%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW302+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 12:25:54 EDT 2023

% Result   : Theorem 44.95s 43.98s
% Output   : Proof 45.01s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SWW302+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 22:25:44 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 44.95/43.98  
% 44.95/43.98  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 44.95/43.98  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.95/43.98  %-----------------------------------------------------
% 44.95/43.98  ncf(matrix, plain, [(52578 ^ _2079949) ^ [_2080006] : [v_P(_2080006, 52573 ^ []), -(v_Q_H(_2080006, 52576 ^ []))], (52584 ^ _2079949) ^ [] : [v_Q(52572 ^ [], 52576 ^ [])], (52575 ^ _2079949) ^ [] : [-(v_P(52572 ^ [], 52573 ^ []))], !, (52517 ^ _776541) ^ [_1831690, _1831692] : [hBOOL(hAPP(hAPP(c_fconj, _1831690), _1831692)), -(hBOOL(_1831692))], (26274 ^ _776541) ^ [_1251042, _1251044] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1251042), _1251044)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1251044), _1251042)))], (4490 ^ _776541) ^ [_844753, _844755] : [_844755 = _844753, -(c_Lazy__Sequence_Oyieldn(_844755) = c_Lazy__Sequence_Oyieldn(_844753))], (22395 ^ _776541) ^ [_1182554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182554), 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)), _1182554)), _1182554)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52495 ^ _776541) ^ [_1831429] : [-(hBOOL(_1831429)), -(hBOOL(hAPP(c_fNot, _1831429)))], (40096 ^ _776541) ^ [_1557470, _1557472, _1557474, _1557476, _1557478, _1557480] : [c_Finite__Set_Ofolding(_1557470, _1557472, _1557474, _1557476), -(hAPP(c_Fun_Ocomp(_1557472, _1557472, _1557472, hAPP(_1557474, _1557478)), hAPP(_1557474, _1557480)) = hAPP(c_Fun_Ocomp(_1557472, _1557472, _1557472, hAPP(_1557474, _1557480)), hAPP(_1557474, _1557478)))], (30948 ^ _776541) ^ [_1331605, _1331607, _1331609] : [class_Orderings_Olinorder(_1331605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331605), _1331607)), 30955 ^ _776541 : [(30962 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331605, tc_HOL_Obool)), _1331607), hAPP(hAPP(c_Set_Oinsert(_1331605), _1331609), c_Orderings_Obot__class_Obot(tc_fun(_1331605, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1331605, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1331605, hAPP(hAPP(c_Set_Oinsert(_1331605), _1331609), _1331607)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331605), _1331609), c_Big__Operators_Olinorder__class_OMin(_1331605, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331605, tc_HOL_Obool)), _1331607), hAPP(hAPP(c_Set_Oinsert(_1331605), _1331609), c_Orderings_Obot__class_Obot(tc_fun(_1331605, tc_HOL_Obool)))))))], (30956 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331605, tc_HOL_Obool)), _1331607), hAPP(hAPP(c_Set_Oinsert(_1331605), _1331609), c_Orderings_Obot__class_Obot(tc_fun(_1331605, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1331605, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1331605, hAPP(hAPP(c_Set_Oinsert(_1331605), _1331609), _1331607)) = _1331609)]]], (24746 ^ _776541) ^ [_1224219] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224219)))], (2776 ^ _776541) ^ [_817608, _817610, _817612, _817614, _817616, _817618] : [-(c_Predicate_ORangeP(_817618, _817614, _817610) = c_Predicate_ORangeP(_817616, _817612, _817608)), _817618 = _817616, _817614 = _817612, _817610 = _817608], (22387 ^ _776541) ^ [_1182401] : [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)), _1182401)), _1182401) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (770 ^ _776541) ^ [_788118, _788120, _788122, _788124, _788126, _788128] : [-(c_Equiv__Relations_Oequiv(_788126, _788122, _788118)), c_Equiv__Relations_Oequiv(_788128, _788124, _788120), _788128 = _788126, _788124 = _788122, _788120 = _788118], (39757 ^ _776541) ^ [_1549384, _1549386, _1549388, _1549390] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549384), _1549386)), 39763 ^ _776541 : [(39766 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549388), hAPP(_1549390, 39762 ^ [_1549384, _1549386, _1549388, _1549390])))], (39764 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549384), 39762 ^ [_1549384, _1549386, _1549388, _1549390]), _1549386)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1549388), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549384, tc_fun(_1549388, tc_HOL_Obool)), _1549386), _1549390))))], (28789 ^ _776541) ^ [_1292767, _1292769] : [c_Int_OBit0(_1292767) = c_Int_OBit1(_1292769)], (45966 ^ _776541) ^ [_1698658, _1698660] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698658)), c_List_Oconcat(_1698658, _1698660)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698658), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1698658))), _1698660)))], (20423 ^ _776541) ^ [_1145008, _1145010, _1145012, _1145014, _1145016] : [class_Fields_Olinordered__field(_1145008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145008), c_Groups_Ozero__class_Ozero(_1145008)), _1145010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145008), _1145010), _1145012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145008), c_Groups_Ozero__class_Ozero(_1145008)), _1145014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145008), _1145014), _1145016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145008), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145008), _1145010), _1145016)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145008), _1145012), _1145014))))], (22695 ^ _776541) ^ [_1187724, _1187726, _1187728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1187724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187724), _1187726)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187724), _1187728))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1187726), _1187728)))], (47416 ^ _776541) ^ [_1729900, _1729902, _1729904] : [hBOOL(hAPP(c_List_Odistinct(_1729900), _1729902)), -(hBOOL(hAPP(c_List_Odistinct(_1729900), c_List_OdropWhile(_1729900, _1729904, _1729902))))], (39384 ^ _776541) ^ [_1539172, _1539174, _1539176, _1539178, _1539180, _1539182] : [class_Groups_Ocomm__monoid__add(_1539172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539174), _1539176)), 39394 ^ _776541 : [(39397 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539178), hAPP(_1539180, 39393 ^ [_1539172, _1539174, _1539176, _1539178, _1539180, _1539182])))], (39395 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539174), 39393 ^ [_1539172, _1539174, _1539176, _1539178, _1539180, _1539182]), _1539176)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539174, _1539172), hAPP(hAPP(c_COMBS(_1539174, tc_fun(_1539178, tc_HOL_Obool), _1539172), hAPP(hAPP(c_COMBB(tc_fun(_1539178, _1539172), tc_fun(tc_fun(_1539178, tc_HOL_Obool), _1539172), _1539174), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539178, _1539172)), _1539182)), _1539180)), _1539176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1539174, _1539178), _1539172), hAPP(c_Product__Type_Oprod_Oprod__case(_1539174, _1539178, _1539172), _1539182)), hAPP(hAPP(c_Product__Type_OSigma(_1539174, _1539178), _1539176), _1539180)))], (25089 ^ _776541) ^ [_1230717, _1230719] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230717, _1230719)), _1230719) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44152 ^ _776541) ^ [_1659418, _1659420, _1659422] : [-(hAPP(c_List_Otl(_1659418), hAPP(hAPP(c_List_Olist_OCons(_1659418), _1659420), _1659422)) = _1659422)], (23275 ^ _776541) ^ [_1198304, _1198306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198304)), 23284 ^ _776541 : [(23287 ^ _776541) ^ [] : [hBOOL(hAPP(_1198306, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23280 ^ [_1198304, _1198306]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 23281 ^ [_1198304, _1198306]), _1198304))))], (23285 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1198306, 23280 ^ [_1198304, _1198306])))]], 23288 ^ _776541 : [(23291 ^ _776541) ^ [] : [hBOOL(hAPP(_1198306, 23280 ^ [_1198304, _1198306]))], (23289 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1198306, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23280 ^ [_1198304, _1198306]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 23281 ^ [_1198304, _1198306]), _1198304)))))]], 23292 ^ _776541 : [(23302 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1198306, 23309 ^ [_1198304, _1198306]))), 23303 ^ _776541 : [(23304 ^ _776541) ^ [_1198851] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1198851), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1198304))), hBOOL(hAPP(_1198306, _1198851))]]], (23293 ^ _776541) ^ [] : [23294 ^ _776541 : [(23295 ^ _776541) ^ [_1198736] : [hBOOL(hAPP(_1198306, _1198736))]], 23297 ^ _776541 : [(23300 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1198306, 23296 ^ [_1198304, _1198306])))], (23298 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23296 ^ [_1198304, _1198306]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1198304))))]]]]], (10535 ^ _776541) ^ [_957688, _957690, _957692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957688, tc_HOL_Obool)), _957690), _957692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957688, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957688, tc_HOL_Obool)), _957692)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957688, tc_HOL_Obool)), _957690))))], (27013 ^ _776541) ^ [_1263137] : [27015 ^ _776541 : [(27018 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27014 ^ [_1263137]))], (27016 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27014 ^ [_1263137]), _1263137)))]], -(c_Nat__Transfer_Onat__set(_1263137))], (40196 ^ _776541) ^ [_1559754, _1559756, _1559758, _1559760, _1559762, _1559764] : [c_Finite__Set_Ofolding(_1559754, _1559756, _1559758, _1559760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559754), _1559762)), -(hBOOL(hAPP(hAPP(c_member(_1559754), _1559764), _1559762))), -(hAPP(_1559760, hAPP(hAPP(c_Set_Oinsert(_1559754), _1559764), _1559762)) = hAPP(c_Fun_Ocomp(_1559756, _1559756, _1559756, hAPP(_1559760, _1559762)), hAPP(_1559758, _1559764)))], (8357 ^ _776541) ^ [_919747, _919749, _919751, _919753] : [class_Lattices_Osemilattice__inf(_919747), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919747), _919749), _919751)), _919753) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919747), _919749), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919747), _919751), _919753)))], (24710 ^ _776541) ^ [_1223612, _1223614] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223612) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223614), -(_1223612 = _1223614)], (25947 ^ _776541) ^ [_1245724] : [25948 ^ _776541 : [(25949 ^ _776541) ^ [_1245781] : [hBOOL(hAPP(_1245724, _1245781))]], 25951 ^ _776541 : [(25954 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1245724, hAPP(c_Int_Onat, 25950 ^ [_1245724]))))], (25952 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25950 ^ [_1245724])))]]], (28603 ^ _776541) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (30760 ^ _776541) ^ [_1328297, _1328299, _1328301] : [class_Orderings_Olinorder(_1328297), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328297), _1328299)), -(c_Big__Operators_Olattice_OInf__fin(_1328297, c_Orderings_Oord__class_Omin(_1328297), hAPP(hAPP(c_Set_Oinsert(_1328297), _1328301), _1328299)) = hAPP(hAPP(c_Finite__Set_Ofold(_1328297, _1328297, c_Orderings_Oord__class_Omin(_1328297)), _1328301), _1328299))], (34147 ^ _776541) ^ [_1410962, _1410964, _1410966] : [class_Fields_Ofield(_1410962), -(_1410964 = c_Groups_Oone__class_Oone(_1410962)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1410962), hAPP(c_Power_Opower__class_Opower(_1410962), _1410964)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1410966)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1410962), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1410962), hAPP(hAPP(c_Power_Opower__class_Opower(_1410962), _1410964), _1410966)), c_Groups_Oone__class_Oone(_1410962))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1410962), _1410964), c_Groups_Oone__class_Oone(_1410962))))], (11220 ^ _776541) ^ [_971340, _971342, _971344] : [class_Groups_Oordered__ab__group__add(_971340), -(hAPP(c_Set_Oimage(_971340, _971340, c_Groups_Ouminus__class_Ouminus(_971340)), c_SetInterval_Oord__class_OatLeastAtMost(_971340, _971342, _971344)) = c_SetInterval_Oord__class_OatLeastAtMost(_971340, hAPP(c_Groups_Ouminus__class_Ouminus(_971340), _971344), hAPP(c_Groups_Ouminus__class_Ouminus(_971340), _971342)))], (46994 ^ _776541) ^ [_1721121] : [-(hAPP(c_List_Orev(_1721121), c_List_Olist_ONil(_1721121)) = c_List_Olist_ONil(_1721121))], (42628 ^ _776541) ^ [_1625228, _1625230] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1625228), _1625230) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1625228, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1625230), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (7730 ^ _776541) ^ [_906110, _906112, _906114] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906110, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906110, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_906110, tc_HOL_Obool), _906112)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_906110, tc_HOL_Obool), _906114))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_906110, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_906110, tc_HOL_Obool), tc_HOL_Obool)), _906112), _906114)))))], (5566 ^ _776541) ^ [_861549, _861551] : [_861551 = _861549, -(tc_Option_Ooption(_861551) = tc_Option_Ooption(_861549))], (25978 ^ _776541) ^ [_1246243] : [25980 ^ _776541 : [(25983 ^ _776541) ^ [] : [hBOOL(hAPP(_1246243, hAPP(c_Int_Onat, 25979 ^ [_1246243])))], (25981 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25979 ^ [_1246243])))]], 25984 ^ _776541 : [(25985 ^ _776541) ^ [_1246376] : [-(hBOOL(hAPP(_1246243, _1246376)))]]], (3828 ^ _776541) ^ [_834030, _834032] : [_834032 = _834030, -(c_New__DSequence_Opos__not__seq(_834032) = c_New__DSequence_Opos__not__seq(_834030))], (44238 ^ _776541) ^ [_1661120, _1661122, _1661124] : [-(hAPP(c_List_Orotate(_1661120, _1661122), _1661124) = hAPP(hAPP(c_List_Oappend(_1661120), hAPP(hAPP(c_List_Odrop(_1661120), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1661122, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661120)), _1661124))), _1661124)), hAPP(hAPP(c_List_Otake(_1661120), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1661122, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661120)), _1661124))), _1661124)))], (17929 ^ _776541) ^ [_1099068, _1099070, _1099072, _1099074] : [class_Rings_Ocomm__semiring__1(_1099068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099070), _1099072)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1099070, _1099068), _1099074), _1099072) = c_Groups_Ozero__class_Ozero(_1099068)), 17938 ^ _776541 : [(17939 ^ _776541) ^ [_1099249] : [hBOOL(hAPP(hAPP(c_member(_1099070), _1099249), _1099072)), hAPP(_1099074, _1099249) = c_Groups_Ozero__class_Ozero(_1099068)]]], (27575 ^ _776541) ^ [_1272594] : [class_Int_Onumber__ring(_1272594), -(hAPP(c_Int_Onumber__class_Onumber__of(_1272594), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1272594))], (36622 ^ _776541) ^ [_1470651, _1470653, _1470655] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1470651), _1470653), _1470655) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470651, tc_fun(tc_fun(_1470651, tc_HOL_Obool), tc_HOL_Obool)), _1470653), hAPP(hAPP(c_COMBC(_1470651, tc_fun(tc_fun(_1470651, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1470651, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470651, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1470651, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1470651, tc_HOL_Obool), tc_HOL_Obool)), _1470651), c_Set_Oinsert(tc_fun(_1470651, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470651, tc_HOL_Obool), tc_fun(_1470651, tc_HOL_Obool), _1470651), c_Relation_OImage(_1470651, _1470651, _1470655)), hAPP(hAPP(c_COMBC(_1470651, tc_fun(_1470651, tc_HOL_Obool), tc_fun(_1470651, tc_HOL_Obool)), c_Set_Oinsert(_1470651)), c_Orderings_Obot__class_Obot(tc_fun(_1470651, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1470651, tc_HOL_Obool), tc_HOL_Obool)))))], (1244 ^ _776541) ^ [_794955, _794957] : [-(class_Divides_Oring__div(_794955)), _794957 = _794955, class_Divides_Oring__div(_794957)], (45497 ^ _776541) ^ [_1688841, _1688843, _1688845, _1688847, _1688849] : [c_List_Olist__all2(_1688841, _1688843, _1688845, _1688847, _1688849), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688841)), _1688847) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688843)), _1688849))], (35551 ^ _776541) ^ [_1439837, _1439839, _1439841] : [35553 ^ _776541 : [(35556 ^ _776541) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1439841, 35552 ^ [_1439837, _1439839, _1439841]))], (35554 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1439837), 35552 ^ [_1439837, _1439839, _1439841]), _1439839)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1439837, tc_Int_Oint), _1439841), _1439839) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1439837, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1439837), c_Int_Onat), _1439841)), _1439839)))], (34391 ^ _776541) ^ [_1416712, _1416714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416712), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1416714, _1416712) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416714), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416712)))], (31032 ^ _776541) ^ [_1333350, _1333352] : [class_Orderings_Olinorder(_1333350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333350), _1333352)), -(_1333352 = c_Orderings_Obot__class_Obot(tc_fun(_1333350, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1333350), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333350), 31045 ^ [_1333350, _1333352]), 31046 ^ [_1333350, _1333352])), hAPP(hAPP(c_Set_Oinsert(_1333350), 31045 ^ [_1333350, _1333352]), hAPP(hAPP(c_Set_Oinsert(_1333350), 31046 ^ [_1333350, _1333352]), c_Orderings_Obot__class_Obot(tc_fun(_1333350, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1333350), c_Big__Operators_Olinorder__class_OMin(_1333350, _1333352)), _1333352)))], (44160 ^ _776541) ^ [_1659579, _1659581, _1659583] : [hBOOL(hAPP(c_List_Odistinct(_1659579), hAPP(c_List_Orotate(_1659579, _1659581), _1659583))), -(hBOOL(hAPP(c_List_Odistinct(_1659579), _1659583)))], (31527 ^ _776541) ^ [_1342604, _1342606, _1342608] : [class_Orderings_Olinorder(_1342604), 31530 ^ _776541 : [(31537 ^ _776541) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342604), _1342606), _1342608) = _1342608, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342604), _1342606), _1342608)))], (31531 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342604), _1342606), _1342608)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342604), _1342606), _1342608) = _1342608)]]], (11284 ^ _776541) ^ [_972623, _972625] : [class_Groups_Oordered__ab__group__add(_972623), -(hAPP(c_Set_Oimage(_972623, _972623, c_Groups_Ouminus__class_Ouminus(_972623)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_972623), _972625)) = hAPP(c_SetInterval_Oord__class_OlessThan(_972623), hAPP(c_Groups_Ouminus__class_Ouminus(_972623), _972625)))], (24812 ^ _776541) ^ [_1225424, _1225426, _1225428, _1225430] : [class_Divides_Osemiring__div(_1225424), -(c_Divides_Odiv__class_Omod(_1225424, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225424), c_Divides_Odiv__class_Omod(_1225424, _1225426, _1225428)), _1225430), _1225428) = c_Divides_Odiv__class_Omod(_1225424, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225424), _1225426), _1225430), _1225428))], (29377 ^ _776541) ^ [_1302967, _1302969, _1302971] : [class_Rings_Olinordered__semidom(_1302967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302967), hAPP(hAPP(c_Power_Opower__class_Opower(_1302967), _1302969), 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(_1302967), _1302971), 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(_1302967), c_Groups_Ozero__class_Ozero(_1302967)), _1302971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302967), _1302969), _1302971)))], (27773 ^ _776541) ^ [_1276004, _1276006] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276004), _1276006), hAPP(c_Int_Onumber__class_Onumber__of(_1276004), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1276004)), class_Fields_Ofield__inverse__zero(_1276004), class_Int_Onumber__ring(_1276004)], (51903 ^ _776541) ^ [_1825214, _1825216] : [-(class_Finite__Set_Ofinite(tc_fun(_1825214, _1825216))), class_Finite__Set_Ofinite(_1825214), class_Finite__Set_Ofinite(_1825216)], (46233 ^ _776541) ^ [_1706365, _1706367, _1706369, _1706371] : [-(c_List_Ofoldr(_1706365, _1706367, _1706369, c_List_Olist_ONil(_1706365), _1706371) = _1706371)], (43120 ^ _776541) ^ [_1635649, _1635651] : [_1635651 = c_List_Olist_ONil(_1635649), -(c_Orderings_Obot__class_Obot(tc_fun(_1635649, tc_HOL_Obool)) = hAPP(c_List_Oset(_1635649), _1635651))], (17647 ^ _776541) ^ [_1094311, _1094313] : [class_Groups_Oordered__ab__group__add(_1094311), 17650 ^ _776541 : [(17657 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094311), _1094313), c_Groups_Ozero__class_Ozero(_1094311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094311), c_Groups_Ozero__class_Ozero(_1094311)), hAPP(c_Groups_Ouminus__class_Ouminus(_1094311), _1094313))))], (17651 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094311), c_Groups_Ozero__class_Ozero(_1094311)), hAPP(c_Groups_Ouminus__class_Ouminus(_1094311), _1094313))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094311), _1094313), c_Groups_Ozero__class_Ozero(_1094311))))]]], (27365 ^ _776541) ^ [_1268848] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1268848) = c_Int_OPls)], (42432 ^ _776541) ^ [_1618958, _1618960, _1618962] : [hBOOL(hAPP(hAPP(c_member(_1618958), _1618960), hAPP(c_List_Oset(_1618958), _1618962))), -(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(_1618958)), _1618962))))], (14795 ^ _776541) ^ [_1043280, _1043282] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043282), _1043280))))], (32702 ^ _776541) ^ [_1370650] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1370650) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370650)))], (2590 ^ _776541) ^ [_814715, _814717] : [_814717 = _814715, -(c_Int_Oint__ge__less__than2(_814717) = c_Int_Oint__ge__less__than2(_814715))], (39595 ^ _776541) ^ [_1544479, _1544481, _1544483, _1544485] : [c_Relation_Orefl__on(_1544479, _1544481, _1544483), hBOOL(hAPP(hAPP(c_member(_1544479), _1544485), _1544481)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544479, _1544479)), hAPP(hAPP(c_Product__Type_OPair(_1544479, _1544479), _1544485), _1544485)), _1544483)))], (45036 ^ _776541) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (52217 ^ _776541) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (9368 ^ _776541) ^ [_937714, _937716, _937718, _937720] : [-(c_Nitpick_Ofold__graph_H(_937714, _937716, _937718, _937720, c_Orderings_Obot__class_Obot(tc_fun(_937714, tc_HOL_Obool)), _937720))], (13826 ^ _776541) ^ [_1023128, _1023130, _1023132] : [class_Groups_Ogroup__add(_1023128), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023128), _1023130), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023128), hAPP(c_Groups_Ouminus__class_Ouminus(_1023128), _1023130)), _1023132)) = _1023132)], (25520 ^ _776541) ^ [_1238178, _1238180, _1238182] : [-(hBOOL(hAPP(_1238178, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1238180), _1238182)))), 25521 ^ _776541 : [(25528 ^ _776541) ^ [_1238346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1238182), _1238346)), _1238180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1238180), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1238182), hAPP(c_Nat_OSuc, _1238346)))), hBOOL(hAPP(_1238178, _1238346))], (25522 ^ _776541) ^ [] : [_1238182 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1238178, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (27959 ^ _776541) ^ [_1279036, _1279038] : [class_Int_Onumber__ring(_1279036), class_Rings_Olinordered__idom(_1279036), 27966 ^ _776541 : [(27973 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279038), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279036), hAPP(c_Int_Onumber__class_Onumber__of(_1279036), _1279038)), c_Groups_Ozero__class_Ozero(_1279036))))], (27967 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279036), hAPP(c_Int_Onumber__class_Onumber__of(_1279036), _1279038)), c_Groups_Ozero__class_Ozero(_1279036))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279038), c_Int_OPls)))]]], (34007 ^ _776541) ^ [_1407877, _1407879] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1407877), _1407879))), -(hAPP(c_Finite__Set_Ocard(_1407877), _1407879) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (326 ^ _776541) ^ [_781460, _781462, _781464, _781466] : [-(c_Wellfounded_OwfP(_781464, _781460)), c_Wellfounded_OwfP(_781466, _781462), _781466 = _781464, _781462 = _781460], (1934 ^ _776541) ^ [_803580, _803582, _803584, _803586] : [-(v_P(_803584, _803580)), v_P(_803586, _803582), _803586 = _803584, _803582 = _803580], (45231 ^ _776541) ^ [_1682453] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682453)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49196 ^ _776541) ^ [_1769651, _1769653, _1769655, _1769657, _1769659] : [c_Relation_Otrans(_1769651, _1769653), hBOOL(hAPP(hAPP(c_member(tc_prod(_1769651, _1769651)), hAPP(hAPP(c_Product__Type_OPair(_1769651, _1769651), _1769655), _1769657)), _1769653)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1769651, _1769651)), hAPP(hAPP(c_Product__Type_OPair(_1769651, _1769651), _1769657), _1769659)), _1769653)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769651, _1769651)), hAPP(hAPP(c_Product__Type_OPair(_1769651, _1769651), _1769655), _1769659)), _1769653)))], (24958 ^ _776541) ^ [_1228514, _1228516, _1228518] : [-(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, _1228514, _1228516)), _1228518), _1228516) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228514), _1228518), _1228516))], (4750 ^ _776541) ^ [_848841, _848843, _848845, _848847] : [-(c_Product__Type_Osnd(_848847, _848843) = c_Product__Type_Osnd(_848845, _848841)), _848847 = _848845, _848843 = _848841], (30154 ^ _776541) ^ [_1317508, _1317510, _1317512] : [class_Orderings_Olinorder(_1317508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317508), _1317510), _1317512)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317508), _1317512), _1317510) = _1317510)], (40741 ^ _776541) ^ [_1573548, _1573550, _1573552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573548, _1573548), tc_HOL_Obool)), c_Relation_OId(_1573548)), _1573550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573548, _1573548), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1573548, _1573548, _1573548), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1573548, _1573548), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573548, _1573552)), _1573550)), _1573552)), _1573550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573548, _1573548), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573548, _1573552)), _1573550)))], (47281 ^ _776541) ^ [_1727087, _1727089, _1727091] : [-(c_List_OtakeWhile(_1727087, _1727089, _1727091) = hAPP(hAPP(c_List_Otake(_1727087), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727087)), c_List_OtakeWhile(_1727087, _1727089, _1727091))), _1727091))], (15436 ^ _776541) ^ [_1055539, _1055541, _1055543] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055539), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055539, tc_HOL_Obool)), _1055541), _1055543))), -(hAPP(c_Finite__Set_Ocard(_1055539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055539, tc_HOL_Obool)), _1055541), _1055543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055539), _1055541)), hAPP(c_Finite__Set_Ocard(_1055539), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055539, tc_HOL_Obool)), _1055541), _1055543))))], (25734 ^ _776541) ^ [_1242242, _1242244, _1242246, _1242248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242244), _1242246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242246), 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), _1242244), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242248, _1242242))), _1242246)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40485 ^ _776541) ^ [_1566563, _1566565, _1566567, _1566569, _1566571] : [_1566563 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1566565, _1566567, _1566563, _1566569), _1566571) = hAPP(c_Product__Type_OPair(_1566565, _1566567), _1566571))], (27473 ^ _776541) ^ [_1270752, _1270754, _1270756] : [class_Groups_Oordered__ab__group__add__abs(_1270752), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270752), hAPP(c_Groups_Oabs__class_Oabs(_1270752), _1270754)), hAPP(c_Groups_Oabs__class_Oabs(_1270752), _1270756))), hAPP(c_Groups_Oabs__class_Oabs(_1270752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270752), _1270756), _1270754)))))], (13802 ^ _776541) ^ [_1022632, _1022634, _1022636] : [class_Groups_Ogroup__add(_1022632), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1022632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022632), _1022634), _1022636)), _1022636) = _1022634)], (19017 ^ _776541) ^ [_1119119, _1119121] : [19019 ^ _776541 : [(19022 ^ _776541) ^ [] : [hBOOL(hAPP(_1119121, 19018 ^ [_1119119, _1119121]))], (19020 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19018 ^ [_1119119, _1119121]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1119119))))]], 19023 ^ _776541 : [(19024 ^ _776541) ^ [_1119274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119274), _1119119)), -(hBOOL(hAPP(_1119121, _1119274)))]]], (15726 ^ _776541) ^ [_1061673, _1061675] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061673), _1061675) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15729 ^ _776541 : [(15732 ^ _776541) ^ [] : [-(_1061675 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15730 ^ _776541) ^ [] : [-(_1061673 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (23992 ^ _776541) ^ [_1210992, _1210994, _1210996, _1210998] : [class_Divides_Osemiring__div(_1210992), -(_1210994 = c_Groups_Ozero__class_Ozero(_1210992)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210992), _1210994), _1210996)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210992), _1210994), _1210998)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210992), _1210996), _1210998))], (8952 ^ _776541) ^ [_931071, _931073, _931075, _931077, _931079, _931081, _931083] : [hBOOL(hAPP(hAPP(c_member(_931071), _931073), _931075)), c_Nitpick_Ofold__graph_H(_931071, _931077, _931079, _931081, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931071, tc_HOL_Obool)), _931075), hAPP(hAPP(c_Set_Oinsert(_931071), _931073), c_Orderings_Obot__class_Obot(tc_fun(_931071, tc_HOL_Obool)))), _931083), -(c_Nitpick_Ofold__graph_H(_931071, _931077, _931079, _931081, _931075, hAPP(hAPP(_931079, _931073), _931083)))], (27693 ^ _776541) ^ [_1274708, _1274710] : [class_Groups_Oordered__ab__group__add__abs(_1274708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274708), _1274710), c_Groups_Ozero__class_Ozero(_1274708))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274708), _1274710) = hAPP(c_Groups_Ouminus__class_Ouminus(_1274708), _1274710))], (36612 ^ _776541) ^ [_1470351, _1470353, _1470355] : [-(hAPP(c_Relation_OField(_1470351), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1470351, _1470351), tc_HOL_Obool)), _1470353), _1470355)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470351, tc_HOL_Obool)), hAPP(c_Relation_OField(_1470351), _1470353)), hAPP(c_Relation_OField(_1470351), _1470355)))], (16747 ^ _776541) ^ [_1077728, _1077730, _1077732, _1077734] : [class_Groups_Ocomm__monoid__add(_1077728), 16750 ^ _776541 : [(16757 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077730)), _1077732))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1077728), _1077734), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1077732, hAPP(c_Nat_OSuc, _1077730))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077728), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1077728), _1077734), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1077732, _1077730))), hAPP(_1077734, hAPP(c_Nat_OSuc, _1077730))))], (16751 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077730)), _1077732)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1077728), _1077734), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1077732, hAPP(c_Nat_OSuc, _1077730))) = c_Groups_Ozero__class_Ozero(_1077728))]]], (33316 ^ _776541) ^ [_1387727, _1387729, _1387731, _1387733, _1387735] : [class_Rings_Osemiring__0(_1387727), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387727), _1387729), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387731, _1387727), _1387733), _1387735)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387731, _1387727), hAPP(hAPP(c_COMBB(_1387727, _1387727, _1387731), hAPP(c_Groups_Otimes__class_Otimes(_1387727), _1387729)), _1387733)), _1387735))], (28897 ^ _776541) ^ [_1294600, _1294602] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1294600), _1294602)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1294600)), c_Int_OBit0(_1294602))))], (17407 ^ _776541) ^ [_1090015, _1090017, _1090019] : [class_Rings_Olinordered__semiring__strict(_1090015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090015), c_Groups_Ozero__class_Ozero(_1090015)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090015), _1090017), _1090019))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090015), c_Groups_Ozero__class_Ozero(_1090015)), _1090019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090015), c_Groups_Ozero__class_Ozero(_1090015)), _1090017)))], (46050 ^ _776541) ^ [_1701482, _1701484, _1701486] : [hAPP(c_List_Ofilter(_1701482, _1701484), _1701486) = _1701486, 46053 ^ _776541 : [(46054 ^ _776541) ^ [_1701573] : [hBOOL(hAPP(hAPP(c_member(_1701482), _1701573), hAPP(c_List_Oset(_1701482), _1701486))), -(hBOOL(hAPP(_1701484, _1701573)))]]], (44154 ^ _776541) ^ [_1659458, _1659460] : [hBOOL(hAPP(c_List_Odistinct(_1659458), _1659460)), -(hBOOL(hAPP(c_List_Odistinct(_1659458), hAPP(c_List_Otl(_1659458), _1659460))))], (47263 ^ _776541) ^ [_1726838, _1726840, _1726842, _1726844] : [hBOOL(hAPP(_1726838, _1726840)), -(c_List_OtakeWhile(_1726842, _1726838, hAPP(hAPP(c_List_Olist_OCons(_1726842), _1726840), _1726844)) = hAPP(hAPP(c_List_Olist_OCons(_1726842), _1726840), c_List_OtakeWhile(_1726842, _1726838, _1726844)))], (52461 ^ _776541) ^ [_1830882] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1830882)))], (34221 ^ _776541) ^ [_1412842, _1412844] : [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(_1412842))), 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)), _1412844)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412842)), hAPP(c_Nat_OSuc, _1412844))))], (34608 ^ _776541) ^ [_1421174, _1421176] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1421174), hAPP(c_Nat_OSuc, _1421176)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1421176), 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)), _1421176)), _1421174))], (46824 ^ _776541) ^ [_1717417, _1717419] : [class_Orderings_Olinorder(_1717417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1717417), _1717419)), 46831 ^ _776541 : [(46836 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1717417), c_List_Olinorder__class_Osorted__list__of__set(_1717417, _1717419))))], (46834 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1717417, c_List_Olinorder__class_Osorted__list__of__set(_1717417, _1717419)))], (46832 ^ _776541) ^ [] : [-(hAPP(c_List_Oset(_1717417), c_List_Olinorder__class_Osorted__list__of__set(_1717417, _1717419)) = _1717419)]]], (48280 ^ _776541) ^ [_1748953, _1748955, _1748957, _1748959] : [c_List_Olist__all(_1748953, _1748955, hAPP(hAPP(c_List_Olist_OCons(_1748953), _1748957), _1748959)), 48283 ^ _776541 : [(48286 ^ _776541) ^ [] : [-(c_List_Olist__all(_1748953, _1748955, _1748959))], (48284 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1748955, _1748957)))]]], (25257 ^ _776541) ^ [_1233757] : [class_Int_Onumber__ring(_1233757), -(hAPP(c_Int_Onumber__class_Onumber__of(_1233757), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233757), c_Groups_Oone__class_Oone(_1233757)))], (32626 ^ _776541) ^ [_1368257, _1368259, _1368261, _1368263, _1368265] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368257, tc_fun(_1368259, tc_HOL_Obool)), _1368261), hAPP(hAPP(c_COMBB(tc_fun(_1368259, tc_HOL_Obool), tc_fun(_1368259, tc_HOL_Obool), _1368257), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368259, tc_HOL_Obool)), _1368263)), _1368265)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368259, tc_HOL_Obool)), _1368263), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368257, tc_fun(_1368259, tc_HOL_Obool)), _1368261), _1368265)))], (30336 ^ _776541) ^ [_1320633, _1320635, _1320637] : [class_Int_Onumber(_1320633), class_Orderings_Oord(_1320633), 30343 ^ _776541 : [(30350 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320633), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320635)), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320637)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320633), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320635)), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320637)) = hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320637))], (30344 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320633), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320635)), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320637))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320633), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320635)), hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320637)) = hAPP(c_Int_Onumber__class_Onumber__of(_1320633), _1320635))]]], (28559 ^ _776541) ^ [_1288979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1288979)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1288979), c_Int_OPls)))], (18972 ^ _776541) ^ [_1118258] : [-(hAPP(c_Nat_OSuc, _1118258) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1118258))], (32870 ^ _776541) ^ [_1375420, _1375422, _1375424, _1375426, _1375428] : [hBOOL(hAPP(hAPP(c_member(_1375420), _1375422), _1375424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375426, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375420, tc_fun(_1375426, tc_HOL_Obool)), _1375424), _1375428)), hAPP(_1375428, _1375422))))], (48438 ^ _776541) ^ [_1752109, _1752111, _1752113, _1752115, _1752117, _1752119, _1752121] : [-(c_New__Random__Sequence_Opos__decr__bind(_1752109, _1752111, _1752113, _1752115, _1752117, _1752119, _1752121) = c_New__DSequence_Opos__decr__bind(_1752109, _1752111, hAPP(hAPP(hAPP(_1752113, _1752117), _1752119), _1752121), hAPP(hAPP(c_COMBC(_1752109, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1752111))), hAPP(hAPP(c_COMBC(_1752109, 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(_1752111)))), hAPP(hAPP(c_COMBC(_1752109, 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(_1752111))))), _1752115), _1752117)), _1752119)), _1752121)))], (2656 ^ _776541) ^ [_815718, _815720, _815722, _815724, _815726, _815728, _815730, _815732, _815734, _815736] : [-(c_Finite__Set_Ofold__graph(_815736, _815732, _815728, _815724, _815720) = c_Finite__Set_Ofold__graph(_815734, _815730, _815726, _815722, _815718)), _815736 = _815734, _815732 = _815730, _815728 = _815726, _815724 = _815722, _815720 = _815718], (22677 ^ _776541) ^ [_1187497, _1187499] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187497), _1187499) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1187499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1187497 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31763 ^ _776541) ^ [_1347277, _1347279, _1347281, _1347283] : [class_Orderings_Olinorder(_1347277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347277), _1347279)), hBOOL(hAPP(hAPP(c_member(_1347277), _1347281), _1347279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347277), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347277), _1347281), _1347283)), hAPP(hAPP(c_Finite__Set_Ofold(_1347277, _1347277, c_Orderings_Oord__class_Omax(_1347277)), _1347283), _1347279))))], (43326 ^ _776541) ^ [_1639964, _1639966, _1639968] : [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), _1639964), _1639966))), -(hBOOL(hAPP(hAPP(_1639968, _1639964), _1639966))), 43333 ^ _776541 : [(43336 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43331 ^ [_1639964, _1639966, _1639968]), 43332 ^ [_1639964, _1639966, _1639968])), -(hBOOL(hAPP(hAPP(_1639968, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43331 ^ [_1639964, _1639966, _1639968]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43332 ^ [_1639964, _1639966, _1639968])))], (43342 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1639968, 43331 ^ [_1639964, _1639966, _1639968]), 43332 ^ [_1639964, _1639966, _1639968]))], (43334 ^ _776541) ^ [] : [-(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), 43331 ^ [_1639964, _1639966, _1639968]), 43332 ^ [_1639964, _1639966, _1639968]))))]]], (1314 ^ _776541) ^ [_795830, _795832] : [-(class_Rings_Oring(_795830)), _795832 = _795830, class_Rings_Oring(_795832)], (5817 ^ _776541) ^ [_868664, _868666, _868668, _868670, _868672, _868674] : [c_Typedef_Otype__definition(_868664, _868666, _868668, _868670, _868672), -(hBOOL(hAPP(hAPP(c_member(_868666), hAPP(_868668, _868674)), _868672)))], (14254 ^ _776541) ^ [_1033062, _1033064, _1033066, _1033068] : [class_Rings_Ocomm__semiring__1(_1033062), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033062), _1033064), _1033066)), _1033068) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033062), _1033064), _1033068)), _1033066))], (31423 ^ _776541) ^ [_1340775, _1340777, _1340779, _1340781, _1340783] : [class_Orderings_Olinorder(_1340775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340775), _1340777), _1340779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340775), _1340781), _1340783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340775), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340775), _1340777), _1340781)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340775), _1340779), _1340783))))], (16606 ^ _776541) ^ [] : [-(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)))], (34329 ^ _776541) ^ [_1415419, _1415421, _1415423] : [-(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), _1415419)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1415421))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1415423))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1415423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1415419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1415419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1415423), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1415421)))))], (4468 ^ _776541) ^ [_844364, _844366, _844368, _844370, _844372, _844374, _844376, _844378, _844380, _844382] : [-(c_Option_Ooption_Ooption__case(_844382, _844378, _844374, _844370, _844366) = c_Option_Ooption_Ooption__case(_844380, _844376, _844372, _844368, _844364)), _844382 = _844380, _844378 = _844376, _844374 = _844372, _844370 = _844368, _844366 = _844364], (23425 ^ _776541) ^ [_1201070, _1201072, _1201074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201070)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1201072), _1201074)), 23432 ^ _776541 : [(23433 ^ _776541) ^ [_1201260] : [23435 ^ _776541 : [(23441 ^ _776541) ^ [] : [-(_1201260 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23437 ^ [_1201070, _1201072, _1201074, _1201260]), 23434 ^ [_1201070, _1201072, _1201074, _1201260]))], (23439 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23437 ^ [_1201070, _1201072, _1201074, _1201260]), _1201074)))], (23436 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23434 ^ [_1201070, _1201072, _1201074, _1201260]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1201070))))]], -(_1201260 = _1201072), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201260), _1201070) = _1201072]]], (16642 ^ _776541) ^ [] : [-(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))))], (27553 ^ _776541) ^ [_1272196, _1272198, _1272200] : [class_Fields_Olinordered__field(_1272196), -(_1272198 = c_Groups_Ozero__class_Ozero(_1272196)), -(hAPP(c_Groups_Oabs__class_Oabs(_1272196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272196), _1272200), _1272198)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272196), hAPP(c_Groups_Oabs__class_Oabs(_1272196), _1272200)), hAPP(c_Groups_Oabs__class_Oabs(_1272196), _1272198)))], (40793 ^ _776541) ^ [_1574841, _1574843, _1574845, _1574847] : [40794 ^ _776541 : [(40797 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574841, _1574841)), _1574843), c_Transitive__Closure_Ortrancl(_1574841, _1574847)))], (40795 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574841, _1574841)), _1574843), c_Transitive__Closure_Ortrancl(_1574841, _1574845)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574841, _1574841)), _1574843), c_Transitive__Closure_Ortrancl(_1574841, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574841, _1574841), tc_HOL_Obool)), _1574845), _1574847)))))], (15292 ^ _776541) ^ [_1052460, _1052462, _1052464, _1052466] : [class_Groups_Ocomm__monoid__mult(_1052460), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052462), _1052464))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052462, _1052460), _1052466), _1052464) = c_Groups_Oone__class_Oone(_1052460))], (40597 ^ _776541) ^ [_1569220, _1569222, _1569224, _1569226] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569220, _1569220)), hAPP(hAPP(c_Product__Type_OPair(_1569220, _1569220), _1569222), _1569224)), _1569226)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569220, _1569220)), hAPP(hAPP(c_Product__Type_OPair(_1569220, _1569220), _1569222), _1569224)), c_Transitive__Closure_Otrancl(_1569220, _1569226))))], (36681 ^ _776541) ^ [_1472161, _1472163, _1472165, _1472167] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1472161, _1472161)), hAPP(hAPP(c_Product__Type_OPair(_1472161, _1472161), _1472163), _1472165)), c_Relation_OId__on(_1472161, _1472167))), 36684 ^ _776541 : [(36687 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472161), _1472163), _1472167)))], (36685 ^ _776541) ^ [] : [-(_1472163 = _1472165)]]], (14260 ^ _776541) ^ [_1033205, _1033207, _1033209, _1033211, _1033213] : [class_Rings_Ocomm__semiring__1(_1033205), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033205), _1033207), _1033209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033205), _1033211), _1033213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033205), _1033207), _1033211)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033205), _1033209), _1033213)))], (48716 ^ _776541) ^ [_1758396, _1758398] : [-(c_List_Oreplicate(_1758396, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1758398) = c_List_Olist_ONil(_1758396))], (49428 ^ _776541) ^ [_1775896, _1775898] : [c_Relation_Otrans(_1775896, hAPP(c_Set_OCollect(tc_prod(_1775896, _1775896)), hAPP(c_Product__Type_Oprod_Oprod__case(_1775896, _1775896, tc_HOL_Obool), _1775898))), -(c_Predicate_Otransp(_1775896, _1775898))], (10974 ^ _776541) ^ [_966248, _966250] : [class_Lattices_Olattice(_966248), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966248), _966250), _966250) = _966250)], (7684 ^ _776541) ^ [_904747, _904749, _904751] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904747, tc_HOL_Obool)), _904749), _904751) = c_Orderings_Obot__class_Obot(tc_fun(_904747, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904747, tc_HOL_Obool)), _904749), _904751) = _904749)], (4002 ^ _776541) ^ [_836983, _836985, _836987, _836989, _836991, _836993, _836995, _836997] : [-(c_Lazy__Sequence_Ohb__bind(_836997, _836993, _836989, _836985) = c_Lazy__Sequence_Ohb__bind(_836995, _836991, _836987, _836983)), _836997 = _836995, _836993 = _836991, _836989 = _836987, _836985 = _836983], (41911 ^ _776541) ^ [_1604529, _1604531, _1604533, _1604535] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604529), tc_List_Olist(_1604529))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604529), tc_List_Olist(_1604529)), _1604531), _1604533)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1604529), c_List_Olistrel1(_1604529, _1604535)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604529)), _1604531) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604529)), _1604533))], (43078 ^ _776541) ^ [_1634917, _1634919] : [-(c_List_Osublist(_1634917, c_List_Olist_ONil(_1634917), _1634919) = c_List_Olist_ONil(_1634917))], (24806 ^ _776541) ^ [_1225289, _1225291, _1225293, _1225295] : [class_Divides_Osemiring__div(_1225289), -(c_Divides_Odiv__class_Omod(_1225289, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225289), _1225291), c_Divides_Odiv__class_Omod(_1225289, _1225293, _1225295)), _1225295) = c_Divides_Odiv__class_Omod(_1225289, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225289), _1225291), _1225293), _1225295))], (48995 ^ _776541) ^ [_1764719, _1764721, _1764723] : [-(c_FunDef_OTHE__default(_1764721, _1764723, _1764719) = c_HOL_OThe(_1764721, _1764719)), 48996 ^ _776541 : [(48997 ^ _776541) ^ [_1764783] : [hBOOL(hAPP(_1764719, _1764783)), 49001 ^ _776541 : [(49004 ^ _776541) ^ [] : [49000 ^ [_1764719, _1764721, _1764723, _1764783] = _1764783], (49002 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1764719, 49000 ^ [_1764719, _1764721, _1764723, _1764783])))]]]]], (22151 ^ _776541) ^ [_1178229, _1178231] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178229)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178231)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178229), _1178231)))], (24788 ^ _776541) ^ [_1224876, _1224878, _1224880, _1224882] : [class_Divides_Osemiring__div(_1224876), -(c_Divides_Odiv__class_Omod(_1224876, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224876), _1224878), _1224880), _1224882) = c_Divides_Odiv__class_Omod(_1224876, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224876), _1224878), c_Divides_Odiv__class_Omod(_1224876, _1224880, _1224882)), _1224882))], (38371 ^ _776541) ^ [_1512031, _1512033, _1512035, _1512037] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512031), _1512033)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512031), _1512035)), -(_1512035 = c_Orderings_Obot__class_Obot(tc_fun(_1512031, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1512031, tc_HOL_Obool), tc_fun(_1512031, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1512031, tc_HOL_Obool), tc_fun(_1512031, tc_HOL_Obool)), _1512033), _1512035)), c_Wellfounded_Omax__ext(_1512031, _1512037)))), 38385 ^ _776541 : [(38388 ^ _776541) ^ [_1512436] : [hBOOL(hAPP(hAPP(c_member(_1512031), _1512436), _1512035)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512031, _1512031)), hAPP(hAPP(c_Product__Type_OPair(_1512031, _1512031), 38384 ^ [_1512031, _1512033, _1512035, _1512037]), _1512436)), _1512037))], (38386 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512031), 38384 ^ [_1512031, _1512033, _1512035, _1512037]), _1512033)))]]], (31593 ^ _776541) ^ [_1343761, _1343763, _1343765, _1343767] : [class_Orderings_Olinorder(_1343761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343761), _1343763), _1343765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343761), _1343763), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343761), _1343765), _1343767))))], (35638 ^ _776541) ^ [_1441799, _1441801, _1441803, _1441805, _1441807] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441799, _1441801, _1441803), _1441805), _1441807) = hAPP(hAPP(_1441805, hAPP(c_Product__Type_Ofst(_1441799, _1441801), _1441807)), hAPP(c_Product__Type_Osnd(_1441799, _1441801), _1441807)))], (49863 ^ _776541) ^ [_1783624, _1783626] : [c_Equiv__Relations_Oequivp(_1783624, _1783626), -(c_Equiv__Relations_Opart__equivp(_1783624, _1783626))], (7599 ^ _776541) ^ [_902354, _902356, _902358, _902360] : [7600 ^ _776541 : [(7601 ^ _776541) ^ [_902464] : [hBOOL(hAPP(hAPP(c_member(_902354), _902464), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902354, tc_HOL_Obool)), _902356), _902358))), hBOOL(hAPP(_902360, _902464))]], 7609 ^ _776541 : [(7612 ^ _776541) ^ [] : [-(hBOOL(hAPP(_902360, 7608 ^ [_902354, _902356, _902358, _902360])))], (7610 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902354), 7608 ^ [_902354, _902356, _902358, _902360]), _902356)))]], 7614 ^ _776541 : [(7617 ^ _776541) ^ [] : [-(hBOOL(hAPP(_902360, 7613 ^ [_902354, _902356, _902358, _902360])))], (7615 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902354), 7613 ^ [_902354, _902356, _902358, _902360]), _902358)))]]], (22167 ^ _776541) ^ [_1178552] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178552)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178552)))], (3066 ^ _776541) ^ [_822143, _822145, _822147, _822149] : [-(c_List_Olexn(_822149, _822145) = c_List_Olexn(_822147, _822143)), _822149 = _822147, _822145 = _822143], (50071 ^ _776541) ^ [_1788116, _1788118, _1788120, _1788122, _1788124, _1788126] : [c_Fun_Oinj__on(_1788116, _1788118, _1788120, _1788122), hBOOL(hAPP(hAPP(c_member(_1788116), _1788124), _1788122)), hAPP(_1788120, _1788124) = _1788126, -(hAPP(c_Hilbert__Choice_Oinv__into(_1788116, _1788118, _1788122, _1788120), _1788126) = _1788124)], (11153 ^ _776541) ^ [_969595, _969597, _969599] : [-(hAPP(c_Set_Oimage(_969595, _969597, _969599), c_Orderings_Obot__class_Obot(tc_fun(_969595, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_969597, tc_HOL_Obool)))], (43092 ^ _776541) ^ [_1635176] : [class_Groups_Omonoid__add(_1635176), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1635176), c_List_Olist_ONil(_1635176)) = c_Groups_Ozero__class_Ozero(_1635176))], (45199 ^ _776541) ^ [_1681922, _1681924] : [_1681922 = _1681924, -(hAPP(c_Code__Numeral_Onat__of, _1681922) = hAPP(c_Code__Numeral_Onat__of, _1681924))], (6965 ^ _776541) ^ [_889588, _889590, _889592] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_889588, tc_HOL_Obool)), _889590), hAPP(c_Set_OPow(_889588), _889592))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889588, tc_HOL_Obool)), _889590), _889592)))], (8525 ^ _776541) ^ [_922982, _922984, _922986, _922988] : [class_Lattices_Osemilattice__sup(_922982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922982), _922984), _922986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922982), _922984), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922982), _922986), _922988))))], (48564 ^ _776541) ^ [_1755654, _1755656, _1755658] : [-(c_List_Oreplicate(_1755654, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755654)), hAPP(c_List_Ofilter(_1755654, hAPP(c_fequal, _1755656)), _1755658)), _1755656) = hAPP(c_List_Ofilter(_1755654, hAPP(c_fequal, _1755656)), _1755658))], (7756 ^ _776541) ^ [_906723, _906725, _906727, _906729] : [hBOOL(hAPP(hAPP(c_member(_906723), _906725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906723, tc_HOL_Obool)), _906727), _906729))), hBOOL(hAPP(hAPP(c_member(_906723), _906725), _906729))], (16765 ^ _776541) ^ [_1078121, _1078123, _1078125] : [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, _1078121)), _1078123)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078121)), _1078125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078123), _1078125)))], (23759 ^ _776541) ^ [_1206836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206836)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4528 ^ _776541) ^ [_845314, _845316] : [_845316 = _845314, -(c_List_Omember(_845316) = c_List_Omember(_845314))], (7362 ^ _776541) ^ [_897183, _897185] : [class_Orderings_Oorder(_897183), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_897183, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_897183), _897185)), hAPP(c_SetInterval_Oord__class_OatLeast(_897183), _897185)) = hAPP(hAPP(c_Set_Oinsert(_897183), _897185), c_Orderings_Obot__class_Obot(tc_fun(_897183, tc_HOL_Obool))))], (39151 ^ _776541) ^ [_1531880, _1531882, _1531884, _1531886, _1531888] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531880, _1531882), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1531880, tc_HOL_Obool)), _1531884), _1531886)), _1531888) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1531880, _1531882), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531880, _1531882), _1531884), _1531888)), hAPP(hAPP(c_Product__Type_OSigma(_1531880, _1531882), _1531886), _1531888)))], (30216 ^ _776541) ^ [_1318568, _1318570, _1318572] : [class_Orderings_Olinorder(_1318568), 30219 ^ _776541 : [(30226 ^ _776541) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318568), _1318570), _1318572) = _1318570, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318568), _1318570), _1318572)))], (30220 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318568), _1318570), _1318572)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318568), _1318570), _1318572) = _1318570)]]], (9906 ^ _776541) ^ [_946280, _946282, _946284] : [class_Orderings_Oorder(_946280), 9909 ^ _776541 : [(9916 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946280), _946282), _946284))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_946280, _946282, _946284) = c_Orderings_Obot__class_Obot(tc_fun(_946280, tc_HOL_Obool)))], (9910 ^ _776541) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_946280, _946282, _946284) = c_Orderings_Obot__class_Obot(tc_fun(_946280, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946280), _946282), _946284))]]], (26272 ^ _776541) ^ [_1251010] : [-(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)), _1251010)) = hAPP(c_Int_Onat, _1251010))], (33180 ^ _776541) ^ [_1384364, _1384366, _1384368] : [hBOOL(hAPP(_1384368, _1384366)), -(hBOOL(hAPP(hAPP(c_member(_1384364), _1384366), hAPP(c_Set_OCollect(_1384364), _1384368))))], (51329 ^ _776541) ^ [_1815585, _1815587, _1815589] : [class_Rings_Odvd(_1815585), class_Rings_Osemiring__0(_1815585), 51336 ^ _776541 : [(51346 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1815587, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815585), _1815589), 51353 ^ [_1815585, _1815587, _1815589])))), 51347 ^ _776541 : [(51348 ^ _776541) ^ [_1815914] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815585), _1815589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815585), _1815914), c_Groups_Ozero__class_Ozero(_1815585)))), hBOOL(hAPP(_1815587, _1815914))]]], (51337 ^ _776541) ^ [] : [51338 ^ _776541 : [(51339 ^ _776541) ^ [_1815777] : [hBOOL(hAPP(_1815587, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815585), _1815589), _1815777)))]], 51341 ^ _776541 : [(51344 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1815587, 51340 ^ [_1815585, _1815587, _1815589])))], (51342 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815585), _1815589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815585), 51340 ^ [_1815585, _1815587, _1815589]), c_Groups_Ozero__class_Ozero(_1815585)))))]]]]], (26254 ^ _776541) ^ [_1250749, _1250751] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1250749, _1250751) = 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), _1250749), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250751))))], (41755 ^ _776541) ^ [_1599646, _1599648, _1599650] : [_1599646 = hAPP(hAPP(c_List_Olist_OCons(_1599648), _1599650), _1599646)], (37622 ^ _776541) ^ [_1492796, _1492798, _1492800, _1492802, _1492804] : [c_Fun_Oinj__on(_1492796, _1492798, _1492800, c_Orderings_Otop__class_Otop(tc_fun(_1492796, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1492796, _1492798, _1492800), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492796, tc_HOL_Obool)), _1492802), _1492804)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492798, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492796, _1492798, _1492800), _1492802)), hAPP(c_Set_Oimage(_1492796, _1492798, _1492800), _1492804)))], (2554 ^ _776541) ^ [_814175, _814177] : [_814177 = _814175, -(c_Wellfounded_Omeasure(_814177) = c_Wellfounded_Omeasure(_814175))], (36938 ^ _776541) ^ [_1477898, _1477900, _1477902, _1477904, _1477906, _1477908] : [c_Equiv__Relations_Oequiv(_1477898, _1477900, _1477902), c_Equiv__Relations_Ocongruent(_1477898, tc_fun(_1477904, tc_HOL_Obool), _1477902, _1477906), hBOOL(hAPP(hAPP(c_member(_1477898), _1477908), _1477900)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477898, tc_fun(_1477904, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1477898, _1477898, _1477902), hAPP(hAPP(c_Set_Oinsert(_1477898), _1477908), c_Orderings_Obot__class_Obot(tc_fun(_1477898, tc_HOL_Obool))))), _1477906) = hAPP(_1477906, _1477908))], (14520 ^ _776541) ^ [_1038387, _1038389] : [14521 ^ _776541 : [(14524 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038389), _1038387))], (14522 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038387), _1038389))]], _1038387 = _1038389], (24940 ^ _776541) ^ [_1228173] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228173, _1228173) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28201 ^ _776541) ^ [_1282886, _1282888] : [class_Int_Onumber__ring(_1282886), -(hAPP(c_Int_Onumber__class_Onumber__of(_1282886), c_Int_Opred(_1282888)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1282886), hAPP(c_Groups_Ouminus__class_Ouminus(_1282886), c_Groups_Oone__class_Oone(_1282886))), hAPP(c_Int_Onumber__class_Onumber__of(_1282886), _1282888)))], (6212 ^ _776541) ^ [_876368, _876370, _876372, _876374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876368, tc_HOL_Obool)), _876370), _876372)), hBOOL(hAPP(_876370, _876374)), -(hBOOL(hAPP(_876372, _876374)))], (36386 ^ _776541) ^ [_1463890] : [-(_1463890 = 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)), _1463890), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (50231 ^ _776541) ^ [_1792015, _1792017] : [50233 ^ _776541 : [(50236 ^ _776541) ^ [] : [hBOOL(hAPP(_1792015, hAPP(c_Code__Numeral_Oof__nat, 50232 ^ [_1792015, _1792017])))], (50234 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50232 ^ [_1792015, _1792017]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1792015, _1792017)))], (19585 ^ _776541) ^ [_1130458, _1130460] : [class_Rings_Olinordered__idom(_1130458), 19588 ^ _776541 : [(19595 ^ _776541) ^ [] : [_1130460 = c_Groups_Ozero__class_Ozero(_1130458), -(c_Groups_Osgn__class_Osgn(_1130458, _1130460) = c_Groups_Ozero__class_Ozero(_1130458))], (19589 ^ _776541) ^ [] : [c_Groups_Osgn__class_Osgn(_1130458, _1130460) = c_Groups_Ozero__class_Ozero(_1130458), -(_1130460 = c_Groups_Ozero__class_Ozero(_1130458))]]], (35042 ^ _776541) ^ [_1430442, _1430444, _1430446, _1430448] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430442, _1430444), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430446), _1430448))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1430442, _1430444) = _1430448)], (41104 ^ _776541) ^ [_1582597, _1582599, _1582601] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582597, _1582599)), hAPP(c_Relation_Oconverse(_1582599, _1582597), _1582601))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582599, _1582597)), _1582601)))], (28881 ^ _776541) ^ [_1294308] : [c_Int_OBit0(_1294308) = c_Int_OMin], (26893 ^ _776541) ^ [_1261050, _1261052] : [class_Int_Oring__char__0(_1261050), 26896 ^ _776541 : [(26903 ^ _776541) ^ [] : [_1261052 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1261050) = hAPP(c_Int_Oring__1__class_Oof__int(_1261050), _1261052))], (26897 ^ _776541) ^ [] : [c_Groups_Ozero__class_Ozero(_1261050) = hAPP(c_Int_Oring__1__class_Oof__int(_1261050), _1261052), -(_1261052 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (49956 ^ _776541) ^ [_1785351, _1785353] : [c_Equiv__Relations_Opart__equivp(_1785351, _1785353), 49960 ^ _776541 : [(49965 ^ _776541) ^ [] : [-(c_Predicate_Otransp(_1785351, _1785353))], (49963 ^ _776541) ^ [] : [-(c_Predicate_Osymp(_1785351, _1785353))], (49961 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1785353, 49959 ^ [_1785351, _1785353]), 49959 ^ [_1785351, _1785353])))]]], (30437 ^ _776541) ^ [_1322616, _1322618, _1322620] : [class_Orderings_Olinorder(_1322616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322616), _1322618)), -(_1322618 = c_Orderings_Obot__class_Obot(tc_fun(_1322616, tc_HOL_Obool))), 30448 ^ _776541 : [(30458 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322616), hAPP(c_Finite__Set_Ofold1(_1322616, c_Orderings_Oord__class_Omin(_1322616)), _1322618)), _1322620))), 30459 ^ _776541 : [(30460 ^ _776541) ^ [_1323005] : [hBOOL(hAPP(hAPP(c_member(_1322616), _1323005), _1322618)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322616), _1323005), _1322620))]]], (30449 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322616), hAPP(c_Finite__Set_Ofold1(_1322616, c_Orderings_Oord__class_Omin(_1322616)), _1322618)), _1322620)), 30453 ^ _776541 : [(30456 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322616), 30452 ^ [_1322616, _1322618, _1322620]), _1322620)))], (30454 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322616), 30452 ^ [_1322616, _1322618, _1322620]), _1322618)))]]]]], (43254 ^ _776541) ^ [_1638227, _1638229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638227)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638229))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638227), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638229)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638227)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638227)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638229))))], (10813 ^ _776541) ^ [_962869, _962871, _962873, _962875] : [class_Orderings_Olinorder(_962869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962869), _962871), _962873)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962869, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962869, _962871), _962875)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962869, _962871), _962873)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962869, _962873), _962875))], (4234 ^ _776541) ^ [_840705, _840707] : [_840707 = _840705, -(c_List_Otake(_840707) = c_List_Otake(_840705))], (33064 ^ _776541) ^ [_1380613, _1380615, _1380617, _1380619, _1380621, _1380623] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380613, tc_fun(_1380615, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380617, _1380613, _1380619), _1380621)), _1380623) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380617, tc_fun(_1380615, tc_HOL_Obool)), _1380621), hAPP(hAPP(c_COMBB(_1380613, tc_fun(_1380615, tc_HOL_Obool), _1380617), _1380623), _1380619)))], (16504 ^ _776541) ^ [_1073712] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073712) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23767 ^ _776541) ^ [_1206987, _1206989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206987), _1206989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206987)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206989))))], (33156 ^ _776541) ^ [_1383474, _1383476, _1383478, _1383480] : [_1383478 = _1383480, -(hAPP(hAPP(c_COMBC(_1383474, tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_fun(_1383476, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383476, tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_fun(_1383476, tc_HOL_Obool)), _1383474), c_COMBC(_1383476, tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383476, tc_prod(_1383474, _1383476)), tc_fun(_1383476, tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool)), _1383474), hAPP(c_COMBB(tc_prod(_1383474, _1383476), tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool), _1383476), c_member(tc_prod(_1383474, _1383476)))), c_Product__Type_OPair(_1383474, _1383476)))), _1383478) = hAPP(hAPP(c_COMBC(_1383474, tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_fun(_1383476, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383476, tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_fun(_1383476, tc_HOL_Obool)), _1383474), c_COMBC(_1383476, tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383476, tc_prod(_1383474, _1383476)), tc_fun(_1383476, tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool)), _1383474), hAPP(c_COMBB(tc_prod(_1383474, _1383476), tc_fun(tc_fun(tc_prod(_1383474, _1383476), tc_HOL_Obool), tc_HOL_Obool), _1383476), c_member(tc_prod(_1383474, _1383476)))), c_Product__Type_OPair(_1383474, _1383476)))), _1383480))], (43038 ^ _776541) ^ [_1634314, _1634316, _1634318, _1634320] : [_1634314 = _1634316, -(c_List_Oremove1(_1634318, _1634314, hAPP(hAPP(c_List_Olist_OCons(_1634318), _1634316), _1634320)) = _1634320)], (9760 ^ _776541) ^ [_943664, _943666, _943668, _943670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943664, tc_HOL_Obool)), _943666), _943668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943664, tc_HOL_Obool)), _943668), _943670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943664, tc_HOL_Obool)), _943666), _943670)))], (16144 ^ _776541) ^ [_1068320, _1068322] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068320)), hAPP(c_Nat_OSuc, _1068322)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1068320), _1068322))], (20387 ^ _776541) ^ [_1144330, _1144332, _1144334] : [class_Fields_Olinordered__field(_1144330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144330), c_Groups_Ozero__class_Ozero(_1144330)), _1144332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144330), _1144334), c_Groups_Ozero__class_Ozero(_1144330))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144330), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144330), _1144332), _1144334)), c_Groups_Ozero__class_Ozero(_1144330))))], (10243 ^ _776541) ^ [_952574, _952576, _952578] : [class_Orderings_Oorder(_952574), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952574, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_952574, _952576), _952578)), hAPP(c_SetInterval_Oord__class_OatLeast(_952574), _952578)) = c_Orderings_Obot__class_Obot(tc_fun(_952574, tc_HOL_Obool)))], (26402 ^ _776541) ^ [_1253025, _1253027] : [hBOOL(hAPP(_1253025, hAPP(c_Int_Onat, _1253027))), 26405 ^ _776541 : [(26412 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253027), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1253025, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26406 ^ _776541) ^ [_1253125] : [_1253027 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1253125), -(hBOOL(hAPP(_1253025, _1253125)))]]], (45110 ^ _776541) ^ [_1679986, _1679988, _1679990, _1679992, _1679994] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679986)), _1679988) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679990)), _1679992), 45113 ^ _776541 : [(45122 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1679986, _1679990), _1679988), _1679992) = _1679994), hAPP(hAPP(c_List_Omap(tc_prod(_1679986, _1679990), _1679986), c_Product__Type_Ofst(_1679986, _1679990)), _1679994) = _1679988, hAPP(hAPP(c_List_Omap(tc_prod(_1679986, _1679990), _1679990), c_Product__Type_Osnd(_1679986, _1679990)), _1679994) = _1679992], (45114 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Ozip(_1679986, _1679990), _1679988), _1679992) = _1679994, 45117 ^ _776541 : [(45120 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1679986, _1679990), _1679990), c_Product__Type_Osnd(_1679986, _1679990)), _1679994) = _1679992)], (45118 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1679986, _1679990), _1679986), c_Product__Type_Ofst(_1679986, _1679990)), _1679994) = _1679988)]]]]], (32476 ^ _776541) ^ [_1361401, _1361403, _1361405] : [-(hAPP(c_Set_OCollect(_1361401), hAPP(hAPP(c_COMBS(_1361401, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361401), c_fimplies), _1361403)), _1361405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361401, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1361401, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1361401), _1361403))), hAPP(c_Set_OCollect(_1361401), _1361405)))], (50171 ^ _776541) ^ [_1790442, _1790444, _1790446, _1790448, _1790450] : [c_Fun_Oinj__on(_1790442, _1790444, _1790446, c_Orderings_Otop__class_Otop(tc_fun(_1790442, tc_HOL_Obool))), 50177 ^ _776541 : [(50180 ^ _776541) ^ [] : [hBOOL(hAPP(_1790448, hAPP(c_Hilbert__Choice_Oinv__into(_1790442, _1790444, c_Orderings_Otop__class_Otop(tc_fun(_1790442, tc_HOL_Obool)), _1790446), 50176 ^ [_1790442, _1790444, _1790446, _1790448, _1790450])))], (50178 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790444), 50176 ^ [_1790442, _1790444, _1790446, _1790448, _1790450]), hAPP(c_Set_Oimage(_1790442, _1790444, _1790446), c_Orderings_Otop__class_Otop(tc_fun(_1790442, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1790448, _1790450)))], (51725 ^ _776541) ^ [_1822592, _1822594] : [51732 ^ _776541 : [(51735 ^ _776541) ^ [] : [_1822592 = _1822594], (51733 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822592), _1822594)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822592), _1822594)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822594), _1822592)))], (43428 ^ _776541) ^ [_1642422, _1642424, _1642426, _1642428, _1642430] : [hAPP(hAPP(c_List_Oappend(_1642422), _1642424), hAPP(hAPP(c_List_Olist_OCons(_1642422), _1642426), c_List_Olist_ONil(_1642422))) = hAPP(hAPP(c_List_Oappend(_1642422), _1642428), hAPP(hAPP(c_List_Olist_OCons(_1642422), _1642430), c_List_Olist_ONil(_1642422))), 43431 ^ _776541 : [(43434 ^ _776541) ^ [] : [-(_1642426 = _1642430)], (43432 ^ _776541) ^ [] : [-(_1642424 = _1642428)]]], (15998 ^ _776541) ^ [_1066041, _1066043] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066041), _1066043))), 16001 ^ _776541 : [(16008 ^ _776541) ^ [] : [_1066041 = _1066043, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066041), hAPP(c_Nat_OSuc, _1066043))))], (16002 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066041), hAPP(c_Nat_OSuc, _1066043))), -(_1066041 = _1066043)]]], (38676 ^ _776541) ^ [_1519595, _1519597, _1519599, _1519601, _1519603] : [-(hAPP(c_Set_Ovimage(_1519595, _1519597, _1519599), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519597, tc_HOL_Obool)), _1519601), _1519603)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519595, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1519595, _1519597, _1519599), _1519601)), hAPP(c_Set_Ovimage(_1519595, _1519597, _1519599), _1519603)))], (29879 ^ _776541) ^ [_1312378, _1312380] : [29880 ^ _776541 : [(29883 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1312380), _1312378))], (29881 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1312378), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1312378, _1312380) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (23872 ^ _776541) ^ [_1208971] : [class_Rings_Osemiring__1(_1208971), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208971), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1208971))], (52055 ^ _776541) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (31293 ^ _776541) ^ [_1338117, _1338119, _1338121] : [class_Orderings_Olinorder(_1338117), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338117), _1338119), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338117), _1338119), _1338121)) = _1338119)], (38106 ^ _776541) ^ [_1506401] : [-(c_Wellfounded_Owf(_1506401, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1506401, _1506401), tc_HOL_Obool))))], (46091 ^ _776541) ^ [_1702243, _1702245, _1702247] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1702243), tc_List_Olist(_1702243)), c_List_Opartition(_1702243, _1702245, _1702247)) = hAPP(c_List_Ofilter(_1702243, _1702245), _1702247))], (43914 ^ _776541) ^ [_1654066, _1654068] : [-(hAPP(c_List_Oset(_1654066), hAPP(c_List_Orotate1(_1654066), _1654068)) = hAPP(c_List_Oset(_1654066), _1654068))], (48104 ^ _776541) ^ [_1745382, _1745384, _1745386] : [-(c_List_Olist__ex(_1745382, _1745384, _1745386)), 48105 ^ _776541 : [(48106 ^ _776541) ^ [_1745439] : [hBOOL(hAPP(hAPP(c_member(_1745382), _1745439), hAPP(c_List_Oset(_1745382), _1745386))), hBOOL(hAPP(_1745384, _1745439))]]], (31012 ^ _776541) ^ [_1332900, _1332902] : [class_Orderings_Olinorder(_1332900), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332900), _1332902)), -(_1332902 = c_Orderings_Obot__class_Obot(tc_fun(_1332900, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1332900), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332900), 31025 ^ [_1332900, _1332902]), 31026 ^ [_1332900, _1332902])), hAPP(hAPP(c_Set_Oinsert(_1332900), 31025 ^ [_1332900, _1332902]), hAPP(hAPP(c_Set_Oinsert(_1332900), 31026 ^ [_1332900, _1332902]), c_Orderings_Obot__class_Obot(tc_fun(_1332900, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1332900), c_Big__Operators_Olattice_OInf__fin(_1332900, c_Orderings_Oord__class_Omin(_1332900), _1332902)), _1332902)))], (1604 ^ _776541) ^ [_799455, _799457] : [-(class_Rings_Olinordered__semiring(_799455)), _799457 = _799455, class_Rings_Olinordered__semiring(_799457)], (34540 ^ _776541) ^ [_1419740, _1419742, _1419744, _1419746, _1419748, _1419750, _1419752] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419740, tc_fun(_1419742, tc_fun(_1419744, tc_HOL_Obool))), _1419746), _1419748), _1419750), _1419752))), 34541 ^ _776541 : [(34542 ^ _776541) ^ [_1419825] : [hBOOL(hAPP(hAPP(c_member(_1419740), _1419825), _1419746)), hBOOL(hAPP(hAPP(hAPP(_1419748, _1419825), _1419750), _1419752))]]], (52023 ^ _776541) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (40759 ^ _776541) ^ [_1574052, _1574054] : [-(c_Transitive__Closure_Ortrancl(_1574052, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574052, _1574052), tc_HOL_Obool)), _1574054), c_Relation_OId(_1574052))) = c_Transitive__Closure_Ortrancl(_1574052, _1574054))], (26649 ^ _776541) ^ [_1257546, _1257548] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257546))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257546)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257548)) = 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), _1257548)))], (34717 ^ _776541) ^ [_1423575] : [-(c_Divides_Odivmod__nat(_1423575, 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)), _1423575))], (12433 ^ _776541) ^ [_994984, _994986, _994988, _994990, _994992] : [c_Finite__Set_Ofolding__one__idem(_994984, _994986, _994988), hBOOL(hAPP(c_Finite__Set_Ofinite(_994984), _994990)), -(_994990 = c_Orderings_Obot__class_Obot(tc_fun(_994984, tc_HOL_Obool))), -(hAPP(_994988, hAPP(hAPP(c_Set_Oinsert(_994984), _994992), _994990)) = hAPP(hAPP(_994986, _994992), hAPP(_994988, _994990)))], (41995 ^ _776541) ^ [_1607130, _1607132, _1607134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607130, _1607130), tc_HOL_Obool)), _1607132), _1607134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607130), tc_List_Olist(_1607130)), tc_HOL_Obool)), c_List_Olistrel(_1607130, _1607132)), c_List_Olistrel(_1607130, _1607134))))], (13898 ^ _776541) ^ [_1024702, _1024704, _1024706] : [class_Groups_Ogroup__add(_1024702), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024702), _1024704), _1024706) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024702), _1024704), hAPP(c_Groups_Ouminus__class_Ouminus(_1024702), _1024706)))], (36478 ^ _776541) ^ [_1466639, _1466641, _1466643, _1466645, _1466647, _1466649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1466639, _1466641), tc_HOL_Obool)), _1466643), _1466645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466639, tc_HOL_Obool)), _1466647), _1466649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466641, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466639, _1466641, _1466643), _1466647)), hAPP(c_Relation_OImage(_1466639, _1466641, _1466645), _1466649))))], (33421 ^ _776541) ^ [_1390503, _1390505, _1390507, _1390509, _1390511, _1390513] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390503, tc_fun(_1390505, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390507, tc_fun(_1390503, tc_HOL_Obool)), _1390509), _1390511)), _1390513) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390507, tc_fun(_1390505, tc_HOL_Obool)), _1390509), hAPP(hAPP(c_COMBC(_1390507, tc_fun(_1390503, tc_fun(_1390505, tc_HOL_Obool)), tc_fun(_1390505, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390503, tc_HOL_Obool), tc_fun(tc_fun(_1390503, tc_fun(_1390505, tc_HOL_Obool)), tc_fun(_1390505, tc_HOL_Obool)), _1390507), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390503, tc_fun(_1390505, tc_HOL_Obool))), _1390511)), _1390513)))], (43206 ^ _776541) ^ [_1637225, _1637227] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637225), tc_List_Olist(_1637225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637225), tc_List_Olist(_1637225)), c_List_Olist_ONil(_1637225)), c_List_Olist_ONil(_1637225))), c_List_Olistrel(_1637225, _1637227))))], (27703 ^ _776541) ^ [_1274873, _1274875] : [class_Groups_Oabs__if(_1274873), 27706 ^ _776541 : [(27713 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274873), _1274875), c_Groups_Ozero__class_Ozero(_1274873)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274873), _1274875) = _1274875)], (27707 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274873), _1274875), c_Groups_Ozero__class_Ozero(_1274873))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274873), _1274875) = hAPP(c_Groups_Ouminus__class_Ouminus(_1274873), _1274875))]]], (2966 ^ _776541) ^ [_820565, _820567] : [_820567 = _820565, -(c_Nitpick_Ofrac(_820567) = c_Nitpick_Ofrac(_820565))], (52089 ^ _776541) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (2022 ^ _776541) ^ [_805667, _805669, _805671, _805673, _805675, _805677, _805679, _805681, _805683, _805685] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_805685, _805681, _805677, _805673, _805669) = c_SetInterval_Oord_OgreaterThanAtMost(_805683, _805679, _805675, _805671, _805667)), _805685 = _805683, _805681 = _805679, _805677 = _805675, _805673 = _805671, _805669 = _805667], (27237 ^ _776541) ^ [_1266672] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266672), 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), _1266672)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1266672)))], (52391 ^ _776541) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (45164 ^ _776541) ^ [_1681093, _1681095] : [-(c_Random_Oselect__weight(_1681093, _1681095) = 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(_1681093, 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, _1681093), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1681093)), _1681095)))), hAPP(hAPP(c_COMBB(_1681093, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1681093, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1681093, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1681093, _1681095))))], (41809 ^ _776541) ^ [_1601003, _1601005, _1601007] : [-(c_List_Oset__Cons(_1601003, _1601005, _1601007) = hAPP(c_Set_OCollect(tc_List_Olist(_1601003)), hAPP(hAPP(c_COMBB(tc_fun(_1601003, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1601003)), c_HOL_OEx(_1601003)), hAPP(hAPP(c_COMBB(tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), tc_fun(_1601003, tc_HOL_Obool), tc_List_Olist(_1601003)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_HOL_Obool, _1601003), c_HOL_OEx(tc_List_Olist(_1601003)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1601003), tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601003, tc_fun(tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool))), tc_fun(tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool))), tc_List_Olist(_1601003)), c_COMBS(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1601003, tc_fun(tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool))), tc_List_Olist(_1601003)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601003), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), _1601003), c_COMBS(tc_List_Olist(_1601003), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1601003)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601003), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1601003), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1601003)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1601003), tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_List_Olist(_1601003))), tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1601003), tc_List_Olist(_1601003)), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), tc_fun(tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_List_Olist(_1601003))), tc_fun(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool))), tc_List_Olist(_1601003)), c_COMBB(tc_fun(tc_List_Olist(_1601003), tc_List_Olist(_1601003)), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), _1601003)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1601003), tc_List_Olist(_1601003)), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), tc_List_Olist(_1601003)), c_COMBB(tc_List_Olist(_1601003), tc_HOL_Obool, tc_List_Olist(_1601003))), c_fequal))), c_List_Olist_OCons(_1601003)))))), hAPP(hAPP(c_COMBC(_1601003, tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool)), _1601003), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1601003))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1601003), c_fconj), hAPP(hAPP(c_COMBC(_1601003, tc_fun(_1601003, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601003)), _1601005)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1601003), tc_fun(tc_List_Olist(_1601003), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1601003))), _1601007)))))))], (37832 ^ _776541) ^ [_1497640, _1497642, _1497644] : [-(c_Fun_Oinj__on(tc_prod(_1497640, _1497642), tc_prod(_1497642, _1497640), hAPP(c_Product__Type_Oprod_Oprod__case(_1497640, _1497642, tc_prod(_1497642, _1497640)), hAPP(c_COMBC(_1497642, _1497640, tc_prod(_1497642, _1497640)), c_Product__Type_OPair(_1497642, _1497640))), _1497644))], (8309 ^ _776541) ^ [_918863, _918865, _918867] : [class_Lattices_Osemilattice__sup(_918863), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918863), _918865), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918863), _918865), _918867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918863), _918865), _918867))], (14376 ^ _776541) ^ [_1035901, _1035903, _1035905, _1035907, _1035909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035901), _1035903)), 14379 ^ _776541 : [(14386 ^ _776541) ^ [] : [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), _1035903), _1035901)), _1035905)), _1035907)), _1035909)), -(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), _1035903), _1035905)), _1035907)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035901), _1035905)), _1035909))))], (14380 ^ _776541) ^ [] : [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), _1035903), _1035905)), _1035907)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035901), _1035905)), _1035909))), -(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), _1035903), _1035901)), _1035905)), _1035907)), _1035909)))]]], (28853 ^ _776541) ^ [_1293834, _1293836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1293834)), c_Int_OBit0(_1293836))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293834), _1293836)))], (12810 ^ _776541) ^ [_1002530, _1002532, _1002534, _1002536] : [class_Lattices_Osemilattice__inf(_1002530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002530), _1002532)), hBOOL(hAPP(hAPP(c_member(_1002530), _1002534), _1002532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002530), hAPP(hAPP(c_Finite__Set_Ofold(_1002530, _1002530, c_Lattices_Osemilattice__inf__class_Oinf(_1002530)), _1002536), _1002532)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1002530), _1002534), _1002536))))], (26675 ^ _776541) ^ [] : [-(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))))], (41098 ^ _776541) ^ [_1582406, _1582408, _1582410, _1582412] : [-(hAPP(c_Relation_Oconverse(_1582406, _1582406), hAPP(hAPP(c_Relation_Oinv__image(_1582408, _1582406), _1582410), _1582412)) = hAPP(hAPP(c_Relation_Oinv__image(_1582408, _1582406), hAPP(c_Relation_Oconverse(_1582408, _1582408), _1582410)), _1582412))], (8185 ^ _776541) ^ [_916297, _916299, _916301, _916303] : [class_Orderings_Oorder(_916297), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916297, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_916297, _916299, _916301)), c_SetInterval_Oord__class_OgreaterThanLessThan(_916297, _916301, _916303)) = c_Orderings_Obot__class_Obot(tc_fun(_916297, tc_HOL_Obool)))], (28395 ^ _776541) ^ [_1286267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286267), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286267)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26477 ^ _776541) ^ [_1254411, _1254413, _1254415, _1254417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1254413), _1254415)), -(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), _1254415), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1254417, _1254411))), _1254413)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1254415), _1254411))))], (50936 ^ _776541) ^ [_1808057, _1808059, _1808061, _1808063, _1808065, _1808067, _1808069, _1808071] : [c_Finite__Set_Ofolding__image(_1808057, _1808059, _1808061, _1808063, _1808065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1808059), _1808067)), 50946 ^ _776541 : [(50949 ^ _776541) ^ [] : [hAPP(_1808069, 50945 ^ [_1808057, _1808059, _1808061, _1808063, _1808065, _1808067, _1808069, _1808071]) = hAPP(_1808071, 50945 ^ [_1808057, _1808059, _1808061, _1808063, _1808065, _1808067, _1808069, _1808071])], (50947 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808059), 50945 ^ [_1808057, _1808059, _1808061, _1808063, _1808065, _1808067, _1808069, _1808071]), _1808067)))]], -(hAPP(hAPP(_1808065, _1808069), _1808067) = hAPP(hAPP(_1808065, _1808071), _1808067))], (17985 ^ _776541) ^ [_1099953, _1099955] : [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), _1099953), _1099955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1099955), _1099953)))], (37478 ^ _776541) ^ [_1489861, _1489863, _1489865, _1489867] : [-(_1489861 = c_Orderings_Obot__class_Obot(tc_fun(_1489863, tc_HOL_Obool))), 37481 ^ _776541 : [(37482 ^ _776541) ^ [] : [-(hAPP(c_Set_Oimage(_1489865, _1489863, 37489 ^ [_1489861, _1489863, _1489865, _1489867]), _1489867) = _1489861), 37483 ^ _776541 : [(37484 ^ _776541) ^ [_1490002] : [c_Fun_Oinj__on(_1489863, _1489865, _1490002, _1489861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489865, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1489863, _1489865, _1490002), _1489861)), _1489867))]]], (37493 ^ _776541) ^ [] : [37494 ^ _776541 : [(37495 ^ _776541) ^ [_1490194] : [hAPP(c_Set_Oimage(_1489865, _1489863, _1490194), _1489867) = _1489861]], 37497 ^ _776541 : [(37500 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489865, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1489863, _1489865, 37496 ^ [_1489861, _1489863, _1489865, _1489867]), _1489861)), _1489867)))], (37498 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1489863, _1489865, 37496 ^ [_1489861, _1489863, _1489865, _1489867], _1489861))]]]]], (29975 ^ _776541) ^ [_1314110, _1314112, _1314114] : [class_Orderings_Olinorder(_1314110), -(_1314112 = c_Orderings_Obot__class_Obot(tc_fun(_1314110, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314110, tc_HOL_Obool)), _1314112), _1314114)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314110), _1314114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314110), hAPP(c_Finite__Set_Ofold1(_1314110, c_Orderings_Oord__class_Omin(_1314110)), _1314114)), hAPP(c_Finite__Set_Ofold1(_1314110, c_Orderings_Oord__class_Omin(_1314110)), _1314112))))], (29775 ^ _776541) ^ [] : [-(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))], (24760 ^ _776541) ^ [_1224425, _1224427] : [class_Divides_Osemiring__div(_1224425), -(c_Divides_Odiv__class_Omod(_1224425, _1224427, _1224427) = c_Groups_Ozero__class_Ozero(_1224425))], (7368 ^ _776541) ^ [_897326, _897328] : [class_Orderings_Olinorder(_897326), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897326, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_897326), _897328)), hAPP(hAPP(c_Set_Oinsert(_897326), _897328), c_Orderings_Obot__class_Obot(tc_fun(_897326, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_897326), _897328))], (52267 ^ _776541) ^ [_1828782] : [class_Lazy__Sequence_Osmall__lazy(_1828782), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1828782)))], (42665 ^ _776541) ^ [_1626040, _1626042, _1626044, _1626046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626040)), _1626042)), _1626044)), -(hAPP(hAPP(c_List_Olist__update(_1626040, _1626042), _1626044), _1626046) = _1626042)], (21759 ^ _776541) ^ [_1170713, _1170715, _1170717, _1170719] : [class_Fields_Olinordered__field__inverse__zero(_1170713), class_Int_Onumber(_1170713), 21766 ^ _776541 : [(21767 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170713), _1170715), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717))), _1170719)), 21770 ^ _776541 : [(21777 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), c_Groups_Ozero__class_Ozero(_1170713)), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717)))), 21780 ^ _776541 : [(21787 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717)), c_Groups_Ozero__class_Ozero(_1170713)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), c_Groups_Ozero__class_Ozero(_1170713)), _1170719)))], (21781 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717)), c_Groups_Ozero__class_Ozero(_1170713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170713), _1170719), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717))), _1170715)))]]], (21771 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), c_Groups_Ozero__class_Ozero(_1170713)), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), _1170715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170713), _1170719), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717)))))]]], (21793 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170713), _1170715), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717))), _1170719))), 21796 ^ _776541 : [(21799 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), _1170715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170713), _1170719), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717))))], (21797 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), c_Groups_Ozero__class_Ozero(_1170713)), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717))))]], 21800 ^ _776541 : [(21803 ^ _776541) ^ [] : [21804 ^ _776541 : [(21807 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170713), _1170719), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717))), _1170715))], (21805 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717)), c_Groups_Ozero__class_Ozero(_1170713))))]], 21808 ^ _776541 : [(21811 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), c_Groups_Ozero__class_Ozero(_1170713)), _1170719))], (21809 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717)), c_Groups_Ozero__class_Ozero(_1170713)))]]], (21801 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170713), c_Groups_Ozero__class_Ozero(_1170713)), hAPP(c_Int_Onumber__class_Onumber__of(_1170713), _1170717)))]]]]], (4098 ^ _776541) ^ [_838573, _838575] : [_838575 = _838573, -(c_New__Random__Sequence_Oneg__single(_838575) = c_New__Random__Sequence_Oneg__single(_838573))], (42363 ^ _776541) ^ [_1617358, _1617360, _1617362] : [-(c_List_Osublist(_1617358, _1617360, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1617362)) = hAPP(hAPP(c_List_Otake(_1617358), _1617362), _1617360))], (6758 ^ _776541) ^ [_885857, _885859, _885861] : [class_Orderings_Oorder(_885857), 6761 ^ _776541 : [(6770 ^ _776541) ^ [] : [-(_885859 = _885861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885857), _885859), _885861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885857), _885861), _885859))], (6762 ^ _776541) ^ [] : [_885859 = _885861, 6765 ^ _776541 : [(6768 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885857), _885861), _885859)))], (6766 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885857), _885859), _885861)))]]]]], (37000 ^ _776541) ^ [_1479674, _1479676, _1479678, _1479680] : [c_Equiv__Relations_Oequivp(_1479674, _1479676), hBOOL(hAPP(hAPP(_1479676, _1479678), _1479680)), -(hBOOL(hAPP(hAPP(_1479676, _1479680), _1479678)))], (37634 ^ _776541) ^ [_1493109, _1493111, _1493113, _1493115, _1493117, _1493119] : [c_Fun_Oinj__on(_1493109, _1493111, _1493113, _1493115), -(hBOOL(hAPP(hAPP(c_member(_1493111), _1493117), hAPP(c_Set_Oimage(_1493109, _1493111, _1493113), _1493115)))), -(c_Fun_Oinj__on(_1493109, _1493111, c_Fun_Ofun__upd(_1493109, _1493111, _1493113, _1493119, _1493117), _1493115))], (11764 ^ _776541) ^ [_982494, _982496, _982498, _982500, _982502, _982504, _982506, _982508] : [c_Finite__Set_Ofolding__image__simple(_982494, _982496, _982498, _982500, _982502, _982504), hBOOL(hAPP(c_Finite__Set_Ofinite(_982496), _982506)), hBOOL(hAPP(c_Finite__Set_Ofinite(_982496), _982508)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982496, tc_HOL_Obool)), _982506), _982508) = c_Orderings_Obot__class_Obot(tc_fun(_982496, tc_HOL_Obool)), -(hAPP(_982504, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982496, tc_HOL_Obool)), _982506), _982508)) = hAPP(hAPP(_982498, hAPP(_982504, _982506)), hAPP(_982504, _982508)))], (7280 ^ _776541) ^ [_895546, _895548, _895550] : [hBOOL(hAPP(hAPP(c_member(_895546), _895548), hAPP(hAPP(c_Set_Oinsert(_895546), _895550), c_Orderings_Obot__class_Obot(tc_fun(_895546, tc_HOL_Obool))))), -(_895548 = _895550)], (15757 ^ _776541) ^ [_1062122, _1062124] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062122), hAPP(c_Nat_OSuc, _1062124)))), 15758 ^ _776541 : [(15761 ^ _776541) ^ [_1062210] : [_1062122 = hAPP(c_Nat_OSuc, _1062210), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062210), _1062124))], (15759 ^ _776541) ^ [] : [_1062122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51005 ^ _776541) ^ [_1809358, _1809360, _1809362] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809358), _1809360)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809358), _1809362))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1809358)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809360), _1809362)))], (52447 ^ _776541) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (6208 ^ _776541) ^ [_876296, _876298] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_876296, tc_HOL_Obool)), _876298)))], (3786 ^ _776541) ^ [_833343, _833345, _833347, _833349, _833351, _833353, _833355, _833357] : [-(c_List_Ofoldl(_833357, _833353, _833349, _833345) = c_List_Ofoldl(_833355, _833351, _833347, _833343)), _833357 = _833355, _833353 = _833351, _833349 = _833347, _833345 = _833343], (13274 ^ _776541) ^ [_1011626, _1011628, _1011630, _1011632, _1011634] : [class_Groups_Ocomm__monoid__mult(_1011626), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011628), _1011630)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011628), _1011632)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011626), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011628, _1011626), _1011634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011628, tc_HOL_Obool)), _1011630), _1011632))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011628, _1011626), _1011634), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011628, tc_HOL_Obool)), _1011630), _1011632))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011626), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011628, _1011626), _1011634), _1011630)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011628, _1011626), _1011634), _1011632)))], (13586 ^ _776541) ^ [_1018348, _1018350, _1018352, _1018354] : [class_Groups_Ocancel__ab__semigroup__add(_1018348), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018348), _1018350), _1018352) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018348), _1018350), _1018354), -(_1018352 = _1018354)], (32328 ^ _776541) ^ [_1357937, _1357939, _1357941, _1357943, _1357945, _1357947] : [hBOOL(hAPP(hAPP(c_member(_1357937), _1357939), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357941, tc_fun(_1357937, tc_HOL_Obool)), _1357943), _1357945))), hBOOL(hAPP(hAPP(c_member(_1357941), _1357947), _1357943)), -(hBOOL(hAPP(hAPP(c_member(_1357937), _1357939), hAPP(_1357945, _1357947))))], (35282 ^ _776541) ^ [_1434922] : [-(_1434922 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1434922), 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)))))], (52017 ^ _776541) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (7640 ^ _776541) ^ [_903240, _903242, _903244, _903246] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903240, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903240, tc_HOL_Obool)), _903242), _903244)), _903246) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903240, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903240, tc_HOL_Obool)), _903242), _903246)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903240, tc_HOL_Obool)), _903244), _903246)))], (36633 ^ _776541) ^ [_1471049, _1471051, _1471053] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471049), _1471051), _1471053) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471049, tc_HOL_Obool), tc_HOL_Obool)), -(_1471051 = c_Orderings_Obot__class_Obot(tc_fun(_1471049, tc_HOL_Obool)))], (6573 ^ _776541) ^ [_882792, _882794] : [class_Orderings_Obot(_882792), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882792), c_Orderings_Obot__class_Obot(_882792)), _882794)))], (25351 ^ _776541) ^ [_1235203, _1235205] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235203), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235205), _1235203)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235205), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235205, _1235203)))], (10493 ^ _776541) ^ [_956805, _956807, _956809] : [hBOOL(hAPP(hAPP(c_member(_956805), _956807), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_956805, tc_HOL_Obool)), _956809))), hBOOL(hAPP(hAPP(c_member(_956805), _956807), _956809))], (278 ^ _776541) ^ [_780824, _780826] : [-(c_Nat__Transfer_Ois__nat(_780824)), _780826 = _780824, c_Nat__Transfer_Ois__nat(_780826)], (13990 ^ _776541) ^ [_1027108, _1027110, _1027112, _1027114, _1027116] : [class_Groups_Ocomm__monoid__add(_1027108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027110), _1027112)), -(hBOOL(hAPP(hAPP(c_member(_1027110), _1027114), _1027112))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027110, _1027108), _1027116), hAPP(hAPP(c_Set_Oinsert(_1027110), _1027114), _1027112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027108), hAPP(_1027116, _1027114)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027110, _1027108), _1027116), _1027112)))], (22503 ^ _776541) ^ [_1184325, _1184327] : [class_Groups_Omonoid__mult(_1184325), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184325), c_Groups_Oone__class_Oone(_1184325)), _1184327) = c_Groups_Oone__class_Oone(_1184325))], (18892 ^ _776541) ^ [_1116807, _1116809, _1116811] : [class_Rings_Olinordered__ring__strict(_1116807), 18895 ^ _776541 : [(18896 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116807), c_Groups_Ozero__class_Ozero(_1116807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116807), _1116809), _1116809)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116807), _1116811), _1116811)))), _1116809 = c_Groups_Ozero__class_Ozero(_1116807), _1116811 = c_Groups_Ozero__class_Ozero(_1116807)], (18906 ^ _776541) ^ [] : [18907 ^ _776541 : [(18910 ^ _776541) ^ [] : [-(_1116811 = c_Groups_Ozero__class_Ozero(_1116807))], (18908 ^ _776541) ^ [] : [-(_1116809 = c_Groups_Ozero__class_Ozero(_1116807))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116807), c_Groups_Ozero__class_Ozero(_1116807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116807), _1116809), _1116809)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116807), _1116811), _1116811)))))]]], (5046 ^ _776541) ^ [_853469, _853471] : [_853471 = _853469, -(c_Lattices_Osemilattice__sup__class_Osup(_853471) = c_Lattices_Osemilattice__sup__class_Osup(_853469))], (7648 ^ _776541) ^ [_903565, _903567, _903569, _903571] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903565, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903565, tc_HOL_Obool)), _903567), _903569)), _903571) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903565, tc_HOL_Obool)), _903567), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903565, tc_HOL_Obool)), _903569), _903571)))], (26060 ^ _776541) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37628 ^ _776541) ^ [_1492979, _1492981, _1492983, _1492985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1492979), hAPP(c_Set_Oimage(_1492981, _1492979, _1492983), _1492985))), hAPP(c_Finite__Set_Ocard(_1492981), _1492985))), c_Fun_Oinj__on(_1492981, _1492979, _1492983, _1492985)], (35384 ^ _776541) ^ [_1436226, _1436228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436228)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436226, _1436228), c_Divides_OposDivAlg(_1436226, _1436228))))], (29017 ^ _776541) ^ [_1296710, _1296712] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1296710)), c_Int_OBit1(_1296712)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296710), _1296712)))], (33220 ^ _776541) ^ [_1385349, _1385351, _1385353, _1385355] : [class_Complete__Lattice_Ocomplete__lattice(_1385349), -(_1385351 = c_Orderings_Obot__class_Obot(tc_fun(_1385353, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385353, _1385349), _1385351), hAPP(c_COMBK(_1385349, _1385353), _1385355)) = _1385355)], (35338 ^ _776541) ^ [_1435642, _1435644, _1435646] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435642, _1435642), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435644), _1435646))), -(_1435642 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1435644 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (32516 ^ _776541) ^ [_1363952, _1363954, _1363956, _1363958, _1363960, _1363962, _1363964] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363952, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363954, tc_fun(_1363952, tc_HOL_Obool)), _1363956), _1363958)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363960, tc_fun(_1363952, tc_HOL_Obool)), _1363962), _1363964)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363954, tc_fun(_1363952, tc_HOL_Obool)), _1363956), hAPP(hAPP(c_COMBB(tc_fun(_1363960, tc_fun(_1363952, tc_HOL_Obool)), tc_fun(_1363952, tc_HOL_Obool), _1363954), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363960, tc_fun(_1363952, tc_HOL_Obool)), _1363962)), hAPP(hAPP(c_COMBC(_1363954, tc_fun(_1363960, tc_fun(_1363952, tc_HOL_Obool)), tc_fun(_1363960, tc_fun(_1363952, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1363952, tc_HOL_Obool), tc_fun(_1363952, tc_HOL_Obool)), tc_fun(tc_fun(_1363960, tc_fun(_1363952, tc_HOL_Obool)), tc_fun(_1363960, tc_fun(_1363952, tc_HOL_Obool))), _1363954), c_COMBB(tc_fun(_1363952, tc_HOL_Obool), tc_fun(_1363952, tc_HOL_Obool), _1363960)), hAPP(hAPP(c_COMBB(tc_fun(_1363952, tc_HOL_Obool), tc_fun(tc_fun(_1363952, tc_HOL_Obool), tc_fun(_1363952, tc_HOL_Obool)), _1363954), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363952, tc_HOL_Obool))), _1363958))), _1363964))))], (8267 ^ _776541) ^ [_917896, _917898, _917900] : [class_Lattices_Olattice(_917896), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917896), _917898), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917896), _917898), _917900)) = _917898)], (30824 ^ _776541) ^ [_1329359, _1329361, _1329363] : [class_Orderings_Olinorder(_1329359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329359), _1329361)), -(c_Big__Operators_Olinorder__class_OMin(_1329359, hAPP(hAPP(c_Set_Oinsert(_1329359), _1329363), _1329361)) = hAPP(hAPP(c_Finite__Set_Ofold(_1329359, _1329359, c_Orderings_Oord__class_Omin(_1329359)), _1329363), _1329361))], (52385 ^ _776541) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (12965 ^ _776541) ^ [_1005316, _1005318, _1005320] : [class_Lattices_Oab__semigroup__idem__mult(_1005316), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005316), _1005318)), -(_1005318 = c_Orderings_Obot__class_Obot(tc_fun(_1005316, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005316), _1005320)), -(_1005320 = c_Orderings_Obot__class_Obot(tc_fun(_1005316, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1005316, c_Groups_Otimes__class_Otimes(_1005316)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1005316, tc_HOL_Obool)), _1005318), _1005320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005316), hAPP(c_Finite__Set_Ofold1(_1005316, c_Groups_Otimes__class_Otimes(_1005316)), _1005318)), hAPP(c_Finite__Set_Ofold1(_1005316, c_Groups_Otimes__class_Otimes(_1005316)), _1005320)))], (40370 ^ _776541) ^ [_1563676, _1563678] : [hBOOL(hAPP(_1563676, c_Hilbert__Choice_OEps(_1563678, _1563676))), -(hBOOL(hAPP(_1563676, 40373 ^ [_1563676, _1563678])))], (16793 ^ _776541) ^ [_1078753, _1078755, _1078757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078755), _1078757)), -(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, _1078753)), _1078755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078753)), _1078757))))], (6780 ^ _776541) ^ [_886184, _886186, _886188] : [class_Orderings_Olinorder(_886184), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886184), _886186), _886188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886184), _886188), _886186)))], (8123 ^ _776541) ^ [_914928, _914930, _914932, _914934] : [class_Orderings_Oorder(_914928), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914928, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914928, _914930, _914932)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914928, _914932, _914934)) = c_Orderings_Obot__class_Obot(tc_fun(_914928, tc_HOL_Obool)))], (43022 ^ _776541) ^ [_1634028, _1634030, _1634032] : [_1634028 = c_List_Olist_ONil(_1634030), -(c_List_Obutlast(_1634030, hAPP(hAPP(c_List_Olist_OCons(_1634030), _1634032), _1634028)) = c_List_Olist_ONil(_1634030))], (43210 ^ _776541) ^ [_1637373, _1637375, _1637377] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637373), tc_List_Olist(_1637373))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637373), tc_List_Olist(_1637373)), _1637375), c_List_Olist_ONil(_1637373))), c_List_Olex(_1637373, _1637377)))], (41714 ^ _776541) ^ [_1597949] : [-(c_Nitpick_Onum(_1597949) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1597949, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1597949)))], (24856 ^ _776541) ^ [_1226398, _1226400, _1226402, _1226404] : [class_Divides_Osemiring__div(_1226398), -(c_Divides_Odiv__class_Omod(_1226398, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226398), _1226400), _1226402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226398), _1226404), _1226402)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226398), c_Divides_Odiv__class_Omod(_1226398, _1226400, _1226404)), _1226402))], (48728 ^ _776541) ^ [_1758642, _1758644, _1758646, _1758648] : [-(hBOOL(hAPP(hAPP(c_member(_1758642), _1758644), hAPP(c_List_Oset(_1758642), c_List_Oreplicate(_1758642, _1758646, _1758648))))), _1758644 = _1758648, -(_1758646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9480 ^ _776541) ^ [_939411, _939413, _939415] : [class_Orderings_Oorder(_939411), 9483 ^ _776541 : [(9484 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939411), _939413), _939415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939411), _939413), _939415))), -(_939413 = _939415)], (9494 ^ _776541) ^ [] : [9495 ^ _776541 : [(9498 ^ _776541) ^ [] : [_939413 = _939415], (9496 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939411), _939413), _939415))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939411), _939413), _939415)))]]], (7728 ^ _776541) ^ [_906030, _906032, _906034] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906030, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_906030, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_906030, tc_HOL_Obool), tc_HOL_Obool)), _906032), _906034))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906030, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_906030, tc_HOL_Obool), _906032)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_906030, tc_HOL_Obool), _906034)))))], (27833 ^ _776541) ^ [_1277004, _1277006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277004)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277004), _1277006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277004), c_Int_OPls)))], (26088 ^ _776541) ^ [_1248046, _1248048] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248046)))), 26091 ^ _776541 : [(26098 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248048)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248046), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248048)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248046), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248048))))], (26092 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248048))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248046), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248048)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248046))]]], (43926 ^ _776541) ^ [_1654358, _1654360] : [hAPP(c_List_Orotate1(_1654358), _1654360) = c_List_Olist_ONil(_1654358), -(_1654360 = c_List_Olist_ONil(_1654358))], (35228 ^ _776541) ^ [_1433916, _1433918, _1433920] : [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), _1433916), _1433918))), -(hBOOL(hAPP(hAPP(_1433920, _1433916), _1433918))), 35235 ^ _776541 : [(35238 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1433920, 35233 ^ [_1433916, _1433918, _1433920]), 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)))), 35234 ^ [_1433916, _1433918, _1433920])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 35233 ^ [_1433916, _1433918, _1433920]), 35234 ^ [_1433916, _1433918, _1433920]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 35234 ^ [_1433916, _1433918, _1433920]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35248 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1433920, 35233 ^ [_1433916, _1433918, _1433920]), 35234 ^ [_1433916, _1433918, _1433920]))], (35236 ^ _776541) ^ [] : [-(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), 35233 ^ [_1433916, _1433918, _1433920]), 35234 ^ [_1433916, _1433918, _1433920]))))]]], (43276 ^ _776541) ^ [_1638753, _1638755, _1638757] : [-(hBOOL(hAPP(hAPP(c_member(_1638753), _1638755), hAPP(c_List_Oset(_1638753), _1638757)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638753)), c_List_Oremove1(_1638753, _1638755, _1638757)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638753)), _1638757))], (28259 ^ _776541) ^ [_1283927, _1283929] : [class_Int_Onumber__ring(_1283927), 28262 ^ _776541 : [(28269 ^ _776541) ^ [] : [c_Int_Oiszero(_1283927, hAPP(c_Int_Onumber__class_Onumber__of(_1283927), 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), _1283929)))), -(c_Groups_Oone__class_Oone(_1283927) = hAPP(c_Int_Onumber__class_Onumber__of(_1283927), _1283929))], (28263 ^ _776541) ^ [] : [c_Groups_Oone__class_Oone(_1283927) = hAPP(c_Int_Onumber__class_Onumber__of(_1283927), _1283929), -(c_Int_Oiszero(_1283927, hAPP(c_Int_Onumber__class_Onumber__of(_1283927), 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), _1283929)))))]]], (5066 ^ _776541) ^ [_853775, _853777, _853779, _853781, _853783, _853785, _853787, _853789] : [-(c_Product__Type_Ocurry(_853789, _853785, _853781, _853777) = c_Product__Type_Ocurry(_853787, _853783, _853779, _853775)), _853789 = _853787, _853785 = _853783, _853781 = _853779, _853777 = _853775], (21297 ^ _776541) ^ [_1161993, _1161995] : [class_Int_Onumber__ring(_1161993), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1161993), hAPP(c_Int_Onumber__class_Onumber__of(_1161993), _1161995)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161993), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161995)))], (35368 ^ _776541) ^ [_1436014, _1436016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436014), 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)), _1436016)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436014, _1436016), c_Divides_OnegDivAlg(_1436014, _1436016))))], (25058 ^ _776541) ^ [_1230249, _1230251] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230249, _1230251) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1230249 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230251), 25061 ^ [_1230249, _1230251]))], (43316 ^ _776541) ^ [_1639757, _1639759, _1639761] : [class_Orderings_Olinorder(_1639757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639757), _1639759)), -(c_List_Olinorder__class_Osorted__list__of__set(_1639757, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639757, tc_HOL_Obool)), _1639759), hAPP(hAPP(c_Set_Oinsert(_1639757), _1639761), c_Orderings_Obot__class_Obot(tc_fun(_1639757, tc_HOL_Obool))))) = c_List_Oremove1(_1639757, _1639761, c_List_Olinorder__class_Osorted__list__of__set(_1639757, _1639759)))], (47958 ^ _776541) ^ [_1742602, _1742604] : [class_Enum_Oenum(_1742602), 47961 ^ _776541 : [(47968 ^ _776541) ^ [] : [hBOOL(hAPP(_1742604, 47969 ^ [_1742602, _1742604])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742602), _1742604)))], (47962 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742602), _1742604)), 47965 ^ _776541 : [(47966 ^ _776541) ^ [_1742728] : [-(hBOOL(hAPP(_1742604, _1742728)))]]]]], (51407 ^ _776541) ^ [_1817054, _1817056, _1817058, _1817060] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817054, _1817056)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817058, _1817060)))), 51408 ^ _776541 : [(51411 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817058), _1817054)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817056), _1817060))], (51409 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817054), _1817056)))]]], (15503 ^ _776541) ^ [_1057119, _1057121, _1057123, _1057125, _1057127] : [class_Groups_Ocomm__monoid__mult(_1057119), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057121), _1057123)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057121), _1057125)), 15517 ^ _776541 : [(15520 ^ _776541) ^ [] : [hAPP(_1057127, 15516 ^ [_1057119, _1057121, _1057123, _1057125, _1057127]) = c_Groups_Oone__class_Oone(_1057119)], (15518 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1057121), 15516 ^ [_1057119, _1057121, _1057123, _1057125, _1057127]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057121, tc_HOL_Obool)), _1057123), _1057125))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1057121, _1057119), _1057127), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1057121, tc_HOL_Obool)), _1057123), _1057125)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057119), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1057121, _1057119), _1057127), _1057123)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1057121, _1057119), _1057127), _1057125)))], (5901 ^ _776541) ^ [_870381, _870383, _870385, _870387] : [_870381 = _870383, 5904 ^ _776541 : [(5911 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870385), _870387), _870383)), -(hBOOL(hAPP(hAPP(c_member(_870385), _870387), _870381)))], (5905 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870385), _870387), _870381)), -(hBOOL(hAPP(hAPP(c_member(_870385), _870387), _870383)))]]], (48274 ^ _776541) ^ [_1748837, _1748839, _1748841] : [c_List_Olist__all(_1748837, _1748839, _1748841), -(c_List_Olist__all(_1748837, _1748839, hAPP(c_List_Orev(_1748837), _1748841)))], (31549 ^ _776541) ^ [_1342967, _1342969, _1342971] : [class_Orderings_Olinorder(_1342967), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342967), _1342969), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342967), _1342969), _1342971))))], (15186 ^ _776541) ^ [_1050537, _1050539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050537), c_Orderings_Otop__class_Otop(tc_fun(_1050537, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1050537), _1050539) = hAPP(c_Finite__Set_Ocard(_1050537), c_Orderings_Otop__class_Otop(tc_fun(_1050537, tc_HOL_Obool))), -(_1050539 = c_Orderings_Otop__class_Otop(tc_fun(_1050537, tc_HOL_Obool)))], (29027 ^ _776541) ^ [_1296903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296903), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1296903)), c_Int_OMin)))], (47040 ^ _776541) ^ [_1722079, _1722081, _1722083, _1722085, _1722087] : [c_List_Olist__all2(_1722079, _1722081, _1722083, _1722085, hAPP(c_List_Orev(_1722081), _1722087)), -(c_List_Olist__all2(_1722079, _1722081, _1722083, hAPP(c_List_Orev(_1722079), _1722085), _1722087))], (40343 ^ _776541) ^ [_1563117, _1563119, _1563121] : [-(c_Hilbert__Choice_OEps(tc_prod(_1563117, _1563119), hAPP(c_Product__Type_Oprod_Oprod__case(_1563117, _1563119, tc_HOL_Obool), _1563121)) = c_Hilbert__Choice_OEps(tc_prod(_1563117, _1563119), hAPP(hAPP(c_COMBS(tc_prod(_1563117, _1563119), _1563119, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1563117, tc_fun(_1563119, tc_HOL_Obool), tc_prod(_1563117, _1563119)), _1563121), c_Product__Type_Ofst(_1563117, _1563119))), c_Product__Type_Osnd(_1563117, _1563119))))], (6963 ^ _776541) ^ [_889543, _889545] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_889543, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_889543, tc_HOL_Obool))), hAPP(c_Set_OPow(_889543), _889545))))], (50243 ^ _776541) ^ [_1792210] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50239 ^ [_1792210]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (39934 ^ _776541) ^ [_1553892, _1553894, _1553896, _1553898, _1553900, _1553902] : [-(hAPP(c_Set_Ovimage(_1553892, _1553894, hAPP(c_Fun_Ocomp(_1553896, _1553894, _1553892, _1553898), _1553900)), _1553902) = hAPP(c_Set_Ovimage(_1553892, _1553896, _1553900), hAPP(c_Set_Ovimage(_1553896, _1553894, _1553898), _1553902)))], (9214 ^ _776541) ^ [_935584, _935586, _935588] : [class_Orderings_Olinorder(_935584), -(_935586 = _935588), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935584), _935586), _935588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935584), _935588), _935586)))], (50910 ^ _776541) ^ [_1807679, _1807681, _1807683] : [c_List_Olist__all(tc_Nat_Onat, _1807679, c_List_Oupt(_1807681, _1807683)), -(c_List_Oall__interval__nat(_1807679, _1807681, _1807683))], (39916 ^ _776541) ^ [_1553408, _1553410, _1553412, _1553414, _1553416, _1553418, _1553420] : [hAPP(c_Fun_Ocomp(_1553408, _1553410, _1553412, _1553414), _1553416) = _1553418, -(hAPP(_1553414, hAPP(_1553416, _1553420)) = hAPP(_1553418, _1553420))], (43916 ^ _776541) ^ [_1654106, _1654108, _1654110, _1654112] : [hBOOL(hAPP(hAPP(c_member(_1654106), _1654108), hAPP(c_List_Oset(_1654106), hAPP(hAPP(c_List_Odrop(_1654106), _1654110), _1654112)))), -(hBOOL(hAPP(hAPP(c_member(_1654106), _1654108), hAPP(c_List_Oset(_1654106), _1654112))))], (26561 ^ _776541) ^ [_1255968, _1255970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255968)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1255968)), _1255970) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1255968), _1255970)))], (41110 ^ _776541) ^ [_1582712, _1582714, _1582716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582714, _1582712)), _1582716)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582712, _1582714)), hAPP(c_Relation_Oconverse(_1582714, _1582712), _1582716))))], (43573 ^ _776541) ^ [_1645779, _1645781, _1645783] : [-(c_List_Olist_ONil(_1645779) = hAPP(hAPP(c_List_Oappend(_1645779), _1645781), _1645783)), _1645781 = c_List_Olist_ONil(_1645779), _1645783 = c_List_Olist_ONil(_1645779)], (15462 ^ _776541) ^ [_1056160, _1056162, _1056164] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056160), _1056162)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056160), _1056164)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056160, tc_HOL_Obool)), _1056162), _1056164) = c_Orderings_Obot__class_Obot(tc_fun(_1056160, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1056160), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056160, tc_HOL_Obool)), _1056162), _1056164)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1056160), _1056162)), hAPP(c_Finite__Set_Ocard(_1056160), _1056164)))], (14336 ^ _776541) ^ [_1035006, _1035008, _1035010, _1035012] : [class_Rings_Ocomm__semiring__1(_1035006), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035006), _1035008), _1035010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035006), _1035012), _1035010)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035006), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035006), _1035008), _1035012)), _1035010))], (28759 ^ _776541) ^ [_1292104, _1292106] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1292104), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1292106)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1292104), 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)))), _1292106)))], (33645 ^ _776541) ^ [_1397868, _1397870, _1397872, _1397874] : [hBOOL(hAPP(hAPP(c_member(_1397870), _1397874), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397868, tc_fun(_1397870, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397868, tc_HOL_Obool))), _1397872))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397868, tc_fun(_1397870, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397868, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1397870, tc_HOL_Obool), tc_fun(_1397870, tc_HOL_Obool), _1397868), hAPP(c_COMBC(_1397870, tc_fun(_1397870, tc_HOL_Obool), tc_HOL_Obool), c_member(_1397870))), _1397872)), _1397874)))], (48704 ^ _776541) ^ [_1758216, _1758218, _1758220] : [c_List_Olist_ONil(_1758216) = c_List_Oreplicate(_1758216, _1758218, _1758220), -(_1758218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25115 ^ _776541) ^ [_1231119] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1231119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231119), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29711 ^ _776541) ^ [_1309294] : [_1309294 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1309294) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39922 ^ _776541) ^ [_1553529, _1553531, _1553533, _1553535, _1553537, _1553539, _1553541, _1553543, _1553545, _1553547, _1553549] : [hAPP(_1553529, hAPP(_1553531, _1553533)) = hAPP(_1553535, hAPP(_1553537, _1553539)), -(hAPP(hAPP(c_Fun_Ocomp(_1553541, _1553543, _1553545, _1553529), _1553531), _1553533) = hAPP(hAPP(c_Fun_Ocomp(_1553547, _1553543, _1553549, _1553535), _1553537), _1553539))], (36284 ^ _776541) ^ [_1461431, _1461433, _1461435, _1461437] : [c_Wellfounded_Omax__extp(_1461431, hAPP(hAPP(c_COMBC(_1461431, tc_fun(tc_prod(_1461431, _1461431), tc_HOL_Obool), tc_fun(_1461431, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461431, tc_fun(tc_fun(tc_prod(_1461431, _1461431), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461431, _1461431), tc_HOL_Obool), tc_fun(_1461431, tc_HOL_Obool)), _1461431), c_COMBC(_1461431, tc_fun(tc_prod(_1461431, _1461431), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461431, tc_prod(_1461431, _1461431)), tc_fun(_1461431, tc_fun(tc_fun(tc_prod(_1461431, _1461431), tc_HOL_Obool), tc_HOL_Obool)), _1461431), hAPP(c_COMBB(tc_prod(_1461431, _1461431), tc_fun(tc_fun(tc_prod(_1461431, _1461431), tc_HOL_Obool), tc_HOL_Obool), _1461431), c_member(tc_prod(_1461431, _1461431)))), c_Product__Type_OPair(_1461431, _1461431)))), _1461433), _1461435, _1461437), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1461431, tc_HOL_Obool), tc_fun(_1461431, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1461431, tc_HOL_Obool), tc_fun(_1461431, tc_HOL_Obool)), _1461435), _1461437)), c_Wellfounded_Omax__ext(_1461431, _1461433))))], (37927 ^ _776541) ^ [_1500419, _1500421, _1500423, _1500425, _1500427, _1500429, _1500431, _1500433] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500419, _1500421)), hAPP(hAPP(c_Product__Type_OPair(_1500419, _1500421), _1500423), _1500425)), _1500427)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500421, _1500429)), hAPP(hAPP(c_Product__Type_OPair(_1500421, _1500429), _1500425), _1500431)), _1500433)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500419, _1500429)), hAPP(hAPP(c_Product__Type_OPair(_1500419, _1500429), _1500423), _1500431)), hAPP(hAPP(c_Relation_Orel__comp(_1500419, _1500421, _1500429), _1500427), _1500433))))], (28887 ^ _776541) ^ [_1294400, _1294402] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1294400)), c_Int_OBit0(_1294402)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1294400), _1294402)))], (28117 ^ _776541) ^ [_1281515] : [class_Rings_Osemiring__1(_1281515), c_Int_Oiszero(_1281515, c_Groups_Oone__class_Oone(_1281515))], (20041 ^ _776541) ^ [_1138396, _1138398, _1138400] : [class_Fields_Olinordered__field__inverse__zero(_1138396), 20044 ^ _776541 : [(20059 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138396), _1138398), _1138400)), c_Groups_Ozero__class_Ozero(_1138396)))), 20060 ^ _776541 : [(20067 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), _1138398), c_Groups_Ozero__class_Ozero(_1138396))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), c_Groups_Ozero__class_Ozero(_1138396)), _1138400))], (20061 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), c_Groups_Ozero__class_Ozero(_1138396)), _1138398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), _1138400), c_Groups_Ozero__class_Ozero(_1138396)))]]], (20045 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138396), _1138398), _1138400)), c_Groups_Ozero__class_Ozero(_1138396))), 20050 ^ _776541 : [(20053 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), _1138400), c_Groups_Ozero__class_Ozero(_1138396))))], (20051 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), c_Groups_Ozero__class_Ozero(_1138396)), _1138398)))]], 20054 ^ _776541 : [(20057 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), c_Groups_Ozero__class_Ozero(_1138396)), _1138400)))], (20055 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138396), _1138398), c_Groups_Ozero__class_Ozero(_1138396))))]]]]], (16486 ^ _776541) ^ [_1073423] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1073423), hAPP(c_Nat_OSuc, _1073423)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1073423), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (52133 ^ _776541) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (32952 ^ _776541) ^ [_1377504, _1377506, _1377508, _1377510, _1377512] : [_1377504 = c_Orderings_Obot__class_Obot(tc_fun(_1377506, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377508, tc_HOL_Obool)), _1377510), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377506, tc_fun(_1377508, tc_HOL_Obool)), _1377504), _1377512)) = _1377510)], (49525 ^ _776541) ^ [_1777445, _1777447, _1777449, _1777451] : [-(c_Wellfounded_Omax__extp(_1777445, _1777447, _1777449, _1777451)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1777445), _1777449)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1777445), _1777451)), -(_1777451 = c_Orderings_Obot__class_Obot(tc_fun(_1777445, tc_HOL_Obool))), 49539 ^ _776541 : [(49542 ^ _776541) ^ [_1777790] : [hBOOL(hAPP(hAPP(c_member(_1777445), _1777790), _1777451)), hBOOL(hAPP(hAPP(_1777447, 49538 ^ [_1777445, _1777447, _1777449, _1777451]), _1777790))], (49540 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777445), 49538 ^ [_1777445, _1777447, _1777449, _1777451]), _1777449)))]]], (2832 ^ _776541) ^ [_818516, _818518, _818520, _818522] : [-(c_Wellfounded_Omax__ext(_818522, _818518) = c_Wellfounded_Omax__ext(_818520, _818516)), _818522 = _818520, _818518 = _818516], (24030 ^ _776541) ^ [_1211583, _1211585] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211583), _1211585)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211583)), _1211585))], (51691 ^ _776541) ^ [_1822026, _1822028] : [-(_1822026 = _1822028), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822026), _1822028)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822028), _1822026))], (3018 ^ _776541) ^ [_821339, _821341] : [_821341 = _821339, -(c_Nitpick_ORep__Frac(_821341) = c_Nitpick_ORep__Frac(_821339))], (28633 ^ _776541) ^ [_1290045] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1290045))) = 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)))), _1290045))], (38796 ^ _776541) ^ [_1522378, _1522380, _1522382, _1522384, _1522386] : [hBOOL(hAPP(hAPP(c_member(_1522378), _1522380), hAPP(c_Set_Ovimage(_1522378, _1522382, _1522384), hAPP(hAPP(c_Set_Oinsert(_1522382), _1522386), c_Orderings_Obot__class_Obot(tc_fun(_1522382, tc_HOL_Obool)))))), -(hAPP(_1522384, _1522380) = _1522386)], (35487 ^ _776541) ^ [_1438631, _1438633, _1438635, _1438637, _1438639, _1438641] : [hAPP(_1438637, hAPP(c_Product__Type_Osnd(_1438635, _1438631), _1438639)) = hAPP(_1438641, hAPP(c_Product__Type_Osnd(_1438635, _1438631), _1438639)), -(hAPP(c_Product__Type_Oapsnd(_1438631, _1438633, _1438635, _1438637), _1438639) = hAPP(c_Product__Type_Oapsnd(_1438631, _1438633, _1438635, _1438641), _1438639))], (14821 ^ _776541) ^ [_1043804, _1043806] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043804), _1043806)), _1043806) = _1043804)], (42319 ^ _776541) ^ [_1616374, _1616376, _1616378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616374, tc_HOL_Obool)), hAPP(c_List_Oset(_1616374), c_List_Osublist(_1616374, _1616376, _1616378))), hAPP(c_List_Oset(_1616374), _1616376))))], (38877 ^ _776541) ^ [_1524267, _1524269] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1524267, _1524267)), _1524269)), 38880 ^ _776541 : [(38887 ^ _776541) ^ [] : [c_Wellfounded_Oacyclic(_1524267, _1524269), -(c_Wellfounded_Owf(_1524267, _1524269))], (38881 ^ _776541) ^ [] : [c_Wellfounded_Owf(_1524267, _1524269), -(c_Wellfounded_Oacyclic(_1524267, _1524269))]]], (50117 ^ _776541) ^ [_1789133, _1789135, _1789137, _1789139] : [c_Fun_Oinj__on(_1789133, _1789135, _1789137, c_Orderings_Otop__class_Otop(tc_fun(_1789133, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1789135, _1789133, c_Hilbert__Choice_Oinv__into(_1789133, _1789135, c_Orderings_Otop__class_Otop(tc_fun(_1789133, tc_HOL_Obool)), _1789137)), hAPP(c_Set_Oimage(_1789133, _1789135, _1789137), _1789139)) = _1789139)], (50135 ^ _776541) ^ [_1789554, _1789556, _1789558, _1789560, _1789562] : [c_Fun_Oinj__on(_1789554, _1789556, _1789558, _1789560), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789554, tc_HOL_Obool)), _1789562), _1789560)), -(hAPP(c_Set_Oimage(_1789556, _1789554, c_Hilbert__Choice_Oinv__into(_1789554, _1789556, _1789560, _1789558)), hAPP(c_Set_Oimage(_1789554, _1789556, _1789558), _1789562)) = _1789562)], (46327 ^ _776541) ^ [_1708253, _1708255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1708253), _1708255)), -(c_List_Oupt(_1708253, hAPP(c_Nat_OSuc, _1708255)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1708253, _1708255)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1708255), c_List_Olist_ONil(tc_Nat_Onat))))], (33282 ^ _776541) ^ [_1386721, _1386723, _1386725, _1386727] : [class_Complete__Lattice_Ocomplete__lattice(_1386721), -(_1386723 = c_Orderings_Obot__class_Obot(tc_fun(_1386725, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386725, _1386721), _1386723), hAPP(c_COMBK(_1386721, _1386725), _1386727)) = _1386727)], (9580 ^ _776541) ^ [_940844, _940846, _940848] : [class_Orderings_Opreorder(_940844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940844), _940846), _940848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940844), _940846), _940848)))], (25375 ^ _776541) ^ [_1235567, _1235569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235569), _1235567))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235569), _1235567) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1235569), _1235567)), _1235567)))], (47275 ^ _776541) ^ [_1727019, _1727021, _1727023, _1727025, _1727027] : [-(hBOOL(hAPP(_1727019, _1727021))), -(c_List_OtakeWhile(_1727023, _1727019, hAPP(hAPP(c_List_Oappend(_1727023), _1727025), hAPP(hAPP(c_List_Olist_OCons(_1727023), _1727021), _1727027))) = c_List_OtakeWhile(_1727023, _1727019, _1727025))], (34860 ^ _776541) ^ [_1427084, _1427086, _1427088, _1427090, _1427092, _1427094] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427084, _1427086, _1427088), _1427090), hAPP(hAPP(c_Product__Type_OPair(_1427084, _1427086), _1427092), _1427094)) = hAPP(hAPP(_1427090, _1427092), _1427094))], (16396 ^ _776541) ^ [_1072189, _1072191] : [class_Groups_Ogroup__add(_1072189), 16399 ^ _776541 : [(16406 ^ _776541) ^ [] : [_1072191 = c_Groups_Ozero__class_Ozero(_1072189), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1072189), _1072191) = c_Groups_Ozero__class_Ozero(_1072189))], (16400 ^ _776541) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1072189), _1072191) = c_Groups_Ozero__class_Ozero(_1072189), -(_1072191 = c_Groups_Ozero__class_Ozero(_1072189))]]], (52035 ^ _776541) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (35481 ^ _776541) ^ [_1438482, _1438484, _1438486, _1438488, _1438490, _1438492] : [hAPP(c_Product__Type_Oapsnd(_1438482, _1438484, _1438486, _1438488), _1438490) = hAPP(c_Product__Type_Oapsnd(_1438482, _1438484, _1438486, _1438492), _1438490), -(hAPP(_1438488, hAPP(c_Product__Type_Osnd(_1438486, _1438482), _1438490)) = hAPP(_1438492, hAPP(c_Product__Type_Osnd(_1438486, _1438482), _1438490)))], (48444 ^ _776541) ^ [_1752313, _1752315, _1752317, _1752319] : [-(c_New__Random__Sequence_Opos__empty(_1752313, _1752315, _1752317, _1752319) = c_New__DSequence_Opos__empty(_1752313))], (45776 ^ _776541) ^ [_1695000, _1695002] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695000)), c_List_Oremdups(_1695000, _1695002)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695000)), _1695002), -(c_List_Oremdups(_1695000, _1695002) = _1695002)], (52373 ^ _776541) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (4658 ^ _776541) ^ [_847377, _847379] : [_847379 = _847377, -(c_DSequence_Ounion(_847379) = c_DSequence_Ounion(_847377))], (45249 ^ _776541) ^ [_1682765] : [-(hAPP(c_Code__Numeral_Onat__of, _1682765) = c_Code__Numeral_Onat__of__aux(_1682765, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7906 ^ _776541) ^ [_909931, _909933, _909935, _909937] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909931, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909931), _909933), _909935)), hAPP(hAPP(c_Set_Oinsert(_909931), _909933), _909937)) = hAPP(hAPP(c_Set_Oinsert(_909931), _909933), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909931, tc_HOL_Obool)), _909935), _909937)))], (47591 ^ _776541) ^ [_1733601, _1733603, _1733605] : [-(c_List_Oinsert(_1733601, _1733603, c_List_Oremdups(_1733601, _1733605)) = c_List_Oremdups(_1733601, c_List_Oinsert(_1733601, _1733603, _1733605)))], (8026 ^ _776541) ^ [_912761, _912763, _912765, _912767] : [hBOOL(hAPP(hAPP(c_member(_912761), _912763), _912765)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912761, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912761), _912763), _912767)), _912765) = hAPP(hAPP(c_Set_Oinsert(_912761), _912763), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912761, tc_HOL_Obool)), _912767), _912765)))], (11816 ^ _776541) ^ [_983652, _983654, _983656] : [class_Lattices_Olattice(_983652), hBOOL(hAPP(c_Finite__Set_Ofinite(_983652), _983654)), hBOOL(hAPP(hAPP(c_member(_983652), _983656), _983654)), 11827 ^ _776541 : [(11834 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983652, tc_HOL_Obool)), _983654), hAPP(hAPP(c_Set_Oinsert(_983652), _983656), c_Orderings_Obot__class_Obot(tc_fun(_983652, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_983652, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_983652, _983654) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_983652), _983656), c_Big__Operators_Olattice__class_OSup__fin(_983652, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983652, tc_HOL_Obool)), _983654), hAPP(hAPP(c_Set_Oinsert(_983652), _983656), c_Orderings_Obot__class_Obot(tc_fun(_983652, tc_HOL_Obool)))))))], (11828 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983652, tc_HOL_Obool)), _983654), hAPP(hAPP(c_Set_Oinsert(_983652), _983656), c_Orderings_Obot__class_Obot(tc_fun(_983652, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_983652, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_983652, _983654) = _983656)]]], (15099 ^ _776541) ^ [_1049147, _1049149] : [class_Groups_Ocomm__monoid__mult(_1049147), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049147), c_Groups_Oone__class_Oone(_1049147)), _1049149) = _1049149)], (30620 ^ _776541) ^ [_1325997, _1325999, _1326001] : [class_Orderings_Olinorder(_1325997), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325997), _1325999)), hBOOL(hAPP(hAPP(c_member(_1325997), _1326001), _1325999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325997), c_Big__Operators_Olinorder__class_OMin(_1325997, _1325999)), _1326001)))], (49279 ^ _776541) ^ [_1771600, _1771602] : [c_Relation_Otrans(_1771600, _1771602), -(c_Relation_Otrans(tc_List_Olist(_1771600), c_List_Olistrel(_1771600, _1771602)))], (25263 ^ _776541) ^ [_1233854] : [class_Int_Onumber__ring(_1233854), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1233854), c_Groups_Oone__class_Oone(_1233854)) = hAPP(c_Int_Onumber__class_Onumber__of(_1233854), c_Int_OMin))], (37576 ^ _776541) ^ [_1491811, _1491813, _1491815, _1491817, _1491819] : [c_Fun_Oinj__on(_1491811, _1491813, _1491815, c_Orderings_Otop__class_Otop(tc_fun(_1491811, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1491811, _1491813, _1491815), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491811, tc_HOL_Obool)), _1491817), _1491819)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491813, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491811, _1491813, _1491815), _1491817)), hAPP(c_Set_Oimage(_1491811, _1491813, _1491815), _1491819)))], (34397 ^ _776541) ^ [_1416818, _1416820] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416818), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 34400 ^ _776541 : [(34409 ^ _776541) ^ [] : [-(c_Nitpick_Onorm__frac(_1416820, _1416818) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1416820), _1416818)), 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), _1416820))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1416818)))), -(_1416820 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1416818 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34401 ^ _776541) ^ [] : [34402 ^ _776541 : [(34405 ^ _776541) ^ [] : [_1416818 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (34403 ^ _776541) ^ [] : [_1416820 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1416820, _1416818) = 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)))]]], (22203 ^ _776541) ^ [_1179240, _1179242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179240), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1179242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179240), _1179242)))], (13866 ^ _776541) ^ [_1023908, _1023910, _1023912, _1023914, _1023916, _1023918] : [class_Rings_Oring(_1023908), 13869 ^ _776541 : [(13876 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1023908), _1023910), _1023916)), _1023912)), _1023914) = _1023918, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023908), _1023910), _1023912)), _1023914) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023908), _1023916), _1023912)), _1023918))], (13870 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023908), _1023910), _1023912)), _1023914) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023908), _1023916), _1023912)), _1023918), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1023908), _1023910), _1023916)), _1023912)), _1023914) = _1023918)]]], (32934 ^ _776541) ^ [_1377049, _1377051, _1377053, _1377055, _1377057] : [-(_1377049 = c_Orderings_Obot__class_Obot(tc_fun(_1377051, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377051, tc_fun(_1377053, tc_HOL_Obool)), _1377049), hAPP(hAPP(c_COMBC(_1377051, tc_fun(_1377053, tc_HOL_Obool), tc_fun(_1377053, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377053, tc_HOL_Obool), tc_fun(tc_fun(_1377053, tc_HOL_Obool), tc_fun(_1377053, tc_HOL_Obool)), _1377051), c_Groups_Ominus__class_Ominus(tc_fun(_1377053, tc_HOL_Obool))), _1377055)), _1377057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377053, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377051, tc_fun(_1377053, tc_HOL_Obool)), _1377049), _1377055)), _1377057))], (10893 ^ _776541) ^ [_964538, _964540, _964542, _964544, _964546] : [class_Groups_Oab__semigroup__mult(_964538), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_964538, _964538, c_Groups_Otimes__class_Otimes(_964538), _964540, _964542), _964544)), hBOOL(hAPP(hAPP(c_member(_964538), _964546), _964542)), -(hBOOL(hAPP(hAPP(c_member(_964538), _964540), _964542))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_964538, _964538, c_Groups_Otimes__class_Otimes(_964538), _964546, hAPP(hAPP(c_Set_Oinsert(_964538), _964540), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964538, tc_HOL_Obool)), _964542), hAPP(hAPP(c_Set_Oinsert(_964538), _964546), c_Orderings_Obot__class_Obot(tc_fun(_964538, tc_HOL_Obool)))))), _964544)))], (5476 ^ _776541) ^ [_860214, _860216] : [_860216 = _860214, -(c_member(_860216) = c_member(_860214))], (16110 ^ _776541) ^ [_1067774, _1067776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067774)), hAPP(c_Nat_OSuc, _1067776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067774), _1067776)))], (45485 ^ _776541) ^ [_1688653, _1688655, _1688657, _1688659] : [c_List_Olist__all2(_1688653, _1688655, _1688657, c_List_Olist_ONil(_1688653), _1688659), -(_1688659 = c_List_Olist_ONil(_1688655))], (29683 ^ _776541) ^ [_1308712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1308712)), -(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), _1308712), 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)))))))], (6522 ^ _776541) ^ [_881849, _881851, _881853] : [class_Orderings_Obot(_881849), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_881851, _881849)), _881853) = c_Orderings_Obot__class_Obot(_881849))], (6256 ^ _776541) ^ [_877103] : [class_Complete__Lattice_Ocomplete__lattice(_877103), -(c_Complete__Lattice_OSup__class_OSup(_877103, c_Orderings_Otop__class_Otop(tc_fun(_877103, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_877103))], (41162 ^ _776541) ^ [_1583665, _1583667, _1583669, _1583671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583665, _1583665)), hAPP(hAPP(c_Product__Type_OPair(_1583665, _1583665), _1583667), _1583669)), c_Transitive__Closure_Ortrancl(_1583665, hAPP(c_Relation_Oconverse(_1583665, _1583665), _1583671)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583665, _1583665)), hAPP(hAPP(c_Product__Type_OPair(_1583665, _1583665), _1583669), _1583667)), c_Transitive__Closure_Ortrancl(_1583665, _1583671))))], (24646 ^ _776541) ^ [_1222451, _1222453, _1222455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222451)), 24649 ^ _776541 : [(24650 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1222453, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222455), _1222451)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222455, _1222451))), 24653 ^ _776541 : [(24654 ^ _776541) ^ [_1222652, _1222654] : [-(hBOOL(hAPP(hAPP(_1222453, _1222654), _1222652))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222652), _1222451)), _1222455 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222451), _1222654)), _1222652)]]], (24668 ^ _776541) ^ [] : [24671 ^ _776541 : [(24674 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24670 ^ [_1222451, _1222453, _1222455]), _1222451)))], (24676 ^ _776541) ^ [] : [-(_1222455 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222451), 24669 ^ [_1222451, _1222453, _1222455])), 24670 ^ [_1222451, _1222453, _1222455]))], (24678 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1222453, 24669 ^ [_1222451, _1222453, _1222455]), 24670 ^ [_1222451, _1222453, _1222455]))], (24672 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24670 ^ [_1222451, _1222453, _1222455])))]], -(hBOOL(hAPP(hAPP(_1222453, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222455), _1222451)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222455, _1222451))))]]], (28565 ^ _776541) ^ [_1289074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1289074), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1289074)), c_Int_OPls)))], (5685 ^ _776541) ^ [_866187, _866189, _866191] : [_866189 = _866191, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(_866187)), _866189), _866191)))], (25311 ^ _776541) ^ [_1234676, _1234678] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234676), _1234678) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1234676 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1234676 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (33579 ^ _776541) ^ [_1394660, _1394662, _1394664] : [class_Groups_Ocomm__monoid__mult(_1394660), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394662, _1394660), hAPP(c_COMBK(_1394660, _1394662), c_Groups_Oone__class_Oone(_1394660))), _1394664) = c_Groups_Oone__class_Oone(_1394660))], (11072 ^ _776541) ^ [_968019, _968021, _968023] : [class_Rings_Oring(_968019), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968019), hAPP(c_Groups_Ouminus__class_Ouminus(_968019), _968021)), _968023) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968019), _968021), hAPP(c_Groups_Ouminus__class_Ouminus(_968019), _968023)))], (52175 ^ _776541) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (47402 ^ _776541) ^ [_1729677, _1729679] : [-(c_List_OdropWhile(_1729677, _1729679, c_List_Olist_ONil(_1729677)) = c_List_Olist_ONil(_1729677))], (44880 ^ _776541) ^ [_1675077, _1675079, _1675081, _1675083, _1675085] : [c_Fun_Oinj__on(_1675077, _1675079, _1675081, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1675077, tc_HOL_Obool)), hAPP(c_List_Oset(_1675077), _1675083)), hAPP(c_List_Oset(_1675077), _1675085))), 44883 ^ _776541 : [(44890 ^ _776541) ^ [] : [_1675083 = _1675085, -(hAPP(hAPP(c_List_Omap(_1675077, _1675079), _1675081), _1675083) = hAPP(hAPP(c_List_Omap(_1675077, _1675079), _1675081), _1675085))], (44884 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Omap(_1675077, _1675079), _1675081), _1675083) = hAPP(hAPP(c_List_Omap(_1675077, _1675079), _1675081), _1675085), -(_1675083 = _1675085)]]], (40737 ^ _776541) ^ [_1573460, _1573462] : [-(c_Transitive__Closure_Otrancl(_1573460, _1573462) = hAPP(hAPP(c_Relation_Orel__comp(_1573460, _1573460, _1573460), _1573462), c_Transitive__Closure_Ortrancl(_1573460, _1573462)))], (9074 ^ _776541) ^ [_933397, _933399, _933401, _933403] : [class_Orderings_Opreorder(_933397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933397), _933399), _933401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933397), _933401), _933403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933397), _933399), _933403)))], (35678 ^ _776541) ^ [_1442545, _1442547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1442545), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442547), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1442545), _1442547) = 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), _1442545), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1442547)))))], (7960 ^ _776541) ^ [_911158, _911160, _911162, _911164, _911166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911158, tc_HOL_Obool)), _911160), _911162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911158, tc_HOL_Obool)), _911164), _911166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911158, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911158, tc_HOL_Obool)), _911160), _911164)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911158, tc_HOL_Obool)), _911162), _911166))))], (13093 ^ _776541) ^ [_1007735, _1007737, _1007739, _1007741, _1007743, _1007745, _1007747, _1007749] : [c_Finite__Set_Ofolding__image__simple(_1007735, _1007737, _1007739, _1007741, _1007743, _1007745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007737), _1007747)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007737), _1007749)), 13107 ^ _776541 : [(13110 ^ _776541) ^ [] : [hAPP(_1007743, 13106 ^ [_1007735, _1007737, _1007739, _1007741, _1007743, _1007745, _1007747, _1007749]) = _1007741], (13108 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007737), 13106 ^ [_1007735, _1007737, _1007739, _1007741, _1007743, _1007745, _1007747, _1007749]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1007737, tc_HOL_Obool)), _1007747), _1007749))))]], -(hAPP(_1007745, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007737, tc_HOL_Obool)), _1007747), _1007749)) = hAPP(hAPP(_1007739, hAPP(_1007745, _1007747)), hAPP(_1007745, _1007749)))], (46956 ^ _776541) ^ [_1720311, _1720313] : [hBOOL(hAPP(c_List_Odistinct(_1720311), hAPP(c_List_Orev(_1720311), _1720313))), -(hBOOL(hAPP(c_List_Odistinct(_1720311), _1720313)))], (19555 ^ _776541) ^ [_1129773, _1129775, _1129777, _1129779] : [class_Rings_Odivision__ring(_1129773), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129773), _1129775), _1129777)), _1129779) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129773), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129773), _1129775), _1129779)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129773), _1129777), _1129779)))], (43890 ^ _776541) ^ [_1653462, _1653464] : [hBOOL(hAPP(c_List_Odistinct(_1653462), _1653464)), -(hBOOL(hAPP(c_List_Odistinct(_1653462), hAPP(c_List_Orotate1(_1653462), _1653464))))], (34684 ^ _776541) ^ [_1422719, _1422721] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1422719, _1422721) = 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), _1422719), _1422721)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1422719, _1422721)))], (17373 ^ _776541) ^ [_1089379, _1089381, _1089383] : [class_Rings_Olinordered__semiring__strict(_1089379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089379), _1089381), c_Groups_Ozero__class_Ozero(_1089379))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089379), c_Groups_Ozero__class_Ozero(_1089379)), _1089383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089379), _1089381), _1089383)), c_Groups_Ozero__class_Ozero(_1089379))))], (52207 ^ _776541) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (14290 ^ _776541) ^ [_1033920, _1033922, _1033924, _1033926] : [class_Rings_Ocomm__semiring__1(_1033920), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033920), _1033922), _1033924)), _1033926) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033920), _1033922), _1033926)), _1033924))], (38414 ^ _776541) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (2956 ^ _776541) ^ [_820416, _820418, _820420, _820422] : [-(c_Nitpick_Oinverse__frac(_820422, _820418) = c_Nitpick_Oinverse__frac(_820420, _820416)), _820422 = _820420, _820418 = _820416], (44350 ^ _776541) ^ [_1663551, _1663553, _1663555, _1663557, _1663559, _1663561] : [-(hAPP(c_List_Ofoldl(_1663551, _1663553, _1663555, _1663557), hAPP(hAPP(c_List_Oappend(_1663553), _1663559), _1663561)) = hAPP(c_List_Ofoldl(_1663551, _1663553, _1663555, hAPP(c_List_Ofoldl(_1663551, _1663553, _1663555, _1663557), _1663559)), _1663561))], (3460 ^ _776541) ^ [_828238, _828240, _828242, _828244] : [-(c_List_OremoveAll(_828244, _828240) = c_List_OremoveAll(_828242, _828238)), _828244 = _828242, _828240 = _828238], (38050 ^ _776541) ^ [_1505275, _1505277, _1505279, _1505281] : [c_Wellfounded_Omax__extp(_1505275, _1505277, _1505279, _1505281), 38053 ^ _776541 : [(38056 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505275), _1505281)))], (38058 ^ _776541) ^ [] : [_1505281 = c_Orderings_Obot__class_Obot(tc_fun(_1505275, tc_HOL_Obool))], (38060 ^ _776541) ^ [_1505491] : [hBOOL(hAPP(hAPP(c_member(_1505275), _1505491), _1505279)), 38064 ^ _776541 : [(38067 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1505277, _1505491), 38063 ^ [_1505275, _1505277, _1505279, _1505281, _1505491])))], (38065 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505275), 38063 ^ [_1505275, _1505277, _1505279, _1505281, _1505491]), _1505281)))]]], (38054 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505275), _1505279)))]]], (11987 ^ _776541) ^ [_987128, _987130, _987132, _987134, _987136] : [11989 ^ _776541 : [(11995 ^ _776541) ^ [] : [hBOOL(hAPP(_987136, 11991 ^ [_987128, _987130, _987132, _987134, _987136]))], (11993 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_987128), 11991 ^ [_987128, _987130, _987132, _987134, _987136]), hAPP(_987134, 11988 ^ [_987128, _987130, _987132, _987134, _987136]))))], (11990 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_987130), 11988 ^ [_987128, _987130, _987132, _987134, _987136]), _987132)))]], 11996 ^ _776541 : [(11997 ^ _776541) ^ [_987438] : [hBOOL(hAPP(hAPP(c_member(_987128), _987438), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987130, tc_fun(_987128, tc_HOL_Obool)), _987132), _987134))), -(hBOOL(hAPP(_987136, _987438)))]]], (29847 ^ _776541) ^ [_1311673, _1311675, _1311677, _1311679] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1311673, _1311675, _1311677, c_Code__Numeral_OSuc__code__numeral(_1311679)) = hAPP(_1311677, _1311679))], (26915 ^ _776541) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (27985 ^ _776541) ^ [_1279447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1279447)), -(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), _1279447))))], (52125 ^ _776541) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (2596 ^ _776541) ^ [_814800, _814802, _814804, _814806, _814808, _814810, _814812, _814814] : [-(c_Recdef_Osame__fst(_814814, _814810, _814806, _814802) = c_Recdef_Osame__fst(_814812, _814808, _814804, _814800)), _814814 = _814812, _814810 = _814808, _814806 = _814804, _814802 = _814800], (2996 ^ _776541) ^ [_821020, _821022, _821024, _821026] : [-(c_Nitpick_Ouminus__frac(_821026, _821022) = c_Nitpick_Ouminus__frac(_821024, _821020)), _821026 = _821024, _821022 = _821020], (33487 ^ _776541) ^ [_1392491, _1392493, _1392495, _1392497, _1392499] : [class_Groups_Ocomm__monoid__mult(_1392491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392493), _1392495)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392493, _1392491), hAPP(hAPP(c_COMBS(_1392493, _1392491, _1392491), hAPP(hAPP(c_COMBB(_1392491, tc_fun(_1392491, _1392491), _1392493), c_Groups_Otimes__class_Otimes(_1392491)), _1392497)), _1392499)), _1392495) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392491), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392493, _1392491), _1392497), _1392495)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392493, _1392491), _1392499), _1392495)))], (49560 ^ _776541) ^ [_1778119, _1778121, _1778123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778119, _1778119), tc_HOL_Obool)), _1778121), _1778123)), c_Relation_Oantisym(_1778119, _1778123), -(c_Relation_Oantisym(_1778119, _1778121))], (34069 ^ _776541) ^ [_1409084, _1409086, _1409088] : [class_Groups_Ocomm__monoid__add(_1409084), class_Groups_Ocomm__monoid__mult(_1409084), c_Nat__Transfer_Onat__set(_1409086), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1409084), _1409088), _1409086) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409084), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1409084, tc_Nat_Onat), _1409088), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1409086)))], (12505 ^ _776541) ^ [_996418, _996420] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_996418, tc_HOL_Obool)), _996420)), 12511 ^ _776541 : [(12514 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_996418), 12510 ^ [_996418, _996420]))], (12512 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_996418, tc_HOL_Obool)), 12510 ^ [_996418, _996420]), _996420)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_996418), c_Complete__Lattice_OSup__class_OSup(tc_fun(_996418, tc_HOL_Obool), _996420))))], (46079 ^ _776541) ^ [_1702030, _1702032, _1702034, _1702036] : [-(hAPP(c_List_Ofilter(_1702030, _1702032), hAPP(c_List_Ofilter(_1702030, _1702034), _1702036)) = hAPP(c_List_Ofilter(_1702030, hAPP(hAPP(c_COMBS(_1702030, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1702030), c_fconj), _1702034)), _1702032)), _1702036))], (8735 ^ _776541) ^ [_926640, _926642, _926644] : [class_Lattices_Olattice(_926640), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926640), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926640), _926642), _926644)), _926644)))], (28373 ^ _776541) ^ [_1285878] : [c_Int_OPls = c_Int_OBit1(_1285878)], (37238 ^ _776541) ^ [_1485258, _1485260] : [-(c_Fun_Oinj__on(_1485258, _1485258, c_COMBI(_1485258), _1485260))], (24956 ^ _776541) ^ [_1228463, _1228465, _1228467] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228463), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228465, _1228467)), _1228467) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228463), _1228465), _1228467))], (35624 ^ _776541) ^ [_1441420, _1441422, _1441424, _1441426, _1441428] : [-(hAPP(c_Product__Type_Ofst(_1441420, _1441422), hAPP(c_Product__Type_Oapsnd(_1441424, _1441422, _1441420, _1441426), _1441428)) = hAPP(c_Product__Type_Ofst(_1441420, _1441424), _1441428))], (34701 ^ _776541) ^ [_1423126, _1423128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1423126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1423126), _1423128)), -(c_Divides_Odivmod__nat(_1423128, _1423126) = 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), _1423128), _1423126)), _1423126))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1423128), _1423126), _1423126)))], (50735 ^ _776541) ^ [_1802037, _1802039, _1802041, _1802043] : [c_Equiv__Relations_Oequivp(_1802037, _1802039), 50741 ^ _776541 : [(50744 ^ _776541) ^ [] : [hBOOL(hAPP(_1802043, 50740 ^ [_1802037, _1802039, _1802041, _1802043]))], (50742 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1802041, 50740 ^ [_1802037, _1802039, _1802041, _1802043])))]], 50747 ^ _776541 : [(50748 ^ _776541) ^ [_1802296] : [hBOOL(hAPP(_1802041, _1802296))]], 50750 ^ _776541 : [(50753 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1802043, 50749 ^ [_1802037, _1802039, _1802041, _1802043])))], (50751 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802037), 50749 ^ [_1802037, _1802039, _1802041, _1802043]), c_Quotient_ORespects(_1802037, _1802039))))]]], (14046 ^ _776541) ^ [_1028246, _1028248, _1028250, _1028252, _1028254, _1028256, _1028258, _1028260] : [c_Finite__Set_Ofolding__image__simple__idem(_1028246, _1028248, _1028250, _1028252, _1028254, _1028256), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028248), _1028258)), -(hAPP(_1028256, hAPP(hAPP(c_Set_Oinsert(_1028248), _1028260), _1028258)) = hAPP(hAPP(_1028250, hAPP(_1028254, _1028260)), hAPP(_1028256, _1028258)))], (38766 ^ _776541) ^ [_1521679, _1521681, _1521683] : [hAPP(c_Relation_ODomain(_1521679, _1521681), _1521683) = c_Orderings_Obot__class_Obot(tc_fun(_1521679, tc_HOL_Obool)), -(_1521683 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521679, _1521681), tc_HOL_Obool)))], (29333 ^ _776541) ^ [_1302180, _1302182] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1302180)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1302182))) = 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), _1302180), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302182))))], (23828 ^ _776541) ^ [_1208191, _1208193] : [class_Rings_Olinordered__semidom(_1208191), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208191), c_Groups_Ozero__class_Ozero(_1208191)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208191), _1208193))))], (10212 ^ _776541) ^ [_951901, _951903, _951905, _951907] : [class_Orderings_Olinorder(_951901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951901), _951903), _951905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951901), _951905), _951907)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951901, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_951901, _951903, _951905)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951901, _951905), _951907)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_951901, _951903, _951907))], (44623 ^ _776541) ^ [_1668742, _1668744, _1668746] : [-(c_List_Olast(_1668742, hAPP(hAPP(c_List_Oappend(_1668742), _1668744), hAPP(hAPP(c_List_Olist_OCons(_1668742), _1668746), c_List_Olist_ONil(_1668742)))) = _1668746)], (41779 ^ _776541) ^ [_1600149, _1600151, _1600153, _1600155, _1600157, _1600159] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600149), tc_List_Olist(_1600149))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600149), tc_List_Olist(_1600149)), hAPP(hAPP(c_List_Olist_OCons(_1600149), _1600151), _1600153)), hAPP(hAPP(c_List_Olist_OCons(_1600149), _1600155), _1600157))), c_List_Olex(_1600149, _1600159))), 41784 ^ _776541 : [(41787 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600149)), _1600153) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600149)), _1600157))], (41785 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600149, _1600149)), hAPP(hAPP(c_Product__Type_OPair(_1600149, _1600149), _1600151), _1600155)), _1600159)))]], 41788 ^ _776541 : [(41791 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600149), tc_List_Olist(_1600149))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600149), tc_List_Olist(_1600149)), _1600153), _1600157)), c_List_Olex(_1600149, _1600159))))], (41789 ^ _776541) ^ [] : [-(_1600151 = _1600155)]]], (37947 ^ _776541) ^ [_1501143, _1501145, _1501147, _1501149, _1501151, _1501153] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1501143, _1501145, _1501147), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501143, _1501145), tc_HOL_Obool)), _1501149), _1501151)), _1501153) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501143, _1501147), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501143, _1501145, _1501147), _1501149), _1501153)), hAPP(hAPP(c_Relation_Orel__comp(_1501143, _1501145, _1501147), _1501151), _1501153)))], (3592 ^ _776541) ^ [_830290, _830292, _830294, _830296, _830298, _830300, _830302, _830304, _830306, _830308] : [-(c_List_Olinorder__class_Oinsort__insert__key(_830308, _830304, _830300, _830296, _830292) = c_List_Olinorder__class_Oinsort__insert__key(_830306, _830302, _830298, _830294, _830290)), _830308 = _830306, _830304 = _830302, _830300 = _830298, _830296 = _830294, _830292 = _830290], (25203 ^ _776541) ^ [_1232854, _1232856] : [class_Int_Onumber__ring(_1232854), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232854), hAPP(c_Int_Onumber__class_Onumber__of(_1232854), c_Int_OMin)), _1232856) = hAPP(c_Groups_Ouminus__class_Ouminus(_1232854), _1232856))], (39139 ^ _776541) ^ [_1531288, _1531290, _1531292, _1531294, _1531296] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531288, _1531290), _1531292), hAPP(hAPP(c_COMBS(_1531288, tc_fun(_1531290, tc_HOL_Obool), tc_fun(_1531290, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531290, tc_HOL_Obool), tc_fun(tc_fun(_1531290, tc_HOL_Obool), tc_fun(_1531290, tc_HOL_Obool)), _1531288), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531290, tc_HOL_Obool))), _1531294)), _1531296)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1531288, _1531290), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531288, _1531290), _1531292), _1531294)), hAPP(hAPP(c_Product__Type_OSigma(_1531288, _1531290), _1531292), _1531296)))], (47269 ^ _776541) ^ [_1726965, _1726967, _1726969, _1726971] : [-(hBOOL(hAPP(_1726965, _1726967))), -(c_List_OtakeWhile(_1726969, _1726965, hAPP(hAPP(c_List_Olist_OCons(_1726969), _1726967), _1726971)) = c_List_Olist_ONil(_1726969))], (22281 ^ _776541) ^ [_1180527, _1180529, _1180531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180527), _1180529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180529), _1180531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180527), _1180531)))], (43086 ^ _776541) ^ [_1635059, _1635061] : [-(c_List_Olistrelp(_1635059, _1635061, c_List_Olist_ONil(_1635059), c_List_Olist_ONil(_1635059)))], (38144 ^ _776541) ^ [_1507010] : [-(c_Wellfounded_Owf(tc_fun(_1507010, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1507010)))], (16446 ^ _776541) ^ [_1072890, _1072892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072890), _1072892)), _1072892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15986 ^ _776541) ^ [_1065826, _1065828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065826)), hAPP(c_Nat_OSuc, _1065828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065826), _1065828)))], (27375 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (30174 ^ _776541) ^ [_1317830, _1317832, _1317834, _1317836] : [class_Orderings_Olinorder(_1317830), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317830), _1317832), _1317834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317830), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317830), _1317836), _1317832)), _1317834)))], (14554 ^ _776541) ^ [_1039040, _1039042, _1039044] : [_1039040 = _1039044, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039040), _1039042) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039044), _1039042))], (22975 ^ _776541) ^ [_1192832, _1192834, _1192836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192832)), _1192832 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1192834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192832), _1192836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192836), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (44198 ^ _776541) ^ [_1660315, _1660317] : [-(c_List_Orotate(_1660315, _1660317) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1660315), tc_List_Olist(_1660315)), _1660317), c_List_Orotate1(_1660315)))], (14570 ^ _776541) ^ [_1039294, _1039296, _1039298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039294), _1039296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039296), _1039298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039294), _1039298)))], (28903 ^ _776541) ^ [_1294719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1294719)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294719), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51507 ^ _776541) ^ [_1818874, _1818876, _1818878, _1818880] : [class_Divides_Osemiring__div(_1818874), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818874), _1818876), _1818878)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1818874), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818874), _1818878), _1818876)), _1818880) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818874), hAPP(hAPP(c_Power_Opower__class_Opower(_1818874), _1818878), _1818880)), hAPP(hAPP(c_Power_Opower__class_Opower(_1818874), _1818876), _1818880)))], (24980 ^ _776541) ^ [_1228914, _1228916, _1228918] : [class_Divides_Osemiring__div(_1228914), -(c_Divides_Odiv__class_Omod(_1228914, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228914), _1228916), _1228918), _1228918) = c_Groups_Ozero__class_Ozero(_1228914))], (5769 ^ _776541) ^ [_867811, _867813, _867815, _867817] : [_867811 = _867813, 5774 ^ _776541 : [(5777 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_867815), _867817), _867813)))], (5775 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_867815), _867817), _867811)))]], 5778 ^ _776541 : [(5781 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_867815), _867817), _867813))], (5779 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_867815), _867817), _867811))]]], (34761 ^ _776541) ^ [_1424976, _1424978] : [class_Rings_Osemiring__1(_1424976), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1424976), _1424978) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1424976, hAPP(hAPP(c_COMBC(_1424976, _1424976, _1424976), c_Groups_Oplus__class_Oplus(_1424976)), c_Groups_Oone__class_Oone(_1424976)), _1424978, c_Groups_Ozero__class_Ozero(_1424976)))], (7348 ^ _776541) ^ [_896892, _896894] : [class_Complete__Lattice_Ocomplete__lattice(_896892), -(c_Complete__Lattice_OInf__class_OInf(_896892, hAPP(hAPP(c_Set_Oinsert(_896892), _896894), c_Orderings_Obot__class_Obot(tc_fun(_896892, tc_HOL_Obool)))) = _896894)], (38201 ^ _776541) ^ [] : [-(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)))))], (46113 ^ _776541) ^ [_1702755] : [-(c_List_Otranspose(_1702755, c_List_Olist_ONil(tc_List_Olist(_1702755))) = c_List_Olist_ONil(tc_List_Olist(_1702755)))], (22497 ^ _776541) ^ [_1184184, _1184186, _1184188] : [class_Groups_Omonoid__mult(_1184184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184184), hAPP(hAPP(c_Power_Opower__class_Opower(_1184184), _1184186), _1184188)), _1184186) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184184), _1184186), hAPP(hAPP(c_Power_Opower__class_Opower(_1184184), _1184186), _1184188)))], (6246 ^ _776541) ^ [_876926] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_876926, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_876926, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_876926, tc_HOL_Obool)))], (13904 ^ _776541) ^ [_1024821, _1024823, _1024825] : [class_Groups_Oab__group__add(_1024821), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024821), _1024823), _1024825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024821), _1024823), hAPP(c_Groups_Ouminus__class_Ouminus(_1024821), _1024825)))], (42447 ^ _776541) ^ [_1619285, _1619287, _1619289] : [-(hBOOL(hAPP(hAPP(c_member(_1619285), _1619287), hAPP(c_List_Oset(_1619285), _1619289)))), 42448 ^ _776541 : [(42449 ^ _776541) ^ [_1619359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619359), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619285)), _1619289))), hAPP(hAPP(c_List_Onth(_1619285), _1619289), _1619359) = _1619287]]], (47247 ^ _776541) ^ [_1726410, _1726412, _1726414, _1726416] : [hBOOL(hAPP(hAPP(c_member(_1726410), _1726412), hAPP(c_List_Oset(_1726410), c_List_OtakeWhile(_1726410, _1726414, _1726416)))), 47250 ^ _776541 : [(47253 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1726414, _1726412)))], (47251 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726410), _1726412), hAPP(c_List_Oset(_1726410), _1726416))))]]], (15023 ^ _776541) ^ [_1047653, _1047655, _1047657, _1047659] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047653), _1047655)), hBOOL(hAPP(hAPP(c_member(_1047653), _1047657), _1047655)), hBOOL(hAPP(hAPP(c_member(_1047653), _1047659), _1047655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1047653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047653, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047653, tc_HOL_Obool)), _1047655), hAPP(hAPP(c_Set_Oinsert(_1047653), _1047657), c_Orderings_Obot__class_Obot(tc_fun(_1047653, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1047653), _1047659), c_Orderings_Obot__class_Obot(tc_fun(_1047653, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1047653), _1047655))))], (37971 ^ _776541) ^ [_1501849, _1501851, _1501853, _1501855] : [hAPP(hAPP(c_Relation_Orel__comp(_1501849, _1501849, _1501849), _1501851), _1501853) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501849, _1501849), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501849, _1501849, _1501849), _1501855), _1501853) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501849, _1501849), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1501849, _1501849, _1501849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501849, _1501849), tc_HOL_Obool)), _1501851), _1501855)), _1501853) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501849, _1501849), tc_HOL_Obool)))], (26979 ^ _776541) ^ [_1262528, _1262530] : [class_Rings_Oring__1(_1262528), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262528), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1262530)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1262528), _1262530))], (42317 ^ _776541) ^ [_1616319, _1616321, _1616323] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616319, tc_HOL_Obool)), hAPP(c_List_Oset(_1616319), hAPP(hAPP(c_List_Otake(_1616319), _1616321), _1616323))), hAPP(c_List_Oset(_1616319), _1616323))))], (27305 ^ _776541) ^ [_1267831, _1267833] : [class_Groups_Oordered__ab__group__add__abs(_1267831), -(hAPP(c_Groups_Oabs__class_Oabs(_1267831), hAPP(c_Groups_Ouminus__class_Ouminus(_1267831), _1267833)) = hAPP(c_Groups_Oabs__class_Oabs(_1267831), _1267833))], (36468 ^ _776541) ^ [_1466112, _1466114, _1466116, _1466118] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1466112, _1466114), _1466116), _1466118) = hAPP(c_Set_OCollect(tc_prod(_1466114, _1466114)), hAPP(c_Product__Type_Oprod_Oprod__case(_1466114, _1466114, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1466114, tc_fun(tc_prod(_1466112, _1466112), tc_HOL_Obool), tc_fun(_1466114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466114, tc_fun(tc_fun(tc_prod(_1466112, _1466112), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1466112, _1466112), tc_HOL_Obool), tc_fun(_1466114, tc_HOL_Obool)), _1466114), c_COMBC(_1466114, tc_fun(tc_prod(_1466112, _1466112), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466114, tc_prod(_1466112, _1466112)), tc_fun(_1466114, tc_fun(tc_fun(tc_prod(_1466112, _1466112), tc_HOL_Obool), tc_HOL_Obool)), _1466114), hAPP(c_COMBB(tc_prod(_1466112, _1466112), tc_fun(tc_fun(tc_prod(_1466112, _1466112), tc_HOL_Obool), tc_HOL_Obool), _1466114), c_member(tc_prod(_1466112, _1466112)))), hAPP(hAPP(c_COMBC(_1466114, tc_fun(_1466114, _1466112), tc_fun(_1466114, tc_prod(_1466112, _1466112))), hAPP(hAPP(c_COMBB(tc_fun(_1466112, tc_prod(_1466112, _1466112)), tc_fun(tc_fun(_1466114, _1466112), tc_fun(_1466114, tc_prod(_1466112, _1466112))), _1466114), c_COMBB(_1466112, tc_prod(_1466112, _1466112), _1466114)), hAPP(hAPP(c_COMBB(_1466112, tc_fun(_1466112, tc_prod(_1466112, _1466112)), _1466114), c_Product__Type_OPair(_1466112, _1466112)), _1466118))), _1466118)))), _1466116))))], (33150 ^ _776541) ^ [_1382925, _1382927, _1382929, _1382931] : [hAPP(hAPP(c_COMBC(_1382925, tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_fun(_1382927, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382927, tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_fun(_1382927, tc_HOL_Obool)), _1382925), c_COMBC(_1382927, tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382927, tc_prod(_1382925, _1382927)), tc_fun(_1382927, tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool)), _1382925), hAPP(c_COMBB(tc_prod(_1382925, _1382927), tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool), _1382927), c_member(tc_prod(_1382925, _1382927)))), c_Product__Type_OPair(_1382925, _1382927)))), _1382929) = hAPP(hAPP(c_COMBC(_1382925, tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_fun(_1382927, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382927, tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_fun(_1382927, tc_HOL_Obool)), _1382925), c_COMBC(_1382927, tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382927, tc_prod(_1382925, _1382927)), tc_fun(_1382927, tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool)), _1382925), hAPP(c_COMBB(tc_prod(_1382925, _1382927), tc_fun(tc_fun(tc_prod(_1382925, _1382927), tc_HOL_Obool), tc_HOL_Obool), _1382927), c_member(tc_prod(_1382925, _1382927)))), c_Product__Type_OPair(_1382925, _1382927)))), _1382931), -(_1382929 = _1382931)], (32598 ^ _776541) ^ [_1367588, _1367590, _1367592, _1367594, _1367596] : [_1367588 = c_Orderings_Obot__class_Obot(tc_fun(_1367590, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367592, tc_HOL_Obool)), _1367594), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367590, tc_fun(_1367592, tc_HOL_Obool)), _1367588), _1367596)) = _1367594)], (23603 ^ _776541) ^ [_1204315, _1204317] : [class_Divides_Osemiring__div(_1204315), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204315), _1204317), c_Groups_Ozero__class_Ozero(_1204315)) = c_Groups_Ozero__class_Ozero(_1204315))], (31729 ^ _776541) ^ [_1346516, _1346518, _1346520, _1346522, _1346524] : [class_Orderings_Olinorder(_1346516), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346516, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1346516, _1346518, _1346520)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1346516, _1346522, _1346524)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1346516, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346516), _1346518), _1346522), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346516), _1346520), _1346524)))], (22551 ^ _776541) ^ [_1185265, _1185267, _1185269] : [class_Rings_Olinordered__semidom(_1185265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185265), c_Groups_Ozero__class_Ozero(_1185265)), _1185267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185265), c_Groups_Ozero__class_Ozero(_1185265)), hAPP(hAPP(c_Power_Opower__class_Opower(_1185265), _1185267), _1185269))))], (35594 ^ _776541) ^ [_1440845, _1440847, _1440849, _1440851] : [-(_1440845 = _1440847), hAPP(c_Product__Type_Ofst(_1440849, _1440851), _1440845) = hAPP(c_Product__Type_Ofst(_1440849, _1440851), _1440847), hAPP(c_Product__Type_Osnd(_1440849, _1440851), _1440845) = hAPP(c_Product__Type_Osnd(_1440849, _1440851), _1440847)], (3040 ^ _776541) ^ [_821658, _821660, _821662, _821664, _821666, _821668, _821670, _821672, _821674, _821676, _821678, _821680] : [-(c_Product__Type_Omap__pair(_821680, _821676, _821672, _821668, _821664, _821660) = c_Product__Type_Omap__pair(_821678, _821674, _821670, _821666, _821662, _821658)), _821680 = _821678, _821676 = _821674, _821672 = _821670, _821668 = _821666, _821664 = _821662, _821660 = _821658], (26677 ^ _776541) ^ [_1257966, _1257968] : [c_Nat__Transfer_Ois__nat(_1257966), c_Nat__Transfer_Ois__nat(_1257968), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1257966, _1257968) = 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, _1257966), hAPP(c_Int_Onat, _1257968))))], (40755 ^ _776541) ^ [_1573918, _1573920] : [-(c_Transitive__Closure_Ortrancl(_1573918, _1573920) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573918, _1573918), tc_HOL_Obool)), c_Relation_OId(_1573918)), hAPP(hAPP(c_Relation_Orel__comp(_1573918, _1573918, _1573918), c_Transitive__Closure_Ortrancl(_1573918, _1573920)), _1573920)))], (46401 ^ _776541) ^ [_1709643, _1709645, _1709647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709643), _1709645)), _1709647)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1709643, _1709647)), _1709645) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709643), _1709645))], (23791 ^ _776541) ^ [_1207449, _1207451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207449), _1207451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207449)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207451))))], (36211 ^ _776541) ^ [_1459571, _1459573, _1459575, _1459577, _1459579, _1459581, _1459583] : [-(hAPP(c_Product__Type_Oapsnd(_1459571, _1459573, _1459575, _1459577), hAPP(c_Product__Type_Oapfst(_1459579, _1459575, _1459571, _1459581), _1459583)) = hAPP(hAPP(c_Product__Type_OPair(_1459575, _1459573), hAPP(_1459581, hAPP(c_Product__Type_Ofst(_1459579, _1459571), _1459583))), hAPP(_1459577, hAPP(c_Product__Type_Osnd(_1459579, _1459571), _1459583))))], (45305 ^ _776541) ^ [_1684377, _1684379, _1684381, _1684383] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684377)), _1684379), c_List_Olists(_1684377, _1684381))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684377)), _1684379), c_List_Olists(_1684377, _1684383))), -(hBOOL(hAPP(c_List_Olistsp(_1684377, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1684377, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1684377, tc_fun(_1684377, tc_HOL_Obool), tc_HOL_Obool), c_member(_1684377)), _1684381)), hAPP(hAPP(c_COMBC(_1684377, tc_fun(_1684377, tc_HOL_Obool), tc_HOL_Obool), c_member(_1684377)), _1684383))), _1684379)))], (45748 ^ _776541) ^ [_1694513, _1694515] : [-(hBOOL(hAPP(c_List_Odistinct(_1694513), c_List_Oremdups(_1694513, _1694515))))], (40528 ^ _776541) ^ [_1567588, _1567590, _1567592, _1567594, _1567596, _1567598, _1567600] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567588, _1567590, _1567592, _1567594), _1567596), _1567598), _1567600) = hAPP(hAPP(_1567598, hAPP(c_Product__Type_Ofst(_1567590, _1567592), hAPP(_1567596, _1567600))), hAPP(c_Product__Type_Osnd(_1567590, _1567592), hAPP(_1567596, _1567600))))], (29579 ^ _776541) ^ [_1306455, _1306457, _1306459] : [class_Int_Onumber__ring(_1306455), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1306455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306455), _1306457), _1306459)), 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(_1306455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306455), hAPP(hAPP(c_Power_Opower__class_Opower(_1306455), _1306457), 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(_1306455), _1306459), 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(_1306455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306455), hAPP(c_Int_Onumber__class_Onumber__of(_1306455), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1306457)), _1306459)))], (45936 ^ _776541) ^ [_1697992, _1697994] : [45938 ^ _776541 : [(45941 ^ _776541) ^ [] : [45937 ^ [_1697992, _1697994] = c_List_Olist_ONil(_1697992)], (45939 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697992)), 45937 ^ [_1697992, _1697994]), hAPP(c_List_Oset(tc_List_Olist(_1697992)), _1697994))))]], -(c_List_Olist_ONil(_1697992) = c_List_Oconcat(_1697992, _1697994))], (14342 ^ _776541) ^ [_1035165, _1035167, _1035169, _1035171] : [class_Rings_Ocomm__semiring__1(_1035165), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035165), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035165), _1035167), _1035169)), _1035171) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035165), _1035167), _1035171)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035165), _1035169), _1035171)))], (29415 ^ _776541) ^ [_1303647, _1303649] : [class_Rings_Olinordered__idom(_1303647), 29418 ^ _776541 : [(29425 ^ _776541) ^ [] : [-(_1303649 = c_Groups_Ozero__class_Ozero(_1303647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303647), c_Groups_Ozero__class_Ozero(_1303647)), hAPP(hAPP(c_Power_Opower__class_Opower(_1303647), _1303649), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29419 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303647), c_Groups_Ozero__class_Ozero(_1303647)), hAPP(hAPP(c_Power_Opower__class_Opower(_1303647), _1303649), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1303649 = c_Groups_Ozero__class_Ozero(_1303647)]]], (30654 ^ _776541) ^ [_1326517, _1326519, _1326521] : [class_Orderings_Olinorder(_1326517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326517), _1326519)), hBOOL(hAPP(hAPP(c_member(_1326517), _1326521), _1326519)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326517), _1326521), c_Big__Operators_Olinorder__class_OMin(_1326517, _1326519)) = c_Big__Operators_Olinorder__class_OMin(_1326517, _1326519))], (45301 ^ _776541) ^ [_1683826, _1683828, _1683830, _1683832] : [-(c_List_Opartition(_1683826, _1683828, hAPP(hAPP(c_List_Olist_OCons(_1683826), _1683830), _1683832)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1683826), tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1683826), tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1683826), tc_fun(tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), tc_fun(tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), tc_List_Olist(_1683826)), c_COMBS(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), tc_fun(tc_List_Olist(_1683826), tc_fun(tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), tc_List_Olist(_1683826)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_fun(tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), tc_List_Olist(_1683826)), hAPP(c_If(tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), hAPP(_1683828, _1683830)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1683826), tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), tc_List_Olist(_1683826)), c_Product__Type_OPair(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), hAPP(c_List_Olist_OCons(_1683826), _1683830))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1683826), tc_fun(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826))), tc_fun(tc_fun(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_fun(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), tc_List_Olist(_1683826)), c_COMBB(tc_List_Olist(_1683826), tc_prod(tc_List_Olist(_1683826), tc_List_Olist(_1683826)), tc_List_Olist(_1683826))), c_Product__Type_OPair(tc_List_Olist(_1683826), tc_List_Olist(_1683826)))), hAPP(c_List_Olist_OCons(_1683826), _1683830)))), c_List_Opartition(_1683826, _1683828, _1683832)))], (48470 ^ _776541) ^ [_1753101, _1753103, _1753105] : [-(c_List_Osplice(_1753101, hAPP(hAPP(c_List_Olist_OCons(_1753101), _1753103), _1753105), c_List_Olist_ONil(_1753101)) = hAPP(hAPP(c_List_Olist_OCons(_1753101), _1753103), _1753105))], (22705 ^ _776541) ^ [_1187920, _1187922] : [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), _1187920), _1187922))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1187920))), -(_1187922 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30499 ^ _776541) ^ [_1323716, _1323718, _1323720] : [class_Orderings_Olinorder(_1323716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323716), _1323718)), -(_1323718 = c_Orderings_Obot__class_Obot(tc_fun(_1323716, tc_HOL_Obool))), 30510 ^ _776541 : [(30511 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323716), _1323720), hAPP(c_Finite__Set_Ofold1(_1323716, c_Orderings_Oord__class_Omin(_1323716)), _1323718))), 30514 ^ _776541 : [(30515 ^ _776541) ^ [_1324009] : [hBOOL(hAPP(hAPP(c_member(_1323716), _1324009), _1323718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323716), _1323720), _1324009)))]]], (30521 ^ _776541) ^ [] : [30523 ^ _776541 : [(30526 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323716), _1323720), 30522 ^ [_1323716, _1323718, _1323720]))], (30524 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323716), 30522 ^ [_1323716, _1323718, _1323720]), _1323718)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323716), _1323720), hAPP(c_Finite__Set_Ofold1(_1323716, c_Orderings_Oord__class_Omin(_1323716)), _1323718))))]]], (36689 ^ _776541) ^ [_1472322, _1472324, _1472326, _1472328] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472322, _1472322)), hAPP(hAPP(c_Product__Type_OPair(_1472322, _1472322), _1472324), _1472326)), c_Relation_OId__on(_1472322, _1472328)))), _1472324 = _1472326, hBOOL(hAPP(hAPP(c_member(_1472322), _1472324), _1472328))], (22385 ^ _776541) ^ [_1182360] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182360)), _1182360) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36278 ^ _776541) ^ [_1461273, _1461275, _1461277, _1461279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1461273), _1461275)), -(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), _1461273), _1461277)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1461275), _1461279))), c_FunDef_Opair__less)))], (6853 ^ _776541) ^ [_887648, _887650, _887652] : [class_Orderings_Olinorder(_887648), 6856 ^ _776541 : [(6863 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887648), _887652), _887650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887648, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887648), _887650)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887648), _887652))))], (6857 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887648, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887648), _887650)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887648), _887652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887648), _887652), _887650)))]]], (25269 ^ _776541) ^ [_1233951, _1233953] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1233951), _1233953), hAPP(c_Int_Onumber__class_Onumber__of(_1233951), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233951), _1233953)), class_Fields_Ofield__inverse__zero(_1233951), class_Int_Onumber__ring(_1233951)], (44731 ^ _776541) ^ [_1670813, _1670815, _1670817, _1670819, _1670821] : [-(hAPP(hAPP(c_List_Odrop(_1670813), _1670815), hAPP(hAPP(c_List_Omap(_1670817, _1670813), _1670819), _1670821)) = hAPP(hAPP(c_List_Omap(_1670817, _1670813), _1670819), hAPP(hAPP(c_List_Odrop(_1670817), _1670815), _1670821)))], (39984 ^ _776541) ^ [_1554944, _1554946, _1554948, _1554950, _1554952] : [class_Groups_Ocomm__monoid__add(_1554944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554946), _1554948)), c_Fun_Oinj__on(_1554946, _1554946, _1554950, _1554948), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554946, _1554944), _1554952), hAPP(c_Set_Oimage(_1554946, _1554946, _1554950), _1554948)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554946, _1554944), hAPP(c_Fun_Ocomp(_1554946, _1554944, _1554946, _1554952), _1554950)), _1554948))], (27399 ^ _776541) ^ [_1269343, _1269345] : [class_Groups_Oordered__ab__group__add__abs(_1269343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269343), c_Groups_Ozero__class_Ozero(_1269343)), _1269345)), -(hAPP(c_Groups_Oabs__class_Oabs(_1269343), _1269345) = _1269345)], (5258 ^ _776541) ^ [_856775, _856777, _856779, _856781] : [-(c_List_Oupt(_856781, _856777) = c_List_Oupt(_856779, _856775)), _856781 = _856779, _856777 = _856775], (7902 ^ _776541) ^ [_909797, _909799, _909801, _909803] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909797, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909797), _909799), _909801)), _909803) = hAPP(hAPP(c_Set_Oinsert(_909797), _909799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909797, tc_HOL_Obool)), _909801), _909803)))], (31465 ^ _776541) ^ [_1341544, _1341546, _1341548] : [class_Orderings_Olinorder(_1341544), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341544), _1341546), _1341548)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341544), _1341548), _1341546) = _1341548)], (18652 ^ _776541) ^ [_1112328, _1112330, _1112332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1112328)), 18655 ^ _776541 : [(18662 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112330), _1112332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112328), _1112330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112328), _1112332))))], (18656 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112328), _1112330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112328), _1112332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112330), _1112332)))]]], (1494 ^ _776541) ^ [_798080, _798082] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_798080)), _798082 = _798080, class_Groups_Oordered__cancel__ab__semigroup__add(_798082)], (13314 ^ _776541) ^ [_1012601, _1012603, _1012605, _1012607, _1012609] : [class_Groups_Ocomm__monoid__mult(_1012601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012603), _1012605)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012603, _1012601), _1012607), hAPP(hAPP(c_Set_Oinsert(_1012603), _1012609), _1012605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012601), hAPP(_1012607, _1012609)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012603, _1012601), _1012607), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012603, tc_HOL_Obool)), _1012605), hAPP(hAPP(c_Set_Oinsert(_1012603), _1012609), c_Orderings_Obot__class_Obot(tc_fun(_1012603, tc_HOL_Obool)))))))], (39743 ^ _776541) ^ [_1548751, _1548753, _1548755, _1548757] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1548751, tc_fun(_1548753, tc_HOL_Obool)), _1548755), _1548757) = hAPP(c_Set_OCollect(_1548753), hAPP(hAPP(c_COMBB(tc_fun(_1548751, tc_HOL_Obool), tc_HOL_Obool, _1548753), c_HOL_OAll(_1548751)), hAPP(hAPP(c_COMBB(tc_fun(_1548751, tc_HOL_Obool), tc_fun(_1548751, tc_HOL_Obool), _1548753), hAPP(c_COMBS(_1548751, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548751), c_fimplies), hAPP(hAPP(c_COMBC(_1548751, tc_fun(_1548751, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548751)), _1548755)))), hAPP(hAPP(c_COMBC(_1548753, tc_fun(_1548751, tc_fun(_1548753, tc_HOL_Obool)), tc_fun(_1548751, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1548753, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1548751, tc_fun(_1548753, tc_HOL_Obool)), tc_fun(_1548751, tc_HOL_Obool)), _1548753), c_COMBB(tc_fun(_1548753, tc_HOL_Obool), tc_HOL_Obool, _1548751)), c_member(_1548753))), _1548757)))))], (47723 ^ _776541) ^ [_1737008, _1737010, _1737012] : [class_Enum_Oenum(_1737008), class_Enum_Oenum(_1737010), 47730 ^ _776541 : [(47737 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737010), hAPP(hAPP(c_COMBB(tc_fun(_1737008, tc_HOL_Obool), tc_HOL_Obool, _1737010), c_Enum_Oenum__class_Oenum__ex(_1737008)), hAPP(hAPP(c_COMBB(tc_fun(_1737008, tc_prod(_1737010, _1737008)), tc_fun(_1737008, tc_HOL_Obool), _1737010), hAPP(c_COMBB(tc_prod(_1737010, _1737008), tc_HOL_Obool, _1737008), _1737012)), c_Product__Type_OPair(_1737010, _1737008))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1737010, _1737008)), _1737012)))], (47731 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1737010, _1737008)), _1737012)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737010), hAPP(hAPP(c_COMBB(tc_fun(_1737008, tc_HOL_Obool), tc_HOL_Obool, _1737010), c_Enum_Oenum__class_Oenum__ex(_1737008)), hAPP(hAPP(c_COMBB(tc_fun(_1737008, tc_prod(_1737010, _1737008)), tc_fun(_1737008, tc_HOL_Obool), _1737010), hAPP(c_COMBB(tc_prod(_1737010, _1737008), tc_HOL_Obool, _1737008), _1737012)), c_Product__Type_OPair(_1737010, _1737008))))))]]], (7682 ^ _776541) ^ [_904711, _904713] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904711, tc_HOL_Obool)), _904713), _904713) = _904713)], (48536 ^ _776541) ^ [_1754557, _1754559, _1754561] : [-(_1754559 = _1754561), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754557, _1754557, hAPP(hAPP(c_COMBB(tc_fun(_1754557, tc_HOL_Obool), tc_fun(_1754557, tc_HOL_Obool), _1754557), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754557), c_fNot)), c_fequal)), _1754559), _1754561)))], (26933 ^ _776541) ^ [_1261658, _1261660, _1261662] : [class_Rings_Olinordered__idom(_1261658), 26936 ^ _776541 : [(26943 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261660), _1261662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261658), hAPP(c_Int_Oring__1__class_Oof__int(_1261658), _1261660)), hAPP(c_Int_Oring__1__class_Oof__int(_1261658), _1261662))))], (26937 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261658), hAPP(c_Int_Oring__1__class_Oof__int(_1261658), _1261660)), hAPP(c_Int_Oring__1__class_Oof__int(_1261658), _1261662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261660), _1261662)))]]], (5877 ^ _776541) ^ [_869976, _869978] : [-(hAPP(c_Set_OCollect(_869976), _869978) = _869978)], (33433 ^ _776541) ^ [_1391090, _1391092, _1391094, _1391096, _1391098, _1391100] : [_1391090 = _1391092, -(hAPP(c_Fun_Ofun__upd(_1391094, _1391096, _1391098, _1391092, _1391100), _1391090) = _1391100)], (40366 ^ _776541) ^ [_1563592, _1563594] : [-(c_Hilbert__Choice_OEps(_1563592, hAPP(c_fequal, _1563594)) = _1563594)], (5010 ^ _776541) ^ [_852913, _852915] : [_852915 = _852913, -(c_Fun_Oid(_852915) = c_Fun_Oid(_852913))], (3906 ^ _776541) ^ [_835203, _835205, _835207, _835209, _835211, _835213, _835215, _835217, _835219, _835221, _835223, _835225, _835227, _835229] : [-(c_New__Random__Sequence_Oneg__decr__bind(_835229, _835225, _835221, _835217, _835213, _835209, _835205) = c_New__Random__Sequence_Oneg__decr__bind(_835227, _835223, _835219, _835215, _835211, _835207, _835203)), _835229 = _835227, _835225 = _835223, _835221 = _835219, _835217 = _835215, _835213 = _835211, _835209 = _835207, _835205 = _835203], (48424 ^ _776541) ^ [_1751815, _1751817, _1751819, _1751821, _1751823] : [_1751815 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1751817, _1751819, _1751821, _1751823), _1751815) = c_Lazy__Sequence_Oempty(_1751819))], (46982 ^ _776541) ^ [_1720865, _1720867, _1720869] : [hAPP(hAPP(c_List_Olist_OCons(_1720865), _1720867), c_List_Olist_ONil(_1720865)) = hAPP(c_List_Orev(_1720865), _1720869), -(_1720869 = hAPP(hAPP(c_List_Olist_OCons(_1720865), _1720867), c_List_Olist_ONil(_1720865)))], (52083 ^ _776541) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (50953 ^ _776541) ^ [_1808462, _1808464, _1808466, _1808468, _1808470] : [-(c_Lazy__Sequence_Omap(_1808462, _1808464, _1808466, c_Lazy__Sequence_Olazy__sequence_OInsert(_1808462, _1808468, _1808470)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1808464, hAPP(_1808466, _1808468), c_Lazy__Sequence_Omap(_1808462, _1808464, _1808466, _1808470)))], (27210 ^ _776541) ^ [_1266151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266151)), 27214 ^ _776541 : [(27217 ^ _776541) ^ [] : [-(_1266151 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 27213 ^ [_1266151]))], (27215 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 27213 ^ [_1266151])))]]], (25010 ^ _776541) ^ [_1229469] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229469), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1229469)], (42693 ^ _776541) ^ [_1626547, _1626549, _1626551, _1626553, _1626555, _1626557, _1626559] : [-(hAPP(hAPP(c_List_Ozip(_1626547, _1626549), hAPP(hAPP(c_List_Olist__update(_1626547, _1626551), _1626553), _1626555)), hAPP(hAPP(c_List_Olist__update(_1626549, _1626557), _1626553), _1626559)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1626547, _1626549), hAPP(hAPP(c_List_Ozip(_1626547, _1626549), _1626551), _1626557)), _1626553), hAPP(hAPP(c_Product__Type_OPair(_1626547, _1626549), _1626555), _1626559)))], (42393 ^ _776541) ^ [_1618095, _1618097, _1618099, _1618101, _1618103] : [hBOOL(hAPP(hAPP(c_member(_1618095), _1618097), hAPP(c_List_Oset(_1618095), _1618099))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618101), hAPP(_1618103, _1618097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618101), c_List_Olist_Olist__size(_1618095, _1618103, _1618099))))], (31475 ^ _776541) ^ [_1341705, _1341707, _1341709] : [class_Orderings_Olinorder(_1341705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341705), _1341707), _1341709)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341705), _1341707), _1341709) = _1341709)], (45455 ^ _776541) ^ [_1687848, _1687850, _1687852, _1687854, _1687856, _1687858, _1687860] : [c_List_Olist__all2(_1687854, _1687850, hAPP(hAPP(c_COMBB(_1687848, tc_fun(_1687850, tc_HOL_Obool), _1687854), _1687852), _1687856), _1687858, _1687860), -(c_List_Olist__all2(_1687848, _1687850, _1687852, hAPP(hAPP(c_List_Omap(_1687854, _1687848), _1687856), _1687858), _1687860))], (46596 ^ _776541) ^ [_1713272, _1713274] : [class_Orderings_Olinorder(_1713272), -(_1713274 = c_List_Olist_ONil(_1713272)), c_List_Olinorder__class_Osorted(_1713272, _1713274), -(c_List_Olinorder__class_Osorted(_1713272, c_List_Obutlast(_1713272, _1713274)))], (46297 ^ _776541) ^ [_1707772, _1707774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707772), _1707774)), -(c_List_Oupt(_1707772, _1707774) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1707772), c_List_Oupt(hAPP(c_Nat_OSuc, _1707772), _1707774)))], (29551 ^ _776541) ^ [_1305936, _1305938, _1305940] : [class_Rings_Olinordered__idom(_1305936), 29554 ^ _776541 : [(29555 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305936), c_Groups_Ozero__class_Ozero(_1305936)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305936), hAPP(hAPP(c_Power_Opower__class_Opower(_1305936), _1305938), 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(_1305936), _1305940), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1305938 = c_Groups_Ozero__class_Ozero(_1305936), _1305940 = c_Groups_Ozero__class_Ozero(_1305936)], (29565 ^ _776541) ^ [] : [29566 ^ _776541 : [(29569 ^ _776541) ^ [] : [-(_1305940 = c_Groups_Ozero__class_Ozero(_1305936))], (29567 ^ _776541) ^ [] : [-(_1305938 = c_Groups_Ozero__class_Ozero(_1305936))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305936), c_Groups_Ozero__class_Ozero(_1305936)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305936), hAPP(hAPP(c_Power_Opower__class_Opower(_1305936), _1305938), 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(_1305936), _1305940), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (52243 ^ _776541) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (50123 ^ _776541) ^ [_1789276, _1789278, _1789280] : [hAPP(c_Set_Oimage(_1789276, _1789278, _1789280), c_Orderings_Otop__class_Otop(tc_fun(_1789276, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1789278, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1789278, _1789276, c_Hilbert__Choice_Oinv__into(_1789276, _1789278, c_Orderings_Otop__class_Otop(tc_fun(_1789276, tc_HOL_Obool)), _1789280), c_Orderings_Otop__class_Otop(tc_fun(_1789278, tc_HOL_Obool))))], (32616 ^ _776541) ^ [_1367980, _1367982, _1367984, _1367986, _1367988] : [-(_1367980 = c_Orderings_Obot__class_Obot(tc_fun(_1367982, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367984, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367982, tc_fun(_1367984, tc_HOL_Obool)), _1367980), _1367986)), _1367988) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367982, tc_fun(_1367984, tc_HOL_Obool)), _1367980), hAPP(hAPP(c_COMBC(_1367982, tc_fun(_1367984, tc_HOL_Obool), tc_fun(_1367984, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1367984, tc_HOL_Obool), tc_fun(tc_fun(_1367984, tc_HOL_Obool), tc_fun(_1367984, tc_HOL_Obool)), _1367982), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367984, tc_HOL_Obool))), _1367986)), _1367988)))], (48770 ^ _776541) ^ [_1759607, _1759609, _1759611] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1759607, _1759609), _1759611) = c_Lazy__Sequence_Oproduct(_1759607, _1759609, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1759607, _1759611), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1759609, _1759611))), class_Lazy__Sequence_Osmall__lazy(_1759607), class_Lazy__Sequence_Osmall__lazy(_1759609)], (7400 ^ _776541) ^ [_898077, _898079, _898081, _898083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898077, tc_HOL_Obool)), _898079), hAPP(hAPP(c_Set_Oinsert(_898077), _898081), _898083)))), 7403 ^ _776541 : [(7406 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898077, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898077, tc_HOL_Obool)), _898079), hAPP(hAPP(c_Set_Oinsert(_898077), _898081), c_Orderings_Obot__class_Obot(tc_fun(_898077, tc_HOL_Obool))))), _898083))], (7404 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898077), _898081), _898079)))]], 7407 ^ _776541 : [(7410 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898077, tc_HOL_Obool)), _898079), _898083))], (7408 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898077), _898081), _898079))]]], (38235 ^ _776541) ^ [_1508727] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1508727)))], (9876 ^ _776541) ^ [_945747, _945749, _945751] : [class_Orderings_Oord(_945747), 9879 ^ _776541 : [(9886 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945747), _945749), _945751)), -(hBOOL(hAPP(hAPP(c_member(_945747), _945749), hAPP(c_SetInterval_Oord__class_OlessThan(_945747), _945751))))], (9880 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945747), _945749), hAPP(c_SetInterval_Oord__class_OlessThan(_945747), _945751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945747), _945749), _945751)))]]], (7186 ^ _776541) ^ [_893643, _893645, _893647, _893649] : [-(hBOOL(hAPP(hAPP(c_member(_893643), _893645), _893647))), -(hBOOL(hAPP(hAPP(c_member(_893643), _893645), _893649))), 7193 ^ _776541 : [(7200 ^ _776541) ^ [] : [_893647 = _893649, -(hAPP(hAPP(c_Set_Oinsert(_893643), _893645), _893647) = hAPP(hAPP(c_Set_Oinsert(_893643), _893645), _893649))], (7194 ^ _776541) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_893643), _893645), _893647) = hAPP(hAPP(c_Set_Oinsert(_893643), _893645), _893649), -(_893647 = _893649)]]], (1714 ^ _776541) ^ [_800830, _800832] : [-(class_Rings_Ocomm__semiring(_800830)), _800832 = _800830, class_Rings_Ocomm__semiring(_800832)], (25875 ^ _776541) ^ [_1244587, _1244589] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244587, _1244589)), _1244587)))], (52397 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (39912 ^ _776541) ^ [_1553291, _1553293, _1553295, _1553297, _1553299, _1553301] : [-(hAPP(hAPP(c_Fun_Ocomp(_1553291, _1553293, _1553295, _1553297), _1553299), _1553301) = hAPP(_1553297, hAPP(_1553299, _1553301)))], (42695 ^ _776541) ^ [_1626639, _1626641, _1626643, _1626645, _1626647, _1626649] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1626639, _1626641), hAPP(hAPP(c_List_Ozip(_1626639, _1626641), _1626643), _1626645)), _1626647), _1626649) = hAPP(hAPP(c_List_Ozip(_1626639, _1626641), hAPP(hAPP(c_List_Olist__update(_1626639, _1626643), _1626647), hAPP(c_Product__Type_Ofst(_1626639, _1626641), _1626649))), hAPP(hAPP(c_List_Olist__update(_1626641, _1626645), _1626647), hAPP(c_Product__Type_Osnd(_1626639, _1626641), _1626649))))], (16741 ^ _776541) ^ [_1077625, _1077627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077625)), _1077627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077625), _1077627)))], (5116 ^ _776541) ^ [_854598, _854600] : [_854600 = _854598, -(c_Orderings_Otop__class_Otop(_854600) = c_Orderings_Otop__class_Otop(_854598))], (22431 ^ _776541) ^ [] : [-(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))))], (44503 ^ _776541) ^ [_1666712, _1666714, _1666716] : [class_Orderings_Olinorder(_1666712), hBOOL(hAPP(hAPP(c_member(_1666712), _1666714), hAPP(c_List_Oset(_1666712), _1666716))), -(c_List_Olinorder__class_Oinsort__insert__key(_1666712, _1666712, c_COMBI(_1666712), _1666714, _1666716) = _1666716)], (16510 ^ _776541) ^ [_1073796, _1073798] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073796), _1073798) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073798), _1073796) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1073796 = _1073798)], (15896 ^ _776541) ^ [_1064269, _1064271] : [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), _1064269), _1064271))), 15899 ^ _776541 : [(15902 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064271)))], (15900 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064269)))]]], (31323 ^ _776541) ^ [_1338862] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1338862), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1338862)], (28769 ^ _776541) ^ [_1292358, _1292360] : [-(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), _1292358)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1292360)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1292358))) = 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), _1292360)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292358)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30702 ^ _776541) ^ [_1327292, _1327294, _1327296] : [class_Orderings_Olinorder(_1327292), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327292), _1327294)), -(_1327296 = c_Orderings_Obot__class_Obot(tc_fun(_1327292, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327292, tc_HOL_Obool)), _1327296), _1327294)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1327292), c_Big__Operators_Olattice_OInf__fin(_1327292, c_Orderings_Oord__class_Omin(_1327292), _1327296)), c_Big__Operators_Olattice_OInf__fin(_1327292, c_Orderings_Oord__class_Omin(_1327292), _1327294)) = c_Big__Operators_Olattice_OInf__fin(_1327292, c_Orderings_Oord__class_Omin(_1327292), _1327294))], (40753 ^ _776541) ^ [_1573874, _1573876] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1573874, _1573874, _1573874), c_Transitive__Closure_Ortrancl(_1573874, _1573876)), c_Transitive__Closure_Ortrancl(_1573874, _1573876)) = c_Transitive__Closure_Ortrancl(_1573874, _1573876))], (7111 ^ _776541) ^ [_892417, _892419] : [-(hBOOL(hAPP(hAPP(c_member(_892417), 7112 ^ [_892417, _892419]), _892419))), -(_892419 = c_Orderings_Obot__class_Obot(tc_fun(_892417, tc_HOL_Obool)))], (47607 ^ _776541) ^ [_1733905, _1733907] : [-(c_List_Oinsert(_1733905, _1733907, c_List_Olist_ONil(_1733905)) = hAPP(hAPP(c_List_Olist_OCons(_1733905), _1733907), c_List_Olist_ONil(_1733905)))], (7274 ^ _776541) ^ [_895375, _895377, _895379, _895381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895375, tc_HOL_Obool)), _895377), _895379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895375, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_895375), _895381), _895377)), hAPP(hAPP(c_Set_Oinsert(_895375), _895381), _895379))))], (42585 ^ _776541) ^ [_1624392, _1624394] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1624392, _1624394) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1624392), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1624394), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14684 ^ _776541) ^ [_1041298, _1041300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041298), _1041300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041298), _1041300))), -(_1041298 = _1041300)], (8573 ^ _776541) ^ [_923797, _923799, _923801] : [class_Lattices_Osemilattice__sup(_923797), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923797), _923799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923797), _923801), _923799))))], (11964 ^ _776541) ^ [_986573, _986575, _986577, _986579] : [c_Finite__Set_Ofolding__one__idem(_986573, _986575, _986577), -(hAPP(hAPP(_986575, _986579), _986579) = _986579)], (20109 ^ _776541) ^ [_1139576, _1139578, _1139580, _1139582] : [class_Fields_Olinordered__field(_1139576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139576), _1139578), _1139580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139576), _1139582), c_Groups_Ozero__class_Ozero(_1139576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139576), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139576), _1139580), _1139582)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139576), _1139578), _1139582))))], (44699 ^ _776541) ^ [_1670160, _1670162] : [-(_1670160 = c_List_Olist_ONil(_1670162)), -(c_Random_Oselect__weight(_1670162, hAPP(hAPP(c_List_Omap(_1670162, tc_prod(tc_Code__Numeral_Ocode__numeral, _1670162)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1670162), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1670160)) = c_Random_Oselect(_1670162, _1670160))], (29777 ^ _776541) ^ [] : [-(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))], (2084 ^ _776541) ^ [_806746, _806748, _806750, _806752, _806754, _806756] : [-(c_Power_Opower_Opower(_806756, _806752, _806748) = c_Power_Opower_Opower(_806754, _806750, _806746)), _806756 = _806754, _806752 = _806750, _806748 = _806746], (24682 ^ _776541) ^ [_1223166, _1223168] : [class_Int_Onumber__ring(_1223166), 24685 ^ _776541 : [(24692 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223168)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223166), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223168)) = hAPP(c_Int_Onumber__class_Onumber__of(_1223166), _1223168))], (24686 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223168))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223166), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223168)) = c_Groups_Ozero__class_Ozero(_1223166))]]], (42587 ^ _776541) ^ [_1624439, _1624441] : [class_Groups_Ocomm__monoid__add(_1624439), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1624439), _1624441) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1624439), hAPP(c_List_Onth(_1624439), _1624441)), 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(_1624439)), _1624441))))], (23635 ^ _776541) ^ [_1204892, _1204894] : [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)), _1204892)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204894))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1204892), _1204894)))], (3568 ^ _776541) ^ [_829904, _829906] : [_829906 = _829904, -(c_SetInterval_Oord__class_OatMost(_829906) = c_SetInterval_Oord__class_OatMost(_829904))], (9184 ^ _776541) ^ [_935118, _935120, _935122] : [class_Orderings_Opreorder(_935118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935118), _935120), _935122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935118), _935122), _935120))], (34610 ^ _776541) ^ [_1421237, _1421239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421237)), _1421239)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421237), _1421239)))], (40518 ^ _776541) ^ [_1567240, _1567242, _1567244, _1567246, _1567248, _1567250, _1567252] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567240, _1567242, _1567244, _1567246), _1567248), _1567250), _1567252) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1567242, _1567244, _1567246), _1567250), hAPP(_1567248, _1567252)))], (28053 ^ _776541) ^ [_1280578, _1280580] : [class_Int_Onumber__ring(_1280578), 28056 ^ _776541 : [(28063 ^ _776541) ^ [] : [c_Int_Oiszero(_1280578, hAPP(c_Int_Onumber__class_Onumber__of(_1280578), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1280580)))), -(c_Groups_Ozero__class_Ozero(_1280578) = hAPP(c_Int_Onumber__class_Onumber__of(_1280578), _1280580))], (28057 ^ _776541) ^ [] : [c_Groups_Ozero__class_Ozero(_1280578) = hAPP(c_Int_Onumber__class_Onumber__of(_1280578), _1280580), -(c_Int_Oiszero(_1280578, hAPP(c_Int_Onumber__class_Onumber__of(_1280578), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1280580)))))]]], (23785 ^ _776541) ^ [_1207344, _1207346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207344)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207344), _1207346)))], (36392 ^ _776541) ^ [_1463935] : [-(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)), _1463935), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (29015 ^ _776541) ^ [_1296677] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1296677)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1296677)))], (28921 ^ _776541) ^ [_1295010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1295010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1295010))))], (52469 ^ _776541) ^ [_1831026, _1831028, _1831030, _1831032, _1831034, _1831036] : [-(hAPP(hAPP(hAPP(c_COMBC(_1831026, _1831028, _1831030), _1831032), _1831034), _1831036) = hAPP(hAPP(_1831032, _1831036), _1831034))], (46277 ^ _776541) ^ [_1707420, _1707422] : [46278 ^ _776541 : [(46281 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707422), _1707420))], (46279 ^ _776541) ^ [] : [_1707422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1707420, _1707422) = c_List_Olist_ONil(tc_Nat_Onat))], (47090 ^ _776541) ^ [_1723016, _1723018] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723016)), hAPP(c_List_Orev(_1723016), _1723018)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723016)), _1723018))], (31234 ^ _776541) ^ [_1337074, _1337076, _1337078] : [class_Orderings_Olinorder(_1337074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337074), _1337076)), 31244 ^ _776541 : [(31247 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337074), 31243 ^ [_1337074, _1337076, _1337078]), _1337078))], (31245 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337074), 31243 ^ [_1337074, _1337076, _1337078]), _1337076)))]], hBOOL(hAPP(hAPP(c_member(_1337074), _1337078), _1337076)), -(c_Big__Operators_Olinorder__class_OMax(_1337074, _1337076) = _1337078)], (49030 ^ _776541) ^ [_1765496, _1765498, _1765500, _1765502, _1765504, _1765506, _1765508] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1765496, tc_fun(_1765498, tc_fun(_1765500, tc_HOL_Obool))), _1765502), _1765504), _1765506), _1765508)), 49034 ^ _776541 : [(49037 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1765504, 49033 ^ [_1765496, _1765498, _1765500, _1765502, _1765504, _1765506, _1765508]), _1765506), _1765508)))], (49035 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765496), 49033 ^ [_1765496, _1765498, _1765500, _1765502, _1765504, _1765506, _1765508]), _1765502)))]]], (1154 ^ _776541) ^ [_793830, _793832] : [-(class_Rings_Olinordered__semiring__1(_793830)), _793832 = _793830, class_Rings_Olinordered__semiring__1(_793832)], (27647 ^ _776541) ^ [_1273661, _1273663, _1273665] : [class_Rings_Oordered__ring__abs(_1273661), -(hAPP(c_Groups_Oabs__class_Oabs(_1273661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273661), _1273663), _1273665)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273661), hAPP(c_Groups_Oabs__class_Oabs(_1273661), _1273663)), hAPP(c_Groups_Oabs__class_Oabs(_1273661), _1273665))), 27654 ^ _776541 : [(27657 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273661), _1273663), c_Groups_Ozero__class_Ozero(_1273661)))], (27655 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273661), c_Groups_Ozero__class_Ozero(_1273661)), _1273663))]], 27658 ^ _776541 : [(27661 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273661), _1273665), c_Groups_Ozero__class_Ozero(_1273661)))], (27659 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273661), c_Groups_Ozero__class_Ozero(_1273661)), _1273665))]]], (45088 ^ _776541) ^ [_1679472, _1679474] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1679472)), hAPP(c_Code__Numeral_Oof__nat, _1679474)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1679472), _1679474)))], (14208 ^ _776541) ^ [_1032134] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1032134)), 14212 ^ _776541 : [(14213 ^ _776541) ^ [_1032214] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1032214), _1032134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032214), 14211 ^ [_1032134])))]]], (24281 ^ _776541) ^ [_1215666, _1215668] : [24282 ^ _776541 : [(24283 ^ _776541) ^ [_1215722] : [_1215668 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215666), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1215722)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215666), _1215668)))], (31577 ^ _776541) ^ [_1343423, _1343425, _1343427, _1343429] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1343423), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343423), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343423), _1343425), _1343427)), _1343429) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343423), _1343425), _1343429)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343423), _1343427), _1343429)))], (51913 ^ _776541) ^ [_1825343, _1825345] : [class_Lattices_Olattice(_1825343), -(class_Lattices_Olattice(tc_fun(_1825345, _1825343)))], (24832 ^ _776541) ^ [_1225842, _1225844, _1225846, _1225848] : [class_Divides_Osemiring__div(_1225842), -(c_Divides_Odiv__class_Omod(_1225842, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225842), _1225844), _1225846), _1225848) = c_Divides_Odiv__class_Omod(_1225842, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225842), _1225844), c_Divides_Odiv__class_Omod(_1225842, _1225846, _1225848)), _1225848))], (22209 ^ _776541) ^ [_1179345, _1179347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179345), _1179347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179345), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1179347)))], (40893 ^ _776541) ^ [_1577237, _1577239, _1577241, _1577243] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577237, _1577237)), hAPP(hAPP(c_Product__Type_OPair(_1577237, _1577237), _1577239), _1577241)), c_Transitive__Closure_Ortrancl(_1577237, _1577243))), -(_1577239 = _1577241), 40900 ^ _776541 : [(40903 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577237, _1577237)), hAPP(hAPP(c_Product__Type_OPair(_1577237, _1577237), _1577239), _1577241)), c_Transitive__Closure_Otrancl(_1577237, _1577243))))], (40901 ^ _776541) ^ [] : [_1577239 = _1577241]]], (39193 ^ _776541) ^ [_1533006, _1533008, _1533010, _1533012] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1533006, _1533008)), hAPP(hAPP(c_Product__Type_OSigma(_1533006, _1533008), hAPP(hAPP(c_Set_Oinsert(_1533006), _1533010), c_Orderings_Obot__class_Obot(tc_fun(_1533006, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1533008, tc_HOL_Obool), _1533006), _1533012))) = hAPP(c_Finite__Set_Ocard(_1533008), _1533012))], (36904 ^ _776541) ^ [_1477063, _1477065, _1477067, _1477069, _1477071] : [c_Equiv__Relations_Oequiv(_1477063, _1477065, _1477067), hBOOL(hAPP(hAPP(c_member(tc_prod(_1477063, _1477063)), hAPP(hAPP(c_Product__Type_OPair(_1477063, _1477063), _1477069), _1477071)), _1477067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477063, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1477063, _1477063, _1477067), hAPP(hAPP(c_Set_Oinsert(_1477063), _1477069), c_Orderings_Obot__class_Obot(tc_fun(_1477063, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1477063, _1477063, _1477067), hAPP(hAPP(c_Set_Oinsert(_1477063), _1477071), c_Orderings_Obot__class_Obot(tc_fun(_1477063, tc_HOL_Obool)))))))], (50801 ^ _776541) ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1803608, _1803610), tc_prod(_1803608, _1803610))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1803608, _1803610), tc_prod(_1803608, _1803610)), hAPP(hAPP(c_Product__Type_OPair(_1803608, _1803610), _1803612), _1803614)), hAPP(hAPP(c_Product__Type_OPair(_1803608, _1803610), _1803616), _1803618))), c_Transitive__Closure_Ortrancl(tc_prod(_1803608, _1803610), _1803620))), hBOOL(hAPP(hAPP(_1803622, _1803612), _1803614)), 50812 ^ _776541 : [(50817 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1803608, _1803610), tc_prod(_1803608, _1803610))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1803608, _1803610), tc_prod(_1803608, _1803610)), hAPP(hAPP(c_Product__Type_OPair(_1803608, _1803610), 50810 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]), 50811 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622])), hAPP(hAPP(c_Product__Type_OPair(_1803608, _1803610), 50814 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]), 50815 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]))), _1803620)))], (50819 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1803622, 50810 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]), 50811 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622])))], (50821 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1803622, 50814 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]), 50815 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]))], (50813 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1803608, _1803610), tc_prod(_1803608, _1803610))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1803608, _1803610), tc_prod(_1803608, _1803610)), hAPP(hAPP(c_Product__Type_OPair(_1803608, _1803610), _1803612), _1803614)), hAPP(hAPP(c_Product__Type_OPair(_1803608, _1803610), 50810 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]), 50811 ^ [_1803608, _1803610, _1803612, _1803614, _1803616, _1803618, _1803620, _1803622]))), c_Transitive__Closure_Ortrancl(tc_prod(_1803608, _1803610), _1803620))))]], -(hBOOL(hAPP(hAPP(_1803622, _1803616), _1803618)))], (17898 ^ _776541) ^ [_1098535, _1098537, _1098539, _1098541] : [class_Rings_Ocomm__semiring__1(_1098535), class_Rings_Ono__zero__divisors(_1098535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098537), _1098539)), 17909 ^ _776541 : [(17919 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1098537, _1098535), _1098541), _1098539) = c_Groups_Ozero__class_Ozero(_1098535)), 17920 ^ _776541 : [(17921 ^ _776541) ^ [_1098913] : [hBOOL(hAPP(hAPP(c_member(_1098537), _1098913), _1098539)), hAPP(_1098541, _1098913) = c_Groups_Ozero__class_Ozero(_1098535)]]], (17910 ^ _776541) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1098537, _1098535), _1098541), _1098539) = c_Groups_Ozero__class_Ozero(_1098535), 17914 ^ _776541 : [(17917 ^ _776541) ^ [] : [-(hAPP(_1098541, 17913 ^ [_1098535, _1098537, _1098539, _1098541]) = c_Groups_Ozero__class_Ozero(_1098535))], (17915 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098537), 17913 ^ [_1098535, _1098537, _1098539, _1098541]), _1098539)))]]]]], (41260 ^ _776541) ^ [_1586139, _1586141, _1586143, _1586145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586139, _1586141), tc_HOL_Obool)), _1586143), _1586145)), c_Relation_Osingle__valued(_1586139, _1586141, _1586145), -(c_Relation_Osingle__valued(_1586139, _1586141, _1586143))], (5448 ^ _776541) ^ [_859772, _859774, _859776, _859778, _859780, _859782] : [-(c_SetInterval_Oord_OgreaterThan(_859782, _859778, _859774) = c_SetInterval_Oord_OgreaterThan(_859780, _859776, _859772)), _859782 = _859780, _859778 = _859776, _859774 = _859772], (33332 ^ _776541) ^ [_1388142, _1388144, _1388146, _1388148] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1388142, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388144, tc_fun(_1388142, tc_HOL_Obool)), _1388146), _1388148)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388144, tc_fun(_1388142, tc_HOL_Obool)), _1388146), hAPP(hAPP(c_COMBB(tc_fun(_1388142, tc_HOL_Obool), tc_fun(_1388142, tc_HOL_Obool), _1388144), c_Groups_Ouminus__class_Ouminus(tc_fun(_1388142, tc_HOL_Obool))), _1388148)))], (47785 ^ _776541) ^ [_1738345, _1738347, _1738349, _1738351] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1738345, _1738347, _1738349, _1738351) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1738345, _1738347), _1738349), _1738351)))], (18015 ^ _776541) ^ [_1100468, _1100470, _1100472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100468), _1100470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100468), _1100472))), 18018 ^ _776541 : [(18021 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100470), _1100472)))], (18019 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100468)))]]], (14981 ^ _776541) ^ [_1046838, _1046840, _1046842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046838), _1046840)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046840), _1046838)), _1046842) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046840), _1046842)), _1046838))], (35778 ^ _776541) ^ [_1444451, _1444453, _1444455, _1444457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444451, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444451, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35779 ^ [_1444451, _1444453, _1444455, _1444457])), _1444453)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444451, 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), 35779 ^ [_1444451, _1444453, _1444455, _1444457]), _1444455))), _1444457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444451, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444451, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1444453)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444451, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1444457))))], (47917 ^ _776541) ^ [_1741686, _1741688, _1741690, _1741692, _1741694] : [-(hAPP(hAPP(c_List_Olist_OCons(_1741686), _1741688), _1741690) = hAPP(c_List_Ofilter(_1741686, _1741692), _1741694)), 47918 ^ _776541 : [(47919 ^ _776541) ^ [_1741814, _1741816] : [_1741694 = hAPP(hAPP(c_List_Oappend(_1741686), _1741816), hAPP(hAPP(c_List_Olist_OCons(_1741686), _1741688), _1741814)), 47925 ^ _776541 : [(47928 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1741692, 47924 ^ [_1741686, _1741688, _1741690, _1741692, _1741694, _1741814, _1741816])))], (47926 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741686), 47924 ^ [_1741686, _1741688, _1741690, _1741692, _1741694, _1741814, _1741816]), hAPP(c_List_Oset(_1741686), _1741816))))]], hBOOL(hAPP(_1741692, _1741688)), _1741690 = hAPP(c_List_Ofilter(_1741686, _1741692), _1741814)]]], (38495 ^ _776541) ^ [_1514526, _1514528, _1514530] : [c_Wellfounded_OwfP(_1514526, _1514528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514526, tc_fun(_1514526, tc_HOL_Obool))), _1514530), _1514528)), -(c_Wellfounded_OwfP(_1514526, _1514530))], (31845 ^ _776541) ^ [_1348650, _1348652, _1348654] : [class_Orderings_Olinorder(_1348650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348650), _1348652)), -(c_Big__Operators_Olinorder__class_OMax(_1348650, hAPP(hAPP(c_Set_Oinsert(_1348650), _1348654), _1348652)) = hAPP(hAPP(c_Finite__Set_Ofold(_1348650, _1348650, c_Orderings_Oord__class_Omax(_1348650)), _1348654), _1348652))], (26236 ^ _776541) ^ [_1250415, _1250417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250417)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1250415)), hAPP(c_Int_Onat, _1250417)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250415), _1250417)))], (25209 ^ _776541) ^ [_1232965, _1232967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232965), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232967), _1232965)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232965, _1232967) = _1232965)], (46704 ^ _776541) ^ [_1715114, _1715116, _1715118] : [class_Orderings_Olinorder(_1715114), -(c_List_Olinorder__class_Osorted(_1715114, hAPP(c_List_Ofilter(_1715114, hAPP(hAPP(c_COMBC(_1715114, _1715114, tc_HOL_Obool), c_fequal), hAPP(_1715116, _1715118))), _1715118)))], (23185 ^ _776541) ^ [] : [-(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))))], (5352 ^ _776541) ^ [_858290, _858292, _858294, _858296, _858298, _858300, _858302, _858304] : [-(c_Lazy__Sequence_Omap(_858304, _858300, _858296, _858292) = c_Lazy__Sequence_Omap(_858302, _858298, _858294, _858290)), _858304 = _858302, _858300 = _858298, _858296 = _858294, _858292 = _858290], (28945 ^ _776541) ^ [_1295423, _1295425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295423), _1295425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295423)), c_Int_OBit1(_1295425))))], (25748 ^ _776541) ^ [_1242501, _1242503, _1242505, _1242507] : [_1242501 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242503), _1242505)), _1242507), -(_1242503 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242501, _1242503) = _1242507), 25755 ^ _776541 : [(25758 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242507), _1242503))], (25756 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242503)))]], 25763 ^ _776541 : [(25766 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242503), _1242507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242507), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25764 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242503))]]], (11618 ^ _776541) ^ [_979781, _979783, _979785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979781, tc_HOL_Obool)), _979783), _979785)), hBOOL(hAPP(c_Finite__Set_Ofinite(_979781), _979785)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979781), _979783)))], (52139 ^ _776541) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (31327 ^ _776541) ^ [_1338917] : [class_Orderings_Olinorder(_1338917), -(c_Finite__Set_Ofun__left__comm__idem(_1338917, _1338917, c_Orderings_Oord__class_Omax(_1338917)))], (50792 ^ _776541) ^ [_1803347, _1803349, _1803351, _1803353, _1803355] : [50794 ^ _776541 : [(50797 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803351, tc_HOL_Obool)), _1803353), hAPP(_1803355, 50793 ^ [_1803347, _1803349, _1803351, _1803353, _1803355])))], (50795 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803347), 50793 ^ [_1803347, _1803349, _1803351, _1803353, _1803355]), _1803349)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803351, tc_HOL_Obool)), _1803353), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1803347, tc_fun(_1803351, tc_HOL_Obool)), _1803349), _1803355))))], (21161 ^ _776541) ^ [_1159371, _1159373, _1159375] : [class_Int_Onumber__ring(_1159371), class_Int_Oring__char__0(_1159371), 21168 ^ _776541 : [(21175 ^ _776541) ^ [] : [_1159373 = _1159375, -(hAPP(c_Int_Onumber__class_Onumber__of(_1159371), _1159373) = hAPP(c_Int_Onumber__class_Onumber__of(_1159371), _1159375))], (21169 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1159371), _1159373) = hAPP(c_Int_Onumber__class_Onumber__of(_1159371), _1159375), -(_1159373 = _1159375)]]], (24032 ^ _776541) ^ [_1211626, _1211628] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211626)), _1211628) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211626), _1211628)))], (11447 ^ _776541) ^ [_976359, _976361, _976363, _976365, _976367] : [c_Finite__Set_Ofolding__one(_976359, _976361, _976363), hBOOL(hAPP(c_Finite__Set_Ofinite(_976359), _976365)), 11454 ^ _776541 : [(11461 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976359, tc_HOL_Obool)), _976365), hAPP(hAPP(c_Set_Oinsert(_976359), _976367), c_Orderings_Obot__class_Obot(tc_fun(_976359, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_976359, tc_HOL_Obool))), -(hAPP(_976363, hAPP(hAPP(c_Set_Oinsert(_976359), _976367), _976365)) = hAPP(hAPP(_976361, _976367), hAPP(_976363, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976359, tc_HOL_Obool)), _976365), hAPP(hAPP(c_Set_Oinsert(_976359), _976367), c_Orderings_Obot__class_Obot(tc_fun(_976359, tc_HOL_Obool)))))))], (11455 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976359, tc_HOL_Obool)), _976365), hAPP(hAPP(c_Set_Oinsert(_976359), _976367), c_Orderings_Obot__class_Obot(tc_fun(_976359, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_976359, tc_HOL_Obool)), -(hAPP(_976363, hAPP(hAPP(c_Set_Oinsert(_976359), _976367), _976365)) = _976367)]]], (32706 ^ _776541) ^ [_1370719, _1370721, _1370723, _1370725] : [_1370719 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1370721, _1370723), 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)), _1370725))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1370721), _1370719)))], (46341 ^ _776541) ^ [_1708526, _1708528] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1708526), _1708528)) = c_List_Oupt(_1708526, _1708528))], (48464 ^ _776541) ^ [_1752968, _1752970, _1752972, _1752974, _1752976] : [-(c_List_Osplice(_1752968, hAPP(hAPP(c_List_Olist_OCons(_1752968), _1752970), _1752972), hAPP(hAPP(c_List_Olist_OCons(_1752968), _1752974), _1752976)) = hAPP(hAPP(c_List_Olist_OCons(_1752968), _1752970), hAPP(hAPP(c_List_Olist_OCons(_1752968), _1752974), c_List_Osplice(_1752968, _1752972, _1752976))))], (34085 ^ _776541) ^ [_1409409, _1409411, _1409413, _1409415] : [class_Groups_Ocomm__monoid__add(_1409409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1409411), _1409413)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409409), _1409415), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1409411, _1409413)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409409), hAPP(_1409415, _1409411)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409409), _1409415), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1409411, _1409413))))], (44581 ^ _776541) ^ [_1668204, _1668206, _1668208] : [_1668204 = c_List_Olist_ONil(_1668206), -(c_List_Olast(_1668206, hAPP(hAPP(c_List_Olist_OCons(_1668206), _1668208), _1668204)) = _1668208)], (34858 ^ _776541) ^ [_1427026, _1427028, _1427030, _1427032, _1427034, _1427036] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427026, _1427028, _1427030), _1427032), hAPP(hAPP(c_Product__Type_OPair(_1427026, _1427028), _1427034), _1427036)) = hAPP(hAPP(_1427032, _1427034), _1427036))], (47609 ^ _776541) ^ [_1733946, _1733948, _1733950, _1733952] : [-(c_List_Oconcat(_1733946, hAPP(hAPP(c_List_Omap(_1733948, tc_List_Olist(_1733946)), _1733950), _1733952)) = c_List_Omaps(_1733948, _1733946, _1733950, _1733952))], (10695 ^ _776541) ^ [_960663, _960665, _960667] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960663, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960663, tc_HOL_Obool)), _960665), _960667)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960663, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960663, tc_HOL_Obool)), _960665)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960663, tc_HOL_Obool)), _960667)))], (34640 ^ _776541) ^ [_1421861, _1421863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421861)), 34643 ^ _776541 : [(34650 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421863), _1421861))), -(c_Divides_OposDivAlg(_1421863, _1421861) = hAPP(c_Divides_Oadjust(_1421861), c_Divides_OposDivAlg(_1421863, 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)))), _1421861))))], (34644 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421863), _1421861)), -(c_Divides_OposDivAlg(_1421863, _1421861) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421863))]]], (16256 ^ _776541) ^ [_1070110, _1070112, _1070114] : [class_Rings_Oring__no__zero__divisors(_1070110), 16259 ^ _776541 : [(16260 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070110), _1070112), _1070114) = c_Groups_Ozero__class_Ozero(_1070110), -(_1070112 = c_Groups_Ozero__class_Ozero(_1070110)), -(_1070114 = c_Groups_Ozero__class_Ozero(_1070110))], (16270 ^ _776541) ^ [] : [16271 ^ _776541 : [(16274 ^ _776541) ^ [] : [_1070114 = c_Groups_Ozero__class_Ozero(_1070110)], (16272 ^ _776541) ^ [] : [_1070112 = c_Groups_Ozero__class_Ozero(_1070110)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070110), _1070112), _1070114) = c_Groups_Ozero__class_Ozero(_1070110))]]], (24309 ^ _776541) ^ [_1216162, _1216164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216162), _1216164)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216164)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216162)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216164), _1216162)))], (52427 ^ _776541) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (47116 ^ _776541) ^ [_1723605, _1723607] : [-(_1723605 = c_List_Olist_ONil(_1723607)), -(hAPP(c_List_Ohd(_1723607), hAPP(c_List_Orev(_1723607), _1723605)) = c_List_Olast(_1723607, _1723605))], (52159 ^ _776541) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (42644 ^ _776541) ^ [_1625476, _1625478, _1625480, _1625482] : [42646 ^ _776541 : [(42649 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1625480, 42645 ^ [_1625476, _1625478, _1625480, _1625482])), hAPP(_1625482, 42645 ^ [_1625476, _1625478, _1625480, _1625482])))], (42647 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625476), 42645 ^ [_1625476, _1625478, _1625480, _1625482]), hAPP(c_List_Oset(_1625476), _1625478))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1625476, _1625480, _1625478)), c_List_Olist_Olist__size(_1625476, _1625482, _1625478))))], (15646 ^ _776541) ^ [_1060341] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060341), hAPP(c_Nat_OSuc, _1060341))))], (8139 ^ _776541) ^ [_915250, _915252, _915254] : [hBOOL(hAPP(hAPP(c_member(_915250), _915252), _915254)), -(hAPP(hAPP(c_Set_Oinsert(_915250), _915252), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915250, tc_HOL_Obool)), _915254), hAPP(hAPP(c_Set_Oinsert(_915250), _915252), c_Orderings_Obot__class_Obot(tc_fun(_915250, tc_HOL_Obool))))) = _915254)], (28639 ^ _776541) ^ [_1290116, _1290118] : [class_Int_Onumber__ring(_1290116), class_Rings_Olinordered__idom(_1290116), 28646 ^ _776541 : [(28653 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1290118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290116), c_Groups_Oone__class_Oone(_1290116)), hAPP(c_Int_Onumber__class_Onumber__of(_1290116), _1290118))))], (28647 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290116), c_Groups_Oone__class_Oone(_1290116)), hAPP(c_Int_Onumber__class_Onumber__of(_1290116), _1290118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1290118)))]]], (45770 ^ _776541) ^ [_1694894, _1694896] : [hBOOL(hAPP(c_List_Odistinct(_1694894), _1694896)), -(c_List_Oremdups(_1694894, _1694896) = _1694896)], (48864 ^ _776541) ^ [_1761587] : [-(c_Lazy__Sequence_Oyieldn(_1761587) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1761587), _1761587, c_Lazy__Sequence_Oyield(_1761587)))], (43858 ^ _776541) ^ [_1652669, _1652671] : [-(hAPP(c_List_Orotate1(_1652669), _1652671) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1652669), _1652669, c_List_Olist_ONil(_1652669), hAPP(hAPP(c_COMBB(tc_List_Olist(_1652669), tc_fun(tc_List_Olist(_1652669), tc_List_Olist(_1652669)), _1652669), hAPP(c_COMBC(tc_List_Olist(_1652669), tc_List_Olist(_1652669), tc_List_Olist(_1652669)), c_List_Oappend(_1652669))), hAPP(hAPP(c_COMBC(_1652669, tc_List_Olist(_1652669), tc_List_Olist(_1652669)), c_List_Olist_OCons(_1652669)), c_List_Olist_ONil(_1652669)))), _1652671))], (18087 ^ _776541) ^ [_1101765, _1101767, _1101769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101765)), 18090 ^ _776541 : [(18097 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101767), _1101769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101765), _1101767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101765), _1101769))))], (18091 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101765), _1101767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101765), _1101769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101767), _1101769)))]]], (51601 ^ _776541) ^ [_1820506, _1820508] : [class_Rings_Ocomm__semiring__1(_1820506), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820506), c_Groups_Oone__class_Oone(_1820506)), _1820508)))], (44196 ^ _776541) ^ [_1660266, _1660268, _1660270] : [-(hAPP(c_List_Orotate1(_1660266), hAPP(c_List_Orotate(_1660266, _1660268), _1660270)) = hAPP(c_List_Orotate(_1660266, _1660268), hAPP(c_List_Orotate1(_1660266), _1660270)))], (48474 ^ _776541) ^ [_1753203, _1753205] : [c_Wellfounded_Oacyclic(_1753203, hAPP(c_Set_OCollect(tc_prod(_1753203, _1753203)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753203, _1753203, tc_HOL_Obool), c_Predicate_Oconversep(_1753203, _1753203, _1753205)))), -(c_Wellfounded_Oacyclic(_1753203, hAPP(c_Set_OCollect(tc_prod(_1753203, _1753203)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753203, _1753203, tc_HOL_Obool), _1753205))))], (2306 ^ _776541) ^ [_810133, _810135, _810137, _810139, _810141, _810143] : [-(c_Nat_Onat_Onat__rec(_810143, _810139, _810135) = c_Nat_Onat_Onat__rec(_810141, _810137, _810133)), _810143 = _810141, _810139 = _810137, _810135 = _810133], (51447 ^ _776541) ^ [_1817779, _1817781] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1817779), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1817781))), 51450 ^ _776541 : [(51453 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817781), _1817779))], (51451 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817779), _1817781)))]]], (41142 ^ _776541) ^ [_1583267, _1583269] : [-(c_Transitive__Closure_Otrancl(_1583267, hAPP(c_Relation_Oconverse(_1583267, _1583267), _1583269)) = hAPP(c_Relation_Oconverse(_1583267, _1583267), c_Transitive__Closure_Otrancl(_1583267, _1583269)))], (34437 ^ _776541) ^ [_1417503, _1417505] : [34438 ^ _776541 : [(34441 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1417505), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34439 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417503), _1417505))]], -(c_Divides_OposDivAlg(_1417503, _1417505) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1417503))], (11042 ^ _776541) ^ [_967404, _967406, _967408, _967410, _967412, _967414] : [c_Finite__Set_Ofun__left__comm(_967404, _967406, _967408), -(hAPP(hAPP(_967408, _967410), hAPP(hAPP(_967408, _967412), _967414)) = hAPP(hAPP(_967408, _967412), hAPP(hAPP(_967408, _967410), _967414)))], (36780 ^ _776541) ^ [_1474401, _1474403, _1474405, _1474407, _1474409, _1474411, _1474413] : [c_Equiv__Relations_Oequiv(_1474401, _1474403, _1474405), hBOOL(hAPP(hAPP(c_member(tc_fun(_1474401, tc_HOL_Obool)), _1474407), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1474401), _1474403), _1474405))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1474401, tc_HOL_Obool)), _1474409), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1474401), _1474403), _1474405))), hBOOL(hAPP(hAPP(c_member(_1474401), _1474411), _1474407)), hBOOL(hAPP(hAPP(c_member(_1474401), _1474413), _1474409)), 36799 ^ _776541 : [(36806 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1474401, _1474401)), hAPP(hAPP(c_Product__Type_OPair(_1474401, _1474401), _1474411), _1474413)), _1474405)), -(_1474407 = _1474409)], (36800 ^ _776541) ^ [] : [_1474407 = _1474409, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1474401, _1474401)), hAPP(hAPP(c_Product__Type_OPair(_1474401, _1474401), _1474411), _1474413)), _1474405)))]]], (302 ^ _776541) ^ [_781142, _781144, _781146, _781148] : [-(c_Nitpick_Owf_H(_781146, _781142)), c_Nitpick_Owf_H(_781148, _781144), _781148 = _781146, _781144 = _781142], (17435 ^ _776541) ^ [_1090525, _1090527, _1090529] : [class_Rings_Olinordered__semiring__strict(_1090525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090525), c_Groups_Ozero__class_Ozero(_1090525)), _1090527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090525), _1090529), c_Groups_Ozero__class_Ozero(_1090525))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090525), _1090529), _1090527)), c_Groups_Ozero__class_Ozero(_1090525))))], (29047 ^ _776541) ^ [_1297253] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297253)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297253))))], (25503 ^ _776541) ^ [_1237874, _1237876, _1237878] : [hBOOL(hAPP(_1237874, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237876), _1237878))), 25508 ^ _776541 : [(25511 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1237874, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25509 ^ _776541) ^ [] : [-(_1237878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25513 ^ _776541 : [(25518 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1237874, 25512 ^ [_1237874, _1237876, _1237878])))], (25516 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237878), hAPP(c_Nat_OSuc, 25512 ^ [_1237874, _1237876, _1237878])))))], (25514 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237878), 25512 ^ [_1237874, _1237876, _1237878])), _1237876)))]]], (33324 ^ _776541) ^ [_1387943, _1387945, _1387947, _1387949] : [class_Groups_Ouminus(_1387943), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1387945, _1387943)), _1387947), _1387949) = hAPP(c_Groups_Ouminus__class_Ouminus(_1387943), hAPP(_1387947, _1387949)))], (2178 ^ _776541) ^ [_808137, _808139, _808141, _808143, _808145, _808147, _808149, _808151] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_808151, _808147, _808143, _808139) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_808149, _808145, _808141, _808137)), _808151 = _808149, _808147 = _808145, _808143 = _808141, _808139 = _808137], (39806 ^ _776541) ^ [_1550739, _1550741, _1550743, _1550745, _1550747, _1550749] : [hBOOL(hAPP(hAPP(c_member(_1550739), _1550741), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550743, _1550745, tc_fun(_1550739, tc_HOL_Obool)), _1550747), _1550749))), 39811 ^ _776541 : [(39814 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550739), _1550741), hAPP(hAPP(_1550747, 39809 ^ [_1550739, _1550741, _1550743, _1550745, _1550747, _1550749]), 39810 ^ [_1550739, _1550741, _1550743, _1550745, _1550747, _1550749]))))], (39812 ^ _776541) ^ [] : [-(_1550749 = hAPP(hAPP(c_Product__Type_OPair(_1550743, _1550745), 39809 ^ [_1550739, _1550741, _1550743, _1550745, _1550747, _1550749]), 39810 ^ [_1550739, _1550741, _1550743, _1550745, _1550747, _1550749]))]]], (25135 ^ _776541) ^ [_1231496, _1231498, _1231500, _1231502] : [class_Divides_Osemiring__div(_1231496), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231496), _1231498), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231496), _1231500), _1231498))), c_Divides_Odiv__class_Omod(_1231496, _1231500, _1231498))), _1231502) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231496), _1231500), _1231502))], (46710 ^ _776541) ^ [_1715229, _1715231, _1715233] : [class_Orderings_Olinorder(_1715229), 46713 ^ _776541 : [(46726 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715229, hAPP(hAPP(c_List_Olist_OCons(_1715229), _1715231), _1715233))), c_List_Olinorder__class_Osorted(_1715229, _1715233), 46732 ^ _776541 : [(46735 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715229), _1715231), 46731 ^ [_1715229, _1715231, _1715233]))], (46733 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715229), 46731 ^ [_1715229, _1715231, _1715233]), hAPP(c_List_Oset(_1715229), _1715233))))]]], (46714 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1715229, hAPP(hAPP(c_List_Olist_OCons(_1715229), _1715231), _1715233)), 46717 ^ _776541 : [(46720 ^ _776541) ^ [_1715415] : [hBOOL(hAPP(hAPP(c_member(_1715229), _1715415), hAPP(c_List_Oset(_1715229), _1715233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715229), _1715231), _1715415)))], (46718 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715229, _1715233))]]]]], (41716 ^ _776541) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46988 ^ _776541) ^ [_1720990, _1720992, _1720994] : [_1720994 = hAPP(hAPP(c_List_Olist_OCons(_1720990), _1720992), c_List_Olist_ONil(_1720990)), -(hAPP(hAPP(c_List_Olist_OCons(_1720990), _1720992), c_List_Olist_ONil(_1720990)) = hAPP(c_List_Orev(_1720990), _1720994))], (52457 ^ _776541) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (18991 ^ _776541) ^ [_1118610, _1118612] : [18999 ^ _776541 : [(19002 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1118612, 18998 ^ [_1118610, _1118612])))], (19000 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18998 ^ [_1118610, _1118612]), _1118610)))]], 18992 ^ _776541 : [(18993 ^ _776541) ^ [_1118679] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1118679), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1118610))), hBOOL(hAPP(_1118612, _1118679))]]], (50955 ^ _776541) ^ [_1808514, _1808516, _1808518] : [-(c_Lazy__Sequence_Omap(_1808514, _1808516, _1808518, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1808514)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1808516))], (33723 ^ _776541) ^ [_1399975, _1399977, _1399979, _1399981, _1399983] : [class_Groups_Ocomm__monoid__add(_1399975), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399977), _1399979)), 33730 ^ _776541 : [(33737 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399977), _1399981), _1399979))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399977, _1399975), hAPP(hAPP(c_COMBC(_1399977, _1399975, _1399975), hAPP(hAPP(c_COMBS(_1399977, _1399975, tc_fun(_1399975, _1399975)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399975, tc_fun(_1399975, _1399975)), _1399977), c_If(_1399975)), hAPP(hAPP(c_COMBC(_1399977, _1399977, tc_HOL_Obool), c_fequal), _1399981))), _1399983)), c_Groups_Ozero__class_Ozero(_1399975))), _1399979) = c_Groups_Ozero__class_Ozero(_1399975))], (33731 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1399977), _1399981), _1399979)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399977, _1399975), hAPP(hAPP(c_COMBC(_1399977, _1399975, _1399975), hAPP(hAPP(c_COMBS(_1399977, _1399975, tc_fun(_1399975, _1399975)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399975, tc_fun(_1399975, _1399975)), _1399977), c_If(_1399975)), hAPP(hAPP(c_COMBC(_1399977, _1399977, tc_HOL_Obool), c_fequal), _1399981))), _1399983)), c_Groups_Ozero__class_Ozero(_1399975))), _1399979) = hAPP(_1399983, _1399981))]]], (24766 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (22159 ^ _776541) ^ [_1178395, _1178397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178395), _1178397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178397))))], (22491 ^ _776541) ^ [_1184025, _1184027, _1184029, _1184031] : [class_Groups_Ocomm__monoid__mult(_1184025), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184025), _1184027), _1184029)), _1184031) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184025), hAPP(hAPP(c_Power_Opower__class_Opower(_1184025), _1184027), _1184031)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184025), _1184029), _1184031)))], (12325 ^ _776541) ^ [_992864, _992866, _992868] : [class_Lattices_Olattice(_992864), hBOOL(hAPP(c_Finite__Set_Ofinite(_992864), _992866)), 12332 ^ _776541 : [(12339 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992864, tc_HOL_Obool)), _992866), hAPP(hAPP(c_Set_Oinsert(_992864), _992868), c_Orderings_Obot__class_Obot(tc_fun(_992864, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992864, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_992864, hAPP(hAPP(c_Set_Oinsert(_992864), _992868), _992866)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_992864), _992868), c_Big__Operators_Olattice__class_OInf__fin(_992864, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992864, tc_HOL_Obool)), _992866), hAPP(hAPP(c_Set_Oinsert(_992864), _992868), c_Orderings_Obot__class_Obot(tc_fun(_992864, tc_HOL_Obool)))))))], (12333 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992864, tc_HOL_Obool)), _992866), hAPP(hAPP(c_Set_Oinsert(_992864), _992868), c_Orderings_Obot__class_Obot(tc_fun(_992864, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992864, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_992864, hAPP(hAPP(c_Set_Oinsert(_992864), _992868), _992866)) = _992868)]]], (14933 ^ _776541) ^ [_1045917, _1045919, _1045921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045917), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045919), _1045921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045917), _1045921)), _1045919)))], (13202 ^ _776541) ^ [_1010246] : [-(c_Finite__Set_Ofun__left__comm__idem(_1010246, tc_fun(_1010246, tc_HOL_Obool), c_Set_Oinsert(_1010246)))], (9502 ^ _776541) ^ [_939709, _939711, _939713] : [class_Orderings_Olinorder(_939709), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939709), _939711), _939713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939709), _939713), _939711)))], (30872 ^ _776541) ^ [_1330281, _1330283, _1330285] : [class_Orderings_Olinorder(_1330281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330281), _1330283)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330281), _1330285)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330281, tc_HOL_Obool)), _1330283), _1330285) = c_Orderings_Obot__class_Obot(tc_fun(_1330281, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330281), c_Big__Operators_Olattice_OInf__fin(_1330281, c_Orderings_Oord__class_Omin(_1330281), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330281, tc_HOL_Obool)), _1330283), _1330285))), c_Big__Operators_Olattice_OInf__fin(_1330281, c_Orderings_Oord__class_Omin(_1330281), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330281, tc_HOL_Obool)), _1330283), _1330285))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330281), c_Big__Operators_Olattice_OInf__fin(_1330281, c_Orderings_Oord__class_Omin(_1330281), _1330283)), c_Big__Operators_Olattice_OInf__fin(_1330281, c_Orderings_Oord__class_Omin(_1330281), _1330285)))], (34315 ^ _776541) ^ [_1415227, _1415229] : [-(c_Divides_OnegDivAlg(_1415227, _1415229) = hAPP(c_Divides_Oadjust(_1415229), c_Divides_OnegDivAlg(_1415227, 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)))), _1415229)))), -(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), _1415227), _1415229)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1415229), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12700 ^ _776541) ^ [_1000449, _1000451, _1000453, _1000455] : [c_Finite__Set_Ofolding__one(_1000449, _1000451, _1000453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000449), _1000455)), -(hAPP(_1000453, _1000455) = hAPP(c_Finite__Set_Ofold1(_1000449, _1000451), _1000455))], (24882 ^ _776541) ^ [_1226959, _1226961, _1226963, _1226965, _1226967, _1226969] : [class_Divides_Oring__div(_1226959), c_Divides_Odiv__class_Omod(_1226959, _1226961, _1226963) = c_Divides_Odiv__class_Omod(_1226959, _1226965, _1226963), c_Divides_Odiv__class_Omod(_1226959, _1226967, _1226963) = c_Divides_Odiv__class_Omod(_1226959, _1226969, _1226963), -(c_Divides_Odiv__class_Omod(_1226959, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1226959), _1226961), _1226967), _1226963) = c_Divides_Odiv__class_Omod(_1226959, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1226959), _1226965), _1226969), _1226963))], (32684 ^ _776541) ^ [_1370258, _1370260, _1370262] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1370258), _1370260), _1370262) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1370258), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370258, tc_Int_Oint), _1370260), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1370262))), class_Groups_Ocomm__monoid__add(_1370258), class_Groups_Ocomm__monoid__mult(_1370258)], (15876 ^ _776541) ^ [_1063942, _1063944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063942), _1063944))))], (22169 ^ _776541) ^ [_1178602, _1178604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178602)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178602), _1178604)))], (34616 ^ _776541) ^ [_1421340, _1421342] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421340), _1421342)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421340)), _1421342)))], (35967 ^ _776541) ^ [_1451111, _1451113, _1451115] : [class_Lattices_Odistrib__lattice(_1451111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451111), _1451113)), -(_1451113 = c_Orderings_Obot__class_Obot(tc_fun(_1451111, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451111), _1451115)), -(_1451115 = c_Orderings_Obot__class_Obot(tc_fun(_1451111, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451111), c_Big__Operators_Olattice__class_OInf__fin(_1451111, _1451113)), c_Big__Operators_Olattice__class_OInf__fin(_1451111, _1451115)) = c_Big__Operators_Olattice__class_OInf__fin(_1451111, hAPP(c_Set_OCollect(_1451111), hAPP(hAPP(c_COMBB(tc_fun(_1451111, tc_HOL_Obool), tc_HOL_Obool, _1451111), c_HOL_OEx(_1451111)), hAPP(hAPP(c_COMBB(tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool)), tc_fun(_1451111, tc_HOL_Obool), _1451111), hAPP(c_COMBB(tc_fun(_1451111, tc_HOL_Obool), tc_HOL_Obool, _1451111), c_HOL_OEx(_1451111))), hAPP(hAPP(c_COMBC(_1451111, tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool)), tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451111, tc_fun(tc_fun(_1451111, tc_HOL_Obool), tc_fun(_1451111, tc_HOL_Obool))), tc_fun(tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool)), tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool))), _1451111), c_COMBS(_1451111, tc_fun(_1451111, tc_HOL_Obool), tc_fun(_1451111, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451111, tc_fun(_1451111, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1451111, tc_fun(tc_fun(_1451111, tc_HOL_Obool), tc_fun(_1451111, tc_HOL_Obool))), _1451111), hAPP(c_COMBB(tc_fun(_1451111, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1451111, tc_HOL_Obool), tc_fun(_1451111, tc_HOL_Obool)), _1451111), c_COMBS(_1451111, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool)), tc_fun(_1451111, tc_fun(_1451111, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1451111), hAPP(c_COMBB(tc_fun(_1451111, tc_HOL_Obool), tc_fun(_1451111, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1451111), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1451111), c_fconj))), hAPP(hAPP(c_COMBC(_1451111, tc_fun(_1451111, tc_fun(_1451111, _1451111)), tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1451111, _1451111), tc_fun(_1451111, tc_HOL_Obool)), tc_fun(tc_fun(_1451111, tc_fun(_1451111, _1451111)), tc_fun(_1451111, tc_fun(_1451111, tc_HOL_Obool))), _1451111), c_COMBB(tc_fun(_1451111, _1451111), tc_fun(_1451111, tc_HOL_Obool), _1451111)), hAPP(hAPP(c_COMBB(tc_fun(_1451111, tc_HOL_Obool), tc_fun(tc_fun(_1451111, _1451111), tc_fun(_1451111, tc_HOL_Obool)), _1451111), c_COMBB(_1451111, tc_HOL_Obool, _1451111)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1451111)))))), hAPP(hAPP(c_COMBC(_1451111, tc_fun(_1451111, tc_HOL_Obool), tc_fun(_1451111, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1451111, tc_HOL_Obool), tc_fun(_1451111, tc_HOL_Obool)), _1451111), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1451111)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1451111), c_fconj), hAPP(hAPP(c_COMBC(_1451111, tc_fun(_1451111, tc_HOL_Obool), tc_HOL_Obool), c_member(_1451111)), _1451113)))), hAPP(hAPP(c_COMBC(_1451111, tc_fun(_1451111, tc_HOL_Obool), tc_HOL_Obool), c_member(_1451111)), _1451115))))))))], (10689 ^ _776541) ^ [_960516, _960518] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960516, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960516, tc_HOL_Obool)), _960518)), _960518) = c_Orderings_Obot__class_Obot(tc_fun(_960516, tc_HOL_Obool)))], (14066 ^ _776541) ^ [_1028730, _1028732, _1028734, _1028736, _1028738] : [class_Groups_Ocomm__monoid__add(_1028730), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028732), _1028734)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028732), _1028736)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1028732, tc_HOL_Obool)), _1028734), _1028736) = c_Orderings_Obot__class_Obot(tc_fun(_1028732, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028732, _1028730), _1028738), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1028732, tc_HOL_Obool)), _1028734), _1028736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028730), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028732, _1028730), _1028738), _1028734)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028732, _1028730), _1028738), _1028736)))], (31325 ^ _776541) ^ [_1338891] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1338891) = _1338891)], (33509 ^ _776541) ^ [_1393031, _1393033] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393031, tc_fun(_1393031, tc_HOL_Obool)), _1393033), hAPP(hAPP(c_COMBC(_1393031, tc_fun(_1393031, tc_HOL_Obool), tc_fun(_1393031, tc_HOL_Obool)), c_Set_Oinsert(_1393031)), c_Orderings_Obot__class_Obot(tc_fun(_1393031, tc_HOL_Obool)))) = _1393033)], (38842 ^ _776541) ^ [_1523437, _1523439, _1523441, _1523443] : [c_Fun_Oinj__on(_1523437, _1523439, _1523441, c_Orderings_Otop__class_Otop(tc_fun(_1523437, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1523437, _1523439, _1523441), hAPP(c_Set_Oimage(_1523437, _1523439, _1523441), _1523443)) = _1523443)], (45404 ^ _776541) ^ [_1686474, _1686476, _1686478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1686474, tc_HOL_Obool)), _1686476), _1686478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1686474), tc_HOL_Obool)), c_List_Olistsp(_1686474, _1686476)), c_List_Olistsp(_1686474, _1686478))))], (37736 ^ _776541) ^ [_1495416, _1495418, _1495420, _1495422] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1495416), _1495418)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495420), _1495422)), 37743 ^ _776541 : [(37744 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1495416), _1495418)), hAPP(c_Finite__Set_Ocard(_1495420), _1495422)))), 37745 ^ _776541 : [(37746 ^ _776541) ^ [_1495627] : [c_Fun_Oinj__on(_1495416, _1495420, _1495627, _1495418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495420, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1495416, _1495420, _1495627), _1495418)), _1495422))]]], (37754 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1495416), _1495418)), hAPP(c_Finite__Set_Ocard(_1495420), _1495422))), 37758 ^ _776541 : [(37761 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495420, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1495416, _1495420, 37757 ^ [_1495416, _1495418, _1495420, _1495422]), _1495418)), _1495422)))], (37759 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1495416, _1495420, 37757 ^ [_1495416, _1495418, _1495420, _1495422], _1495418))]]]]], (22181 ^ _776541) ^ [_1178818, _1178820] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1178818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178820), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1178818, _1178820))], (28439 ^ _776541) ^ [_1286990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1286990)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1286990), c_Int_OMin)))], (48440 ^ _776541) ^ [_1752220, _1752222, _1752224, _1752226, _1752228] : [-(hAPP(c_New__DSequence_Oneg__bind(_1752220, _1752222, _1752224, _1752226), _1752228) = c_Lazy__Sequence_Ohb__bind(_1752220, _1752222, hAPP(_1752224, _1752228), hAPP(hAPP(c_COMBC(_1752220, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1752222))), _1752226), _1752228)))], (31925 ^ _776541) ^ [_1350106, _1350108] : [class_Orderings_Olinorder(_1350106), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350106), _1350108)), -(_1350108 = c_Orderings_Obot__class_Obot(tc_fun(_1350106, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1350106), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350106), 31938 ^ [_1350106, _1350108]), 31939 ^ [_1350106, _1350108])), hAPP(hAPP(c_Set_Oinsert(_1350106), 31938 ^ [_1350106, _1350108]), hAPP(hAPP(c_Set_Oinsert(_1350106), 31939 ^ [_1350106, _1350108]), c_Orderings_Obot__class_Obot(tc_fun(_1350106, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1350106), c_Big__Operators_Olinorder__class_OMax(_1350106, _1350108)), _1350108)))], (7136 ^ _776541) ^ [_892777, _892779, _892781] : [-(hAPP(hAPP(c_Set_Oinsert(_892777), _892779), hAPP(hAPP(c_Set_Oinsert(_892777), _892779), _892781)) = hAPP(hAPP(c_Set_Oinsert(_892777), _892779), _892781))], (25594 ^ _776541) ^ [_1239527, _1239529, _1239531] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239527)))), 25597 ^ _776541 : [(25604 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239529)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239527)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239529)), _1239531)) = 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), _1239527), _1239529))), _1239531))], (25598 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239529))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239527)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239529)), _1239531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239527)), _1239531))]]], (7180 ^ _776541) ^ [_893519, _893521, _893523, _893525] : [hBOOL(hAPP(hAPP(c_member(_893519), _893521), _893523)), -(hBOOL(hAPP(hAPP(c_member(_893519), _893521), hAPP(hAPP(c_Set_Oinsert(_893519), _893525), _893523))))], (2712 ^ _776541) ^ [_816626, _816628, _816630, _816632, _816634, _816636] : [-(c_FunDef_Oin__rel(_816636, _816632, _816628) = c_FunDef_Oin__rel(_816634, _816630, _816626)), _816636 = _816634, _816632 = _816630, _816628 = _816626], (18276 ^ _776541) ^ [_1105182, _1105184, _1105186, _1105188] : [class_Rings_Olinordered__semiring__strict(_1105182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105182), _1105184), _1105186)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105182), _1105184), _1105188))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105182), c_Groups_Ozero__class_Ozero(_1105182)), _1105184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105182), _1105186), _1105188)))], (28571 ^ _776541) ^ [_1289187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1289187))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1289187)))], (41592 ^ _776541) ^ [_1594912, _1594914, _1594916, _1594918, _1594920] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594912, _1594912)), hAPP(hAPP(c_Product__Type_OPair(_1594912, _1594912), _1594914), _1594916)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594912, _1594912), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1594918)), _1594920))), 41596 ^ _776541 : [(41599 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594912, _1594912)), hAPP(hAPP(c_Product__Type_OPair(_1594912, _1594912), 41595 ^ [_1594912, _1594914, _1594916, _1594918, _1594920]), _1594916)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594912, _1594912), tc_HOL_Obool), _1594918), _1594920))))], (41597 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594912, _1594912)), hAPP(hAPP(c_Product__Type_OPair(_1594912, _1594912), _1594914), 41595 ^ [_1594912, _1594914, _1594916, _1594918, _1594920])), _1594920)))]]], (10841 ^ _776541) ^ [_963521, _963523, _963525, _963527] : [class_Orderings_Olinorder(_963521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963521), _963523), _963525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963521), _963525), _963527)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963521, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963521, _963523), _963525)), c_SetInterval_Oord__class_OatLeastAtMost(_963521, _963525, _963527)) = c_SetInterval_Oord__class_OatLeastAtMost(_963521, _963523, _963527))], (22819 ^ _776541) ^ [_1189913, _1189915, _1189917, _1189919] : [class_Rings_Olinordered__semidom(_1189913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189913), c_Groups_Oone__class_Oone(_1189913)), _1189915)), 22826 ^ _776541 : [(22833 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189917), _1189919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189913), hAPP(hAPP(c_Power_Opower__class_Opower(_1189913), _1189915), _1189917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189913), _1189915), _1189919))))], (22827 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189913), hAPP(hAPP(c_Power_Opower__class_Opower(_1189913), _1189915), _1189917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189913), _1189915), _1189919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189917), _1189919)))]]], (41688 ^ _776541) ^ [_1597440, _1597442, _1597444] : [c_Nitpick_Oless__frac(_1597440, _1597442, _1597444), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597440), c_Nitpick_Oplus__frac(_1597440, _1597442, c_Nitpick_Ouminus__frac(_1597440, _1597444)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34325 ^ _776541) ^ [_1415299, _1415301] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415299)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415301)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415301))), 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), _1415299)), c_Int_Onat)))))], (51473 ^ _776541) ^ [_1818256, _1818258] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818256), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1818258)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818258), _1818256)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818256), _1818258)))], (45022 ^ _776541) ^ [_1678273, _1678275] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1678273)), hAPP(c_Code__Numeral_Oof__nat, _1678275)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1678273), _1678275)))], (32093 ^ _776541) ^ [_1353158, _1353160, _1353162] : [class_Orderings_Olinorder(_1353158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353158), _1353160)), -(hBOOL(hAPP(hAPP(c_member(_1353158), _1353162), _1353160))), -(_1353160 = c_Orderings_Obot__class_Obot(tc_fun(_1353158, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1353158, c_Orderings_Oord__class_Omax(_1353158), hAPP(hAPP(c_Set_Oinsert(_1353158), _1353162), _1353160)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353158), _1353162), c_Big__Operators_Olattice_OSup__fin(_1353158, c_Orderings_Oord__class_Omax(_1353158), _1353160)))], (8585 ^ _776541) ^ [_924011, _924013, _924015] : [class_Lattices_Osemilattice__sup(_924011), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924011), _924013), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924011), _924013), _924015))))], (44862 ^ _776541) ^ [_1674052, _1674054] : [-(hAPP(hAPP(c_List_Ozip(_1674052, _1674052), _1674054), _1674054) = hAPP(hAPP(c_List_Omap(_1674052, tc_prod(_1674052, _1674052)), hAPP(hAPP(c_COMBS(_1674052, _1674052, tc_prod(_1674052, _1674052)), c_Product__Type_OPair(_1674052, _1674052)), c_COMBI(_1674052))), _1674054))], (44631 ^ _776541) ^ [_1668942, _1668944, _1668946, _1668948] : [hAPP(hAPP(c_List_Oappend(_1668942), _1668944), hAPP(hAPP(c_List_Olist_OCons(_1668942), _1668946), c_List_Olist_ONil(_1668942))) = _1668948, 44634 ^ _776541 : [(44639 ^ _776541) ^ [] : [-(c_List_Olast(_1668942, _1668948) = _1668946)], (44637 ^ _776541) ^ [] : [-(c_List_Obutlast(_1668942, _1668948) = _1668944)], (44635 ^ _776541) ^ [] : [_1668948 = c_List_Olist_ONil(_1668942)]]], (38251 ^ _776541) ^ [_1508993, _1508995] : [hBOOL(hAPP(hAPP(c_member(_1508993), 38252 ^ [_1508993, _1508995]), c_Wellfounded_Oacc(_1508993, _1508995))), -(c_Wellfounded_Owf(_1508993, _1508995))], (35616 ^ _776541) ^ [_1441263, _1441265, _1441267, _1441269, _1441271] : [hAPP(c_Product__Type_Ofst(_1441263, _1441265), hAPP(hAPP(c_Product__Type_OPair(_1441263, _1441265), _1441267), _1441269)) = _1441271, -(_1441267 = _1441271)], (2128 ^ _776541) ^ [_807414, _807416, _807418, _807420] : [-(c_Nat__Transfer_Otsub(_807420, _807416) = c_Nat__Transfer_Otsub(_807418, _807414)), _807420 = _807418, _807416 = _807414], (25093 ^ _776541) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17892 ^ _776541) ^ [_1098402, _1098404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1098402), hAPP(c_Nat_OSuc, _1098404))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1098402, hAPP(c_Nat_OSuc, _1098404)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1098404)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1098402, _1098404)))], (45473 ^ _776541) ^ [_1688444, _1688446, _1688448, _1688450] : [c_List_Olist__all2(_1688444, _1688446, _1688448, _1688450, c_List_Olist_ONil(_1688446)), -(_1688450 = c_List_Olist_ONil(_1688444))], (44405 ^ _776541) ^ [_1664565, _1664567, _1664569, _1664571, _1664573] : [c_Finite__Set_Ofun__left__comm__idem(_1664565, _1664567, _1664569), -(hAPP(hAPP(c_Finite__Set_Ofold(_1664565, _1664567, _1664569), _1664571), hAPP(c_List_Oset(_1664565), _1664573)) = hAPP(c_List_Ofoldl(_1664567, _1664565, hAPP(c_COMBC(_1664565, _1664567, _1664567), _1664569), _1664571), _1664573))], (28219 ^ _776541) ^ [_1283215, _1283217, _1283219] : [class_Int_Onumber__ring(_1283215), 28222 ^ _776541 : [(28229 ^ _776541) ^ [] : [c_Int_Oiszero(_1283215, hAPP(c_Int_Onumber__class_Onumber__of(_1283215), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283217), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1283219)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1283215), _1283217) = hAPP(c_Int_Onumber__class_Onumber__of(_1283215), _1283219))], (28223 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1283215), _1283217) = hAPP(c_Int_Onumber__class_Onumber__of(_1283215), _1283219), -(c_Int_Oiszero(_1283215, hAPP(c_Int_Onumber__class_Onumber__of(_1283215), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283217), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1283219)))))]]], (46257 ^ _776541) ^ [_1706895, _1706897, _1706899] : [-(c_List_Osublist(_1706895, _1706897, _1706899) = hAPP(hAPP(c_List_Omap(tc_prod(_1706895, tc_Nat_Onat), _1706895), c_Product__Type_Ofst(_1706895, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1706895, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1706895, 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(_1706895, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1706895, tc_Nat_Onat))), _1706899)), hAPP(hAPP(c_List_Ozip(_1706895, tc_Nat_Onat), _1706897), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706895)), _1706897))))))], (23878 ^ _776541) ^ [_1209058, _1209060, _1209062] : [class_Rings_Olinordered__semidom(_1209058), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209058), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209058), _1209060)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209058), _1209062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209060), _1209062)))], (19995 ^ _776541) ^ [_1137423, _1137425, _1137427, _1137429, _1137431] : [class_Fields_Ofield__inverse__zero(_1137423), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137423), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137423), _1137425), _1137427)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137423), _1137429), _1137431)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137423), _1137425), _1137429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137423), _1137427), _1137431)))], (28803 ^ _776541) ^ [_1292976] : [c_Int_OPls = c_Int_OBit0(_1292976), -(c_Int_OPls = _1292976)], (32270 ^ _776541) ^ [_1356763] : [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), _1356763))), 32273 ^ _776541 : [(32280 ^ _776541) ^ [] : [-(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), _1356763))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1356763)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1356763)), 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), _1356763)))))], (32274 ^ _776541) ^ [] : [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), _1356763)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1356763)) = 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), _1356763))))]]], (1724 ^ _776541) ^ [_800955, _800957] : [-(class_Nat_Osemiring__char__0(_800955)), _800957 = _800955, class_Nat_Osemiring__char__0(_800957)], (8829 ^ _776541) ^ [_928421, _928423, _928425, _928427, _928429] : [class_Groups_Oordered__ab__group__add(_928421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_928421), _928423), _928425) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_928421), _928427), _928429), 8836 ^ _776541 : [(8843 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928421), _928427), _928429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928421), _928423), _928425)))], (8837 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928421), _928423), _928425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928421), _928427), _928429)))]]], (44513 ^ _776541) ^ [_1666883, _1666885, _1666887] : [class_Orderings_Olinorder(_1666883), -(hAPP(c_List_Oset(_1666883), c_List_Olinorder__class_Oinsort__insert__key(_1666883, _1666883, c_COMBI(_1666883), _1666885, _1666887)) = hAPP(hAPP(c_Set_Oinsert(_1666883), _1666885), hAPP(c_List_Oset(_1666883), _1666887)))], (43090 ^ _776541) ^ [_1635133, _1635135, _1635137] : [-(hAPP(hAPP(c_List_Ozip(_1635133, _1635135), _1635137), c_List_Olist_ONil(_1635135)) = c_List_Olist_ONil(tc_prod(_1635133, _1635135)))], (26148 ^ _776541) ^ [_1249029, _1249031] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1249029)), hAPP(c_Int_Onat, _1249031)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249029), _1249031))], (46411 ^ _776541) ^ [_1709853] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1709853) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1709853))))], (3936 ^ _776541) ^ [_835792, _835794, _835796, _835798, _835800, _835802, _835804, _835806] : [-(c_New__DSequence_Oneg__decr__bind(_835806, _835802, _835798, _835794) = c_New__DSequence_Oneg__decr__bind(_835804, _835800, _835796, _835792)), _835806 = _835804, _835802 = _835800, _835798 = _835796, _835794 = _835792], (43412 ^ _776541) ^ [_1642051, _1642053, _1642055, _1642057, _1642059] : [-(hAPP(hAPP(c_List_Olist_OCons(_1642051), _1642053), _1642055) = hAPP(hAPP(c_List_Oappend(_1642051), _1642057), _1642059)), 43413 ^ _776541 : [(43420 ^ _776541) ^ [_1642234] : [hAPP(hAPP(c_List_Olist_OCons(_1642051), _1642053), _1642234) = _1642057, _1642055 = hAPP(hAPP(c_List_Oappend(_1642051), _1642234), _1642059)], (43414 ^ _776541) ^ [] : [_1642057 = c_List_Olist_ONil(_1642051), hAPP(hAPP(c_List_Olist_OCons(_1642051), _1642053), _1642055) = _1642059]]], (4294 ^ _776541) ^ [_841577, _841579, _841581, _841583] : [-(c_List_Oconcat(_841583, _841579) = c_List_Oconcat(_841581, _841577)), _841583 = _841581, _841579 = _841577], (13216 ^ _776541) ^ [_1010433] : [class_Lattices_Osemilattice__inf(_1010433), -(c_Finite__Set_Ofun__left__comm__idem(_1010433, _1010433, c_Lattices_Osemilattice__inf__class_Oinf(_1010433)))], (37222 ^ _776541) ^ [_1484965, _1484967, _1484969, _1484971, _1484973] : [c_Fun_Oinj__on(_1484965, _1484967, _1484969, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484965, tc_HOL_Obool)), _1484971), _1484973)), 37225 ^ _776541 : [(37232 ^ _776541) ^ [] : [_1484971 = _1484973, -(hAPP(c_Set_Oimage(_1484965, _1484967, _1484969), _1484971) = hAPP(c_Set_Oimage(_1484965, _1484967, _1484969), _1484973))], (37226 ^ _776541) ^ [] : [hAPP(c_Set_Oimage(_1484965, _1484967, _1484969), _1484971) = hAPP(c_Set_Oimage(_1484965, _1484967, _1484969), _1484973), -(_1484971 = _1484973)]]], (46526 ^ _776541) ^ [_1712134, _1712136] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1712134, _1712136)))], (34715 ^ _776541) ^ [_1423523, _1423525, _1423527, _1423529] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423523, _1423525, _1423527), hAPP(c_Nat_OSuc, _1423529)) = hAPP(hAPP(_1423527, _1423529), hAPP(c_Nat_Onat_Onat__rec(_1423523, _1423525, _1423527), _1423529)))], (3006 ^ _776541) ^ [_821169, _821171] : [_821171 = _821169, -(c_Nitpick_Odenom(_821171) = c_Nitpick_Odenom(_821169))], (34594 ^ _776541) ^ [_1420895, _1420897, _1420899, _1420901, _1420903, _1420905] : [hBOOL(hAPP(hAPP(_1420895, _1420897), _1420899)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420901, tc_fun(_1420903, tc_HOL_Obool))), _1420895), _1420905), _1420897), _1420899)))], (13758 ^ _776541) ^ [_1021666, _1021668, _1021670, _1021672] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1021666), 13761 ^ _776541 : [(13768 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021666), _1021670), _1021672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021666), _1021668), _1021670)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021666), _1021668), _1021672))))], (13762 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021666), _1021668), _1021670)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021666), _1021668), _1021672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021666), _1021670), _1021672)))]]], (13538 ^ _776541) ^ [_1017508, _1017510, _1017512, _1017514] : [class_Groups_Oab__semigroup__add(_1017508), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017508), _1017510), _1017512)), _1017514) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017508), _1017510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017508), _1017512), _1017514)))], (28593 ^ _776541) ^ [_1289510, _1289512] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289510), _1289512), hAPP(c_Int_Onumber__class_Onumber__of(_1289510), c_Int_OBit1(c_Int_OPls))) = _1289512), class_Fields_Ofield(_1289510), class_Int_Onumber__ring(_1289510)], (45664 ^ _776541) ^ [_1692439, _1692441] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1692439), tc_fun(_1692439, tc_HOL_Obool), c_List_Oset(_1692439)), hAPP(c_List_Oset(tc_List_Olist(_1692439)), c_Enum_Osublists(_1692439, _1692441))) = hAPP(c_Set_OPow(_1692439), hAPP(c_List_Oset(_1692439), _1692441)))], (4246 ^ _776541) ^ [_840875, _840877] : [_840877 = _840875, -(c_List_Odrop(_840877) = c_List_Odrop(_840875))], (8453 ^ _776541) ^ [_921712, _921714, _921716, _921718, _921720] : [class_Lattices_Osemilattice__sup(_921712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921712), _921714), _921716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921712), _921718), _921720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921712), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921712), _921714), _921718)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921712), _921716), _921720))))], (41383 ^ _776541) ^ [_1589096, _1589098, _1589100, _1589102, _1589104] : [c_Relation_Osingle__valued(_1589096, _1589098, hAPP(c_Relation_Oconverse(_1589098, _1589096), _1589100)), -(hAPP(c_Relation_OImage(_1589098, _1589096, _1589100), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589098, tc_HOL_Obool)), _1589102), _1589104)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589096, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1589098, _1589096, _1589100), _1589102)), hAPP(c_Relation_OImage(_1589098, _1589096, _1589100), _1589104)))], (16188 ^ _776541) ^ [_1069097, _1069099] : [class_Groups_Omonoid__add(_1069097), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069097), _1069099), c_Groups_Ozero__class_Ozero(_1069097)) = _1069099)], (51229 ^ _776541) ^ [_1813861, _1813863, _1813865, _1813867] : [class_Rings_Odvd(_1813861), _1813863 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813861), _1813865), _1813867), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813861), _1813865), _1813863)))], (49434 ^ _776541) ^ [_1776005, _1776007, _1776009, _1776011, _1776013] : [c_Predicate_Otransp(_1776005, _1776007), hBOOL(hAPP(hAPP(_1776007, _1776009), _1776011)), hBOOL(hAPP(hAPP(_1776007, _1776011), _1776013)), -(hBOOL(hAPP(hAPP(_1776007, _1776009), _1776013)))], (44112 ^ _776541) ^ [_1658908, _1658910, _1658912] : [_1658908 = c_List_Olist_ONil(_1658910), -(hAPP(c_List_Ohd(_1658910), hAPP(hAPP(c_List_Oappend(_1658910), _1658908), _1658912)) = hAPP(c_List_Ohd(_1658910), _1658912))], (29851 ^ _776541) ^ [_1311743, _1311745, _1311747, _1311749] : [29853 ^ _776541 : [(29858 ^ _776541) ^ [] : [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(_1311747, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29852 ^ [_1311743, _1311745, _1311747, _1311749]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1311747, 29852 ^ [_1311743, _1311745, _1311747, _1311749])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29856 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29852 ^ [_1311743, _1311745, _1311747, _1311749]), _1311745)))], (29854 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1311743), 29852 ^ [_1311743, _1311745, _1311747, _1311749])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1311743), _1311745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1311747, _1311743)), _1311749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311749), hAPP(_1311747, _1311745))), 29872 ^ _776541 : [(29877 ^ _776541) ^ [] : [-(hAPP(_1311747, 29871 ^ [_1311743, _1311745, _1311747, _1311749]) = _1311749)], (29875 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29871 ^ [_1311743, _1311745, _1311747, _1311749]), _1311745)))], (29873 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1311743), 29871 ^ [_1311743, _1311745, _1311747, _1311749])))]]], (8002 ^ _776541) ^ [_912122, _912124, _912126, _912128] : [hBOOL(hAPP(hAPP(c_member(_912122), _912124), _912126)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912122, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912122), _912124), _912128)), _912126) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912122, tc_HOL_Obool)), _912128), _912126))], (41737 ^ _776541) ^ [_1598490, _1598492, _1598494] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598490)), _1598492) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598490)), _1598494)), _1598492 = _1598494], (46389 ^ _776541) ^ [_1709422, _1709424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709422), _1709424)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1709422, _1709424)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1709424), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10693 ^ _776541) ^ [_960614, _960616] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960614, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960614, tc_HOL_Obool)), _960616)), _960616) = c_Orderings_Otop__class_Otop(tc_fun(_960614, tc_HOL_Obool)))], (32572 ^ _776541) ^ [_1365768, _1365770, _1365772, _1365774] : [hBOOL(hAPP(hAPP(c_member(_1365768), _1365774), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365768, tc_HOL_Obool)), _1365770), _1365772))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365768, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1365768, tc_fun(_1365768, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365768)), _1365770)), hAPP(hAPP(c_COMBC(_1365768, tc_fun(_1365768, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365768)), _1365772)), _1365774)))], (7664 ^ _776541) ^ [_904167, _904169, _904171, _904173] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904167, tc_HOL_Obool)), _904169), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904167, tc_HOL_Obool)), _904171), _904173)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904167, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904167, tc_HOL_Obool)), _904169), _904171)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904167, tc_HOL_Obool)), _904169), _904173)))], (23730 ^ _776541) ^ [_1206318] : [23731 ^ _776541 : [(23732 ^ _776541) ^ [_1206375] : [hBOOL(hAPP(_1206318, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206375)))]], 23734 ^ _776541 : [(23737 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1206318, 23733 ^ [_1206318])))], (23735 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23733 ^ [_1206318])))]]], (50534 ^ _776541) ^ [_1797973, _1797975, _1797977, _1797979] : [c_Fun_Obij__betw(_1797973, _1797975, _1797977, _1797979, c_Orderings_Obot__class_Obot(tc_fun(_1797975, tc_HOL_Obool))), -(_1797979 = c_Orderings_Obot__class_Obot(tc_fun(_1797973, tc_HOL_Obool)))], (34267 ^ _776541) ^ [_1414095, _1414097, _1414099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414095), _1414097)), -(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)), _1414095)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414099), _1414097)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1414099), _1414095)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1414097), _1414095)))], (40425 ^ _776541) ^ [_1564946, _1564948, _1564950] : [40427 ^ _776541 : [(40430 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1564946), 40426 ^ [_1564946, _1564948, _1564950]), c_Wellfounded_Oacc(_1564946, _1564950)))], (40428 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564946, _1564946)), hAPP(hAPP(c_Product__Type_OPair(_1564946, _1564946), 40426 ^ [_1564946, _1564948, _1564950]), _1564948)), _1564950)))]], -(hBOOL(hAPP(hAPP(c_member(_1564946), _1564948), c_Wellfounded_Oacc(_1564946, _1564950))))], (10773 ^ _776541) ^ [_962098, _962100, _962102, _962104, _962106] : [class_Orderings_Olinorder(_962098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962098, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962098, _962100), _962102)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962098, _962104), _962106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962098), _962102), _962100))), 10784 ^ _776541 : [(10787 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962098), _962102), _962106)))], (10785 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962098), _962104), _962100)))]]], (24722 ^ _776541) ^ [_1223803, _1223805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1223803), _1223805)), -(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)), _1223803)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223805))))], (48203 ^ _776541) ^ [] : [-(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))))], (2420 ^ _776541) ^ [_812032, _812034, _812036, _812038, _812040, _812042, _812044, _812046] : [-(c_Nitpick_Opair__box_OPairBox(_812046, _812042, _812038, _812034) = c_Nitpick_Opair__box_OPairBox(_812044, _812040, _812036, _812032)), _812046 = _812044, _812042 = _812040, _812038 = _812036, _812034 = _812032], (24930 ^ _776541) ^ [_1227963, _1227965] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227963), _1227965)), _1227963)))], (19567 ^ _776541) ^ [_1130075, _1130077, _1130079, _1130081] : [class_Rings_Odivision__ring(_1130075), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130075), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130075), _1130077), _1130079)), _1130081) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130075), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130075), _1130077), _1130081)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130075), _1130079), _1130081)))], (23815 ^ _776541) ^ [_1207958, _1207960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1207958), _1207960)), -(_1207960 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1207958), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23818 ^ [_1207958, _1207960])))], (26256 ^ _776541) ^ [_1250797] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1250797))), -(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), _1250797)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1214 ^ _776541) ^ [_794580, _794582] : [-(class_Rings_Oordered__ring(_794580)), _794582 = _794580, class_Rings_Oordered__ring(_794582)], (51867 ^ _776541) ^ [_1824740, _1824742] : [class_Lattices_Obounded__lattice(_1824740), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1824742, _1824740)))], (11970 ^ _776541) ^ [_986692, _986694, _986696, _986698, _986700] : [11972 ^ _776541 : [(11975 ^ _776541) ^ [] : [hBOOL(hAPP(_986700, 11971 ^ [_986692, _986694, _986696, _986698, _986700]))], (11973 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_986692), 11971 ^ [_986692, _986694, _986696, _986698, _986700]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986694, tc_fun(_986692, tc_HOL_Obool)), _986696), _986698))))]], 11976 ^ _776541 : [(11977 ^ _776541) ^ [_986914] : [hBOOL(hAPP(hAPP(c_member(_986694), _986914), _986696)), 11980 ^ _776541 : [(11981 ^ _776541) ^ [_987011] : [hBOOL(hAPP(hAPP(c_member(_986692), _987011), hAPP(_986698, _986914))), -(hBOOL(hAPP(_986700, _987011)))]]]]], (3534 ^ _776541) ^ [_829377, _829379] : [_829379 = _829377, -(c_SetInterval_Oord__class_OlessThan(_829379) = c_SetInterval_Oord__class_OlessThan(_829377))], (34419 ^ _776541) ^ [_1417116, _1417118, _1417120, _1417122, _1417124] : [-(c_Nat_Onat_Onat__case(_1417116, _1417118, _1417120, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417122)), _1417124)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1417116), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417122))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417116, _1417116), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1417116, tc_fun(_1417116, _1417116)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417116, tc_fun(_1417116, _1417116)), tc_Int_Oint), c_If(_1417116)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1417116, _1417118, _1417120, _1417124))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417116, tc_Int_Oint), _1417120), 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)), _1417124)))))], (49694 ^ _776541) ^ [_1781053, _1781055] : [c_Relation_Osym(_1781053, _1781055), -(c_Relation_Osym(_1781053, hAPP(c_Relation_Oconverse(_1781053, _1781053), _1781055)))], (14592 ^ _776541) ^ [_1039586] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039586), _1039586)))], (51919 ^ _776541) ^ [_1825422, _1825424] : [class_Orderings_Oorder(_1825422), -(class_Orderings_Oorder(tc_fun(_1825424, _1825422)))], (28951 ^ _776541) ^ [_1295545, _1295547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295545)), c_Int_OBit1(_1295547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295545), _1295547)))], (32888 ^ _776541) ^ [_1375941, _1375943, _1375945, _1375947, _1375949] : [hBOOL(hAPP(hAPP(c_member(_1375941), _1375943), _1375945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375947, tc_HOL_Obool)), hAPP(_1375949, _1375943)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375941, tc_fun(_1375947, tc_HOL_Obool)), _1375945), _1375949))))], (49570 ^ _776541) ^ [_1778278, _1778280] : [-(c_Relation_Oantisym(_1778278, c_Relation_OId__on(_1778278, _1778280)))], (16334 ^ _776541) ^ [_1071286, _1071288] : [class_Groups_Ogroup__add(_1071286), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071286), _1071288), _1071288) = c_Groups_Ozero__class_Ozero(_1071286))], (29812 ^ _776541) ^ [_1311060, _1311062, _1311064] : [29814 ^ _776541 : [(29819 ^ _776541) ^ [] : [hBOOL(hAPP(_1311062, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 29813 ^ [_1311060, _1311062, _1311064]), _1311060)))], (29817 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1311062, 29813 ^ [_1311060, _1311062, _1311064])))], (29815 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29813 ^ [_1311060, _1311062, _1311064]), _1311060)))]], hBOOL(hAPP(_1311062, _1311064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1311064), _1311060)), -(hBOOL(hAPP(_1311062, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25385 ^ _776541) ^ [_1235715, _1235717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235715)), 25388 ^ _776541 : [(25395 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235717), _1235715))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235717), _1235715) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1235717), _1235715)), _1235715)))], (25389 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235717), _1235715)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235717), _1235715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16432 ^ _776541) ^ [_1072739] : [-(_1072739 = 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)), _1072739)))], (28093 ^ _776541) ^ [_1281200] : [-(c_Int_Osucc(c_Int_Opred(_1281200)) = _1281200)], (16284 ^ _776541) ^ [_1070507, _1070509] : [class_Rings_Omult__zero(_1070507), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070507), c_Groups_Ozero__class_Ozero(_1070507)), _1070509) = c_Groups_Ozero__class_Ozero(_1070507))], (22479 ^ _776541) ^ [_1183815, _1183817, _1183819] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183815), _1183817)), _1183819) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183817), _1183819)))], (25858 ^ _776541) ^ [_1244253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244253), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1244253 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 25861 ^ [_1244253]))))], (34672 ^ _776541) ^ [_1422443, _1422445, _1422447, _1422449, _1422451] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1422443, _1422445, _1422447), _1422449), _1422451)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1422443, _1422445)), hAPP(hAPP(c_Product__Type_OPair(_1422443, _1422445), _1422449), _1422451)), _1422447)))], (18160 ^ _776541) ^ [_1102987] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102987) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1102987))], (10477 ^ _776541) ^ [_956522, _956524, _956526] : [class_Groups_Oordered__ab__group__add(_956522), 10480 ^ _776541 : [(10487 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956522), _956526), hAPP(c_Groups_Ouminus__class_Ouminus(_956522), _956524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956522), _956524), hAPP(c_Groups_Ouminus__class_Ouminus(_956522), _956526))))], (10481 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956522), _956524), hAPP(c_Groups_Ouminus__class_Ouminus(_956522), _956526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956522), _956526), hAPP(c_Groups_Ouminus__class_Ouminus(_956522), _956524))))]]], (7548 ^ _776541) ^ [_901032, _901034, _901036, _901038] : [hBOOL(hAPP(_901032, _901034)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901036, tc_HOL_Obool)), _901032), _901038), _901034)))], (39455 ^ _776541) ^ [_1541079, _1541081, _1541083, _1541085, _1541087, _1541089, _1541091] : [-(hAPP(c_Product__Type_Ofst(_1541079, _1541081), hAPP(c_Product__Type_Omap__pair(_1541083, _1541079, _1541085, _1541081, _1541087, _1541089), _1541091)) = hAPP(_1541087, hAPP(c_Product__Type_Ofst(_1541083, _1541085), _1541091)))], (44260 ^ _776541) ^ [_1661598, _1661600, _1661602, _1661604] : [-(hAPP(c_List_Ofoldl(_1661598, _1661600, _1661602, _1661604), c_List_Olist_ONil(_1661600)) = _1661604)], (26949 ^ _776541) ^ [_1261935, _1261937, _1261939] : [class_Rings_Oring__1(_1261935), -(hAPP(c_Int_Oring__1__class_Oof__int(_1261935), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261937), _1261939)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1261935), hAPP(c_Int_Oring__1__class_Oof__int(_1261935), _1261937)), hAPP(c_Int_Oring__1__class_Oof__int(_1261935), _1261939)))], (52403 ^ _776541) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (32536 ^ _776541) ^ [_1364698, _1364700, _1364702, _1364704, _1364706] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364698, tc_fun(_1364700, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364698, tc_HOL_Obool)), _1364702), _1364704)), _1364706) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364700, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364698, tc_fun(_1364700, tc_HOL_Obool)), _1364702), _1364706)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364698, tc_fun(_1364700, tc_HOL_Obool)), _1364704), _1364706)))], (6386 ^ _776541) ^ [_879613] : [c_Orderings_Otop__class_Otop(tc_fun(_879613, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_879613, tc_HOL_Obool))], (3882 ^ _776541) ^ [_834863, _834865] : [_834865 = _834863, -(c_Enum_Oenum__class_Oenum__all(_834865) = c_Enum_Oenum__class_Oenum__all(_834863))], (11750 ^ _776541) ^ [_982169, _982171, _982173, _982175, _982177, _982179, _982181, _982183] : [c_Finite__Set_Ofolding__image__simple(_982169, _982171, _982173, _982175, _982177, _982179), hBOOL(hAPP(c_Finite__Set_Ofinite(_982171), _982181)), hBOOL(hAPP(hAPP(c_member(_982171), _982183), _982181)), -(hAPP(_982179, _982181) = hAPP(hAPP(_982173, hAPP(_982177, _982183)), hAPP(_982179, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982171, tc_HOL_Obool)), _982181), hAPP(hAPP(c_Set_Oinsert(_982171), _982183), c_Orderings_Obot__class_Obot(tc_fun(_982171, tc_HOL_Obool)))))))], (43266 ^ _776541) ^ [_1638444, _1638446] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1638444), tc_List_Olist(_1638444), c_List_Olistrel(_1638444, _1638446)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1638444)), c_List_Olist_ONil(_1638444)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1638444), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1638444)), c_List_Olist_ONil(_1638444)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1638444), tc_HOL_Obool))))], (1634 ^ _776541) ^ [_799830, _799832] : [-(class_Groups_Ocomm__monoid__mult(_799830)), _799832 = _799830, class_Groups_Ocomm__monoid__mult(_799832)], (29801 ^ _776541) ^ [_1310863, _1310865, _1310867] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1310863, _1310865) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1310867, _1310865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1310867), _1310863)), -(_1310863 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1310865), 29808 ^ [_1310863, _1310865, _1310867])))], (23065 ^ _776541) ^ [_1194445, _1194447] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1194445, _1194447))))], (43525 ^ _776541) ^ [_1644577, _1644579, _1644581, _1644583, _1644585] : [-(hAPP(hAPP(c_List_Oappend(_1644577), _1644579), _1644581) = hAPP(hAPP(c_List_Oappend(_1644577), _1644583), _1644585)), 43526 ^ _776541 : [(43533 ^ _776541) ^ [_1644801] : [hAPP(hAPP(c_List_Oappend(_1644577), _1644579), _1644801) = _1644583, _1644581 = hAPP(hAPP(c_List_Oappend(_1644577), _1644801), _1644585)], (43527 ^ _776541) ^ [_1644689] : [_1644579 = hAPP(hAPP(c_List_Oappend(_1644577), _1644583), _1644689), hAPP(hAPP(c_List_Oappend(_1644577), _1644689), _1644581) = _1644585]]], (14913 ^ _776541) ^ [_1045545, _1045547, _1045549, _1045551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045545), _1045547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045549), _1045551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045545), _1045549)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045547), _1045551))))], (14580 ^ _776541) ^ [_1039457, _1039459] : [_1039457 = _1039459, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039457), _1039459)))], (37240 ^ _776541) ^ [_1485287, _1485289, _1485291, _1485293, _1485295] : [c_Fun_Oinj__on(_1485287, _1485289, _1485291, _1485293), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1485287, tc_HOL_Obool)), _1485295), _1485293)), -(c_Fun_Oinj__on(_1485287, _1485289, _1485291, _1485295))], (3748 ^ _776541) ^ [_832744, _832746, _832748, _832750, _832752, _832754, _832756, _832758] : [-(c_List_Omaps(_832758, _832754, _832750, _832746) = c_List_Omaps(_832756, _832752, _832748, _832744)), _832758 = _832756, _832754 = _832752, _832750 = _832748, _832746 = _832744], (26124 ^ _776541) ^ [_1248620, _1248622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248620)), 26127 ^ _776541 : [(26134 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248622), _1248620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1248622)), hAPP(c_Int_Onat, _1248620))))], (26128 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1248622)), hAPP(c_Int_Onat, _1248620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248622), _1248620)))]]], (36380 ^ _776541) ^ [_1463799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1463799)), -(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))), _1463799)), c_FunDef_Omax__weak)))], (14302 ^ _776541) ^ [_1034240, _1034242, _1034244, _1034246, _1034248] : [class_Rings_Ocomm__semiring__1(_1034240), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034240), _1034242), _1034244)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034240), _1034246), _1034248)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034240), _1034246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034240), _1034242), _1034244)), _1034248)))], (42329 ^ _776541) ^ [_1616628, _1616630, _1616632, _1616634] : [hBOOL(hAPP(hAPP(c_member(_1616628), _1616630), hAPP(c_List_Oset(_1616628), hAPP(hAPP(c_List_Olist_OCons(_1616628), _1616632), _1616634)))), -(_1616630 = _1616632), -(hBOOL(hAPP(hAPP(c_member(_1616628), _1616630), hAPP(c_List_Oset(_1616628), _1616634))))], (12077 ^ _776541) ^ [_988781, _988783, _988785] : [class_Lattices_Olattice(_988781), hBOOL(hAPP(c_Finite__Set_Ofinite(_988781), _988783)), hBOOL(hAPP(hAPP(c_member(_988781), _988785), _988783)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_988781), _988785), c_Big__Operators_Olattice__class_OSup__fin(_988781, _988783)) = _988785)], (35622 ^ _776541) ^ [_1441376, _1441378, _1441380, _1441382] : [-(hAPP(c_Product__Type_Ofst(_1441376, _1441378), hAPP(hAPP(c_Product__Type_OPair(_1441376, _1441378), _1441380), _1441382)) = _1441380)], (25913 ^ _776541) ^ [_1245242, _1245244] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245242, _1245244)) = _1245244), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1245242), _1245244) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245242, _1245244)))], (41274 ^ _776541) ^ [_1586384, _1586386, _1586388] : [c_Relation_Ototal__on(_1586384, _1586386, hAPP(c_Relation_Oconverse(_1586384, _1586384), _1586388)), -(c_Relation_Ototal__on(_1586384, _1586386, _1586388))], (42279 ^ _776541) ^ [_1615143, _1615145, _1615147, _1615149] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615143), tc_List_Olist(_1615143))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615143), tc_List_Olist(_1615143)), _1615145), _1615147)), c_List_Olexord(_1615143, _1615149)))), 42280 ^ _776541 : [(42287 ^ _776541) ^ [_1615450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1615450), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615143)), _1615145)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615143)), _1615147)))), hAPP(hAPP(c_List_Otake(_1615143), _1615450), _1615145) = hAPP(hAPP(c_List_Otake(_1615143), _1615450), _1615147), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615143, _1615143)), hAPP(hAPP(c_Product__Type_OPair(_1615143, _1615143), hAPP(hAPP(c_List_Onth(_1615143), _1615145), _1615450)), hAPP(hAPP(c_List_Onth(_1615143), _1615147), _1615450))), _1615149))], (42281 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615143)), _1615145)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615143)), _1615147))), hAPP(hAPP(c_List_Otake(_1615143), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615143)), _1615145)), _1615147) = _1615145]]], (2688 ^ _776541) ^ [_816256, _816258, _816260, _816262] : [-(c_Divides_Odivmod__nat__rel(_816262, _816258) = c_Divides_Odivmod__nat__rel(_816260, _816256)), _816262 = _816260, _816258 = _816256], (48644 ^ _776541) ^ [_1757218, _1757220, _1757222, _1757224, _1757226] : [c_List_Oreplicate(_1757218, _1757220, _1757222) = c_List_Oreplicate(_1757218, _1757224, _1757226), 48647 ^ _776541 : [(48650 ^ _776541) ^ [] : [-(_1757220 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1757222 = _1757226)], (48648 ^ _776541) ^ [] : [-(_1757220 = _1757224)]]], (49052 ^ _776541) ^ [_1765994, _1765996] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765994, _1765996), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1765994)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46188 ^ _776541) ^ [_1704466, _1704468] : [46190 ^ _776541 : [(46193 ^ _776541) ^ [] : [46189 ^ [_1704466, _1704468] = c_List_Olist_ONil(_1704466)], (46191 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704466)), 46189 ^ [_1704466, _1704468]), hAPP(c_List_Oset(tc_List_Olist(_1704466)), _1704468))))]], -(c_List_Otranspose(_1704466, _1704468) = c_List_Olist_ONil(tc_List_Olist(_1704466)))], (39179 ^ _776541) ^ [_1532640, _1532642, _1532644, _1532646, _1532648, _1532650] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532640, _1532642)), hAPP(hAPP(c_Product__Type_OPair(_1532640, _1532642), _1532644), _1532646)), hAPP(hAPP(c_Product__Type_OSigma(_1532640, _1532642), _1532648), _1532650))), -(hBOOL(hAPP(hAPP(c_member(_1532642), _1532646), hAPP(_1532650, _1532644))))], (39095 ^ _776541) ^ [_1529745, _1529747, _1529749] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1529745, _1529747), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529745, _1529747), _1529749), hAPP(c_COMBK(tc_fun(_1529747, tc_HOL_Obool), _1529745), c_Orderings_Otop__class_Otop(tc_fun(_1529747, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1529745, _1529747), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529745, tc_HOL_Obool)), _1529749)), hAPP(c_COMBK(tc_fun(_1529747, tc_HOL_Obool), _1529745), c_Orderings_Otop__class_Otop(tc_fun(_1529747, tc_HOL_Obool)))))], (43797 ^ _776541) ^ [_1650847, _1650849, _1650851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1650847), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650849)), _1650851))), -(hAPP(hAPP(c_List_Otake(_1650849), hAPP(c_Nat_OSuc, _1650847)), _1650851) = hAPP(hAPP(c_List_Oappend(_1650849), hAPP(hAPP(c_List_Otake(_1650849), _1650847), _1650851)), hAPP(hAPP(c_List_Olist_OCons(_1650849), hAPP(hAPP(c_List_Onth(_1650849), _1650851), _1650847)), c_List_Olist_ONil(_1650849))))], (36545 ^ _776541) ^ [_1468580] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1468580)) = _1468580)], (52141 ^ _776541) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (36659 ^ _776541) ^ [_1471593, _1471595] : [-(c_Relation_OId__on(_1471593, _1471595) = hAPP(c_Product__Type_Oprod_Oprod__case(_1471593, _1471593, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1471593, tc_HOL_Obool, tc_fun(_1471593, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471593, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1471593, tc_HOL_Obool)), _1471593), c_COMBC(_1471593, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471593, tc_HOL_Obool), tc_fun(_1471593, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1471593), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1471593), c_fconj)), c_fequal))), _1471595)))], (49096 ^ _776541) ^ [_1766740, _1766742, _1766744] : [49098 ^ _776541 : [(49101 ^ _776541) ^ [] : [hBOOL(hAPP(_1766740, 49097 ^ [_1766740, _1766742, _1766744]))], (49099 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49097 ^ [_1766740, _1766742, _1766744]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1766742, _1766744))))]], -(c_List_Oall__interval__int(_1766740, _1766742, _1766744))], (11278 ^ _776541) ^ [_972500, _972502] : [class_Groups_Oordered__ab__group__add(_972500), -(hAPP(c_Set_Oimage(_972500, _972500, c_Groups_Ouminus__class_Ouminus(_972500)), hAPP(c_SetInterval_Oord__class_OlessThan(_972500), _972502)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_972500), hAPP(c_Groups_Ouminus__class_Ouminus(_972500), _972502)))], (26072 ^ _776541) ^ [_1247818] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1247818))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1247818)) = _1247818)], (25540 ^ _776541) ^ [_1238591, _1238593] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238591) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238593), 25543 ^ _776541 : [(25550 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238591)))), 25553 ^ _776541 : [(25560 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238593)))), -(_1238591 = _1238593)], (25554 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238593))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238591) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (25544 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238591))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238593)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (40883 ^ _776541) ^ [_1576970, _1576972, _1576974, _1576976, _1576978] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576970, _1576970)), hAPP(hAPP(c_Product__Type_OPair(_1576970, _1576970), _1576972), _1576974)), _1576976)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576970, _1576970)), hAPP(hAPP(c_Product__Type_OPair(_1576970, _1576970), _1576974), _1576978)), c_Transitive__Closure_Ortrancl(_1576970, _1576976))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576970, _1576970)), hAPP(hAPP(c_Product__Type_OPair(_1576970, _1576970), _1576972), _1576978)), c_Transitive__Closure_Otrancl(_1576970, _1576976))))], (32392 ^ _776541) ^ [_1359361, _1359363, _1359365, _1359367, _1359369, _1359371] : [hBOOL(hAPP(hAPP(c_member(_1359361), _1359363), _1359365)), hBOOL(hAPP(hAPP(_1359367, _1359363), _1359369)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359361, tc_fun(_1359371, tc_HOL_Obool)), _1359365), _1359367), _1359369)))], (36547 ^ _776541) ^ [_1468609, _1468611] : [-(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), _1468609), _1468611)), 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), _1468611), _1468609)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (39473 ^ _776541) ^ [_1541602, _1541604, _1541606, _1541608, _1541610, _1541612, _1541614, _1541616, _1541618, _1541620] : [hAPP(c_Set_Oimage(_1541602, _1541604, _1541606), _1541608) = _1541610, hAPP(c_Set_Oimage(_1541612, _1541614, _1541616), _1541618) = _1541620, -(hAPP(c_Set_Oimage(tc_prod(_1541602, _1541612), tc_prod(_1541604, _1541614), c_Product__Type_Omap__pair(_1541602, _1541604, _1541612, _1541614, _1541606, _1541616)), hAPP(hAPP(c_Product__Type_OSigma(_1541602, _1541612), _1541608), hAPP(c_COMBK(tc_fun(_1541612, tc_HOL_Obool), _1541602), _1541618))) = hAPP(hAPP(c_Product__Type_OSigma(_1541604, _1541614), _1541610), hAPP(c_COMBK(tc_fun(_1541614, tc_HOL_Obool), _1541604), _1541620)))], (16578 ^ _776541) ^ [_1074810, _1074812, _1074814] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074810), _1074812) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074810), _1074814), -(_1074810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1074812 = _1074814)], (45096 ^ _776541) ^ [_1679638, _1679640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1679638), _1679640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1679638)), hAPP(c_Code__Numeral_Oof__nat, _1679640))))], (9570 ^ _776541) ^ [_940684, _940686, _940688] : [class_Orderings_Olinorder(_940684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940684), _940686), _940688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940684), _940688), _940686))], (27287 ^ _776541) ^ [_1267472, _1267474, _1267476] : [class_Rings_Olinordered__idom(_1267472), -(hAPP(c_Groups_Oabs__class_Oabs(_1267472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267472), _1267474), _1267476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267472), hAPP(c_Groups_Oabs__class_Oabs(_1267472), _1267474)), hAPP(c_Groups_Oabs__class_Oabs(_1267472), _1267476)))], (41720 ^ _776541) ^ [_1598020, _1598022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41721 ^ [_1598020, _1598022]), hAPP(_1598020, 41721 ^ [_1598020, _1598022]))), -(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)), _1598020)), _1598022)))))], (14428 ^ _776541) ^ [_1037062, _1037064, _1037066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037062), _1037064)), 14431 ^ _776541 : [(14438 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037066), _1037062)), _1037064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037066), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037064), _1037062))))], (14432 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037066), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037064), _1037062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037066), _1037062)), _1037064)))]]], (22907 ^ _776541) ^ [_1191628, _1191630, _1191632, _1191634] : [class_Rings_Olinordered__semidom(_1191628), hAPP(hAPP(c_Power_Opower__class_Opower(_1191628), _1191630), _1191632) = hAPP(hAPP(c_Power_Opower__class_Opower(_1191628), _1191634), _1191632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191628), c_Groups_Ozero__class_Ozero(_1191628)), _1191630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191628), c_Groups_Ozero__class_Ozero(_1191628)), _1191634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1191632)), -(_1191630 = _1191634)], (47084 ^ _776541) ^ [_1722911, _1722913] : [class_Groups_Ocomm__monoid__add(_1722911), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722911), hAPP(c_List_Orev(_1722911), _1722913)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1722911), _1722913))], (5697 ^ _776541) ^ [_866399, _866401, _866403] : [_866401 = _866403, -(hAPP(c_Hoare__Mirabelle_ORep__triple(_866399), _866401) = hAPP(c_Hoare__Mirabelle_ORep__triple(_866399), _866403))], (23089 ^ _776541) ^ [_1194844, _1194846, _1194848, _1194850, _1194852, _1194854] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194844), _1194846)), _1194848) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194850), _1194852)), _1194854), 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), _1194850), _1194852)), _1194854)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194848), _1194844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194850), _1194844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194852), _1194846)))], (11612 ^ _776541) ^ [_979656, _979658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979656, _979658)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_979656, _979658), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979658), c_Orderings_Otop__class_Otop(tc_fun(_979658, tc_HOL_Obool)))))], (43878 ^ _776541) ^ [_1653237, _1653239, _1653241] : [hBOOL(hAPP(c_List_Odistinct(_1653237), _1653239)), -(hBOOL(hAPP(c_List_Odistinct(_1653237), hAPP(hAPP(c_List_Odrop(_1653237), _1653241), _1653239))))], (44417 ^ _776541) ^ [_1664825, _1664827] : [class_Complete__Lattice_Ocomplete__lattice(_1664825), -(c_Complete__Lattice_OInf__class_OInf(_1664825, hAPP(c_List_Oset(_1664825), _1664827)) = hAPP(c_List_Ofoldl(_1664825, _1664825, c_Lattices_Osemilattice__inf__class_Oinf(_1664825), c_Orderings_Otop__class_Otop(_1664825)), _1664827))], (28243 ^ _776541) ^ [_1283668, _1283670] : [class_Int_Onumber__ring(_1283668), 28246 ^ _776541 : [(28253 ^ _776541) ^ [] : [c_Int_Oiszero(_1283668, hAPP(c_Int_Onumber__class_Onumber__of(_1283668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283670), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1283668), _1283670) = c_Groups_Oone__class_Oone(_1283668))], (28247 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1283668), _1283670) = c_Groups_Oone__class_Oone(_1283668), -(c_Int_Oiszero(_1283668, hAPP(c_Int_Onumber__class_Onumber__of(_1283668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283670), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (41017 ^ _776541) ^ [_1580101] : [-(c_Relation_OId(_1580101) = hAPP(c_Set_OCollect(tc_prod(_1580101, _1580101)), hAPP(hAPP(c_COMBB(tc_fun(_1580101, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1580101, _1580101)), c_HOL_OEx(_1580101)), hAPP(hAPP(c_COMBC(tc_prod(_1580101, _1580101), tc_fun(_1580101, tc_prod(_1580101, _1580101)), tc_fun(_1580101, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1580101, _1580101), tc_HOL_Obool), tc_fun(tc_fun(_1580101, tc_prod(_1580101, _1580101)), tc_fun(_1580101, tc_HOL_Obool)), tc_prod(_1580101, _1580101)), c_COMBB(tc_prod(_1580101, _1580101), tc_HOL_Obool, _1580101)), c_fequal)), hAPP(hAPP(c_COMBS(_1580101, _1580101, tc_prod(_1580101, _1580101)), c_Product__Type_OPair(_1580101, _1580101)), c_COMBI(_1580101))))))], (40401 ^ _776541) ^ [_1564223, _1564225, _1564227, _1564229] : [-(c_Hilbert__Choice_OEps(tc_prod(_1564223, _1564225), hAPP(c_Product__Type_Oprod_Oprod__case(_1564223, _1564225, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1564223, tc_fun(_1564225, tc_HOL_Obool), tc_fun(_1564225, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1564225, tc_HOL_Obool), tc_fun(_1564225, tc_HOL_Obool)), _1564223), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564225)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1564223), c_fconj), hAPP(c_fequal, _1564227)))), hAPP(c_fequal, _1564229)))) = hAPP(hAPP(c_Product__Type_OPair(_1564223, _1564225), _1564227), _1564229))], (36604 ^ _776541) ^ [_1470165] : [-(hAPP(c_Relation_OField(_1470165), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1470165, _1470165), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1470165, tc_HOL_Obool)))], (25401 ^ _776541) ^ [_1235987, _1235989, _1235991] : [hBOOL(hAPP(_1235987, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235989), _1235991))), 25404 ^ _776541 : [(25411 ^ _776541) ^ [] : [-(_1235991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25414 ^ _776541 : [(25415 ^ _776541) ^ [_1236239, _1236241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1236239), _1235991)), _1235989 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235991), _1236241)), _1236239), -(hBOOL(hAPP(_1235987, _1236241)))]]], (25405 ^ _776541) ^ [] : [_1235991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1235987, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (29203 ^ _776541) ^ [_1299933] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1299933)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1299933)))], (37820 ^ _776541) ^ [_1497486, _1497488] : [-(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)), _1497486), _1497488))], (38562 ^ _776541) ^ [_1516254, _1516256, _1516258] : [-(c_HOL_OThe(tc_prod(_1516254, _1516256), hAPP(c_Product__Type_Oprod_Oprod__case(_1516254, _1516256, tc_HOL_Obool), _1516258)) = c_HOL_OThe(tc_prod(_1516254, _1516256), hAPP(hAPP(c_COMBS(tc_prod(_1516254, _1516256), _1516256, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1516254, tc_fun(_1516256, tc_HOL_Obool), tc_prod(_1516254, _1516256)), _1516258), c_Product__Type_Ofst(_1516254, _1516256))), c_Product__Type_Osnd(_1516254, _1516256))))], (45277 ^ _776541) ^ [_1683227, _1683229, _1683231, _1683233, _1683235] : [c_List_Opartition(_1683227, _1683229, _1683231) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683227), tc_List_Olist(_1683227)), _1683233), _1683235), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1683227, tc_HOL_Obool)), hAPP(c_List_Oset(_1683227), _1683233)), hAPP(c_List_Oset(_1683227), _1683235)) = hAPP(c_List_Oset(_1683227), _1683231))], (8090 ^ _776541) ^ [_914132, _914134, _914136] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914132, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_914132, tc_HOL_Obool), _914134)), _914136) = c_Orderings_Obot__class_Obot(tc_fun(_914132, tc_HOL_Obool)), 8093 ^ _776541 : [(8094 ^ _776541) ^ [_914267] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_914132, tc_HOL_Obool)), _914267), _914134)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914132, tc_HOL_Obool)), _914267), _914136) = c_Orderings_Obot__class_Obot(tc_fun(_914132, tc_HOL_Obool)))]]], (32540 ^ _776541) ^ [_1364844, _1364846, _1364848, _1364850] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364844, tc_fun(_1364846, tc_HOL_Obool)), _1364848), _1364850) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1364846, tc_HOL_Obool), hAPP(c_Set_Oimage(_1364844, tc_fun(_1364846, tc_HOL_Obool), _1364850), _1364848)))], (39513 ^ _776541) ^ [_1542672, _1542674, _1542676] : [c_Relation_Orefl__on(_1542672, _1542674, _1542676), 39516 ^ _776541 : [(39519 ^ _776541) ^ [_1542854] : [hBOOL(hAPP(hAPP(c_member(_1542672), _1542854), _1542674)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542672, _1542672)), hAPP(hAPP(c_Product__Type_OPair(_1542672, _1542672), _1542854), _1542854)), _1542676)))], (39517 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542672, _1542672), tc_HOL_Obool)), _1542676), hAPP(hAPP(c_Product__Type_OSigma(_1542672, _1542672), _1542674), hAPP(c_COMBK(tc_fun(_1542672, tc_HOL_Obool), _1542672), _1542674)))))]]], (47076 ^ _776541) ^ [_1722775, _1722777, _1722779] : [_1722777 = hAPP(c_List_Orev(_1722775), _1722779), -(hAPP(c_List_Orev(_1722775), _1722777) = _1722779)], (2118 ^ _776541) ^ [_807265, _807267, _807269, _807271] : [-(c_Int_Onat__aux(_807271, _807267) = c_Int_Onat__aux(_807269, _807265)), _807271 = _807269, _807267 = _807265], (43633 ^ _776541) ^ [_1646828, _1646830, _1646832] : [_1646832 = c_List_Olist_ONil(_1646828), -(hAPP(hAPP(c_List_Oappend(_1646828), _1646830), _1646832) = _1646830)], (51817 ^ _776541) ^ [_1824034, _1824036, _1824038] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824034), _1824036)), _1824036 = _1824038, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824034), _1824038)))], (19711 ^ _776541) ^ [_1132430, _1132432] : [class_Rings_Odivision__ring__inverse__zero(_1132430), 19714 ^ _776541 : [(19721 ^ _776541) ^ [] : [-(_1132432 = c_Groups_Ozero__class_Ozero(_1132430)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132430), _1132432), _1132432) = c_Groups_Oone__class_Oone(_1132430))], (19715 ^ _776541) ^ [] : [_1132432 = c_Groups_Ozero__class_Ozero(_1132430), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132430), _1132432), _1132432) = c_Groups_Ozero__class_Ozero(_1132430))]]], (20997 ^ _776541) ^ [_1155758, _1155760, _1155762, _1155764, _1155766] : [class_Fields_Ofield(_1155758), hBOOL(hAPP(c_Finite__Set_Ofinite(_1155760), _1155762)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1155760), _1155764)), 21011 ^ _776541 : [(21014 ^ _776541) ^ [] : [-(hAPP(_1155766, 21010 ^ [_1155758, _1155760, _1155762, _1155764, _1155766]) = c_Groups_Ozero__class_Ozero(_1155758))], (21012 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1155760), 21010 ^ [_1155758, _1155760, _1155762, _1155764, _1155766]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1155760, tc_HOL_Obool)), _1155762), _1155764))))]], 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= hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1708732), _1708730))], (48961 ^ _776541) ^ [_1763710, _1763712, _1763714, _1763716] : [class_Groups_Ocomm__monoid__add(_1763710), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1763712, tc_HOL_Obool)), _1763714)), 48971 ^ _776541 : [(48974 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1763712), 48970 ^ [_1763710, _1763712, _1763714, _1763716]))], (48972 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1763712, tc_HOL_Obool)), 48970 ^ [_1763710, _1763712, _1763714, _1763716]), _1763714)))]], 48978 ^ _776541 : [(48982 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1763712, tc_HOL_Obool)), 48980 ^ [_1763710, _1763712, _1763714, _1763716]), _1763714)))], (48979 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1763712, tc_HOL_Obool)), 48977 ^ [_1763710, _1763712, _1763714, _1763716]), _1763714)))], (48991 ^ _776541) ^ [] : [hAPP(_1763716, 48985 ^ [_1763710, _1763712, _1763714, _1763716]) = 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hAPP(hAPP(c_List_Oappend(_1650140), _1650142), _1650144), _1650146) = hAPP(hAPP(c_List_Oappend(_1650140), c_List_Osublist(_1650140, _1650142, _1650146)), c_List_Osublist(_1650140, _1650144, 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(_1650140)), _1650142)))), _1650146)))))], (4544 ^ _776541) ^ [_845548, _845550, _845552, _845554] : [-(c_HOL_OThe(_845554, _845550) = c_HOL_OThe(_845552, _845548)), _845554 = _845552, _845550 = _845548], (23813 ^ _776541) ^ [_1207897, _1207899] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207897)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207899)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207897), _1207899)))], (29133 ^ _776541) ^ [_1298700, _1298702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298700), _1298702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298700)), c_Int_OBit1(_1298702))))], (8050 ^ _776541) ^ [_913264, _913266, _913268, _913270] : [hBOOL(hAPP(hAPP(c_member(_913264), _913266), _913268)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913264, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913264), _913266), _913270)), _913268) = hAPP(hAPP(c_Set_Oinsert(_913264), _913266), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913264, tc_HOL_Obool)), _913270), _913268)))], (20903 ^ _776541) ^ [_1153995, _1153997, _1153999, _1154001] : [class_Fields_Olinordered__field__inverse__zero(_1153995), 20906 ^ _776541 : [(20907 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153995), _1153997), _1153999)), _1154001)), 20910 ^ _776541 : [(20917 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), c_Groups_Ozero__class_Ozero(_1153995)), _1153999))), 20920 ^ _776541 : [(20927 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), _1153999), c_Groups_Ozero__class_Ozero(_1153995)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), c_Groups_Ozero__class_Ozero(_1153995)), _1154001)))], (20921 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), _1153999), c_Groups_Ozero__class_Ozero(_1153995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153995), _1154001), _1153999)), _1153997)))]]], (20911 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), c_Groups_Ozero__class_Ozero(_1153995)), _1153999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), _1153997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153995), _1154001), _1153999))))]]], (20933 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153995), _1153997), _1153999)), _1154001))), 20936 ^ _776541 : [(20939 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), _1153997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153995), _1154001), _1153999)))], (20937 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), c_Groups_Ozero__class_Ozero(_1153995)), _1153999)))]], 20940 ^ _776541 : [(20943 ^ _776541) ^ [] : [20944 ^ _776541 : [(20947 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153995), _1154001), _1153999)), _1153997))], (20945 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), _1153999), c_Groups_Ozero__class_Ozero(_1153995))))]], 20948 ^ _776541 : [(20951 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153995), c_Groups_Ozero__class_Ozero(_1153995)), _1154001))], (20949 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), _1153999), c_Groups_Ozero__class_Ozero(_1153995)))]]], (20941 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153995), c_Groups_Ozero__class_Ozero(_1153995)), _1153999))]]]]], (34295 ^ _776541) ^ [_1414682, _1414684] : [-(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), _1414682)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414684), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1414682))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (29717 ^ _776541) ^ [_1309370] : [-(_1309370 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 29720 ^ _776541 : [(29727 ^ _776541) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1309370, 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, _1309370) = 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), _1309370), 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)))], (29721 ^ _776541) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1309370, 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, _1309370) = 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), _1309370), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (34015 ^ _776541) ^ [_1408017, _1408019, _1408021, _1408023] : [class_Complete__Lattice_Ocomplete__lattice(_1408017), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408019), _1408021)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408019, _1408017), _1408021), _1408023) = hAPP(hAPP(c_Finite__Set_Ofold(_1408019, _1408017, hAPP(hAPP(c_COMBB(_1408017, tc_fun(_1408017, _1408017), _1408019), c_Lattices_Osemilattice__inf__class_Oinf(_1408017)), _1408023)), c_Orderings_Otop__class_Otop(_1408017)), _1408021))], (24397 ^ _776541) ^ [_1217756, _1217758] : [class_Rings_Olinordered__semidom(_1217756), 24400 ^ _776541 : [(24407 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217756), c_Groups_Ozero__class_Ozero(_1217756)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217756), _1217758))))], (24401 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217756), c_Groups_Ozero__class_Ozero(_1217756)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217756), _1217758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217758)))]]], (42717 ^ _776541) ^ [_1627218, _1627220, _1627222, _1627224, _1627226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627218, tc_HOL_Obool)), hAPP(c_List_Oset(_1627218), _1627220)), _1627222)), hBOOL(hAPP(hAPP(c_member(_1627218), _1627224), _1627222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627218, tc_HOL_Obool)), hAPP(c_List_Oset(_1627218), hAPP(hAPP(c_List_Olist__update(_1627218, _1627220), _1627226), _1627224))), _1627222)))], (16707 ^ _776541) ^ [_1077073, _1077075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077073), _1077075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077073)), _1077075)))], (38582 ^ _776541) ^ [_1517080, _1517082, _1517084, _1517086] : [hBOOL(hAPP(c_Predicate_ORangeP(_1517080, _1517082, hAPP(hAPP(c_COMBC(_1517080, tc_fun(tc_prod(_1517080, _1517082), tc_HOL_Obool), tc_fun(_1517082, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517082, tc_fun(tc_fun(tc_prod(_1517080, _1517082), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517080, _1517082), tc_HOL_Obool), tc_fun(_1517082, tc_HOL_Obool)), _1517080), c_COMBC(_1517082, tc_fun(tc_prod(_1517080, _1517082), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517082, tc_prod(_1517080, _1517082)), tc_fun(_1517082, tc_fun(tc_fun(tc_prod(_1517080, _1517082), tc_HOL_Obool), tc_HOL_Obool)), _1517080), hAPP(c_COMBB(tc_prod(_1517080, _1517082), tc_fun(tc_fun(tc_prod(_1517080, _1517082), tc_HOL_Obool), tc_HOL_Obool), _1517082), c_member(tc_prod(_1517080, _1517082)))), c_Product__Type_OPair(_1517080, _1517082)))), _1517084)), _1517086)), -(hBOOL(hAPP(hAPP(c_member(_1517082), _1517086), hAPP(c_Relation_ORange(_1517080, _1517082), _1517084))))], (16917 ^ _776541) ^ [_1080943, _1080945, _1080947] : [class_Rings_Oordered__cancel__semiring(_1080943), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080943), _1080945), _1080947)), c_Groups_Ozero__class_Ozero(_1080943)))), 16922 ^ _776541 : [(16929 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080943), _1080945), c_Groups_Ozero__class_Ozero(_1080943))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080943), c_Groups_Ozero__class_Ozero(_1080943)), _1080947))], (16923 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080943), c_Groups_Ozero__class_Ozero(_1080943)), _1080945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080943), _1080947), c_Groups_Ozero__class_Ozero(_1080943)))]]], (37644 ^ _776541) ^ [_1493257] : [-(c_Fun_Oinj__on(_1493257, tc_fun(_1493257, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1493257, tc_fun(_1493257, tc_HOL_Obool), tc_fun(_1493257, tc_HOL_Obool)), c_Set_Oinsert(_1493257)), c_Orderings_Obot__class_Obot(tc_fun(_1493257, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1493257, tc_HOL_Obool))))], (23866 ^ _776541) ^ [_1208833, _1208835] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208833), _1208835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208833)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208835)))], (32474 ^ _776541) ^ [_1361324, _1361326, _1361328, _1361330, _1361332] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361324, tc_fun(_1361326, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1361324), _1361328), _1361330)), _1361332) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361326, tc_HOL_Obool)), hAPP(_1361332, _1361328)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361324, tc_fun(_1361326, tc_HOL_Obool)), _1361330), _1361332)))], (23063 ^ _776541) ^ [_1194412, _1194414] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1194412), _1194414))))], (48754 ^ _776541) ^ [_1759095, _1759097, _1759099] : [-(_1759095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1759097), c_List_Oreplicate(_1759097, _1759095, _1759099)) = hAPP(hAPP(c_Set_Oinsert(_1759097), _1759099), c_Orderings_Obot__class_Obot(tc_fun(_1759097, tc_HOL_Obool))))], (7206 ^ _776541) ^ [_894009, _894011, _894013, _894015] : [hBOOL(hAPP(hAPP(c_member(_894009), _894011), hAPP(hAPP(c_Set_Oinsert(_894009), _894013), _894015))), -(_894011 = _894013), -(hBOOL(hAPP(hAPP(c_member(_894009), _894011), _894015)))], (18192 ^ _776541) ^ [_1103656, _1103658, _1103660] : [class_Groups_Oordered__comm__monoid__add(_1103656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103656), _1103658), c_Groups_Ozero__class_Ozero(_1103656))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103656), _1103660), c_Groups_Ozero__class_Ozero(_1103656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103656), _1103658), _1103660)), c_Groups_Ozero__class_Ozero(_1103656))))], (4584 ^ _776541) ^ [_846152, _846154, _846156, _846158, _846160, _846162, _846164, _846166, _846168, _846170] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_846170, _846166, _846162, _846158, _846154) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_846168, _846164, _846160, _846156, _846152)), _846170 = _846168, _846166 = _846164, _846162 = _846160, _846158 = _846156, _846154 = _846152], (19479 ^ _776541) ^ [_1128318, _1128320, _1128322, _1128324, _1128326] : [class_Groups_Ocomm__monoid__add(_1128318), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128320), _1128322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128320, tc_HOL_Obool)), _1128324), _1128322)), 19493 ^ _776541 : [(19496 ^ _776541) ^ [] : [hAPP(_1128326, 19492 ^ [_1128318, _1128320, _1128322, _1128324, _1128326]) = c_Groups_Ozero__class_Ozero(_1128318)], (19494 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1128320), 19492 ^ [_1128318, _1128320, _1128322, _1128324, _1128326]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1128320, tc_HOL_Obool)), _1128322), _1128324))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128320, _1128318), _1128326), _1128322) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128320, _1128318), _1128326), _1128324))], (31823 ^ _776541) ^ [_1348301, _1348303, _1348305] : [class_Orderings_Olinorder(_1348301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348301), _1348303)), -(_1348303 = c_Orderings_Obot__class_Obot(tc_fun(_1348301, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348301), _1348305)), -(_1348305 = c_Orderings_Obot__class_Obot(tc_fun(_1348301, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1348301, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1348301, tc_HOL_Obool)), _1348303), _1348305)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348301), c_Big__Operators_Olinorder__class_OMax(_1348301, _1348303)), c_Big__Operators_Olinorder__class_OMax(_1348301, _1348305)))], (52367 ^ _776541) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (21315 ^ _776541) ^ [_1162334, _1162336, _1162338] : [class_Int_Onumber(_1162334), class_Orderings_Olinorder(_1162334), 21322 ^ _776541 : [(21329 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162334), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162338)), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162336)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162334), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162336)), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162338))))], (21323 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162334), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162336)), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162338))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162334), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162338)), hAPP(c_Int_Onumber__class_Onumber__of(_1162334), _1162336)))]]], (2860 ^ _776541) ^ [_818966, _818968] : [_818968 = _818966, -(c_Relation_OField(_818968) = c_Relation_OField(_818966))], (32668 ^ _776541) ^ [_1369763, _1369765, _1369767, _1369769, _1369771] : [class_Groups_Ocomm__monoid__add(_1369763), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369763), _1369765), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1369767), _1369769)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1369771), _1369769))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369763), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1369763, tc_Nat_Onat), _1369765), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1369769))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1369767), _1369771)))], (52249 ^ _776541) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52171 ^ _776541) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (47530 ^ _776541) ^ [_1732493, _1732495] : [class_Orderings_Olinorder(_1732493), 47533 ^ _776541 : [(47554 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732493, _1732495)), 47555 ^ _776541 : [(47558 ^ _776541) ^ [_1733053, _1733055] : [_1732495 = hAPP(hAPP(c_List_Olist_OCons(_1732493), _1733053), _1733055), 47564 ^ _776541 : [(47567 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732493), _1733053), 47563 ^ [_1732493, _1732495, _1733053, _1733055]))], (47565 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732493), 47563 ^ [_1732493, _1732495, _1733053, _1733055]), hAPP(c_List_Oset(_1732493), _1733055))))]], c_List_Olinorder__class_Osorted(_1732493, _1733055)], (47556 ^ _776541) ^ [] : [_1732495 = c_List_Olist_ONil(_1732493)]]], (47534 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1732493, _1732495), -(_1732495 = c_List_Olist_ONil(_1732493)), 47543 ^ _776541 : [(47546 ^ _776541) ^ [_1732827] : [hBOOL(hAPP(hAPP(c_member(_1732493), _1732827), hAPP(c_List_Oset(_1732493), 47541 ^ [_1732493, _1732495]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732493), 47542 ^ [_1732493, _1732495]), _1732827)))], (47552 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732493, 47541 ^ [_1732493, _1732495]))], (47544 ^ _776541) ^ [] : [-(_1732495 = hAPP(hAPP(c_List_Olist_OCons(_1732493), 47542 ^ [_1732493, _1732495]), 47541 ^ [_1732493, _1732495]))]]]]], (38893 ^ _776541) ^ [_1524488, _1524490] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1524488, _1524488)), _1524490)), c_Wellfounded_Oacyclic(_1524488, _1524490), -(c_Wellfounded_Owf(_1524488, _1524490))], (41314 ^ _776541) ^ [_1587247, _1587249, _1587251] : [41317 ^ _776541 : [(41323 ^ _776541) ^ [] : [41316 ^ [_1587247, _1587249, _1587251] = 41319 ^ [_1587247, _1587249, _1587251]], (41321 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587247, _1587249)), hAPP(hAPP(c_Product__Type_OPair(_1587247, _1587249), 41315 ^ [_1587247, _1587249, _1587251]), 41319 ^ [_1587247, _1587249, _1587251])), _1587251)))], (41318 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587247, _1587249)), hAPP(hAPP(c_Product__Type_OPair(_1587247, _1587249), 41315 ^ [_1587247, _1587249, _1587251]), 41316 ^ [_1587247, _1587249, _1587251])), _1587251)))]], -(c_Relation_Osingle__valued(_1587247, _1587249, _1587251))], (5462 ^ _776541) ^ [_859993, _859995, _859997, _859999, _860001, _860003] : [-(c_SetInterval_Oord_OatLeast(_860003, _859999, _859995) = c_SetInterval_Oord_OatLeast(_860001, _859997, _859993)), _860003 = _860001, _859999 = _859997, _859995 = _859993], (46407 ^ _776541) ^ [_1709774, _1709776] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1709774, _1709776) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1709774), hAPP(c_Nat_OSuc, _1709776))))], (38448 ^ _776541) ^ [_1513627, _1513629] : [-(c_Set_Othe__elem(_1513627, _1513629) = c_HOL_OThe(_1513627, hAPP(hAPP(c_COMBB(tc_fun(_1513627, tc_HOL_Obool), tc_HOL_Obool, _1513627), hAPP(c_fequal, _1513629)), hAPP(hAPP(c_COMBC(_1513627, tc_fun(_1513627, tc_HOL_Obool), tc_fun(_1513627, tc_HOL_Obool)), c_Set_Oinsert(_1513627)), c_Orderings_Obot__class_Obot(tc_fun(_1513627, tc_HOL_Obool))))))], (28091 ^ _776541) ^ [_1281154, _1281156] : [-(c_Nitpick_Oint__lcm(_1281154, _1281156) = 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), _1281154)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1281156)))))], (44080 ^ _776541) ^ [_1658105, _1658107, _1658109, _1658111, _1658113] : [-(hAPP(hAPP(c_List_Ozip(_1658105, _1658107), _1658109), hAPP(hAPP(c_List_Oappend(_1658107), _1658111), _1658113)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1658105, _1658107)), hAPP(hAPP(c_List_Ozip(_1658105, _1658107), hAPP(hAPP(c_List_Otake(_1658105), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658107)), _1658111)), _1658109)), _1658111)), hAPP(hAPP(c_List_Ozip(_1658105, _1658107), hAPP(hAPP(c_List_Odrop(_1658105), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658107)), _1658111)), _1658109)), _1658113)))], (38558 ^ _776541) ^ [_1516132, _1516134, _1516136, _1516138] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516132, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1516134, _1516132), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1516134, _1516132), tc_HOL_Obool)), _1516136), _1516138))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1516132, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1516134, _1516132), _1516136)), hAPP(c_Relation_ORange(_1516134, _1516132), _1516138)))))], (33743 ^ _776541) ^ [_1400513, _1400515, _1400517, _1400519, _1400521] : [hBOOL(hAPP(hAPP(c_member(_1400513), _1400515), _1400517)), -(hAPP(c_Set_Oimage(_1400513, _1400519, hAPP(c_COMBK(_1400519, _1400513), _1400521)), _1400517) = hAPP(hAPP(c_Set_Oinsert(_1400519), _1400521), c_Orderings_Obot__class_Obot(tc_fun(_1400519, tc_HOL_Obool))))], (7816 ^ _776541) ^ [_907999, _908001, _908003, _908005] : [hBOOL(hAPP(hAPP(c_member(_907999), _908001), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907999, tc_HOL_Obool)), _908003), _908005))), -(hBOOL(hAPP(hAPP(c_member(_907999), _908001), _908005)))], (41068 ^ _776541) ^ [_1581539, _1581541, _1581543, _1581545, _1581547] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581539, _1581541)), hAPP(hAPP(c_Product__Type_OPair(_1581539, _1581541), _1581543), _1581545)), hAPP(c_Relation_Oconverse(_1581541, _1581539), _1581547))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581541, _1581539)), hAPP(hAPP(c_Product__Type_OPair(_1581541, _1581539), _1581545), _1581543)), _1581547)))], (43144 ^ _776541) ^ [_1636099, _1636101, _1636103, _1636105] : [hAPP(hAPP(c_List_Olist__update(_1636099, _1636101), _1636103), _1636105) = c_List_Olist_ONil(_1636099), -(_1636101 = c_List_Olist_ONil(_1636099))], (52341 ^ _776541) ^ [_1829727, _1829729] : [-(class_HOL_Oequal(tc_prod(_1829727, _1829729)))], (43098 ^ _776541) ^ [_1635282, _1635284] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635282)), _1635284) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1635284 = c_List_Olist_ONil(_1635282))], (12447 ^ _776541) ^ [_995200, _995202, _995204, _995206, _995208] : [c_Finite__Set_Ofolding__one__idem(_995200, _995202, _995204), hBOOL(hAPP(c_Finite__Set_Ofinite(_995200), _995206)), -(_995208 = c_Orderings_Obot__class_Obot(tc_fun(_995200, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_995200, tc_HOL_Obool)), _995208), _995206)), -(hAPP(hAPP(_995202, hAPP(_995204, _995208)), hAPP(_995204, _995206)) = hAPP(_995204, _995206))], (26597 ^ _776541) ^ [_1256599, _1256601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256599)), 26600 ^ _776541 : [(26607 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256599), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1256599)), _1256601)))], (26601 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1256599)), _1256601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256599), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256601))))]]], (7286 ^ _776541) ^ [_895661, _895663, _895665] : [_895663 = _895665, -(hBOOL(hAPP(hAPP(c_member(_895661), _895663), hAPP(hAPP(c_Set_Oinsert(_895661), _895665), c_Orderings_Obot__class_Obot(tc_fun(_895661, tc_HOL_Obool))))))], (45926 ^ _776541) ^ [_1697786, _1697788] : [c_List_Olist_ONil(_1697786) = c_List_Oconcat(_1697786, _1697788), 45929 ^ _776541 : [(45930 ^ _776541) ^ [_1697877] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697786)), _1697877), hAPP(c_List_Oset(tc_List_Olist(_1697786)), _1697788))), -(_1697877 = c_List_Olist_ONil(_1697786))]]], (31703 ^ _776541) ^ [_1345951, _1345953, _1345955] : [class_Orderings_Olinorder(_1345951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345951), _1345953)), hBOOL(hAPP(hAPP(c_member(_1345951), _1345955), _1345953)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345951), _1345955), c_Big__Operators_Olinorder__class_OMax(_1345951, _1345953)) = c_Big__Operators_Olinorder__class_OMax(_1345951, _1345953))], (4044 ^ _776541) ^ [_837670, _837672, _837674, _837676, _837678, _837680, _837682, _837684] : [-(c_New__DSequence_Oneg__bind(_837684, _837680, _837676, _837672) = c_New__DSequence_Oneg__bind(_837682, _837678, _837674, _837670)), _837684 = _837682, _837680 = _837678, _837676 = _837674, _837672 = _837670], (22345 ^ _776541) ^ [_1181679, _1181681] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1181679), _1181681)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181679), _1181681) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52383 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (22477 ^ _776541) ^ [_1183758, _1183760, _1183762] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1183760), _1183762)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183758), _1183760)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183758), _1183762)))], (17869 ^ _776541) ^ [_1097966, _1097968, _1097970] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097966), _1097968)), 17872 ^ _776541 : [(17873 ^ _776541) ^ [] : [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(_1097966, tc_Nat_Onat), _1097970), _1097968))), 17876 ^ _776541 : [(17877 ^ _776541) ^ [_1098134] : [hBOOL(hAPP(hAPP(c_member(_1097966), _1098134), _1097968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1097970, _1098134))))]]], (17883 ^ _776541) ^ [] : [17885 ^ _776541 : [(17888 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1097970, 17884 ^ [_1097966, _1097968, _1097970])))], (17886 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097966), 17884 ^ [_1097966, _1097968, _1097970]), _1097968)))]], -(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(_1097966, tc_Nat_Onat), _1097970), _1097968))))]]], (49379 ^ _776541) ^ [_1773938, _1773940, _1773942, _1773944] : [class_Complete__Lattice_Ocomplete__lattice(_1773938), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1773940, _1773938), _1773942), _1773944) = c_Complete__Lattice_OSup__class_OSup(_1773938, hAPP(c_Set_OCollect(_1773938), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773940, _1773938), tc_HOL_Obool), tc_HOL_Obool, _1773938), c_HOL_OEx(tc_fun(_1773940, _1773938))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773940, _1773938), tc_HOL_Obool), tc_fun(tc_fun(_1773940, _1773938), tc_HOL_Obool), _1773938), hAPP(c_COMBS(tc_fun(_1773940, _1773938), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1773940, _1773938)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1773940, _1773938), tc_fun(tc_fun(_1773940, _1773938), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1773940, _1773938))), _1773942)))), hAPP(hAPP(c_COMBC(_1773938, tc_fun(tc_fun(_1773940, _1773938), _1773938), tc_fun(tc_fun(_1773940, _1773938), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773938, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1773940, _1773938), _1773938), tc_fun(tc_fun(_1773940, _1773938), tc_HOL_Obool)), _1773938), c_COMBB(_1773938, tc_HOL_Obool, tc_fun(_1773940, _1773938))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1773940, _1773938), _1773940, _1773938), c_COMBI(tc_fun(_1773940, _1773938))), _1773944)))))))], (42735 ^ _776541) ^ [_1627656, _1627658, _1627660, _1627662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627658)), _1627660))), 42738 ^ _776541 : [(42745 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Onth(_1627658), _1627660), _1627656) = _1627662, -(hAPP(hAPP(c_List_Olist__update(_1627658, _1627660), _1627656), _1627662) = _1627660)], (42739 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1627658, _1627660), _1627656), _1627662) = _1627660, -(hAPP(hAPP(c_List_Onth(_1627658), _1627660), _1627656) = _1627662)]]], (16596 ^ _776541) ^ [_1075065, _1075067] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1075065, _1075067)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1075065), hAPP(c_Nat_OSuc, _1075067)))], (5324 ^ _776541) ^ [_857816, _857818] : [_857818 = _857816, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_857818) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_857816))], (31959 ^ _776541) ^ [_1350748, _1350750, _1350752] : [class_Orderings_Olinorder(_1350748), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350748), _1350750)), hBOOL(hAPP(hAPP(c_member(_1350748), _1350752), _1350750)), 31970 ^ _776541 : [(31977 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350748, tc_HOL_Obool)), _1350750), hAPP(hAPP(c_Set_Oinsert(_1350748), _1350752), c_Orderings_Obot__class_Obot(tc_fun(_1350748, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1350748, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1350748, c_Orderings_Oord__class_Omax(_1350748), _1350750) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350748), _1350752), c_Big__Operators_Olattice_OSup__fin(_1350748, c_Orderings_Oord__class_Omax(_1350748), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350748, tc_HOL_Obool)), _1350750), hAPP(hAPP(c_Set_Oinsert(_1350748), _1350752), c_Orderings_Obot__class_Obot(tc_fun(_1350748, tc_HOL_Obool)))))))], (31971 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350748, tc_HOL_Obool)), _1350750), hAPP(hAPP(c_Set_Oinsert(_1350748), _1350752), c_Orderings_Obot__class_Obot(tc_fun(_1350748, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1350748, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1350748, c_Orderings_Oord__class_Omax(_1350748), _1350750) = _1350752)]]], (32462 ^ _776541) ^ [_1361047, _1361049, _1361051, _1361053, _1361055] : [_1361047 = c_Orderings_Obot__class_Obot(tc_fun(_1361049, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361049, tc_fun(_1361051, tc_HOL_Obool)), _1361047), hAPP(hAPP(c_COMBB(tc_fun(_1361051, tc_HOL_Obool), tc_fun(_1361051, tc_HOL_Obool), _1361049), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361051, tc_HOL_Obool)), _1361053)), _1361055)) = c_Orderings_Obot__class_Obot(tc_fun(_1361051, tc_HOL_Obool)))], (8191 ^ _776541) ^ [_916424, _916426, _916428, _916430] : [class_Lattices_Olattice(_916424), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916424), _916426), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916424), _916428), _916430))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916424), _916426), _916428)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916424), _916426), _916430)))))], (15702 ^ _776541) ^ [_1061305, _1061307] : [hAPP(c_Nat_OSuc, _1061305) = hAPP(c_Nat_OSuc, _1061307), -(_1061305 = _1061307)], (14136 ^ _776541) ^ [_1030387, _1030389, _1030391, _1030393, _1030395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030387), _1030389)), 14139 ^ _776541 : [(14146 ^ _776541) ^ [] : [_1030393 = 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), _1030389), _1030387)), _1030391)), _1030395), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030387), _1030391)), _1030393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030389), _1030391)), _1030395))], (14140 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030387), _1030391)), _1030393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030389), _1030391)), _1030395), -(_1030393 = 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), _1030389), _1030387)), _1030391)), _1030395))]]], (16620 ^ _776541) ^ [_1075478, _1075480, _1075482, _1075484] : [class_Groups_Ocomm__monoid__add(_1075478), 16623 ^ _776541 : [(16630 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075480), _1075482))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1075480, _1075478), _1075484), _1075482) = c_Groups_Ozero__class_Ozero(_1075478))], (16624 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075480), _1075482)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1075480, _1075478), _1075484), _1075482) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075478, _1075480, c_Groups_Oplus__class_Oplus(_1075478)), _1075484), c_Groups_Ozero__class_Ozero(_1075478)), _1075482))]]], (48194 ^ _776541) ^ [_1747393, _1747395, _1747397] : [48196 ^ _776541 : [(48199 ^ _776541) ^ [] : [hBOOL(hAPP(_1747395, hAPP(hAPP(c_List_Onth(_1747393), _1747397), 48195 ^ [_1747393, _1747395, _1747397])))], (48197 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48195 ^ [_1747393, _1747395, _1747397]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747393)), _1747397))))]], -(c_List_Olist__all(_1747393, _1747395, _1747397))], (49980 ^ _776541) ^ [_1786019, _1786021, _1786023] : [hAPP(c_Fun_Ocomp(_1786021, _1786019, _1786019, c_Hilbert__Choice_Oinv__into(_1786019, _1786021, c_Orderings_Otop__class_Otop(tc_fun(_1786019, tc_HOL_Obool)), _1786023)), _1786023) = c_Fun_Oid(_1786019), -(c_Fun_Oinj__on(_1786019, _1786021, _1786023, c_Orderings_Otop__class_Otop(tc_fun(_1786019, tc_HOL_Obool))))], (10140 ^ _776541) ^ [_950248, _950250, _950252, _950254, _950256, _950258, _950260] : [c_Nitpick_Ofold__graph_H(_950248, _950250, _950252, _950254, _950256, hAPP(hAPP(_950252, _950258), _950260)), 10145 ^ _776541 : [(10148 ^ _776541) ^ [] : [-(hAPP(hAPP(_950252, _950258), _950260) = _950254)], (10146 ^ _776541) ^ [] : [-(_950256 = c_Orderings_Obot__class_Obot(tc_fun(_950248, tc_HOL_Obool)))]], 10151 ^ _776541 : [(10156 ^ _776541) ^ [] : [-(c_Nitpick_Ofold__graph_H(_950248, _950250, _950252, _950254, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950248, tc_HOL_Obool)), _950256), hAPP(hAPP(c_Set_Oinsert(_950248), 10149 ^ [_950248, _950250, _950252, _950254, _950256, _950258, _950260]), c_Orderings_Obot__class_Obot(tc_fun(_950248, tc_HOL_Obool)))), 10150 ^ [_950248, _950250, _950252, _950254, _950256, _950258, _950260]))], (10154 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_950248), 10149 ^ [_950248, _950250, _950252, _950254, _950256, _950258, _950260]), _950256)))], (10152 ^ _776541) ^ [] : [-(hAPP(hAPP(_950252, _950258), _950260) = hAPP(hAPP(_950252, 10149 ^ [_950248, _950250, _950252, _950254, _950256, _950258, _950260]), 10150 ^ [_950248, _950250, _950252, _950254, _950256, _950258, _950260]))]]], (13910 ^ _776541) ^ [_1024940, _1024942, _1024944] : [class_Groups_Ogroup__add(_1024940), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024940), _1024942), hAPP(c_Groups_Ouminus__class_Ouminus(_1024940), _1024944)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024940), _1024942), _1024944))], (19241 ^ _776541) ^ [_1123676, _1123678, _1123680] : [hAPP(c_Finite__Set_Ocard(_1123676), _1123678) = hAPP(c_Nat_OSuc, _1123680), 19246 ^ _776541 : [(19249 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1123676), 19244 ^ [_1123676, _1123678, _1123680]), 19245 ^ [_1123676, _1123678, _1123680]))], (19251 ^ _776541) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1123676), 19245 ^ [_1123676, _1123678, _1123680]) = _1123680)], (19253 ^ _776541) ^ [] : [_1123680 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(19245 ^ [_1123676, _1123678, _1123680] = c_Orderings_Obot__class_Obot(tc_fun(_1123676, tc_HOL_Obool)))], (19247 ^ _776541) ^ [] : [-(_1123678 = hAPP(hAPP(c_Set_Oinsert(_1123676), 19244 ^ [_1123676, _1123678, _1123680]), 19245 ^ [_1123676, _1123678, _1123680]))]]], (35742 ^ _776541) ^ [_1443804, _1443806, _1443808] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1443804, _1443806), _1443808))), _1443804 = 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), _1443808)), _1443806)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443808)), 35749 ^ _776541 : [(35752 ^ _776541) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1443808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35750 ^ _776541) ^ [] : [-(_1443806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 35753 ^ _776541 : [(35756 ^ _776541) ^ [] : [35757 ^ _776541 : [(35760 ^ _776541) ^ [] : [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), _1443808))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443808)), _1443806))], (35758 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443806)))]], 35765 ^ _776541 : [(35768 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1443806), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443808))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443808)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35766 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443806))]]], (35754 ^ _776541) ^ [] : [_1443806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50385 ^ _776541) ^ [_1795223, _1795225, _1795227, _1795229, _1795231] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1795223, _1795225, tc_HOL_Obool, _1795227), _1795229), _1795231)), -(hBOOL(hAPP(_1795227, hAPP(hAPP(c_Product__Type_OPair(_1795223, _1795225), _1795229), _1795231))))], (5040 ^ _776541) ^ [_853384, _853386] : [_853386 = _853384, -(c_Orderings_Obot__class_Obot(_853386) = c_Orderings_Obot__class_Obot(_853384))], (36663 ^ _776541) ^ [_1471726, _1471728, _1471730] : [-(hAPP(c_Relation_OImage(_1471726, _1471726, c_Relation_OId__on(_1471726, _1471728)), _1471730) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471726, tc_HOL_Obool)), _1471728), _1471730))], (37266 ^ _776541) ^ [_1485765, _1485767, _1485769, _1485771] : [c_Fun_Oinj__on(_1485765, _1485767, _1485769, _1485771), 37269 ^ _776541 : [(37270 ^ _776541) ^ [_1485873] : [hBOOL(hAPP(hAPP(c_member(_1485765), _1485873), _1485771)), 37273 ^ _776541 : [(37274 ^ _776541) ^ [_1485975] : [hBOOL(hAPP(hAPP(c_member(_1485765), _1485975), _1485771)), hAPP(_1485769, _1485873) = hAPP(_1485769, _1485975), -(_1485873 = _1485975)]]]]], (12824 ^ _776541) ^ [_1002797, _1002799] : [class_Complete__Lattice_Ocomplete__lattice(_1002797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002797), _1002799)), -(c_Complete__Lattice_OSup__class_OSup(_1002797, _1002799) = hAPP(hAPP(c_Finite__Set_Ofold(_1002797, _1002797, c_Lattices_Osemilattice__sup__class_Osup(_1002797)), c_Orderings_Obot__class_Obot(_1002797)), _1002799))], (17663 ^ _776541) ^ [_1094585, _1094587] : [class_Groups_Olinordered__ab__group__add(_1094585), 17666 ^ _776541 : [(17673 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094585), _1094587), c_Groups_Ozero__class_Ozero(_1094585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094585), _1094587), hAPP(c_Groups_Ouminus__class_Ouminus(_1094585), _1094587))))], (17667 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094585), _1094587), hAPP(c_Groups_Ouminus__class_Ouminus(_1094585), _1094587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094585), _1094587), c_Groups_Ozero__class_Ozero(_1094585))))]]], (52075 ^ _776541) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (44176 ^ _776541) ^ [_1659874, _1659876, _1659878] : [-(c_List_Orotate(_1659874, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659876), _1659878)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1659874), tc_List_Olist(_1659874), tc_List_Olist(_1659874), c_List_Orotate(_1659874, _1659876)), c_List_Orotate(_1659874, _1659878)))], (43308 ^ _776541) ^ [_1639388, _1639390, _1639392, _1639394, _1639396, _1639398] : [-(hAPP(c_List_Olist_Olist__case(_1639388, _1639390, _1639392, _1639394), hAPP(hAPP(c_List_Olist_OCons(_1639390), _1639396), _1639398)) = hAPP(hAPP(_1639394, _1639396), _1639398))], (52151 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (39836 ^ _776541) ^ [_1551722, _1551724, _1551726, _1551728, _1551730, _1551732] : [c_Fun_Oinj__on(_1551722, _1551724, _1551726, _1551728), 39839 ^ _776541 : [(39846 ^ _776541) ^ [] : [c_Fun_Oinj__on(_1551722, _1551730, hAPP(c_Fun_Ocomp(_1551724, _1551730, _1551722, _1551732), _1551726), _1551728), -(c_Fun_Oinj__on(_1551724, _1551730, _1551732, hAPP(c_Set_Oimage(_1551722, _1551724, _1551726), _1551728)))], (39840 ^ _776541) ^ [] : [c_Fun_Oinj__on(_1551724, _1551730, _1551732, hAPP(c_Set_Oimage(_1551722, _1551724, _1551726), _1551728)), -(c_Fun_Oinj__on(_1551722, _1551730, hAPP(c_Fun_Ocomp(_1551724, _1551730, _1551722, _1551732), _1551726), _1551728))]]], (11202 ^ _776541) ^ [_970847, _970849, _970851, _970853, _970855] : [hBOOL(hAPP(hAPP(c_member(_970847), _970849), _970851)), -(hAPP(hAPP(c_Set_Oinsert(_970853), hAPP(_970855, _970849)), hAPP(c_Set_Oimage(_970847, _970853, _970855), _970851)) = hAPP(c_Set_Oimage(_970847, _970853, _970855), _970851))], (36079 ^ _776541) ^ [_1455852] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1455852)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1455852)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35690 ^ _776541) ^ [_1442803, _1442805, _1442807, _1442809, _1442811] : [hBOOL(hAPP(hAPP(_1442803, _1442805), _1442807)), -(hBOOL(hAPP(hAPP(_1442803, hAPP(c_Product__Type_Osnd(_1442809, _1442811), hAPP(hAPP(c_Product__Type_OPair(_1442809, _1442811), _1442807), _1442805))), hAPP(c_Product__Type_Ofst(_1442809, _1442811), hAPP(hAPP(c_Product__Type_OPair(_1442809, _1442811), _1442807), _1442805)))))], (16683 ^ _776541) ^ [_1076635, _1076637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1076635)), _1076637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076635), _1076637)))], (32596 ^ _776541) ^ [_1367493, _1367495, _1367497, _1367499, _1367501] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367493, tc_fun(_1367495, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1367493), _1367497), _1367499)), _1367501) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367495, tc_HOL_Obool)), hAPP(_1367501, _1367497)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367493, tc_fun(_1367495, tc_HOL_Obool)), _1367499), _1367501)))], (48298 ^ _776541) ^ [_1749261, _1749263, _1749265] : [48300 ^ _776541 : [(48303 ^ _776541) ^ [] : [hBOOL(hAPP(_1749265, 48299 ^ [_1749261, _1749263, _1749265]))], (48301 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749261), 48299 ^ [_1749261, _1749263, _1749265]), hAPP(c_List_Oset(_1749261), _1749263))))]], -(c_List_Olist__all(_1749261, _1749265, _1749263))], (52129 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (39341 ^ _776541) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (32229 ^ _776541) ^ [_1355847, _1355849, _1355851] : [class_Orderings_Olinorder(_1355847), hAPP(_1355849, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355847), 32234 ^ [_1355847, _1355849, _1355851]), 32235 ^ [_1355847, _1355849, _1355851])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355847), hAPP(_1355849, 32234 ^ [_1355847, _1355849, _1355851])), hAPP(_1355849, 32235 ^ [_1355847, _1355849, _1355851])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355847), _1355851)), -(_1355851 = c_Orderings_Obot__class_Obot(tc_fun(_1355847, tc_HOL_Obool))), -(hAPP(_1355849, c_Big__Operators_Olinorder__class_OMax(_1355847, _1355851)) = c_Big__Operators_Olinorder__class_OMax(_1355847, hAPP(c_Set_Oimage(_1355847, _1355847, _1355849), _1355851)))], (48268 ^ _776541) ^ [_1748748, _1748750, _1748752] : [c_List_Olist__all(_1748748, _1748750, hAPP(c_List_Orev(_1748748), _1748752)), -(c_List_Olist__all(_1748748, _1748750, _1748752))], (41923 ^ _776541) ^ [_1604898, _1604900, _1604902, _1604904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604898), tc_List_Olist(_1604898))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604898), tc_List_Olist(_1604898)), _1604900), _1604902)), c_List_Olistrel1(_1604898, hAPP(c_Relation_Oconverse(_1604898, _1604898), _1604904)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604898), tc_List_Olist(_1604898))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604898), tc_List_Olist(_1604898)), _1604900), _1604902)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1604898), tc_List_Olist(_1604898)), c_List_Olistrel1(_1604898, _1604904)))))], (40170 ^ _776541) ^ [_1559259, _1559261, _1559263, _1559265] : [c_Finite__Set_Ofolding(_1559259, _1559261, _1559263, _1559265), -(hAPP(_1559265, c_Orderings_Obot__class_Obot(tc_fun(_1559259, tc_HOL_Obool))) = c_Fun_Oid(_1559261))], (36502 ^ _776541) ^ [_1467362, _1467364, _1467366, _1467368, _1467370, _1467372] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467362, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1467364, _1467362, _1467366), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1467368, tc_fun(_1467364, tc_HOL_Obool)), _1467370), _1467372))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1467368, tc_fun(_1467362, tc_HOL_Obool)), _1467370), hAPP(hAPP(c_COMBB(tc_fun(_1467364, tc_HOL_Obool), tc_fun(_1467362, tc_HOL_Obool), _1467368), c_Relation_OImage(_1467364, _1467362, _1467366)), _1467372)))))], (23069 ^ _776541) ^ [_1194507] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194507) = _1194507)], (8990 ^ _776541) ^ [_932098, _932100, _932102, _932104, _932106] : [class_Orderings_Oorder(_932098), 8993 ^ _776541 : [(9014 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932098, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_932098, _932100, _932102)), c_SetInterval_Oord__class_OatLeastAtMost(_932098, _932104, _932106)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932104), _932106)), 9017 ^ _776541 : [(9020 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932104), _932100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932102), _932106)), 9027 ^ _776541 : [(9030 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932098), _932102), _932106))], (9028 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932098), _932104), _932100))]]], (9018 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932100), _932102)))]]], (8994 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932098, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_932098, _932100, _932102)), c_SetInterval_Oord__class_OatLeastAtMost(_932098, _932104, _932106))), 8997 ^ _776541 : [(8998 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932100), _932102)), 9001 ^ _776541 : [(9006 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932098), _932104), _932100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932098), _932102), _932106)))], (9004 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932102), _932106)))], (9002 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932104), _932100)))]]], (9012 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932098), _932104), _932106)))]]]]], (44982 ^ _776541) ^ [_1677286, _1677288, _1677290, _1677292] : [class_Rings_Osemiring__1(_1677286), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677286), hAPP(hAPP(c_List_Omap(_1677288, _1677286), hAPP(c_COMBK(_1677286, _1677288), _1677290)), _1677292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1677286), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1677286), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677288)), _1677292))), _1677290))], (29287 ^ _776541) ^ [_1301367] : [-(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)))), _1301367) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1301367)))], (45678 ^ _776541) ^ [_1692860, _1692862, _1692864] : [-(hAPP(c_List_Oset(tc_List_Olist(_1692860)), c_Enum_On__lists(_1692860, _1692862, _1692864)) = hAPP(c_Set_OCollect(tc_List_Olist(_1692860)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1692860), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1692860)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1692860), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1692860)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1692860)))), _1692862))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1692860), tc_fun(_1692860, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1692860, tc_HOL_Obool), tc_fun(tc_fun(_1692860, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1692860)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1692860, tc_HOL_Obool))), c_List_Oset(_1692860))), hAPP(c_List_Oset(_1692860), _1692864)))))], (30598 ^ _776541) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (6388 ^ _776541) ^ [_879646, _879648, _879650] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_879646, tc_HOL_Obool)), _879648), _879650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879646, tc_HOL_Obool)), _879648), c_Complete__Lattice_OSup__class_OSup(tc_fun(_879646, tc_HOL_Obool), _879650))))], (19521 ^ _776541) ^ [_1129220, _1129222] : [class_Rings_Olinordered__idom(_1129220), 19524 ^ _776541 : [(19531 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129220), _1129222), c_Groups_Ozero__class_Ozero(_1129220))), -(c_Groups_Osgn__class_Osgn(_1129220, _1129222) = hAPP(c_Groups_Ouminus__class_Ouminus(_1129220), c_Groups_Oone__class_Oone(_1129220)))], (19525 ^ _776541) ^ [] : [c_Groups_Osgn__class_Osgn(_1129220, _1129222) = hAPP(c_Groups_Ouminus__class_Ouminus(_1129220), c_Groups_Oone__class_Oone(_1129220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129220), _1129222), c_Groups_Ozero__class_Ozero(_1129220))))]]], (47257 ^ _776541) ^ [_1726651, _1726653, _1726655, _1726657, _1726659] : [-(hAPP(hAPP(c_List_Ozip(_1726651, _1726653), _1726655), c_List_OtakeWhile(_1726653, _1726657, _1726659)) = c_List_OtakeWhile(tc_prod(_1726651, _1726653), hAPP(c_Fun_Ocomp(_1726653, tc_HOL_Obool, tc_prod(_1726651, _1726653), _1726657), c_Product__Type_Osnd(_1726651, _1726653)), hAPP(hAPP(c_List_Ozip(_1726651, _1726653), _1726655), _1726659)))], (28761 ^ _776541) ^ [_1292153, _1292155] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1292153), _1292155) = 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), _1292153)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1292155)))))], (39004 ^ _776541) ^ [_1527551, _1527553, _1527555, _1527557] : [hBOOL(hAPP(c_Predicate_ODomainP(_1527551, _1527553, _1527555), _1527557)), -(hBOOL(hAPP(hAPP(_1527555, _1527557), 39007 ^ [_1527551, _1527553, _1527555, _1527557])))], (1544 ^ _776541) ^ [_798705, _798707] : [-(class_Groups_Oordered__ab__semigroup__add(_798705)), _798707 = _798705, class_Groups_Oordered__ab__semigroup__add(_798707)], (24986 ^ _776541) ^ [_1229019, _1229021, _1229023, _1229025] : [class_Divides_Osemiring__div(_1229019), -(c_Divides_Odiv__class_Omod(_1229019, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229019), _1229021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229019), _1229023), _1229025)), _1229023) = c_Divides_Odiv__class_Omod(_1229019, _1229021, _1229023))], (32308 ^ _776541) ^ [_1357539, _1357541, _1357543, _1357545, _1357547, _1357549] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357539, tc_fun(_1357541, tc_HOL_Obool)), _1357543), _1357545), _1357547)), -(hBOOL(hAPP(hAPP(_1357545, _1357549), _1357547))), hBOOL(hAPP(hAPP(c_member(_1357539), _1357549), _1357543))], (10685 ^ _776541) ^ [_960426] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960426, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_960426, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_960426, tc_HOL_Obool)))], (29217 ^ _776541) ^ [_1300228] : [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), _1300228))), 29220 ^ _776541 : [(29223 ^ _776541) ^ [] : [-(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(_1300228)))))], (29221 ^ _776541) ^ [] : [-(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(_1300228)))))]]], (49628 ^ _776541) ^ [_1779498, _1779500] : [c_Relation_Oantisym(_1779498, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779498, _1779498), tc_HOL_Obool)), _1779500), c_Relation_OId(_1779498))), -(c_Relation_Oantisym(_1779498, _1779500))], (23145 ^ _776541) ^ [_1195865, _1195867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195865)), -(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), _1195865), _1195867))))], (42931 ^ _776541) ^ [_1632096, _1632098] : [class_Groups_Ocomm__monoid__add(_1632096), hBOOL(hAPP(c_List_Odistinct(_1632096), _1632098)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1632096), _1632098) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1632096, _1632096), c_COMBI(_1632096)), hAPP(c_List_Oset(_1632096), _1632098)))], (39483 ^ _776541) ^ [_1541903, _1541905, _1541907, _1541909] : [c_Wellfounded_Owf(_1541903, _1541905), c_Fun_Oinj__on(_1541903, _1541907, _1541909, c_Orderings_Otop__class_Otop(tc_fun(_1541903, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1541907, hAPP(c_Set_Oimage(tc_prod(_1541903, _1541903), tc_prod(_1541907, _1541907), c_Product__Type_Omap__pair(_1541903, _1541907, _1541903, _1541907, _1541909, _1541909)), _1541905)))], (24086 ^ _776541) ^ [_1212459, _1212461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212459)), 24089 ^ _776541 : [(24096 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212461)), -(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), _1212461), _1212459))))], (24090 ^ _776541) ^ [] : [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), _1212461), _1212459))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212461)))]]], (45225 ^ _776541) ^ [_1682342, _1682344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682342)), hAPP(c_Code__Numeral_Onat__of, _1682344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1682342), _1682344)))], (1824 ^ _776541) ^ [_802205, _802207] : [-(class_Rings_Osemiring(_802205)), _802207 = _802205, class_Rings_Osemiring(_802207)], (2358 ^ _776541) ^ [_810953, _810955, _810957, _810959, _810961, _810963, _810965, _810967] : [-(c_Nitpick_Oprod(_810967, _810963, _810959, _810955) = c_Nitpick_Oprod(_810965, _810961, _810957, _810953)), _810967 = _810965, _810963 = _810961, _810959 = _810957, _810955 = _810953], (46996 ^ _776541) ^ [_1721168, _1721170] : [c_List_Olist_ONil(_1721168) = hAPP(c_List_Orev(_1721168), _1721170), -(_1721170 = c_List_Olist_ONil(_1721168))], (50307 ^ _776541) ^ [_1793498, _1793500, _1793502, _1793504, _1793506] : [c_Fun_Obij__betw(_1793498, _1793500, _1793502, c_Orderings_Otop__class_Otop(tc_fun(_1793498, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793500, tc_HOL_Obool))), c_Fun_Obij__betw(_1793504, _1793498, _1793506, c_Orderings_Otop__class_Otop(tc_fun(_1793504, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793498, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1793504, _1793500, c_Orderings_Otop__class_Otop(tc_fun(_1793504, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1793498, _1793500, _1793504, _1793502), _1793506)) = hAPP(c_Fun_Ocomp(_1793498, _1793504, _1793500, c_Hilbert__Choice_Oinv__into(_1793504, _1793498, c_Orderings_Otop__class_Otop(tc_fun(_1793504, tc_HOL_Obool)), _1793506)), c_Hilbert__Choice_Oinv__into(_1793498, _1793500, c_Orderings_Otop__class_Otop(tc_fun(_1793498, tc_HOL_Obool)), _1793502)))], (48430 ^ _776541) ^ [_1751912, _1751914, _1751916, _1751918, _1751920] : [-(_1751912 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1751914, _1751916, _1751918, _1751920), _1751912) = hAPP(c_Lazy__Sequence_Obind(_1751914, _1751916, hAPP(_1751918, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1751912), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1751914, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1751916)), _1751920), _1751912)))], (42137 ^ _776541) ^ [_1611503, _1611505, _1611507] : [c_Relation_Orefl__on(_1611503, _1611505, _1611507), -(c_Relation_Orefl__on(tc_List_Olist(_1611503), c_List_Olists(_1611503, _1611505), c_List_Olistrel(_1611503, _1611507)))], (28343 ^ _776541) ^ [_1285316, _1285318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285316), _1285318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1285316)), c_Int_OBit1(_1285318))))], (35785 ^ _776541) ^ [_1444781, _1444783, _1444785] : [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), _1444781), _1444783))), -(hBOOL(hAPP(hAPP(_1444785, _1444781), _1444783))), 35792 ^ _776541 : [(35795 ^ _776541) ^ [] : [-(35791 ^ [_1444781, _1444783, _1444785] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1444785, 35791 ^ [_1444781, _1444783, _1444785]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 35790 ^ [_1444781, _1444783, _1444785], 35791 ^ [_1444781, _1444783, _1444785]))))], (35801 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1444785, 35790 ^ [_1444781, _1444783, _1444785]), 35791 ^ [_1444781, _1444783, _1444785]))], (35793 ^ _776541) ^ [] : [-(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), 35790 ^ [_1444781, _1444783, _1444785]), 35791 ^ [_1444781, _1444783, _1444785]))))]]], (45315 ^ _776541) ^ [_1684654, _1684656] : [-(hBOOL(hAPP(c_List_Olistsp(_1684654, _1684656), c_List_Olist_ONil(_1684654))))], (38022 ^ _776541) ^ [_1503356, _1503358, _1503360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1503356, _1503356), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1503356, _1503356, _1503356), _1503358), _1503360)), _1503358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1503356, tc_HOL_Obool), tc_fun(_1503356, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1503356, tc_HOL_Obool), tc_fun(_1503356, tc_HOL_Obool), tc_fun(_1503356, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1503356, _1503358)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1503356, tc_HOL_Obool), tc_fun(_1503356, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1503356, _1503360)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1503356, tc_HOL_Obool), tc_fun(_1503356, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1503356, tc_HOL_Obool), tc_fun(_1503356, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1503356, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1503356, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1503356, tc_HOL_Obool), tc_fun(_1503356, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1503356, _1503358))))], (4496 ^ _776541) ^ [_844838, _844840, _844842, _844844, _844846, _844848] : [-(c_Lazy__Sequence_Oanamorph(_844848, _844844, _844840) = c_Lazy__Sequence_Oanamorph(_844846, _844842, _844838)), _844848 = _844846, _844844 = _844842, _844840 = _844838], (35856 ^ _776541) ^ [_1446589] : [-(c_Wellfounded_Ofinite__psubset(_1446589) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1446589, tc_HOL_Obool), tc_fun(_1446589, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1446589, tc_HOL_Obool), tc_fun(_1446589, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1446589, tc_HOL_Obool), tc_fun(tc_fun(_1446589, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446589, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1446589, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1446589, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446589, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1446589, tc_HOL_Obool)), c_COMBS(tc_fun(_1446589, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1446589, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446589, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1446589, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1446589, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1446589, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1446589)))))], (30126 ^ _776541) ^ [_1317010, _1317012, _1317014, _1317016] : [class_Orderings_Olinorder(_1317010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317010), _1317012), _1317014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317010), _1317012), _1317016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317010), _1317012), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317010), _1317014), _1317016))))], (52099 ^ _776541) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (15716 ^ _776541) ^ [_1061525] : [hAPP(c_Nat_OSuc, _1061525) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14444 ^ _776541) ^ [_1037351, _1037353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037351), _1037353)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037353), _1037351)), _1037351) = _1037353)], (43541 ^ _776541) ^ [_1644965, _1644967, _1644969, _1644971] : [-(hAPP(hAPP(c_List_Oappend(_1644965), hAPP(hAPP(c_List_Oappend(_1644965), _1644967), _1644969)), _1644971) = hAPP(hAPP(c_List_Oappend(_1644965), _1644967), hAPP(hAPP(c_List_Oappend(_1644965), _1644969), _1644971)))], (28031 ^ _776541) ^ [_1280255, _1280257] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280255), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280255)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280257)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1280255), _1280257)))], (47442 ^ _776541) ^ [_1730447, _1730449, _1730451, _1730453, _1730455] : [-(c_List_OdropWhile(_1730447, _1730449, _1730451) = hAPP(hAPP(c_List_Olist_OCons(_1730447), _1730453), _1730455)), _1730451 = hAPP(hAPP(c_List_Oappend(_1730447), c_List_OtakeWhile(_1730447, _1730449, _1730451)), hAPP(hAPP(c_List_Olist_OCons(_1730447), _1730453), _1730455)), -(hBOOL(hAPP(_1730449, _1730453)))], (26188 ^ _776541) ^ [_1249687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249687)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1249687)) = _1249687)], (5098 ^ _776541) ^ [_854297, _854299, _854301, _854303, _854305, _854307, _854309, _854311] : [-(c_Hilbert__Choice_Oinv__into(_854311, _854307, _854303, _854299) = c_Hilbert__Choice_Oinv__into(_854309, _854305, _854301, _854297)), _854311 = _854309, _854307 = _854305, _854303 = _854301, _854299 = _854297], (21303 ^ _776541) ^ [_1162104, _1162106, _1162108, _1162110] : [class_Rings_Ocomm__semiring__1(_1162104), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1162104), hAPP(hAPP(c_Power_Opower__class_Opower(_1162104), _1162106), _1162108)), _1162110) = hAPP(hAPP(c_Power_Opower__class_Opower(_1162104), _1162106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162108), _1162110)))], (6989 ^ _776541) ^ [_890136, _890138, _890140] : [class_Orderings_Oord(_890136), 6992 ^ _776541 : [(6999 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890136), _890138), _890140)), -(hBOOL(hAPP(hAPP(c_member(_890136), _890138), hAPP(c_SetInterval_Oord__class_OatMost(_890136), _890140))))], (6993 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890136), _890138), hAPP(c_SetInterval_Oord__class_OatMost(_890136), _890140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890136), _890138), _890140)))]]], (20743 ^ _776541) ^ [_1151050, _1151052, _1151054, _1151056] : [class_Fields_Ofield__inverse__zero(_1151050), -(_1151052 = c_Groups_Ozero__class_Ozero(_1151050)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151050), _1151054), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151050), _1151056), _1151052)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151050), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151050), _1151056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151050), _1151054), _1151052))), _1151052))], (19561 ^ _776541) ^ [_1129932, _1129934, _1129936, _1129938] : [class_Rings_Odivision__ring(_1129932), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129932), _1129934), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129932), _1129936), _1129938)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129932), _1129934), _1129936)), _1129938))], (51749 ^ _776541) ^ [_1822981, _1822983] : [-(_1822981 = _1822983), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822981), _1822983)), 51756 ^ _776541 : [(51759 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822983), _1822981))], (51757 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822981), _1822983)))]]], (51879 ^ _776541) ^ [_1824898, _1824900] : [class_Lattices_Olattice(_1824898), -(class_Lattices_Osemilattice__inf(tc_fun(_1824900, _1824898)))], (31717 ^ _776541) ^ [_1346186, _1346188, _1346190, _1346192, _1346194] : [class_Orderings_Olinorder(_1346186), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346186, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1346186, _1346188, _1346190)), c_SetInterval_Oord__class_OatLeastAtMost(_1346186, _1346192, _1346194)) = c_SetInterval_Oord__class_OatLeastAtMost(_1346186, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346186), _1346188), _1346192), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346186), _1346190), _1346194)))], (43448 ^ _776541) ^ [_1642875, _1642877, _1642879, _1642881, _1642883, _1642885] : [hAPP(hAPP(c_List_Olist_OCons(_1642875), _1642877), _1642879) = _1642881, _1642883 = hAPP(hAPP(c_List_Oappend(_1642875), _1642879), _1642885), -(hAPP(hAPP(c_List_Olist_OCons(_1642875), _1642877), _1642883) = hAPP(hAPP(c_List_Oappend(_1642875), _1642881), _1642885))], (20481 ^ _776541) ^ [_1146109, _1146111, _1146113] : [class_Fields_Olinordered__field(_1146109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146109), _1146111), c_Groups_Ozero__class_Ozero(_1146109))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146109), _1146113), c_Groups_Ozero__class_Ozero(_1146109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146109), c_Groups_Ozero__class_Ozero(_1146109)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146109), _1146111), _1146113))))], (51761 ^ _776541) ^ [_1823172, _1823174] : [_1823172 = _1823174, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823172), _1823174)))], (33230 ^ _776541) ^ [_1385504, _1385506, _1385508, _1385510] : [c_Orderings_Obot__class_Obot(tc_fun(_1385504, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385506, tc_fun(_1385504, tc_HOL_Obool)), _1385508), _1385510), 33233 ^ _776541 : [(33234 ^ _776541) ^ [_1385620] : [hBOOL(hAPP(hAPP(c_member(_1385506), _1385620), _1385508)), -(hAPP(_1385510, _1385620) = c_Orderings_Obot__class_Obot(tc_fun(_1385504, tc_HOL_Obool)))]]], (36651 ^ _776541) ^ [_1471424, _1471426, _1471428] : [_1471426 = c_Orderings_Obot__class_Obot(tc_fun(_1471424, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471424, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471424), _1471426), _1471428))], (14204 ^ _776541) ^ [_1032020, _1032022] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1032020, _1032022))))], (45614 ^ _776541) ^ [_1691377, _1691379, _1691381, _1691383, _1691385, _1691387] : [c_List_Olist__all2(_1691377, _1691379, _1691381, _1691383, _1691385), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691387), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691379)), _1691385))), -(hBOOL(hAPP(hAPP(_1691381, hAPP(hAPP(c_List_Onth(_1691377), _1691383), _1691387)), hAPP(hAPP(c_List_Onth(_1691379), _1691385), _1691387))))], (13413 ^ _776541) ^ [_1014841, _1014843, _1014845, _1014847] : [class_Lattices_Osemilattice__inf(_1014841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014841), _1014843)), 13423 ^ _776541 : [(13426 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014841), _1014845), 13422 ^ [_1014841, _1014843, _1014845, _1014847]))], (13424 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014841), 13422 ^ [_1014841, _1014843, _1014845, _1014847]), _1014843)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014841), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1014841), _1014845), _1014847)), hAPP(hAPP(c_Finite__Set_Ofold(_1014841, _1014841, c_Lattices_Osemilattice__inf__class_Oinf(_1014841)), _1014847), _1014843))))], (25004 ^ _776541) ^ [_1229364, _1229366, _1229368] : [class_Divides_Osemiring__div(_1229364), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1229364), c_Divides_Odiv__class_Omod(_1229364, _1229366, _1229368)), _1229368) = c_Groups_Ozero__class_Ozero(_1229364))], (12035 ^ _776541) ^ [_988082, _988084, _988086] : [class_Lattices_Olattice(_988082), hBOOL(hAPP(c_Finite__Set_Ofinite(_988082), _988084)), hBOOL(hAPP(hAPP(c_member(_988082), _988086), _988084)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_988082), _988086), c_Big__Operators_Olattice__class_OSup__fin(_988082, _988084)) = c_Big__Operators_Olattice__class_OSup__fin(_988082, _988084))], (39019 ^ _776541) ^ [_1527981] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1527981), c_Int_OInteg)), -(_1527981 = hAPP(c_Int_ORep__Integ, 39022 ^ [_1527981]))], (7878 ^ _776541) ^ [_909237, _909239] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909237, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_909237, tc_HOL_Obool))), _909239) = c_Orderings_Obot__class_Obot(tc_fun(_909237, tc_HOL_Obool)))], (42207 ^ _776541) ^ [_1613417, _1613419, _1613421] : [_1613417 = _1613419, 42210 ^ _776541 : [(42213 ^ _776541) ^ [_1613565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613565), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613421)), _1613417))), -(hAPP(hAPP(c_List_Onth(_1613421), _1613417), _1613565) = hAPP(hAPP(c_List_Onth(_1613421), _1613419), _1613565))], (42211 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613421)), _1613417) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613421)), _1613419))]]], (52287 ^ _776541) ^ [_1829034, _1829036] : [-(class_HOL_Oequal(tc_sum(_1829034, _1829036)))], (26056 ^ _776541) ^ [_1247541, _1247543] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247541), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247543), _1247541)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247543), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247543, _1247541)))], (10371 ^ _776541) ^ [_954645, _954647, _954649] : [class_Lattices_Oboolean__algebra(_954645), 10374 ^ _776541 : [(10381 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954645), _954649), _954647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954645), hAPP(c_Groups_Ouminus__class_Ouminus(_954645), _954647)), hAPP(c_Groups_Ouminus__class_Ouminus(_954645), _954649))))], (10375 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954645), hAPP(c_Groups_Ouminus__class_Ouminus(_954645), _954647)), hAPP(c_Groups_Ouminus__class_Ouminus(_954645), _954649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954645), _954649), _954647)))]]], (31287 ^ _776541) ^ [_1338008, _1338010, _1338012] : [class_Orderings_Olinorder(_1338008), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338008), _1338010), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338008), _1338010), _1338012)) = _1338010)], (50253 ^ _776541) ^ [_1792378, _1792380] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1792378), _1792380))), -(c_Quickcheck_Obeyond(_1792378, _1792380) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (42575 ^ _776541) ^ [_1624113, _1624115, _1624117, _1624119, _1624121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624113), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624115)), _1624117))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624113), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624119)), _1624121))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1624115, _1624119)), hAPP(hAPP(c_List_Ozip(_1624115, _1624119), _1624117), _1624121)), _1624113) = hAPP(hAPP(c_Product__Type_OPair(_1624115, _1624119), hAPP(hAPP(c_List_Onth(_1624115), _1624117), _1624113)), hAPP(hAPP(c_List_Onth(_1624119), _1624121), _1624113)))], (4340 ^ _776541) ^ [_842266, _842268] : [_842268 = _842266, -(c_If(_842268) = c_If(_842266))], (43962 ^ _776541) ^ [_1655094, _1655096, _1655098, _1655100] : [-(hAPP(hAPP(c_List_Odrop(_1655094), _1655096), hAPP(hAPP(c_List_Oappend(_1655094), _1655098), _1655100)) = hAPP(hAPP(c_List_Oappend(_1655094), hAPP(hAPP(c_List_Odrop(_1655094), _1655096), _1655098)), hAPP(hAPP(c_List_Odrop(_1655094), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655096), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655094)), _1655098))), _1655100)))], (19627 ^ _776541) ^ [_1131128, _1131130, _1131132, _1131134] : [class_Rings_Odivision__ring(_1131128), -(_1131130 = c_Groups_Ozero__class_Ozero(_1131128)), _1131132 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131128), _1131134), _1131130), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131128), _1131132), _1131130) = _1131134)], (37987 ^ _776541) ^ [_1502259, _1502261, _1502263, _1502265] : [hBOOL(hAPP(hAPP(c_member(_1502259), _1502261), c_Wellfounded_Oacc(_1502259, _1502263))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1502259, _1502259)), hAPP(hAPP(c_Product__Type_OPair(_1502259, _1502259), _1502265), _1502261)), _1502263)), -(hBOOL(hAPP(hAPP(c_member(_1502259), _1502265), c_Wellfounded_Oacc(_1502259, _1502263))))], (40368 ^ _776541) ^ [_1563623, _1563625] : [-(c_Hilbert__Choice_OEps(_1563623, hAPP(hAPP(c_COMBC(_1563623, _1563623, tc_HOL_Obool), c_fequal), _1563625)) = _1563625)], (15692 ^ _776541) ^ [_1061124] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1061124)], (44383 ^ _776541) ^ [_1664163, _1664165, _1664167, _1664169, _1664171] : [class_Orderings_Olinorder(_1664163), 44386 ^ _776541 : [(44395 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1664165), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1664165, _1664163, _1664167), _1664169), _1664171)))), -(hBOOL(hAPP(hAPP(c_member(_1664165), _1664169), hAPP(c_List_Oset(_1664165), _1664171)))), hBOOL(hAPP(c_List_Odistinct(_1664165), _1664171))], (44387 ^ _776541) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1664165), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1664165, _1664163, _1664167), _1664169), _1664171))), 44390 ^ _776541 : [(44393 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1664165), _1664171)))], (44391 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1664165), _1664169), hAPP(c_List_Oset(_1664165), _1664171)))]]]]], (38314 ^ _776541) ^ [_1510418] : [class_Orderings_Owellorder(_1510418), -(c_Wellfounded_Owf(_1510418, hAPP(c_Set_OCollect(tc_prod(_1510418, _1510418)), hAPP(c_Product__Type_Oprod_Oprod__case(_1510418, _1510418, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1510418)))))], (49967 ^ _776541) ^ [_1785511, _1785513] : [c_Equiv__Relations_Opart__equivp(_1785511, _1785513), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1785511, tc_HOL_Obool)), 49970 ^ [_1785511, _1785513]), hAPP(hAPP(c_COMBB(tc_fun(_1785511, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1785511, tc_HOL_Obool)), c_HOL_OEx(_1785511)), hAPP(hAPP(c_COMBB(tc_fun(_1785511, tc_HOL_Obool), tc_fun(_1785511, tc_HOL_Obool), tc_fun(_1785511, tc_HOL_Obool)), hAPP(c_COMBS(_1785511, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785511), c_fconj), hAPP(hAPP(c_COMBS(_1785511, _1785511, tc_HOL_Obool), _1785513), c_COMBI(_1785511))))), hAPP(hAPP(c_COMBC(tc_fun(_1785511, tc_HOL_Obool), tc_fun(_1785511, tc_fun(_1785511, tc_HOL_Obool)), tc_fun(_1785511, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1785511, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1785511, tc_fun(_1785511, tc_HOL_Obool)), tc_fun(_1785511, tc_HOL_Obool)), tc_fun(_1785511, tc_HOL_Obool)), c_COMBB(tc_fun(_1785511, tc_HOL_Obool), tc_HOL_Obool, _1785511)), c_fequal)), _1785513))))))], (38229 ^ _776541) ^ [_1508609, _1508611, _1508613] : [c_Wellfounded_Owf(_1508609, _1508611), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508609, _1508609)), hAPP(hAPP(c_Product__Type_OPair(_1508609, _1508609), _1508613), _1508613)), _1508611))], (12179 ^ _776541) ^ [_990331, _990333, _990335] : [class_Lattices_Olattice(_990331), hBOOL(hAPP(c_Finite__Set_Ofinite(_990331), _990333)), -(_990335 = c_Orderings_Obot__class_Obot(tc_fun(_990331, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990331, tc_HOL_Obool)), _990335), _990333)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_990331), c_Big__Operators_Olattice__class_OInf__fin(_990331, _990335)), c_Big__Operators_Olattice__class_OInf__fin(_990331, _990333)) = c_Big__Operators_Olattice__class_OInf__fin(_990331, _990333))], (35172 ^ _776541) ^ [_1432929, _1432931] : [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), _1432929), _1432931))), 35175 ^ _776541 : [(35182 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432931), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 35185 ^ _776541 : [(35194 ^ _776541) ^ [] : [-(c_Nitpick_Onorm__frac(_1432929, _1432931) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1432929), _1432931)), 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), _1432929))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1432931)))), -(_1432929 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1432931 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35186 ^ _776541) ^ [] : [35187 ^ _776541 : [(35190 ^ _776541) ^ [] : [_1432931 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35188 ^ _776541) ^ [] : [_1432929 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1432929, _1432931) = 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)))]]], (35176 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432931), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1432929, _1432931) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1432929), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1432931)))]]], (29039 ^ _776541) ^ [_1297099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1297099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1297099))))], (48607 ^ _776541) ^ [_1756444, _1756446, _1756448, _1756450] : [48608 ^ _776541 : [(48611 ^ _776541) ^ [] : [_1756446 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48609 ^ _776541) ^ [] : [hBOOL(hAPP(_1756450, _1756448))]], 48612 ^ _776541 : [(48613 ^ _776541) ^ [_1756569] : [hBOOL(hAPP(hAPP(c_member(_1756444), _1756569), hAPP(c_List_Oset(_1756444), c_List_Oreplicate(_1756444, _1756446, _1756448)))), -(hBOOL(hAPP(_1756450, _1756569)))]]], (47573 ^ _776541) ^ [_1733374, _1733376, _1733378] : [hBOOL(hAPP(hAPP(c_member(_1733374), _1733376), hAPP(c_List_Oset(_1733374), _1733378))), -(c_List_Oinsert(_1733374, _1733376, _1733378) = _1733378)], (22867 ^ _776541) ^ [_1190818, _1190820, _1190822, _1190824] : [class_Rings_Olinordered__semidom(_1190818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190820), _1190822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190818), c_Groups_Oone__class_Oone(_1190818)), _1190824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190818), hAPP(hAPP(c_Power_Opower__class_Opower(_1190818), _1190824), _1190820)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190818), _1190824), _1190822))))], (39308 ^ _776541) ^ [_1537332, _1537334, _1537336, _1537338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537334, _1537332), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1537332, tc_prod(_1537334, _1537332), 39304 ^ [_1537332, _1537334, _1537336, _1537338]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537334, tc_fun(_1537332, tc_HOL_Obool)), _1537336), _1537338))), hAPP(hAPP(c_Product__Type_OSigma(_1537334, _1537332), _1537336), _1537338))))], (26433 ^ _776541) ^ [_1253569, _1253571, _1253573] : [hBOOL(hAPP(_1253569, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1253571, _1253573))), 26436 ^ _776541 : [(26443 ^ _776541) ^ [] : [-(_1253573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26446 ^ _776541 : [(26447 ^ _776541) ^ [_1253817, _1253819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1253817), _1253573)), _1253571 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1253573), _1253819)), _1253817), -(hBOOL(hAPP(_1253569, _1253817)))]]], (26437 ^ _776541) ^ [] : [_1253573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1253569, _1253571)))]]], (49210 ^ _776541) ^ [_1769964, _1769966] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1769964, tc_HOL_Obool), _1769966) = hAPP(c_Set_OCollect(_1769964), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769964, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1769964), c_HOL_OEx(tc_fun(_1769964, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769964, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1769964, tc_HOL_Obool), tc_HOL_Obool), _1769964), hAPP(c_COMBS(tc_fun(_1769964, 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(_1769964, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769964, tc_HOL_Obool), tc_fun(tc_fun(_1769964, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769964, tc_HOL_Obool))), _1769966)))), c_member(_1769964)))))], (39195 ^ _776541) ^ [_1533079, _1533081, _1533083, _1533085, _1533087, _1533089] : [hBOOL(hAPP(hAPP(c_member(_1533079), _1533081), _1533083)), 39198 ^ _776541 : [(39205 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533085, tc_HOL_Obool)), _1533087), _1533089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533085, _1533079), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533085, _1533079), _1533087), hAPP(c_COMBK(tc_fun(_1533079, tc_HOL_Obool), _1533085), _1533083))), hAPP(hAPP(c_Product__Type_OSigma(_1533085, _1533079), _1533089), hAPP(c_COMBK(tc_fun(_1533079, tc_HOL_Obool), _1533085), _1533083)))))], (39199 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533085, _1533079), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533085, _1533079), _1533087), hAPP(c_COMBK(tc_fun(_1533079, tc_HOL_Obool), _1533085), _1533083))), hAPP(hAPP(c_Product__Type_OSigma(_1533085, _1533079), _1533089), hAPP(c_COMBK(tc_fun(_1533079, tc_HOL_Obool), _1533085), _1533083)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533085, tc_HOL_Obool)), _1533087), _1533089)))]]], (51925 ^ _776541) ^ [_1825501, _1825503] : [class_Orderings_Otop(_1825501), -(class_Orderings_Otop(tc_fun(_1825503, _1825501)))], (22215 ^ _776541) ^ [_1179456, _1179458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179456), _1179458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179456), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1179458)))], (35452 ^ _776541) ^ [_1437715, _1437717, _1437719] : [35454 ^ _776541 : [(35457 ^ _776541) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1437719, 35453 ^ [_1437715, _1437717, _1437719]))], (35455 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437715), 35453 ^ [_1437715, _1437717, _1437719]), _1437717)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1437715, tc_Int_Oint), _1437719), _1437717) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1437715, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1437715), c_Int_Onat), _1437719)), _1437717)))], (11704 ^ _776541) ^ [_981334, _981336, _981338, _981340] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981334), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981334, tc_HOL_Obool)), _981336), hAPP(hAPP(c_Set_Oinsert(_981334), _981338), _981340)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981334), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981334, tc_HOL_Obool)), _981336), _981340))))], (15690 ^ _776541) ^ [_1061089] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1061089)], (36752 ^ _776541) ^ [_1473822, _1473824, _1473826, _1473828, _1473830] : [c_Equiv__Relations_Oequiv(_1473822, _1473824, _1473826), hBOOL(hAPP(hAPP(c_member(tc_fun(_1473822, tc_HOL_Obool)), _1473828), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473822), _1473824), _1473826))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1473822, tc_HOL_Obool)), _1473830), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473822), _1473824), _1473826))), -(_1473828 = _1473830), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473822, tc_HOL_Obool)), _1473828), _1473830) = c_Orderings_Obot__class_Obot(tc_fun(_1473822, tc_HOL_Obool)))], (52277 ^ _776541) ^ [_1828905, _1828907] : [-(class_Finite__Set_Ofinite(tc_sum(_1828905, _1828907))), class_Finite__Set_Ofinite(_1828905), class_Finite__Set_Ofinite(_1828907)], (52273 ^ _776541) ^ [_1828857] : [-(class_HOL_Oequal(tc_List_Olist(_1828857)))], (31809 ^ _776541) ^ [_1348066, _1348068, _1348070] : [class_Orderings_Olinorder(_1348066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348066), _1348068)), hBOOL(hAPP(hAPP(c_member(_1348066), _1348070), _1348068)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348066), _1348070), c_Big__Operators_Olattice_OInf__fin(_1348066, c_Orderings_Oord__class_Omin(_1348066), _1348068)) = _1348070)], (46140 ^ _776541) ^ [_1703278, _1703280, _1703282, _1703284] : [-(hBOOL(hAPP(_1703278, _1703280))), -(hAPP(c_List_OremoveAll(_1703282, _1703280), hAPP(c_List_Ofilter(_1703282, _1703278), _1703284)) = hAPP(c_List_Ofilter(_1703282, _1703278), _1703284))], (40258 ^ _776541) ^ [_1561307, _1561309, _1561311, _1561313, _1561315, _1561317] : [c_Finite__Set_Ofolding__idem(_1561307, _1561309, _1561311, _1561313), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561307), _1561315)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561307), _1561317)), -(hAPP(_1561313, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1561307, tc_HOL_Obool)), _1561315), _1561317)) = hAPP(c_Fun_Ocomp(_1561309, _1561309, _1561309, hAPP(_1561313, _1561315)), hAPP(_1561313, _1561317)))], (40763 ^ _776541) ^ [_1574166, _1574168] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574166, _1574166), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574166, _1574168)), c_Relation_OId(_1574166)) = c_Transitive__Closure_Ortrancl(_1574166, _1574168))], (14392 ^ _776541) ^ [_1036292, _1036294, _1036296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036292), _1036294)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036296), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036294), _1036292)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036296), _1036292)), _1036294))], (43908 ^ _776541) ^ [_1653891, _1653893, _1653895, _1653897, _1653899] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1653891, _1653893)), _1653895), hAPP(hAPP(c_List_Ozip(_1653891, _1653893), _1653897), _1653899)) = hAPP(hAPP(c_List_Ozip(_1653891, _1653893), hAPP(hAPP(c_List_Odrop(_1653891), _1653895), _1653897)), hAPP(hAPP(c_List_Odrop(_1653893), _1653895), _1653899)))], (13832 ^ _776541) ^ [_1023247, _1023249, _1023251] : [class_Groups_Ogroup__add(_1023247), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023247), hAPP(c_Groups_Ouminus__class_Ouminus(_1023247), _1023249)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023247), _1023249), _1023251)) = _1023251)], (26765 ^ _776541) ^ [_1259281, _1259283] : [class_Int_Onumber__ring(_1259281), -(hAPP(c_Int_Onumber__class_Onumber__of(_1259281), _1259283) = hAPP(c_Int_Oring__1__class_Oof__int(_1259281), _1259283))], (25121 ^ _776541) ^ [_1231204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231204), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1231204)))], (50393 ^ _776541) ^ [_1795404, _1795406, _1795408, _1795410] : [c_Fun_Obij__betw(_1795404, _1795406, _1795408, c_Orderings_Otop__class_Otop(tc_fun(_1795404, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1795406, tc_HOL_Obool))), 50396 ^ _776541 : [(50403 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795406), _1795410)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1795404), hAPP(c_Set_Ovimage(_1795404, _1795406, _1795408), _1795410))))], (50397 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795404), hAPP(c_Set_Ovimage(_1795404, _1795406, _1795408), _1795410))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1795406), _1795410)))]]], (3804 ^ _776541) ^ [_833644, _833646] : [_833646 = _833644, -(c_Enum_Oenum__class_Oenum__ex(_833646) = c_Enum_Oenum__class_Oenum__ex(_833644))], (14500 ^ _776541) ^ [_1038276, _1038278] : [-(_1038276 = _1038278), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038276), _1038278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038278), _1038276)))], (50259 ^ _776541) ^ [_1792424] : [-(c_Quickcheck_Obeyond(_1792424, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (23779 ^ _776541) ^ [_1207218, _1207220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207218), _1207220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207218)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207220))))], (23870 ^ _776541) ^ [_1208925, _1208927] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208925)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208927)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208925), _1208927)))], (42123 ^ _776541) ^ [_1611231] : [-(c_List_Olists(_1611231, c_Orderings_Otop__class_Otop(tc_fun(_1611231, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1611231), tc_HOL_Obool)))], (18668 ^ _776541) ^ [_1112611, _1112613, _1112615] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1112611), _1112613)), 18671 ^ _776541 : [(18691 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112611, tc_Nat_Onat), _1112615), _1112613) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 18692 ^ _776541 : [(18693 ^ _776541) ^ [_1113092] : [hBOOL(hAPP(hAPP(c_member(_1112611), _1113092), _1112613)), hAPP(_1112615, _1113092) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 18701 ^ _776541 : [(18706 ^ _776541) ^ [] : [hAPP(_1112615, 18700 ^ [_1112611, _1112613, _1112615, _1113092]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18704 ^ _776541) ^ [] : [_1113092 = 18700 ^ [_1112611, _1112613, _1112615, _1113092]], (18702 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112611), 18700 ^ [_1112611, _1112613, _1112615, _1113092]), _1112613)))]]]]], (18672 ^ _776541) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112611, tc_Nat_Onat), _1112615), _1112613) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 18676 ^ _776541 : [(18681 ^ _776541) ^ [_1112931] : [hBOOL(hAPP(hAPP(c_member(_1112611), _1112931), _1112613)), -(18675 ^ [_1112611, _1112613, _1112615] = _1112931), -(hAPP(_1112615, _1112931) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18679 ^ _776541) ^ [] : [-(hAPP(_1112615, 18675 ^ [_1112611, _1112613, _1112615]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18677 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112611), 18675 ^ [_1112611, _1112613, _1112615]), _1112613)))]]]]], (10623 ^ _776541) ^ [_959232, _959234] : [class_Lattices_Oboolean__algebra(_959232), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959232), _959234), hAPP(c_Groups_Ouminus__class_Ouminus(_959232), _959234)) = c_Orderings_Obot__class_Obot(_959232))], (28139 ^ _776541) ^ [_1281857] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1281857), c_Int_OMin) = c_Int_Opred(_1281857))], (43200 ^ _776541) ^ [_1637024, _1637026, _1637028] : [-(hAPP(hAPP(c_List_Otake(_1637024), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1637024), _1637026), _1637028)) = hAPP(hAPP(c_List_Olist_OCons(_1637024), _1637026), c_List_Olist_ONil(_1637024)))], (44212 ^ _776541) ^ [_1660577, _1660579, _1660581] : [-(hAPP(c_List_Orotate(_1660577, hAPP(c_Nat_OSuc, _1660579)), _1660581) = hAPP(c_List_Orotate1(_1660577), hAPP(c_List_Orotate(_1660577, _1660579), _1660581)))], (52301 ^ _776541) ^ [_1829217] : [class_Finite__Set_Ofinite(_1829217), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1829217)))], (20831 ^ _776541) ^ [_1152612, _1152614, _1152616] : [class_Fields_Olinordered__field(_1152612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152612), _1152614), _1152616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152612), _1152614), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152612), _1152614), _1152616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152612), c_Groups_Oone__class_Oone(_1152612)), c_Groups_Oone__class_Oone(_1152612))))))], (36231 ^ _776541) ^ [_1460147, _1460149, _1460151, _1460153, _1460155, _1460157, _1460159] : [-(hAPP(c_Product__Type_Oapsnd(_1460147, _1460149, _1460151, _1460153), hAPP(c_Product__Type_Oapfst(_1460155, _1460151, _1460147, _1460157), _1460159)) = hAPP(c_Product__Type_Oapfst(_1460155, _1460151, _1460149, _1460157), hAPP(c_Product__Type_Oapsnd(_1460147, _1460149, _1460155, _1460153), _1460159)))], (11942 ^ _776541) ^ [_986200, _986202, _986204, _986206, _986208, _986210] : [-(_986200 = _986202), -(hAPP(c_Fun_Ofun__upd(_986204, _986206, _986208, _986202, _986210), _986200) = hAPP(_986208, _986200))], (47899 ^ _776541) ^ [_1741168, _1741170, _1741172, _1741174, _1741176] : [hAPP(hAPP(c_List_Olist_OCons(_1741168), _1741170), _1741172) = hAPP(c_List_Ofilter(_1741168, _1741174), _1741176), 47904 ^ _776541 : [(47913 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1741174, _1741170)))], (47915 ^ _776541) ^ [] : [-(_1741172 = hAPP(c_List_Ofilter(_1741168, _1741174), 47903 ^ [_1741168, _1741170, _1741172, _1741174, _1741176]))], (47907 ^ _776541) ^ [_1741482] : [hBOOL(hAPP(hAPP(c_member(_1741168), _1741482), hAPP(c_List_Oset(_1741168), 47902 ^ [_1741168, _1741170, _1741172, _1741174, _1741176]))), hBOOL(hAPP(_1741174, _1741482))], (47905 ^ _776541) ^ [] : [-(_1741176 = hAPP(hAPP(c_List_Oappend(_1741168), 47902 ^ [_1741168, _1741170, _1741172, _1741174, _1741176]), hAPP(hAPP(c_List_Olist_OCons(_1741168), _1741170), 47903 ^ [_1741168, _1741170, _1741172, _1741174, _1741176])))]]], (25079 ^ _776541) ^ [_1230573, _1230575] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230573), _1230575) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230573, _1230575) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (11894 ^ _776541) ^ [_985460, _985462, _985464, _985466, _985468] : [c_Finite__Set_Ofolding__one__idem(_985460, _985462, _985464), hBOOL(hAPP(c_Finite__Set_Ofinite(_985460), _985466)), -(_985466 = c_Orderings_Obot__class_Obot(tc_fun(_985460, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_985460), _985468)), -(_985468 = c_Orderings_Obot__class_Obot(tc_fun(_985460, tc_HOL_Obool))), -(hAPP(_985464, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985460, tc_HOL_Obool)), _985466), _985468)) = hAPP(hAPP(_985462, hAPP(_985464, _985466)), hAPP(_985464, _985468)))], (37502 ^ _776541) ^ [_1490319, _1490321, _1490323] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490319), _1490321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490319, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1490319, _1490319, _1490323), _1490321)), _1490321)), c_Fun_Oinj__on(_1490319, _1490319, _1490323, _1490321), -(hAPP(c_Set_Oimage(_1490319, _1490319, _1490323), _1490321) = _1490321)], (28891 ^ _776541) ^ [_1294499, _1294501] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1294499)), c_Int_OBit0(_1294501))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1294499), _1294501)))], (34725 ^ _776541) ^ [_1423703, _1423705] : [-(c_Divides_Odivmod__nat(_1423703, _1423705) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1423703), _1423705)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1423703, _1423705)))], (41156 ^ _776541) ^ [_1583530, _1583532, _1583534] : [-(hAPP(c_Relation_ORange(_1583530, _1583532), hAPP(c_Relation_Oconverse(_1583532, _1583530), _1583534)) = hAPP(c_Relation_ODomain(_1583532, _1583530), _1583534))], (38362 ^ _776541) ^ [_1511638, _1511640, _1511642, _1511644] : [38364 ^ _776541 : [(38367 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1511640, hAPP(_1511642, 38363 ^ [_1511638, _1511640, _1511642, _1511644]))), hAPP(_1511640, 38363 ^ [_1511638, _1511640, _1511642, _1511644])))], (38365 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1511638, 38363 ^ [_1511638, _1511640, _1511642, _1511644])))]], -(c_Wellfounded_Owf(_1511644, hAPP(c_Set_OCollect(tc_prod(_1511644, _1511644)), hAPP(c_Product__Type_Oprod_Oprod__case(_1511644, _1511644, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1511644, tc_HOL_Obool), tc_fun(_1511644, tc_HOL_Obool), _1511644), hAPP(c_COMBS(_1511644, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511644), c_fconj), _1511638))), hAPP(hAPP(c_COMBC(_1511644, tc_fun(_1511644, _1511644), tc_fun(_1511644, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511644, tc_HOL_Obool), tc_fun(tc_fun(_1511644, _1511644), tc_fun(_1511644, tc_HOL_Obool)), _1511644), c_COMBB(_1511644, tc_HOL_Obool, _1511644)), c_fequal)), _1511642))))))], (20075 ^ _776541) ^ [_1138986, _1138988, _1138990] : [class_Fields_Olinordered__field__inverse__zero(_1138986), 20078 ^ _776541 : [(20093 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), c_Groups_Ozero__class_Ozero(_1138986)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138986), _1138988), _1138990)))), 20094 ^ _776541 : [(20101 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), _1138988), c_Groups_Ozero__class_Ozero(_1138986))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), _1138990), c_Groups_Ozero__class_Ozero(_1138986)))], (20095 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), c_Groups_Ozero__class_Ozero(_1138986)), _1138988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), c_Groups_Ozero__class_Ozero(_1138986)), _1138990))]]], (20079 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), c_Groups_Ozero__class_Ozero(_1138986)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138986), _1138988), _1138990))), 20084 ^ _776541 : [(20087 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), c_Groups_Ozero__class_Ozero(_1138986)), _1138990)))], (20085 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), c_Groups_Ozero__class_Ozero(_1138986)), _1138988)))]], 20088 ^ _776541 : [(20091 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), _1138990), c_Groups_Ozero__class_Ozero(_1138986))))], (20089 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138986), _1138988), c_Groups_Ozero__class_Ozero(_1138986))))]]]]], (41823 ^ _776541) ^ [_1601784, _1601786, _1601788] : [-(c_Random_Oselect__weight(_1601784, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1601784)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1601784), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1601786)), _1601788)) = c_Random_Oselect__weight(_1601784, _1601788))], (52487 ^ _776541) ^ [] : [-(hBOOL(c_fTrue))], (52167 ^ _776541) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (18886 ^ _776541) ^ [_1116710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116710)), -(_1116710 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116710), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (32928 ^ _776541) ^ [_1376842, _1376844, _1376846, _1376848, _1376850] : [_1376842 = c_Orderings_Obot__class_Obot(tc_fun(_1376844, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376844, tc_fun(_1376846, tc_HOL_Obool)), _1376842), hAPP(hAPP(c_COMBC(_1376844, tc_fun(_1376846, tc_HOL_Obool), tc_fun(_1376846, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376846, tc_HOL_Obool), tc_fun(tc_fun(_1376846, tc_HOL_Obool), tc_fun(_1376846, tc_HOL_Obool)), _1376844), c_Groups_Ominus__class_Ominus(tc_fun(_1376846, tc_HOL_Obool))), _1376848)), _1376850)) = c_Orderings_Otop__class_Otop(tc_fun(_1376846, tc_HOL_Obool)))], (52153 ^ _776541) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (45335 ^ _776541) ^ [_1685062, _1685064, _1685066, _1685068] : [hBOOL(hAPP(c_List_Olistsp(_1685062, _1685064), hAPP(hAPP(c_List_Olist_OCons(_1685062), _1685066), _1685068))), 45338 ^ _776541 : [(45341 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1685062, _1685064), _1685068)))], (45339 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1685064, _1685066)))]]], (11782 ^ _776541) ^ [_982883, _982885, _982887, _982889, _982891, _982893, _982895, _982897] : [c_Finite__Set_Ofolding__image__simple(_982883, _982885, _982887, _982889, _982891, _982893), hBOOL(hAPP(c_Finite__Set_Ofinite(_982885), _982895)), -(hAPP(_982893, hAPP(hAPP(c_Set_Oinsert(_982885), _982897), _982895)) = hAPP(hAPP(_982887, hAPP(_982891, _982897)), hAPP(_982893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982885, tc_HOL_Obool)), _982895), hAPP(hAPP(c_Set_Oinsert(_982885), _982897), c_Orderings_Obot__class_Obot(tc_fun(_982885, tc_HOL_Obool)))))))], (20227 ^ _776541) ^ [_1141724, _1141726, _1141728] : [class_Fields_Olinordered__field__inverse__zero(_1141724), 20230 ^ _776541 : [(20245 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), c_Groups_Ozero__class_Ozero(_1141724)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141724), _1141726), _1141728)))), 20246 ^ _776541 : [(20253 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), _1141726), c_Groups_Ozero__class_Ozero(_1141724))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), _1141728), c_Groups_Ozero__class_Ozero(_1141724)))], (20247 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), c_Groups_Ozero__class_Ozero(_1141724)), _1141726)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), c_Groups_Ozero__class_Ozero(_1141724)), _1141728))]]], (20231 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), c_Groups_Ozero__class_Ozero(_1141724)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141724), _1141726), _1141728))), 20236 ^ _776541 : [(20239 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), c_Groups_Ozero__class_Ozero(_1141724)), _1141728)))], (20237 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), c_Groups_Ozero__class_Ozero(_1141724)), _1141726)))]], 20240 ^ _776541 : [(20243 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), _1141728), c_Groups_Ozero__class_Ozero(_1141724))))], (20241 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141724), _1141726), c_Groups_Ozero__class_Ozero(_1141724))))]]]]], (38483 ^ _776541) ^ [_1514334, _1514336, _1514338] : [c_Wellfounded_OwfP(_1514334, _1514336), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1514334, _1514336), _1514338)))], (34803 ^ _776541) ^ [_1425899, _1425901, _1425903, _1425905] : [class_Rings_Osemiring__1(_1425899), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1425899, _1425901, hAPP(c_Nat_OSuc, _1425903), _1425905) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1425899, _1425901, _1425903, hAPP(_1425901, _1425905)))], (16318 ^ _776541) ^ [_1071045, _1071047, _1071049] : [class_Groups_Oab__group__add(_1071045), 16321 ^ _776541 : [(16328 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071045), _1071047), _1071049) = c_Groups_Ozero__class_Ozero(_1071045), -(_1071047 = _1071049)], (16322 ^ _776541) ^ [] : [_1071047 = _1071049, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071045), _1071047), _1071049) = c_Groups_Ozero__class_Ozero(_1071045))]]], (24377 ^ _776541) ^ [_1217392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217392)), -(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), _1217392))))], (7850 ^ _776541) ^ [_908716, _908718, _908720] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_908716, tc_HOL_Obool)), _908718), _908720) = c_Orderings_Obot__class_Obot(tc_fun(_908716, tc_HOL_Obool)), 7853 ^ _776541 : [(7854 ^ _776541) ^ [_908840] : [hBOOL(hAPP(hAPP(c_member(_908716), _908840), _908718)), 7857 ^ _776541 : [(7858 ^ _776541) ^ [_908930] : [hBOOL(hAPP(hAPP(c_member(_908716), _908930), _908720)), _908840 = _908930]]]]], (8100 ^ _776541) ^ [_914400, _914402, _914404] : [8102 ^ _776541 : [(8105 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914400, tc_HOL_Obool)), 8101 ^ [_914400, _914402, _914404]), _914404) = c_Orderings_Obot__class_Obot(tc_fun(_914400, tc_HOL_Obool))], (8103 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_914400, tc_HOL_Obool)), 8101 ^ [_914400, _914402, _914404]), _914402)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914400, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_914400, tc_HOL_Obool), _914402)), _914404) = c_Orderings_Obot__class_Obot(tc_fun(_914400, tc_HOL_Obool)))], (4622 ^ _776541) ^ [_846775, _846777, _846779, _846781, _846783, _846785, _846787, _846789] : [-(c_Product__Type_Oscomp(_846789, _846785, _846781, _846777) = c_Product__Type_Oscomp(_846787, _846783, _846779, _846775)), _846789 = _846787, _846785 = _846783, _846781 = _846779, _846777 = _846775], (29267 ^ _776541) ^ [] : [-(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))))], (3184 ^ _776541) ^ [_823942, _823944, _823946, _823948] : [-(c_Big__Operators_Olattice__class_OInf__fin(_823948, _823944) = c_Big__Operators_Olattice__class_OInf__fin(_823946, _823942)), _823948 = _823946, _823944 = _823942], (5376 ^ _776541) ^ [_858676, _858678] : [_858678 = _858676, -(c_Finite__Set_Ofinite(_858678) = c_Finite__Set_Ofinite(_858676))], (14883 ^ _776541) ^ [_1044943, _1044945, _1044947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044943), _1044945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044943), _1044947)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044945), _1044947))))], (37674 ^ _776541) ^ [_1493841, _1493843, _1493845, _1493847] : [c_Fun_Oinj__on(_1493841, _1493843, _1493845, c_Orderings_Otop__class_Otop(tc_fun(_1493841, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493843, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493841, _1493843, _1493845), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1493841, tc_HOL_Obool)), _1493847))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1493843, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493841, _1493843, _1493845), _1493847)))))], (33062 ^ _776541) ^ [_1380579, _1380581] : [-(hAPP(c_Set_Oimage(_1380579, _1380579, c_COMBI(_1380579)), _1380581) = _1380581)], (38588 ^ _776541) ^ [_1517431, _1517433, _1517435, _1517437] : [hBOOL(hAPP(hAPP(c_member(_1517433), _1517437), hAPP(c_Relation_ORange(_1517431, _1517433), _1517435))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1517431, _1517433, hAPP(hAPP(c_COMBC(_1517431, tc_fun(tc_prod(_1517431, _1517433), tc_HOL_Obool), tc_fun(_1517433, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517433, tc_fun(tc_fun(tc_prod(_1517431, _1517433), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517431, _1517433), tc_HOL_Obool), tc_fun(_1517433, tc_HOL_Obool)), _1517431), c_COMBC(_1517433, tc_fun(tc_prod(_1517431, _1517433), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517433, tc_prod(_1517431, _1517433)), tc_fun(_1517433, tc_fun(tc_fun(tc_prod(_1517431, _1517433), tc_HOL_Obool), tc_HOL_Obool)), _1517431), hAPP(c_COMBB(tc_prod(_1517431, _1517433), tc_fun(tc_fun(tc_prod(_1517431, _1517433), tc_HOL_Obool), tc_HOL_Obool), _1517433), c_member(tc_prod(_1517431, _1517433)))), c_Product__Type_OPair(_1517431, _1517433)))), _1517435)), _1517437)))], (14228 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (41729 ^ _776541) ^ [_1598288, _1598290, _1598292, _1598294, _1598296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598288), tc_List_Olist(_1598288))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598288), tc_List_Olist(_1598288)), _1598290), _1598292)), hAPP(c_List_Olexn(_1598288, _1598294), _1598296))), 41732 ^ _776541 : [(41735 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598288)), _1598292) = _1598296)], (41733 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598288)), _1598290) = _1598296)]]], (32484 ^ _776541) ^ [_1361702, _1361704, _1361706, _1361708] : [hBOOL(hAPP(hAPP(c_member(_1361702), _1361708), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361702, tc_HOL_Obool)), _1361704), _1361706))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361702, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1361702, tc_fun(_1361702, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361702)), _1361704)), hAPP(hAPP(c_COMBC(_1361702, tc_fun(_1361702, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361702)), _1361706)), _1361708)))], (26797 ^ _776541) ^ [_1259728, _1259730] : [c_Nat__Transfer_Ois__nat(_1259728), c_Nat__Transfer_Ois__nat(_1259730), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259728), _1259730)))], (39538 ^ _776541) ^ [_1543337, _1543339, _1543341, _1543343, _1543345, _1543347] : [-(_1543337 = c_Orderings_Obot__class_Obot(tc_fun(_1543339, tc_HOL_Obool))), 39544 ^ _776541 : [(39547 ^ _776541) ^ [] : [c_Fun_Oinj__on(_1543341, _1543343, _1543345, hAPP(_1543347, 39543 ^ [_1543337, _1543339, _1543341, _1543343, _1543345, _1543347]))], (39545 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543339), 39543 ^ [_1543337, _1543339, _1543341, _1543343, _1543345, _1543347]), _1543337)))]], -(c_Fun_Oinj__on(_1543341, _1543343, _1543345, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1543339, tc_fun(_1543341, tc_HOL_Obool)), _1543337), _1543347)))], (648 ^ _776541) ^ [_786295, _786297, _786299, _786301, _786303, _786305, _786307, _786309] : [-(c_Nat__Transfer_Otransfer__morphism(_786307, _786303, _786299, _786295)), c_Nat__Transfer_Otransfer__morphism(_786309, _786305, _786301, _786297), _786309 = _786307, _786305 = _786303, _786301 = _786299, _786297 = _786295], (45255 ^ _776541) ^ [_1682865, _1682867] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1682865), _1682867) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682865)), hAPP(c_Code__Numeral_Onat__of, _1682867))))], (44106 ^ _776541) ^ [_1658838, _1658840, _1658842] : [-(_1658838 = c_List_Olist_ONil(_1658840)), -(hAPP(c_List_Ohd(_1658840), hAPP(hAPP(c_List_Oappend(_1658840), _1658838), _1658842)) = hAPP(c_List_Ohd(_1658840), _1658838))], (37010 ^ _776541) ^ [_1479831, _1479833, _1479835] : [c_Equiv__Relations_Oequivp(_1479831, _1479833), -(hBOOL(hAPP(hAPP(_1479833, _1479835), _1479835)))], (40925 ^ _776541) ^ [_1578039, _1578041, _1578043, _1578045, _1578047] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578039, _1578039)), hAPP(hAPP(c_Product__Type_OPair(_1578039, _1578039), _1578041), _1578043)), c_Transitive__Closure_Ortrancl(_1578039, _1578045))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578039, _1578039)), hAPP(hAPP(c_Product__Type_OPair(_1578039, _1578039), _1578043), _1578047)), c_Transitive__Closure_Otrancl(_1578039, _1578045))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578039, _1578039)), hAPP(hAPP(c_Product__Type_OPair(_1578039, _1578039), _1578041), _1578047)), c_Transitive__Closure_Otrancl(_1578039, _1578045))))], (11792 ^ _776541) ^ [_983146, _983148, _983150] : [class_Lattices_Olattice(_983146), hBOOL(hAPP(c_Finite__Set_Ofinite(_983146), _983148)), hBOOL(hAPP(hAPP(c_member(_983146), _983150), _983148)), 11803 ^ _776541 : [(11810 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983146, tc_HOL_Obool)), _983148), hAPP(hAPP(c_Set_Oinsert(_983146), _983150), c_Orderings_Obot__class_Obot(tc_fun(_983146, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_983146, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_983146, _983148) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_983146), _983150), c_Big__Operators_Olattice__class_OInf__fin(_983146, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983146, tc_HOL_Obool)), _983148), hAPP(hAPP(c_Set_Oinsert(_983146), _983150), c_Orderings_Obot__class_Obot(tc_fun(_983146, tc_HOL_Obool)))))))], (11804 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983146, tc_HOL_Obool)), _983148), hAPP(hAPP(c_Set_Oinsert(_983146), _983150), c_Orderings_Obot__class_Obot(tc_fun(_983146, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_983146, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_983146, _983148) = _983150)]]], (29655 ^ _776541) ^ [_1308152, _1308154, _1308156] : [class_Rings_Olinordered__idom(_1308152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308152), _1308154), c_Groups_Ozero__class_Ozero(_1308152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308152), hAPP(hAPP(c_Power_Opower__class_Opower(_1308152), _1308154), 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)))), _1308156)))), c_Groups_Ozero__class_Ozero(_1308152))))], (25085 ^ _776541) ^ [_1230662] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230662), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6606 ^ _776541) ^ [_883524, _883526, _883528] : [class_Orderings_Olinorder(_883524), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883524), _883526), _883528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883524), _883528), _883526)))], (18530 ^ _776541) ^ [_1110026, _1110028] : [hAPP(c_Finite__Set_Ocard(_1110026), _1110028) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1110028 = c_Orderings_Obot__class_Obot(tc_fun(_1110026, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110026), _1110028))], (434 ^ _776541) ^ [_783090, _783092] : [-(class_Rings_Oinverse(_783090)), _783092 = _783090, class_Rings_Oinverse(_783092)], (11644 ^ _776541) ^ [_980210, _980212, _980214] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980210), _980212)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980210), _980214)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980210), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980210, tc_HOL_Obool)), _980212), _980214))))], (18290 ^ _776541) ^ [_1105451, _1105453, _1105455, _1105457] : [class_Rings_Olinordered__semiring__strict(_1105451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105451), _1105453), _1105455)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105451), _1105457), _1105455))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105451), c_Groups_Ozero__class_Ozero(_1105451)), _1105455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105451), _1105453), _1105457)))], (7356 ^ _776541) ^ [_897040, _897042] : [class_Orderings_Olinorder(_897040), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897040, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_897040), _897042), c_Orderings_Obot__class_Obot(tc_fun(_897040, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_897040), _897042)) = hAPP(c_SetInterval_Oord__class_OatLeast(_897040), _897042))], (39449 ^ _776541) ^ [_1540860, _1540862, _1540864, _1540866, _1540868, _1540870, _1540872, _1540874, _1540876] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540860, _1540862)), hAPP(hAPP(c_Product__Type_OPair(_1540860, _1540862), _1540864), _1540866)), _1540868)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540870, _1540872)), hAPP(hAPP(c_Product__Type_OPair(_1540870, _1540872), hAPP(_1540874, _1540864)), hAPP(_1540876, _1540866))), hAPP(c_Set_Oimage(tc_prod(_1540860, _1540862), tc_prod(_1540870, _1540872), c_Product__Type_Omap__pair(_1540860, _1540870, _1540862, _1540872, _1540874, _1540876)), _1540868))))], (39111 ^ _776541) ^ [_1530482, _1530484, _1530486, _1530488, _1530490, _1530492, _1530494, _1530496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530482, _1530484), tc_HOL_Obool)), _1530486), hAPP(hAPP(c_Product__Type_OSigma(_1530482, _1530484), _1530488), hAPP(c_COMBK(tc_fun(_1530484, tc_HOL_Obool), _1530482), _1530490)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530484, _1530492), tc_HOL_Obool)), _1530494), hAPP(hAPP(c_Product__Type_OSigma(_1530484, _1530492), _1530490), hAPP(c_COMBK(tc_fun(_1530492, tc_HOL_Obool), _1530484), _1530496)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530482, _1530492), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530482, _1530484, _1530492), _1530486), _1530494)), hAPP(hAPP(c_Product__Type_OSigma(_1530482, _1530492), _1530488), hAPP(c_COMBK(tc_fun(_1530492, tc_HOL_Obool), _1530482), _1530496)))))], (16074 ^ _776541) ^ [_1067191, _1067193] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067191)), _1067193) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067191), _1067193)))], (6877 ^ _776541) ^ [_888110, _888112, _888114] : [class_Orderings_Oorder(_888110), 6880 ^ _776541 : [(6887 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888110), _888112), _888114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888110, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_888110), _888112)), hAPP(c_SetInterval_Oord__class_OatMost(_888110), _888114))))], (6881 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888110, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_888110), _888112)), hAPP(c_SetInterval_Oord__class_OatMost(_888110), _888114))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888110), _888112), _888114)))]]], (52029 ^ _776541) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (16358 ^ _776541) ^ [_1071640] : [class_Groups_Ogroup__add(_1071640), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1071640), c_Groups_Ozero__class_Ozero(_1071640)) = c_Groups_Ozero__class_Ozero(_1071640))], (40959 ^ _776541) ^ [_1578728, _1578730, _1578732, _1578734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578728, _1578728)), hAPP(hAPP(c_Product__Type_OPair(_1578728, _1578728), _1578730), _1578732)), c_Transitive__Closure_Ortrancl(_1578728, _1578734))), hBOOL(hAPP(hAPP(c_member(_1578728), _1578732), c_Wellfounded_Oacc(_1578728, _1578734))), -(hBOOL(hAPP(hAPP(c_member(_1578728), _1578730), c_Wellfounded_Oacc(_1578728, _1578734))))], (14813 ^ _776541) ^ [_1043614, _1043616, _1043618] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043614), _1043616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043618), _1043616)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043614), _1043618))], (9542 ^ _776541) ^ [_940252, _940254, _940256] : [class_Orderings_Oorder(_940252), -(_940254 = _940256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940252), _940254), _940256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940252), _940254), _940256)))], (40399 ^ _776541) ^ [_1564145, _1564147, _1564149] : [-(c_Hilbert__Choice_OEps(tc_prod(_1564145, _1564147), _1564149) = c_Hilbert__Choice_OEps(tc_prod(_1564145, _1564147), hAPP(c_Product__Type_Oprod_Oprod__case(_1564145, _1564147, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1564147, tc_prod(_1564145, _1564147)), tc_fun(_1564147, tc_HOL_Obool), _1564145), hAPP(c_COMBB(tc_prod(_1564145, _1564147), tc_HOL_Obool, _1564147), _1564149)), c_Product__Type_OPair(_1564145, _1564147)))))], (46333 ^ _776541) ^ [_1708382, _1708384, _1708386] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1708382), c_List_Oupt(_1708384, _1708386)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708384), _1708382), _1708386))], (6051 ^ _776541) ^ [_873240, _873242, _873244, _873246, _873248] : [-(hBOOL(hAPP(hAPP(c_member(_873240), _873242), c_SetInterval_Oord_OatLeastAtMost(_873240, _873244, _873246, _873248)))), hBOOL(hAPP(hAPP(_873244, _873246), _873242)), hBOOL(hAPP(hAPP(_873244, _873242), _873248))], (12538 ^ _776541) ^ [_997080, _997082, _997084] : [class_Lattices_Olattice(_997080), hAPP(_997082, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_997080), 12543 ^ [_997080, _997082, _997084]), 12544 ^ [_997080, _997082, _997084])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_997080), hAPP(_997082, 12543 ^ [_997080, _997082, _997084])), hAPP(_997082, 12544 ^ [_997080, _997082, _997084])), hBOOL(hAPP(c_Finite__Set_Ofinite(_997080), _997084)), -(_997084 = c_Orderings_Obot__class_Obot(tc_fun(_997080, tc_HOL_Obool))), -(hAPP(_997082, c_Big__Operators_Olattice__class_OSup__fin(_997080, _997084)) = c_Big__Operators_Olattice__class_OSup__fin(_997080, hAPP(c_Set_Oimage(_997080, _997080, _997082), _997084)))], (17975 ^ _776541) ^ [_1099779, _1099781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1099781), _1099779)), _1099781)))], (14628 ^ _776541) ^ [_1040333, _1040335, _1040337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040333), _1040335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040333), _1040337)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040335), _1040337))))], (51495 ^ _776541) ^ [_1818666, _1818668] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818666), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818668))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818666), _1818668)))], (49726 ^ _776541) ^ [_1781533, _1781535, _1781537] : [c_Relation_Osym(_1781533, _1781535), c_Relation_Osym(_1781533, _1781537), -(c_Relation_Osym(_1781533, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1781533, _1781533), tc_HOL_Obool)), _1781535), _1781537)))], (47353 ^ _776541) ^ [_1728633, _1728635, _1728637] : [hBOOL(hAPP(c_List_Odistinct(_1728633), _1728635)), hBOOL(hAPP(hAPP(c_member(_1728633), _1728637), hAPP(c_List_Oset(_1728633), _1728635))), -(c_List_OdropWhile(_1728633, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728633), c_fNot), hAPP(hAPP(c_COMBC(_1728633, _1728633, tc_HOL_Obool), c_fequal), _1728637)), hAPP(c_List_Orev(_1728633), _1728635)) = hAPP(hAPP(c_List_Olist_OCons(_1728633), _1728637), hAPP(c_List_Orev(_1728633), c_List_OtakeWhile(_1728633, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728633), c_fNot), hAPP(hAPP(c_COMBC(_1728633, _1728633, tc_HOL_Obool), c_fequal), _1728637)), _1728635))))], (16979 ^ _776541) ^ [_1082118, _1082120, _1082122, _1082124, _1082126] : [class_Rings_Oordered__semiring(_1082118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082118), _1082120), _1082122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082118), _1082124), _1082126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082118), c_Groups_Ozero__class_Ozero(_1082118)), _1082120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082118), c_Groups_Ozero__class_Ozero(_1082118)), _1082124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082118), _1082120), _1082124)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082118), _1082122), _1082126))))], (18570 ^ _776541) ^ [_1110726, _1110728, _1110730] : [-(hBOOL(hAPP(_1110726, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110728), _1110730)))), 18573 ^ _776541 : [(18576 ^ _776541) ^ [] : [hBOOL(hAPP(_1110726, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18574 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110728), _1110730)))]], 18578 ^ _776541 : [(18581 ^ _776541) ^ [] : [hBOOL(hAPP(_1110726, 18577 ^ [_1110726, _1110728, _1110730]))], (18579 ^ _776541) ^ [] : [-(_1110728 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110730), 18577 ^ [_1110726, _1110728, _1110730]))]]], (39049 ^ _776541) ^ [_1528593, _1528595, _1528597, _1528599, _1528601, _1528603] : [hBOOL(hAPP(hAPP(c_member(_1528593), _1528595), _1528597)), 39052 ^ _776541 : [(39059 ^ _776541) ^ [] : [_1528601 = _1528603, -(hAPP(hAPP(c_Product__Type_OSigma(_1528599, _1528593), _1528601), hAPP(c_COMBK(tc_fun(_1528593, tc_HOL_Obool), _1528599), _1528597)) = hAPP(hAPP(c_Product__Type_OSigma(_1528599, _1528593), _1528603), hAPP(c_COMBK(tc_fun(_1528593, tc_HOL_Obool), _1528599), _1528597)))], (39053 ^ _776541) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1528599, _1528593), _1528601), hAPP(c_COMBK(tc_fun(_1528593, tc_HOL_Obool), _1528599), _1528597)) = hAPP(hAPP(c_Product__Type_OSigma(_1528599, _1528593), _1528603), hAPP(c_COMBK(tc_fun(_1528593, tc_HOL_Obool), _1528599), _1528597)), -(_1528601 = _1528603)]]], (14196 ^ _776541) ^ [_1031902] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1031902))))], (38564 ^ _776541) ^ [_1516335, _1516337] : [c_Wellfounded_Owf(_1516335, _1516337), -(c_Wellfounded_OwfP(_1516335, c_FunDef_Oin__rel(_1516335, _1516335, _1516337)))], (26831 ^ _776541) ^ [_1260172, _1260174] : [c_Nat__Transfer_Ois__nat(_1260172), c_Nat__Transfer_Ois__nat(_1260174), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1260172), _1260174)))], (41668 ^ _776541) ^ [_1596969, _1596971, _1596973] : [-(c_Product__Type_Ointernal__split(_1596969, _1596971, _1596973) = c_Product__Type_Oprod_Oprod__case(_1596969, _1596971, _1596973))], (6700 ^ _776541) ^ [_884974, _884976, _884978, _884980] : [class_Orderings_Oorder(_884974), _884976 = _884978, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884974), _884980), _884978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884974), _884980), _884976)))], (45014 ^ _776541) ^ [_1678082, _1678084, _1678086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678084)), _1678086))), -(hAPP(c_Random_Opick(_1678084, hAPP(hAPP(c_List_Omap(_1678084, tc_prod(tc_Code__Numeral_Ocode__numeral, _1678084)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1678084), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1678086)), hAPP(c_Code__Numeral_Oof__nat, _1678082)) = hAPP(hAPP(c_List_Onth(_1678084), _1678086), _1678082))], (29119 ^ _776541) ^ [_1298410] : [-(c_Int_Osucc(c_Int_OBit0(_1298410)) = c_Int_OBit1(_1298410))], (50105 ^ _776541) ^ [_1788843, _1788845, _1788847] : [c_Fun_Oinj__on(_1788843, _1788845, _1788847, c_Orderings_Otop__class_Otop(tc_fun(_1788843, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1788845, _1788843, c_Hilbert__Choice_Oinv__into(_1788843, _1788845, c_Orderings_Otop__class_Otop(tc_fun(_1788843, tc_HOL_Obool)), _1788847)), c_Orderings_Otop__class_Otop(tc_fun(_1788845, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1788843, tc_HOL_Obool)))], (47301 ^ _776541) ^ [_1727426, _1727428, _1727430, _1727432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727428)), c_List_OtakeWhile(_1727428, _1727430, _1727432)))), -(hAPP(hAPP(c_List_Onth(_1727428), c_List_OtakeWhile(_1727428, _1727430, _1727432)), _1727426) = hAPP(hAPP(c_List_Onth(_1727428), _1727432), _1727426))], (38442 ^ _776541) ^ [_1513474, _1513476] : [-(c_Nitpick_Onumber__of__frac(_1513474, _1513476) = c_Nitpick_OAbs__Frac(_1513474, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1513476), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9370 ^ _776541) ^ [_937752, _937754, _937756, _937758] : [-(c_Nitpick_Ofold__graph_H(_937752, _937754, _937756, _937758, c_Orderings_Obot__class_Obot(tc_fun(_937752, tc_HOL_Obool)), _937758))], (11078 ^ _776541) ^ [_968148, _968150, _968152] : [class_Rings_Oring(_968148), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968148), hAPP(c_Groups_Ouminus__class_Ouminus(_968148), _968150)), hAPP(c_Groups_Ouminus__class_Ouminus(_968148), _968152)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968148), _968150), _968152))], (13688 ^ _776541) ^ [_1020308, _1020310, _1020312, _1020314] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020308), 13691 ^ _776541 : [(13698 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020308), _1020310), _1020314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020308), _1020310), _1020312)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020308), _1020314), _1020312))))], (13692 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020308), _1020310), _1020312)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020308), _1020314), _1020312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020308), _1020310), _1020314)))]]], (22893 ^ _776541) ^ [_1191345, _1191347, _1191349] : [class_Rings_Olinordered__semidom(_1191345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191345), c_Groups_Ozero__class_Ozero(_1191345)), _1191347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191345), _1191347), c_Groups_Oone__class_Oone(_1191345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191345), _1191347), hAPP(hAPP(c_Power_Opower__class_Opower(_1191345), _1191347), _1191349))), hAPP(hAPP(c_Power_Opower__class_Opower(_1191345), _1191347), _1191349))))], (9060 ^ _776541) ^ [_933164, _933166, _933168, _933170] : [class_Orderings_Oorder(_933164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933164), _933166), _933168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933164), _933170), _933166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933164), _933170), _933168)))], (37773 ^ _776541) ^ [] : [-(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))], (46097 ^ _776541) ^ [_1702409, _1702411, _1702413, _1702415, _1702417] : [-(hAPP(c_List_Ofilter(_1702409, _1702411), hAPP(hAPP(c_List_Omap(_1702413, _1702409), _1702415), _1702417)) = hAPP(hAPP(c_List_Omap(_1702413, _1702409), _1702415), hAPP(c_List_Ofilter(_1702413, hAPP(c_Fun_Ocomp(_1702409, tc_HOL_Obool, _1702413, _1702411), _1702415)), _1702417)))], (42653 ^ _776541) ^ [_1625726, _1625728, _1625730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625726), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1625728))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1625728), _1625726), _1625730)) = 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), _1625728)), _1625730)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1625728), _1625726)))], (51239 ^ _776541) ^ [_1814026, _1814028, _1814030, _1814032, _1814034] : [class_Rings_Ocomm__semiring__1(_1814026), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814026), _1814028), _1814030)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814026), _1814032), _1814034)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814026), _1814028), _1814032)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814026), _1814030), _1814034))))], (52119 ^ _776541) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (40286 ^ _776541) ^ [_1561859, _1561861, _1561863, _1561865, _1561867, _1561869, _1561871] : [c_Finite__Set_Ofolding__idem(_1561859, _1561861, _1561863, _1561865), -(hAPP(c_Fun_Ocomp(_1561861, _1561861, _1561867, hAPP(_1561863, _1561869)), hAPP(c_Fun_Ocomp(_1561861, _1561861, _1561867, hAPP(_1561863, _1561869)), _1561871)) = hAPP(c_Fun_Ocomp(_1561861, _1561861, _1561867, hAPP(_1561863, _1561869)), _1561871))], (19737 ^ _776541) ^ [_1132800, _1132802, _1132804] : [class_Rings_Odivision__ring(_1132800), -(_1132802 = c_Groups_Ozero__class_Ozero(_1132800)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1132800), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132800), _1132804), _1132802)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132800), _1132804), hAPP(c_Groups_Ouminus__class_Ouminus(_1132800), _1132802)))], (43076 ^ _776541) ^ [_1634882, _1634884] : [-(hAPP(hAPP(c_List_Otake(_1634882), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1634884) = c_List_Olist_ONil(_1634882))], (43050 ^ _776541) ^ [_1634479, _1634481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1634479), _1634481)), -(c_List_Oupto(_1634481, _1634479) = c_List_Olist_ONil(tc_Int_Oint))], (52131 ^ _776541) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (37763 ^ _776541) ^ [_1495943, _1495945, _1495947, _1495949] : [c_Fun_Oinj__on(_1495943, tc_fun(tc_fun(_1495943, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1495943, tc_fun(tc_prod(_1495943, _1495943), tc_HOL_Obool), tc_fun(tc_fun(_1495943, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495943, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1495943, _1495943), tc_HOL_Obool), tc_fun(tc_fun(_1495943, tc_HOL_Obool), tc_HOL_Obool)), _1495943), c_Equiv__Relations_Oquotient(_1495943)), hAPP(hAPP(c_COMBC(_1495943, tc_fun(_1495943, tc_HOL_Obool), tc_fun(_1495943, tc_HOL_Obool)), c_Set_Oinsert(_1495943)), c_Orderings_Obot__class_Obot(tc_fun(_1495943, tc_HOL_Obool))))), _1495945), _1495947), hBOOL(hAPP(hAPP(c_member(_1495943), _1495949), _1495947)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495943), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495943, tc_HOL_Obool)), _1495947), hAPP(hAPP(c_Set_Oinsert(_1495943), _1495949), c_Orderings_Obot__class_Obot(tc_fun(_1495943, tc_HOL_Obool))))), _1495945) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1495943, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495943), _1495947), _1495945)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495943), hAPP(hAPP(c_Set_Oinsert(_1495943), _1495949), c_Orderings_Obot__class_Obot(tc_fun(_1495943, tc_HOL_Obool)))), _1495945)))], (49058 ^ _776541) ^ [_1766121, _1766123, _1766125] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766121) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1766121, _1766123, _1766125)], (48120 ^ _776541) ^ [_1745685, _1745687, _1745689] : [c_List_Olist__ex(_1745685, _1745687, _1745689), -(c_List_Olist__ex(_1745685, _1745687, hAPP(c_List_Orev(_1745685), _1745689)))], (50528 ^ _776541) ^ [_1797866, _1797868, _1797870, _1797872] : [c_Fun_Obij__betw(_1797866, _1797868, _1797870, c_Orderings_Obot__class_Obot(tc_fun(_1797866, tc_HOL_Obool)), _1797872), -(_1797872 = c_Orderings_Obot__class_Obot(tc_fun(_1797868, tc_HOL_Obool)))], (14056 ^ _776541) ^ [_1028461, _1028463, _1028465, _1028467, _1028469] : [class_Groups_Ocomm__monoid__add(_1028461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028463), _1028465)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028463, _1028461), _1028467), hAPP(hAPP(c_Set_Oinsert(_1028463), _1028469), _1028465)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028461), hAPP(_1028467, _1028469)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028463, _1028461), _1028467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1028463, tc_HOL_Obool)), _1028465), hAPP(hAPP(c_Set_Oinsert(_1028463), _1028469), c_Orderings_Obot__class_Obot(tc_fun(_1028463, tc_HOL_Obool)))))))], (15406 ^ _776541) ^ [_1054800, _1054802, _1054804] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054800), _1054802)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054800), _1054804)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054800), _1054802)), hAPP(c_Finite__Set_Ocard(_1054800), _1054804)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054800), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054800, tc_HOL_Obool)), _1054802), _1054804))), hAPP(c_Finite__Set_Ocard(_1054800), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054800, tc_HOL_Obool)), _1054802), _1054804))))], (27581 ^ _776541) ^ [_1272681] : [class_Int_Onumber__ring(_1272681), -(c_Groups_Ozero__class_Ozero(_1272681) = hAPP(c_Int_Onumber__class_Onumber__of(_1272681), c_Int_OPls))], (39439 ^ _776541) ^ [_1540575, _1540577, _1540579, _1540581, _1540583, _1540585] : [hAPP(c_Set_Oimage(_1540575, _1540577, _1540579), c_Orderings_Otop__class_Otop(tc_fun(_1540575, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1540577, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1540581, _1540583, _1540585), c_Orderings_Otop__class_Otop(tc_fun(_1540581, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1540583, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1540575, _1540581), tc_prod(_1540577, _1540583), c_Product__Type_Omap__pair(_1540575, _1540577, _1540581, _1540583, _1540579, _1540585)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1540575, _1540581), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1540577, _1540583), tc_HOL_Obool)))], (670 ^ _776541) ^ [_786648, _786650, _786652, _786654, _786656, _786658] : [-(c_List_Olist__ex1(_786656, _786652, _786648)), c_List_Olist__ex1(_786658, _786654, _786650), _786658 = _786656, _786654 = _786652, _786650 = _786648], (29013 ^ _776541) ^ [_1296634, _1296636] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1296634)), c_Int_OBit1(_1296636)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1296634), _1296636)))], (36462 ^ _776541) ^ [_1465935, _1465937, _1465939, _1465941, _1465943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1465939, _1465935)), hAPP(hAPP(c_Product__Type_OPair(_1465939, _1465935), _1465943), _1465937)), _1465941)), -(hBOOL(hAPP(hAPP(c_member(_1465935), _1465937), hAPP(c_Relation_OImage(_1465939, _1465935, _1465941), hAPP(hAPP(c_Set_Oinsert(_1465939), _1465943), c_Orderings_Obot__class_Obot(tc_fun(_1465939, tc_HOL_Obool)))))))], (47617 ^ _776541) ^ [_1734138, _1734140] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1734138)), _1734140)), 47623 ^ _776541 : [(47626 ^ _776541) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1734138), 47622 ^ [_1734138, _1734140]))], (47624 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734138)), 47622 ^ [_1734138, _1734140]), hAPP(c_List_Oset(tc_List_Olist(_1734138)), _1734140))))]], 47630 ^ _776541 : [(47634 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734138)), 47632 ^ [_1734138, _1734140]), hAPP(c_List_Oset(tc_List_Olist(_1734138)), _1734140))))], (47636 ^ _776541) ^ [] : [47629 ^ [_1734138, _1734140] = 47632 ^ [_1734138, _1734140]], (47638 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1734138, tc_HOL_Obool)), hAPP(c_List_Oset(_1734138), 47629 ^ [_1734138, _1734140])), hAPP(c_List_Oset(_1734138), 47632 ^ [_1734138, _1734140])) = c_Orderings_Obot__class_Obot(tc_fun(_1734138, tc_HOL_Obool))], (47631 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734138)), 47629 ^ [_1734138, _1734140]), hAPP(c_List_Oset(tc_List_Olist(_1734138)), _1734140))))]], -(hBOOL(hAPP(c_List_Odistinct(_1734138), c_List_Oconcat(_1734138, _1734140))))], (26078 ^ _776541) ^ [_1247860] : [-(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)), _1247860)) = _1247860)], (8068 ^ _776541) ^ [_913688, _913690, _913692, _913694] : [-(hBOOL(hAPP(hAPP(c_member(_913688), _913690), _913692))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913688, tc_HOL_Obool)), _913692), hAPP(hAPP(c_Set_Oinsert(_913688), _913690), _913694)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913688, tc_HOL_Obool)), _913692), _913694))], (12736 ^ _776541) ^ [_1001199, _1001201, _1001203] : [class_Complete__Lattice_Ocomplete__lattice(_1001199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001199), _1001201)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1001199), _1001203), c_Complete__Lattice_OSup__class_OSup(_1001199, _1001201)) = hAPP(hAPP(c_Finite__Set_Ofold(_1001199, _1001199, c_Lattices_Osemilattice__sup__class_Osup(_1001199)), _1001203), _1001201))], (27979 ^ _776541) ^ [_1279362] : [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), _1279362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1279362)))], (39065 ^ _776541) ^ [_1528946, _1528948, _1528950] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528946, _1528948), c_Orderings_Obot__class_Obot(tc_fun(_1528946, tc_HOL_Obool))), _1528950) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528946, _1528948), tc_HOL_Obool)))], (45672 ^ _776541) ^ [_1692723, _1692725] : [hBOOL(hAPP(c_List_Odistinct(_1692723), _1692725)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1692723, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692723), tc_fun(_1692723, tc_HOL_Obool)), c_List_Oset(_1692723)), c_Enum_Osublists(_1692723, _1692725)))))], (18554 ^ _776541) ^ [_1110442, _1110444, _1110446] : [hBOOL(hAPP(_1110442, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110444), _1110446))), 18557 ^ _776541 : [(18564 ^ _776541) ^ [_1110627] : [_1110444 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110446), _1110627), -(hBOOL(hAPP(_1110442, _1110627)))], (18558 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110444), _1110446)), -(hBOOL(hAPP(_1110442, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (7690 ^ _776541) ^ [_904880, _904882, _904884] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904880, tc_HOL_Obool)), _904882), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904880, tc_HOL_Obool)), _904884), _904882)) = c_Orderings_Obot__class_Obot(tc_fun(_904880, tc_HOL_Obool)))], (50491 ^ _776541) ^ [_1797257, _1797259, _1797261, _1797263, _1797265] : [c_Fun_Obij__betw(_1797257, _1797259, _1797261, _1797263, _1797265), 50494 ^ _776541 : [(50501 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797259), _1797265)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1797257), _1797263)))], (50495 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797257), _1797263)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1797259), _1797265)))]]], (50415 ^ _776541) ^ [_1795861, _1795863, _1795865] : [c_Fun_Obij__betw(_1795861, _1795863, _1795865, c_Orderings_Otop__class_Otop(tc_fun(_1795861, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1795863, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1795861, _1795863, _1795865, c_Orderings_Otop__class_Otop(tc_fun(_1795861, tc_HOL_Obool))))], (12389 ^ _776541) ^ [_994159, _994161, _994163] : [class_Lattices_Olattice(_994159), hBOOL(hAPP(c_Finite__Set_Ofinite(_994159), _994161)), hBOOL(hAPP(c_Finite__Set_Ofinite(_994159), _994163)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994159, tc_HOL_Obool)), _994161), _994163) = c_Orderings_Obot__class_Obot(tc_fun(_994159, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994159), c_Big__Operators_Olattice__class_OInf__fin(_994159, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_994159, tc_HOL_Obool)), _994161), _994163))), c_Big__Operators_Olattice__class_OInf__fin(_994159, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994159, tc_HOL_Obool)), _994161), _994163))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994159), c_Big__Operators_Olattice__class_OInf__fin(_994159, _994161)), c_Big__Operators_Olattice__class_OInf__fin(_994159, _994163)))], (45365 ^ _776541) ^ [_1685654, _1685656, _1685658, _1685660] : [hBOOL(hAPP(c_List_Olistsp(_1685654, hAPP(hAPP(c_COMBS(_1685654, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1685654), c_fconj), _1685656)), _1685658)), _1685660)), 45368 ^ _776541 : [(45371 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1685654, _1685658), _1685660)))], (45369 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1685654, _1685656), _1685660)))]]], (40687 ^ _776541) ^ [_1571481, _1571483, _1571485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571481, _1571481), tc_HOL_Obool)), _1571483), _1571485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571481, _1571481), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1571481, _1571481, _1571481), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1571481, _1571481), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571481, _1571483)), _1571485)), _1571483)), _1571485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571481, _1571481), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571481, _1571483)), _1571485)))], (40937 ^ _776541) ^ [_1578348] : [-(hAPP(c_Relation_ORange(_1578348, _1578348), c_Relation_OId(_1578348)) = c_Orderings_Otop__class_Otop(tc_fun(_1578348, tc_HOL_Obool)))], (30770 ^ _776541) ^ [_1328488, _1328490, _1328492] : [class_Orderings_Olinorder(_1328488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328488), _1328490)), -(_1328490 = c_Orderings_Obot__class_Obot(tc_fun(_1328488, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1328488, hAPP(hAPP(c_Set_Oinsert(_1328488), _1328492), _1328490)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328488), _1328492), c_Big__Operators_Olinorder__class_OMin(_1328488, _1328490)))], (42845 ^ _776541) ^ [_1630155, _1630157, _1630159] : [hBOOL(hAPP(c_List_Odistinct(_1630155), hAPP(hAPP(c_List_Olist_OCons(_1630155), _1630157), _1630159))), 42848 ^ _776541 : [(42851 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1630155), _1630159)))], (42849 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630155), _1630157), hAPP(c_List_Oset(_1630155), _1630159)))]]], (22331 ^ _776541) ^ [_1181310, _1181312, _1181314] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181310), _1181312)), _1181314) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181310), _1181314)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181312), _1181314)))], (36551 ^ _776541) ^ [_1468691] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1468691) = 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), _1468691), 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))))))], (44850 ^ _776541) ^ [_1673840, _1673842, _1673844, _1673846] : [hAPP(hAPP(c_List_Omap(_1673840, _1673842), _1673844), _1673846) = c_List_Olist_ONil(_1673842), -(_1673846 = c_List_Olist_ONil(_1673840))], (33263 ^ _776541) ^ [_1386262, _1386264, _1386266, _1386268] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386262, tc_fun(_1386264, tc_HOL_Obool)), _1386266), _1386268) = c_Orderings_Obot__class_Obot(tc_fun(_1386264, tc_HOL_Obool)), 33266 ^ _776541 : [(33267 ^ _776541) ^ [_1386378] : [hBOOL(hAPP(hAPP(c_member(_1386262), _1386378), _1386266)), -(hAPP(_1386268, _1386378) = c_Orderings_Obot__class_Obot(tc_fun(_1386264, tc_HOL_Obool)))]]], (7512 ^ _776541) ^ [_900360, _900362, _900364, _900366] : [hBOOL(hAPP(hAPP(c_member(_900360), _900362), _900364)), -(hBOOL(hAPP(hAPP(c_member(_900360), _900362), _900366))), -(hBOOL(hAPP(hAPP(c_member(_900360), _900362), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900360, tc_HOL_Obool)), _900364), _900366))))], (42151 ^ _776541) ^ [_1611804, _1611806, _1611808, _1611810] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611804)), hAPP(hAPP(c_List_Olist_OCons(_1611804), _1611806), _1611808)), c_List_Olists(_1611804, _1611810)))), hBOOL(hAPP(hAPP(c_member(_1611804), _1611806), _1611810)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611804)), _1611808), c_List_Olists(_1611804, _1611810)))], (42990 ^ _776541) ^ [_1633410, _1633412, _1633414] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633410), tc_List_Olist(_1633410))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633410), tc_List_Olist(_1633410)), _1633412), c_List_Olist_ONil(_1633410))), c_List_Olistrel(_1633410, _1633414))), -(_1633412 = c_List_Olist_ONil(_1633410))], (38556 ^ _776541) ^ [_1516098, _1516100] : [-(c_Divides_Odivmod__nat(_1516098, _1516100) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1516098, _1516100)))], (39147 ^ _776541) ^ [_1531655, _1531657, _1531659, _1531661, _1531663] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531655, _1531657), _1531659), hAPP(hAPP(c_COMBS(_1531655, tc_fun(_1531657, tc_HOL_Obool), tc_fun(_1531657, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531657, tc_HOL_Obool), tc_fun(tc_fun(_1531657, tc_HOL_Obool), tc_fun(_1531657, tc_HOL_Obool)), _1531655), c_Groups_Ominus__class_Ominus(tc_fun(_1531657, tc_HOL_Obool))), _1531661)), _1531663)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1531655, _1531657), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531655, _1531657), _1531659), _1531661)), hAPP(hAPP(c_Product__Type_OSigma(_1531655, _1531657), _1531659), _1531663)))], (29117 ^ _776541) ^ [_1298379] : [-(c_Int_Osucc(c_Int_OBit1(_1298379)) = c_Int_OBit0(c_Int_Osucc(_1298379)))], (25087 ^ _776541) ^ [_1230688] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230688, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1230688)], (4334 ^ _776541) ^ [_842181, _842183] : [_842183 = _842181, -(c_Set_Oinsert(_842183) = c_Set_Oinsert(_842181))], (13502 ^ _776541) ^ [_1016774, _1016776] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1016774), _1016776))))], (33591 ^ _776541) ^ [] : [-(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)))], (23071 ^ _776541) ^ [_1194548, _1194550] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194548)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194550))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1194548), _1194550)))], (34626 ^ _776541) ^ [_1421539, _1421541] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421539)), _1421541) = 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), _1421539)), _1421541))], (8038 ^ _776541) ^ [_913099, _913101, _913103, _913105] : [-(hBOOL(hAPP(hAPP(c_member(_913099), _913101), _913103))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913099, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913099), _913101), _913105)), _913103) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913099, tc_HOL_Obool)), _913105), _913103))], (49869 ^ _776541) ^ [_1783716, _1783718] : [c_Equiv__Relations_Opart__equivp(_1783716, _1783718), 49873 ^ _776541 : [(49886 ^ _776541) ^ [_1784058, _1784060] : [-(hBOOL(hAPP(hAPP(_1783718, _1784060), _1784058))), hBOOL(hAPP(hAPP(_1783718, _1784060), _1784060)), hBOOL(hAPP(hAPP(_1783718, _1784058), _1784058)), hAPP(_1783718, _1784060) = hAPP(_1783718, _1784058)], (49876 ^ _776541) ^ [_1783889, _1783891] : [hBOOL(hAPP(hAPP(_1783718, _1783891), _1783889)), 49879 ^ _776541 : [(49884 ^ _776541) ^ [] : [-(hAPP(_1783718, _1783891) = hAPP(_1783718, _1783889))], (49882 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1783718, _1783889), _1783889)))], (49880 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1783718, _1783891), _1783891)))]]], (49874 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1783718, 49872 ^ [_1783716, _1783718]), 49872 ^ [_1783716, _1783718])))]]], (33889 ^ _776541) ^ [_1404530, _1404532] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1404530), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1404532))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1404530), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404532))), 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))))], (7722 ^ _776541) ^ [_905823, _905825, _905827] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_905823, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_905823, tc_HOL_Obool), tc_HOL_Obool)), _905825), _905827)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905823, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_905823, tc_HOL_Obool), _905825)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_905823, tc_HOL_Obool), _905827)))], (51483 ^ _776541) ^ [_1818443, _1818445] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818443), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818445))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818445), _1818443)))], (11550 ^ _776541) ^ [_978431] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_978431)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_978431), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_978431), c_Orderings_Otop__class_Otop(tc_fun(_978431, tc_HOL_Obool)))))], (45187 ^ _776541) ^ [_1681735] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1681735)) = _1681735)], (830 ^ _776541) ^ [_788966, _788968, _788970, _788972] : [-(c_Predicate_Otransp(_788970, _788966)), c_Predicate_Otransp(_788972, _788968), _788972 = _788970, _788968 = _788966], (26585 ^ _776541) ^ [_1256423] : [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, _1256423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1256423)))], (35070 ^ _776541) ^ [_1431075, _1431077, _1431079, _1431081, _1431083, _1431085] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1431075, _1431077, _1431079, _1431081, c_Nitpick_Opair__box_OPairBox(_1431075, _1431077, _1431083, _1431085)) = hAPP(hAPP(_1431081, _1431083), _1431085))], (26719 ^ _776541) ^ [_1258635, _1258637, _1258639] : [class_Int_Oring__char__0(_1258635), 26722 ^ _776541 : [(26729 ^ _776541) ^ [] : [_1258637 = _1258639, -(hAPP(c_Int_Oring__1__class_Oof__int(_1258635), _1258637) = hAPP(c_Int_Oring__1__class_Oof__int(_1258635), _1258639))], (26723 ^ _776541) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1258635), _1258637) = hAPP(c_Int_Oring__1__class_Oof__int(_1258635), _1258639), -(_1258637 = _1258639)]]], (31753 ^ _776541) ^ [_1347120, _1347122] : [class_Orderings_Olinorder(_1347120), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347120), _1347122)), -(c_Big__Operators_Olinorder__class_OMax(_1347120, _1347122) = hAPP(c_Finite__Set_Ofold1(_1347120, c_Orderings_Oord__class_Omax(_1347120)), _1347122))], (9050 ^ _776541) ^ [_933004, _933006, _933008] : [class_Orderings_Opreorder(_933004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933004), _933006), _933008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933004), _933008), _933006))], (11710 ^ _776541) ^ [_981487, _981489, _981491, _981493] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981487), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981487, tc_HOL_Obool)), _981489), _981493))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981487), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981487, tc_HOL_Obool)), _981489), hAPP(hAPP(c_Set_Oinsert(_981487), _981491), _981493)))))], (14266 ^ _776541) ^ [_1033382, _1033384, _1033386] : [class_Rings_Ocomm__semiring__1(_1033382), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033382), _1033384), _1033386) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033382), _1033386), _1033384))], (28981 ^ _776541) ^ [_1296056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1296056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1296056))))], (39265 ^ _776541) ^ [_1534756, _1534758, _1534760, _1534762, _1534764, _1534766] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1534756, _1534758), hAPP(hAPP(c_Set_Oinsert(_1534756), _1534760), _1534762)), hAPP(c_COMBK(tc_fun(_1534758, tc_HOL_Obool), _1534756), hAPP(hAPP(c_Set_Oinsert(_1534758), _1534764), _1534766))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1534756, _1534758)), hAPP(hAPP(c_Product__Type_OPair(_1534756, _1534758), _1534760), _1534764)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1534756, _1534758), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1534756, _1534758), _1534762), hAPP(c_COMBK(tc_fun(_1534758, tc_HOL_Obool), _1534756), hAPP(hAPP(c_Set_Oinsert(_1534758), _1534764), _1534766)))), hAPP(hAPP(c_Product__Type_OSigma(_1534756, _1534758), hAPP(hAPP(c_Set_Oinsert(_1534756), _1534760), _1534762)), hAPP(c_COMBK(tc_fun(_1534758, tc_HOL_Obool), _1534756), _1534766)))))], (6818 ^ _776541) ^ [_886932, _886934, _886936] : [class_Complete__Lattice_Ocomplete__lattice(_886932), 6824 ^ _776541 : [(6827 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886932), _886936), 6823 ^ [_886932, _886934, _886936]))], (6825 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886932), 6823 ^ [_886932, _886934, _886936]), _886934)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886932), _886936), c_Complete__Lattice_OInf__class_OInf(_886932, _886934))))], (48794 ^ _776541) ^ [_1760057, _1760059, _1760061, _1760063, _1760065] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1760057, _1760059, _1760061) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1760057, _1760063, _1760065)), _1760059 = _1760063, _1760061 = _1760065], (33174 ^ _776541) ^ [_1384261, _1384263, _1384265] : [hBOOL(hAPP(hAPP(c_member(_1384261), _1384263), hAPP(c_Set_OCollect(_1384261), _1384265))), -(hBOOL(hAPP(_1384265, _1384263)))], (10617 ^ _776541) ^ [_959127, _959129] : [class_Lattices_Oboolean__algebra(_959127), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959127), hAPP(c_Groups_Ouminus__class_Ouminus(_959127), _959129)), _959129) = c_Orderings_Obot__class_Obot(_959127))], (22303 ^ _776541) ^ [_1180868, _1180870] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180868)), _1180870) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180868), _1180870)))], (49119 ^ _776541) ^ [_1767488, _1767490, _1767492] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1767488, _1767490, _1767492, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1767490)], (7822 ^ _776541) ^ [_908130, _908132] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908130, tc_HOL_Obool)), _908132), _908132) = c_Orderings_Obot__class_Obot(tc_fun(_908130, tc_HOL_Obool)))], (7998 ^ _776541) ^ [_912001, _912003] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912001, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_912001, tc_HOL_Obool))), _912003) = _912003)], (21821 ^ _776541) ^ [_1171919, _1171921] : [-(_1171919 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1171921), _1171919) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1171921), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1171921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171919), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (38862 ^ _776541) ^ [_1523879, _1523881, _1523883, _1523885] : [hBOOL(hAPP(hAPP(c_member(_1523879), _1523881), hAPP(c_Relation_ODomain(_1523879, _1523883), _1523885))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523879, _1523883)), hAPP(hAPP(c_Product__Type_OPair(_1523879, _1523883), _1523881), 38865 ^ [_1523879, _1523881, _1523883, _1523885])), _1523885)))], (6925 ^ _776541) ^ [_888935, _888937, _888939] : [class_Orderings_Olinorder(_888935), 6928 ^ _776541 : [(6935 ^ _776541) ^ [] : [_888937 = _888939, -(hAPP(c_SetInterval_Oord__class_OatLeast(_888935), _888937) = hAPP(c_SetInterval_Oord__class_OatLeast(_888935), _888939))], (6929 ^ _776541) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_888935), _888937) = hAPP(c_SetInterval_Oord__class_OatLeast(_888935), _888939), -(_888937 = _888939)]]], (38245 ^ _776541) ^ [_1508891, _1508893] : [c_Wellfounded_Owf(_1508891, _1508893), 38248 ^ _776541 : [(38249 ^ _776541) ^ [_1508960] : [-(hBOOL(hAPP(hAPP(c_member(_1508891), _1508960), c_Wellfounded_Oacc(_1508891, _1508893))))]]], (40040 ^ _776541) ^ [_1556168, _1556170, _1556172, _1556174, _1556176, _1556178] : [c_Finite__Set_Ofolding(_1556168, _1556170, _1556172, _1556174), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556168), _1556176)), hBOOL(hAPP(hAPP(c_member(_1556168), _1556178), _1556176)), -(hAPP(_1556174, _1556176) = hAPP(c_Fun_Ocomp(_1556170, _1556170, _1556170, hAPP(_1556174, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556168, tc_HOL_Obool)), _1556176), hAPP(hAPP(c_Set_Oinsert(_1556168), _1556178), c_Orderings_Obot__class_Obot(tc_fun(_1556168, tc_HOL_Obool)))))), hAPP(_1556172, _1556178)))], (50979 ^ _776541) ^ [_1808922, _1808924] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808922), _1808924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1808924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1808922), _1808924)))], (18976 ^ _776541) ^ [_1118319, _1118321] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118319), hAPP(c_Nat_OSuc, _1118321)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118319), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1118321))], (39077 ^ _776541) ^ [_1529390, _1529392, _1529394, _1529396] : [hAPP(hAPP(c_Product__Type_OSigma(_1529390, _1529392), _1529394), hAPP(c_COMBK(tc_fun(_1529392, tc_HOL_Obool), _1529390), _1529396)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529390, _1529392), tc_HOL_Obool)), -(_1529394 = c_Orderings_Obot__class_Obot(tc_fun(_1529390, tc_HOL_Obool))), -(_1529396 = c_Orderings_Obot__class_Obot(tc_fun(_1529392, tc_HOL_Obool)))], (38195 ^ _776541) ^ [_1507956, _1507958] : [c_Wellfounded_Owf(_1507956, _1507958), -(c_Wellfounded_Owf(tc_fun(_1507956, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1507956, _1507958)))], (11218 ^ _776541) ^ [_971256, _971258, _971260, _971262, _971264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971256, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971256, tc_HOL_Obool)), hAPP(c_Set_Oimage(_971258, _971256, _971260), _971262)), hAPP(c_Set_Oimage(_971258, _971256, _971260), _971264))), hAPP(c_Set_Oimage(_971258, _971256, _971260), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971258, tc_HOL_Obool)), _971262), _971264)))))], (44547 ^ _776541) ^ [_1667564, _1667566, _1667568] : [44548 ^ _776541 : [(44549 ^ _776541) ^ [_1667653, _1667655] : [_1667566 = hAPP(hAPP(c_List_Olist_OCons(_1667564), _1667655), _1667653)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667564), tc_List_Olist(_1667564))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667564), tc_List_Olist(_1667564)), c_List_Olist_ONil(_1667564)), _1667566)), c_List_Olexord(_1667564, _1667568))))], (41300 ^ _776541) ^ [_1586873, _1586875, _1586877] : [c_Relation_Osingle__valued(_1586873, _1586875, _1586877), 41303 ^ _776541 : [(41304 ^ _776541) ^ [_1586994, _1586996] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586873, _1586875)), hAPP(hAPP(c_Product__Type_OPair(_1586873, _1586875), _1586996), _1586994)), _1586877)), 41307 ^ _776541 : [(41308 ^ _776541) ^ [_1587120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586873, _1586875)), hAPP(hAPP(c_Product__Type_OPair(_1586873, _1586875), _1586996), _1587120)), _1586877)), -(_1586994 = _1587120)]]]]], (21102 ^ _776541) ^ [_1158183, _1158185, _1158187, _1158189] : [class_Groups_Ocomm__monoid__mult(_1158183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158185), _1158187)), 21112 ^ _776541 : [(21115 ^ _776541) ^ [] : [hAPP(_1158189, 21111 ^ [_1158183, _1158185, _1158187, _1158189]) = c_Groups_Oone__class_Oone(_1158183)], (21113 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1158185), 21111 ^ [_1158183, _1158185, _1158187, _1158189]), _1158187)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1158183, _1158185, c_Groups_Otimes__class_Otimes(_1158183)), _1158189), c_Groups_Oone__class_Oone(_1158183)), _1158187) = c_Groups_Oone__class_Oone(_1158183))], (43260 ^ _776541) ^ [_1638386, _1638388] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638386)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638388)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638386), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638388)) = c_List_Olist_ONil(tc_Int_Oint))], (28037 ^ _776541) ^ [_1280319, _1280321] : [class_Int_Onumber__ring(_1280319), 28040 ^ _776541 : [(28047 ^ _776541) ^ [] : [c_Int_Oiszero(_1280319, hAPP(c_Int_Onumber__class_Onumber__of(_1280319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1280321), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1280319), _1280321) = c_Groups_Ozero__class_Ozero(_1280319))], (28041 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1280319), _1280321) = c_Groups_Ozero__class_Ozero(_1280319), -(c_Int_Oiszero(_1280319, hAPP(c_Int_Onumber__class_Onumber__of(_1280319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1280321), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (47652 ^ _776541) ^ [_1735128, _1735130] : [-(c_Wellfounded_Owf(_1735128, c_List_Omeasures(_1735128, _1735130)))], (4702 ^ _776541) ^ [_848069, _848071] : [_848071 = _848069, -(c_DSequence_Osingle(_848071) = c_DSequence_Osingle(_848069))], (50369 ^ _776541) ^ [_1794911, _1794913, _1794915, _1794917, _1794919, _1794921, _1794923, _1794925] : [c_Fun_Obij__betw(_1794911, _1794913, _1794915, _1794917, _1794919), c_Fun_Obij__betw(_1794913, _1794921, _1794923, _1794919, _1794925), -(c_Fun_Obij__betw(_1794911, _1794921, hAPP(c_Fun_Ocomp(_1794913, _1794921, _1794911, _1794923), _1794915), _1794917, _1794925))], (24698 ^ _776541) ^ [_1223421, _1223423] : [_1223421 = _1223423, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223421) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223423))], (6457 ^ _776541) ^ [_880853, _880855] : [_880855 = c_Orderings_Obot__class_Obot(tc_fun(_880853, tc_HOL_Obool)), 6460 ^ _776541 : [(6461 ^ _776541) ^ [_880933] : [hBOOL(hAPP(hAPP(c_member(_880853), _880933), _880855))]]], (33082 ^ _776541) ^ [_1381208, _1381210, _1381212, _1381214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1381208, _1381210)), hAPP(hAPP(c_Product__Type_OPair(_1381208, _1381210), _1381212), _1381214)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1381208, _1381210), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381208, tc_fun(_1381210, tc_HOL_Obool))), _1381212), _1381214)))], (3432 ^ _776541) ^ [_827796, _827798, _827800, _827802, _827804, _827806] : [-(c_Enum_On__lists(_827806, _827802, _827798) = c_Enum_On__lists(_827804, _827800, _827796)), _827806 = _827804, _827802 = _827800, _827798 = _827796], (1404 ^ _776541) ^ [_796955, _796957] : [-(class_Lattices_Odistrib__lattice(_796955)), _796957 = _796955, class_Lattices_Odistrib__lattice(_796957)], (14634 ^ _776541) ^ [_1040456, _1040458, _1040460, _1040462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040456), _1040458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040460), _1040462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040456), _1040460)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040458), _1040462))))], (8781 ^ _776541) ^ [_927383, _927385] : [class_Lattices_Obounded__lattice__bot(_927383), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927383), c_Orderings_Obot__class_Obot(_927383)), _927385) = _927385)], (23401 ^ _776541) ^ [_1200598, _1200600, _1200602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200598)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1200600), _1200602)), 23408 ^ _776541 : [(23409 ^ _776541) ^ [_1200794] : [23411 ^ _776541 : [(23417 ^ _776541) ^ [] : [-(_1200794 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23413 ^ [_1200598, _1200600, _1200602, _1200794]), 23410 ^ [_1200598, _1200600, _1200602, _1200794]))], (23415 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23413 ^ [_1200598, _1200600, _1200602, _1200794]), _1200602)))], (23412 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23410 ^ [_1200598, _1200600, _1200602, _1200794]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1200598))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200600), _1200794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200600), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1200794), _1200598))))]]], (33109 ^ _776541) ^ [_1381846, _1381848, _1381850, _1381852, _1381854] : [-(hBOOL(hAPP(hAPP(c_member(_1381846), _1381848), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381850, tc_fun(_1381846, tc_HOL_Obool)), _1381852), _1381854)))), 33110 ^ _776541 : [(33111 ^ _776541) ^ [_1381928] : [hBOOL(hAPP(hAPP(c_member(_1381850), _1381928), _1381852)), hBOOL(hAPP(hAPP(c_member(_1381846), _1381848), hAPP(_1381854, _1381928)))]]], (43751 ^ _776541) ^ [_1649612, _1649614, _1649616, _1649618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649612), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649614)), _1649616))), -(hAPP(hAPP(c_List_Onth(_1649614), hAPP(hAPP(c_List_Oappend(_1649614), _1649616), _1649618)), _1649612) = hAPP(hAPP(c_List_Onth(_1649614), _1649616), _1649612))], (49700 ^ _776541) ^ [_1781159, _1781161] : [c_Relation_Osym(_1781159, _1781161), -(hAPP(c_Relation_Oconverse(_1781159, _1781159), _1781161) = _1781161)], (7556 ^ _776541) ^ [_901282, _901284, _901286, _901288] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901282, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901282, tc_HOL_Obool)), _901284), _901286)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901282, tc_HOL_Obool)), _901288), _901286)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901282, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901282, tc_HOL_Obool)), _901284), _901286)), _901288))], (45561 ^ _776541) ^ [_1690093, _1690095, _1690097, _1690099, _1690101, _1690103, _1690105] : [c_List_Olist__all2(_1690093, _1690095, _1690097, _1690099, _1690101), c_List_Olist__all2(_1690093, _1690095, _1690097, _1690103, _1690105), -(c_List_Olist__all2(_1690093, _1690095, _1690097, hAPP(hAPP(c_List_Oappend(_1690093), _1690099), _1690103), hAPP(hAPP(c_List_Oappend(_1690095), _1690101), _1690105)))], (28019 ^ _776541) ^ [_1280063, _1280065, _1280067] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280063), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280063)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280065)), _1280067)) = 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), _1280063), _1280065))), _1280067))], (38905 ^ _776541) ^ [_1524713, _1524715, _1524717, _1524719, _1524721] : [c_Fun_Oinj__on(_1524713, _1524715, _1524717, c_Orderings_Otop__class_Otop(tc_fun(_1524713, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524715, tc_HOL_Obool)), _1524719), hAPP(c_Set_Oimage(_1524713, _1524715, _1524717), _1524721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524713, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1524713, _1524715, _1524717), _1524719)), _1524721)))], (51543 ^ _776541) ^ [_1819510, _1819512, _1819514, _1819516] : [class_Divides_Osemiring__div(_1819510), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819510), _1819512), _1819514)), 51550 ^ _776541 : [(51557 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819510), _1819512), _1819516)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819510), _1819512), c_Divides_Odiv__class_Omod(_1819510, _1819516, _1819514))))], (51551 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819510), _1819512), c_Divides_Odiv__class_Omod(_1819510, _1819516, _1819514))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819510), _1819512), _1819516)))]]], (14498 ^ _776541) ^ [_1038252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038252), _1038252))], (34379 ^ _776541) ^ [_1416519, _1416521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416519), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416521)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416519)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416521))], (45662 ^ _776541) ^ [_1692369, _1692371, _1692373, _1692375] : [-(hAPP(c_List_Oset(tc_prod(_1692369, _1692371)), c_Enum_Oproduct(_1692369, _1692371, _1692373, _1692375)) = hAPP(hAPP(c_Product__Type_OSigma(_1692369, _1692371), hAPP(c_List_Oset(_1692369), _1692373)), hAPP(c_COMBK(tc_fun(_1692371, tc_HOL_Obool), _1692369), hAPP(c_List_Oset(_1692371), _1692375))))], (4926 ^ _776541) ^ [_851601, _851603, _851605, _851607] : [-(c_Relation_Oconverse(_851607, _851603) = c_Relation_Oconverse(_851605, _851601)), _851607 = _851605, _851603 = _851601], (15968 ^ _776541) ^ [_1065556, _1065558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065556), hAPP(c_Nat_OSuc, _1065558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065556), _1065558))), -(_1065556 = _1065558)], (36490 ^ _776541) ^ [_1466982, _1466984, _1466986, _1466988, _1466990, _1466992] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1466982, _1466982)), hAPP(hAPP(c_Product__Type_OPair(_1466982, _1466982), _1466984), _1466986)), hAPP(hAPP(c_Relation_Oinv__image(_1466988, _1466982), _1466990), _1466992))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1466988, _1466988)), hAPP(hAPP(c_Product__Type_OPair(_1466988, _1466988), hAPP(_1466992, _1466984)), hAPP(_1466992, _1466986))), _1466990)))], (21132 ^ _776541) ^ [_1158724, _1158726, _1158728, _1158730, _1158732, _1158734] : [class_Groups_Oab__semigroup__mult(_1158724), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158726), _1158728)), 21142 ^ _776541 : [(21145 ^ _776541) ^ [] : [hAPP(_1158730, 21141 ^ [_1158724, _1158726, _1158728, _1158730, _1158732, _1158734]) = hAPP(_1158732, 21141 ^ [_1158724, _1158726, _1158728, _1158730, _1158732, _1158734])], (21143 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1158726), 21141 ^ [_1158724, _1158726, _1158728, _1158730, _1158732, _1158734]), _1158728)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1158724, _1158726, c_Groups_Otimes__class_Otimes(_1158724)), _1158730), _1158734), _1158728) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1158724, _1158726, c_Groups_Otimes__class_Otimes(_1158724)), _1158732), _1158734), _1158728))], (34628 ^ _776541) ^ [_1421584, _1421586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421586)), -(c_Divides_OposDivAlg(_1421584, _1421586) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1421584), _1421586)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1421584, _1421586)))], (29285 ^ _776541) ^ [_1301332] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301332), 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, _1301332)))], (42751 ^ _776541) ^ [_1627950, _1627952, _1627954, _1627956, _1627958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627952)), _1627954))), 42754 ^ _776541 : [(42761 ^ _776541) ^ [] : [-(_1627950 = _1627956), -(hAPP(hAPP(c_List_Onth(_1627952), hAPP(hAPP(c_List_Olist__update(_1627952, _1627954), _1627950), _1627958)), _1627956) = hAPP(hAPP(c_List_Onth(_1627952), _1627954), _1627956))], (42755 ^ _776541) ^ [] : [_1627950 = _1627956, -(hAPP(hAPP(c_List_Onth(_1627952), hAPP(hAPP(c_List_Olist__update(_1627952, _1627954), _1627950), _1627958)), _1627956) = _1627958)]]], (1274 ^ _776541) ^ [_795330, _795332] : [-(class_Int_Onumber__ring(_795330)), _795332 = _795330, class_Int_Onumber__ring(_795332)], (50165 ^ _776541) ^ [_1790287, _1790289, _1790291] : [hAPP(c_Fun_Ocomp(_1790287, _1790289, _1790289, _1790291), c_Hilbert__Choice_Oinv__into(_1790287, _1790289, c_Orderings_Otop__class_Otop(tc_fun(_1790287, tc_HOL_Obool)), _1790291)) = c_Fun_Oid(_1790289), -(hAPP(c_Set_Oimage(_1790287, _1790289, _1790291), c_Orderings_Otop__class_Otop(tc_fun(_1790287, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790289, tc_HOL_Obool)))], (37088 ^ _776541) ^ [_1481372, _1481374, _1481376, _1481378, _1481380, _1481382, _1481384, _1481386, _1481388] : [c_Equiv__Relations_Oequiv(_1481372, _1481374, _1481376), c_Equiv__Relations_Oequiv(_1481378, _1481380, _1481382), c_Equiv__Relations_Ocongruent2(_1481372, _1481378, tc_fun(_1481384, tc_HOL_Obool), _1481376, _1481382, _1481386), hBOOL(hAPP(hAPP(c_member(_1481378), _1481388), _1481380)), -(c_Equiv__Relations_Ocongruent(_1481372, tc_fun(_1481384, tc_HOL_Obool), _1481376, hAPP(hAPP(c_COMBB(tc_fun(_1481378, tc_fun(_1481384, tc_HOL_Obool)), tc_fun(_1481384, tc_HOL_Obool), _1481372), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481378, tc_fun(_1481384, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1481378, _1481378, _1481382), hAPP(hAPP(c_Set_Oinsert(_1481378), _1481388), c_Orderings_Obot__class_Obot(tc_fun(_1481378, tc_HOL_Obool)))))), _1481386)))], (7692 ^ _776541) ^ [_904934, _904936, _904938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904934, tc_HOL_Obool)), _904936), _904938)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904934, tc_HOL_Obool)), _904936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904934, tc_HOL_Obool)), _904938), _904936)) = _904938)], (44044 ^ _776541) ^ [_1657179, _1657181, _1657183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657179), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657181)), _1657183))), -(hAPP(hAPP(c_List_Olist_OCons(_1657181), hAPP(hAPP(c_List_Onth(_1657181), _1657183), _1657179)), hAPP(hAPP(c_List_Odrop(_1657181), hAPP(c_Nat_OSuc, _1657179)), _1657183)) = hAPP(hAPP(c_List_Odrop(_1657181), _1657179), _1657183))], (40629 ^ _776541) ^ [_1569934, _1569936, _1569938, _1569940, _1569942] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569934, _1569934)), hAPP(hAPP(c_Product__Type_OPair(_1569934, _1569934), _1569936), _1569938)), _1569940)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569934, _1569934)), hAPP(hAPP(c_Product__Type_OPair(_1569934, _1569934), _1569938), _1569942)), _1569940)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569934, _1569934)), hAPP(hAPP(c_Product__Type_OPair(_1569934, _1569934), _1569936), _1569942)), c_Transitive__Closure_Otrancl(_1569934, _1569940))))], (33517 ^ _776541) ^ [_1393272, _1393274, _1393276, _1393278, _1393280] : [-(_1393272 = c_Orderings_Obot__class_Obot(tc_fun(_1393274, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393274, tc_fun(_1393276, tc_HOL_Obool)), _1393272), hAPP(hAPP(c_COMBB(tc_fun(_1393276, tc_HOL_Obool), tc_fun(_1393276, tc_HOL_Obool), _1393274), hAPP(c_Set_Oinsert(_1393276), _1393278)), _1393280)) = hAPP(hAPP(c_Set_Oinsert(_1393276), _1393278), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393274, tc_fun(_1393276, tc_HOL_Obool)), _1393272), _1393280)))], (40522 ^ _776541) ^ [_1567353, _1567355, _1567357, _1567359, _1567361, _1567363, _1567365, _1567367, _1567369] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1567353, _1567355, _1567357, _1567359), hAPP(hAPP(c_Product__Type_Oscomp(_1567353, _1567361, _1567363, tc_prod(_1567355, _1567357)), _1567365), _1567367)), _1567369) = hAPP(hAPP(c_Product__Type_Oscomp(_1567353, _1567361, _1567363, _1567359), _1567365), hAPP(hAPP(c_COMBC(_1567361, tc_fun(_1567355, tc_fun(_1567357, _1567359)), tc_fun(_1567363, _1567359)), hAPP(hAPP(c_COMBB(tc_fun(_1567363, tc_prod(_1567355, _1567357)), tc_fun(tc_fun(_1567355, tc_fun(_1567357, _1567359)), tc_fun(_1567363, _1567359)), _1567361), c_Product__Type_Oscomp(_1567363, _1567355, _1567357, _1567359)), _1567367)), _1567369)))], (41270 ^ _776541) ^ [_1586306, _1586308] : [-(c_Relation_Osingle__valued(_1586306, _1586306, c_Relation_OId__on(_1586306, _1586308)))], (36209 ^ _776541) ^ [_1459493, _1459495, _1459497, _1459499, _1459501, _1459503, _1459505] : [-(hAPP(c_Product__Type_Oapfst(_1459493, _1459495, _1459497, _1459499), hAPP(c_Product__Type_Oapsnd(_1459501, _1459497, _1459493, _1459503), _1459505)) = hAPP(hAPP(c_Product__Type_OPair(_1459495, _1459497), hAPP(_1459499, hAPP(c_Product__Type_Ofst(_1459493, _1459501), _1459505))), hAPP(_1459503, hAPP(c_Product__Type_Osnd(_1459493, _1459501), _1459505))))], (27563 ^ _776541) ^ [_1272354, _1272356, _1272358] : [class_Rings_Olinordered__idom(_1272354), -(hAPP(c_Groups_Oabs__class_Oabs(_1272354), hAPP(hAPP(c_Power_Opower__class_Opower(_1272354), hAPP(c_Groups_Ouminus__class_Ouminus(_1272354), _1272356)), _1272358)) = hAPP(c_Groups_Oabs__class_Oabs(_1272354), hAPP(hAPP(c_Power_Opower__class_Opower(_1272354), _1272356), _1272358)))], (50873 ^ _776541) ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647] : [50876 ^ _776541 : [(50883 ^ _776541) ^ [] : [hAPP(hAPP(_1806645, 50874 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647]), 50878 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647]) = hAPP(hAPP(_1806645, 50875 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647]), 50879 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647])], (50881 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1806641, _1806641)), hAPP(hAPP(c_Product__Type_OPair(_1806641, _1806641), 50878 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647]), 50879 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647])), _1806643)))], (50877 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1806637, _1806637)), hAPP(hAPP(c_Product__Type_OPair(_1806637, _1806637), 50874 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647]), 50875 ^ [_1806637, _1806639, _1806641, _1806643, _1806645, _1806647])), _1806639)))]], -(c_Equiv__Relations_Ocongruent2(_1806637, _1806641, _1806647, _1806639, _1806643, _1806645))], (27613 ^ _776541) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (46267 ^ _776541) ^ [_1707318, _1707320] : [c_List_Oupt(_1707318, _1707320) = c_List_Olist_ONil(tc_Nat_Onat), -(_1707320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707320), _1707318)))], (45906 ^ _776541) ^ [_1697432, _1697434, _1697436, _1697438] : [class_Orderings_Olinorder(_1697432), 45909 ^ _776541 : [(45916 ^ _776541) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1697434), _1697438)), -(hBOOL(hAPP(c_List_Odistinct(_1697434), c_List_Olinorder__class_Osort__key(_1697434, _1697432, _1697436, _1697438))))], (45910 ^ _776541) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1697434), c_List_Olinorder__class_Osort__key(_1697434, _1697432, _1697436, _1697438))), -(hBOOL(hAPP(c_List_Odistinct(_1697434), _1697438)))]]], (40847 ^ _776541) ^ [_1576185, _1576187, _1576189] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576185, _1576185)), hAPP(hAPP(c_Product__Type_OPair(_1576185, _1576185), _1576187), _1576189)), c_Relation_OId(_1576185))), -(_1576187 = _1576189)], (41420 ^ _776541) ^ [_1589952, _1589954] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589952, _1589952), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1589954) = _1589954)], (16725 ^ _776541) ^ [_1077384, _1077386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077384), _1077386)), 16728 ^ _776541 : [(16735 ^ _776541) ^ [] : [_1077386 = _1077384, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077386), hAPP(c_Nat_OSuc, _1077384))))], (16729 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077386), hAPP(c_Nat_OSuc, _1077384))), -(_1077386 = _1077384)]]], (37078 ^ _776541) ^ [_1481173, _1481175, _1481177, _1481179, _1481181, _1481183] : [c_Equiv__Relations_Ocongruent(_1481173, _1481175, _1481177, _1481179), hBOOL(hAPP(hAPP(c_member(tc_prod(_1481173, _1481173)), hAPP(hAPP(c_Product__Type_OPair(_1481173, _1481173), _1481181), _1481183)), _1481177)), -(hAPP(_1481179, _1481181) = hAPP(_1481179, _1481183))], (32518 ^ _776541) ^ [_1364155, _1364157, _1364159] : [-(hAPP(c_Set_OCollect(_1364155), hAPP(hAPP(c_COMBS(_1364155, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364155), c_fdisj), _1364157)), _1364159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364155, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1364155), _1364157)), hAPP(c_Set_OCollect(_1364155), _1364159)))], (52459 ^ _776541) ^ [_1830858] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1830858)))], (13964 ^ _776541) ^ [_1026376, _1026378, _1026380, _1026382, _1026384, _1026386] : [class_Rings_Oordered__ring(_1026376), 13967 ^ _776541 : [(13974 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026376), _1026382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026376), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026376), _1026384), _1026378)), _1026380)), _1026386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026376), _1026378), _1026380)), _1026382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026376), _1026384), _1026380)), _1026386))))], (13968 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026376), _1026378), _1026380)), _1026382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026376), _1026384), _1026380)), _1026386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026376), _1026382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026376), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026376), _1026384), _1026378)), _1026380)), _1026386))))]]], (37945 ^ _776541) ^ [_1501052, _1501054, _1501056, _1501058, _1501060, _1501062] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1501052, _1501054, _1501056), _1501058), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501054, _1501056), tc_HOL_Obool)), _1501060), _1501062)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501052, _1501056), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501052, _1501054, _1501056), _1501058), _1501060)), hAPP(hAPP(c_Relation_Orel__comp(_1501052, _1501054, _1501056), _1501058), _1501062)))], (18125 ^ _776541) ^ [_1102433, _1102435] : [_1102433 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102433), _1102435), -(_1102435 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1102433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32876 ^ _776541) ^ [_1375585, _1375587, _1375589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375585, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1375585, tc_fun(_1375585, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375585)), _1375587)), hAPP(hAPP(c_COMBC(_1375585, tc_fun(_1375585, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375585)), _1375589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375585, tc_HOL_Obool)), _1375587), _1375589)))], (47104 ^ _776541) ^ [_1723407, _1723409, _1723411, _1723413] : [_1723409 = hAPP(hAPP(c_List_Oappend(_1723407), hAPP(c_List_Orev(_1723407), _1723413)), hAPP(hAPP(c_List_Olist_OCons(_1723407), _1723411), c_List_Olist_ONil(_1723407))), -(hAPP(c_List_Orev(_1723407), _1723409) = hAPP(hAPP(c_List_Olist_OCons(_1723407), _1723411), _1723413))], (49602 ^ _776541) ^ [_1778837, _1778839] : [c_Relation_Oantisym(_1778837, _1778839), 49605 ^ _776541 : [(49606 ^ _776541) ^ [_1778949, _1778951] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778837, _1778837)), hAPP(hAPP(c_Product__Type_OPair(_1778837, _1778837), _1778951), _1778949)), _1778839)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778837, _1778837)), hAPP(hAPP(c_Product__Type_OPair(_1778837, _1778837), _1778949), _1778951)), _1778839)), -(_1778951 = _1778949)]]], (15302 ^ _776541) ^ [_1052584, _1052586, _1052588, _1052590] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052584), _1052586)), hBOOL(hAPP(hAPP(c_member(_1052584), _1052588), _1052586)), -(hBOOL(hAPP(hAPP(c_member(_1052584), _1052588), _1052590))), -(hAPP(c_Finite__Set_Ocard(_1052584), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052584, tc_HOL_Obool)), _1052586), hAPP(hAPP(c_Set_Oinsert(_1052584), _1052588), _1052590))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1052584), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052584, tc_HOL_Obool)), _1052586), _1052590))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46265 ^ _776541) ^ [_1707277] : [-(c_List_Oupt(_1707277, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (10699 ^ _776541) ^ [_960809, _960811] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960809, tc_HOL_Obool)), _960811) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960809, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_960809, tc_HOL_Obool))), _960811))], (3766 ^ _776541) ^ [_833045, _833047, _833049, _833051] : [-(c_List_Olex(_833051, _833047) = c_List_Olex(_833049, _833045)), _833051 = _833049, _833047 = _833045], (26276 ^ _776541) ^ [_1251097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1251097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251097)))], (34882 ^ _776541) ^ [_1427415, _1427417, _1427419, _1427421, _1427423, _1427425, _1427427, _1427429] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427415, _1427417, _1427419), _1427421), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427423, _1427425, tc_prod(_1427415, _1427417)), _1427427), _1427429)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427423, _1427425, _1427419), hAPP(hAPP(c_COMBB(tc_fun(_1427425, tc_prod(_1427415, _1427417)), tc_fun(_1427425, _1427419), _1427423), hAPP(c_COMBB(tc_prod(_1427415, _1427417), _1427419, _1427425), hAPP(c_Product__Type_Oprod_Oprod__case(_1427415, _1427417, _1427419), _1427421))), _1427427)), _1427429))], (1334 ^ _776541) ^ [_796080, _796082] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_796080)), _796082 = _796080, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_796082)], (52005 ^ _776541) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (44118 ^ _776541) ^ [_1659021, _1659023, _1659025] : [-(_1659021 = c_List_Olist_ONil(_1659023)), -(hAPP(c_List_Ohd(_1659023), hAPP(hAPP(c_List_Oappend(_1659023), _1659021), _1659025)) = hAPP(c_List_Ohd(_1659023), _1659021))], (43304 ^ _776541) ^ [_1639137] : [-(c_List_Olistset(_1639137, c_List_Olist_ONil(tc_fun(_1639137, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639137)), c_List_Olist_ONil(_1639137)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639137), tc_HOL_Obool))))], (49297 ^ _776541) ^ [_1771858, _1771860] : [c_Relation_Otrans(_1771858, _1771860), -(c_Transitive__Closure_Otrancl(_1771858, _1771860) = _1771860)], (4574 ^ _776541) ^ [_846003, _846005, _846007, _846009] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_846009, _846005) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_846007, _846003)), _846009 = _846007, _846005 = _846003], (18005 ^ _776541) ^ [_1100295, _1100297] : [-(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), _1100295), _1100297)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100297))], (33094 ^ _776541) ^ [_1381497, _1381499] : [hBOOL(hAPP(hAPP(c_member(_1381497), _1381499), c_Orderings_Obot__class_Obot(tc_fun(_1381497, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381497, tc_HOL_Obool)), _1381499)))], (14486 ^ _776541) ^ [_1038067, _1038069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038067), _1038069)), _1038067 = _1038069], (23848 ^ _776541) ^ [_1208529, _1208531] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208529)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208531)), _1208529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1208531 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33016 ^ _776541) ^ [_1379320, _1379322] : [-(hAPP(c_Set_OCollect(_1379320), hAPP(c_fequal, _1379322)) = hAPP(hAPP(c_Set_Oinsert(_1379320), _1379322), c_Orderings_Obot__class_Obot(tc_fun(_1379320, tc_HOL_Obool))))], (20329 ^ _776541) ^ [_1143302, _1143304, _1143306, _1143308] : [class_Fields_Ofield__inverse__zero(_1143302), -(_1143304 = c_Groups_Ozero__class_Ozero(_1143302)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143302), _1143306), _1143304)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143302), _1143308), _1143304)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143302), _1143306), _1143308))], (42105 ^ _776541) ^ [_1610597, _1610599, _1610601, _1610603, _1610605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610597), tc_List_Olist(_1610597))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610597), tc_List_Olist(_1610597)), _1610599), hAPP(hAPP(c_List_Olist_OCons(_1610597), _1610601), _1610603))), c_List_Olistrel(_1610597, _1610605))), 42110 ^ _776541 : [(42115 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610597), tc_List_Olist(_1610597))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610597), tc_List_Olist(_1610597)), 42109 ^ [_1610597, _1610599, _1610601, _1610603, _1610605]), _1610603)), c_List_Olistrel(_1610597, _1610605))))], (42113 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610597, _1610597)), hAPP(hAPP(c_Product__Type_OPair(_1610597, _1610597), 42108 ^ [_1610597, _1610599, _1610601, _1610603, _1610605]), _1610601)), _1610605)))], (42111 ^ _776541) ^ [] : [-(_1610599 = hAPP(hAPP(c_List_Olist_OCons(_1610597), 42108 ^ [_1610597, _1610599, _1610601, _1610603, _1610605]), 42109 ^ [_1610597, _1610599, _1610601, _1610603, _1610605]))]]], (29797 ^ _776541) ^ [_1310791] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1310791)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1310791)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37394 ^ _776541) ^ [_1488160, _1488162, _1488164, _1488166] : [c_Fun_Oinj__on(_1488160, _1488162, _1488164, c_Orderings_Otop__class_Otop(tc_fun(_1488160, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1488160, tc_fun(_1488166, _1488162), hAPP(hAPP(c_COMBB(_1488162, tc_fun(_1488166, _1488162), _1488160), c_COMBK(_1488162, _1488166)), _1488164), c_Orderings_Otop__class_Otop(tc_fun(_1488160, tc_HOL_Obool))))], (27635 ^ _776541) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (24351 ^ _776541) ^ [_1216967, _1216969, _1216971] : [class_Divides_Osemiring__div(_1216967), -(_1216969 = c_Groups_Ozero__class_Ozero(_1216967)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216967), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216967), _1216969), _1216971)), _1216969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216967), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216967), _1216971), _1216969)), c_Groups_Oone__class_Oone(_1216967)))], (24734 ^ _776541) ^ [_1224034, _1224036] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224034) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224036), -(_1224034 = _1224036)], (1914 ^ _776541) ^ [_803330, _803332] : [-(class_Nat_Osize(_803330)), _803332 = _803330, class_Nat_Osize(_803332)], (10871 ^ _776541) ^ [_964120, _964122, _964124] : [class_Orderings_Oorder(_964120), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964120, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_964120), _964122)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964120, _964122), _964124)) = c_Orderings_Obot__class_Obot(tc_fun(_964120, tc_HOL_Obool)))], (19004 ^ _776541) ^ [_1118865, _1118867] : [19006 ^ _776541 : [(19009 ^ _776541) ^ [] : [hBOOL(hAPP(_1118867, 19005 ^ [_1118865, _1118867]))], (19007 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19005 ^ [_1118865, _1118867]), _1118865)))]], 19010 ^ _776541 : [(19011 ^ _776541) ^ [_1119016] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1119016), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1118865))), -(hBOOL(hAPP(_1118867, _1119016)))]]], (22191 ^ _776541) ^ [_1179009, _1179011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179011), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179009), _1179011)))], (13385 ^ _776541) ^ [_1014191, _1014193, _1014195, _1014197, _1014199] : [class_Groups_Ocomm__monoid__add(_1014191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014193), _1014195)), hBOOL(hAPP(hAPP(c_member(_1014193), _1014197), _1014195)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014193, _1014191), _1014199), _1014195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014191), hAPP(_1014199, _1014197)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014193, _1014191), _1014199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014193, tc_HOL_Obool)), _1014195), hAPP(hAPP(c_Set_Oinsert(_1014193), _1014197), c_Orderings_Obot__class_Obot(tc_fun(_1014193, tc_HOL_Obool)))))))], (19537 ^ _776541) ^ [_1129482, _1129484] : [class_Rings_Olinordered__idom(_1129482), -(c_Groups_Osgn__class_Osgn(_1129482, c_Groups_Osgn__class_Osgn(_1129482, _1129484)) = c_Groups_Osgn__class_Osgn(_1129482, _1129484))], (38772 ^ _776541) ^ [_1521792, _1521794, _1521796] : [_1521796 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521792, _1521794), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1521792, _1521794), _1521796) = c_Orderings_Obot__class_Obot(tc_fun(_1521792, tc_HOL_Obool)))], (1234 ^ _776541) ^ [_794830, _794832] : [-(class_Groups_Ogroup__add(_794830)), _794832 = _794830, class_Groups_Ogroup__add(_794832)], (34363 ^ _776541) ^ [_1416246, _1416248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1416246)), 34366 ^ _776541 : [(34373 ^ _776541) ^ [] : [-(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), _1416248), _1416246)))), -(c_Divides_OnegDivAlg(_1416248, _1416246) = hAPP(c_Divides_Oadjust(_1416246), c_Divides_OnegDivAlg(_1416248, 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)))), _1416246))))], (34367 ^ _776541) ^ [] : [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), _1416248), _1416246))), -(c_Divides_OnegDivAlg(_1416248, _1416246) = 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), _1416248), _1416246)))]]], (45078 ^ _776541) ^ [_1679231, _1679233, _1679235, _1679237] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679231)), _1679233) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679235)), _1679237), -(hAPP(hAPP(c_List_Omap(tc_prod(_1679231, _1679235), _1679235), c_Product__Type_Osnd(_1679231, _1679235)), hAPP(hAPP(c_List_Ozip(_1679231, _1679235), _1679233), _1679237)) = _1679237)], (24818 ^ _776541) ^ [_1225559, _1225561, _1225563, _1225565, _1225567, _1225569] : [class_Divides_Osemiring__div(_1225559), c_Divides_Odiv__class_Omod(_1225559, _1225561, _1225563) = c_Divides_Odiv__class_Omod(_1225559, _1225565, _1225563), c_Divides_Odiv__class_Omod(_1225559, _1225567, _1225563) = c_Divides_Odiv__class_Omod(_1225559, _1225569, _1225563), -(c_Divides_Odiv__class_Omod(_1225559, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225559), _1225561), _1225567), _1225563) = c_Divides_Odiv__class_Omod(_1225559, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225559), _1225565), _1225569), _1225563))], (33002 ^ _776541) ^ [_1379033, _1379035, _1379037] : [hBOOL(hAPP(_1379033, _1379035)), -(hAPP(c_Set_OCollect(_1379037), hAPP(hAPP(c_COMBS(_1379037, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1379037), c_fconj), hAPP(c_fequal, _1379035))), _1379033)) = hAPP(hAPP(c_Set_Oinsert(_1379037), _1379035), c_Orderings_Obot__class_Obot(tc_fun(_1379037, tc_HOL_Obool))))], (10333 ^ _776541) ^ [_954013, _954015] : [class_Lattices_Oboolean__algebra(_954013), -(hAPP(c_Groups_Ouminus__class_Ouminus(_954013), hAPP(c_Groups_Ouminus__class_Ouminus(_954013), _954015)) = _954015)], (8261 ^ _776541) ^ [_917797, _917799] : [class_Lattices_Obounded__lattice__top(_917797), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917797), _917799), c_Orderings_Otop__class_Otop(_917797)) = c_Orderings_Otop__class_Otop(_917797))], (26531 ^ _776541) ^ [_1255410, _1255412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255412)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1255410)), hAPP(c_Int_Onat, _1255412)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255410), _1255412)))], (48317 ^ _776541) ^ [_1749651, _1749653, _1749655] : [c_List_Olist__all(_1749651, _1749653, _1749655), 48320 ^ _776541 : [(48321 ^ _776541) ^ [_1749732] : [hBOOL(hAPP(hAPP(c_member(_1749651), _1749732), hAPP(c_List_Oset(_1749651), _1749655))), -(hBOOL(hAPP(_1749653, _1749732)))]]], (34463 ^ _776541) ^ [_1417896, _1417898, _1417900, _1417902, _1417904, _1417906] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417896, tc_fun(_1417898, tc_HOL_Obool))), _1417900), _1417902), _1417904), _1417906)), -(hBOOL(hAPP(hAPP(_1417900, _1417904), _1417906))), -(hBOOL(hAPP(hAPP(_1417902, _1417904), _1417906)))], (17969 ^ _776541) ^ [_1099734, _1099736] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1099734), _1099736))), -(hAPP(c_Finite__Set_Ocard(_1099734), _1099736) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44326 ^ _776541) ^ [_1662983, _1662985, _1662987, _1662989, _1662991, _1662993] : [-(hAPP(c_List_Ofoldl(_1662983, _1662985, _1662987, _1662989), hAPP(hAPP(c_List_Olist_OCons(_1662985), _1662991), _1662993)) = hAPP(c_List_Ofoldl(_1662983, _1662985, _1662987, hAPP(hAPP(_1662987, _1662989), _1662991)), _1662993))], (14895 ^ _776541) ^ [_1045189, _1045191] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045189), _1045191)), _1045189)))], (52415 ^ _776541) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (51263 ^ _776541) ^ [_1814476, _1814478, _1814480, _1814482] : [class_Rings_Ocomm__semiring__1(_1814476), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814476), _1814478), _1814480)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814476), _1814478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814476), _1814480), _1814482))))], (24992 ^ _776541) ^ [_1229146, _1229148, _1229150, _1229152] : [class_Divides_Osemiring__div(_1229146), -(c_Divides_Odiv__class_Omod(_1229146, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229146), _1229148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229146), _1229150), _1229152)), _1229152) = c_Divides_Odiv__class_Omod(_1229146, _1229148, _1229152))], (17243 ^ _776541) ^ [_1086958, _1086960, _1086962] : [class_Groups_Oordered__comm__monoid__add(_1086958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086958), c_Groups_Ozero__class_Ozero(_1086958)), _1086960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086958), c_Groups_Ozero__class_Ozero(_1086958)), _1086962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086958), c_Groups_Ozero__class_Ozero(_1086958)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086958), _1086960), _1086962))))], (41062 ^ _776541) ^ [_1581298] : [-(hAPP(c_Relation_Oconverse(_1581298, _1581298), c_Relation_OId(_1581298)) = c_Relation_OId(_1581298))], (46069 ^ _776541) ^ [_1701874, _1701876, _1701878] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1701874, tc_HOL_Obool)), hAPP(c_List_Oset(_1701874), hAPP(c_List_Ofilter(_1701874, _1701876), _1701878))), hAPP(c_List_Oset(_1701874), _1701878))))], (26200 ^ _776541) ^ [_1249831, _1249833] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249831) = _1249833, 26203 ^ _776541 : [(26206 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249833)))], (26204 ^ _776541) ^ [] : [-(_1249831 = hAPP(c_Int_Onat, _1249833))]]], (30852 ^ _776541) ^ [_1329793, _1329795, _1329797] : [class_Orderings_Olinorder(_1329793), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329793), _1329795)), 30859 ^ _776541 : [(30866 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329793, tc_HOL_Obool)), _1329795), hAPP(hAPP(c_Set_Oinsert(_1329793), _1329797), c_Orderings_Obot__class_Obot(tc_fun(_1329793, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1329793, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1329793, c_Orderings_Oord__class_Omin(_1329793), hAPP(hAPP(c_Set_Oinsert(_1329793), _1329797), _1329795)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329793), _1329797), c_Big__Operators_Olattice_OInf__fin(_1329793, c_Orderings_Oord__class_Omin(_1329793), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329793, tc_HOL_Obool)), _1329795), hAPP(hAPP(c_Set_Oinsert(_1329793), _1329797), c_Orderings_Obot__class_Obot(tc_fun(_1329793, tc_HOL_Obool)))))))], (30860 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329793, tc_HOL_Obool)), _1329795), hAPP(hAPP(c_Set_Oinsert(_1329793), _1329797), c_Orderings_Obot__class_Obot(tc_fun(_1329793, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1329793, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1329793, c_Orderings_Oord__class_Omin(_1329793), hAPP(hAPP(c_Set_Oinsert(_1329793), _1329797), _1329795)) = _1329797)]]], (24395 ^ _776541) ^ [_1217719] : [-(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, _1217719)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43012 ^ _776541) ^ [_1633854, _1633856, _1633858] : [hBOOL(hAPP(c_List_Odistinct(_1633854), _1633856)), -(hBOOL(hAPP(c_List_Odistinct(_1633854), c_List_Oremove1(_1633854, _1633858, _1633856))))], (39724 ^ _776541) ^ [_1548000, _1548002, _1548004, _1548006] : [c_Equiv__Relations_Ocongruent(_1548000, _1548002, _1548004, _1548006), 39727 ^ _776541 : [(39728 ^ _776541) ^ [_1548145] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548000, _1548000)), _1548145), _1548004)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548000, _1548000, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548000, tc_fun(_1548000, _1548002), tc_fun(_1548000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548002, tc_HOL_Obool), tc_fun(tc_fun(_1548000, _1548002), tc_fun(_1548000, tc_HOL_Obool)), _1548000), c_COMBB(_1548002, tc_HOL_Obool, _1548000)), hAPP(hAPP(c_COMBB(_1548002, tc_fun(_1548002, tc_HOL_Obool), _1548000), c_fequal), _1548006))), _1548006)), _1548145)))]]], (48442 ^ _776541) ^ [_1752281, _1752283] : [-(hAPP(c_New__DSequence_Opos__empty(_1752281), _1752283) = c_Lazy__Sequence_Oempty(_1752281))], (44733 ^ _776541) ^ [_1670874, _1670876, _1670878, _1670880] : [-(_1670874 = c_List_Olist_ONil(_1670876)), -(hAPP(c_List_Ohd(_1670878), hAPP(hAPP(c_List_Omap(_1670876, _1670878), _1670880), _1670874)) = hAPP(_1670880, hAPP(c_List_Ohd(_1670876), _1670874)))], (49105 ^ _776541) ^ [_1766916, _1766918, _1766920, _1766922] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1766916, _1766918, _1766920, c_Code__Numeral_OSuc__code__numeral(_1766922)) = hAPP(hAPP(_1766920, _1766922), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1766916, _1766918, _1766920, _1766922)))], (32424 ^ _776541) ^ [_1360079, _1360081, _1360083] : [-(hAPP(hAPP(c_Set_Oinsert(_1360079), _1360081), _1360083) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360079, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1360079), hAPP(hAPP(c_COMBC(_1360079, _1360079, tc_HOL_Obool), c_fequal), _1360081))), _1360083))], (52077 ^ _776541) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (20619 ^ _776541) ^ [_1148763, _1148765, _1148767, _1148769] : [class_Fields_Olinordered__field(_1148763), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148763), c_Groups_Ozero__class_Ozero(_1148763)), _1148765)), 20626 ^ _776541 : [(20633 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148763), _1148767), _1148765)), _1148769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148763), _1148767), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148763), _1148769), _1148765))))], (20627 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148763), _1148767), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148763), _1148769), _1148765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148763), _1148767), _1148765)), _1148769)))]]], (31383 ^ _776541) ^ [_1339978, _1339980, _1339982, _1339984] : [class_Orderings_Olinorder(_1339978), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339978), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339978), _1339980), _1339982)), _1339984) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339978), _1339980), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339978), _1339982), _1339984)))], (40322 ^ _776541) ^ [_1562609, _1562611, _1562613, _1562615, _1562617, _1562619, _1562621, _1562623] : [class_Groups_Ocomm__monoid__mult(_1562609), c_Fun_Oinj__on(_1562611, _1562613, _1562615, _1562617), _1562619 = hAPP(c_Set_Oimage(_1562611, _1562613, _1562615), _1562617), 40336 ^ _776541 : [(40339 ^ _776541) ^ [] : [hAPP(_1562621, 40335 ^ [_1562609, _1562611, _1562613, _1562615, _1562617, _1562619, _1562621, _1562623]) = hAPP(hAPP(c_Fun_Ocomp(_1562613, _1562609, _1562611, _1562623), _1562615), 40335 ^ [_1562609, _1562611, _1562613, _1562615, _1562617, _1562619, _1562621, _1562623])], (40337 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562611), 40335 ^ [_1562609, _1562611, _1562613, _1562615, _1562617, _1562619, _1562621, _1562623]), _1562617)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1562613, _1562609), _1562623), _1562619) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1562611, _1562609), _1562621), _1562617))], (26384 ^ _776541) ^ [_1252709, _1252711] : [26385 ^ _776541 : [(26388 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252711))], (26386 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252709))]], 26389 ^ _776541 : [(26396 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252709), _1252711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1252709)), hAPP(c_Int_Onat, _1252711))))], (26390 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1252709)), hAPP(c_Int_Onat, _1252711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252709), _1252711)))]]], (48448 ^ _776541) ^ [_1752472, _1752474, _1752476, _1752478, _1752480] : [-(hAPP(c_New__DSequence_Opos__bind(_1752472, _1752474, _1752476, _1752478), _1752480) = hAPP(c_Lazy__Sequence_Obind(_1752472, _1752474, hAPP(_1752476, _1752480)), hAPP(hAPP(c_COMBC(_1752472, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1752474)), _1752478), _1752480)))], (34307 ^ _776541) ^ [_1415068, _1415070] : [34308 ^ _776541 : [(34311 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1415070), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34309 ^ _776541) ^ [] : [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), _1415068), _1415070)))]], -(c_Divides_OnegDivAlg(_1415068, _1415070) = 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), _1415068), _1415070)))], (19324 ^ _776541) ^ [_1125443] : [class_Rings_Oring__1(_1125443), -(hBOOL(hAPP(hAPP(c_member(_1125443), c_Groups_Ozero__class_Ozero(_1125443)), c_Int_Oring__1__class_OInts(_1125443))))], (12161 ^ _776541) ^ [_990017, _990019, _990021] : [class_Lattices_Olattice(_990017), hBOOL(hAPP(c_Finite__Set_Ofinite(_990017), _990019)), -(_990021 = c_Orderings_Obot__class_Obot(tc_fun(_990017, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990017, tc_HOL_Obool)), _990021), _990019)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_990017), c_Big__Operators_Olattice__class_OSup__fin(_990017, _990021)), c_Big__Operators_Olattice__class_OSup__fin(_990017, _990019)) = c_Big__Operators_Olattice__class_OSup__fin(_990017, _990019))], (52359 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (21995 ^ _776541) ^ [_1175233, _1175235, _1175237, _1175239] : [class_Fields_Olinordered__field__inverse__zero(_1175233), class_Int_Onumber(_1175233), 22002 ^ _776541 : [(22003 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), _1175235), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175233), _1175237), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)))), 22006 ^ _776541 : [(22013 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), c_Groups_Ozero__class_Ozero(_1175233)), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)))), 22016 ^ _776541 : [(22023 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)), c_Groups_Ozero__class_Ozero(_1175233)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), _1175235), c_Groups_Ozero__class_Ozero(_1175233))))], (22017 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)), c_Groups_Ozero__class_Ozero(_1175233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), _1175237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175233), _1175235), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)))))]]], (22007 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), c_Groups_Ozero__class_Ozero(_1175233)), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175233), _1175235), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239))), _1175237)))]]], (22029 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), _1175235), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175233), _1175237), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239))))), 22032 ^ _776541 : [(22035 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175233), _1175235), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239))), _1175237))], (22033 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), c_Groups_Ozero__class_Ozero(_1175233)), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239))))]], 22036 ^ _776541 : [(22039 ^ _776541) ^ [] : [22040 ^ _776541 : [(22043 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), _1175237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175233), _1175235), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239))))], (22041 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)), c_Groups_Ozero__class_Ozero(_1175233))))]], 22044 ^ _776541 : [(22047 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175233), _1175235), c_Groups_Ozero__class_Ozero(_1175233)))], (22045 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)), c_Groups_Ozero__class_Ozero(_1175233)))]]], (22037 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175233), c_Groups_Ozero__class_Ozero(_1175233)), hAPP(c_Int_Onumber__class_Onumber__of(_1175233), _1175239)))]]]]], (40943 ^ _776541) ^ [_1578432, _1578434, _1578436, _1578438] : [-(hBOOL(hAPP(hAPP(c_member(_1578432), _1578434), hAPP(c_Relation_ODomain(_1578432, _1578432), _1578436)))), 40946 ^ _776541 : [(40953 ^ _776541) ^ [] : [_1578434 = _1578438, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578432, _1578432)), hAPP(hAPP(c_Product__Type_OPair(_1578432, _1578432), _1578434), _1578438)), c_Transitive__Closure_Ortrancl(_1578432, _1578436))))], (40947 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578432, _1578432)), hAPP(hAPP(c_Product__Type_OPair(_1578432, _1578432), _1578434), _1578438)), c_Transitive__Closure_Ortrancl(_1578432, _1578436))), -(_1578434 = _1578438)]]], (31269 ^ _776541) ^ [_1337660, _1337662, _1337664] : [class_Orderings_Olinorder(_1337660), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337660), _1337662)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337660), _1337664)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337660, tc_HOL_Obool)), _1337662), _1337664) = c_Orderings_Obot__class_Obot(tc_fun(_1337660, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1337660), c_Big__Operators_Olinorder__class_OMax(_1337660, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337660, tc_HOL_Obool)), _1337662), _1337664))), c_Big__Operators_Olinorder__class_OMax(_1337660, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337660, tc_HOL_Obool)), _1337662), _1337664))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1337660), c_Big__Operators_Olinorder__class_OMax(_1337660, _1337662)), c_Big__Operators_Olinorder__class_OMax(_1337660, _1337664)))], (21433 ^ _776541) ^ [_1164948, _1164950] : [class_Int_Onumber__ring(_1164948), -(hBOOL(hAPP(hAPP(c_member(_1164948), hAPP(c_Int_Onumber__class_Onumber__of(_1164948), _1164950)), c_Int_Oring__1__class_OInts(_1164948))))], (52009 ^ _776541) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (18426 ^ _776541) ^ [_1108065, _1108067, _1108069, _1108071, _1108073] : [class_Rings_Olinordered__semiring__strict(_1108065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108065), _1108067), _1108069)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108065), _1108071), _1108073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108065), c_Groups_Ozero__class_Ozero(_1108065)), _1108069)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108065), c_Groups_Ozero__class_Ozero(_1108065)), _1108071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108065), _1108067), _1108071)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108065), _1108069), _1108073))))], (2796 ^ _776541) ^ [_817914, _817916, _817918, _817920, _817922, _817924, _817926, _817928] : [-(c_Product__Type_Oapsnd(_817928, _817924, _817920, _817916) = c_Product__Type_Oapsnd(_817926, _817922, _817918, _817914)), _817928 = _817926, _817924 = _817922, _817920 = _817918, _817916 = _817914], (41422 ^ _776541) ^ [_1589989, _1589991, _1589993] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589989, _1589989, _1589989), _1589991), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589989, _1589989), tc_HOL_Obool), _1589993), _1589991)) = hAPP(hAPP(c_Relation_Orel__comp(_1589989, _1589989, _1589989), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589989, _1589989), tc_HOL_Obool), _1589993), _1589991)), _1589991))], (8787 ^ _776541) ^ [_927478, _927480] : [class_Lattices_Obounded__lattice__bot(_927478), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927478), _927480), c_Orderings_Obot__class_Obot(_927478)) = c_Orderings_Obot__class_Obot(_927478))], (33453 ^ _776541) ^ [_1391571, _1391573, _1391575, _1391577] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1391571, tc_HOL_Obool), tc_fun(_1391573, tc_HOL_Obool)), _1391575), hAPP(hAPP(c_COMBC(tc_fun(_1391571, tc_HOL_Obool), tc_fun(_1391571, tc_fun(_1391573, tc_HOL_Obool)), tc_fun(_1391573, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391571, tc_fun(_1391573, tc_HOL_Obool))), _1391577)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391571, tc_fun(_1391573, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1391571, tc_HOL_Obool), _1391575)), _1391577))], (23914 ^ _776541) ^ [] : [-(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))], (46694 ^ _776541) ^ [_1714927, _1714929, _1714931, _1714933, _1714935] : [class_Orderings_Olinorder(_1714927), c_List_Olinorder__class_Osorted(_1714927, hAPP(hAPP(c_List_Omap(_1714929, _1714927), _1714931), _1714933)), -(c_List_Olinorder__class_Osorted(_1714927, hAPP(hAPP(c_List_Omap(_1714929, _1714927), _1714931), hAPP(c_List_Ofilter(_1714929, _1714935), _1714933))))], (28307 ^ _776541) ^ [_1284713] : [_1284713 = c_Int_OMin, -(c_Int_OBit1(_1284713) = c_Int_OMin)], (11694 ^ _776541) ^ [_981122, _981124, _981126, _981128, _981130] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981122), _981124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981126, tc_HOL_Obool)), _981128), hAPP(c_Set_Oimage(_981122, _981126, _981130), _981124))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981126), _981128)))], (42037 ^ _776541) ^ [_1608305, _1608307, _1608309, _1608311] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608305), tc_List_Olist(_1608305))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608305), tc_List_Olist(_1608305)), _1608307), _1608309)), c_List_Olistrel(_1608305, _1608311))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608305), tc_List_Olist(_1608305))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608305), tc_List_Olist(_1608305)), _1608307), _1608309)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1608305), c_List_Olistrel1(_1608305, _1608311)))))], (8637 ^ _776541) ^ [_924968, _924970, _924972, _924974] : [class_Lattices_Osemilattice__inf(_924968), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924968), _924970), _924972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924968), _924970), _924974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924968), _924970), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924968), _924972), _924974))))], (45467 ^ _776541) ^ [_1688220, _1688222, _1688224, _1688226, _1688228, _1688230, _1688232] : [c_List_Olist__all2(_1688220, _1688228, hAPP(hAPP(c_COMBC(_1688220, tc_fun(_1688228, _1688222), tc_fun(_1688228, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1688222, tc_HOL_Obool), tc_fun(tc_fun(_1688228, _1688222), tc_fun(_1688228, tc_HOL_Obool)), _1688220), c_COMBB(_1688222, tc_HOL_Obool, _1688228)), _1688224)), _1688230), _1688226, _1688232), -(c_List_Olist__all2(_1688220, _1688222, _1688224, _1688226, hAPP(hAPP(c_List_Omap(_1688228, _1688222), _1688230), _1688232)))], (32374 ^ _776541) ^ [_1358933, _1358935, _1358937] : [32375 ^ _776541 : [(32378 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358933), hAPP(c_Set_OCollect(_1358933), _1358937)))], (32376 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358933), hAPP(c_Set_OCollect(_1358933), _1358935)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1358933), hAPP(c_Set_OCollect(_1358933), hAPP(hAPP(c_COMBS(_1358933, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1358933), c_fconj), _1358935)), _1358937)))))], (47238 ^ _776541) ^ [_1726222, _1726224, _1726226] : [47240 ^ _776541 : [(47243 ^ _776541) ^ [] : [hBOOL(hAPP(_1726224, 47239 ^ [_1726222, _1726224, _1726226]))], (47241 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726222), 47239 ^ [_1726222, _1726224, _1726226]), hAPP(c_List_Oset(_1726222), _1726226))))]], -(c_List_OtakeWhile(_1726222, _1726224, _1726226) = _1726226)], (4966 ^ _776541) ^ [_852205, _852207, _852209, _852211] : [-(c_Quickcheck_Obeyond(_852211, _852207) = c_Quickcheck_Obeyond(_852209, _852205)), _852211 = _852209, _852207 = _852205], (26631 ^ _776541) ^ [_1257230, _1257232] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257230))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257230)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257232)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40403 ^ _776541) ^ [_1564329, _1564331, _1564333, _1564335, _1564337, _1564339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564329, tc_HOL_Obool)), _1564331), _1564333)), 40409 ^ _776541 : [(40412 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564335, tc_HOL_Obool)), hAPP(_1564337, 40408 ^ [_1564329, _1564331, _1564333, _1564335, _1564337, _1564339])), hAPP(_1564339, 40408 ^ [_1564329, _1564331, _1564333, _1564335, _1564337, _1564339])))], (40410 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564329), 40408 ^ [_1564329, _1564331, _1564333, _1564335, _1564337, _1564339]), _1564331)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564329, _1564335), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1564329, _1564335), _1564331), _1564337)), hAPP(hAPP(c_Product__Type_OSigma(_1564329, _1564335), _1564333), _1564339))))], (42380 ^ _776541) ^ [_1617776, _1617778, _1617780] : [42382 ^ _776541 : [(42385 ^ _776541) ^ [] : [hBOOL(hAPP(_1617780, hAPP(hAPP(c_List_Onth(_1617776), _1617778), 42381 ^ [_1617776, _1617778, _1617780])))], (42383 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42381 ^ [_1617776, _1617778, _1617780]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617776)), _1617778))))]], 42386 ^ _776541 : [(42387 ^ _776541) ^ [_1617978] : [hBOOL(hAPP(hAPP(c_member(_1617776), _1617978), hAPP(c_List_Oset(_1617776), _1617778))), -(hBOOL(hAPP(_1617780, _1617978)))]]], (1976 ^ _776541) ^ [_804962, _804964] : [_804964 = _804962, -(c_Hoare__Mirabelle_OAbs__triple(_804964) = c_Hoare__Mirabelle_OAbs__triple(_804962))], (47026 ^ _776541) ^ [_1721723, _1721725, _1721727, _1721729] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721723)), _1721725) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721727)), _1721729), -(hAPP(hAPP(c_List_Ozip(_1721723, _1721727), hAPP(c_List_Orev(_1721723), _1721725)), hAPP(c_List_Orev(_1721727), _1721729)) = hAPP(c_List_Orev(tc_prod(_1721723, _1721727)), hAPP(hAPP(c_List_Ozip(_1721723, _1721727), _1721725), _1721729)))], (26645 ^ _776541) ^ [_1257452] : [-(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), _1257452)) = 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), _1257452))))], (39605 ^ _776541) ^ [_1544685, _1544687] : [c_Predicate_Oreflp(_1544685, _1544687), -(c_Relation_Orefl__on(_1544685, c_Orderings_Otop__class_Otop(tc_fun(_1544685, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544685, _1544685)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544685, _1544685, tc_HOL_Obool), _1544687))))], (29597 ^ _776541) ^ [_1306940, _1306942, _1306944] : [class_Rings_Ocomm__semiring__1(_1306940), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1306940), _1306942), 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)))), _1306944))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306940), _1306942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306940), hAPP(hAPP(c_Power_Opower__class_Opower(_1306940), _1306942), _1306944)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306940), _1306942), _1306944))))], (51965 ^ _776541) ^ [_1826025, _1826027] : [-(class_Enum_Oenum(tc_fun(_1826025, _1826027))), class_Enum_Oenum(_1826025), class_Enum_Oenum(_1826027)], (28841 ^ _776541) ^ [_1293611, _1293613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1293611)), c_Int_OBit0(_1293613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293611), _1293613)))], (30536 ^ _776541) ^ [_1324381, _1324383, _1324385] : [class_Orderings_Olinorder(_1324381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324381), _1324383)), hBOOL(hAPP(hAPP(c_member(_1324381), _1324385), _1324383)), 30547 ^ _776541 : [(30554 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324381, tc_HOL_Obool)), _1324383), hAPP(hAPP(c_Set_Oinsert(_1324381), _1324385), c_Orderings_Obot__class_Obot(tc_fun(_1324381, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324381, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1324381, _1324383) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324381), _1324385), c_Big__Operators_Olinorder__class_OMin(_1324381, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324381, tc_HOL_Obool)), _1324383), hAPP(hAPP(c_Set_Oinsert(_1324381), _1324385), c_Orderings_Obot__class_Obot(tc_fun(_1324381, tc_HOL_Obool)))))))], (30548 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324381, tc_HOL_Obool)), _1324383), hAPP(hAPP(c_Set_Oinsert(_1324381), _1324385), c_Orderings_Obot__class_Obot(tc_fun(_1324381, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324381, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1324381, _1324383) = _1324385)]]], (18041 ^ _776541) ^ [_1100967, _1100969, _1100971] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100967), _1100969)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100971), _1100969)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100967), _1100971))], (50247 ^ _776541) ^ [_1792291, _1792293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1792291), _1792293)), -(c_Quickcheck_Obeyond(_1792291, _1792293) = _1792293)], (43018 ^ _776541) ^ [_1633957] : [-(hBOOL(hAPP(c_List_Odistinct(_1633957), c_List_Olist_ONil(_1633957))))], (5837 ^ _776541) ^ [_869147, _869149, _869151] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869147, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869147)), tc_HOL_Obool)), _869149), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869147, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869147)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_869147)))), hBOOL(hAPP(_869151, hAPP(c_Hoare__Mirabelle_ORep__triple(_869147), 5842 ^ [_869147, _869149, _869151]))), -(hBOOL(hAPP(_869151, _869149)))], (21291 ^ _776541) ^ [_1161882, _1161884] : [class_Int_Onumber__ring(_1161882), -(hAPP(c_Int_Onumber__class_Onumber__of(_1161882), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161884)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1161882), hAPP(c_Int_Onumber__class_Onumber__of(_1161882), _1161884)))], (32402 ^ _776541) ^ [_1359558] : [-(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)), _1359558)))))], (13529 ^ _776541) ^ [_1017329] : [13531 ^ _776541 : [(13534 ^ _776541) ^ [_1017439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 13530 ^ [_1017329, _1017439]), _1017439))], (13532 ^ _776541) ^ [_1017405] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 13530 ^ [_1017329, _1017405]), _1017329)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1017329)))], (42941 ^ _776541) ^ [_1632282, _1632284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1632282), _1632284)), -(c_Nitpick_Ocard_H(_1632282, _1632284) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632282)), c_Hilbert__Choice_OEps(tc_List_Olist(_1632282), hAPP(hAPP(c_COMBS(tc_List_Olist(_1632282), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1632282)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1632282), tc_fun(_1632282, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1632282, tc_HOL_Obool), tc_fun(tc_fun(_1632282, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1632282)), c_fequal), c_List_Oset(_1632282))), _1632284))), c_List_Odistinct(_1632282)))))], (1704 ^ _776541) ^ [_800705, _800707] : [-(class_Divides_Osemiring__div(_800705)), _800707 = _800705, class_Divides_Osemiring__div(_800707)], (50111 ^ _776541) ^ [_1788990, _1788992, _1788994, _1788996] : [c_Fun_Oinj__on(_1788990, _1788992, _1788994, c_Orderings_Otop__class_Otop(tc_fun(_1788990, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1788992, _1788990, c_Hilbert__Choice_Oinv__into(_1788990, _1788992, c_Orderings_Otop__class_Otop(tc_fun(_1788990, tc_HOL_Obool)), _1788994)), hAPP(c_Set_Oimage(_1788990, _1788992, _1788994), _1788996)) = _1788996)], (40354 ^ _776541) ^ [_1563395, _1563397] : [40355 ^ _776541 : [(40356 ^ _776541) ^ [_1563441] : [hBOOL(hAPP(_1563395, _1563441))]], -(hBOOL(hAPP(_1563395, c_Hilbert__Choice_OEps(_1563397, _1563395))))], (40705 ^ _776541) ^ [_1572441, _1572443, _1572445, _1572447] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572441, _1572441)), hAPP(hAPP(c_Product__Type_OPair(_1572441, _1572441), _1572445), _1572447)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572441, _1572441), tc_HOL_Obool)), _1572443), c_Relation_OId(_1572441)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572441, tc_fun(_1572441, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1572441, tc_fun(tc_prod(_1572441, _1572441), tc_HOL_Obool), tc_fun(_1572441, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572441, tc_fun(tc_fun(tc_prod(_1572441, _1572441), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1572441, _1572441), tc_HOL_Obool), tc_fun(_1572441, tc_HOL_Obool)), _1572441), c_COMBC(_1572441, tc_fun(tc_prod(_1572441, _1572441), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572441, tc_prod(_1572441, _1572441)), tc_fun(_1572441, tc_fun(tc_fun(tc_prod(_1572441, _1572441), tc_HOL_Obool), tc_HOL_Obool)), _1572441), hAPP(c_COMBB(tc_prod(_1572441, _1572441), tc_fun(tc_fun(tc_prod(_1572441, _1572441), tc_HOL_Obool), tc_HOL_Obool), _1572441), c_member(tc_prod(_1572441, _1572441)))), c_Product__Type_OPair(_1572441, _1572441)))), _1572443)), c_fequal), _1572445), _1572447)))], (38175 ^ _776541) ^ [_1507637, _1507639, _1507641] : [c_Wellfounded_Owf(_1507637, _1507639), -(c_Wellfounded_Owf(_1507637, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1507637, _1507637), tc_HOL_Obool)), _1507641), _1507639)))], (7260 ^ _776541) ^ [_895062, _895064, _895066] : [hAPP(hAPP(c_Set_Oinsert(_895062), _895064), c_Orderings_Obot__class_Obot(tc_fun(_895062, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_895062), _895066), c_Orderings_Obot__class_Obot(tc_fun(_895062, tc_HOL_Obool))), -(_895064 = _895066)], (27106 ^ _776541) ^ [_1264562, _1264564] : [class_Rings_Olinordered__idom(_1264562), 27109 ^ _776541 : [(27116 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264562), c_Groups_Ozero__class_Ozero(_1264562)), hAPP(c_Int_Oring__1__class_Oof__int(_1264562), _1264564))))], (27110 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264562), c_Groups_Ozero__class_Ozero(_1264562)), hAPP(c_Int_Oring__1__class_Oof__int(_1264562), _1264564))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264564)))]]], (32656 ^ _776541) ^ [_1369467, _1369469, _1369471, _1369473] : [-(hBOOL(hAPP(hAPP(c_member(_1369467), _1369469), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369467, tc_HOL_Obool)), _1369471), hAPP(c_Set_OCollect(_1369467), _1369473))))), hBOOL(hAPP(hAPP(c_member(_1369467), _1369469), _1369471)), hBOOL(hAPP(_1369473, _1369469))], (8279 ^ _776541) ^ [_918148, _918150, _918152, _918154] : [class_Lattices_Olattice(_918148), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918148), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918148), _918150), _918152)), _918154) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918148), _918150), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918148), _918152), _918154)))], (21367 ^ _776541) ^ [_1163409, _1163411, _1163413] : [class_Rings_Ocomm__semiring__1(_1163409), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163409), hAPP(hAPP(c_Power_Opower__class_Opower(_1163409), _1163411), _1163413)), _1163411) = hAPP(hAPP(c_Power_Opower__class_Opower(_1163409), _1163411), hAPP(c_Nat_OSuc, _1163413)))], (30082 ^ _776541) ^ [_1316171] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1316171) = c_Orderings_Oord__class_Omin(_1316171)), class_Lattices_Osemilattice__inf(_1316171), class_Orderings_Olinorder(_1316171)], (49305 ^ _776541) ^ [_1771966, _1771968] : [-(c_Relation_Otrans(_1771966, c_Transitive__Closure_Ortrancl(_1771966, _1771968)))], (51641 ^ _776541) ^ [_1821207] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821207), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1821207 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27377 ^ _776541) ^ [_1268987, _1268989] : [class_Groups_Oordered__ab__group__add__abs(_1268987), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268987), c_Groups_Ozero__class_Ozero(_1268987)), hAPP(c_Groups_Oabs__class_Oabs(_1268987), _1268989))))], (24200 ^ _776541) ^ [_1214258, _1214260, _1214262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214258), 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)), _1214260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214260), _1214262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214258), _1214260)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214258), _1214262))))], (36332 ^ _776541) ^ [_1462819, _1462821, _1462823, _1462825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1462819), _1462821)), -(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), _1462819), _1462823)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1462821), _1462825))), c_FunDef_Opair__leq)))], (39427 ^ _776541) ^ [_1540273, _1540275, _1540277, _1540279, _1540281] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540273, _1540275)), _1540277), hAPP(hAPP(c_Product__Type_OSigma(_1540273, _1540275), _1540279), _1540281))), 39431 ^ _776541 : [(39437 ^ _776541) ^ [] : [-(_1540277 = hAPP(hAPP(c_Product__Type_OPair(_1540273, _1540275), 39430 ^ [_1540273, _1540275, _1540277, _1540279, _1540281]), 39433 ^ [_1540273, _1540275, _1540277, _1540279, _1540281]))], (39435 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540275), 39433 ^ [_1540273, _1540275, _1540277, _1540279, _1540281]), hAPP(_1540281, 39430 ^ [_1540273, _1540275, _1540277, _1540279, _1540281]))))], (39432 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540273), 39430 ^ [_1540273, _1540275, _1540277, _1540279, _1540281]), _1540279)))]]], (22509 ^ _776541) ^ [_1184424, _1184426, _1184428, _1184430] : [class_Groups_Omonoid__mult(_1184424), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184424), _1184426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184428), _1184430)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1184424), hAPP(hAPP(c_Power_Opower__class_Opower(_1184424), _1184426), _1184428)), _1184430))], (44228 ^ _776541) ^ [_1660938, _1660940] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660938)), hAPP(c_List_Otl(_1660938), _1660940)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660938)), _1660940)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (33611 ^ _776541) ^ [_1395883, _1395885, _1395887, _1395889, _1395891, _1395893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1395885, _1395887)), hAPP(hAPP(c_Product__Type_OPair(_1395885, _1395887), _1395891), _1395893)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395883, tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395883, tc_HOL_Obool))), _1395889))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395883, tc_fun(_1395885, tc_fun(_1395887, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1395883, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool), tc_fun(_1395885, tc_fun(_1395887, tc_HOL_Obool)), _1395883), hAPP(c_COMBC(_1395885, tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool), tc_fun(_1395887, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395887, tc_fun(tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool), tc_fun(_1395887, tc_HOL_Obool)), _1395885), c_COMBC(_1395887, tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395887, tc_prod(_1395885, _1395887)), tc_fun(_1395887, tc_fun(tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool), tc_HOL_Obool)), _1395885), hAPP(c_COMBB(tc_prod(_1395885, _1395887), tc_fun(tc_fun(tc_prod(_1395885, _1395887), tc_HOL_Obool), tc_HOL_Obool), _1395887), c_member(tc_prod(_1395885, _1395887)))), c_Product__Type_OPair(_1395885, _1395887))))), _1395889)), _1395891), _1395893)))], (11688 ^ _776541) ^ [_981013, _981015, _981017, _981019, _981021, _981023] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_981013, _981015, _981017, _981019, _981021), _981023)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981013), _981021)))], (42982 ^ _776541) ^ [_1633282, _1633284, _1633286, _1633288] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633282) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1633284), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633282)), hAPP(hAPP(c_List_Olist_OCons(_1633284), _1633286), _1633288)) = hAPP(hAPP(c_List_Olist_OCons(_1633284), _1633286), hAPP(hAPP(c_List_Otake(_1633284), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633282)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1633288)))], (25800 ^ _776541) ^ [_1243393, _1243395] : [-(_1243393 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25803 ^ _776541 : [(25810 ^ _776541) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243395, _1243393) = 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), _1243395)), _1243393) = 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), _1243395), _1243393))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25804 ^ _776541) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243395, _1243393) = 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), _1243395)), _1243393) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243395), _1243393)))]]], (34385 ^ _776541) ^ [_1416630, _1416632] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416630), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416632)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416630)) = 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), _1416632), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416630)))), 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)))], (13796 ^ _776541) ^ [_1022473, _1022475, _1022477, _1022479] : [class_Rings_Ocomm__semiring(_1022473), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022473), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022473), _1022475), _1022477)), _1022479) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022473), _1022475), _1022479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022473), _1022477), _1022479)))], (28859 ^ _776541) ^ [_1293935, _1293937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293935), _1293937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1293935)), c_Int_OBit0(_1293937))))], (15904 ^ _776541) ^ [_1064392, _1064394] : [-(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), _1064392), _1064394)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064394))], (34994 ^ _776541) ^ [_1429447] : [-(c_Int_Oint__ge__less__than2(_1429447) = 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), _1429447)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (22165 ^ _776541) ^ [_1178506, _1178508] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178506)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178508)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178506), _1178508)))], (18468 ^ _776541) ^ [_1108869, _1108871, _1108873, _1108875] : [class_Rings_Olinordered__ring__strict(_1108869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108869), c_Groups_Ozero__class_Ozero(_1108869)), _1108871)), 18475 ^ _776541 : [(18482 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108869), _1108873), _1108875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108869), _1108871), _1108873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108869), _1108871), _1108875))))], (18476 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108869), _1108871), _1108873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108869), _1108871), _1108875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108869), _1108873), _1108875)))]]], (32175 ^ _776541) ^ [_1354762, _1354764, _1354766] : [class_Orderings_Olinorder(_1354762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354762), _1354764)), -(hBOOL(hAPP(hAPP(c_member(_1354762), _1354766), _1354764))), -(c_Big__Operators_Olattice_OSup__fin(_1354762, c_Orderings_Oord__class_Omax(_1354762), hAPP(hAPP(c_Set_Oinsert(_1354762), _1354766), _1354764)) = hAPP(hAPP(c_Finite__Set_Ofold(_1354762, _1354762, c_Orderings_Oord__class_Omax(_1354762)), _1354766), _1354764))], (47122 ^ _776541) ^ [_1723656, _1723658] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723656), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1723656))), c_List_Otranspose(_1723656, _1723658)))))], (43381 ^ _776541) ^ [_1641387, _1641389, _1641391, _1641393, _1641395] : [-(hAPP(hAPP(c_List_Oappend(_1641387), _1641389), _1641391) = hAPP(hAPP(c_List_Olist_OCons(_1641387), _1641393), _1641395)), 43382 ^ _776541 : [(43389 ^ _776541) ^ [_1641570] : [_1641389 = hAPP(hAPP(c_List_Olist_OCons(_1641387), _1641393), _1641570), hAPP(hAPP(c_List_Oappend(_1641387), _1641570), _1641391) = _1641395], (43383 ^ _776541) ^ [] : [_1641389 = c_List_Olist_ONil(_1641387), _1641391 = hAPP(hAPP(c_List_Olist_OCons(_1641387), _1641393), _1641395)]]], (31359 ^ _776541) ^ [_1339442, _1339444, _1339446] : [class_Orderings_Olinorder(_1339442), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339442), _1339444), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339442), _1339444), _1339446)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339442), _1339444), _1339446))], (47383 ^ _776541) ^ [_1729285, _1729287, _1729289] : [c_List_OdropWhile(_1729285, _1729287, _1729289) = c_List_Olist_ONil(_1729285), 47386 ^ _776541 : [(47387 ^ _776541) ^ [_1729376] : [hBOOL(hAPP(hAPP(c_member(_1729285), _1729376), hAPP(c_List_Oset(_1729285), _1729289))), -(hBOOL(hAPP(_1729287, _1729376)))]]], (540 ^ _776541) ^ [_784625, _784627, _784629, _784631, _784633, _784635, _784637, _784639, _784641, _784643] : [-(c_Typedef_Otype__definition(_784641, _784637, _784633, _784629, _784625)), c_Typedef_Otype__definition(_784643, _784639, _784635, _784631, _784627), _784643 = _784641, _784639 = _784637, _784635 = _784633, _784631 = _784629, _784627 = _784625], (32418 ^ _776541) ^ [_1359922, _1359924] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359922), _1359924)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1359922, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1359922, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1359922, tc_HOL_Obool), tc_fun(_1359922, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1359922, tc_HOL_Obool))), _1359924)))))], (40186 ^ _776541) ^ [_1559553, _1559555, _1559557, _1559559, _1559561, _1559563, _1559565] : [c_Finite__Set_Ofolding__image(_1559553, _1559555, _1559557, _1559559, _1559561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559555), _1559563)), -(hAPP(hAPP(_1559561, _1559565), _1559563) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559553, _1559555, _1559557), _1559565), _1559559), _1559563))], (6222 ^ _776541) ^ [_876533, _876535, _876537, _876539] : [hBOOL(hAPP(_876533, _876535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876537, tc_HOL_Obool)), _876533), _876539)), -(hBOOL(hAPP(_876539, _876535)))], (36400 ^ _776541) ^ [] : [-(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)))], (39734 ^ _776541) ^ [_1548376, _1548378, _1548380, _1548382] : [39736 ^ _776541 : [(39739 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548376, _1548376, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548376, tc_fun(_1548376, _1548378), tc_fun(_1548376, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548378, tc_HOL_Obool), tc_fun(tc_fun(_1548376, _1548378), tc_fun(_1548376, tc_HOL_Obool)), _1548376), c_COMBB(_1548378, tc_HOL_Obool, _1548376)), hAPP(hAPP(c_COMBB(_1548378, tc_fun(_1548378, tc_HOL_Obool), _1548376), c_fequal), _1548382))), _1548382)), 39735 ^ [_1548376, _1548378, _1548380, _1548382]))], (39737 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548376, _1548376)), 39735 ^ [_1548376, _1548378, _1548380, _1548382]), _1548380)))]], -(c_Equiv__Relations_Ocongruent(_1548376, _1548378, _1548380, _1548382))], (11167 ^ _776541) ^ [_969888, _969890, _969892, _969894, _969896] : [-(hAPP(c_Set_Oimage(_969888, _969890, _969892), hAPP(hAPP(c_Set_Oinsert(_969888), _969894), _969896)) = hAPP(hAPP(c_Set_Oinsert(_969890), hAPP(_969892, _969894)), hAPP(c_Set_Oimage(_969888, _969890, _969892), _969896)))], (23211 ^ _776541) ^ [_1197004, _1197006, _1197008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197004)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197006), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1197008)), 23218 ^ _776541 : [(23219 ^ _776541) ^ [_1197212] : [23221 ^ _776541 : [(23227 ^ _776541) ^ [] : [-(_1197212 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23223 ^ [_1197004, _1197006, _1197008, _1197212]), 23220 ^ [_1197004, _1197006, _1197008, _1197212]))], (23225 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23223 ^ [_1197004, _1197006, _1197008, _1197212]), _1197008)))], (23222 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23220 ^ [_1197004, _1197006, _1197008, _1197212]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1197004))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197006), _1197212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197006), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197212), _1197004))))]]], (26619 ^ _776541) ^ [_1256961, _1256963] : [class_Int_Onumber__ring(_1256961), -(hAPP(c_Int_Onumber__class_Onumber__of(_1256961), c_Int_Osucc(_1256963)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256961), c_Groups_Oone__class_Oone(_1256961)), hAPP(c_Int_Onumber__class_Onumber__of(_1256961), _1256963)))], (47124 ^ _776541) ^ [_1723702, _1723704] : [-(hAPP(c_List_Orev(_1723702), _1723704) = hAPP(c_List_Ofoldl(tc_List_Olist(_1723702), _1723702, hAPP(c_COMBC(_1723702, tc_List_Olist(_1723702), tc_List_Olist(_1723702)), c_List_Olist_OCons(_1723702)), c_List_Olist_ONil(_1723702)), _1723704))], (42795 ^ _776541) ^ [_1629000, _1629002, _1629004, _1629006] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629000), tc_List_Olist(_1629000))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629000), tc_List_Olist(_1629000)), _1629002), _1629004)), c_List_Olistrel1(_1629000, _1629006)))), 42796 ^ _776541 : [(42797 ^ _776541) ^ [_1629133, _1629135] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629000, _1629000)), hAPP(hAPP(c_Product__Type_OPair(_1629000, _1629000), hAPP(hAPP(c_List_Onth(_1629000), _1629002), _1629133)), _1629135)), _1629006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629133), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629000)), _1629002))), _1629004 = hAPP(hAPP(c_List_Olist__update(_1629000, _1629002), _1629133), _1629135)]]], (42367 ^ _776541) ^ [_1617465, _1617467, _1617469] : [42369 ^ _776541 : [(42372 ^ _776541) ^ [] : [hBOOL(hAPP(_1617469, 42368 ^ [_1617465, _1617467, _1617469]))], (42370 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617465), 42368 ^ [_1617465, _1617467, _1617469]), hAPP(c_List_Oset(_1617465), _1617467))))]], 42373 ^ _776541 : [(42374 ^ _776541) ^ [_1617649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1617649), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617465)), _1617467))), -(hBOOL(hAPP(_1617469, hAPP(hAPP(c_List_Onth(_1617465), _1617467), _1617649))))]]], (24565 ^ _776541) ^ [_1220899, _1220901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1220899), _1220901)), -(c_Nat__Transfer_Otsub(_1220901, _1220899) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220901), _1220899))], (32864 ^ _776541) ^ [_1374813, _1374815, _1374817, _1374819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool)), _1374817), _1374819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374813, tc_fun(_1374815, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1374813, tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_fun(_1374815, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374815, tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_fun(_1374815, tc_HOL_Obool)), _1374813), c_COMBC(_1374815, tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374815, tc_prod(_1374813, _1374815)), tc_fun(_1374815, tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool)), _1374813), hAPP(c_COMBB(tc_prod(_1374813, _1374815), tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool), _1374815), c_member(tc_prod(_1374813, _1374815)))), c_Product__Type_OPair(_1374813, _1374815)))), _1374817)), hAPP(hAPP(c_COMBC(_1374813, tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_fun(_1374815, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374815, tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_fun(_1374815, tc_HOL_Obool)), _1374813), c_COMBC(_1374815, tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374815, tc_prod(_1374813, _1374815)), tc_fun(_1374815, tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool)), _1374813), hAPP(c_COMBB(tc_prod(_1374813, _1374815), tc_fun(tc_fun(tc_prod(_1374813, _1374815), tc_HOL_Obool), tc_HOL_Obool), _1374815), c_member(tc_prod(_1374813, _1374815)))), c_Product__Type_OPair(_1374813, _1374815)))), _1374819))))], (22961 ^ _776541) ^ [_1192603, _1192605, _1192607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192603)), _1192603 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1192605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192603), _1192607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192605), _1192603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1192607)))], (51783 ^ _776541) ^ [_1823491, _1823493] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823491), _1823493)), 51788 ^ _776541 : [(51791 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823493), _1823491))], (51789 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823491), _1823493)))]], -(_1823491 = _1823493)], (16290 ^ _776541) ^ [_1070606, _1070608] : [class_Rings_Ocomm__semiring__1(_1070606), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070606), c_Groups_Ozero__class_Ozero(_1070606)), _1070608) = c_Groups_Ozero__class_Ozero(_1070606))], (13852 ^ _776541) ^ [_1023637, _1023639, _1023641, _1023643, _1023645] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1023637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023637), _1023639), _1023641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023637), _1023643), _1023645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023637), _1023639), _1023643)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023637), _1023641), _1023645))))], (11562 ^ _776541) ^ [_978682, _978684] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_978682, _978684)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_978682, _978684), tc_HOL_Obool)))), 11565 ^ _776541 : [(11568 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_978684), c_Orderings_Otop__class_Otop(tc_fun(_978684, tc_HOL_Obool)))))], (11566 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_978682), c_Orderings_Otop__class_Otop(tc_fun(_978682, tc_HOL_Obool)))))]]], (23701 ^ _776541) ^ [_1205902] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1205902) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1205902 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41033 ^ _776541) ^ [_1580502, _1580504, _1580506, _1580508, _1580510] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580502, _1580502)), hAPP(hAPP(c_Product__Type_OPair(_1580502, _1580502), _1580504), _1580506)), c_Transitive__Closure_Ortrancl(_1580502, _1580508))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580502, _1580502), tc_HOL_Obool)), _1580508), hAPP(hAPP(c_Product__Type_OSigma(_1580502, _1580502), _1580510), hAPP(c_COMBK(tc_fun(_1580502, tc_HOL_Obool), _1580502), _1580510)))), -(_1580504 = _1580506), -(hBOOL(hAPP(hAPP(c_member(_1580502), _1580504), _1580510)))], (584 ^ _776541) ^ [_785339, _785341] : [-(c_List_Onat__list(_785339)), _785341 = _785339, c_List_Onat__list(_785341)], (43138 ^ _776541) ^ [_1635967, _1635969] : [-(c_List_Olist_Olist__size(_1635967, _1635969, c_List_Olist_ONil(_1635967)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30560 ^ _776541) ^ [_1324887, _1324889, _1324891] : [class_Orderings_Olinorder(_1324887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324887), _1324889)), hBOOL(hAPP(hAPP(c_member(_1324887), _1324891), _1324889)), 30571 ^ _776541 : [(30578 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324887, tc_HOL_Obool)), _1324889), hAPP(hAPP(c_Set_Oinsert(_1324887), _1324891), c_Orderings_Obot__class_Obot(tc_fun(_1324887, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324887, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1324887, c_Orderings_Oord__class_Omin(_1324887), _1324889) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324887), _1324891), c_Big__Operators_Olattice_OInf__fin(_1324887, c_Orderings_Oord__class_Omin(_1324887), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324887, tc_HOL_Obool)), _1324889), hAPP(hAPP(c_Set_Oinsert(_1324887), _1324891), c_Orderings_Obot__class_Obot(tc_fun(_1324887, tc_HOL_Obool)))))))], (30572 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324887, tc_HOL_Obool)), _1324889), hAPP(hAPP(c_Set_Oinsert(_1324887), _1324891), c_Orderings_Obot__class_Obot(tc_fun(_1324887, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324887, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1324887, c_Orderings_Oord__class_Omin(_1324887), _1324889) = _1324891)]]], (36396 ^ _776541) ^ [] : [-(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)))))], (32768 ^ _776541) ^ [_1371912, _1371914, _1371916, _1371918, _1371920] : [class_Groups_Ocomm__monoid__add(_1371912), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371914, _1371912), hAPP(hAPP(c_COMBS(_1371914, _1371912, _1371912), hAPP(hAPP(c_COMBB(_1371912, tc_fun(_1371912, _1371912), _1371914), c_Groups_Oplus__class_Oplus(_1371912)), _1371916)), _1371918)), _1371920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1371912), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371914, _1371912), _1371916), _1371920)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371914, _1371912), _1371918), _1371920)))], (36553 ^ _776541) ^ [_1468735, _1468737, _1468739, _1468741] : [-(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), _1468735), _1468737)), 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), _1468739), _1468741)), 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), _1468735), _1468739)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468737), _1468741))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (42305 ^ _776541) ^ [_1616037, _1616039, _1616041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616037)), _1616039)), _1616041)), -(hAPP(hAPP(c_List_Otake(_1616037), _1616041), _1616039) = _1616039)], (29699 ^ _776541) ^ [_1309020, _1309022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309020)), -(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)))), _1309022)), 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)))), _1309020)) = 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, _1309022, _1309020))))], (10951 ^ _776541) ^ [_965773, _965775, _965777, _965779, _965781, _965783, _965785] : [c_Finite__Set_Ofun__left__comm(_965773, _965775, _965777), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_965773, _965775, _965777, _965779, _965781), _965783)), hBOOL(hAPP(hAPP(c_member(_965773), _965785), _965781)), 10963 ^ _776541 : [(10966 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_965773, _965775, _965777, _965779, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965773, tc_HOL_Obool)), _965781), hAPP(hAPP(c_Set_Oinsert(_965773), _965785), c_Orderings_Obot__class_Obot(tc_fun(_965773, tc_HOL_Obool))))), 10962 ^ [_965773, _965775, _965777, _965779, _965781, _965783, _965785])))], (10964 ^ _776541) ^ [] : [-(_965783 = hAPP(hAPP(_965777, _965785), 10962 ^ [_965773, _965775, _965777, _965779, _965781, _965783, _965785]))]]], (43212 ^ _776541) ^ [_1637447, _1637449, _1637451] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637447), tc_List_Olist(_1637447))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637447), tc_List_Olist(_1637447)), c_List_Olist_ONil(_1637447)), _1637449)), c_List_Olex(_1637447, _1637451)))], (28331 ^ _776541) ^ [_1285093, _1285095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285093), _1285095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1285093)), c_Int_OBit1(_1285095))))], (39693 ^ _776541) ^ [_1547294] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39689 ^ [_1547294]), c_Int_OInteg)))], (34197 ^ _776541) ^ [_1412256, _1412258] : [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(_1412256))), 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)), _1412258)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412256)), hAPP(c_Nat_OSuc, _1412258))))], (47020 ^ _776541) ^ [_1721559, _1721561] : [-(hAPP(c_List_Orev(_1721559), c_List_Oconcat(_1721559, _1721561)) = c_List_Oconcat(_1721559, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1721559), tc_List_Olist(_1721559)), c_List_Orev(_1721559)), hAPP(c_List_Orev(tc_List_Olist(_1721559)), _1721561))))], (41094 ^ _776541) ^ [_1582290, _1582292, _1582294, _1582296] : [-(hAPP(c_Relation_Oconverse(_1582290, _1582292), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582290, _1582292), tc_HOL_Obool)), _1582294), _1582296)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582292, _1582290), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1582290, _1582292), _1582294)), hAPP(c_Relation_Oconverse(_1582290, _1582292), _1582296)))], (22595 ^ _776541) ^ [_1185940, _1185942, _1185944] : [class_Rings_Olinordered__semidom(_1185940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185940), c_Groups_Oone__class_Oone(_1185940)), _1185942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185940), c_Groups_Oone__class_Oone(_1185940)), hAPP(hAPP(c_Power_Opower__class_Opower(_1185940), _1185942), _1185944))))], (9194 ^ _776541) ^ [_935278, _935280, _935282] : [class_Orderings_Opreorder(_935278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935278), _935280), _935282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935278), _935282), _935280))], (27138 ^ _776541) ^ [_1265077, _1265079] : [class_Rings_Oring__1(_1265077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265079)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1265077), hAPP(c_Int_Onat, _1265079)) = hAPP(c_Int_Oring__1__class_Oof__int(_1265077), _1265079))], (49261 ^ _776541) ^ [_1771318, _1771320] : [c_Relation_Otrans(_1771318, hAPP(c_Relation_Oconverse(_1771318, _1771318), _1771320)), -(c_Relation_Otrans(_1771318, _1771320))], (7836 ^ _776541) ^ [_908429, _908431, _908433] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908429, tc_HOL_Obool)), _908431), _908433) = c_Orderings_Obot__class_Obot(tc_fun(_908429, tc_HOL_Obool))), _908431 = c_Orderings_Obot__class_Obot(tc_fun(_908429, tc_HOL_Obool)), _908433 = c_Orderings_Obot__class_Obot(tc_fun(_908429, tc_HOL_Obool))], (40416 ^ _776541) ^ [_1564719, _1564721, _1564723] : [-(hBOOL(hAPP(hAPP(c_member(_1564719), _1564721), c_Wellfounded_Oacc(_1564719, _1564723)))), 40420 ^ _776541 : [(40423 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1564719), 40419 ^ [_1564719, _1564721, _1564723]), c_Wellfounded_Oacc(_1564719, _1564723)))], (40421 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564719, _1564719)), hAPP(hAPP(c_Product__Type_OPair(_1564719, _1564719), 40419 ^ [_1564719, _1564721, _1564723]), _1564721)), _1564723)))]]], (44088 ^ _776541) ^ [_1658401, _1658403, _1658405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658401), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658403)), _1658405))), -(hAPP(hAPP(c_List_Oappend(_1658403), hAPP(hAPP(c_List_Otake(_1658403), _1658401), _1658405)), hAPP(hAPP(c_List_Olist_OCons(_1658403), hAPP(c_List_Ohd(_1658403), hAPP(hAPP(c_List_Odrop(_1658403), _1658401), _1658405))), c_List_Olist_ONil(_1658403))) = hAPP(hAPP(c_List_Otake(_1658403), hAPP(c_Nat_OSuc, _1658401)), _1658405))], (44148 ^ _776541) ^ [_1659312, _1659314, _1659316] : [-(hAPP(hAPP(c_List_Odrop(_1659312), _1659314), hAPP(c_List_Otl(_1659312), _1659316)) = hAPP(c_List_Otl(_1659312), hAPP(hAPP(c_List_Odrop(_1659312), _1659314), _1659316)))], (4916 ^ _776541) ^ [_851452, _851454, _851456, _851458] : [-(c_Relation_Oinv__image(_851458, _851454) = c_Relation_Oinv__image(_851456, _851452)), _851458 = _851456, _851454 = _851452], (39936 ^ _776541) ^ [_1553954, _1553956, _1553958] : [-(hAPP(c_Fun_Ocomp(_1553954, _1553956, _1553954, _1553958), c_Fun_Oid(_1553954)) = _1553958)], (28169 ^ _776541) ^ [_1282349, _1282351, _1282353] : [class_Rings_Osemiring__1(_1282349), hBOOL(hAPP(hAPP(c_member(_1282349), _1282351), c_Nat_Osemiring__1__class_ONats(_1282349))), hBOOL(hAPP(hAPP(c_member(_1282349), _1282353), c_Nat_Osemiring__1__class_ONats(_1282349))), -(hBOOL(hAPP(hAPP(c_member(_1282349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282349), _1282351), _1282353)), c_Nat_Osemiring__1__class_ONats(_1282349))))], (20995 ^ _776541) ^ [_1155710, _1155712] : [-(c_Sum__Type_OPlus(_1155710, _1155712, c_Orderings_Otop__class_Otop(tc_fun(_1155710, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1155712, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1155710, _1155712), tc_HOL_Obool)))], (5620 ^ _776541) ^ [_862336, _862338, _862340, _862342, _862344, _862346] : [-(c_COMBB(_862346, _862342, _862338) = c_COMBB(_862344, _862340, _862336)), _862346 = _862344, _862342 = _862340, _862338 = _862336], (34215 ^ _776541) ^ [_1412715, _1412717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412715)), hAPP(c_Nat_OSuc, _1412717))), -(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(_1412715))), 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)), _1412717)))))], (6186 ^ _776541) ^ [_875901, _875903] : [-(hBOOL(hAPP(hAPP(c_member(_875901), _875903), c_Orderings_Otop__class_Otop(tc_fun(_875901, tc_HOL_Obool)))))], (28725 ^ _776541) ^ [_1291481, _1291483] : [class_Int_Onumber__ring(_1291481), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1291481), c_Groups_Oone__class_Oone(_1291481)), hAPP(c_Int_Onumber__class_Onumber__of(_1291481), _1291483)) = hAPP(c_Int_Onumber__class_Onumber__of(_1291481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1291483)))], (46227 ^ _776541) ^ [_1706078, _1706080, _1706082, _1706084] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706078)), _1706080))), c_List_Ofoldr(tc_List_Olist(_1706082), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1706082)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1706082))), _1706084, 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(_1706078)), _1706080)), c_List_Ofoldr(tc_List_Olist(_1706082), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1706082)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706082), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1706082)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1706082)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1706082), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1706082)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706082), tc_List_Olist(_1706082), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1706082)))), _1706084), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (41837 ^ _776541) ^ [_1602191, _1602193, _1602195, _1602197, _1602199, _1602201] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602191), tc_List_Olist(_1602191))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602191), tc_List_Olist(_1602191)), hAPP(hAPP(c_List_Olist_OCons(_1602191), _1602193), _1602195)), hAPP(hAPP(c_List_Olist_OCons(_1602191), _1602197), _1602199))), c_List_Olexord(_1602191, _1602201)))), 41838 ^ _776541 : [(41841 ^ _776541) ^ [] : [_1602193 = _1602197, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602191), tc_List_Olist(_1602191))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602191), tc_List_Olist(_1602191)), _1602195), _1602199)), c_List_Olexord(_1602191, _1602201)))], (41839 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602191, _1602191)), hAPP(hAPP(c_Product__Type_OPair(_1602191, _1602191), _1602193), _1602197)), _1602201))]]], (32849 ^ _776541) ^ [_1373928, _1373930, _1373932, _1373934, _1373936] : [32851 ^ _776541 : [(32854 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373928, tc_HOL_Obool)), hAPP(_1373934, 32850 ^ [_1373928, _1373930, _1373932, _1373934, _1373936])), _1373936))], (32852 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373930), 32850 ^ [_1373928, _1373930, _1373932, _1373934, _1373936]), _1373932)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373928, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1373930, tc_fun(_1373928, tc_HOL_Obool)), _1373932), _1373934)), _1373936)))], (12345 ^ _776541) ^ [_993334, _993336, _993338] : [class_Lattices_Olattice(_993334), hBOOL(hAPP(c_Finite__Set_Ofinite(_993334), _993336)), hBOOL(hAPP(c_Finite__Set_Ofinite(_993334), _993338)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_993334, tc_HOL_Obool)), _993336), _993338) = c_Orderings_Obot__class_Obot(tc_fun(_993334, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_993334), c_Big__Operators_Olattice__class_OSup__fin(_993334, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993334, tc_HOL_Obool)), _993336), _993338))), c_Big__Operators_Olattice__class_OSup__fin(_993334, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_993334, tc_HOL_Obool)), _993336), _993338))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_993334), c_Big__Operators_Olattice__class_OSup__fin(_993334, _993336)), c_Big__Operators_Olattice__class_OSup__fin(_993334, _993338)))], (3354 ^ _776541) ^ [_826593, _826595, _826597, _826599, _826601, _826603, _826605, _826607] : [-(c_Enum_Oproduct(_826607, _826603, _826599, _826595) = c_Enum_Oproduct(_826605, _826601, _826597, _826593)), _826607 = _826605, _826603 = _826601, _826599 = _826597, _826595 = _826593], (7071 ^ _776541) ^ [_891651, _891653, _891655] : [class_Orderings_Oorder(_891651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891651), _891653), _891655)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_891651, _891655, _891653) = c_Orderings_Obot__class_Obot(tc_fun(_891651, tc_HOL_Obool)))], (34067 ^ _776541) ^ [_1409012, _1409014, _1409016] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1409012, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1409014)), _1409016) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409012, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1409012, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1409014)), _1409016)), hAPP(_1409016, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29645 ^ _776541) ^ [_1307957, _1307959, _1307961] : [class_Rings_Olinordered__idom(_1307957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307957), c_Groups_Ozero__class_Ozero(_1307957)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307957), _1307959), 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)))), _1307961))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307957), c_Groups_Ozero__class_Ozero(_1307957)), _1307959)))], (33821 ^ _776541) ^ [_1402954, _1402956, _1402958, _1402960] : [class_Rings_Osemiring__1(_1402954), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1402956, _1402954), hAPP(c_COMBK(_1402954, _1402956), _1402958)), _1402960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402954), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1402954), hAPP(c_Finite__Set_Ocard(_1402956), _1402960))), _1402958))], (42065 ^ _776541) ^ [_1609632, _1609634, _1609636, _1609638, _1609640] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609632), tc_List_Olist(_1609632))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609632), tc_List_Olist(_1609632)), hAPP(hAPP(c_List_Olist_OCons(_1609632), _1609634), _1609636)), _1609638)), c_List_Olistrel(_1609632, _1609640))), 42070 ^ _776541 : [(42075 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609632), tc_List_Olist(_1609632))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609632), tc_List_Olist(_1609632)), _1609636), 42069 ^ [_1609632, _1609634, _1609636, _1609638, _1609640])), c_List_Olistrel(_1609632, _1609640))))], (42073 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609632, _1609632)), hAPP(hAPP(c_Product__Type_OPair(_1609632, _1609632), _1609634), 42068 ^ [_1609632, _1609634, _1609636, _1609638, _1609640])), _1609640)))], (42071 ^ _776541) ^ [] : [-(_1609638 = hAPP(hAPP(c_List_Olist_OCons(_1609632), 42068 ^ [_1609632, _1609634, _1609636, _1609638, _1609640]), 42069 ^ [_1609632, _1609634, _1609636, _1609638, _1609640]))]]], (29061 ^ _776541) ^ [_1297480] : [-(c_Int_Opred(c_Int_OBit1(_1297480)) = c_Int_OBit0(_1297480))], (43990 ^ _776541) ^ [_1655805, _1655807, _1655809, _1655811] : [-(_1655805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1655807), _1655805), hAPP(hAPP(c_List_Olist_OCons(_1655807), _1655809), _1655811)) = hAPP(hAPP(c_List_Odrop(_1655807), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655805), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1655811))], (10677 ^ _776541) ^ [_960260, _960262] : [_960262 = c_Orderings_Obot__class_Obot(tc_fun(_960260, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960260, tc_HOL_Obool)), _960262), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960260, tc_HOL_Obool)), _960262))))], (16695 ^ _776541) ^ [_1076854, _1076856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076854), _1076856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076854), hAPP(c_Nat_OSuc, _1076856))))], (6248 ^ _776541) ^ [_876968] : [class_Complete__Lattice_Ocomplete__lattice(_876968), -(c_Complete__Lattice_OSup__class_OSup(_876968, c_Orderings_Obot__class_Obot(tc_fun(_876968, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_876968))], (28909 ^ _776541) ^ [_1294814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294814), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1294814)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22239 ^ _776541) ^ [_1179847, _1179849, _1179851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179847), _1179849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179851), _1179847)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179851), _1179849))))], (26007 ^ _776541) ^ [_1246709, _1246711] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246709, _1246711) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1246709 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246711), 26010 ^ [_1246709, _1246711]))], (46646 ^ _776541) ^ [_1713980, _1713982, _1713984, _1713986] : [class_Orderings_Olinorder(_1713980), -(c_List_Olinorder__class_Osorted(_1713980, hAPP(hAPP(c_List_Omap(_1713982, _1713980), _1713984), c_List_Olinorder__class_Osort__key(_1713982, _1713980, _1713984, _1713986))))], (47500 ^ _776541) ^ [_1731781, _1731783, _1731785, _1731787] : [47502 ^ _776541 : [(47507 ^ _776541) ^ [] : [hBOOL(hAPP(_1731787, hAPP(hAPP(c_List_Onth(_1731783), _1731785), 47501 ^ [_1731781, _1731783, _1731785, _1731787])))], (47505 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47501 ^ [_1731781, _1731783, _1731785, _1731787]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731783)), _1731785))))], (47503 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47501 ^ [_1731781, _1731783, _1731785, _1731787]), _1731781)))]], 47510 ^ _776541 : [(47513 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1731787, hAPP(hAPP(c_List_Onth(_1731783), _1731785), _1731781))))], (47511 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731781), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731783)), _1731785))))]], -(c_List_OtakeWhile(_1731783, _1731787, _1731785) = hAPP(hAPP(c_List_Otake(_1731783), _1731781), _1731785))], (43904 ^ _776541) ^ [_1653799, _1653801, _1653803, _1653805] : [-(hAPP(hAPP(c_List_Odrop(_1653799), _1653801), hAPP(hAPP(c_List_Odrop(_1653799), _1653803), _1653805)) = hAPP(hAPP(c_List_Odrop(_1653799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653801), _1653803)), _1653805))], (12766 ^ _776541) ^ [_1001756, _1001758, _1001760, _1001762, _1001764] : [c_Finite__Set_Ofolding__one__idem(_1001756, _1001758, _1001760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001756), _1001762)), -(hAPP(_1001760, hAPP(hAPP(c_Set_Oinsert(_1001756), _1001764), _1001762)) = hAPP(hAPP(c_Finite__Set_Ofold(_1001756, _1001756, _1001758), _1001764), _1001762))], (28451 ^ _776541) ^ [_1287198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1287198)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1287198), c_Int_OMin)))], (38998 ^ _776541) ^ [_1527425, _1527427, _1527429, _1527431, _1527433] : [hBOOL(hAPP(hAPP(_1527425, _1527427), _1527429)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1527431, _1527433, _1527425), _1527427)))], (37981 ^ _776541) ^ [_1502122, _1502124, _1502126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502122, _1502122), tc_HOL_Obool)), _1502124), _1502126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502122, tc_HOL_Obool)), c_Wellfounded_Oacc(_1502122, _1502126)), c_Wellfounded_Oacc(_1502122, _1502124))))], (38712 ^ _776541) ^ [_1520474, _1520476, _1520478, _1520480, _1520482, _1520484] : [-(hAPP(c_Set_Ovimage(_1520474, _1520476, _1520478), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1520480, tc_fun(_1520476, tc_HOL_Obool)), _1520482), _1520484)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1520480, tc_fun(_1520474, tc_HOL_Obool)), _1520482), hAPP(hAPP(c_COMBB(tc_fun(_1520476, tc_HOL_Obool), tc_fun(_1520474, tc_HOL_Obool), _1520480), c_Set_Ovimage(_1520474, _1520476, _1520478)), _1520484)))], (5300 ^ _776541) ^ [_857446, _857448, _857450, _857452] : [-(c_Lazy__Sequence_Oflat(_857452, _857448) = c_Lazy__Sequence_Oflat(_857450, _857446)), _857452 = _857450, _857448 = _857446], (1574 ^ _776541) ^ [_799080, _799082] : [-(class_Rings_Oordered__cancel__semiring(_799080)), _799082 = _799080, class_Rings_Oordered__cancel__semiring(_799082)], (40617 ^ _776541) ^ [_1569714, _1569716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569714, _1569714)), c_Transitive__Closure_Otrancl(_1569714, _1569716))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569714, _1569714)), _1569716)))], (20261 ^ _776541) ^ [_1142314, _1142316, _1142318, _1142320] : [class_Fields_Ofield__inverse__zero(_1142314), 20264 ^ _776541 : [(20265 ^ _776541) ^ [] : [_1142316 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142314), _1142318), _1142320), 20268 ^ _776541 : [(20275 ^ _776541) ^ [] : [_1142320 = c_Groups_Ozero__class_Ozero(_1142314), -(_1142316 = c_Groups_Ozero__class_Ozero(_1142314))], (20269 ^ _776541) ^ [] : [-(_1142320 = c_Groups_Ozero__class_Ozero(_1142314)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142314), _1142316), _1142320) = _1142318)]]], (20281 ^ _776541) ^ [] : [-(_1142316 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142314), _1142318), _1142320)), 20284 ^ _776541 : [(20287 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142314), _1142316), _1142320) = _1142318], (20285 ^ _776541) ^ [] : [_1142320 = c_Groups_Ozero__class_Ozero(_1142314)]], 20288 ^ _776541 : [(20291 ^ _776541) ^ [] : [_1142316 = c_Groups_Ozero__class_Ozero(_1142314)], (20289 ^ _776541) ^ [] : [-(_1142320 = c_Groups_Ozero__class_Ozero(_1142314))]]]]], (15057 ^ _776541) ^ [] : [-(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))], (28637 ^ _776541) ^ [] : [-(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)))))], (5823 ^ _776541) ^ [_868775, _868777, _868779] : [5825 ^ _776541 : [(5828 ^ _776541) ^ [] : [hBOOL(hAPP(_868777, hAPP(c_Hoare__Mirabelle_OAbs__triple(_868775), 5824 ^ [_868775, _868777, _868779])))], (5826 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_868775, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _868775)), tc_HOL_Obool)), 5824 ^ [_868775, _868777, _868779]), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_868775, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _868775)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_868775)))))]], -(hBOOL(hAPP(_868777, _868779)))], (6588 ^ _776541) ^ [_883101, _883103, _883105] : [hBOOL(hAPP(hAPP(c_member(_883101), _883103), c_Complete__Lattice_OSup__class_OSup(tc_fun(_883101, tc_HOL_Obool), _883105))), 6592 ^ _776541 : [(6595 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_883101, tc_HOL_Obool)), 6591 ^ [_883101, _883103, _883105]), _883105)))], (6593 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_883101), _883103), 6591 ^ [_883101, _883103, _883105])))]]], (19082 ^ _776541) ^ [_1120375, _1120377] : [class_Rings_Olinordered__idom(_1120375), 19085 ^ _776541 : [(19092 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120375), _1120377), c_Groups_Ozero__class_Ozero(_1120375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120375), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120375), _1120377), _1120377)), c_Groups_Ozero__class_Ozero(_1120375))))], (19086 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120375), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120375), _1120377), _1120377)), c_Groups_Ozero__class_Ozero(_1120375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120375), _1120377), c_Groups_Ozero__class_Ozero(_1120375))))]]], (46040 ^ _776541) ^ [_1701229, _1701231, _1701233] : [hBOOL(hAPP(c_List_Odistinct(_1701229), _1701231)), -(hBOOL(hAPP(c_List_Odistinct(_1701229), hAPP(c_List_Ofilter(_1701229, _1701233), _1701231))))], (41619 ^ _776541) ^ [_1595744, _1595746] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595744, _1595744)), _1595746), c_Relation_OId(_1595744))), -(_1595746 = hAPP(hAPP(c_Product__Type_OPair(_1595744, _1595744), 41622 ^ [_1595744, _1595746]), 41622 ^ [_1595744, _1595746]))], (48574 ^ _776541) ^ [_1755918, _1755920, _1755922] : [-(hAPP(c_List_Orev(_1755918), c_List_Oreplicate(_1755918, _1755920, _1755922)) = c_List_Oreplicate(_1755918, _1755920, _1755922))], (44872 ^ _776541) ^ [_1674686, _1674688, _1674690, _1674692, _1674694, _1674696, _1674698, _1674700] : [-(hAPP(hAPP(c_List_Ozip(_1674686, _1674688), hAPP(hAPP(c_List_Omap(_1674690, _1674686), _1674692), _1674694)), hAPP(hAPP(c_List_Omap(_1674696, _1674688), _1674698), _1674700)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674690, _1674696), tc_prod(_1674686, _1674688)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674690, _1674696, tc_prod(_1674686, _1674688)), hAPP(hAPP(c_COMBC(_1674690, tc_fun(_1674696, _1674688), tc_fun(_1674696, tc_prod(_1674686, _1674688))), hAPP(hAPP(c_COMBB(tc_fun(_1674688, tc_prod(_1674686, _1674688)), tc_fun(tc_fun(_1674696, _1674688), tc_fun(_1674696, tc_prod(_1674686, _1674688))), _1674690), c_COMBB(_1674688, tc_prod(_1674686, _1674688), _1674696)), hAPP(hAPP(c_COMBB(_1674686, tc_fun(_1674688, tc_prod(_1674686, _1674688)), _1674690), c_Product__Type_OPair(_1674686, _1674688)), _1674692))), _1674698))), hAPP(hAPP(c_List_Ozip(_1674690, _1674696), _1674694), _1674700)))], (46433 ^ _776541) ^ [_1710386, _1710388, _1710390] : [46434 ^ _776541 : [(46437 ^ _776541) ^ [] : [_1710390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46435 ^ _776541) ^ [] : [-(_1710386 = c_List_Olist_ONil(tc_List_Olist(_1710388)))]], 46441 ^ _776541 : [(46444 ^ _776541) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710388)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1710388)), _1710386), 46440 ^ [_1710386, _1710388, _1710390])) = _1710390], (46442 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46440 ^ [_1710386, _1710388, _1710390]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710388))), _1710386))))]], -(c_List_Otranspose(_1710388, _1710386) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1710388)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1710388)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1710388), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1710388)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1710388)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1710388), hAPP(hAPP(c_COMBB(tc_List_Olist(_1710388), tc_fun(tc_Nat_Onat, _1710388), tc_Nat_Onat), c_List_Onth(_1710388)), hAPP(c_List_Onth(tc_List_Olist(_1710388)), _1710386))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710388))), _1710386)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1710390)))], (23916 ^ _776541) ^ [] : [-(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)))], (36422 ^ _776541) ^ [_1464458, _1464460, _1464462, _1464464] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464458), _1464464) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464462), _1464460), -(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), _1464458), _1464460)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1464462), _1464464))), c_Int_Ointrel)))], (634 ^ _776541) ^ [_786102, _786104, _786106, _786108] : [-(c_FunDef_Ois__measure(_786106, _786102)), c_FunDef_Ois__measure(_786108, _786104), _786108 = _786106, _786104 = _786102], (35604 ^ _776541) ^ [_1441032, _1441034, _1441036, _1441038] : [hAPP(c_Product__Type_Ofst(_1441032, _1441034), _1441036) = hAPP(c_Product__Type_Ofst(_1441032, _1441034), _1441038), hAPP(c_Product__Type_Osnd(_1441032, _1441034), _1441036) = hAPP(c_Product__Type_Osnd(_1441032, _1441034), _1441038), -(_1441036 = _1441038)], (7740 ^ _776541) ^ [_906386, _906388, _906390, _906392] : [-(hBOOL(hAPP(hAPP(c_member(_906386), _906388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906386, tc_HOL_Obool)), _906390), _906392)))), hBOOL(hAPP(hAPP(c_member(_906386), _906388), _906390)), -(hBOOL(hAPP(hAPP(c_member(_906386), _906388), _906392)))], (33304 ^ _776541) ^ [_1387205, _1387207, _1387209, _1387211, _1387213, _1387215, _1387217] : [class_Rings_Osemiring__0(_1387205), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387205), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387207, _1387205), _1387209), _1387211)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387213, _1387205), _1387215), _1387217)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387207, _1387205), hAPP(hAPP(c_COMBC(_1387207, tc_fun(_1387213, tc_HOL_Obool), _1387205), hAPP(hAPP(c_COMBB(tc_fun(_1387213, _1387205), tc_fun(tc_fun(_1387213, tc_HOL_Obool), _1387205), _1387207), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387213, _1387205)), hAPP(hAPP(c_COMBC(_1387207, tc_fun(_1387213, _1387205), tc_fun(_1387213, _1387205)), hAPP(hAPP(c_COMBB(tc_fun(_1387205, _1387205), tc_fun(tc_fun(_1387213, _1387205), tc_fun(_1387213, _1387205)), _1387207), c_COMBB(_1387205, _1387205, _1387213)), hAPP(hAPP(c_COMBB(_1387205, tc_fun(_1387205, _1387205), _1387207), c_Groups_Otimes__class_Otimes(_1387205)), _1387209))), _1387215))), _1387217)), _1387211))], (39551 ^ _776541) ^ [_1543629, _1543631] : [-(c_Relation_Orefl__on(_1543629, _1543631, c_Relation_OId__on(_1543629, _1543631)))], (9512 ^ _776541) ^ [_939829, _939831, _939833] : [class_Orderings_Olinorder(_939829), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939829), _939831), _939833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939829), _939833), _939831)))], (32926 ^ _776541) ^ [_1376765, _1376767] : [-(hAPP(c_Set_OPow(_1376765), _1376767) = hAPP(c_Set_OCollect(tc_fun(_1376765, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1376765, tc_HOL_Obool), tc_fun(_1376765, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1376765, tc_HOL_Obool))), _1376767)))], (33144 ^ _776541) ^ [_1382763, _1382765, _1382767] : [_1382765 = _1382767, -(hAPP(hAPP(c_COMBC(_1382763, tc_fun(_1382763, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382763)), _1382765) = hAPP(hAPP(c_COMBC(_1382763, tc_fun(_1382763, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382763)), _1382767))], (32988 ^ _776541) ^ [_1378669, _1378671, _1378673] : [-(hAPP(hAPP(c_Set_Oinsert(_1378669), _1378671), _1378673) = hAPP(c_Set_OCollect(_1378669), hAPP(hAPP(c_COMBS(_1378669, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378669), c_fdisj), hAPP(hAPP(c_COMBC(_1378669, _1378669, tc_HOL_Obool), c_fequal), _1378671))), hAPP(hAPP(c_COMBC(_1378669, tc_fun(_1378669, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378669)), _1378673))))], (27745 ^ _776541) ^ [_1275592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275592)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1275592 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39047 ^ _776541) ^ [_1528503, _1528505, _1528507, _1528509] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528503, _1528505), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1528503, tc_HOL_Obool), _1528507)), _1528509) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1528503, tc_HOL_Obool), tc_fun(tc_prod(_1528503, _1528505), tc_HOL_Obool)), _1528507), hAPP(hAPP(c_COMBC(tc_fun(_1528503, tc_HOL_Obool), tc_fun(_1528503, tc_fun(_1528505, tc_HOL_Obool)), tc_fun(tc_prod(_1528503, _1528505), tc_HOL_Obool)), c_Product__Type_OSigma(_1528503, _1528505)), _1528509)))], (42173 ^ _776541) ^ [_1612328, _1612330, _1612332, _1612334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612328), tc_List_Olist(_1612328))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612328), tc_List_Olist(_1612328)), _1612330), _1612332)), c_List_Olistrel(_1612328, _1612334))), 42176 ^ _776541 : [(42179 ^ _776541) ^ [_1612557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612557), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612328)), _1612330))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612328, _1612328)), hAPP(hAPP(c_Product__Type_OPair(_1612328, _1612328), hAPP(hAPP(c_List_Onth(_1612328), _1612330), _1612557)), hAPP(hAPP(c_List_Onth(_1612328), _1612332), _1612557))), _1612334)))], (42177 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612328)), _1612330) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612328)), _1612332))]]], (27341 ^ _776541) ^ [_1268396, _1268398, _1268400] : [class_Fields_Olinordered__field__inverse__zero(_1268396), -(hAPP(c_Groups_Oabs__class_Oabs(_1268396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268396), _1268398), _1268400)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268396), hAPP(c_Groups_Oabs__class_Oabs(_1268396), _1268398)), hAPP(c_Groups_Oabs__class_Oabs(_1268396), _1268400)))], (27371 ^ _776541) ^ [] : [c_Int_OPls = c_Int_OMin], (23061 ^ _776541) ^ [_1194381, _1194383] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1194381, _1194383))))], (19304 ^ _776541) ^ [_1125060, _1125062] : [class_Rings_Olinordered__idom(_1125060), hBOOL(hAPP(hAPP(c_member(_1125060), _1125062), c_Int_Oring__1__class_OInts(_1125060))), 19311 ^ _776541 : [(19318 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125060), _1125062), c_Groups_Ozero__class_Ozero(_1125060))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125060), c_Groups_Oone__class_Oone(_1125060)), _1125062)), _1125062)), c_Groups_Ozero__class_Ozero(_1125060))))], (19312 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125060), c_Groups_Oone__class_Oone(_1125060)), _1125062)), _1125062)), c_Groups_Ozero__class_Ozero(_1125060))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125060), _1125062), c_Groups_Ozero__class_Ozero(_1125060))))]]], (2950 ^ _776541) ^ [_820331, _820333] : [_820333 = _820331, -(c_Int_Oring__1__class_Oof__int(_820333) = c_Int_Oring__1__class_Oof__int(_820331))], (28755 ^ _776541) ^ [_1292000, _1292002] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1292000)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1292002)) = 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)))), _1292000)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1292002)))], (14610 ^ _776541) ^ [_1039986, _1039988, _1039990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039988), _1039990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039986), _1039988)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039986), _1039990))))], (18880 ^ _776541) ^ [_1116651, _1116653] : [-(_1116651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116651), _1116653) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116651), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1116653)))], (19428 ^ _776541) ^ [_1127288, _1127290, _1127292, _1127294] : [19429 ^ _776541 : [(19432 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1127292), _1127294)))], (19430 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1127288), _1127290)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1127288, _1127292)), c_Sum__Type_OPlus(_1127288, _1127292, _1127290, _1127294)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52393 ^ _776541) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (25243 ^ _776541) ^ [_1233527, _1233529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233527)), 25246 ^ _776541 : [(25249 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233529, _1233527)), _1233527)))], (25247 ^ _776541) ^ [] : [-(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, _1233529, _1233527))))]]], (3024 ^ _776541) ^ [_821424, _821426] : [_821426 = _821424, -(c_HOL_Obool_Obool__size(_821426) = c_HOL_Obool_Obool__size(_821424))], (31647 ^ _776541) ^ [_1344669, _1344671, _1344673] : [class_Int_Onumber(_1344669), class_Orderings_Oord(_1344669), 31654 ^ _776541 : [(31661 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344669), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344671)), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344673)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344669), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344671)), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344673)) = hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344671))], (31655 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344669), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344671)), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344673))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344669), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344671)), hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344673)) = hAPP(c_Int_Onumber__class_Onumber__of(_1344669), _1344673))]]], (14530 ^ _776541) ^ [_1038562, _1038564] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038562), _1038564) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038564), _1038562))], (7642 ^ _776541) ^ [_903324, _903326, _903328, _903330] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903324, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903324, tc_HOL_Obool)), _903326), _903328)), _903330) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903324, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903324, tc_HOL_Obool)), _903326), _903330)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903324, tc_HOL_Obool)), _903328), _903330)))], (26112 ^ _776541) ^ [_1248440] : [hAPP(c_Int_Onat, _1248440) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248440), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41935 ^ _776541) ^ [_1605389, _1605391, _1605393, _1605395, _1605397, _1605399] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605389), tc_List_Olist(_1605389))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605389), tc_List_Olist(_1605389)), hAPP(hAPP(c_List_Olist_OCons(_1605389), _1605391), _1605393)), hAPP(hAPP(c_List_Olist_OCons(_1605389), _1605395), _1605397))), c_List_Olistrel1(_1605389, _1605399))), 41940 ^ _776541 : [(41943 ^ _776541) ^ [] : [-(_1605393 = _1605397)], (41941 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605389, _1605389)), hAPP(hAPP(c_Product__Type_OPair(_1605389, _1605389), _1605391), _1605395)), _1605399)))]], 41944 ^ _776541 : [(41947 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605389), tc_List_Olist(_1605389))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605389), tc_List_Olist(_1605389)), _1605393), _1605397)), c_List_Olistrel1(_1605389, _1605399))))], (41945 ^ _776541) ^ [] : [-(_1605391 = _1605395)]]], (5917 ^ _776541) ^ [_870642, _870644, _870646, _870648] : [_870642 = _870644, 5920 ^ _776541 : [(5927 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870646), _870644), _870648)), -(hBOOL(hAPP(hAPP(c_member(_870646), _870642), _870648)))], (5921 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870646), _870642), _870648)), -(hBOOL(hAPP(hAPP(c_member(_870646), _870644), _870648)))]]], (30890 ^ _776541) ^ [_1330653, _1330655, _1330657] : [class_Orderings_Olinorder(_1330653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330653), _1330655)), -(_1330655 = c_Orderings_Obot__class_Obot(tc_fun(_1330653, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330653), _1330657)), -(_1330657 = c_Orderings_Obot__class_Obot(tc_fun(_1330653, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330653, tc_HOL_Obool)), _1330655), _1330657) = c_Orderings_Obot__class_Obot(tc_fun(_1330653, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1330653, c_Orderings_Oord__class_Omin(_1330653), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330653, tc_HOL_Obool)), _1330655), _1330657)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330653), c_Big__Operators_Olattice_OInf__fin(_1330653, c_Orderings_Oord__class_Omin(_1330653), _1330655)), c_Big__Operators_Olattice_OInf__fin(_1330653, c_Orderings_Oord__class_Omin(_1330653), _1330657)))], (33398 ^ _776541) ^ [_1389853, _1389855, _1389857, _1389859, _1389861] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389853, tc_fun(_1389855, tc_HOL_Obool)), _1389857), _1389859), _1389861)), 33402 ^ _776541 : [(33405 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1389859, 33401 ^ [_1389853, _1389855, _1389857, _1389859, _1389861]), _1389861)))], (33403 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389853), 33401 ^ [_1389853, _1389855, _1389857, _1389859, _1389861]), _1389857)))]]], (17175 ^ _776541) ^ [_1085751, _1085753, _1085755] : [class_Rings_Olinordered__ring__strict(_1085751), 17178 ^ _776541 : [(17193 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), c_Groups_Ozero__class_Ozero(_1085751)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085751), _1085753), _1085755)))), 17194 ^ _776541 : [(17201 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), _1085753), c_Groups_Ozero__class_Ozero(_1085751))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), _1085755), c_Groups_Ozero__class_Ozero(_1085751)))], (17195 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), c_Groups_Ozero__class_Ozero(_1085751)), _1085753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), c_Groups_Ozero__class_Ozero(_1085751)), _1085755))]]], (17179 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), c_Groups_Ozero__class_Ozero(_1085751)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085751), _1085753), _1085755))), 17184 ^ _776541 : [(17187 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), c_Groups_Ozero__class_Ozero(_1085751)), _1085755)))], (17185 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), c_Groups_Ozero__class_Ozero(_1085751)), _1085753)))]], 17188 ^ _776541 : [(17191 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), _1085755), c_Groups_Ozero__class_Ozero(_1085751))))], (17189 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085751), _1085753), c_Groups_Ozero__class_Ozero(_1085751))))]]]]], (22413 ^ _776541) ^ [_1182849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1182849)))], (25127 ^ _776541) ^ [_1231295] : [-(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, _1231295))))))], (15978 ^ _776541) ^ [_1065668, _1065670] : [15979 ^ _776541 : [(15982 ^ _776541) ^ [] : [_1065668 = _1065670], (15980 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065668), _1065670))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065668), hAPP(c_Nat_OSuc, _1065670))))], (36986 ^ _776541) ^ [_1479445, _1479447, _1479449, _1479451, _1479453] : [c_Equiv__Relations_Oequivp(_1479445, _1479447), hBOOL(hAPP(hAPP(_1479447, _1479449), _1479451)), hBOOL(hAPP(hAPP(_1479447, _1479451), _1479453)), -(hBOOL(hAPP(hAPP(_1479447, _1479449), _1479453)))], (14586 ^ _776541) ^ [_1039540, _1039542] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039540), _1039542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039542), _1039540)))], (33915 ^ _776541) ^ [_1405213, _1405215] : [-(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)), _1405213)), 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), _1405215), _1405213))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1405213), _1405215))], (27881 ^ _776541) ^ [_1277827, _1277829] : [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), _1277827)), _1277829))), _1277827 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1277829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34996 ^ _776541) ^ [_1429493] : [-(c_Int_Oint__ge__less__than(_1429493) = 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), _1429493)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36866 ^ _776541) ^ [_1476182, _1476184, _1476186, _1476188, _1476190] : [c_Equiv__Relations_Oequiv(_1476182, _1476184, _1476186), hBOOL(hAPP(hAPP(c_member(_1476182), _1476188), _1476184)), hBOOL(hAPP(hAPP(c_member(_1476182), _1476190), _1476184)), 36877 ^ _776541 : [(36884 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476182, _1476182)), hAPP(hAPP(c_Product__Type_OPair(_1476182, _1476182), _1476188), _1476190)), _1476186)), -(hAPP(c_Relation_OImage(_1476182, _1476182, _1476186), hAPP(hAPP(c_Set_Oinsert(_1476182), _1476188), c_Orderings_Obot__class_Obot(tc_fun(_1476182, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1476182, _1476182, _1476186), hAPP(hAPP(c_Set_Oinsert(_1476182), _1476190), c_Orderings_Obot__class_Obot(tc_fun(_1476182, tc_HOL_Obool)))))], (36878 ^ _776541) ^ [] : [hAPP(c_Relation_OImage(_1476182, _1476182, _1476186), hAPP(hAPP(c_Set_Oinsert(_1476182), _1476188), c_Orderings_Obot__class_Obot(tc_fun(_1476182, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1476182, _1476182, _1476186), hAPP(hAPP(c_Set_Oinsert(_1476182), _1476190), c_Orderings_Obot__class_Obot(tc_fun(_1476182, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476182, _1476182)), hAPP(hAPP(c_Product__Type_OPair(_1476182, _1476182), _1476188), _1476190)), _1476186)))]]], (7005 ^ _776541) ^ [_890404, _890406, _890408] : [class_Orderings_Oord(_890404), 7008 ^ _776541 : [(7015 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890404), _890408), _890406)), -(hBOOL(hAPP(hAPP(c_member(_890404), _890406), hAPP(c_SetInterval_Oord__class_OatLeast(_890404), _890408))))], (7009 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890404), _890406), hAPP(c_SetInterval_Oord__class_OatLeast(_890404), _890408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890404), _890408), _890406)))]]], (32478 ^ _776541) ^ [_1361503, _1361505, _1361507, _1361509] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361503, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1361503, tc_fun(_1361503, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361503)), _1361505)), hAPP(hAPP(c_COMBC(_1361503, tc_fun(_1361503, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361503)), _1361507)), _1361509)), -(hBOOL(hAPP(hAPP(c_member(_1361503), _1361509), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361503, tc_HOL_Obool)), _1361505), _1361507))))], (42630 ^ _776541) ^ [_1625271, _1625273] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1625271, _1625273) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1625271), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1625273)))], (35515 ^ _776541) ^ [_1439195, _1439197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439195)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439197)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439195, _1439197) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1439195, _1439197)))], (33352 ^ _776541) ^ [_1388671, _1388673, _1388675, _1388677] : [-(hAPP(c_Set_OPow(_1388671), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388673, tc_fun(_1388671, tc_HOL_Obool)), _1388675), _1388677)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388673, tc_fun(tc_fun(_1388671, tc_HOL_Obool), tc_HOL_Obool)), _1388675), hAPP(hAPP(c_COMBB(tc_fun(_1388671, tc_HOL_Obool), tc_fun(tc_fun(_1388671, tc_HOL_Obool), tc_HOL_Obool), _1388673), c_Set_OPow(_1388671)), _1388677)))], (8333 ^ _776541) ^ [_919347, _919349, _919351] : [class_Lattices_Olattice(_919347), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919347), _919349), _919351) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919347), _919351), _919349))], (46231 ^ _776541) ^ [_1706306, _1706308, _1706310, _1706312, _1706314, _1706316] : [-(c_List_Ofoldr(_1706306, _1706308, _1706310, hAPP(hAPP(c_List_Olist_OCons(_1706306), _1706312), _1706314), _1706316) = hAPP(hAPP(_1706310, _1706312), c_List_Ofoldr(_1706306, _1706308, _1706310, _1706314, _1706316)))], (33249 ^ _776541) ^ [_1385963, _1385965, _1385967] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385963, tc_fun(_1385965, tc_HOL_Obool)), _1385967), hAPP(c_COMBK(tc_fun(_1385965, tc_HOL_Obool), _1385963), c_Orderings_Obot__class_Obot(tc_fun(_1385965, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1385965, tc_HOL_Obool)))], (44352 ^ _776541) ^ [_1663616] : [class_Groups_Omonoid__add(_1663616), -(c_List_Omonoid__add__class_Olistsum(_1663616) = c_List_Ofoldl(_1663616, _1663616, c_Groups_Oplus__class_Oplus(_1663616), c_Groups_Ozero__class_Ozero(_1663616)))], (44767 ^ _776541) ^ [_1671582, _1671584, _1671586, _1671588, _1671590] : [hAPP(hAPP(c_List_Omap(_1671582, _1671584), _1671586), _1671588) = hAPP(hAPP(c_List_Omap(_1671582, _1671584), _1671586), _1671590), c_Fun_Oinj__on(_1671582, _1671584, _1671586, c_Orderings_Otop__class_Otop(tc_fun(_1671582, tc_HOL_Obool))), -(_1671588 = _1671590)], (19056 ^ _776541) ^ [_1119870, _1119872] : [19058 ^ _776541 : [(19061 ^ _776541) ^ [] : [hBOOL(hAPP(_1119872, 19057 ^ [_1119870, _1119872]))], (19059 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19057 ^ [_1119870, _1119872]), _1119870)))]], 19062 ^ _776541 : [(19063 ^ _776541) ^ [_1120020] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1120020), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119870))), -(hBOOL(hAPP(_1119872, _1120020)))]]], (15914 ^ _776541) ^ [_1064547, _1064549, _1064551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064547), _1064549)), 15917 ^ _776541 : [(15937 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1064547, tc_Nat_Onat), _1064551), _1064549) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 15938 ^ _776541 : [(15939 ^ _776541) ^ [_1065028] : [hBOOL(hAPP(hAPP(c_member(_1064547), _1065028), _1064549)), hAPP(_1064551, _1065028) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15947 ^ _776541 : [(15952 ^ _776541) ^ [] : [hAPP(_1064551, 15946 ^ [_1064547, _1064549, _1064551, _1065028]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15950 ^ _776541) ^ [] : [_1065028 = 15946 ^ [_1064547, _1064549, _1064551, _1065028]], (15948 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1064547), 15946 ^ [_1064547, _1064549, _1064551, _1065028]), _1064549)))]]]]], (15918 ^ _776541) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1064547, tc_Nat_Onat), _1064551), _1064549) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15922 ^ _776541 : [(15927 ^ _776541) ^ [_1064867] : [hBOOL(hAPP(hAPP(c_member(_1064547), _1064867), _1064549)), -(15921 ^ [_1064547, _1064549, _1064551] = _1064867), -(hAPP(_1064551, _1064867) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15925 ^ _776541) ^ [] : [-(hAPP(_1064551, 15921 ^ [_1064547, _1064549, _1064551]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15923 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1064547), 15921 ^ [_1064547, _1064549, _1064551]), _1064549)))]]]]], (10613 ^ _776541) ^ [_959043, _959045, _959047, _959049] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_959043, _959045, _959047, _959049, c_Orderings_Obot__class_Obot(tc_fun(_959043, tc_HOL_Obool))), _959049)))], (7890 ^ _776541) ^ [_909504, _909506, _909508, _909510, _909512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909504, tc_HOL_Obool)), _909506), _909508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909504, tc_HOL_Obool)), _909510), _909512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909504, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909504, tc_HOL_Obool)), _909506), _909512)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909504, tc_HOL_Obool)), _909508), _909510))))], (21261 ^ _776541) ^ [_1161167, _1161169, _1161171] : [class_Int_Onumber__ring(_1161167), -(hAPP(c_Int_Onumber__class_Onumber__of(_1161167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1161169), _1161171)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161167), hAPP(c_Int_Onumber__class_Onumber__of(_1161167), _1161169)), hAPP(c_Int_Onumber__class_Onumber__of(_1161167), _1161171)))], (3194 ^ _776541) ^ [_824091, _824093, _824095, _824097] : [-(c_Big__Operators_Olinorder__class_OMin(_824097, _824093) = c_Big__Operators_Olinorder__class_OMin(_824095, _824091)), _824097 = _824095, _824093 = _824091], (8321 ^ _776541) ^ [_919113, _919115, _919117] : [class_Lattices_Osemilattice__sup(_919113), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919113), _919115), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919113), _919115), _919117)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919113), _919115), _919117))], (51837 ^ _776541) ^ [_1824336, _1824338] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824336), _1824338)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824338), _1824336)), -(_1824336 = _1824338)], (8753 ^ _776541) ^ [_926961, _926963, _926965] : [class_Lattices_Obounded__lattice__bot(_926961), 8756 ^ _776541 : [(8765 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926961), _926963), _926965) = c_Orderings_Obot__class_Obot(_926961)), _926963 = c_Orderings_Obot__class_Obot(_926961), _926965 = c_Orderings_Obot__class_Obot(_926961)], (8757 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926961), _926963), _926965) = c_Orderings_Obot__class_Obot(_926961), 8760 ^ _776541 : [(8763 ^ _776541) ^ [] : [-(_926965 = c_Orderings_Obot__class_Obot(_926961))], (8761 ^ _776541) ^ [] : [-(_926963 = c_Orderings_Obot__class_Obot(_926961))]]]]], (6254 ^ _776541) ^ [_877061] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_877061, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_877061, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_877061, tc_HOL_Obool)))], (4304 ^ _776541) ^ [_841726, _841728] : [_841728 = _841726, -(c_List_Oappend(_841728) = c_List_Oappend(_841726))], (40719 ^ _776541) ^ [_1573042, _1573044] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573042, _1573042)), hAPP(hAPP(c_Product__Type_OPair(_1573042, _1573042), _1573044), _1573044)), c_Relation_OId(_1573042))))], (5783 ^ _776541) ^ [_868074, _868076, _868078, _868080, _868082, _868084, _868086] : [c_Typedef_Otype__definition(_868074, _868076, _868078, _868080, _868082), hBOOL(hAPP(hAPP(c_member(_868076), _868084), _868082)), hBOOL(hAPP(hAPP(c_member(_868076), _868086), _868082)), 5794 ^ _776541 : [(5801 ^ _776541) ^ [] : [_868084 = _868086, -(hAPP(_868080, _868084) = hAPP(_868080, _868086))], (5795 ^ _776541) ^ [] : [hAPP(_868080, _868084) = hAPP(_868080, _868086), -(_868084 = _868086)]]], (20639 ^ _776541) ^ [_1149144, _1149146, _1149148, _1149150] : [class_Fields_Olinordered__field__inverse__zero(_1149144), 20642 ^ _776541 : [(20643 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149144), _1149146), _1149148)), _1149150)), 20646 ^ _776541 : [(20653 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), c_Groups_Ozero__class_Ozero(_1149144)), _1149148))), 20656 ^ _776541 : [(20663 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), _1149148), c_Groups_Ozero__class_Ozero(_1149144)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), c_Groups_Ozero__class_Ozero(_1149144)), _1149150)))], (20657 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), _1149148), c_Groups_Ozero__class_Ozero(_1149144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149144), _1149150), _1149148)), _1149146)))]]], (20647 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), c_Groups_Ozero__class_Ozero(_1149144)), _1149148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), _1149146), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149144), _1149150), _1149148))))]]], (20669 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149144), _1149146), _1149148)), _1149150))), 20672 ^ _776541 : [(20675 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), _1149146), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149144), _1149150), _1149148)))], (20673 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), c_Groups_Ozero__class_Ozero(_1149144)), _1149148)))]], 20676 ^ _776541 : [(20679 ^ _776541) ^ [] : [20680 ^ _776541 : [(20683 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149144), _1149150), _1149148)), _1149146))], (20681 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), _1149148), c_Groups_Ozero__class_Ozero(_1149144))))]], 20684 ^ _776541 : [(20687 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), c_Groups_Ozero__class_Ozero(_1149144)), _1149150))], (20685 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), _1149148), c_Groups_Ozero__class_Ozero(_1149144)))]]], (20677 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149144), c_Groups_Ozero__class_Ozero(_1149144)), _1149148))]]]]], (22943 ^ _776541) ^ [_1192264, _1192266, _1192268, _1192270] : [class_Rings_Olinordered__semidom(_1192264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1192266), _1192268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192264), c_Groups_Ozero__class_Ozero(_1192264)), _1192270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192264), _1192270), c_Groups_Oone__class_Oone(_1192264))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192264), hAPP(hAPP(c_Power_Opower__class_Opower(_1192264), _1192270), _1192268)), hAPP(hAPP(c_Power_Opower__class_Opower(_1192264), _1192270), _1192266))))], (38491 ^ _776541) ^ [_1514461, _1514463] : [-(c_HOL_OThe(_1514461, hAPP(c_fequal, _1514463)) = _1514463)], (15196 ^ _776541) ^ [_1050724, _1050726] : [class_Rings_Olinordered__semidom(_1050724), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050724), _1050726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050724), _1050726), c_Groups_Oone__class_Oone(_1050724)))))], (37806 ^ _776541) ^ [_1497219, _1497221] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497219), _1497221)), -(_1497221 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1497219, 37810 ^ [_1497219, _1497221]), 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)), 37809 ^ [_1497219, _1497221]))))], (51033 ^ _776541) ^ [_1809872, _1809874, _1809876, _1809878] : [class_Rings_Ocomm__ring(_1809872), class_Rings_Odvd(_1809872), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809872), _1809874), _1809876)), 51044 ^ _776541 : [(51051 ^ _776541) ^ [_1810298, _1810300] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809872), _1809874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809872), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1809872), _1810300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1809872), _1810298), _1809876))), _1809878))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809872), _1809874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809872), _1810300), _1809878))))], (51045 ^ _776541) ^ [_1810125, _1810127] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809872), _1809874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809872), _1810127), _1809878))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809872), _1809874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809872), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1809872), _1810127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1809872), _1810125), _1809876))), _1809878))))]]], (2972 ^ _776541) ^ [_820650, _820652, _820654, _820656] : [-(c_Nitpick_OAbs__Frac(_820656, _820652) = c_Nitpick_OAbs__Frac(_820654, _820650)), _820656 = _820654, _820652 = _820650], (11924 ^ _776541) ^ [_985960, _985962, _985964, _985966, _985968, _985970] : [-(_985960 = _985962), -(hAPP(c_Fun_Ofun__upd(_985964, _985966, _985968, _985962, _985970), _985960) = hAPP(_985968, _985960))], (36043 ^ _776541) ^ [_1454237, _1454239, _1454241] : [class_Orderings_Olinorder(_1454237), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454237), _1454239)), -(_1454239 = c_Orderings_Obot__class_Obot(tc_fun(_1454237, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454237), _1454241)), -(_1454241 = c_Orderings_Obot__class_Obot(tc_fun(_1454237, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1454237), c_Big__Operators_Olattice_OSup__fin(_1454237, c_Orderings_Oord__class_Omax(_1454237), _1454239)), c_Big__Operators_Olattice_OSup__fin(_1454237, c_Orderings_Oord__class_Omax(_1454237), _1454241)) = c_Big__Operators_Olattice_OSup__fin(_1454237, c_Orderings_Oord__class_Omax(_1454237), hAPP(c_Set_OCollect(_1454237), hAPP(hAPP(c_COMBB(tc_fun(_1454237, tc_HOL_Obool), tc_HOL_Obool, _1454237), c_HOL_OEx(_1454237)), hAPP(hAPP(c_COMBB(tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool)), tc_fun(_1454237, tc_HOL_Obool), _1454237), hAPP(c_COMBB(tc_fun(_1454237, tc_HOL_Obool), tc_HOL_Obool, _1454237), c_HOL_OEx(_1454237))), hAPP(hAPP(c_COMBC(_1454237, tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool)), tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1454237, tc_fun(tc_fun(_1454237, tc_HOL_Obool), tc_fun(_1454237, tc_HOL_Obool))), tc_fun(tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool)), tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool))), _1454237), c_COMBS(_1454237, tc_fun(_1454237, tc_HOL_Obool), tc_fun(_1454237, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1454237, tc_fun(_1454237, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1454237, tc_fun(tc_fun(_1454237, tc_HOL_Obool), tc_fun(_1454237, tc_HOL_Obool))), _1454237), hAPP(c_COMBB(tc_fun(_1454237, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1454237, tc_HOL_Obool), tc_fun(_1454237, tc_HOL_Obool)), _1454237), c_COMBS(_1454237, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool)), tc_fun(_1454237, tc_fun(_1454237, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1454237), hAPP(c_COMBB(tc_fun(_1454237, tc_HOL_Obool), tc_fun(_1454237, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1454237), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1454237), c_fconj))), hAPP(hAPP(c_COMBC(_1454237, tc_fun(_1454237, tc_fun(_1454237, _1454237)), tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1454237, _1454237), tc_fun(_1454237, tc_HOL_Obool)), tc_fun(tc_fun(_1454237, tc_fun(_1454237, _1454237)), tc_fun(_1454237, tc_fun(_1454237, tc_HOL_Obool))), _1454237), c_COMBB(tc_fun(_1454237, _1454237), tc_fun(_1454237, tc_HOL_Obool), _1454237)), hAPP(hAPP(c_COMBB(tc_fun(_1454237, tc_HOL_Obool), tc_fun(tc_fun(_1454237, _1454237), tc_fun(_1454237, tc_HOL_Obool)), _1454237), c_COMBB(_1454237, tc_HOL_Obool, _1454237)), c_fequal))), c_Orderings_Oord__class_Omin(_1454237)))))), hAPP(hAPP(c_COMBC(_1454237, tc_fun(_1454237, tc_HOL_Obool), tc_fun(_1454237, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1454237, tc_HOL_Obool), tc_fun(_1454237, tc_HOL_Obool)), _1454237), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1454237)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1454237), c_fconj), hAPP(hAPP(c_COMBC(_1454237, tc_fun(_1454237, tc_HOL_Obool), tc_HOL_Obool), c_member(_1454237)), _1454239)))), hAPP(hAPP(c_COMBC(_1454237, tc_fun(_1454237, tc_HOL_Obool), tc_HOL_Obool), c_member(_1454237)), _1454241))))))))], (17303 ^ _776541) ^ [_1088048, _1088050, _1088052, _1088054] : [class_Rings_Olinordered__ring__strict(_1088048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088048), _1088050), _1088052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088048), _1088054), c_Groups_Ozero__class_Ozero(_1088048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088048), _1088052), _1088054)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088048), _1088050), _1088054))))], (2584 ^ _776541) ^ [_814630, _814632] : [_814632 = _814630, -(c_Int_Oint__ge__less__than(_814632) = c_Int_Oint__ge__less__than(_814630))], (1694 ^ _776541) ^ [_800580, _800582] : [-(class_Groups_Osemigroup__add(_800580)), _800582 = _800580, class_Groups_Osemigroup__add(_800582)], (10929 ^ _776541) ^ [_965268, _965270] : [-(_965268 = c_Orderings_Obot__class_Obot(tc_fun(_965270, tc_HOL_Obool))), 10934 ^ _776541 : [(10937 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_965270), 10932 ^ [_965268, _965270]), 10933 ^ [_965268, _965270]))], (10935 ^ _776541) ^ [] : [-(_965268 = hAPP(hAPP(c_Set_Oinsert(_965270), 10932 ^ [_965268, _965270]), 10933 ^ [_965268, _965270]))]]], (44655 ^ _776541) ^ [_1669377, _1669379] : [-(_1669377 = c_List_Olist_ONil(_1669379)), -(hAPP(hAPP(c_List_Oappend(_1669379), c_List_Obutlast(_1669379, _1669377)), hAPP(hAPP(c_List_Olist_OCons(_1669379), c_List_Olast(_1669379, _1669377)), c_List_Olist_ONil(_1669379))) = _1669377)], (42508 ^ _776541) ^ [_1622263, _1622265, _1622267, _1622269] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1622263, _1622265))), hAPP(hAPP(c_List_Ozip(_1622263, _1622265), _1622267), _1622269)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622263)), _1622267)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622265)), _1622269)))], (938 ^ _776541) ^ [_790612, _790614, _790616, _790618] : [-(c_Wellfounded_Owf(_790616, _790612)), c_Wellfounded_Owf(_790618, _790614), _790618 = _790616, _790614 = _790612], (23115 ^ _776541) ^ [_1195349, _1195351, _1195353, _1195355, _1195357] : [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), _1195349), _1195351)), _1195353)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195349), _1195355)), _1195357))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195357), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195349), _1195357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195349), _1195353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195355), _1195351)))], (15059 ^ _776541) ^ [_1048550, _1048552] : [class_Groups_Oone(_1048550), 15062 ^ _776541 : [(15069 ^ _776541) ^ [] : [_1048552 = c_Groups_Oone__class_Oone(_1048550), -(c_Groups_Oone__class_Oone(_1048550) = _1048552)], (15063 ^ _776541) ^ [] : [c_Groups_Oone__class_Oone(_1048550) = _1048552, -(_1048552 = c_Groups_Oone__class_Oone(_1048550))]]], (50602 ^ _776541) ^ [_1799400, _1799402, _1799404] : [c_Fun_Oinj__on(_1799400, _1799402, _1799404, c_Orderings_Otop__class_Otop(tc_fun(_1799400, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1799400, _1799402, _1799404), c_Orderings_Otop__class_Otop(tc_fun(_1799400, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799402, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1799400, _1799402, _1799404, c_Orderings_Otop__class_Otop(tc_fun(_1799400, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799402, tc_HOL_Obool))))], (11586 ^ _776541) ^ [_979170, _979172] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979170, tc_HOL_Obool)), hAPP(c_Set_OPow(_979170), _979172))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979170), _979172)))], (23139 ^ _776541) ^ [_1195802, _1195804] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195802), _1195804))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1195804, _1195802) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1195804), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1195804), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1195802)))], (4038 ^ _776541) ^ [_837585, _837587] : [_837587 = _837585, -(c_New__DSequence_Opos__empty(_837587) = c_New__DSequence_Opos__empty(_837585))], (33599 ^ _776541) ^ [_1395148, _1395150, _1395152, _1395154] : [hBOOL(hAPP(hAPP(c_member(_1395150), _1395154), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395148, tc_fun(_1395150, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395148, tc_HOL_Obool))), _1395152))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395148, tc_fun(_1395150, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395148, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1395150, tc_HOL_Obool), tc_fun(_1395150, tc_HOL_Obool), _1395148), hAPP(c_COMBC(_1395150, tc_fun(_1395150, tc_HOL_Obool), tc_HOL_Obool), c_member(_1395150))), _1395152)), _1395154)))], (43597 ^ _776541) ^ [_1646209, _1646211, _1646213] : [_1646209 = hAPP(hAPP(c_List_Oappend(_1646211), _1646213), _1646209), -(_1646213 = c_List_Olist_ONil(_1646211))], (44050 ^ _776541) ^ [_1657350, _1657352, _1657354, _1657356] : [-(hAPP(c_List_Orotate1(_1657350), c_List_Olist_ONil(_1657350)) = c_List_Olist_ONil(_1657350))], (6394 ^ _776541) ^ [_879777, _879779, _879781] : [class_Complete__Lattice_Ocomplete__lattice(_879777), hBOOL(hAPP(hAPP(c_member(_879777), _879779), _879781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879777), _879779), c_Complete__Lattice_OSup__class_OSup(_879777, _879781))))], (48698 ^ _776541) ^ [_1758105, _1758107, _1758109] : [_1758107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1758105, _1758107, _1758109) = c_List_Olist_ONil(_1758105))], (29177 ^ _776541) ^ [_1299494, _1299496] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1299494)), _1299496) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299494), _1299496))), _1299496))], (25181 ^ _776541) ^ [_1232479, _1232481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232479)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232481), _1232479)), _1232479) = _1232481)], (7126 ^ _776541) ^ [_892637, _892639, _892641, _892643] : [hBOOL(hAPP(hAPP(c_member(_892637), _892639), hAPP(hAPP(c_Set_Oinsert(_892637), _892641), _892643))), -(_892639 = _892641), -(hBOOL(hAPP(hAPP(c_member(_892637), _892639), _892643)))], (45624 ^ _776541) ^ [_1691594, _1691596, _1691598, _1691600, _1691602, _1691604, _1691606, _1691608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691594), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691596)), _1691598))), c_List_Olist__all2(_1691596, _1691600, _1691602, _1691598, _1691604), hBOOL(hAPP(hAPP(_1691602, _1691606), _1691608)), -(c_List_Olist__all2(_1691596, _1691600, _1691602, hAPP(hAPP(c_List_Olist__update(_1691596, _1691598), _1691594), _1691606), hAPP(hAPP(c_List_Olist__update(_1691600, _1691604), _1691594), _1691608)))], (3718 ^ _776541) ^ [_832289, _832291] : [_832291 = _832289, -(c_List_Omonoid__add__class_Olistsum(_832291) = c_List_Omonoid__add__class_Olistsum(_832289))], (32554 ^ _776541) ^ [_1365271, _1365273, _1365275, _1365277, _1365279] : [_1365271 = c_Orderings_Obot__class_Obot(tc_fun(_1365273, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365273, tc_fun(_1365275, tc_HOL_Obool)), _1365271), hAPP(hAPP(c_COMBB(tc_fun(_1365275, tc_HOL_Obool), tc_fun(_1365275, tc_HOL_Obool), _1365273), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365275, tc_HOL_Obool)), _1365277)), _1365279)) = c_Orderings_Otop__class_Otop(tc_fun(_1365275, tc_HOL_Obool)))], (5550 ^ _776541) ^ [_861315, _861317] : [_861317 = _861315, -(tc_List_Olist(_861317) = tc_List_Olist(_861315))], (24118 ^ _776541) ^ [_1212950, _1212952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212950)), 24121 ^ _776541 : [(24130 ^ _776541) ^ [] : [-(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), _1212950), _1212952)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212952), _1212950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212952))], (24122 ^ _776541) ^ [] : [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), _1212950), _1212952))), 24125 ^ _776541 : [(24128 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212952)))], (24126 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212952), _1212950)))]]]]], (39471 ^ _776541) ^ [_1541479, _1541481, _1541483, _1541485, _1541487, _1541489] : [-(c_Product__Type_Omap__pair(_1541479, _1541481, _1541483, _1541485, _1541487, _1541489) = hAPP(c_Product__Type_Oprod_Oprod__case(_1541479, _1541483, tc_prod(_1541481, _1541485)), hAPP(hAPP(c_COMBC(_1541479, tc_fun(_1541483, _1541485), tc_fun(_1541483, tc_prod(_1541481, _1541485))), hAPP(hAPP(c_COMBB(tc_fun(_1541485, tc_prod(_1541481, _1541485)), tc_fun(tc_fun(_1541483, _1541485), tc_fun(_1541483, tc_prod(_1541481, _1541485))), _1541479), c_COMBB(_1541485, tc_prod(_1541481, _1541485), _1541483)), hAPP(hAPP(c_COMBB(_1541481, tc_fun(_1541485, tc_prod(_1541481, _1541485)), _1541479), c_Product__Type_OPair(_1541481, _1541485)), _1541487))), _1541489)))], (1998 ^ _776541) ^ [_805281, _805283] : [_805283 = _805281, -(c_Hoare__Mirabelle_ORep__triple(_805283) = c_Hoare__Mirabelle_ORep__triple(_805281))], (24042 ^ _776541) ^ [_1211809] : [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)), _1211809))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1211809)))], (27725 ^ _776541) ^ [_1275234, _1275236, _1275238] : [class_Fields_Olinordered__field__inverse__zero(_1275234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275234), c_Groups_Ozero__class_Ozero(_1275234)), _1275236)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275234), hAPP(c_Groups_Oabs__class_Oabs(_1275234), _1275238)), _1275236) = hAPP(c_Groups_Oabs__class_Oabs(_1275234), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275234), _1275238), _1275236)))], (45820 ^ _776541) ^ [_1695792, _1695794] : [-(hAPP(c_List_OremoveAll(_1695792, _1695794), c_List_Olist_ONil(_1695792)) = c_List_Olist_ONil(_1695792))], (33855 ^ _776541) ^ [_1403787, _1403789, _1403791, _1403793] : [class_Groups_Ocomm__monoid__mult(_1403787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403789), _1403791)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403789, _1403787), hAPP(c_COMBK(_1403787, _1403789), _1403793)), _1403791) = hAPP(hAPP(c_Power_Opower__class_Opower(_1403787), _1403793), hAPP(c_Finite__Set_Ocard(_1403789), _1403791)))], (43866 ^ _776541) ^ [_1652956, _1652958, _1652960] : [-(hAPP(hAPP(c_List_Oappend(_1652956), hAPP(hAPP(c_List_Otake(_1652956), _1652958), _1652960)), hAPP(hAPP(c_List_Odrop(_1652956), _1652958), _1652960)) = _1652960)], (49331 ^ _776541) ^ [_1772409, _1772411, _1772413] : [c_List_Olist__ex(_1772409, _1772411, _1772413), 49335 ^ _776541 : [(49338 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1772411, 49334 ^ [_1772409, _1772411, _1772413])))], (49336 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772409), 49334 ^ [_1772409, _1772411, _1772413]), hAPP(c_List_Oset(_1772409), _1772413))))]]], (16845 ^ _776541) ^ [_1079711, _1079713, _1079715] : [class_Groups_Oordered__comm__monoid__add(_1079711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079711), c_Groups_Ozero__class_Ozero(_1079711)), _1079713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079711), c_Groups_Ozero__class_Ozero(_1079711)), _1079715)), 16856 ^ _776541 : [(16865 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079711), _1079713), _1079715) = c_Groups_Ozero__class_Ozero(_1079711)), _1079713 = c_Groups_Ozero__class_Ozero(_1079711), _1079715 = c_Groups_Ozero__class_Ozero(_1079711)], (16857 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079711), _1079713), _1079715) = c_Groups_Ozero__class_Ozero(_1079711), 16860 ^ _776541 : [(16863 ^ _776541) ^ [] : [-(_1079715 = c_Groups_Ozero__class_Ozero(_1079711))], (16861 ^ _776541) ^ [] : [-(_1079713 = c_Groups_Ozero__class_Ozero(_1079711))]]]]], (6728 ^ _776541) ^ [_885412, _885414, _885416] : [class_Orderings_Oorder(_885412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885412), _885414), _885416)), 6735 ^ _776541 : [(6742 ^ _776541) ^ [] : [_885416 = _885414, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885412), _885416), _885414)))], (6736 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885412), _885416), _885414)), -(_885416 = _885414)]]], (42467 ^ _776541) ^ [_1619868, _1619870, _1619872] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1619868), _1619870)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1619868)), hAPP(c_Set_OCollect(tc_List_Olist(_1619868)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1619868), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1619868)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1619868), tc_fun(_1619868, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1619868, tc_HOL_Obool), tc_fun(tc_fun(_1619868, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1619868)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1619868, tc_HOL_Obool))), c_List_Oset(_1619868))), _1619870))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1619868), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1619868)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1619868)))), _1619872))))))], (10387 ^ _776541) ^ [_954928, _954930, _954932] : [class_Groups_Oordered__ab__group__add(_954928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954928), _954930), _954932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954928), hAPP(c_Groups_Ouminus__class_Ouminus(_954928), _954932)), hAPP(c_Groups_Ouminus__class_Ouminus(_954928), _954930))))], (22097 ^ _776541) ^ [_1177201, _1177203, _1177205, _1177207] : [class_Rings_Olinordered__semidom(_1177201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177201), c_Groups_Oone__class_Oone(_1177201)), _1177203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177201), hAPP(hAPP(c_Power_Opower__class_Opower(_1177201), _1177203), _1177205)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177201), _1177203), _1177207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177205), _1177207)))], (36589 ^ _776541) ^ [_1469889, _1469891] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1469889, _1469889)), hAPP(hAPP(c_Product__Type_OPair(_1469889, _1469889), 36590 ^ [_1469889, _1469891]), 36590 ^ [_1469889, _1469891])), _1469891))), -(c_Relation_Oirrefl(_1469889, _1469891))], (9718 ^ _776541) ^ [_942908, _942910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942908, tc_HOL_Obool)), _942910), c_Orderings_Obot__class_Obot(tc_fun(_942908, tc_HOL_Obool))))], (16194 ^ _776541) ^ [_1069192, _1069194] : [class_Groups_Ocomm__monoid__add(_1069192), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069192), _1069194), c_Groups_Ozero__class_Ozero(_1069192)) = _1069194)], (44320 ^ _776541) ^ [_1662846, _1662848, _1662850, _1662852, _1662854] : [class_Orderings_Olinorder(_1662846), -(hAPP(c_List_Oset(_1662848), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662848, _1662846, _1662850), _1662852), _1662854)) = hAPP(hAPP(c_Set_Oinsert(_1662848), _1662852), hAPP(c_List_Oset(_1662848), _1662854)))], (49229 ^ _776541) ^ [_1770430, _1770432] : [49230 ^ _776541 : [(49231 ^ _776541) ^ [_1770496] : [hBOOL(hAPP(_1770432, _1770496))]], 49233 ^ _776541 : [(49236 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1770432, 49232 ^ [_1770430, _1770432])))], (49234 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770430), 49232 ^ [_1770430, _1770432]), c_Orderings_Otop__class_Otop(tc_fun(_1770430, tc_HOL_Obool)))))]]], (39691 ^ _776541) ^ [_1547266] : [-(_1547266 = hAPP(c_Int_OAbs__Integ, 39689 ^ [_1547266]))], (52081 ^ _776541) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (36452 ^ _776541) ^ [_1465606] : [-(c_Wellfounded_Omeasure(_1465606) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1465606), c_Wellfounded_Oless__than))], (34735 ^ _776541) ^ [_1424063, _1424065] : [class_Rings_Oring__1(_1424063), 34738 ^ _776541 : [(34745 ^ _776541) ^ [] : [-(_1424065 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34748 ^ _776541 : [(34755 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424065), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1424063), _1424065) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1424063), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1424063, _1424063)), tc_fun(tc_Int_Oint, _1424063)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1424063, _1424063), _1424063), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1424063, _1424063)), tc_fun(tc_Int_Oint, _1424063)), tc_Int_Oint), c_COMBB(tc_fun(_1424063, _1424063), _1424063, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1424063, tc_fun(tc_fun(_1424063, _1424063), _1424063), tc_Int_Oint), c_HOL_OLet(_1424063, _1424063)), c_Int_Oring__1__class_Oof__int(_1424063)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1424063, _1424063), tc_fun(_1424063, _1424063)), hAPP(hAPP(c_COMBB(tc_fun(_1424063, tc_fun(_1424063, _1424063)), tc_fun(tc_fun(_1424063, _1424063), tc_fun(_1424063, _1424063)), tc_Int_Oint), c_COMBS(_1424063, _1424063, _1424063)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1424063, _1424063), tc_fun(_1424063, tc_fun(_1424063, _1424063))), hAPP(hAPP(c_COMBB(tc_fun(_1424063, tc_fun(_1424063, _1424063)), tc_fun(tc_fun(_1424063, _1424063), tc_fun(_1424063, tc_fun(_1424063, _1424063))), tc_Int_Oint), c_COMBB(_1424063, tc_fun(_1424063, _1424063), _1424063)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1424063, tc_fun(_1424063, _1424063)), tc_Int_Oint), c_If(_1424063)), 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(_1424063, _1424063, _1424063), c_Groups_Oplus__class_Oplus(_1424063)), c_COMBI(_1424063))))), hAPP(hAPP(c_COMBC(_1424063, _1424063, _1424063), hAPP(hAPP(c_COMBB(_1424063, tc_fun(_1424063, _1424063), _1424063), c_Groups_Oplus__class_Oplus(_1424063)), hAPP(hAPP(c_COMBS(_1424063, _1424063, _1424063), c_Groups_Oplus__class_Oplus(_1424063)), c_COMBI(_1424063)))), c_Groups_Oone__class_Oone(_1424063))))), c_Divides_Odivmod__int(_1424065, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34749 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424065), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1424063), _1424065) = hAPP(c_Groups_Ouminus__class_Ouminus(_1424063), hAPP(c_Int_Oring__1__class_Oof__int(_1424063), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1424065))))]]], (34739 ^ _776541) ^ [] : [_1424065 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1424063), _1424065) = c_Groups_Ozero__class_Ozero(_1424063))]]], (46259 ^ _776541) ^ [_1706998, _1707000, _1707002, _1707004] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1706998, tc_Nat_Onat), _1706998), c_Product__Type_Ofst(_1706998, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1706998, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1706998, 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(_1706998, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1706998, tc_Nat_Onat))), _1707000)), hAPP(hAPP(c_List_Ozip(_1706998, tc_Nat_Onat), _1707002), c_List_Oupt(_1707004, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707004), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706998)), _1707002)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1706998, tc_Nat_Onat), _1706998), c_Product__Type_Ofst(_1706998, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1706998, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1706998, 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(_1706998, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1706998, 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(_1706998, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1706998, tc_Nat_Onat))), _1707004))), _1707000)), hAPP(hAPP(c_List_Ozip(_1706998, tc_Nat_Onat), _1707002), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706998)), _1707002))))))], (14348 ^ _776541) ^ [_1035324, _1035326, _1035328, _1035330, _1035332] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1035324), 14351 ^ _776541 : [(14352 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035326), _1035330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035328), _1035332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035326), _1035332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035328), _1035330)), -(_1035326 = _1035328), -(_1035330 = _1035332)], (14362 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035326), _1035330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035328), _1035332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035326), _1035332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035328), _1035330))), 14365 ^ _776541 : [(14368 ^ _776541) ^ [] : [_1035330 = _1035332], (14366 ^ _776541) ^ [] : [_1035326 = _1035328]]]]], (24902 ^ _776541) ^ [_1227385, _1227387, _1227389, _1227391] : [class_Divides_Oring__div(_1227385), -(c_Divides_Odiv__class_Omod(_1227385, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227385), _1227387), _1227389), _1227391) = c_Divides_Odiv__class_Omod(_1227385, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227385), c_Divides_Odiv__class_Omod(_1227385, _1227387, _1227391)), _1227389), _1227391))], (16014 ^ _776541) ^ [_1066274, _1066276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066274), _1066276))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066274), hAPP(c_Nat_OSuc, _1066276))), -(_1066276 = _1066274)], (46415 ^ _776541) ^ [_1709937, _1709939, _1709941, _1709943] : [class_Groups_Ocomm__monoid__add(_1709937), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1709937), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1709937), _1709939), c_List_Oupt(_1709941, _1709943))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1709937), _1709939), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1709941, _1709943))))], (18950 ^ _776541) ^ [_1117883, _1117885, _1117887] : [class_Rings_Olinordered__ring__strict(_1117883), 18953 ^ _776541 : [(18962 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117883), _1117885), _1117885)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117883), _1117887), _1117887)) = c_Groups_Ozero__class_Ozero(_1117883)), _1117885 = c_Groups_Ozero__class_Ozero(_1117883), _1117887 = c_Groups_Ozero__class_Ozero(_1117883)], (18954 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117883), _1117885), _1117885)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117883), _1117887), _1117887)) = c_Groups_Ozero__class_Ozero(_1117883), 18957 ^ _776541 : [(18960 ^ _776541) ^ [] : [-(_1117887 = c_Groups_Ozero__class_Ozero(_1117883))], (18958 ^ _776541) ^ [] : [-(_1117885 = c_Groups_Ozero__class_Ozero(_1117883))]]]]], (44641 ^ _776541) ^ [_1669131, _1669133, _1669135, _1669137] : [-(hAPP(hAPP(c_List_Oappend(_1669131), _1669133), hAPP(hAPP(c_List_Olist_OCons(_1669131), _1669135), c_List_Olist_ONil(_1669131))) = _1669137), -(_1669137 = c_List_Olist_ONil(_1669131)), c_List_Obutlast(_1669131, _1669137) = _1669133, c_List_Olast(_1669131, _1669137) = _1669135], (9248 ^ _776541) ^ [_935978, _935980, _935982] : [class_Orderings_Olinorder(_935978), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935978), _935980), _935982))), -(_935980 = _935982), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935978), _935982), _935980)))], (49317 ^ _776541) ^ [_1772155] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1772155, tc_HOL_Obool) = c_Set_OBex(_1772155))], (974 ^ _776541) ^ [_791158, _791160, _791162, _791164, _791166, _791168, _791170, _791172, _791174, _791176, _791178, _791180] : [-(c_Equiv__Relations_Ocongruent2(_791178, _791174, _791170, _791166, _791162, _791158)), c_Equiv__Relations_Ocongruent2(_791180, _791176, _791172, _791168, _791164, _791160), _791180 = _791178, _791176 = _791174, _791172 = _791170, _791168 = _791166, _791164 = _791162, _791160 = _791158], (39099 ^ _776541) ^ [_1529929, _1529931, _1529933, _1529935, _1529937, _1529939] : [class_Groups_Ocomm__monoid__mult(_1529929), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529931, _1529929), hAPP(hAPP(c_COMBC(_1529931, tc_fun(_1529933, tc_HOL_Obool), _1529929), hAPP(hAPP(c_COMBB(tc_fun(_1529933, _1529929), tc_fun(tc_fun(_1529933, tc_HOL_Obool), _1529929), _1529931), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529933, _1529929)), _1529935)), _1529937)), _1529939) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1529931, _1529933), _1529929), hAPP(c_Product__Type_Oprod_Oprod__case(_1529931, _1529933, _1529929), _1529935)), hAPP(hAPP(c_Product__Type_OSigma(_1529931, _1529933), _1529939), hAPP(c_COMBK(tc_fun(_1529933, tc_HOL_Obool), _1529931), _1529937))))], (46285 ^ _776541) ^ [_1707553, _1707555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707553), _1707555)), -(c_List_Oupt(_1707555, _1707553) = c_List_Olist_ONil(tc_Nat_Onat))], (28281 ^ _776541) ^ [_1284313, _1284315] : [class_Int_Onumber__ring(_1284313), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1284313), c_Groups_Oone__class_Oone(_1284313)), hAPP(c_Int_Onumber__class_Onumber__of(_1284313), _1284315)) = hAPP(c_Int_Onumber__class_Onumber__of(_1284313), 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), _1284315))))], (29335 ^ _776541) ^ [_1302232] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1302232), _1302232)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1302232)], (9164 ^ _776541) ^ [_934826, _934828, _934830] : [class_Orderings_Oorder(_934826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934826), _934828), _934830)), _934830 = _934828], (28313 ^ _776541) ^ [_1284809, _1284811] : [c_Int_OBit1(_1284809) = c_Int_OBit1(_1284811), -(_1284809 = _1284811)], (46395 ^ _776541) ^ [_1709533, _1709535] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1709533, _1709535)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1709533), hAPP(c_Nat_OSuc, _1709535)))], (14702 ^ _776541) ^ [_1041556, _1041558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041556), _1041558)), 14705 ^ _776541 : [(14708 ^ _776541) ^ [] : [_1041556 = _1041558], (14706 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041556), _1041558)))]]], (41192 ^ _776541) ^ [_1584628, _1584630, _1584632, _1584634, _1584636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584630, tc_HOL_Obool)), _1584634), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584630, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584628, _1584630, hAPP(c_Relation_Oconverse(_1584630, _1584628), _1584632)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584628, tc_HOL_Obool)), _1584636))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584628, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584630, _1584628, _1584632), _1584634)), _1584636)))], (43982 ^ _776541) ^ [_1655591, _1655593, _1655595, _1655597] : [-(hAPP(hAPP(c_List_Odrop(_1655591), _1655593), hAPP(hAPP(c_List_Olist_OCons(_1655591), _1655595), _1655597)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1655591), hAPP(hAPP(c_List_Olist_OCons(_1655591), _1655595), _1655597), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1655591), tc_List_Olist(_1655591)), c_List_Odrop(_1655591)), _1655597), _1655593))], (7824 ^ _776541) ^ [_908171, _908173] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908171, tc_HOL_Obool)), _908173), c_Orderings_Obot__class_Obot(tc_fun(_908171, tc_HOL_Obool))) = _908173)], (52387 ^ _776541) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (6497 ^ _776541) ^ [_881498, _881500] : [hAPP(c_Set_OCollect(_881498), _881500) = c_Orderings_Obot__class_Obot(tc_fun(_881498, tc_HOL_Obool)), 6500 ^ _776541 : [(6501 ^ _776541) ^ [_881583] : [hBOOL(hAPP(_881500, _881583))]]], (10659 ^ _776541) ^ [_959916, _959918] : [class_Lattices_Oboolean__algebra(_959916), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959916), hAPP(c_Groups_Ouminus__class_Ouminus(_959916), _959918)), _959918) = c_Orderings_Otop__class_Otop(_959916))], (52409 ^ _776541) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (49756 ^ _776541) ^ [_1782008, _1782010, _1782012, _1782014] : [c_Relation_Osym(_1782008, _1782010), -(c_Relation_Osym(_1782012, hAPP(hAPP(c_Relation_Oinv__image(_1782008, _1782012), _1782010), _1782014)))], (52013 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (16937 ^ _776541) ^ [_1081319, _1081321, _1081323] : [class_Rings_Oordered__ring(_1081319), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081319), c_Groups_Ozero__class_Ozero(_1081319)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081319), _1081321), _1081323)))), 16942 ^ _776541 : [(16949 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081319), _1081321), c_Groups_Ozero__class_Ozero(_1081319))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081319), _1081323), c_Groups_Ozero__class_Ozero(_1081319)))], (16943 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081319), c_Groups_Ozero__class_Ozero(_1081319)), _1081321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081319), c_Groups_Ozero__class_Ozero(_1081319)), _1081323))]]], (11084 ^ _776541) ^ [_968277, _968279, _968281] : [class_Rings_Oidom(_968277), 11087 ^ _776541 : [(11088 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968277), _968279), _968279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968277), _968281), _968281), -(_968279 = _968281), -(_968279 = hAPP(c_Groups_Ouminus__class_Ouminus(_968277), _968281))], (11098 ^ _776541) ^ [] : [11099 ^ _776541 : [(11102 ^ _776541) ^ [] : [_968279 = hAPP(c_Groups_Ouminus__class_Ouminus(_968277), _968281)], (11100 ^ _776541) ^ [] : [_968279 = _968281]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968277), _968279), _968279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968277), _968281), _968281))]]], (26661 ^ _776541) ^ [_1257742, _1257744] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257742))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257742)), _1257744) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257744))], (47214 ^ _776541) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (10883 ^ _776541) ^ [_964382, _964384, _964386, _964388, _964390] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_964382, _964382, _964384, _964386, _964388), _964390)), -(hBOOL(hAPP(hAPP(c_member(_964382), _964386), _964388))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_964382, _964384, hAPP(hAPP(c_Set_Oinsert(_964382), _964386), _964388)), _964390)))], (49397 ^ _776541) ^ [_1775267, _1775269, _1775271, _1775273] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775267), _1775269)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1775267), _1775271)), -(_1775271 = c_Orderings_Obot__class_Obot(tc_fun(_1775267, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1775267, _1775273, _1775269, _1775271)), 49411 ^ _776541 : [(49414 ^ _776541) ^ [_1775612] : [hBOOL(hAPP(hAPP(c_member(_1775267), _1775612), _1775271)), hBOOL(hAPP(hAPP(_1775273, 49410 ^ [_1775267, _1775269, _1775271, _1775273]), _1775612))], (49412 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775267), 49410 ^ [_1775267, _1775269, _1775271, _1775273]), _1775269)))]]], (35505 ^ _776541) ^ [_1439032, _1439034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439032), 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)), _1439034)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439032, _1439034) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1439032, _1439034)))], (38338 ^ _776541) ^ [_1511150, _1511152, _1511154, _1511156] : [c_FunDef_Oreduction__pair(_1511150, _1511152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511150, _1511150), tc_HOL_Obool)), _1511154), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511150, _1511150), tc_HOL_Obool), tc_fun(tc_prod(_1511150, _1511150), tc_HOL_Obool)), _1511152))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511150, _1511150), tc_HOL_Obool)), _1511156), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1511150, _1511150), tc_HOL_Obool), tc_fun(tc_prod(_1511150, _1511150), tc_HOL_Obool)), _1511152))), c_Wellfounded_Owf(_1511150, _1511156), -(c_Wellfounded_Owf(_1511150, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1511150, _1511150), tc_HOL_Obool)), _1511154), _1511156)))], (7466 ^ _776541) ^ [_899468, _899470, _899472, _899474] : [hBOOL(hAPP(_899468, _899470)), hBOOL(hAPP(_899472, _899470)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_899474, tc_HOL_Obool)), _899468), _899472), _899470)))], (46178 ^ _776541) ^ [_1704256, _1704258] : [c_List_Otranspose(_1704256, _1704258) = c_List_Olist_ONil(tc_List_Olist(_1704256)), 46181 ^ _776541 : [(46182 ^ _776541) ^ [_1704351] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704256)), _1704351), hAPP(c_List_Oset(tc_List_Olist(_1704256)), _1704258))), -(_1704351 = c_List_Olist_ONil(_1704256))]]], (33891 ^ _776541) ^ [_1404581, _1404583, _1404585] : [class_Groups_Ocomm__monoid__add(_1404581), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404581), _1404583), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404585))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404581), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404581), _1404583), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1404585))), hAPP(_1404583, _1404585)))], (13148 ^ _776541) ^ [_1009007, _1009009, _1009011, _1009013, _1009015] : [class_Groups_Oab__group__add(_1009007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009009), _1009011)), 13155 ^ _776541 : [(13162 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1009009), _1009013), _1009011))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009009, _1009007), _1009015), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009009, tc_HOL_Obool)), _1009011), hAPP(hAPP(c_Set_Oinsert(_1009009), _1009013), c_Orderings_Obot__class_Obot(tc_fun(_1009009, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009009, _1009007), _1009015), _1009011))], (13156 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1009009), _1009013), _1009011)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009009, _1009007), _1009015), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009009, tc_HOL_Obool)), _1009011), hAPP(hAPP(c_Set_Oinsert(_1009009), _1009013), c_Orderings_Obot__class_Obot(tc_fun(_1009009, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009007), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009009, _1009007), _1009015), _1009011)), hAPP(_1009015, _1009013)))]]], (35312 ^ _776541) ^ [_1435281, _1435283, _1435285, _1435287, _1435289, _1435291] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435281, _1435283), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435285), _1435287))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435281, _1435283), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435289), _1435291))), -(_1435283 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1435287 = _1435291)], (35688 ^ _776541) ^ [_1442736, _1442738, _1442740, _1442742, _1442744] : [-(c_Product__Type_Oprod_Oprod__size(_1442736, _1442738, _1442740, _1442742, _1442744) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1442740, hAPP(c_Product__Type_Ofst(_1442736, _1442738), _1442744))), hAPP(_1442742, hAPP(c_Product__Type_Osnd(_1442736, _1442738), _1442744)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39247 ^ _776541) ^ [_1534428, _1534430, _1534432, _1534434] : [-(_1534428 = c_Orderings_Obot__class_Obot(tc_fun(_1534430, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1534432, _1534430), _1534432, c_Product__Type_Ofst(_1534432, _1534430)), hAPP(hAPP(c_Product__Type_OSigma(_1534432, _1534430), _1534434), hAPP(c_COMBK(tc_fun(_1534430, tc_HOL_Obool), _1534432), _1534428))) = _1534434)], (3658 ^ _776541) ^ [_831347, _831349, _831351, _831353, _831355, _831357, _831359, _831361, _831363, _831365] : [-(c_List_Ofoldr(_831365, _831361, _831357, _831353, _831349) = c_List_Ofoldr(_831363, _831359, _831355, _831351, _831347)), _831365 = _831363, _831361 = _831359, _831357 = _831355, _831353 = _831351, _831349 = _831347], (45723 ^ _776541) ^ [_1693887, _1693889, _1693891, _1693893] : [45725 ^ _776541 : [(45728 ^ _776541) ^ [] : [hBOOL(hAPP(_1693891, hAPP(hAPP(c_List_Onth(_1693887), _1693889), 45724 ^ [_1693887, _1693889, _1693891, _1693893])))], (45726 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45724 ^ [_1693887, _1693889, _1693891, _1693893]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693887)), _1693889))))]], hBOOL(hAPP(hAPP(c_member(_1693887), _1693893), hAPP(c_List_Oset(_1693887), _1693889))), -(hBOOL(hAPP(_1693891, _1693893)))], (13294 ^ _776541) ^ [_1012193, _1012195, _1012197, _1012199] : [-(hBOOL(hAPP(hAPP(c_member(_1012193), _1012195), _1012197))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012193, tc_Nat_Onat), _1012199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012193, tc_HOL_Obool)), _1012197), hAPP(hAPP(c_Set_Oinsert(_1012193), _1012195), c_Orderings_Obot__class_Obot(tc_fun(_1012193, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012193, tc_Nat_Onat), _1012199), _1012197))], (14098 ^ _776541) ^ [_1029486, _1029488, _1029490] : [class_Rings_Ocomm__ring__1(_1029486), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029486), _1029488), _1029490) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029486), _1029488), hAPP(c_Groups_Ouminus__class_Ouminus(_1029486), _1029490)))], (18178 ^ _776541) ^ [_1103320, _1103322] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1103320)), _1103322) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1103320, _1103322))], (18176 ^ _776541) ^ [_1103284, _1103286] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1103284), _1103286) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1103284, _1103286))], (29207 ^ _776541) ^ [_1299999, _1300001] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1299999)), c_Int_OBit1(_1300001)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1299999)), _1300001)))], (29227 ^ _776541) ^ [_1300385, _1300387] : [class_Int_Onumber__ring(_1300385), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300385), _1300387), hAPP(c_Int_Onumber__class_Onumber__of(_1300385), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300385), _1300387), _1300387))], (51937 ^ _776541) ^ [_1825659, _1825661] : [class_Orderings_Obot(_1825659), -(class_Orderings_Obot(tc_fun(_1825661, _1825659)))], (46127 ^ _776541) ^ [_1703047, _1703049, _1703051] : [46129 ^ _776541 : [(46132 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1703049, 46128 ^ [_1703047, _1703049, _1703051])))], (46130 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703047), 46128 ^ [_1703047, _1703049, _1703051]), hAPP(c_List_Oset(_1703047), _1703051))))]], -(hAPP(c_List_Ofilter(_1703047, _1703049), _1703051) = c_List_Olist_ONil(_1703047))], (29371 ^ _776541) ^ [_1302858, _1302860] : [class_Rings_Olinordered__idom(_1302858), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302858), c_Groups_Ozero__class_Ozero(_1302858)), hAPP(hAPP(c_Power_Opower__class_Opower(_1302858), _1302860), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (45828 ^ _776541) ^ [_1695929, _1695931] : [_1695931 = c_List_Olist_ONil(_1695929), -(c_List_Oremdups(_1695929, _1695931) = c_List_Olist_ONil(_1695929))], (24972 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (50671 ^ _776541) ^ [_1800804, _1800806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800804), _1800806)), -(c_Fun_Obij__betw(_1800804, tc_Nat_Onat, 50674 ^ [_1800804, _1800806], _1800806, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1800804), _1800806))))], (50729 ^ _776541) ^ [_1801926, _1801928, _1801930] : [hBOOL(hAPP(hAPP(_1801930, _1801928), _1801928)), -(hBOOL(hAPP(hAPP(c_member(_1801926), _1801928), c_Quotient_ORespects(_1801926, _1801930))))], (3888 ^ _776541) ^ [_834948, _834950] : [_834950 = _834948, -(c_Groups_Oabs__class_Oabs(_834950) = c_Groups_Oabs__class_Oabs(_834948))], (17587 ^ _776541) ^ [_1093276, _1093278, _1093280] : [class_Groups_Oordered__ab__group__add(_1093276), 17590 ^ _776541 : [(17597 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093276), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1093276), _1093278), _1093280)), c_Groups_Ozero__class_Ozero(_1093276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093276), _1093278), _1093280)))], (17591 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093276), _1093278), _1093280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093276), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1093276), _1093278), _1093280)), c_Groups_Ozero__class_Ozero(_1093276))))]]], (3328 ^ _776541) ^ [_826210, _826212] : [_826212 = _826210, -(c_Int_OBit1(_826212) = c_Int_OBit1(_826210))], (40669 ^ _776541) ^ [_1571002, _1571004, _1571006, _1571008] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571002, _1571002)), _1571004), c_Transitive__Closure_Otrancl(_1571002, _1571006))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571002, _1571002), tc_HOL_Obool)), _1571006), _1571008)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571002, _1571002)), _1571004), c_Transitive__Closure_Otrancl(_1571002, _1571008))))], (14466 ^ _776541) ^ [_1037721, _1037723, _1037725] : [14467 ^ _776541 : [(14470 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1037725, _1037723), _1037721))], (14468 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037721), _1037723)))]], 14473 ^ _776541 : [(14476 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1037725, _1037723), _1037721))], (14474 ^ _776541) ^ [] : [-(_1037721 = _1037723)]], 14479 ^ _776541 : [(14482 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1037725, _1037723), _1037721))], (14480 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037723), _1037721)))]], -(hBOOL(hAPP(hAPP(_1037725, _1037723), _1037721)))], (44587 ^ _776541) ^ [_1668303, _1668305, _1668307] : [-(_1668303 = c_List_Olist_ONil(_1668305)), -(c_List_Olast(_1668305, hAPP(hAPP(c_List_Olist_OCons(_1668305), _1668307), _1668303)) = c_List_Olast(_1668305, _1668303))], (522 ^ _776541) ^ [_784356, _784358, _784360, _784362, _784364, _784366] : [-(c_Finite__Set_Ofun__left__comm__idem(_784364, _784360, _784356)), c_Finite__Set_Ofun__left__comm__idem(_784366, _784362, _784358), _784366 = _784364, _784362 = _784360, _784358 = _784356], (14740 ^ _776541) ^ [_1042210, _1042212, _1042214, _1042216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042210), _1042212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042214), _1042216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042210), _1042214)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042212), _1042216))))], (40757 ^ _776541) ^ [_1573975, _1573977, _1573979] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573975, _1573975), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573975, _1573975), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573975, _1573977)), c_Transitive__Closure_Ortrancl(_1573975, _1573979))), c_Transitive__Closure_Ortrancl(_1573975, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573975, _1573975), tc_HOL_Obool)), _1573977), _1573979)))))], (40853 ^ _776541) ^ [_1576302, _1576304, _1576306] : [_1576304 = _1576306, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576302, _1576302)), hAPP(hAPP(c_Product__Type_OPair(_1576302, _1576302), _1576304), _1576306)), c_Relation_OId(_1576302))))], (52161 ^ _776541) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (37284 ^ _776541) ^ [_1486150, _1486152, _1486154, _1486156] : [37286 ^ _776541 : [(37290 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486150), 37288 ^ [_1486150, _1486152, _1486154, _1486156]), _1486156)))], (37292 ^ _776541) ^ [] : [-(hAPP(_1486154, 37285 ^ [_1486150, _1486152, _1486154, _1486156]) = hAPP(_1486154, 37288 ^ [_1486150, _1486152, _1486154, _1486156]))], (37294 ^ _776541) ^ [] : [37285 ^ [_1486150, _1486152, _1486154, _1486156] = 37288 ^ [_1486150, _1486152, _1486154, _1486156]], (37287 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486150), 37285 ^ [_1486150, _1486152, _1486154, _1486156]), _1486156)))]], -(c_Fun_Oinj__on(_1486150, _1486152, _1486154, _1486156))], (23629 ^ _776541) ^ [_1204787, _1204789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1204787), _1204789)), -(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)), _1204787)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204789))))], (33056 ^ _776541) ^ [_1380354, _1380356, _1380358, _1380360, _1380362, _1380364] : [-(hAPP(c_Set_Oimage(_1380354, _1380356, _1380358), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380360, tc_fun(_1380354, tc_HOL_Obool)), _1380362), _1380364)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380360, tc_fun(_1380356, tc_HOL_Obool)), _1380362), hAPP(hAPP(c_COMBB(tc_fun(_1380354, tc_HOL_Obool), tc_fun(_1380356, tc_HOL_Obool), _1380360), c_Set_Oimage(_1380354, _1380356, _1380358)), _1380364)))], (3498 ^ _776541) ^ [_828837, _828839, _828841, _828843] : [-(c_Random_Oselect__weight(_828843, _828839) = c_Random_Oselect__weight(_828841, _828837)), _828843 = _828841, _828839 = _828837], (37864 ^ _776541) ^ [_1498251, _1498253, _1498255, _1498257] : [c_Fun_Oinj__on(_1498251, _1498253, _1498255, _1498257), -(hAPP(c_Set_Oimage(_1498253, _1498251, c_Fun_Othe__inv__into(_1498251, _1498253, _1498257, _1498255)), hAPP(c_Set_Oimage(_1498251, _1498253, _1498255), _1498257)) = _1498257)], (39241 ^ _776541) ^ [_1534271, _1534273, _1534275, _1534277] : [_1534271 = c_Orderings_Obot__class_Obot(tc_fun(_1534273, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1534275, _1534273), _1534275, c_Product__Type_Ofst(_1534275, _1534273)), hAPP(hAPP(c_Product__Type_OSigma(_1534275, _1534273), _1534277), hAPP(c_COMBK(tc_fun(_1534273, tc_HOL_Obool), _1534275), _1534271))) = c_Orderings_Obot__class_Obot(tc_fun(_1534275, tc_HOL_Obool)))], (12672 ^ _776541) ^ [_999882, _999884, _999886, _999888, _999890, _999892] : [c_Finite__Set_Ofun__left__comm(_999882, _999884, _999886), hBOOL(hAPP(c_Finite__Set_Ofinite(_999882), _999888)), -(hAPP(hAPP(_999886, _999890), hAPP(hAPP(c_Finite__Set_Ofold(_999882, _999884, _999886), _999892), _999888)) = hAPP(hAPP(c_Finite__Set_Ofold(_999882, _999884, _999886), hAPP(hAPP(_999886, _999890), _999892)), _999888))], (11161 ^ _776541) ^ [_969771, _969773, _969775, _969777] : [_969777 = c_Orderings_Obot__class_Obot(tc_fun(_969773, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_969771, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_969773, _969771, _969775), _969777))], (42947 ^ _776541) ^ [_1632519, _1632521] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1632519), _1632521))), -(c_Nitpick_Ocard_H(_1632519, _1632521) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40733 ^ _776541) ^ [_1573372, _1573374] : [-(c_Transitive__Closure_Otrancl(_1573372, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573372, _1573372), tc_HOL_Obool)), _1573374), c_Relation_OId(_1573372))) = c_Transitive__Closure_Ortrancl(_1573372, _1573374))], (46852 ^ _776541) ^ [_1717879, _1717881] : [class_Orderings_Olinorder(_1717879), 46855 ^ _776541 : [(46856 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1717879, _1717881), 46859 ^ _776541 : [(46860 ^ _776541) ^ [_1718050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718050), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717879)), _1717881))), 46863 ^ _776541 : [(46864 ^ _776541) ^ [_1718167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718167), _1718050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717879), hAPP(hAPP(c_List_Onth(_1717879), _1717881), _1718167)), hAPP(hAPP(c_List_Onth(_1717879), _1717881), _1718050))))]]]]], (46870 ^ _776541) ^ [] : [46872 ^ _776541 : [(46878 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717879), hAPP(hAPP(c_List_Onth(_1717879), _1717881), 46874 ^ [_1717879, _1717881])), hAPP(hAPP(c_List_Onth(_1717879), _1717881), 46871 ^ [_1717879, _1717881])))], (46876 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46874 ^ [_1717879, _1717881]), 46871 ^ [_1717879, _1717881])))], (46873 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46871 ^ [_1717879, _1717881]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717879)), _1717881))))]], -(c_List_Olinorder__class_Osorted(_1717879, _1717881))]]], (51381 ^ _776541) ^ [_1816545, _1816547, _1816549, _1816551, _1816553] : [class_Rings_Ocomm__semiring__1(_1816545), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816545), hAPP(hAPP(c_Power_Opower__class_Opower(_1816545), _1816547), _1816549)), _1816551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1816553), _1816549)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816545), hAPP(hAPP(c_Power_Opower__class_Opower(_1816545), _1816547), _1816553)), _1816551)))], (28933 ^ _776541) ^ [_1295206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295206), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295206)), c_Int_OPls)))], (22189 ^ _776541) ^ [_1178965] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178965), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1178965)], (43194 ^ _776541) ^ [_1636975, _1636977] : [-(_1636977 = c_List_Olist_ONil(_1636975)), -(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(_1636975)), _1636977))))], (42351 ^ _776541) ^ [_1617067, _1617069, _1617071, _1617073] : [-(hBOOL(hAPP(hAPP(c_member(_1617067), _1617069), hAPP(c_List_Oset(_1617067), _1617071)))), hBOOL(hAPP(hAPP(c_member(_1617067), _1617069), hAPP(c_List_Oset(_1617067), c_List_Osublist(_1617067, _1617071, _1617073))))], (49764 ^ _776541) ^ [_1782152, _1782154, _1782156] : [c_Equiv__Relations_Oequiv(_1782152, _1782154, _1782156), 49767 ^ _776541 : [(49772 ^ _776541) ^ [] : [-(c_Relation_Otrans(_1782152, _1782156))], (49770 ^ _776541) ^ [] : [-(c_Relation_Osym(_1782152, _1782156))], (49768 ^ _776541) ^ [] : [-(c_Relation_Orefl__on(_1782152, _1782154, _1782156))]]], (34958 ^ _776541) ^ [_1428781, _1428783] : [_1428781 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1428783, _1428781) = 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), _1428783)))], (51669 ^ _776541) ^ [_1821659, _1821661, _1821663, _1821665] : [class_Rings_Ocomm__semiring__1(_1821659), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821659), _1821661), _1821663)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821659), _1821663), _1821665)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821659), _1821661), _1821665)))], (40761 ^ _776541) ^ [_1574099, _1574101, _1574103] : [-(c_Transitive__Closure_Ortrancl(_1574099, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574099, _1574099), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574099, _1574101)), c_Transitive__Closure_Ortrancl(_1574099, _1574103))) = c_Transitive__Closure_Ortrancl(_1574099, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574099, _1574099), tc_HOL_Obool)), _1574101), _1574103)))], (47404 ^ _776541) ^ [_1729725, _1729727, _1729729, _1729731] : [hBOOL(hAPP(_1729725, _1729727)), -(c_List_OdropWhile(_1729729, _1729725, hAPP(hAPP(c_List_Olist_OCons(_1729729), _1729727), _1729731)) = c_List_OdropWhile(_1729729, _1729725, _1729731))], (37032 ^ _776541) ^ [_1480233, _1480235] : [-(c_Equiv__Relations_Oequivp(_1480233, _1480235)), 37037 ^ _776541 : [(37040 ^ _776541) ^ [] : [hAPP(_1480235, 37033 ^ [_1480233, _1480235]) = hAPP(_1480235, 37034 ^ [_1480233, _1480235])], (37038 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1480235, 37033 ^ [_1480233, _1480235]), 37034 ^ [_1480233, _1480235])))]], 37041 ^ _776541 : [(37044 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1480235, 37033 ^ [_1480233, _1480235]), 37034 ^ [_1480233, _1480235]))], (37042 ^ _776541) ^ [] : [-(hAPP(_1480235, 37033 ^ [_1480233, _1480235]) = hAPP(_1480235, 37034 ^ [_1480233, _1480235]))]]], (24393 ^ _776541) ^ [_1217685] : [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, _1217685)))))], (39617 ^ _776541) ^ [_1544921, _1544923, _1544925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544921, _1544921), tc_HOL_Obool)), _1544923), hAPP(hAPP(c_Product__Type_OSigma(_1544921, _1544921), _1544925), hAPP(c_COMBK(tc_fun(_1544921, tc_HOL_Obool), _1544921), _1544925)))), 39623 ^ _776541 : [(39626 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544921, _1544921)), hAPP(hAPP(c_Product__Type_OPair(_1544921, _1544921), 39622 ^ [_1544921, _1544923, _1544925]), 39622 ^ [_1544921, _1544923, _1544925])), _1544923))], (39624 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544921), 39622 ^ [_1544921, _1544923, _1544925]), _1544925)))]], -(c_Relation_Orefl__on(_1544921, _1544925, _1544923))], (33368 ^ _776541) ^ [_1389164, _1389166, _1389168, _1389170] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389164, tc_fun(_1389166, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1389164, tc_HOL_Obool), _1389168)), _1389170) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1389164, tc_HOL_Obool), tc_fun(_1389166, tc_HOL_Obool)), _1389168), hAPP(hAPP(c_COMBC(tc_fun(_1389164, tc_HOL_Obool), tc_fun(_1389164, tc_fun(_1389166, tc_HOL_Obool)), tc_fun(_1389166, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389164, tc_fun(_1389166, tc_HOL_Obool))), _1389170)))], (398 ^ _776541) ^ [_782552, _782554, _782556, _782558, _782560, _782562] : [-(c_Relation_Ototal__on(_782560, _782556, _782552)), c_Relation_Ototal__on(_782562, _782558, _782554), _782562 = _782560, _782558 = _782556, _782554 = _782552], (51989 ^ _776541) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (43675 ^ _776541) ^ [_1647631, _1647633, _1647635, _1647637, _1647639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647631), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647633)), _1647635))), -(hAPP(hAPP(c_List_Olist__update(_1647633, hAPP(hAPP(c_List_Oappend(_1647633), _1647635), _1647637)), _1647631), _1647639) = hAPP(hAPP(c_List_Oappend(_1647633), hAPP(hAPP(c_List_Olist__update(_1647633, _1647635), _1647631), _1647639)), _1647637))], (13168 ^ _776541) ^ [_1009477, _1009479, _1009481, _1009483, _1009485] : [class_Groups_Ocomm__monoid__mult(_1009477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009479), _1009481)), hBOOL(hAPP(hAPP(c_member(_1009479), _1009483), _1009481)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009479, _1009477), _1009485), _1009481) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009477), hAPP(_1009485, _1009483)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009479, _1009477), _1009485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009479, tc_HOL_Obool)), _1009481), hAPP(hAPP(c_Set_Oinsert(_1009479), _1009483), c_Orderings_Obot__class_Obot(tc_fun(_1009479, tc_HOL_Obool)))))))], (10615 ^ _776541) ^ [_959085, _959087, _959089, _959091] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_959085, _959087, _959089, _959091, c_Orderings_Obot__class_Obot(tc_fun(_959085, tc_HOL_Obool))), _959091)))], (24952 ^ _776541) ^ [_1228361, _1228363, _1228365] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228361), _1228363), _1228365) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228361), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228363, _1228365)), _1228365))], (48674 ^ _776541) ^ [_1757668, _1757670, _1757672, _1757674] : [-(hAPP(hAPP(c_List_Oappend(_1757668), c_List_Oreplicate(_1757668, _1757670, _1757672)), c_List_Oreplicate(_1757668, _1757674, _1757672)) = hAPP(hAPP(c_List_Oappend(_1757668), c_List_Oreplicate(_1757668, _1757674, _1757672)), c_List_Oreplicate(_1757668, _1757670, _1757672)))], (40582 ^ _776541) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (33525 ^ _776541) ^ [_1393407, _1393409, _1393411, _1393413] : [_1393407 = c_Orderings_Obot__class_Obot(tc_fun(_1393409, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393409, tc_fun(_1393411, tc_HOL_Obool)), _1393407), hAPP(c_COMBK(tc_fun(_1393411, tc_HOL_Obool), _1393409), _1393413)) = c_Orderings_Otop__class_Otop(tc_fun(_1393411, tc_HOL_Obool)))], (36742 ^ _776541) ^ [_1473615, _1473617, _1473619, _1473621] : [c_Equiv__Relations_Oequiv(_1473615, _1473617, _1473619), hBOOL(hAPP(hAPP(c_member(_1473615), _1473621), _1473617)), -(hBOOL(hAPP(hAPP(c_member(_1473615), _1473621), hAPP(c_Relation_OImage(_1473615, _1473615, _1473619), hAPP(hAPP(c_Set_Oinsert(_1473615), _1473621), c_Orderings_Obot__class_Obot(tc_fun(_1473615, tc_HOL_Obool)))))))], (6188 ^ _776541) ^ [_875938, _875940, _875942, _875944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875938, tc_HOL_Obool)), _875940), _875942)), hBOOL(hAPP(hAPP(c_member(_875938), _875944), _875940)), -(hBOOL(hAPP(hAPP(c_member(_875938), _875944), _875942)))], (48418 ^ _776541) ^ [_1751717, _1751719, _1751721, _1751723, _1751725] : [-(_1751717 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1751719, _1751721, _1751723, _1751725), _1751717) = c_Lazy__Sequence_Ohb__bind(_1751719, _1751721, hAPP(_1751723, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1751717), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1751719, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1751721))), _1751725), _1751717)))], (45193 ^ _776541) ^ [_1681837, _1681839] : [hAPP(c_Code__Numeral_Onat__of, _1681837) = hAPP(c_Code__Numeral_Onat__of, _1681839), -(_1681837 = _1681839)], (39109 ^ _776541) ^ [_1530367, _1530369, _1530371, _1530373, _1530375] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530367, _1530369), _1530371), hAPP(hAPP(c_COMBS(_1530367, tc_fun(_1530369, tc_HOL_Obool), tc_fun(_1530369, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530369, tc_HOL_Obool), tc_fun(tc_fun(_1530369, tc_HOL_Obool), tc_fun(_1530369, tc_HOL_Obool)), _1530367), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530369, tc_HOL_Obool))), _1530373)), _1530375)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530367, _1530369), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530367, _1530369), _1530371), _1530373)), hAPP(hAPP(c_Product__Type_OSigma(_1530367, _1530369), _1530371), _1530375)))], (12269 ^ _776541) ^ [_991920, _991922, _991924] : [class_Lattices_Olattice(_991920), hBOOL(hAPP(c_Finite__Set_Ofinite(_991920), _991922)), -(hBOOL(hAPP(hAPP(c_member(_991920), _991924), _991922))), -(_991922 = c_Orderings_Obot__class_Obot(tc_fun(_991920, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_991920, hAPP(hAPP(c_Set_Oinsert(_991920), _991924), _991922)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_991920), _991924), c_Big__Operators_Olattice__class_OSup__fin(_991920, _991922)))], (52051 ^ _776541) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (38680 ^ _776541) ^ [_1519743, _1519745, _1519747, _1519749, _1519751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519743, tc_HOL_Obool)), _1519745), _1519747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519749, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1519749, _1519743, _1519751), _1519745)), hAPP(c_Set_Ovimage(_1519749, _1519743, _1519751), _1519747))))], (29097 ^ _776541) ^ [_1298086, _1298088] : [class_Int_Onumber__ring(_1298086), class_Int_Oring__char__0(_1298086), 29104 ^ _776541 : [(29111 ^ _776541) ^ [] : [c_Int_Oiszero(_1298086, hAPP(c_Int_Onumber__class_Onumber__of(_1298086), _1298088)), -(c_Int_Oiszero(_1298086, hAPP(c_Int_Onumber__class_Onumber__of(_1298086), c_Int_OBit0(_1298088))))], (29105 ^ _776541) ^ [] : [c_Int_Oiszero(_1298086, hAPP(c_Int_Onumber__class_Onumber__of(_1298086), c_Int_OBit0(_1298088))), -(c_Int_Oiszero(_1298086, hAPP(c_Int_Onumber__class_Onumber__of(_1298086), _1298088)))]]], (19330 ^ _776541) ^ [_1125538, _1125540, _1125542] : [class_Rings_Oring__1(_1125538), hBOOL(hAPP(hAPP(c_member(_1125538), _1125540), c_Int_Oring__1__class_OInts(_1125538))), hBOOL(hAPP(hAPP(c_member(_1125538), _1125542), c_Int_Oring__1__class_OInts(_1125538))), -(hBOOL(hAPP(hAPP(c_member(_1125538), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125538), _1125540), _1125542)), c_Int_Oring__1__class_OInts(_1125538))))], (14750 ^ _776541) ^ [_1042401, _1042403, _1042405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042401), _1042403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042401), _1042405)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042403), _1042405))))], (34952 ^ _776541) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (244 ^ _776541) ^ [_780381, _780383] : [-(class_Fields_Ofield__inverse__zero(_780381)), _780383 = _780381, class_Fields_Ofield__inverse__zero(_780383)], (45638 ^ _776541) ^ [_1691893, _1691895, _1691897, _1691899, _1691901, _1691903, _1691905, _1691907] : [c_List_Olist__all2(_1691893, _1691895, _1691897, _1691899, _1691901), hBOOL(hAPP(hAPP(_1691897, _1691903), _1691905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691895)), _1691901))), -(c_List_Olist__all2(_1691893, _1691895, _1691897, hAPP(hAPP(c_List_Olist__update(_1691893, _1691899), _1691907), _1691903), hAPP(hAPP(c_List_Olist__update(_1691895, _1691901), _1691907), _1691905)))], (14728 ^ _776541) ^ [_1041988, _1041990, _1041992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041988), _1041990)), _1041992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041988), _1041992)))], (29609 ^ _776541) ^ [_1307233, _1307235] : [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), _1307233))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1307235))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1307233))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1307235)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1307233)))], (26020 ^ _776541) ^ [_1246922, _1246924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246922), _1246924))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246922, _1246924) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1246922), _1246924), _1246924))], (42185 ^ _776541) ^ [_1612736, _1612738, _1612740, _1612742] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612736), tc_List_Olist(_1612736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612736), tc_List_Olist(_1612736)), _1612738), _1612740)), c_List_Olistrel(_1612736, _1612742)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612736)), _1612738) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612736)), _1612740), 42191 ^ _776541 : [(42194 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612736, _1612736)), hAPP(hAPP(c_Product__Type_OPair(_1612736, _1612736), hAPP(hAPP(c_List_Onth(_1612736), _1612738), 42190 ^ [_1612736, _1612738, _1612740, _1612742])), hAPP(hAPP(c_List_Onth(_1612736), _1612740), 42190 ^ [_1612736, _1612738, _1612740, _1612742]))), _1612742))], (42192 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42190 ^ [_1612736, _1612738, _1612740, _1612742]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612736)), _1612738))))]]], (43803 ^ _776541) ^ [_1651067, _1651069, _1651071, _1651073, _1651075, _1651077] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651067), tc_List_Olist(_1651067))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651067), tc_List_Olist(_1651067)), hAPP(hAPP(c_List_Oappend(_1651067), _1651069), hAPP(hAPP(c_List_Olist_OCons(_1651067), _1651071), c_List_Olist_ONil(_1651067)))), hAPP(hAPP(c_List_Oappend(_1651067), _1651073), hAPP(hAPP(c_List_Olist_OCons(_1651067), _1651075), c_List_Olist_ONil(_1651067))))), c_List_Olistrel1(_1651067, _1651077))), 43808 ^ _776541 : [(43811 ^ _776541) ^ [] : [-(_1651071 = _1651075)], (43809 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651067), tc_List_Olist(_1651067))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651067), tc_List_Olist(_1651067)), _1651069), _1651073)), c_List_Olistrel1(_1651067, _1651077))))]], 43812 ^ _776541 : [(43815 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651067, _1651067)), hAPP(hAPP(c_Product__Type_OPair(_1651067, _1651067), _1651071), _1651075)), _1651077)))], (43813 ^ _776541) ^ [] : [-(_1651069 = _1651073)]]], (27317 ^ _776541) ^ [_1268041] : [class_Groups_Oordered__ab__group__add__abs(_1268041), -(hAPP(c_Groups_Oabs__class_Oabs(_1268041), c_Groups_Ozero__class_Ozero(_1268041)) = c_Groups_Ozero__class_Ozero(_1268041))], (28489 ^ _776541) ^ [_1287831] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1287831)), c_Int_OPls))], (38187 ^ _776541) ^ [_1507851, _1507853, _1507855] : [c_Wellfounded_Owf(_1507851, _1507853), -(c_Wellfounded_Owf(_1507851, c_Wellfounded_Omlex__prod(_1507851, _1507855, _1507853)))], (34588 ^ _776541) ^ [_1420762, _1420764, _1420766, _1420768, _1420770, _1420772] : [hBOOL(hAPP(hAPP(_1420762, _1420764), _1420766)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420768, tc_fun(_1420770, tc_HOL_Obool))), _1420772), _1420762), _1420764), _1420766)))], (28111 ^ _776541) ^ [_1281438] : [class_Rings_Osemiring__1(_1281438), -(c_Int_Oiszero(_1281438, c_Groups_Ozero__class_Ozero(_1281438)))], (7619 ^ _776541) ^ [_902753, _902755, _902757, _902759] : [7633 ^ _776541 : [(7636 ^ _776541) ^ [] : [-(hBOOL(hAPP(_902759, 7632 ^ [_902753, _902755, _902757, _902759])))], (7634 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902753), 7632 ^ [_902753, _902755, _902757, _902759]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902753, tc_HOL_Obool)), _902755), _902757))))]], 7620 ^ _776541 : [(7627 ^ _776541) ^ [_902962] : [hBOOL(hAPP(hAPP(c_member(_902753), _902962), _902757)), hBOOL(hAPP(_902759, _902962))], (7621 ^ _776541) ^ [_902866] : [hBOOL(hAPP(hAPP(c_member(_902753), _902866), _902755)), hBOOL(hAPP(_902759, _902866))]]], (2930 ^ _776541) ^ [_820025, _820027, _820029, _820031, _820033, _820035] : [-(c_Nitpick_Oof__frac(_820035, _820031, _820027) = c_Nitpick_Oof__frac(_820033, _820029, _820025)), _820035 = _820033, _820031 = _820029, _820027 = _820025], (52149 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (3408 ^ _776541) ^ [_827426, _827428, _827430, _827432] : [-(c_Enum_Oenum__the(_827432, _827428) = c_Enum_Oenum__the(_827430, _827426)), _827432 = _827430, _827428 = _827426], (9228 ^ _776541) ^ [_935719, _935721, _935723] : [class_Orderings_Olinorder(_935719), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935719), _935721), _935723))), 9235 ^ _776541 : [(9242 ^ _776541) ^ [] : [_935723 = _935721, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935719), _935723), _935721))], (9236 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935719), _935723), _935721))), -(_935723 = _935721)]]], (43242 ^ _776541) ^ [_1638027, _1638029, _1638031, _1638033] : [_1638027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1638029), _1638027), hAPP(hAPP(c_List_Olist_OCons(_1638029), _1638031), _1638033)) = c_List_Olist_ONil(_1638029))], (34954 ^ _776541) ^ [_1428673, _1428675] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1428673), _1428675)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1428673), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428675)))], (33066 ^ _776541) ^ [_1380690, _1380692, _1380694, _1380696, _1380698, _1380700] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380690, tc_fun(_1380692, tc_HOL_Obool)), _1380694), hAPP(hAPP(c_COMBB(_1380696, tc_fun(_1380692, tc_HOL_Obool), _1380690), _1380698), _1380700)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380696, tc_fun(_1380692, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380690, _1380696, _1380700), _1380694)), _1380698))], (40751 ^ _776541) ^ [_1573823, _1573825] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1573823, _1573823, _1573823), _1573825), c_Transitive__Closure_Ortrancl(_1573823, _1573825)) = hAPP(hAPP(c_Relation_Orel__comp(_1573823, _1573823, _1573823), c_Transitive__Closure_Ortrancl(_1573823, _1573825)), _1573825))], (48576 ^ _776541) ^ [_1755958, _1755960, _1755962, _1755964] : [-(hAPP(hAPP(c_List_Otake(_1755958), _1755960), c_List_Oreplicate(_1755958, _1755962, _1755964)) = c_List_Oreplicate(_1755958, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1755960), _1755962), _1755964))], (49021 ^ _776541) ^ [_1765238, _1765240, _1765242, _1765244, _1765246, _1765248, _1765250] : [49023 ^ _776541 : [(49026 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1765242, 49022 ^ [_1765238, _1765240, _1765242, _1765244, _1765246, _1765248, _1765250]), _1765244), _1765246))], (49024 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765238), 49022 ^ [_1765238, _1765240, _1765242, _1765244, _1765246, _1765248, _1765250]), _1765240)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1765238, tc_fun(_1765248, tc_fun(_1765250, tc_HOL_Obool))), _1765240), _1765242), _1765244), _1765246)))], (44130 ^ _776541) ^ [_1659128, _1659130] : [-(_1659128 = c_List_Olist_ONil(_1659130)), -(hAPP(c_List_Ohd(_1659130), _1659128) = hAPP(hAPP(c_List_Onth(_1659130), _1659128), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22051 ^ _776541) ^ [_1176347, _1176349, _1176351, _1176353] : [class_Rings_Olinordered__semidom(_1176347), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176347), _1176349), _1176351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176347), c_Groups_Ozero__class_Ozero(_1176347)), _1176349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176347), hAPP(hAPP(c_Power_Opower__class_Opower(_1176347), _1176349), _1176353)), hAPP(hAPP(c_Power_Opower__class_Opower(_1176347), _1176351), _1176353))))], (42327 ^ _776541) ^ [_1616564, _1616566, _1616568, _1616570] : [-(hAPP(hAPP(c_List_Otake(_1616564), hAPP(c_Nat_OSuc, _1616566)), hAPP(hAPP(c_List_Olist_OCons(_1616564), _1616568), _1616570)) = hAPP(hAPP(c_List_Olist_OCons(_1616564), _1616568), hAPP(hAPP(c_List_Otake(_1616564), _1616566), _1616570)))], (36523 ^ _776541) ^ [_1467921, _1467923, _1467925, _1467927, _1467929] : [-(hBOOL(hAPP(hAPP(c_member(_1467921), _1467923), hAPP(c_Relation_OImage(_1467925, _1467921, _1467927), _1467929)))), 36524 ^ _776541 : [(36525 ^ _776541) ^ [_1468007] : [hBOOL(hAPP(hAPP(c_member(_1467925), _1468007), _1467929)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1467925, _1467921)), hAPP(hAPP(c_Product__Type_OPair(_1467925, _1467921), _1468007), _1467923)), _1467927))]]], (16040 ^ _776541) ^ [_1066649, _1066651, _1066653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066649), _1066651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066651), _1066653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1066649)), _1066653)))], (52535 ^ _776541) ^ [_1831951, _1831953] : [hBOOL(hAPP(hAPP(c_fdisj, _1831951), _1831953)), -(hBOOL(_1831951)), -(hBOOL(_1831953))], (5889 ^ _776541) ^ [_870189, _870191, _870193] : [hBOOL(hAPP(hAPP(c_member(_870189), _870191), _870193)), -(hBOOL(hAPP(_870193, _870191)))], (41583 ^ _776541) ^ [_1594600, _1594602, _1594604, _1594606, _1594608] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594600, _1594600)), hAPP(hAPP(c_Product__Type_OPair(_1594600, _1594600), _1594602), _1594604)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594600, _1594600), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1594606)), _1594608))), 41587 ^ _776541 : [(41590 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594600, _1594600)), hAPP(hAPP(c_Product__Type_OPair(_1594600, _1594600), 41586 ^ [_1594600, _1594602, _1594604, _1594606, _1594608]), _1594604)), _1594608)))], (41588 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594600, _1594600)), hAPP(hAPP(c_Product__Type_OPair(_1594600, _1594600), _1594602), 41586 ^ [_1594600, _1594602, _1594604, _1594606, _1594608])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594600, _1594600), tc_HOL_Obool), _1594606), _1594608))))]]], (25219 ^ _776541) ^ [_1233122, _1233124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233122), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25222 ^ _776541 : [(25225 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233122), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233124, _1233122))))], (25223 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233124, _1233122)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (45233 ^ _776541) ^ [_1682484] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1682484)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1682484))], (41455 ^ _776541) ^ [_1590879, _1590881, _1590883] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590879, _1590879)), hAPP(hAPP(c_Product__Type_OPair(_1590879, _1590879), _1590881), _1590881)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590879, _1590879), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590883))))], (10691 ^ _776541) ^ [_960565, _960567] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960565, tc_HOL_Obool)), _960567), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960565, tc_HOL_Obool)), _960567)) = c_Orderings_Otop__class_Otop(tc_fun(_960565, tc_HOL_Obool)))], (27525 ^ _776541) ^ [_1271709, _1271711] : [class_Groups_Oordered__ab__group__add__abs(_1271709), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271709), hAPP(c_Groups_Ouminus__class_Ouminus(_1271709), _1271711)), hAPP(c_Groups_Oabs__class_Oabs(_1271709), _1271711))))], (33943 ^ _776541) ^ [_1405822, _1405824, _1405826, _1405828, _1405830] : [class_Groups_Ocomm__monoid__add(_1405822), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405824), _1405826)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405824, _1405822), _1405828), hAPP(c_Set_OCollect(_1405824), hAPP(hAPP(c_COMBS(_1405824, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1405824), c_fconj), hAPP(hAPP(c_COMBC(_1405824, tc_fun(_1405824, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405824)), _1405826))), hAPP(hAPP(c_COMBC(_1405824, tc_fun(_1405824, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405824)), _1405830)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405824, _1405822), hAPP(hAPP(c_COMBC(_1405824, _1405822, _1405822), hAPP(hAPP(c_COMBS(_1405824, _1405822, tc_fun(_1405822, _1405822)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1405822, tc_fun(_1405822, _1405822)), _1405824), c_If(_1405822)), hAPP(hAPP(c_COMBC(_1405824, tc_fun(_1405824, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405824)), _1405830))), _1405828)), c_Groups_Ozero__class_Ozero(_1405822))), _1405826))], (44617 ^ _776541) ^ [_1668689, _1668691] : [-(_1668689 = c_List_Olist_ONil(_1668691)), -(hBOOL(hAPP(hAPP(c_member(_1668691), c_List_Olast(_1668691, _1668689)), hAPP(c_List_Oset(_1668691), _1668689))))], (6164 ^ _776541) ^ [_875458, _875460, _875462, _875464] : [hBOOL(hAPP(hAPP(c_member(_875458), _875460), c_Complete__Lattice_OInf__class_OInf(tc_fun(_875458, tc_HOL_Obool), _875462))), hBOOL(hAPP(hAPP(c_member(tc_fun(_875458, tc_HOL_Obool)), _875464), _875462)), -(hBOOL(hAPP(hAPP(c_member(_875458), _875460), _875464)))], (8651 ^ _776541) ^ [_925217, _925219, _925221] : [class_Lattices_Osemilattice__inf(_925217), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925217), _925219), _925221)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925217), _925221), _925219) = _925219)], (37526 ^ _776541) ^ [_1490745, _1490747] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490745), c_Orderings_Otop__class_Otop(tc_fun(_1490745, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1490745, _1490745, _1490747), c_Orderings_Otop__class_Otop(tc_fun(_1490745, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1490745, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1490745, _1490745, _1490747, c_Orderings_Otop__class_Otop(tc_fun(_1490745, tc_HOL_Obool))))], (31311 ^ _776541) ^ [_1338544, _1338546, _1338548, _1338550] : [class_Orderings_Olinorder(_1338544), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338544), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338544), _1338546), _1338548)), _1338550) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338544), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338544), _1338546), _1338550)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338544), _1338548), _1338550)))], (50277 ^ _776541) ^ [_1792870, _1792872] : [-(c_Fun_Obij__betw(_1792870, _1792870, c_Fun_Oid(_1792870), _1792872, _1792872))], (29305 ^ _776541) ^ [_1301680, _1301682, _1301684] : [class_Groups_Omonoid__mult(_1301680), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301680), _1301682), 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)))), _1301684)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1301680), hAPP(hAPP(c_Power_Opower__class_Opower(_1301680), _1301682), _1301684)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (23693 ^ _776541) ^ [_1205832] : [-(_1205832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205832), _1205832) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (27255 ^ _776541) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48668 ^ _776541) ^ [_1757553, _1757555, _1757557, _1757559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757553), _1757555)), -(hAPP(hAPP(c_List_Onth(_1757557), c_List_Oreplicate(_1757557, _1757555, _1757559)), _1757553) = _1757559)], (45343 ^ _776541) ^ [_1685205, _1685207, _1685209, _1685211] : [-(hBOOL(hAPP(c_List_Olistsp(_1685205, _1685207), hAPP(hAPP(c_List_Olist_OCons(_1685205), _1685209), _1685211)))), hBOOL(hAPP(_1685207, _1685209)), hBOOL(hAPP(c_List_Olistsp(_1685205, _1685207), _1685211))], (37582 ^ _776541) ^ [_1491994, _1491996, _1491998, _1492000] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491994), _1491996)), 37585 ^ _776541 : [(37592 ^ _776541) ^ [] : [hAPP(c_Finite__Set_Ocard(_1491998), hAPP(c_Set_Oimage(_1491994, _1491998, _1492000), _1491996)) = hAPP(c_Finite__Set_Ocard(_1491994), _1491996), -(c_Fun_Oinj__on(_1491994, _1491998, _1492000, _1491996))], (37586 ^ _776541) ^ [] : [c_Fun_Oinj__on(_1491994, _1491998, _1492000, _1491996), -(hAPP(c_Finite__Set_Ocard(_1491998), hAPP(c_Set_Oimage(_1491994, _1491998, _1492000), _1491996)) = hAPP(c_Finite__Set_Ocard(_1491994), _1491996))]]], (5084 ^ _776541) ^ [_854076, _854078, _854080, _854082, _854084, _854086] : [-(c_Set_Ovimage(_854086, _854082, _854078) = c_Set_Ovimage(_854084, _854080, _854076)), _854086 = _854084, _854082 = _854080, _854078 = _854076], (2560 ^ _776541) ^ [_814260, _814262, _814264, _814266] : [-(c_Wellfounded_Omin__ext(_814266, _814262) = c_Wellfounded_Omin__ext(_814264, _814260)), _814266 = _814264, _814262 = _814260], (32968 ^ _776541) ^ [_1377944, _1377946, _1377948, _1377950, _1377952] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377944, tc_HOL_Obool)), _1377946), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377948, tc_fun(_1377944, tc_HOL_Obool)), _1377950), _1377952)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377948, tc_fun(_1377944, tc_HOL_Obool)), _1377950), hAPP(hAPP(c_COMBB(tc_fun(_1377944, tc_HOL_Obool), tc_fun(_1377944, tc_HOL_Obool), _1377948), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377944, tc_HOL_Obool)), _1377946)), _1377952)))], (14422 ^ _776541) ^ [_1036925, _1036927, _1036929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036925), _1036927)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036929), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036927), _1036925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036929), _1036927)), _1036925))], (25881 ^ _776541) ^ [_1244727] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1244727)) = _1244727)], (51105 ^ _776541) ^ [_1811496, _1811498, _1811500, _1811502, _1811504] : [class_Divides_Osemiring__div(_1811496), -(_1811498 = c_Groups_Ozero__class_Ozero(_1811496)), -(_1811500 = c_Groups_Ozero__class_Ozero(_1811496)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811496), _1811498), _1811502)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811496), _1811500), _1811504)), 51124 ^ _776541 : [(51131 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811496), _1811502), _1811500) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811496), _1811498), _1811504), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811496), _1811502), _1811498) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811496), _1811504), _1811500))], (51125 ^ _776541) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811496), _1811502), _1811498) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811496), _1811504), _1811500), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811496), _1811502), _1811500) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811496), _1811498), _1811504))]]], (41929 ^ _776541) ^ [_1605127, _1605129, _1605131, _1605133] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605127), tc_List_Olist(_1605127))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605127), tc_List_Olist(_1605127)), _1605129), _1605131)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1605127), tc_List_Olist(_1605127)), c_List_Olistrel1(_1605127, _1605133)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605127), tc_List_Olist(_1605127))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605127), tc_List_Olist(_1605127)), _1605129), _1605131)), c_List_Olistrel1(_1605127, hAPP(c_Relation_Oconverse(_1605127, _1605127), _1605133)))))], (42524 ^ _776541) ^ [_1622747, _1622749, _1622751] : [-(_1622747 = _1622749), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622751)), _1622747) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622751)), _1622749), 42530 ^ _776541 : [(42533 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1622751, _1622751, tc_HOL_Obool), c_fequal), 42529 ^ [_1622747, _1622749, _1622751]))], (42531 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622751, _1622751)), 42529 ^ [_1622747, _1622749, _1622751]), hAPP(c_List_Oset(tc_prod(_1622751, _1622751)), hAPP(hAPP(c_List_Ozip(_1622751, _1622751), _1622747), _1622749)))))]]], (35298 ^ _776541) ^ [_1435077, _1435079, _1435081, _1435083, _1435085, _1435087] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435077, _1435079), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435081), _1435083))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435077, _1435079), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435085), _1435087))), -(_1435079 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1435081 = _1435085)], (40801 ^ _776541) ^ [_1575066, _1575068, _1575070, _1575072, _1575074] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575066, _1575066)), hAPP(hAPP(c_Product__Type_OPair(_1575066, _1575066), _1575068), _1575070)), _1575072)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575066, _1575066)), hAPP(hAPP(c_Product__Type_OPair(_1575066, _1575066), _1575070), _1575074)), c_Transitive__Closure_Ortrancl(_1575066, _1575072))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575066, _1575066)), hAPP(hAPP(c_Product__Type_OPair(_1575066, _1575066), _1575068), _1575074)), c_Transitive__Closure_Ortrancl(_1575066, _1575072))))], (37216 ^ _776541) ^ [_1484882, _1484884] : [class_Groups_Oordered__ab__group__add(_1484882), -(c_Fun_Oinj__on(_1484882, _1484882, c_Groups_Ouminus__class_Ouminus(_1484882), _1484884))], (43184 ^ _776541) ^ [_1636784, _1636786] : [-(c_List_Osublist(_1636784, _1636786, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1636784))], (45515 ^ _776541) ^ [_1689144, _1689146, _1689148, _1689150, _1689152, _1689154] : [c_List_Olist__all2(_1689144, _1689146, _1689148, _1689150, _1689152), -(c_List_Olist__all2(_1689144, _1689146, _1689148, hAPP(hAPP(c_List_Otake(_1689144), _1689154), _1689150), hAPP(hAPP(c_List_Otake(_1689146), _1689154), _1689152)))], (3164 ^ _776541) ^ [_823644, _823646, _823648, _823650] : [-(c_Finite__Set_Ofold1(_823650, _823646) = c_Finite__Set_Ofold1(_823648, _823644)), _823650 = _823648, _823646 = _823644], (38644 ^ _776541) ^ [_1518900, _1518902, _1518904] : [c_Wellfounded_Owf(_1518900, _1518902), c_Wellfounded_Owf(_1518900, _1518904), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518900, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1518900, _1518900), _1518902)), hAPP(c_Relation_ORange(_1518900, _1518900), _1518904)) = c_Orderings_Obot__class_Obot(tc_fun(_1518900, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1518900, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518900, _1518900), tc_HOL_Obool)), _1518902), _1518904)))], (44206 ^ _776541) ^ [_1660420, _1660422, _1660424] : [-(hAPP(hAPP(c_List_Otake(_1660420), _1660422), hAPP(c_List_Otl(_1660420), _1660424)) = hAPP(c_List_Otl(_1660420), hAPP(hAPP(c_List_Otake(_1660420), hAPP(c_Nat_OSuc, _1660422)), _1660424)))], (38552 ^ _776541) ^ [_1515977, _1515979, _1515981, _1515983, _1515985] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1515977, _1515979, _1515981), _1515983), _1515985) = c_HOL_OThe(_1515979, c_Finite__Set_Ofold__graph(_1515977, _1515979, _1515981, _1515983, _1515985)))], (5691 ^ _776541) ^ [_866304, _866306, _866308] : [hAPP(c_Hoare__Mirabelle_ORep__triple(_866304), _866306) = hAPP(c_Hoare__Mirabelle_ORep__triple(_866304), _866308), -(_866306 = _866308)], (43088 ^ _776541) ^ [_1635090, _1635092, _1635094] : [-(hAPP(hAPP(c_List_Ozip(_1635090, _1635092), c_List_Olist_ONil(_1635090)), _1635094) = c_List_Olist_ONil(tc_prod(_1635090, _1635092)))], (25879 ^ _776541) ^ [_1244674, _1244676, _1244678] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244674), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244676, _1244678)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244674), _1244676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244674), _1244678)))], (14596 ^ _776541) ^ [_1039665, _1039667] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039665), _1039667) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039667), _1039665))], (9922 ^ _776541) ^ [_946499, _946501, _946503] : [class_Orderings_Oorder(_946499), 9925 ^ _776541 : [(9932 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946499), _946501), _946503))), -(c_Orderings_Obot__class_Obot(tc_fun(_946499, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_946499, _946501, _946503))], (9926 ^ _776541) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_946499, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_946499, _946501, _946503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946499), _946501), _946503))]]], (16701 ^ _776541) ^ [_1076974, _1076976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1076974)), _1076976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076974), _1076976)))], (5743 ^ _776541) ^ [_867153, _867155] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867153, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867153)), tc_HOL_Obool)), _867155), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867153, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867153)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867153)))), -(hAPP(c_Hoare__Mirabelle_ORep__triple(_867153), hAPP(c_Hoare__Mirabelle_OAbs__triple(_867153), _867155)) = _867155)], (52489 ^ _776541) ^ [_1831353] : [hBOOL(hAPP(c_fNot, _1831353)), hBOOL(_1831353)], (9822 ^ _776541) ^ [_944827, _944829, _944831] : [class_Complete__Lattice_Ocomplete__lattice(_944827), class_Orderings_Olinorder(_944827), 9829 ^ _776541 : [(9839 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944827), _944829), c_Complete__Lattice_OSup__class_OSup(_944827, _944831)))), 9840 ^ _776541 : [(9841 ^ _776541) ^ [_945133] : [hBOOL(hAPP(hAPP(c_member(_944827), _945133), _944831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944827), _944829), _945133))]]], (9830 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944827), _944829), c_Complete__Lattice_OSup__class_OSup(_944827, _944831))), 9834 ^ _776541 : [(9837 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944827), _944829), 9833 ^ [_944827, _944829, _944831])))], (9835 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944827), 9833 ^ [_944827, _944829, _944831]), _944831)))]]]]], (13474 ^ _776541) ^ [_1016198, _1016200, _1016202, _1016204, _1016206, _1016208, _1016210, _1016212] : [c_Finite__Set_Ofolding__image__simple__idem(_1016198, _1016200, _1016202, _1016204, _1016206, _1016208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016200), _1016210)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016200), _1016212)), -(hAPP(_1016208, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016200, tc_HOL_Obool)), _1016210), _1016212)) = hAPP(hAPP(_1016202, hAPP(_1016208, _1016210)), hAPP(_1016208, _1016212)))], (27257 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (32914 ^ _776541) ^ [_1376546, _1376548, _1376550, _1376552, _1376554] : [class_Complete__Lattice_Ocomplete__lattice(_1376546), hBOOL(hAPP(hAPP(c_member(_1376548), _1376550), _1376552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376546), hAPP(_1376554, _1376550)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376548, _1376546), _1376552), _1376554))))], (16484 ^ _776541) ^ [_1073397] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073397) = _1073397)], (10046 ^ _776541) ^ [_948436, _948438] : [class_Orderings_Oorder(_948436), -(c_SetInterval_Oord__class_OatLeastAtMost(_948436, _948438, _948438) = hAPP(hAPP(c_Set_Oinsert(_948436), _948438), c_Orderings_Obot__class_Obot(tc_fun(_948436, tc_HOL_Obool))))], (40524 ^ _776541) ^ [_1567480, _1567482, _1567484, _1567486] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1567480, _1567482, _1567484, tc_prod(_1567482, _1567484)), _1567486), c_Product__Type_OPair(_1567482, _1567484)) = _1567486)], (36398 ^ _776541) ^ [] : [-(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)))], (29081 ^ _776541) ^ [_1297812] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1297812)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1297812))))], (46046 ^ _776541) ^ [_1701336, _1701338, _1701340] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701336)), hAPP(c_List_Ofilter(_1701336, _1701338), _1701340))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701336)), _1701340))))], (15640 ^ _776541) ^ [_1060232, _1060234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060232), _1060234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060232)), hAPP(c_Nat_OSuc, _1060234))))], (45219 ^ _776541) ^ [_1682237, _1682239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1682237), _1682239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682237)), hAPP(c_Code__Numeral_Onat__of, _1682239))))], (43172 ^ _776541) ^ [_1636610, _1636612, _1636614, _1636616] : [-(hBOOL(hAPP(hAPP(c_member(_1636610), _1636612), hAPP(c_List_Oset(_1636610), _1636614)))), hBOOL(hAPP(hAPP(c_member(_1636610), _1636612), hAPP(c_List_Oset(_1636610), c_List_Oremove1(_1636610, _1636616, _1636614))))], (34686 ^ _776541) ^ [_1422778, _1422780] : [c_Nitpick_Orefl_H(_1422778, _1422780), 34689 ^ _776541 : [(34690 ^ _776541) ^ [_1422856] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1422778, _1422778)), hAPP(hAPP(c_Product__Type_OPair(_1422778, _1422778), _1422856), _1422856)), _1422780)))]]], (26252 ^ _776541) ^ [_1250717] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250717))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33362 ^ _776541) ^ [_1389013, _1389015, _1389017, _1389019, _1389021, _1389023] : [class_Complete__Lattice_Ocomplete__lattice(_1389013), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389015, tc_fun(_1389017, _1389013)), _1389019), _1389021), _1389023) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389015, _1389013), _1389019), hAPP(hAPP(c_COMBC(_1389015, _1389017, _1389013), _1389021), _1389023)))], (42512 ^ _776541) ^ [_1622436, _1622438, _1622440] : [_1622436 = _1622438, 42515 ^ _776541 : [(42518 ^ _776541) ^ [_1622592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622440, _1622440)), _1622592), hAPP(c_List_Oset(tc_prod(_1622440, _1622440)), hAPP(hAPP(c_List_Ozip(_1622440, _1622440), _1622436), _1622438)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1622440, _1622440, tc_HOL_Obool), c_fequal), _1622592)))], (42516 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622440)), _1622436) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622440)), _1622438))]]], (44948 ^ _776541) ^ [_1676529, _1676531, _1676533, _1676535] : [c_Fun_Oinj__on(_1676529, _1676531, _1676533, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1676529, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1676529), tc_fun(_1676529, tc_HOL_Obool), c_List_Oset(_1676529)), _1676535))), -(c_Fun_Oinj__on(tc_List_Olist(_1676529), tc_List_Olist(_1676531), hAPP(c_List_Omap(_1676529, _1676531), _1676533), _1676535))], (33196 ^ _776541) ^ [_1384731, _1384733, _1384735] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1384731), hAPP(c_Set_OCollect(_1384731), hAPP(hAPP(c_COMBS(_1384731, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1384731), c_fdisj), _1384733)), _1384735))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384731), hAPP(c_Set_OCollect(_1384731), _1384733))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384731), hAPP(c_Set_OCollect(_1384731), _1384735)))], (34699 ^ _776541) ^ [_1423065] : [-(c_Divides_Oadjust(_1423065) = 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)), _1423065))))), 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)), _1423065))))), 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))))))))], (7638 ^ _776541) ^ [_903156, _903158, _903160, _903162] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903156, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903156, tc_HOL_Obool)), _903158), _903160)), _903162) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903156, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903156, tc_HOL_Obool)), _903158), _903162)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903156, tc_HOL_Obool)), _903160), _903162)))], (8215 ^ _776541) ^ [_917044, _917046, _917048, _917050, _917052] : [class_Lattices_Olattice(_917044), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917046, _917044)), _917048), _917050), _917052) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917044), hAPP(_917048, _917052)), hAPP(_917050, _917052)))], (3614 ^ _776541) ^ [_830679, _830681, _830683, _830685] : [-(c_List_Olinorder__class_Osorted__list__of__set(_830685, _830681) = c_List_Olinorder__class_Osorted__list__of__set(_830683, _830679)), _830685 = _830683, _830681 = _830679], (33119 ^ _776541) ^ [_1382119, _1382121, _1382123, _1382125, _1382127] : [hBOOL(hAPP(hAPP(c_member(_1382119), _1382121), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382123, tc_fun(_1382119, tc_HOL_Obool)), _1382125), _1382127))), 33122 ^ _776541 : [(33123 ^ _776541) ^ [_1382243] : [hBOOL(hAPP(hAPP(c_member(_1382123), _1382243), _1382125)), -(hBOOL(hAPP(hAPP(c_member(_1382119), _1382121), hAPP(_1382127, _1382243))))]]], (51995 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (20349 ^ _776541) ^ [_1143626, _1143628, _1143630, _1143632, _1143634] : [class_Fields_Ofield(_1143626), -(_1143628 = c_Groups_Ozero__class_Ozero(_1143626)), -(_1143630 = c_Groups_Ozero__class_Ozero(_1143626)), 20360 ^ _776541 : [(20367 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143626), _1143632), _1143630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143626), _1143634), _1143628), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143626), _1143632), _1143628) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143626), _1143634), _1143630))], (20361 ^ _776541) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143626), _1143632), _1143628) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143626), _1143634), _1143630), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143626), _1143632), _1143630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143626), _1143634), _1143628))]]], (51573 ^ _776541) ^ [_1820024, _1820026, _1820028, _1820030] : [class_Divides_Osemiring__div(_1820024), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820024), _1820026), _1820028)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820024), _1820026), _1820030)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820024), _1820026), c_Divides_Odiv__class_Omod(_1820024, _1820028, _1820030))))], (50645 ^ _776541) ^ [_1800318, _1800320, _1800322, _1800324, _1800326, _1800328] : [c_Fun_Oinj__on(_1800318, _1800320, _1800322, _1800324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800320, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1800318, _1800320, _1800322), _1800324)), _1800326)), c_Fun_Oinj__on(_1800320, _1800318, _1800328, _1800326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800318, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1800320, _1800318, _1800328), _1800326)), _1800324)), -(c_Fun_Obij__betw(_1800318, _1800320, 50660 ^ [_1800318, _1800320, _1800322, _1800324, _1800326, _1800328], _1800324, _1800326))], (35634 ^ _776541) ^ [_1441663, _1441665] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1441663, _1441665) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1441663, _1441665)))], (11372 ^ _776541) ^ [_974815, _974817, _974819, _974821, _974823] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974815, _974817, hAPP(hAPP(c_Set_Oinsert(_974815), _974819), _974821)), _974823))), 11373 ^ _776541 : [(11374 ^ _776541) ^ [_974919, _974921] : [hAPP(hAPP(c_Set_Oinsert(_974815), _974819), _974821) = hAPP(hAPP(c_Set_Oinsert(_974815), _974921), _974919), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974815, _974815, _974817, _974921, _974919), _974823)), -(hBOOL(hAPP(hAPP(c_member(_974815), _974921), _974919)))]]], (36296 ^ _776541) ^ [_1462207, _1462209, _1462211, _1462213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462207), _1462209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462211), _1462213)), -(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), _1462207), _1462211)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1462209), _1462213))), c_FunDef_Opair__leq)))], (49582 ^ _776541) ^ [_1778462, _1778464] : [c_Relation_Oantisym(_1778462, _1778464), -(c_Relation_Oantisym(_1778462, hAPP(c_Relation_Oconverse(_1778462, _1778462), _1778464)))], (34445 ^ _776541) ^ [_1417644, _1417646] : [-(c_Divides_OposDivAlg(_1417644, _1417646) = hAPP(c_Divides_Oadjust(_1417646), c_Divides_OposDivAlg(_1417644, 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)))), _1417646)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417644), _1417646))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1417646), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25024 ^ _776541) ^ [_1229718, _1229720, _1229722] : [-(_1229718 = 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), _1229718), _1229720)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229718), _1229722)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229720), _1229722))], (41483 ^ _776541) ^ [_1591743, _1591745, _1591747] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591743, _1591743)), _1591745), c_Transitive__Closure_Otrancl(_1591743, _1591747))), 41487 ^ _776541 : [(41490 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591743, _1591743)), _1591745), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591743, _1591743), tc_HOL_Obool), 41486 ^ [_1591743, _1591745, _1591747]), _1591747))))], (41488 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41486 ^ [_1591743, _1591745, _1591747])))]]], (52355 ^ _776541) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (17809 ^ _776541) ^ [_1097050, _1097052, _1097054] : [class_Groups_Ogroup__add(_1097050), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097050), _1097052), _1097054) = c_Groups_Ozero__class_Ozero(_1097050), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097050), _1097052) = _1097054)], (45168 ^ _776541) ^ [_1681265, _1681267, _1681269, _1681271, _1681273] : [class_Groups_Omonoid__add(_1681265), class_Groups_Oordered__ab__semigroup__add(_1681265), 45178 ^ _776541 : [(45181 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681265), hAPP(_1681271, 45177 ^ [_1681265, _1681267, _1681269, _1681271, _1681273])), hAPP(_1681273, 45177 ^ [_1681265, _1681267, _1681269, _1681271, _1681273])))], (45179 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1681267), 45177 ^ [_1681265, _1681267, _1681269, _1681271, _1681273]), hAPP(c_List_Oset(_1681267), _1681269))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681265), hAPP(c_List_Omonoid__add__class_Olistsum(_1681265), hAPP(hAPP(c_List_Omap(_1681267, _1681265), _1681271), _1681269))), hAPP(c_List_Omonoid__add__class_Olistsum(_1681265), hAPP(hAPP(c_List_Omap(_1681267, _1681265), _1681273), _1681269)))))], (22887 ^ _776541) ^ [_1191248, _1191250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1191248)), -(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), _1191248), _1191250))))], (52241 ^ _776541) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (34884 ^ _776541) ^ [] : [-(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)))))], (28457 ^ _776541) ^ [_1287293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1287293), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1287293)), c_Int_OMin)))], (264 ^ _776541) ^ [_780631, _780633, _780635, _780637] : [-(c_Nitpick_Orefl_H(_780635, _780631)), c_Nitpick_Orefl_H(_780637, _780633), _780637 = _780635, _780633 = _780631], (37250 ^ _776541) ^ [_1485456, _1485458, _1485460, _1485462, _1485464] : [c_Fun_Oinj__on(_1485456, _1485458, _1485460, _1485462), c_Fun_Oinj__on(_1485456, _1485458, _1485460, _1485464), -(c_Fun_Oinj__on(_1485456, _1485458, _1485460, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485456, tc_HOL_Obool)), _1485462), _1485464)))], (6957 ^ _776541) ^ [_889417, _889419] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_889417, tc_HOL_Obool)), _889419), hAPP(c_Set_OPow(_889417), _889419))))], (29793 ^ _776541) ^ [] : [-(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))], (12844 ^ _776541) ^ [_1003135, _1003137, _1003139] : [class_Lattices_Olattice(_1003135), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003135), _1003137)), -(c_Big__Operators_Olattice__class_OSup__fin(_1003135, hAPP(hAPP(c_Set_Oinsert(_1003135), _1003139), _1003137)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003135, _1003135, c_Lattices_Osemilattice__sup__class_Osup(_1003135)), _1003139), _1003137))], (24002 ^ _776541) ^ [_1211154, _1211156] : [class_Divides_Osemiring__div(_1211154), -(_1211156 = c_Groups_Ozero__class_Ozero(_1211154)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1211154), _1211156), _1211156) = c_Groups_Oone__class_Oone(_1211154))], (30266 ^ _776541) ^ [_1319387, _1319389, _1319391, _1319393] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1319387), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319387), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319387), _1319389), _1319391)), _1319393) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319387), _1319389), _1319393)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319387), _1319391), _1319393)))], (36549 ^ _776541) ^ [] : [-(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))))))], (44936 ^ _776541) ^ [_1676223, _1676225] : [class_Groups_Oordered__ab__group__add__abs(_1676223), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676223), hAPP(c_Groups_Oabs__class_Oabs(_1676223), hAPP(c_List_Omonoid__add__class_Olistsum(_1676223), _1676225))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676223), hAPP(hAPP(c_List_Omap(_1676223, _1676223), c_Groups_Oabs__class_Oabs(_1676223)), _1676225)))))], (38535 ^ _776541) ^ [_1515433, _1515435, _1515437, _1515439] : [-(c_HOL_OThe(tc_prod(_1515433, _1515435), hAPP(c_Product__Type_Oprod_Oprod__case(_1515433, _1515435, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1515433, tc_fun(_1515435, tc_HOL_Obool), tc_fun(_1515435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1515435, tc_HOL_Obool), tc_fun(_1515435, tc_HOL_Obool)), _1515433), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1515435)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515433), c_fconj), hAPP(c_fequal, _1515437)))), hAPP(c_fequal, _1515439)))) = hAPP(hAPP(c_Product__Type_OPair(_1515433, _1515435), _1515437), _1515439))], (18061 ^ _776541) ^ [_1101331, _1101333, _1101335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101331), _1101333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101335), _1101331)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101335), _1101333))))], (14901 ^ _776541) ^ [_1045299, _1045301, _1045303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045299), _1045301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045299), _1045303)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045301), _1045303))))], (40150 ^ _776541) ^ [_1558793, _1558795, _1558797, _1558799, _1558801, _1558803, _1558805, _1558807] : [c_Finite__Set_Ofolding(_1558793, _1558795, _1558797, _1558799), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558793), _1558801)), -(hAPP(c_Fun_Ocomp(_1558795, _1558795, _1558803, hAPP(_1558797, _1558805)), hAPP(c_Fun_Ocomp(_1558795, _1558795, _1558803, hAPP(_1558799, _1558801)), _1558807)) = hAPP(c_Fun_Ocomp(_1558795, _1558795, _1558803, hAPP(_1558799, _1558801)), hAPP(c_Fun_Ocomp(_1558795, _1558795, _1558803, hAPP(_1558797, _1558805)), _1558807)))], (51993 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (51987 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (41895 ^ _776541) ^ [_1603936, _1603938] : [-(c_List_Olistrel1(_1603936, hAPP(c_Relation_Oconverse(_1603936, _1603936), _1603938)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1603936), tc_List_Olist(_1603936)), c_List_Olistrel1(_1603936, _1603938)))], (33577 ^ _776541) ^ [_1394621] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1394621, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1394621), hAPP(c_COMBK(tc_HOL_Obool, _1394621), c_fTrue)))], (38509 ^ _776541) ^ [_1514830, _1514832] : [-(hAPP(c_Relation_ORange(_1514830, _1514832), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514830, _1514832), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1514832, tc_HOL_Obool)))], (36557 ^ _776541) ^ [_1468888] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468888) = 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, _1468888)), 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))))))))], (32676 ^ _776541) ^ [_1369999, _1370001] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1369999, 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(_1369999, tc_HOL_Obool)), tc_fun(_1369999, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1369999, tc_HOL_Obool)), tc_fun(_1369999, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1369999, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1370001)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1369999, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1370001))], (27034 ^ _776541) ^ [_1263449] : [-(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)), _1263449)))], (40605 ^ _776541) ^ [_1569452, _1569454, _1569456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569452, _1569452)), _1569454), _1569456)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569452, _1569452)), _1569454), c_Transitive__Closure_Otrancl(_1569452, _1569456))))], (45788 ^ _776541) ^ [_1695232, _1695234] : [-(hAPP(c_List_Oset(_1695232), c_List_Oremdups(_1695232, _1695234)) = hAPP(c_List_Oset(_1695232), _1695234))], (45166 ^ _776541) ^ [_1681177, _1681179] : [-(c_Random_Oselect(_1681177, _1681179) = 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(_1681177, 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(_1681177)), _1681179)))), hAPP(hAPP(c_COMBB(_1681177, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1681177, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1681177, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1681177, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1681177), _1681179)), c_Code__Numeral_Onat__of))))], (40272 ^ _776541) ^ [_1561588, _1561590, _1561592, _1561594, _1561596, _1561598] : [c_Finite__Set_Ofolding__idem(_1561588, _1561590, _1561592, _1561594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561588), _1561596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1561588, tc_HOL_Obool)), _1561598), _1561596)), -(hAPP(c_Fun_Ocomp(_1561590, _1561590, _1561590, hAPP(_1561594, _1561596)), hAPP(_1561594, _1561598)) = hAPP(_1561594, _1561596))], (36083 ^ _776541) ^ [_1455944, _1455946, _1455948, _1455950] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455944, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36084 ^ [_1455944, _1455946, _1455948, _1455950])), _1455946) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455944, 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), 36084 ^ [_1455944, _1455946, _1455948, _1455950]), _1455948))), _1455950), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455944, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455946) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455944, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455950))], (1674 ^ _776541) ^ [_800330, _800332] : [-(class_Groups_Ocomm__monoid__add(_800330)), _800332 = _800330, class_Groups_Ocomm__monoid__add(_800332)], (10116 ^ _776541) ^ [_949758, _949760, _949762, _949764] : [class_Orderings_Olinorder(_949758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949758), _949760), _949762)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949758), _949762), _949764)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_949758, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949758, _949760, _949762)), c_SetInterval_Oord__class_OgreaterThanLessThan(_949758, _949762, _949764)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_949758, _949760, _949764))], (32990 ^ _776541) ^ [_1378766, _1378768, _1378770] : [hBOOL(hAPP(_1378766, _1378768)), -(hAPP(c_Set_OCollect(_1378770), hAPP(hAPP(c_COMBS(_1378770, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378770), c_fconj), hAPP(hAPP(c_COMBC(_1378770, _1378770, tc_HOL_Obool), c_fequal), _1378768))), _1378766)) = hAPP(hAPP(c_Set_Oinsert(_1378770), _1378768), c_Orderings_Obot__class_Obot(tc_fun(_1378770, tc_HOL_Obool))))], (46486 ^ _776541) ^ [_1711564, _1711566, _1711568] : [class_Orderings_Olinorder(_1711564), c_List_Olinorder__class_Osorted(_1711564, _1711566), -(c_List_Olinorder__class_Osorted(_1711564, c_List_Olinorder__class_Oinsort__insert__key(_1711564, _1711564, c_COMBI(_1711564), _1711568, _1711566)))], (19579 ^ _776541) ^ [_1130329, _1130331, _1130333] : [class_Rings_Odivision__ring(_1130329), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130329), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130329), _1130331), _1130333)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130329), hAPP(c_Groups_Ouminus__class_Ouminus(_1130329), _1130331)), _1130333))], (45742 ^ _776541) ^ [_1694334, _1694336, _1694338, _1694340, _1694342] : [c_Fun_Oinj__on(_1694334, _1694336, _1694338, hAPP(hAPP(c_Set_Oinsert(_1694334), _1694340), hAPP(c_List_Oset(_1694334), _1694342))), -(hAPP(hAPP(c_List_Omap(_1694334, _1694336), _1694338), hAPP(c_List_OremoveAll(_1694334, _1694340), _1694342)) = hAPP(c_List_OremoveAll(_1694336, hAPP(_1694338, _1694340)), hAPP(hAPP(c_List_Omap(_1694334, _1694336), _1694338), _1694342)))], (37462 ^ _776541) ^ [_1489551, _1489553, _1489555, _1489557, _1489559] : [c_Fun_Oinj__on(_1489551, _1489553, _1489555, c_Orderings_Otop__class_Otop(tc_fun(_1489551, tc_HOL_Obool))), 37465 ^ _776541 : [(37472 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1489551), _1489557), _1489559)), -(hBOOL(hAPP(hAPP(c_member(_1489553), hAPP(_1489555, _1489557)), hAPP(c_Set_Oimage(_1489551, _1489553, _1489555), _1489559))))], (37466 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1489553), hAPP(_1489555, _1489557)), hAPP(c_Set_Oimage(_1489551, _1489553, _1489555), _1489559))), -(hBOOL(hAPP(hAPP(c_member(_1489551), _1489557), _1489559)))]]], (11175 ^ _776541) ^ [_970127, _970129, _970131, _970133, _970135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970127, tc_HOL_Obool)), _970129), hAPP(c_Set_Oimage(_970131, _970127, _970133), _970135))), 11179 ^ _776541 : [(11182 ^ _776541) ^ [] : [-(_970129 = hAPP(c_Set_Oimage(_970131, _970127, _970133), 11178 ^ [_970127, _970129, _970131, _970133, _970135]))], (11180 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970131, tc_HOL_Obool)), 11178 ^ [_970127, _970129, _970131, _970133, _970135]), _970135)))]]], (18103 ^ _776541) ^ [_1102048, _1102050] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1102048), _1102050)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39938 ^ _776541) ^ [_1553991, _1553993, _1553995] : [-(hAPP(c_Fun_Ocomp(_1553991, _1553991, _1553993, c_Fun_Oid(_1553991)), _1553995) = _1553995)], (11386 ^ _776541) ^ [_975176, _975178, _975180, _975182, _975184, _975186, _975188] : [c_Finite__Set_Ofun__left__comm(_975176, _975178, _975180), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975176, _975178, _975180, _975182, hAPP(hAPP(c_Set_Oinsert(_975176), _975184), _975186)), _975188)), -(hBOOL(hAPP(hAPP(c_member(_975176), _975184), _975186))), 11398 ^ _776541 : [(11401 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975176, _975178, _975180, _975182, _975186), 11397 ^ [_975176, _975178, _975180, _975182, _975184, _975186, _975188])))], (11399 ^ _776541) ^ [] : [-(_975188 = hAPP(hAPP(_975180, _975184), 11397 ^ [_975176, _975178, _975180, _975182, _975184, _975186, _975188]))]]], (30020 ^ _776541) ^ [_1314903, _1314905] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1314903)), hAPP(c_Nat_OSuc, _1314905)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1314903), _1314905)))], (29211 ^ _776541) ^ [_1300089, _1300091] : [class_Int_Onumber__ring(_1300089), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300089), c_Groups_Oone__class_Oone(_1300089)), c_Groups_Oone__class_Oone(_1300089))), hAPP(c_Int_Onumber__class_Onumber__of(_1300089), _1300091)) = hAPP(c_Int_Onumber__class_Onumber__of(_1300089), c_Int_OBit0(_1300091)))], (42781 ^ _776541) ^ [_1628582, _1628584] : [-(c_List_Obutlast(_1628582, _1628584) = hAPP(hAPP(c_List_Otake(_1628582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628582)), _1628584)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1628584))], (41248 ^ _776541) ^ [_1585946] : [-(c_Relation_Osingle__valued(_1585946, _1585946, c_Relation_OId(_1585946)))], (1354 ^ _776541) ^ [_796330, _796332] : [-(class_Complete__Lattice_Ocomplete__lattice(_796330)), _796332 = _796330, class_Complete__Lattice_Ocomplete__lattice(_796332)], (46309 ^ _776541) ^ [_1707929, _1707931, _1707933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707929), _1707931)), -(c_List_Oupt(_1707929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707931), _1707933)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1707929, _1707931)), c_List_Oupt(_1707931, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707931), _1707933))))], (19813 ^ _776541) ^ [_1134117, _1134119, _1134121, _1134123] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1134117, _1134119)), c_Sum__Type_OPlus(_1134117, _1134119, _1134121, _1134123))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1134119), _1134123)))], (1924 ^ _776541) ^ [_803455, _803457] : [-(hBOOL(_803455)), _803457 = _803455, hBOOL(_803457)], (40717 ^ _776541) ^ [_1572993, _1572995, _1572997] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572993, _1572993)), hAPP(hAPP(c_Product__Type_OPair(_1572993, _1572993), _1572995), _1572995)), c_Transitive__Closure_Ortrancl(_1572993, _1572997))))], (11030 ^ _776541) ^ [_967222, _967224] : [class_Lattices_Oab__semigroup__idem__mult(_967222), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967222), _967224), _967224) = _967224)], (23087 ^ _776541) ^ [_1194816] : [-(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)), _1194816))))], (40086 ^ _776541) ^ [_1557143, _1557145, _1557147, _1557149, _1557151, _1557153] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1557143, _1557145), _1557143, tc_prod(_1557147, _1557149), c_Product__Type_Ofst(_1557143, _1557145)), c_Product__Type_Omap__pair(_1557147, _1557143, _1557149, _1557145, _1557151, _1557153)) = hAPP(c_Fun_Ocomp(_1557147, _1557143, tc_prod(_1557147, _1557149), _1557151), c_Product__Type_Ofst(_1557147, _1557149)))], (46255 ^ _776541) ^ [_1706834, _1706836] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1706834))), c_List_Otranspose(_1706834, _1706836)) = c_List_Ofoldr(tc_List_Olist(_1706834), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1706834)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1706834))), _1706836, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13980 ^ _776541) ^ [_1026815, _1026817, _1026819, _1026821] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1026815), _1026817)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026815), _1026819)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1026815, tc_Nat_Onat), _1026821), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1026815, tc_HOL_Obool)), _1026817), _1026819)) = 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(_1026815, tc_Nat_Onat), _1026821), _1026817)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1026815, tc_Nat_Onat), _1026821), _1026819))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1026815, tc_Nat_Onat), _1026821), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026815, tc_HOL_Obool)), _1026817), _1026819))))], (33042 ^ _776541) ^ [_1379929, _1379931, _1379933, _1379935] : [class_Groups_Oordered__ab__group__add__abs(_1379929), -(hAPP(c_Groups_Oabs__class_Oabs(_1379929), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1379931, _1379929), hAPP(hAPP(c_COMBB(_1379929, _1379929, _1379931), c_Groups_Oabs__class_Oabs(_1379929)), _1379933)), _1379935)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1379931, _1379929), hAPP(hAPP(c_COMBB(_1379929, _1379929, _1379931), c_Groups_Oabs__class_Oabs(_1379929)), _1379933)), _1379935))], (34531 ^ _776541) ^ [_1419522, _1419524, _1419526, _1419528, _1419530, _1419532, _1419534] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419522, tc_fun(_1419524, tc_fun(_1419526, tc_HOL_Obool))), _1419528), _1419530), _1419532), _1419534)), 34535 ^ _776541 : [(34538 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1419530, 34534 ^ [_1419522, _1419524, _1419526, _1419528, _1419530, _1419532, _1419534]), _1419532), _1419534)))], (34536 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419522), 34534 ^ [_1419522, _1419524, _1419526, _1419528, _1419530, _1419532, _1419534]), _1419528)))]]], (49293 ^ _776541) ^ [_1771802, _1771804] : [-(c_Relation_Otrans(_1771802, c_Relation_OId__on(_1771802, _1771804)))], (49998 ^ _776541) ^ [_1786436] : [-(c_Hilbert__Choice_Oinv__into(_1786436, _1786436, c_Orderings_Otop__class_Otop(tc_fun(_1786436, tc_HOL_Obool)), c_Fun_Oid(_1786436)) = c_Fun_Oid(_1786436))], (23017 ^ _776541) ^ [_1193533, _1193535, _1193537, _1193539, _1193541] : [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), _1193533), _1193535)), _1193537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193533), _1193539)), _1193541))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193537), _1193533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193541), _1193533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193535), _1193539)))], (46060 ^ _776541) ^ [_1701682, _1701684, _1701686] : [46062 ^ _776541 : [(46065 ^ _776541) ^ [] : [hBOOL(hAPP(_1701684, 46061 ^ [_1701682, _1701684, _1701686]))], (46063 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1701682), 46061 ^ [_1701682, _1701684, _1701686]), hAPP(c_List_Oset(_1701682), _1701686))))]], -(hAPP(c_List_Ofilter(_1701682, _1701684), _1701686) = _1701686)], (47098 ^ _776541) ^ [_1723258, _1723260, _1723262, _1723264] : [hAPP(c_List_Orev(_1723258), _1723260) = hAPP(hAPP(c_List_Olist_OCons(_1723258), _1723262), _1723264), -(_1723260 = hAPP(hAPP(c_List_Oappend(_1723258), hAPP(c_List_Orev(_1723258), _1723264)), hAPP(hAPP(c_List_Olist_OCons(_1723258), _1723262), c_List_Olist_ONil(_1723258))))], (13134 ^ _776541) ^ [_1008682, _1008684, _1008686, _1008688, _1008690] : [class_Rings_Oring(_1008682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008684), _1008686)), hBOOL(hAPP(hAPP(c_member(_1008684), _1008688), _1008686)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008684, _1008682), _1008690), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008684, tc_HOL_Obool)), _1008686), hAPP(hAPP(c_Set_Oinsert(_1008684), _1008688), c_Orderings_Obot__class_Obot(tc_fun(_1008684, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1008682), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008684, _1008682), _1008690), _1008686)), hAPP(_1008690, _1008688)))], (35501 ^ _776541) ^ [_1438943, _1438945, _1438947] : [-(hAPP(c_Product__Type_Osnd(_1438943, _1438945), _1438947) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1438943, _1438945, _1438945), hAPP(c_COMBK(tc_fun(_1438945, _1438945), _1438943), c_COMBI(_1438945))), _1438947))], (17099 ^ _776541) ^ [_1084396, _1084398, _1084400] : [class_Rings_Oordered__cancel__semiring(_1084396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084396), c_Groups_Ozero__class_Ozero(_1084396)), _1084398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084396), _1084400), c_Groups_Ozero__class_Ozero(_1084396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084396), _1084400), _1084398)), c_Groups_Ozero__class_Ozero(_1084396))))], (16763 ^ _776541) ^ [_1078064, _1078066] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1078064), _1078066)), hAPP(c_Nat_OSuc, _1078064))))], (12558 ^ _776541) ^ [_997483, _997485, _997487, _997489] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_997483), _997485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997483, tc_HOL_Obool)), _997485), _997487)), hBOOL(hAPP(_997489, c_Orderings_Obot__class_Obot(tc_fun(_997483, tc_HOL_Obool)))), 12573 ^ _776541 : [(12574 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_997483), 12572 ^ [_997483, _997485, _997487, _997489])))], (12578 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_997483), 12571 ^ [_997483, _997485, _997487, _997489]), 12572 ^ [_997483, _997485, _997487, _997489]))], (12582 ^ _776541) ^ [] : [hBOOL(hAPP(_997489, hAPP(hAPP(c_Set_Oinsert(_997483), 12571 ^ [_997483, _997485, _997487, _997489]), 12572 ^ [_997483, _997485, _997487, _997489])))], (12580 ^ _776541) ^ [] : [-(hBOOL(hAPP(_997489, 12572 ^ [_997483, _997485, _997487, _997489])))], (12576 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997483), 12571 ^ [_997483, _997485, _997487, _997489]), _997487)))]], -(hBOOL(hAPP(_997489, _997485)))], (41250 ^ _776541) ^ [_1585972, _1585974, _1585976, _1585978, _1585980] : [c_Relation_Osingle__valued(_1585972, _1585974, _1585976), c_Relation_Osingle__valued(_1585974, _1585978, _1585980), -(c_Relation_Osingle__valued(_1585972, _1585978, hAPP(hAPP(c_Relation_Orel__comp(_1585972, _1585974, _1585978), _1585976), _1585980)))], (1644 ^ _776541) ^ [_799955, _799957] : [-(class_Groups_Oab__semigroup__add(_799955)), _799957 = _799955, class_Groups_Oab__semigroup__add(_799957)], (15794 ^ _776541) ^ [_1062742, _1062744] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1062742), _1062744), 15799 ^ _776541 : [(15802 ^ _776541) ^ [] : [-(_1062744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15800 ^ _776541) ^ [] : [-(_1062742 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 15803 ^ _776541 : [(15806 ^ _776541) ^ [] : [-(_1062744 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15804 ^ _776541) ^ [] : [-(_1062742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (52169 ^ _776541) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (29197 ^ _776541) ^ [_1299832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299832), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1299832)), c_Int_OMin)))], (52063 ^ _776541) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (41053 ^ _776541) ^ [_1580962, _1580964, _1580966, _1580968, _1580970] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580962, _1580962)), hAPP(hAPP(c_Product__Type_OPair(_1580962, _1580962), hAPP(_1580964, hAPP(c_Nat_OSuc, 41054 ^ [_1580962, _1580964, _1580966, _1580968, _1580970]))), hAPP(_1580964, 41054 ^ [_1580962, _1580964, _1580966, _1580968, _1580970]))), c_Transitive__Closure_Ortrancl(_1580962, _1580966))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580962, _1580962)), hAPP(hAPP(c_Product__Type_OPair(_1580962, _1580962), hAPP(_1580964, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1580968), _1580970))), hAPP(_1580964, _1580968))), c_Transitive__Closure_Ortrancl(_1580962, _1580966))))], (46882 ^ _776541) ^ [_1718603, _1718605, _1718607, _1718609] : [class_Orderings_Olinorder(_1718603), c_List_Olinorder__class_Osorted(_1718603, _1718605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718607), _1718609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718609), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718603)), _1718605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718603), hAPP(hAPP(c_List_Onth(_1718603), _1718605), _1718607)), hAPP(hAPP(c_List_Onth(_1718603), _1718605), _1718609))))], (31341 ^ _776541) ^ [_1339133, _1339135] : [class_Orderings_Olinorder(_1339133), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339133), _1339135), _1339135) = _1339135)], (22275 ^ _776541) ^ [_1180481, _1180483] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180481), _1180483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180483), _1180481)))], (4824 ^ _776541) ^ [_849980, _849982] : [_849982 = _849980, -(c_List_Oset(_849982) = c_List_Oset(_849980))], (39575 ^ _776541) ^ [_1544089, _1544091, _1544093, _1544095, _1544097] : [c_Relation_Orefl__on(_1544089, _1544091, _1544093), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544089, _1544089)), hAPP(hAPP(c_Product__Type_OPair(_1544089, _1544089), _1544095), _1544097)), _1544093)), -(hBOOL(hAPP(hAPP(c_member(_1544089), _1544097), _1544091)))], (3158 ^ _776541) ^ [_823559, _823561] : [_823561 = _823559, -(c_List_Orotate1(_823561) = c_List_Orotate1(_823559))], (16492 ^ _776541) ^ [_1073544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073544), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1073544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44054 ^ _776541) ^ [_1657462, _1657464, _1657466, _1657468] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657462) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1657464), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657462)), hAPP(hAPP(c_List_Olist_OCons(_1657464), _1657466), _1657468)) = hAPP(hAPP(c_List_Olist_OCons(_1657464), _1657466), _1657468))], (5392 ^ _776541) ^ [_858910, _858912] : [_858912 = _858910, -(c_Groups_Otimes__class_Otimes(_858912) = c_Groups_Otimes__class_Otimes(_858910))], (8435 ^ _776541) ^ [_921398, _921400] : [class_Lattices_Osemilattice__inf(_921398), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921398), _921400), _921400) = _921400)], (384 ^ _776541) ^ [_782359, _782361, _782363, _782365] : [-(c_Relation_Oirrefl(_782363, _782359)), c_Relation_Oirrefl(_782365, _782361), _782365 = _782363, _782361 = _782359], (40497 ^ _776541) ^ [_1566748, _1566750, _1566752, _1566754, _1566756, _1566758, _1566760, _1566762] : [class_Groups_Ocomm__monoid__add(_1566748), c_Fun_Oinj__on(_1566750, _1566752, _1566754, _1566756), _1566758 = hAPP(c_Set_Oimage(_1566750, _1566752, _1566754), _1566756), 40511 ^ _776541 : [(40514 ^ _776541) ^ [] : [hAPP(_1566760, 40510 ^ [_1566748, _1566750, _1566752, _1566754, _1566756, _1566758, _1566760, _1566762]) = hAPP(_1566762, hAPP(_1566754, 40510 ^ [_1566748, _1566750, _1566752, _1566754, _1566756, _1566758, _1566760, _1566762]))], (40512 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566750), 40510 ^ [_1566748, _1566750, _1566752, _1566754, _1566756, _1566758, _1566760, _1566762]), _1566756)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566752, _1566748), _1566762), _1566758) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566750, _1566748), _1566760), _1566756))], (27611 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (46032 ^ _776541) ^ [_1701049, _1701051, _1701053] : [-(hAPP(c_List_Ofilter(_1701049, _1701051), c_List_Oconcat(_1701049, _1701053)) = c_List_Oconcat(_1701049, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1701049), tc_List_Olist(_1701049)), c_List_Ofilter(_1701049, _1701051)), _1701053)))], (42833 ^ _776541) ^ [_1629895, _1629897, _1629899, _1629901] : [hBOOL(hAPP(c_List_Odistinct(_1629895), _1629897)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1629895, _1629899)), hAPP(hAPP(c_List_Ozip(_1629895, _1629899), _1629897), _1629901))))], (46219 ^ _776541) ^ [_1705854] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1705854)), c_List_Otranspose__rel(_1705854)), c_List_Olist_ONil(tc_List_Olist(_1705854)))), -(c_List_Otranspose(_1705854, c_List_Olist_ONil(tc_List_Olist(_1705854))) = c_List_Olist_ONil(tc_List_Olist(_1705854)))], (46838 ^ _776541) ^ [_1717638, _1717640, _1717642] : [class_Orderings_Olinorder(_1717638), hBOOL(hAPP(hAPP(c_member(_1717638), _1717640), hAPP(c_List_Oset(_1717638), _1717642))), c_List_Olinorder__class_Osorted(_1717638, _1717642), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1717638, _1717638, c_COMBI(_1717638)), _1717640), c_List_Oremove1(_1717638, _1717640, _1717642)) = _1717642)], (49992 ^ _776541) ^ [_1786287, _1786289, _1786291, _1786293, _1786295] : [c_Fun_Oinj__on(_1786287, _1786289, _1786291, c_Orderings_Otop__class_Otop(tc_fun(_1786287, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1786289, _1786293, _1786287, hAPP(c_Fun_Ocomp(_1786287, _1786293, _1786289, _1786295), c_Hilbert__Choice_Oinv__into(_1786287, _1786289, c_Orderings_Otop__class_Otop(tc_fun(_1786287, tc_HOL_Obool)), _1786291))), _1786291) = _1786295)], (21361 ^ _776541) ^ [_1163278, _1163280, _1163282] : [class_Rings_Ocomm__semiring__1(_1163278), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163278), _1163280), hAPP(hAPP(c_Power_Opower__class_Opower(_1163278), _1163280), _1163282)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1163278), _1163280), hAPP(c_Nat_OSuc, _1163282)))], (41186 ^ _776541) ^ [_1584437, _1584439, _1584441, _1584443, _1584445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584437, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584439, _1584437, _1584441), _1584443)), _1584445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584439, tc_HOL_Obool)), _1584443), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584439, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584437, _1584439, hAPP(c_Relation_Oconverse(_1584439, _1584437), _1584441)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584437, tc_HOL_Obool)), _1584445))))))], (49486 ^ _776541) ^ [_1776736, _1776738, _1776740, _1776742] : [c_Predicate_Osymp(_1776736, _1776738), hBOOL(hAPP(hAPP(_1776738, _1776740), _1776742)), -(hBOOL(hAPP(hAPP(_1776738, _1776742), _1776740)))], (33631 ^ _776541) ^ [] : [-(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)))], (17141 ^ _776541) ^ [_1085161, _1085163, _1085165] : [class_Rings_Olinordered__ring__strict(_1085161), 17144 ^ _776541 : [(17159 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085161), _1085163), _1085165)), c_Groups_Ozero__class_Ozero(_1085161)))), 17160 ^ _776541 : [(17167 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), _1085163), c_Groups_Ozero__class_Ozero(_1085161))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), c_Groups_Ozero__class_Ozero(_1085161)), _1085165))], (17161 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), c_Groups_Ozero__class_Ozero(_1085161)), _1085163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), _1085165), c_Groups_Ozero__class_Ozero(_1085161)))]]], (17145 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085161), _1085163), _1085165)), c_Groups_Ozero__class_Ozero(_1085161))), 17150 ^ _776541 : [(17153 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), _1085165), c_Groups_Ozero__class_Ozero(_1085161))))], (17151 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), c_Groups_Ozero__class_Ozero(_1085161)), _1085163)))]], 17154 ^ _776541 : [(17157 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), c_Groups_Ozero__class_Ozero(_1085161)), _1085165)))], (17155 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085161), _1085163), c_Groups_Ozero__class_Ozero(_1085161))))]]]]], (28605 ^ _776541) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (22351 ^ _776541) ^ [_1181774, _1181776] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181774), _1181776) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1181774), _1181776)))], (38464 ^ _776541) ^ [_1513962, _1513964, _1513966, _1513968, _1513970] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513962, _1513964)), hAPP(hAPP(c_Product__Type_OPair(_1513962, _1513964), _1513966), _1513968)), _1513970)), -(hBOOL(hAPP(hAPP(c_member(_1513964), _1513968), hAPP(c_Relation_ORange(_1513962, _1513964), _1513970))))], (30100 ^ _776541) ^ [_1316516, _1316518, _1316520, _1316522] : [class_Orderings_Olinorder(_1316516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316516), _1316518), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316516), _1316520), _1316522))), 30107 ^ _776541 : [(30110 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316516), _1316518), _1316522)))], (30108 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316516), _1316518), _1316520)))]]], (19549 ^ _776541) ^ [_1129674, _1129676] : [class_Rings_Odivision__ring__inverse__zero(_1129674), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129674), _1129676), c_Groups_Ozero__class_Ozero(_1129674)) = c_Groups_Ozero__class_Ozero(_1129674))], (52053 ^ _776541) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (52215 ^ _776541) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (40997 ^ _776541) ^ [_1579633, _1579635, _1579637, _1579639] : [c_Wellfounded_Oacyclic(_1579633, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579633, _1579633)), hAPP(hAPP(c_Product__Type_OPair(_1579633, _1579633), _1579635), _1579637)), _1579639)), 41000 ^ _776541 : [(41003 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579633, _1579633)), hAPP(hAPP(c_Product__Type_OPair(_1579633, _1579633), _1579637), _1579635)), c_Transitive__Closure_Ortrancl(_1579633, _1579639)))], (41001 ^ _776541) ^ [] : [-(c_Wellfounded_Oacyclic(_1579633, _1579639))]]], (11226 ^ _776541) ^ [_971471, _971473, _971475, _971477, _971479] : [c_Typedef_Otype__definition(_971471, _971473, _971475, _971477, _971479), -(hAPP(c_Set_Oimage(_971473, _971471, _971477), _971479) = c_Orderings_Otop__class_Otop(tc_fun(_971471, tc_HOL_Obool)))], (33537 ^ _776541) ^ [_1393612, _1393614, _1393616] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393612, tc_fun(_1393614, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1393612, tc_HOL_Obool))), _1393616) = c_Orderings_Otop__class_Otop(tc_fun(_1393614, tc_HOL_Obool)))], (13246 ^ _776541) ^ [_1011015, _1011017, _1011019, _1011021, _1011023] : [class_Groups_Ocomm__monoid__mult(_1011015), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011017), _1011019)), -(hBOOL(hAPP(hAPP(c_member(_1011017), _1011021), _1011019))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011017, _1011015), _1011023), hAPP(hAPP(c_Set_Oinsert(_1011017), _1011021), _1011019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011015), hAPP(_1011023, _1011021)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011017, _1011015), _1011023), _1011019)))], (41743 ^ _776541) ^ [_1598582, _1598584] : [-(c_List_Olenlex(_1598582, _1598584) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1598582), tc_List_Olist(_1598582), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1598582), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598582), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), tc_List_Olist(_1598582)), c_COMBS(tc_List_Olist(_1598582), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1598582)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1598582)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1598582), tc_fun(tc_List_Olist(_1598582), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1598582), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), tc_List_Olist(_1598582)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1598582))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1598582)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1598582))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1598582)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1598582), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598582), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), tc_List_Olist(_1598582)), c_COMBS(tc_List_Olist(_1598582), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1598582)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1598582)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1598582), tc_fun(tc_List_Olist(_1598582), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1598582), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), tc_List_Olist(_1598582)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1598582))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1598582)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1598582))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1598582)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1598582), tc_fun(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598582), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598582), tc_HOL_Obool)), tc_List_Olist(_1598582)), c_COMBC(tc_List_Olist(_1598582), tc_fun(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598582), tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582))), tc_fun(tc_List_Olist(_1598582), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1598582)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1598582)), c_member(tc_prod(tc_List_Olist(_1598582), tc_List_Olist(_1598582))))), c_Product__Type_OPair(tc_List_Olist(_1598582), tc_List_Olist(_1598582))))), c_List_Olex(_1598582, _1598584)))))))], (4448 ^ _776541) ^ [_844066, _844068, _844070, _844072] : [-(c_Lazy__Sequence_Osmall__lazy_H(_844072, _844068) = c_Lazy__Sequence_Osmall__lazy_H(_844070, _844066)), _844072 = _844070, _844068 = _844066], (36404 ^ _776541) ^ [_1464074, _1464076] : [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), _1464074), _1464076)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1464074), _1464076)))], (41064 ^ _776541) ^ [_1581331, _1581333, _1581335, _1581337, _1581339] : [-(hAPP(c_Relation_Oconverse(_1581331, _1581333), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581335, tc_fun(tc_prod(_1581331, _1581333), tc_HOL_Obool)), _1581337), _1581339)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581335, tc_fun(tc_prod(_1581333, _1581331), tc_HOL_Obool)), _1581337), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1581331, _1581333), tc_HOL_Obool), tc_fun(tc_prod(_1581333, _1581331), tc_HOL_Obool), _1581335), c_Relation_Oconverse(_1581331, _1581333)), _1581339)))], (24964 ^ _776541) ^ [_1228649, _1228651] : [-(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, _1228649, _1228651)), _1228651) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228649), _1228651))], (9708 ^ _776541) ^ [_942711, _942713, _942715, _942717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942711, tc_HOL_Obool)), _942713), _942715)), hBOOL(hAPP(hAPP(c_member(_942711), _942717), _942713)), -(hBOOL(hAPP(hAPP(c_member(_942711), _942717), _942715)))], (18186 ^ _776541) ^ [_1103507, _1103509, _1103511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103507), _1103509)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103511), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103509), _1103507))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1103511), _1103507)), hAPP(c_Nat_OSuc, _1103509)))], (20165 ^ _776541) ^ [_1140624, _1140626, _1140628] : [class_Fields_Olinordered__field(_1140624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140624), c_Groups_Ozero__class_Ozero(_1140624)), _1140626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140624), _1140628), c_Groups_Ozero__class_Ozero(_1140624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140624), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140624), _1140626), _1140628)), c_Groups_Ozero__class_Ozero(_1140624))))], (44569 ^ _776541) ^ [_1668037, _1668039, _1668041] : [_1668037 = c_List_Olist_ONil(_1668039), -(c_List_Olast(_1668039, hAPP(hAPP(c_List_Olist_OCons(_1668039), _1668041), _1668037)) = _1668041)], (19947 ^ _776541) ^ [_1136504, _1136506, _1136508, _1136510] : [class_Fields_Olinordered__field(_1136504), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136504), _1136506), c_Groups_Ozero__class_Ozero(_1136504))), 19954 ^ _776541 : [(19961 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136504), _1136510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136504), _1136508), _1136506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136504), _1136508), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136504), _1136510), _1136506))))], (19955 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136504), _1136508), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136504), _1136510), _1136506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136504), _1136510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136504), _1136508), _1136506))))]]], (42077 ^ _776541) ^ [_1610021, _1610023, _1610025, _1610027, _1610029, _1610031] : [hBOOL(hAPP(hAPP(_1610021, _1610023), _1610025)), c_List_Olistrelp(_1610027, _1610021, _1610029, _1610031), -(c_List_Olistrelp(_1610027, _1610021, hAPP(hAPP(c_List_Olist_OCons(_1610027), _1610023), _1610029), hAPP(hAPP(c_List_Olist_OCons(_1610027), _1610025), _1610031)))], (45750 ^ _776541) ^ [_1694545, _1694547] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694545)), c_List_Oremdups(_1694545, _1694547))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694545)), _1694547))))], (49974 ^ _776541) ^ [_1785890, _1785892, _1785894] : [c_Fun_Oinj__on(_1785890, _1785892, _1785894, c_Orderings_Otop__class_Otop(tc_fun(_1785890, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785892, _1785890, _1785890, c_Hilbert__Choice_Oinv__into(_1785890, _1785892, c_Orderings_Otop__class_Otop(tc_fun(_1785890, tc_HOL_Obool)), _1785894)), _1785894) = c_Fun_Oid(_1785890))], (15011 ^ _776541) ^ [_1047431, _1047433, _1047435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047431), _1047433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047431), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047433), _1047435))))], (42167 ^ _776541) ^ [_1612164, _1612166, _1612168] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612164)), _1612166), c_Wellfounded_Oacc(tc_List_Olist(_1612164), c_List_Olistrel1(_1612164, _1612168)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612164)), _1612166), c_List_Olists(_1612164, c_Wellfounded_Oacc(_1612164, _1612168)))))], (7174 ^ _776541) ^ [_893410, _893412, _893414] : [hBOOL(hAPP(hAPP(c_member(_893410), _893412), _893414)), -(hAPP(hAPP(c_Set_Oinsert(_893410), _893412), _893414) = _893414)], (18786 ^ _776541) ^ [_1114937, _1114939, _1114941, _1114943] : [class_Groups_Ocomm__monoid__add(_1114937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114939), _1114941)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114937), _1114943), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1114939, _1114941)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114937), hAPP(_1114943, _1114939)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114937), _1114943), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1114939), _1114941))))], (48692 ^ _776541) ^ [_1758018, _1758020, _1758022] : [c_List_Oreplicate(_1758018, _1758020, _1758022) = c_List_Olist_ONil(_1758018), -(_1758020 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26625 ^ _776541) ^ [_1257080, _1257082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257080), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1257080), _1257082)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1257080))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1257082))))], (41198 ^ _776541) ^ [_1584825, _1584827, _1584829] : [c_Relation_Orefl__on(_1584825, _1584827, _1584829), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584825, _1584825), tc_HOL_Obool)), _1584829), hAPP(hAPP(c_Relation_Orel__comp(_1584825, _1584825, _1584825), hAPP(c_Relation_Oconverse(_1584825, _1584825), _1584829)), _1584829))))], (28325 ^ _776541) ^ [_1284992, _1284994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1284992)), c_Int_OBit1(_1284994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284992), _1284994)))], (21285 ^ _776541) ^ [_1161747, _1161749, _1161751] : [class_Int_Onumber__ring(_1161747), -(hAPP(c_Int_Onumber__class_Onumber__of(_1161747), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1161749), _1161751)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161747), hAPP(c_Int_Onumber__class_Onumber__of(_1161747), _1161749)), hAPP(c_Int_Onumber__class_Onumber__of(_1161747), _1161751)))], (50291 ^ _776541) ^ [_1793196, _1793198, _1793200, _1793202, _1793204, _1793206] : [c_Fun_Obij__betw(_1793196, _1793198, _1793200, _1793202, _1793204), hBOOL(hAPP(hAPP(c_member(_1793196), _1793206), _1793202)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1793198, _1793196, _1793204, c_Hilbert__Choice_Oinv__into(_1793196, _1793198, _1793202, _1793200)), _1793206) = hAPP(_1793200, _1793206))], (25816 ^ _776541) ^ [_1243676, _1243678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243676)), -(c_SMT_Oz3mod(_1243678, _1243676) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243678, _1243676))], (11316 ^ _776541) ^ [_973232, _973234, _973236, _973238] : [hAPP(c_Set_Oimage(_973232, _973234, _973236), c_Orderings_Otop__class_Otop(tc_fun(_973232, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_973234, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973234, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973234, tc_HOL_Obool)), hAPP(c_Set_Oimage(_973232, _973234, _973236), _973238))), hAPP(c_Set_Oimage(_973232, _973234, _973236), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973232, tc_HOL_Obool)), _973238)))))], (50353 ^ _776541) ^ [_1794620, _1794622, _1794624, _1794626, _1794628, _1794630, _1794632, _1794634] : [c_Fun_Obij__betw(_1794620, _1794622, _1794624, _1794626, _1794628), 50356 ^ _776541 : [(50363 ^ _776541) ^ [] : [c_Fun_Obij__betw(_1794620, _1794630, hAPP(c_Fun_Ocomp(_1794622, _1794630, _1794620, _1794632), _1794624), _1794626, _1794634), -(c_Fun_Obij__betw(_1794622, _1794630, _1794632, _1794628, _1794634))], (50357 ^ _776541) ^ [] : [c_Fun_Obij__betw(_1794622, _1794630, _1794632, _1794628, _1794634), -(c_Fun_Obij__betw(_1794620, _1794630, hAPP(c_Fun_Ocomp(_1794622, _1794630, _1794620, _1794632), _1794624), _1794626, _1794634))]]], (32666 ^ _776541) ^ [_1369670, _1369672, _1369674] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369670, tc_HOL_Obool)), _1369672), _1369674) = hAPP(c_Set_OCollect(_1369670), hAPP(hAPP(c_COMBS(_1369670, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369670), c_fconj), hAPP(hAPP(c_COMBC(_1369670, tc_fun(_1369670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1369670)), _1369672))), hAPP(hAPP(c_COMBC(_1369670, tc_fun(_1369670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1369670)), _1369674))))], (33210 ^ _776541) ^ [_1385128, _1385130, _1385132] : [-(hAPP(hAPP(c_Set_Oinsert(_1385128), _1385130), hAPP(c_Set_OCollect(_1385128), _1385132)) = hAPP(c_Set_OCollect(_1385128), hAPP(hAPP(c_COMBS(_1385128, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1385128), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1385128), c_fNot), hAPP(hAPP(c_COMBC(_1385128, _1385128, tc_HOL_Obool), c_fequal), _1385130)))), _1385132)))], (39816 ^ _776541) ^ [_1551008, _1551010, _1551012, _1551014, _1551016, _1551018] : [-(hAPP(c_Set_Ovimage(_1551008, tc_prod(_1551010, _1551012), _1551014), hAPP(hAPP(c_Product__Type_OSigma(_1551010, _1551012), _1551016), hAPP(c_COMBK(tc_fun(_1551012, tc_HOL_Obool), _1551010), _1551018))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551008, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1551008, _1551010, hAPP(c_Fun_Ocomp(tc_prod(_1551010, _1551012), _1551010, _1551008, c_Product__Type_Ofst(_1551010, _1551012)), _1551014)), _1551016)), hAPP(c_Set_Ovimage(_1551008, _1551012, hAPP(c_Fun_Ocomp(tc_prod(_1551010, _1551012), _1551012, _1551008, c_Product__Type_Osnd(_1551010, _1551012)), _1551014)), _1551018)))], (33088 ^ _776541) ^ [_1381386, _1381388] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381386, tc_HOL_Obool)), _1381388)), -(hBOOL(hAPP(hAPP(c_member(_1381386), _1381388), c_Orderings_Obot__class_Obot(tc_fun(_1381386, tc_HOL_Obool)))))], (6790 ^ _776541) ^ [_886302, _886304, _886306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886302, tc_HOL_Obool)), _886304), _886306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_886302, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_886302, _886304)), c_Predicate_OPowp(_886302, _886306))))], (34157 ^ _776541) ^ [_1411164, _1411166] : [class_Rings_Ocomm__semiring__1(_1411164), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411164), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411164), c_Groups_Oone__class_Oone(_1411164)), c_Groups_Oone__class_Oone(_1411164))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411164), c_Nat_Osemiring__1__class_Oof__nat(_1411164)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1411166))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411164), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1411164), _1411166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411164), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1411164), _1411166)), c_Groups_Oone__class_Oone(_1411164))))], (24321 ^ _776541) ^ [_1216412, _1216414, _1216416] : [class_Rings_Oring__1(_1216412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216414), _1216416)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216416), _1216414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216412), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216412), _1216416)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216412), _1216414)))], (50263 ^ _776541) ^ [_1792508, _1792510, _1792512, _1792514] : [c_Fun_Obij__betw(_1792508, _1792510, _1792512, c_Orderings_Otop__class_Otop(tc_fun(_1792508, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792510, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1792508, _1792510, _1792512), hAPP(c_Set_OCollect(_1792508), _1792514)) = hAPP(c_Set_OCollect(_1792510), hAPP(hAPP(c_COMBB(_1792508, tc_HOL_Obool, _1792510), _1792514), c_Hilbert__Choice_Oinv__into(_1792508, _1792510, c_Orderings_Otop__class_Otop(tc_fun(_1792508, tc_HOL_Obool)), _1792512))))], (20513 ^ _776541) ^ [_1146723, _1146725, _1146727, _1146729] : [class_Fields_Olinordered__field(_1146723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146723), _1146725), _1146727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146723), c_Groups_Ozero__class_Ozero(_1146723)), _1146729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146723), c_Groups_Ozero__class_Ozero(_1146723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146723), _1146727), _1146725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146723), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146723), _1146729), _1146727)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146723), _1146729), _1146725))))], (38756 ^ _776541) ^ [_1521402, _1521404, _1521406, _1521408] : [hAPP(c_Set_Oimage(_1521402, _1521404, _1521406), c_Orderings_Otop__class_Otop(tc_fun(_1521402, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1521404, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1521402, _1521404, _1521406), hAPP(c_Set_Ovimage(_1521402, _1521404, _1521406), _1521408)) = _1521408)], (31178 ^ _776541) ^ [_1336082, _1336084] : [class_Orderings_Olinorder(_1336082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336082), _1336084)), -(_1336084 = c_Orderings_Obot__class_Obot(tc_fun(_1336082, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1336082), c_Big__Operators_Olinorder__class_OMax(_1336082, _1336084)), _1336084)))], (43872 ^ _776541) ^ [_1653106, _1653108, _1653110, _1653112, _1653114] : [hAPP(hAPP(c_List_Odrop(_1653106), _1653108), _1653110) = hAPP(hAPP(c_List_Olist_OCons(_1653106), _1653112), _1653114), -(hAPP(hAPP(c_List_Onth(_1653106), _1653110), _1653108) = _1653112)], (43314 ^ _776541) ^ [_1639530, _1639532, _1639534, _1639536, _1639538] : [-(hAPP(hAPP(c_List_Ozip(_1639530, _1639532), _1639534), hAPP(hAPP(c_List_Olist_OCons(_1639532), _1639536), _1639538)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1639530, _1639532)), _1639530, c_List_Olist_ONil(tc_prod(_1639530, _1639532)), hAPP(hAPP(c_COMBC(_1639530, tc_fun(tc_List_Olist(_1639530), tc_List_Olist(tc_prod(_1639530, _1639532))), tc_fun(tc_List_Olist(_1639530), tc_List_Olist(tc_prod(_1639530, _1639532)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1639530, _1639532)), tc_List_Olist(tc_prod(_1639530, _1639532))), tc_fun(tc_fun(tc_List_Olist(_1639530), tc_List_Olist(tc_prod(_1639530, _1639532))), tc_fun(tc_List_Olist(_1639530), tc_List_Olist(tc_prod(_1639530, _1639532)))), _1639530), c_COMBB(tc_List_Olist(tc_prod(_1639530, _1639532)), tc_List_Olist(tc_prod(_1639530, _1639532)), tc_List_Olist(_1639530))), hAPP(hAPP(c_COMBB(tc_prod(_1639530, _1639532), tc_fun(tc_List_Olist(tc_prod(_1639530, _1639532)), tc_List_Olist(tc_prod(_1639530, _1639532))), _1639530), c_List_Olist_OCons(tc_prod(_1639530, _1639532))), hAPP(hAPP(c_COMBC(_1639530, _1639532, tc_prod(_1639530, _1639532)), c_Product__Type_OPair(_1639530, _1639532)), _1639536)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1639530), tc_List_Olist(_1639532), tc_List_Olist(tc_prod(_1639530, _1639532))), c_List_Ozip(_1639530, _1639532)), _1639538))), _1639534))], (52109 ^ _776541) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (48619 ^ _776541) ^ [_1756717, _1756719, _1756721, _1756723] : [48626 ^ _776541 : [(48629 ^ _776541) ^ [] : [_1756719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48627 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1756723, _1756721)))]], 48620 ^ _776541 : [(48621 ^ _776541) ^ [_1756789] : [hBOOL(hAPP(hAPP(c_member(_1756717), _1756789), hAPP(c_List_Oset(_1756717), c_List_Oreplicate(_1756717, _1756719, _1756721)))), hBOOL(hAPP(_1756723, _1756789))]]], (27361 ^ _776541) ^ [_1268793] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1268793), c_Int_OPls) = _1268793)], (7772 ^ _776541) ^ [_907030, _907032, _907034, _907036] : [7773 ^ _776541 : [(7776 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907030), _907032), _907036))], (7774 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907030), _907032), _907034))]], -(hBOOL(hAPP(hAPP(c_member(_907030), _907032), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907030, tc_HOL_Obool)), _907034), _907036))))], (32704 ^ _776541) ^ [_1370682] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1370682)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370682)), 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))))], (8849 ^ _776541) ^ [_928776, _928778, _928780] : [class_Orderings_Olinorder(_928776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928776), _928778), _928780)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928776, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_928776), _928778), c_Orderings_Obot__class_Obot(tc_fun(_928776, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_928776, _928778, _928780)) = c_SetInterval_Oord__class_OatLeastAtMost(_928776, _928778, _928780))], (1744 ^ _776541) ^ [_801205, _801207] : [-(class_Orderings_Opreorder(_801205)), _801207 = _801205, class_Orderings_Opreorder(_801207)], (6490 ^ _776541) ^ [_881426, _881428] : [-(hBOOL(hAPP(_881428, 6491 ^ [_881426, _881428]))), -(c_Orderings_Obot__class_Obot(tc_fun(_881426, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_881426), _881428))], (48288 ^ _776541) ^ [_1749080, _1749082, _1749084, _1749086] : [-(c_List_Olist__all(_1749080, _1749082, hAPP(hAPP(c_List_Olist_OCons(_1749080), _1749084), _1749086))), hBOOL(hAPP(_1749082, _1749084)), c_List_Olist__all(_1749080, _1749082, _1749086)], (16228 ^ _776541) ^ [_1069718, _1069720, _1069722] : [class_Rings_Ono__zero__divisors(_1069718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069718), _1069720), _1069722) = c_Groups_Ozero__class_Ozero(_1069718), -(_1069720 = c_Groups_Ozero__class_Ozero(_1069718)), -(_1069722 = c_Groups_Ozero__class_Ozero(_1069718))], (2892 ^ _776541) ^ [_819434, _819436, _819438, _819440] : [-(c_Nitpick_Oint__lcm(_819440, _819436) = c_Nitpick_Oint__lcm(_819438, _819434)), _819440 = _819438, _819436 = _819434], (34950 ^ _776541) ^ [_1428593, _1428595, _1428597, _1428599, _1428601, _1428603] : [-(hAPP(c_Product__Type_Oapsnd(_1428593, _1428595, _1428597, _1428599), hAPP(hAPP(c_Product__Type_OPair(_1428597, _1428593), _1428601), _1428603)) = hAPP(hAPP(c_Product__Type_OPair(_1428597, _1428595), _1428601), hAPP(_1428599, _1428603)))], (40590 ^ _776541) ^ [_1569146, _1569148] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569146, _1569146)), hAPP(hAPP(c_Product__Type_OPair(_1569146, _1569146), 40591 ^ [_1569146, _1569148]), 40591 ^ [_1569146, _1569148])), c_Transitive__Closure_Otrancl(_1569146, _1569148)))), -(c_Wellfounded_Oacyclic(_1569146, _1569148))], (39822 ^ _776541) ^ [_1551312, _1551314, _1551316, _1551318, _1551320, _1551322, _1551324, _1551326, _1551328, _1551330, _1551332] : [-(hAPP(c_Product__Type_Omap__pair(_1551312, _1551314, _1551316, _1551318, _1551320, _1551322), hAPP(c_Product__Type_Omap__pair(_1551324, _1551312, _1551326, _1551316, _1551328, _1551330), _1551332)) = hAPP(c_Product__Type_Omap__pair(_1551324, _1551314, _1551326, _1551318, hAPP(c_Fun_Ocomp(_1551312, _1551314, _1551324, _1551320), _1551328), hAPP(c_Fun_Ocomp(_1551316, _1551318, _1551326, _1551322), _1551330)), _1551332))], (41626 ^ _776541) ^ [_1595886, _1595888] : [-(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)))), _1595886)) = 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)))), _1595888))), 41628 ^ _776541 : [(41631 ^ _776541) ^ [] : [41632 ^ _776541 : [(41635 ^ _776541) ^ [] : [hBOOL(hAPP(_1595888, 41627 ^ [_1595886, _1595888]))], (41633 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1595886, 41627 ^ [_1595886, _1595888])))]], 41636 ^ _776541 : [(41639 ^ _776541) ^ [] : [hBOOL(hAPP(_1595886, 41627 ^ [_1595886, _1595888]))], (41637 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1595888, 41627 ^ [_1595886, _1595888])))]]], (41629 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41627 ^ [_1595886, _1595888])))]]], (3854 ^ _776541) ^ [_834421, _834423, _834425, _834427, _834429, _834431] : [-(c_List_OtakeWhile(_834431, _834427, _834423) = c_List_OtakeWhile(_834429, _834425, _834421)), _834431 = _834429, _834427 = _834425, _834423 = _834421], (35708 ^ _776541) ^ [_1443213, _1443215] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1443213), _1443215) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1443213, _1443215)))], (27363 ^ _776541) ^ [_1268822] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1268822) = _1268822)], (44222 ^ _776541) ^ [_1660823, _1660825, _1660827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660823)), _1660825)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1660823, _1660827), _1660825) = _1660825)], (15734 ^ _776541) ^ [_1061784, _1061786] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061784), _1061786) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1061784 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1061786 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50279 ^ _776541) ^ [_1792900, _1792902, _1792904] : [c_Fun_Obij__betw(_1792900, _1792902, _1792904, c_Orderings_Otop__class_Otop(tc_fun(_1792900, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792902, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1792902, _1792900, c_Hilbert__Choice_Oinv__into(_1792900, _1792902, c_Orderings_Otop__class_Otop(tc_fun(_1792900, tc_HOL_Obool)), _1792904), c_Orderings_Otop__class_Otop(tc_fun(_1792902, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792900, tc_HOL_Obool))))], (41124 ^ _776541) ^ [_1582970, _1582972] : [c_Wellfounded_Oacyclic(_1582970, _1582972), -(c_Wellfounded_Oacyclic(_1582970, hAPP(c_Relation_Oconverse(_1582970, _1582970), _1582972)))], (27991 ^ _776541) ^ [_1279547, _1279549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279547), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279547)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279549)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279549))], (52353 ^ _776541) ^ [_1829883, _1829885] : [-(class_Nat_Osize(tc_prod(_1829883, _1829885)))], (6971 ^ _776541) ^ [_889735, _889737, _889739] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_889735, tc_HOL_Obool)), _889737), hAPP(c_Set_OPow(_889735), _889739))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889735, tc_HOL_Obool)), _889737), _889739)))], (24012 ^ _776541) ^ [_1211268] : [class_Rings_Osemiring__1(_1211268), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211268), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1211268))], (33186 ^ _776541) ^ [_1384473, _1384475] : [-(hAPP(c_Set_OCollect(_1384473), hAPP(hAPP(c_COMBC(_1384473, tc_fun(_1384473, tc_HOL_Obool), tc_HOL_Obool), c_member(_1384473)), _1384475)) = _1384475)], (52371 ^ _776541) ^ [_1830060] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1830060)))], (40434 ^ _776541) ^ [_1565205, _1565207, _1565209, _1565211] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1565205, tc_HOL_Obool), tc_fun(_1565205, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1565205, tc_HOL_Obool), tc_fun(_1565205, tc_HOL_Obool)), _1565207), _1565209)), c_Wellfounded_Omax__ext(_1565205, _1565211))), 40437 ^ _776541 : [(40440 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565205), _1565209)))], (40442 ^ _776541) ^ [] : [_1565209 = c_Orderings_Obot__class_Obot(tc_fun(_1565205, tc_HOL_Obool))], (40444 ^ _776541) ^ [_1565499] : [hBOOL(hAPP(hAPP(c_member(_1565205), _1565499), _1565207)), 40448 ^ _776541 : [(40451 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565205, _1565205)), hAPP(hAPP(c_Product__Type_OPair(_1565205, _1565205), _1565499), 40447 ^ [_1565205, _1565207, _1565209, _1565211, _1565499])), _1565211)))], (40449 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565205), 40447 ^ [_1565205, _1565207, _1565209, _1565211, _1565499]), _1565209)))]]], (40438 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565205), _1565207)))]]], (33897 ^ _776541) ^ [_1404734, _1404736, _1404738] : [class_Groups_Ocomm__monoid__add(_1404734), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404734), _1404736), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404738))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404734), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404734), _1404736), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1404738))), hAPP(_1404736, hAPP(c_Nat_OSuc, _1404738))))], (39630 ^ _776541) ^ [_1545267, _1545269, _1545271, _1545273] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1545267), _1545269))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545271), hAPP(c_Set_Oimage(_1545267, _1545271, _1545273), _1545269))), 39638 ^ _776541 : [(39641 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1545267), hAPP(c_Set_OCollect(_1545267), hAPP(hAPP(c_COMBS(_1545267, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545267), c_fconj), hAPP(hAPP(c_COMBC(_1545267, tc_fun(_1545267, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545267)), _1545269))), hAPP(hAPP(c_COMBC(_1545267, _1545271, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1545271, tc_fun(_1545271, tc_HOL_Obool), _1545267), c_fequal), _1545273)), hAPP(_1545273, 39637 ^ [_1545267, _1545269, _1545271, _1545273]))))))], (39639 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545267), 39637 ^ [_1545267, _1545269, _1545271, _1545273]), _1545269)))]]], (33497 ^ _776541) ^ [_1392776, _1392778, _1392780, _1392782, _1392784] : [_1392776 = c_Orderings_Obot__class_Obot(tc_fun(_1392778, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1392780), _1392782), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392778, tc_fun(_1392780, tc_HOL_Obool)), _1392776), _1392784)) = hAPP(hAPP(c_Set_Oinsert(_1392780), _1392782), c_Orderings_Obot__class_Obot(tc_fun(_1392780, tc_HOL_Obool))))], (2206 ^ _776541) ^ [_808587, _808589, _808591, _808593, _808595, _808597] : [-(c_Random_Ominus__shift(_808597, _808593, _808589) = c_Random_Ominus__shift(_808595, _808591, _808587)), _808597 = _808595, _808593 = _808591, _808589 = _808587], (8927 ^ _776541) ^ [_930476, _930478, _930480] : [class_Orderings_Olinorder(_930476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930476), _930478), _930480)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_930476, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_930476), _930478)), c_SetInterval_Oord__class_OatLeastAtMost(_930476, _930478, _930480)) = hAPP(c_SetInterval_Oord__class_OatMost(_930476), _930480))], (34135 ^ _776541) ^ [_1410818] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1410818))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1410818)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15262 ^ _776541) ^ [_1051931, _1051933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1051931), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1051933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051933), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1051931))))), -(_1051931 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1051933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051933), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1051931))))], (7762 ^ _776541) ^ [_906876, _906878, _906880, _906882] : [hBOOL(hAPP(hAPP(c_member(_906876), _906878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906876, tc_HOL_Obool)), _906880), _906882))), -(hBOOL(hAPP(hAPP(c_member(_906876), _906878), _906880))), -(hBOOL(hAPP(hAPP(c_member(_906876), _906878), _906882)))], (44599 ^ _776541) ^ [_1668466, _1668468, _1668470] : [-(_1668466 = c_List_Olist_ONil(_1668468)), -(c_List_Olast(_1668468, hAPP(hAPP(c_List_Oappend(_1668468), _1668470), _1668466)) = c_List_Olast(_1668468, _1668466))], (45822 ^ _776541) ^ [_1695842, _1695844] : [c_List_Oremdups(_1695842, _1695844) = c_List_Olist_ONil(_1695842), -(_1695844 = c_List_Olist_ONil(_1695842))], (26268 ^ _776541) ^ [_1250948] : [-(c_Int_Osucc(_1250948) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1250948), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41749 ^ _776541) ^ [_1599495, _1599497, _1599499, _1599501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599495)), _1599497)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599495)), _1599499))), _1599497 = hAPP(hAPP(c_List_Olist_OCons(_1599495), _1599501), _1599499)], (42232 ^ _776541) ^ [_1614019, _1614021, _1614023, _1614025] : [-(hAPP(hAPP(c_List_Onth(_1614019), hAPP(hAPP(c_List_Olist_OCons(_1614019), _1614021), _1614023)), hAPP(c_Nat_OSuc, _1614025)) = hAPP(hAPP(c_List_Onth(_1614019), _1614023), _1614025))], (13576 ^ _776541) ^ [_1018181, _1018183, _1018185, _1018187] : [class_Groups_Ocancel__semigroup__add(_1018181), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018181), _1018183), _1018185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018181), _1018183), _1018187), -(_1018185 = _1018187)], (10086 ^ _776541) ^ [_949123, _949125, _949127] : [class_Orderings_Oorder(_949123), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949123, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_949123), _949125)), c_SetInterval_Oord__class_OatLeastAtMost(_949123, _949125, _949127)) = c_Orderings_Obot__class_Obot(tc_fun(_949123, tc_HOL_Obool)))], (33568 ^ _776541) ^ [_1394391, _1394393, _1394395, _1394397] : [33570 ^ _776541 : [(33573 ^ _776541) ^ [] : [hAPP(_1394397, 33569 ^ [_1394391, _1394393, _1394395, _1394397]) = c_Orderings_Otop__class_Otop(tc_fun(_1394393, tc_HOL_Obool))], (33571 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394391), 33569 ^ [_1394391, _1394393, _1394395, _1394397]), _1394395)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394391, tc_fun(_1394393, tc_HOL_Obool)), _1394395), _1394397) = c_Orderings_Otop__class_Otop(tc_fun(_1394393, tc_HOL_Obool)))], (3706 ^ _776541) ^ [_832119, _832121] : [_832121 = _832119, -(c_List_Oreturn__list(_832121) = c_List_Oreturn__list(_832119))], (39107 ^ _776541) ^ [_1530257, _1530259, _1530261, _1530263, _1530265] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530257, _1530259), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530257, tc_HOL_Obool)), _1530261), _1530263)), hAPP(c_COMBK(tc_fun(_1530259, tc_HOL_Obool), _1530257), _1530265)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530257, _1530259), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530257, _1530259), _1530261), hAPP(c_COMBK(tc_fun(_1530259, tc_HOL_Obool), _1530257), _1530265))), hAPP(hAPP(c_Product__Type_OSigma(_1530257, _1530259), _1530263), hAPP(c_COMBK(tc_fun(_1530259, tc_HOL_Obool), _1530257), _1530265))))], (8285 ^ _776541) ^ [_918291, _918293, _918295, _918297] : [class_Lattices_Osemilattice__sup(_918291), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918291), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918291), _918293), _918295)), _918297) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918291), _918293), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918291), _918295), _918297)))], (34602 ^ _776541) ^ [_1421060, _1421062, _1421064, _1421066] : [-(c_Nat_Onat_Onat__case(_1421060, _1421062, _1421064, hAPP(c_Nat_OSuc, _1421066)) = hAPP(_1421064, _1421066))], (14668 ^ _776541) ^ [_1041074, _1041076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041074), _1041076)), -(_1041074 = _1041076), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041074), _1041076)))], (45146 ^ _776541) ^ [_1680610, _1680612, _1680614, _1680616] : [class_Groups_Ocomm__monoid__add(_1680610), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1680610), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1680610), _1680612), c_List_Oupto(_1680614, _1680616))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1680610), _1680612), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1680614, _1680616))))], (41706 ^ _776541) ^ [_1597797, _1597799, _1597801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597797), c_Nitpick_Oplus__frac(_1597797, _1597799, c_Nitpick_Ouminus__frac(_1597797, _1597801)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1597797, _1597799, _1597801))], (20841 ^ _776541) ^ [_1152827, _1152829, _1152831] : [class_Fields_Olinordered__field(_1152827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152827), _1152829), _1152831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152827), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152827), _1152829), _1152831)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152827), c_Groups_Oone__class_Oone(_1152827)), c_Groups_Oone__class_Oone(_1152827)))), _1152831)))], (33273 ^ _776541) ^ [_1386491, _1386493, _1386495, _1386497] : [33275 ^ _776541 : [(33278 ^ _776541) ^ [] : [hAPP(_1386497, 33274 ^ [_1386491, _1386493, _1386495, _1386497]) = c_Orderings_Obot__class_Obot(tc_fun(_1386493, tc_HOL_Obool))], (33276 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386491), 33274 ^ [_1386491, _1386493, _1386495, _1386497]), _1386495)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386491, tc_fun(_1386493, tc_HOL_Obool)), _1386495), _1386497) = c_Orderings_Obot__class_Obot(tc_fun(_1386493, tc_HOL_Obool)))], (14236 ^ _776541) ^ [_1032633, _1032635, _1032637, _1032639] : [class_Rings_Ocomm__semiring__1(_1032633), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032633), _1032635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032633), _1032637), _1032639)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032633), _1032637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032633), _1032635), _1032639)))], (38523 ^ _776541) ^ [_1515124, _1515126, _1515128, _1515130] : [-(hAPP(c_Relation_ORange(_1515124, _1515126), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1515124, _1515126), tc_HOL_Obool)), _1515128), _1515130)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1515126, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1515124, _1515126), _1515128)), hAPP(c_Relation_ORange(_1515124, _1515126), _1515130)))], (26811 ^ _776541) ^ [_1259906, _1259908] : [c_Nat__Transfer_Ois__nat(_1259906), c_Nat__Transfer_Ois__nat(_1259908), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1259906), _1259908)))], (18123 ^ _776541) ^ [_1102395, _1102397] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1102395), hAPP(c_Nat_OSuc, _1102397)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1102395, _1102397))], (32741 ^ _776541) ^ [_1371394, _1371396, _1371398, _1371400, _1371402] : [class_Complete__Lattice_Ocomplete__lattice(_1371394), class_Orderings_Olinorder(_1371394), 32748 ^ _776541 : [(32758 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371394), _1371396), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1371398, _1371394), _1371400), _1371402)))), 32759 ^ _776541 : [(32760 ^ _776541) ^ [_1371742] : [hBOOL(hAPP(hAPP(c_member(_1371398), _1371742), _1371400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371394), _1371396), hAPP(_1371402, _1371742)))]]], (32749 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371394), _1371396), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1371398, _1371394), _1371400), _1371402))), 32753 ^ _776541 : [(32756 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371394), _1371396), hAPP(_1371402, 32752 ^ [_1371394, _1371396, _1371398, _1371400, _1371402]))))], (32754 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1371398), 32752 ^ [_1371394, _1371396, _1371398, _1371400, _1371402]), _1371400)))]]]]], (43996 ^ _776541) ^ [_1655877, _1655879, _1655881, _1655883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1655877), _1655879)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655881)), _1655883))), -(hAPP(hAPP(c_List_Onth(_1655881), hAPP(hAPP(c_List_Odrop(_1655881), _1655877), _1655883)), _1655879) = hAPP(hAPP(c_List_Onth(_1655881), _1655883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1655877), _1655879)))], (25091 ^ _776541) ^ [_1230752, _1230754, _1230756] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230752), _1230754)), _1230756) = 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), _1230752), _1230756)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230754), _1230756))), 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, _1230752, _1230756)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230754, _1230756))), _1230756)))], (7458 ^ _776541) ^ [_899323, _899325, _899327, _899329] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_899323, tc_HOL_Obool)), _899325), _899327), _899329)), 7461 ^ _776541 : [(7464 ^ _776541) ^ [] : [-(hBOOL(hAPP(_899327, _899329)))], (7462 ^ _776541) ^ [] : [-(hBOOL(hAPP(_899325, _899329)))]]], (11528 ^ _776541) ^ [_978058, _978060] : [class_Finite__Set_Ofinite(_978058), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_978058), _978060)))], (17959 ^ _776541) ^ [_1099564, _1099566] : [17960 ^ _776541 : [(17963 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099566))], (17961 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099564))]], -(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), _1099564), _1099566))))], (35710 ^ _776541) ^ [_1443268, _1443270, _1443272] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1443268, _1443270), _1443272)), 35713 ^ _776541 : [(35722 ^ _776541) ^ [] : [-(_1443270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35725 ^ _776541 : [(35734 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443270))), 35737 ^ _776541 : [(35740 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443272)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35738 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1443270), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443272))))]]], (35726 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443270)), 35729 ^ _776541 : [(35732 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443272)), _1443270)))], (35730 ^ _776541) ^ [] : [-(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), _1443272))))]]]]], (35716 ^ _776541) ^ [] : [_1443270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1443272) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35714 ^ _776541) ^ [] : [-(_1443268 = 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), _1443272)), _1443270)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443272)))]]], (51219 ^ _776541) ^ [_1813682, _1813684, _1813686, _1813688] : [class_Rings_Ocomm__semiring__1(_1813682), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813682), _1813684), _1813686)), _1813688)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813682), _1813684), _1813688)))], (29169 ^ _776541) ^ [_1299369, _1299371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299369), _1299371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299369)), c_Int_OBit0(_1299371))))], (28469 ^ _776541) ^ [_1287489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1287489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287489))))], (24272 ^ _776541) ^ [] : [-(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))], (43310 ^ _776541) ^ [_1639443, _1639445, _1639447, _1639449] : [-(hAPP(c_List_Olist_Olist__case(_1639443, _1639445, _1639447, _1639449), c_List_Olist_ONil(_1639445)) = _1639447)], (41100 ^ _776541) ^ [_1582465, _1582467, _1582469] : [-(hAPP(c_Relation_Oconverse(_1582465, _1582467), hAPP(c_Relation_Oconverse(_1582467, _1582465), _1582469)) = _1582469)], (23179 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (17997 ^ _776541) ^ [_1100172, _1100174] : [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), _1100172), _1100174))), 18000 ^ _776541 : [(18003 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100174)))], (18001 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100172)))]]], (35640 ^ _776541) ^ [_1441858, _1441860, _1441862, _1441864, _1441866] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441858, _1441860, _1441862), _1441864), _1441866) = hAPP(hAPP(_1441864, hAPP(c_Product__Type_Ofst(_1441858, _1441860), _1441866)), hAPP(c_Product__Type_Osnd(_1441858, _1441860), _1441866)))], (9624 ^ _776541) ^ [_941431, _941433, _941435] : [class_Orderings_Oorder(_941431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941431), _941433), _941435)), -(_941433 = _941435), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941431), _941433), _941435)))], (16122 ^ _776541) ^ [_1067990, _1067992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067990), _1067992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067990), hAPP(c_Nat_OSuc, _1067992))))], (46117 ^ _776541) ^ [_1702842, _1702844, _1702846] : [hAPP(c_List_Ofilter(_1702842, _1702844), _1702846) = c_List_Olist_ONil(_1702842), 46120 ^ _776541 : [(46121 ^ _776541) ^ [_1702939] : [hBOOL(hAPP(hAPP(c_member(_1702842), _1702939), hAPP(c_List_Oset(_1702842), _1702846))), hBOOL(hAPP(_1702844, _1702939))]]], (43084 ^ _776541) ^ [_1635028, _1635030] : [-(c_List_Olistrelp(_1635028, _1635030, c_List_Olist_ONil(_1635028), c_List_Olist_ONil(_1635028)))], (16102 ^ _776541) ^ [_1067610, _1067612] : [16103 ^ _776541 : [(16106 ^ _776541) ^ [] : [_1067610 = hAPP(c_Nat_OSuc, _1067612)], (16104 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067610), _1067612))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067610), hAPP(c_Nat_OSuc, _1067612))))], (49422 ^ _776541) ^ [_1775793, _1775795] : [c_Predicate_Otransp(_1775793, _1775795), -(c_Relation_Otrans(_1775793, hAPP(c_Set_OCollect(tc_prod(_1775793, _1775793)), hAPP(c_Product__Type_Oprod_Oprod__case(_1775793, _1775793, tc_HOL_Obool), _1775795))))], (18814 ^ _776541) ^ [_1115484, _1115486, _1115488, _1115490] : [class_Groups_Ocomm__monoid__mult(_1115484), 18817 ^ _776541 : [(18824 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1115486), _1115488))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1115486, _1115484), _1115490), _1115488) = c_Groups_Oone__class_Oone(_1115484))], (18818 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1115486), _1115488)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1115486, _1115484), _1115490), _1115488) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1115484, _1115486, c_Groups_Otimes__class_Otimes(_1115484)), _1115490), c_Groups_Oone__class_Oone(_1115484)), _1115488))]]], (42691 ^ _776541) ^ [_1626495, _1626497, _1626499, _1626501] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626495)), hAPP(hAPP(c_List_Olist__update(_1626495, _1626497), _1626499), _1626501)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626495)), _1626497))], (20571 ^ _776541) ^ [_1147844, _1147846, _1147848, _1147850] : [class_Fields_Olinordered__field(_1147844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147844), c_Groups_Ozero__class_Ozero(_1147844)), _1147846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147844), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147844), _1147848), _1147846)), _1147850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147844), _1147848), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147844), _1147850), _1147846))))], (39123 ^ _776541) ^ [_1530942, _1530944, _1530946, _1530948] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530942), _1530944)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530946), _1530948)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1530942, _1530946)), hAPP(hAPP(c_Product__Type_OSigma(_1530942, _1530946), _1530944), hAPP(c_COMBK(tc_fun(_1530946, tc_HOL_Obool), _1530942), _1530948)))))], (23511 ^ _776541) ^ [_1202675, _1202677, _1202679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202675)), 23517 ^ _776541 : [(23520 ^ _776541) ^ [] : [hBOOL(hAPP(_1202677, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23516 ^ [_1202675, _1202677, _1202679]), _1202675)))], (23518 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1202677, 23516 ^ [_1202675, _1202677, _1202679])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202679)), 23525 ^ _776541 : [(23526 ^ _776541) ^ [_1202964] : [hBOOL(hAPP(_1202677, _1202964)), -(hBOOL(hAPP(_1202677, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202679), _1202675)))))]]], (40377 ^ _776541) ^ [_1563775, _1563777] : [40378 ^ _776541 : [(40379 ^ _776541) ^ [_1563821] : [hBOOL(hAPP(_1563775, _1563821))]], -(hBOOL(hAPP(_1563775, c_Hilbert__Choice_OEps(_1563777, _1563775))))], (2160 ^ _776541) ^ [_807882, _807884] : [_807884 = _807882, -(c_HOL_Oequal__class_Oequal(_807884) = c_HOL_Oequal__class_Oequal(_807882))], (32904 ^ _776541) ^ [_1376355, _1376357, _1376359, _1376361, _1376363] : [class_Complete__Lattice_Ocomplete__lattice(_1376355), hBOOL(hAPP(hAPP(c_member(_1376357), _1376359), _1376361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376355), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376357, _1376355), _1376361), _1376363)), hAPP(_1376363, _1376359))))], (36838 ^ _776541) ^ [_1475582, _1475584, _1475586, _1475588, _1475590] : [c_Equiv__Relations_Oequiv(_1475582, _1475584, _1475586), 36841 ^ _776541 : [(36852 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475582, _1475582)), hAPP(hAPP(c_Product__Type_OPair(_1475582, _1475582), _1475588), _1475590)), _1475586))), hAPP(c_Relation_OImage(_1475582, _1475582, _1475586), hAPP(hAPP(c_Set_Oinsert(_1475582), _1475588), c_Orderings_Obot__class_Obot(tc_fun(_1475582, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1475582, _1475582, _1475586), hAPP(hAPP(c_Set_Oinsert(_1475582), _1475590), c_Orderings_Obot__class_Obot(tc_fun(_1475582, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1475582), _1475588), _1475584)), hBOOL(hAPP(hAPP(c_member(_1475582), _1475590), _1475584))], (36842 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1475582, _1475582)), hAPP(hAPP(c_Product__Type_OPair(_1475582, _1475582), _1475588), _1475590)), _1475586)), 36845 ^ _776541 : [(36850 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475582), _1475590), _1475584)))], (36848 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475582), _1475588), _1475584)))], (36846 ^ _776541) ^ [] : [-(hAPP(c_Relation_OImage(_1475582, _1475582, _1475586), hAPP(hAPP(c_Set_Oinsert(_1475582), _1475588), c_Orderings_Obot__class_Obot(tc_fun(_1475582, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1475582, _1475582, _1475586), hAPP(hAPP(c_Set_Oinsert(_1475582), _1475590), c_Orderings_Obot__class_Obot(tc_fun(_1475582, tc_HOL_Obool)))))]]]]], (23067 ^ _776541) ^ [_1194476, _1194478] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1194476, _1194478))))], (9088 ^ _776541) ^ [_933630, _933632, _933634, _933636] : [class_Orderings_Oorder(_933630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933630), _933632), _933634)), _933632 = _933636, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933630), _933636), _933634)))], (9740 ^ _776541) ^ [_943306, _943308, _943310, _943312] : [class_Lattices_Osemilattice__inf(_943306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943306), _943308), _943310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_943306), _943308), _943312)), _943310)))], (8020 ^ _776541) ^ [_912528, _912530, _912532] : [-(hAPP(hAPP(c_Set_Oinsert(_912528), _912530), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912528, tc_HOL_Obool)), _912532), hAPP(hAPP(c_Set_Oinsert(_912528), _912530), c_Orderings_Obot__class_Obot(tc_fun(_912528, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_912528), _912530), _912532))], (1524 ^ _776541) ^ [_798455, _798457] : [-(class_Groups_Olinordered__ab__semigroup__add(_798455)), _798457 = _798455, class_Groups_Olinordered__ab__semigroup__add(_798457)], (1794 ^ _776541) ^ [_801830, _801832] : [-(class_Rings_Osemiring__0(_801830)), _801832 = _801830, class_Rings_Osemiring__0(_801832)], (23858 ^ _776541) ^ [_1208678, _1208680] : [class_Rings_Olinordered__semidom(_1208678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208678), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208678), _1208680)), c_Groups_Ozero__class_Ozero(_1208678)))], (34231 ^ _776541) ^ [_1413113, _1413115, _1413117] : [class_Int_Onumber__ring(_1413113), 34234 ^ _776541 : [(34241 ^ _776541) ^ [] : [-(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), _1413115)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1413113), _1413117), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1413115))) = c_Groups_Oone__class_Oone(_1413113))], (34235 ^ _776541) ^ [] : [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), _1413115))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1413113), _1413117), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1413115))) = hAPP(hAPP(c_HOL_OLet(_1413113, _1413113), hAPP(hAPP(c_Power_Opower__class_Opower(_1413113), _1413117), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413115))), hAPP(hAPP(c_COMBS(_1413113, _1413113, _1413113), hAPP(hAPP(c_COMBB(_1413113, tc_fun(_1413113, _1413113), _1413113), c_Groups_Otimes__class_Otimes(_1413113)), hAPP(c_Groups_Otimes__class_Otimes(_1413113), _1413117))), c_COMBI(_1413113))))]]], (33058 ^ _776541) ^ [_1380438, _1380440, _1380442, _1380444, _1380446, _1380448] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380438, tc_fun(_1380440, tc_HOL_Obool)), _1380442), hAPP(hAPP(c_COMBB(_1380444, tc_fun(_1380440, tc_HOL_Obool), _1380438), _1380446), _1380448)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380444, tc_fun(_1380440, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380438, _1380444, _1380448), _1380442)), _1380446))], (29011 ^ _776541) ^ [_1296591, _1296593] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1296591)), c_Int_OBit0(_1296593)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1296591), _1296593)))], (36600 ^ _776541) ^ [_1470011, _1470013, _1470015, _1470017] : [-(hAPP(c_Relation_OField(_1470011), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1470011, _1470011)), hAPP(hAPP(c_Product__Type_OPair(_1470011, _1470011), _1470013), _1470015)), _1470017)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470011, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1470011), _1470013), hAPP(hAPP(c_Set_Oinsert(_1470011), _1470015), c_Orderings_Obot__class_Obot(tc_fun(_1470011, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1470011), _1470017)))], (15276 ^ _776541) ^ [_1052227, _1052229, _1052231] : [class_Groups_Ocomm__monoid__mult(_1052227), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052229, _1052227), _1052231), c_Orderings_Obot__class_Obot(tc_fun(_1052229, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1052227))], (15694 ^ _776541) ^ [_1061159] : [_1061159 = hAPP(c_Nat_OSuc, _1061159)], (7579 ^ _776541) ^ [_901869, _901871, _901873, _901875] : [7583 ^ _776541 : [(7586 ^ _776541) ^ [] : [hBOOL(hAPP(_901875, 7582 ^ [_901869, _901871, _901873, _901875]))], (7584 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901869), 7582 ^ [_901869, _901871, _901873, _901875]), _901871)))]], 7588 ^ _776541 : [(7591 ^ _776541) ^ [] : [hBOOL(hAPP(_901875, 7587 ^ [_901869, _901871, _901873, _901875]))], (7589 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901869), 7587 ^ [_901869, _901871, _901873, _901875]), _901873)))]], 7592 ^ _776541 : [(7593 ^ _776541) ^ [_902202] : [hBOOL(hAPP(hAPP(c_member(_901869), _902202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901869, tc_HOL_Obool)), _901871), _901873))), -(hBOOL(hAPP(_901875, _902202)))]]], (42632 ^ _776541) ^ [_1625324] : [c_List_Onat__list(_1625324), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1625324)))], (28885 ^ _776541) ^ [_1294367] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1294367)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1294367)))], (32632 ^ _776541) ^ [_1368546, _1368548, _1368550, _1368552, _1368554] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368546, tc_HOL_Obool)), _1368548), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368550, tc_fun(_1368546, tc_HOL_Obool)), _1368552), _1368554)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368550, tc_fun(_1368546, tc_HOL_Obool)), _1368552), hAPP(hAPP(c_COMBB(tc_fun(_1368546, tc_HOL_Obool), tc_fun(_1368546, tc_HOL_Obool), _1368550), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368546, tc_HOL_Obool)), _1368548)), _1368554)))], (17711 ^ _776541) ^ [_1095395, _1095397] : [class_Groups_Oordered__ab__group__add(_1095395), 17714 ^ _776541 : [(17721 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095395), _1095397), c_Groups_Ozero__class_Ozero(_1095395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095395), c_Groups_Ozero__class_Ozero(_1095395)), hAPP(c_Groups_Ouminus__class_Ouminus(_1095395), _1095397))))], (17715 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095395), c_Groups_Ozero__class_Ozero(_1095395)), hAPP(c_Groups_Ouminus__class_Ouminus(_1095395), _1095397))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095395), _1095397), c_Groups_Ozero__class_Ozero(_1095395))))]]], (12646 ^ _776541) ^ [_999419, _999421, _999423, _999425] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_999419, _999421, _999423), _999425), c_Orderings_Obot__class_Obot(tc_fun(_999419, tc_HOL_Obool))) = _999425)], (26354 ^ _776541) ^ [_1252293, _1252295] : [_1252293 = hAPP(c_Int_Onat, _1252295), 26357 ^ _776541 : [(26364 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252295))), -(_1252293 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26358 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252295)), -(_1252295 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252293))]]], (44896 ^ _776541) ^ [_1675402, _1675404, _1675406, _1675408, _1675410] : [hAPP(hAPP(c_List_Omap(_1675402, _1675404), _1675406), _1675408) = hAPP(hAPP(c_List_Omap(_1675402, _1675404), _1675406), _1675410), c_Fun_Oinj__on(_1675402, _1675404, _1675406, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1675402, tc_HOL_Obool)), hAPP(c_List_Oset(_1675402), _1675408)), hAPP(c_List_Oset(_1675402), _1675410))), -(_1675408 = _1675410)], (46303 ^ _776541) ^ [_1707883, _1707885] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707883), _1707885))), -(c_List_Oupt(_1707883, _1707885) = c_List_Olist_ONil(tc_Nat_Onat))], (43681 ^ _776541) ^ [_1647806, _1647808, _1647810, _1647812, _1647814] : [-(hAPP(hAPP(c_List_Olist__update(_1647806, hAPP(hAPP(c_List_Oappend(_1647806), _1647808), hAPP(hAPP(c_List_Olist_OCons(_1647806), _1647810), _1647812))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647806)), _1647808)), _1647814) = hAPP(hAPP(c_List_Oappend(_1647806), _1647808), hAPP(hAPP(c_List_Olist_OCons(_1647806), _1647814), _1647812)))], (8495 ^ _776541) ^ [_922481, _922483, _922485] : [class_Lattices_Osemilattice__sup(_922481), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922481), _922483), _922485)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922481), _922485), _922483) = _922485)], (41601 ^ _776541) ^ [_1595224, _1595226, _1595228, _1595230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595224, _1595224)), hAPP(hAPP(c_Product__Type_OPair(_1595224, _1595224), _1595226), _1595228)), c_Transitive__Closure_Otrancl(_1595224, _1595230))), 41605 ^ _776541 : [(41608 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595224, _1595224)), hAPP(hAPP(c_Product__Type_OPair(_1595224, _1595224), 41604 ^ [_1595224, _1595226, _1595228, _1595230]), _1595228)), c_Transitive__Closure_Ortrancl(_1595224, _1595230))))], (41606 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595224, _1595224)), hAPP(hAPP(c_Product__Type_OPair(_1595224, _1595224), _1595226), 41604 ^ [_1595224, _1595226, _1595228, _1595230])), _1595230)))]]], (22419 ^ _776541) ^ [_1182949, _1182951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182949), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1182951), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182949), _1182951)))], (51169 ^ _776541) ^ [_1812723, _1812725, _1812727, _1812729] : [class_Divides_Osemiring__div(_1812723), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812723), _1812725), _1812727)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812723), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812723), _1812727), _1812725)), _1812729) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812723), _1812727), _1812729)), _1812725))], (41670 ^ _776541) ^ [_1597004, _1597006, _1597008, _1597010, _1597012, _1597014] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1597004, _1597006, _1597008), _1597010), hAPP(hAPP(c_Product__Type_OPair(_1597004, _1597006), _1597012), _1597014)) = hAPP(hAPP(_1597010, _1597012), _1597014))], (11489 ^ _776541) ^ [_977258, _977260, _977262] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977258), _977260)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977258), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977258, tc_HOL_Obool)), _977260), _977262))))], (43884 ^ _776541) ^ [_1653363, _1653365] : [hBOOL(hAPP(c_List_Odistinct(_1653363), hAPP(c_List_Orotate1(_1653363), _1653365))), -(hBOOL(hAPP(c_List_Odistinct(_1653363), _1653365)))], (30008 ^ _776541) ^ [_1314732, _1314734] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1314732), _1314734) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1314732), _1314734))], (40478 ^ _776541) ^ [_1566344, _1566346, _1566348] : [c_Wellfounded_Owf(_1566344, _1566346), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566344, _1566344)), hAPP(hAPP(c_Product__Type_OPair(_1566344, _1566344), hAPP(_1566348, hAPP(c_Nat_OSuc, 40481 ^ [_1566344, _1566346, _1566348]))), hAPP(_1566348, 40481 ^ [_1566344, _1566346, _1566348]))), _1566346))], (43186 ^ _776541) ^ [_1636815, _1636817, _1636819] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636815, tc_HOL_Obool)), hAPP(c_List_Oset(_1636815), c_List_Oremove1(_1636815, _1636817, _1636819))), hAPP(c_List_Oset(_1636815), _1636819))))], (32630 ^ _776541) ^ [_1368456, _1368458, _1368460, _1368462, _1368464] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368456, tc_HOL_Obool)), _1368458), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368460, tc_fun(_1368456, tc_HOL_Obool)), _1368462), _1368464)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368460, tc_fun(_1368456, tc_HOL_Obool)), _1368462), hAPP(hAPP(c_COMBB(tc_fun(_1368456, tc_HOL_Obool), tc_fun(_1368456, tc_HOL_Obool), _1368460), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368456, tc_HOL_Obool)), _1368458)), _1368464)))], (43603 ^ _776541) ^ [_1646304, _1646306, _1646308] : [_1646308 = c_List_Olist_ONil(_1646306), -(_1646304 = hAPP(hAPP(c_List_Oappend(_1646306), _1646308), _1646304))], (24287 ^ _776541) ^ [_1215807, _1215809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215807)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215809)))), 24290 ^ _776541 : [(24293 ^ _776541) ^ [] : [-(_1215809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24291 ^ _776541) ^ [] : [-(_1215807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (33931 ^ _776541) ^ [_1405526, _1405528, _1405530] : [hBOOL(hAPP(c_Predicate_OPowp(_1405526, hAPP(hAPP(c_COMBC(_1405526, tc_fun(_1405526, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405526)), _1405528)), _1405530)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1405526, tc_HOL_Obool)), _1405530), hAPP(c_Set_OPow(_1405526), _1405528))))], (49942 ^ _776541) ^ [_1785122, _1785124, _1785126, _1785128, _1785130] : [c_Equiv__Relations_Opart__equivp(_1785122, _1785124), hBOOL(hAPP(hAPP(_1785124, _1785126), _1785128)), hBOOL(hAPP(hAPP(_1785124, _1785128), _1785130)), -(hBOOL(hAPP(hAPP(_1785124, _1785126), _1785130)))], (16520 ^ _776541) ^ [_1073967, _1073969, _1073971] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073967), _1073969) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073971), _1073969), -(_1073967 = _1073971), -(_1073969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51081 ^ _776541) ^ [_1811098, _1811100, _1811102, _1811104] : [class_Divides_Osemiring__div(_1811098), -(_1811100 = c_Groups_Ozero__class_Ozero(_1811098)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811098), _1811100), _1811102)), 51092 ^ _776541 : [(51099 ^ _776541) ^ [] : [_1811102 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811098), _1811104), _1811100), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811098), _1811102), _1811100) = _1811104)], (51093 ^ _776541) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811098), _1811102), _1811100) = _1811104, -(_1811102 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811098), _1811104), _1811100))]]], (36090 ^ _776541) ^ [_1456224] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1456224) = _1456224)], (34809 ^ _776541) ^ [_1426028, _1426030, _1426032] : [hBOOL(hAPP(_1426028, 34810 ^ [_1426028, _1426030, _1426032])), 34813 ^ _776541 : [(34814 ^ _776541) ^ [_1426139, _1426141] : [-(hBOOL(hAPP(_1426028, hAPP(hAPP(c_Product__Type_OPair(_1426030, _1426032), _1426141), _1426139))))]]], (52265 ^ _776541) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (17803 ^ _776541) ^ [_1096945, _1096947] : [class_Groups_Oab__group__add(_1096945), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096945), hAPP(c_Groups_Ouminus__class_Ouminus(_1096945), _1096947)), _1096947) = c_Groups_Ozero__class_Ozero(_1096945))], (8203 ^ _776541) ^ [_916770, _916772, _916774, _916776, _916778] : [class_Groups_Ominus(_916770), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916772, _916770)), _916774), _916776), _916778) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_916770), hAPP(_916774, _916778)), hAPP(_916776, _916778)))], (21243 ^ _776541) ^ [_1160728, _1160730, _1160732] : [class_Int_Onumber__ring(_1160728), -(hAPP(c_Int_Onumber__class_Onumber__of(_1160728), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1160730), _1160732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160728), hAPP(c_Int_Onumber__class_Onumber__of(_1160728), _1160730)), hAPP(c_Int_Onumber__class_Onumber__of(_1160728), _1160732)))], (23255 ^ _776541) ^ [_1197896, _1197898, _1197900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197896)), 23258 ^ _776541 : [(23259 ^ _776541) ^ [_1198030] : [23261 ^ _776541 : [(23267 ^ _776541) ^ [] : [-(_1198030 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23263 ^ [_1197896, _1197898, _1197900, _1198030]), 23260 ^ [_1197896, _1197898, _1197900, _1198030]))], (23265 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23263 ^ [_1197896, _1197898, _1197900, _1198030]), _1197898)))], (23262 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23260 ^ [_1197896, _1197898, _1197900, _1198030]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1197896))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197900), _1198030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198030), _1197896))))]]], (16092 ^ _776541) ^ [_1067492, _1067494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067492), hAPP(c_Nat_OSuc, _1067494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067492), _1067494))), -(_1067492 = hAPP(c_Nat_OSuc, _1067494))], (16677 ^ _776541) ^ [_1076536, _1076538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076536), _1076538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1076536)), _1076538)))], (16815 ^ _776541) ^ [_1079173, _1079175] : [class_Groups_Olinordered__ab__group__add(_1079173), 16818 ^ _776541 : [(16825 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079173), _1079175), c_Groups_Ozero__class_Ozero(_1079173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079173), _1079175), _1079175)), c_Groups_Ozero__class_Ozero(_1079173))))], (16819 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079173), _1079175), _1079175)), c_Groups_Ozero__class_Ozero(_1079173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079173), _1079175), c_Groups_Ozero__class_Ozero(_1079173))))]]], (5234 ^ _776541) ^ [_856405, _856407, _856409, _856411, _856413, _856415] : [-(c_Lazy__Sequence_Oappend(_856415, _856411, _856407) = c_Lazy__Sequence_Oappend(_856413, _856409, _856405)), _856415 = _856413, _856411 = _856409, _856407 = _856405], (5848 ^ _776541) ^ [_869421, _869423] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869421, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869421)), tc_HOL_Obool)), _869423), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869421, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869421)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_869421)))), -(_869423 = hAPP(c_Hoare__Mirabelle_ORep__triple(_869421), 5851 ^ [_869421, _869423]))], (35461 ^ _776541) ^ [_1437945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1437945)), 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), _1437945)) = 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), _1437945))))))], (47491 ^ _776541) ^ [_1731660, _1731662, _1731664] : [47493 ^ _776541 : [(47496 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1731662, 47492 ^ [_1731660, _1731662, _1731664])))], (47494 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1731660), 47492 ^ [_1731660, _1731662, _1731664]), hAPP(c_List_Oset(_1731660), c_List_OdropWhile(_1731660, _1731662, _1731664)))))]], -(c_List_OtakeWhile(_1731660, _1731662, _1731664) = hAPP(c_List_Ofilter(_1731660, _1731662), _1731664))], (49008 ^ _776541) ^ [_1764977, _1764979, _1764981] : [-(c_FunDef_OTHE__default(_1764979, _1764981, _1764977) = _1764981), 49010 ^ _776541 : [(49013 ^ _776541) ^ [_1765099] : [hBOOL(hAPP(_1764977, _1765099)), -(_1765099 = 49009 ^ [_1764977, _1764979, _1764981])], (49011 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1764977, 49009 ^ [_1764977, _1764979, _1764981])))]]], (26050 ^ _776541) ^ [_1247430] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247430) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247430)))], (39011 ^ _776541) ^ [_1527666, _1527668, _1527670, _1527672] : [39012 ^ _776541 : [(39013 ^ _776541) ^ [_1527720] : [hBOOL(hAPP(hAPP(_1527670, _1527672), _1527720))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1527666, _1527668, _1527670), _1527672)))], (45253 ^ _776541) ^ [_1682831] : [-(c_Code__Numeral_OSuc__code__numeral(_1682831) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1682831))))], (38155 ^ _776541) ^ [_1507258, _1507260, _1507262, _1507264, _1507266, _1507268, _1507270] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1507258, _1507260, _1507262, _1507264, _1507266), _1507268), _1507270))), 38156 ^ _776541 : [(38157 ^ _776541) ^ [_1507329] : [hBOOL(hAPP(hAPP(_1507264, _1507268), _1507329)), hBOOL(hAPP(hAPP(_1507266, _1507329), _1507270))]]], (38203 ^ _776541) ^ [_1508063, _1508065, _1508067] : [c_Wellfounded_Owf(_1508063, _1508065), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508063, _1508063)), hAPP(hAPP(c_Product__Type_OPair(_1508063, _1508063), _1508067), _1508067)), _1508065))], (26841 ^ _776541) ^ [_1260307, _1260309] : [c_Nat__Transfer_Ois__nat(_1260307), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1260307), _1260309)))], (26106 ^ _776541) ^ [_1248337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248337), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1248337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11952 ^ _776541) ^ [_986373, _986375, _986377, _986379, _986381] : [c_Fun_Ofun__upd(_986373, _986375, _986377, _986379, _986381) = _986377, -(hAPP(_986377, _986379) = _986381)], (16600 ^ _776541) ^ [_1075145] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075145), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28143 ^ _776541) ^ [_1281916] : [class_Int_Onumber__ring(_1281916), -(c_Int_Oiszero(_1281916, hAPP(c_Int_Onumber__class_Onumber__of(_1281916), c_Int_OPls)))], (27605 ^ _776541) ^ [_1273077, _1273079] : [class_Rings_Olinordered__idom(_1273077), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273077), c_Groups_Osgn__class_Osgn(_1273077, _1273079)), hAPP(c_Groups_Oabs__class_Oabs(_1273077), _1273079)) = _1273079)], (32542 ^ _776541) ^ [_1364919, _1364921, _1364923, _1364925, _1364927] : [_1364919 = c_Orderings_Obot__class_Obot(tc_fun(_1364921, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364921, tc_fun(_1364923, tc_HOL_Obool)), _1364919), hAPP(hAPP(c_COMBC(_1364921, tc_fun(_1364923, tc_HOL_Obool), tc_fun(_1364923, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1364923, tc_HOL_Obool), tc_fun(tc_fun(_1364923, tc_HOL_Obool), tc_fun(_1364923, tc_HOL_Obool)), _1364921), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364923, tc_HOL_Obool))), _1364925)), _1364927)) = c_Orderings_Otop__class_Otop(tc_fun(_1364923, tc_HOL_Obool)))], (35150 ^ _776541) ^ [_1432606, _1432608] : [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), _1432606), _1432608))), 35153 ^ _776541 : [(35162 ^ _776541) ^ [] : [-(c_Divides_OposDivAlg(_1432606, _1432608) = hAPP(c_Divides_Oadjust(_1432608), c_Divides_OposDivAlg(_1432606, 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)))), _1432608)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432606), _1432608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1432608), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35154 ^ _776541) ^ [] : [35155 ^ _776541 : [(35158 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1432608), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35156 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432606), _1432608))]], -(c_Divides_OposDivAlg(_1432606, _1432608) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1432606))]]], (36003 ^ _776541) ^ [_1452696, _1452698, _1452700] : [class_Lattices_Odistrib__lattice(_1452696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452696), _1452698)), -(_1452698 = c_Orderings_Obot__class_Obot(tc_fun(_1452696, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452696), _1452700)), -(_1452700 = c_Orderings_Obot__class_Obot(tc_fun(_1452696, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452696), c_Big__Operators_Olattice__class_OSup__fin(_1452696, _1452698)), c_Big__Operators_Olattice__class_OSup__fin(_1452696, _1452700)) = c_Big__Operators_Olattice__class_OSup__fin(_1452696, hAPP(c_Set_OCollect(_1452696), hAPP(hAPP(c_COMBB(tc_fun(_1452696, tc_HOL_Obool), tc_HOL_Obool, _1452696), c_HOL_OEx(_1452696)), hAPP(hAPP(c_COMBB(tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool)), tc_fun(_1452696, tc_HOL_Obool), _1452696), hAPP(c_COMBB(tc_fun(_1452696, tc_HOL_Obool), tc_HOL_Obool, _1452696), c_HOL_OEx(_1452696))), hAPP(hAPP(c_COMBC(_1452696, tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool)), tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1452696, tc_fun(tc_fun(_1452696, tc_HOL_Obool), tc_fun(_1452696, tc_HOL_Obool))), tc_fun(tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool)), tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool))), _1452696), c_COMBS(_1452696, tc_fun(_1452696, tc_HOL_Obool), tc_fun(_1452696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1452696, tc_fun(_1452696, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1452696, tc_fun(tc_fun(_1452696, tc_HOL_Obool), tc_fun(_1452696, tc_HOL_Obool))), _1452696), hAPP(c_COMBB(tc_fun(_1452696, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1452696, tc_HOL_Obool), tc_fun(_1452696, tc_HOL_Obool)), _1452696), c_COMBS(_1452696, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool)), tc_fun(_1452696, tc_fun(_1452696, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1452696), hAPP(c_COMBB(tc_fun(_1452696, tc_HOL_Obool), tc_fun(_1452696, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1452696), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452696), c_fconj))), hAPP(hAPP(c_COMBC(_1452696, tc_fun(_1452696, tc_fun(_1452696, _1452696)), tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1452696, _1452696), tc_fun(_1452696, tc_HOL_Obool)), tc_fun(tc_fun(_1452696, tc_fun(_1452696, _1452696)), tc_fun(_1452696, tc_fun(_1452696, tc_HOL_Obool))), _1452696), c_COMBB(tc_fun(_1452696, _1452696), tc_fun(_1452696, tc_HOL_Obool), _1452696)), hAPP(hAPP(c_COMBB(tc_fun(_1452696, tc_HOL_Obool), tc_fun(tc_fun(_1452696, _1452696), tc_fun(_1452696, tc_HOL_Obool)), _1452696), c_COMBB(_1452696, tc_HOL_Obool, _1452696)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1452696)))))), hAPP(hAPP(c_COMBC(_1452696, tc_fun(_1452696, tc_HOL_Obool), tc_fun(_1452696, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1452696, tc_HOL_Obool), tc_fun(_1452696, tc_HOL_Obool)), _1452696), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1452696)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452696), c_fconj), hAPP(hAPP(c_COMBC(_1452696, tc_fun(_1452696, tc_HOL_Obool), tc_HOL_Obool), c_member(_1452696)), _1452698)))), hAPP(hAPP(c_COMBC(_1452696, tc_fun(_1452696, tc_HOL_Obool), tc_HOL_Obool), c_member(_1452696)), _1452700))))))))], (13114 ^ _776541) ^ [_1008236, _1008238, _1008240, _1008242, _1008244, _1008246] : [c_Finite__Set_Ofun__left__comm__idem(_1008236, _1008238, _1008240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008236), _1008242)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1008236, _1008238, _1008240), _1008244), hAPP(hAPP(c_Set_Oinsert(_1008236), _1008246), _1008242)) = hAPP(hAPP(_1008240, _1008246), hAPP(hAPP(c_Finite__Set_Ofold(_1008236, _1008238, _1008240), _1008244), _1008242)))], (33633 ^ _776541) ^ [_1397461, _1397463, _1397465, _1397467, _1397469] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1397461), hAPP(c_Set_Oimage(_1397463, _1397461, _1397465), c_Orderings_Otop__class_Otop(tc_fun(_1397463, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1397467), hAPP(c_Set_Oimage(_1397463, _1397467, hAPP(hAPP(c_COMBB(_1397461, _1397467, _1397463), _1397469), _1397465)), c_Orderings_Otop__class_Otop(tc_fun(_1397463, tc_HOL_Obool))))))], (4228 ^ _776541) ^ [_840620, _840622] : [_840622 = _840620, -(c_List_Orev(_840622) = c_List_Orev(_840620))], (49646 ^ _776541) ^ [_1779797, _1779799, _1779801, _1779803, _1779805, _1779807] : [-(c_Partial__Function_Ofun__lub(_1779797, _1779799, _1779801, _1779803, _1779805, _1779807) = hAPP(_1779803, hAPP(c_Set_OCollect(_1779797), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779801, _1779797), tc_HOL_Obool), tc_HOL_Obool, _1779797), c_HOL_OEx(tc_fun(_1779801, _1779797))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779801, _1779797), tc_HOL_Obool), tc_fun(tc_fun(_1779801, _1779797), tc_HOL_Obool), _1779797), hAPP(c_COMBS(tc_fun(_1779801, _1779797), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1779801, _1779797)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1779801, _1779797), tc_fun(tc_fun(_1779801, _1779797), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1779801, _1779797))), _1779805)))), hAPP(hAPP(c_COMBC(_1779797, tc_fun(tc_fun(_1779801, _1779797), _1779797), tc_fun(tc_fun(_1779801, _1779797), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779797, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1779801, _1779797), _1779797), tc_fun(tc_fun(_1779801, _1779797), tc_HOL_Obool)), _1779797), c_COMBB(_1779797, tc_HOL_Obool, tc_fun(_1779801, _1779797))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1779801, _1779797), _1779801, _1779797), c_COMBI(tc_fun(_1779801, _1779797))), _1779807)))))))], (43543 ^ _776541) ^ [_1645026, _1645028, _1645030] : [class_Groups_Omonoid__add(_1645026), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645026), hAPP(hAPP(c_List_Oappend(_1645026), _1645028), _1645030)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645026), hAPP(c_List_Omonoid__add__class_Olistsum(_1645026), _1645028)), hAPP(c_List_Omonoid__add__class_Olistsum(_1645026), _1645030)))], (43216 ^ _776541) ^ [_1637604, _1637606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1637604), _1637606)), -(c_List_Oupto(_1637604, _1637606) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1637604), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1637604), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1637606)))], (24341 ^ _776541) ^ [_1216789, _1216791, _1216793, _1216795] : [class_Divides_Osemiring__div(_1216789), -(_1216791 = c_Groups_Ozero__class_Ozero(_1216789)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216789), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216789), _1216793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216789), _1216795), _1216791))), _1216791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216789), _1216795), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216789), _1216793), _1216791)))], (5248 ^ _776541) ^ [_856626, _856628, _856630, _856632] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_856632, _856628) = c_SetInterval_Oord__class_OatLeastLessThan(_856630, _856626)), _856632 = _856630, _856628 = _856626], (15696 ^ _776541) ^ [_1061194] : [hAPP(c_Nat_OSuc, _1061194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20193 ^ _776541) ^ [_1141134, _1141136, _1141138] : [class_Fields_Olinordered__field__inverse__zero(_1141134), 20196 ^ _776541 : [(20211 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141134), _1141136), _1141138)), c_Groups_Ozero__class_Ozero(_1141134)))), 20212 ^ _776541 : [(20219 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), _1141136), c_Groups_Ozero__class_Ozero(_1141134))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), c_Groups_Ozero__class_Ozero(_1141134)), _1141138))], (20213 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), c_Groups_Ozero__class_Ozero(_1141134)), _1141136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), _1141138), c_Groups_Ozero__class_Ozero(_1141134)))]]], (20197 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141134), _1141136), _1141138)), c_Groups_Ozero__class_Ozero(_1141134))), 20202 ^ _776541 : [(20205 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), _1141138), c_Groups_Ozero__class_Ozero(_1141134))))], (20203 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), c_Groups_Ozero__class_Ozero(_1141134)), _1141136)))]], 20206 ^ _776541 : [(20209 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), c_Groups_Ozero__class_Ozero(_1141134)), _1141138)))], (20207 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141134), _1141136), c_Groups_Ozero__class_Ozero(_1141134))))]]]]], (42303 ^ _776541) ^ [_1615982, _1615984, _1615986] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1615982, tc_HOL_Obool)), hAPP(c_List_Oset(_1615982), _1615984)), hAPP(c_List_Oset(_1615982), hAPP(hAPP(c_List_Olist_OCons(_1615982), _1615986), _1615984)))))], (22715 ^ _776541) ^ [_1188026, _1188028] : [22716 ^ _776541 : [(22719 ^ _776541) ^ [] : [_1188028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22717 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188026))]], -(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), _1188026), _1188028))))], (37050 ^ _776541) ^ [_1480585, _1480587, _1480589, _1480591, _1480593, _1480595, _1480597, _1480599] : [c_Equiv__Relations_Oequiv(_1480585, _1480587, _1480589), c_Equiv__Relations_Ocongruent2(_1480585, _1480591, _1480593, _1480589, _1480595, _1480597), hBOOL(hAPP(hAPP(c_member(_1480585), _1480599), _1480587)), -(c_Equiv__Relations_Ocongruent(_1480591, _1480593, _1480595, hAPP(_1480597, _1480599)))], (40542 ^ _776541) ^ [_1567907, _1567909] : [c_Wellfounded_Owf(_1567907, _1567909), 40545 ^ _776541 : [(40546 ^ _776541) ^ [_1568039] : [40547 ^ _776541 : [(40548 ^ _776541) ^ [_1568144] : [hBOOL(hAPP(hAPP(c_member(_1567907), _1568144), _1568039))]], 40550 ^ _776541 : [(40553 ^ _776541) ^ [_1568266] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567907, _1567907)), hAPP(hAPP(c_Product__Type_OPair(_1567907, _1567907), _1568266), 40549 ^ [_1567907, _1567909, _1568039])), _1567909)), hBOOL(hAPP(hAPP(c_member(_1567907), _1568266), _1568039))], (40551 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567907), 40549 ^ [_1567907, _1567909, _1568039]), _1568039)))]]]]], (8273 ^ _776541) ^ [_918005, _918007, _918009, _918011] : [class_Lattices_Osemilattice__sup(_918005), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918005), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918005), _918007), _918009)), _918011) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918005), _918007), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918005), _918009), _918011)))], (34331 ^ _776541) ^ [_1415500, _1415502, _1415504] : [class_Int_Onumber__ring(_1415500), 34334 ^ _776541 : [(34341 ^ _776541) ^ [] : [-(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), _1415502)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1415500), hAPP(c_Int_Onumber__class_Onumber__of(_1415500), _1415504)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1415502))) = c_Groups_Oone__class_Oone(_1415500))], (34335 ^ _776541) ^ [] : [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), _1415502))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1415500), hAPP(c_Int_Onumber__class_Onumber__of(_1415500), _1415504)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1415502))) = hAPP(hAPP(c_HOL_OLet(_1415500, _1415500), hAPP(hAPP(c_Power_Opower__class_Opower(_1415500), hAPP(c_Int_Onumber__class_Onumber__of(_1415500), _1415504)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415502))), hAPP(hAPP(c_COMBS(_1415500, _1415500, _1415500), hAPP(hAPP(c_COMBB(_1415500, tc_fun(_1415500, _1415500), _1415500), c_Groups_Otimes__class_Otimes(_1415500)), hAPP(c_Groups_Otimes__class_Otimes(_1415500), hAPP(c_Int_Onumber__class_Onumber__of(_1415500), _1415504)))), c_COMBI(_1415500))))]]], (45874 ^ _776541) ^ [_1696771, _1696773, _1696775] : [-(hAPP(c_List_Oset(_1696771), hAPP(c_List_OremoveAll(_1696771, _1696773), _1696775)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1696771, tc_HOL_Obool)), hAPP(c_List_Oset(_1696771), _1696775)), hAPP(hAPP(c_Set_Oinsert(_1696771), _1696773), c_Orderings_Obot__class_Obot(tc_fun(_1696771, tc_HOL_Obool)))))], (50129 ^ _776541) ^ [_1789423, _1789425, _1789427, _1789429, _1789431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789423, tc_HOL_Obool)), _1789425), hAPP(c_Set_Oimage(_1789427, _1789423, _1789429), _1789431))), -(c_Fun_Oinj__on(_1789423, _1789427, c_Hilbert__Choice_Oinv__into(_1789427, _1789423, _1789431, _1789429), _1789425))], (46781 ^ _776541) ^ [_1716602, _1716604, _1716606, _1716608, _1716610, _1716612] : [class_Orderings_Olinorder(_1716602), c_List_Olinorder__class_Osorted(_1716602, hAPP(hAPP(c_List_Omap(_1716604, _1716602), _1716606), _1716608)), hBOOL(hAPP(_1716610, _1716612)), -(hAPP(c_List_Ofilter(_1716604, _1716610), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716604, _1716602, _1716606), _1716612), _1716608)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716604, _1716602, _1716606), _1716612), hAPP(c_List_Ofilter(_1716604, _1716610), _1716608)))], (26755 ^ _776541) ^ [_1259146, _1259148] : [c_Nat__Transfer_Onat__set(_1259146), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1259148), _1259146)), -(c_Nat__Transfer_Ois__nat(_1259148))], (8793 ^ _776541) ^ [_927577, _927579] : [class_Lattices_Obounded__lattice__bot(_927577), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927577), c_Orderings_Obot__class_Obot(_927577)), _927579) = c_Orderings_Obot__class_Obot(_927577))], (7021 ^ _776541) ^ [_890672, _890674] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_890672, tc_HOL_Obool), tc_HOL_Obool)), _890674), hAPP(c_Set_OPow(_890672), c_Complete__Lattice_OSup__class_OSup(tc_fun(_890672, tc_HOL_Obool), _890674)))))], (15824 ^ _776541) ^ [_1063167, _1063169] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063167), _1063169) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15829 ^ _776541 : [(15832 ^ _776541) ^ [] : [-(_1063169 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15830 ^ _776541) ^ [] : [-(_1063167 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 15833 ^ _776541 : [(15836 ^ _776541) ^ [] : [-(_1063169 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15834 ^ _776541) ^ [] : [-(_1063167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (45876 ^ _776541) ^ [_1696838, _1696840] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696838)), c_List_Oremdups(_1696838, c_List_Oconcat(_1696838, _1696840))) = hAPP(c_Finite__Set_Ocard(_1696838), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1696838), tc_fun(_1696838, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1696838)), _1696840)), c_List_Oset(_1696838))))], (17345 ^ _776541) ^ [_1088855, _1088857, _1088859, _1088861] : [class_Rings_Olinordered__semiring__strict(_1088855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088855), _1088857), _1088859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088855), c_Groups_Ozero__class_Ozero(_1088855)), _1088861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088855), _1088857), _1088861)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088855), _1088859), _1088861))))], (2886 ^ _776541) ^ [_819349, _819351] : [_819351 = _819349, -(c_Nat_Ofunpow(_819351) = c_Nat_Ofunpow(_819349))], (23739 ^ _776541) ^ [_1206479] : [23741 ^ _776541 : [(23744 ^ _776541) ^ [] : [hBOOL(hAPP(_1206479, 23740 ^ [_1206479]))], (23742 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23740 ^ [_1206479])))]], 23745 ^ _776541 : [(23746 ^ _776541) ^ [_1206606] : [-(hBOOL(hAPP(_1206479, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206606))))]]], (29269 ^ _776541) ^ [] : [-(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))))], (6262 ^ _776541) ^ [_877196] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_877196, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_877196, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_877196, tc_HOL_Obool)))], (41506 ^ _776541) ^ [_1592290, _1592292, _1592294, _1592296, _1592298] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592290, _1592290)), hAPP(hAPP(c_Product__Type_OPair(_1592290, _1592290), _1592292), _1592294)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592290, _1592290), tc_HOL_Obool), _1592296), _1592298))), 41511 ^ _776541 : [(41514 ^ _776541) ^ [] : [-(_1592292 = _1592294)], (41512 ^ _776541) ^ [] : [-(_1592296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41517 ^ _776541 : [(41522 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592290, _1592290)), hAPP(hAPP(c_Product__Type_OPair(_1592290, _1592290), 41515 ^ [_1592290, _1592292, _1592294, _1592296, _1592298]), _1592294)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592290, _1592290), tc_HOL_Obool), 41516 ^ [_1592290, _1592292, _1592294, _1592296, _1592298]), _1592298))))], (41520 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592290, _1592290)), hAPP(hAPP(c_Product__Type_OPair(_1592290, _1592290), _1592292), 41515 ^ [_1592290, _1592292, _1592294, _1592296, _1592298])), _1592298)))], (41518 ^ _776541) ^ [] : [-(_1592296 = hAPP(c_Nat_OSuc, 41516 ^ [_1592290, _1592292, _1592294, _1592296, _1592298]))]]], (11147 ^ _776541) ^ [_969478, _969480, _969482, _969484] : [_969484 = c_Orderings_Obot__class_Obot(tc_fun(_969478, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_969478, _969480, _969482), _969484) = c_Orderings_Obot__class_Obot(tc_fun(_969480, tc_HOL_Obool)))], (7486 ^ _776541) ^ [_899799, _899801, _899803, _899805] : [7487 ^ _776541 : [(7490 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899799), _899801), _899805))], (7488 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899799), _899801), _899803))]], -(hBOOL(hAPP(hAPP(c_member(_899799), _899801), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899799, tc_HOL_Obool)), _899805), _899803))))], (5404 ^ _776541) ^ [_859080, _859082, _859084, _859086, _859088, _859090, _859092, _859094] : [-(c_SetInterval_Oord_OatLeastAtMost(_859094, _859090, _859086, _859082) = c_SetInterval_Oord_OatLeastAtMost(_859092, _859088, _859084, _859080)), _859094 = _859092, _859090 = _859088, _859086 = _859084, _859082 = _859080], (8817 ^ _776541) ^ [_928153, _928155, _928157, _928159] : [class_Lattices_Odistrib__lattice(_928153), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928153), _928155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928153), _928157), _928159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928153), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928153), _928155), _928157)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928153), _928155), _928159)))], (48077 ^ _776541) ^ [_1744955, _1744957, _1744959, _1744961] : [c_List_Olist__ex(_1744955, _1744957, hAPP(hAPP(c_List_Oappend(_1744955), _1744959), _1744961)), -(c_List_Olist__ex(_1744955, _1744957, _1744959)), -(c_List_Olist__ex(_1744955, _1744957, _1744961))], (43126 ^ _776541) ^ [_1635767, _1635769] : [hAPP(c_List_Oset(_1635767), _1635769) = c_Orderings_Obot__class_Obot(tc_fun(_1635767, tc_HOL_Obool)), -(_1635769 = c_List_Olist_ONil(_1635767))], (48154 ^ _776541) ^ [_1746333, _1746335, _1746337] : [-(hBOOL(hAPP(hAPP(c_member(_1746333), _1746335), hAPP(c_List_Oset(_1746333), _1746337)))), 48155 ^ _776541 : [(48156 ^ _776541) ^ [_1746422] : [48157 ^ _776541 : [(48158 ^ _776541) ^ [_1746495] : [_1746337 = hAPP(hAPP(c_List_Oappend(_1746333), _1746422), hAPP(hAPP(c_List_Olist_OCons(_1746333), _1746335), _1746495))]], -(hBOOL(hAPP(hAPP(c_member(_1746333), _1746335), hAPP(c_List_Oset(_1746333), _1746422))))]]], (3508 ^ _776541) ^ [_828986, _828988] : [_828988 = _828986, -(c_List_Otranspose__rel(_828988) = c_List_Otranspose__rel(_828986))], (38525 ^ _776541) ^ [_1515196, _1515198, _1515200] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1515196, _1515198)), _1515200)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515198), hAPP(c_Relation_ORange(_1515196, _1515198), _1515200))))], (15956 ^ _776541) ^ [_1065390, _1065392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065390), _1065392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065392), hAPP(c_Nat_OSuc, _1065390))))], (36914 ^ _776541) ^ [_1477344, _1477346, _1477348, _1477350, _1477352] : [c_Equiv__Relations_Oequiv(_1477344, _1477346, _1477348), hBOOL(hAPP(hAPP(c_member(_1477344), _1477350), _1477346)), hBOOL(hAPP(hAPP(c_member(_1477344), _1477352), _1477346)), 36925 ^ _776541 : [(36932 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477344, _1477344)), hAPP(hAPP(c_Product__Type_OPair(_1477344, _1477344), _1477350), _1477352)), _1477348)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477344), hAPP(hAPP(c_Set_Oinsert(_1477344), _1477350), c_Orderings_Obot__class_Obot(tc_fun(_1477344, tc_HOL_Obool)))), _1477348) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477344), hAPP(hAPP(c_Set_Oinsert(_1477344), _1477352), c_Orderings_Obot__class_Obot(tc_fun(_1477344, tc_HOL_Obool)))), _1477348))], (36926 ^ _776541) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477344), hAPP(hAPP(c_Set_Oinsert(_1477344), _1477350), c_Orderings_Obot__class_Obot(tc_fun(_1477344, tc_HOL_Obool)))), _1477348) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477344), hAPP(hAPP(c_Set_Oinsert(_1477344), _1477352), c_Orderings_Obot__class_Obot(tc_fun(_1477344, tc_HOL_Obool)))), _1477348), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477344, _1477344)), hAPP(hAPP(c_Product__Type_OPair(_1477344, _1477344), _1477350), _1477352)), _1477348)))]]], (34111 ^ _776541) ^ [_1410293, _1410295] : [hAPP(c_Nat_OSuc, _1410293) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410295), -(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(_1410295))), 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)), _1410293))))))], (13612 ^ _776541) ^ [_1018843, _1018845, _1018847, _1018849, _1018851, _1018853, _1018855] : [c_Finite__Set_Ofolding__image__simple__idem(_1018843, _1018845, _1018847, _1018849, _1018851, _1018853), -(hAPP(hAPP(_1018847, _1018855), _1018855) = _1018855)], (28337 ^ _776541) ^ [_1285215, _1285217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1285215)), c_Int_OBit1(_1285217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285215), _1285217)))], (39087 ^ _776541) ^ [_1529552, _1529554, _1529556, _1529558] : [39088 ^ _776541 : [(39091 ^ _776541) ^ [] : [_1529558 = c_Orderings_Obot__class_Obot(tc_fun(_1529554, tc_HOL_Obool))], (39089 ^ _776541) ^ [] : [_1529556 = c_Orderings_Obot__class_Obot(tc_fun(_1529552, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1529552, _1529554), _1529556), hAPP(c_COMBK(tc_fun(_1529554, tc_HOL_Obool), _1529552), _1529558)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529552, _1529554), tc_HOL_Obool)))], (51827 ^ _776541) ^ [_1824187, _1824189] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824187), _1824189)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824189), _1824187)), -(_1824187 = _1824189)], (28621 ^ _776541) ^ [] : [-(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)))], (52485 ^ _776541) ^ [] : [hBOOL(c_fFalse)], (45806 ^ _776541) ^ [_1695567] : [-(c_List_Oremdups(_1695567, c_List_Olist_ONil(_1695567)) = c_List_Olist_ONil(_1695567))], (17085 ^ _776541) ^ [_1084141, _1084143, _1084145] : [class_Rings_Oordered__cancel__semiring(_1084141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084141), _1084143), c_Groups_Ozero__class_Ozero(_1084141))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084141), c_Groups_Ozero__class_Ozero(_1084141)), _1084145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084141), _1084143), _1084145)), c_Groups_Ozero__class_Ozero(_1084141))))], (33703 ^ _776541) ^ [_1399465, _1399467, _1399469, _1399471, _1399473] : [class_Groups_Ocomm__monoid__add(_1399465), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399467), _1399469)), 33710 ^ _776541 : [(33717 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399467), _1399471), _1399469))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399467, _1399465), hAPP(hAPP(c_COMBC(_1399467, _1399465, _1399465), hAPP(hAPP(c_COMBS(_1399467, _1399465, tc_fun(_1399465, _1399465)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399465, tc_fun(_1399465, _1399465)), _1399467), c_If(_1399465)), hAPP(c_fequal, _1399471))), _1399473)), c_Groups_Ozero__class_Ozero(_1399465))), _1399469) = c_Groups_Ozero__class_Ozero(_1399465))], (33711 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1399467), _1399471), _1399469)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399467, _1399465), hAPP(hAPP(c_COMBC(_1399467, _1399465, _1399465), hAPP(hAPP(c_COMBS(_1399467, _1399465, tc_fun(_1399465, _1399465)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399465, tc_fun(_1399465, _1399465)), _1399467), c_If(_1399465)), hAPP(c_fequal, _1399471))), _1399473)), c_Groups_Ozero__class_Ozero(_1399465))), _1399469) = hAPP(_1399473, _1399471))]]], (18172 ^ _776541) ^ [_1103213, _1103215] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1103213, _1103215)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103215), hAPP(c_Nat_OSuc, _1103213)))], (29145 ^ _776541) ^ [_1298923, _1298925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298923), _1298925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298923)), c_Int_OBit1(_1298925))))], (9786 ^ _776541) ^ [_944195, _944197, _944199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944195, tc_HOL_Obool)), _944197), _944199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944195, tc_HOL_Obool)), _944197), _944199))), -(_944197 = _944199)], (17463 ^ _776541) ^ [_1091035, _1091037, _1091039] : [class_Rings_Olinordered__semiring__strict(_1091035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091035), c_Groups_Ozero__class_Ozero(_1091035)), _1091037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091035), c_Groups_Ozero__class_Ozero(_1091035)), _1091039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091035), c_Groups_Ozero__class_Ozero(_1091035)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091035), _1091037), _1091039))))], (39555 ^ _776541) ^ [_1543695, _1543697, _1543699, _1543701, _1543703] : [c_Relation_Orefl__on(_1543695, _1543697, _1543699), c_Relation_Orefl__on(_1543695, _1543701, _1543703), -(c_Relation_Orefl__on(_1543695, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543695, tc_HOL_Obool)), _1543697), _1543701), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543695, _1543695), tc_HOL_Obool)), _1543699), _1543703)))], (52115 ^ _776541) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (45924 ^ _776541) ^ [_1697720, _1697722, _1697724] : [-(c_List_Oconcat(_1697720, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697720)), _1697722), _1697724)) = hAPP(hAPP(c_List_Oappend(_1697720), _1697722), c_List_Oconcat(_1697720, _1697724)))], (33292 ^ _776541) ^ [_1386855, _1386857, _1386859, _1386861] : [class_Groups_Oab__group__add(_1386855), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1386857, _1386855), hAPP(hAPP(c_COMBB(_1386855, _1386855, _1386857), c_Groups_Ouminus__class_Ouminus(_1386855)), _1386859)), _1386861) = hAPP(c_Groups_Ouminus__class_Ouminus(_1386855), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1386857, _1386855), _1386859), _1386861)))], (40697 ^ _776541) ^ [_1571752, _1571754, _1571756, _1571758] : [-(c_Transitive__Closure_Otrancl(_1571752, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1571752, _1571752)), hAPP(hAPP(c_Product__Type_OPair(_1571752, _1571752), _1571754), _1571756)), _1571758)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571752, _1571752), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571752, _1571758)), hAPP(c_Set_OCollect(tc_prod(_1571752, _1571752)), hAPP(c_Product__Type_Oprod_Oprod__case(_1571752, _1571752, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1571752, tc_fun(_1571752, tc_HOL_Obool), tc_fun(_1571752, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1571752, tc_HOL_Obool), tc_fun(_1571752, tc_HOL_Obool)), _1571752), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1571752)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571752), c_fconj), hAPP(hAPP(c_COMBC(_1571752, tc_fun(tc_prod(_1571752, _1571752), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1571752, _1571752), tc_fun(tc_fun(tc_prod(_1571752, _1571752), tc_HOL_Obool), tc_HOL_Obool), _1571752), c_member(tc_prod(_1571752, _1571752))), hAPP(hAPP(c_COMBC(_1571752, _1571752, tc_prod(_1571752, _1571752)), c_Product__Type_OPair(_1571752, _1571752)), _1571754))), c_Transitive__Closure_Ortrancl(_1571752, _1571758))))), hAPP(hAPP(c_COMBC(_1571752, tc_fun(tc_prod(_1571752, _1571752), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1571752, _1571752), tc_fun(tc_fun(tc_prod(_1571752, _1571752), tc_HOL_Obool), tc_HOL_Obool), _1571752), c_member(tc_prod(_1571752, _1571752))), hAPP(c_Product__Type_OPair(_1571752, _1571752), _1571756))), c_Transitive__Closure_Ortrancl(_1571752, _1571758)))))))], (6210 ^ _776541) ^ [_876328, _876330] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876328, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_876328, tc_HOL_Obool))), _876330)))], (1594 ^ _776541) ^ [_799330, _799332] : [-(class_Groups_Ocancel__semigroup__add(_799330)), _799332 = _799330, class_Groups_Ocancel__semigroup__add(_799332)], (38114 ^ _776541) ^ [_1506531, _1506533, _1506535, _1506537] : [c_Wellfounded_Owf(_1506531, _1506533), c_Wellfounded_Owf(_1506535, _1506537), -(c_Wellfounded_Owf(tc_prod(_1506531, _1506535), c_Wellfounded_Olex__prod(_1506531, _1506535, _1506533, _1506537)))], (1058 ^ _776541) ^ [_792510, _792512, _792514, _792516, _792518, _792520, _792522, _792524, _792526, _792528] : [-(c_Finite__Set_Ofolding__image(_792526, _792522, _792518, _792514, _792510)), c_Finite__Set_Ofolding__image(_792528, _792524, _792520, _792516, _792512), _792528 = _792526, _792524 = _792522, _792520 = _792518, _792516 = _792514, _792512 = _792510], (16771 ^ _776541) ^ [_1078252, _1078254, _1078256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078254), _1078256)), -(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, _1078252)), _1078254)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078252)), _1078256))))], (25297 ^ _776541) ^ [_1234375, _1234377] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234375, _1234377) = 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), _1234375), _1234377) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1234377), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234375, _1234377)))], (29799 ^ _776541) ^ [_1310828] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1310828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1310828)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25907 ^ _776541) ^ [_1245143, _1245145] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245143, _1245145)) = _1245145, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1245143), _1245145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2258 ^ _776541) ^ [_809431, _809433] : [_809433 = _809431, -(c_SetInterval_Oord__class_OatLeast(_809433) = c_SetInterval_Oord__class_OatLeast(_809431))], (10665 ^ _776541) ^ [_960021, _960023] : [class_Lattices_Oboolean__algebra(_960021), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960021), _960023), hAPP(c_Groups_Ouminus__class_Ouminus(_960021), _960023)) = c_Orderings_Otop__class_Otop(_960021))], (31411 ^ _776541) ^ [_1340552, _1340554, _1340556, _1340558] : [class_Orderings_Olinorder(_1340552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340552), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340552), _1340554), _1340556)), _1340558)), 31418 ^ _776541 : [(31421 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340552), _1340556), _1340558)))], (31419 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340552), _1340554), _1340558)))]]], (38979 ^ _776541) ^ [_1527083, _1527085] : [-(c_Nitpick_Owf_H(_1527083, _1527085)), c_Wellfounded_Oacyclic(_1527083, _1527085), 38984 ^ _776541 : [(38987 ^ _776541) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (38985 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1527083, _1527083)), _1527085))]]], (26164 ^ _776541) ^ [_1249295, _1249297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249297)), 26171 ^ _776541 : [(26178 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249295), _1249297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1249295)), hAPP(c_Int_Onat, _1249297))))], (26172 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1249295)), hAPP(c_Int_Onat, _1249297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249295), _1249297)))]]], (52127 ^ _776541) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (43436 ^ _776541) ^ [_1642599, _1642601, _1642603, _1642605, _1642607] : [-(hAPP(hAPP(c_List_Oappend(_1642599), _1642601), hAPP(hAPP(c_List_Olist_OCons(_1642599), _1642603), c_List_Olist_ONil(_1642599))) = hAPP(hAPP(c_List_Oappend(_1642599), _1642605), hAPP(hAPP(c_List_Olist_OCons(_1642599), _1642607), c_List_Olist_ONil(_1642599)))), _1642601 = _1642605, _1642603 = _1642607], (46138 ^ _776541) ^ [_1703238, _1703240] : [-(c_List_OremoveAll(_1703238, _1703240) = c_List_Ofilter(_1703238, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1703238), c_fNot), hAPP(c_fequal, _1703240))))], (1184 ^ _776541) ^ [_794205, _794207] : [-(class_Rings_Olinordered__ring(_794205)), _794207 = _794205, class_Rings_Olinordered__ring(_794207)], (14797 ^ _776541) ^ [_1043316, _1043318, _1043320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043316), _1043318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043316), _1043320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043320), _1043318)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043320), _1043316))))], (44667 ^ _776541) ^ [_1669515, _1669517, _1669519] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669515)), _1669517), c_List_Olists(_1669515, _1669519))), -(_1669517 = c_List_Olist_ONil(_1669515)), 44676 ^ _776541 : [(44681 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669515)), 44675 ^ [_1669515, _1669517, _1669519]), c_List_Olists(_1669515, _1669519))))], (44679 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1669515), 44674 ^ [_1669515, _1669517, _1669519]), _1669519)))], (44677 ^ _776541) ^ [] : [-(_1669517 = hAPP(hAPP(c_List_Olist_OCons(_1669515), 44674 ^ [_1669515, _1669517, _1669519]), 44675 ^ [_1669515, _1669517, _1669519]))]]], (26304 ^ _776541) ^ [_1251532, _1251534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251534)), 26311 ^ _776541 : [(26318 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251532), _1251534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251532)), hAPP(c_Int_Onat, _1251534))))], (26312 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251532)), hAPP(c_Int_Onat, _1251534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251532), _1251534)))]]], (52225 ^ _776541) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52043 ^ _776541) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (8221 ^ _776541) ^ [_917181, _917183] : [class_Lattices_Obounded__lattice__top(_917181), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917181), c_Orderings_Otop__class_Otop(_917181)), _917183) = _917183)], (43868 ^ _776541) ^ [_1653007, _1653009, _1653011] : [-(hAPP(hAPP(c_List_Odrop(_1653007), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1653007), _1653009), _1653011)) = _1653011)], (15660 ^ _776541) ^ [_1060579, _1060581] : [class_Groups_Ozero(_1060579), 15663 ^ _776541 : [(15670 ^ _776541) ^ [] : [_1060581 = c_Groups_Ozero__class_Ozero(_1060579), -(c_Groups_Ozero__class_Ozero(_1060579) = _1060581)], (15664 ^ _776541) ^ [] : [c_Groups_Ozero__class_Ozero(_1060579) = _1060581, -(_1060581 = c_Groups_Ozero__class_Ozero(_1060579))]]], (22291 ^ _776541) ^ [_1180690, _1180692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180690), _1180692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180692), _1180690)), -(_1180690 = _1180692)], (28189 ^ _776541) ^ [_1282688] : [class_Rings_Osemiring__1(_1282688), -(hBOOL(hAPP(hAPP(c_member(_1282688), c_Groups_Oone__class_Oone(_1282688)), c_Nat_Osemiring__1__class_ONats(_1282688))))], (28625 ^ _776541) ^ [_1289904, _1289906] : [class_Groups_Omonoid__mult(_1289904), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1289904), _1289906), 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(_1289904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289904), _1289906), _1289906)), _1289906))], (48786 ^ _776541) ^ [_1759936, _1759938, _1759940, _1759942, _1759944] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1759936, _1759938, _1759940) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1759936, _1759942, _1759944), 48789 ^ _776541 : [(48792 ^ _776541) ^ [] : [-(_1759940 = _1759944)], (48790 ^ _776541) ^ [] : [-(_1759938 = _1759942)]]], (22343 ^ _776541) ^ [_1181607, _1181609, _1181611] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181607), _1181609)), _1181611) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181607), _1181611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181609), _1181611)))], (44178 ^ _776541) ^ [_1659930, _1659932, _1659934] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659930)), hAPP(c_List_Orotate(_1659930, _1659932), _1659934)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659930)), _1659934))], (45571 ^ _776541) ^ [_1690292, _1690294, _1690296, _1690298, _1690300, _1690302] : [c_List_Olist__all2(_1690292, _1690294, _1690296, _1690298, _1690300), -(c_List_Olist__all2(_1690292, _1690294, _1690296, hAPP(hAPP(c_List_Odrop(_1690292), _1690302), _1690298), hAPP(hAPP(c_List_Odrop(_1690294), _1690302), _1690300)))], (37961 ^ _776541) ^ [_1501576, _1501578, _1501580, _1501582] : [hAPP(hAPP(c_Relation_Orel__comp(_1501576, _1501576, _1501576), _1501578), _1501580) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501576, _1501576), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501576, _1501576, _1501576), _1501578), _1501582) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501576, _1501576), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1501576, _1501576, _1501576), _1501578), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501576, _1501576), tc_HOL_Obool)), _1501580), _1501582)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501576, _1501576), tc_HOL_Obool)))], (38258 ^ _776541) ^ [_1509126, _1509128] : [hAPP(hAPP(c_Relation_Orel__comp(_1509126, _1509126, _1509126), _1509128), _1509128) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509126, _1509126), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1509126, _1509128))], (10687 ^ _776541) ^ [_960467, _960469] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960467, tc_HOL_Obool)), _960469), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960467, tc_HOL_Obool)), _960469)) = c_Orderings_Obot__class_Obot(tc_fun(_960467, tc_HOL_Obool)))], (40711 ^ _776541) ^ [_1572868, _1572870, _1572872] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572868, _1572868)), _1572870), _1572872)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572868, _1572868)), _1572870), c_Transitive__Closure_Ortrancl(_1572868, _1572872))))], (7224 ^ _776541) ^ [_894308, _894310, _894312] : [-(hBOOL(hAPP(hAPP(c_member(_894308), _894310), hAPP(hAPP(c_Set_Oinsert(_894308), _894310), _894312))))], (48586 ^ _776541) ^ [_1756099, _1756101, _1756103] : [-(_1756099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1756101, c_List_Oreplicate(_1756101, _1756099, _1756103)) = _1756103)], (45211 ^ _776541) ^ [_1682113, _1682115] : [_1682113 = _1682115, -(hAPP(c_Code__Numeral_Onat__of, _1682113) = hAPP(c_Code__Numeral_Onat__of, _1682115))], (48838 ^ _776541) ^ [_1760784, _1760786, _1760788] : [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), _1760784), _1760786))), -(hBOOL(hAPP(hAPP(_1760788, _1760784), _1760786))), 48845 ^ _776541 : [(48848 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48843 ^ [_1760784, _1760786, _1760788]), 48844 ^ [_1760784, _1760786, _1760788]))), -(hBOOL(hAPP(hAPP(_1760788, 48843 ^ [_1760784, _1760786, _1760788]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48844 ^ [_1760784, _1760786, _1760788]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48854 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1760788, 48843 ^ [_1760784, _1760786, _1760788]), 48844 ^ [_1760784, _1760786, _1760788]))], (48846 ^ _776541) ^ [] : [-(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), 48843 ^ [_1760784, _1760786, _1760788]), 48844 ^ [_1760784, _1760786, _1760788]))))]]], (27231 ^ _776541) ^ [_1266581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266581), 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), _1266581)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27821 ^ _776541) ^ [_1276779, _1276781] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276779)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276781)))), 27824 ^ _776541 : [(27827 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1276781))], (27825 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276779), _1276781)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276779), _1276781))], (9610 ^ _776541) ^ [_941259, _941261, _941263] : [class_Orderings_Oorder(_941259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941259), _941261), _941263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941259), _941261), _941263))), -(_941261 = _941263)], (27807 ^ _776541) ^ [] : [-(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))))], (15854 ^ _776541) ^ [_1063577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063577)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063577), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1063577)], (35560 ^ _776541) ^ [_1440067, _1440069, _1440071] : [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), _1440067), _1440069))), -(hBOOL(hAPP(hAPP(_1440071, _1440067), _1440069))), 35567 ^ _776541 : [(35570 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 35566 ^ [_1440067, _1440069, _1440071]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1440071, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 35565 ^ [_1440067, _1440069, _1440071])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 35566 ^ [_1440067, _1440069, _1440071]))))], (35576 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1440071, 35565 ^ [_1440067, _1440069, _1440071]), 35566 ^ [_1440067, _1440069, _1440071]))], (35568 ^ _776541) ^ [] : [-(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), 35565 ^ [_1440067, _1440069, _1440071]), 35566 ^ [_1440067, _1440069, _1440071]))))]]], (7090 ^ _776541) ^ [_892012, _892014] : [hBOOL(hAPP(hAPP(c_member(_892012), 7091 ^ [_892012, _892014]), _892014)), -(c_Orderings_Otop__class_Otop(tc_fun(_892012, tc_HOL_Obool)) = _892014)], (16610 ^ _776541) ^ [_1075283, _1075285, _1075287, _1075289] : [class_Groups_Ocomm__monoid__add(_1075283), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075285), _1075287)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1075285, _1075283), _1075289), _1075287) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075283, _1075285, c_Groups_Oplus__class_Oplus(_1075283)), _1075289), c_Groups_Ozero__class_Ozero(_1075283)), _1075287))], (26917 ^ _776541) ^ [_1261381, _1261383, _1261385] : [class_Rings_Olinordered__idom(_1261381), 26920 ^ _776541 : [(26927 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261383), _1261385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261381), hAPP(c_Int_Oring__1__class_Oof__int(_1261381), _1261383)), hAPP(c_Int_Oring__1__class_Oof__int(_1261381), _1261385))))], (26921 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261381), hAPP(c_Int_Oring__1__class_Oof__int(_1261381), _1261383)), hAPP(c_Int_Oring__1__class_Oof__int(_1261381), _1261385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261383), _1261385)))]]], (40298 ^ _776541) ^ [_1562137, _1562139, _1562141, _1562143, _1562145, _1562147] : [c_Finite__Set_Ofolding__idem(_1562137, _1562139, _1562141, _1562143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562137), _1562145)), hBOOL(hAPP(hAPP(c_member(_1562137), _1562147), _1562145)), -(hAPP(c_Fun_Ocomp(_1562139, _1562139, _1562139, hAPP(_1562143, _1562145)), hAPP(_1562141, _1562147)) = hAPP(_1562143, _1562145))], (7306 ^ _776541) ^ [_896095, _896097, _896099, _896101] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896095, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_896095), _896097), _896099)), _896101))), hBOOL(hAPP(hAPP(c_member(_896095), _896097), _896101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896095, tc_HOL_Obool)), _896099), _896101))], (45860 ^ _776541) ^ [_1696489, _1696491, _1696493] : [-(hBOOL(hAPP(hAPP(c_member(_1696489), _1696491), hAPP(c_List_Oset(_1696489), _1696493)))), -(c_List_Oremdups(_1696489, hAPP(hAPP(c_List_Olist_OCons(_1696489), _1696491), _1696493)) = hAPP(hAPP(c_List_Olist_OCons(_1696489), _1696491), c_List_Oremdups(_1696489, _1696493)))], (29239 ^ _776541) ^ [_1300619] : [class_Int_Onumber__ring(_1300619), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300619), c_Groups_Oone__class_Oone(_1300619)), c_Groups_Oone__class_Oone(_1300619)) = hAPP(c_Int_Onumber__class_Onumber__of(_1300619), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (50479 ^ _776541) ^ [_1797081, _1797083, _1797085] : [c_Fun_Obij__betw(_1797081, _1797081, c_Fun_Oid(_1797081), _1797083, _1797085), -(_1797083 = _1797085)], (6316 ^ _776541) ^ [_878255, _878257, _878259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_878255, tc_HOL_Obool), tc_HOL_Obool)), _878257), _878259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878255, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_878255, tc_HOL_Obool), _878259)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_878255, tc_HOL_Obool), _878257))))], (35036 ^ _776541) ^ [_1430347, _1430349, _1430351] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430347, _1430349), _1430351)), -(c_Divides_Odivmod__nat(_1430347, _1430349) = _1430351)], (6287 ^ _776541) ^ [_877672, _877674, _877676] : [class_Complete__Lattice_Ocomplete__lattice(_877672), 6290 ^ _776541 : [(6291 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877672), c_Complete__Lattice_OSup__class_OSup(_877672, _877674)), _877676)), 6294 ^ _776541 : [(6295 ^ _776541) ^ [_877830] : [hBOOL(hAPP(hAPP(c_member(_877672), _877830), _877674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877672), _877830), _877676)))]]], (6301 ^ _776541) ^ [] : [6303 ^ _776541 : [(6306 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877672), 6302 ^ [_877672, _877674, _877676]), _877676))], (6304 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877672), 6302 ^ [_877672, _877674, _877676]), _877674)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877672), c_Complete__Lattice_OSup__class_OSup(_877672, _877674)), _877676)))]]], (33605 ^ _776541) ^ [_1395400, _1395402, _1395404, _1395406, _1395408, _1395410] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395400, tc_fun(_1395402, tc_fun(_1395404, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1395400, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool), tc_fun(_1395402, tc_fun(_1395404, tc_HOL_Obool)), _1395400), hAPP(c_COMBC(_1395402, tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool), tc_fun(_1395404, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395404, tc_fun(tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool), tc_fun(_1395404, tc_HOL_Obool)), _1395402), c_COMBC(_1395404, tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395404, tc_prod(_1395402, _1395404)), tc_fun(_1395404, tc_fun(tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool), tc_HOL_Obool)), _1395402), hAPP(c_COMBB(tc_prod(_1395402, _1395404), tc_fun(tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool), tc_HOL_Obool), _1395404), c_member(tc_prod(_1395402, _1395404)))), c_Product__Type_OPair(_1395402, _1395404))))), _1395406)), _1395408), _1395410)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1395402, _1395404)), hAPP(hAPP(c_Product__Type_OPair(_1395402, _1395404), _1395408), _1395410)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395400, tc_fun(tc_prod(_1395402, _1395404), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395400, tc_HOL_Obool))), _1395406))))], (10279 ^ _776541) ^ [_953195, _953197] : [class_Groups_Ogroup__add(_953195), -(hAPP(c_Groups_Ouminus__class_Ouminus(_953195), hAPP(c_Groups_Ouminus__class_Ouminus(_953195), _953197)) = _953197)], (27619 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (50023 ^ _776541) ^ [_1787058, _1787060, _1787062, _1787064] : [hAPP(c_Set_Oimage(_1787058, _1787060, _1787062), c_Orderings_Otop__class_Otop(tc_fun(_1787058, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1787060, tc_HOL_Obool)), -(hAPP(_1787062, hAPP(c_Hilbert__Choice_Oinv__into(_1787058, _1787060, c_Orderings_Otop__class_Otop(tc_fun(_1787058, tc_HOL_Obool)), _1787062), _1787064)) = _1787064)], (10571 ^ _776541) ^ [_958320, _958322, _958324, _958326, _958328] : [class_Orderings_Olinorder(_958320), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958320, _958322), _958324) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958320, _958326), _958328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958320), _958322), _958324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958320), _958326), _958328)), -(_958322 = _958326)], (33549 ^ _776541) ^ [_1393911, _1393913, _1393915, _1393917] : [33551 ^ _776541 : [(33554 ^ _776541) ^ [] : [hAPP(_1393917, 33550 ^ [_1393911, _1393913, _1393915, _1393917]) = c_Orderings_Otop__class_Otop(tc_fun(_1393911, tc_HOL_Obool))], (33552 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1393913), 33550 ^ [_1393911, _1393913, _1393915, _1393917]), _1393915)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1393911, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393913, tc_fun(_1393911, tc_HOL_Obool)), _1393915), _1393917))], (49574 ^ _776541) ^ [_1778331] : [-(c_Relation_Oantisym(_1778331, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1778331, _1778331), tc_HOL_Obool))))], (28427 ^ _776541) ^ [_1286806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1286806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1286806)))], (43056 ^ _776541) ^ [_1634572, _1634574] : [-(hAPP(hAPP(c_List_Otake(_1634572), _1634574), c_List_Olist_ONil(_1634572)) = c_List_Olist_ONil(_1634572))], (11606 ^ _776541) ^ [_979543, _979545, _979547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979543), _979547)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979543), hAPP(hAPP(c_Set_Oinsert(_979543), _979545), _979547))))], (28889 ^ _776541) ^ [_1294443, _1294445] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1294443)), _1294445) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1294443), _1294445)))], (31603 ^ _776541) ^ [_1343940, _1343942, _1343944, _1343946] : [class_Orderings_Olinorder(_1343940), 31606 ^ _776541 : [(31615 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343940), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343940), _1343942), _1343944)), _1343946))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343940), _1343942), _1343946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343940), _1343944), _1343946))], (31607 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343940), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343940), _1343942), _1343944)), _1343946)), 31610 ^ _776541 : [(31613 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343940), _1343944), _1343946)))], (31611 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343940), _1343942), _1343946)))]]]]], (5214 ^ _776541) ^ [_856107, _856109, _856111, _856113] : [-(c_Transitive__Closure_Ortrancl(_856113, _856109) = c_Transitive__Closure_Ortrancl(_856111, _856107)), _856113 = _856111, _856109 = _856107], (1294 ^ _776541) ^ [_795580, _795582] : [-(class_Groups_Oabs__if(_795580)), _795582 = _795580, class_Groups_Oabs__if(_795582)], (4784 ^ _776541) ^ [_849360, _849362, _849364, _849366, _849368, _849370, _849372, _849374] : [-(c_Wellfounded_Olex__prod(_849374, _849370, _849366, _849362) = c_Wellfounded_Olex__prod(_849372, _849368, _849364, _849360)), _849374 = _849372, _849370 = _849368, _849366 = _849364, _849362 = _849360], (32131 ^ _776541) ^ [_1353895, _1353897, _1353899] : [class_Orderings_Olinorder(_1353895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353895), _1353897)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353895), _1353899)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353895, tc_HOL_Obool)), _1353897), _1353899) = c_Orderings_Obot__class_Obot(tc_fun(_1353895, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353895), c_Big__Operators_Olattice_OSup__fin(_1353895, c_Orderings_Oord__class_Omax(_1353895), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353895, tc_HOL_Obool)), _1353897), _1353899))), c_Big__Operators_Olattice_OSup__fin(_1353895, c_Orderings_Oord__class_Omax(_1353895), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353895, tc_HOL_Obool)), _1353897), _1353899))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353895), c_Big__Operators_Olattice_OSup__fin(_1353895, c_Orderings_Oord__class_Omax(_1353895), _1353897)), c_Big__Operators_Olattice_OSup__fin(_1353895, c_Orderings_Oord__class_Omax(_1353895), _1353899)))], (27843 ^ _776541) ^ [_1277134, _1277136] : [27844 ^ _776541 : [(27847 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277134), c_Int_OPls))], (27845 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277134), _1277136))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277134)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277136))))], (41793 ^ _776541) ^ [_1600547, _1600549, _1600551, _1600553, _1600555, _1600557] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600547), tc_List_Olist(_1600547))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600547), tc_List_Olist(_1600547)), hAPP(hAPP(c_List_Olist_OCons(_1600547), _1600549), _1600551)), hAPP(hAPP(c_List_Olist_OCons(_1600547), _1600553), _1600555))), c_List_Olex(_1600547, _1600557)))), 41794 ^ _776541 : [(41801 ^ _776541) ^ [] : [_1600549 = _1600553, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600547), tc_List_Olist(_1600547))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600547), tc_List_Olist(_1600547)), _1600551), _1600555)), c_List_Olex(_1600547, _1600557)))], (41795 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600547, _1600547)), hAPP(hAPP(c_Product__Type_OPair(_1600547, _1600547), _1600549), _1600553)), _1600557)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600547)), _1600551) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600547)), _1600555)]]], (38276 ^ _776541) ^ [_1509676, _1509678] : [c_Wellfounded_Owf(_1509676, _1509678), 38280 ^ _776541 : [(38281 ^ _776541) ^ [_1509812] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1509676, _1509676)), hAPP(hAPP(c_Product__Type_OPair(_1509676, _1509676), hAPP(_1509812, hAPP(c_Nat_OSuc, 38279 ^ [_1509676, _1509678, _1509812]))), hAPP(_1509812, 38279 ^ [_1509676, _1509678, _1509812]))), _1509678))]]], (38028 ^ _776541) ^ [_1503757, _1503759, _1503761, _1503763, _1503765, _1503767, _1503769] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1503757, _1503759, _1503761, hAPP(hAPP(c_COMBC(_1503757, tc_fun(tc_prod(_1503757, _1503759), tc_HOL_Obool), tc_fun(_1503759, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503759, tc_fun(tc_fun(tc_prod(_1503757, _1503759), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1503757, _1503759), tc_HOL_Obool), tc_fun(_1503759, tc_HOL_Obool)), _1503757), c_COMBC(_1503759, tc_fun(tc_prod(_1503757, _1503759), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503759, tc_prod(_1503757, _1503759)), tc_fun(_1503759, tc_fun(tc_fun(tc_prod(_1503757, _1503759), tc_HOL_Obool), tc_HOL_Obool)), _1503757), hAPP(c_COMBB(tc_prod(_1503757, _1503759), tc_fun(tc_fun(tc_prod(_1503757, _1503759), tc_HOL_Obool), tc_HOL_Obool), _1503759), c_member(tc_prod(_1503757, _1503759)))), c_Product__Type_OPair(_1503757, _1503759)))), _1503763), hAPP(hAPP(c_COMBC(_1503759, tc_fun(tc_prod(_1503759, _1503761), tc_HOL_Obool), tc_fun(_1503761, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503761, tc_fun(tc_fun(tc_prod(_1503759, _1503761), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1503759, _1503761), tc_HOL_Obool), tc_fun(_1503761, tc_HOL_Obool)), _1503759), c_COMBC(_1503761, tc_fun(tc_prod(_1503759, _1503761), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503761, tc_prod(_1503759, _1503761)), tc_fun(_1503761, tc_fun(tc_fun(tc_prod(_1503759, _1503761), tc_HOL_Obool), tc_HOL_Obool)), _1503759), hAPP(c_COMBB(tc_prod(_1503759, _1503761), tc_fun(tc_fun(tc_prod(_1503759, _1503761), tc_HOL_Obool), tc_HOL_Obool), _1503761), c_member(tc_prod(_1503759, _1503761)))), c_Product__Type_OPair(_1503759, _1503761)))), _1503765)), _1503767), _1503769)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1503757, _1503761)), hAPP(hAPP(c_Product__Type_OPair(_1503757, _1503761), _1503767), _1503769)), hAPP(hAPP(c_Relation_Orel__comp(_1503757, _1503759, _1503761), _1503763), _1503765))))], (49039 ^ _776541) ^ [_1765722, _1765724] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1765722)), _1765724)), 49043 ^ _776541 : [(49044 ^ _776541) ^ [_1765823] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765722)), _1765823), _1765724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765722)), _1765823)), 49042 ^ [_1765722, _1765724])))]]], (36470 ^ _776541) ^ [_1466353, _1466355, _1466357] : [-(hAPP(c_Relation_OImage(_1466353, _1466355, _1466357), c_Orderings_Obot__class_Obot(tc_fun(_1466353, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1466355, tc_HOL_Obool)))], (1504 ^ _776541) ^ [_798205, _798207] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_798205)), _798207 = _798205, class_Groups_Oordered__ab__semigroup__add__imp__le(_798207)], (45479 ^ _776541) ^ [_1688535, _1688537, _1688539, _1688541] : [_1688541 = c_List_Olist_ONil(_1688535), -(c_List_Olist__all2(_1688535, _1688537, _1688539, _1688541, c_List_Olist_ONil(_1688537)))], (32604 ^ _776541) ^ [_1367721, _1367723, _1367725, _1367727, _1367729] : [-(_1367721 = c_Orderings_Obot__class_Obot(tc_fun(_1367723, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367725, tc_HOL_Obool)), _1367727), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367723, tc_fun(_1367725, tc_HOL_Obool)), _1367721), _1367729)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367723, tc_fun(_1367725, tc_HOL_Obool)), _1367721), hAPP(hAPP(c_COMBB(tc_fun(_1367725, tc_HOL_Obool), tc_fun(_1367725, tc_HOL_Obool), _1367723), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367725, tc_HOL_Obool)), _1367727)), _1367729)))], (11252 ^ _776541) ^ [_971942, _971944, _971946] : [class_Groups_Oordered__ab__group__add(_971942), -(hAPP(c_Set_Oimage(_971942, _971942, c_Groups_Ouminus__class_Ouminus(_971942)), c_SetInterval_Oord__class_OgreaterThanLessThan(_971942, _971944, _971946)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_971942, hAPP(c_Groups_Ouminus__class_Ouminus(_971942), _971946), hAPP(c_Groups_Ouminus__class_Ouminus(_971942), _971944)))], (32286 ^ _776541) ^ [_1357053] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1357053)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1357053)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33076 ^ _776541) ^ [_1381051, _1381053, _1381055, _1381057] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381051, tc_fun(_1381053, tc_HOL_Obool))), _1381055), _1381057)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1381051, _1381053)), hAPP(hAPP(c_Product__Type_OPair(_1381051, _1381053), _1381055), _1381057)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1381051, _1381053), tc_HOL_Obool)))))], (42565 ^ _776541) ^ [_1623878, _1623880, _1623882, _1623884] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623878, _1623878)), hAPP(hAPP(c_Product__Type_OPair(_1623878, _1623878), _1623880), _1623882)), hAPP(c_List_Oset(tc_prod(_1623878, _1623878)), hAPP(hAPP(c_List_Ozip(_1623878, _1623878), _1623884), _1623884))))), hBOOL(hAPP(hAPP(c_member(_1623878), _1623880), hAPP(c_List_Oset(_1623878), _1623884))), _1623880 = _1623882], (16066 ^ _776541) ^ [_1067039, _1067041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067039)), hAPP(c_Nat_OSuc, _1067041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067039), _1067041)))], (39665 ^ _776541) ^ [_1546458, _1546460, _1546462] : [-(c_Relation_Orefl__on(_1546458, _1546460, _1546462)), 39669 ^ _776541 : [(39672 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1546458, _1546458, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1546458, tc_fun(_1546458, tc_HOL_Obool), tc_fun(_1546458, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546458, tc_HOL_Obool), tc_fun(_1546458, tc_HOL_Obool)), _1546458), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546458)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546458), c_fconj), hAPP(hAPP(c_COMBC(_1546458, tc_fun(_1546458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546458)), _1546460)))), hAPP(hAPP(c_COMBC(_1546458, tc_fun(_1546458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546458)), _1546460))), 39668 ^ [_1546458, _1546460, _1546462]))], (39670 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546458, _1546458)), 39668 ^ [_1546458, _1546460, _1546462]), _1546462)))]], 39674 ^ _776541 : [(39677 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546458, _1546458)), hAPP(hAPP(c_Product__Type_OPair(_1546458, _1546458), 39673 ^ [_1546458, _1546460, _1546462]), 39673 ^ [_1546458, _1546460, _1546462])), _1546462))], (39675 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546458), 39673 ^ [_1546458, _1546460, _1546462]), _1546460)))]]], (37722 ^ _776541) ^ [_1495141, _1495143, _1495145, _1495147, _1495149] : [c_Fun_Oinj__on(_1495141, _1495143, _1495145, _1495147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495143, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1495141, _1495143, _1495145), _1495147)), _1495149)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495143), _1495149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1495141), _1495147)), hAPP(c_Finite__Set_Ocard(_1495143), _1495149))))], (16340 ^ _776541) ^ [_1071381, _1071383] : [class_Groups_Ogroup__add(_1071381), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071381), _1071383), c_Groups_Ozero__class_Ozero(_1071381)) = _1071383)], (27789 ^ _776541) ^ [_1276258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276258), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276258) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6340 ^ _776541) ^ [_878750, _878752, _878754] : [_878750 = _878752, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878754, tc_HOL_Obool)), _878752), _878750)))], (48656 ^ _776541) ^ [_1757354, _1757356, _1757358, _1757360, _1757362] : [-(c_List_Oreplicate(_1757354, _1757356, _1757358) = c_List_Oreplicate(_1757354, _1757360, _1757362)), _1757356 = _1757360, 48661 ^ _776541 : [(48664 ^ _776541) ^ [] : [_1757358 = _1757362], (48662 ^ _776541) ^ [] : [_1757356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43208 ^ _776541) ^ [_1637299, _1637301, _1637303] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637299), tc_List_Olist(_1637299))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637299), tc_List_Olist(_1637299)), _1637301), c_List_Olist_ONil(_1637299))), c_List_Olexord(_1637299, _1637303)))], (32622 ^ _776541) ^ [_1368107, _1368109, _1368111] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368107, tc_HOL_Obool)), _1368109), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1368107, tc_HOL_Obool), _1368111)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1368107, tc_HOL_Obool), tc_fun(_1368107, tc_HOL_Obool)), _1368111), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368107, tc_HOL_Obool)), _1368109)))], (4534 ^ _776541) ^ [_845399, _845401, _845403, _845405] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_845405, _845401) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_845403, _845399)), _845405 = _845403, _845401 = _845399], (7316 ^ _776541) ^ [_896303, _896305, _896307, _896309] : [-(hBOOL(hAPP(hAPP(c_member(_896303), _896305), _896307))), 7319 ^ _776541 : [(7326 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896303, tc_HOL_Obool)), _896307), _896309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896303, tc_HOL_Obool)), _896307), hAPP(hAPP(c_Set_Oinsert(_896303), _896305), _896309))))], (7320 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896303, tc_HOL_Obool)), _896307), hAPP(hAPP(c_Set_Oinsert(_896303), _896305), _896309))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896303, tc_HOL_Obool)), _896307), _896309)))]]], (42638 ^ _776541) ^ [_1625397] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1625397)), -(c_List_Onat__list(_1625397))], (51737 ^ _776541) ^ [_1822784, _1822786] : [51744 ^ _776541 : [(51747 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822786), _1822784))], (51745 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822784), _1822786)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822784), _1822786)), -(_1822784 = _1822786)], (28867 ^ _776541) ^ [_1294085] : [-(c_Int_OBit0(_1294085) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1294085), _1294085))], (22339 ^ _776541) ^ [_1181510, _1181512] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181510), _1181512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181510), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181512)))], (10445 ^ _776541) ^ [_955956, _955958, _955960] : [class_Groups_Oordered__ab__group__add(_955956), 10448 ^ _776541 : [(10455 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955956), _955960), _955958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955956), hAPP(c_Groups_Ouminus__class_Ouminus(_955956), _955958)), hAPP(c_Groups_Ouminus__class_Ouminus(_955956), _955960))))], (10449 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955956), hAPP(c_Groups_Ouminus__class_Ouminus(_955956), _955958)), hAPP(c_Groups_Ouminus__class_Ouminus(_955956), _955960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955956), _955960), _955958)))]]], (45878 ^ _776541) ^ [_1696904, _1696906] : [class_Orderings_Olinorder(_1696904), -(c_List_Olinorder__class_Osorted__list__of__set(_1696904, hAPP(c_List_Oset(_1696904), _1696906)) = c_List_Olinorder__class_Osort__key(_1696904, _1696904, c_COMBI(_1696904), c_List_Oremdups(_1696904, _1696906)))], (24914 ^ _776541) ^ [_1227655, _1227657, _1227659, _1227661] : [class_Divides_Oring__div(_1227655), c_Divides_Odiv__class_Omod(_1227655, _1227657, _1227659) = c_Divides_Odiv__class_Omod(_1227655, _1227661, _1227659), -(c_Divides_Odiv__class_Omod(_1227655, hAPP(c_Groups_Ouminus__class_Ouminus(_1227655), _1227657), _1227659) = c_Divides_Odiv__class_Omod(_1227655, hAPP(c_Groups_Ouminus__class_Ouminus(_1227655), _1227661), _1227659))], (49157 ^ _776541) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (48889 ^ _776541) ^ [_1762199, _1762201] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762199), c_List_Olist_ONil(_1762199)), _1762201))], (8423 ^ _776541) ^ [_921198, _921200, _921202] : [class_Lattices_Osemilattice__inf(_921198), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921198), _921200), _921202) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921198), _921202), _921200))], (11540 ^ _776541) ^ [_978224, _978226] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_978224), c_Orderings_Otop__class_Otop(tc_fun(_978224, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978226), c_Orderings_Otop__class_Otop(tc_fun(_978226, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_978224, _978226)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_978224, _978226), tc_HOL_Obool)))))], (29245 ^ _776541) ^ [_1300726] : [class_Rings_Osemiring__1(_1300726), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300726), c_Groups_Ozero__class_Ozero(_1300726)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1300726))], (40729 ^ _776541) ^ [_1573291, _1573293] : [-(c_Transitive__Closure_Otrancl(_1573291, c_Transitive__Closure_Ortrancl(_1573291, _1573293)) = c_Transitive__Closure_Ortrancl(_1573291, _1573293))], (43486 ^ _776541) ^ [_1643753, _1643755, _1643757, _1643759] : [hAPP(hAPP(c_List_Oappend(_1643753), _1643755), _1643757) = hAPP(hAPP(c_List_Oappend(_1643753), _1643759), _1643757), -(_1643755 = _1643759)], (47424 ^ _776541) ^ [_1730068, _1730070, _1730072, _1730074, _1730076] : [hBOOL(hAPP(hAPP(c_member(_1730068), _1730070), hAPP(c_List_Oset(_1730068), _1730072))), -(hBOOL(hAPP(_1730074, _1730070))), -(c_List_OdropWhile(_1730068, _1730074, hAPP(hAPP(c_List_Oappend(_1730068), _1730072), _1730076)) = hAPP(hAPP(c_List_Oappend(_1730068), c_List_OdropWhile(_1730068, _1730074, _1730072)), _1730076))], (24970 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11054 ^ _776541) ^ [_967682] : [class_Groups_Oab__semigroup__mult(_967682), -(c_Finite__Set_Ofun__left__comm(_967682, _967682, c_Groups_Otimes__class_Otimes(_967682)))], (164 ^ _776541) ^ [_779243, _779245, _779247, _779249, _779251, _779253, _779255, _779257, _779259, _779261] : [-(c_Big__Operators_Ocomm__monoid__big(_779259, _779255, _779251, _779247, _779243)), c_Big__Operators_Ocomm__monoid__big(_779261, _779257, _779253, _779249, _779245), _779261 = _779259, _779257 = _779255, _779253 = _779251, _779249 = _779247, _779245 = _779243], (32496 ^ _776541) ^ [_1362591, _1362593, _1362595, _1362597, _1362599, _1362601] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1362591, _1362593)), hAPP(hAPP(c_Product__Type_OPair(_1362591, _1362593), _1362599), _1362601)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool)), _1362595), _1362597))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362591, tc_fun(_1362593, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1362591, tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_fun(_1362593, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362593, tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_fun(_1362593, tc_HOL_Obool)), _1362591), c_COMBC(_1362593, tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362593, tc_prod(_1362591, _1362593)), tc_fun(_1362593, tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool)), _1362591), hAPP(c_COMBB(tc_prod(_1362591, _1362593), tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool), _1362593), c_member(tc_prod(_1362591, _1362593)))), c_Product__Type_OPair(_1362591, _1362593)))), _1362595)), hAPP(hAPP(c_COMBC(_1362591, tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_fun(_1362593, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362593, tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_fun(_1362593, tc_HOL_Obool)), _1362591), c_COMBC(_1362593, tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362593, tc_prod(_1362591, _1362593)), tc_fun(_1362593, tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool)), _1362591), hAPP(c_COMBB(tc_prod(_1362591, _1362593), tc_fun(tc_fun(tc_prod(_1362591, _1362593), tc_HOL_Obool), tc_HOL_Obool), _1362593), c_member(tc_prod(_1362591, _1362593)))), c_Product__Type_OPair(_1362591, _1362593)))), _1362597)), _1362599), _1362601)))], (47014 ^ _776541) ^ [_1721462, _1721464] : [_1721464 = c_List_Olist_ONil(_1721462), -(hAPP(c_List_Orev(_1721462), _1721464) = c_List_Olist_ONil(_1721462))], (5422 ^ _776541) ^ [_859381, _859383] : [_859383 = _859381, -(c_Groups_Ominus__class_Ominus(_859383) = c_Groups_Ominus__class_Ominus(_859381))], (32406 ^ _776541) ^ [_1359620, _1359622, _1359624, _1359626] : [class_Groups_Oordered__ab__group__add__abs(_1359620), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359620), hAPP(c_Groups_Oabs__class_Oabs(_1359620), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359622, _1359620), _1359624), _1359626))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359622, _1359620), hAPP(hAPP(c_COMBB(_1359620, _1359620, _1359622), c_Groups_Oabs__class_Oabs(_1359620)), _1359624)), _1359626))))], (13342 ^ _776541) ^ [_1013265, _1013267, _1013269, _1013271, _1013273] : [class_Groups_Ocomm__monoid__mult(_1013265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013267), _1013269)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013267), _1013271)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013267, tc_HOL_Obool)), _1013269), _1013271) = c_Orderings_Obot__class_Obot(tc_fun(_1013267, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1013267, _1013265), _1013273), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013267, tc_HOL_Obool)), _1013269), _1013271)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013265), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1013267, _1013265), _1013273), _1013269)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1013267, _1013265), _1013273), _1013271)))], (33208 ^ _776541) ^ [_1385044, _1385046, _1385048, _1385050, _1385052] : [-(hAPP(hAPP(c_Set_Oinsert(_1385044), _1385046), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385048, tc_fun(_1385044, tc_HOL_Obool)), _1385050), _1385052)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385048, tc_fun(_1385044, tc_HOL_Obool)), _1385050), hAPP(hAPP(c_COMBB(tc_fun(_1385044, tc_HOL_Obool), tc_fun(_1385044, tc_HOL_Obool), _1385048), hAPP(c_Set_Oinsert(_1385044), _1385046)), _1385052)))], (15396 ^ _776541) ^ [_1054609, _1054611, _1054613] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054609), _1054611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1054609, tc_HOL_Obool)), _1054613), _1054611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054609), _1054613)), hAPP(c_Finite__Set_Ocard(_1054609), _1054611))))], (36456 ^ _776541) ^ [_1465764, _1465766, _1465768, _1465770, _1465772] : [hBOOL(hAPP(hAPP(c_member(_1465764), _1465766), hAPP(c_Relation_OImage(_1465768, _1465764, _1465770), hAPP(hAPP(c_Set_Oinsert(_1465768), _1465772), c_Orderings_Obot__class_Obot(tc_fun(_1465768, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1465768, _1465764)), hAPP(hAPP(c_Product__Type_OPair(_1465768, _1465764), _1465772), _1465766)), _1465770)))], (22641 ^ _776541) ^ [_1186748, _1186750, _1186752] : [class_Power_Opower(_1186748), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186748), _1186750), hAPP(c_Nat_OSuc, _1186752)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186748), _1186750), hAPP(hAPP(c_Power_Opower__class_Opower(_1186748), _1186750), _1186752)))], (22153 ^ _776541) ^ [_1178290, _1178292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178290)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178290), _1178292)))], (9892 ^ _776541) ^ [_946015, _946017, _946019, _946021] : [class_Orderings_Olinorder(_946015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946015), _946017), _946019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946015), _946019), _946021)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946015, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_946015, _946017, _946019)), c_SetInterval_Oord__class_OatLeastAtMost(_946015, _946019, _946021)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_946015, _946017, _946021))], (41879 ^ _776541) ^ [_1603544, _1603546, _1603548, _1603550] : [hBOOL(hAPP(hAPP(c_member(_1603544), _1603546), c_Wellfounded_Oacc(_1603544, _1603548))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1603544)), _1603550), c_Wellfounded_Oacc(tc_List_Olist(_1603544), c_List_Olistrel1(_1603544, _1603548)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1603544)), hAPP(hAPP(c_List_Olist_OCons(_1603544), _1603546), _1603550)), c_Wellfounded_Oacc(tc_List_Olist(_1603544), c_List_Olistrel1(_1603544, _1603548)))))], (5528 ^ _776541) ^ [_860996, _860998] : [_860998 = _860996, -(c_Power_Opower__class_Opower(_860998) = c_Power_Opower__class_Opower(_860996))], (33240 ^ _776541) ^ [_1385733, _1385735, _1385737, _1385739] : [33242 ^ _776541 : [(33245 ^ _776541) ^ [] : [hAPP(_1385739, 33241 ^ [_1385733, _1385735, _1385737, _1385739]) = c_Orderings_Obot__class_Obot(tc_fun(_1385733, tc_HOL_Obool))], (33243 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1385735), 33241 ^ [_1385733, _1385735, _1385737, _1385739]), _1385737)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1385733, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385735, tc_fun(_1385733, tc_HOL_Obool)), _1385737), _1385739))], (16787 ^ _776541) ^ [_1078622, _1078624, _1078626] : [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, _1078622)), _1078624)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078622)), _1078626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078624), _1078626)))], (40615 ^ _776541) ^ [_1569659, _1569661] : [-(hAPP(c_Relation_ORange(_1569659, _1569659), c_Transitive__Closure_Otrancl(_1569659, _1569661)) = hAPP(c_Relation_ORange(_1569659, _1569659), _1569661))], (5286 ^ _776541) ^ [_857225, _857227, _857229, _857231, _857233, _857235] : [-(c_Lazy__Sequence_Obind(_857235, _857231, _857227) = c_Lazy__Sequence_Obind(_857233, _857229, _857225)), _857235 = _857233, _857231 = _857229, _857227 = _857225], (38903 ^ _776541) ^ [_1524631, _1524633, _1524635, _1524637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524631, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524631, _1524633), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1524631, _1524633), tc_HOL_Obool)), _1524635), _1524637))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524631, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524631, _1524633), _1524635)), hAPP(c_Relation_ODomain(_1524631, _1524633), _1524637)))))], (43028 ^ _776541) ^ [_1634131, _1634133, _1634135] : [-(_1634131 = c_List_Olist_ONil(_1634133)), -(c_List_Obutlast(_1634133, hAPP(hAPP(c_List_Olist_OCons(_1634133), _1634135), _1634131)) = hAPP(hAPP(c_List_Olist_OCons(_1634133), _1634135), c_List_Obutlast(_1634133, _1634131)))], (29497 ^ _776541) ^ [_1304856, _1304858, _1304860] : [class_Rings_Ocomm__semiring__1(_1304856), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1304856), _1304858), 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)))), _1304860)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304856), hAPP(hAPP(c_Power_Opower__class_Opower(_1304856), _1304858), _1304860)), hAPP(hAPP(c_Power_Opower__class_Opower(_1304856), _1304858), _1304860)))], (44593 ^ _776541) ^ [_1668359, _1668361, _1668363] : [_1668359 = c_List_Olist_ONil(_1668361), -(c_List_Olast(_1668361, hAPP(hAPP(c_List_Oappend(_1668361), _1668363), _1668359)) = c_List_Olast(_1668361, _1668363))], (43737 ^ _776541) ^ [_1649316, _1649318, _1649320] : [-(hBOOL(hAPP(c_List_Odistinct(_1649316), hAPP(hAPP(c_List_Oappend(_1649316), _1649318), _1649320)))), hBOOL(hAPP(c_List_Odistinct(_1649316), _1649318)), hBOOL(hAPP(c_List_Odistinct(_1649316), _1649320)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1649316, tc_HOL_Obool)), hAPP(c_List_Oset(_1649316), _1649318)), hAPP(c_List_Oset(_1649316), _1649320)) = c_Orderings_Obot__class_Obot(tc_fun(_1649316, tc_HOL_Obool))], (52245 ^ _776541) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52177 ^ _776541) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (35048 ^ _776541) ^ [_1430553, _1430555, _1430557, _1430559] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430553, _1430555), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430557), _1430559))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1430553), _1430555) = _1430557)], (34013 ^ _776541) ^ [_1407924] : [-(c_Finite__Set_Ofun__left__comm__idem(_1407924, tc_fun(_1407924, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1407924, tc_HOL_Obool), tc_fun(tc_fun(_1407924, tc_HOL_Obool), tc_fun(_1407924, tc_HOL_Obool)), _1407924), hAPP(c_COMBC(tc_fun(_1407924, tc_HOL_Obool), tc_fun(_1407924, tc_HOL_Obool), tc_fun(_1407924, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1407924, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1407924, tc_fun(_1407924, tc_HOL_Obool), tc_fun(_1407924, tc_HOL_Obool)), c_Set_Oinsert(_1407924)), c_Orderings_Obot__class_Obot(tc_fun(_1407924, tc_HOL_Obool))))))], (12878 ^ _776541) ^ [_1003757, _1003759, _1003761, _1003763, _1003765, _1003767] : [c_Finite__Set_Ofun__left__comm(_1003757, _1003759, _1003761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003757), _1003763)), -(hBOOL(hAPP(hAPP(c_member(_1003757), _1003765), _1003763))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1003757, _1003759, _1003761), _1003767), hAPP(hAPP(c_Set_Oinsert(_1003757), _1003765), _1003763)) = hAPP(hAPP(_1003761, _1003765), hAPP(hAPP(c_Finite__Set_Ofold(_1003757, _1003759, _1003761), _1003767), _1003763)))], (11948 ^ _776541) ^ [_986258, _986260, _986262, _986264, _986266] : [-(hAPP(c_Fun_Ofun__upd(_986258, _986260, _986262, _986264, _986266), _986264) = _986266)], (22989 ^ _776541) ^ [_1193061, _1193063, _1193065] : [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), _1193061), _1193063)), _1193065))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193065), _1193061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193063)))], (39335 ^ _776541) ^ [_1538109, _1538111] : [-(c_Product__Type_Oapsnd(_1538109, _1538109, _1538111, c_Fun_Oid(_1538109)) = c_Fun_Oid(tc_prod(_1538111, _1538109)))], (19891 ^ _776541) ^ [_1135405, _1135407, _1135409, _1135411] : [class_Fields_Olinordered__field__inverse__zero(_1135405), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135405), _1135407), _1135409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135405), _1135411), c_Groups_Ozero__class_Ozero(_1135405))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135405), c_Groups_Ozero__class_Ozero(_1135405)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135405), _1135407), _1135409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135405), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135405), _1135411), _1135407)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135405), _1135411), _1135409))))], (4122 ^ _776541) ^ [_838959, _838961, _838963, _838965] : [-(c_New__DSequence_Oneg__single(_838965, _838961) = c_New__DSequence_Oneg__single(_838963, _838959)), _838965 = _838963, _838961 = _838959], (8805 ^ _776541) ^ [_927835, _927837, _927839, _927841] : [class_Lattices_Odistrib__lattice(_927835), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927835), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927835), _927837), _927839)), _927841) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927835), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927835), _927837), _927841)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927835), _927839), _927841)))], (16172 ^ _776541) ^ [_1068856, _1068858] : [class_Groups_Olinordered__ab__group__add(_1068856), 16175 ^ _776541 : [(16182 ^ _776541) ^ [] : [_1068858 = c_Groups_Ozero__class_Ozero(_1068856), -(c_Groups_Ozero__class_Ozero(_1068856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068856), _1068858), _1068858))], (16176 ^ _776541) ^ [] : [c_Groups_Ozero__class_Ozero(_1068856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068856), _1068858), _1068858), -(_1068858 = c_Groups_Ozero__class_Ozero(_1068856))]]], (48550 ^ _776541) ^ [_1755091, _1755093, _1755095, _1755097, _1755099] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1755093, _1755091)), hAPP(hAPP(c_Product__Type_OPair(_1755093, _1755091), _1755097), _1755099)), hAPP(c_Relation_Oconverse(_1755091, _1755093), _1755095))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1755091, _1755093, hAPP(hAPP(c_COMBC(_1755091, tc_fun(tc_prod(_1755091, _1755093), tc_HOL_Obool), tc_fun(_1755093, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1755093, tc_fun(tc_fun(tc_prod(_1755091, _1755093), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1755091, _1755093), tc_HOL_Obool), tc_fun(_1755093, tc_HOL_Obool)), _1755091), c_COMBC(_1755093, tc_fun(tc_prod(_1755091, _1755093), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1755093, tc_prod(_1755091, _1755093)), tc_fun(_1755093, tc_fun(tc_fun(tc_prod(_1755091, _1755093), tc_HOL_Obool), tc_HOL_Obool)), _1755091), hAPP(c_COMBB(tc_prod(_1755091, _1755093), tc_fun(tc_fun(tc_prod(_1755091, _1755093), tc_HOL_Obool), tc_HOL_Obool), _1755093), c_member(tc_prod(_1755091, _1755093)))), c_Product__Type_OPair(_1755091, _1755093)))), _1755095)), _1755097), _1755099)))], (16128 ^ _776541) ^ [_1068093, _1068095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068093), hAPP(c_Nat_OSuc, _1068095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068093), _1068095))), -(_1068093 = hAPP(c_Nat_OSuc, _1068095))], (34656 ^ _776541) ^ [_1422101, _1422103] : [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), _1422101))), 34659 ^ _776541 : [(34666 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422103)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422101)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422103), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422101)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422101)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422103), 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), _1422101)))))], (34660 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422103)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422101))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422103), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422101)) = 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), _1422103)))]]], (39745 ^ _776541) ^ [_1548916, _1548918] : [class_Complete__Lattice_Ocomplete__lattice(_1548916), -(c_Complete__Lattice_OInf__class_OInf(_1548916, _1548918) = c_Complete__Lattice_OSup__class_OSup(_1548916, hAPP(c_Set_OCollect(_1548916), hAPP(hAPP(c_COMBB(tc_fun(_1548916, tc_HOL_Obool), tc_HOL_Obool, _1548916), c_HOL_OAll(_1548916)), hAPP(hAPP(c_COMBB(tc_fun(_1548916, tc_HOL_Obool), tc_fun(_1548916, tc_HOL_Obool), _1548916), hAPP(c_COMBS(_1548916, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548916), c_fimplies), hAPP(hAPP(c_COMBC(_1548916, tc_fun(_1548916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548916)), _1548918)))), c_Orderings_Oord__class_Oless__eq(_1548916))))))], (40941 ^ _776541) ^ [] : [-(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))))], (11360 ^ _776541) ^ [_974424, _974426, _974428, _974430, _974432] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974424, _974426, hAPP(hAPP(c_Set_Oinsert(_974424), _974428), _974430)), _974432)), 11365 ^ _776541 : [(11370 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974424), 11363 ^ [_974424, _974426, _974428, _974430, _974432]), 11364 ^ [_974424, _974426, _974428, _974430, _974432]))], (11368 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974424, _974424, _974426, 11363 ^ [_974424, _974426, _974428, _974430, _974432], 11364 ^ [_974424, _974426, _974428, _974430, _974432]), _974432)))], (11366 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_974424), _974428), _974430) = hAPP(hAPP(c_Set_Oinsert(_974424), 11363 ^ [_974424, _974426, _974428, _974430, _974432]), 11364 ^ [_974424, _974426, _974428, _974430, _974432]))]]], (19372 ^ _776541) ^ [_1126303] : [class_Rings_Oring__1(_1126303), -(hBOOL(hAPP(hAPP(c_member(_1126303), c_Groups_Oone__class_Oone(_1126303)), c_Int_Oring__1__class_OInts(_1126303))))], (15111 ^ _776541) ^ [_1049337, _1049339, _1049341] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049337), _1049339)), 15114 ^ _776541 : [(15115 ^ _776541) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049337, tc_Nat_Onat), _1049341), _1049339) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 15118 ^ _776541 : [(15119 ^ _776541) ^ [_1049499] : [hBOOL(hAPP(hAPP(c_member(_1049337), _1049499), _1049339)), -(hAPP(_1049341, _1049499) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (15125 ^ _776541) ^ [] : [15127 ^ _776541 : [(15130 ^ _776541) ^ [] : [hAPP(_1049341, 15126 ^ [_1049337, _1049339, _1049341]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (15128 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049337), 15126 ^ [_1049337, _1049339, _1049341]), _1049339)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049337, tc_Nat_Onat), _1049341), _1049339) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (28355 ^ _776541) ^ [_1285539, _1285541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285539), _1285541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285539)), c_Int_OBit1(_1285541))))], (38537 ^ _776541) ^ [_1515560, _1515562, _1515564, _1515566] : [hBOOL(hAPP(hAPP(c_member(_1515560), _1515562), hAPP(c_Relation_ORange(_1515564, _1515560), _1515566))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515564, _1515560)), hAPP(hAPP(c_Product__Type_OPair(_1515564, _1515560), 38540 ^ [_1515560, _1515562, _1515564, _1515566]), _1515562)), _1515566)))], (5610 ^ _776541) ^ [_862187, _862189, _862191, _862193] : [-(c_COMBK(_862193, _862189) = c_COMBK(_862191, _862187)), _862193 = _862191, _862189 = _862187], (10835 ^ _776541) ^ [_963372, _963374, _963376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963372, tc_HOL_Obool)), _963374), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_963372, tc_HOL_Obool)), _963376))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963372, tc_HOL_Obool)), _963374), _963376) = c_Orderings_Obot__class_Obot(tc_fun(_963372, tc_HOL_Obool)))], (44864 ^ _776541) ^ [_1674116, _1674118, _1674120, _1674122, _1674124, _1674126] : [-(hAPP(hAPP(c_List_Ozip(_1674116, _1674118), _1674120), hAPP(hAPP(c_List_Omap(_1674122, _1674118), _1674124), _1674126)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674116, _1674122), tc_prod(_1674116, _1674118)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674116, _1674122, tc_prod(_1674116, _1674118)), hAPP(hAPP(c_COMBC(_1674116, tc_fun(_1674122, _1674118), tc_fun(_1674122, tc_prod(_1674116, _1674118))), hAPP(hAPP(c_COMBB(tc_fun(_1674118, tc_prod(_1674116, _1674118)), tc_fun(tc_fun(_1674122, _1674118), tc_fun(_1674122, tc_prod(_1674116, _1674118))), _1674116), c_COMBB(_1674118, tc_prod(_1674116, _1674118), _1674122)), c_Product__Type_OPair(_1674116, _1674118))), _1674124))), hAPP(hAPP(c_List_Ozip(_1674116, _1674122), _1674120), _1674126)))], (14532 ^ _776541) ^ [_1038599, _1038601, _1038603] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038599), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038601), _1038603)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038599), _1038603)))], (45132 ^ _776541) ^ [_1680434, _1680436, _1680438] : [-(c_List_Olist_Olist__size(_1680434, _1680436, _1680438) = 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(_1680434, tc_Nat_Onat), _1680436), _1680438))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680434)), _1680438)))], (23187 ^ _776541) ^ [_1196520, _1196522, _1196524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196520)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196522), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1196524)), 23194 ^ _776541 : [(23195 ^ _776541) ^ [_1196728] : [23197 ^ _776541 : [(23203 ^ _776541) ^ [] : [-(_1196728 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23199 ^ [_1196520, _1196522, _1196524, _1196728]), 23196 ^ [_1196520, _1196522, _1196524, _1196728]))], (23201 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23199 ^ [_1196520, _1196522, _1196524, _1196728]), _1196524)))], (23198 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23196 ^ [_1196520, _1196522, _1196524, _1196728]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1196520))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196728), _1196522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196728), _1196520)), _1196522)))]]], (7786 ^ _776541) ^ [_907346, _907348, _907350, _907352] : [hBOOL(hAPP(hAPP(c_member(_907346), _907348), _907350)), -(hBOOL(hAPP(hAPP(c_member(_907346), _907348), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907346, tc_HOL_Obool)), _907352), _907350))))], (14398 ^ _776541) ^ [_1036447, _1036449, _1036451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036447), _1036449)), _1036451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036447), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036451), _1036449))))], (50485 ^ _776541) ^ [_1797166, _1797168, _1797170] : [_1797168 = _1797170, -(c_Fun_Obij__betw(_1797166, _1797166, c_Fun_Oid(_1797166), _1797168, _1797170))], (7650 ^ _776541) ^ [_903638, _903640, _903642, _903644] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903638, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903638, tc_HOL_Obool)), _903640), _903642)), _903644) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903638, tc_HOL_Obool)), _903640), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903638, tc_HOL_Obool)), _903642), _903644)))], (46940 ^ _776541) ^ [_1719840, _1719842, _1719844, _1719846] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719840), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719840))), _1719842))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719844), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719840))), c_List_Otranspose(_1719840, _1719842)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719846), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719840))), hAPP(c_List_Ofilter(tc_List_Olist(_1719840), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1719840)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719844)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719840)))), _1719842)))), -(hAPP(hAPP(c_List_Onth(_1719840), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719840)), c_List_Otranspose(_1719840, _1719842)), _1719844)), _1719846) = hAPP(hAPP(c_List_Onth(_1719840), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719840)), _1719842), _1719846)), _1719844))], (31747 ^ _776541) ^ [_1346977, _1346979, _1346981, _1346983] : [class_Orderings_Olinorder(_1346977), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346977, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1346977), _1346979)), c_SetInterval_Oord__class_OatLeastAtMost(_1346977, _1346981, _1346983)) = c_SetInterval_Oord__class_OatLeastAtMost(_1346977, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346977), _1346979), _1346981), _1346983))], (52205 ^ _776541) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (39681 ^ _776541) ^ [_1547099, _1547101] : [39683 ^ _776541 : [(39686 ^ _776541) ^ [] : [hBOOL(hAPP(_1547099, hAPP(c_Int_OAbs__Integ, 39682 ^ [_1547099, _1547101])))], (39684 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39682 ^ [_1547099, _1547101]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1547099, _1547101)))], (2814 ^ _776541) ^ [_818215, _818217, _818219, _818221, _818223, _818225, _818227, _818229] : [-(c_Product__Type_Oapfst(_818229, _818225, _818221, _818217) = c_Product__Type_Oapfst(_818227, _818223, _818219, _818215)), _818229 = _818227, _818225 = _818223, _818221 = _818219, _818217 = _818215], (12197 ^ _776541) ^ [_990645, _990647, _990649] : [class_Lattices_Olattice(_990645), hBOOL(hAPP(c_Finite__Set_Ofinite(_990645), _990647)), -(_990647 = c_Orderings_Obot__class_Obot(tc_fun(_990645, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_990645), _990649)), -(_990649 = c_Orderings_Obot__class_Obot(tc_fun(_990645, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_990645, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_990645, tc_HOL_Obool)), _990647), _990649)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_990645), c_Big__Operators_Olattice__class_OSup__fin(_990645, _990647)), c_Big__Operators_Olattice__class_OSup__fin(_990645, _990649)))], (12023 ^ _776541) ^ [_987868, _987870] : [class_Lattices_Olattice(_987868), -(c_Big__Operators_Olattice__class_OInf__fin(_987868, hAPP(hAPP(c_Set_Oinsert(_987868), _987870), c_Orderings_Obot__class_Obot(tc_fun(_987868, tc_HOL_Obool)))) = _987870)], (38219 ^ _776541) ^ [_1508395, _1508397, _1508399, _1508401] : [c_Wellfounded_Owf(_1508395, _1508397), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508395, _1508395)), hAPP(hAPP(c_Product__Type_OPair(_1508395, _1508395), _1508399), _1508401)), _1508397)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508395, _1508395)), hAPP(hAPP(c_Product__Type_OPair(_1508395, _1508395), _1508401), _1508399)), _1508397))], (37814 ^ _776541) ^ [_1497350, _1497352] : [37815 ^ _776541 : [(37816 ^ _776541) ^ [_1497414, _1497416] : [_1497352 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1497350, _1497414), 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)), _1497416)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497350), _1497352)))], (10104 ^ _776541) ^ [_949504, _949506, _949508, _949510] : [class_Orderings_Oorder(_949504), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949504, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949504, _949506, _949508)), c_SetInterval_Oord__class_OgreaterThanLessThan(_949504, _949508, _949510)) = c_Orderings_Obot__class_Obot(tc_fun(_949504, tc_HOL_Obool)))], (1284 ^ _776541) ^ [_795455, _795457] : [-(class_Groups_Osgn__if(_795455)), _795457 = _795455, class_Groups_Osgn__if(_795457)], (41449 ^ _776541) ^ [_1590736, _1590738, _1590740, _1590742] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590736, _1590736)), hAPP(hAPP(c_Product__Type_OPair(_1590736, _1590736), _1590738), _1590740)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590736, _1590736), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590742))), -(_1590738 = _1590740)], (14600 ^ _776541) ^ [_1039765, _1039767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039765), _1039767)), _1039765))], (41092 ^ _776541) ^ [_1582221, _1582223, _1582225, _1582227, _1582229] : [-(hAPP(c_Relation_Oconverse(_1582221, _1582223), hAPP(hAPP(c_Relation_Orel__comp(_1582221, _1582225, _1582223), _1582227), _1582229)) = hAPP(hAPP(c_Relation_Orel__comp(_1582223, _1582225, _1582221), hAPP(c_Relation_Oconverse(_1582225, _1582223), _1582229)), hAPP(c_Relation_Oconverse(_1582221, _1582225), _1582227)))], (52455 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (10729 ^ _776541) ^ [_961426, _961428, _961430] : [class_Orderings_Oorder(_961426), 10732 ^ _776541 : [(10739 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961426), _961428), _961430))), -(c_Orderings_Obot__class_Obot(tc_fun(_961426, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961426, _961428), _961430))], (10733 ^ _776541) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_961426, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961426, _961428), _961430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961426), _961428), _961430))]]], (38300 ^ _776541) ^ [_1510157, _1510159, _1510161] : [c_Wellfounded_Owf(_1510157, _1510159), c_Wellfounded_Owf(_1510157, _1510161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510157, _1510157), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510157, _1510157, _1510157), _1510159), _1510161)), _1510159)), -(c_Wellfounded_Owf(_1510157, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510157, _1510157), tc_HOL_Obool)), _1510159), _1510161)))], (34824 ^ _776541) ^ [_1426380, _1426382, _1426384, _1426386, _1426388, _1426390] : [hAPP(hAPP(c_Product__Type_OPair(_1426380, _1426382), _1426384), _1426386) = hAPP(hAPP(c_Product__Type_OPair(_1426380, _1426382), _1426388), _1426390), 34827 ^ _776541 : [(34830 ^ _776541) ^ [] : [-(_1426386 = _1426390)], (34828 ^ _776541) ^ [] : [-(_1426384 = _1426388)]]], (48412 ^ _776541) ^ [_1751620, _1751622, _1751624, _1751626, _1751628] : [_1751620 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1751622, _1751624, _1751626, _1751628), _1751620) = c_Lazy__Sequence_Ohit__bound(_1751624))], (18304 ^ _776541) ^ [_1105720, _1105722, _1105724, _1105726] : [class_Rings_Olinordered__semiring__strict(_1105720), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105720), _1105722), _1105724)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105720), _1105722), _1105726))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105720), c_Groups_Ozero__class_Ozero(_1105720)), _1105722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105720), _1105724), _1105726)))], (45922 ^ _776541) ^ [_1697688] : [-(c_List_Oconcat(_1697688, c_List_Olist_ONil(tc_List_Olist(_1697688))) = c_List_Olist_ONil(_1697688))], (47975 ^ _776541) ^ [_1742855, _1742857] : [class_Enum_Oenum(_1742855), 47978 ^ _776541 : [(47986 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742855), _1742857)), 47989 ^ _776541 : [(47990 ^ _776541) ^ [_1743073] : [-(hBOOL(hAPP(_1742857, _1743073)))]]], (47979 ^ _776541) ^ [] : [hBOOL(hAPP(_1742857, 47980 ^ [_1742855, _1742857])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742855), _1742857)))]]], (45782 ^ _776541) ^ [_1695113, _1695115] : [c_List_Oremdups(_1695113, _1695115) = _1695115, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695113)), c_List_Oremdups(_1695113, _1695115)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695113)), _1695115))], (46026 ^ _776541) ^ [_1700560, _1700562, _1700564] : [-(c_Enum_On__lists(_1700560, hAPP(c_Nat_OSuc, _1700562), _1700564) = c_List_Oconcat(tc_List_Olist(_1700560), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700560), tc_List_Olist(tc_List_Olist(_1700560))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700560), tc_List_Olist(_1700560), tc_List_Olist(tc_List_Olist(_1700560))), hAPP(hAPP(c_COMBB(tc_fun(_1700560, tc_List_Olist(_1700560)), tc_fun(tc_List_Olist(_1700560), tc_List_Olist(tc_List_Olist(_1700560))), tc_List_Olist(_1700560)), c_List_Omap(_1700560, tc_List_Olist(_1700560))), hAPP(c_COMBC(_1700560, tc_List_Olist(_1700560), tc_List_Olist(_1700560)), c_List_Olist_OCons(_1700560)))), _1700564)), c_Enum_On__lists(_1700560, _1700562, _1700564))))], (43510 ^ _776541) ^ [_1644246, _1644248, _1644250, _1644252, _1644254] : [hAPP(hAPP(c_List_Oappend(_1644246), _1644248), _1644250) = hAPP(hAPP(c_List_Oappend(_1644246), _1644252), _1644254), 43516 ^ _776541 : [(43519 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1644246), 43513 ^ [_1644246, _1644248, _1644250, _1644252, _1644254]), _1644250) = _1644254)], (43517 ^ _776541) ^ [] : [-(_1644248 = hAPP(hAPP(c_List_Oappend(_1644246), _1644252), 43513 ^ [_1644246, _1644248, _1644250, _1644252, _1644254]))]], 43520 ^ _776541 : [(43523 ^ _776541) ^ [] : [-(_1644250 = hAPP(hAPP(c_List_Oappend(_1644246), 43513 ^ [_1644246, _1644248, _1644250, _1644252, _1644254]), _1644254))], (43521 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1644246), _1644248), 43513 ^ [_1644246, _1644248, _1644250, _1644252, _1644254]) = _1644252)]]], (6983 ^ _776541) ^ [_889991, _889993, _889995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889991, tc_HOL_Obool)), _889993), _889995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_889991, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_889991), _889993)), hAPP(c_Set_OPow(_889991), _889995))))], (37016 ^ _776541) ^ [_1479935, _1479937] : [c_Equiv__Relations_Oequivp(_1479935, _1479937), 37019 ^ _776541 : [(37026 ^ _776541) ^ [_1480128, _1480130] : [hAPP(_1479937, _1480130) = hAPP(_1479937, _1480128), -(hBOOL(hAPP(hAPP(_1479937, _1480130), _1480128)))], (37020 ^ _776541) ^ [_1480029, _1480031] : [hBOOL(hAPP(hAPP(_1479937, _1480031), _1480029)), -(hAPP(_1479937, _1480031) = hAPP(_1479937, _1480029))]]], (3388 ^ _776541) ^ [_827128, _827130, _827132, _827134] : [-(c_HOL_OLet(_827134, _827130) = c_HOL_OLet(_827132, _827128)), _827134 = _827132, _827130 = _827128], (27795 ^ _776541) ^ [_1276363] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276363), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276363), c_Int_OPls)))], (6450 ^ _776541) ^ [_880802, _880804] : [-(hBOOL(hAPP(hAPP(c_member(_880802), 6451 ^ [_880802, _880804]), _880804))), -(_880804 = c_Orderings_Obot__class_Obot(tc_fun(_880802, tc_HOL_Obool)))], (52363 ^ _776541) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (29391 ^ _776541) ^ [_1303230, _1303232, _1303234] : [class_Rings_Olinordered__semidom(_1303230), hAPP(hAPP(c_Power_Opower__class_Opower(_1303230), _1303232), 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(_1303230), _1303234), 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(_1303230), c_Groups_Ozero__class_Ozero(_1303230)), _1303232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303230), c_Groups_Ozero__class_Ozero(_1303230)), _1303234)), -(_1303232 = _1303234)], (18162 ^ _776541) ^ [_1103016, _1103018, _1103020, _1103022, _1103024, _1103026, _1103028] : [c_Finite__Set_Ofolding__image__simple(_1103016, _1103018, _1103020, _1103022, _1103024, _1103026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1103018), _1103028)), -(hAPP(_1103026, _1103028) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1103016, _1103018, _1103020), _1103024), _1103022), _1103028))], (49319 ^ _776541) ^ [_1772183, _1772185] : [c_Relation_Otrans(_1772183, _1772185), -(c_Relation_Otrans(_1772183, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1772183, _1772183), tc_HOL_Obool)), _1772185), c_Relation_OId(_1772183))))], (43222 ^ _776541) ^ [_1637721, _1637723] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1637721), _1637723))), -(c_List_Oupto(_1637721, _1637723) = c_List_Olist_ONil(tc_Int_Oint))], (9652 ^ _776541) ^ [_941779, _941781, _941783, _941785] : [class_Orderings_Opreorder(_941779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941779), _941781), _941783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941779), _941783), _941785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941779), _941781), _941785)))], (13714 ^ _776541) ^ [_1020810, _1020812, _1020814, _1020816] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020810), _1020812), _1020814)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020810), _1020816), _1020814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020810), _1020812), _1020816)))], (27148 ^ _776541) ^ [_1265234] : [c_Nat__Transfer_Onat__set(_1265234), 27151 ^ _776541 : [(27158 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265234))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1265234)))], (27152 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1265234)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265234))))]]], (49712 ^ _776541) ^ [_1781335, _1781337] : [c_Relation_Osym(_1781335, _1781337), -(c_Relation_Osym(tc_List_Olist(_1781335), c_List_Olistrel(_1781335, _1781337)))], (49086 ^ _776541) ^ [_1766559, _1766561, _1766563] : [c_List_Oall__interval__int(_1766559, _1766561, _1766563), 49089 ^ _776541 : [(49090 ^ _776541) ^ [_1766637] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1766637), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1766561, _1766563))), -(hBOOL(hAPP(_1766559, _1766637)))]]], (10917 ^ _776541) ^ [_965018, _965020, _965022, _965024] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_965018, _965020, hAPP(hAPP(c_Set_Oinsert(_965018), _965022), c_Orderings_Obot__class_Obot(tc_fun(_965018, tc_HOL_Obool)))), _965024)), -(_965022 = _965024)], (40979 ^ _776541) ^ [_1579191, _1579193, _1579195, _1579197] : [c_Wellfounded_Owf(_1579191, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579191, _1579191)), hAPP(hAPP(c_Product__Type_OPair(_1579191, _1579191), _1579193), _1579195)), _1579197)), 40982 ^ _776541 : [(40985 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579191, _1579191)), hAPP(hAPP(c_Product__Type_OPair(_1579191, _1579191), _1579195), _1579193)), c_Transitive__Closure_Ortrancl(_1579191, _1579197)))], (40983 ^ _776541) ^ [] : [-(c_Wellfounded_Owf(_1579191, _1579197))]]], (25865 ^ _776541) ^ [_1244366, _1244368] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1244366), _1244368) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244366, _1244368)), _1244368))], (15808 ^ _776541) ^ [_1062926, _1062928] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1062926), _1062928)), 15809 ^ _776541 : [(15816 ^ _776541) ^ [] : [_1062926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1062928 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15810 ^ _776541) ^ [] : [_1062926 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062928 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (11302 ^ _776541) ^ [_972992, _972994, _972996, _972998, _973000] : [class_Groups_Oab__semigroup__mult(_972992), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_972992, _972992, c_Groups_Otimes__class_Otimes(_972992), _972994, _972996), _972998)), -(hBOOL(hAPP(hAPP(c_member(_972992), _972994), _972996))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_972992, _972992, c_Groups_Otimes__class_Otimes(_972992), _973000, hAPP(hAPP(c_Set_Oinsert(_972992), _972994), _972996)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972992), _973000), _972998))))], (44729 ^ _776541) ^ [_1670778] : [-(hAPP(c_List_Omap(_1670778, _1670778), c_COMBI(_1670778)) = c_Fun_Oid(tc_List_Olist(_1670778)))], (25169 ^ _776541) ^ [_1232243, _1232245, _1232247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232243)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232243), _1232245)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232243), _1232247)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232245), _1232247))], (8157 ^ _776541) ^ [_915689, _915691] : [class_Orderings_Oorder(_915689), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915689, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915689), _915691), c_Orderings_Obot__class_Obot(tc_fun(_915689, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_915689), _915691)) = hAPP(hAPP(c_Set_Oinsert(_915689), _915691), c_Orderings_Obot__class_Obot(tc_fun(_915689, tc_HOL_Obool))))], (46409 ^ _776541) ^ [_1709815, _1709817] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1709815, _1709817) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1709815), _1709817)))], (38619 ^ _776541) ^ [_1518327, _1518329, _1518331, _1518333] : [hBOOL(hAPP(c_Predicate_ORangeP(_1518327, _1518329, _1518331), _1518333)), -(hBOOL(hAPP(hAPP(_1518331, 38622 ^ [_1518327, _1518329, _1518331, _1518333]), _1518333)))], (9348 ^ _776541) ^ [_937359, _937361, _937363, _937365, _937367] : [class_Groups_Oordered__ab__group__add(_937359), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937359), _937361), _937363) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937359), _937365), _937367), 9355 ^ _776541 : [(9362 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937359), _937365), _937367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937359), _937361), _937363)))], (9356 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937359), _937361), _937363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937359), _937365), _937367)))]]], (35586 ^ _776541) ^ [_1440694, _1440696, _1440698, _1440700] : [_1440694 = _1440696, 35589 ^ _776541 : [(35592 ^ _776541) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1440698, _1440700), _1440694) = hAPP(c_Product__Type_Osnd(_1440698, _1440700), _1440696))], (35590 ^ _776541) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1440698, _1440700), _1440694) = hAPP(c_Product__Type_Ofst(_1440698, _1440700), _1440696))]]], (38668 ^ _776541) ^ [_1519364, _1519366, _1519368, _1519370, _1519372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519364, _1519366)), hAPP(hAPP(c_Product__Type_OPair(_1519364, _1519366), _1519368), _1519370)), _1519372)), -(hBOOL(hAPP(hAPP(c_member(_1519364), _1519368), hAPP(c_Relation_ODomain(_1519364, _1519366), _1519372))))], (33887 ^ _776541) ^ [_1404489] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1404489) = 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), _1404489), c_Int_Onat)))))], (8133 ^ _776541) ^ [_915173, _915175, _915177] : [-(hBOOL(hAPP(hAPP(c_member(_915173), _915175), _915177))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915173, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915173), _915175), _915177)), hAPP(hAPP(c_Set_Oinsert(_915173), _915175), c_Orderings_Obot__class_Obot(tc_fun(_915173, tc_HOL_Obool)))) = _915177)], (26591 ^ _776541) ^ [_1256508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1256508)), -(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, _1256508))))], (32456 ^ _776541) ^ [_1360902, _1360904, _1360906, _1360908, _1360910] : [-(_1360902 = c_Orderings_Obot__class_Obot(tc_fun(_1360904, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360904, tc_fun(_1360906, tc_HOL_Obool)), _1360902), hAPP(hAPP(c_COMBC(_1360904, tc_fun(_1360906, tc_HOL_Obool), tc_fun(_1360906, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360906, tc_HOL_Obool), tc_fun(tc_fun(_1360906, tc_HOL_Obool), tc_fun(_1360906, tc_HOL_Obool)), _1360904), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360906, tc_HOL_Obool))), _1360908)), _1360910)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360906, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360904, tc_fun(_1360906, tc_HOL_Obool)), _1360902), _1360908)), _1360910))], (39337 ^ _776541) ^ [_1538146, _1538148] : [-(hAPP(c_Fun_Oid(_1538146), _1538148) = _1538148)], (36974 ^ _776541) ^ [_1478797, _1478799] : [c_Equiv__Relations_Oequiv(_1478797, c_Orderings_Otop__class_Otop(tc_fun(_1478797, tc_HOL_Obool)), _1478799), -(c_Equiv__Relations_Oequivp(_1478797, hAPP(hAPP(c_COMBC(_1478797, tc_fun(tc_prod(_1478797, _1478797), tc_HOL_Obool), tc_fun(_1478797, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478797, tc_fun(tc_fun(tc_prod(_1478797, _1478797), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1478797, _1478797), tc_HOL_Obool), tc_fun(_1478797, tc_HOL_Obool)), _1478797), c_COMBC(_1478797, tc_fun(tc_prod(_1478797, _1478797), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478797, tc_prod(_1478797, _1478797)), tc_fun(_1478797, tc_fun(tc_fun(tc_prod(_1478797, _1478797), tc_HOL_Obool), tc_HOL_Obool)), _1478797), hAPP(c_COMBB(tc_prod(_1478797, _1478797), tc_fun(tc_fun(tc_prod(_1478797, _1478797), tc_HOL_Obool), tc_HOL_Obool), _1478797), c_member(tc_prod(_1478797, _1478797)))), c_Product__Type_OPair(_1478797, _1478797)))), _1478799)))], (35614 ^ _776541) ^ [_1441217, _1441219, _1441221] : [-(hAPP(c_Product__Type_Ofst(_1441217, _1441219), _1441221) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441217, _1441219, _1441217), c_COMBK(_1441217, _1441219)), _1441221))], (43922 ^ _776541) ^ [_1654251, _1654253, _1654255] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654251, tc_HOL_Obool)), hAPP(c_List_Oset(_1654251), hAPP(hAPP(c_List_Odrop(_1654251), _1654253), _1654255))), hAPP(c_List_Oset(_1654251), _1654255))))], (14202 ^ _776541) ^ [_1031992] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1031992))))], (50103 ^ _776541) ^ [_1788775, _1788777, _1788779, _1788781] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1788775, _1788777, c_Orderings_Otop__class_Otop(tc_fun(_1788775, tc_HOL_Obool)), _1788779), _1788781) = c_Hilbert__Choice_OEps(_1788775, hAPP(hAPP(c_COMBC(_1788775, _1788777, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1788777, tc_fun(_1788777, tc_HOL_Obool), _1788775), c_fequal), _1788779)), _1788781)))], (47162 ^ _776541) ^ [_1724675, _1724677, _1724679] : [class_Orderings_Olinorder(_1724675), c_List_Olinorder__class_Osorted(_1724675, hAPP(c_List_Orev(_1724675), _1724677)), 47169 ^ _776541 : [(47176 ^ _776541) ^ [] : [-(_1724677 = c_List_Olist_ONil(_1724675)), -(c_List_Ofoldr(_1724675, _1724675, c_Orderings_Oord__class_Omax(_1724675), _1724677, _1724679) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1724675), hAPP(hAPP(c_List_Onth(_1724675), _1724677), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1724679))], (47170 ^ _776541) ^ [] : [_1724677 = c_List_Olist_ONil(_1724675), -(c_List_Ofoldr(_1724675, _1724675, c_Orderings_Oord__class_Omax(_1724675), _1724677, _1724679) = _1724679)]]], (52001 ^ _776541) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (46215 ^ _776541) ^ [_1705728, _1705730] : [-(c_Random_Opick(_1705728, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1705728), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1705728, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1705728, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1705728)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1705730)) = c_Random_Opick(_1705728, _1705730))], (48558 ^ _776541) ^ [_1755597, _1755599, _1755601] : [-(_1755597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1755599), c_List_Oreplicate(_1755599, _1755597, _1755601)) = c_List_Oreplicate(_1755599, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1755597), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1755601))], (49986 ^ _776541) ^ [_1786154, _1786156, _1786158] : [c_Fun_Oinj__on(_1786154, _1786156, _1786158, c_Orderings_Otop__class_Otop(tc_fun(_1786154, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1786156, _1786154, _1786154, c_Hilbert__Choice_Oinv__into(_1786154, _1786156, c_Orderings_Otop__class_Otop(tc_fun(_1786154, tc_HOL_Obool)), _1786158)), _1786158) = c_Fun_Oid(_1786154))], (1874 ^ _776541) ^ [_802830, _802832] : [-(class_Int_Onumber(_802830)), _802832 = _802830, class_Int_Onumber(_802832)], (7226 ^ _776541) ^ [_894365, _894367, _894369] : [c_Orderings_Obot__class_Obot(tc_fun(_894365, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_894365), _894367), _894369)], (11184 ^ _776541) ^ [_970331, _970333, _970335, _970337, _970339] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970331, tc_HOL_Obool)), _970333), hAPP(c_Set_Oimage(_970335, _970331, _970337), _970339)))), 11185 ^ _776541 : [(11186 ^ _776541) ^ [_970411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970335, tc_HOL_Obool)), _970411), _970339)), _970333 = hAPP(c_Set_Oimage(_970335, _970331, _970337), _970411)]]], (210 ^ _776541) ^ [_779938, _779940, _779942, _779944] : [-(c_Int_Oiszero(_779942, _779938)), c_Int_Oiszero(_779944, _779940), _779944 = _779942, _779940 = _779938], (30784 ^ _776541) ^ [_1328696, _1328698, _1328700] : [class_Orderings_Olinorder(_1328696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328696), _1328698)), -(_1328700 = c_Orderings_Obot__class_Obot(tc_fun(_1328696, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328696, tc_HOL_Obool)), _1328700), _1328698)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328696), c_Big__Operators_Olinorder__class_OMin(_1328696, _1328700)), c_Big__Operators_Olinorder__class_OMin(_1328696, _1328698)) = c_Big__Operators_Olinorder__class_OMin(_1328696, _1328698))], (12726 ^ _776541) ^ [_1000976, _1000978, _1000980, _1000982] : [class_Lattices_Osemilattice__inf(_1000976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000976), _1000978)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1000976, _1000976, c_Lattices_Osemilattice__inf__class_Oinf(_1000976)), _1000980), hAPP(hAPP(c_Set_Oinsert(_1000976), _1000982), _1000978)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1000976), _1000982), hAPP(hAPP(c_Finite__Set_Ofold(_1000976, _1000976, c_Lattices_Osemilattice__inf__class_Oinf(_1000976)), _1000980), _1000978)))], (7418 ^ _776541) ^ [_898589, _898591, _898593] : [class_Orderings_Oorder(_898589), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_898589, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_898589, _898591, _898593)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_898589), _898593)) = c_Orderings_Obot__class_Obot(tc_fun(_898589, tc_HOL_Obool)))], (46472 ^ _776541) ^ [_1711352, _1711354] : [class_Orderings_Olinorder(_1711352), -(c_List_Olinorder__class_Osorted(_1711352, hAPP(hAPP(c_List_Olist_OCons(_1711352), _1711354), c_List_Olist_ONil(_1711352))))], (27447 ^ _776541) ^ [_1270125, _1270127, _1270129, _1270131, _1270133] : [class_Rings_Olinordered__idom(_1270125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270125), hAPP(c_Groups_Oabs__class_Oabs(_1270125), _1270127)), _1270129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270125), hAPP(c_Groups_Oabs__class_Oabs(_1270125), _1270131)), _1270133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270125), hAPP(c_Groups_Oabs__class_Oabs(_1270125), _1270127)), hAPP(c_Groups_Oabs__class_Oabs(_1270125), _1270131))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270125), _1270129), _1270133))))], (7140 ^ _776541) ^ [_892910, _892912, _892914, _892916] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_892910), _892912), _892914), _892916)), -(_892912 = _892916), -(hBOOL(hAPP(_892914, _892916)))], (40389 ^ _776541) ^ [_1563985, _1563987, _1563989] : [40390 ^ _776541 : [(40391 ^ _776541) ^ [_1564039] : [hBOOL(hAPP(_1563985, _1564039))]], _1563987 = c_Hilbert__Choice_OEps(_1563989, _1563985), -(hBOOL(hAPP(_1563985, _1563987)))], (16598 ^ _776541) ^ [_1075107] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1075107)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1075107), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1075107)))], (28289 ^ _776541) ^ [_1284470] : [c_Int_OMin = c_Int_OBit1(_1284470), -(c_Int_OMin = _1284470)], (21395 ^ _776541) ^ [_1164127, _1164129, _1164131, _1164133] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164127), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164127), _1164129), _1164131)), hAPP(c_Int_Onumber__class_Onumber__of(_1164127), _1164133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164127), _1164129), hAPP(c_Int_Onumber__class_Onumber__of(_1164127), _1164133))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164127), _1164131), hAPP(c_Int_Onumber__class_Onumber__of(_1164127), _1164133)))), class_Int_Onumber(_1164127), class_Rings_Oring(_1164127)], (44230 ^ _776541) ^ [_1660988, _1660990, _1660992] : [-(hAPP(c_List_Otl(_1660988), hAPP(hAPP(c_List_Otake(_1660988), _1660990), _1660992)) = hAPP(hAPP(c_List_Otake(_1660988), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1660990), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1660988), _1660992)))], (43282 ^ _776541) ^ [_1638823, _1638825] : [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), _1638823), _1638825))), 43285 ^ _776541 : [(43292 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1638823), _1638825))), -(c_List_Oupto(_1638823, _1638825) = c_List_Olist_ONil(tc_Int_Oint))], (43286 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1638823), _1638825)), -(c_List_Oupto(_1638823, _1638825) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1638823), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1638823), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1638825)))]]], (30184 ^ _776541) ^ [_1318009, _1318011, _1318013, _1318015] : [class_Orderings_Olinorder(_1318009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318009), _1318011), _1318013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318009), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318009), _1318011), _1318015)), _1318013)))], (39884 ^ _776541) ^ [_1552632, _1552634, _1552636, _1552638, _1552640, _1552642] : [-(hAPP(hAPP(c_Fun_Ocomp(_1552632, _1552634, _1552636, _1552638), _1552640), _1552642) = hAPP(_1552638, hAPP(_1552640, _1552642)))], (29928 ^ _776541) ^ [_1313203, _1313205] : [_1313203 = _1313205, -(c_Random_Oinc__shift(_1313203, _1313205) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (2220 ^ _776541) ^ [_808808, _808810, _808812, _808814] : [-(c_Random_Oinc__shift(_808814, _808810) = c_Random_Oinc__shift(_808812, _808808)), _808814 = _808812, _808810 = _808808], (52181 ^ _776541) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (43932 ^ _776541) ^ [_1654449, _1654451] : [_1654451 = c_List_Olist_ONil(_1654449), -(hAPP(c_List_Orotate1(_1654449), _1654451) = c_List_Olist_ONil(_1654449))], (32970 ^ _776541) ^ [_1378034, _1378036, _1378038, _1378040, _1378042] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378034, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378036, tc_fun(_1378034, tc_HOL_Obool)), _1378038), _1378040)), _1378042) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378036, tc_fun(_1378034, tc_HOL_Obool)), _1378038), hAPP(hAPP(c_COMBC(_1378036, tc_fun(_1378034, tc_HOL_Obool), tc_fun(_1378034, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378034, tc_HOL_Obool), tc_fun(tc_fun(_1378034, tc_HOL_Obool), tc_fun(_1378034, tc_HOL_Obool)), _1378036), c_Groups_Ominus__class_Ominus(tc_fun(_1378034, tc_HOL_Obool))), _1378040)), _1378042)))], (51367 ^ _776541) ^ [_1816278, _1816280, _1816282, _1816284, _1816286] : [class_Rings_Ocomm__semiring__1(_1816278), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816278), _1816280), _1816282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1816284), _1816286)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816278), hAPP(hAPP(c_Power_Opower__class_Opower(_1816278), _1816280), _1816284)), hAPP(hAPP(c_Power_Opower__class_Opower(_1816278), _1816282), _1816286))))], (31723 ^ _776541) ^ [_1346345, _1346347, _1346349, _1346351, _1346353] : [class_Orderings_Olinorder(_1346345), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346345, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346345, _1346347), _1346349)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346345, _1346351), _1346353)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346345, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346345), _1346347), _1346351)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346345), _1346349), _1346353)))], (7934 ^ _776541) ^ [_910591, _910593, _910595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910591, tc_HOL_Obool)), _910593), _910595)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910591, tc_HOL_Obool)), _910593), _910595) = _910595)], (16458 ^ _776541) ^ [_1073010, _1073012] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073010), _1073012) = _1073010, -(_1073012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34105 ^ _776541) ^ [_1410011, _1410013, _1410015] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1410011), _1410013)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410011, tc_HOL_Obool)), _1410015), _1410013) = hAPP(hAPP(c_Finite__Set_Ofold(_1410011, tc_fun(_1410011, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1410011, tc_HOL_Obool), tc_fun(tc_fun(_1410011, tc_HOL_Obool), tc_fun(_1410011, tc_HOL_Obool)), _1410011), hAPP(c_COMBC(tc_fun(_1410011, tc_HOL_Obool), tc_fun(_1410011, tc_HOL_Obool), tc_fun(_1410011, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1410011, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1410011, tc_fun(_1410011, tc_HOL_Obool), tc_fun(_1410011, tc_HOL_Obool)), c_Set_Oinsert(_1410011)), c_Orderings_Obot__class_Obot(tc_fun(_1410011, tc_HOL_Obool))))), _1410015), _1410013))], (29045 ^ _776541) ^ [_1297188, _1297190] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297188))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297190))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297188)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297190)))], (44066 ^ _776541) ^ [_1657678, _1657680, _1657682, _1657684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657678), _1657680)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657682)), _1657684))), -(hAPP(hAPP(c_List_Otake(_1657682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657678), _1657680)), _1657684) = hAPP(hAPP(c_List_Oappend(_1657682), hAPP(hAPP(c_List_Otake(_1657682), _1657678), _1657684)), hAPP(hAPP(c_List_Otake(_1657682), _1657680), hAPP(hAPP(c_List_Odrop(_1657682), _1657678), _1657684))))], (29233 ^ _776541) ^ [_1300502, _1300504] : [class_Int_Onumber__ring(_1300502), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300502), hAPP(c_Int_Onumber__class_Onumber__of(_1300502), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1300504) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300502), _1300504), _1300504))], (24794 ^ _776541) ^ [_1225011, _1225013, _1225015, _1225017] : [class_Divides_Osemiring__div(_1225011), -(c_Divides_Odiv__class_Omod(_1225011, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225011), _1225013), _1225015), _1225017) = c_Divides_Odiv__class_Omod(_1225011, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225011), c_Divides_Odiv__class_Omod(_1225011, _1225013, _1225017)), _1225015), _1225017))], (7672 ^ _776541) ^ [_904457, _904459, _904461] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904457, tc_HOL_Obool)), _904459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904457, tc_HOL_Obool)), _904461), _904459)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904457, tc_HOL_Obool)), _904459), _904461))], (8417 ^ _776541) ^ [_921089, _921091, _921093] : [class_Lattices_Olattice(_921089), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921089), _921091), _921093) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921089), _921093), _921091))], (30584 ^ _776541) ^ [_1325411, _1325413, _1325415] : [class_Orderings_Olinorder(_1325411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325411), _1325413)), -(hBOOL(hAPP(hAPP(c_member(_1325411), _1325415), _1325413))), -(c_Big__Operators_Olinorder__class_OMin(_1325411, hAPP(hAPP(c_Set_Oinsert(_1325411), _1325415), _1325413)) = hAPP(hAPP(c_Finite__Set_Ofold(_1325411, _1325411, c_Orderings_Oord__class_Omin(_1325411)), _1325415), _1325413))], (42659 ^ _776541) ^ [_1625887, _1625889, _1625891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1625887), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625889)), _1625891))), -(c_List_Obutlast(_1625889, hAPP(hAPP(c_List_Otake(_1625889), _1625887), _1625891)) = hAPP(hAPP(c_List_Otake(_1625889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1625887), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1625891))], (52413 ^ _776541) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (14720 ^ _776541) ^ [_1041837, _1041839, _1041841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041837), _1041839)), _1041841)), 14723 ^ _776541 : [(14726 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041839), _1041841)))], (14724 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041837), _1041841)))]]], (1104 ^ _776541) ^ [_793205, _793207] : [-(class_Groups_Oordered__ab__group__add__abs(_793205)), _793207 = _793205, class_Groups_Oordered__ab__group__add__abs(_793207)], (7354 ^ _776541) ^ [_896999, _897001] : [-(c_Set_Othe__elem(_896999, hAPP(hAPP(c_Set_Oinsert(_896999), _897001), c_Orderings_Obot__class_Obot(tc_fun(_896999, tc_HOL_Obool)))) = _897001)], (7676 ^ _776541) ^ [_904577, _904579, _904581] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904577, tc_HOL_Obool)), _904579), _904581) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904577, tc_HOL_Obool)), _904581), _904579))], (45888 ^ _776541) ^ [_1697111, _1697113, _1697115] : [class_Orderings_Olinorder(_1697111), -(c_List_Olinorder__class_Osort__key(_1697113, _1697111, _1697115, c_List_Olist_ONil(_1697113)) = c_List_Olist_ONil(_1697113))], (50755 ^ _776541) ^ [_1802409, _1802411, _1802413, _1802415] : [c_Equiv__Relations_Oequivp(_1802409, _1802411), -(c_Quotient_OBabs(_1802409, _1802413, c_Quotient_ORespects(_1802409, _1802411), _1802415) = _1802415)], (15087 ^ _776541) ^ [_1048957, _1048959] : [class_Groups_Ocomm__monoid__mult(_1048957), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048957), _1048959), c_Groups_Oone__class_Oone(_1048957)) = _1048959)], (27617 ^ _776541) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (43777 ^ _776541) ^ [_1650219, _1650221, _1650223, _1650225, _1650227, _1650229, _1650231, _1650233] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650219, _1650219)), hAPP(hAPP(c_Product__Type_OPair(_1650219, _1650219), _1650221), _1650223)), _1650225)), _1650227 = hAPP(hAPP(c_List_Oappend(_1650219), _1650229), hAPP(hAPP(c_List_Olist_OCons(_1650219), _1650221), _1650231)), _1650233 = hAPP(hAPP(c_List_Oappend(_1650219), _1650229), hAPP(hAPP(c_List_Olist_OCons(_1650219), _1650223), _1650231)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650219), tc_List_Olist(_1650219))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650219), tc_List_Olist(_1650219)), _1650227), _1650233)), c_List_Olistrel1(_1650219, _1650225))))], (44661 ^ _776541) ^ [_1669435, _1669437] : [-(_1669435 = c_List_Olist_ONil(_1669437)), -(c_List_Olast(_1669437, _1669435) = hAPP(hAPP(c_List_Onth(_1669437), _1669435), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669437)), _1669435)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (39017 ^ _776541) ^ [_1527784, _1527786, _1527788, _1527790, _1527792, _1527794] : [-(hAPP(c_Set_Oimage(_1527784, tc_prod(_1527786, _1527788), hAPP(hAPP(c_COMBS(_1527784, _1527788, tc_prod(_1527786, _1527788)), hAPP(hAPP(c_COMBB(_1527786, tc_fun(_1527788, tc_prod(_1527786, _1527788)), _1527784), c_Product__Type_OPair(_1527786, _1527788)), _1527790)), _1527792)), _1527794) = hAPP(hAPP(c_Product__Type_OSigma(_1527786, _1527788), hAPP(c_Set_Oimage(_1527784, _1527786, _1527790), _1527794)), hAPP(hAPP(c_COMBB(tc_fun(_1527784, tc_HOL_Obool), tc_fun(_1527788, tc_HOL_Obool), _1527786), c_Set_Oimage(_1527784, _1527788, _1527792)), hAPP(hAPP(c_COMBC(_1527786, tc_fun(_1527784, tc_HOL_Obool), tc_fun(_1527784, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1527784, tc_HOL_Obool), tc_fun(tc_fun(_1527784, tc_HOL_Obool), tc_fun(_1527784, tc_HOL_Obool)), _1527786), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1527784, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527786, tc_HOL_Obool), tc_fun(_1527784, tc_HOL_Obool), _1527786), c_Set_Ovimage(_1527784, _1527786, _1527790)), hAPP(hAPP(c_COMBC(_1527786, tc_fun(_1527786, tc_HOL_Obool), tc_fun(_1527786, tc_HOL_Obool)), c_Set_Oinsert(_1527786)), c_Orderings_Obot__class_Obot(tc_fun(_1527786, tc_HOL_Obool)))))), _1527794))))], (37064 ^ _776541) ^ [_1480836, _1480838, _1480840, _1480842, _1480844, _1480846, _1480848, _1480850, _1480852, _1480854] : [c_Equiv__Relations_Ocongruent2(_1480836, _1480838, _1480840, _1480842, _1480844, _1480846), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480836, _1480836)), hAPP(hAPP(c_Product__Type_OPair(_1480836, _1480836), _1480848), _1480850)), _1480842)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480838, _1480838)), hAPP(hAPP(c_Product__Type_OPair(_1480838, _1480838), _1480852), _1480854)), _1480844)), -(hAPP(hAPP(_1480846, _1480848), _1480852) = hAPP(hAPP(_1480846, _1480850), _1480854))], (52473 ^ _776541) ^ [_1831133, _1831135] : [hBOOL(hAPP(hAPP(c_fequal, _1831133), _1831135)), -(_1831133 = _1831135)], (42510 ^ _776541) ^ [_1622331, _1622333, _1622335, _1622337, _1622339, _1622341] : [-(hAPP(hAPP(c_List_Ozip(_1622331, _1622333), hAPP(hAPP(c_List_Olist_OCons(_1622331), _1622335), _1622337)), hAPP(hAPP(c_List_Olist_OCons(_1622333), _1622339), _1622341)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1622331, _1622333)), hAPP(hAPP(c_Product__Type_OPair(_1622331, _1622333), _1622335), _1622339)), hAPP(hAPP(c_List_Ozip(_1622331, _1622333), _1622337), _1622341)))], (6871 ^ _776541) ^ [_887981, _887983, _887985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887981, tc_HOL_Obool)), _887983), _887985)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_887981, tc_HOL_Obool)), _887983), hAPP(c_Set_OPow(_887981), _887985))))], (35378 ^ _776541) ^ [_1436169, _1436171] : [-(_1436169 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436171, _1436169), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1436171), _1436169)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1436171, _1436169)))))], (52195 ^ _776541) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (27467 ^ _776541) ^ [_1270599, _1270601, _1270603] : [class_Groups_Oordered__ab__group__add__abs(_1270599), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270599), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270599), hAPP(c_Groups_Oabs__class_Oabs(_1270599), _1270601)), hAPP(c_Groups_Oabs__class_Oabs(_1270599), _1270603))), hAPP(c_Groups_Oabs__class_Oabs(_1270599), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270599), _1270601), _1270603)))))], (29351 ^ _776541) ^ [_1302508, _1302510] : [class_Fields_Olinordered__field__inverse__zero(_1302508), class_Int_Onumber__ring(_1302508), 29358 ^ _776541 : [(29365 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302508), c_Groups_Ozero__class_Ozero(_1302508)), _1302510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302508), c_Groups_Ozero__class_Ozero(_1302508)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302508), _1302510), hAPP(c_Int_Onumber__class_Onumber__of(_1302508), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29359 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302508), c_Groups_Ozero__class_Ozero(_1302508)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302508), _1302510), hAPP(c_Int_Onumber__class_Onumber__of(_1302508), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302508), c_Groups_Ozero__class_Ozero(_1302508)), _1302510)))]]], (50061 ^ _776541) ^ [_1787935, _1787937, _1787939, _1787941, _1787943] : [c_Fun_Oinj__on(_1787935, _1787937, _1787939, _1787941), hBOOL(hAPP(hAPP(c_member(_1787935), _1787943), _1787941)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1787935, _1787937, _1787941, _1787939), hAPP(_1787939, _1787943)) = _1787943)], (25147 ^ _776541) ^ [_1231796, _1231798, _1231800] : [class_Divides_Osemiring__div(_1231796), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231796), _1231798), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231796), _1231800), _1231798))), c_Divides_Odiv__class_Omod(_1231796, _1231800, _1231798)) = _1231800)], (51683 ^ _776541) ^ [_1821907, _1821909] : [_1821907 = _1821909, 51686 ^ _776541 : [(51689 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821909), _1821907)))], (51687 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821907), _1821909)))]]], (32061 ^ _776541) ^ [_1352600, _1352602, _1352604] : [class_Orderings_Olinorder(_1352600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352600), _1352602)), -(_1352602 = c_Orderings_Obot__class_Obot(tc_fun(_1352600, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352600), _1352604)), -(_1352604 = c_Orderings_Obot__class_Obot(tc_fun(_1352600, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1352600, c_Orderings_Oord__class_Omax(_1352600), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352600, tc_HOL_Obool)), _1352602), _1352604)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352600), c_Big__Operators_Olattice_OSup__fin(_1352600, c_Orderings_Oord__class_Omax(_1352600), _1352602)), c_Big__Operators_Olattice_OSup__fin(_1352600, c_Orderings_Oord__class_Omax(_1352600), _1352604)))], (42262 ^ _776541) ^ [_1614603, _1614605, _1614607, _1614609] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614603), tc_List_Olist(_1614603))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614603), tc_List_Olist(_1614603)), _1614605), _1614607)), c_List_Olexord(_1614603, _1614609))), 42267 ^ _776541 : [(42270 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1614603), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614603)), _1614605)), _1614607) = _1614605)], (42268 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614603)), _1614605)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614603)), _1614607))))]], 42272 ^ _776541 : [(42277 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614603, _1614603)), hAPP(hAPP(c_Product__Type_OPair(_1614603, _1614603), hAPP(hAPP(c_List_Onth(_1614603), _1614605), 42271 ^ [_1614603, _1614605, _1614607, _1614609])), hAPP(hAPP(c_List_Onth(_1614603), _1614607), 42271 ^ [_1614603, _1614605, _1614607, _1614609]))), _1614609)))], (42275 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1614603), 42271 ^ [_1614603, _1614605, _1614607, _1614609]), _1614605) = hAPP(hAPP(c_List_Otake(_1614603), 42271 ^ [_1614603, _1614605, _1614607, _1614609]), _1614607))], (42273 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42271 ^ [_1614603, _1614605, _1614607, _1614609]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614603)), _1614605)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614603)), _1614607)))))]]], (27323 ^ _776541) ^ [_1268132, _1268134] : [class_Groups_Oordered__ab__group__add__abs(_1268132), 27326 ^ _776541 : [(27333 ^ _776541) ^ [] : [_1268134 = c_Groups_Ozero__class_Ozero(_1268132), -(hAPP(c_Groups_Oabs__class_Oabs(_1268132), _1268134) = c_Groups_Ozero__class_Ozero(_1268132))], (27327 ^ _776541) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1268132), _1268134) = c_Groups_Ozero__class_Ozero(_1268132), -(_1268134 = c_Groups_Ozero__class_Ozero(_1268132))]]], (46662 ^ _776541) ^ [_1714274, _1714276, _1714278, _1714280, _1714282] : [class_Orderings_Olinorder(_1714274), c_List_Olinorder__class_Osorted(_1714274, hAPP(hAPP(c_List_Omap(_1714276, _1714274), _1714278), _1714280)), -(c_List_Olinorder__class_Osorted(_1714274, hAPP(hAPP(c_List_Omap(_1714276, _1714274), _1714278), c_List_Oremove1(_1714276, _1714282, _1714280))))], (16604 ^ _776541) ^ [_1075215] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1075215)) = hAPP(c_Nat_OSuc, _1075215))], (7298 ^ _776541) ^ [_895922, _895924, _895926, _895928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895922, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_895922), _895924), _895926)), _895928)), 7301 ^ _776541 : [(7304 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895922, tc_HOL_Obool)), _895926), _895928)))], (7302 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895922), _895924), _895928)))]]], (35989 ^ _776541) ^ [_1452210, _1452212, _1452214] : [class_Lattices_Odistrib__lattice(_1452210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452210), _1452212)), -(_1452212 = c_Orderings_Obot__class_Obot(tc_fun(_1452210, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452210), _1452214), c_Big__Operators_Olattice__class_OSup__fin(_1452210, _1452212)) = c_Big__Operators_Olattice__class_OSup__fin(_1452210, hAPP(c_Set_OCollect(_1452210), hAPP(hAPP(c_COMBB(tc_fun(_1452210, tc_HOL_Obool), tc_HOL_Obool, _1452210), c_HOL_OEx(_1452210)), hAPP(hAPP(c_COMBC(_1452210, tc_fun(_1452210, tc_HOL_Obool), tc_fun(_1452210, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452210, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1452210, tc_HOL_Obool), tc_fun(_1452210, tc_HOL_Obool)), _1452210), c_COMBS(_1452210, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452210, tc_HOL_Obool), tc_fun(_1452210, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1452210), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452210), c_fconj)), hAPP(hAPP(c_COMBC(_1452210, tc_fun(_1452210, _1452210), tc_fun(_1452210, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452210, tc_HOL_Obool), tc_fun(tc_fun(_1452210, _1452210), tc_fun(_1452210, tc_HOL_Obool)), _1452210), c_COMBB(_1452210, tc_HOL_Obool, _1452210)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452210), _1452214))))), hAPP(hAPP(c_COMBC(_1452210, tc_fun(_1452210, tc_HOL_Obool), tc_HOL_Obool), c_member(_1452210)), _1452212))))))], (48860 ^ _776541) ^ [_1761332, _1761334, _1761336] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1761332, _1761334), _1761336) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1761332, tc_Lazy__Sequence_Olazy__sequence(_1761332)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1761332, tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1761332, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat)), _1761332), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1761332), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1761332)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1761332, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761332), tc_Nat_Onat)), _1761332), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1761332))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1761332), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1761334))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1761332, _1761334))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1761332), _1761336)))], (22521 ^ _776541) ^ [_1184722, _1184724] : [class_Groups_Omonoid__mult(_1184722), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184722), _1184724), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1184724)], (28541 ^ _776541) ^ [_1288692, _1288694] : [class_Int_Onumber__ring(_1288692), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288692), _1288694), hAPP(c_Int_Onumber__class_Onumber__of(_1288692), c_Int_OBit1(c_Int_OPls))) = _1288694)], (24024 ^ _776541) ^ [_1211458, _1211460, _1211462] : [class_Rings_Osemiring__1(_1211458), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211458), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211460), _1211462)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1211458), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211458), _1211460)), _1211462))], (44705 ^ _776541) ^ [_1670222, _1670224, _1670226] : [c_Fun_Oinj__on(_1670222, _1670224, _1670226, c_Orderings_Otop__class_Otop(tc_fun(_1670222, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1670222), tc_List_Olist(_1670224), hAPP(c_List_Omap(_1670222, _1670224), _1670226), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670222), tc_HOL_Obool))))], (28757 ^ _776541) ^ [_1292055, _1292057] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1292055)))), _1292057) = 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)))), _1292055)), _1292057))], (8775 ^ _776541) ^ [_927288, _927290] : [class_Lattices_Obounded__lattice__bot(_927288), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927288), _927290), c_Orderings_Obot__class_Obot(_927288)) = _927290)], (52263 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (880 ^ _776541) ^ [_789705, _789707, _789709, _789711, _789713, _789715, _789717, _789719, _789721, _789723] : [-(c_Fun_Obij__betw(_789721, _789717, _789713, _789709, _789705)), c_Fun_Obij__betw(_789723, _789719, _789715, _789711, _789707), _789723 = _789721, _789719 = _789717, _789715 = _789713, _789711 = _789709, _789707 = _789705], (42438 ^ _776541) ^ [_1619097, _1619099, _1619101] : [hBOOL(hAPP(hAPP(c_member(_1619097), _1619099), hAPP(c_List_Oset(_1619097), _1619101))), 42442 ^ _776541 : [(42445 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1619097), _1619101), 42441 ^ [_1619097, _1619099, _1619101]) = _1619099)], (42443 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42441 ^ [_1619097, _1619099, _1619101]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619097)), _1619101))))]]], (17859 ^ _776541) ^ [_1097842, _1097844, _1097846, _1097848] : [class_Groups_Ocomm__monoid__add(_1097842), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1097844), _1097846))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097844, _1097842), _1097848), _1097846) = c_Groups_Ozero__class_Ozero(_1097842))], (5604 ^ _776541) ^ [_862102, _862104] : [_862104 = _862102, -(c_COMBI(_862104) = c_COMBI(_862102))], (5648 ^ _776541) ^ [_862778, _862780, _862782, _862784, _862786, _862788] : [-(c_COMBS(_862788, _862784, _862780) = c_COMBS(_862786, _862782, _862778)), _862788 = _862786, _862784 = _862782, _862780 = _862778], (7732 ^ _776541) ^ [_906211, _906213, _906215, _906217] : [hBOOL(hAPP(hAPP(c_member(_906211), _906213), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906211, tc_HOL_Obool)), _906215), _906217))), 7735 ^ _776541 : [(7738 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_906211), _906213), _906217))], (7736 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_906211), _906213), _906215)))]]], (12710 ^ _776541) ^ [_1000614, _1000616, _1000618] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000614), _1000616)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000614, tc_HOL_Obool)), _1000616), _1000618) = hAPP(hAPP(c_Finite__Set_Ofold(_1000614, tc_fun(_1000614, tc_HOL_Obool), c_Set_Oinsert(_1000614)), _1000618), _1000616))], (15680 ^ _776541) ^ [_1060875] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060875)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1060875)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1060875), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (19543 ^ _776541) ^ [_1129575, _1129577] : [class_Rings_Odivision__ring(_1129575), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129575), c_Groups_Ozero__class_Ozero(_1129575)), _1129577) = c_Groups_Ozero__class_Ozero(_1129575))], (44739 ^ _776541) ^ [_1670938, _1670940, _1670942, _1670944, _1670946] : [-(hAPP(hAPP(c_List_Omap(_1670938, _1670940), _1670942), hAPP(hAPP(c_List_Oappend(_1670938), _1670944), _1670946)) = hAPP(hAPP(c_List_Oappend(_1670940), hAPP(hAPP(c_List_Omap(_1670938, _1670940), _1670942), _1670944)), hAPP(hAPP(c_List_Omap(_1670938, _1670940), _1670942), _1670946)))], (12133 ^ _776541) ^ [_989601, _989603, _989605] : [class_Lattices_Olattice(_989601), hBOOL(hAPP(c_Finite__Set_Ofinite(_989601), _989603)), -(_989603 = c_Orderings_Obot__class_Obot(tc_fun(_989601, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_989601, hAPP(hAPP(c_Set_Oinsert(_989601), _989605), _989603)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_989601), _989605), c_Big__Operators_Olattice__class_OSup__fin(_989601, _989603)))], (41168 ^ _776541) ^ [_1583846, _1583848, _1583850, _1583852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583846, _1583846)), hAPP(hAPP(c_Product__Type_OPair(_1583846, _1583846), _1583848), _1583850)), c_Transitive__Closure_Ortrancl(_1583846, _1583852))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583846, _1583846)), hAPP(hAPP(c_Product__Type_OPair(_1583846, _1583846), _1583850), _1583848)), c_Transitive__Closure_Ortrancl(_1583846, hAPP(c_Relation_Oconverse(_1583846, _1583846), _1583852)))))], (2620 ^ _776541) ^ [_815186, _815188] : [_815188 = _815186, -(c_Nitpick_Oone__frac(_815188) = c_Nitpick_Oone__frac(_815186))], (33008 ^ _776541) ^ [_1379192, _1379194, _1379196] : [-(hBOOL(hAPP(_1379192, _1379194))), -(hAPP(c_Set_OCollect(_1379196), hAPP(hAPP(c_COMBS(_1379196, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1379196), c_fconj), hAPP(c_fequal, _1379194))), _1379192)) = c_Orderings_Obot__class_Obot(tc_fun(_1379196, tc_HOL_Obool)))], (23773 ^ _776541) ^ [_1207113, _1207115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207113)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207113), _1207115)))], (51607 ^ _776541) ^ [_1820599, _1820601] : [class_Rings_Ocomm__semiring__1(_1820599), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820599), c_Groups_Ozero__class_Ozero(_1820599)), _1820601)), -(_1820601 = c_Groups_Ozero__class_Ozero(_1820599))], (44813 ^ _776541) ^ [_1672897, _1672899, _1672901, _1672903] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672897)), hAPP(hAPP(c_List_Omap(_1672899, _1672897), _1672901), _1672903)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672899)), _1672903))], (23946 ^ _776541) ^ [_1210268, _1210270, _1210272, _1210274] : [class_Divides_Osemiring__div(_1210268), 23949 ^ _776541 : [(23956 ^ _776541) ^ [] : [-(_1210270 = c_Groups_Ozero__class_Ozero(_1210268)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210268), _1210270), _1210272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210268), _1210270), _1210274)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210268), _1210272), _1210274))], (23950 ^ _776541) ^ [] : [_1210270 = c_Groups_Ozero__class_Ozero(_1210268), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210268), _1210270), _1210272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210268), _1210270), _1210274)) = c_Groups_Ozero__class_Ozero(_1210268))]]], (28583 ^ _776541) ^ [_1289359, _1289361] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289359), _1289361), hAPP(c_Int_Onumber__class_Onumber__of(_1289359), c_Int_OBit1(c_Int_OPls))) = _1289361), class_Fields_Ofield(_1289359), class_Int_Onumber__ring(_1289359)], (50839 ^ _776541) ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1805319, _1805321), tc_prod(_1805319, _1805321))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1805319, _1805321), tc_prod(_1805319, _1805321)), hAPP(hAPP(c_Product__Type_OPair(_1805319, _1805321), _1805323), _1805325)), hAPP(hAPP(c_Product__Type_OPair(_1805319, _1805321), _1805327), _1805329))), c_Transitive__Closure_Ortrancl(tc_prod(_1805319, _1805321), _1805331))), hBOOL(hAPP(hAPP(_1805333, _1805327), _1805329)), 50852 ^ _776541 : [(50855 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1805319, _1805321), tc_prod(_1805319, _1805321))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1805319, _1805321), tc_prod(_1805319, _1805321)), hAPP(hAPP(c_Product__Type_OPair(_1805319, _1805321), 50850 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333]), 50851 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333])), hAPP(hAPP(c_Product__Type_OPair(_1805319, _1805321), _1805327), _1805329))), c_Transitive__Closure_Ortrancl(tc_prod(_1805319, _1805321), _1805331))))], (50857 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1805333, 50850 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333]), 50851 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333])))], (50859 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1805333, 50848 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333]), 50849 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333]))], (50853 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1805319, _1805321), tc_prod(_1805319, _1805321))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1805319, _1805321), tc_prod(_1805319, _1805321)), hAPP(hAPP(c_Product__Type_OPair(_1805319, _1805321), 50848 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333]), 50849 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333])), hAPP(hAPP(c_Product__Type_OPair(_1805319, _1805321), 50850 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333]), 50851 ^ [_1805319, _1805321, _1805323, _1805325, _1805327, _1805329, _1805331, _1805333]))), _1805331)))]], -(hBOOL(hAPP(hAPP(_1805333, _1805323), _1805325)))], (46688 ^ _776541) ^ [_1714764, _1714766, _1714768, _1714770, _1714772] : [class_Orderings_Olinorder(_1714764), -(c_List_Olinorder__class_Osorted(_1714764, hAPP(hAPP(c_List_Omap(_1714766, _1714764), _1714768), hAPP(c_List_Ofilter(_1714766, hAPP(hAPP(c_COMBC(_1714766, _1714764, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1714764, tc_fun(_1714764, tc_HOL_Obool), _1714766), c_fequal), _1714768)), hAPP(_1714770, _1714772))), _1714772))))], (28993 ^ _776541) ^ [_1296261, _1296263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296261), _1296263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296261)), c_Int_OBit0(_1296263))))], (43703 ^ _776541) ^ [_1648350, _1648352, _1648354] : [-(c_List_Obutlast(_1648350, hAPP(hAPP(c_List_Oappend(_1648350), _1648352), hAPP(hAPP(c_List_Olist_OCons(_1648350), _1648354), c_List_Olist_ONil(_1648350)))) = _1648352)], (6597 ^ _776541) ^ [_883293, _883295, _883297] : [6599 ^ _776541 : [(6602 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883293, tc_HOL_Obool)), _883297), 6598 ^ [_883293, _883295, _883297]))], (6600 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_883293, tc_HOL_Obool)), 6598 ^ [_883293, _883295, _883297]), _883295)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883293, tc_HOL_Obool)), _883297), c_Complete__Lattice_OInf__class_OInf(tc_fun(_883293, tc_HOL_Obool), _883295))))], (8291 ^ _776541) ^ [_918434, _918436, _918438, _918440] : [class_Lattices_Osemilattice__sup(_918434), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918434), _918436), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918434), _918438), _918440)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918434), _918438), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918434), _918436), _918440)))], (14219 ^ _776541) ^ [_1032321] : [14221 ^ _776541 : [(14224 ^ _776541) ^ [_1032431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14220 ^ [_1032321, _1032431]), _1032431))], (14222 ^ _776541) ^ [_1032397] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14220 ^ [_1032321, _1032397]), _1032321)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1032321)))], (47760 ^ _776541) ^ [_1737690, _1737692] : [class_Enum_Oenum(_1737690), 47763 ^ _776541 : [(47771 ^ _776541) ^ [] : [47772 ^ _776541 : [(47773 ^ _776541) ^ [_1737870] : [hBOOL(hAPP(_1737692, _1737870))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737690), _1737692)))], (47764 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737690), _1737692)), -(hBOOL(hAPP(_1737692, 47767 ^ [_1737690, _1737692])))]]], (44190 ^ _776541) ^ [_1660165, _1660167, _1660169] : [_1660169 = c_List_Olist_ONil(_1660165), -(hAPP(c_List_Orotate(_1660165, _1660167), _1660169) = c_List_Olist_ONil(_1660165))], (38264 ^ _776541) ^ [_1509257, _1509259, _1509261] : [c_Wellfounded_Owf(_1509257, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509257, _1509257), tc_HOL_Obool)), _1509259), _1509261)), -(c_Wellfounded_Owf(_1509257, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509257, _1509257), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509257, _1509257), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509257, _1509257, _1509257), _1509259), _1509259)), hAPP(hAPP(c_Relation_Orel__comp(_1509257, _1509257, _1509257), _1509261), _1509259))), _1509261)))], (34934 ^ _776541) ^ [_1428233, _1428235] : [-(_1428233 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34937 ^ _776541 : [(34944 ^ _776541) ^ [] : [-(_1428235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1428233, _1428235) = 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, _1428235))), 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)), _1428235)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428233))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428235), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428233), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1428233, _1428235)), 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), _1428235))))), c_Divides_Opdivmod(_1428233, _1428235)))))], (34938 ^ _776541) ^ [] : [_1428235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1428233, _1428235) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428233))]]], (37919 ^ _776541) ^ [_1499624, _1499626, _1499628] : [hBOOL(hAPP(hAPP(c_member(_1499624), _1499628), c_Wellfounded_Oacc(_1499624, _1499626))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1499624, hAPP(hAPP(c_COMBC(_1499624, tc_fun(tc_prod(_1499624, _1499624), tc_HOL_Obool), tc_fun(_1499624, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499624, tc_fun(tc_fun(tc_prod(_1499624, _1499624), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499624, _1499624), tc_HOL_Obool), tc_fun(_1499624, tc_HOL_Obool)), _1499624), c_COMBC(_1499624, tc_fun(tc_prod(_1499624, _1499624), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499624, tc_prod(_1499624, _1499624)), tc_fun(_1499624, tc_fun(tc_fun(tc_prod(_1499624, _1499624), tc_HOL_Obool), tc_HOL_Obool)), _1499624), hAPP(c_COMBB(tc_prod(_1499624, _1499624), tc_fun(tc_fun(tc_prod(_1499624, _1499624), tc_HOL_Obool), tc_HOL_Obool), _1499624), c_member(tc_prod(_1499624, _1499624)))), c_Product__Type_OPair(_1499624, _1499624)))), _1499626)), _1499628)))], (25867 ^ _776541) ^ [_1244409, _1244411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1244409), _1244411)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244409, _1244411) = _1244409)], (41447 ^ _776541) ^ [_1590697, _1590699] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590697, _1590697), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590699) = c_Relation_OId(_1590697))], (31389 ^ _776541) ^ [_1340121, _1340123, _1340125, _1340127] : [class_Orderings_Olinorder(_1340121), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340121), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340121), _1340123), _1340125)), _1340127) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340121), _1340123), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340121), _1340125), _1340127)))], (3030 ^ _776541) ^ [_821509, _821511, _821513, _821515] : [-(c_List_Olenlex(_821515, _821511) = c_List_Olenlex(_821513, _821509)), _821515 = _821513, _821511 = _821509], (35858 ^ _776541) ^ [_1446749, _1446751, _1446753] : [class_Orderings_Olinorder(_1446749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446749), _1446751)), -(_1446751 = c_Orderings_Obot__class_Obot(tc_fun(_1446749, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446749), _1446753)), -(_1446753 = c_Orderings_Obot__class_Obot(tc_fun(_1446749, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1446749), c_Big__Operators_Olattice_OInf__fin(_1446749, c_Orderings_Oord__class_Omin(_1446749), _1446751)), c_Big__Operators_Olattice_OInf__fin(_1446749, c_Orderings_Oord__class_Omin(_1446749), _1446753)) = c_Big__Operators_Olattice_OInf__fin(_1446749, c_Orderings_Oord__class_Omin(_1446749), hAPP(c_Set_OCollect(_1446749), hAPP(hAPP(c_COMBB(tc_fun(_1446749, tc_HOL_Obool), tc_HOL_Obool, _1446749), c_HOL_OEx(_1446749)), hAPP(hAPP(c_COMBB(tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool)), tc_fun(_1446749, tc_HOL_Obool), _1446749), hAPP(c_COMBB(tc_fun(_1446749, tc_HOL_Obool), tc_HOL_Obool, _1446749), c_HOL_OEx(_1446749))), hAPP(hAPP(c_COMBC(_1446749, tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool)), tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446749, tc_fun(tc_fun(_1446749, tc_HOL_Obool), tc_fun(_1446749, tc_HOL_Obool))), tc_fun(tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool)), tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool))), _1446749), c_COMBS(_1446749, tc_fun(_1446749, tc_HOL_Obool), tc_fun(_1446749, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446749, tc_fun(_1446749, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1446749, tc_fun(tc_fun(_1446749, tc_HOL_Obool), tc_fun(_1446749, tc_HOL_Obool))), _1446749), hAPP(c_COMBB(tc_fun(_1446749, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1446749, tc_HOL_Obool), tc_fun(_1446749, tc_HOL_Obool)), _1446749), c_COMBS(_1446749, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool)), tc_fun(_1446749, tc_fun(_1446749, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1446749), hAPP(c_COMBB(tc_fun(_1446749, tc_HOL_Obool), tc_fun(_1446749, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1446749), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1446749), c_fconj))), hAPP(hAPP(c_COMBC(_1446749, tc_fun(_1446749, tc_fun(_1446749, _1446749)), tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1446749, _1446749), tc_fun(_1446749, tc_HOL_Obool)), tc_fun(tc_fun(_1446749, tc_fun(_1446749, _1446749)), tc_fun(_1446749, tc_fun(_1446749, tc_HOL_Obool))), _1446749), c_COMBB(tc_fun(_1446749, _1446749), tc_fun(_1446749, tc_HOL_Obool), _1446749)), hAPP(hAPP(c_COMBB(tc_fun(_1446749, tc_HOL_Obool), tc_fun(tc_fun(_1446749, _1446749), tc_fun(_1446749, tc_HOL_Obool)), _1446749), c_COMBB(_1446749, tc_HOL_Obool, _1446749)), c_fequal))), c_Orderings_Oord__class_Omax(_1446749)))))), hAPP(hAPP(c_COMBC(_1446749, tc_fun(_1446749, tc_HOL_Obool), tc_fun(_1446749, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1446749, tc_HOL_Obool), tc_fun(_1446749, tc_HOL_Obool)), _1446749), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1446749)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1446749), c_fconj), hAPP(hAPP(c_COMBC(_1446749, tc_fun(_1446749, tc_HOL_Obool), tc_HOL_Obool), c_member(_1446749)), _1446751)))), hAPP(hAPP(c_COMBC(_1446749, tc_fun(_1446749, tc_HOL_Obool), tc_HOL_Obool), c_member(_1446749)), _1446753))))))))], (19881 ^ _776541) ^ [_1135240, _1135242] : [class_Rings_Olinordered__idom(_1135240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135240), _1135242), c_Groups_Ozero__class_Ozero(_1135240))), -(c_Groups_Osgn__class_Osgn(_1135240, _1135242) = hAPP(c_Groups_Ouminus__class_Ouminus(_1135240), c_Groups_Oone__class_Oone(_1135240)))], (22561 ^ _776541) ^ [_1185448, _1185450, _1185452] : [class_Power_Opower(_1185448), class_Rings_Omult__zero(_1185448), class_Rings_Ono__zero__divisors(_1185448), class_Rings_Ozero__neq__one(_1185448), 22576 ^ _776541 : [(22585 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1185448), _1185450), _1185452) = c_Groups_Ozero__class_Ozero(_1185448)), _1185450 = c_Groups_Ozero__class_Ozero(_1185448), -(_1185452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22577 ^ _776541) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1185448), _1185450), _1185452) = c_Groups_Ozero__class_Ozero(_1185448), 22580 ^ _776541 : [(22583 ^ _776541) ^ [] : [_1185452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22581 ^ _776541) ^ [] : [-(_1185450 = c_Groups_Ozero__class_Ozero(_1185448))]]]]], (11570 ^ _776541) ^ [_978847, _978849] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_978847, _978849)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_978847, _978849), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978847), c_Orderings_Otop__class_Otop(tc_fun(_978847, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978849), c_Orderings_Otop__class_Otop(tc_fun(_978849, tc_HOL_Obool))))], (27665 ^ _776541) ^ [_1274056, _1274058, _1274060] : [class_Groups_Oordered__ab__group__add__abs(_1274056), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274056), hAPP(c_Groups_Oabs__class_Oabs(_1274056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274056), _1274058), _1274060))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274056), hAPP(c_Groups_Oabs__class_Oabs(_1274056), _1274058)), hAPP(c_Groups_Oabs__class_Oabs(_1274056), _1274060)))))], (9938 ^ _776541) ^ [_946718, _946720, _946722] : [class_Orderings_Oord(_946718), 9941 ^ _776541 : [(9948 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946718), _946722), _946720)), -(hBOOL(hAPP(hAPP(c_member(_946718), _946720), hAPP(c_SetInterval_Oord__class_OgreaterThan(_946718), _946722))))], (9942 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_946718), _946720), hAPP(c_SetInterval_Oord__class_OgreaterThan(_946718), _946722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946718), _946722), _946720)))]]], (34229 ^ _776541) ^ [_1413041, _1413043] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1413041)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413043)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413043))), 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, _1413041))), 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), _1413041)), c_Int_Onat)))))], (38396 ^ _776541) ^ [] : [-(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))))], (12796 ^ _776541) ^ [_1002263, _1002265, _1002267, _1002269] : [class_Lattices_Osemilattice__sup(_1002263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002263), _1002265)), hBOOL(hAPP(hAPP(c_member(_1002263), _1002267), _1002265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002263), _1002267), _1002269)), hAPP(hAPP(c_Finite__Set_Ofold(_1002263, _1002263, c_Lattices_Osemilattice__sup__class_Osup(_1002263)), _1002269), _1002265))))], (20179 ^ _776541) ^ [_1140879, _1140881, _1140883] : [class_Fields_Olinordered__field(_1140879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140879), c_Groups_Ozero__class_Ozero(_1140879)), _1140881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140879), c_Groups_Ozero__class_Ozero(_1140879)), _1140883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140879), c_Groups_Ozero__class_Ozero(_1140879)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140879), _1140881), _1140883))))], (7374 ^ _776541) ^ [_897469, _897471, _897473, _897475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897469, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897469, tc_HOL_Obool)), _897471), hAPP(hAPP(c_Set_Oinsert(_897469), _897473), c_Orderings_Obot__class_Obot(tc_fun(_897469, tc_HOL_Obool))))), _897475)), hBOOL(hAPP(hAPP(c_member(_897469), _897473), _897471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897469, tc_HOL_Obool)), _897471), hAPP(hAPP(c_Set_Oinsert(_897469), _897473), _897475))))], (6141 ^ _776541) ^ [_875035, _875037, _875039, _875041] : [hBOOL(hAPP(_875035, _875037)), hBOOL(hAPP(hAPP(c_member(_875039), _875037), _875041)), 6149 ^ _776541 : [(6152 ^ _776541) ^ [] : [-(hBOOL(hAPP(_875035, 6148 ^ [_875035, _875037, _875039, _875041])))], (6150 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_875039), 6148 ^ [_875035, _875037, _875039, _875041]), _875041)))]]], (49062 ^ _776541) ^ [_1766209, _1766211, _1766213] : [c_List_Olist__all(tc_Int_Oint, _1766209, c_List_Oupto(_1766211, _1766213)), -(c_List_Oall__interval__int(_1766209, _1766211, _1766213))], (12854 ^ _776541) ^ [_1003320, _1003322, _1003324] : [class_Lattices_Olattice(_1003320), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003320), _1003322)), -(c_Big__Operators_Olattice__class_OInf__fin(_1003320, hAPP(hAPP(c_Set_Oinsert(_1003320), _1003324), _1003322)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003320, _1003320, c_Lattices_Osemilattice__inf__class_Oinf(_1003320)), _1003324), _1003322))], (47313 ^ _776541) ^ [_1727746, _1727748] : [-(_1727746 = c_List_Olist_ONil(_1727748)), hBOOL(hAPP(c_List_Odistinct(_1727748), _1727746)), -(c_List_OtakeWhile(_1727748, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1727748), c_fNot), hAPP(hAPP(c_COMBC(_1727748, _1727748, tc_HOL_Obool), c_fequal), c_List_Olast(_1727748, _1727746))), _1727746) = c_List_Obutlast(_1727748, _1727746))], (33372 ^ _776541) ^ [_1389371, _1389373, _1389375, _1389377, _1389379, _1389381] : [c_Nitpick_Opair__box_OPairBox(_1389371, _1389373, _1389375, _1389377) = c_Nitpick_Opair__box_OPairBox(_1389371, _1389373, _1389379, _1389381), 33375 ^ _776541 : [(33378 ^ _776541) ^ [] : [-(_1389377 = _1389381)], (33376 ^ _776541) ^ [] : [-(_1389375 = _1389379)]]], (38094 ^ _776541) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (37546 ^ _776541) ^ [_1491135, _1491137, _1491139, _1491141, _1491143] : [c_Fun_Oinj__on(_1491135, _1491137, _1491139, c_Orderings_Otop__class_Otop(tc_fun(_1491135, tc_HOL_Obool))), 37549 ^ _776541 : [(37556 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491135, tc_HOL_Obool)), _1491141), _1491143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491137, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491135, _1491137, _1491139), _1491141)), hAPP(c_Set_Oimage(_1491135, _1491137, _1491139), _1491143))))], (37550 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491137, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491135, _1491137, _1491139), _1491141)), hAPP(c_Set_Oimage(_1491135, _1491137, _1491139), _1491143))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491135, tc_HOL_Obool)), _1491141), _1491143)))]]], (40681 ^ _776541) ^ [_1571272, _1571274, _1571276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571272, _1571272), tc_HOL_Obool)), _1571274), hAPP(hAPP(c_Product__Type_OSigma(_1571272, _1571272), _1571276), hAPP(c_COMBK(tc_fun(_1571272, tc_HOL_Obool), _1571272), _1571276)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571272, _1571272), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571272, _1571274)), hAPP(hAPP(c_Product__Type_OSigma(_1571272, _1571272), _1571276), hAPP(c_COMBK(tc_fun(_1571272, tc_HOL_Obool), _1571272), _1571276)))))], (37193 ^ _776541) ^ [] : [-(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))], (40110 ^ _776541) ^ [_1557849, _1557851, _1557853, _1557855, _1557857, _1557859, _1557861, _1557863] : [c_Finite__Set_Ofolding__image(_1557849, _1557851, _1557853, _1557855, _1557857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557851), _1557859)), -(hAPP(hAPP(_1557857, hAPP(hAPP(c_COMBS(_1557851, _1557849, _1557849), hAPP(hAPP(c_COMBB(_1557849, tc_fun(_1557849, _1557849), _1557851), _1557853), _1557861)), _1557863)), _1557859) = hAPP(hAPP(_1557853, hAPP(hAPP(_1557857, _1557861), _1557859)), hAPP(hAPP(_1557857, _1557863), _1557859)))], (16160 ^ _776541) ^ [_1068666, _1068668] : [class_Groups_Omonoid__add(_1068666), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068666), c_Groups_Ozero__class_Ozero(_1068666)), _1068668) = _1068668)], (44268 ^ _776541) ^ [_1661743, _1661745, _1661747] : [class_Orderings_Olinorder(_1661743), -(c_List_Oremove1(_1661743, _1661745, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661743, _1661743, c_COMBI(_1661743)), _1661745), _1661747)) = _1661747)], (45591 ^ _776541) ^ [_1690800, _1690802, _1690804, _1690806, _1690808] : [-(c_List_Olist__all2(_1690800, _1690802, _1690804, _1690806, _1690808)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690800)), _1690806) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690802)), _1690808), 45597 ^ _776541 : [(45600 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1690804, hAPP(hAPP(c_List_Onth(_1690800), _1690806), 45596 ^ [_1690800, _1690802, _1690804, _1690806, _1690808])), hAPP(hAPP(c_List_Onth(_1690802), _1690808), 45596 ^ [_1690800, _1690802, _1690804, _1690806, _1690808])))], (45598 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45596 ^ [_1690800, _1690802, _1690804, _1690806, _1690808]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690800)), _1690806))))]]], (31667 ^ _776541) ^ [_1345061, _1345063, _1345065, _1345067] : [class_Orderings_Olinorder(_1345061), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345061), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345061), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345061), _1345063), _1345065)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345061), _1345063), _1345067))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345061), _1345063), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345061), _1345065), _1345067)))))], (25335 ^ _776541) ^ [_1234977, _1234979] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234977), _1234979) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 25336 ^ _776541 : [(25343 ^ _776541) ^ [] : [_1234977 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1234979 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (25337 ^ _776541) ^ [] : [_1234977 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1234979 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (29063 ^ _776541) ^ [_1297521] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1297521)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1297521), c_Int_OPls)))], (46962 ^ _776541) ^ [_1720410, _1720412] : [hBOOL(hAPP(c_List_Odistinct(_1720410), _1720412)), -(hBOOL(hAPP(c_List_Odistinct(_1720410), hAPP(c_List_Orev(_1720410), _1720412))))], (45866 ^ _776541) ^ [_1696563, _1696565] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696563)), c_List_Oremdups(_1696563, _1696565)) = hAPP(c_Finite__Set_Ocard(_1696563), hAPP(c_List_Oset(_1696563), _1696565)))], (52431 ^ _776541) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (12049 ^ _776541) ^ [_988317, _988319, _988321] : [class_Lattices_Olattice(_988317), hBOOL(hAPP(c_Finite__Set_Ofinite(_988317), _988319)), hBOOL(hAPP(hAPP(c_member(_988317), _988321), _988319)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_988317), _988321), c_Big__Operators_Olattice__class_OInf__fin(_988317, _988319)) = _988321)], (29573 ^ _776541) ^ [_1306311, _1306313, _1306315] : [class_Rings_Olinordered__idom(_1306311), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306311), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306311), hAPP(hAPP(c_Power_Opower__class_Opower(_1306311), _1306313), 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(_1306311), _1306315), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1306311)))], (36535 ^ _776541) ^ [_1468278, _1468280, _1468282] : [class_Rings_Oring__1(_1468278), -(hAPP(c_Int_Oring__1__class_Oof__int(_1468278), 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), _1468280), _1468282)), 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(_1468278), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1468278), _1468280)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1468278), _1468282)))], (39227 ^ _776541) ^ [_1533846, _1533848, _1533850, _1533852] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1533846, _1533848)), hAPP(hAPP(c_Product__Type_OSigma(_1533846, _1533848), _1533850), hAPP(c_COMBK(tc_fun(_1533848, tc_HOL_Obool), _1533846), _1533852)))), -(_1533850 = c_Orderings_Obot__class_Obot(tc_fun(_1533846, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533848), _1533852)))], (26771 ^ _776541) ^ [_1259376] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259376) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1259376))], (29733 ^ _776541) ^ [] : [-(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)))], (9426 ^ _776541) ^ [_938600, _938602, _938604] : [class_Orderings_Olinorder(_938600), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938600), _938602), _938604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938600), _938604), _938602)))], (29175 ^ _776541) ^ [] : [-(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))))], (24946 ^ _776541) ^ [_1228273, _1228275] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228273)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228275)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228273), _1228275)))], (8467 ^ _776541) ^ [_921983, _921985, _921987, _921989] : [class_Lattices_Osemilattice__sup(_921983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921983), _921985), _921987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921983), _921989), _921987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921983), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921983), _921985), _921989)), _921987)))], (48676 ^ _776541) ^ [_1757729, _1757731, _1757733, _1757735] : [-(c_List_Oreplicate(_1757729, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1757731), _1757733), _1757735) = hAPP(hAPP(c_List_Oappend(_1757729), c_List_Oreplicate(_1757729, _1757731, _1757735)), c_List_Oreplicate(_1757729, _1757733, _1757735)))], (46030 ^ _776541) ^ [_1700906, _1700908] : [-(c_List_Oconcat(_1700906, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700906), tc_List_Olist(_1700906)), c_List_Olist_Olist__case(tc_List_Olist(_1700906), _1700906, c_List_Olist_ONil(_1700906), hAPP(hAPP(c_COMBB(tc_List_Olist(_1700906), tc_fun(tc_List_Olist(_1700906), tc_List_Olist(_1700906)), _1700906), c_COMBK(tc_List_Olist(_1700906), tc_List_Olist(_1700906))), hAPP(hAPP(c_COMBC(_1700906, tc_List_Olist(_1700906), tc_List_Olist(_1700906)), c_List_Olist_OCons(_1700906)), c_List_Olist_ONil(_1700906))))), _1700908)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700906), _1700906), c_List_Ohd(_1700906)), hAPP(c_List_Ofilter(tc_List_Olist(_1700906), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700906)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700906), tc_List_Olist(_1700906), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700906)))), _1700908)))], (32642 ^ _776541) ^ [_1369142, _1369144, _1369146, _1369148, _1369150] : [class_Lattices_Olattice(_1369142), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369144, _1369142)), _1369146), _1369148), _1369150) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1369142), hAPP(_1369146, _1369150)), hAPP(_1369148, _1369150)))], (23469 ^ _776541) ^ [_1201928, _1201930, _1201932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201928)), 23472 ^ _776541 : [(23473 ^ _776541) ^ [_1202062] : [23475 ^ _776541 : [(23481 ^ _776541) ^ [] : [-(_1202062 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23477 ^ [_1201928, _1201930, _1201932, _1202062]), 23474 ^ [_1201928, _1201930, _1201932, _1202062]))], (23479 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23477 ^ [_1201928, _1201930, _1201932, _1202062]), _1201930)))], (23476 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23474 ^ [_1201928, _1201930, _1201932, _1202062]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1201928))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202062), _1201932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202062), _1201928)), _1201932)))]]], (38416 ^ _776541) ^ [_1512973, _1512975, _1512977, _1512979] : [38418 ^ _776541 : [(38421 ^ _776541) ^ [] : [c_Wellfounded_Owf(_1512975, hAPP(_1512977, 38417 ^ [_1512973, _1512975, _1512977, _1512979]))], (38419 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1512973, 38417 ^ [_1512973, _1512975, _1512977, _1512979])))]], -(c_Wellfounded_Owf(tc_prod(_1512979, _1512975), c_Recdef_Osame__fst(_1512979, _1512975, _1512973, _1512977)))], (34227 ^ _776541) ^ [_1412975, _1412977] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412975)), hAPP(c_Nat_OSuc, _1412977)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1412975))), 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, _1412977))), 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)), _1412977)))))], (19819 ^ _776541) ^ [_1134230, _1134232] : [class_Rings_Olinordered__idom(_1134230), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134230), c_Groups_Ozero__class_Ozero(_1134230)), _1134232)), -(c_Groups_Osgn__class_Osgn(_1134230, _1134232) = c_Groups_Oone__class_Oone(_1134230))], (34928 ^ _776541) ^ [_1428155, _1428157] : [_1428155 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1428155, _1428157) = 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)))], (33340 ^ _776541) ^ [_1388375, _1388377, _1388379, _1388381, _1388383] : [class_Fields_Ofield(_1388375), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388375), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388377, _1388375), _1388379), _1388381)), _1388383) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388377, _1388375), hAPP(hAPP(c_COMBC(_1388377, _1388375, _1388375), hAPP(hAPP(c_COMBB(_1388375, tc_fun(_1388375, _1388375), _1388377), c_Rings_Oinverse__class_Odivide(_1388375)), _1388379)), _1388383)), _1388381))], (47599 ^ _776541) ^ [_1733745, _1733747, _1733749] : [hBOOL(hAPP(hAPP(c_member(_1733745), _1733747), hAPP(c_List_Oset(_1733745), _1733749))), -(c_List_Oinsert(_1733745, _1733747, _1733749) = _1733749)], (23748 ^ _776541) ^ [_1206636] : [hBOOL(hAPP(_1206636, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23749 ^ [_1206636]))), 23752 ^ _776541 : [(23753 ^ _776541) ^ [_1206736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206736)), -(hBOOL(hAPP(_1206636, _1206736)))]]], (33334 ^ _776541) ^ [_1388224, _1388226, _1388228, _1388230, _1388232, _1388234] : [class_Complete__Lattice_Ocomplete__lattice(_1388224), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388226, tc_fun(_1388228, _1388224)), _1388230), _1388232), _1388234) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388226, _1388224), _1388230), hAPP(hAPP(c_COMBC(_1388226, _1388228, _1388224), _1388232), _1388234)))], (33805 ^ _776541) ^ [_1402421, _1402423, _1402425, _1402427] : [-(hAPP(c_Set_Oimage(_1402421, _1402423, _1402425), _1402427) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402421, tc_fun(_1402423, tc_HOL_Obool)), _1402427), hAPP(hAPP(c_COMBC(_1402421, tc_fun(_1402423, tc_HOL_Obool), tc_fun(_1402423, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1402423, tc_fun(tc_fun(_1402423, tc_HOL_Obool), tc_fun(_1402423, tc_HOL_Obool)), _1402421), c_Set_Oinsert(_1402423)), _1402425)), c_Orderings_Obot__class_Obot(tc_fun(_1402423, tc_HOL_Obool)))))], (46321 ^ _776541) ^ [_1708204, _1708206] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1708204), _1708206))), -(c_List_Oupt(_1708204, hAPP(c_Nat_OSuc, _1708206)) = c_List_Olist_ONil(tc_Nat_Onat))], (46672 ^ _776541) ^ [_1714457, _1714459, _1714461, _1714463, _1714465] : [class_Orderings_Olinorder(_1714457), 46675 ^ _776541 : [(46682 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1714457, hAPP(hAPP(c_List_Omap(_1714459, _1714457), _1714461), _1714465)), -(c_List_Olinorder__class_Osorted(_1714457, hAPP(hAPP(c_List_Omap(_1714459, _1714457), _1714461), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1714459, _1714457, _1714461), _1714463), _1714465))))], (46676 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1714457, hAPP(hAPP(c_List_Omap(_1714459, _1714457), _1714461), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1714459, _1714457, _1714461), _1714463), _1714465))), -(c_List_Olinorder__class_Osorted(_1714457, hAPP(hAPP(c_List_Omap(_1714459, _1714457), _1714461), _1714465)))]]], (10461 ^ _776541) ^ [_956239, _956241, _956243] : [class_Groups_Oordered__ab__group__add(_956239), 10464 ^ _776541 : [(10471 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956239), hAPP(c_Groups_Ouminus__class_Ouminus(_956239), _956243)), _956241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956239), hAPP(c_Groups_Ouminus__class_Ouminus(_956239), _956241)), _956243)))], (10465 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956239), hAPP(c_Groups_Ouminus__class_Ouminus(_956239), _956241)), _956243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956239), hAPP(c_Groups_Ouminus__class_Ouminus(_956239), _956243)), _956241)))]]], (12626 ^ _776541) ^ [_998984, _998986, _998988, _998990, _998992] : [c_Finite__Set_Ofolding__one__idem(_998984, _998986, _998988), hAPP(_998990, hAPP(hAPP(_998986, 12631 ^ [_998984, _998986, _998988, _998990, _998992]), 12632 ^ [_998984, _998986, _998988, _998990, _998992])) = hAPP(hAPP(_998986, hAPP(_998990, 12631 ^ [_998984, _998986, _998988, _998990, _998992])), hAPP(_998990, 12632 ^ [_998984, _998986, _998988, _998990, _998992])), hBOOL(hAPP(c_Finite__Set_Ofinite(_998984), _998992)), -(_998992 = c_Orderings_Obot__class_Obot(tc_fun(_998984, tc_HOL_Obool))), -(hAPP(_998990, hAPP(_998988, _998992)) = hAPP(_998988, hAPP(c_Set_Oimage(_998984, _998984, _998990), _998992)))], (25481 ^ _776541) ^ [_1237472, _1237474, _1237476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237472)), 25484 ^ _776541 : [(25485 ^ _776541) ^ [] : [-(_1237474 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237476), _1237472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237472), _1237474)), _1237476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237472), hAPP(c_Nat_OSuc, _1237474))))], (25495 ^ _776541) ^ [] : [_1237474 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237476), _1237472), 25498 ^ _776541 : [(25501 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237472), hAPP(c_Nat_OSuc, _1237474)))))], (25499 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237472), _1237474)), _1237476)))]]]]], (49754 ^ _776541) ^ [_1781963, _1781965] : [-(c_Relation_Osym(_1781963, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1781963, _1781963), tc_HOL_Obool)), _1781965), hAPP(c_Relation_Oconverse(_1781963, _1781963), _1781965))))], (41574 ^ _776541) ^ [_1594292, _1594294, _1594296, _1594298, _1594300] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594292, _1594292)), hAPP(hAPP(c_Product__Type_OPair(_1594292, _1594292), _1594294), _1594296)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594292, _1594292), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1594298)), _1594300))), 41578 ^ _776541 : [(41581 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594292, _1594292)), hAPP(hAPP(c_Product__Type_OPair(_1594292, _1594292), 41577 ^ [_1594292, _1594294, _1594296, _1594298, _1594300]), _1594296)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594292, _1594292), tc_HOL_Obool), _1594298), _1594300))))], (41579 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594292, _1594292)), hAPP(hAPP(c_Product__Type_OPair(_1594292, _1594292), _1594294), 41577 ^ [_1594292, _1594294, _1594296, _1594298, _1594300])), _1594300)))]]], (11296 ^ _776541) ^ [_972869, _972871] : [class_Groups_Oordered__ab__group__add(_972869), -(hAPP(c_Set_Oimage(_972869, _972869, c_Groups_Ouminus__class_Ouminus(_972869)), hAPP(c_SetInterval_Oord__class_OatMost(_972869), _972871)) = hAPP(c_SetInterval_Oord__class_OatLeast(_972869), hAPP(c_Groups_Ouminus__class_Ouminus(_972869), _972871)))], (50934 ^ _776541) ^ [_1808011, _1808013, _1808015, _1808017] : [-(hAPP(c_Lazy__Sequence_Obind(_1808011, _1808013, _1808015), _1808017) = c_Lazy__Sequence_Oflat(_1808013, c_Lazy__Sequence_Omap(_1808011, tc_Lazy__Sequence_Olazy__sequence(_1808013), _1808017, _1808015)))], (5939 ^ _776541) ^ [_871016, _871018, _871020] : [_871018 = _871020, -(hBOOL(hAPP(hAPP(c_member(_871016), _871018), hAPP(c_fequal, _871020))))], (27569 ^ _776541) ^ [_1272493, _1272495] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1272493), _1272495)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1272493) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (3470 ^ _776541) ^ [_828387, _828389, _828391, _828393, _828395, _828397, _828399, _828401] : [-(c_List_Olist_Olist__case(_828401, _828397, _828393, _828389) = c_List_Olist_Olist__case(_828399, _828395, _828391, _828387)), _828401 = _828399, _828397 = _828395, _828393 = _828391, _828389 = _828387], (43657 ^ _776541) ^ [_1647254, _1647256, _1647258] : [_1647254 = c_List_Olist_ONil(_1647256), -(c_List_Obutlast(_1647256, hAPP(hAPP(c_List_Oappend(_1647256), _1647258), _1647254)) = c_List_Obutlast(_1647256, _1647258))], (444 ^ _776541) ^ [_783215, _783217, _783219, _783221, _783223, _783225] : [-(c_Nitpick_Oless__frac(_783223, _783219, _783215)), c_Nitpick_Oless__frac(_783225, _783221, _783217), _783225 = _783223, _783221 = _783219, _783217 = _783215], (26525 ^ _776541) ^ [_1255287, _1255289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255287)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255287), _1255289)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1255287)), hAPP(c_Int_Onat, _1255289)))], (12688 ^ _776541) ^ [_1000220, _1000222, _1000224] : [-(hAPP(c_Finite__Set_Ofold1(_1000220, _1000222), hAPP(hAPP(c_Set_Oinsert(_1000220), _1000224), c_Orderings_Obot__class_Obot(tc_fun(_1000220, tc_HOL_Obool)))) = _1000224)], (2982 ^ _776541) ^ [_820799, _820801, _820803, _820805, _820807, _820809] : [-(c_Nitpick_Oplus__frac(_820809, _820805, _820801) = c_Nitpick_Oplus__frac(_820807, _820803, _820799)), _820809 = _820807, _820805 = _820803, _820801 = _820799], (46397 ^ _776541) ^ [_1709573, _1709575] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1709573, _1709575) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1709573, hAPP(c_Nat_OSuc, _1709575))))], (44216 ^ _776541) ^ [_1660710, _1660712, _1660714] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1660710, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660712)), _1660714)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1660712, _1660710), _1660714) = _1660714)], (38718 ^ _776541) ^ [_1520715, _1520717, _1520719, _1520721, _1520723] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1520715, _1520717, _1520719), _1520721), _1520723)), -(hBOOL(hAPP(_1520721, hAPP(_1520719, _1520723))))], (31317 ^ _776541) ^ [_1338703, _1338705, _1338707, _1338709] : [class_Orderings_Olinorder(_1338703), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338703), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338703), _1338705), _1338707)), _1338709) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338703), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338703), _1338705), _1338709)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338703), _1338707), _1338709)))], (2636 ^ _776541) ^ [_815420, _815422, _815424, _815426] : [-(c_Nitpick_Onorm__frac(_815426, _815422) = c_Nitpick_Onorm__frac(_815424, _815420)), _815426 = _815424, _815422 = _815420], (52003 ^ _776541) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (43563 ^ _776541) ^ [_1645597, _1645599] : [-(hAPP(hAPP(c_List_Oappend(_1645597), c_List_Olist_ONil(_1645597)), _1645599) = _1645599)], (39281 ^ _776541) ^ [_1535216, _1535218, _1535220, _1535222, _1535224, _1535226, _1535228, _1535230] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1535216, _1535218), tc_fun(tc_prod(_1535220, _1535222), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535216, _1535218), _1535224), hAPP(c_COMBK(tc_fun(_1535218, tc_HOL_Obool), _1535216), _1535226))), hAPP(c_Product__Type_Oprod_Oprod__case(_1535216, _1535218, tc_fun(tc_prod(_1535220, _1535222), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1535216, tc_fun(_1535218, tc_fun(_1535220, tc_fun(_1535222, tc_HOL_Obool))), tc_fun(_1535218, tc_fun(tc_prod(_1535220, _1535222), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1535220, tc_fun(_1535222, tc_HOL_Obool)), tc_fun(tc_prod(_1535220, _1535222), tc_HOL_Obool)), tc_fun(tc_fun(_1535218, tc_fun(_1535220, tc_fun(_1535222, tc_HOL_Obool))), tc_fun(_1535218, tc_fun(tc_prod(_1535220, _1535222), tc_HOL_Obool))), _1535216), c_COMBB(tc_fun(_1535220, tc_fun(_1535222, tc_HOL_Obool)), tc_fun(tc_prod(_1535220, _1535222), tc_HOL_Obool), _1535218)), hAPP(hAPP(c_COMBB(tc_fun(_1535220, tc_HOL_Obool), tc_fun(tc_fun(_1535220, tc_fun(_1535222, tc_HOL_Obool)), tc_fun(tc_prod(_1535220, _1535222), tc_HOL_Obool)), _1535216), c_Product__Type_OSigma(_1535220, _1535222)), _1535228))), hAPP(hAPP(c_COMBB(tc_fun(_1535222, tc_HOL_Obool), tc_fun(_1535220, tc_fun(_1535222, tc_HOL_Obool)), _1535218), c_COMBK(tc_fun(_1535222, tc_HOL_Obool), _1535220)), _1535230)))) = hAPP(hAPP(c_Product__Type_OSigma(_1535220, _1535222), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535216, tc_fun(_1535220, tc_HOL_Obool)), _1535224), _1535228)), hAPP(c_COMBK(tc_fun(_1535222, tc_HOL_Obool), _1535220), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535218, tc_fun(_1535222, tc_HOL_Obool)), _1535226), _1535230))))], (40210 ^ _776541) ^ [_1559990, _1559992, _1559994, _1559996, _1559998, _1560000] : [c_Finite__Set_Ofolding(_1559990, _1559992, _1559994, _1559996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559990), _1559998)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559990), _1560000)), -(hAPP(c_Fun_Ocomp(_1559992, _1559992, _1559992, hAPP(_1559996, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1559990, tc_HOL_Obool)), _1559998), _1560000))), hAPP(_1559996, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1559990, tc_HOL_Obool)), _1559998), _1560000))) = hAPP(c_Fun_Ocomp(_1559992, _1559992, _1559992, hAPP(_1559996, _1559998)), hAPP(_1559996, _1560000)))], (28445 ^ _776541) ^ [_1287085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1287085), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1287085)), c_Int_OMin)))], (49373 ^ _776541) ^ [_1773495, _1773497, _1773499, _1773501] : [class_Complete__Lattice_Ocomplete__lattice(_1773495), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1773497, _1773495), _1773499), _1773501) = c_Complete__Lattice_OSup__class_OSup(_1773495, hAPP(c_Set_OCollect(_1773495), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773497, _1773495), tc_HOL_Obool), tc_HOL_Obool, _1773495), c_HOL_OEx(tc_fun(_1773497, _1773495))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773497, _1773495), tc_HOL_Obool), tc_fun(tc_fun(_1773497, _1773495), tc_HOL_Obool), _1773495), hAPP(c_COMBS(tc_fun(_1773497, _1773495), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1773497, _1773495)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1773497, _1773495), tc_fun(tc_fun(_1773497, _1773495), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1773497, _1773495))), _1773499)))), hAPP(hAPP(c_COMBC(_1773495, tc_fun(tc_fun(_1773497, _1773495), _1773495), tc_fun(tc_fun(_1773497, _1773495), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773495, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1773497, _1773495), _1773495), tc_fun(tc_fun(_1773497, _1773495), tc_HOL_Obool)), _1773495), c_COMBB(_1773495, tc_HOL_Obool, tc_fun(_1773497, _1773495))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1773497, _1773495), _1773497, _1773495), c_COMBI(tc_fun(_1773497, _1773495))), _1773501)))))))], (39525 ^ _776541) ^ [_1542989, _1542991, _1542993] : [-(c_Relation_Orefl__on(_1542989, _1542991, _1542993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542989, _1542989), tc_HOL_Obool)), _1542993), hAPP(hAPP(c_Product__Type_OSigma(_1542989, _1542989), _1542991), hAPP(c_COMBK(tc_fun(_1542989, tc_HOL_Obool), _1542989), _1542991)))), 39531 ^ _776541 : [(39534 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542989, _1542989)), hAPP(hAPP(c_Product__Type_OPair(_1542989, _1542989), 39530 ^ [_1542989, _1542991, _1542993]), 39530 ^ [_1542989, _1542991, _1542993])), _1542993))], (39532 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542989), 39530 ^ [_1542989, _1542991, _1542993]), _1542991)))]]], (41136 ^ _776541) ^ [_1583170, _1583172, _1583174] : [c_Relation_Orefl__on(_1583170, _1583172, _1583174), -(c_Relation_Orefl__on(_1583170, _1583172, hAPP(c_Relation_Oconverse(_1583170, _1583170), _1583174)))], (34203 ^ _776541) ^ [_1412404, _1412406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412404)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412406))), -(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(_1412406))), 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), _1412404)), c_Int_Onat))))))], (49706 ^ _776541) ^ [_1781244, _1781246] : [hAPP(c_Relation_Oconverse(_1781244, _1781244), _1781246) = _1781246, -(c_Relation_Osym(_1781244, _1781246))], (38626 ^ _776541) ^ [_1518442, _1518444, _1518446, _1518448] : [38627 ^ _776541 : [(38628 ^ _776541) ^ [_1518496] : [hBOOL(hAPP(hAPP(_1518446, _1518496), _1518448))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1518442, _1518444, _1518446), _1518448)))], (21267 ^ _776541) ^ [_1161302, _1161304, _1161306] : [class_Int_Onumber__ring(_1161302), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161302), hAPP(c_Int_Onumber__class_Onumber__of(_1161302), _1161304)), hAPP(c_Int_Onumber__class_Onumber__of(_1161302), _1161306)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1161304), _1161306)))], (32514 ^ _776541) ^ [_1363843, _1363845, _1363847, _1363849, _1363851] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363843, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363845, tc_fun(_1363843, tc_HOL_Obool)), _1363847), _1363849)), _1363851) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363845, tc_fun(_1363843, tc_HOL_Obool)), _1363847), hAPP(hAPP(c_COMBC(_1363845, tc_fun(_1363843, tc_HOL_Obool), tc_fun(_1363843, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363843, tc_HOL_Obool), tc_fun(tc_fun(_1363843, tc_HOL_Obool), tc_fun(_1363843, tc_HOL_Obool)), _1363845), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363843, tc_HOL_Obool))), _1363849)), _1363851)))], (5176 ^ _776541) ^ [_855508, _855510, _855512, _855514, _855516, _855518, _855520, _855522] : [-(c_Quotient_OBabs(_855522, _855518, _855514, _855510) = c_Quotient_OBabs(_855520, _855516, _855512, _855508)), _855522 = _855520, _855518 = _855516, _855514 = _855512, _855510 = _855508], (14404 ^ _776541) ^ [_1036566, _1036568, _1036570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036570), _1036568))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036566), _1036568)), _1036570)))], (28975 ^ _776541) ^ [_1295973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1295973))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1295973)))], (43769 ^ _776541) ^ [_1650037, _1650039, _1650041, _1650043, _1650045] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1650037), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650039)), _1650041)))), -(hAPP(hAPP(c_List_Olist__update(_1650039, hAPP(hAPP(c_List_Oappend(_1650039), _1650041), _1650043)), _1650037), _1650045) = hAPP(hAPP(c_List_Oappend(_1650039), _1650041), hAPP(hAPP(c_List_Olist__update(_1650039, _1650043), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1650037), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650039)), _1650041))), _1650045)))], (27259 ^ _776541) ^ [_1266918, _1266920] : [class_Groups_Oordered__ab__group__add__abs(_1266918), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266918), _1266920), hAPP(c_Groups_Oabs__class_Oabs(_1266918), _1266920))))], (5731 ^ _776541) ^ [_866898] : [class_HOL_Oequal(_866898), -(c_fequal = c_HOL_Oequal__class_Oequal(_866898))], (47128 ^ _776541) ^ [_1723823, _1723825, _1723827] : [-(hAPP(c_List_Orev(_1723823), hAPP(hAPP(c_List_Odrop(_1723823), _1723825), _1723827)) = hAPP(hAPP(c_List_Otake(_1723823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723823)), _1723827)), _1723825)), hAPP(c_List_Orev(_1723823), _1723827)))], (8405 ^ _776541) ^ [_920855, _920857, _920859] : [class_Lattices_Osemilattice__inf(_920855), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920855), _920857), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920855), _920857), _920859)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920855), _920857), _920859))], (19845 ^ _776541) ^ [_1134632, _1134634, _1134636, _1134638] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1134632), _1134634)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134636), _1134638)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1134632, _1134636)), c_Sum__Type_OPlus(_1134632, _1134636, _1134634, _1134638)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1134632), _1134634)), hAPP(c_Finite__Set_Ocard(_1134636), _1134638)))], (1144 ^ _776541) ^ [_793705, _793707] : [-(class_Rings_Oring__no__zero__divisors(_793705)), _793707 = _793705, class_Rings_Oring__no__zero__divisors(_793707)], (38991 ^ _776541) ^ [_1527260, _1527262, _1527264, _1527266] : [hBOOL(hAPP(hAPP(c_member(_1527260), _1527262), hAPP(c_Relation_ODomain(_1527260, _1527264), _1527266))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527260, _1527264)), hAPP(hAPP(c_Product__Type_OPair(_1527260, _1527264), _1527262), 38994 ^ [_1527260, _1527262, _1527264, _1527266])), _1527266)))], (8032 ^ _776541) ^ [_912932, _912934, _912936, _912938] : [hBOOL(hAPP(hAPP(c_member(_912932), _912934), _912936)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912932, tc_HOL_Obool)), _912936), hAPP(hAPP(c_Set_Oinsert(_912932), _912934), _912938)) = hAPP(hAPP(c_Set_Oinsert(_912932), _912934), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912932, tc_HOL_Obool)), _912936), _912938)))], (31691 ^ _776541) ^ [_1345685, _1345687] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1345685), _1345687)), _1345687) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1345685), _1345687))], (28749 ^ _776541) ^ [_1291859, _1291861] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1291859))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1291861)) = 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)))), _1291859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1291861)))], (10192 ^ _776541) ^ [_951475, _951477, _951479] : [class_Orderings_Olinorder(_951475), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951475), _951477), _951479)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951475, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_951475), _951477), c_Orderings_Obot__class_Obot(tc_fun(_951475, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_951475, _951477, _951479)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951475, _951477), _951479))], (27851 ^ _776541) ^ [_1277295, _1277297] : [class_Int_Onumber__ring(_1277295), class_Rings_Olinordered__idom(_1277295), 27858 ^ _776541 : [(27865 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277295), hAPP(c_Int_Onumber__class_Onumber__of(_1277295), _1277297)), c_Groups_Ozero__class_Ozero(_1277295)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1277295), hAPP(c_Int_Onumber__class_Onumber__of(_1277295), _1277297)) = hAPP(c_Int_Onumber__class_Onumber__of(_1277295), _1277297))], (27859 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277295), hAPP(c_Int_Onumber__class_Onumber__of(_1277295), _1277297)), c_Groups_Ozero__class_Ozero(_1277295))), -(hAPP(c_Groups_Oabs__class_Oabs(_1277295), hAPP(c_Int_Onumber__class_Onumber__of(_1277295), _1277297)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1277295), hAPP(c_Int_Onumber__class_Onumber__of(_1277295), _1277297)))]]], (21477 ^ _776541) ^ [_1165661, _1165663, _1165665, _1165667] : [class_Fields_Ofield__inverse__zero(_1165661), class_Int_Onumber(_1165661), 21484 ^ _776541 : [(21485 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165661), _1165663) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165661), _1165665), _1165667), 21488 ^ _776541 : [(21495 ^ _776541) ^ [] : [_1165667 = c_Groups_Ozero__class_Ozero(_1165661), -(hAPP(c_Int_Onumber__class_Onumber__of(_1165661), _1165663) = c_Groups_Ozero__class_Ozero(_1165661))], (21489 ^ _776541) ^ [] : [-(_1165667 = c_Groups_Ozero__class_Ozero(_1165661)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165661), hAPP(c_Int_Onumber__class_Onumber__of(_1165661), _1165663)), _1165667) = _1165665)]]], (21501 ^ _776541) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1165661), _1165663) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165661), _1165665), _1165667)), 21504 ^ _776541 : [(21507 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165661), hAPP(c_Int_Onumber__class_Onumber__of(_1165661), _1165663)), _1165667) = _1165665], (21505 ^ _776541) ^ [] : [_1165667 = c_Groups_Ozero__class_Ozero(_1165661)]], 21508 ^ _776541 : [(21511 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165661), _1165663) = c_Groups_Ozero__class_Ozero(_1165661)], (21509 ^ _776541) ^ [] : [-(_1165667 = c_Groups_Ozero__class_Ozero(_1165661))]]]]], (30070 ^ _776541) ^ [_1315885, _1315887, _1315889, _1315891] : [class_Orderings_Olinorder(_1315885), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315885), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315885), _1315887), _1315889)), _1315891) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315885), _1315887), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315885), _1315889), _1315891)))], (29005 ^ _776541) ^ [_1296484, _1296486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296484), _1296486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296484)), c_Int_OBit0(_1296486))))], (28751 ^ _776541) ^ [_1291910, _1291912] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1291910))), _1291912) = 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)))), _1291910), _1291912))], (14857 ^ _776541) ^ [_1044509, _1044511, _1044513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044509), _1044511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044509), _1044513)), 14864 ^ _776541 : [(14871 ^ _776541) ^ [] : [_1044511 = _1044513, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044511), _1044509) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044513), _1044509))], (14865 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044511), _1044509) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044513), _1044509), -(_1044511 = _1044513)]]], (22881 ^ _776541) ^ [_1191083, _1191085, _1191087] : [class_Rings_Oring__1(_1191083), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191083), hAPP(c_Groups_Ouminus__class_Ouminus(_1191083), _1191085)), _1191087) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191083), hAPP(hAPP(c_Power_Opower__class_Opower(_1191083), hAPP(c_Groups_Ouminus__class_Ouminus(_1191083), c_Groups_Oone__class_Oone(_1191083))), _1191087)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191083), _1191085), _1191087)))], (9556 ^ _776541) ^ [_940468, _940470, _940472] : [class_Orderings_Oorder(_940468), -(_940470 = _940472), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940468), _940472), _940470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940468), _940472), _940470)))], (4818 ^ _776541) ^ [_849895, _849897] : [_849897 = _849895, -(c_Set_OBex(_849897) = c_Set_OBex(_849895))], (46071 ^ _776541) ^ [_1701923, _1701925, _1701927, _1701929] : [-(hBOOL(hAPP(_1701923, _1701925))), -(c_List_Oremove1(_1701927, _1701925, hAPP(c_List_Ofilter(_1701927, _1701923), _1701929)) = hAPP(c_List_Ofilter(_1701927, _1701923), _1701929))], (25303 ^ _776541) ^ [_1234434, _1234436] : [-(_1234434 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234436), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234434), _1234436))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234434, _1234436)))], (45848 ^ _776541) ^ [_1696245, _1696247, _1696249] : [hBOOL(hAPP(c_List_Odistinct(_1696245), _1696247)), -(c_List_Oremove1(_1696245, _1696249, _1696247) = hAPP(c_List_OremoveAll(_1696245, _1696249), _1696247))], (34483 ^ _776541) ^ [_1418257, _1418259, _1418261, _1418263, _1418265, _1418267] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418257, tc_fun(_1418259, tc_HOL_Obool))), _1418261), _1418263), _1418265), _1418267)), 34486 ^ _776541 : [(34489 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1418263, _1418265), _1418267)))], (34487 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1418261, _1418265), _1418267)))]]], (10911 ^ _776541) ^ [_964882, _964884, _964886, _964888] : [c_Finite__Set_Ofolding__one(_964882, _964884, _964886), -(hAPP(_964886, hAPP(hAPP(c_Set_Oinsert(_964882), _964888), c_Orderings_Obot__class_Obot(tc_fun(_964882, tc_HOL_Obool)))) = _964888)], (32610 ^ _776541) ^ [_1367847, _1367849, _1367851, _1367853, _1367855] : [_1367847 = c_Orderings_Obot__class_Obot(tc_fun(_1367849, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367851, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367849, tc_fun(_1367851, tc_HOL_Obool)), _1367847), _1367853)), _1367855) = _1367855)], (17215 ^ _776541) ^ [_1086450, _1086452, _1086454, _1086456] : [class_Rings_Olinordered__semidom(_1086450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086450), c_Groups_Ozero__class_Ozero(_1086450)), _1086452)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086450), _1086454), _1086456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086450), _1086454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086450), _1086452), _1086456))))], (25175 ^ _776541) ^ [_1232374, _1232376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232374)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232374), _1232376)), _1232374) = _1232376)], (29087 ^ _776541) ^ [_1297913, _1297915] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1297913)), c_Int_OBit0(_1297915)))], (37646 ^ _776541) ^ [_1493313] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1493313)), c_Int_OInteg)))], (45577 ^ _776541) ^ [_1690421, _1690423, _1690425] : [-(c_Enum_Oproduct(_1690421, _1690423, c_List_Olist_ONil(_1690421), _1690425) = c_List_Olist_ONil(tc_prod(_1690421, _1690423)))], (51847 ^ _776541) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (26042 ^ _776541) ^ [_1247242, _1247244, _1247246] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247242), _1247244)), _1247246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247242), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247244), _1247246))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247242), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247244, _1247246))), _1247246)))], (42506 ^ _776541) ^ [_1622187, _1622189, _1622191, _1622193, _1622195] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1622187, _1622189)), _1622191), hAPP(hAPP(c_List_Ozip(_1622187, _1622189), _1622193), _1622195)) = hAPP(hAPP(c_List_Ozip(_1622187, _1622189), hAPP(hAPP(c_List_Otake(_1622187), _1622191), _1622193)), hAPP(hAPP(c_List_Otake(_1622189), _1622191), _1622195)))], (12987 ^ _776541) ^ [_1005695, _1005697, _1005699] : [class_Lattices_Olattice(_1005695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005695), _1005697)), -(hBOOL(hAPP(hAPP(c_member(_1005695), _1005699), _1005697))), -(c_Big__Operators_Olattice__class_OSup__fin(_1005695, hAPP(hAPP(c_Set_Oinsert(_1005695), _1005699), _1005697)) = hAPP(hAPP(c_Finite__Set_Ofold(_1005695, _1005695, c_Lattices_Osemilattice__sup__class_Osup(_1005695)), _1005699), _1005697))], (25097 ^ _776541) ^ [_1230882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230882)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1230882) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1230882), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (6503 ^ _776541) ^ [_881606, _881608] : [-(hBOOL(hAPP(_881608, 6504 ^ [_881606, _881608]))), -(hAPP(c_Set_OCollect(_881606), _881608) = c_Orderings_Obot__class_Obot(tc_fun(_881606, tc_HOL_Obool)))], (44302 ^ _776541) ^ [_1662445, _1662447, _1662449, _1662451] : [class_Orderings_Olinorder(_1662445), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662445, _1662445, c_COMBI(_1662445)), _1662447), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662445, _1662445, c_COMBI(_1662445)), _1662449), _1662451)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662445, _1662445, c_COMBI(_1662445)), _1662449), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662445, _1662445, c_COMBI(_1662445)), _1662447), _1662451)))], (20821 ^ _776541) ^ [_1152434, _1152436, _1152438, _1152440] : [class_Fields_Ofield(_1152434), -(_1152436 = c_Groups_Ozero__class_Ozero(_1152434)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152434), _1152438), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152434), _1152440), _1152436)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152434), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152434), _1152436), _1152438)), _1152440)), _1152436))], (2166 ^ _776541) ^ [_807967, _807969] : [_807969 = _807967, -(c_Int_Osucc(_807969) = c_Int_Osucc(_807967))], (48262 ^ _776541) ^ [_1748613, _1748615, _1748617] : [c_FunDef_Ois__measure(_1748613, _1748615), -(c_FunDef_Ois__measure(tc_prod(_1748613, _1748617), hAPP(hAPP(c_COMBB(_1748613, tc_Nat_Onat, tc_prod(_1748613, _1748617)), _1748615), c_Product__Type_Ofst(_1748613, _1748617))))], (36606 ^ _776541) ^ [_1470206, _1470208, _1470210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1470206, _1470206), tc_HOL_Obool)), _1470208), _1470210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470206, tc_HOL_Obool)), hAPP(c_Relation_OField(_1470206), _1470208)), hAPP(c_Relation_OField(_1470206), _1470210))))], (19727 ^ _776541) ^ [_1132652, _1132654, _1132656] : [class_Rings_Odivision__ring(_1132652), -(_1132654 = c_Groups_Ozero__class_Ozero(_1132652)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132652), hAPP(c_Groups_Ouminus__class_Ouminus(_1132652), _1132656)), hAPP(c_Groups_Ouminus__class_Ouminus(_1132652), _1132654)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132652), _1132656), _1132654))], (28869 ^ _776541) ^ [_1294131, _1294133] : [c_Int_OBit0(_1294131) = c_Int_OBit0(_1294133), -(_1294131 = _1294133)], (1734 ^ _776541) ^ [_801080, _801082] : [-(class_Rings_Ozero__neq__one(_801080)), _801082 = _801080, class_Rings_Ozero__neq__one(_801082)], (29337 ^ _776541) ^ [_1302267, _1302269] : [class_Fields_Olinordered__field__inverse__zero(_1302267), class_Int_Onumber__ring(_1302267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302267), c_Groups_Ozero__class_Ozero(_1302267)), _1302269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302267), c_Groups_Ozero__class_Ozero(_1302267)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302267), _1302269), hAPP(c_Int_Onumber__class_Onumber__of(_1302267), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (52465 ^ _776541) ^ [_1830936, _1830938, _1830940, _1830942] : [-(hAPP(hAPP(c_COMBK(_1830936, _1830938), _1830940), _1830942) = _1830940)], (46241 ^ _776541) ^ [_1706515, _1706517, _1706519, _1706521, _1706523, _1706525, _1706527] : [-(c_List_Ofoldr(_1706515, _1706517, _1706519, hAPP(hAPP(c_List_Omap(_1706521, _1706515), _1706523), _1706525), _1706527) = c_List_Ofoldr(_1706521, _1706517, hAPP(c_Fun_Ocomp(_1706515, tc_fun(_1706517, _1706517), _1706521, _1706519), _1706523), _1706525, _1706527))], (5496 ^ _776541) ^ [_860520, _860522, _860524, _860526, _860528, _860530] : [-(c_Divides_Odiv__class_Omod(_860530, _860526, _860522) = c_Divides_Odiv__class_Omod(_860528, _860524, _860520)), _860530 = _860528, _860526 = _860524, _860522 = _860520], (52039 ^ _776541) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (42095 ^ _776541) ^ [_1610400, _1610402, _1610404, _1610406, _1610408, _1610410] : [-(c_List_Olistrelp(_1610400, _1610402, hAPP(hAPP(c_List_Olist_OCons(_1610400), _1610404), _1610406), hAPP(hAPP(c_List_Olist_OCons(_1610400), _1610408), _1610410))), hBOOL(hAPP(hAPP(_1610402, _1610404), _1610408)), c_List_Olistrelp(_1610400, _1610402, _1610406, _1610410)], (45090 ^ _776541) ^ [_1679533, _1679535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1679533)), hAPP(c_Code__Numeral_Oof__nat, _1679535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1679533), _1679535)))], (45217 ^ _776541) ^ [] : [-(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))))], (40859 ^ _776541) ^ [_1576446, _1576448, _1576450, _1576452] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576446, _1576446)), hAPP(hAPP(c_Product__Type_OPair(_1576446, _1576446), _1576448), _1576450)), c_Transitive__Closure_Ortrancl(_1576446, _1576452))), -(_1576448 = _1576450), 40866 ^ _776541 : [(40869 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576446, _1576446)), hAPP(hAPP(c_Product__Type_OPair(_1576446, _1576446), _1576448), _1576450)), c_Transitive__Closure_Otrancl(_1576446, _1576452))))], (40867 ^ _776541) ^ [] : [_1576448 = _1576450]]], (43763 ^ _776541) ^ [_1649868, _1649870, _1649872, _1649874, _1649876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649868), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649870)), _1649872))), -(hAPP(hAPP(c_List_Olist__update(_1649870, hAPP(hAPP(c_List_Oappend(_1649870), _1649872), _1649874)), _1649868), _1649876) = hAPP(hAPP(c_List_Oappend(_1649870), hAPP(hAPP(c_List_Olist__update(_1649870, _1649872), _1649868), _1649876)), _1649874))], (33511 ^ _776541) ^ [_1393109, _1393111, _1393113, _1393115, _1393117] : [_1393109 = c_Orderings_Obot__class_Obot(tc_fun(_1393111, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393111, tc_fun(_1393113, tc_HOL_Obool)), _1393109), hAPP(hAPP(c_COMBB(tc_fun(_1393113, tc_HOL_Obool), tc_fun(_1393113, tc_HOL_Obool), _1393111), hAPP(c_Set_Oinsert(_1393113), _1393115)), _1393117)) = c_Orderings_Obot__class_Obot(tc_fun(_1393113, tc_HOL_Obool)))], (24932 ^ _776541) ^ [_1227999, _1228001, _1228003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227999), _1228001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227999), _1228003)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228001), _1228003))))], (31873 ^ _776541) ^ [_1349072, _1349074, _1349076] : [class_Orderings_Olinorder(_1349072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349072), _1349074)), 31880 ^ _776541 : [(31887 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349072, tc_HOL_Obool)), _1349074), hAPP(hAPP(c_Set_Oinsert(_1349072), _1349076), c_Orderings_Obot__class_Obot(tc_fun(_1349072, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349072, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1349072, hAPP(hAPP(c_Set_Oinsert(_1349072), _1349076), _1349074)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349072), _1349076), c_Big__Operators_Olinorder__class_OMax(_1349072, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349072, tc_HOL_Obool)), _1349074), hAPP(hAPP(c_Set_Oinsert(_1349072), _1349076), c_Orderings_Obot__class_Obot(tc_fun(_1349072, tc_HOL_Obool)))))))], (31881 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349072, tc_HOL_Obool)), _1349074), hAPP(hAPP(c_Set_Oinsert(_1349072), _1349076), c_Orderings_Obot__class_Obot(tc_fun(_1349072, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349072, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1349072, hAPP(hAPP(c_Set_Oinsert(_1349072), _1349076), _1349074)) = _1349076)]]], (42256 ^ _776541) ^ [_1614501, _1614503, _1614505, _1614507] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614501) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1614503), hAPP(hAPP(c_List_Olist_OCons(_1614503), _1614505), _1614507)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614501)) = hAPP(hAPP(c_List_Onth(_1614503), _1614507), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614501)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (26973 ^ _776541) ^ [_1262393, _1262395, _1262397] : [class_Rings_Oring__1(_1262393), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1262395), _1262397)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1262393), hAPP(c_Int_Oring__1__class_Oof__int(_1262393), _1262395)), hAPP(c_Int_Oring__1__class_Oof__int(_1262393), _1262397)))], (43902 ^ _776541) ^ [_1653732, _1653734, _1653736, _1653738] : [-(hAPP(hAPP(c_List_Otake(_1653732), _1653734), hAPP(hAPP(c_List_Odrop(_1653732), _1653736), _1653738)) = hAPP(hAPP(c_List_Odrop(_1653732), _1653736), hAPP(hAPP(c_List_Otake(_1653732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653734), _1653736)), _1653738)))], (43156 ^ _776541) ^ [_1636310, _1636312, _1636314, _1636316] : [-(_1636310 = _1636312), 43159 ^ _776541 : [(43166 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1636314), _1636310), hAPP(c_List_Oset(_1636314), _1636316))), -(hBOOL(hAPP(hAPP(c_member(_1636314), _1636310), hAPP(c_List_Oset(_1636314), c_List_Oremove1(_1636314, _1636312, _1636316)))))], (43160 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1636314), _1636310), hAPP(c_List_Oset(_1636314), c_List_Oremove1(_1636314, _1636312, _1636316)))), -(hBOOL(hAPP(hAPP(c_member(_1636314), _1636310), hAPP(c_List_Oset(_1636314), _1636316))))]]], (20013 ^ _776541) ^ [_1137858, _1137860, _1137862, _1137864] : [class_Fields_Olinordered__field__inverse__zero(_1137858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137858), _1137860), _1137862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137858), _1137864), c_Groups_Ozero__class_Ozero(_1137858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137858), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137858), _1137862), _1137864)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137858), _1137860), _1137864))))], (8869 ^ _776541) ^ [_929194, _929196, _929198] : [class_Orderings_Olinorder(_929194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929194), _929196), _929198)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_929194, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_929194, _929196, _929198)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_929194), _929198)) = hAPP(c_SetInterval_Oord__class_OatLeast(_929194), _929196))], (12892 ^ _776541) ^ [_1004009, _1004011, _1004013, _1004015, _1004017] : [c_Finite__Set_Ofolding__one(_1004009, _1004011, _1004013), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004009), _1004015)), -(hBOOL(hAPP(hAPP(c_member(_1004009), _1004017), _1004015))), -(hAPP(_1004013, hAPP(hAPP(c_Set_Oinsert(_1004009), _1004017), _1004015)) = hAPP(hAPP(c_Finite__Set_Ofold(_1004009, _1004009, _1004011), _1004017), _1004015))], (32634 ^ _776541) ^ [_1368636, _1368638, _1368640, _1368642, _1368644] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368636, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368638, tc_fun(_1368636, tc_HOL_Obool)), _1368640), _1368642)), _1368644) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368638, tc_fun(_1368636, tc_HOL_Obool)), _1368640), hAPP(hAPP(c_COMBC(_1368638, tc_fun(_1368636, tc_HOL_Obool), tc_fun(_1368636, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368636, tc_HOL_Obool), tc_fun(tc_fun(_1368636, tc_HOL_Obool), tc_fun(_1368636, tc_HOL_Obool)), _1368638), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368636, tc_HOL_Obool))), _1368642)), _1368644)))], (41700 ^ _776541) ^ [_1597686, _1597688, _1597690] : [c_Nitpick_Oless__eq__frac(_1597686, _1597688, _1597690), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597686), c_Nitpick_Oplus__frac(_1597686, _1597688, c_Nitpick_Ouminus__frac(_1597686, _1597690)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (1094 ^ _776541) ^ [_793080, _793082] : [-(class_Rings_Olinordered__semiring__1__strict(_793080)), _793082 = _793080, class_Rings_Olinordered__semiring__1__strict(_793082)], (48352 ^ _776541) ^ [_1750320, _1750322, _1750324, _1750326] : [-(c_List_Olist__ex1(_1750320, _1750322, hAPP(hAPP(c_List_Olist_OCons(_1750320), _1750324), _1750326))), 48355 ^ _776541 : [(48358 ^ _776541) ^ [] : [c_List_Olist__all(_1750320, hAPP(hAPP(c_COMBS(_1750320, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1750320), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750320), c_fNot), _1750322))), hAPP(c_fequal, _1750324)), _1750326)], (48356 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1750322, _1750324)))]], 48359 ^ _776541 : [(48362 ^ _776541) ^ [] : [c_List_Olist__ex1(_1750320, _1750322, _1750326)], (48360 ^ _776541) ^ [] : [hBOOL(hAPP(_1750322, _1750324))]]], (40108 ^ _776541) ^ [_1557778, _1557780, _1557782, _1557784, _1557786, _1557788] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1557778, _1557780), _1557780, tc_prod(_1557782, _1557784), c_Product__Type_Osnd(_1557778, _1557780)), c_Product__Type_Omap__pair(_1557782, _1557778, _1557784, _1557780, _1557786, _1557788)) = hAPP(c_Fun_Ocomp(_1557784, _1557780, tc_prod(_1557782, _1557784), _1557788), c_Product__Type_Osnd(_1557782, _1557784)))], (52189 ^ _776541) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (7828 ^ _776541) ^ [_908276, _908278, _908280] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908276, tc_HOL_Obool)), _908278), _908280) = c_Orderings_Obot__class_Obot(tc_fun(_908276, tc_HOL_Obool)), 7831 ^ _776541 : [(7834 ^ _776541) ^ [] : [-(_908280 = c_Orderings_Obot__class_Obot(tc_fun(_908276, tc_HOL_Obool)))], (7832 ^ _776541) ^ [] : [-(_908278 = c_Orderings_Obot__class_Obot(tc_fun(_908276, tc_HOL_Obool)))]]], (26066 ^ _776541) ^ [_1247737] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1247737)), -(hAPP(c_Int_Onat, _1247737) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31583 ^ _776541) ^ [_1343582, _1343584, _1343586, _1343588] : [class_Orderings_Olinorder(_1343582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343582), _1343584), _1343586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343582), _1343584), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343582), _1343588), _1343586))))], (7646 ^ _776541) ^ [_903492, _903494, _903496, _903498] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903492, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903492, tc_HOL_Obool)), _903494), _903496)), _903498) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903492, tc_HOL_Obool)), _903494), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903492, tc_HOL_Obool)), _903496), _903498)))], (41993 ^ _776541) ^ [_1607070, _1607072, _1607074] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607070), tc_List_Olist(_1607070))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607070), tc_List_Olist(_1607070)), _1607072), _1607072)), c_List_Olistrel(_1607070, c_Transitive__Closure_Ortrancl(_1607070, _1607074)))))], (37422 ^ _776541) ^ [_1488707, _1488709, _1488711, _1488713, _1488715] : [c_Fun_Oinj__on(_1488707, _1488709, _1488711, _1488713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1488707, tc_HOL_Obool)), _1488715), _1488713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1488709, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1488707, _1488709, _1488711), _1488715)), hAPP(c_Set_Oimage(_1488707, _1488709, _1488711), _1488713))))], (37400 ^ _776541) ^ [_1488307, _1488309, _1488311, _1488313, _1488315] : [c_Fun_Oinj__on(_1488307, _1488309, _1488311, c_Orderings_Otop__class_Otop(tc_fun(_1488307, tc_HOL_Obool))), 37403 ^ _776541 : [(37410 ^ _776541) ^ [] : [_1488313 = _1488315, -(hAPP(c_Set_Oimage(_1488307, _1488309, _1488311), _1488313) = hAPP(c_Set_Oimage(_1488307, _1488309, _1488311), _1488315))], (37404 ^ _776541) ^ [] : [hAPP(c_Set_Oimage(_1488307, _1488309, _1488311), _1488313) = hAPP(c_Set_Oimage(_1488307, _1488309, _1488311), _1488315), -(_1488313 = _1488315)]]], (11066 ^ _776541) ^ [_967890, _967892, _967894] : [class_Rings_Oring(_967890), -(hAPP(c_Groups_Ouminus__class_Ouminus(_967890), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967890), _967892), _967894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967890), hAPP(c_Groups_Ouminus__class_Ouminus(_967890), _967892)), _967894))], (40453 ^ _776541) ^ [_1565711, _1565713, _1565715, _1565717] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1565711, tc_HOL_Obool), tc_fun(_1565711, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1565711, tc_HOL_Obool), tc_fun(_1565711, tc_HOL_Obool)), _1565713), _1565715)), c_Wellfounded_Omax__ext(_1565711, _1565717)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565711), _1565713)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565711), _1565715)), -(_1565715 = c_Orderings_Obot__class_Obot(tc_fun(_1565711, tc_HOL_Obool))), 40467 ^ _776541 : [(40470 ^ _776541) ^ [_1566116] : [hBOOL(hAPP(hAPP(c_member(_1565711), _1566116), _1565715)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565711, _1565711)), hAPP(hAPP(c_Product__Type_OPair(_1565711, _1565711), 40466 ^ [_1565711, _1565713, _1565715, _1565717]), _1566116)), _1565717))], (40468 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565711), 40466 ^ [_1565711, _1565713, _1565715, _1565717]), _1565713)))]]], (14018 ^ _776541) ^ [_1027608, _1027610, _1027612, _1027614, _1027616] : [class_Groups_Ocomm__monoid__add(_1027608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027610), _1027612)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027610), _1027614)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027608), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027610, _1027608), _1027616), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027610, tc_HOL_Obool)), _1027612), _1027614))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027610, _1027608), _1027616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027610, tc_HOL_Obool)), _1027612), _1027614))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027608), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027610, _1027608), _1027616), _1027612)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027610, _1027608), _1027616), _1027614)))], (30678 ^ _776541) ^ [_1326915, _1326917] : [class_Orderings_Olinorder(_1326915), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326915), _1326917)), -(c_Big__Operators_Olinorder__class_OMin(_1326915, _1326917) = hAPP(c_Finite__Set_Ofold1(_1326915, c_Orderings_Oord__class_Omin(_1326915)), _1326917))], (37368 ^ _776541) ^ [_1487736, _1487738, _1487740, _1487742, _1487744] : [c_Fun_Oinj__on(_1487736, _1487738, _1487740, c_Orderings_Otop__class_Otop(tc_fun(_1487736, tc_HOL_Obool))), 37371 ^ _776541 : [(37378 ^ _776541) ^ [] : [_1487742 = _1487744, -(hAPP(_1487740, _1487742) = hAPP(_1487740, _1487744))], (37372 ^ _776541) ^ [] : [hAPP(_1487740, _1487742) = hAPP(_1487740, _1487744), -(_1487742 = _1487744)]]], (6579 ^ _776541) ^ [_882885, _882887, _882889] : [6581 ^ _776541 : [(6584 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_882885), _882889), 6580 ^ [_882885, _882887, _882889]))], (6582 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_882885, tc_HOL_Obool)), 6580 ^ [_882885, _882887, _882889]), _882887)))]], -(hBOOL(hAPP(hAPP(c_member(_882885), _882889), c_Complete__Lattice_OInf__class_OInf(tc_fun(_882885, tc_HOL_Obool), _882887))))], (40383 ^ _776541) ^ [_1563881, _1563883] : [40384 ^ _776541 : [(40385 ^ _776541) ^ [_1563927] : [hBOOL(hAPP(_1563881, _1563927))]], -(hBOOL(hAPP(_1563881, c_Hilbert__Choice_OEps(_1563883, _1563881))))], (48836 ^ _776541) ^ [_1760752] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1760752) = c_Lazy__Sequence_Osmall__lazy_H(_1760752, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1760752)))], (24960 ^ _776541) ^ [_1228565, _1228567] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228565, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228567)) = 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), _1228565), _1228567)))], (50245 ^ _776541) ^ [_1792245, _1792247, _1792249, _1792251] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1792245, _1792247, _1792249, _1792251, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1792247)) = _1792249)], (39940 ^ _776541) ^ [_1554028, _1554030, _1554032, _1554034, _1554036, _1554038, _1554040] : [hAPP(c_Fun_Ocomp(_1554028, _1554030, _1554032, _1554034), _1554036) = hAPP(c_Fun_Ocomp(_1554030, _1554030, _1554032, c_Fun_Oid(_1554030)), _1554038), -(hAPP(_1554034, hAPP(_1554036, _1554040)) = hAPP(_1554038, _1554040))], (51209 ^ _776541) ^ [_1813503, _1813505, _1813507, _1813509] : [class_Rings_Ocomm__semiring__1(_1813503), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813503), _1813505), _1813507)), _1813509)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813503), _1813507), _1813509)))], (52021 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (49291 ^ _776541) ^ [_1771774] : [-(c_Relation_Otrans(tc_fun(_1771774, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1771774)))], (42301 ^ _776541) ^ [_1615948, _1615950] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1615948), hAPP(c_List_Oset(_1615948), _1615950))))], (24214 ^ _776541) ^ [_1214503, _1214505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214503), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214505), _1214503)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214503), _1214505) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19259 ^ _776541) ^ [_1124094, _1124096, _1124098] : [-(hAPP(c_Finite__Set_Ocard(_1124094), _1124096) = hAPP(c_Nat_OSuc, _1124098)), 19260 ^ _776541 : [(19261 ^ _776541) ^ [_1124194, _1124196] : [_1124096 = hAPP(hAPP(c_Set_Oinsert(_1124094), _1124196), _1124194), -(hBOOL(hAPP(hAPP(c_member(_1124094), _1124196), _1124194))), hAPP(c_Finite__Set_Ocard(_1124094), _1124194) = _1124098, 19272 ^ _776541 : [(19275 ^ _776541) ^ [] : [_1124194 = c_Orderings_Obot__class_Obot(tc_fun(_1124094, tc_HOL_Obool))], (19273 ^ _776541) ^ [] : [-(_1124098 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (23532 ^ _776541) ^ [_1203087, _1203089, _1203091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203087)), 23538 ^ _776541 : [(23541 ^ _776541) ^ [] : [hBOOL(hAPP(_1203089, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23537 ^ [_1203087, _1203089, _1203091]), _1203087)))], (23539 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1203089, 23537 ^ [_1203087, _1203089, _1203091])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203091)), 23546 ^ _776541 : [(23547 ^ _776541) ^ [_1203376] : [hBOOL(hAPP(_1203089, _1203376)), -(hBOOL(hAPP(_1203089, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1203376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203091), _1203087)))))]]], (15775 ^ _776541) ^ [_1062437] : [_1062437 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062437), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (34141 ^ _776541) ^ [_1410907] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1410907)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1410907)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410907)), 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)))))], (6831 ^ _776541) ^ [_887188, _887190, _887192] : [class_Complete__Lattice_Ocomplete__lattice(_887188), 6837 ^ _776541 : [(6840 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887188), 6836 ^ [_887188, _887190, _887192]), _887192))], (6838 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887188), 6836 ^ [_887188, _887190, _887192]), _887190)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887188), c_Complete__Lattice_OSup__class_OSup(_887188, _887190)), _887192)))], (47664 ^ _776541) ^ [_1735517, _1735519, _1735521, _1735523, _1735525] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1735517, _1735517)), hAPP(hAPP(c_Product__Type_OPair(_1735517, _1735517), _1735519), _1735521)), c_List_Omeasures(_1735517, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1735517, tc_Nat_Onat)), _1735523), _1735525)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1735523, _1735519)), hAPP(_1735523, _1735521)))), 47671 ^ _776541 : [(47674 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1735517, _1735517)), hAPP(hAPP(c_Product__Type_OPair(_1735517, _1735517), _1735519), _1735521)), c_List_Omeasures(_1735517, _1735525))))], (47672 ^ _776541) ^ [] : [-(hAPP(_1735523, _1735519) = hAPP(_1735523, _1735521))]]], (3638 ^ _776541) ^ [_831049, _831051, _831053, _831055] : [-(c_List_Orotate(_831055, _831051) = c_List_Orotate(_831053, _831049)), _831055 = _831053, _831051 = _831049], (41767 ^ _776541) ^ [_1599892, _1599894, _1599896, _1599898, _1599900] : [-(hAPP(hAPP(c_List_Olist_OCons(_1599892), _1599894), _1599896) = hAPP(hAPP(c_List_Olist_OCons(_1599892), _1599898), _1599900)), _1599894 = _1599898, _1599896 = _1599900], (43112 ^ _776541) ^ [_1635502] : [-(hAPP(c_List_Oset(_1635502), c_List_Olist_ONil(_1635502)) = c_Orderings_Obot__class_Obot(tc_fun(_1635502, tc_HOL_Obool)))], (11732 ^ _776541) ^ [_981924, _981926, _981928, _981930, _981932] : [c_Finite__Set_Ofolding__one(_981924, _981926, _981928), hBOOL(hAPP(c_Finite__Set_Ofinite(_981924), _981930)), -(hBOOL(hAPP(hAPP(c_member(_981924), _981932), _981930))), -(_981930 = c_Orderings_Obot__class_Obot(tc_fun(_981924, tc_HOL_Obool))), -(hAPP(_981928, hAPP(hAPP(c_Set_Oinsert(_981924), _981932), _981930)) = hAPP(hAPP(_981926, _981932), hAPP(_981928, _981930)))], (46048 ^ _776541) ^ [_1701388, _1701390, _1701392] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701388)), hAPP(c_List_Ofilter(_1701388, _1701390), _1701392))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701388)), hAPP(c_List_Ofilter(_1701388, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1701388), c_fNot), _1701390)), _1701392))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701388)), _1701392))], (39818 ^ _776541) ^ [_1551122, _1551124, _1551126, _1551128, _1551130, _1551132, _1551134, _1551136, _1551138, _1551140] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1551122, _1551124), tc_prod(_1551126, _1551128), tc_prod(_1551130, _1551132), c_Product__Type_Omap__pair(_1551122, _1551126, _1551124, _1551128, _1551134, _1551136)), c_Product__Type_Omap__pair(_1551130, _1551122, _1551132, _1551124, _1551138, _1551140)) = c_Product__Type_Omap__pair(_1551130, _1551126, _1551132, _1551128, hAPP(c_Fun_Ocomp(_1551122, _1551126, _1551130, _1551134), _1551138), hAPP(c_Fun_Ocomp(_1551124, _1551128, _1551132, _1551136), _1551140)))], (49212 ^ _776541) ^ [_1770092, _1770094] : [c_Relation_Otrans(_1770092, _1770094), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1770092, _1770092), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1770092, _1770092, _1770092), _1770094), _1770094)), _1770094)))], (42413 ^ _776541) ^ [_1618511, _1618513, _1618515] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618511)), _1618513), c_List_Olists(_1618511, _1618515))), 42416 ^ _776541 : [(42417 ^ _776541) ^ [_1618619] : [hBOOL(hAPP(hAPP(c_member(_1618511), _1618619), hAPP(c_List_Oset(_1618511), _1618513))), -(hBOOL(hAPP(hAPP(c_member(_1618511), _1618619), _1618515)))]]], (36565 ^ _776541) ^ [_1469140, _1469142, _1469144, _1469146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469140), _1469146)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469144), _1469142))), -(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), _1469140), _1469142)), 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), _1469144), _1469146)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (8691 ^ _776541) ^ [_925897, _925899, _925901, _925903] : [class_Lattices_Osemilattice__inf(_925897), 8694 ^ _776541 : [(8703 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925897), _925899), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925897), _925901), _925903)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925897), _925899), _925901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925897), _925899), _925903))], (8695 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925897), _925899), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925897), _925901), _925903))), 8698 ^ _776541 : [(8701 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925897), _925899), _925903)))], (8699 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925897), _925899), _925901)))]]]]], (50010 ^ _776541) ^ [_1786708, _1786710, _1786712] : [hAPP(c_Set_Oimage(_1786708, _1786710, _1786712), c_Orderings_Otop__class_Otop(tc_fun(_1786708, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1786710, tc_HOL_Obool)), 50013 ^ _776541 : [(50014 ^ _776541) ^ [_1786819] : [-(hAPP(_1786712, hAPP(c_Hilbert__Choice_Oinv__into(_1786708, _1786710, c_Orderings_Otop__class_Otop(tc_fun(_1786708, tc_HOL_Obool)), _1786712), _1786819)) = _1786819)]]], (14158 ^ _776541) ^ [_1030949, _1030951, _1030953, _1030955, _1030957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030949), _1030951)), 14161 ^ _776541 : [(14168 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030955), 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), _1030951), _1030949)), _1030953)), _1030957))), -(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), _1030949), _1030953)), _1030955)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030951), _1030953)), _1030957))))], (14162 ^ _776541) ^ [] : [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), _1030949), _1030953)), _1030955)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030951), _1030953)), _1030957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030955), 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), _1030951), _1030949)), _1030953)), _1030957))))]]], (14548 ^ _776541) ^ [_1038941, _1038943, _1038945] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038941), _1038943) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038945), _1038943), -(_1038941 = _1038945)], (6238 ^ _776541) ^ [_876791] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_876791, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_876791, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_876791, tc_HOL_Obool)))], (36338 ^ _776541) ^ [_1462956, _1462958, _1462960, _1462962] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462956), _1462958)), 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)), _1462956), _1462960)), 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)), _1462958), _1462962)), 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)), _1462958), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462960), _1462962))), c_FunDef_Omin__weak)))], (34055 ^ _776541) ^ [_1408705, _1408707] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408705)), 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)), _1408705))), 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, _1408707))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (39105 ^ _776541) ^ [_1530174, _1530176, _1530178, _1530180, _1530182] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530174, _1530176), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530174, tc_HOL_Obool)), _1530178), _1530180)), _1530182) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530174, _1530176), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530174, _1530176), _1530178), _1530182)), hAPP(hAPP(c_Product__Type_OSigma(_1530174, _1530176), _1530180), _1530182)))], (17565 ^ _776541) ^ [_1092883, _1092885] : [class_Rings_Olinordered__ring(_1092883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092883), _1092885), _1092885)), c_Groups_Ozero__class_Ozero(_1092883)))], (5224 ^ _776541) ^ [_856256, _856258, _856260, _856262] : [-(c_Product__Type_OPair(_856262, _856258) = c_Product__Type_OPair(_856260, _856256)), _856262 = _856260, _856258 = _856256], (27311 ^ _776541) ^ [_1267936, _1267938] : [class_Groups_Oordered__ab__group__add__abs(_1267936), -(hAPP(c_Groups_Oabs__class_Oabs(_1267936), hAPP(c_Groups_Oabs__class_Oabs(_1267936), _1267938)) = hAPP(c_Groups_Oabs__class_Oabs(_1267936), _1267938))], (40811 ^ _776541) ^ [_1575333, _1575335, _1575337, _1575339, _1575341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575333, _1575333)), hAPP(hAPP(c_Product__Type_OPair(_1575333, _1575333), _1575335), _1575337)), c_Transitive__Closure_Ortrancl(_1575333, _1575339))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575333, _1575333)), hAPP(hAPP(c_Product__Type_OPair(_1575333, _1575333), _1575337), _1575341)), _1575339)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575333, _1575333)), hAPP(hAPP(c_Product__Type_OPair(_1575333, _1575333), _1575335), _1575341)), c_Transitive__Closure_Ortrancl(_1575333, _1575339))))], (11232 ^ _776541) ^ [_971584, _971586, _971588, _971590, _971592] : [c_Typedef_Otype__definition(_971584, _971586, _971588, _971590, _971592), -(hAPP(c_Set_Oimage(_971584, _971586, _971588), c_Orderings_Otop__class_Otop(tc_fun(_971584, tc_HOL_Obool))) = _971592)], (32966 ^ _776541) ^ [_1377835, _1377837, _1377839, _1377841, _1377843] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377835, tc_fun(_1377837, tc_HOL_Obool)), _1377839), hAPP(hAPP(c_COMBC(_1377835, tc_fun(_1377837, tc_HOL_Obool), tc_fun(_1377837, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377837, tc_HOL_Obool), tc_fun(tc_fun(_1377837, tc_HOL_Obool), tc_fun(_1377837, tc_HOL_Obool)), _1377835), c_Groups_Ominus__class_Ominus(tc_fun(_1377837, tc_HOL_Obool))), _1377841)), _1377843)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377837, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377835, tc_fun(_1377837, tc_HOL_Obool)), _1377839), _1377841)), _1377843))], (45461 ^ _776541) ^ [_1688023, _1688025, _1688027, _1688029, _1688031, _1688033, _1688035] : [c_List_Olist__all2(_1688023, _1688025, _1688027, _1688029, hAPP(hAPP(c_List_Omap(_1688031, _1688025), _1688033), _1688035)), -(c_List_Olist__all2(_1688023, _1688031, hAPP(hAPP(c_COMBC(_1688023, tc_fun(_1688031, _1688025), tc_fun(_1688031, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1688025, tc_HOL_Obool), tc_fun(tc_fun(_1688031, _1688025), tc_fun(_1688031, tc_HOL_Obool)), _1688023), c_COMBB(_1688025, tc_HOL_Obool, _1688031)), _1688027)), _1688033), _1688029, _1688035))], (11266 ^ _776541) ^ [_972230, _972232, _972234] : [class_Groups_Oordered__ab__group__add(_972230), -(hAPP(c_Set_Oimage(_972230, _972230, c_Groups_Ouminus__class_Ouminus(_972230)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_972230, _972232), _972234)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_972230, hAPP(c_Groups_Ouminus__class_Ouminus(_972230), _972234), hAPP(c_Groups_Ouminus__class_Ouminus(_972230), _972232)))], (41504 ^ _776541) ^ [_1592262] : [-(c_Nat_Ofunpow(_1592262) = c_Nat_Ocompow(_1592262, _1592262))], (40292 ^ _776541) ^ [_1562016, _1562018, _1562020, _1562022, _1562024] : [c_Finite__Set_Ofolding__idem(_1562016, _1562018, _1562020, _1562022), -(hAPP(c_Fun_Ocomp(_1562018, _1562018, _1562018, hAPP(_1562020, _1562024)), hAPP(_1562020, _1562024)) = hAPP(_1562020, _1562024))], (18762 ^ _776541) ^ [_1114426, _1114428, _1114430, _1114432] : [class_Groups_Ocomm__monoid__add(_1114426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114428), _1114430)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114426), _1114432), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1114428), _1114430)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114426), hAPP(_1114432, _1114428)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114426), _1114432), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1114428)), _1114430))))], (7680 ^ _776541) ^ [_904675, _904677] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904675, tc_HOL_Obool)), _904677), _904677) = _904677)], (5855 ^ _776541) ^ [_869612, _869614, _869616, _869618, _869620, _869622, _869624] : [c_Typedef_Otype__definition(_869612, _869614, _869616, _869618, _869620), 5858 ^ _776541 : [(5865 ^ _776541) ^ [] : [_869622 = _869624, -(hAPP(_869616, _869622) = hAPP(_869616, _869624))], (5859 ^ _776541) ^ [] : [hAPP(_869616, _869622) = hAPP(_869616, _869624), -(_869622 = _869624)]]], (33346 ^ _776541) ^ [_1388558, _1388560, _1388562, _1388564, _1388566] : [c_Finite__Set_Ofun__left__comm__idem(_1388558, _1388560, _1388562), -(c_Finite__Set_Ofun__left__comm__idem(_1388564, _1388560, hAPP(hAPP(c_COMBB(_1388558, tc_fun(_1388560, _1388560), _1388564), _1388562), _1388566)))], (45020 ^ _776541) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (1394 ^ _776541) ^ [_796830, _796832] : [-(class_Lattices_Osemilattice__inf(_796830)), _796832 = _796830, class_Lattices_Osemilattice__inf(_796832)], (38146 ^ _776541) ^ [_1507068, _1507070, _1507072, _1507074, _1507076, _1507078, _1507080] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1507068, _1507070, _1507072, _1507074, _1507076), _1507078), _1507080)), 38150 ^ _776541 : [(38153 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1507076, 38149 ^ [_1507068, _1507070, _1507072, _1507074, _1507076, _1507078, _1507080]), _1507080)))], (38151 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1507074, _1507078), 38149 ^ [_1507068, _1507070, _1507072, _1507074, _1507076, _1507078, _1507080])))]]], (24728 ^ _776541) ^ [_1223908, _1223910] : [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)), _1223908)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1223908), _1223910)))], (12363 ^ _776541) ^ [_993682, _993684, _993686] : [class_Lattices_Olattice(_993682), hBOOL(hAPP(c_Finite__Set_Ofinite(_993682), _993684)), -(_993684 = c_Orderings_Obot__class_Obot(tc_fun(_993682, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_993682), _993686)), -(_993686 = c_Orderings_Obot__class_Obot(tc_fun(_993682, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_993682, tc_HOL_Obool)), _993684), _993686) = c_Orderings_Obot__class_Obot(tc_fun(_993682, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_993682, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993682, tc_HOL_Obool)), _993684), _993686)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_993682), c_Big__Operators_Olattice__class_OSup__fin(_993682, _993684)), c_Big__Operators_Olattice__class_OSup__fin(_993682, _993686)))], (48446 ^ _776541) ^ [_1752349, _1752351, _1752353, _1752355, _1752357, _1752359, _1752361] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1752349, _1752351, _1752353, _1752355), _1752357), _1752359), _1752361) = c_New__DSequence_Oneg__bind(_1752349, _1752351, hAPP(hAPP(hAPP(_1752353, _1752357), _1752359), _1752361), hAPP(hAPP(c_COMBC(_1752349, 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(_1752351)))), hAPP(hAPP(c_COMBC(_1752349, 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(_1752351))))), hAPP(hAPP(c_COMBC(_1752349, 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(_1752351)))))), _1752355), _1752357)), _1752359)), _1752361)))], (9322 ^ _776541) ^ [_936904, _936906, _936908] : [class_Orderings_Oorder(_936904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936904), _936906), _936908)), -(c_SetInterval_Oord__class_OatLeastAtMost(_936904, _936908, _936906) = c_Orderings_Obot__class_Obot(tc_fun(_936904, tc_HOL_Obool)))], (2522 ^ _776541) ^ [_813637, _813639, _813641, _813643, _813645, _813647, _813649, _813651, _813653, _813655] : [-(c_Product__Type_Oprod_Oprod__rec(_813655, _813651, _813647, _813643, _813639) = c_Product__Type_Oprod_Oprod__rec(_813653, _813649, _813645, _813641, _813637)), _813655 = _813653, _813651 = _813649, _813647 = _813645, _813643 = _813641, _813639 = _813637], (33623 ^ _776541) ^ [_1396882, _1396884, _1396886, _1396888, _1396890, _1396892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1396884, _1396886)), hAPP(hAPP(c_Product__Type_OPair(_1396884, _1396886), _1396890), _1396892)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396882, tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396882, tc_HOL_Obool))), _1396888))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396882, tc_fun(_1396884, tc_fun(_1396886, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1396882, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool), tc_fun(_1396884, tc_fun(_1396886, tc_HOL_Obool)), _1396882), hAPP(c_COMBC(_1396884, tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool), tc_fun(_1396886, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396886, tc_fun(tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool), tc_fun(_1396886, tc_HOL_Obool)), _1396884), c_COMBC(_1396886, tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396886, tc_prod(_1396884, _1396886)), tc_fun(_1396886, tc_fun(tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool), tc_HOL_Obool)), _1396884), hAPP(c_COMBB(tc_prod(_1396884, _1396886), tc_fun(tc_fun(tc_prod(_1396884, _1396886), tc_HOL_Obool), tc_HOL_Obool), _1396886), c_member(tc_prod(_1396884, _1396886)))), c_Product__Type_OPair(_1396884, _1396886))))), _1396888)), _1396890), _1396892)))], (8962 ^ _776541) ^ [_931310, _931312, _931314] : [class_Orderings_Olinorder(_931310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931310), _931312), _931314)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931310, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_931310, _931312, _931314)), hAPP(c_SetInterval_Oord__class_OatLeast(_931310), _931314)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_931310), _931312))], (36543 ^ _776541) ^ [_1468455, _1468457, _1468459, _1468461] : [-(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), _1468455), _1468457)), 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), _1468459), _1468461)), 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), _1468455), _1468459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1468457), _1468461))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1468455), _1468461)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1468457), _1468459)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (16060 ^ _776541) ^ [_1066936, _1066938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1066936)), _1066938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066936), _1066938)))], (35358 ^ _776541) ^ [_1435884, _1435886, _1435888, _1435890] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435884, _1435886), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435888), _1435890))), -(_1435886 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435884), _1435886) = _1435888)], (39585 ^ _776541) ^ [_1544284, _1544286, _1544288, _1544290, _1544292] : [c_Relation_Orefl__on(_1544284, _1544286, _1544288), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544284, _1544284)), hAPP(hAPP(c_Product__Type_OPair(_1544284, _1544284), _1544290), _1544292)), _1544288)), -(hBOOL(hAPP(hAPP(c_member(_1544284), _1544290), _1544286)))], (41971 ^ _776541) ^ [_1606400, _1606402, _1606404, _1606406] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1606400), tc_List_Olist(_1606400), c_List_Olistrel(_1606400, _1606402)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1606400)), hAPP(hAPP(c_List_Olist_OCons(_1606400), _1606404), _1606406)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1606400), tc_HOL_Obool)))) = c_List_Oset__Cons(_1606400, hAPP(c_Relation_OImage(_1606400, _1606400, _1606402), hAPP(hAPP(c_Set_Oinsert(_1606400), _1606404), c_Orderings_Obot__class_Obot(tc_fun(_1606400, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1606400), tc_List_Olist(_1606400), c_List_Olistrel(_1606400, _1606402)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1606400)), _1606406), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1606400), tc_HOL_Obool))))))], (46506 ^ _776541) ^ [_1711848, _1711850, _1711852] : [class_Orderings_Olinorder(_1711848), c_List_Olinorder__class_Osorted(_1711848, _1711850), -(c_List_Olinorder__class_Osorted(_1711848, c_List_Oremove1(_1711848, _1711852, _1711850)))], (51713 ^ _776541) ^ [_1822382, _1822384] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822382), _1822384))), 51714 ^ _776541 : [(51715 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822382), _1822384)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822384), _1822382)))], (51721 ^ _776541) ^ [] : [_1822382 = _1822384]]], (23699 ^ _776541) ^ [] : [-(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))], (36130 ^ _776541) ^ [_1457562, _1457564, _1457566, _1457568, _1457570, _1457572, _1457574, _1457576] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1457562, _1457564), tc_prod(_1457562, _1457564))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1457562, _1457564), tc_prod(_1457562, _1457564)), hAPP(hAPP(c_Product__Type_OPair(_1457562, _1457564), _1457566), _1457568)), hAPP(hAPP(c_Product__Type_OPair(_1457562, _1457564), _1457570), _1457572))), c_Wellfounded_Olex__prod(_1457562, _1457564, _1457574, _1457576)))), 36131 ^ _776541 : [(36134 ^ _776541) ^ [] : [_1457566 = _1457570, hBOOL(hAPP(hAPP(c_member(tc_prod(_1457564, _1457564)), hAPP(hAPP(c_Product__Type_OPair(_1457564, _1457564), _1457568), _1457572)), _1457576))], (36132 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457562, _1457562)), hAPP(hAPP(c_Product__Type_OPair(_1457562, _1457562), _1457566), _1457570)), _1457574))]]], (27771 ^ _776541) ^ [_1275968, _1275970] : [-(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), _1275968)), _1275970))))], (15482 ^ _776541) ^ [_1056624, _1056626, _1056628, _1056630, _1056632] : [class_Groups_Ocomm__monoid__mult(_1056624), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056626), _1056628)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056626), _1056630)), 15496 ^ _776541 : [(15499 ^ _776541) ^ [] : [hAPP(_1056632, 15495 ^ [_1056624, _1056626, _1056628, _1056630, _1056632]) = c_Groups_Oone__class_Oone(_1056624)], (15497 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1056626), 15495 ^ [_1056624, _1056626, _1056628, _1056630, _1056632]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056626, tc_HOL_Obool)), _1056628), _1056630))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056626, _1056624), _1056632), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056626, tc_HOL_Obool)), _1056628), _1056630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056624), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056626, _1056624), _1056632), _1056628)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056626, _1056624), _1056632), _1056630)))], (44232 ^ _776541) ^ [_1661043, _1661045, _1661047] : [-(_1661043 = c_List_Olist_ONil(_1661045)), -(hAPP(hAPP(c_List_Otake(_1661045), hAPP(c_Nat_OSuc, _1661047)), _1661043) = hAPP(hAPP(c_List_Olist_OCons(_1661045), hAPP(c_List_Ohd(_1661045), _1661043)), hAPP(hAPP(c_List_Otake(_1661045), _1661047), hAPP(c_List_Otl(_1661045), _1661043))))], (28295 ^ _776541) ^ [_1284545] : [c_Int_OMin = _1284545, -(c_Int_OMin = c_Int_OBit1(_1284545))], (104 ^ _776541) ^ [_778153, _778155, _778157, _778159, _778161, _778163, _778165, _778167, _778169, _778171, _778173, _778175] : [-(c_Finite__Set_Ofolding__image__simple__idem(_778173, _778169, _778165, _778161, _778157, _778153)), c_Finite__Set_Ofolding__image__simple__idem(_778175, _778171, _778167, _778163, _778159, _778155), _778175 = _778173, _778171 = _778169, _778167 = _778165, _778163 = _778161, _778159 = _778157, _778155 = _778153], (26735 ^ _776541) ^ [_1258876, _1258878] : [c_Nat__Transfer_Onat__set(_1258876), c_Nat__Transfer_Onat__set(_1258878), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258876), _1258878)))], (38446 ^ _776541) ^ [_1513552, _1513554, _1513556] : [-(hAPP(c_Relation_ORange(_1513552, _1513554), hAPP(c_Set_OCollect(tc_prod(_1513552, _1513554)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513552, _1513554, tc_HOL_Obool), _1513556))) = hAPP(c_Set_OCollect(_1513554), hAPP(hAPP(c_COMBB(tc_fun(_1513552, tc_HOL_Obool), tc_HOL_Obool, _1513554), c_HOL_OEx(_1513552)), hAPP(c_COMBC(_1513552, _1513554, tc_HOL_Obool), _1513556))))], (134 ^ _776541) ^ [_778698, _778700, _778702, _778704, _778706, _778708, _778710, _778712, _778714, _778716, _778718, _778720] : [-(c_Finite__Set_Ofolding__image__simple(_778718, _778714, _778710, _778706, _778702, _778698)), c_Finite__Set_Ofolding__image__simple(_778720, _778716, _778712, _778708, _778704, _778700), _778720 = _778718, _778716 = _778714, _778712 = _778710, _778708 = _778706, _778704 = _778702, _778700 = _778698], (6869 ^ _776541) ^ [_887940] : [-(hAPP(c_Set_OPow(_887940), c_Orderings_Otop__class_Otop(tc_fun(_887940, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_887940, tc_HOL_Obool), tc_HOL_Obool)))], (16346 ^ _776541) ^ [_1071476] : [class_Rings_Ozero__neq__one(_1071476), c_Groups_Oone__class_Oone(_1071476) = c_Groups_Ozero__class_Ozero(_1071476)], (15164 ^ _776541) ^ [_1050207, _1050209] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050207), _1050209) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1050207 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1050209 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (1992 ^ _776541) ^ [_805196, _805198] : [_805198 = _805196, -(c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_805198) = c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_805196))], (52187 ^ _776541) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (5330 ^ _776541) ^ [_857901, _857903, _857905, _857907, _857909, _857911, _857913, _857915, _857917, _857919] : [-(c_New__DSequence_Opos__map(_857919, _857915, _857911, _857907, _857903) = c_New__DSequence_Opos__map(_857917, _857913, _857909, _857905, _857901)), _857919 = _857917, _857915 = _857913, _857911 = _857909, _857907 = _857905, _857903 = _857901], (16072 ^ _776541) ^ [_1067148, _1067150] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067148)), _1067150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067148), hAPP(c_Nat_OSuc, _1067150)))], (43358 ^ _776541) ^ [_1640689, _1640691, _1640693, _1640695, _1640697] : [-(_1640689 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1640691, _1640693, _1640695), _1640689), _1640697) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1640693), _1640691), tc_prod(_1640693, _1640691), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640693), _1640691), c_List_Olist_ONil(_1640693)), _1640697), hAPP(c_Product__Type_Oprod_Oprod__case(_1640693, _1640691, tc_prod(tc_List_Olist(_1640693), _1640691)), hAPP(hAPP(c_COMBC(_1640693, tc_fun(_1640691, tc_prod(tc_List_Olist(_1640693), _1640691)), tc_fun(_1640691, tc_prod(tc_List_Olist(_1640693), _1640691))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1640693), _1640691), tc_prod(tc_List_Olist(_1640693), _1640691)), tc_fun(tc_fun(_1640691, tc_prod(tc_List_Olist(_1640693), _1640691)), tc_fun(_1640691, tc_prod(tc_List_Olist(_1640693), _1640691))), _1640693), c_COMBB(tc_prod(tc_List_Olist(_1640693), _1640691), tc_prod(tc_List_Olist(_1640693), _1640691), _1640691)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640693), tc_fun(_1640691, tc_prod(tc_List_Olist(_1640693), _1640691))), tc_fun(tc_prod(tc_List_Olist(_1640693), _1640691), tc_prod(tc_List_Olist(_1640693), _1640691)), _1640693), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1640693), _1640691, tc_prod(tc_List_Olist(_1640693), _1640691))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640693), tc_List_Olist(_1640693)), tc_fun(tc_List_Olist(_1640693), tc_fun(_1640691, tc_prod(tc_List_Olist(_1640693), _1640691))), _1640693), hAPP(c_COMBB(tc_List_Olist(_1640693), tc_fun(_1640691, tc_prod(tc_List_Olist(_1640693), _1640691)), tc_List_Olist(_1640693)), c_Product__Type_OPair(tc_List_Olist(_1640693), _1640691))), c_List_Olist_OCons(_1640693))))), hAPP(c_Lazy__Sequence_Oanamorph(_1640691, _1640693, _1640695), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1640689), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1640695, _1640697)))], (33683 ^ _776541) ^ [_1398909, _1398911, _1398913, _1398915] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1398909, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1398911)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1398909, tc_HOL_Obool), tc_Nat_Onat), _1398913), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1398915))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1398909, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1398915, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398911), _1398915))), _1398913))], (39565 ^ _776541) ^ [_1543892, _1543894, _1543896, _1543898, _1543900] : [c_Relation_Orefl__on(_1543892, _1543894, _1543896), c_Relation_Orefl__on(_1543892, _1543898, _1543900), -(c_Relation_Orefl__on(_1543892, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543892, tc_HOL_Obool)), _1543894), _1543898), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1543892, _1543892), tc_HOL_Obool)), _1543896), _1543900)))], (44286 ^ _776541) ^ [_1662104, _1662106, _1662108, _1662110, _1662112, _1662114] : [class_Orderings_Olinorder(_1662104), -(hAPP(_1662106, _1662108) = hAPP(_1662106, _1662110)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662112, _1662104, _1662106), _1662110), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662112, _1662104, _1662106), _1662108), _1662114)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662112, _1662104, _1662106), _1662108), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662112, _1662104, _1662106), _1662110), _1662114)))], (7504 ^ _776541) ^ [_900185, _900187, _900189, _900191] : [hBOOL(hAPP(hAPP(c_member(_900185), _900187), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_900185, tc_HOL_Obool)), _900189), _900191))), 7507 ^ _776541 : [(7510 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900185), _900187), _900191)))], (7508 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900185), _900187), _900189)))]]], (15634 ^ _776541) ^ [_1060151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060151), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44296 ^ _776541) ^ [_1662294, _1662296, _1662298, _1662300] : [class_Groups_Osemigroup__add(_1662294), -(hAPP(c_List_Ofoldl(_1662294, _1662294, c_Groups_Oplus__class_Oplus(_1662294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1662294), _1662296), _1662298)), _1662300) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1662294), _1662296), hAPP(c_List_Ofoldl(_1662294, _1662294, c_Groups_Oplus__class_Oplus(_1662294), _1662298), _1662300)))], (19157 ^ _776541) ^ [_1121639, _1121641, _1121643, _1121645, _1121647] : [class_Groups_Oordered__comm__monoid__add(_1121639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121641), _1121643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1121641, tc_HOL_Obool)), _1121645), _1121643)), 19171 ^ _776541 : [(19174 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121639), c_Groups_Ozero__class_Ozero(_1121639)), hAPP(_1121647, 19170 ^ [_1121639, _1121641, _1121643, _1121645, _1121647])))], (19172 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1121641), 19170 ^ [_1121639, _1121641, _1121643, _1121645, _1121647]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1121641, tc_HOL_Obool)), _1121643), _1121645))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121639), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1121641, _1121639), _1121647), _1121645)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1121641, _1121639), _1121647), _1121643))))], (51861 ^ _776541) ^ [_1824661, _1824663] : [class_Lattices_Obounded__lattice(_1824661), -(class_Lattices_Obounded__lattice__top(tc_fun(_1824663, _1824661)))], (36657 ^ _776541) ^ [_1471547, _1471549] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471547), c_Orderings_Obot__class_Obot(tc_fun(_1471547, tc_HOL_Obool))), _1471549) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471547, tc_HOL_Obool), tc_HOL_Obool)))], (11048 ^ _776541) ^ [_967539, _967541, _967543, _967545] : [class_Groups_Oab__semigroup__mult(_967539), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967539), _967541), _967543)), _967545) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967539), _967541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967539), _967543), _967545)))], (3242 ^ _776541) ^ [_824831, _824833, _824835, _824837, _824839, _824841, _824843, _824845, _824847, _824849] : [-(c_Fun_Ofun__upd(_824849, _824845, _824841, _824837, _824833) = c_Fun_Ofun__upd(_824847, _824843, _824839, _824835, _824831)), _824849 = _824847, _824845 = _824843, _824841 = _824839, _824837 = _824835, _824833 = _824831], (4252 ^ _776541) ^ [_840960, _840962, _840964, _840966] : [-(c_List_Olast(_840966, _840962) = c_List_Olast(_840964, _840960)), _840966 = _840964, _840962 = _840960], (24862 ^ _776541) ^ [_1226541, _1226543, _1226545, _1226547] : [class_Divides_Osemiring__div(_1226541), -(c_Divides_Odiv__class_Omod(_1226541, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226541), c_Divides_Odiv__class_Omod(_1226541, _1226543, _1226545)), _1226547), _1226545) = c_Divides_Odiv__class_Omod(_1226541, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226541), _1226543), _1226547), _1226545))], (16482 ^ _776541) ^ [_1073368] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073368), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1073368)], (1884 ^ _776541) ^ [_802955, _802957] : [-(class_Groups_Oone(_802955)), _802957 = _802955, class_Groups_Oone(_802957)], (32894 ^ _776541) ^ [_1376088, _1376090, _1376092, _1376094, _1376096] : [class_Groups_Ocomm__monoid__add(_1376088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376090), _1376092)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1376090, _1376088), hAPP(hAPP(c_COMBS(_1376090, _1376088, _1376088), hAPP(hAPP(c_COMBB(_1376088, tc_fun(_1376088, _1376088), _1376090), c_Groups_Oplus__class_Oplus(_1376088)), _1376094)), _1376096)), _1376092) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376088), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1376090, _1376088), _1376094), _1376092)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1376090, _1376088), _1376096), _1376092)))], (40312 ^ _776541) ^ [_1562402, _1562404, _1562406, _1562408, _1562410, _1562412] : [c_Finite__Set_Ofolding__idem(_1562402, _1562404, _1562406, _1562408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562402), _1562410)), -(hAPP(_1562408, hAPP(hAPP(c_Set_Oinsert(_1562402), _1562412), _1562410)) = hAPP(c_Fun_Ocomp(_1562404, _1562404, _1562404, hAPP(_1562408, _1562410)), hAPP(_1562406, _1562412)))], (51137 ^ _776541) ^ [_1812107, _1812109, _1812111] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1812107), _1812109)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1812107), _1812111))), -(_1812107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812109), _1812111)))], (38193 ^ _776541) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (14654 ^ _776541) ^ [_1040828, _1040830, _1040832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040828), _1040830)), _1040832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040828), _1040832)))], (9036 ^ _776541) ^ [_932869, _932871, _932873] : [class_Orderings_Olinorder(_932869), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932869), _932871), _932873))), -(_932871 = _932873), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932869), _932873), _932871)))], (49060 ^ _776541) ^ [_1766154, _1766156, _1766158, _1766160] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1766154, _1766156, _1766158, _1766160, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766156)) = _1766158)], (28987 ^ _776541) ^ [_1296160, _1296162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296160)), c_Int_OBit0(_1296162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296160), _1296162)))], (6264 ^ _776541) ^ [_877238, _877240, _877242] : [class_Complete__Lattice_Ocomplete__lattice(_877238), 6267 ^ _776541 : [(6268 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877238), _877240), c_Complete__Lattice_OInf__class_OInf(_877238, _877242))), 6271 ^ _776541 : [(6272 ^ _776541) ^ [_877396] : [hBOOL(hAPP(hAPP(c_member(_877238), _877396), _877242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877238), _877240), _877396)))]]], (6278 ^ _776541) ^ [] : [6280 ^ _776541 : [(6283 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877238), _877240), 6279 ^ [_877238, _877240, _877242]))], (6281 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877238), 6279 ^ [_877238, _877240, _877242]), _877242)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877238), _877240), c_Complete__Lattice_OInf__class_OInf(_877238, _877242))))]]], (29225 ^ _776541) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (18262 ^ _776541) ^ [_1104927, _1104929, _1104931] : [class_Groups_Oordered__comm__monoid__add(_1104927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104927), c_Groups_Ozero__class_Ozero(_1104927)), _1104929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104927), c_Groups_Ozero__class_Ozero(_1104927)), _1104931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104927), c_Groups_Ozero__class_Ozero(_1104927)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104927), _1104929), _1104931))))], (45040 ^ _776541) ^ [_1678561, _1678563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1678561)), hAPP(c_Code__Numeral_Oof__nat, _1678563))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678561), _1678563)))], (47094 ^ _776541) ^ [_1723117, _1723119, _1723121, _1723123, _1723125] : [-(hAPP(c_List_Ofoldl(_1723117, _1723119, _1723121, _1723123), _1723125) = c_List_Ofoldr(_1723119, _1723117, hAPP(c_COMBC(_1723117, _1723119, _1723117), _1723121), hAPP(c_List_Orev(_1723119), _1723125), _1723123))], (48858 ^ _776541) ^ [_1761236, _1761238] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1761236)), _1761238) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1761236, tc_Lazy__Sequence_Olazy__sequence(_1761236)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1761236, tc_Lazy__Sequence_Olazy__sequence(_1761236), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761236), tc_Nat_Onat), _1761236), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1761236), 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(_1761236)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1761236)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1761236), _1761238)))], (47371 ^ _776541) ^ [_1729078, _1729080, _1729082] : [class_Orderings_Olinorder(_1729078), c_List_Olinorder__class_Osorted(_1729078, _1729080), -(c_List_Olinorder__class_Osorted(_1729078, c_List_OdropWhile(_1729078, _1729082, _1729080)))], (41457 ^ _776541) ^ [_1590937, _1590939, _1590941, _1590943, _1590945, _1590947] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590937, _1590937)), hAPP(hAPP(c_Product__Type_OPair(_1590937, _1590937), _1590939), _1590941)), _1590943)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590937, _1590937)), hAPP(hAPP(c_Product__Type_OPair(_1590937, _1590937), _1590941), _1590945)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590937, _1590937), tc_HOL_Obool), _1590947), _1590943))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590937, _1590937)), hAPP(hAPP(c_Product__Type_OPair(_1590937, _1590937), _1590939), _1590945)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590937, _1590937), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590947)), _1590943))))], (51253 ^ _776541) ^ [_1814297, _1814299, _1814301, _1814303] : [class_Rings_Ocomm__semiring__1(_1814297), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814297), _1814299), _1814301)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814297), _1814299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814297), _1814303), _1814301))))], (41224 ^ _776541) ^ [_1585298, _1585300, _1585302] : [-(hAPP(c_Relation_Oconverse(_1585298, _1585300), _1585302) = hAPP(c_Set_OCollect(tc_prod(_1585300, _1585298)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585300, _1585298, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1585300, tc_fun(tc_prod(_1585298, _1585300), tc_HOL_Obool), tc_fun(_1585298, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585298, tc_fun(tc_fun(tc_prod(_1585298, _1585300), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585298, _1585300), tc_HOL_Obool), tc_fun(_1585298, tc_HOL_Obool)), _1585300), c_COMBC(_1585298, tc_fun(tc_prod(_1585298, _1585300), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585298, tc_prod(_1585298, _1585300)), tc_fun(_1585298, tc_fun(tc_fun(tc_prod(_1585298, _1585300), tc_HOL_Obool), tc_HOL_Obool)), _1585300), hAPP(c_COMBB(tc_prod(_1585298, _1585300), tc_fun(tc_fun(tc_prod(_1585298, _1585300), tc_HOL_Obool), tc_HOL_Obool), _1585298), c_member(tc_prod(_1585298, _1585300)))), hAPP(c_COMBC(_1585298, _1585300, tc_prod(_1585298, _1585300)), c_Product__Type_OPair(_1585298, _1585300))))), _1585302))))], (25822 ^ _776541) ^ [_1243765, _1243767] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243765))), -(c_SMT_Oz3mod(_1243767, _1243765) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243767, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243765)))], (48500 ^ _776541) ^ [_1753822, _1753824, _1753826, _1753828, _1753830] : [hBOOL(hAPP(hAPP(_1753826, _1753830), _1753828)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1753822, _1753824, _1753826), _1753828), _1753830)))], (29331 ^ _776541) ^ [_1302136] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1302136))), 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), _1302136), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (52467 ^ _776541) ^ [_1830974, _1830976, _1830978, _1830980, _1830982, _1830984] : [-(hAPP(hAPP(hAPP(c_COMBB(_1830974, _1830976, _1830978), _1830980), _1830982), _1830984) = hAPP(_1830980, hAPP(_1830982, _1830984)))], (41242 ^ _776541) ^ [_1585829, _1585831, _1585833] : [c_Relation_Ototal__on(_1585829, _1585831, _1585833), -(c_Relation_Ototal__on(_1585829, _1585831, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1585829, _1585829), tc_HOL_Obool)), _1585833), c_Relation_OId(_1585829))))], (11672 ^ _776541) ^ [_980735, _980737, _980739] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980735), _980737)), 11675 ^ _776541 : [(11682 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980735), _980739)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980735, tc_HOL_Obool)), _980739), _980737))))], (11676 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980735, tc_HOL_Obool)), _980739), _980737))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980735), _980739)))]]], (23761 ^ _776541) ^ [_1206882, _1206884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206882)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206882), _1206884)))], (43964 ^ _776541) ^ [_1655197, _1655199, _1655201, _1655203] : [hAPP(hAPP(c_List_Oappend(_1655197), _1655199), _1655201) = _1655203, 43967 ^ _776541 : [(43970 ^ _776541) ^ [] : [-(_1655201 = hAPP(hAPP(c_List_Odrop(_1655197), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655197)), _1655199)), _1655203))], (43968 ^ _776541) ^ [] : [-(_1655199 = hAPP(hAPP(c_List_Otake(_1655197), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655197)), _1655199)), _1655203))]]], (45283 ^ _776541) ^ [_1683396, _1683398, _1683400, _1683402, _1683404] : [c_List_Opartition(_1683396, _1683398, _1683400) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683396), tc_List_Olist(_1683396)), _1683402), _1683404), 45286 ^ _776541 : [(45293 ^ _776541) ^ [_1683658] : [hBOOL(hAPP(hAPP(c_member(_1683396), _1683658), hAPP(c_List_Oset(_1683396), _1683404))), hBOOL(hAPP(_1683398, _1683658))], (45287 ^ _776541) ^ [_1683549] : [hBOOL(hAPP(hAPP(c_member(_1683396), _1683549), hAPP(c_List_Oset(_1683396), _1683402))), -(hBOOL(hAPP(_1683398, _1683549)))]]], (44789 ^ _776541) ^ [_1672235, _1672237, _1672239, _1672241, _1672243] : [class_Rings_Osemiring__0(_1672235), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672235), hAPP(hAPP(c_List_Omap(_1672237, _1672235), hAPP(hAPP(c_COMBB(_1672235, _1672235, _1672237), hAPP(c_Groups_Otimes__class_Otimes(_1672235), _1672239)), _1672241)), _1672243)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1672235), _1672239), hAPP(c_List_Omonoid__add__class_Olistsum(_1672235), hAPP(hAPP(c_List_Omap(_1672237, _1672235), _1672241), _1672243))))], (1982 ^ _776541) ^ [_805047, _805049, _805051, _805053] : [-(tc_Datatype_Onode(_805053, _805049) = tc_Datatype_Onode(_805051, _805047)), _805053 = _805051, _805049 = _805047], (15202 ^ _776541) ^ [_1050833, _1050835, _1050837] : [class_Rings_Olinordered__semidom(_1050833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050833), c_Groups_Oone__class_Oone(_1050833)), _1050835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050833), c_Groups_Oone__class_Oone(_1050833)), _1050837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050833), c_Groups_Oone__class_Oone(_1050833)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050833), _1050835), _1050837))))], (45299 ^ _776541) ^ [_1683778, _1683780] : [-(c_List_Opartition(_1683778, _1683780, c_List_Olist_ONil(_1683778)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683778), tc_List_Olist(_1683778)), c_List_Olist_ONil(_1683778)), c_List_Olist_ONil(_1683778)))], (8008 ^ _776541) ^ [_912292, _912294, _912296, _912298] : [hBOOL(hAPP(hAPP(c_member(_912292), _912294), _912296)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912292, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912292), _912294), _912298)), _912296) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912292, tc_HOL_Obool)), _912298), _912296))], (36290 ^ _776541) ^ [_1461816, _1461818, _1461820, _1461822] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1461816, tc_HOL_Obool), tc_fun(_1461816, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1461816, tc_HOL_Obool), tc_fun(_1461816, tc_HOL_Obool)), _1461820), _1461822)), c_Wellfounded_Omax__ext(_1461816, _1461818))), -(c_Wellfounded_Omax__extp(_1461816, hAPP(hAPP(c_COMBC(_1461816, tc_fun(tc_prod(_1461816, _1461816), tc_HOL_Obool), tc_fun(_1461816, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461816, tc_fun(tc_fun(tc_prod(_1461816, _1461816), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461816, _1461816), tc_HOL_Obool), tc_fun(_1461816, tc_HOL_Obool)), _1461816), c_COMBC(_1461816, tc_fun(tc_prod(_1461816, _1461816), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461816, tc_prod(_1461816, _1461816)), tc_fun(_1461816, tc_fun(tc_fun(tc_prod(_1461816, _1461816), tc_HOL_Obool), tc_HOL_Obool)), _1461816), hAPP(c_COMBB(tc_prod(_1461816, _1461816), tc_fun(tc_fun(tc_prod(_1461816, _1461816), tc_HOL_Obool), tc_HOL_Obool), _1461816), c_member(tc_prod(_1461816, _1461816)))), c_Product__Type_OPair(_1461816, _1461816)))), _1461818), _1461820, _1461822))], (41477 ^ _776541) ^ [_1591563, _1591565, _1591567] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591563, _1591563), hAPP(c_Nat_OSuc, _1591565)), _1591567) = hAPP(c_Fun_Ocomp(_1591563, _1591563, _1591563, _1591567), hAPP(hAPP(c_Nat_Ocompow(_1591563, _1591563), _1591565), _1591567)))], (14993 ^ _776541) ^ [_1047112, _1047114, _1047116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047112), _1047114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047112), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047116), _1047114))))], (28753 ^ _776541) ^ [_1291955, _1291957] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1291955, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1291957)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1291955, 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)))), _1291957)))], (48742 ^ _776541) ^ [_1758922, _1758924, _1758926] : [-(_1758922 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1758924), c_List_Oreplicate(_1758924, _1758922, _1758926)) = hAPP(hAPP(c_Set_Oinsert(_1758924), _1758926), c_Orderings_Obot__class_Obot(tc_fun(_1758924, tc_HOL_Obool))))], (40781 ^ _776541) ^ [_1574565, _1574567, _1574569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574565, _1574565), tc_HOL_Obool)), _1574567), _1574569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574565, _1574565), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574565, _1574567)), c_Transitive__Closure_Ortrancl(_1574565, _1574569))))], (11592 ^ _776541) ^ [_979275, _979277] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979275), _979277)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979275, tc_HOL_Obool)), hAPP(c_Set_OPow(_979275), _979277))))], (48012 ^ _776541) ^ [_1743547, _1743549, _1743551, _1743553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743547), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743549)), _1743551))), 48018 ^ _776541 : [(48021 ^ _776541) ^ [] : [hBOOL(hAPP(_1743553, 48017 ^ [_1743547, _1743549, _1743551, _1743553]))], (48019 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743549), 48017 ^ [_1743547, _1743549, _1743551, _1743553]), hAPP(c_List_Oset(_1743549), _1743551))))]], -(hBOOL(hAPP(_1743553, hAPP(hAPP(c_List_Onth(_1743549), _1743551), _1743547))))], (1894 ^ _776541) ^ [_803080, _803082] : [-(class_Rings_Odvd(_803080)), _803082 = _803080, class_Rings_Odvd(_803082)], (52095 ^ _776541) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (34083 ^ _776541) ^ [_1409329, _1409331, _1409333] : [-(hAPP(c_Divides_Oadjust(_1409329), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1409331), _1409333)) = 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), _1409333), _1409329)), 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)))), _1409331)), 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)))), _1409331)), _1409333))))], (52213 ^ _776541) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (13544 ^ _776541) ^ [_1017651, _1017653, _1017655, _1017657] : [class_Groups_Ocancel__semigroup__add(_1017651), 13547 ^ _776541 : [(13554 ^ _776541) ^ [] : [_1017655 = _1017657, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017651), _1017653), _1017655) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017651), _1017653), _1017657))], (13548 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017651), _1017653), _1017655) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017651), _1017653), _1017657), -(_1017655 = _1017657)]]], (25425 ^ _776541) ^ [_1236424, _1236426, _1236428] : [-(hBOOL(hAPP(_1236424, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1236426), _1236428)))), 25428 ^ _776541 : [(25431 ^ _776541) ^ [] : [hBOOL(hAPP(_1236424, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25429 ^ _776541) ^ [] : [-(_1236428 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25432 ^ _776541 : [(25437 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25435 ^ [_1236424, _1236426, _1236428]), _1236428)))], (25439 ^ _776541) ^ [] : [-(_1236426 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1236428), 25434 ^ [_1236424, _1236426, _1236428])), 25435 ^ [_1236424, _1236426, _1236428]))], (25441 ^ _776541) ^ [] : [hBOOL(hAPP(_1236424, 25434 ^ [_1236424, _1236426, _1236428]))], (25433 ^ _776541) ^ [] : [_1236428 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23151 ^ _776541) ^ [_1195962, _1195964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195964)), -(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), _1195962), _1195964))))], (49391 ^ _776541) ^ [_1774824, _1774826, _1774828, _1774830] : [class_Complete__Lattice_Ocomplete__lattice(_1774824), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1774826, _1774824), _1774828), _1774830) = c_Complete__Lattice_OInf__class_OInf(_1774824, hAPP(c_Set_OCollect(_1774824), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774826, _1774824), tc_HOL_Obool), tc_HOL_Obool, _1774824), c_HOL_OEx(tc_fun(_1774826, _1774824))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774826, _1774824), tc_HOL_Obool), tc_fun(tc_fun(_1774826, _1774824), tc_HOL_Obool), _1774824), hAPP(c_COMBS(tc_fun(_1774826, _1774824), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774826, _1774824)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774826, _1774824), tc_fun(tc_fun(_1774826, _1774824), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774826, _1774824))), _1774828)))), hAPP(hAPP(c_COMBC(_1774824, tc_fun(tc_fun(_1774826, _1774824), _1774824), tc_fun(tc_fun(_1774826, _1774824), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774824, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774826, _1774824), _1774824), tc_fun(tc_fun(_1774826, _1774824), tc_HOL_Obool)), _1774824), c_COMBB(_1774824, tc_HOL_Obool, tc_fun(_1774826, _1774824))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774826, _1774824), _1774826, _1774824), c_COMBI(tc_fun(_1774826, _1774824))), _1774830)))))))], (43585 ^ _776541) ^ [_1645995, _1645997, _1645999] : [_1645995 = hAPP(hAPP(c_List_Oappend(_1645997), _1645995), _1645999), -(_1645999 = c_List_Olist_ONil(_1645997))], (20783 ^ _776541) ^ [_1151762, _1151764, _1151766, _1151768, _1151770] : [class_Fields_Ofield(_1151762), -(_1151764 = c_Groups_Ozero__class_Ozero(_1151762)), -(_1151766 = c_Groups_Ozero__class_Ozero(_1151762)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151762), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151762), _1151768), _1151764)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151762), _1151770), _1151766)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151762), _1151768), _1151766)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151762), _1151770), _1151764))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151762), _1151764), _1151766)))], (27593 ^ _776541) ^ [_1272869, _1272871] : [class_Int_Onumber__ring(_1272869), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272869), _1272871), hAPP(c_Int_Onumber__class_Onumber__of(_1272869), c_Int_OPls)) = _1272871)], (48486 ^ _776541) ^ [_1753491, _1753493, _1753495, _1753497] : [-(c_Predicate_Oconversep(_1753491, _1753493, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1753491, tc_fun(_1753493, tc_HOL_Obool))), _1753495), _1753497)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1753493, tc_fun(_1753491, tc_HOL_Obool))), c_Predicate_Oconversep(_1753491, _1753493, _1753495)), c_Predicate_Oconversep(_1753491, _1753493, _1753497)))], (31495 ^ _776541) ^ [_1342045, _1342047, _1342049, _1342051] : [class_Orderings_Olinorder(_1342045), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342045), _1342047), _1342049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342045), _1342047), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342045), _1342049), _1342051))))], (26038 ^ _776541) ^ [_1247132, _1247134, _1247136] : [-(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), _1247132), _1247134)), _1247136), _1247134) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247136, _1247134))], (5166 ^ _776541) ^ [_855359, _855361, _855363, _855365] : [-(c_Quotient_ORespects(_855365, _855361) = c_Quotient_ORespects(_855363, _855359)), _855365 = _855363, _855361 = _855359], (10339 ^ _776541) ^ [_954108, _954110, _954112, _954114] : [class_Groups_Ouminus(_954108), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_954110, _954108)), _954112), _954114) = hAPP(c_Groups_Ouminus__class_Ouminus(_954108), hAPP(_954112, _954114)))], (11141 ^ _776541) ^ [_969367, _969369, _969371, _969373] : [hAPP(c_Set_Oimage(_969367, _969369, _969371), _969373) = c_Orderings_Obot__class_Obot(tc_fun(_969369, tc_HOL_Obool)), -(_969373 = c_Orderings_Obot__class_Obot(tc_fun(_969367, tc_HOL_Obool)))], (40833 ^ _776541) ^ [_1575907] : [-(c_Transitive__Closure_Ortrancl(_1575907, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575907, _1575907), tc_HOL_Obool))) = c_Relation_OId(_1575907))], (41745 ^ _776541) ^ [_1599138, _1599140, _1599142] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599138)), c_List_Osublist(_1599138, _1599140, _1599142)) = 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(_1599138)), _1599140)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1599142)))))], (25927 ^ _776541) ^ [_1245427, _1245429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245429)), 25934 ^ _776541 : [(25941 ^ _776541) ^ [] : [_1245427 = _1245429, -(hAPP(c_Int_Onat, _1245427) = hAPP(c_Int_Onat, _1245429))], (25935 ^ _776541) ^ [] : [hAPP(c_Int_Onat, _1245427) = hAPP(c_Int_Onat, _1245429), -(_1245427 = _1245429)]]], (32678 ^ _776541) ^ [_1370095, _1370097, _1370099, _1370101] : [class_Groups_Ocomm__monoid__add(_1370095), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370095), _1370097), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1370099), hAPP(c_Nat_OSuc, _1370101))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370095), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370095, tc_Nat_Onat), _1370097), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370099, _1370101)))], (35636 ^ _776541) ^ [_1441698, _1441700, _1441702, _1441704, _1441706, _1441708] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1441698, _1441700), _1441700, _1441702), hAPP(hAPP(c_COMBB(_1441704, tc_fun(_1441700, _1441702), tc_prod(_1441698, _1441700)), _1441706), hAPP(hAPP(c_COMBB(_1441698, _1441704, tc_prod(_1441698, _1441700)), _1441708), c_Product__Type_Ofst(_1441698, _1441700)))), c_Product__Type_Osnd(_1441698, _1441700)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1441698, _1441700, _1441702), hAPP(hAPP(c_COMBB(_1441704, tc_fun(_1441700, _1441702), _1441698), _1441706), _1441708)))], (15594 ^ _776541) ^ [_1059188, _1059190, _1059192, _1059194, _1059196] : [class_Groups_Ocomm__monoid__mult(_1059188), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059190), _1059192)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059190), _1059194)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059188), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059188, _1059190, c_Groups_Otimes__class_Otimes(_1059188)), _1059196), c_Groups_Oone__class_Oone(_1059188)), _1059192)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059188, _1059190, c_Groups_Otimes__class_Otimes(_1059188)), _1059196), c_Groups_Oone__class_Oone(_1059188)), _1059194)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059188), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059188, _1059190, c_Groups_Otimes__class_Otimes(_1059188)), _1059196), c_Groups_Oone__class_Oone(_1059188)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1059190, tc_HOL_Obool)), _1059192), _1059194))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059188, _1059190, c_Groups_Otimes__class_Otimes(_1059188)), _1059196), c_Groups_Oone__class_Oone(_1059188)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1059190, tc_HOL_Obool)), _1059192), _1059194))))], (36213 ^ _776541) ^ [_1459649, _1459651, _1459653, _1459655, _1459657] : [-(hAPP(c_Product__Type_Ofst(_1459649, _1459651), hAPP(c_Product__Type_Oapfst(_1459653, _1459649, _1459651, _1459655), _1459657)) = hAPP(_1459655, hAPP(c_Product__Type_Ofst(_1459653, _1459651), _1459657)))], (50977 ^ _776541) ^ [_1808897] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1808897)))], (35642 ^ _776541) ^ [_1441917, _1441919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441917), 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)), _1441919)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1441917), _1441919) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1441917, _1441919)))], (16380 ^ _776541) ^ [_1071963, _1071965] : [class_Groups_Olinordered__ab__group__add(_1071963), 16383 ^ _776541 : [(16390 ^ _776541) ^ [] : [_1071965 = c_Groups_Ozero__class_Ozero(_1071963), -(_1071965 = hAPP(c_Groups_Ouminus__class_Ouminus(_1071963), _1071965))], (16384 ^ _776541) ^ [] : [_1071965 = hAPP(c_Groups_Ouminus__class_Ouminus(_1071963), _1071965), -(_1071965 = c_Groups_Ozero__class_Ozero(_1071963))]]], (25018 ^ _776541) ^ [_1229609, _1229611, _1229613] : [_1229609 = 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), _1229609), _1229611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229609), _1229613)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52315 ^ _776541) ^ [_1829391] : [-(class_Nat_Osize(tc_Option_Ooption(_1829391)))], (19681 ^ _776541) ^ [_1132014, _1132016, _1132018] : [class_Rings_Odivision__ring(_1132014), -(_1132016 = c_Groups_Ozero__class_Ozero(_1132014)), 19688 ^ _776541 : [(19695 ^ _776541) ^ [] : [_1132018 = _1132016, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132014), _1132018), _1132016) = c_Groups_Oone__class_Oone(_1132014))], (19689 ^ _776541) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132014), _1132018), _1132016) = c_Groups_Oone__class_Oone(_1132014), -(_1132018 = _1132016)]]], (52523 ^ _776541) ^ [_1831777, _1831779] : [hBOOL(_1831777), -(hBOOL(hAPP(hAPP(c_fdisj, _1831777), _1831779)))], (48748 ^ _776541) ^ [_1758994, _1758996, _1758998] : [_1758994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1758996), c_List_Oreplicate(_1758996, _1758994, _1758998)) = c_Orderings_Obot__class_Obot(tc_fun(_1758996, tc_HOL_Obool)))], (32797 ^ _776541) ^ [_1372607, _1372609, _1372611, _1372613, _1372615] : [class_Complete__Lattice_Ocomplete__lattice(_1372607), 32800 ^ _776541 : [(32801 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372607), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1372609, _1372607), _1372611), _1372613)), _1372615)), 32804 ^ _776541 : [(32805 ^ _776541) ^ [_1372788] : [hBOOL(hAPP(hAPP(c_member(_1372609), _1372788), _1372611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372607), hAPP(_1372613, _1372788)), _1372615)))]]], (32811 ^ _776541) ^ [] : [32813 ^ _776541 : [(32816 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372607), hAPP(_1372613, 32812 ^ [_1372607, _1372609, _1372611, _1372613, _1372615])), _1372615))], (32814 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372609), 32812 ^ [_1372607, _1372609, _1372611, _1372613, _1372615]), _1372611)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372607), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1372609, _1372607), _1372611), _1372613)), _1372615)))]]], (16508 ^ _776541) ^ [_1073767] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073767), _1073767) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46652 ^ _776541) ^ [_1714087, _1714089, _1714091, _1714093, _1714095] : [class_Orderings_Olinorder(_1714087), c_List_Olinorder__class_Osorted(_1714087, hAPP(hAPP(c_List_Omap(_1714089, _1714087), _1714091), _1714093)), -(c_List_Olinorder__class_Osorted(_1714087, hAPP(hAPP(c_List_Omap(_1714089, _1714087), _1714091), c_List_Olinorder__class_Oinsort__insert__key(_1714089, _1714087, _1714091, _1714095, _1714093))))], (15228 ^ _776541) ^ [_1051378, _1051380] : [class_Rings_Ocomm__semiring__1(_1051378), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051378), _1051380), _1051380) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051378), c_Groups_Oone__class_Oone(_1051378)), c_Groups_Oone__class_Oone(_1051378))), _1051380))], (36614 ^ _776541) ^ [_1470418, _1470420] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1470418, _1470418)), _1470420)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1470418), hAPP(c_Relation_OField(_1470418), _1470420))))], (32560 ^ _776541) ^ [_1365440, _1365442, _1365444, _1365446, _1365448] : [-(_1365440 = c_Orderings_Obot__class_Obot(tc_fun(_1365442, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365442, tc_fun(_1365444, tc_HOL_Obool)), _1365440), hAPP(hAPP(c_COMBB(tc_fun(_1365444, tc_HOL_Obool), tc_fun(_1365444, tc_HOL_Obool), _1365442), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365444, tc_HOL_Obool)), _1365446)), _1365448)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365444, tc_HOL_Obool)), _1365446), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365442, tc_fun(_1365444, tc_HOL_Obool)), _1365440), _1365448)))], (50916 ^ _776541) ^ [_1807764, _1807766, _1807768] : [c_List_Oall__interval__nat(_1807764, _1807766, _1807768), -(c_List_Olist__all(tc_Nat_Onat, _1807764, c_List_Oupt(_1807766, _1807768)))], (25706 ^ _776541) ^ [_1241706, _1241708, _1241710, _1241712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241708), _1241710)), -(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), _1241710), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241712, _1241706))), _1241708)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241710), _1241706))))], (4708 ^ _776541) ^ [_848154, _848156, _848158, _848160, _848162, _848164, _848166, _848168] : [-(c_Random__Sequence_Omap(_848168, _848164, _848160, _848156) = c_Random__Sequence_Omap(_848166, _848162, _848158, _848154)), _848168 = _848166, _848164 = _848162, _848160 = _848158, _848156 = _848154], (8056 ^ _776541) ^ [_913429, _913431, _913433, _913435] : [-(hBOOL(hAPP(hAPP(c_member(_913429), _913431), _913433))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913429, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913429), _913431), _913435)), _913433) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913429, tc_HOL_Obool)), _913435), _913433))], (28511 ^ _776541) ^ [_1288187] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1288187), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1288187)), c_Int_OMin)))], (23489 ^ _776541) ^ [_1202345, _1202347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202345), _1202347)), -(c_Nat__Transfer_Otsub(_1202347, _1202345) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202347), _1202345))], (7652 ^ _776541) ^ [_903711, _903713, _903715] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903711, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903711, tc_HOL_Obool)), _903713), _903715)), _903715) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903711, tc_HOL_Obool)), _903713), _903715))], (28787 ^ _776541) ^ [_1292726, _1292728] : [c_Int_OBit1(_1292726) = c_Int_OBit0(_1292728)], (10072 ^ _776541) ^ [_948858, _948860, _948862, _948864] : [class_Orderings_Olinorder(_948858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948858), _948860), _948862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948858), _948862), _948864)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948858, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_948858, _948860, _948862)), c_SetInterval_Oord__class_OgreaterThanAtMost(_948858, _948862, _948864)) = c_SetInterval_Oord__class_OatLeastAtMost(_948858, _948860, _948864))], (49303 ^ _776541) ^ [_1771941] : [-(c_Relation_Otrans(_1771941, c_Relation_OId(_1771941)))], (46229 ^ _776541) ^ [_1706247, _1706249, _1706251, _1706253, _1706255, _1706257] : [-(c_List_Ofoldr(_1706247, _1706249, _1706251, hAPP(hAPP(c_List_Oappend(_1706247), _1706253), _1706255), _1706257) = c_List_Ofoldr(_1706247, _1706249, _1706251, _1706253, c_List_Ofoldr(_1706247, _1706249, _1706251, _1706255, _1706257)))], (10994 ^ _776541) ^ [_966474, _966476, _966478, _966480, _966482, _966484] : [_966474 = hAPP(_966476, _966478), hBOOL(hAPP(hAPP(c_member(_966480), _966478), _966482)), -(hBOOL(hAPP(hAPP(c_member(_966484), _966474), hAPP(c_Set_Oimage(_966480, _966484, _966476), _966482))))], (36665 ^ _776541) ^ [_1471774, _1471776, _1471778, _1471780] : [hBOOL(hAPP(hAPP(c_member(_1471774), _1471776), _1471778)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1471774, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1471774, _1471774, _1471780), hAPP(hAPP(c_Set_Oinsert(_1471774), _1471776), c_Orderings_Obot__class_Obot(tc_fun(_1471774, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471774), _1471778), _1471780))))], (6528 ^ _776541) ^ [_881946, _881948] : [-(hBOOL(hAPP(hAPP(c_member(_881946), _881948), c_Orderings_Otop__class_Otop(tc_fun(_881946, tc_HOL_Obool)))))], (26687 ^ _776541) ^ [_1258125, _1258127] : [class_Rings_Oring__1(_1258125), 26690 ^ _776541 : [(26697 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258127), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1258125), _1258127) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1258125), hAPP(c_Int_Onat, _1258127)))], (26691 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258127), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1258125), _1258127) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258125), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1258125), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1258127)))))]]], (16146 ^ _776541) ^ [_1068363, _1068365, _1068367] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068363)), _1068365)), hAPP(c_Nat_OSuc, _1068367)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1068363), _1068365)), _1068367))], (33531 ^ _776541) ^ [_1393544, _1393546, _1393548, _1393550] : [-(_1393544 = c_Orderings_Obot__class_Obot(tc_fun(_1393546, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393546, tc_fun(_1393548, tc_HOL_Obool)), _1393544), hAPP(c_COMBK(tc_fun(_1393548, tc_HOL_Obool), _1393546), _1393550)) = _1393550)], (4910 ^ _776541) ^ [_851367, _851369] : [_851369 = _851367, -(c_Relation_OId(_851369) = c_Relation_OId(_851367))], (40915 ^ _776541) ^ [_1577766, _1577768, _1577770, _1577772, _1577774] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577766, _1577766)), hAPP(hAPP(c_Product__Type_OPair(_1577766, _1577766), _1577768), _1577770)), c_Transitive__Closure_Otrancl(_1577766, _1577772))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577766, _1577766)), hAPP(hAPP(c_Product__Type_OPair(_1577766, _1577766), _1577770), _1577774)), c_Transitive__Closure_Ortrancl(_1577766, _1577772))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577766, _1577766)), hAPP(hAPP(c_Product__Type_OPair(_1577766, _1577766), _1577768), _1577774)), c_Transitive__Closure_Otrancl(_1577766, _1577772))))], (39946 ^ _776541) ^ [_1554169, _1554171, _1554173, _1554175, _1554177, _1554179] : [class_Groups_Ocomm__monoid__add(_1554169), c_Fun_Oinj__on(_1554171, _1554173, _1554175, _1554177), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554173, _1554169), _1554179), hAPP(c_Set_Oimage(_1554171, _1554173, _1554175), _1554177)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554171, _1554169), hAPP(c_Fun_Ocomp(_1554173, _1554169, _1554171, _1554179), _1554175)), _1554177))], (14296 ^ _776541) ^ [_1034063, _1034065, _1034067, _1034069, _1034071] : [class_Rings_Ocomm__semiring__1(_1034063), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034063), _1034065), _1034067)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034063), _1034069), _1034071)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034063), _1034065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034063), _1034067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034063), _1034069), _1034071))))], (50664 ^ _776541) ^ [_1800685, _1800687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800685), _1800687)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1800685, 50667 ^ [_1800685, _1800687], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1800685), _1800687)), _1800687))], (3204 ^ _776541) ^ [_824240, _824242, _824244, _824246] : [-(c_Big__Operators_Olinorder__class_OMax(_824246, _824242) = c_Big__Operators_Olinorder__class_OMax(_824244, _824240)), _824246 = _824244, _824242 = _824240], (10052 ^ _776541) ^ [_948545, _948547, _948549, _948551, _948553] : [class_Groups_Oab__group__add(_948545), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948545), _948547), _948549) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948545), _948551), _948553), 10059 ^ _776541 : [(10066 ^ _776541) ^ [] : [_948551 = _948553, -(_948547 = _948549)], (10060 ^ _776541) ^ [] : [_948547 = _948549, -(_948551 = _948553)]]], (31919 ^ _776541) ^ [_1350019] : [class_Orderings_Oord(_1350019), -(c_Orderings_Oord__class_Omax(_1350019) = c_Orderings_Oord_Omax(_1350019, c_Orderings_Oord__class_Oless__eq(_1350019)))], (46263 ^ _776541) ^ [_1707240, _1707242] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1707240), _1707242) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1707240, _1707242)))], (46976 ^ _776541) ^ [_1720716, _1720718, _1720720] : [_1720718 = hAPP(hAPP(c_List_Olist_OCons(_1720716), _1720720), c_List_Olist_ONil(_1720716)), -(hAPP(c_List_Orev(_1720716), _1720718) = hAPP(hAPP(c_List_Olist_OCons(_1720716), _1720720), c_List_Olist_ONil(_1720716)))], (46421 ^ _776541) ^ [_1710080, _1710082, _1710084, _1710086] : [class_Groups_Ocomm__monoid__add(_1710080), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1710080), _1710082), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1710084, _1710086))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1710080), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1710080), _1710082), c_List_Oupt(_1710084, _1710086))))], (50546 ^ _776541) ^ [_1798189, _1798191, _1798193, _1798195, _1798197] : [c_Fun_Obij__betw(_1798189, _1798191, _1798193, _1798195, _1798197), -(c_Fun_Obij__betw(_1798191, _1798189, c_Fun_Othe__inv__into(_1798189, _1798191, _1798195, _1798193), _1798197, _1798195))], (33995 ^ _776541) ^ [_1407608, _1407610] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1407608), _1407610)), -(hAPP(c_Finite__Set_Ocard(_1407608), _1407610) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1407608, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1407608), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407610))], (18634 ^ _776541) ^ [_1111989, _1111991, _1111993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111989), _1111991)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111993), _1111991))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111989), _1111993)))], (6893 ^ _776541) ^ [_888402, _888404, _888406] : [class_Orderings_Oorder(_888402), 6896 ^ _776541 : [(6903 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888402), _888406), _888404)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888402, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_888402), _888404)), hAPP(c_SetInterval_Oord__class_OatLeast(_888402), _888406))))], (6897 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888402, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_888402), _888404)), hAPP(c_SetInterval_Oord__class_OatLeast(_888402), _888406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888402), _888406), _888404)))]]], (48893 ^ _776541) ^ [_1762281, _1762283, _1762285, _1762287] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762281), hAPP(hAPP(c_List_Olist_OCons(_1762281), _1762283), _1762285)), _1762287)), -(_1762283 = _1762287), -(hBOOL(hAPP(hAPP(c_List_Omember(_1762281), _1762285), _1762287)))], (41811 ^ _776541) ^ [_1601553, _1601555, _1601557, _1601559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1601553), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1601555), _1601557))), -(hAPP(c_Random_Opick(_1601555, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1601555)), _1601557), _1601559)), _1601553) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1601555), _1601557))], (23035 ^ _776541) ^ [_1193882, _1193884, _1193886, _1193888, _1193890, _1193892] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193882), _1193884)), _1193886) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193888), _1193890)), _1193892), 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), _1193888), _1193890)), _1193892))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193892), _1193888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193888), _1193882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193884), _1193890)))], (44441 ^ _776541) ^ [_1665327, _1665329, _1665331] : [class_Orderings_Olinorder(_1665327), -(c_Big__Operators_Olinorder__class_OMax(_1665327, hAPP(c_List_Oset(_1665327), hAPP(hAPP(c_List_Olist_OCons(_1665327), _1665329), _1665331))) = hAPP(c_List_Ofoldl(_1665327, _1665327, c_Orderings_Oord__class_Omax(_1665327), _1665329), _1665331))], (18234 ^ _776541) ^ [_1104419, _1104421, _1104423, _1104425] : [class_Groups_Oordered__comm__monoid__add(_1104419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104419), c_Groups_Ozero__class_Ozero(_1104419)), _1104421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104419), _1104423), _1104425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104419), _1104423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104419), _1104421), _1104425))))], (30600 ^ _776541) ^ [_1325643, _1325645] : [class_Orderings_Olinorder(_1325643), -(c_Big__Operators_Olinorder__class_OMin(_1325643, hAPP(hAPP(c_Set_Oinsert(_1325643), _1325645), c_Orderings_Obot__class_Obot(tc_fun(_1325643, tc_HOL_Obool)))) = _1325645)], (34163 ^ _776541) ^ [_1411365, _1411367, _1411369, _1411371] : [class_Groups_Oab__group__add(_1411365), 34166 ^ _776541 : [(34173 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411367), _1411369))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411365), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1411365, _1411365), hAPP(hAPP(c_COMBB(_1411365, tc_fun(_1411365, _1411365), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1411365)), _1411371)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411365, tc_Nat_Onat), _1411371), 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, _1411367, _1411369)) = c_Groups_Ozero__class_Ozero(_1411365))], (34167 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411367), _1411369)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411365), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1411365, _1411365), hAPP(hAPP(c_COMBB(_1411365, tc_fun(_1411365, _1411365), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1411365)), _1411371)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411365, tc_Nat_Onat), _1411371), 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, _1411367, _1411369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1411365), hAPP(_1411371, _1411367)), hAPP(_1411371, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1411369), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (27219 ^ _776541) ^ [_1266281, _1266283, _1266285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1266283), 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), _1266283), _1266285))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1266281))), _1266285)))], (8799 ^ _776541) ^ [_927676, _927678, _927680, _927682] : [class_Lattices_Odistrib__lattice(_927676), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927676), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927676), _927678), _927680)), _927682) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927676), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927676), _927678), _927682)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927676), _927680), _927682)))], (42988 ^ _776541) ^ [_1633371, _1633373] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1633371)), c_List_Olist_ONil(_1633371)), c_List_Olists(_1633371, _1633373))))], (24224 ^ _776541) ^ [_1214664, _1214666, _1214668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214664), _1214666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214664), _1214668)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214666), _1214668))))], (3624 ^ _776541) ^ [_830828, _830830, _830832, _830834, _830836, _830838] : [-(c_List_Oremove1(_830838, _830834, _830830) = c_List_Oremove1(_830836, _830832, _830828)), _830838 = _830836, _830834 = _830832, _830830 = _830828], (14819 ^ _776541) ^ [_1043767, _1043769] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043767), _1043769)), _1043767) = _1043769)], (45668 ^ _776541) ^ [_1692545] : [-(c_Enum_Osublists(_1692545, c_List_Olist_ONil(_1692545)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1692545)), c_List_Olist_ONil(_1692545)), c_List_Olist_ONil(tc_List_Olist(_1692545))))], (29545 ^ _776541) ^ [_1305793, _1305795, _1305797] : [class_Rings_Olinordered__idom(_1305793), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305793), c_Groups_Ozero__class_Ozero(_1305793)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305793), hAPP(hAPP(c_Power_Opower__class_Opower(_1305793), _1305795), 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(_1305793), _1305797), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (22389 ^ _776541) ^ [_1182445] : [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)), _1182445)), _1182445)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182445), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41712 ^ _776541) ^ [_1597914] : [-(c_Nitpick_Odenom(_1597914) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1597914, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1597914)))], (594 ^ _776541) ^ [_785464, _785466, _785468, _785470, _785472, _785474, _785476, _785478, _785480, _785482] : [-(c_List_Olist__all2(_785480, _785476, _785472, _785468, _785464)), c_List_Olist__all2(_785482, _785478, _785474, _785470, _785466), _785482 = _785480, _785478 = _785476, _785474 = _785472, _785470 = _785468, _785466 = _785464], (38704 ^ _776541) ^ [_1520307, _1520309, _1520311, _1520313, _1520315] : [hBOOL(hAPP(hAPP(c_member(_1520311), hAPP(_1520313, _1520309)), _1520315)), -(hBOOL(hAPP(hAPP(c_member(_1520307), _1520309), hAPP(c_Set_Ovimage(_1520307, _1520311, _1520313), _1520315))))], (41226 ^ _776541) ^ [_1585474, _1585476, _1585478, _1585480, _1585482, _1585484] : [c_Relation_Osingle__valued(_1585474, _1585476, hAPP(c_Relation_Oconverse(_1585476, _1585474), _1585478)), -(_1585480 = c_Orderings_Obot__class_Obot(tc_fun(_1585482, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1585476, _1585474, _1585478), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585482, tc_fun(_1585476, tc_HOL_Obool)), _1585480), _1585484)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585482, tc_fun(_1585474, tc_HOL_Obool)), _1585480), hAPP(hAPP(c_COMBB(tc_fun(_1585476, tc_HOL_Obool), tc_fun(_1585474, tc_HOL_Obool), _1585482), c_Relation_OImage(_1585476, _1585474, _1585478)), _1585484)))], (8747 ^ _776541) ^ [_926854, _926856, _926858] : [class_Lattices_Olattice(_926854), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926854), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926854), _926856), _926858)), _926856)))], (21385 ^ _776541) ^ [_1163884, _1163886, _1163888, _1163890] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163884), hAPP(c_Int_Onumber__class_Onumber__of(_1163884), _1163886)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163884), _1163888), _1163890)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163884), hAPP(c_Int_Onumber__class_Onumber__of(_1163884), _1163886)), _1163888)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163884), hAPP(c_Int_Onumber__class_Onumber__of(_1163884), _1163886)), _1163890))), class_Int_Onumber(_1163884), class_Rings_Oring(_1163884)], (34522 ^ _776541) ^ [_1419232, _1419234, _1419236, _1419238, _1419240, _1419242, _1419244] : [34524 ^ _776541 : [(34527 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1419240, 34523 ^ [_1419232, _1419234, _1419236, _1419238, _1419240, _1419242, _1419244]), _1419242), _1419244))], (34525 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419232), 34523 ^ [_1419232, _1419234, _1419236, _1419238, _1419240, _1419242, _1419244]), _1419238)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419232, tc_fun(_1419234, tc_fun(_1419236, tc_HOL_Obool))), _1419238), _1419240), _1419242), _1419244)))], (25305 ^ _776541) ^ [_1234481, _1234483, _1234485] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234481), _1234483)), _1234485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234481), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234483), _1234485))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234481), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234483, _1234485))), _1234485)))], (23501 ^ _776541) ^ [_1202490, _1202492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202492)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1202492), _1202490)), _1202492) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1202492), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202490), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (19279 ^ _776541) ^ [_1124516, _1124518, _1124520, _1124522, _1124524] : [class_Groups_Ocomm__monoid__add(_1124516), class_Groups_Oordered__ab__semigroup__add(_1124516), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124518), _1124520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1124518, tc_HOL_Obool)), _1124522), _1124520)), 19297 ^ _776541 : [(19300 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124516), c_Groups_Ozero__class_Ozero(_1124516)), hAPP(_1124524, 19296 ^ [_1124516, _1124518, _1124520, _1124522, _1124524])))], (19298 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1124518), 19296 ^ [_1124516, _1124518, _1124520, _1124522, _1124524]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1124518, tc_HOL_Obool)), _1124520), _1124522))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124516), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1124518, _1124516), _1124524), _1124522)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1124518, _1124516), _1124524), _1124520))))], (7716 ^ _776541) ^ [_905632, _905634, _905636, _905638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905632, tc_HOL_Obool)), _905638), _905634)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905632, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905632, tc_HOL_Obool)), _905634), _905636)), _905638) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905632, tc_HOL_Obool)), _905634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905632, tc_HOL_Obool)), _905636), _905638)))], (14528 ^ _776541) ^ [_1038534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038534), _1038534))], (51489 ^ _776541) ^ [_1818544, _1818546] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818546), _1818544)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818544), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818546))))], (25840 ^ _776541) ^ [_1244007] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244007))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244007)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8937 ^ _776541) ^ [_930671, _930673, _930675, _930677, _930679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930671, tc_HOL_Obool)), _930673), _930675)), 8943 ^ _776541 : [(8948 ^ _776541) ^ [] : [hBOOL(hAPP(_930679, 8942 ^ [_930671, _930673, _930675, _930677, _930679]))], (8946 ^ _776541) ^ [] : [-(hBOOL(hAPP(_930677, 8942 ^ [_930671, _930673, _930675, _930677, _930679])))], (8944 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930671), 8942 ^ [_930671, _930673, _930675, _930677, _930679]), _930673)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930671, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930671, tc_HOL_Obool)), _930673), hAPP(c_Set_OCollect(_930671), _930677))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930671, tc_HOL_Obool)), _930675), hAPP(c_Set_OCollect(_930671), _930679)))))], (22455 ^ _776541) ^ [_1183490] : [_1183490 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1183490) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (3334 ^ _776541) ^ [_826295, _826297, _826299, _826301] : [-(c_List_Olistsp(_826301, _826297) = c_List_Olistsp(_826299, _826295)), _826301 = _826299, _826297 = _826295], (13025 ^ _776541) ^ [_1006394, _1006396, _1006398] : [class_Groups_Oab__semigroup__mult(_1006394), -(_1006396 = c_Orderings_Obot__class_Obot(tc_fun(_1006394, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006394), _1006396)), -(hBOOL(hAPP(hAPP(c_member(_1006394), _1006398), _1006396))), -(hAPP(c_Finite__Set_Ofold1(_1006394, c_Groups_Otimes__class_Otimes(_1006394)), hAPP(hAPP(c_Set_Oinsert(_1006394), _1006398), _1006396)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006394), _1006398), hAPP(c_Finite__Set_Ofold1(_1006394, c_Groups_Otimes__class_Otimes(_1006394)), _1006396)))], (26985 ^ _776541) ^ [_1262629, _1262631] : [class_Rings_Oring__1(_1262629), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262629), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1262631)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1262629), hAPP(c_Int_Oring__1__class_Oof__int(_1262629), _1262631)))], (32958 ^ _776541) ^ [_1377637, _1377639, _1377641, _1377643, _1377645] : [-(_1377637 = c_Orderings_Obot__class_Obot(tc_fun(_1377639, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377641, tc_HOL_Obool)), _1377643), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377639, tc_fun(_1377641, tc_HOL_Obool)), _1377637), _1377645)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377639, tc_fun(_1377641, tc_HOL_Obool)), _1377637), hAPP(hAPP(c_COMBB(tc_fun(_1377641, tc_HOL_Obool), tc_fun(_1377641, tc_HOL_Obool), _1377639), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377641, tc_HOL_Obool)), _1377643)), _1377645)))], (13808 ^ _776541) ^ [_1022741, _1022743, _1022745] : [class_Groups_Ogroup__add(_1022741), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022741), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1022741), _1022743), _1022745)), _1022745) = _1022743)], (22659 ^ _776541) ^ [_1187129, _1187131, _1187133, _1187135] : [class_Fields_Ofield(_1187129), -(_1187131 = c_Groups_Ozero__class_Ozero(_1187129)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187129), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187129), _1187133), _1187131)), _1187135) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187129), hAPP(hAPP(c_Power_Opower__class_Opower(_1187129), _1187133), _1187135)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187129), _1187131), _1187135)))], (22369 ^ _776541) ^ [_1182089, _1182091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182089), _1182091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1182089), _1182091)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20851 ^ _776541) ^ [_1153042, _1153044, _1153046, _1153048] : [class_Fields_Olinordered__field__inverse__zero(_1153042), 20854 ^ _776541 : [(20855 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), _1153044), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153042), _1153046), _1153048))), 20858 ^ _776541 : [(20865 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), c_Groups_Ozero__class_Ozero(_1153042)), _1153048))), 20868 ^ _776541 : [(20875 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), _1153048), c_Groups_Ozero__class_Ozero(_1153042)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), _1153044), c_Groups_Ozero__class_Ozero(_1153042))))], (20869 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), _1153048), c_Groups_Ozero__class_Ozero(_1153042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), _1153046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153042), _1153044), _1153048))))]]], (20859 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), c_Groups_Ozero__class_Ozero(_1153042)), _1153048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153042), _1153044), _1153048)), _1153046)))]]], (20881 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), _1153044), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153042), _1153046), _1153048)))), 20884 ^ _776541 : [(20887 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153042), _1153044), _1153048)), _1153046))], (20885 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), c_Groups_Ozero__class_Ozero(_1153042)), _1153048)))]], 20888 ^ _776541 : [(20891 ^ _776541) ^ [] : [20892 ^ _776541 : [(20895 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), _1153046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153042), _1153044), _1153048)))], (20893 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), _1153048), c_Groups_Ozero__class_Ozero(_1153042))))]], 20896 ^ _776541 : [(20899 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153042), _1153044), c_Groups_Ozero__class_Ozero(_1153042)))], (20897 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), _1153048), c_Groups_Ozero__class_Ozero(_1153042)))]]], (20889 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153042), c_Groups_Ozero__class_Ozero(_1153042)), _1153048))]]]]], (47008 ^ _776541) ^ [_1721371, _1721373] : [hAPP(c_List_Orev(_1721371), _1721373) = c_List_Olist_ONil(_1721371), -(_1721373 = c_List_Olist_ONil(_1721371))], (22273 ^ _776541) ^ [_1180457] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180457), _1180457)))], (50451 ^ _776541) ^ [_1796498, _1796500, _1796502, _1796504] : [c_Fun_Obij__betw(_1796498, _1796500, _1796502, _1796504, c_Orderings_Otop__class_Otop(tc_fun(_1796500, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1796498, _1796500, _1796502), c_Orderings_Otop__class_Otop(tc_fun(_1796498, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1796500, tc_HOL_Obool)))], (52137 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (19641 ^ _776541) ^ [_1131358, _1131360, _1131362, _1131364] : [class_Rings_Odivision__ring(_1131358), -(_1131360 = c_Groups_Ozero__class_Ozero(_1131358)), 19648 ^ _776541 : [(19655 ^ _776541) ^ [] : [_1131362 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131358), _1131364), _1131360), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131358), _1131362), _1131360) = _1131364)], (19649 ^ _776541) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131358), _1131362), _1131360) = _1131364, -(_1131362 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131358), _1131364), _1131360))]]], (41889 ^ _776541) ^ [_1603785, _1603787, _1603789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1603785, _1603785), tc_HOL_Obool)), _1603787), _1603789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1603785), tc_List_Olist(_1603785)), tc_HOL_Obool)), c_List_Olistrel1(_1603785, _1603787)), c_List_Olistrel1(_1603785, _1603789))))], (26909 ^ _776541) ^ [_1261276] : [class_Rings_Oring__1(_1261276), -(hAPP(c_Int_Oring__1__class_Oof__int(_1261276), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1261276))], (24850 ^ _776541) ^ [_1226255, _1226257, _1226259, _1226261] : [class_Divides_Osemiring__div(_1226255), -(c_Divides_Odiv__class_Omod(_1226255, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226255), _1226257), _1226259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226255), _1226257), _1226261)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226255), _1226257), c_Divides_Odiv__class_Omod(_1226255, _1226259, _1226261)))], (6310 ^ _776541) ^ [_878106, _878108, _878110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_878106, tc_HOL_Obool), tc_HOL_Obool)), _878108), _878110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878106, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_878106, tc_HOL_Obool), _878108)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_878106, tc_HOL_Obool), _878110))))], (18862 ^ _776541) ^ [_1116414, _1116416] : [_1116414 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116414), _1116416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36541 ^ _776541) ^ [] : [-(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))))))], (11598 ^ _776541) ^ [_979386] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_979386), c_Orderings_Obot__class_Obot(tc_fun(_979386, tc_HOL_Obool)))))], (25103 ^ _776541) ^ [_1230987] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1230987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230987)))], (28375 ^ _776541) ^ [_1285912] : [c_Int_OBit1(_1285912) = c_Int_OPls], (46528 ^ _776541) ^ [_1712162, _1712164, _1712166] : [class_Orderings_Olinorder(_1712162), c_List_Olinorder__class_Osorted(_1712162, _1712164), -(c_List_Olinorder__class_Osorted(_1712162, hAPP(hAPP(c_List_Odrop(_1712162), _1712166), _1712164)))], (2444 ^ _776541) ^ [_812418, _812420] : [_812420 = _812418, -(c_Int_OBit0(_812420) = c_Int_OBit0(_812418))], (27479 ^ _776541) ^ [_1270905, _1270907, _1270909] : [class_Groups_Oordered__ab__group__add__abs(_1270905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270905), hAPP(c_Groups_Oabs__class_Oabs(_1270905), _1270907)), _1270909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270905), hAPP(c_Groups_Ouminus__class_Ouminus(_1270905), _1270907)), _1270909)))], (35939 ^ _776541) ^ [_1450139, _1450141, _1450143] : [class_Groups_Olinordered__ab__semigroup__add(_1450139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450139), _1450141)), -(_1450141 = c_Orderings_Obot__class_Obot(tc_fun(_1450139, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450139), _1450143), c_Big__Operators_Olinorder__class_OMin(_1450139, _1450141)) = c_Big__Operators_Olinorder__class_OMin(_1450139, hAPP(c_Set_OCollect(_1450139), hAPP(hAPP(c_COMBB(tc_fun(_1450139, tc_HOL_Obool), tc_HOL_Obool, _1450139), c_HOL_OEx(_1450139)), hAPP(hAPP(c_COMBC(_1450139, tc_fun(_1450139, tc_HOL_Obool), tc_fun(_1450139, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450139, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1450139, tc_HOL_Obool), tc_fun(_1450139, tc_HOL_Obool)), _1450139), c_COMBS(_1450139, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450139, tc_HOL_Obool), tc_fun(_1450139, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1450139), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1450139), c_fconj)), hAPP(hAPP(c_COMBC(_1450139, tc_fun(_1450139, _1450139), tc_fun(_1450139, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450139, tc_HOL_Obool), tc_fun(tc_fun(_1450139, _1450139), tc_fun(_1450139, tc_HOL_Obool)), _1450139), c_COMBB(_1450139, tc_HOL_Obool, _1450139)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1450139), _1450143))))), hAPP(hAPP(c_COMBC(_1450139, tc_fun(_1450139, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450139)), _1450141))))))], (48917 ^ _776541) ^ [_1762711, _1762713, _1762715] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762711), _1762715), _1762713)), -(hBOOL(hAPP(hAPP(c_member(_1762711), _1762713), hAPP(c_List_Oset(_1762711), _1762715))))], (22335 ^ _776541) ^ [_1181424, _1181426] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181424), _1181426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181424)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181426)))], (25921 ^ _776541) ^ [_1245328, _1245330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245330, _1245328)), _1245328)))], (34622 ^ _776541) ^ [_1421449, _1421451] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1421449), hAPP(c_Nat_OSuc, _1421451)) = 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), _1421449), _1421451)))], (26487 ^ _776541) ^ [_1254616, _1254618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254618)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254616), _1254618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1254616)), hAPP(c_Int_Onat, _1254618)))], (29163 ^ _776541) ^ [_1299268, _1299270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299268)), c_Int_OBit0(_1299270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299268), _1299270)))], (42019 ^ _776541) ^ [_1607842, _1607844] : [-(c_List_Olistrel(_1607842, c_Transitive__Closure_Ortrancl(_1607842, _1607844)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607842), c_List_Olistrel1(_1607842, _1607844)))], (11950 ^ _776541) ^ [_986298, _986300, _986302, _986304, _986306, _986308] : [-(c_Fun_Ofun__upd(_986298, _986300, c_Fun_Ofun__upd(_986298, _986300, _986302, _986304, _986306), _986304, _986308) = c_Fun_Ofun__upd(_986298, _986300, _986302, _986304, _986308))], (39503 ^ _776541) ^ [_1542321, _1542323, _1542325, _1542327, _1542329, _1542331, _1542333, _1542335] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542321, _1542323)), _1542325), hAPP(c_Set_Oimage(tc_prod(_1542327, _1542329), tc_prod(_1542321, _1542323), c_Product__Type_Omap__pair(_1542327, _1542321, _1542329, _1542323, _1542331, _1542333)), _1542335))), 39508 ^ _776541 : [(39511 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542327, _1542329)), hAPP(hAPP(c_Product__Type_OPair(_1542327, _1542329), 39506 ^ [_1542321, _1542323, _1542325, _1542327, _1542329, _1542331, _1542333, _1542335]), 39507 ^ [_1542321, _1542323, _1542325, _1542327, _1542329, _1542331, _1542333, _1542335])), _1542335)))], (39509 ^ _776541) ^ [] : [-(_1542325 = hAPP(hAPP(c_Product__Type_OPair(_1542321, _1542323), hAPP(_1542331, 39506 ^ [_1542321, _1542323, _1542325, _1542327, _1542329, _1542331, _1542333, _1542335])), hAPP(_1542333, 39507 ^ [_1542321, _1542323, _1542325, _1542327, _1542329, _1542331, _1542333, _1542335])))]]], (27899 ^ _776541) ^ [_1278112, _1278114] : [class_Int_Onumber__ring(_1278112), class_Rings_Olinordered__idom(_1278112), 27906 ^ _776541 : [(27913 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1278114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278112), c_Groups_Ozero__class_Ozero(_1278112)), hAPP(c_Int_Onumber__class_Onumber__of(_1278112), _1278114))))], (27907 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278112), c_Groups_Ozero__class_Ozero(_1278112)), hAPP(c_Int_Onumber__class_Onumber__of(_1278112), _1278114))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1278114)))]]], (33979 ^ _776541) ^ [_1407202, _1407204, _1407206] : [class_Int_Onumber__ring(_1407202), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1407202), hAPP(c_Int_Onumber__class_Onumber__of(_1407202), _1407204)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1407206))) = hAPP(hAPP(c_HOL_OLet(_1407202, _1407202), hAPP(hAPP(c_Power_Opower__class_Opower(_1407202), hAPP(c_Int_Onumber__class_Onumber__of(_1407202), _1407204)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407206))), hAPP(hAPP(c_COMBS(_1407202, _1407202, _1407202), c_Groups_Otimes__class_Otimes(_1407202)), c_COMBI(_1407202))))], (13430 ^ _776541) ^ [_1015205, _1015207, _1015209, _1015211] : [class_Lattices_Osemilattice__sup(_1015205), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015205), _1015207)), 13440 ^ _776541 : [(13443 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015205), 13439 ^ [_1015205, _1015207, _1015209, _1015211]), _1015209))], (13441 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1015205), 13439 ^ [_1015205, _1015207, _1015209, _1015211]), _1015207)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015205), hAPP(hAPP(c_Finite__Set_Ofold(_1015205, _1015205, c_Lattices_Osemilattice__sup__class_Osup(_1015205)), _1015211), _1015207)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1015205), _1015209), _1015211))))], (41272 ^ _776541) ^ [_1586335, _1586337] : [-(c_Relation_Ototal__on(_1586335, c_Orderings_Obot__class_Obot(tc_fun(_1586335, tc_HOL_Obool)), _1586337))], (48087 ^ _776541) ^ [_1745067, _1745069, _1745071, _1745073] : [48088 ^ _776541 : [(48091 ^ _776541) ^ [] : [c_List_Olist__ex(_1745067, _1745069, _1745073)], (48089 ^ _776541) ^ [] : [c_List_Olist__ex(_1745067, _1745069, _1745071)]], -(c_List_Olist__ex(_1745067, _1745069, hAPP(hAPP(c_List_Oappend(_1745067), _1745071), _1745073)))], (44429 ^ _776541) ^ [_1665069, _1665071, _1665073] : [class_Lattices_Olattice(_1665069), -(c_Big__Operators_Olattice__class_OInf__fin(_1665069, hAPP(c_List_Oset(_1665069), hAPP(hAPP(c_List_Olist_OCons(_1665069), _1665071), _1665073))) = hAPP(c_List_Ofoldl(_1665069, _1665069, c_Lattices_Osemilattice__inf__class_Oinf(_1665069), _1665071), _1665073))], (40120 ^ _776541) ^ [_1558110, _1558112, _1558114, _1558116, _1558118, _1558120, _1558122] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1558110, _1558112, _1558114), hAPP(c_Fun_Ocomp(_1558116, tc_fun(_1558112, _1558114), _1558110, _1558118), _1558120)), _1558122) = hAPP(hAPP(_1558118, hAPP(_1558120, hAPP(c_Product__Type_Ofst(_1558110, _1558112), _1558122))), hAPP(c_Product__Type_Osnd(_1558110, _1558112), _1558122)))], (43561 ^ _776541) ^ [_1645536, _1645538, _1645540] : [-(hAPP(c_List_Oset(_1645536), hAPP(hAPP(c_List_Oappend(_1645536), _1645538), _1645540)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1645536, tc_HOL_Obool)), hAPP(c_List_Oset(_1645536), _1645538)), hAPP(c_List_Oset(_1645536), _1645540)))], (38752 ^ _776541) ^ [_1521305, _1521307, _1521309] : [-(hAPP(c_Set_Ovimage(_1521305, _1521307, _1521309), c_Orderings_Obot__class_Obot(tc_fun(_1521307, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1521305, tc_HOL_Obool)))], (47198 ^ _776541) ^ [_1725299, _1725301, _1725303] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725299), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1725299))), _1725301))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725303), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1725299))), _1725301))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1725299))), hAPP(c_List_Ofilter(tc_List_Olist(_1725299), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1725299)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725303)), c_Nat_Osize__class_Osize(tc_List_Olist(_1725299)))), c_List_Otranspose(_1725299, _1725301))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725299)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1725299)), _1725301), _1725303)))], (50391 ^ _776541) ^ [_1795348, _1795350, _1795352, _1795354, _1795356, _1795358] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1795348, _1795350, _1795352, _1795354), _1795356), _1795358) = hAPP(_1795354, hAPP(hAPP(c_Product__Type_OPair(_1795348, _1795350), _1795356), _1795358)))], (38730 ^ _776541) ^ [_1520935, _1520937] : [-(hAPP(c_Relation_ODomain(_1520935, _1520935), c_Relation_OId__on(_1520935, _1520937)) = _1520937)], (44150 ^ _776541) ^ [_1659365, _1659367, _1659369] : [-(hAPP(c_List_Otl(_1659365), hAPP(hAPP(c_List_Odrop(_1659365), _1659367), _1659369)) = hAPP(hAPP(c_List_Odrop(_1659365), _1659367), hAPP(c_List_Otl(_1659365), _1659369)))], (34870 ^ _776541) ^ [_1427282, _1427284] : [-(c_Divides_Odivmod__nat(_1427284, _1427282) = 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), _1427284), _1427282), _1427282))), -(_1427282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1427284), _1427282)))], (51849 ^ _776541) ^ [_1824503, _1824505] : [class_Lattices_Obounded__lattice(_1824503), -(class_Lattices_Obounded__lattice(tc_fun(_1824505, _1824503)))], (24307 ^ _776541) ^ [_1216128] : [-(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), _1216128))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (38955 ^ _776541) ^ [_1526240, _1526242, _1526244, _1526246] : [hBOOL(hAPP(c_Predicate_ODomainP(_1526240, _1526242, hAPP(hAPP(c_COMBC(_1526240, tc_fun(tc_prod(_1526240, _1526242), tc_HOL_Obool), tc_fun(_1526242, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526242, tc_fun(tc_fun(tc_prod(_1526240, _1526242), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526240, _1526242), tc_HOL_Obool), tc_fun(_1526242, tc_HOL_Obool)), _1526240), c_COMBC(_1526242, tc_fun(tc_prod(_1526240, _1526242), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526242, tc_prod(_1526240, _1526242)), tc_fun(_1526242, tc_fun(tc_fun(tc_prod(_1526240, _1526242), tc_HOL_Obool), tc_HOL_Obool)), _1526240), hAPP(c_COMBB(tc_prod(_1526240, _1526242), tc_fun(tc_fun(tc_prod(_1526240, _1526242), tc_HOL_Obool), tc_HOL_Obool), _1526242), c_member(tc_prod(_1526240, _1526242)))), c_Product__Type_OPair(_1526240, _1526242)))), _1526244)), _1526246)), -(hBOOL(hAPP(hAPP(c_member(_1526240), _1526246), hAPP(c_Relation_ODomain(_1526240, _1526242), _1526244))))], (26543 ^ _776541) ^ [_1255635, _1255637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255635), _1255637)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1255637), _1255635)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1255637)), hAPP(c_Int_Onat, _1255635)))], (5598 ^ _776541) ^ [_862017, _862019] : [_862019 = _862017, -(tc_Lazy__Sequence_Olazy__sequence(_862019) = tc_Lazy__Sequence_Olazy__sequence(_862017))], (4976 ^ _776541) ^ [_852354, _852356, _852358, _852360, _852362, _852364, _852366, _852368, _852370, _852372] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_852372, _852368, _852364, _852360, _852356) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_852370, _852366, _852362, _852358, _852354)), _852372 = _852370, _852368 = _852366, _852364 = _852362, _852360 = _852358, _852356 = _852354], (4222 ^ _776541) ^ [_840535, _840537] : [_840537 = _840535, -(c_List_Otl(_840537) = c_List_Otl(_840535))], (27353 ^ _776541) ^ [_1268664, _1268666] : [class_Rings_Olinordered__idom(_1268664), -(hAPP(c_Groups_Oabs__class_Oabs(_1268664), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1268664), _1268666)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1268664), _1268666))], (19344 ^ _776541) ^ [_1125793, _1125795, _1125797] : [class_Rings_Oring__1(_1125793), hBOOL(hAPP(hAPP(c_member(_1125793), _1125795), c_Int_Oring__1__class_OInts(_1125793))), hBOOL(hAPP(hAPP(c_member(_1125793), _1125797), c_Int_Oring__1__class_OInts(_1125793))), -(hBOOL(hAPP(hAPP(c_member(_1125793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125793), _1125795), _1125797)), c_Int_Oring__1__class_OInts(_1125793))))], (19981 ^ _776541) ^ [_1137154, _1137156, _1137158, _1137160] : [class_Fields_Olinordered__field(_1137154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137154), c_Groups_Ozero__class_Ozero(_1137154)), _1137156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137154), _1137158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137154), _1137160), _1137156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137154), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137154), _1137158), _1137156)), _1137160)))], (10158 ^ _776541) ^ [_950685, _950687, _950689, _950691, _950693, _950695, _950697] : [-(c_Nitpick_Ofold__graph_H(_950685, _950687, _950689, _950691, _950693, hAPP(hAPP(_950689, _950695), _950697))), 10159 ^ _776541 : [(10166 ^ _776541) ^ [_950914, _950916] : [hAPP(hAPP(_950689, _950695), _950697) = hAPP(hAPP(_950689, _950916), _950914), hBOOL(hAPP(hAPP(c_member(_950685), _950916), _950693)), c_Nitpick_Ofold__graph_H(_950685, _950687, _950689, _950691, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950685, tc_HOL_Obool)), _950693), hAPP(hAPP(c_Set_Oinsert(_950685), _950916), c_Orderings_Obot__class_Obot(tc_fun(_950685, tc_HOL_Obool)))), _950914)], (10160 ^ _776541) ^ [] : [_950693 = c_Orderings_Obot__class_Obot(tc_fun(_950685, tc_HOL_Obool)), hAPP(hAPP(_950689, _950695), _950697) = _950691]]], (40939 ^ _776541) ^ [_1578384] : [-(c_Relation_Orefl__on(_1578384, c_Orderings_Otop__class_Otop(tc_fun(_1578384, tc_HOL_Obool)), c_Relation_OId(_1578384)))], (26507 ^ _776541) ^ [_1254989, _1254991] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1254989) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1254991), 26510 ^ _776541 : [(26513 ^ _776541) ^ [] : [-(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), _1254991))))], (26511 ^ _776541) ^ [] : [-(_1254989 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1254991)))]]], (8623 ^ _776541) ^ [_924719, _924721, _924723, _924725] : [class_Lattices_Osemilattice__inf(_924719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924719), _924721), _924723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924719), _924721), _924725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924719), _924721), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924719), _924723), _924725))))], (16050 ^ _776541) ^ [_1066818, _1066820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066818), hAPP(c_Nat_OSuc, _1066820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066818), _1066820))), -(_1066818 = _1066820)], (47261 ^ _776541) ^ [_1726790, _1726792] : [-(c_List_OtakeWhile(_1726790, _1726792, c_List_Olist_ONil(_1726790)) = c_List_Olist_ONil(_1726790))], (44868 ^ _776541) ^ [_1674439, _1674441, _1674443, _1674445, _1674447, _1674449, _1674451, _1674453] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674439, _1674441), _1674443), _1674445), hAPP(hAPP(c_List_Ozip(_1674439, _1674441), hAPP(hAPP(c_List_Omap(_1674447, _1674439), _1674449), _1674451)), _1674453)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674447, _1674441), _1674443), hAPP(c_Product__Type_Oprod_Oprod__case(_1674447, _1674441, _1674443), hAPP(hAPP(c_COMBB(tc_fun(_1674441, tc_prod(_1674439, _1674441)), tc_fun(_1674441, _1674443), _1674447), hAPP(c_COMBB(tc_prod(_1674439, _1674441), _1674443, _1674441), _1674445)), hAPP(hAPP(c_COMBB(_1674439, tc_fun(_1674441, tc_prod(_1674439, _1674441)), _1674447), c_Product__Type_OPair(_1674439, _1674441)), _1674449)))), hAPP(hAPP(c_List_Ozip(_1674447, _1674441), _1674451), _1674453)))], (42345 ^ _776541) ^ [_1616923, _1616925, _1616927, _1616929] : [hBOOL(hAPP(hAPP(c_member(_1616923), _1616925), hAPP(c_List_Oset(_1616923), hAPP(hAPP(c_List_Otake(_1616923), _1616927), _1616929)))), -(hBOOL(hAPP(hAPP(c_member(_1616923), _1616925), hAPP(c_List_Oset(_1616923), _1616929))))], (44743 ^ _776541) ^ [_1671080, _1671082, _1671084, _1671086] : [-(hAPP(c_List_Oset(_1671080), hAPP(hAPP(c_List_Omap(_1671082, _1671080), _1671084), _1671086)) = hAPP(c_Set_Oimage(_1671082, _1671080, _1671084), hAPP(c_List_Oset(_1671082), _1671086)))], (16412 ^ _776541) ^ [_1072421, _1072423] : [class_Groups_Olinordered__ab__group__add(_1072421), 16415 ^ _776541 : [(16422 ^ _776541) ^ [] : [_1072423 = c_Groups_Ozero__class_Ozero(_1072421), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1072421), _1072423) = _1072423)], (16416 ^ _776541) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1072421), _1072423) = _1072423, -(_1072423 = c_Groups_Ozero__class_Ozero(_1072421))]]], (52401 ^ _776541) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (45886 ^ _776541) ^ [_1697059, _1697061, _1697063] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1697059), tc_List_Olist(_1697059), c_List_Oappend(_1697059), _1697061), _1697063) = hAPP(hAPP(c_List_Oappend(_1697059), _1697061), c_List_Oconcat(_1697059, _1697063)))], (23719 ^ _776541) ^ [_1206148] : [-(hBOOL(hAPP(_1206148, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23726 ^ [_1206148])))), 23720 ^ _776541 : [(23721 ^ _776541) ^ [_1206200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206200)), hBOOL(hAPP(_1206148, _1206200))]]], (47307 ^ _776541) ^ [_1727579, _1727581, _1727583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727579)), c_List_OtakeWhile(_1727579, _1727581, _1727583))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727579)), _1727583))), hBOOL(hAPP(_1727581, hAPP(hAPP(c_List_Onth(_1727579), _1727583), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727579)), c_List_OtakeWhile(_1727579, _1727581, _1727583)))))], (38714 ^ _776541) ^ [_1520558, _1520560, _1520562, _1520564, _1520566] : [-(hAPP(c_Set_Ovimage(_1520558, _1520560, _1520562), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520560, tc_HOL_Obool)), _1520564), _1520566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520558, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1520558, _1520560, _1520562), _1520564)), hAPP(c_Set_Ovimage(_1520558, _1520560, _1520562), _1520566)))], (22723 ^ _776541) ^ [_1188163, _1188165, _1188167, _1188169] : [class_Rings_Olinordered__semidom(_1188163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188163), hAPP(hAPP(c_Power_Opower__class_Opower(_1188163), _1188165), _1188167)), hAPP(hAPP(c_Power_Opower__class_Opower(_1188163), _1188169), _1188167))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188163), c_Groups_Ozero__class_Ozero(_1188163)), _1188169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188163), _1188165), _1188169)))], (25369 ^ _776541) ^ [_1235517] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235517)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235517)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235517))], (52557 ^ _776541) ^ [_1832172, _1832174] : [hBOOL(hAPP(hAPP(c_fimplies, _1832172), _1832174)), hBOOL(_1832172), -(hBOOL(_1832174))], (45373 ^ _776541) ^ [_1685827, _1685829, _1685831, _1685833] : [-(hBOOL(hAPP(c_List_Olistsp(_1685827, hAPP(hAPP(c_COMBS(_1685827, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1685827), c_fconj), _1685829)), _1685831)), _1685833))), hBOOL(hAPP(c_List_Olistsp(_1685827, _1685829), _1685833)), hBOOL(hAPP(c_List_Olistsp(_1685827, _1685831), _1685833))], (14945 ^ _776541) ^ [_1046161, _1046163, _1046165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046161), _1046163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046161), _1046165)), 14952 ^ _776541 : [(14959 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046163), _1046165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046163), _1046161)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046165), _1046161))))], (14953 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046163), _1046161)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046165), _1046161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046163), _1046165)))]]], (2916 ^ _776541) ^ [_819804, _819806, _819808, _819810, _819812, _819814] : [-(c_Nitpick_Otimes__frac(_819814, _819810, _819806) = c_Nitpick_Otimes__frac(_819812, _819808, _819804)), _819814 = _819812, _819810 = _819808, _819806 = _819804], (32978 ^ _776541) ^ [_1378280, _1378282, _1378284, _1378286, _1378288] : [class_Groups_Oab__group__add(_1378280), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378282, _1378280), hAPP(hAPP(c_COMBS(_1378282, _1378280, _1378280), hAPP(hAPP(c_COMBB(_1378280, tc_fun(_1378280, _1378280), _1378282), c_Groups_Ominus__class_Ominus(_1378280)), _1378284)), _1378286)), _1378288) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1378280), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378282, _1378280), _1378284), _1378288)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378282, _1378280), _1378286), _1378288)))], (12906 ^ _776541) ^ [_1004231, _1004233, _1004235] : [class_Lattices_Osemilattice__inf(_1004231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004231), _1004233)), hBOOL(hAPP(hAPP(c_member(_1004231), _1004235), _1004233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004231), hAPP(c_Finite__Set_Ofold1(_1004231, c_Lattices_Osemilattice__inf__class_Oinf(_1004231)), _1004233)), _1004235)))], (39401 ^ _776541) ^ [_1539649, _1539651, _1539653, _1539655] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539649), _1539651)), 39407 ^ _776541 : [(39410 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539653), hAPP(_1539655, 39406 ^ [_1539649, _1539651, _1539653, _1539655])))], (39408 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539649), 39406 ^ [_1539649, _1539651, _1539653, _1539655]), _1539651)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1539649, _1539653)), hAPP(hAPP(c_Product__Type_OSigma(_1539649, _1539653), _1539651), _1539655)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539649, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1539653, tc_HOL_Obool), tc_Nat_Onat, _1539649), c_Finite__Set_Ocard(_1539653)), _1539655)), _1539651))], (21335 ^ _776541) ^ [_1162661, _1162663, _1162665, _1162667] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162661), _1162663), _1162665)), hAPP(c_Int_Onumber__class_Onumber__of(_1162661), _1162667)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162661), _1162663), hAPP(c_Int_Onumber__class_Onumber__of(_1162661), _1162667))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162661), _1162665), hAPP(c_Int_Onumber__class_Onumber__of(_1162661), _1162667)))), class_Int_Onumber(_1162661), class_Rings_Osemiring(_1162661)], (13260 ^ _776541) ^ [_1011265, _1011267, _1011269, _1011271, _1011273] : [class_Groups_Ocomm__monoid__mult(_1011265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011267), _1011269)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011267), _1011271)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011265), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011267, _1011265), _1011273), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011267, tc_HOL_Obool)), _1011269), _1011271))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011267, _1011265), _1011273), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011267, tc_HOL_Obool)), _1011269), _1011271))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011265), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011267, _1011265), _1011273), _1011269)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011267, _1011265), _1011273), _1011271)))], (15366 ^ _776541) ^ [_1054040, _1054042, _1054044] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054040), _1054042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1054040, tc_HOL_Obool)), _1054044), _1054042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054040), _1054042)), hAPP(c_Finite__Set_Ocard(_1054040), _1054044))), -(_1054044 = _1054042)], (39874 ^ _776541) ^ [_1552433, _1552435, _1552437, _1552439, _1552441] : [c_Fun_Oinj__on(_1552433, _1552435, _1552437, c_Orderings_Otop__class_Otop(tc_fun(_1552433, tc_HOL_Obool))), c_Fun_Oinj__on(_1552439, _1552433, _1552441, c_Orderings_Otop__class_Otop(tc_fun(_1552439, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1552439, _1552435, hAPP(c_Fun_Ocomp(_1552433, _1552435, _1552439, _1552437), _1552441), c_Orderings_Otop__class_Otop(tc_fun(_1552439, tc_HOL_Obool))))], (43110 ^ _776541) ^ [_1635470] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635470)), c_List_Olist_ONil(_1635470)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3446 ^ _776541) ^ [_828017, _828019, _828021, _828023, _828025, _828027] : [-(c_List_Opartition(_828027, _828023, _828019) = c_List_Opartition(_828025, _828021, _828017)), _828027 = _828025, _828023 = _828021, _828019 = _828017], (18840 ^ _776541) ^ [_1115951] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1115951), c_Orderings_Otop__class_Otop(tc_fun(_1115951, 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(_1115951), c_Orderings_Otop__class_Otop(tc_fun(_1115951, tc_HOL_Obool))))))], (6530 ^ _776541) ^ [_881983, _881985] : [class_Orderings_Otop(_881983), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881983), _881985), c_Orderings_Otop__class_Otop(_881983))))], (29639 ^ _776541) ^ [_1307742, _1307744, _1307746] : [class_Int_Onumber__ring(_1307742), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1307742), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1307742), _1307744), _1307746)), 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(_1307742), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1307742), hAPP(hAPP(c_Power_Opower__class_Opower(_1307742), _1307744), 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(_1307742), _1307746), 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(_1307742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307742), hAPP(c_Int_Onumber__class_Onumber__of(_1307742), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1307744)), _1307746)))], (47126 ^ _776541) ^ [_1723757, _1723759, _1723761] : [-(hAPP(c_List_Orev(_1723757), hAPP(hAPP(c_List_Otake(_1723757), _1723759), _1723761)) = hAPP(hAPP(c_List_Odrop(_1723757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723757)), _1723761)), _1723759)), hAPP(c_List_Orev(_1723757), _1723761)))], (33423 ^ _776541) ^ [_1390622, _1390624, _1390626, _1390628, _1390630, _1390632] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390622, tc_fun(_1390624, tc_HOL_Obool)), _1390626), hAPP(hAPP(c_COMBC(_1390622, tc_fun(_1390628, tc_fun(_1390624, tc_HOL_Obool)), tc_fun(_1390624, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390628, tc_HOL_Obool), tc_fun(tc_fun(_1390628, tc_fun(_1390624, tc_HOL_Obool)), tc_fun(_1390624, tc_HOL_Obool)), _1390622), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390628, tc_fun(_1390624, tc_HOL_Obool))), _1390630)), _1390632)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390628, tc_fun(_1390624, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390622, tc_fun(_1390628, tc_HOL_Obool)), _1390626), _1390630)), _1390632))], (35805 ^ _776541) ^ [_1445218, _1445220] : [hAPP(c_Int_ORep__Integ, _1445218) = hAPP(c_Int_ORep__Integ, _1445220), -(_1445218 = _1445220)], (27373 ^ _776541) ^ [] : [c_Int_OMin = c_Int_OPls], (51795 ^ _776541) ^ [_1823685, _1823687] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823685), _1823687)), -(_1823685 = _1823687), 51802 ^ _776541 : [(51805 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823687), _1823685))], (51803 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823685), _1823687)))]]], (23495 ^ _776541) ^ [_1202444, _1202446] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202444), _1202446))), -(c_Nat__Transfer_Otsub(_1202446, _1202444) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27299 ^ _776541) ^ [_1267740] : [class_Rings_Olinordered__idom(_1267740), -(hAPP(c_Groups_Oabs__class_Oabs(_1267740), c_Groups_Oone__class_Oone(_1267740)) = c_Groups_Oone__class_Oone(_1267740))], (41060 ^ _776541) ^ [_1581255, _1581257] : [-(c_Transitive__Closure_Ortrancl(_1581255, hAPP(c_Relation_Oconverse(_1581255, _1581255), _1581257)) = hAPP(c_Relation_Oconverse(_1581255, _1581255), c_Transitive__Closure_Ortrancl(_1581255, _1581257)))], (33701 ^ _776541) ^ [_1399408, _1399410, _1399412] : [-(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)), _1399408)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1399410, _1399412)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399410), _1399408), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399412), _1399408)))], (50379 ^ _776541) ^ [_1795098, _1795100, _1795102, _1795104, _1795106] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1795098, _1795100, tc_HOL_Obool, _1795102), _1795104), _1795106)), -(hBOOL(hAPP(_1795102, hAPP(hAPP(c_Product__Type_OPair(_1795098, _1795100), _1795104), _1795106))))], (46954 ^ _776541) ^ [_1720263, _1720265] : [-(c_Fun_Oinj__on(tc_List_Olist(_1720263), tc_List_Olist(_1720263), c_List_Orev(_1720263), _1720265))], (44878 ^ _776541) ^ [_1674975, _1674977, _1674979, _1674981, _1674983, _1674985, _1674987] : [-(hAPP(c_List_Ofoldl(_1674975, _1674977, _1674979, _1674981), hAPP(hAPP(c_List_Omap(_1674983, _1674977), _1674985), _1674987)) = hAPP(c_List_Ofoldl(_1674975, _1674983, hAPP(hAPP(c_COMBC(_1674975, tc_fun(_1674983, _1674977), tc_fun(_1674983, _1674975)), hAPP(hAPP(c_COMBB(tc_fun(_1674977, _1674975), tc_fun(tc_fun(_1674983, _1674977), tc_fun(_1674983, _1674975)), _1674975), c_COMBB(_1674977, _1674975, _1674983)), _1674979)), _1674985), _1674981), _1674987))], (28433 ^ _776541) ^ [_1286889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1286889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1286889))))], (28155 ^ _776541) ^ [_1282094, _1282096, _1282098] : [class_Rings_Osemiring__1(_1282094), hBOOL(hAPP(hAPP(c_member(_1282094), _1282096), c_Nat_Osemiring__1__class_ONats(_1282094))), hBOOL(hAPP(hAPP(c_member(_1282094), _1282098), c_Nat_Osemiring__1__class_ONats(_1282094))), -(hBOOL(hAPP(hAPP(c_member(_1282094), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1282094), _1282096), _1282098)), c_Nat_Osemiring__1__class_ONats(_1282094))))], (9174 ^ _776541) ^ [_934972, _934974, _934976] : [class_Orderings_Oorder(_934972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934972), _934974), _934976)), _934974 = _934976], (33048 ^ _776541) ^ [_1380102, _1380104, _1380106, _1380108] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380102, tc_fun(_1380104, tc_HOL_Obool)), _1380106), _1380108) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1380104, tc_HOL_Obool), hAPP(c_Set_Oimage(_1380102, tc_fun(_1380104, tc_HOL_Obool), _1380108), _1380106)))], (25285 ^ _776541) ^ [_1234214, _1234216] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234214, _1234216) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234214, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234216)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234214, _1234216)), _1234216))], (18948 ^ _776541) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17317 ^ _776541) ^ [_1088317, _1088319, _1088321, _1088323] : [class_Rings_Olinordered__comm__semiring__strict(_1088317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088317), _1088319), _1088321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088317), c_Groups_Ozero__class_Ozero(_1088317)), _1088323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088317), _1088323), _1088319)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088317), _1088323), _1088321))))], (43268 ^ _776541) ^ [_1638521, _1638523] : [-(c_List_Oset__Cons(_1638521, _1638523, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1638521)), c_List_Olist_ONil(_1638521)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1638521), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1638521, tc_List_Olist(_1638521), hAPP(hAPP(c_COMBC(_1638521, tc_List_Olist(_1638521), tc_List_Olist(_1638521)), c_List_Olist_OCons(_1638521)), c_List_Olist_ONil(_1638521))), _1638523))], (4936 ^ _776541) ^ [_851750, _851752] : [_851752 = _851750, -(c_HOL_OEx(_851752) = c_HOL_OEx(_851750))], (26655 ^ _776541) ^ [_1257663, _1257665] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257663)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257665)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257665))))], (28401 ^ _776541) ^ [_1286380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1286380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1286380)))], (23840 ^ _776541) ^ [_1208412, _1208414] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208412)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208414), 23843 ^ _776541 : [(23846 ^ _776541) ^ [] : [-(_1208414 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23844 ^ _776541) ^ [] : [-(_1208412 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (13560 ^ _776541) ^ [_1017916, _1017918, _1017920, _1017922] : [class_Groups_Ocancel__semigroup__add(_1017916), 13563 ^ _776541 : [(13570 ^ _776541) ^ [] : [_1017918 = _1017922, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017916), _1017918), _1017920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017916), _1017922), _1017920))], (13564 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017916), _1017918), _1017920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017916), _1017922), _1017920), -(_1017918 = _1017922)]]], (27074 ^ _776541) ^ [_1264047, _1264049] : [class_Rings_Olinordered__idom(_1264047), 27077 ^ _776541 : [(27084 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264047), c_Groups_Ozero__class_Ozero(_1264047)), hAPP(c_Int_Oring__1__class_Oof__int(_1264047), _1264049))))], (27078 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264047), c_Groups_Ozero__class_Ozero(_1264047)), hAPP(c_Int_Oring__1__class_Oof__int(_1264047), _1264049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264049)))]]], (7880 ^ _776541) ^ [_909283, _909285, _909287, _909289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909283, tc_HOL_Obool)), _909285), _909287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909283, tc_HOL_Obool)), _909287), _909289)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909283, tc_HOL_Obool)), _909287), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909283, tc_HOL_Obool)), _909289), _909285)) = _909285)], (35626 ^ _776541) ^ [_1441471, _1441473, _1441475] : [-(hAPP(hAPP(c_Product__Type_OPair(_1441471, _1441473), hAPP(c_Product__Type_Ofst(_1441471, _1441473), _1441475)), hAPP(c_Product__Type_Osnd(_1441471, _1441473), _1441475)) = _1441475)], (41443 ^ _776541) ^ [_1590552, _1590554, _1590556] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590552, _1590552), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590554)), _1590556) = hAPP(hAPP(c_Relation_Orel__comp(_1590552, _1590552, _1590552), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590552, _1590552), tc_HOL_Obool), _1590554), _1590556)), _1590556))], (52097 ^ _776541) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (18220 ^ _776541) ^ [_1104166, _1104168, _1104170, _1104172] : [class_Groups_Oordered__comm__monoid__add(_1104166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104166), c_Groups_Ozero__class_Ozero(_1104166)), _1104168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104166), _1104170), _1104172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104166), _1104170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104166), _1104168), _1104172))))], (46028 ^ _776541) ^ [_1700680, _1700682, _1700684, _1700686] : [-(c_List_Otranspose(_1700680, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700680)), hAPP(hAPP(c_List_Olist_OCons(_1700680), _1700682), _1700684)), _1700686)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700680)), hAPP(hAPP(c_List_Olist_OCons(_1700680), _1700682), c_List_Oconcat(_1700680, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700680), tc_List_Olist(_1700680)), c_List_Olist_Olist__case(tc_List_Olist(_1700680), _1700680, c_List_Olist_ONil(_1700680), hAPP(hAPP(c_COMBB(tc_List_Olist(_1700680), tc_fun(tc_List_Olist(_1700680), tc_List_Olist(_1700680)), _1700680), c_COMBK(tc_List_Olist(_1700680), tc_List_Olist(_1700680))), hAPP(hAPP(c_COMBC(_1700680, tc_List_Olist(_1700680), tc_List_Olist(_1700680)), c_List_Olist_OCons(_1700680)), c_List_Olist_ONil(_1700680))))), _1700686)))), c_List_Otranspose(_1700680, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700680)), _1700684), c_List_Oconcat(tc_List_Olist(_1700680), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700680), tc_List_Olist(tc_List_Olist(_1700680))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1700680)), _1700680, c_List_Olist_ONil(tc_List_Olist(_1700680)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1700680), tc_List_Olist(tc_List_Olist(_1700680))), _1700680), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700680), tc_List_Olist(tc_List_Olist(_1700680)), tc_List_Olist(tc_List_Olist(_1700680))), c_List_Olist_OCons(tc_List_Olist(_1700680))), c_List_Olist_ONil(tc_List_Olist(_1700680)))))), _1700686))))))], (50409 ^ _776541) ^ [_1795694, _1795696, _1795698, _1795700] : [c_Fun_Obij__betw(_1795694, _1795696, _1795698, c_Orderings_Otop__class_Otop(tc_fun(_1795694, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1795696, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1795694, _1795696, _1795698), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1795694, tc_HOL_Obool)), _1795700)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1795696, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1795694, _1795696, _1795698), _1795700)))], (5879 ^ _776541) ^ [_870006, _870008, _870010, _870012] : [_870006 = _870008, hBOOL(hAPP(hAPP(c_member(_870010), _870008), _870012)), -(hBOOL(hAPP(hAPP(c_member(_870010), _870006), _870012)))], (21373 ^ _776541) ^ [_1163540, _1163542, _1163544, _1163546] : [class_Int_Onumber__ring(_1163540), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163540), hAPP(c_Int_Onumber__class_Onumber__of(_1163540), _1163542)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163540), hAPP(c_Int_Onumber__class_Onumber__of(_1163540), _1163544)), _1163546)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163540), hAPP(c_Int_Onumber__class_Onumber__of(_1163540), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1163542), _1163544))), _1163546))], (49127 ^ _776541) ^ [_1767701, _1767703, _1767705, _1767707, _1767709, _1767711, _1767713] : [hBOOL(hAPP(hAPP(_1767701, hAPP(c_Product__Type_Osnd(_1767703, _1767705), _1767707)), hAPP(c_Product__Type_Ofst(_1767703, _1767705), _1767707))), 49134 ^ _776541 : [(49137 ^ _776541) ^ [] : [hBOOL(hAPP(_1767709, hAPP(hAPP(_1767711, 49132 ^ [_1767701, _1767703, _1767705, _1767707, _1767709, _1767711, _1767713]), 49133 ^ [_1767701, _1767703, _1767705, _1767707, _1767709, _1767711, _1767713])))], (49135 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1767701, 49133 ^ [_1767701, _1767703, _1767705, _1767707, _1767709, _1767711, _1767713]), 49132 ^ [_1767701, _1767703, _1767705, _1767707, _1767709, _1767711, _1767713])))]], -(hBOOL(hAPP(_1767709, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1767703, _1767705, _1767713), _1767711), _1767707))))], (29603 ^ _776541) ^ [_1307109, _1307111] : [class_Rings_Oring__1(_1307109), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1307109), hAPP(c_Groups_Ouminus__class_Ouminus(_1307109), c_Groups_Oone__class_Oone(_1307109))), 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)))), _1307111)) = c_Groups_Oone__class_Oone(_1307109))], (52567 ^ _776541) ^ [_1832307, _1832309] : [v_Q_H(_1832309, _1832307), -(v_Q(_1832309, _1832307))], (7332 ^ _776541) ^ [_896611, _896613, _896615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896611, tc_HOL_Obool)), _896613), hAPP(hAPP(c_Set_Oinsert(_896611), _896615), c_Orderings_Obot__class_Obot(tc_fun(_896611, tc_HOL_Obool))))), -(_896613 = c_Orderings_Obot__class_Obot(tc_fun(_896611, tc_HOL_Obool))), -(_896613 = hAPP(hAPP(c_Set_Oinsert(_896611), _896615), c_Orderings_Obot__class_Obot(tc_fun(_896611, tc_HOL_Obool))))], (46024 ^ _776541) ^ [_1700473, _1700475, _1700477, _1700479] : [-(c_List_Oconcat(_1700473, hAPP(hAPP(c_List_Omap(_1700475, tc_List_Olist(_1700473)), hAPP(hAPP(c_COMBC(_1700475, tc_List_Olist(_1700473), tc_List_Olist(_1700473)), hAPP(hAPP(c_COMBB(_1700473, tc_fun(tc_List_Olist(_1700473), tc_List_Olist(_1700473)), _1700475), c_List_Olist_OCons(_1700473)), _1700477)), c_List_Olist_ONil(_1700473))), _1700479)) = hAPP(hAPP(c_List_Omap(_1700475, _1700473), _1700477), _1700479))], (38124 ^ _776541) ^ [_1506684, _1506686] : [-(c_Wellfounded_Owf(_1506684, hAPP(c_Wellfounded_Omeasure(_1506684), _1506686)))], (36101 ^ _776541) ^ [_1456494, _1456496, _1456498, _1456500, _1456502, _1456504] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1456494), _1456496)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456498), _1456500)), 36111 ^ _776541 : [(36114 ^ _776541) ^ [] : [hAPP(c_Finite__Set_Ocard(_1456494), hAPP(c_Set_OCollect(_1456494), hAPP(hAPP(c_COMBS(_1456494, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1456494), c_fconj), hAPP(hAPP(c_COMBC(_1456494, tc_fun(_1456494, tc_HOL_Obool), tc_HOL_Obool), c_member(_1456494)), _1456496))), hAPP(hAPP(c_COMBC(_1456494, _1456498, tc_HOL_Obool), _1456502), 36110 ^ [_1456494, _1456496, _1456498, _1456500, _1456502, _1456504])))) = hAPP(_1456504, 36110 ^ [_1456494, _1456496, _1456498, _1456500, _1456502, _1456504])], (36112 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456498), 36110 ^ [_1456494, _1456496, _1456498, _1456500, _1456502, _1456504]), _1456500)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456494, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1456498, tc_HOL_Obool), tc_Nat_Onat, _1456494), c_Finite__Set_Ocard(_1456498)), hAPP(hAPP(c_COMBB(tc_fun(_1456498, tc_HOL_Obool), tc_fun(_1456498, tc_HOL_Obool), _1456494), c_Set_OCollect(_1456498)), hAPP(hAPP(c_COMBB(tc_fun(_1456498, tc_HOL_Obool), tc_fun(_1456498, tc_HOL_Obool), _1456494), hAPP(c_COMBS(_1456498, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1456498), c_fconj), hAPP(hAPP(c_COMBC(_1456498, tc_fun(_1456498, tc_HOL_Obool), tc_HOL_Obool), c_member(_1456498)), _1456500)))), _1456502)))), _1456496) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456498, tc_Nat_Onat), _1456504), _1456500))], (8591 ^ _776541) ^ [_924118, _924120, _924122] : [class_Lattices_Olattice(_924118), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924118), _924120), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924118), _924120), _924122))))], (49369 ^ _776541) ^ [_1773127, _1773129, _1773131, _1773133] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1773127, tc_fun(_1773129, tc_HOL_Obool)), _1773131), _1773133) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1773129, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1773129, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773127, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1773129, tc_HOL_Obool)), c_HOL_OEx(_1773127)), hAPP(hAPP(c_COMBB(tc_fun(_1773127, tc_HOL_Obool), tc_fun(_1773127, tc_HOL_Obool), tc_fun(_1773129, tc_HOL_Obool)), hAPP(c_COMBS(_1773127, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1773127), c_fconj), hAPP(hAPP(c_COMBC(_1773127, tc_fun(_1773127, tc_HOL_Obool), tc_HOL_Obool), c_member(_1773127)), _1773131)))), hAPP(hAPP(c_COMBC(tc_fun(_1773129, tc_HOL_Obool), tc_fun(_1773127, tc_fun(_1773129, tc_HOL_Obool)), tc_fun(_1773127, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773129, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1773127, tc_fun(_1773129, tc_HOL_Obool)), tc_fun(_1773127, tc_HOL_Obool)), tc_fun(_1773129, tc_HOL_Obool)), c_COMBB(tc_fun(_1773129, tc_HOL_Obool), tc_HOL_Obool, _1773127)), c_fequal)), _1773133))))))], (42557 ^ _776541) ^ [_1623679, 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882424, _882422)), _882426), _882428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882422), hAPP(_882426, _882430)), hAPP(_882428, _882430))))], (23449 ^ _776541) ^ [_1201520, _1201522, _1201524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201520)), 23452 ^ _776541 : [(23453 ^ _776541) ^ [_1201654] : [23455 ^ _776541 : [(23461 ^ _776541) ^ [] : [-(_1201654 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23457 ^ [_1201520, _1201522, _1201524, _1201654]), 23454 ^ [_1201520, _1201522, _1201524, _1201654]))], (23459 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23457 ^ [_1201520, _1201522, _1201524, _1201654]), _1201522)))], (23456 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23454 ^ [_1201520, _1201522, _1201524, _1201654]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1201520))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201524), _1201654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201654), _1201520))))]]], (7876 ^ _776541) ^ [_909191, _909193] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909191, tc_HOL_Obool)), _909193), c_Orderings_Obot__class_Obot(tc_fun(_909191, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_909191, tc_HOL_Obool)))], (15270 ^ _776541) ^ [_1052118, _1052120, _1052122] : [class_Groups_Ocomm__monoid__mult(_1052118), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052120, _1052118), _1052122), c_Orderings_Obot__class_Obot(tc_fun(_1052120, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1052118))], (16889 ^ _776541) ^ [_1080435, _1080437, _1080439, _1080441] : [class_Groups_Oordered__comm__monoid__add(_1080435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080435), c_Groups_Ozero__class_Ozero(_1080435)), _1080437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080435), _1080439), _1080441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080435), _1080439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080435), _1080441), _1080437))))], (17531 ^ _776541) ^ [_1092277, _1092279, _1092281, _1092283] : [class_Rings_Olinordered__ring__strict(_1092277), 17534 ^ _776541 : [(17549 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092277), _1092279), _1092281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092277), _1092283), _1092281)))), 17550 ^ _776541 : [(17557 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), _1092281), c_Groups_Ozero__class_Ozero(_1092277))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), _1092283), _1092279))], (17551 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), c_Groups_Ozero__class_Ozero(_1092277)), _1092281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), _1092279), _1092283))]]], (17535 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092277), _1092279), _1092281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092277), _1092283), _1092281))), 17540 ^ _776541 : [(17543 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), _1092279), _1092283)))], (17541 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), c_Groups_Ozero__class_Ozero(_1092277)), _1092281)))]], 17544 ^ _776541 : [(17547 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), _1092283), _1092279)))], (17545 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092277), _1092281), c_Groups_Ozero__class_Ozero(_1092277))))]]]]], (42021 ^ _776541) ^ [_1607881, _1607883, _1607885, _1607887] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607881), tc_List_Olist(_1607881))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607881), tc_List_Olist(_1607881)), _1607883), _1607885)), c_List_Olistrel1(_1607881, _1607887))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607881), tc_List_Olist(_1607881))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607881), tc_List_Olist(_1607881)), _1607883), _1607885)), c_List_Olistrel(_1607881, c_Transitive__Closure_Ortrancl(_1607881, _1607887)))))], (12063 ^ _776541) ^ [_988546, _988548, _988550] : [class_Lattices_Olattice(_988546), hBOOL(hAPP(c_Finite__Set_Ofinite(_988546), _988548)), hBOOL(hAPP(hAPP(c_member(_988546), _988550), _988548)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_988546), _988550), c_Big__Operators_Olattice__class_OInf__fin(_988546, _988548)) = c_Big__Operators_Olattice__class_OInf__fin(_988546, _988548))], (36366 ^ _776541) ^ [_1463518, _1463520, _1463522, _1463524] : 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hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1463522), _1463524))), c_FunDef_Omin__strict)))], (10110 ^ _776541) ^ [_949631, _949633, _949635] : [class_Orderings_Oorder(_949631), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949631, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949631, _949633, _949635)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949631), _949635)) = c_Orderings_Obot__class_Obot(tc_fun(_949631, tc_HOL_Obool)))], (7118 ^ _776541) ^ [_892472, _892474, _892476, _892478] : [7119 ^ _776541 : [(7122 ^ _776541) ^ [] : [_892474 = _892478], (7120 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_892472), _892474), _892476))]], -(hBOOL(hAPP(hAPP(c_member(_892472), _892474), hAPP(hAPP(c_Set_Oinsert(_892472), _892478), _892476))))], (52027 ^ _776541) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (16206 ^ _776541) ^ [_1069382, _1069384] : [class_Rings_Ocomm__semiring__1(_1069382), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069382), _1069384), c_Groups_Ozero__class_Ozero(_1069382)) = _1069384)], (8671 ^ _776541) ^ [_925539, _925541, _925543, _925545] : [class_Lattices_Osemilattice__inf(_925539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925539), _925541), _925543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925539), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925539), _925545), _925541)), _925543)))], (15682 ^ _776541) ^ [_1060919, _1060921] : [hAPP(_1060919, 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), _1060919), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060921)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1060919), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1060921)))], (33465 ^ _776541) ^ [_1391958, _1391960, _1391962, _1391964] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1391958), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391960, tc_Int_Oint), _1391962), _1391964)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391960, _1391958), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1391958, _1391960), c_Int_Oring__1__class_Oof__int(_1391958)), _1391962)), _1391964)), class_Groups_Ocomm__monoid__mult(_1391958), class_Rings_Oring__1(_1391958)], (11916 ^ _776541) ^ [_985825, _985827, _985829, _985831] : [-(c_Fun_Ofun__upd(_985825, _985827, _985829, _985831, hAPP(_985829, _985831)) = _985829)], (36488 ^ _776541) ^ [_1466878, _1466880, _1466882, _1466884, _1466886] : [-(hAPP(c_Relation_OImage(_1466878, _1466880, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1466878, _1466880), tc_HOL_Obool)), _1466882), _1466884)), _1466886) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466880, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466878, _1466880, _1466882), _1466886)), hAPP(c_Relation_OImage(_1466878, _1466880, _1466884), _1466886)))], (31092 ^ _776541) ^ [_1334612, _1334614] : [class_Groups_Olinordered__ab__group__add(_1334612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334612), _1334614)), -(_1334614 = c_Orderings_Obot__class_Obot(tc_fun(_1334612, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1334612), c_Big__Operators_Olinorder__class_OMax(_1334612, _1334614)) = c_Big__Operators_Olinorder__class_OMin(_1334612, hAPP(c_Set_Oimage(_1334612, _1334612, c_Groups_Ouminus__class_Ouminus(_1334612)), _1334614)))], (30012 ^ _776541) ^ [_1314798] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1314798) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19178 ^ _776541) ^ [_1122125, _1122127, _1122129, _1122131, _1122133] : [class_Groups_Ocomm__monoid__mult(_1122125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122127), _1122129)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122127), _1122131)), 19192 ^ _776541 : [(19195 ^ _776541) ^ [] : [hAPP(_1122133, 19191 ^ [_1122125, _1122127, _1122129, _1122131, _1122133]) = c_Groups_Oone__class_Oone(_1122125)], (19193 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1122127), 19191 ^ [_1122125, _1122127, _1122129, _1122131, _1122133]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1122127, tc_HOL_Obool)), _1122129), _1122131))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1122125, _1122127, c_Groups_Otimes__class_Otimes(_1122125)), _1122133), c_Groups_Oone__class_Oone(_1122125)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1122127, tc_HOL_Obool)), _1122129), _1122131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122125), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1122125, _1122127, c_Groups_Otimes__class_Otimes(_1122125)), _1122133), c_Groups_Oone__class_Oone(_1122125)), _1122129)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1122125, _1122127, c_Groups_Otimes__class_Otimes(_1122125)), _1122133), c_Groups_Oone__class_Oone(_1122125)), _1122131)))], (8131 ^ _776541) ^ [_915116, _915118, _915120] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_915116, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_915116, tc_HOL_Obool)), _915118), _915120)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915116, tc_HOL_Obool)), _915118), c_Complete__Lattice_OInf__class_OInf(tc_fun(_915116, tc_HOL_Obool), _915120)))], (16662 ^ _776541) ^ [_1076234, _1076236] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076234), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076236), _1076234)))))], (4132 ^ _776541) ^ [_839108, _839110, _839112, _839114] : [-(c_Lazy__Sequence_Ohb__single(_839114, _839110) = c_Lazy__Sequence_Ohb__single(_839112, _839108)), _839114 = _839112, _839110 = _839108], (39153 ^ _776541) ^ [_1531963, _1531965] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531963, _1531965), c_Orderings_Otop__class_Otop(tc_fun(_1531963, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1531965, tc_HOL_Obool), _1531963), c_Orderings_Otop__class_Otop(tc_fun(_1531965, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1531963, _1531965), tc_HOL_Obool)))], (48307 ^ _776541) ^ [_1749437, _1749439, _1749441] : [c_List_Olist__all(_1749437, _1749441, _1749439), 48310 ^ _776541 : [(48311 ^ _776541) ^ [_1749518] : [hBOOL(hAPP(hAPP(c_member(_1749437), _1749518), hAPP(c_List_Oset(_1749437), _1749439))), -(hBOOL(hAPP(_1749441, _1749518)))]]], (38427 ^ _776541) ^ [_1513185, _1513187, _1513189, _1513191] : [-(_1513185 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1513187, tc_HOL_Obool), tc_HOL_Obool))), 38433 ^ _776541 : [(38436 ^ _776541) ^ [] : [c_Fun_Oinj__on(_1513187, _1513189, _1513191, 38432 ^ [_1513185, _1513187, _1513189, _1513191])], (38434 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1513187, tc_HOL_Obool)), 38432 ^ [_1513185, _1513187, _1513189, _1513191]), _1513185)))]], -(c_Fun_Oinj__on(_1513187, _1513189, _1513191, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1513187, tc_HOL_Obool), _1513185)))], (14534 ^ _776541) ^ [_1038650, _1038652, _1038654] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038650), _1038652)), _1038654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038652), _1038654)))], (42198 ^ _776541) ^ [_1613179, _1613181, _1613183] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613179, _1613179)), hAPP(hAPP(c_Product__Type_OPair(_1613179, _1613179), 42199 ^ [_1613179, _1613181, _1613183]), 42199 ^ [_1613179, _1613181, _1613183])), _1613181))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613179), tc_List_Olist(_1613179))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613179), tc_List_Olist(_1613179)), _1613183), _1613183)), c_List_Olexord(_1613179, _1613181)))], (7848 ^ _776541) ^ [_908657, _908659] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908657, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_908657, tc_HOL_Obool))), _908659) = _908659)], (22407 ^ _776541) ^ [_1182770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1182770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182770)))], (46496 ^ _776541) ^ [_1711711, _1711713] : [class_Orderings_Olinorder(_1711711), c_List_Olinorder__class_Osorted(_1711711, _1711713), -(c_List_Olinorder__class_Osorted(_1711711, hAPP(c_List_Otl(_1711711), _1711713)))], (48374 ^ _776541) ^ [_1750740, _1750742, _1750744] : [c_List_Olist__ex1(_1750740, _1750742, _1750744), 48378 ^ _776541 : [(48383 ^ _776541) ^ [_1750986] : [-(_1750986 = 48377 ^ [_1750740, _1750742, _1750744]), hBOOL(hAPP(hAPP(c_member(_1750740), _1750986), hAPP(c_List_Oset(_1750740), _1750744))), hBOOL(hAPP(_1750742, _1750986))], (48381 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1750742, 48377 ^ [_1750740, _1750742, _1750744])))], (48379 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750740), 48377 ^ [_1750740, _1750742, _1750744]), hAPP(c_List_Oset(_1750740), _1750744))))]]], (27919 ^ _776541) ^ [_1278417, _1278419] : [class_Int_Onumber__ring(_1278417), class_Rings_Olinordered__idom(_1278417), 27926 ^ _776541 : [(27933 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1278419), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278417), hAPP(c_Int_Onumber__class_Onumber__of(_1278417), _1278419)), c_Groups_Ozero__class_Ozero(_1278417))))], (27927 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278417), hAPP(c_Int_Onumber__class_Onumber__of(_1278417), _1278419)), c_Groups_Ozero__class_Ozero(_1278417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1278419), c_Int_OPls)))]]], (41080 ^ _776541) ^ [_1581879, _1581881, _1581883, _1581885, _1581887] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581879, _1581881)), hAPP(hAPP(c_Product__Type_OPair(_1581879, _1581881), _1581883), _1581885)), _1581887)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581881, _1581879)), hAPP(hAPP(c_Product__Type_OPair(_1581881, _1581879), _1581885), _1581883)), hAPP(c_Relation_Oconverse(_1581879, _1581881), _1581887))))], (43906 ^ _776541) ^ [_1653858, _1653860] : [-(hAPP(hAPP(c_List_Odrop(_1653858), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1653860) = _1653860)], (7416 ^ _776541) ^ [_898515, _898517, _898519] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898515, tc_HOL_Obool)), _898517), _898519) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_898515, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898515, tc_HOL_Obool)), _898517), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898515, tc_HOL_Obool)), _898519), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_898515, tc_HOL_Obool), tc_HOL_Obool))))))], (51653 ^ _776541) ^ [_1821375, _1821377, _1821379, _1821381] : [class_Rings_Ocomm__semiring__1(_1821375), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821375), _1821377), _1821379)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821375), hAPP(hAPP(c_Power_Opower__class_Opower(_1821375), _1821377), _1821381)), hAPP(hAPP(c_Power_Opower__class_Opower(_1821375), _1821379), _1821381))))], (15037 ^ _776541) ^ [_1048008, _1048010, _1048012] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048008), _1048010)), hBOOL(hAPP(hAPP(c_member(_1048008), _1048012), _1048010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1048008), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048008, tc_HOL_Obool)), _1048010), hAPP(hAPP(c_Set_Oinsert(_1048008), _1048012), c_Orderings_Obot__class_Obot(tc_fun(_1048008, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1048008), _1048010))))], (1204 ^ _776541) ^ [_794455, _794457] : [-(class_Groups_Oab__group__add(_794455)), _794457 = _794455, class_Groups_Oab__group__add(_794457)], (27637 ^ _776541) ^ [_1273460, _1273462, _1273464] : [class_Rings_Olinordered__idom(_1273460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273460), c_Groups_Ozero__class_Ozero(_1273460)), _1273462)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273460), hAPP(c_Groups_Oabs__class_Oabs(_1273460), _1273464)), _1273462) = hAPP(c_Groups_Oabs__class_Oabs(_1273460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273460), _1273464), _1273462)))], (512 ^ _776541) ^ [_784231, _784233] : [-(class_Lattices_Oab__semigroup__idem__mult(_784231)), _784233 = _784231, class_Lattices_Oab__semigroup__idem__mult(_784233)], (14807 ^ _776541) ^ [_1043503, _1043505, _1043507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043503), _1043505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043503), _1043507)), _1043505)))], (29431 ^ _776541) ^ [_1303871, _1303873, _1303875] : [class_Rings_Olinordered__idom(_1303871), 29434 ^ _776541 : [(29443 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1303871), hAPP(hAPP(c_Power_Opower__class_Opower(_1303871), _1303873), 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(_1303871), _1303875), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1303871)), _1303873 = c_Groups_Ozero__class_Ozero(_1303871), _1303875 = c_Groups_Ozero__class_Ozero(_1303871)], (29435 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1303871), hAPP(hAPP(c_Power_Opower__class_Opower(_1303871), _1303873), 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(_1303871), _1303875), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1303871), 29438 ^ _776541 : [(29441 ^ _776541) ^ [] : [-(_1303875 = c_Groups_Ozero__class_Ozero(_1303871))], (29439 ^ _776541) ^ [] : [-(_1303873 = c_Groups_Ozero__class_Ozero(_1303871))]]]]], (27629 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (6025 ^ _776541) ^ [_872707, _872709, _872711, _872713] : [hBOOL(hAPP(hAPP(_872711, _872709), _872713)), -(hBOOL(hAPP(hAPP(c_member(_872707), _872709), c_SetInterval_Oord_OlessThan(_872707, _872711, _872713))))], (4606 ^ _776541) ^ [_846541, _846543, _846545, _846547] : [-(c_List_Oupto(_846547, _846543) = c_List_Oupto(_846545, _846541)), _846547 = _846545, _846543 = _846541], (49113 ^ _776541) ^ [_1767109, _1767111, _1767113, _1767115] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1767109), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1767111, _1767113, _1767109, _1767115) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1767111, 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(_1767111)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1767113, _1767115)), 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(_1767111)))), 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(_1767111)))), 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(_1767111)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1767111, 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(_1767111)))), 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(_1767111)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1767111, _1767113, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1767109), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1767115))), 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(_1767111)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767111))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767111)))), 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(_1767111)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1767111, 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(_1767111)))), 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(_1767111)))), 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(_1767111))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767111)))), 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(_1767111)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767111)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767111))))), tc_prod(_1767111, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1767111)), hAPP(hAPP(c_COMBB(_1767111, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767111)))), tc_prod(_1767111, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1767111)), c_Product__Type_Ofst(_1767111, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (46610 ^ _776541) ^ [_1713464, _1713466] : [class_Orderings_Olinorder(_1713464), c_List_Olinorder__class_Osorted(_1713464, _1713466), -(c_List_Olinorder__class_Osorted(_1713464, c_List_Oremdups(_1713464, _1713466)))], (48225 ^ _776541) ^ [_1747954] : [class_Nat_Osize(_1747954), -(c_FunDef_Ois__measure(_1747954, c_Nat_Osize__class_Osize(_1747954)))], (7826 ^ _776541) ^ [_908212, _908214] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908212, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_908212, tc_HOL_Obool))), _908214) = c_Orderings_Obot__class_Obot(tc_fun(_908212, tc_HOL_Obool)))], (48114 ^ _776541) ^ [_1745596, _1745598, _1745600] : [c_List_Olist__ex(_1745596, _1745598, hAPP(c_List_Orev(_1745596), _1745600)), -(c_List_Olist__ex(_1745596, _1745598, _1745600))], (41349 ^ _776541) ^ [_1588124, _1588126, _1588128] : [41351 ^ _776541 : [(41352 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588124), 41350 ^ [_1588124, _1588126, _1588128]), _1588126)))], (41357 ^ _776541) ^ [] : [41350 ^ [_1588124, _1588126, _1588128] = 41353 ^ [_1588124, _1588126, _1588128]], (41361 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588124, _1588124)), hAPP(hAPP(c_Product__Type_OPair(_1588124, _1588124), 41353 ^ [_1588124, _1588126, _1588128]), 41350 ^ [_1588124, _1588126, _1588128])), _1588128))], (41359 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588124, _1588124)), hAPP(hAPP(c_Product__Type_OPair(_1588124, _1588124), 41350 ^ [_1588124, _1588126, _1588128]), 41353 ^ [_1588124, _1588126, _1588128])), _1588128))], (41355 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588124), 41353 ^ [_1588124, _1588126, _1588128]), _1588126)))]], -(c_Relation_Ototal__on(_1588124, _1588126, _1588128))], (35348 ^ _776541) ^ [_1435758, _1435760, _1435762, _1435764] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435758, _1435760), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435762), _1435764))), -(_1435760 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1435758, _1435760) = _1435764)], (50616 ^ _776541) ^ [_1799689, _1799691, _1799693, _1799695, _1799697] : [c_Fun_Obij__betw(_1799689, _1799691, _1799693, c_Orderings_Otop__class_Otop(tc_fun(_1799689, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799691, tc_HOL_Obool))), 50619 ^ _776541 : [(50626 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799691, tc_HOL_Obool)), _1799695), hAPP(c_Set_Oimage(_1799689, _1799691, _1799693), _1799697))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799689, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1799689, _1799691, _1799693), _1799695)), _1799697)))], (50620 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799689, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1799689, _1799691, _1799693), _1799695)), _1799697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799691, tc_HOL_Obool)), _1799695), hAPP(c_Set_Oimage(_1799689, _1799691, _1799693), _1799697))))]]], (27435 ^ _776541) ^ [_1269868, _1269870] : [class_Groups_Oordered__ab__group__add__abs(_1269868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269868), hAPP(c_Groups_Oabs__class_Oabs(_1269868), _1269870)), c_Groups_Ozero__class_Ozero(_1269868)))], (23591 ^ _776541) ^ [_1204104] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204104) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (3488 ^ _776541) ^ [_828688, _828690, _828692, _828694] : [-(c_Random_Opick(_828694, _828690) = c_Random_Opick(_828692, _828688)), _828694 = _828692, _828690 = _828688], (27293 ^ _776541) ^ [_1267611, _1267613, _1267615] : [class_Groups_Oordered__ab__group__add__abs(_1267611), -(hAPP(c_Groups_Oabs__class_Oabs(_1267611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1267611), _1267613), _1267615)) = hAPP(c_Groups_Oabs__class_Oabs(_1267611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1267611), _1267615), _1267613)))], (13948 ^ _776541) ^ [_1025937, _1025939, _1025941, _1025943, _1025945, _1025947] : [class_Rings_Oordered__ring(_1025937), 13951 ^ _776541 : [(13958 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025937), _1025939), _1025945)), _1025941)), _1025943)), _1025947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025937), _1025939), _1025941)), _1025943)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025937), _1025945), _1025941)), _1025947))))], (13952 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025937), _1025939), _1025941)), _1025943)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025937), _1025945), _1025941)), _1025947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025937), _1025939), _1025945)), _1025941)), _1025943)), _1025947)))]]], (1344 ^ _776541) ^ [_796205, _796207] : [-(class_Orderings_Owellorder(_796205)), _796207 = _796205, class_Orderings_Owellorder(_796207)], (5967 ^ _776541) ^ [_871574, _871576, _871578, _871580, _871582, _871584, _871586] : [c_Typedef_Otype__definition(_871574, _871576, _871578, _871580, _871582), hBOOL(hAPP(hAPP(c_member(_871576), _871584), _871582)), hBOOL(hAPP(_871586, hAPP(_871578, 5976 ^ [_871574, _871576, _871578, _871580, _871582, _871584, _871586]))), -(hBOOL(hAPP(_871586, _871584)))], (39820 ^ _776541) ^ [_1551217, _1551219, _1551221, _1551223, _1551225, _1551227, _1551229, _1551231, _1551233, _1551235] : [-(c_Product__Type_Omap__pair(_1551217, _1551219, _1551221, _1551223, hAPP(c_Fun_Ocomp(_1551225, _1551219, _1551217, _1551227), _1551229), hAPP(c_Fun_Ocomp(_1551231, _1551223, _1551221, _1551233), _1551235)) = hAPP(c_Fun_Ocomp(tc_prod(_1551225, _1551231), tc_prod(_1551219, _1551223), tc_prod(_1551217, _1551221), c_Product__Type_Omap__pair(_1551225, _1551219, _1551231, _1551223, _1551227, _1551233)), c_Product__Type_Omap__pair(_1551217, _1551225, _1551221, _1551231, _1551229, _1551235)))], (39770 ^ _776541) ^ [_1549671, _1549673] : [39772 ^ _776541 : [(39775 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1549673), 39771 ^ [_1549671, _1549673]))], (39773 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39771 ^ [_1549671, _1549673]), _1549671)))]], -(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)), _1549673), _1549671))], (43695 ^ _776541) ^ [_1648125, _1648127, _1648129, _1648131] : [43696 ^ _776541 : [(43699 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648125), _1648127), hAPP(c_List_Oset(_1648125), c_List_Obutlast(_1648125, _1648131))))], (43697 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648125), _1648127), hAPP(c_List_Oset(_1648125), c_List_Obutlast(_1648125, _1648129))))]], -(hBOOL(hAPP(hAPP(c_member(_1648125), _1648127), hAPP(c_List_Oset(_1648125), c_List_Obutlast(_1648125, hAPP(hAPP(c_List_Oappend(_1648125), _1648129), _1648131))))))], (45102 ^ _776541) ^ [_1679749, _1679751] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1679749)), hAPP(c_Code__Numeral_Oof__nat, _1679751)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1679749), _1679751)))], (11348 ^ _776541) ^ [_974007, _974009, _974011, _974013, _974015] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974007, _974009, hAPP(hAPP(c_Set_Oinsert(_974007), _974011), _974013)), _974015)), 11353 ^ _776541 : [(11358 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974007), 11351 ^ [_974007, _974009, _974011, _974013, _974015]), 11352 ^ [_974007, _974009, _974011, _974013, _974015]))], (11356 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974007, _974007, _974009, 11351 ^ [_974007, _974009, _974011, _974013, _974015], 11352 ^ [_974007, _974009, _974011, _974013, _974015]), _974015)))], (11354 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_974007), _974011), _974013) = hAPP(hAPP(c_Set_Oinsert(_974007), 11351 ^ [_974007, _974009, _974011, _974013, _974015]), 11352 ^ [_974007, _974009, _974011, _974013, _974015]))]]], (25656 ^ _776541) ^ [_1240747, _1240749, _1240751] : [-(hBOOL(hAPP(_1240747, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1240749, _1240751)))), 25659 ^ _776541 : [(25662 ^ _776541) ^ [] : [hBOOL(hAPP(_1240747, _1240749))], (25660 ^ _776541) ^ [] : [-(_1240751 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 25665 ^ _776541 : [(25666 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240751)))], (25672 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25668 ^ [_1240747, _1240749, _1240751]), _1240751)))], (25676 ^ _776541) ^ [] : [hBOOL(hAPP(_1240747, 25668 ^ [_1240747, _1240749, _1240751]))], (25674 ^ _776541) ^ [] : [-(_1240749 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240751), 25667 ^ [_1240747, _1240749, _1240751])), 25668 ^ [_1240747, _1240749, _1240751]))], (25670 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25668 ^ [_1240747, _1240749, _1240751])))]], 25677 ^ _776541 : [(25678 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240751), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25684 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25680 ^ [_1240747, _1240749, _1240751]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25688 ^ _776541) ^ [] : [hBOOL(hAPP(_1240747, 25680 ^ [_1240747, _1240749, _1240751]))], (25686 ^ _776541) ^ [] : [-(_1240749 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240751), 25679 ^ [_1240747, _1240749, _1240751])), 25680 ^ [_1240747, _1240749, _1240751]))], (25682 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240751), 25680 ^ [_1240747, _1240749, _1240751])))]]], (46480 ^ _776541) ^ [_1711475, _1711477] : [class_Orderings_Olinorder(_1711475), -(c_List_Olinorder__class_Osorted(_1711475, c_List_Olinorder__class_Osort__key(_1711475, _1711475, c_COMBI(_1711475), _1711477)))], (42976 ^ _776541) ^ [_1633159, _1633161, _1633163, _1633165] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633159) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1633161), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633159)), hAPP(hAPP(c_List_Olist_OCons(_1633161), _1633163), _1633165)) = c_List_Olist_ONil(_1633161))], (47847 ^ _776541) ^ [_1739757, _1739759, _1739761, _1739763, _1739765] : [class_Orderings_Olinorder(_1739757), 47853 ^ _776541 : [(47856 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1739757), hAPP(_1739763, _1739765)), hAPP(_1739763, 47852 ^ [_1739757, _1739759, _1739761, _1739763, _1739765])))], (47854 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739759), 47852 ^ [_1739757, _1739759, _1739761, _1739763, _1739765]), hAPP(c_List_Oset(_1739759), _1739761))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739759, _1739757, _1739763), _1739765), _1739761) = hAPP(hAPP(c_List_Olist_OCons(_1739759), _1739765), _1739761))], (8022 ^ _776541) ^ [_912595, _912597, _912599, _912601] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912595, tc_HOL_Obool)), _912597), hAPP(hAPP(c_Set_Oinsert(_912595), _912599), _912601)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912595, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912595, tc_HOL_Obool)), _912597), hAPP(hAPP(c_Set_Oinsert(_912595), _912599), c_Orderings_Obot__class_Obot(tc_fun(_912595, tc_HOL_Obool))))), _912601))], (5703 ^ _776541) ^ [_866500] : [class_HOL_Oequal(_866500), -(c_HOL_Oequal__class_Oequal(_866500) = c_fequal)], (47688 ^ _776541) ^ [_1736119, _1736121, _1736123, _1736125, _1736127, _1736129, _1736131, _1736133] : [47690 ^ _776541 : [(47693 ^ _776541) ^ [] : [hAPP(c_Fun_Ocomp(_1736123, _1736123, _1736125, hAPP(_1736127, 47689 ^ [_1736119, _1736121, _1736123, _1736125, _1736127, _1736129, _1736131, _1736133])), _1736129) = hAPP(c_Fun_Ocomp(_1736125, _1736123, _1736125, _1736129), hAPP(_1736131, 47689 ^ [_1736119, _1736121, _1736123, _1736125, _1736127, _1736129, _1736131, _1736133]))], (47691 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736119), 47689 ^ [_1736119, _1736121, _1736123, _1736125, _1736127, _1736129, _1736131, _1736133]), hAPP(c_List_Oset(_1736119), _1736121))))]], -(hAPP(c_List_Ofoldl(_1736123, _1736119, hAPP(c_COMBC(_1736119, _1736123, _1736123), _1736127), hAPP(_1736129, _1736133)), _1736121) = hAPP(_1736129, hAPP(c_List_Ofoldl(_1736125, _1736119, hAPP(c_COMBC(_1736119, _1736125, _1736125), _1736131), _1736133), _1736121)))], (50723 ^ _776541) ^ [_1801821, _1801823, _1801825] : [hBOOL(hAPP(hAPP(c_member(_1801821), _1801823), c_Quotient_ORespects(_1801821, _1801825))), -(hBOOL(hAPP(hAPP(_1801825, _1801823), _1801823)))], (37858 ^ _776541) ^ [_1498124, _1498126, _1498128, _1498130] : [c_Fun_Oinj__on(_1498124, _1498126, _1498128, c_Orderings_Otop__class_Otop(tc_fun(_1498124, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1498124, _1498126, c_Orderings_Otop__class_Otop(tc_fun(_1498124, tc_HOL_Obool)), _1498128), hAPP(_1498128, _1498130)) = _1498130)], (45834 ^ _776541) ^ [_1696022, _1696024, _1696026, _1696028] : [-(c_List_Oremdups(_1696022, hAPP(hAPP(c_List_Omap(_1696024, _1696022), _1696026), c_List_Oremdups(_1696024, _1696028))) = c_List_Oremdups(_1696022, hAPP(hAPP(c_List_Omap(_1696024, _1696022), _1696026), _1696028)))], (18360 ^ _776541) ^ [_1106796, _1106798, _1106800, _1106802, _1106804] : [class_Rings_Olinordered__semiring__strict(_1106796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106796), _1106798), _1106800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106796), _1106802), _1106804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106796), c_Groups_Ozero__class_Ozero(_1106796)), _1106798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106796), c_Groups_Ozero__class_Ozero(_1106796)), _1106802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106796), _1106798), _1106802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106796), _1106800), _1106804))))], (43645 ^ _776541) ^ [_1647042, _1647044, _1647046] : [_1647044 = c_List_Olist_ONil(_1647042), -(hAPP(hAPP(c_List_Oappend(_1647042), _1647044), _1647046) = _1647046)], (13222 ^ _776541) ^ [_1010512, _1010514, _1010516, _1010518] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1010512), _1010514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010512, tc_HOL_Obool)), _1010514), _1010516)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010512, tc_Nat_Onat), _1010518), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010512, tc_HOL_Obool)), _1010516), _1010514)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010512, tc_Nat_Onat), _1010518), _1010516)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010512, tc_Nat_Onat), _1010518), _1010514)))], (20339 ^ _776541) ^ [_1143464, _1143466, _1143468, _1143470] : [class_Fields_Ofield__inverse__zero(_1143464), -(_1143466 = c_Groups_Ozero__class_Ozero(_1143464)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143464), _1143466), _1143468)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143464), _1143466), _1143470)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143464), _1143468), _1143470))], (32694 ^ _776541) ^ [_1370449, _1370451, _1370453, _1370455, _1370457] : [class_Groups_Ocomm__monoid__add(_1370449), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370449), _1370451), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370453), _1370455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370457), _1370455))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370449), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370449, tc_Nat_Onat), _1370451), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1370455))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370453, _1370457)))], (25903 ^ _776541) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28025 ^ _776541) ^ [_1280150, _1280152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280150), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280150)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280152)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37888 ^ _776541) ^ [_1498802, _1498804, _1498806, _1498808, _1498810] : [class_Groups_Ocomm__monoid__add(_1498802), class_Groups_Ocomm__monoid__mult(_1498802), _1498804 = _1498806, c_Nat__Transfer_Onat__set(_1498806), 37906 ^ _776541 : [(37909 ^ _776541) ^ [] : [hAPP(_1498808, 37905 ^ [_1498802, _1498804, _1498806, _1498808, _1498810]) = hAPP(_1498810, 37905 ^ [_1498802, _1498804, _1498806, _1498808, _1498810])], (37907 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37905 ^ [_1498802, _1498804, _1498806, _1498808, _1498810])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1498802), _1498808), _1498804) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1498802), _1498810), _1498806))], (46353 ^ _776541) ^ [_1708776, _1708778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708776)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708778))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708776), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708778)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708776)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708776)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708778))))], (50507 ^ _776541) ^ [_1797512, _1797514, _1797516, _1797518] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797512), _1797514)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1797516), _1797518)), 50514 ^ _776541 : [(50521 ^ _776541) ^ [] : [hAPP(c_Finite__Set_Ocard(_1797512), _1797514) = hAPP(c_Finite__Set_Ocard(_1797516), _1797518), -(c_Fun_Obij__betw(_1797512, _1797516, 50524 ^ [_1797512, _1797514, _1797516, _1797518], _1797514, _1797518))], (50515 ^ _776541) ^ [] : [50516 ^ _776541 : [(50517 ^ _776541) ^ [_1797701] : [c_Fun_Obij__betw(_1797512, _1797516, _1797701, _1797514, _1797518)]], -(hAPP(c_Finite__Set_Ocard(_1797512), _1797514) = hAPP(c_Finite__Set_Ocard(_1797516), _1797518))]]], (27621 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (31120 ^ _776541) ^ [_1335012, _1335014, _1335016, _1335018] : [class_Orderings_Olinorder(_1335012), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335012), _1335014)), 31130 ^ _776541 : [(31133 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335012), _1335016), 31129 ^ [_1335012, _1335014, _1335016, _1335018]))], (31131 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335012), 31129 ^ [_1335012, _1335014, _1335016, _1335018]), _1335014)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335012), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335012), _1335016), _1335018)), hAPP(hAPP(c_Finite__Set_Ofold(_1335012, _1335012, c_Orderings_Oord__class_Omin(_1335012)), _1335018), _1335014))))], (52113 ^ _776541) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (18382 ^ _776541) ^ [_1107219, _1107221, _1107223, _1107225, _1107227] : [class_Rings_Olinordered__semiring__strict(_1107219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107219), _1107221), _1107223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107219), _1107225), _1107227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107219), c_Groups_Ozero__class_Ozero(_1107219)), _1107221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107219), c_Groups_Ozero__class_Ozero(_1107219)), _1107225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107219), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107219), _1107221), _1107225)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107219), _1107223), _1107227))))], (52157 ^ _776541) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (15866 ^ _776541) ^ [_1063783, _1063785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063785), _1063783))))], (41395 ^ _776541) ^ [_1589486, _1589488] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589486, _1589486)), hAPP(hAPP(c_Product__Type_OPair(_1589486, _1589486), 41396 ^ [_1589486, _1589488]), 41396 ^ [_1589486, _1589488])), c_Transitive__Closure_Otrancl(_1589486, _1589488)))), -(c_Wellfounded_Oacyclic(_1589486, _1589488))], (45410 ^ _776541) ^ [_1686627, _1686629, _1686631] : [hBOOL(hAPP(c_List_Olistsp(_1686627, hAPP(hAPP(c_COMBC(_1686627, tc_fun(_1686627, tc_HOL_Obool), tc_HOL_Obool), c_member(_1686627)), _1686629)), _1686631)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1686627)), _1686631), c_List_Olists(_1686627, _1686629))))], (50614 ^ _776541) ^ [_1799648, _1799650, _1799652, _1799654] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1799648, _1799650, _1799652), c_Product__Type_Ocurry(_1799648, _1799650, _1799652, _1799654)) = _1799654)], (49658 ^ _776541) ^ [_1780212, _1780214] : [c_Relation_Osym(_1780212, _1780214), 49661 ^ _776541 : [(49662 ^ _776541) ^ [_1780318, _1780320] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780212, _1780212)), hAPP(hAPP(c_Product__Type_OPair(_1780212, _1780212), _1780320), _1780318)), _1780214)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780212, _1780212)), hAPP(hAPP(c_Product__Type_OPair(_1780212, _1780212), _1780318), _1780320)), _1780214)))]]], (11208 ^ _776541) ^ [_970994, _970996, _970998, _971000, _971002] : [_970994 = hAPP(_970996, _970998), -(hBOOL(hAPP(hAPP(c_member(_971000), _970994), hAPP(c_Set_Oimage(_971002, _971000, _970996), c_Orderings_Otop__class_Otop(tc_fun(_971002, tc_HOL_Obool))))))], (32839 ^ _776541) ^ [_1373670, _1373672, _1373674, _1373676, _1373678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373670, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1373672, tc_fun(_1373670, tc_HOL_Obool)), _1373674), _1373676)), _1373678)), 32842 ^ _776541 : [(32843 ^ _776541) ^ [_1373803] : [hBOOL(hAPP(hAPP(c_member(_1373672), _1373803), _1373674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373670, tc_HOL_Obool)), hAPP(_1373676, _1373803)), _1373678)))]]], (42699 ^ _776541) ^ [_1626786, _1626788, _1626790, _1626792, _1626794, _1626796] : [-(_1626786 = _1626788), -(hAPP(hAPP(c_List_Olist__update(_1626790, hAPP(hAPP(c_List_Olist__update(_1626790, _1626792), _1626786), _1626794)), _1626788), _1626796) = hAPP(hAPP(c_List_Olist__update(_1626790, hAPP(hAPP(c_List_Olist__update(_1626790, _1626792), _1626788), _1626796)), _1626786), _1626794))], (21018 ^ _776541) ^ [_1156275, _1156277, _1156279, _1156281] : [c_Sum__Type_OPlus(_1156275, _1156277, _1156279, _1156281) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1156275, _1156277), tc_HOL_Obool)), 21021 ^ _776541 : [(21024 ^ _776541) ^ [] : [-(_1156281 = c_Orderings_Obot__class_Obot(tc_fun(_1156277, tc_HOL_Obool)))], (21022 ^ _776541) ^ [] : [-(_1156279 = c_Orderings_Obot__class_Obot(tc_fun(_1156275, tc_HOL_Obool)))]]], (48366 ^ _776541) ^ [] : [-(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)))], (6043 ^ _776541) ^ [_873091, _873093, _873095, _873097, _873099] : [hBOOL(hAPP(hAPP(c_member(_873091), _873093), c_SetInterval_Oord_OatLeastAtMost(_873091, _873095, _873097, _873099))), 6046 ^ _776541 : [(6049 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_873095, _873093), _873099)))], (6047 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_873095, _873097), _873093)))]]], (45814 ^ _776541) ^ [_1695699, _1695701] : [_1695701 = c_List_Olist_ONil(_1695699), -(c_List_Olist_ONil(_1695699) = c_List_Oremdups(_1695699, _1695701))], (24998 ^ _776541) ^ [_1229273, _1229275] : [class_Divides_Osemiring__div(_1229273), -(c_Divides_Odiv__class_Omod(_1229273, _1229275, c_Groups_Oone__class_Oone(_1229273)) = c_Groups_Ozero__class_Ozero(_1229273))], (21553 ^ _776541) ^ [_1166851, _1166853, _1166855, _1166857] : [class_Fields_Ofield__inverse__zero(_1166851), class_Int_Onumber(_1166851), 21560 ^ _776541 : [(21561 ^ _776541) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166851), _1166853), hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855)) = _1166857, 21564 ^ _776541 : [(21571 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855) = c_Groups_Ozero__class_Ozero(_1166851), -(_1166857 = c_Groups_Ozero__class_Ozero(_1166851))], (21565 ^ _776541) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855) = c_Groups_Ozero__class_Ozero(_1166851)), -(_1166853 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166851), _1166857), hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855)))]]], (21577 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166851), _1166853), hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855)) = _1166857), 21580 ^ _776541 : [(21583 ^ _776541) ^ [] : [_1166853 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166851), _1166857), hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855))], (21581 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855) = c_Groups_Ozero__class_Ozero(_1166851)]], 21584 ^ _776541 : [(21587 ^ _776541) ^ [] : [_1166857 = c_Groups_Ozero__class_Ozero(_1166851)], (21585 ^ _776541) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1166851), _1166855) = c_Groups_Ozero__class_Ozero(_1166851))]]]]], (11036 ^ _776541) ^ [_967313, _967315] : [class_Lattices_Oab__semigroup__idem__mult(_967313), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967313), _967315), _967315) = _967315)], (24908 ^ _776541) ^ [_1227520, _1227522, _1227524, _1227526] : [class_Divides_Oring__div(_1227520), -(c_Divides_Odiv__class_Omod(_1227520, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227520), _1227522), _1227524), _1227526) = c_Divides_Odiv__class_Omod(_1227520, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227520), _1227522), c_Divides_Odiv__class_Omod(_1227520, _1227524, _1227526)), _1227526))], (46007 ^ _776541) ^ [_1699832, _1699834, _1699836] : [c_List_Oconcat(_1699832, _1699834) = c_List_Oconcat(_1699832, _1699836), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699832))), _1699834) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699832))), _1699836), 46017 ^ _776541 : [(46020 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1699832), tc_List_Olist(_1699832), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699832), tc_fun(tc_List_Olist(_1699832), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699832), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1699832), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699832), tc_HOL_Obool)), tc_List_Olist(_1699832)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1699832))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1699832)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1699832))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1699832)))), 46016 ^ [_1699832, _1699834, _1699836]))], (46018 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1699832), tc_List_Olist(_1699832))), 46016 ^ [_1699832, _1699834, _1699836]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1699832), tc_List_Olist(_1699832))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1699832), tc_List_Olist(_1699832)), _1699834), _1699836)))))]], -(_1699834 = _1699836)], (35817 ^ _776541) ^ [_1445394, _1445396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1445394)), -(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(_1445394), _1445396))), _1445394)))], (12255 ^ _776541) ^ [_991587, _991589, _991591, _991593, _991595, _991597, _991599, _991601] : [c_Finite__Set_Ofolding__image__simple(_991587, _991589, _991591, _991593, _991595, _991597), hBOOL(hAPP(c_Finite__Set_Ofinite(_991589), _991599)), hBOOL(hAPP(c_Finite__Set_Ofinite(_991589), _991601)), -(hAPP(hAPP(_991591, hAPP(_991597, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991589, tc_HOL_Obool)), _991599), _991601))), hAPP(_991597, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_991589, tc_HOL_Obool)), _991599), _991601))) = hAPP(hAPP(_991591, hAPP(_991597, _991599)), hAPP(_991597, _991601)))], (25187 ^ _776541) ^ [_1232584, _1232586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1232584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232586), _1232584)), _1232586)))], (234 ^ _776541) ^ [_780256, _780258] : [-(class_Fields_Olinordered__field(_780256)), _780258 = _780256, class_Fields_Olinordered__field(_780258)], (15005 ^ _776541) ^ [_1047334, _1047336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047334), _1047336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047334), _1047336)))], (30094 ^ _776541) ^ [_1316357, _1316359, _1316361, _1316363] : [class_Groups_Oordered__ab__group__add(_1316357), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1316357), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316357), _1316359), _1316361)), _1316363) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316357), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1316357), _1316359), _1316363)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1316357), _1316361), _1316363)))], (5592 ^ _776541) ^ [_861932, _861934] : [_861934 = _861932, -(tc_Hoare__Mirabelle_Otriple(_861934) = tc_Hoare__Mirabelle_Otriple(_861932))], (42463 ^ _776541) ^ [_1619664, _1619666] : [-(c_List_Olists(_1619664, _1619666) = hAPP(c_Set_OCollect(tc_List_Olist(_1619664)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1619664), tc_fun(_1619664, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1619664, tc_HOL_Obool), tc_fun(tc_fun(_1619664, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1619664)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1619664, tc_HOL_Obool))), c_List_Oset(_1619664))), _1619666)))], (20151 ^ _776541) ^ [_1140369, _1140371, _1140373] : [class_Fields_Olinordered__field(_1140369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140369), _1140371), c_Groups_Ozero__class_Ozero(_1140369))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140369), c_Groups_Ozero__class_Ozero(_1140369)), _1140373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140369), _1140371), _1140373)), c_Groups_Ozero__class_Ozero(_1140369))))], (13232 ^ _776541) ^ [_1010765, _1010767, _1010769, _1010771, _1010773] : [class_Groups_Ocomm__monoid__mult(_1010765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010767), _1010769)), -(hBOOL(hAPP(hAPP(c_member(_1010767), _1010771), _1010769))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1010767, _1010765), _1010773), hAPP(hAPP(c_Set_Oinsert(_1010767), _1010771), _1010769)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010765), hAPP(_1010773, _1010771)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1010767, _1010765), _1010773), _1010769)))], (3322 ^ _776541) ^ [_826125, _826127] : [_826127 = _826125, -(c_Lazy__Sequence_Ohb__not__seq(_826127) = c_Lazy__Sequence_Ohb__not__seq(_826125))], (33024 ^ _776541) ^ [_1379586, _1379588, _1379590, _1379592] : [_1379586 = c_Orderings_Obot__class_Obot(tc_fun(_1379588, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1379588, _1379590, hAPP(c_COMBK(_1379590, _1379588), _1379592)), _1379586) = c_Orderings_Obot__class_Obot(tc_fun(_1379590, tc_HOL_Obool)))], (21423 ^ _776541) ^ [_1164765, _1164767, _1164769] : [class_Rings_Oring__1(_1164765), hBOOL(hAPP(hAPP(c_member(_1164765), _1164767), c_Int_Oring__1__class_OInts(_1164765))), -(hBOOL(hAPP(hAPP(c_member(_1164765), hAPP(hAPP(c_Power_Opower__class_Opower(_1164765), _1164767), _1164769)), c_Int_Oring__1__class_OInts(_1164765))))], (38560 ^ _776541) ^ [_1516214, _1516216, _1516218] : [-(hAPP(c_Finite__Set_Ofold1(_1516214, _1516216), _1516218) = c_HOL_OThe(_1516214, c_Finite__Set_Ofold1Set(_1516214, _1516216, _1516218)))], (36555 ^ _776541) ^ [_1468836, _1468838] : [-(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), _1468836), _1468838)), 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), _1468836), _1468838))], (52059 ^ _776541) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (52433 ^ _776541) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (36952 ^ _776541) ^ [_1478199, _1478201, _1478203, _1478205, _1478207, _1478209, _1478211, _1478213, _1478215, _1478217] : [c_Equiv__Relations_Oequiv(_1478199, _1478201, _1478203), c_Equiv__Relations_Oequiv(_1478205, _1478207, _1478209), c_Equiv__Relations_Ocongruent2(_1478199, _1478205, tc_fun(_1478211, tc_HOL_Obool), _1478203, _1478209, _1478213), hBOOL(hAPP(hAPP(c_member(_1478199), _1478215), _1478201)), hBOOL(hAPP(hAPP(c_member(_1478205), _1478217), _1478207)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478199, tc_fun(_1478211, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1478199, _1478199, _1478203), hAPP(hAPP(c_Set_Oinsert(_1478199), _1478215), c_Orderings_Obot__class_Obot(tc_fun(_1478199, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1478205, tc_fun(_1478211, tc_HOL_Obool)), tc_fun(_1478211, tc_HOL_Obool), _1478199), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478205, tc_fun(_1478211, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1478205, _1478205, _1478209), hAPP(hAPP(c_Set_Oinsert(_1478205), _1478217), c_Orderings_Obot__class_Obot(tc_fun(_1478205, tc_HOL_Obool)))))), _1478213)) = hAPP(hAPP(_1478213, _1478215), _1478217))], (47656 ^ _776541) ^ [_1735225, _1735227] : [-(c_List_Omeasures(_1735225, _1735227) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1735225), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1735225, tc_List_Olist(tc_fun(_1735225, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1735225, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1735225, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1735225), c_List_Omap(tc_fun(_1735225, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1735225, tc_Nat_Onat), _1735225, tc_Nat_Onat), c_COMBI(tc_fun(_1735225, tc_Nat_Onat))))), _1735227)))], (51943 ^ _776541) ^ [_1825738, _1825740] : [class_Groups_Ouminus(_1825738), -(class_Groups_Ouminus(tc_fun(_1825740, _1825738)))], (6941 ^ _776541) ^ [_889176, _889178, _889180] : [class_Orderings_Olinorder(_889176), 6944 ^ _776541 : [(6951 ^ _776541) ^ [] : [_889178 = _889180, -(hAPP(c_SetInterval_Oord__class_OatMost(_889176), _889178) = hAPP(c_SetInterval_Oord__class_OatMost(_889176), _889180))], (6945 ^ _776541) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_889176), _889178) = hAPP(c_SetInterval_Oord__class_OatMost(_889176), _889180), -(_889178 = _889180)]]], (27281 ^ _776541) ^ [_1267345, _1267347] : [class_Rings_Olinordered__idom(_1267345), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267345), hAPP(c_Groups_Oabs__class_Oabs(_1267345), _1267347)), hAPP(c_Groups_Oabs__class_Oabs(_1267345), _1267347)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267345), _1267347), _1267347))], (40787 ^ _776541) ^ [_1574708, _1574710, _1574712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1574708, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1574708, _1574708, _1574710), _1574712)), _1574712)), -(hAPP(c_Relation_OImage(_1574708, _1574708, c_Transitive__Closure_Ortrancl(_1574708, _1574710)), _1574712) = _1574712)], (23864 ^ _776541) ^ [_1208794, _1208796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208794)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208796))))], (43114 ^ _776541) ^ [_1635552, _1635554] : [c_Orderings_Obot__class_Obot(tc_fun(_1635552, tc_HOL_Obool)) = hAPP(c_List_Oset(_1635552), _1635554), -(_1635554 = c_List_Olist_ONil(_1635552))], (48578 ^ _776541) ^ [_1756005, _1756007, _1756009] : [-(_1756005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1756007), c_List_Oreplicate(_1756007, _1756005, _1756009)) = _1756009)], (190 ^ _776541) ^ [_779688, _779690] : [-(class_Rings_Odivision__ring__inverse__zero(_779688)), _779690 = _779688, class_Rings_Odivision__ring__inverse__zero(_779690)], (24331 ^ _776541) ^ [_1216611, _1216613, _1216615, _1216617] : [class_Divides_Osemiring__div(_1216611), -(_1216613 = c_Groups_Ozero__class_Ozero(_1216611)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216611), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216611), _1216615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216611), _1216613), _1216617))), _1216613) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216611), _1216617), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216611), _1216615), _1216613)))], (32996 ^ _776541) ^ [_1378939, _1378941, _1378943] : [-(hBOOL(hAPP(_1378939, _1378941))), -(hAPP(c_Set_OCollect(_1378943), hAPP(hAPP(c_COMBS(_1378943, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378943), c_fconj), hAPP(hAPP(c_COMBC(_1378943, _1378943, tc_HOL_Obool), c_fequal), _1378941))), _1378939)) = c_Orderings_Obot__class_Obot(tc_fun(_1378943, tc_HOL_Obool)))], (48678 ^ _776541) ^ [_1757799, _1757801, _1757803, _1757805] : [hBOOL(hAPP(_1757799, _1757801)), -(hAPP(c_List_Ofilter(_1757803, _1757799), c_List_Oreplicate(_1757803, _1757805, _1757801)) = c_List_Oreplicate(_1757803, _1757805, _1757801))], (36446 ^ _776541) ^ [_1465469, _1465471] : [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)), _1465469), _1465471)), 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)), _1465469), 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)), _1465471), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (27042 ^ _776541) ^ [_1263567, _1263569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263567)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1263567, _1263569)))], (7958 ^ _776541) ^ [_911112, _911114] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911112, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_911112, tc_HOL_Obool))), _911114) = c_Orderings_Otop__class_Otop(tc_fun(_911112, tc_HOL_Obool)))], (52251 ^ _776541) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (7678 ^ _776541) ^ [_904626, _904628, _904630] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904626, tc_HOL_Obool)), _904628), _904630) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904626, tc_HOL_Obool)), _904630), _904628))], (1484 ^ _776541) ^ [_797955, _797957] : [-(class_Enum_Oenum(_797955)), _797957 = _797955, class_Enum_Oenum(_797957)], (8014 ^ _776541) ^ [_912441, _912443, _912445, _912447] : [-(hBOOL(hAPP(hAPP(c_member(_912441), _912443), _912445))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912441, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912441), _912443), _912447)), _912445) = hAPP(hAPP(c_Set_Oinsert(_912441), _912443), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912441, tc_HOL_Obool)), _912447), _912445)))], (14774 ^ _776541) ^ [_1042883, _1042885, _1042887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042885), _1042887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042883), _1042885)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042883), _1042887))))], (9332 ^ _776541) ^ [_937067, _937069, _937071] : [class_Orderings_Olinorder(_937067), 9335 ^ _776541 : [(9342 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937067), _937069), _937071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937067, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_937067), _937069)), hAPP(c_SetInterval_Oord__class_OlessThan(_937067), _937071))))], (9336 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937067, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_937067), _937069)), hAPP(c_SetInterval_Oord__class_OlessThan(_937067), _937071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937067), _937069), _937071)))]]], (48144 ^ _776541) ^ [_1746078, _1746080, _1746082] : [hBOOL(hAPP(hAPP(c_member(_1746078), _1746080), hAPP(c_List_Oset(_1746078), _1746082))), 48149 ^ _776541 : [(48152 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1746078), _1746080), hAPP(c_List_Oset(_1746078), 48147 ^ [_1746078, _1746080, _1746082])))], (48150 ^ _776541) ^ [] : [-(_1746082 = hAPP(hAPP(c_List_Oappend(_1746078), 48147 ^ [_1746078, _1746080, _1746082]), hAPP(hAPP(c_List_Olist_OCons(_1746078), _1746080), 48148 ^ [_1746078, _1746080, _1746082])))]]], (33681 ^ _776541) ^ [_1398780, _1398782, _1398784, _1398786, _1398788] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398780, tc_fun(_1398782, tc_HOL_Obool)), _1398784), hAPP(hAPP(c_COMBS(_1398780, tc_fun(_1398782, tc_HOL_Obool), tc_fun(_1398782, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398782, tc_HOL_Obool), tc_fun(tc_fun(_1398782, tc_HOL_Obool), tc_fun(_1398782, tc_HOL_Obool)), _1398780), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398782, tc_HOL_Obool))), _1398786)), _1398788)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398782, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1398782, tc_HOL_Obool), hAPP(c_Set_Oimage(_1398780, tc_fun(_1398782, tc_HOL_Obool), _1398786), _1398784))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1398782, tc_HOL_Obool), hAPP(c_Set_Oimage(_1398780, tc_fun(_1398782, tc_HOL_Obool), _1398788), _1398784))))], (32189 ^ _776541) ^ [_1354982, _1354984] : [class_Orderings_Olinorder(_1354982), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354982), _1354984)), -(_1354984 = c_Orderings_Obot__class_Obot(tc_fun(_1354982, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1354982), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354982), 32202 ^ [_1354982, _1354984]), 32203 ^ [_1354982, _1354984])), hAPP(hAPP(c_Set_Oinsert(_1354982), 32202 ^ [_1354982, _1354984]), hAPP(hAPP(c_Set_Oinsert(_1354982), 32203 ^ [_1354982, _1354984]), c_Orderings_Obot__class_Obot(tc_fun(_1354982, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1354982), c_Big__Operators_Olattice_OSup__fin(_1354982, c_Orderings_Oord__class_Omax(_1354982), _1354984)), _1354984)))], (5122 ^ _776541) ^ [_854683, _854685, _854687, _854689, _854691, _854693] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_854693, _854689, _854685) = c_SetInterval_Oord__class_OatLeastAtMost(_854691, _854687, _854683)), _854693 = _854691, _854689 = _854687, _854685 = _854683], (32412 ^ _776541) ^ [_1359783, _1359785, _1359787, _1359789] : [class_Groups_Oordered__ab__group__add__abs(_1359783), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359783), c_Groups_Ozero__class_Ozero(_1359783)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359785, _1359783), hAPP(hAPP(c_COMBB(_1359783, _1359783, _1359785), c_Groups_Oabs__class_Oabs(_1359783)), _1359787)), _1359789))))], (25846 ^ _776541) ^ [_1244098] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244098)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244098)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1244098)))], (19909 ^ _776541) ^ [_1135764, _1135766, _1135768, _1135770] : [class_Fields_Olinordered__field(_1135764), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135764), _1135766), _1135768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135764), c_Groups_Ozero__class_Ozero(_1135764)), _1135770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135764), c_Groups_Ozero__class_Ozero(_1135764)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135764), _1135768), _1135766))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135764), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135764), _1135770), _1135768)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135764), _1135770), _1135766))))], (45424 ^ _776541) ^ [_1687013, _1687015, _1687017, _1687019, _1687021] : [c_List_Olist__all2(_1687013, _1687015, _1687017, _1687019, _1687021), 45427 ^ _776541 : [(45430 ^ _776541) ^ [_1687179] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1687013, _1687015)), _1687179), hAPP(c_List_Oset(tc_prod(_1687013, _1687015)), hAPP(hAPP(c_List_Ozip(_1687013, _1687015), _1687019), _1687021)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687013, _1687015, tc_HOL_Obool), _1687017), _1687179)))], (45428 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687013)), _1687019) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687015)), _1687021))]]], (24018 ^ _776541) ^ [_1211355, _1211357] : [class_Rings_Oring__1(_1211355), -(hBOOL(hAPP(hAPP(c_member(_1211355), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211355), _1211357)), c_Int_Oring__1__class_OInts(_1211355))))], (34493 ^ _776541) ^ [_1418514, _1418516, _1418518, _1418520, _1418522] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418514, tc_fun(_1418516, tc_HOL_Obool)), _1418518), _1418520), _1418522)), 34496 ^ _776541 : [(34497 ^ _776541) ^ [_1418623] : [hBOOL(hAPP(hAPP(c_member(_1418514), _1418623), _1418518)), -(hBOOL(hAPP(hAPP(_1418520, _1418623), _1418522)))]]], (7750 ^ _776541) ^ [_906592, _906594, _906596, _906598] : [hBOOL(hAPP(hAPP(c_member(_906592), _906594), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906592, tc_HOL_Obool)), _906596), _906598))), -(hBOOL(hAPP(hAPP(c_member(_906592), _906594), _906596)))], (45503 ^ _776541) ^ [_1688976, _1688978, _1688980] : [_1688976 = _1688978, -(c_List_Olist__all2(_1688980, _1688980, c_fequal, _1688976, _1688978))], (34964 ^ _776541) ^ [_1428870, _1428872] : [-(_1428870 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1428872, _1428870) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428872), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428870)))], (14734 ^ _776541) ^ [_1042099, _1042101, _1042103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042099), _1042101)), _1042103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042101), _1042103)))], (47654 ^ _776541) ^ [_1735171, _1735173, _1735175] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1735171, _1735171)), hAPP(hAPP(c_Product__Type_OPair(_1735171, _1735171), _1735173), _1735175)), c_List_Omeasures(_1735171, c_List_Olist_ONil(tc_fun(_1735171, tc_Nat_Onat)))))], (47796 ^ _776541) ^ [_1738608, _1738610, _1738612, _1738614, _1738616] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738608)), _1738610) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738612)), _1738614), 47802 ^ _776541 : [(47805 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1738616, hAPP(hAPP(c_List_Onth(_1738608), _1738610), 47801 ^ [_1738608, _1738610, _1738612, _1738614, _1738616])), hAPP(hAPP(c_List_Onth(_1738612), _1738614), 47801 ^ [_1738608, _1738610, _1738612, _1738614, _1738616])))], (47803 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47801 ^ [_1738608, _1738610, _1738612, _1738614, _1738616]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738608)), _1738610))))]], -(c_List_Olist__all2(_1738608, _1738612, _1738616, _1738610, _1738614))], (32924 ^ _776541) ^ [_1376737] : [-(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)))), _1376737))))], (15282 ^ _776541) ^ [_1052336, _1052338, _1052340, _1052342] : [class_Groups_Ocomm__monoid__mult(_1052336), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052338), _1052340))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052338, _1052336), _1052342), _1052340) = c_Groups_Oone__class_Oone(_1052336))], (31299 ^ _776541) ^ [_1338226, _1338228, _1338230, _1338232] : [class_Orderings_Olinorder(_1338226), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338226), _1338228), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338226), _1338230), _1338232)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338226), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338226), _1338228), _1338230)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338226), _1338228), _1338232)))], (27801 ^ _776541) ^ [_1276450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276450), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276450))], (13672 ^ _776541) ^ [_1020001, _1020003, _1020005, _1020007] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020001), 13675 ^ _776541 : [(13682 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020001), _1020005), _1020007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020001), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020001), _1020003), _1020005)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020001), _1020003), _1020007))))], (13676 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020001), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020001), _1020003), _1020005)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020001), _1020003), _1020007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020001), _1020005), _1020007)))]]], (40526 ^ _776541) ^ [_1567526, _1567528, _1567530, _1567532, _1567534, _1567536, _1567538] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567526, _1567528, _1567530, _1567532), _1567534), _1567536), _1567538) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1567528, _1567530, _1567532), _1567536), hAPP(_1567534, _1567538)))], (7726 ^ _776541) ^ [_905960, _905962, _905964] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_905960, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_905960, tc_HOL_Obool), tc_HOL_Obool)), _905962), _905964)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905960, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_905960, tc_HOL_Obool), _905962)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_905960, tc_HOL_Obool), _905964)))], (36306 ^ _776541) ^ [_1462410, _1462412, _1462414, _1462416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462410), _1462412)), 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)), _1462414), _1462410)), 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)), _1462416), _1462412)), 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)), _1462414), _1462416)), _1462412)), c_FunDef_Omax__strict)))], (19747 ^ _776541) ^ [_1132948, _1132950] : [class_Rings_Olinordered__idom(_1132948), 19750 ^ _776541 : [(19757 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132948), _1132950), c_Groups_Ozero__class_Ozero(_1132948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132948), c_Groups_Osgn__class_Osgn(_1132948, _1132950)), c_Groups_Ozero__class_Ozero(_1132948))))], (19751 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132948), c_Groups_Osgn__class_Osgn(_1132948, _1132950)), c_Groups_Ozero__class_Ozero(_1132948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132948), _1132950), c_Groups_Ozero__class_Ozero(_1132948))))]]], (42003 ^ _776541) ^ [_1607334, _1607336, _1607338, _1607340] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607334), tc_List_Olist(_1607334))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607334), tc_List_Olist(_1607334)), _1607336), _1607338)), c_List_Olistrel(_1607334, _1607340))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607334)), _1607336) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607334)), _1607338))], (38762 ^ _776541) ^ [_1521545, _1521547, _1521549, _1521551] : [-(hAPP(c_Set_Ovimage(_1521545, _1521547, _1521549), _1521551) = hAPP(c_Set_OCollect(_1521545), hAPP(hAPP(c_COMBC(_1521545, tc_fun(_1521547, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1521547, tc_fun(tc_fun(_1521547, tc_HOL_Obool), tc_HOL_Obool), _1521545), c_member(_1521547)), _1521549)), _1521551)))], (51979 ^ _776541) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (21149 ^ _776541) ^ [_1159129] : [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), _1159129))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159129) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159129)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41074 ^ _776541) ^ [_1581706, _1581708, _1581710, _1581712, _1581714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581708, _1581706)), hAPP(hAPP(c_Product__Type_OPair(_1581708, _1581706), _1581712), _1581710)), _1581714)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581706, _1581708)), hAPP(hAPP(c_Product__Type_OPair(_1581706, _1581708), _1581710), _1581712)), hAPP(c_Relation_Oconverse(_1581708, _1581706), _1581714))))], (44725 ^ _776541) ^ [_1670672, _1670674, _1670676, _1670678, _1670680] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1670672), tc_List_Olist(_1670674), tc_List_Olist(_1670676), hAPP(c_List_Omap(_1670672, _1670674), _1670678)), hAPP(c_List_Omap(_1670676, _1670672), _1670680)) = hAPP(c_List_Omap(_1670676, _1670674), hAPP(c_Fun_Ocomp(_1670672, _1670674, _1670676, _1670678), _1670680)))], (5572 ^ _776541) ^ [_861634, _861636, _861638, _861640] : [-(tc_Nitpick_Opair__box(_861640, _861636) = tc_Nitpick_Opair__box(_861638, _861634)), _861640 = _861638, _861636 = _861634], (37562 ^ _776541) ^ [_1491476, _1491478, _1491480, _1491482, _1491484, _1491486] : [c_Fun_Oinj__on(_1491476, _1491478, _1491480, _1491482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491476, tc_HOL_Obool)), _1491484), _1491482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491476, tc_HOL_Obool)), _1491486), _1491482)), -(hAPP(c_Set_Oimage(_1491476, _1491478, _1491480), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491476, tc_HOL_Obool)), _1491484), _1491486)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491478, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491476, _1491478, _1491480), _1491484)), hAPP(c_Set_Oimage(_1491476, _1491478, _1491480), _1491486)))], (28081 ^ _776541) ^ [_1280995, _1280997] : [class_Int_Onumber__ring(_1280995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1280997)), -(hBOOL(hAPP(hAPP(c_member(_1280995), hAPP(c_Int_Onumber__class_Onumber__of(_1280995), _1280997)), c_Nat_Osemiring__1__class_ONats(_1280995))))], (6463 ^ _776541) ^ [_880984, _880986] : [6464 ^ _776541 : [(6465 ^ _776541) ^ [_881037] : [hBOOL(hAPP(hAPP(c_member(_880984), _881037), _880986))]], _880986 = c_Orderings_Obot__class_Obot(tc_fun(_880984, tc_HOL_Obool))], (52261 ^ _776541) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (5428 ^ _776541) ^ [_859466, _859468] : [_859468 = _859466, -(c_Orderings_Oord__class_Oless__eq(_859468) = c_Orderings_Oord__class_Oless__eq(_859466))], (43364 ^ _776541) ^ [_1640983, _1640985, _1640987, _1640989] : [-(c_List_Osublist(_1640983, hAPP(hAPP(c_List_Olist_OCons(_1640983), _1640985), _1640987), _1640989) = hAPP(hAPP(c_List_Oappend(_1640983), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1640983)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1640989)), hAPP(hAPP(c_List_Olist_OCons(_1640983), _1640985), c_List_Olist_ONil(_1640983))), c_List_Olist_ONil(_1640983))), c_List_Osublist(_1640983, _1640987, 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)), _1640989)))))], (29021 ^ _776541) ^ [_1296808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1296808)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296808), c_Int_OMin)))], (46343 ^ _776541) ^ [_1708563, _1708565, _1708567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708563), _1708565)), _1708567)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1708565), c_List_Oupt(_1708563, _1708567)) = c_List_Oupt(_1708563, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708563), _1708565)))], (5268 ^ _776541) ^ [_856924, _856926, _856928, _856930, _856932, _856934, _856936, _856938] : [-(c_Fun_Ocomp(_856938, _856934, _856930, _856926) = c_Fun_Ocomp(_856936, _856932, _856928, _856924)), _856938 = _856936, _856934 = _856932, _856930 = _856928, _856926 = _856924], (4412 ^ _776541) ^ [_843526, _843528, _843530, _843532, _843534, _843536] : [-(c_New__DSequence_Opos__union(_843536, _843532, _843528) = c_New__DSequence_Opos__union(_843534, _843530, _843526)), _843536 = _843534, _843532 = _843530, _843528 = _843526], (23918 ^ _776541) ^ [_1209721, _1209723, _1209725] : [class_Rings_Olinordered__semidom(_1209721), 23921 ^ _776541 : [(23928 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209723), _1209725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209721), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209721), _1209723)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209721), _1209725))))], (23922 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209721), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209721), _1209723)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209721), _1209725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209723), _1209725)))]]], (32700 ^ _776541) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17727 ^ _776541) ^ [_1095669, _1095671] : [class_Groups_Oordered__ab__group__add(_1095669), 17730 ^ _776541 : [(17737 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095669), c_Groups_Ozero__class_Ozero(_1095669)), _1095671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095669), hAPP(c_Groups_Ouminus__class_Ouminus(_1095669), _1095671)), c_Groups_Ozero__class_Ozero(_1095669))))], (17731 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095669), hAPP(c_Groups_Ouminus__class_Ouminus(_1095669), _1095671)), c_Groups_Ozero__class_Ozero(_1095669))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095669), c_Groups_Ozero__class_Ozero(_1095669)), _1095671)))]]], (27615 ^ _776541) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42671 ^ _776541) ^ [_1626159, _1626161, _1626163, _1626165, _1626167] : [-(_1626159 = _1626161), -(hAPP(hAPP(c_List_Onth(_1626163), hAPP(hAPP(c_List_Olist__update(_1626163, _1626165), _1626159), _1626167)), _1626161) = hAPP(hAPP(c_List_Onth(_1626163), _1626165), _1626161))], (42131 ^ _776541) ^ [_1611404, _1611406, _1611408] : [c_Equiv__Relations_Oequiv(_1611404, _1611406, _1611408), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1611404), c_List_Olists(_1611404, _1611406), c_List_Olistrel(_1611404, _1611408)))], (38832 ^ _776541) ^ [_1523256, _1523258, _1523260, _1523262] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523256), _1523258)), c_Fun_Oinj__on(_1523260, _1523256, _1523262, c_Orderings_Otop__class_Otop(tc_fun(_1523260, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523260), hAPP(c_Set_Ovimage(_1523260, _1523256, _1523262), _1523258))))], (40530 ^ _776541) ^ [_1567676, _1567678] : [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), _1567676), _1567678)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1567676), _1567678)))], (40160 ^ _776541) ^ [_1559046, _1559048, _1559050, _1559052, _1559054, _1559056] : [c_Finite__Set_Ofolding(_1559046, _1559048, _1559050, _1559052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559046), _1559054)), -(hAPP(c_Fun_Ocomp(_1559048, _1559048, _1559048, hAPP(_1559050, _1559056)), hAPP(_1559052, _1559054)) = hAPP(c_Fun_Ocomp(_1559048, _1559048, _1559048, hAPP(_1559052, _1559054)), hAPP(_1559050, _1559056)))], (16574 ^ _776541) ^ [_1074737] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074737), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38450 ^ _776541) ^ [_1513712, _1513714] : [c_Wellfounded_OwfP(_1513712, _1513714), -(c_Wellfounded_Owf(_1513712, hAPP(c_Set_OCollect(tc_prod(_1513712, _1513712)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513712, _1513712, tc_HOL_Obool), _1513714))))], (46146 ^ _776541) ^ [_1703338, _1703340, _1703342] : [-(c_List_Oremdups(_1703338, hAPP(c_List_Ofilter(_1703338, _1703340), _1703342)) = hAPP(c_List_Ofilter(_1703338, _1703340), c_List_Oremdups(_1703338, _1703342)))], (5540 ^ _776541) ^ [_861166, _861168, _861170, _861172] : [-(tc_fun(_861172, _861168) = tc_fun(_861170, _861166)), _861172 = _861170, _861168 = _861166], (15769 ^ _776541) ^ [_1062356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062356), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1062356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28349 ^ _776541) ^ [_1285438, _1285440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285438)), c_Int_OBit1(_1285440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285438), _1285440)))], (30688 ^ _776541) ^ [_1327072, _1327074, _1327076] : [class_Orderings_Olinorder(_1327072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327072), _1327074)), -(_1327074 = c_Orderings_Obot__class_Obot(tc_fun(_1327072, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1327072, c_Orderings_Oord__class_Omin(_1327072), hAPP(hAPP(c_Set_Oinsert(_1327072), _1327076), _1327074)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1327072), _1327076), c_Big__Operators_Olattice_OInf__fin(_1327072, c_Orderings_Oord__class_Omin(_1327072), _1327074)))], (49169 ^ _776541) ^ [_1768789, _1768791] : [c_Relation_Otrans(_1768789, _1768791), 49172 ^ _776541 : [(49173 ^ _776541) ^ [_1768925, _1768927] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768789, _1768789)), hAPP(hAPP(c_Product__Type_OPair(_1768789, _1768789), _1768927), _1768925)), _1768791)), 49176 ^ _776541 : [(49177 ^ _776541) ^ [_1769068] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768789, _1768789)), hAPP(hAPP(c_Product__Type_OPair(_1768789, _1768789), _1768925), _1769068)), _1768791)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768789, _1768789)), hAPP(hAPP(c_Product__Type_OPair(_1768789, _1768789), _1768927), _1769068)), _1768791)))]]]]], (1474 ^ _776541) ^ [_797830, _797832] : [-(class_Finite__Set_Ofinite(_797830)), _797832 = _797830, class_Finite__Set_Ofinite(_797832)], (27783 ^ _776541) ^ [_1276171] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276171) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276171), c_Int_OPls)))], (51975 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (20531 ^ _776541) ^ [_1147082, _1147084, _1147086, _1147088] : [class_Fields_Olinordered__field(_1147082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147082), _1147084), c_Groups_Ozero__class_Ozero(_1147082))), 20538 ^ _776541 : [(20545 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147082), _1147088), _1147084)), _1147086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147082), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147082), _1147086), _1147084)), _1147088)))], (20539 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147082), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147082), _1147086), _1147084)), _1147088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147082), _1147088), _1147084)), _1147086)))]]], (33425 ^ _776541) ^ [_1390741, _1390743, _1390745, _1390747, _1390749, _1390751] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390741, tc_fun(_1390743, tc_HOL_Obool)), _1390745), hAPP(hAPP(c_COMBC(_1390741, tc_fun(_1390747, tc_fun(_1390743, tc_HOL_Obool)), tc_fun(_1390743, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390747, tc_HOL_Obool), tc_fun(tc_fun(_1390747, tc_fun(_1390743, tc_HOL_Obool)), tc_fun(_1390743, tc_HOL_Obool)), _1390741), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390747, tc_fun(_1390743, tc_HOL_Obool))), _1390749)), _1390751)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390747, tc_fun(_1390743, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390741, tc_fun(_1390747, tc_HOL_Obool)), _1390745), _1390749)), _1390751))], (51891 ^ _776541) ^ [_1825056, _1825058] : [class_Lattices_Oboolean__algebra(_1825056), -(class_Lattices_Oboolean__algebra(tc_fun(_1825058, _1825056)))], (16799 ^ _776541) ^ [_1078890, _1078892] : [class_Groups_Olinordered__ab__group__add(_1078890), 16802 ^ _776541 : [(16809 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078890), c_Groups_Ozero__class_Ozero(_1078890)), _1078892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078890), c_Groups_Ozero__class_Ozero(_1078890)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078890), _1078892), _1078892))))], (16803 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078890), c_Groups_Ozero__class_Ozero(_1078890)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078890), _1078892), _1078892))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078890), c_Groups_Ozero__class_Ozero(_1078890)), _1078892)))]]], (52275 ^ _776541) ^ [_1828881] : [-(class_Nat_Osize(tc_List_Olist(_1828881)))], (14787 ^ _776541) ^ [_1043130, _1043132] : [14788 ^ _776541 : [(14789 ^ _776541) ^ [_1043180] : [_1043132 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043130), _1043180)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043130), _1043132)))], (14450 ^ _776541) ^ [_1037462, _1037464, _1037466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037462), _1037464)), 14453 ^ _776541 : [(14460 ^ _776541) ^ [] : [_1037464 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037466), _1037462), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037464), _1037462) = _1037466)], (14454 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037464), _1037462) = _1037466, -(_1037464 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037466), _1037462))]]], (2752 ^ _776541) ^ [_817238, _817240, _817242, _817244] : [-(c_Predicate_OPowp(_817244, _817240) = c_Predicate_OPowp(_817242, _817238)), _817244 = _817242, _817240 = _817238], (17843 ^ _776541) ^ [_1097609, _1097611, _1097613] : [class_Groups_Ocomm__monoid__add(_1097609), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097611, _1097609), _1097613), c_Orderings_Obot__class_Obot(tc_fun(_1097611, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1097609))], (7216 ^ _776541) ^ [_894143, _894145, _894147, _894149] : [7217 ^ _776541 : [(7220 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894143), _894145), _894149))], (7218 ^ _776541) ^ [] : [_894145 = _894147]], -(hBOOL(hAPP(hAPP(c_member(_894143), _894145), hAPP(hAPP(c_Set_Oinsert(_894143), _894147), _894149))))], (3724 ^ _776541) ^ [_832374, _832376, _832378, _832380] : [-(c_List_Oremdups(_832380, _832376) = c_List_Oremdups(_832378, _832374)), _832380 = _832378, _832376 = _832374], (37925 ^ _776541) ^ [_1499971, _1499973, _1499975, _1499977, _1499979] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1499971, _1499973, _1499975), _1499977), _1499979) = hAPP(c_Set_OCollect(tc_prod(_1499971, _1499975)), hAPP(c_Product__Type_Oprod_Oprod__case(_1499971, _1499975, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1499975, tc_fun(_1499973, tc_HOL_Obool)), tc_fun(_1499975, tc_HOL_Obool), _1499971), hAPP(c_COMBB(tc_fun(_1499973, tc_HOL_Obool), tc_HOL_Obool, _1499975), c_HOL_OEx(_1499973))), hAPP(hAPP(c_COMBC(_1499971, tc_fun(_1499975, tc_fun(_1499973, tc_HOL_Obool)), tc_fun(_1499975, tc_fun(_1499973, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1499973, tc_HOL_Obool), tc_fun(_1499973, tc_HOL_Obool)), tc_fun(tc_fun(_1499975, tc_fun(_1499973, tc_HOL_Obool)), tc_fun(_1499975, tc_fun(_1499973, tc_HOL_Obool))), _1499971), c_COMBB(tc_fun(_1499973, tc_HOL_Obool), tc_fun(_1499973, tc_HOL_Obool), _1499975)), hAPP(hAPP(c_COMBB(tc_fun(_1499973, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1499973, tc_HOL_Obool), tc_fun(_1499973, tc_HOL_Obool)), _1499971), c_COMBS(_1499973, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499973, tc_HOL_Obool), tc_fun(_1499973, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1499971), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499973), c_fconj)), hAPP(hAPP(c_COMBC(_1499971, tc_fun(tc_prod(_1499971, _1499973), tc_HOL_Obool), tc_fun(_1499973, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499973, tc_fun(tc_fun(tc_prod(_1499971, _1499973), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499971, _1499973), tc_HOL_Obool), tc_fun(_1499973, tc_HOL_Obool)), _1499971), c_COMBC(_1499973, tc_fun(tc_prod(_1499971, _1499973), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499973, tc_prod(_1499971, _1499973)), tc_fun(_1499973, tc_fun(tc_fun(tc_prod(_1499971, _1499973), tc_HOL_Obool), tc_HOL_Obool)), _1499971), hAPP(c_COMBB(tc_prod(_1499971, _1499973), tc_fun(tc_fun(tc_prod(_1499971, _1499973), tc_HOL_Obool), tc_HOL_Obool), _1499973), c_member(tc_prod(_1499971, _1499973)))), c_Product__Type_OPair(_1499971, _1499973)))), _1499977))))), hAPP(hAPP(c_COMBC(_1499975, tc_fun(tc_prod(_1499973, _1499975), tc_HOL_Obool), tc_fun(_1499973, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499973, tc_fun(tc_fun(tc_prod(_1499973, _1499975), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499973, _1499975), tc_HOL_Obool), tc_fun(_1499973, tc_HOL_Obool)), _1499975), c_COMBC(_1499973, tc_fun(tc_prod(_1499973, _1499975), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499973, tc_prod(_1499973, _1499975)), tc_fun(_1499973, tc_fun(tc_fun(tc_prod(_1499973, _1499975), tc_HOL_Obool), tc_HOL_Obool)), _1499975), hAPP(c_COMBB(tc_prod(_1499973, _1499975), tc_fun(tc_fun(tc_prod(_1499973, _1499975), tc_HOL_Obool), tc_HOL_Obool), _1499973), c_member(tc_prod(_1499973, _1499975)))), hAPP(c_COMBC(_1499973, _1499975, tc_prod(_1499973, _1499975)), c_Product__Type_OPair(_1499973, _1499975))))), _1499979))))))], (29887 ^ _776541) ^ [_1312513, _1312515] : [-(c_Random_Olog(_1312513, _1312515) = 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(_1312513, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1312515), _1312513)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1312513), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1312515), _1312513)))], (47454 ^ _776541) ^ [_1730711, _1730713, _1730715, _1730717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730711), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730713)), c_List_OdropWhile(_1730713, _1730715, _1730717)))), -(hAPP(hAPP(c_List_Onth(_1730713), c_List_OdropWhile(_1730713, _1730715, _1730717)), _1730711) = hAPP(hAPP(c_List_Onth(_1730713), _1730717), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1730711), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730713)), c_List_OtakeWhile(_1730713, _1730715, _1730717)))))], (24770 ^ _776541) ^ [_1224557, _1224559, _1224561] : [class_Divides_Osemiring__div(_1224557), -(c_Divides_Odiv__class_Omod(_1224557, c_Divides_Odiv__class_Omod(_1224557, _1224559, _1224561), _1224561) = c_Divides_Odiv__class_Omod(_1224557, _1224559, _1224561))], (14004 ^ _776541) ^ [_1027358, _1027360, _1027362, _1027364, _1027366] : [class_Groups_Ocomm__monoid__add(_1027358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027360), _1027362)), -(hBOOL(hAPP(hAPP(c_member(_1027360), _1027364), _1027362))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027360, _1027358), _1027366), hAPP(hAPP(c_Set_Oinsert(_1027360), _1027364), _1027362)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027358), hAPP(_1027366, _1027364)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027360, _1027358), _1027366), _1027362)))], (3834 ^ _776541) ^ [_834115, _834117, _834119, _834121, _834123, _834125] : [-(c_List_OdropWhile(_834125, _834121, _834117) = c_List_OdropWhile(_834123, _834119, _834115)), _834125 = _834123, _834121 = _834119, _834117 = _834115], (28847 ^ _776541) ^ [_1293712, _1293714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293712), _1293714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1293712)), c_Int_OBit0(_1293714))))], (46399 ^ _776541) ^ [_1709611] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1709611) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1709611)))], (7864 ^ _776541) ^ [_909030, _909032, _909034] : [7866 ^ _776541 : [(7872 ^ _776541) ^ [] : [-(7865 ^ [_909030, _909032, _909034] = 7868 ^ [_909030, _909032, _909034])], (7870 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_909030), 7868 ^ [_909030, _909032, _909034]), _909034)))], (7867 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_909030), 7865 ^ [_909030, _909032, _909034]), _909032)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909030, tc_HOL_Obool)), _909032), _909034) = c_Orderings_Obot__class_Obot(tc_fun(_909030, tc_HOL_Obool)))], (22929 ^ _776541) ^ [_1192003, _1192005, _1192007] : [class_Rings_Olinordered__semidom(_1192003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192003), c_Groups_Ozero__class_Ozero(_1192003)), _1192005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192003), _1192005), c_Groups_Oone__class_Oone(_1192003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192003), hAPP(hAPP(c_Power_Opower__class_Opower(_1192003), _1192005), hAPP(c_Nat_OSuc, _1192007))), c_Groups_Oone__class_Oone(_1192003))))], (15962 ^ _776541) ^ [_1065435, _1065437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065437), hAPP(c_Nat_OSuc, _1065435))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065435), _1065437))], (16719 ^ _776541) ^ [_1077281, _1077283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077281), _1077283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077281)), _1077283)))], (29151 ^ _776541) ^ [_1299045, _1299047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299045)), c_Int_OBit0(_1299047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299045), _1299047)))], (6430 ^ _776541) ^ [_880423, _880425, _880427, _880429] : [hBOOL(hAPP(hAPP(c_member(_880423), _880425), _880427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880423, tc_HOL_Obool)), _880427), _880429)), -(hBOOL(hAPP(hAPP(c_member(_880423), _880425), _880429)))], (29121 ^ _776541) ^ [_1298439, _1298441] : [class_Int_Onumber__ring(_1298439), -(hAPP(c_Int_Onumber__class_Onumber__of(_1298439), c_Int_OBit0(_1298441)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298439), c_Groups_Ozero__class_Ozero(_1298439)), hAPP(c_Int_Onumber__class_Onumber__of(_1298439), _1298441))), hAPP(c_Int_Onumber__class_Onumber__of(_1298439), _1298441)))], (39331 ^ _776541) ^ [_1538043, _1538045] : [-(c_Fun_Oinj__on(_1538043, _1538043, c_Fun_Oid(_1538043), _1538045))], (31985 ^ _776541) ^ [_1351290, _1351292, _1351294] : [class_Orderings_Olinorder(_1351290), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351290), _1351292)), hBOOL(hAPP(hAPP(c_member(_1351290), _1351294), _1351292)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351290), _1351294), c_Big__Operators_Olattice_OSup__fin(_1351290, c_Orderings_Oord__class_Omax(_1351290), _1351292)) = c_Big__Operators_Olattice_OSup__fin(_1351290, c_Orderings_Oord__class_Omax(_1351290), _1351292))], (742 ^ _776541) ^ [_787732, _787734, _787736, _787738] : [-(c_Wellfounded_Oacyclic(_787736, _787732)), c_Wellfounded_Oacyclic(_787738, _787734), _787738 = _787736, _787734 = _787732], (35923 ^ _776541) ^ [_1449373, _1449375] : [-(hAPP(c_Set_OPow(_1449373), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1449373, tc_HOL_Obool)), _1449375)) = hAPP(c_Set_OCollect(tc_fun(_1449373, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1449373, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1449373, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1449373, tc_HOL_Obool), tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1449373, tc_HOL_Obool)), c_COMBS(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1449373, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1449373, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1449373, tc_HOL_Obool), tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_fun(_1449373, tc_HOL_Obool)), tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_fun(_1449373, tc_HOL_Obool)), tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1449373, tc_HOL_Obool)), c_COMBB(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1449373, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1449373, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449373, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1449373, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1449373, tc_HOL_Obool)), _1449375)), c_Set_OPow(_1449373))))))], (17057 ^ _776541) ^ [_1083617, _1083619, _1083621, _1083623] : [class_Rings_Oordered__semiring(_1083617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083617), _1083619), _1083621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083617), c_Groups_Ozero__class_Ozero(_1083617)), _1083623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083617), _1083619), _1083623)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083617), _1083621), _1083623))))], (29837 ^ _776541) ^ [_1311518, _1311520] : [_1311518 = _1311520, -(c_Code__Numeral_OSuc__code__numeral(_1311518) = c_Code__Numeral_OSuc__code__numeral(_1311520))], (25012 ^ _776541) ^ [_1229498, _1229500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1229498), _1229500)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229498), _1229500) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35840 ^ _776541) ^ [_1446191, _1446193, _1446195, _1446197, _1446199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1446191, _1446193)), hAPP(_1446191, _1446195))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1446197, _1446197)), hAPP(hAPP(c_Product__Type_OPair(_1446197, _1446197), _1446193), _1446195)), _1446199)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446197, _1446197)), hAPP(hAPP(c_Product__Type_OPair(_1446197, _1446197), _1446193), _1446195)), c_Wellfounded_Omlex__prod(_1446197, _1446191, _1446199))))], (49668 ^ _776541) ^ [_1780475, _1780477] : [49671 ^ _776541 : [(49674 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780475, _1780475)), hAPP(hAPP(c_Product__Type_OPair(_1780475, _1780475), 49670 ^ [_1780475, _1780477]), 49669 ^ [_1780475, _1780477])), _1780477))], (49672 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780475, _1780475)), hAPP(hAPP(c_Product__Type_OPair(_1780475, _1780475), 49669 ^ [_1780475, _1780477]), 49670 ^ [_1780475, _1780477])), _1780477)))]], -(c_Relation_Osym(_1780475, _1780477))], (36474 ^ _776541) ^ [_1466471, _1466473, _1466475, _1466477, _1466479, _1466481] : [-(hAPP(c_Relation_OImage(_1466471, _1466473, _1466475), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1466477, tc_fun(_1466471, tc_HOL_Obool)), _1466479), _1466481)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1466477, tc_fun(_1466473, tc_HOL_Obool)), _1466479), hAPP(hAPP(c_COMBB(tc_fun(_1466471, tc_HOL_Obool), tc_fun(_1466473, tc_HOL_Obool), _1466477), c_Relation_OImage(_1466471, _1466473, _1466475)), _1466481)))], (7138 ^ _776541) ^ [_892828, _892830, _892832, _892834] : [-(hAPP(hAPP(c_Set_Oinsert(_892828), _892830), hAPP(hAPP(c_Set_Oinsert(_892828), _892832), _892834)) = hAPP(hAPP(c_Set_Oinsert(_892828), _892832), hAPP(hAPP(c_Set_Oinsert(_892828), _892830), _892834)))], (7228 ^ _776541) ^ [_894420, _894422, _894424] : [hAPP(hAPP(c_Set_Oinsert(_894420), _894422), _894424) = c_Orderings_Obot__class_Obot(tc_fun(_894420, tc_HOL_Obool))], (27048 ^ _776541) ^ [_1263654, _1263656] : [c_Nat__Transfer_Onat__set(_1263654), c_Nat__Transfer_Onat__set(_1263656), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1263654), _1263656) = 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), _1263654)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1263656))))], (25834 ^ _776541) ^ [_1243935, _1243937] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1243935)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243935)), _1243937)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1243935))), _1243937))], (42117 ^ _776541) ^ [_1610986, _1610988, _1610990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610986, _1610986), tc_HOL_Obool)), _1610988), hAPP(hAPP(c_Product__Type_OSigma(_1610986, _1610986), _1610990), hAPP(c_COMBK(tc_fun(_1610986, tc_HOL_Obool), _1610986), _1610990)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610986), tc_List_Olist(_1610986)), tc_HOL_Obool)), c_List_Olistrel(_1610986, _1610988)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1610986), tc_List_Olist(_1610986)), c_List_Olists(_1610986, _1610990)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1610986), tc_HOL_Obool), tc_List_Olist(_1610986)), c_List_Olists(_1610986, _1610990))))))], (43080 ^ _776541) ^ [_1634950, _1634952, _1634954, _1634956] : [-(c_List_Oremove1(_1634950, _1634952, c_List_Oremove1(_1634950, _1634954, _1634956)) = c_List_Oremove1(_1634950, _1634954, c_List_Oremove1(_1634950, _1634952, _1634956)))], (16538 ^ _776541) ^ [_1074240, _1074242, _1074244] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074240), _1074242) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074240), _1074244), -(_1074242 = _1074244), -(_1074240 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4952 ^ _776541) ^ [_851984, _851986, _851988, _851990, _851992, _851994] : [-(c_Finite__Set_Ofold__image(_851994, _851990, _851986) = c_Finite__Set_Ofold__image(_851992, _851988, _851984)), _851994 = _851992, _851990 = _851988, _851986 = _851984], (9130 ^ _776541) ^ [_934287, _934289, _934291, _934293] : [class_Orderings_Oord(_934287), _934289 = _934291, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934287), _934291), _934293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934287), _934289), _934293)))], (25692 ^ _776541) ^ [_1241459, _1241461, _1241463, _1241465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241461), _1241463)), -(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), _1241463), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241465, _1241459))), _1241461))))], (42899 ^ _776541) ^ [_1631204, _1631206] : [hBOOL(hAPP(c_List_Odistinct(_1631204), _1631206)), 42902 ^ _776541 : [(42903 ^ _776541) ^ [_1631336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631336), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631204)), _1631206))), 42906 ^ _776541 : [(42907 ^ _776541) ^ [_1631463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631463), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631204)), _1631206))), -(_1631336 = _1631463), hAPP(hAPP(c_List_Onth(_1631204), _1631206), _1631336) = hAPP(hAPP(c_List_Onth(_1631204), _1631206), _1631463)]]]]], (32348 ^ _776541) ^ [_1358375, _1358377, _1358379, _1358381, _1358383, _1358385, _1358387, _1358389] : [hBOOL(hAPP(hAPP(c_member(_1358375), _1358377), _1358379)), hBOOL(hAPP(hAPP(hAPP(_1358381, _1358377), _1358383), _1358385)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358375, tc_fun(_1358387, tc_fun(_1358389, tc_HOL_Obool))), _1358379), _1358381), _1358383), _1358385)))], (45393 ^ _776541) ^ [_1686252, _1686254, _1686256] : [45395 ^ _776541 : [(45398 ^ _776541) ^ [] : [hBOOL(hAPP(_1686254, 45394 ^ [_1686252, _1686254, _1686256]))], (45396 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686252), 45394 ^ [_1686252, _1686254, _1686256]), hAPP(c_List_Oset(_1686252), _1686256))))]], -(hBOOL(hAPP(c_List_Olistsp(_1686252, _1686254), _1686256)))], (48883 ^ _776541) ^ [_1762068, _1762070, _1762072] : [hBOOL(hAPP(hAPP(c_member(_1762068), _1762072), hAPP(c_List_Oset(_1762068), _1762070))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1762068), _1762070), _1762072)))], (1584 ^ _776541) ^ [_799205, _799207] : [-(class_Rings_Oordered__comm__semiring(_799205)), _799207 = _799205, class_Rings_Oordered__comm__semiring(_799207)], (52069 ^ _776541) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (41467 ^ _776541) ^ [_1591250, _1591252, _1591254, _1591256, _1591258, _1591260] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591250, _1591250)), hAPP(hAPP(c_Product__Type_OPair(_1591250, _1591250), _1591252), _1591254)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591250, _1591250), tc_HOL_Obool), _1591256), _1591258))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591250, _1591250)), hAPP(hAPP(c_Product__Type_OPair(_1591250, _1591250), _1591254), _1591260)), _1591258)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591250, _1591250)), hAPP(hAPP(c_Product__Type_OPair(_1591250, _1591250), _1591252), _1591260)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591250, _1591250), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1591256)), _1591258))))], (44471 ^ _776541) ^ [_1666068, _1666070] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1666068), hAPP(c_List_Oset(tc_Nat_Onat), _1666070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1666068), 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)), _1666070))))], (50989 ^ _776541) ^ [_1809075, _1809077, _1809079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1809075)), 50992 ^ _776541 : [(50999 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809077), _1809079)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809075), _1809077)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809075), _1809079))))], (50993 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809075), _1809077)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809075), _1809079))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809077), _1809079)))]]], (11004 ^ _776541) ^ [_966667, _966669] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966667, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966667, tc_HOL_Obool)), _966669)) = _966669)], (17421 ^ _776541) ^ [_1090270, _1090272, _1090274] : [class_Rings_Olinordered__semiring__strict(_1090270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090270), c_Groups_Ozero__class_Ozero(_1090270)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090270), _1090272), _1090274))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090270), c_Groups_Ozero__class_Ozero(_1090270)), _1090272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090270), c_Groups_Ozero__class_Ozero(_1090270)), _1090274)))], (18868 ^ _776541) ^ [_1116497, _1116499] : [-(_1116497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116497), _1116499) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116497), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1116499)))], (52011 ^ _776541) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (1304 ^ _776541) ^ [_795705, _795707] : [-(class_Rings_Oring__1(_795705)), _795707 = _795705, class_Rings_Oring__1(_795707)], (6686 ^ _776541) ^ [_884755, _884757, _884759, _884761] : [class_Orderings_Oord(_884755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884755), _884757), _884759)), _884759 = _884761, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884755), _884757), _884761)))], (36671 ^ _776541) ^ [_1471945, _1471947, _1471949, _1471951] : [_1471945 = _1471947, hBOOL(hAPP(hAPP(c_member(_1471949), _1471945), _1471951)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1471949, _1471949)), hAPP(hAPP(c_Product__Type_OPair(_1471949, _1471949), _1471945), _1471947)), c_Relation_OId__on(_1471949, _1471951))))], (2450 ^ _776541) ^ [_812503, _812505, _812507, _812509] : [-(c_Nitpick_Onat__gcd(_812509, _812505) = c_Nitpick_Onat__gcd(_812507, _812503)), _812509 = _812507, _812505 = _812503], (39163 ^ _776541) ^ [_1532248, _1532250, _1532252, _1532254, _1532256, _1532258] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532248, _1532250)), hAPP(hAPP(c_Product__Type_OPair(_1532248, _1532250), _1532252), _1532254)), hAPP(hAPP(c_Product__Type_OSigma(_1532248, _1532250), _1532256), _1532258)))), hBOOL(hAPP(hAPP(c_member(_1532248), _1532252), _1532256)), hBOOL(hAPP(hAPP(c_member(_1532250), _1532254), hAPP(_1532258, _1532252)))], (32538 ^ _776541) ^ [_1364787, _1364789, _1364791, _1364793] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1364787, tc_HOL_Obool), hAPP(c_Set_Oimage(_1364789, tc_fun(_1364787, tc_HOL_Obool), _1364791), _1364793)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364789, tc_fun(_1364787, tc_HOL_Obool)), _1364793), _1364791))], (34455 ^ _776541) ^ [_1417713, _1417715, _1417717, _1417719, _1417721, _1417723] : [34456 ^ _776541 : [(34459 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1417719, _1417715), _1417717))], (34457 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1417713, _1417715), _1417717))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417721, tc_fun(_1417723, tc_HOL_Obool))), _1417719), _1417713), _1417715), _1417717)))], (34912 ^ _776541) ^ [_1427918, _1427920] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427918))), 34915 ^ _776541 : [(34922 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427920))), -(c_Divides_Odivmod__int(_1427918, _1427920) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427918), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427920))))], (34916 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427920)), -(c_Divides_Odivmod__int(_1427918, _1427920) = c_Divides_OnegDivAlg(_1427918, _1427920))]]], (18846 ^ _776541) ^ [_1116068, _1116070, _1116072] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1116068), _1116070)), -(hAPP(c_Finite__Set_Ocard(_1116068), hAPP(hAPP(c_Set_Oinsert(_1116068), _1116072), _1116070)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1116068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1116068, tc_HOL_Obool)), _1116070), hAPP(hAPP(c_Set_Oinsert(_1116068), _1116072), c_Orderings_Obot__class_Obot(tc_fun(_1116068, tc_HOL_Obool)))))))], (44344 ^ _776541) ^ [_1663428, _1663430, _1663432, _1663434] : [class_Orderings_Olinorder(_1663428), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663430, _1663428, _1663432), _1663434), c_List_Olist_ONil(_1663430)) = hAPP(hAPP(c_List_Olist_OCons(_1663430), _1663434), c_List_Olist_ONil(_1663430)))], (15788 ^ _776541) ^ [_1062627] : [15789 ^ _776541 : [(15790 ^ _776541) ^ [_1062669] : [_1062627 = hAPP(c_Nat_OSuc, _1062669)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062627)))], (17645 ^ _776541) ^ [_1094279] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1094279)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1094279)], (46158 ^ _776541) ^ [_1703742, _1703744, _1703746] : [-(hAPP(c_List_Oset(_1703742), hAPP(c_List_Ofilter(_1703742, _1703744), _1703746)) = hAPP(c_Set_OCollect(_1703742), hAPP(hAPP(c_COMBS(_1703742, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1703742), c_fconj), hAPP(hAPP(c_COMBC(_1703742, tc_fun(_1703742, tc_HOL_Obool), tc_HOL_Obool), c_member(_1703742)), hAPP(c_List_Oset(_1703742), _1703746)))), _1703744)))], (50145 ^ _776541) ^ [_1789757, _1789759, _1789761, _1789763, _1789765, _1789767, _1789769] : [c_Fun_Oinj__on(_1789757, _1789759, _1789761, hAPP(c_Set_Oimage(_1789763, _1789757, _1789765), _1789767)), c_Fun_Oinj__on(_1789763, _1789757, _1789765, _1789767), hBOOL(hAPP(hAPP(c_member(_1789759), _1789769), hAPP(c_Set_Oimage(_1789757, _1789759, _1789761), hAPP(c_Set_Oimage(_1789763, _1789757, _1789765), _1789767)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1789763, _1789759, _1789767, hAPP(c_Fun_Ocomp(_1789757, _1789759, _1789763, _1789761), _1789765)), _1789769) = hAPP(hAPP(c_Fun_Ocomp(_1789757, _1789763, _1789759, c_Hilbert__Choice_Oinv__into(_1789763, _1789757, _1789767, _1789765)), c_Hilbert__Choice_Oinv__into(_1789757, _1789759, hAPP(c_Set_Oimage(_1789763, _1789757, _1789765), _1789767), _1789761)), _1789769))], (28609 ^ _776541) ^ [_1289715] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1289715)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1289715)))], (45764 ^ _776541) ^ [_1694787, _1694789, _1694791] : [hBOOL(hAPP(c_List_Odistinct(_1694787), _1694789)), -(hBOOL(hAPP(c_List_Odistinct(_1694787), hAPP(c_List_OremoveAll(_1694787, _1694791), _1694789))))], (42125 ^ _776541) ^ [_1611269, _1611271, _1611273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611269, tc_HOL_Obool)), _1611271), _1611273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1611269), tc_HOL_Obool)), c_List_Olists(_1611269, _1611271)), c_List_Olists(_1611269, _1611273))))], (29463 ^ _776541) ^ [_1304433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1304433), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1304433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1304433 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29283 ^ _776541) ^ [] : [-(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))))))], (26082 ^ _776541) ^ [_1247944, _1247946] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247944))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247944), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247946)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18448 ^ _776541) ^ [_1108488, _1108490, _1108492, _1108494] : [class_Rings_Olinordered__ring__strict(_1108488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108488), _1108490), c_Groups_Ozero__class_Ozero(_1108488))), 18455 ^ _776541 : [(18462 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108488), _1108494), _1108492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108488), _1108490), _1108492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108488), _1108490), _1108494))))], (18456 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108488), _1108490), _1108492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108488), _1108490), _1108494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108488), _1108494), _1108492)))]]], (36065 ^ _776541) ^ [_1455354, _1455356, _1455358] : [class_Orderings_Olinorder(_1455354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455354), _1455356)), -(_1455356 = c_Orderings_Obot__class_Obot(tc_fun(_1455354, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1455354), _1455358), c_Big__Operators_Olattice_OSup__fin(_1455354, c_Orderings_Oord__class_Omax(_1455354), _1455356)) = c_Big__Operators_Olattice_OSup__fin(_1455354, c_Orderings_Oord__class_Omax(_1455354), hAPP(c_Set_OCollect(_1455354), hAPP(hAPP(c_COMBB(tc_fun(_1455354, tc_HOL_Obool), tc_HOL_Obool, _1455354), c_HOL_OEx(_1455354)), hAPP(hAPP(c_COMBC(_1455354, tc_fun(_1455354, tc_HOL_Obool), tc_fun(_1455354, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455354, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1455354, tc_HOL_Obool), tc_fun(_1455354, tc_HOL_Obool)), _1455354), c_COMBS(_1455354, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455354, tc_HOL_Obool), tc_fun(_1455354, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1455354), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1455354), c_fconj)), hAPP(hAPP(c_COMBC(_1455354, tc_fun(_1455354, _1455354), tc_fun(_1455354, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455354, tc_HOL_Obool), tc_fun(tc_fun(_1455354, _1455354), tc_fun(_1455354, tc_HOL_Obool)), _1455354), c_COMBB(_1455354, tc_HOL_Obool, _1455354)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1455354), _1455358))))), hAPP(hAPP(c_COMBC(_1455354, tc_fun(_1455354, tc_HOL_Obool), tc_HOL_Obool), c_member(_1455354)), _1455356))))))], (33407 ^ _776541) ^ [_1390041, _1390043, _1390045, _1390047, _1390049] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390041, tc_fun(_1390043, tc_HOL_Obool)), _1390045), _1390047), _1390049))), 33408 ^ _776541 : [(33409 ^ _776541) ^ [_1390113] : [hBOOL(hAPP(hAPP(c_member(_1390041), _1390113), _1390045)), hBOOL(hAPP(hAPP(_1390047, _1390113), _1390049))]]], (3214 ^ _776541) ^ [_824389, _824391, _824393, _824395, _824397, _824399] : [-(c_Big__Operators_Olattice_OInf__fin(_824399, _824395, _824391) = c_Big__Operators_Olattice_OInf__fin(_824397, _824393, _824389)), _824399 = _824397, _824395 = _824393, _824391 = _824389], (27090 ^ _776541) ^ [_1264300, _1264302] : [class_Rings_Olinordered__idom(_1264300), 27093 ^ _776541 : [(27100 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1264302), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264300), hAPP(c_Int_Oring__1__class_Oof__int(_1264300), _1264302)), c_Groups_Ozero__class_Ozero(_1264300))))], (27094 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264300), hAPP(c_Int_Oring__1__class_Oof__int(_1264300), _1264302)), c_Groups_Ozero__class_Ozero(_1264300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1264302), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (24954 ^ _776541) ^ [_1228412, _1228414, _1228416] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228412), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228414, _1228416)), _1228416) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228412), _1228414), _1228416))], (4876 ^ _776541) ^ [_850848, _850850, _850852, _850854, _850856, _850858] : [-(c_Relation_Orel__comp(_850858, _850854, _850850) = c_Relation_Orel__comp(_850856, _850852, _850848)), _850858 = _850856, _850854 = _850852, _850850 = _850848], (32510 ^ _776541) ^ [_1363663, _1363665, _1363667, _1363669, _1363671] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363663, tc_HOL_Obool)), _1363665), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363667, tc_fun(_1363663, tc_HOL_Obool)), _1363669), _1363671)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363667, tc_fun(_1363663, tc_HOL_Obool)), _1363669), hAPP(hAPP(c_COMBB(tc_fun(_1363663, tc_HOL_Obool), tc_fun(_1363663, tc_HOL_Obool), _1363667), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363663, tc_HOL_Obool)), _1363665)), _1363671)))], (18033 ^ _776541) ^ [_1100818, _1100820, _1100822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100818), _1100820)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100822), _1100820))), 18036 ^ _776541 : [(18039 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100818), _1100822)))], (18037 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100820)))]]], (51155 ^ _776541) ^ [_1812402, _1812404, _1812406, _1812408, _1812410] : [class_Divides_Osemiring__div(_1812402), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812402), _1812404), _1812406)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812402), _1812408), _1812410)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812402), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812402), _1812406), _1812404)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812402), _1812410), _1812408)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812402), _1812406), _1812410)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812402), _1812404), _1812408)))], (40345 ^ _776541) ^ [_1563198, _1563200] : [40347 ^ _776541 : [(40350 ^ _776541) ^ [] : [40346 ^ [_1563198, _1563200] = c_Orderings_Obot__class_Obot(tc_fun(_1563198, tc_HOL_Obool))], (40348 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563198, tc_HOL_Obool)), 40346 ^ [_1563198, _1563200]), hAPP(c_Relation_OImage(_1563198, _1563198, _1563200), 40346 ^ [_1563198, _1563200]))))]], -(c_Wellfounded_Owf(_1563198, _1563200))], (24443 ^ _776541) ^ [_1218496, _1218498, _1218500] : [hBOOL(hAPP(_1218496, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1218498), _1218500))), 24446 ^ _776541 : [(24471 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218500), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24474 ^ _776541 : [(24475 ^ _776541) ^ [_1219160] : [-(hBOOL(hAPP(_1218496, _1219160))), 24476 ^ _776541 : [(24477 ^ _776541) ^ [_1219234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218500), _1219234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1219234), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1218498 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218500), _1219160)), _1219234)]]]]], (24453 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218500)), 24456 ^ _776541 : [(24457 ^ _776541) ^ [_1218830] : [-(hBOOL(hAPP(_1218496, _1218830))), 24458 ^ _776541 : [(24459 ^ _776541) ^ [_1218901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218901), _1218500)), _1218498 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218500), _1218830)), _1218901)]]]]], (24447 ^ _776541) ^ [] : [_1218500 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1218496, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14542 ^ _776541) ^ [_1038818, _1038820, _1038822] : [_1038820 = _1038822, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038818), _1038820) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038818), _1038822))], (31685 ^ _776541) ^ [_1345546, _1345548, _1345550] : [class_Groups_Olinordered__ab__group__add(_1345546), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1345546), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345546), _1345548), _1345550)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345546), hAPP(c_Groups_Ouminus__class_Ouminus(_1345546), _1345548)), hAPP(c_Groups_Ouminus__class_Ouminus(_1345546), _1345550)))], (16671 ^ _776541) ^ [_1076401, _1076403] : [16672 ^ _776541 : [(16673 ^ _776541) ^ [_1076454] : [_1076403 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076401), _1076454))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076401), _1076403)))], (13288 ^ _776541) ^ [_1012002, _1012004, _1012006, _1012008] : [hBOOL(hAPP(hAPP(c_member(_1012002), _1012004), _1012006)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012002, tc_Nat_Onat), _1012008), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012002, tc_HOL_Obool)), _1012006), hAPP(hAPP(c_Set_Oinsert(_1012002), _1012004), c_Orderings_Obot__class_Obot(tc_fun(_1012002, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012002, tc_Nat_Onat), _1012008), _1012006)), hAPP(_1012008, _1012004)))], (46478 ^ _776541) ^ [_1711447, _1711449] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1711447, _1711449)))], (15144 ^ _776541) ^ [_1049909, _1049911] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049909), _1049911)), _1049909 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1049911 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (43651 ^ _776541) ^ [_1647143, _1647145, _1647147] : [_1647143 = _1647145, -(_1647143 = hAPP(hAPP(c_List_Oappend(_1647147), c_List_Olist_ONil(_1647147)), _1647145))], (24768 ^ _776541) ^ [_1224530] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1224530, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35850 ^ _776541) ^ [_1446438, _1446440, _1446442, _1446444, _1446446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1446438, _1446440)), hAPP(_1446438, _1446442))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446444, _1446444)), hAPP(hAPP(c_Product__Type_OPair(_1446444, _1446444), _1446440), _1446442)), c_Wellfounded_Omlex__prod(_1446444, _1446438, _1446446))))], (3954 ^ _776541) ^ [_836093, _836095, _836097, _836099, _836101, _836103, _836105, _836107, _836109, _836111, _836113, _836115, _836117, _836119] : [-(c_New__Random__Sequence_Opos__decr__bind(_836119, _836115, _836111, _836107, _836103, _836099, _836095) = c_New__Random__Sequence_Opos__decr__bind(_836117, _836113, _836109, _836105, _836101, _836097, _836093)), _836119 = _836117, _836115 = _836113, _836111 = _836109, _836107 = _836105, _836103 = _836101, _836099 = _836097, _836095 = _836093], (31437 ^ _776541) ^ [_1341046, _1341048, _1341050, _1341052] : [class_Orderings_Olinorder(_1341046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341046), _1341048), _1341050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341046), _1341052), _1341050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341046), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341046), _1341048), _1341052)), _1341050)))], (30040 ^ _776541) ^ [_1315240, _1315242, _1315244] : [class_Orderings_Olinorder(_1315240), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315240), _1315242), _1315244) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315240), _1315244), _1315242))], (34209 ^ _776541) ^ [_1412549, _1412551] : [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(_1412551))), 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), _1412549)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412549)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412551))))], (38410 ^ _776541) ^ [_1512862, _1512864] : [-(c_List_Olex(_1512862, _1512864) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1512862), tc_List_Olist(_1512862)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1512862, _1512864)))], (49360 ^ _776541) ^ [_1772967, _1772969, _1772971] : [c_List_Olist__ex(_1772967, _1772971, _1772969), 49364 ^ _776541 : [(49367 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1772971, 49363 ^ [_1772967, _1772969, _1772971])))], (49365 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772967), 49363 ^ [_1772967, _1772969, _1772971]), hAPP(c_List_Oset(_1772967), _1772969))))]]], (9284 ^ _776541) ^ [_936363, _936365, _936367] : [class_Orderings_Olinorder(_936363), 9287 ^ _776541 : [(9288 ^ _776541) ^ [] : [-(_936365 = _936367), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936363), _936365), _936367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936363), _936367), _936365)))], (9298 ^ _776541) ^ [] : [9299 ^ _776541 : [(9302 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936363), _936367), _936365))], (9300 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936363), _936365), _936367))]], _936365 = _936367]]], (39649 ^ _776541) ^ [_1545839, _1545841, _1545843] : [c_Relation_Orefl__on(_1545839, _1545841, _1545843), 39652 ^ _776541 : [(39659 ^ _776541) ^ [_1546323] : [hBOOL(hAPP(hAPP(c_member(_1545839), _1546323), _1545841)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545839, _1545839)), hAPP(hAPP(c_Product__Type_OPair(_1545839, _1545839), _1546323), _1546323)), _1545843)))], (39653 ^ _776541) ^ [_1546050] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545839, _1545839)), _1546050), _1545843)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545839, _1545839, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1545839, tc_fun(_1545839, tc_HOL_Obool), tc_fun(_1545839, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1545839, tc_HOL_Obool), tc_fun(_1545839, tc_HOL_Obool)), _1545839), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545839)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545839), c_fconj), hAPP(hAPP(c_COMBC(_1545839, tc_fun(_1545839, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545839)), _1545841)))), hAPP(hAPP(c_COMBC(_1545839, tc_fun(_1545839, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545839)), _1545841))), _1546050)))]]], (47002 ^ _776541) ^ [_1721259, _1721261] : [_1721261 = c_List_Olist_ONil(_1721259), -(c_List_Olist_ONil(_1721259) = hAPP(c_List_Orev(_1721259), _1721261))], (19131 ^ _776541) ^ [_1121270, _1121272, _1121274, _1121276, _1121278, _1121280, _1121282] : [c_Big__Operators_Ocomm__monoid__big(_1121270, _1121272, _1121274, _1121276, _1121278), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1121272), _1121280))), -(hAPP(hAPP(_1121278, _1121282), _1121280) = _1121276)], (29191 ^ _776541) ^ [_1299737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1299737)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299737), c_Int_OMin)))], (10949 ^ _776541) ^ [_965691, _965693, _965695] : [-(hAPP(c_Set_OPow(_965691), hAPP(hAPP(c_Set_Oinsert(_965691), _965693), _965695)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_965691, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_965691), _965695)), hAPP(c_Set_Oimage(tc_fun(_965691, tc_HOL_Obool), tc_fun(_965691, tc_HOL_Obool), hAPP(c_Set_Oinsert(_965691), _965693)), hAPP(c_Set_OPow(_965691), _965695))))], (42603 ^ _776541) ^ [_1624752] : [42605 ^ _776541 : [(42608 ^ _776541) ^ [] : [42604 ^ [_1624752] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42606 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42604 ^ [_1624752]), hAPP(c_List_Oset(tc_Nat_Onat), _1624752))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1624752) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35252 ^ _776541) ^ [_1434402, _1434404] : [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), _1434402), _1434404))), 35255 ^ _776541 : [(35262 ^ _776541) ^ [] : [-(_1434404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1434402, _1434404) = c_Nitpick_Onat__gcd(_1434404, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1434402, _1434404)))], (35256 ^ _776541) ^ [] : [_1434404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1434402, _1434404) = _1434402)]]], (7670 ^ _776541) ^ [_904397, _904399, _904401] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904397, tc_HOL_Obool)), _904399), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904397, tc_HOL_Obool)), _904399), _904401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904397, tc_HOL_Obool)), _904399), _904401))], (49074 ^ _776541) ^ [_1766403, _1766405, _1766407] : [c_List_Olist__ex(tc_Int_Oint, _1766403, c_List_Oupto(_1766405, _1766407)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1766403), _1766405, _1766407)], (14560 ^ _776541) ^ [_1039145, _1039147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039145), _1039147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039147), _1039145)), -(_1039145 = _1039147)], (43870 ^ _776541) ^ [_1653050, _1653052, _1653054, _1653056] : [-(hAPP(hAPP(c_List_Odrop(_1653050), hAPP(c_Nat_OSuc, _1653052)), hAPP(hAPP(c_List_Olist_OCons(_1653050), _1653054), _1653056)) = hAPP(hAPP(c_List_Odrop(_1653050), _1653052), _1653056))], (480 ^ _776541) ^ [_783753, _783755] : [-(c_Nat__Transfer_Onat__set(_783753)), _783755 = _783753, c_Nat__Transfer_Onat__set(_783755)], (49125 ^ _776541) ^ [_1767630, _1767632, _1767634, _1767636] : [-(c_Random__Sequence_Omap(_1767630, _1767632, _1767634, _1767636) = c_Random__Sequence_Obind(_1767630, _1767632, _1767636, hAPP(c_Fun_Ocomp(_1767632, 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(_1767632)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1767630, c_Random__Sequence_Osingle(_1767632)), _1767634)))], (7430 ^ _776541) ^ [_898843, _898845, _898847] : [class_Orderings_Olinorder(_898843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898843), _898845), _898847)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898843, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_898843, _898845, _898847)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_898843), _898847)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_898843), _898845))], (19613 ^ _776541) ^ [_1130898, _1130900, _1130902, _1130904] : [class_Rings_Odivision__ring(_1130898), -(_1130900 = c_Groups_Ozero__class_Ozero(_1130898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130898), _1130902), _1130900) = _1130904, -(_1130902 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130898), _1130904), _1130900))], (4760 ^ _776541) ^ [_848990, _848992, _848994, _848996] : [-(c_Product__Type_Ofst(_848996, _848992) = c_Product__Type_Ofst(_848994, _848990)), _848996 = _848994, _848992 = _848990], (38794 ^ _776541) ^ [_1522293, _1522295, _1522297, _1522299] : [-(hAPP(c_Set_Ovimage(_1522293, _1522295, _1522297), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1522295, tc_HOL_Obool), _1522299)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1522295, tc_HOL_Obool), tc_fun(_1522293, tc_HOL_Obool)), _1522299), c_Set_Ovimage(_1522293, _1522295, _1522297)))], (41180 ^ _776541) ^ [_1584220, _1584222, _1584224, _1584226] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584220, _1584220)), hAPP(hAPP(c_Product__Type_OPair(_1584220, _1584220), _1584222), _1584224)), hAPP(c_Relation_Oconverse(_1584220, _1584220), c_Transitive__Closure_Otrancl(_1584220, _1584226)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584220, _1584220)), hAPP(hAPP(c_Product__Type_OPair(_1584220, _1584220), _1584222), _1584224)), c_Transitive__Closure_Otrancl(_1584220, hAPP(c_Relation_Oconverse(_1584220, _1584220), _1584226)))))], (45205 ^ _776541) ^ [_1682028, _1682030] : [hAPP(c_Code__Numeral_Onat__of, _1682028) = hAPP(c_Code__Numeral_Onat__of, _1682030), -(_1682028 = _1682030)], (26673 ^ _776541) ^ [_1257911, _1257913] : [-(c_Int_Onat__aux(_1257911, _1257913) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1257911)), _1257913))], (42727 ^ _776541) ^ [_1627451, _1627453, _1627455, _1627457] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627451, tc_HOL_Obool)), hAPP(c_List_Oset(_1627451), hAPP(hAPP(c_List_Olist__update(_1627451, _1627453), _1627455), _1627457))), hAPP(hAPP(c_Set_Oinsert(_1627451), _1627457), hAPP(c_List_Oset(_1627451), _1627453)))))], (40969 ^ _776541) ^ [_1578949, _1578951, _1578953, _1578955] : [hBOOL(hAPP(hAPP(c_member(_1578949), _1578951), c_Wellfounded_Oacc(_1578949, _1578953))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578949, _1578949)), hAPP(hAPP(c_Product__Type_OPair(_1578949, _1578949), _1578955), _1578951)), c_Transitive__Closure_Ortrancl(_1578949, _1578953))), -(hBOOL(hAPP(hAPP(c_member(_1578949), _1578955), c_Wellfounded_Oacc(_1578949, _1578953))))], (9970 ^ _776541) ^ [_947205, _947207, _947209] : [class_Orderings_Oorder(_947205), 9973 ^ _776541 : [(9980 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947205), _947207), _947209))), -(c_Orderings_Obot__class_Obot(tc_fun(_947205, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_947205, _947207, _947209))], (9974 ^ _776541) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_947205, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_947205, _947207, _947209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947205), _947207), _947209))]]], (31485 ^ _776541) ^ [_1341866, _1341868, _1341870, _1341872] : [class_Orderings_Olinorder(_1341866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341866), _1341868), _1341870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341866), _1341868), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341866), _1341872), _1341870))))], (45257 ^ _776541) ^ [_1682911] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1682911), 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, _1682911)) = _1682911)], (18206 ^ _776541) ^ [_1103911, _1103913, _1103915] : [class_Groups_Oordered__comm__monoid__add(_1103911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103911), _1103913), c_Groups_Ozero__class_Ozero(_1103911))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103911), _1103915), c_Groups_Ozero__class_Ozero(_1103911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103911), _1103913), _1103915)), c_Groups_Ozero__class_Ozero(_1103911))))], (48760 ^ _776541) ^ [_1759157, _1759159, _1759161] : [-(hAPP(c_List_Oset(_1759157), c_List_Oreplicate(_1759157, hAPP(c_Nat_OSuc, _1759159), _1759161)) = hAPP(hAPP(c_Set_Oinsert(_1759157), _1759161), c_Orderings_Obot__class_Obot(tc_fun(_1759157, tc_HOL_Obool))))], (22263 ^ _776541) ^ [_1180303, _1180305] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180303), _1180305))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180303), _1180305)), -(_1180303 = _1180305)], (2270 ^ _776541) ^ [_809601, _809603, _809605, _809607] : [-(c_Orderings_Oord_Omax(_809607, _809603) = c_Orderings_Oord_Omax(_809605, _809601)), _809607 = _809605, _809603 = _809601], (49054 ^ _776541) ^ [_1766027, _1766029] : [-(c_Lazy__Sequence_Oappend(_1766027, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766027), _1766029) = _1766029)], (49932 ^ _776541) ^ [_1784965, _1784967, _1784969, _1784971] : [c_Equiv__Relations_Opart__equivp(_1784965, _1784967), hBOOL(hAPP(hAPP(_1784967, _1784969), _1784971)), -(hBOOL(hAPP(hAPP(_1784967, _1784971), _1784969)))], (15360 ^ _776541) ^ [_1053907, _1053909, _1053911] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053907), _1053909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1053907), _1053909)), hAPP(c_Finite__Set_Ocard(_1053907), hAPP(hAPP(c_Set_Oinsert(_1053907), _1053911), _1053909)))))], (44208 ^ _776541) ^ [_1660476, _1660478, _1660480] : [-(hAPP(c_List_Orotate(_1660476, _1660478), _1660480) = hAPP(c_List_Orotate(_1660476, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1660478, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660476)), _1660480))), _1660480))], (24754 ^ _776541) ^ [_1224338, _1224340] : [class_Divides_Osemiring__div(_1224338), -(c_Divides_Odiv__class_Omod(_1224338, _1224340, c_Groups_Ozero__class_Ozero(_1224338)) = _1224340)], (52223 ^ _776541) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (10653 ^ _776541) ^ [_959777, _959779, _959781] : [class_Lattices_Oboolean__algebra(_959777), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959777), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959777), _959779), _959781)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959777), hAPP(c_Groups_Ouminus__class_Ouminus(_959777), _959779)), hAPP(c_Groups_Ouminus__class_Ouminus(_959777), _959781)))], (33030 ^ _776541) ^ [_1379707, _1379709, _1379711, _1379713] : [-(_1379707 = c_Orderings_Obot__class_Obot(tc_fun(_1379709, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1379709, _1379711, hAPP(c_COMBK(_1379711, _1379709), _1379713)), _1379707) = hAPP(hAPP(c_Set_Oinsert(_1379711), _1379713), c_Orderings_Obot__class_Obot(tc_fun(_1379711, tc_HOL_Obool))))], (49325 ^ _776541) ^ [_1772292, _1772294, _1772296, _1772298] : [c_Relation_Otrans(_1772292, _1772294), -(c_Relation_Otrans(_1772296, hAPP(hAPP(c_Relation_Oinv__image(_1772292, _1772296), _1772294), _1772298)))], (6154 ^ _776541) ^ [_875261, _875263, _875265, _875267] : [hBOOL(hAPP(hAPP(c_member(_875261), _875263), c_Complete__Lattice_OInf__class_OInf(tc_fun(_875261, tc_HOL_Obool), _875265))), hBOOL(hAPP(hAPP(c_member(tc_fun(_875261, tc_HOL_Obool)), _875267), _875265)), -(hBOOL(hAPP(hAPP(c_member(_875261), _875263), _875267)))], (41524 ^ _776541) ^ [_1592732, _1592734, _1592736, _1592738, _1592740] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592732, _1592732)), hAPP(hAPP(c_Product__Type_OPair(_1592732, _1592732), _1592734), _1592736)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592732, _1592732), tc_HOL_Obool), _1592738), _1592740))), 41529 ^ _776541 : [(41532 ^ _776541) ^ [] : [-(_1592734 = _1592736)], (41530 ^ _776541) ^ [] : [-(_1592738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41535 ^ _776541 : [(41540 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592732, _1592732)), hAPP(hAPP(c_Product__Type_OPair(_1592732, _1592732), 41533 ^ [_1592732, _1592734, _1592736, _1592738, _1592740]), _1592736)), _1592740)))], (41538 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592732, _1592732)), hAPP(hAPP(c_Product__Type_OPair(_1592732, _1592732), _1592734), 41533 ^ [_1592732, _1592734, _1592736, _1592738, _1592740])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592732, _1592732), tc_HOL_Obool), 41534 ^ [_1592732, _1592734, _1592736, _1592738, _1592740]), _1592740))))], (41536 ^ _776541) ^ [] : [-(_1592738 = hAPP(c_Nat_OSuc, 41534 ^ [_1592732, _1592734, _1592736, _1592738, _1592740]))]]], (11930 ^ _776541) ^ [_986012, _986014, _986016, _986018, _986020, _986022, _986024] : [-(_986012 = _986014), -(c_Fun_Ofun__upd(_986016, _986018, c_Fun_Ofun__upd(_986016, _986018, _986020, _986012, _986022), _986014, _986024) = c_Fun_Ofun__upd(_986016, _986018, c_Fun_Ofun__upd(_986016, _986018, _986020, _986014, _986024), _986012, _986022))], (19807 ^ _776541) ^ [_1134004, _1134006, _1134008, _1134010] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1134004, _1134006)), c_Sum__Type_OPlus(_1134004, _1134006, _1134008, _1134010))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1134004), _1134008)))], (32444 ^ _776541) ^ [_1360569, _1360571, _1360573, _1360575, _1360577] : [-(_1360569 = c_Orderings_Obot__class_Obot(tc_fun(_1360571, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360573, tc_HOL_Obool)), _1360575), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360571, tc_fun(_1360573, tc_HOL_Obool)), _1360569), _1360577)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360571, tc_fun(_1360573, tc_HOL_Obool)), _1360569), hAPP(hAPP(c_COMBB(tc_fun(_1360573, tc_HOL_Obool), tc_fun(_1360573, tc_HOL_Obool), _1360571), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360573, tc_HOL_Obool)), _1360575)), _1360577)))], (49458 ^ _776541) ^ [_1776372, _1776374] : [-(c_Equiv__Relations_Oequivp(_1776372, _1776374)), c_Predicate_Oreflp(_1776372, _1776374), c_Predicate_Osymp(_1776372, _1776374), c_Predicate_Otransp(_1776372, _1776374)], (31210 ^ _776541) ^ [_1336568, _1336570, _1336572] : [class_Orderings_Olinorder(_1336568), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336568), _1336570)), hBOOL(hAPP(hAPP(c_member(_1336568), _1336572), _1336570)), 31221 ^ _776541 : [(31228 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336568, tc_HOL_Obool)), _1336570), hAPP(hAPP(c_Set_Oinsert(_1336568), _1336572), c_Orderings_Obot__class_Obot(tc_fun(_1336568, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1336568, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1336568, _1336570) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1336568), _1336572), c_Big__Operators_Olinorder__class_OMax(_1336568, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336568, tc_HOL_Obool)), _1336570), hAPP(hAPP(c_Set_Oinsert(_1336568), _1336572), c_Orderings_Obot__class_Obot(tc_fun(_1336568, tc_HOL_Obool)))))))], (31222 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336568, tc_HOL_Obool)), _1336570), hAPP(hAPP(c_Set_Oinsert(_1336568), _1336572), c_Orderings_Obot__class_Obot(tc_fun(_1336568, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1336568, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1336568, _1336570) = _1336572)]]], (45704 ^ _776541) ^ [_1693413, _1693415, _1693417, _1693419] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693413)), _1693415), hAPP(c_List_Oset(tc_List_Olist(_1693413)), c_Enum_On__lists(_1693413, _1693417, _1693419)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693413)), _1693415) = _1693417)], (31405 ^ _776541) ^ [_1340393, _1340395, _1340397, _1340399] : [class_Groups_Oordered__ab__group__add(_1340393), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1340393), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340393), _1340395), _1340397)), _1340399) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1340393), _1340395), _1340399)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1340393), _1340397), _1340399)))], (52165 ^ _776541) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (24305 ^ _776541) ^ [_1216093] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1216093)) = 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), _1216093)))], (43458 ^ _776541) ^ [_1643105, _1643107, _1643109, _1643111] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643105)), hAPP(hAPP(c_List_Oappend(_1643105), _1643107), _1643109)), c_List_Olists(_1643105, _1643111))), 43461 ^ _776541 : [(43464 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643105)), _1643109), c_List_Olists(_1643105, _1643111))))], (43462 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643105)), _1643107), c_List_Olists(_1643105, _1643111))))]]], (35531 ^ _776541) ^ [_1439469, _1439471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439471), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439469, _1439471) = 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), _1439469), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1439471)))))], (33188 ^ _776541) ^ [_1384536, _1384538, _1384540] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384536), hAPP(c_Set_OCollect(_1384536), hAPP(hAPP(c_COMBS(_1384536, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1384536), c_fdisj), _1384538)), _1384540)))), 33191 ^ _776541 : [(33194 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1384536), hAPP(c_Set_OCollect(_1384536), _1384540))))], (33192 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1384536), hAPP(c_Set_OCollect(_1384536), _1384538))))]]], (5995 ^ _776541) ^ [_872108, _872110, _872112, _872114] : [hBOOL(hAPP(hAPP(c_member(_872108), _872110), c_SetInterval_Oord_OatMost(_872108, _872112, _872114))), -(hBOOL(hAPP(hAPP(_872112, _872110), _872114)))], (43104 ^ _776541) ^ [_1635373, _1635375] : [_1635375 = c_List_Olist_ONil(_1635373), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635373)), _1635375) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7674 ^ _776541) ^ [_904517, _904519, _904521] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904517, tc_HOL_Obool)), _904519), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904517, tc_HOL_Obool)), _904519), _904521)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904517, tc_HOL_Obool)), _904519), _904521))], (4208 ^ _776541) ^ [_840314, _840316, _840318, _840320, _840322, _840324] : [-(c_Predicate_Oconversep(_840324, _840320, _840316) = c_Predicate_Oconversep(_840322, _840318, _840314)), _840324 = _840322, _840320 = _840318, _840316 = _840314], (9394 ^ _776541) ^ [_938182, _938184, _938186] : [class_Orderings_Olinorder(_938182), 9397 ^ _776541 : [(9404 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938182), _938186), _938184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938182), _938184), _938186))], (9398 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938182), _938184), _938186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938182), _938186), _938184)))]]], (29779 ^ _776541) ^ [_1310593, _1310595] : [_1310593 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1310593, _1310595) = _1310595)], (29922 ^ _776541) ^ [_1313139, _1313141, _1313143] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1313139), _1313141))), -(c_Random_Ominus__shift(_1313143, _1313139, _1313141) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1313139), _1313141))], (38764 ^ _776541) ^ [_1521617, _1521619] : [-(hAPP(c_Relation_ODomain(_1521617, _1521619), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521617, _1521619), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1521617, tc_HOL_Obool)))], (47365 ^ _776541) ^ [_1728972, _1728974, _1728976] : [-(c_List_OdropWhile(_1728972, _1728974, _1728976) = c_List_Olist_ONil(_1728972)), hBOOL(hAPP(_1728974, hAPP(c_List_Ohd(_1728972), c_List_OdropWhile(_1728972, _1728974, _1728976))))], (4840 ^ _776541) ^ [_850214, _850216, _850218, _850220] : [-(c_Complete__Lattice_OInf__class_OInf(_850220, _850216) = c_Complete__Lattice_OInf__class_OInf(_850218, _850214)), _850220 = _850218, _850216 = _850214], (22383 ^ _776541) ^ [_1182331] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1182331), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1182331)], (34129 ^ _776541) ^ [_1410683, _1410685] : [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(_1410683))), 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)), _1410685))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410683) = hAPP(c_Nat_OSuc, _1410685))], (11012 ^ _776541) ^ [_966833, _966835, _966837] : [_966835 = _966837, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966833, tc_HOL_Obool)), _966835) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966833, tc_HOL_Obool)), _966837))], (32638 ^ _776541) ^ [_1368948, _1368950, _1368952, _1368954, _1368956] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1368948, tc_fun(_1368950, tc_HOL_Obool)), _1368952), hAPP(hAPP(c_COMBS(_1368948, tc_fun(_1368950, tc_HOL_Obool), tc_fun(_1368950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368950, tc_HOL_Obool), tc_fun(tc_fun(_1368950, tc_HOL_Obool), tc_fun(_1368950, tc_HOL_Obool)), _1368948), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368950, tc_HOL_Obool))), _1368954)), _1368956)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368950, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1368948, tc_fun(_1368950, tc_HOL_Obool)), _1368952), _1368954)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1368948, tc_fun(_1368950, tc_HOL_Obool)), _1368952), _1368956)))], (10980 ^ _776541) ^ [_966339, _966341, _966343] : [class_Rings_Olinordered__idom(_966339), -(_966341 = _966343), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966339), _966341), _966343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966339), _966343), _966341)))], (23641 ^ _776541) ^ [_1205003, _1205005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205005)), -(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), _1205003), _1205005))))], (3148 ^ _776541) ^ [_823410, _823412, _823414, _823416] : [-(c_Nat_Ocompow(_823416, _823412) = c_Nat_Ocompow(_823414, _823410)), _823416 = _823414, _823412 = _823410], (490 ^ _776541) ^ [_783878, _783880, _783882, _783884, _783886, _783888, _783890, _783892] : [-(c_List_Olistrelp(_783890, _783886, _783882, _783878)), c_List_Olistrelp(_783892, _783888, _783884, _783880), _783892 = _783890, _783888 = _783886, _783884 = _783882, _783880 = _783878], (6128 ^ _776541) ^ [_874787, _874789, _874791] : [6136 ^ _776541 : [(6139 ^ _776541) ^ [] : [-(hBOOL(hAPP(_874791, 6135 ^ [_874787, _874789, _874791])))], (6137 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874787), 6135 ^ [_874787, _874789, _874791]), _874789)))]], 6129 ^ _776541 : [(6130 ^ _776541) ^ [_874862] : [hBOOL(hAPP(hAPP(c_member(_874787), _874862), _874789)), hBOOL(hAPP(_874791, _874862))]]], (27036 ^ _776541) ^ [_1263474] : [class_Int_Onumber__ring(_1263474), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263474), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1263474), c_Int_OMin))], (52357 ^ _776541) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (2252 ^ _776541) ^ [_809346, _809348] : [_809348 = _809346, -(c_Nat_Onat_Onat__size(_809348) = c_Nat_Onat_Onat__size(_809346))], (33162 ^ _776541) ^ [_1384029, _1384031, _1384033] : [hBOOL(hAPP(hAPP(c_member(_1384029), _1384031), hAPP(c_Set_OCollect(_1384029), _1384033))), -(hBOOL(hAPP(_1384033, _1384031)))], (41280 ^ _776541) ^ [_1586475, _1586477, _1586479] : [c_Relation_Ototal__on(_1586475, _1586477, _1586479), -(c_Relation_Ototal__on(_1586475, _1586477, hAPP(c_Relation_Oconverse(_1586475, _1586475), _1586479)))], (34273 ^ _776541) ^ [_1414247, _1414249, _1414251] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414247), _1414249))), 34276 ^ _776541 : [(34283 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414251), _1414249))), -(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)), _1414247)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414251), _1414249)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34277 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414251), _1414249)), -(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)), _1414247)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414251), _1414249)) = 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))))]]], (21647 ^ _776541) ^ [_1168575, _1168577, _1168579, _1168581] : [class_Fields_Olinordered__field__inverse__zero(_1168575), class_Int_Onumber(_1168575), 21654 ^ _776541 : [(21655 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168575), _1168579), _1168581))), 21658 ^ _776541 : [(21665 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), c_Groups_Ozero__class_Ozero(_1168575)), _1168581))), 21668 ^ _776541 : [(21675 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), _1168581), c_Groups_Ozero__class_Ozero(_1168575)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), c_Groups_Ozero__class_Ozero(_1168575))))], (21669 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), _1168581), c_Groups_Ozero__class_Ozero(_1168575))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), _1168579), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), _1168581))))]]], (21659 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), c_Groups_Ozero__class_Ozero(_1168575)), _1168581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), _1168581)), _1168579)))]]], (21681 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168575), _1168579), _1168581)))), 21684 ^ _776541 : [(21687 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), _1168581)), _1168579))], (21685 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), c_Groups_Ozero__class_Ozero(_1168575)), _1168581)))]], 21688 ^ _776541 : [(21691 ^ _776541) ^ [] : [21692 ^ _776541 : [(21695 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), _1168579), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), _1168581)))], (21693 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), _1168581), c_Groups_Ozero__class_Ozero(_1168575))))]], 21696 ^ _776541 : [(21699 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), hAPP(c_Int_Onumber__class_Onumber__of(_1168575), _1168577)), c_Groups_Ozero__class_Ozero(_1168575)))], (21697 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), _1168581), c_Groups_Ozero__class_Ozero(_1168575)))]]], (21689 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168575), c_Groups_Ozero__class_Ozero(_1168575)), _1168581))]]]]], (22675 ^ _776541) ^ [_1187456] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187456) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5150 ^ _776541) ^ [_855125, _855127] : [_855127 = _855125, -(c_Finite__Set_Ocard(_855127) = c_Finite__Set_Ocard(_855125))], (37708 ^ _776541) ^ [_1494802, _1494804, _1494806, _1494808, _1494810] : [-(c_Fun_Oinj__on(_1494802, _1494804, _1494806, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494802, tc_HOL_Obool)), _1494808), _1494810))), c_Fun_Oinj__on(_1494802, _1494804, _1494806, _1494808), c_Fun_Oinj__on(_1494802, _1494804, _1494806, _1494810), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494804, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1494802, _1494804, _1494806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494802, tc_HOL_Obool)), _1494808), _1494810))), hAPP(c_Set_Oimage(_1494802, _1494804, _1494806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494802, tc_HOL_Obool)), _1494810), _1494808))) = c_Orderings_Obot__class_Obot(tc_fun(_1494804, tc_HOL_Obool))], (29755 ^ _776541) ^ [_1310098, _1310100, _1310102] : [29757 ^ _776541 : [(29760 ^ _776541) ^ [] : [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(_1310100, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29756 ^ [_1310098, _1310100, _1310102]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1310100, 29756 ^ [_1310098, _1310100, _1310102])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29758 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29756 ^ [_1310098, _1310100, _1310102]), _1310098)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1310100, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1310102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1310102), hAPP(_1310100, _1310098))), 29770 ^ _776541 : [(29773 ^ _776541) ^ [] : [-(hAPP(_1310100, 29769 ^ [_1310098, _1310100, _1310102]) = _1310102)], (29771 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29769 ^ [_1310098, _1310100, _1310102]), _1310098)))]]], (34191 ^ _776541) ^ [_1412129, _1412131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412129)), hAPP(c_Nat_OSuc, _1412131))), -(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(_1412129))), 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)), _1412131)))))], (46335 ^ _776541) ^ [_1708427, _1708429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708427), _1708429)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1708427, _1708429)) = _1708427)], (21439 ^ _776541) ^ [_1165051, _1165053, _1165055, _1165057] : [class_Fields_Ofield__inverse__zero(_1165051), class_Int_Onumber(_1165051), 21446 ^ _776541 : [(21447 ^ _776541) ^ [] : [_1165053 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165051), _1165055), hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057)), 21450 ^ _776541 : [(21457 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057) = c_Groups_Ozero__class_Ozero(_1165051), -(_1165053 = c_Groups_Ozero__class_Ozero(_1165051))], (21451 ^ _776541) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057) = c_Groups_Ozero__class_Ozero(_1165051)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165051), _1165053), hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057)) = _1165055)]]], (21463 ^ _776541) ^ [] : [-(_1165053 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165051), _1165055), hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057))), 21466 ^ _776541 : [(21469 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165051), _1165053), hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057)) = _1165055], (21467 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057) = c_Groups_Ozero__class_Ozero(_1165051)]], 21470 ^ _776541 : [(21473 ^ _776541) ^ [] : [_1165053 = c_Groups_Ozero__class_Ozero(_1165051)], (21471 ^ _776541) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1165051), _1165057) = c_Groups_Ozero__class_Ozero(_1165051))]]]]], (3344 ^ _776541) ^ [_826444, _826446, _826448, _826450] : [-(c_List_Olists(_826450, _826446) = c_List_Olists(_826448, _826444)), _826450 = _826448, _826446 = _826444], (35628 ^ _776541) ^ [_1441519, _1441521, _1441523] : [-(_1441519 = hAPP(hAPP(c_Product__Type_OPair(_1441521, _1441523), hAPP(c_Product__Type_Ofst(_1441521, _1441523), _1441519)), hAPP(c_Product__Type_Osnd(_1441521, _1441523), _1441519)))], (52511 ^ _776541) ^ [_1831603, _1831605] : [hBOOL(hAPP(hAPP(c_fconj, _1831603), _1831605)), -(hBOOL(_1831603))], (39069 ^ _776541) ^ [_1529066, _1529068, _1529070, _1529072, _1529074, _1529076] : [class_Groups_Ocomm__monoid__add(_1529066), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1529068, _1529066), hAPP(hAPP(c_COMBC(_1529068, tc_fun(_1529070, tc_HOL_Obool), _1529066), hAPP(hAPP(c_COMBB(tc_fun(_1529070, _1529066), tc_fun(tc_fun(_1529070, tc_HOL_Obool), _1529066), _1529068), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1529070, _1529066)), _1529072)), _1529074)), _1529076) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1529068, _1529070), _1529066), hAPP(c_Product__Type_Oprod_Oprod__case(_1529068, _1529070, _1529066), _1529072)), hAPP(hAPP(c_Product__Type_OSigma(_1529068, _1529070), _1529076), hAPP(c_COMBK(tc_fun(_1529070, tc_HOL_Obool), _1529068), _1529074))))], (39906 ^ _776541) ^ [_1553144, _1553146, _1553148, _1553150, _1553152, _1553154, _1553156, _1553158, _1553160] : [hAPP(c_Fun_Ocomp(_1553144, _1553146, _1553148, _1553150), _1553152) = hAPP(c_Fun_Ocomp(_1553154, _1553146, _1553148, _1553156), _1553158), -(hAPP(_1553150, hAPP(_1553152, _1553160)) = hAPP(_1553156, hAPP(_1553158, _1553160)))], (47291 ^ _776541) ^ [_1727268, _1727270, _1727272, _1727274, _1727276] : [hBOOL(hAPP(hAPP(c_member(_1727268), _1727270), hAPP(c_List_Oset(_1727268), _1727272))), -(hBOOL(hAPP(_1727274, _1727270))), -(c_List_OtakeWhile(_1727268, _1727274, hAPP(hAPP(c_List_Oappend(_1727268), _1727272), _1727276)) = c_List_OtakeWhile(_1727268, _1727274, _1727272))], (40845 ^ _776541) ^ [_1576128, _1576130, _1576132] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1576128, _1576130, _1576130), _1576132), c_Relation_OId(_1576130)) = _1576132)], (52381 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (2438 ^ _776541) ^ [_812333, _812335] : [_812335 = _812333, -(c_Divides_Oadjust(_812335) = c_Divides_Oadjust(_812333))], (10499 ^ _776541) ^ [_956929, _956931, _956933] : [hBOOL(hAPP(hAPP(c_member(_956929), _956931), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_956929, tc_HOL_Obool)), _956933))), hBOOL(hAPP(hAPP(c_member(_956929), _956931), _956933))], (20373 ^ _776541) ^ [_1144075, _1144077, _1144079] : [class_Fields_Olinordered__field(_1144075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144075), c_Groups_Ozero__class_Ozero(_1144075)), _1144077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144075), c_Groups_Ozero__class_Ozero(_1144075)), _1144079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144075), c_Groups_Ozero__class_Ozero(_1144075)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144075), _1144077), _1144079))))], (16664 ^ _776541) ^ [_1076288, _1076290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076288), _1076290)), -(_1076290 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076288), 16667 ^ [_1076288, _1076290])))], (30282 ^ _776541) ^ [_1319725, _1319727, _1319729, _1319731] : [class_Orderings_Olinorder(_1319725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319725), _1319727), _1319729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319725), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319725), _1319727), _1319731)), _1319729)))], (4178 ^ _776541) ^ [_839859, _839861] : [_839861 = _839859, -(c_New__Random__Sequence_Opos__single(_839861) = c_New__Random__Sequence_Opos__single(_839859))], (45185 ^ _776541) ^ [_1681689, _1681691] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1681689), _1681691) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1681689)), hAPP(c_Code__Numeral_Onat__of, _1681691))))], (23623 ^ _776541) ^ [_1204661, _1204663] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204661)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204663))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1204661), _1204663)))], (35917 ^ _776541) ^ [_1449012, _1449014, _1449016, _1449018] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449012), hAPP(c_Set_OCollect(_1449012), _1449014))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1449016), hAPP(c_Set_OCollect(_1449016), hAPP(hAPP(c_COMBB(tc_fun(_1449012, tc_HOL_Obool), tc_HOL_Obool, _1449016), c_HOL_OEx(_1449012)), hAPP(hAPP(c_COMBC(_1449016, tc_fun(_1449012, tc_HOL_Obool), tc_fun(_1449012, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449012, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1449012, tc_HOL_Obool), tc_fun(_1449012, tc_HOL_Obool)), _1449016), c_COMBS(_1449012, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449012, tc_HOL_Obool), tc_fun(_1449012, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1449016), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1449012), c_fconj)), hAPP(hAPP(c_COMBC(_1449016, tc_fun(_1449012, _1449016), tc_fun(_1449012, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449016, tc_HOL_Obool), tc_fun(tc_fun(_1449012, _1449016), tc_fun(_1449012, tc_HOL_Obool)), _1449016), c_COMBB(_1449016, tc_HOL_Obool, _1449012)), c_fequal)), _1449018)))), _1449014))))))], (45084 ^ _776541) ^ [] : [-(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))], (16713 ^ _776541) ^ [_1077178, _1077180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077178), _1077180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077178), hAPP(c_Nat_OSuc, _1077180))))], (38961 ^ _776541) ^ [_1526591, _1526593, _1526595, _1526597] : [hBOOL(hAPP(hAPP(c_member(_1526591), _1526597), hAPP(c_Relation_ODomain(_1526591, _1526593), _1526595))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1526591, _1526593, hAPP(hAPP(c_COMBC(_1526591, tc_fun(tc_prod(_1526591, _1526593), tc_HOL_Obool), tc_fun(_1526593, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526593, tc_fun(tc_fun(tc_prod(_1526591, _1526593), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526591, _1526593), tc_HOL_Obool), tc_fun(_1526593, tc_HOL_Obool)), _1526591), c_COMBC(_1526593, tc_fun(tc_prod(_1526591, _1526593), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526593, tc_prod(_1526591, _1526593)), tc_fun(_1526593, tc_fun(tc_fun(tc_prod(_1526591, _1526593), tc_HOL_Obool), tc_HOL_Obool)), _1526591), hAPP(c_COMBB(tc_prod(_1526591, _1526593), tc_fun(tc_fun(tc_prod(_1526591, _1526593), tc_HOL_Obool), tc_HOL_Obool), _1526593), c_member(tc_prod(_1526591, _1526593)))), c_Product__Type_OPair(_1526591, _1526593)))), _1526595)), _1526597)))], (38724 ^ _776541) ^ [_1520822, _1520824, _1520826, _1520828, _1520830] : [hBOOL(hAPP(_1520828, hAPP(_1520826, _1520830))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1520822, _1520824, _1520826), _1520828), _1520830)))], (47743 ^ _776541) ^ [_1737447, _1737449] : [class_Enum_Oenum(_1737447), 47746 ^ _776541 : [(47753 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737447), _1737449)), -(hBOOL(hAPP(_1737449, 47756 ^ [_1737447, _1737449])))], (47747 ^ _776541) ^ [] : [47748 ^ _776541 : [(47749 ^ _776541) ^ [_1737549] : [hBOOL(hAPP(_1737449, _1737549))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737447), _1737449)))]]], (22433 ^ _776541) ^ [_1183183, _1183185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183183)), 22436 ^ _776541 : [(22445 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1183183), _1183185) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1183183 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1183185 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (22437 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1183183), _1183185) = c_Groups_Oone__class_Oone(tc_Int_Oint), 22440 ^ _776541 : [(22443 ^ _776541) ^ [] : [-(_1183185 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22441 ^ _776541) ^ [] : [-(_1183183 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (32858 ^ _776541) ^ [_1374212, _1374214, _1374216, _1374218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374212, tc_fun(_1374214, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1374212, tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_fun(_1374214, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374214, tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_fun(_1374214, tc_HOL_Obool)), _1374212), c_COMBC(_1374214, tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374214, tc_prod(_1374212, _1374214)), tc_fun(_1374214, tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool)), _1374212), hAPP(c_COMBB(tc_prod(_1374212, _1374214), tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool), _1374214), c_member(tc_prod(_1374212, _1374214)))), c_Product__Type_OPair(_1374212, _1374214)))), _1374216)), hAPP(hAPP(c_COMBC(_1374212, tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_fun(_1374214, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374214, tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_fun(_1374214, tc_HOL_Obool)), _1374212), c_COMBC(_1374214, tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374214, tc_prod(_1374212, _1374214)), tc_fun(_1374214, tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool)), _1374212), hAPP(c_COMBB(tc_prod(_1374212, _1374214), tc_fun(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool), tc_HOL_Obool), _1374214), c_member(tc_prod(_1374212, _1374214)))), c_Product__Type_OPair(_1374212, _1374214)))), _1374218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1374212, _1374214), tc_HOL_Obool)), _1374216), _1374218)))], (24740 ^ _776541) ^ [_1224119, _1224121] : [_1224119 = _1224121, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224119) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224121))], (15174 ^ _776541) ^ [_1050350] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1050350)) = _1050350)], (43492 ^ _776541) ^ [_1643862, _1643864, _1643866, _1643868] : [_1643864 = _1643868, -(hAPP(hAPP(c_List_Oappend(_1643862), _1643864), _1643866) = hAPP(hAPP(c_List_Oappend(_1643862), _1643868), _1643866))], (8179 ^ _776541) ^ [_916170, _916172, _916174] : [class_Orderings_Oorder(_916170), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916170, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_916170), _916172)), c_SetInterval_Oord__class_OgreaterThanLessThan(_916170, _916172, _916174)) = c_Orderings_Obot__class_Obot(tc_fun(_916170, tc_HOL_Obool)))], (35495 ^ _776541) ^ [_1438830, _1438832, _1438834, _1438836, _1438838] : [hAPP(c_Product__Type_Osnd(_1438830, _1438832), hAPP(hAPP(c_Product__Type_OPair(_1438830, _1438832), _1438834), _1438836)) = _1438838, -(_1438836 = _1438838)], (35054 ^ _776541) ^ [_1430668, _1430670] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430668, _1430670), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1430668), _1430670)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1430668, _1430670)))))], (44210 ^ _776541) ^ [_1660526, _1660528, _1660530] : [-(hAPP(hAPP(c_List_Odrop(_1660526), hAPP(c_Nat_OSuc, _1660528)), _1660530) = hAPP(hAPP(c_List_Odrop(_1660526), _1660528), hAPP(c_List_Otl(_1660526), _1660530)))], (21379 ^ _776541) ^ [_1163709, _1163711, _1163713, _1163715] : [class_Int_Onumber__ring(_1163709), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163709), hAPP(c_Int_Onumber__class_Onumber__of(_1163709), _1163711)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163709), _1163713), hAPP(c_Int_Onumber__class_Onumber__of(_1163709), _1163715))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163709), hAPP(c_Int_Onumber__class_Onumber__of(_1163709), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1163711), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163715)))), _1163713))], (16024 ^ _776541) ^ [_1066422, _1066424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066422), _1066424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066422), hAPP(c_Nat_OSuc, _1066424))))], (39465 ^ _776541) ^ [_1541352, _1541354, _1541356, _1541358] : [-(c_Product__Type_Oapfst(_1541352, _1541354, _1541356, _1541358) = c_Product__Type_Omap__pair(_1541352, _1541354, _1541356, _1541356, _1541358, c_Fun_Oid(_1541356)))], (48524 ^ _776541) ^ [_1754290, _1754292, _1754294, _1754296, _1754298] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754290, _1754292, _1754294), _1754296), _1754298)), -(hBOOL(hAPP(hAPP(_1754294, _1754298), _1754296)))], (37997 ^ _776541) ^ [_1502492, _1502494, _1502496] : [hBOOL(hAPP(hAPP(c_member(_1502492), _1502494), c_Wellfounded_Oacc(_1502492, _1502496))), 38000 ^ _776541 : [(38001 ^ _776541) ^ [_1502606] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1502492, _1502492)), hAPP(hAPP(c_Product__Type_OPair(_1502492, _1502492), _1502606), _1502494)), _1502496)), -(hBOOL(hAPP(hAPP(c_member(_1502492), _1502606), c_Wellfounded_Oacc(_1502492, _1502496))))]]], (9694 ^ _776541) ^ [_942478, _942480, _942482, _942484] : [class_Orderings_Oorder(_942478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942478), _942480), _942482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942478), _942484), _942480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942478), _942484), _942482)))], (45191 ^ _776541) ^ [_1681793] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1681793)) = _1681793)], (26324 ^ _776541) ^ [_1251862, _1251864] : [hAPP(c_Int_Onat, _1251862) = _1251864, 26327 ^ _776541 : [(26334 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251862))), -(_1251864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26328 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251862)), -(_1251862 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251864))]]], (27225 ^ _776541) ^ [_1266428, _1266430, _1266432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266432), 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), _1266432), _1266430))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1266428)))))], (52201 ^ _776541) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (14768 ^ _776541) ^ [_1042764, _1042766, _1042768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042764), _1042766)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042764), _1042768))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042766), _1042768)))], (7952 ^ _776541) ^ [_910970, _910972, _910974] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910970, tc_HOL_Obool)), _910972), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910970, tc_HOL_Obool)), _910974), _910972))))], (44487 ^ _776541) ^ [_1666349, _1666351, _1666353, _1666355] : [44488 ^ _776541 : [(44489 ^ _776541) ^ [_1666446, _1666448] : [_1666349 = hAPP(hAPP(c_List_Olist_OCons(_1666351), _1666448), _1666446)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666351), tc_List_Olist(_1666351))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666351), tc_List_Olist(_1666351)), _1666353), hAPP(hAPP(c_List_Oappend(_1666351), _1666353), _1666349))), c_List_Olexord(_1666351, _1666355))))], (13820 ^ _776541) ^ [_1022989, _1022991, _1022993] : [class_Groups_Ogroup__add(_1022989), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1022989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022989), _1022991), _1022993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022989), hAPP(c_Groups_Ouminus__class_Ouminus(_1022989), _1022993)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022989), _1022991)))], (756 ^ _776541) ^ [_787925, _787927, _787929, _787931] : [-(c_Relation_Oantisym(_787929, _787925)), c_Relation_Oantisym(_787931, _787927), _787931 = _787929, _787927 = _787925], (41481 ^ _776541) ^ [_1591689, _1591691] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591689, _1591689), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1591691) = c_Fun_Oid(_1591689))], (11006 ^ _776541) ^ [_966726, _966728, _966730] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966726, tc_HOL_Obool)), _966728) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966726, tc_HOL_Obool)), _966730), -(_966728 = _966730)], (38283 ^ _776541) ^ [_1509879, _1509881] : [38285 ^ _776541 : [(38286 ^ _776541) ^ [_1509904] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509879, _1509879)), hAPP(hAPP(c_Product__Type_OPair(_1509879, _1509879), hAPP(38284 ^ [_1509879, _1509881], hAPP(c_Nat_OSuc, _1509904))), hAPP(38284 ^ [_1509879, _1509881], _1509904))), _1509881)))]], -(c_Wellfounded_Owf(_1509879, _1509881))], (23133 ^ _776541) ^ [_1195713, _1195715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195713), _1195715)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1195715, _1195713) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (50435 ^ _776541) ^ [_1796226, _1796228, _1796230, _1796232, _1796234] : [-(c_Fun_Obij__betw(_1796226, _1796228, _1796230, _1796232, _1796234)), c_Fun_Oinj__on(_1796226, _1796228, _1796230, _1796232), hAPP(c_Set_Oimage(_1796226, _1796228, _1796230), _1796232) = _1796234], (5034 ^ _776541) ^ [_853299, _853301] : [_853301 = _853299, -(c_Lattices_Osemilattice__inf__class_Oinf(_853301) = c_Lattices_Osemilattice__inf__class_Oinf(_853299))], (26224 ^ _776541) ^ [_1250199, _1250201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250199), hAPP(c_Int_Onat, _1250201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250199)), _1250201)))], (29179 ^ _776541) ^ [_1299553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1299553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1299553)))], (28883 ^ _776541) ^ [_1294342] : [c_Int_OMin = c_Int_OBit0(_1294342)], (952 ^ _776541) ^ [_790805, _790807, _790809, _790811, _790813, _790815, _790817, _790819] : [-(c_Equiv__Relations_Ocongruent(_790817, _790813, _790809, _790805)), c_Equiv__Relations_Ocongruent(_790819, _790815, _790811, _790807), _790819 = _790817, _790815 = _790813, _790811 = _790809, _790807 = _790805], (28069 ^ _776541) ^ [_1280843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1280843), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280843)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48820 ^ _776541) ^ [_1760496, _1760498] : [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), _1760496), _1760498))), 48823 ^ _776541 : [(48830 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760496), _1760498))), -(c_Lazy__Sequence_Osmall__lazy_H(_1760496, _1760498) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1760498), c_Lazy__Sequence_Osmall__lazy_H(_1760496, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1760498), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48824 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760496), _1760498)), -(c_Lazy__Sequence_Osmall__lazy_H(_1760496, _1760498) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (50427 ^ _776541) ^ [_1796097, _1796099, _1796101, _1796103, _1796105] : [c_Fun_Obij__betw(_1796097, _1796099, _1796101, _1796103, _1796105), 50430 ^ _776541 : [(50433 ^ _776541) ^ [] : [-(hAPP(c_Set_Oimage(_1796097, _1796099, _1796101), _1796103) = _1796105)], (50431 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1796097, _1796099, _1796101, _1796103))]]], (52155 ^ _776541) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (30606 ^ _776541) ^ [_1325750, _1325752, _1325754] : [class_Orderings_Olinorder(_1325750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325750), _1325752)), hBOOL(hAPP(hAPP(c_member(_1325750), _1325754), _1325752)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325750), _1325754), c_Big__Operators_Olattice_OInf__fin(_1325750, c_Orderings_Oord__class_Omin(_1325750), _1325752)) = c_Big__Operators_Olattice_OInf__fin(_1325750, c_Orderings_Oord__class_Omin(_1325750), _1325752))], (47082 ^ _776541) ^ [_1722876, _1722878] : [-(hAPP(c_List_Orev(_1722876), hAPP(c_List_Orev(_1722876), _1722878)) = _1722878)], (28241 ^ _776541) ^ [_1283625, _1283627] : [-(c_Nitpick_Onat__lcm(_1283625, _1283627) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1283625), _1283627)), c_Nitpick_Onat__gcd(_1283625, _1283627)))], (28475 ^ _776541) ^ [_1287590] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1287590)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1287590))))], (32940 ^ _776541) ^ [_1377194, _1377196, _1377198, _1377200, _1377202] : [_1377194 = c_Orderings_Obot__class_Obot(tc_fun(_1377196, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377198, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377196, tc_fun(_1377198, tc_HOL_Obool)), _1377194), _1377200)), _1377202) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377198, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1377198, tc_HOL_Obool))), _1377202))], (43306 ^ _776541) ^ [_1639187, _1639189, _1639191, _1639193, _1639195] : [-(hAPP(hAPP(c_List_Ozip(_1639187, _1639189), hAPP(hAPP(c_List_Olist_OCons(_1639187), _1639191), _1639193)), _1639195) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1639187, _1639189)), _1639189, c_List_Olist_ONil(tc_prod(_1639187, _1639189)), hAPP(hAPP(c_COMBC(_1639189, tc_fun(tc_List_Olist(_1639189), tc_List_Olist(tc_prod(_1639187, _1639189))), tc_fun(tc_List_Olist(_1639189), tc_List_Olist(tc_prod(_1639187, _1639189)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1639187, _1639189)), tc_List_Olist(tc_prod(_1639187, _1639189))), tc_fun(tc_fun(tc_List_Olist(_1639189), tc_List_Olist(tc_prod(_1639187, _1639189))), tc_fun(tc_List_Olist(_1639189), tc_List_Olist(tc_prod(_1639187, _1639189)))), _1639189), c_COMBB(tc_List_Olist(tc_prod(_1639187, _1639189)), tc_List_Olist(tc_prod(_1639187, _1639189)), tc_List_Olist(_1639189))), hAPP(hAPP(c_COMBB(tc_prod(_1639187, _1639189), tc_fun(tc_List_Olist(tc_prod(_1639187, _1639189)), tc_List_Olist(tc_prod(_1639187, _1639189))), _1639189), c_List_Olist_OCons(tc_prod(_1639187, _1639189))), hAPP(c_Product__Type_OPair(_1639187, _1639189), _1639191)))), hAPP(c_List_Ozip(_1639187, _1639189), _1639193))), _1639195))], (42616 ^ _776541) ^ [_1624978, _1624980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624978), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1624980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1624980), _1624978)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1624980))))], (30014 ^ _776541) ^ [_1314824] : [class_Orderings_Olinorder(_1314824), -(c_Finite__Set_Ofun__left__comm__idem(_1314824, _1314824, c_Orderings_Oord__class_Omin(_1314824)))], (50269 ^ _776541) ^ [_1792689, _1792691, _1792693, _1792695, _1792697, _1792699] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1792689, _1792691, _1792693, _1792695), _1792697), _1792699) = hAPP(_1792695, hAPP(hAPP(c_Product__Type_OPair(_1792689, _1792691), _1792697), _1792699)))], (35394 ^ _776541) ^ [_1436379, _1436381, _1436383, _1436385, _1436387, _1436389, _1436391] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436379, _1436381), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436383), _1436385))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436387, _1436381), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436389), _1436391))), -(_1436381 = 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), _1436379), _1436387), _1436381), 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), _1436383), _1436389)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436385), _1436391)), _1436381))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436385), _1436391), _1436381)))))], (48472 ^ _776541) ^ [_1753150, _1753152, _1753154] : [-(hAPP(c_New__DSequence_Opos__single(_1753150, _1753152), _1753154) = hAPP(c_Lazy__Sequence_Osingle(_1753150), _1753152))], (27625 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (32209 ^ _776541) ^ [_1355432, _1355434, _1355436] : [class_Orderings_Olinorder(_1355432), hAPP(_1355434, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355432), 32214 ^ [_1355432, _1355434, _1355436]), 32215 ^ [_1355432, _1355434, _1355436])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355432), hAPP(_1355434, 32214 ^ [_1355432, _1355434, _1355436])), hAPP(_1355434, 32215 ^ [_1355432, _1355434, _1355436])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355432), _1355436)), -(_1355436 = c_Orderings_Obot__class_Obot(tc_fun(_1355432, tc_HOL_Obool))), -(hAPP(_1355434, c_Big__Operators_Olattice_OSup__fin(_1355432, c_Orderings_Oord__class_Omax(_1355432), _1355436)) = c_Big__Operators_Olattice_OSup__fin(_1355432, c_Orderings_Oord__class_Omax(_1355432), hAPP(c_Set_Oimage(_1355432, _1355432, _1355434), _1355436)))], (34301 ^ _776541) ^ [_1414736, _1414738, _1414740, _1414742] : [class_Rings_Ocomm__semiring__1(_1414736), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414736), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414736), c_Groups_Oone__class_Oone(_1414736)), c_Groups_Oone__class_Oone(_1414736))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414736), hAPP(hAPP(c_COMBB(_1414736, _1414736, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1414736), _1414738)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1414736, _1414736), hAPP(hAPP(c_COMBB(_1414736, tc_fun(_1414736, _1414736), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1414736)), c_Nat_Osemiring__1__class_Oof__nat(_1414736))), _1414740))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1414742))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414736), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1414736), _1414742)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414736), _1414738), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414736), _1414738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414736), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1414736), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1414742), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1414740)))))], (32584 ^ _776541) ^ [_1366173, _1366175, _1366177, _1366179, _1366181, _1366183] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366173, tc_fun(_1366175, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1366173, tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_fun(_1366175, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366175, tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_fun(_1366175, tc_HOL_Obool)), _1366173), c_COMBC(_1366175, tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366175, tc_prod(_1366173, _1366175)), tc_fun(_1366175, tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool)), _1366173), hAPP(c_COMBB(tc_prod(_1366173, _1366175), tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool), _1366175), c_member(tc_prod(_1366173, _1366175)))), c_Product__Type_OPair(_1366173, _1366175)))), _1366177)), hAPP(hAPP(c_COMBC(_1366173, tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_fun(_1366175, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366175, tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_fun(_1366175, tc_HOL_Obool)), _1366173), c_COMBC(_1366175, tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366175, tc_prod(_1366173, _1366175)), tc_fun(_1366175, tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool)), _1366173), hAPP(c_COMBB(tc_prod(_1366173, _1366175), tc_fun(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool), tc_HOL_Obool), _1366175), c_member(tc_prod(_1366173, _1366175)))), c_Product__Type_OPair(_1366173, _1366175)))), _1366179)), _1366181), _1366183)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1366173, _1366175)), hAPP(hAPP(c_Product__Type_OPair(_1366173, _1366175), _1366181), _1366183)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1366173, _1366175), tc_HOL_Obool)), _1366177), _1366179))))], (28631 ^ _776541) ^ [] : [-(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))))))], (45688 ^ _776541) ^ [_1693143, _1693145] : [-(c_Enum_On__lists(_1693143, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1693145) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1693143)), c_List_Olist_ONil(_1693143)), c_List_Olist_ONil(tc_List_Olist(_1693143))))], (24254 ^ _776541) ^ [_1215191, _1215193, _1215195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215191)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1215195), _1215191)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215193), _1215195)), _1215191))], (36243 ^ _776541) ^ [_1460417, _1460419, _1460421, _1460423, _1460425, _1460427] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1460417, tc_HOL_Obool), tc_fun(_1460417, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1460417, tc_HOL_Obool), tc_fun(_1460417, tc_HOL_Obool)), _1460419), _1460421)), c_Wellfounded_Omax__ext(_1460417, _1460423))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1460417, tc_HOL_Obool), tc_fun(_1460417, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1460417, tc_HOL_Obool), tc_fun(_1460417, tc_HOL_Obool)), _1460425), _1460427)), c_Wellfounded_Omax__ext(_1460417, _1460423))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1460417, tc_HOL_Obool), tc_fun(_1460417, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1460417, tc_HOL_Obool), tc_fun(_1460417, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460417, tc_HOL_Obool)), _1460419), _1460425)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460417, tc_HOL_Obool)), _1460421), _1460427))), c_Wellfounded_Omax__ext(_1460417, _1460423))))], (34729 ^ _776541) ^ [_1423878, _1423880, _1423882, _1423884, _1423886, _1423888, _1423890] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1423878, _1423880)), hAPP(hAPP(c_Product__Type_OPair(_1423878, _1423880), _1423882), _1423884)), _1423886)), -(hBOOL(hAPP(hAPP(c_member(_1423888), hAPP(hAPP(_1423890, _1423882), _1423884)), hAPP(c_Set_Oimage(tc_prod(_1423878, _1423880), _1423888, hAPP(c_Product__Type_Oprod_Oprod__case(_1423878, _1423880, _1423888), _1423890)), _1423886))))], (44477 ^ _776541) ^ [_1666177, _1666179, _1666181, _1666183, _1666185] : [class_Orderings_Olinorder(_1666177), -(hBOOL(hAPP(hAPP(c_member(_1666177), hAPP(_1666179, _1666181)), hAPP(c_Set_Oimage(_1666183, _1666177, _1666179), hAPP(c_List_Oset(_1666183), _1666185))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1666183, _1666177, _1666179, _1666181, _1666185) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1666183, _1666177, _1666179), _1666181), _1666185))], (22187 ^ _776541) ^ [_1178939] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1178939) = _1178939)], (45024 ^ _776541) ^ [_1678334, _1678336] : [hAPP(c_Code__Numeral_Oof__nat, _1678334) = hAPP(c_Code__Numeral_Oof__nat, _1678336), -(_1678334 = _1678336)], (49385 ^ _776541) ^ [_1774381, _1774383, _1774385, _1774387] : [class_Complete__Lattice_Ocomplete__lattice(_1774381), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1774383, _1774381), _1774385), _1774387) = c_Complete__Lattice_OInf__class_OInf(_1774381, hAPP(c_Set_OCollect(_1774381), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774383, _1774381), tc_HOL_Obool), tc_HOL_Obool, _1774381), c_HOL_OEx(tc_fun(_1774383, _1774381))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774383, _1774381), tc_HOL_Obool), tc_fun(tc_fun(_1774383, _1774381), tc_HOL_Obool), _1774381), hAPP(c_COMBS(tc_fun(_1774383, _1774381), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774383, _1774381)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774383, _1774381), tc_fun(tc_fun(_1774383, _1774381), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774383, _1774381))), _1774385)))), hAPP(hAPP(c_COMBC(_1774381, tc_fun(tc_fun(_1774383, _1774381), _1774381), tc_fun(tc_fun(_1774383, _1774381), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774381, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774383, _1774381), _1774381), tc_fun(tc_fun(_1774383, _1774381), tc_HOL_Obool)), _1774381), c_COMBB(_1774381, tc_HOL_Obool, tc_fun(_1774383, _1774381))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774383, _1774381), _1774383, _1774381), c_COMBI(tc_fun(_1774383, _1774381))), _1774387)))))))], (39133 ^ _776541) ^ [_1531145, _1531147, _1531149] : [c_Equiv__Relations_Oequiv(_1531145, _1531147, _1531149), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531145, _1531145), tc_HOL_Obool)), _1531149), hAPP(hAPP(c_Product__Type_OSigma(_1531145, _1531145), _1531147), hAPP(c_COMBK(tc_fun(_1531145, tc_HOL_Obool), _1531145), _1531147)))))], (33380 ^ _776541) ^ [_1389498, _1389500, _1389502, _1389504, _1389506, _1389508] : [-(c_Nitpick_Opair__box_OPairBox(_1389498, _1389500, _1389502, _1389504) = c_Nitpick_Opair__box_OPairBox(_1389498, _1389500, _1389506, _1389508)), _1389502 = _1389506, _1389504 = _1389508], (49572 ^ _776541) ^ [_1778306] : [-(c_Relation_Oantisym(_1778306, c_Relation_OId(_1778306)))], (19607 ^ _776541) ^ [_1130771, _1130773, _1130775] : [class_Rings_Olinordered__idom(_1130771), -(c_Groups_Osgn__class_Osgn(_1130771, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130771), _1130773), _1130775)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130771), c_Groups_Osgn__class_Osgn(_1130771, _1130773)), c_Groups_Osgn__class_Osgn(_1130771, _1130775)))], (7558 ^ _776541) ^ [_901366, _901368, _901370] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901366, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901366, tc_HOL_Obool)), _901368), _901370)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901366, tc_HOL_Obool)), _901368), _901370)) = _901368)], (50711 ^ _776541) ^ [_1801607, _1801609, _1801611] : [hBOOL(hAPP(c_Quotient_ORespects(_1801607, _1801609), _1801611)), -(hBOOL(hAPP(hAPP(_1801609, _1801611), _1801611)))], (8209 ^ _776541) ^ [_916907, _916909, _916911, _916913, _916915] : [class_Lattices_Olattice(_916907), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916909, _916907)), _916911), _916913), _916915) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916907), hAPP(_916911, _916915)), hAPP(_916913, _916915)))], (38476 ^ _776541) ^ [_1514216, _1514218] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1514216, _1514218), 38477 ^ [_1514216, _1514218])), -(c_Wellfounded_OwfP(_1514216, _1514218))], (46968 ^ _776541) ^ [_1720515, _1720517, _1720519] : [-(hAPP(c_List_Orev(_1720515), hAPP(hAPP(c_List_Oappend(_1720515), _1720517), _1720519)) = hAPP(hAPP(c_List_Oappend(_1720515), hAPP(c_List_Orev(_1720515), _1720519)), hAPP(c_List_Orev(_1720515), _1720517)))], (2490 ^ _776541) ^ [_813099, _813101, _813103, _813105] : [-(c_Divides_OposDivAlg(_813105, _813101) = c_Divides_OposDivAlg(_813103, _813099)), _813105 = _813103, _813101 = _813099], (39237 ^ _776541) ^ [_1534010, _1534012, _1534014, _1534016] : [-(hAPP(c_Set_OCollect(tc_prod(_1534010, _1534012)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534010, _1534012, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1534010, tc_fun(_1534012, tc_HOL_Obool), tc_fun(_1534012, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534012, tc_HOL_Obool), tc_fun(_1534012, tc_HOL_Obool)), _1534010), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534012)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534010), c_fconj), _1534014))), _1534016))) = hAPP(hAPP(c_Product__Type_OSigma(_1534010, _1534012), hAPP(c_Set_OCollect(_1534010), _1534014)), hAPP(c_COMBK(tc_fun(_1534012, tc_HOL_Obool), _1534010), hAPP(c_Set_OCollect(_1534012), _1534016))))], (12287 ^ _776541) ^ [_992157, _992159, _992161] : [class_Lattices_Olattice(_992157), hBOOL(hAPP(c_Finite__Set_Ofinite(_992157), _992159)), -(hBOOL(hAPP(hAPP(c_member(_992157), _992161), _992159))), -(_992159 = c_Orderings_Obot__class_Obot(tc_fun(_992157, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_992157, hAPP(hAPP(c_Set_Oinsert(_992157), _992161), _992159)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_992157), _992161), c_Big__Operators_Olattice__class_OInf__fin(_992157, _992159)))], (16200 ^ _776541) ^ [_1069287, _1069289] : [class_Rings_Ocomm__semiring__1(_1069287), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069287), c_Groups_Ozero__class_Ozero(_1069287)), _1069289) = _1069289)], (26515 ^ _776541) ^ [_1255122, _1255124] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255122) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255124)), _1255122 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255124)), 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), _1255124)))], (44719 ^ _776541) ^ [_1670465, _1670467, _1670469, _1670471, _1670473, _1670475] : [-(hAPP(hAPP(c_List_Omap(_1670465, _1670467), _1670469), hAPP(hAPP(c_List_Omap(_1670471, _1670465), _1670473), _1670475)) = hAPP(hAPP(c_List_Omap(_1670471, _1670467), hAPP(c_Fun_Ocomp(_1670465, _1670467, _1670471, _1670469), _1670473)), _1670475))], (16296 ^ _776541) ^ [_1070705, _1070707] : [class_Rings_Ocomm__semiring__1(_1070705), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070705), _1070707), c_Groups_Ozero__class_Ozero(_1070705)) = c_Groups_Ozero__class_Ozero(_1070705))], (37698 ^ _776541) ^ [_1494535, _1494537, _1494539, _1494541, _1494543] : [c_Fun_Oinj__on(_1494535, _1494537, _1494539, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494535, tc_HOL_Obool)), _1494541), _1494543)), 37701 ^ _776541 : [(37706 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494537, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1494535, _1494537, _1494539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494535, tc_HOL_Obool)), _1494541), _1494543))), hAPP(c_Set_Oimage(_1494535, _1494537, _1494539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494535, tc_HOL_Obool)), _1494543), _1494541))) = c_Orderings_Obot__class_Obot(tc_fun(_1494537, tc_HOL_Obool)))], (37704 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1494535, _1494537, _1494539, _1494543))], (37702 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1494535, _1494537, _1494539, _1494541))]]], (29831 ^ _776541) ^ [_1311437, _1311439] : [c_Code__Numeral_OSuc__code__numeral(_1311437) = c_Code__Numeral_OSuc__code__numeral(_1311439), -(_1311437 = _1311439)], (52443 ^ _776541) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (28195 ^ _776541) ^ [_1282783, _1282785] : [class_Rings_Osemiring__1(_1282783), -(hBOOL(hAPP(hAPP(c_member(_1282783), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1282783), _1282785)), c_Nat_Osemiring__1__class_ONats(_1282783))))], (1414 ^ _776541) ^ [_797080, _797082] : [-(class_Lattices_Oboolean__algebra(_797080)), _797082 = _797080, class_Lattices_Oboolean__algebra(_797082)], (16472 ^ _776541) ^ [_1073225, _1073227] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073225), _1073227) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1073227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9804 ^ _776541) ^ [_944500, _944502, _944504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944500, tc_HOL_Obool)), _944502), _944504)), 9807 ^ _776541 : [(9810 ^ _776541) ^ [] : [_944502 = _944504], (9808 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944500, tc_HOL_Obool)), _944502), _944504)))]]], (44060 ^ _776541) ^ [_1657597, _1657599, _1657601, _1657603] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657597) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1657599), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657597)), hAPP(hAPP(c_List_Olist_OCons(_1657599), _1657601), _1657603)) = hAPP(hAPP(c_List_Odrop(_1657599), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657597)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1657603))], (50317 ^ _776541) ^ [_1793783, _1793785, _1793787, _1793789, _1793791, _1793793] : [c_Fun_Obij__betw(_1793783, _1793785, _1793787, c_Orderings_Otop__class_Otop(tc_fun(_1793783, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793785, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793783, _1793785, _1793787), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1793789, tc_fun(_1793783, tc_HOL_Obool)), _1793791), _1793793)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1793789, tc_fun(_1793785, tc_HOL_Obool)), _1793791), hAPP(hAPP(c_COMBB(tc_fun(_1793783, tc_HOL_Obool), tc_fun(_1793785, tc_HOL_Obool), _1793789), c_Set_Oimage(_1793783, _1793785, _1793787)), _1793793)))], (16530 ^ _776541) ^ [_1074079, _1074081, _1074083] : [16531 ^ _776541 : [(16534 ^ _776541) ^ [] : [_1074081 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16532 ^ _776541) ^ [] : [_1074079 = _1074083]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074079), _1074081) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074083), _1074081))], (9770 ^ _776541) ^ [_943861, _943863, _943865, _943867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943861, tc_HOL_Obool)), _943863), _943865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943861, tc_HOL_Obool)), _943865), _943867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943861, tc_HOL_Obool)), _943863), _943867)))], (10701 ^ _776541) ^ [_960858, _960860, _960862] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960858, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960858, tc_HOL_Obool)), _960860), _960862)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960858, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960858, tc_HOL_Obool)), _960860)), _960862))], (45265 ^ _776541) ^ [_1683054, _1683056] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1683054), _1683056) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1683054)), hAPP(c_Code__Numeral_Onat__of, _1683056))))], (17775 ^ _776541) ^ [_1096479, _1096481] : [class_Groups_Ogroup__add(_1096479), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096479), _1096481), hAPP(c_Groups_Ouminus__class_Ouminus(_1096479), _1096481)) = c_Groups_Ozero__class_Ozero(_1096479))], (32338 ^ _776541) ^ [_1358154, _1358156, _1358158, _1358160, _1358162, _1358164] : [hBOOL(hAPP(hAPP(c_member(_1358154), _1358156), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358158, tc_fun(_1358154, tc_HOL_Obool)), _1358160), _1358162))), -(hBOOL(hAPP(hAPP(c_member(_1358154), _1358156), hAPP(_1358162, _1358164)))), hBOOL(hAPP(hAPP(c_member(_1358158), _1358164), _1358160))], (38576 ^ _776541) ^ [_1516744, _1516746] : [c_Wellfounded_Owf(_1516744, _1516746), -(c_Wellfounded_OwfP(_1516744, hAPP(hAPP(c_COMBC(_1516744, tc_fun(tc_prod(_1516744, _1516744), tc_HOL_Obool), tc_fun(_1516744, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516744, tc_fun(tc_fun(tc_prod(_1516744, _1516744), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516744, _1516744), tc_HOL_Obool), tc_fun(_1516744, tc_HOL_Obool)), _1516744), c_COMBC(_1516744, tc_fun(tc_prod(_1516744, _1516744), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516744, tc_prod(_1516744, _1516744)), tc_fun(_1516744, tc_fun(tc_fun(tc_prod(_1516744, _1516744), tc_HOL_Obool), tc_HOL_Obool)), _1516744), hAPP(c_COMBB(tc_prod(_1516744, _1516744), tc_fun(tc_fun(tc_prod(_1516744, _1516744), tc_HOL_Obool), tc_HOL_Obool), _1516744), c_member(tc_prod(_1516744, _1516744)))), c_Product__Type_OPair(_1516744, _1516744)))), _1516746)))], (9666 ^ _776541) ^ [_942012, _942014, _942016, _942018] : [class_Orderings_Oorder(_942012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942012), _942014), _942016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942012), _942018), _942014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942012), _942018), _942016)))], (36394 ^ _776541) ^ [] : [-(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)))))], (8375 ^ _776541) ^ [_920176, _920178, _920180, _920182] : [class_Lattices_Osemilattice__inf(_920176), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920176), _920178), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920176), _920180), _920182)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920176), _920180), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920176), _920178), _920182)))], (2626 ^ _776541) ^ [_815271, _815273, _815275, _815277] : [-(c_Nitpick_Onumber__of__frac(_815277, _815273) = c_Nitpick_Onumber__of__frac(_815275, _815271)), _815277 = _815275, _815273 = _815271], (4726 ^ _776541) ^ [_848455, _848457, _848459, _848461, _848463, _848465, _848467, _848469] : [-(c_Random__Sequence_Obind(_848469, _848465, _848461, _848457) = c_Random__Sequence_Obind(_848467, _848463, _848459, _848455)), _848469 = _848467, _848465 = _848463, _848461 = _848459, _848457 = _848455], (36436 ^ _776541) ^ [_1464728, _1464730, _1464732] : [-(c_Wellfounded_Omlex__prod(_1464728, _1464730, _1464732) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1464728), _1464728), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1464728, c_Wellfounded_Oless__than, _1464732)), hAPP(hAPP(c_COMBS(_1464728, _1464728, tc_prod(tc_Nat_Onat, _1464728)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1464728, tc_prod(tc_Nat_Onat, _1464728)), _1464728), c_Product__Type_OPair(tc_Nat_Onat, _1464728)), _1464730)), c_COMBI(_1464728))))], (47096 ^ _776541) ^ [_1723174, _1723176, _1723178] : [-(hAPP(c_List_Orev(_1723174), hAPP(hAPP(c_List_Olist_OCons(_1723174), _1723176), _1723178)) = hAPP(hAPP(c_List_Oappend(_1723174), hAPP(c_List_Orev(_1723174), _1723178)), hAPP(hAPP(c_List_Olist_OCons(_1723174), _1723176), c_List_Olist_ONil(_1723174))))], (52545 ^ _776541) ^ [_1832045, _1832047] : [-(hBOOL(_1832045)), -(hBOOL(hAPP(hAPP(c_fimplies, _1832045), _1832047)))], (35125 ^ _776541) ^ [_1432097, _1432099, _1432101] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1432097, _1432099), _1432101)), 35128 ^ _776541 : [(35129 ^ _776541) ^ [_1432182] : [hBOOL(hAPP(hAPP(_1432099, _1432182), _1432101)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1432097, _1432099), _1432182)))]]], (18914 ^ _776541) ^ [_1117182, _1117184, _1117186] : [class_Rings_Olinordered__ring(_1117182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117182), _1117184), _1117184)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117182), _1117186), _1117186))), c_Groups_Ozero__class_Ozero(_1117182)))], (5382 ^ _776541) ^ [_858761, _858763, _858765, _858767] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_858767, _858763) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_858765, _858761)), _858767 = _858765, _858763 = _858761], (45235 ^ _776541) ^ [] : [-(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))], (42053 ^ _776541) ^ [_1608872, _1608874, _1608876, _1608878] : [c_List_Olistrelp(_1608872, hAPP(hAPP(c_COMBC(_1608872, tc_fun(tc_prod(_1608872, _1608872), tc_HOL_Obool), tc_fun(_1608872, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608872, tc_fun(tc_fun(tc_prod(_1608872, _1608872), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1608872, _1608872), tc_HOL_Obool), tc_fun(_1608872, tc_HOL_Obool)), _1608872), c_COMBC(_1608872, tc_fun(tc_prod(_1608872, _1608872), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608872, tc_prod(_1608872, _1608872)), tc_fun(_1608872, tc_fun(tc_fun(tc_prod(_1608872, _1608872), tc_HOL_Obool), tc_HOL_Obool)), _1608872), hAPP(c_COMBB(tc_prod(_1608872, _1608872), tc_fun(tc_fun(tc_prod(_1608872, _1608872), tc_HOL_Obool), tc_HOL_Obool), _1608872), c_member(tc_prod(_1608872, _1608872)))), c_Product__Type_OPair(_1608872, _1608872)))), _1608874), _1608876, _1608878), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608872), tc_List_Olist(_1608872))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608872), tc_List_Olist(_1608872)), _1608876), _1608878)), c_List_Olistrel(_1608872, _1608874))))], (10697 ^ _776541) ^ [_960736, _960738, _960740] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960736, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960736, tc_HOL_Obool)), _960738), _960740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960736, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960736, tc_HOL_Obool)), _960738)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960736, tc_HOL_Obool)), _960740)))], (38778 ^ _776541) ^ [_1521911, _1521913, _1521915, _1521917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521911, _1521913), tc_HOL_Obool)), _1521915), _1521917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521911, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1521911, _1521913), _1521915)), hAPP(c_Relation_ODomain(_1521911, _1521913), _1521917))))], (5510 ^ _776541) ^ [_860741, _860743] : [_860743 = _860741, -(c_Groups_Ozero__class_Ozero(_860743) = c_Groups_Ozero__class_Ozero(_860741))], (43202 ^ _776541) ^ [_1637092, _1637094, _1637096] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637092), tc_List_Olist(_1637092))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637092), tc_List_Olist(_1637092)), _1637094), c_List_Olist_ONil(_1637092))), c_List_Olistrel1(_1637092, _1637096)))], (11194 ^ _776541) ^ [_970576, _970578, _970580, _970582, _970584] : [-(hAPP(c_Set_Oimage(_970576, _970578, _970580), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_970576, tc_HOL_Obool)), _970582), _970584)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_970578, tc_HOL_Obool)), hAPP(c_Set_Oimage(_970576, _970578, _970580), _970582)), hAPP(c_Set_Oimage(_970576, _970578, _970580), _970584)))], (39751 ^ _776541) ^ [_1549143, _1549145] : [class_Complete__Lattice_Ocomplete__lattice(_1549143), -(c_Complete__Lattice_OSup__class_OSup(_1549143, _1549145) = c_Complete__Lattice_OInf__class_OInf(_1549143, hAPP(c_Set_OCollect(_1549143), hAPP(hAPP(c_COMBB(tc_fun(_1549143, tc_HOL_Obool), tc_HOL_Obool, _1549143), c_HOL_OAll(_1549143)), hAPP(hAPP(c_COMBB(tc_fun(_1549143, tc_HOL_Obool), tc_fun(_1549143, tc_HOL_Obool), _1549143), hAPP(c_COMBS(_1549143, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549143), c_fimplies), hAPP(hAPP(c_COMBC(_1549143, tc_fun(_1549143, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549143)), _1549145)))), hAPP(c_COMBC(_1549143, _1549143, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1549143)))))))], (40536 ^ _776541) ^ [_1567781, _1567783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1567781), _1567783)), -(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), _1567781), _1567783)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (41905 ^ _776541) ^ [_1604294, _1604296, _1604298, _1604300, _1604302] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604294), tc_List_Olist(_1604294))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604294), tc_List_Olist(_1604294)), _1604296), _1604298)), c_List_Olistrel1(_1604294, _1604300))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604294), tc_List_Olist(_1604294))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604294), tc_List_Olist(_1604294)), hAPP(hAPP(c_List_Olist_OCons(_1604294), _1604302), _1604296)), hAPP(hAPP(c_List_Olist_OCons(_1604294), _1604302), _1604298))), c_List_Olistrel1(_1604294, _1604300))))], (6382 ^ _776541) ^ [_879529, _879531] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879529, tc_HOL_Obool)), _879531), _879531)))], (14616 ^ _776541) ^ [_1040111, _1040113, _1040115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040111), _1040113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040113), _1040115))))], (13073 ^ _776541) ^ [_1007312, _1007314, _1007316] : [class_Lattices_Oab__semigroup__idem__mult(_1007312), hAPP(_1007314, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007312), 13078 ^ [_1007312, _1007314, _1007316]), 13079 ^ [_1007312, _1007314, _1007316])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007312), hAPP(_1007314, 13078 ^ [_1007312, _1007314, _1007316])), hAPP(_1007314, 13079 ^ [_1007312, _1007314, _1007316])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007312), _1007316)), -(_1007316 = c_Orderings_Obot__class_Obot(tc_fun(_1007312, tc_HOL_Obool))), -(hAPP(_1007314, hAPP(c_Finite__Set_Ofold1(_1007312, c_Groups_Otimes__class_Otimes(_1007312)), _1007316)) = hAPP(c_Finite__Set_Ofold1(_1007312, c_Groups_Otimes__class_Otimes(_1007312)), hAPP(c_Set_Oimage(_1007312, _1007312, _1007314), _1007316)))], (5136 ^ _776541) ^ [_854904, _854906, _854908, _854910, _854912, _854914] : [-(c_Set_Oimage(_854914, _854910, _854906) = c_Set_Oimage(_854912, _854908, _854904)), _854914 = _854912, _854910 = _854908, _854906 = _854904], (11495 ^ _776541) ^ [_977375, _977377] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_977375), c_Complete__Lattice_OInf__class_OInf(tc_fun(_977375, tc_HOL_Obool), _977377)))), 11496 ^ _776541 : [(11497 ^ _776541) ^ [_977439] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_977375, tc_HOL_Obool)), _977439), _977377)), hBOOL(hAPP(c_Finite__Set_Ofinite(_977375), _977439))]]], (22527 ^ _776541) ^ [_1184813, _1184815, _1184817] : [class_Rings_Olinordered__semidom(_1184813), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184813), c_Groups_Ozero__class_Ozero(_1184813)), _1184815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184813), c_Groups_Ozero__class_Ozero(_1184813)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184813), _1184815), _1184817))))], (36330 ^ _776541) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (14370 ^ _776541) ^ [_1035742, _1035744, _1035746, _1035748] : [class_Rings_Ocomm__semiring__1(_1035742), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035742), _1035744), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035742), _1035746), _1035748)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035742), _1035744), _1035746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035742), _1035744), _1035748)))], (48231 ^ _776541) ^ [_1748031, _1748033] : [-(c_FunDef_Ois__measure(_1748031, _1748033))], (52031 ^ _776541) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (50029 ^ _776541) ^ [_1787205, _1787207, _1787209, _1787211] : [hAPP(c_Set_Oimage(_1787205, _1787207, _1787209), c_Orderings_Otop__class_Otop(tc_fun(_1787205, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1787207, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1787205, _1787207, _1787209), hAPP(c_Set_Oimage(_1787207, _1787205, c_Hilbert__Choice_Oinv__into(_1787205, _1787207, c_Orderings_Otop__class_Otop(tc_fun(_1787205, tc_HOL_Obool)), _1787209)), _1787211)) = _1787211)], (29591 ^ _776541) ^ [_1306787, _1306789, _1306791] : [class_Groups_Omonoid__mult(_1306787), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1306787), _1306789), 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)))), _1306791))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306787), _1306789), hAPP(hAPP(c_Power_Opower__class_Opower(_1306787), hAPP(hAPP(c_Power_Opower__class_Opower(_1306787), _1306789), _1306791)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (42697 ^ _776541) ^ [_1626732, _1626734, _1626736, _1626738, _1626740] : [-(hAPP(hAPP(c_List_Olist__update(_1626732, hAPP(hAPP(c_List_Olist__update(_1626732, _1626734), _1626736), _1626738)), _1626736), _1626740) = hAPP(hAPP(c_List_Olist__update(_1626732, _1626734), _1626736), _1626740))], (27631 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (29845 ^ _776541) ^ [_1311648] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1311648)], (11018 ^ _776541) ^ [_966946, _966948, _966950, _966952, _966954] : [hAPP(c_Set_Oimage(_966946, _966948, _966950), _966952) = _966954, -(hAPP(c_Set_Oimage(tc_fun(_966946, tc_HOL_Obool), tc_fun(_966948, tc_HOL_Obool), c_Set_Oimage(_966946, _966948, _966950)), hAPP(c_Set_OPow(_966946), _966952)) = hAPP(c_Set_OPow(_966948), _966954))], (52399 ^ _776541) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (42707 ^ _776541) ^ [_1626963, _1626965, _1626967, _1626969, _1626971] : [-(hAPP(hAPP(c_List_Olist__update(_1626963, hAPP(hAPP(c_List_Olist_OCons(_1626963), _1626965), _1626967)), hAPP(c_Nat_OSuc, _1626969)), _1626971) = hAPP(hAPP(c_List_Olist_OCons(_1626963), _1626965), hAPP(hAPP(c_List_Olist__update(_1626963, _1626967), _1626969), _1626971)))], (37608 ^ _776541) ^ [_1492461, _1492463, _1492465, _1492467, _1492469, _1492471] : [c_Fun_Oinj__on(_1492461, _1492463, _1492465, _1492467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492461, tc_HOL_Obool)), _1492469), _1492467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492461, tc_HOL_Obool)), _1492471), _1492467)), -(hAPP(c_Set_Oimage(_1492461, _1492463, _1492465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492461, tc_HOL_Obool)), _1492469), _1492471)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492463, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492461, _1492463, _1492465), _1492469)), hAPP(c_Set_Oimage(_1492461, _1492463, _1492465), _1492471)))], (44988 ^ _776541) ^ [_1677445, _1677447, _1677449, _1677451, _1677453] : [class_Groups_Ocomm__monoid__add(_1677445), hBOOL(hAPP(hAPP(c_member(_1677447), _1677449), hAPP(c_List_Oset(_1677447), _1677451))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677445), hAPP(hAPP(c_List_Omap(_1677447, _1677445), _1677453), _1677451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1677445), hAPP(_1677453, _1677449)), hAPP(c_List_Omonoid__add__class_Olistsum(_1677445), hAPP(hAPP(c_List_Omap(_1677447, _1677445), _1677453), c_List_Oremove1(_1677447, _1677449, _1677451)))))], (17947 ^ _776541) ^ [_1099398, _1099400] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1099398, _1099400)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1099400)), _1099398))], (15860 ^ _776541) ^ [_1063674, _1063676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063674), hAPP(c_Nat_OSuc, _1063676))), _1063674)))], (15081 ^ _776541) ^ [_1048862, _1048864] : [class_Rings_Ocomm__semiring__1(_1048862), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048862), c_Groups_Oone__class_Oone(_1048862)), _1048864) = _1048864)], (31625 ^ _776541) ^ [_1344320, _1344322, _1344324, _1344326] : [class_Orderings_Olinorder(_1344320), 31628 ^ _776541 : [(31629 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344320), _1344322), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344320), _1344324), _1344326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344320), _1344322), _1344324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344320), _1344322), _1344326)))], (31639 ^ _776541) ^ [] : [31640 ^ _776541 : [(31643 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344320), _1344322), _1344326))], (31641 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344320), _1344322), _1344324))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344320), _1344322), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344320), _1344324), _1344326))))]]], (52049 ^ _776541) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (32882 ^ _776541) ^ [_1375760, _1375762, _1375764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375760, tc_HOL_Obool)), _1375762), _1375764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375760, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1375760, tc_fun(_1375760, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375760)), _1375762)), hAPP(hAPP(c_COMBC(_1375760, tc_fun(_1375760, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375760)), _1375764))))], (48780 ^ _776541) ^ [_1759770, _1759772, _1759774, _1759776] : [-(hAPP(c_New__DSequence_Opos__union(_1759770, _1759772, _1759774), _1759776) = c_Lazy__Sequence_Oappend(_1759770, hAPP(_1759772, _1759776), hAPP(_1759774, _1759776)))], (36645 ^ _776541) ^ [_1471307, _1471309, _1471311] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471307, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471307), _1471309), _1471311), -(_1471309 = c_Orderings_Obot__class_Obot(tc_fun(_1471307, tc_HOL_Obool)))], (39888 ^ _776541) ^ [_1552732, _1552734, _1552736, _1552738] : [c_Finite__Set_Ofun__left__comm__idem(_1552732, _1552734, _1552736), -(hAPP(c_Fun_Ocomp(_1552734, _1552734, _1552734, hAPP(_1552736, _1552738)), hAPP(_1552736, _1552738)) = hAPP(_1552736, _1552738))], (52163 ^ _776541) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (362 ^ _776541) ^ [_782006, _782008, _782010, _782012, _782014, _782016, _782018, _782020] : [-(c_Finite__Set_Ofolding__idem(_782018, _782014, _782010, _782006)), c_Finite__Set_Ofolding__idem(_782020, _782016, _782012, _782008), _782020 = _782018, _782016 = _782014, _782012 = _782010, _782008 = _782006], (45984 ^ _776541) ^ [_1699105, _1699107, _1699109] : [45986 ^ _776541 : [(45989 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1699105), tc_List_Olist(_1699105), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699105), tc_fun(tc_List_Olist(_1699105), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699105), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1699105), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699105), tc_HOL_Obool)), tc_List_Olist(_1699105)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1699105))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1699105)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1699105))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1699105)))), 45985 ^ [_1699105, _1699107, _1699109]))], (45987 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1699105), tc_List_Olist(_1699105))), 45985 ^ [_1699105, _1699107, _1699109]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1699105), tc_List_Olist(_1699105))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1699105), tc_List_Olist(_1699105)), _1699107), _1699109)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699105))), _1699107) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699105))), _1699109), 45994 ^ _776541 : [(46001 ^ _776541) ^ [] : [_1699107 = _1699109, -(c_List_Oconcat(_1699105, _1699107) = c_List_Oconcat(_1699105, _1699109))], (45995 ^ _776541) ^ [] : [c_List_Oconcat(_1699105, _1699107) = c_List_Oconcat(_1699105, _1699109), -(_1699107 = _1699109)]]], (38820 ^ _776541) ^ [_1522947, _1522949, _1522951, _1522953, _1522955] : [hAPP(c_Set_Oimage(_1522947, _1522949, _1522951), c_Orderings_Otop__class_Otop(tc_fun(_1522947, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522949, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522947, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522947, _1522949, _1522951), _1522953)), _1522955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522949, tc_HOL_Obool)), _1522953), hAPP(c_Set_Oimage(_1522947, _1522949, _1522951), _1522955))))], (47938 ^ _776541) ^ [_1742212, _1742214, _1742216, _1742218] : [class_Orderings_Oorder(_1742212), class_Enum_Oenum(_1742214), 47945 ^ _776541 : [(47952 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742214), hAPP(hAPP(c_COMBS(_1742214, _1742212, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1742212, tc_fun(_1742212, tc_HOL_Obool), _1742214), c_Orderings_Oord__class_Oless__eq(_1742212)), _1742216)), _1742218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1742214, _1742212)), _1742216), _1742218)))], (47946 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1742214, _1742212)), _1742216), _1742218)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742214), hAPP(hAPP(c_COMBS(_1742214, _1742212, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1742212, tc_fun(_1742212, tc_HOL_Obool), _1742214), c_Orderings_Oord__class_Oless__eq(_1742212)), _1742216)), _1742218))))]]], (14308 ^ _776541) ^ [_1034417, _1034419, _1034421, _1034423, _1034425] : [class_Rings_Ocomm__semiring__1(_1034417), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034417), _1034419), _1034421)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034417), _1034423), _1034425)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034417), _1034419), _1034423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034417), _1034421), _1034425)))], (15344 ^ _776541) ^ [_1053543, _1053545, _1053547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053543), _1053545)), 15347 ^ _776541 : [(15354 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1053543), _1053547), _1053545))), -(hAPP(c_Finite__Set_Ocard(_1053543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053543, tc_HOL_Obool)), _1053545), hAPP(hAPP(c_Set_Oinsert(_1053543), _1053547), c_Orderings_Obot__class_Obot(tc_fun(_1053543, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1053543), _1053545))], (15348 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1053543), _1053547), _1053545)), -(hAPP(c_Finite__Set_Ocard(_1053543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053543, tc_HOL_Obool)), _1053545), hAPP(hAPP(c_Set_Oinsert(_1053543), _1053547), c_Orderings_Obot__class_Obot(tc_fun(_1053543, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1053543), _1053545)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (7536 ^ _776541) ^ [_900810, _900812, _900814, _900816] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_900810, tc_HOL_Obool)), _900812), _900814), _900816)), -(hBOOL(hAPP(_900812, _900816)))], (41408 ^ _776541) ^ [_1589665, _1589667, _1589669, _1589671] : [-(hAPP(_1589665, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589667, _1589667), _1589669), _1589665), _1589671)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589667, _1589667), _1589669), _1589665), hAPP(_1589665, _1589671)))], (28141 ^ _776541) ^ [_1281888] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1281888) = c_Int_Opred(_1281888))], (40122 ^ _776541) ^ [_1558187, _1558189, _1558191, _1558193, _1558195, _1558197, _1558199, _1558201] : [c_Finite__Set_Ofolding(_1558187, _1558189, _1558191, _1558193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558187), _1558195)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558187), _1558197)), -(hAPP(c_Fun_Ocomp(_1558189, _1558189, _1558199, hAPP(_1558193, _1558197)), hAPP(c_Fun_Ocomp(_1558189, _1558189, _1558199, hAPP(_1558193, _1558195)), _1558201)) = hAPP(c_Fun_Ocomp(_1558189, _1558189, _1558199, hAPP(_1558193, _1558195)), hAPP(c_Fun_Ocomp(_1558189, _1558189, _1558199, hAPP(_1558193, _1558197)), _1558201)))], (7266 ^ _776541) ^ [_895193, _895195, _895197] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895193, tc_HOL_Obool)), _895195), hAPP(hAPP(c_Set_Oinsert(_895193), _895197), _895195))))], (52451 ^ _776541) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (5194 ^ _776541) ^ [_855809, _855811, _855813, _855815] : [-(c_Transitive__Closure_Otrancl(_855815, _855811) = c_Transitive__Closure_Otrancl(_855813, _855809)), _855815 = _855813, _855811 = _855809], (9849 ^ _776541) ^ [_945287, _945289, _945291] : [class_Complete__Lattice_Ocomplete__lattice(_945287), class_Orderings_Olinorder(_945287), 9856 ^ _776541 : [(9866 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945287), c_Complete__Lattice_OInf__class_OInf(_945287, _945289)), _945291))), 9867 ^ _776541 : [(9868 ^ _776541) ^ [_945593] : [hBOOL(hAPP(hAPP(c_member(_945287), _945593), _945289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945287), _945593), _945291))]]], (9857 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945287), c_Complete__Lattice_OInf__class_OInf(_945287, _945289)), _945291)), 9861 ^ _776541 : [(9864 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945287), 9860 ^ [_945287, _945289, _945291]), _945291)))], (9862 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945287), 9860 ^ [_945287, _945289, _945291]), _945289)))]]]]], (1754 ^ _776541) ^ [_801330, _801332] : [-(class_Orderings_Olinorder(_801330)), _801332 = _801330, class_Orderings_Olinorder(_801332)], (48814 ^ _776541) ^ [_1760434, _1760436] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760434), _1760436))), -(c_Lazy__Sequence_Osmall__lazy_H(_1760434, _1760436) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1760436), c_Lazy__Sequence_Osmall__lazy_H(_1760434, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1760436), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49068 ^ _776541) ^ [_1766294, _1766296, _1766298] : [c_List_Oall__interval__int(_1766294, _1766296, _1766298), -(c_List_Olist__all(tc_Int_Oint, _1766294, c_List_Oupto(_1766296, _1766298)))], (38854 ^ _776541) ^ [_1523700, _1523702, _1523704, _1523706] : [-(hBOOL(hAPP(hAPP(c_member(_1523700), _1523702), _1523704))), -(hAPP(c_Set_Ovimage(_1523706, _1523700, hAPP(c_COMBK(_1523700, _1523706), _1523702)), _1523704) = c_Orderings_Obot__class_Obot(tc_fun(_1523706, tc_HOL_Obool)))], (2646 ^ _776541) ^ [_815569, _815571, _815573, _815575] : [-(c_Set_Othe__elem(_815575, _815571) = c_Set_Othe__elem(_815573, _815569)), _815575 = _815573, _815571 = _815569], (45416 ^ _776541) ^ [_1686766, _1686768, _1686770] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1686766)), _1686770), c_List_Olists(_1686766, _1686768))), -(hBOOL(hAPP(c_List_Olistsp(_1686766, hAPP(hAPP(c_COMBC(_1686766, tc_fun(_1686766, tc_HOL_Obool), tc_HOL_Obool), c_member(_1686766)), _1686768)), _1686770)))], (11662 ^ _776541) ^ [_980554, _980556, _980558] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_980554), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980554, tc_HOL_Obool)), _980556), _980558)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_980554), _980556)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980554), _980558))], (31679 ^ _776541) ^ [_1345407, _1345409, _1345411] : [class_Groups_Olinordered__ab__group__add(_1345407), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1345407), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345407), _1345409), _1345411)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345407), hAPP(c_Groups_Ouminus__class_Ouminus(_1345407), _1345409)), hAPP(c_Groups_Ouminus__class_Ouminus(_1345407), _1345411)))], (24034 ^ _776541) ^ [_1211669, _1211671] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211669)), _1211671) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211669), _1211671)))], (29313 ^ _776541) ^ [] : [-(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)))))], (17257 ^ _776541) ^ [_1087213, _1087215] : [class_Groups_Olinordered__ab__group__add(_1087213), 17260 ^ _776541 : [(17267 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087213), _1087215), c_Groups_Ozero__class_Ozero(_1087213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087213), _1087215), _1087215)), c_Groups_Ozero__class_Ozero(_1087213))))], (17261 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087213), _1087215), _1087215)), c_Groups_Ozero__class_Ozero(_1087213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087213), _1087215), c_Groups_Ozero__class_Ozero(_1087213))))]]], (36025 ^ _776541) ^ [_1453813, _1453815, _1453817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1453813, tc_HOL_Obool), tc_fun(_1453813, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1453813, tc_HOL_Obool), tc_fun(_1453813, tc_HOL_Obool)), _1453815), _1453817)), c_Wellfounded_Ofinite__psubset(_1453813))), 36028 ^ _776541 : [(36031 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1453813), _1453817)))], (36029 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1453813, tc_HOL_Obool)), _1453815), _1453817)))]]], (33629 ^ _776541) ^ [_1397371, _1397373, _1397375, _1397377, _1397379] : [-(hAPP(c_Set_Oimage(_1397371, _1397373, hAPP(hAPP(c_COMBB(_1397375, _1397373, _1397371), _1397377), _1397379)), c_Orderings_Otop__class_Otop(tc_fun(_1397371, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1397375, _1397373, _1397377), hAPP(c_Set_Oimage(_1397371, _1397375, _1397379), c_Orderings_Otop__class_Otop(tc_fun(_1397371, tc_HOL_Obool)))))], (17113 ^ _776541) ^ [_1084651, _1084653, _1084655] : [class_Rings_Oordered__cancel__semiring(_1084651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084651), c_Groups_Ozero__class_Ozero(_1084651)), _1084653)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084651), _1084655), c_Groups_Ozero__class_Ozero(_1084651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084651), _1084653), _1084655)), c_Groups_Ozero__class_Ozero(_1084651))))], (36253 ^ _776541) ^ [_1460810, _1460812, _1460814, _1460816, _1460818] : [class_Groups_Ocomm__monoid__add(_1460810), class_Groups_Ocomm__monoid__mult(_1460810), _1460812 = _1460814, c_Nat__Transfer_Onat__set(_1460814), 36271 ^ _776541 : [(36274 ^ _776541) ^ [] : [hAPP(_1460816, 36270 ^ [_1460810, _1460812, _1460814, _1460816, _1460818]) = hAPP(_1460818, 36270 ^ [_1460810, _1460812, _1460814, _1460816, _1460818])], (36272 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36270 ^ [_1460810, _1460812, _1460814, _1460816, _1460818])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1460810), _1460816), _1460812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1460810), _1460818), _1460814))], (48233 ^ _776541) ^ [_1748056, _1748058] : [-(c_FunDef_Ois__measure(_1748056, _1748058))], (27064 ^ _776541) ^ [_1263906, _1263908] : [c_Nat__Transfer_Onat__set(_1263906), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1263908), _1263906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263908)))], (44747 ^ _776541) ^ [_1671188, _1671190, _1671192, _1671194, _1671196] : [-(hAPP(hAPP(c_List_Otake(_1671188), _1671190), hAPP(hAPP(c_List_Omap(_1671192, _1671188), _1671194), _1671196)) = hAPP(hAPP(c_List_Omap(_1671192, _1671188), _1671194), hAPP(hAPP(c_List_Otake(_1671192), _1671190), _1671196)))], (40012 ^ _776541) ^ [_1555494, _1555496, _1555498, _1555500, _1555502, _1555504, _1555506] : [c_Fun_Oinj__on(_1555494, _1555496, _1555498, hAPP(c_Set_Oimage(_1555500, _1555494, _1555502), _1555504)), c_Fun_Oinj__on(_1555500, _1555494, _1555502, _1555504), hBOOL(hAPP(hAPP(c_member(_1555496), _1555506), hAPP(c_Set_Oimage(_1555494, _1555496, _1555498), hAPP(c_Set_Oimage(_1555500, _1555494, _1555502), _1555504)))), -(hAPP(c_Fun_Othe__inv__into(_1555500, _1555496, _1555504, hAPP(c_Fun_Ocomp(_1555494, _1555496, _1555500, _1555498), _1555502)), _1555506) = hAPP(hAPP(c_Fun_Ocomp(_1555494, _1555500, _1555496, c_Fun_Othe__inv__into(_1555500, _1555494, _1555504, _1555502)), c_Fun_Othe__inv__into(_1555494, _1555496, hAPP(c_Set_Oimage(_1555500, _1555494, _1555502), _1555504), _1555498)), _1555506))], (14602 ^ _776541) ^ [_1039813, _1039815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039813), _1039815)), _1039815))], (7654 ^ _776541) ^ [_903771, _903773, _903775] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903771, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903771, tc_HOL_Obool)), _903773), _903775)), _903775) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903771, tc_HOL_Obool)), _903773), _903775))], (37943 ^ _776541) ^ [_1500997, _1500999, _1501001, _1501003] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500997, _1500999, _1501001), _1501003), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500999, _1501001), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500997, _1501001), tc_HOL_Obool)))], (47339 ^ _776541) ^ [_1728271, _1728273] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1728271), _1728273) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1728271)), c_List_Oembed__list(_1728273))))], (24154 ^ _776541) ^ [_1213517, _1213519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213519), 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), _1213517), _1213519)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45030 ^ _776541) ^ [_1678419, _1678421] : [_1678419 = _1678421, -(hAPP(c_Code__Numeral_Oof__nat, _1678419) = hAPP(c_Code__Numeral_Oof__nat, _1678421))], (32438 ^ _776541) ^ [_1360436, _1360438, _1360440, _1360442, _1360444] : [_1360436 = c_Orderings_Obot__class_Obot(tc_fun(_1360438, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360440, tc_HOL_Obool)), _1360442), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360438, tc_fun(_1360440, tc_HOL_Obool)), _1360436), _1360444)) = _1360442)], (10178 ^ _776541) ^ [_951206, _951208, _951210, _951212] : [class_Orderings_Olinorder(_951206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951206), _951208), _951210)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951206), _951210), _951212)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951206, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_951206, _951208, _951210)), c_SetInterval_Oord__class_OgreaterThanLessThan(_951206, _951210, _951212)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951206, _951208), _951212))], (51767 ^ _776541) ^ [_1823259, _1823261] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823259), _1823261)), 51770 ^ _776541 : [(51777 ^ _776541) ^ [] : [_1823261 = _1823259, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823261), _1823259)))], (51771 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823261), _1823259)), -(_1823261 = _1823259)]]], (41949 ^ _776541) ^ [_1605759, _1605761, _1605763, _1605765, _1605767, _1605769] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605759), tc_List_Olist(_1605759))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605759), tc_List_Olist(_1605759)), hAPP(hAPP(c_List_Olist_OCons(_1605759), _1605761), _1605763)), hAPP(hAPP(c_List_Olist_OCons(_1605759), _1605765), _1605767))), c_List_Olistrel1(_1605759, _1605769)))), 41950 ^ _776541 : [(41957 ^ _776541) ^ [] : [_1605761 = _1605765, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605759), tc_List_Olist(_1605759))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605759), tc_List_Olist(_1605759)), _1605763), _1605767)), c_List_Olistrel1(_1605759, _1605769)))], (41951 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605759, _1605759)), hAPP(hAPP(c_Product__Type_OPair(_1605759, _1605759), _1605761), _1605765)), _1605769)), _1605763 = _1605767]]], (37214 ^ _776541) ^ [_1484848, _1484850, _1484852] : [-(c_Fun_Oinj__on(_1484848, _1484850, _1484852, c_Orderings_Obot__class_Obot(tc_fun(_1484848, tc_HOL_Obool))))], (42863 ^ _776541) ^ [_1630516, _1630518] : [hBOOL(hAPP(c_List_Odistinct(_1630516), _1630518)), -(hAPP(c_Finite__Set_Ocard(_1630516), hAPP(c_List_Oset(_1630516), _1630518)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630516)), _1630518))], (13738 ^ _776541) ^ [_1021276, _1021278, _1021280, _1021282] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1021276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021276), _1021278), _1021280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021276), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021276), _1021282), _1021278)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021276), _1021282), _1021280))))], (8661 ^ _776541) ^ [_925378, _925380, _925382] : [class_Lattices_Osemilattice__inf(_925378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925378), _925380), _925382)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925378), _925380), _925382) = _925380)], (34998 ^ _776541) ^ [_1429539, _1429541, _1429543, _1429545, _1429547] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1429539, _1429541), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1429543), _1429545))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429541)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429547), _1429539), _1429541), 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), _1429547), _1429543)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429547), _1429545)), _1429541))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429547), _1429545), _1429541)))))], (21064 ^ _776541) ^ [_1157219, _1157221, _1157223, _1157225] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1157219, tc_Nat_Onat), _1157221), _1157223) = hAPP(c_Nat_OSuc, _1157225), 21068 ^ _776541 : [(21071 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1157221, 21067 ^ [_1157219, _1157221, _1157223, _1157225]))))], (21069 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1157219), 21067 ^ [_1157219, _1157221, _1157223, _1157225]), _1157223)))]]], (51433 ^ _776541) ^ [_1817525, _1817527, _1817529] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817525), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1817527), _1817529))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817525), _1817529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1817529), _1817527)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817525), _1817527)))], (40176 ^ _776541) ^ [_1559364, _1559366, _1559368, _1559370, _1559372, _1559374] : [c_Finite__Set_Ofolding(_1559364, _1559366, _1559368, _1559370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559364), _1559372)), -(hAPP(hAPP(_1559370, _1559372), _1559374) = hAPP(hAPP(c_Finite__Set_Ofold(_1559364, _1559366, _1559368), _1559374), _1559372))], (24413 ^ _776541) ^ [_1218009, _1218011, _1218013, _1218015] : [_1218009 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218011), _1218013)), _1218015), -(_1218011 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1218009), _1218011) = _1218013), 24420 ^ _776541 : [(24423 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218015), _1218011))], (24421 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218011)))]], 24428 ^ _776541 : [(24431 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218011), _1218015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1218015), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24429 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218011))]]], (42238 ^ _776541) ^ [_1614188, _1614190, _1614192, _1614194] : [_1614188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1614190), hAPP(hAPP(c_List_Olist_OCons(_1614190), _1614192), _1614194)), _1614188) = _1614192)], (42043 ^ _776541) ^ [_1608516, _1608518, _1608520, _1608522, _1608524, _1608526] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608516, _1608516)), hAPP(hAPP(c_Product__Type_OPair(_1608516, _1608516), _1608518), _1608520)), _1608522)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608516), tc_List_Olist(_1608516))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608516), tc_List_Olist(_1608516)), _1608524), _1608526)), c_List_Olistrel(_1608516, _1608522))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608516), tc_List_Olist(_1608516))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608516), tc_List_Olist(_1608516)), hAPP(hAPP(c_List_Olist_OCons(_1608516), _1608518), _1608524)), hAPP(hAPP(c_List_Olist_OCons(_1608516), _1608520), _1608526))), c_List_Olistrel(_1608516, _1608522))))], (41643 ^ _776541) ^ [_1596207, _1596209, _1596211, _1596213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596207, _1596209)), _1596211), hAPP(c_Relation_Oconverse(_1596209, _1596207), _1596213))), 41648 ^ _776541 : [(41651 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596209, _1596207)), hAPP(hAPP(c_Product__Type_OPair(_1596209, _1596207), 41646 ^ [_1596207, _1596209, _1596211, _1596213]), 41647 ^ [_1596207, _1596209, _1596211, _1596213])), _1596213)))], (41649 ^ _776541) ^ [] : [-(_1596211 = hAPP(hAPP(c_Product__Type_OPair(_1596207, _1596209), 41647 ^ [_1596207, _1596209, _1596211, _1596213]), 41646 ^ [_1596207, _1596209, _1596211, _1596213]))]]], (52183 ^ _776541) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (38444 ^ _776541) ^ [_1513511, _1513513, _1513515] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1513511), _1513513), _1513515) = c_Nitpick_OAbs__Frac(_1513511, c_Nitpick_Onorm__frac(_1513513, _1513515)))], (26208 ^ _776541) ^ [_1249946, _1249948] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249946) = _1249948), _1249946 = hAPP(c_Int_Onat, _1249948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249948))], (45353 ^ _776541) ^ [_1685384, _1685386, _1685388, _1685390] : [hBOOL(hAPP(c_List_Olistsp(_1685384, _1685386), _1685388)), hBOOL(hAPP(c_List_Olistsp(_1685384, _1685390), _1685388)), -(hBOOL(hAPP(c_List_Olistsp(_1685384, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1685384, tc_HOL_Obool)), _1685386), _1685390)), _1685388)))], (7530 ^ _776541) ^ [_900699, _900701, _900703, _900705] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_900699, tc_HOL_Obool)), _900701), _900703), _900705)), -(hBOOL(hAPP(_900703, _900705)))], (39295 ^ _776541) ^ [_1536003, _1536005, _1536007, _1536009, _1536011, _1536013, _1536015] : [class_Rings_Osemiring__0(_1536003), c_Fun_Oinj__on(tc_prod(_1536005, _1536007), _1536003, hAPP(c_Product__Type_Oprod_Oprod__case(_1536005, _1536007, _1536003), hAPP(hAPP(c_COMBC(_1536005, tc_fun(_1536007, _1536003), tc_fun(_1536007, _1536003)), hAPP(hAPP(c_COMBB(tc_fun(_1536003, _1536003), tc_fun(tc_fun(_1536007, _1536003), tc_fun(_1536007, _1536003)), _1536005), c_COMBB(_1536003, _1536003, _1536007)), hAPP(hAPP(c_COMBB(_1536003, tc_fun(_1536003, _1536003), _1536005), c_Groups_Otimes__class_Otimes(_1536003)), _1536009))), _1536011)), hAPP(hAPP(c_Product__Type_OSigma(_1536005, _1536007), _1536013), hAPP(c_COMBK(tc_fun(_1536007, tc_HOL_Obool), _1536005), _1536015))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1536003), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536005, _1536003), _1536009), _1536013)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536007, _1536003), _1536011), _1536015)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536003, _1536003), c_Fun_Oid(_1536003)), hAPP(c_Set_OCollect(_1536003), hAPP(hAPP(c_COMBB(tc_fun(_1536005, tc_HOL_Obool), tc_HOL_Obool, _1536003), c_HOL_OEx(_1536005)), hAPP(hAPP(c_COMBB(tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool)), tc_fun(_1536005, tc_HOL_Obool), _1536003), hAPP(c_COMBB(tc_fun(_1536007, tc_HOL_Obool), tc_HOL_Obool, _1536005), c_HOL_OEx(_1536007))), hAPP(hAPP(c_COMBC(_1536003, tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool)), tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536005, tc_fun(tc_fun(_1536007, tc_HOL_Obool), tc_fun(_1536007, tc_HOL_Obool))), tc_fun(tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool)), tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool))), _1536003), c_COMBS(_1536005, tc_fun(_1536007, tc_HOL_Obool), tc_fun(_1536007, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536005, tc_fun(_1536007, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1536005, tc_fun(tc_fun(_1536007, tc_HOL_Obool), tc_fun(_1536007, tc_HOL_Obool))), _1536003), hAPP(c_COMBB(tc_fun(_1536007, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1536007, tc_HOL_Obool), tc_fun(_1536007, tc_HOL_Obool)), _1536005), c_COMBS(_1536007, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool)), tc_fun(_1536005, tc_fun(_1536007, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1536003), hAPP(c_COMBB(tc_fun(_1536007, tc_HOL_Obool), tc_fun(_1536007, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1536005), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536007), c_fconj))), hAPP(hAPP(c_COMBC(_1536003, tc_fun(_1536005, tc_fun(_1536007, _1536003)), tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1536007, _1536003), tc_fun(_1536007, tc_HOL_Obool)), tc_fun(tc_fun(_1536005, tc_fun(_1536007, _1536003)), tc_fun(_1536005, tc_fun(_1536007, tc_HOL_Obool))), _1536003), c_COMBB(tc_fun(_1536007, _1536003), tc_fun(_1536007, tc_HOL_Obool), _1536005)), hAPP(hAPP(c_COMBB(tc_fun(_1536003, tc_HOL_Obool), tc_fun(tc_fun(_1536007, _1536003), tc_fun(_1536007, tc_HOL_Obool)), _1536003), c_COMBB(_1536003, tc_HOL_Obool, _1536007)), c_fequal))), hAPP(hAPP(c_COMBC(_1536005, tc_fun(_1536007, _1536003), tc_fun(_1536007, _1536003)), hAPP(hAPP(c_COMBB(tc_fun(_1536003, _1536003), tc_fun(tc_fun(_1536007, _1536003), tc_fun(_1536007, _1536003)), _1536005), c_COMBB(_1536003, _1536003, _1536007)), hAPP(hAPP(c_COMBB(_1536003, tc_fun(_1536003, _1536003), _1536005), c_Groups_Otimes__class_Otimes(_1536003)), _1536009))), _1536011)))))), hAPP(hAPP(c_COMBC(_1536005, tc_fun(_1536007, tc_HOL_Obool), tc_fun(_1536007, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1536007, tc_HOL_Obool), tc_fun(_1536007, tc_HOL_Obool)), _1536005), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536007)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536005), c_fconj), hAPP(hAPP(c_COMBC(_1536005, tc_fun(_1536005, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536005)), _1536013)))), hAPP(hAPP(c_COMBC(_1536007, tc_fun(_1536007, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536007)), _1536015))))))))], (43352 ^ _776541) ^ [_1640566, _1640568, _1640570, _1640572, _1640574] : [_1640566 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1640568, _1640570, _1640572), _1640566), _1640574) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640570), _1640568), c_List_Olist_ONil(_1640570)), _1640574))], (51179 ^ _776541) ^ [_1812936, _1812938, _1812940] : [class_Divides_Osemiring__div(_1812936), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812936), _1812938), _1812940)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812936), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812936), _1812940), _1812938)), _1812938) = _1812940)], (22789 ^ _776541) ^ [_1189450, _1189452] : [class_Power_Opower(_1189450), class_Rings_Osemiring__0(_1189450), 22796 ^ _776541 : [(22803 ^ _776541) ^ [] : [-(_1189452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1189450), c_Groups_Ozero__class_Ozero(_1189450)), _1189452) = c_Groups_Ozero__class_Ozero(_1189450))], (22797 ^ _776541) ^ [] : [_1189452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1189450), c_Groups_Ozero__class_Ozero(_1189450)), _1189452) = c_Groups_Oone__class_Oone(_1189450))]]], (7448 ^ _776541) ^ [_899193, _899195, _899197, _899199] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899193, tc_HOL_Obool)), _899195), _899197), _899199)), -(hBOOL(hAPP(_899195, _899199))), -(hBOOL(hAPP(_899197, _899199)))], (38398 ^ _776541) ^ [_1512680, _1512682] : [c_Wellfounded_Owf(_1512680, _1512682), -(c_Wellfounded_Owf(tc_List_Olist(_1512680), c_List_Olex(_1512680, _1512682)))], (8233 ^ _776541) ^ [_917371, _917373, _917375] : [class_Lattices_Obounded__lattice__top(_917371), 8236 ^ _776541 : [(8245 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917371), _917373), _917375) = c_Orderings_Otop__class_Otop(_917371)), _917373 = c_Orderings_Otop__class_Otop(_917371), _917375 = c_Orderings_Otop__class_Otop(_917371)], (8237 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917371), _917373), _917375) = c_Orderings_Otop__class_Otop(_917371), 8240 ^ _776541 : [(8243 ^ _776541) ^ [] : [-(_917375 = c_Orderings_Otop__class_Otop(_917371))], (8241 ^ _776541) ^ [] : [-(_917373 = c_Orderings_Otop__class_Otop(_917371))]]]]], (43002 ^ _776541) ^ [_1633703, _1633705] : [-(_1633703 = c_List_Olist_ONil(_1633705)), hBOOL(hAPP(c_List_Odistinct(_1633705), _1633703)), -(hBOOL(hAPP(c_List_Odistinct(_1633705), c_List_Obutlast(_1633705, _1633703))))], (26230 ^ _776541) ^ [_1250304, _1250306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250304)), _1250306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250304), hAPP(c_Int_Onat, _1250306))))], (26040 ^ _776541) ^ [_1247179, _1247181, _1247183] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247179, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247181), _1247183)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247181), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247179), _1247181), _1247183))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247179, _1247181)))], (30802 ^ _776541) ^ [_1329010, _1329012, _1329014] : [class_Orderings_Olinorder(_1329010), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329010), _1329012)), -(_1329012 = c_Orderings_Obot__class_Obot(tc_fun(_1329010, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329010), _1329014)), -(_1329014 = c_Orderings_Obot__class_Obot(tc_fun(_1329010, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1329010, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329010, tc_HOL_Obool)), _1329012), _1329014)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329010), c_Big__Operators_Olinorder__class_OMin(_1329010, _1329012)), c_Big__Operators_Olinorder__class_OMin(_1329010, _1329014)))], (16490 ^ _776541) ^ [_1073507] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073507)))], (25227 ^ _776541) ^ [_1233271, _1233273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233271), 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, _1233273, _1233271)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10429 ^ _776541) ^ [_955673, _955675, _955677] : [class_Groups_Oordered__ab__group__add(_955673), 10432 ^ _776541 : [(10439 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955673), _955677), hAPP(c_Groups_Ouminus__class_Ouminus(_955673), _955675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955673), _955675), hAPP(c_Groups_Ouminus__class_Ouminus(_955673), _955677))))], (10433 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955673), _955675), hAPP(c_Groups_Ouminus__class_Ouminus(_955673), _955677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955673), _955677), hAPP(c_Groups_Ouminus__class_Ouminus(_955673), _955675))))]]], (5895 ^ _776541) ^ [_870282, _870284, _870286] : [hBOOL(hAPP(_870286, _870284)), -(hBOOL(hAPP(hAPP(c_member(_870282), _870284), _870286)))], (40839 ^ _776541) ^ [_1576021, _1576023] : [-(c_Relation_Orefl__on(_1576021, c_Orderings_Otop__class_Otop(tc_fun(_1576021, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1576021, _1576023)))], (14200 ^ _776541) ^ [_1031961, _1031963] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1031961, _1031963))))], (11238 ^ _776541) ^ [_971697, _971699, _971701, _971703, _971705, _971707, _971709] : [c_Finite__Set_Ofun__left__comm(_971697, _971699, _971701), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_971697, _971699, _971701, _971703, _971705), _971707)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_971697, _971699, _971701, _971703, _971705), _971709)), -(_971709 = _971707)], (43950 ^ _776541) ^ [_1654846, _1654848, _1654850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654846)), _1654850)), _1654848)), -(hAPP(hAPP(c_List_Odrop(_1654846), _1654848), _1654850) = c_List_Olist_ONil(_1654846))], (48460 ^ _776541) ^ [_1752862, _1752864, _1752866, _1752868, _1752870] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1752862), _1752864), _1752866), _1752868), _1752870) = c_New__DSequence_Opos__single(_1752862, _1752864))], (28781 ^ _776541) ^ [_1292591, _1292593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292591)), -(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)))), _1292593))), 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)))), _1292591)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1292593), _1292591))], (8297 ^ _776541) ^ [_918577, _918579, _918581, _918583] : [class_Lattices_Olattice(_918577), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918577), _918579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918577), _918581), _918583)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918577), _918581), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918577), _918579), _918583)))], (37298 ^ _776541) ^ [_1486542, _1486544, _1486546, _1486548, _1486550, _1486552] : [c_Fun_Oinj__on(_1486542, _1486544, _1486546, _1486548), hAPP(_1486546, _1486550) = hAPP(_1486546, _1486552), hBOOL(hAPP(hAPP(c_member(_1486542), _1486550), _1486548)), hBOOL(hAPP(hAPP(c_member(_1486542), _1486552), _1486548)), -(_1486550 = _1486552)], (36533 ^ _776541) ^ [_1468187, _1468189, _1468191, _1468193] : [-(hAPP(c_Relation_OImage(_1468187, _1468189, _1468191), _1468193) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1468187, tc_fun(_1468189, tc_HOL_Obool)), _1468193), hAPP(hAPP(c_COMBB(tc_fun(_1468187, tc_HOL_Obool), tc_fun(_1468189, tc_HOL_Obool), _1468187), c_Relation_OImage(_1468187, _1468189, _1468191)), hAPP(hAPP(c_COMBC(_1468187, tc_fun(_1468187, tc_HOL_Obool), tc_fun(_1468187, tc_HOL_Obool)), c_Set_Oinsert(_1468187)), c_Orderings_Obot__class_Obot(tc_fun(_1468187, tc_HOL_Obool))))))], (42545 ^ _776541) ^ [_1623296, _1623298, _1623300, _1623302, _1623304, _1623306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623296, _1623298)), hAPP(hAPP(c_Product__Type_OPair(_1623296, _1623298), _1623300), _1623302)), hAPP(c_List_Oset(tc_prod(_1623296, _1623298)), hAPP(hAPP(c_List_Ozip(_1623296, _1623298), _1623304), _1623306)))), -(hBOOL(hAPP(hAPP(c_member(_1623298), _1623302), hAPP(c_List_Oset(_1623298), _1623306))))], (16430 ^ _776541) ^ [_1072705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072705), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37834 ^ _776541) ^ [_1497698, _1497700, _1497702, _1497704, _1497706] : [c_Fun_Oinj__on(_1497698, _1497700, _1497702, _1497704), hBOOL(hAPP(hAPP(c_member(_1497698), _1497706), _1497704)), -(hAPP(c_Fun_Othe__inv__into(_1497698, _1497700, _1497704, _1497702), hAPP(_1497702, _1497706)) = _1497706)], (21255 ^ _776541) ^ [_1160998, _1161000, _1161002, _1161004] : [class_Int_Onumber__ring(_1160998), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160998), hAPP(c_Int_Onumber__class_Onumber__of(_1160998), _1161000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160998), hAPP(c_Int_Onumber__class_Onumber__of(_1160998), _1161002)), _1161004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160998), hAPP(c_Int_Onumber__class_Onumber__of(_1160998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1161000), _1161002))), _1161004))], (17331 ^ _776541) ^ [_1088586, _1088588, _1088590, _1088592] : [class_Rings_Olinordered__semiring__strict(_1088586), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088586), _1088588), _1088590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088586), c_Groups_Ozero__class_Ozero(_1088586)), _1088592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088586), _1088592), _1088588)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088586), _1088592), _1088590))))], (51981 ^ _776541) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (44605 ^ _776541) ^ [_1668532, _1668534, _1668536] : [_1668532 = c_List_Olist_ONil(_1668534), -(c_List_Olast(_1668534, hAPP(hAPP(c_List_Oappend(_1668534), _1668536), _1668532)) = c_List_Olast(_1668534, _1668536))], (4510 ^ _776541) ^ [_845059, _845061] : [_845061 = _845059, -(c_Lazy__Sequence_Oyield(_845061) = c_Lazy__Sequence_Oyield(_845059))], (33558 ^ _776541) ^ [_1394162, _1394164, _1394166, _1394168] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394162, tc_fun(_1394164, tc_HOL_Obool)), _1394166), _1394168) = c_Orderings_Otop__class_Otop(tc_fun(_1394164, tc_HOL_Obool)), 33561 ^ _776541 : [(33562 ^ _776541) ^ [_1394278] : [hBOOL(hAPP(hAPP(c_member(_1394162), _1394278), _1394166)), -(hAPP(_1394168, _1394278) = c_Orderings_Otop__class_Otop(tc_fun(_1394164, tc_HOL_Obool)))]]], (16452 ^ _776541) ^ [_1072974] : [-(_1072974 = 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)), _1072974)))], (52479 ^ _776541) ^ [_1831222, _1831224] : [_1831222 = _1831224, -(hBOOL(hAPP(hAPP(c_fequal, _1831222), _1831224)))], (8859 ^ _776541) ^ [_928985, _928987, _928989] : [class_Orderings_Olinorder(_928985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928985), _928987), _928989)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928985, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_928985, _928987, _928989)), hAPP(hAPP(c_Set_Oinsert(_928985), _928989), c_Orderings_Obot__class_Obot(tc_fun(_928985, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_928985, _928987, _928989))], (4516 ^ _776541) ^ [_845144, _845146] : [_845146 = _845144, -(c_List_Olist_ONil(_845146) = c_List_Olist_ONil(_845144))], (1854 ^ _776541) ^ [_802580, _802582] : [-(class_Power_Opower(_802580)), _802582 = _802580, class_Power_Opower(_802582)], (33129 ^ _776541) ^ [_1382362, _1382364, _1382366, _1382368, _1382370] : [33131 ^ _776541 : [(33134 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1382362), _1382364), hAPP(_1382370, 33130 ^ [_1382362, _1382364, _1382366, _1382368, _1382370])))], (33132 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382366), 33130 ^ [_1382362, _1382364, _1382366, _1382368, _1382370]), _1382368)))]], -(hBOOL(hAPP(hAPP(c_member(_1382362), _1382364), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382366, tc_fun(_1382362, tc_HOL_Obool)), _1382368), _1382370))))], (8381 ^ _776541) ^ [_920319, _920321, _920323, _920325] : [class_Lattices_Olattice(_920319), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920319), _920321), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920319), _920323), _920325)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920319), _920323), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920319), _920321), _920325)))], (48891 ^ _776541) ^ [_1762233] : [-(c_List_Omember(_1762233) = c_List_Oset(_1762233))], (44280 ^ _776541) ^ [_1661967, _1661969, _1661971] : [class_Groups_Omonoid__add(_1661967), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1661967), _1661969), hAPP(c_List_Ofoldl(_1661967, _1661967, c_Groups_Oplus__class_Oplus(_1661967), c_Groups_Ozero__class_Ozero(_1661967)), _1661971)) = hAPP(c_List_Ofoldl(_1661967, _1661967, c_Groups_Oplus__class_Oplus(_1661967), _1661969), _1661971))], (8303 ^ _776541) ^ [_918720, _918722, _918724, _918726] : [class_Lattices_Osemilattice__sup(_918720), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918720), _918722), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918720), _918724), _918726)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918720), _918724), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918720), _918722), _918726)))], (41479 ^ _776541) ^ [_1591619, _1591621, _1591623, _1591625] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591619, _1591619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1591621), _1591623)), _1591625) = hAPP(c_Fun_Ocomp(_1591619, _1591619, _1591619, hAPP(hAPP(c_Nat_Ocompow(_1591619, _1591619), _1591621), _1591625)), hAPP(hAPP(c_Nat_Ocompow(_1591619, _1591619), _1591623), _1591625)))], (27249 ^ _776541) ^ [_1266827] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266827), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1266827)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1266827)))], (29523 ^ _776541) ^ [_1305397, _1305399, _1305401] : [class_Rings_Olinordered__idom(_1305397), 29526 ^ _776541 : [(29535 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305397), hAPP(hAPP(c_Power_Opower__class_Opower(_1305397), _1305399), 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(_1305397), _1305401), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1305397)))), _1305399 = c_Groups_Ozero__class_Ozero(_1305397), _1305401 = c_Groups_Ozero__class_Ozero(_1305397)], (29527 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305397), hAPP(hAPP(c_Power_Opower__class_Opower(_1305397), _1305399), 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(_1305397), _1305401), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1305397))), 29530 ^ _776541 : [(29533 ^ _776541) ^ [] : [-(_1305401 = c_Groups_Ozero__class_Ozero(_1305397))], (29531 ^ _776541) ^ [] : [-(_1305399 = c_Groups_Ozero__class_Ozero(_1305397))]]]]], (4850 ^ _776541) ^ [_850363, _850365, _850367, _850369, _850371, _850373, _850375, _850377, _850379, _850381, _850383, _850385] : [-(c_Partial__Function_Ofun__lub(_850385, _850381, _850377, _850373, _850369, _850365) = c_Partial__Function_Ofun__lub(_850383, _850379, _850375, _850371, _850367, _850363)), _850385 = _850383, _850381 = _850379, _850377 = _850375, _850373 = _850371, _850369 = _850367, _850365 = _850363], (32318 ^ _776541) ^ [_1357740, _1357742, _1357744, _1357746, _1357748, _1357750] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357740, tc_fun(_1357742, tc_HOL_Obool)), _1357744), _1357746), _1357748)), hBOOL(hAPP(hAPP(c_member(_1357740), _1357750), _1357744)), -(hBOOL(hAPP(hAPP(_1357746, _1357750), _1357748)))], (10317 ^ _776541) ^ [_953772, _953774, _953776] : [class_Groups_Ogroup__add(_953772), 10320 ^ _776541 : [(10327 ^ _776541) ^ [] : [_953774 = _953776, -(hAPP(c_Groups_Ouminus__class_Ouminus(_953772), _953774) = hAPP(c_Groups_Ouminus__class_Ouminus(_953772), _953776))], (10321 ^ _776541) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_953772), _953774) = hAPP(c_Groups_Ouminus__class_Ouminus(_953772), _953776), -(_953774 = _953776)]]], (24315 ^ _776541) ^ [_1216291, _1216293] : [class_Rings_Osemiring__1(_1216291), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216291), hAPP(c_Nat_OSuc, _1216293)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216291), c_Groups_Oone__class_Oone(_1216291)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216291), _1216293)))], (14694 ^ _776541) ^ [_1041404, _1041406] : [14695 ^ _776541 : [(14698 ^ _776541) ^ [] : [_1041404 = _1041406], (14696 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041404), _1041406))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041404), _1041406)))], (44553 ^ _776541) ^ [_1667747, _1667749, _1667751, _1667753] : [-(_1667747 = c_List_Olist_ONil(_1667749)), 44556 ^ _776541 : [(44563 ^ _776541) ^ [] : [-(_1667751 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667749)), _1667747)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1667749, hAPP(hAPP(c_List_Olist__update(_1667749, _1667747), _1667751), _1667753)) = c_List_Olast(_1667749, _1667747))], (44557 ^ _776541) ^ [] : [_1667751 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667749)), _1667747)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1667749, hAPP(hAPP(c_List_Olist__update(_1667749, _1667747), _1667751), _1667753)) = _1667753)]]], (48480 ^ _776541) ^ [_1753344, _1753346] : [c_Wellfounded_Oacyclic(_1753344, hAPP(c_Set_OCollect(tc_prod(_1753344, _1753344)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753344, _1753344, tc_HOL_Obool), _1753346))), -(c_Wellfounded_Oacyclic(_1753344, hAPP(c_Set_OCollect(tc_prod(_1753344, _1753344)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753344, _1753344, tc_HOL_Obool), c_Predicate_Oconversep(_1753344, _1753344, _1753346)))))], (6115 ^ _776541) ^ [_874533, _874535, _874537, _874539] : [6117 ^ _776541 : [(6120 ^ _776541) ^ [] : [hBOOL(hAPP(_874537, 6116 ^ [_874533, _874535, _874537, _874539]))], (6118 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874533), 6116 ^ [_874533, _874535, _874537, _874539]), _874535)))]], -(hBOOL(hAPP(_874537, _874539))), hBOOL(hAPP(hAPP(c_member(_874533), _874539), _874535))], (44807 ^ _776541) ^ [_1672746, _1672748, _1672750, _1672752, _1672754, _1672756, _1672758] : [hAPP(hAPP(c_List_Omap(_1672746, _1672748), _1672750), _1672752) = hAPP(hAPP(c_List_Omap(_1672754, _1672748), _1672756), _1672758), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672746)), _1672752) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672754)), _1672758))], (10517 ^ _776541) ^ [_957251, _957253, _957255] : [class_Groups_Oab__group__add(_957251), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957251), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957251), _957253), _957255)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957251), _957255), _957253))], (37106 ^ _776541) ^ [_1481799, _1481801, _1481803, _1481805, _1481807, _1481809, _1481811] : [c_Equiv__Relations_Oequiv(_1481799, _1481801, _1481803), c_Equiv__Relations_Ocongruent(_1481799, tc_fun(_1481805, tc_HOL_Obool), _1481803, _1481807), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481799, tc_fun(_1481805, tc_HOL_Obool)), _1481809), _1481807) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481799, tc_fun(_1481805, tc_HOL_Obool)), _1481811), _1481807), hBOOL(hAPP(hAPP(c_member(tc_fun(_1481799, tc_HOL_Obool)), _1481809), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481799), _1481801), _1481803))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1481799, tc_HOL_Obool)), _1481811), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481799), _1481801), _1481803))), 37128 ^ _776541 : [(37132 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481799), 37130 ^ [_1481799, _1481801, _1481803, _1481805, _1481807, _1481809, _1481811]), _1481801)))], (37134 ^ _776541) ^ [] : [-(hAPP(_1481807, 37127 ^ [_1481799, _1481801, _1481803, _1481805, _1481807, _1481809, _1481811]) = hAPP(_1481807, 37130 ^ [_1481799, _1481801, _1481803, _1481805, _1481807, _1481809, _1481811]))], (37136 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1481799, _1481799)), hAPP(hAPP(c_Product__Type_OPair(_1481799, _1481799), 37127 ^ [_1481799, _1481801, _1481803, _1481805, _1481807, _1481809, _1481811]), 37130 ^ [_1481799, _1481801, _1481803, _1481805, _1481807, _1481809, _1481811])), _1481803))], (37129 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481799), 37127 ^ [_1481799, _1481801, _1481803, _1481805, _1481807, _1481809, _1481811]), _1481801)))]], -(_1481809 = _1481811)], (16302 ^ _776541) ^ [_1070804, _1070806, _1070808] : [class_Groups_Ogroup__add(_1070804), 16305 ^ _776541 : [(16312 ^ _776541) ^ [] : [_1070806 = _1070808, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070804), _1070806), _1070808) = c_Groups_Ozero__class_Ozero(_1070804))], (16306 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070804), _1070806), _1070808) = c_Groups_Ozero__class_Ozero(_1070804), -(_1070806 = _1070808)]]], (35662 ^ _776541) ^ [_1442245] : [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), _1442245))), -(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), _1442245)) = 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), _1442245))))], (924 ^ _776541) ^ [_790419, _790421, _790423, _790425] : [-(c_Equiv__Relations_Oequivp(_790423, _790419)), c_Equiv__Relations_Oequivp(_790425, _790421), _790425 = _790423, _790421 = _790419], (39713 ^ _776541) ^ [_1547665, _1547667, _1547669] : [39715 ^ _776541 : [(39718 ^ _776541) ^ [] : [hBOOL(hAPP(_1547667, 39714 ^ [_1547665, _1547667, _1547669]))], (39716 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547665), 39714 ^ [_1547665, _1547667, _1547669]), _1547669)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1547665, _1547667), _1547669)))], (12241 ^ _776541) ^ [_991343, _991345, _991347, _991349, _991351, _991353, _991355, _991357] : [c_Finite__Set_Ofolding__image__simple(_991343, _991345, _991347, _991349, _991351, _991353), hBOOL(hAPP(c_Finite__Set_Ofinite(_991345), _991355)), -(hBOOL(hAPP(hAPP(c_member(_991345), _991357), _991355))), -(hAPP(_991353, hAPP(hAPP(c_Set_Oinsert(_991345), _991357), _991355)) = hAPP(hAPP(_991347, hAPP(_991351, _991357)), hAPP(_991353, _991355)))], (15708 ^ _776541) ^ [_1061390, _1061392] : [_1061390 = _1061392, -(hAPP(c_Nat_OSuc, _1061390) = hAPP(c_Nat_OSuc, _1061392))], (2172 ^ _776541) ^ [_808052, _808054] : [_808054 = _808052, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808054) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808052))], (17043 ^ _776541) ^ [_1083348, _1083350, _1083352, _1083354] : [class_Rings_Oordered__semiring(_1083348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083348), _1083350), _1083352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083348), c_Groups_Ozero__class_Ozero(_1083348)), _1083354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083348), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083348), _1083354), _1083350)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083348), _1083354), _1083352))))], (14877 ^ _776541) ^ [_1044832, _1044834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044832), _1044834)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044834), _1044832)) = _1044832)], (27339 ^ _776541) ^ [_1268364] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1268364)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1268364))], (52435 ^ _776541) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (24610 ^ _776541) ^ [_1221718, _1221720, _1221722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221718), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24613 ^ _776541 : [(24614 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1221720, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221722), _1221718)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1221722, _1221718))), 24617 ^ _776541 : [(24618 ^ _776541) ^ [_1221928, _1221930] : [-(hBOOL(hAPP(hAPP(_1221720, _1221930), _1221928))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221718), _1221928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1221928), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1221722 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1221718), _1221930)), _1221928)]]], (24632 ^ _776541) ^ [] : [24635 ^ _776541 : [(24638 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24634 ^ [_1221718, _1221720, _1221722]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24640 ^ _776541) ^ [] : [-(_1221722 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1221718), 24633 ^ [_1221718, _1221720, _1221722])), 24634 ^ [_1221718, _1221720, _1221722]))], (24642 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1221720, 24633 ^ [_1221718, _1221720, _1221722]), 24634 ^ [_1221718, _1221720, _1221722]))], (24636 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221718), 24634 ^ [_1221718, _1221720, _1221722])))]], -(hBOOL(hAPP(hAPP(_1221720, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221722), _1221718)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1221722, _1221718))))]]], (7230 ^ _776541) ^ [_894484, _894486, _894488, _894490, _894492] : [hAPP(hAPP(c_Set_Oinsert(_894484), _894486), hAPP(hAPP(c_Set_Oinsert(_894484), _894488), c_Orderings_Obot__class_Obot(tc_fun(_894484, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_894484), _894490), hAPP(hAPP(c_Set_Oinsert(_894484), _894492), c_Orderings_Obot__class_Obot(tc_fun(_894484, tc_HOL_Obool)))), 7235 ^ _776541 : [(7238 ^ _776541) ^ [] : [-(_894488 = _894492)], (7236 ^ _776541) ^ [] : [-(_894486 = _894490)]], 7239 ^ _776541 : [(7242 ^ _776541) ^ [] : [-(_894488 = _894490)], (7240 ^ _776541) ^ [] : [-(_894486 = _894492)]]], (39185 ^ _776541) ^ [_1532801, _1532803, _1532805, _1532807, _1532809, _1532811] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532801, _1532803)), hAPP(hAPP(c_Product__Type_OPair(_1532801, _1532803), _1532805), _1532807)), hAPP(hAPP(c_Product__Type_OSigma(_1532801, _1532803), _1532809), _1532811))), 39188 ^ _776541 : [(39191 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532803), _1532807), hAPP(_1532811, _1532805))))], (39189 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532801), _1532805), _1532809)))]]], (38594 ^ _776541) ^ [_1517800, _1517802, _1517804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517800, tc_HOL_Obool)), _1517802), hAPP(hAPP(c_Set_Oinsert(_1517800), _1517804), c_Orderings_Obot__class_Obot(tc_fun(_1517800, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1517800, _1517804, _1517802) = _1517804)], (52257 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (43068 ^ _776541) ^ [_1634739, _1634741, _1634743] : [43069 ^ _776541 : [(43072 ^ _776541) ^ [] : [_1634743 = c_List_Olist_ONil(_1634739)], (43070 ^ _776541) ^ [] : [_1634741 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1634739), _1634741), _1634743) = c_List_Olist_ONil(_1634739))], (2264 ^ _776541) ^ [_809516, _809518] : [_809518 = _809516, -(c_SetInterval_Oord__class_OgreaterThan(_809518) = c_SetInterval_Oord__class_OgreaterThan(_809516))], (44370 ^ _776541) ^ [_1663937, _1663939] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663937), _1663939) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1663937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44376 ^ _776541 : [(44379 ^ _776541) ^ [] : [44375 ^ [_1663937, _1663939] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44377 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44375 ^ [_1663937, _1663939]), hAPP(c_List_Oset(tc_Nat_Onat), _1663939))))]]], (44836 ^ _776541) ^ [_1673567, _1673569, _1673571, _1673573] : [c_List_Olist_ONil(_1673567) = hAPP(hAPP(c_List_Omap(_1673569, _1673567), _1673571), _1673573), -(_1673573 = c_List_Olist_ONil(_1673569))], (47393 ^ _776541) ^ [_1729485, _1729487, _1729489] : [47395 ^ _776541 : [(47398 ^ _776541) ^ [] : [hBOOL(hAPP(_1729487, 47394 ^ [_1729485, _1729487, _1729489]))], (47396 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729485), 47394 ^ [_1729485, _1729487, _1729489]), hAPP(c_List_Oset(_1729485), _1729489))))]], -(c_List_OdropWhile(_1729485, _1729487, _1729489) = c_List_Olist_ONil(_1729485))], (41144 ^ _776541) ^ [_1583310, _1583312] : [c_Wellfounded_Owf(_1583310, hAPP(c_Relation_Oconverse(_1583310, _1583310), _1583312)), -(c_Wellfounded_Owf(_1583310, hAPP(c_Relation_Oconverse(_1583310, _1583310), c_Transitive__Closure_Otrancl(_1583310, _1583312))))], (10263 ^ _776541) ^ [_952940, _952942, _952944] : [class_Orderings_Olinorder(_952940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952940), _952942), _952944)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952940, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_952940, _952942), _952944)), hAPP(c_SetInterval_Oord__class_OatLeast(_952940), _952944)) = hAPP(c_SetInterval_Oord__class_OatLeast(_952940), _952942))], (39703 ^ _776541) ^ [_1547482, _1547484, _1547486] : [hBOOL(hAPP(c_Predicate_OPowp(_1547482, _1547484), _1547486)), 39706 ^ _776541 : [(39707 ^ _776541) ^ [_1547566] : [hBOOL(hAPP(hAPP(c_member(_1547482), _1547566), _1547486)), -(hBOOL(hAPP(_1547484, _1547566)))]]], (38678 ^ _776541) ^ [_1519669, _1519671, _1519673, _1519675, _1519677] : [-(hAPP(c_Set_Ovimage(_1519669, _1519671, _1519673), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519671, tc_HOL_Obool)), _1519675), _1519677)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519669, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1519669, _1519671, _1519673), _1519675)), hAPP(c_Set_Ovimage(_1519669, _1519671, _1519673), _1519677)))], (14660 ^ _776541) ^ [_1040939, _1040941] : [14661 ^ _776541 : [(14664 ^ _776541) ^ [] : [_1040939 = _1040941], (14662 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040939), _1040941))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040939), _1040941)))], (24050 ^ _776541) ^ [_1211933, _1211935] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211933), _1211935) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1211935 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24059 ^ _776541 : [(24062 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211933), _1211935)))], (24060 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211933)))]], 24063 ^ _776541 : [(24066 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211935), _1211933)))], (24064 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211933), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (8741 ^ _776541) ^ [_926747, _926749, _926751] : [class_Lattices_Osemilattice__inf(_926747), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926747), _926749), _926751)), _926749)))], (39722 ^ _776541) ^ [_1547845, _1547847, _1547849, _1547851] : [-(hAPP(c_Set_OCollect(_1547845), hAPP(hAPP(c_COMBB(tc_fun(_1547847, tc_HOL_Obool), tc_HOL_Obool, _1547845), c_HOL_OAll(_1547847)), hAPP(hAPP(c_COMBB(tc_fun(_1547847, tc_HOL_Obool), tc_fun(_1547847, tc_HOL_Obool), _1547845), hAPP(c_COMBS(_1547847, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547847), c_fimplies), hAPP(hAPP(c_COMBC(_1547847, tc_fun(_1547847, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547847)), _1547849)))), _1547851))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1547847, tc_fun(_1547845, tc_HOL_Obool)), _1547849), hAPP(hAPP(c_COMBB(tc_fun(_1547845, tc_HOL_Obool), tc_fun(_1547845, tc_HOL_Obool), _1547847), c_Set_OCollect(_1547845)), hAPP(c_COMBC(_1547845, _1547847, tc_HOL_Obool), _1547851))))], (43910 ^ _776541) ^ [_1653967, _1653969] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653967)), hAPP(c_List_Orotate1(_1653967), _1653969)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653967)), _1653969))], (6536 ^ _776541) ^ [_882076, _882078, _882080, _882082] : [class_Orderings_Oord(_882076), 6539 ^ _776541 : [(6546 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882076), hAPP(_882080, 6547 ^ [_882076, _882078, _882080, _882082])), hAPP(_882082, 6547 ^ [_882076, _882078, _882080, _882082]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882078, _882076)), _882080), _882082)))], (6540 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882078, _882076)), _882080), _882082)), 6543 ^ _776541 : [(6544 ^ _776541) ^ [_882233] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882076), hAPP(_882080, _882233)), hAPP(_882082, _882233))))]]]]], (31192 ^ _776541) ^ [_1336262, _1336264, _1336266] : [class_Orderings_Olinorder(_1336262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336262, tc_HOL_Obool)), _1336264), _1336266)), -(_1336264 = c_Orderings_Obot__class_Obot(tc_fun(_1336262, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336262), _1336266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336262), c_Big__Operators_Olinorder__class_OMax(_1336262, _1336264)), c_Big__Operators_Olinorder__class_OMax(_1336262, _1336266))))], (38967 ^ _776541) ^ [_1526963, _1526965] : [c_Nitpick_Owf_H(_1526963, _1526965), 38970 ^ _776541 : [(38973 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1526963, _1526963)), _1526965))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (38971 ^ _776541) ^ [] : [-(c_Wellfounded_Oacyclic(_1526963, _1526965))]]], (46375 ^ _776541) ^ [_1709181, _1709183, _1709185, _1709187] : [-(c_List_Oupt(_1709181, _1709183) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1709185), _1709187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709181), _1709183)), _1709181 = _1709185, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709181), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1709183) = _1709187], (28123 ^ _776541) ^ [_1281608, _1281610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1281608), _1281610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1281608)), _1281610)))], (40905 ^ _776541) ^ [_1577499, _1577501, _1577503, _1577505, _1577507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577499, _1577499)), hAPP(hAPP(c_Product__Type_OPair(_1577499, _1577499), _1577501), _1577503)), c_Transitive__Closure_Ortrancl(_1577499, _1577505))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577499, _1577499)), hAPP(hAPP(c_Product__Type_OPair(_1577499, _1577499), _1577503), _1577507)), _1577505)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577499, _1577499)), hAPP(hAPP(c_Product__Type_OPair(_1577499, _1577499), _1577501), _1577507)), c_Transitive__Closure_Otrancl(_1577499, _1577505))))], (46243 ^ _776541) ^ [_1706582, _1706584, _1706586] : [class_Groups_Omonoid__add(_1706582), -(hAPP(c_List_Ofoldl(_1706582, _1706582, c_Groups_Oplus__class_Oplus(_1706582), _1706584), _1706586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706582), _1706584), c_List_Ofoldr(_1706582, _1706582, c_Groups_Oplus__class_Oplus(_1706582), _1706586, c_Groups_Ozero__class_Ozero(_1706582))))], (36152 ^ _776541) ^ [_1458242, _1458244, _1458246, _1458248, _1458250] : [class_Groups_Oordered__ab__group__add(_1458242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458244), _1458246)), 36162 ^ _776541 : [(36165 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458242), c_Groups_Ozero__class_Ozero(_1458242)), hAPP(_1458248, 36161 ^ [_1458242, _1458244, _1458246, _1458248, _1458250])))], (36163 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458244), 36161 ^ [_1458242, _1458244, _1458246, _1458248, _1458250]), _1458246)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458244, _1458242), _1458248), _1458246) = c_Groups_Ozero__class_Ozero(_1458242), hBOOL(hAPP(hAPP(c_member(_1458244), _1458250), _1458246)), -(hAPP(_1458248, _1458250) = c_Groups_Ozero__class_Ozero(_1458242))], (39347 ^ _776541) ^ [_1538309, _1538311, _1538313, _1538315] : [class_Groups_Ocomm__monoid__add(_1538309), c_Fun_Oinj__on(_1538311, _1538309, _1538313, _1538315), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538311, _1538309), _1538313), _1538315) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538309, _1538309), c_Fun_Oid(_1538309)), hAPP(c_Set_Oimage(_1538311, _1538309, _1538313), _1538315)))], (30986 ^ _776541) ^ [_1332423, _1332425, _1332427] : [class_Orderings_Olinorder(_1332423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332423), _1332425)), -(_1332425 = c_Orderings_Obot__class_Obot(tc_fun(_1332423, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332423), _1332427)), -(_1332427 = c_Orderings_Obot__class_Obot(tc_fun(_1332423, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332423, tc_HOL_Obool)), _1332425), _1332427) = c_Orderings_Obot__class_Obot(tc_fun(_1332423, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1332423, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332423, tc_HOL_Obool)), _1332425), _1332427)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332423), c_Big__Operators_Olinorder__class_OMin(_1332423, _1332425)), c_Big__Operators_Olinorder__class_OMin(_1332423, _1332427)))], (13748 ^ _776541) ^ [_1021471, _1021473, _1021475, _1021477] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1021471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021471), _1021473), _1021475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021471), _1021473), _1021477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021471), _1021475), _1021477))))], (23707 ^ _776541) ^ [_1205979] : [_1205979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1205979) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50825 ^ _776541) ^ [_1804738, _1804740, _1804742, _1804744, _1804746, _1804748, _1804750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1804738, _1804740), tc_prod(_1804738, _1804740))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1804738, _1804740), tc_prod(_1804738, _1804740)), hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), _1804742), _1804744)), hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), _1804746), _1804748))), c_Transitive__Closure_Ortrancl(tc_prod(_1804738, _1804740), _1804750))), -(hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), _1804742), _1804744) = hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), _1804746), _1804748)), 50834 ^ _776541 : [(50837 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1804738, _1804740), tc_prod(_1804738, _1804740))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1804738, _1804740), tc_prod(_1804738, _1804740)), hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), 50832 ^ [_1804738, _1804740, _1804742, _1804744, _1804746, _1804748, _1804750]), 50833 ^ [_1804738, _1804740, _1804742, _1804744, _1804746, _1804748, _1804750])), hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), _1804746), _1804748))), c_Transitive__Closure_Ortrancl(tc_prod(_1804738, _1804740), _1804750))))], (50835 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1804738, _1804740), tc_prod(_1804738, _1804740))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1804738, _1804740), tc_prod(_1804738, _1804740)), hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), _1804742), _1804744)), hAPP(hAPP(c_Product__Type_OPair(_1804738, _1804740), 50832 ^ [_1804738, _1804740, _1804742, _1804744, _1804746, _1804748, _1804750]), 50833 ^ [_1804738, _1804740, _1804742, _1804744, _1804746, _1804748, _1804750]))), _1804750)))]]], (18506 ^ _776541) ^ [_1109573, _1109575, _1109577] : [class_Rings_Olinordered__idom(_1109573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109573), c_Groups_Ozero__class_Ozero(_1109573)), _1109575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109573), c_Groups_Ozero__class_Ozero(_1109573)), _1109577)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109573), _1109577), c_Groups_Oone__class_Oone(_1109573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109573), _1109575), _1109577)), _1109575)))], (48720 ^ _776541) ^ [_1758499, _1758501, _1758503, _1758505] : [hBOOL(hAPP(hAPP(c_member(_1758499), _1758501), hAPP(c_List_Oset(_1758499), c_List_Oreplicate(_1758499, _1758503, _1758505)))), 48723 ^ _776541 : [(48726 ^ _776541) ^ [] : [_1758503 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48724 ^ _776541) ^ [] : [-(_1758501 = _1758505)]]], (45976 ^ _776541) ^ [_1698904, _1698906, _1698908] : [-(c_List_Oconcat(_1698904, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1698904)), _1698906), _1698908)) = hAPP(hAPP(c_List_Oappend(_1698904), c_List_Oconcat(_1698904, _1698906)), c_List_Oconcat(_1698904, _1698908)))], (35204 ^ _776541) ^ [_1433421, _1433423, _1433425] : [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), _1433421), _1433423))), -(hBOOL(hAPP(hAPP(_1433425, _1433421), _1433423))), 35211 ^ _776541 : [(35214 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1433425, 35209 ^ [_1433421, _1433423, _1433425]), 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)))), 35210 ^ [_1433421, _1433423, _1433425])))), -(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), 35209 ^ [_1433421, _1433423, _1433425]), 35210 ^ [_1433421, _1433423, _1433425])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 35210 ^ [_1433421, _1433423, _1433425]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35224 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1433425, 35209 ^ [_1433421, _1433423, _1433425]), 35210 ^ [_1433421, _1433423, _1433425]))], (35212 ^ _776541) ^ [] : [-(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), 35209 ^ [_1433421, _1433423, _1433425]), 35210 ^ [_1433421, _1433423, _1433425]))))]]], (10968 ^ _776541) ^ [_966157, _966159] : [class_Lattices_Olattice(_966157), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_966157), _966159), _966159) = _966159)], (50000 ^ _776541) ^ [_1786473, _1786475, _1786477, _1786479, _1786481, _1786483] : [hAPP(c_Set_Oimage(_1786473, _1786475, _1786477), _1786479) = _1786481, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1786475, tc_HOL_Obool)), _1786483), _1786481)), -(hAPP(c_Set_Oimage(_1786473, _1786475, _1786477), hAPP(c_Set_Oimage(_1786475, _1786473, c_Hilbert__Choice_Oinv__into(_1786473, _1786475, _1786479, _1786477)), _1786483)) = _1786483)], (21237 ^ _776541) ^ [_1160569, _1160571, _1160573, _1160575] : [class_Rings_Ocomm__semiring__1(_1160569), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1160569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160569), _1160571), _1160573)), _1160575) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160569), hAPP(hAPP(c_Power_Opower__class_Opower(_1160569), _1160571), _1160575)), hAPP(hAPP(c_Power_Opower__class_Opower(_1160569), _1160573), _1160575)))], (6658 ^ _776541) ^ [_884323, _884325, _884327] : [class_Orderings_Oorder(_884323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884323), _884325), _884327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884323), _884327), _884325)), -(_884325 = _884327)], (31983 ^ _776541) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (46315 ^ _776541) ^ [_1708081, _1708083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1708081), _1708083)), -(c_List_Oupt(_1708081, hAPP(c_Nat_OSuc, _1708083)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1708081, _1708083)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1708083), c_List_Olist_ONil(tc_Nat_Onat))))], (44966 ^ _776541) ^ [_1676954, _1676956, _1676958] : [c_Fun_Oinj__on(_1676954, _1676956, _1676958, c_Orderings_Otop__class_Otop(tc_fun(_1676954, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1676954), tc_List_Olist(_1676956), hAPP(c_List_Omap(_1676954, _1676956), _1676958), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676954), tc_HOL_Obool))))], (14823 ^ _776541) ^ [_1043841, _1043843, _1043845] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043841), _1043843)), _1043845) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043841), _1043845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043843), _1043845)))], (35503 ^ _776541) ^ [_1438997, _1438999] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1438997, _1438999) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1438997, _1438999)))], (39306 ^ _776541) ^ [_1537278, _1537280, _1537282, _1537284] : [-(c_Fun_Oinj__on(_1537278, tc_prod(_1537280, _1537278), 39304 ^ [_1537278, _1537280, _1537282, _1537284], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537280, tc_fun(_1537278, tc_HOL_Obool)), _1537282), _1537284)))], (41965 ^ _776541) ^ [_1606187, _1606189, _1606191, _1606193, _1606195] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606187, _1606187)), hAPP(hAPP(c_Product__Type_OPair(_1606187, _1606187), _1606189), _1606191)), _1606193)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606187), tc_List_Olist(_1606187))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606187), tc_List_Olist(_1606187)), hAPP(hAPP(c_List_Olist_OCons(_1606187), _1606189), _1606195)), hAPP(hAPP(c_List_Olist_OCons(_1606187), _1606191), _1606195))), c_List_Olistrel1(_1606187, _1606193))))], (50889 ^ _776541) ^ [_1807262, _1807264, _1807266] : [c_List_Oall__interval__nat(_1807262, _1807264, _1807266), 50892 ^ _776541 : [(50893 ^ _776541) ^ [_1807342] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807342), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1807264), _1807266))), -(hBOOL(hAPP(_1807262, _1807342)))]]], (11936 ^ _776541) ^ [_986103, _986105, _986107, _986109, _986111, _986113] : [_986103 = _986105, -(hAPP(c_Fun_Ofun__upd(_986107, _986109, _986111, _986105, _986113), _986103) = _986113)], (14104 ^ _776541) ^ [_1029605, _1029607, _1029609, _1029611, _1029613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029605), _1029607)), 14107 ^ _776541 : [(14114 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029611), 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), _1029607), _1029605)), _1029609)), _1029613))), -(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), _1029605), _1029609)), _1029611)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029607), _1029609)), _1029613))))], (14108 ^ _776541) ^ [] : [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), _1029605), _1029609)), _1029611)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029607), _1029609)), _1029613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029611), 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), _1029607), _1029605)), _1029609)), _1029613))))]]], (7424 ^ _776541) ^ [_898716, _898718, _898720] : [class_Orderings_Oorder(_898716), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_898716, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_898716, _898718, _898720)), hAPP(c_SetInterval_Oord__class_OatLeast(_898716), _898720)) = c_Orderings_Obot__class_Obot(tc_fun(_898716, tc_HOL_Obool)))], (52041 ^ _776541) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (13188 ^ _776541) ^ [_1009923, _1009925, _1009927, _1009929, _1009931] : [class_Groups_Oab__group__add(_1009923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1009925), _1009927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1009927), _1009929)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009923), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1009923), _1009931), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1009925), _1009929))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1009923), _1009931), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1009925), _1009927))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1009923), _1009931), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1009927), _1009929)))], (52365 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (20495 ^ _776541) ^ [_1146364, _1146366, _1146368, _1146370] : [class_Fields_Olinordered__field(_1146364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146364), _1146366), _1146368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146364), _1146370), c_Groups_Ozero__class_Ozero(_1146364))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146364), c_Groups_Ozero__class_Ozero(_1146364)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146364), _1146366), _1146368))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146364), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146364), _1146370), _1146366)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146364), _1146370), _1146368))))], (3382 ^ _776541) ^ [_827043, _827045] : [_827045 = _827043, -(c_Set_OPow(_827045) = c_Set_OPow(_827043))], (42685 ^ _776541) ^ [_1626416, _1626418, _1626420, _1626422] : [-(_1626416 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626418)), _1626420)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1626418, hAPP(hAPP(c_List_Olist__update(_1626418, _1626420), _1626416), _1626422)) = hAPP(hAPP(c_List_Olist__update(_1626418, c_List_Obutlast(_1626418, _1626420)), _1626416), _1626422))], (27461 ^ _776541) ^ [_1270436, _1270438, _1270440] : [class_Groups_Oordered__ab__group__add__abs(_1270436), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270436), hAPP(c_Groups_Oabs__class_Oabs(_1270436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270436), hAPP(c_Groups_Oabs__class_Oabs(_1270436), _1270438)), hAPP(c_Groups_Oabs__class_Oabs(_1270436), _1270440)))), hAPP(c_Groups_Oabs__class_Oabs(_1270436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270436), _1270438), _1270440)))))], (18548 ^ _776541) ^ [_1110325, _1110327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1110325), _1110327))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110325), _1110327)))], (13210 ^ _776541) ^ [_1010354] : [class_Lattices_Osemilattice__sup(_1010354), -(c_Finite__Set_Ofun__left__comm__idem(_1010354, _1010354, c_Lattices_Osemilattice__sup__class_Osup(_1010354)))], (25321 ^ _776541) ^ [_1234793, _1234795] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234793), _1234795) = c_Groups_Oone__class_Oone(tc_Int_Oint), 25326 ^ _776541 : [(25329 ^ _776541) ^ [] : [-(_1234795 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25327 ^ _776541) ^ [] : [-(_1234793 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 25330 ^ _776541 : [(25333 ^ _776541) ^ [] : [-(_1234795 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25331 ^ _776541) ^ [] : [-(_1234793 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (35776 ^ _776541) ^ [_1444413] : [-(hAPP(c_Int_Onat, _1444413) = 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, _1444413)), 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)))))))], (2098 ^ _776541) ^ [_806967, _806969, _806971, _806973] : [-(c_SMT_Oz3div(_806973, _806969) = c_SMT_Oz3div(_806971, _806967)), _806973 = _806971, _806969 = _806967], (37941 ^ _776541) ^ [_1500942, _1500944, _1500946, _1500948] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500942, _1500944, _1500946), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500942, _1500944), tc_HOL_Obool))), _1500948) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500942, _1500946), tc_HOL_Obool)))], (45604 ^ _776541) ^ [_1691160, _1691162, _1691164, _1691166, _1691168, _1691170] : [c_List_Olist__all2(_1691160, _1691162, _1691164, _1691166, _1691168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691170), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691160)), _1691166))), -(hBOOL(hAPP(hAPP(_1691164, hAPP(hAPP(c_List_Onth(_1691160), _1691166), _1691170)), hAPP(hAPP(c_List_Onth(_1691162), _1691168), _1691170))))], (17797 ^ _776541) ^ [_1096840, _1096842] : [class_Groups_Ogroup__add(_1096840), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096840), hAPP(c_Groups_Ouminus__class_Ouminus(_1096840), _1096842)), _1096842) = c_Groups_Ozero__class_Ozero(_1096840))], (22337 ^ _776541) ^ [_1181470, _1181472] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181470), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181472)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181470), _1181472))], (45072 ^ _776541) ^ [_1679074, _1679076, _1679078, _1679080] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679074)), _1679076) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679078)), _1679080), -(hAPP(hAPP(c_List_Omap(tc_prod(_1679074, _1679078), _1679074), c_Product__Type_Ofst(_1679074, _1679078)), hAPP(hAPP(c_List_Ozip(_1679074, _1679078), _1679076), _1679080)) = _1679076)], (51527 ^ _776541) ^ [_1819260, _1819262, _1819264] : [class_Divides_Osemiring__div(_1819260), 51530 ^ _776541 : [(51537 ^ _776541) ^ [] : [c_Divides_Odiv__class_Omod(_1819260, _1819264, _1819262) = c_Groups_Ozero__class_Ozero(_1819260), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819260), _1819262), _1819264)))], (51531 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819260), _1819262), _1819264)), -(c_Divides_Odiv__class_Omod(_1819260, _1819264, _1819262) = c_Groups_Ozero__class_Ozero(_1819260))]]], (16903 ^ _776541) ^ [_1080688, _1080690, _1080692] : [class_Groups_Oordered__comm__monoid__add(_1080688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080688), _1080690), c_Groups_Ozero__class_Ozero(_1080688))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080688), _1080692), c_Groups_Ozero__class_Ozero(_1080688))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080688), _1080690), _1080692)), c_Groups_Ozero__class_Ozero(_1080688))))], (47024 ^ _776541) ^ [_1721674, _1721676, _1721678] : [-(hAPP(c_List_Orev(_1721674), hAPP(c_List_Ofilter(_1721674, _1721676), _1721678)) = hAPP(c_List_Ofilter(_1721674, _1721676), hAPP(c_List_Orev(_1721674), _1721678)))], (46349 ^ _776541) ^ [_1708700, _1708702] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1708700, _1708702))))], (28553 ^ _776541) ^ [_1288880] : [class_Int_Onumber__ring(_1288880), -(hAPP(c_Int_Onumber__class_Onumber__of(_1288880), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1288880))], (52239 ^ _776541) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52463 ^ _776541) ^ [_1830906, _1830908] : [-(hAPP(c_COMBI(_1830906), _1830908) = _1830908)], (49812 ^ _776541) ^ [_1782835, _1782837] : [c_Predicate_Osymp(_1782835, _1782837), -(c_Relation_Osym(_1782835, hAPP(c_Set_OCollect(tc_prod(_1782835, _1782835)), hAPP(c_Product__Type_Oprod_Oprod__case(_1782835, _1782835, tc_HOL_Obool), _1782837))))], (10789 ^ _776541) ^ [_962379, _962381, _962383, _962385] : [class_Orderings_Olinorder(_962379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962379), _962381), _962383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962379), _962383), _962385)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962379, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962379, _962381), _962383)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962379, _962383), _962385)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962379, _962381), _962385))], (39461 ^ _776541) ^ [_1541270, _1541272, _1541274] : [-(hAPP(c_Product__Type_Omap__pair(_1541270, _1541270, _1541272, _1541272, c_COMBI(_1541270), c_COMBI(_1541272)), _1541274) = _1541274)], (10024 ^ _776541) ^ [_948092, _948094, _948096, _948098] : [class_Orderings_Oorder(_948092), 10027 ^ _776541 : [(10036 ^ _776541) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_948092, _948094, _948096) = hAPP(hAPP(c_Set_Oinsert(_948092), _948098), c_Orderings_Obot__class_Obot(tc_fun(_948092, tc_HOL_Obool)))), _948094 = _948096, _948096 = _948098], (10028 ^ _776541) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_948092, _948094, _948096) = hAPP(hAPP(c_Set_Oinsert(_948092), _948098), c_Orderings_Obot__class_Obot(tc_fun(_948092, tc_HOL_Obool))), 10031 ^ _776541 : [(10034 ^ _776541) ^ [] : [-(_948096 = _948098)], (10032 ^ _776541) ^ [] : [-(_948094 = _948096)]]]]], (33849 ^ _776541) ^ [_1403686] : [class_Orderings_Olinorder(_1403686), -(c_Orderings_Oord_Omin(_1403686, hAPP(c_COMBC(_1403686, _1403686, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1403686))) = c_Orderings_Oord__class_Omax(_1403686))], (44918 ^ _776541) ^ [_1675885, _1675887, _1675889, _1675891] : [hBOOL(hAPP(c_List_Odistinct(_1675885), hAPP(hAPP(c_List_Omap(_1675887, _1675885), _1675889), _1675891))), 44921 ^ _776541 : [(44924 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1675887, _1675885, _1675889, hAPP(c_List_Oset(_1675887), _1675891)))], (44922 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1675887), _1675891)))]]], (7384 ^ _776541) ^ [_897745, _897747, _897749, _897751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897745, tc_HOL_Obool)), _897747), hAPP(hAPP(c_Set_Oinsert(_897745), _897749), _897751))), 7387 ^ _776541 : [(7394 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_897745), _897749), _897747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897745, tc_HOL_Obool)), _897747), _897751)))], (7388 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_897745), _897749), _897747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897745, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897745, tc_HOL_Obool)), _897747), hAPP(hAPP(c_Set_Oinsert(_897745), _897749), c_Orderings_Obot__class_Obot(tc_fun(_897745, tc_HOL_Obool))))), _897751)))]]], (34327 ^ _776541) ^ [_1415362, _1415364] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415362)), hAPP(c_Nat_OSuc, _1415364)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415362))), 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)), _1415364)))))], (45140 ^ _776541) ^ [_1680528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1680528)), _1680528 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29953 ^ _776541) ^ [_1313623, _1313625, _1313627] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1313623), _1313625)), hBOOL(hAPP(_1313627, c_Orderings_Obot__class_Obot(tc_fun(_1313623, tc_HOL_Obool)))), 29964 ^ _776541 : [(29967 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1313623), 29962 ^ [_1313623, _1313625, _1313627]), 29963 ^ [_1313623, _1313625, _1313627]))], (29969 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1313627, 29963 ^ [_1313623, _1313625, _1313627])))], (29971 ^ _776541) ^ [] : [hBOOL(hAPP(_1313627, hAPP(hAPP(c_Set_Oinsert(_1313623), 29962 ^ [_1313623, _1313625, _1313627]), 29963 ^ [_1313623, _1313625, _1313627])))], (29965 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1313623), 29963 ^ [_1313623, _1313625, _1313627])))]], -(hBOOL(hAPP(_1313627, _1313625)))], (32506 ^ _776541) ^ [_1363464, _1363466, _1363468, _1363470, _1363472] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363464, tc_fun(_1363466, tc_HOL_Obool)), _1363468), hAPP(hAPP(c_COMBB(tc_fun(_1363466, tc_HOL_Obool), tc_fun(_1363466, tc_HOL_Obool), _1363464), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363466, tc_HOL_Obool)), _1363470)), _1363472)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363466, tc_HOL_Obool)), _1363470), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363464, tc_fun(_1363466, tc_HOL_Obool)), _1363468), _1363472)))], (14416 ^ _776541) ^ [_1036814, _1036816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036814), _1036816)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036816), _1036814)) = _1036816)], (39928 ^ _776541) ^ [_1553692, _1553694, _1553696, _1553698, _1553700, _1553702, _1553704] : [-(hAPP(c_Fun_Ocomp(_1553692, _1553694, _1553696, _1553698), c_Fun_Ofun__upd(_1553696, _1553692, _1553700, _1553702, _1553704)) = c_Fun_Ofun__upd(_1553696, _1553694, hAPP(c_Fun_Ocomp(_1553692, _1553694, _1553696, _1553698), _1553700), _1553702, hAPP(_1553698, _1553704)))], (32432 ^ _776541) ^ [_1360291, _1360293, _1360295, _1360297, _1360299] : [-(_1360291 = c_Orderings_Obot__class_Obot(tc_fun(_1360293, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360295, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360293, tc_fun(_1360295, tc_HOL_Obool)), _1360291), _1360297)), _1360299) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360293, tc_fun(_1360295, tc_HOL_Obool)), _1360291), hAPP(hAPP(c_COMBC(_1360293, tc_fun(_1360295, tc_HOL_Obool), tc_fun(_1360295, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360295, tc_HOL_Obool), tc_fun(tc_fun(_1360295, tc_HOL_Obool), tc_fun(_1360295, tc_HOL_Obool)), _1360293), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360295, tc_HOL_Obool))), _1360297)), _1360299)))], (44459 ^ _776541) ^ [_1665726, _1665728, _1665730, _1665732] : [class_Complete__Lattice_Ocomplete__lattice(_1665726), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1665728, _1665726), hAPP(c_List_Oset(_1665728), _1665730)), _1665732) = hAPP(c_List_Ofoldl(_1665726, _1665728, hAPP(c_COMBC(_1665728, _1665726, _1665726), hAPP(hAPP(c_COMBB(_1665726, tc_fun(_1665726, _1665726), _1665728), c_Lattices_Osemilattice__sup__class_Osup(_1665726)), _1665732)), c_Orderings_Obot__class_Obot(_1665726)), _1665730))], (31106 ^ _776541) ^ [_1334812, _1334814] : [class_Groups_Olinordered__ab__group__add(_1334812), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334812), _1334814)), -(_1334814 = c_Orderings_Obot__class_Obot(tc_fun(_1334812, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1334812), c_Big__Operators_Olinorder__class_OMin(_1334812, _1334814)) = c_Big__Operators_Olinorder__class_OMax(_1334812, hAPP(c_Set_Oimage(_1334812, _1334812, c_Groups_Ouminus__class_Ouminus(_1334812)), _1334814)))], (36454 ^ _776541) ^ [_1465637, _1465639, _1465641, _1465643] : [-(hAPP(c_Relation_OImage(_1465637, _1465639, _1465641), hAPP(hAPP(c_Set_Oinsert(_1465637), _1465643), c_Orderings_Obot__class_Obot(tc_fun(_1465637, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1465639), hAPP(hAPP(c_COMBC(_1465639, tc_fun(tc_prod(_1465637, _1465639), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1465637, _1465639), tc_fun(tc_fun(tc_prod(_1465637, _1465639), tc_HOL_Obool), tc_HOL_Obool), _1465639), c_member(tc_prod(_1465637, _1465639))), hAPP(c_Product__Type_OPair(_1465637, _1465639), _1465643))), _1465641)))], (7554 ^ _776541) ^ [_901143, _901145, _901147, _901149] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901143, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901143, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901143, tc_HOL_Obool)), _901145), _901147)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901143, tc_HOL_Obool)), _901147), _901149))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901143, tc_HOL_Obool)), _901149), _901145)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901143, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901143, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901143, tc_HOL_Obool)), _901145), _901147)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901143, tc_HOL_Obool)), _901147), _901149))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901143, tc_HOL_Obool)), _901149), _901145)))], (19927 ^ _776541) ^ [_1136123, _1136125, _1136127, _1136129] : [class_Fields_Olinordered__field(_1136123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136123), _1136125), c_Groups_Ozero__class_Ozero(_1136123))), 19934 ^ _776541 : [(19941 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136123), _1136129), _1136125)), _1136127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136123), _1136127), _1136125)), _1136129)))], (19935 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136123), _1136127), _1136125)), _1136129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136123), _1136129), _1136125)), _1136127)))]]], (35493 ^ _776541) ^ [_1438786, _1438788, _1438790, _1438792] : [-(hAPP(c_Product__Type_Osnd(_1438786, _1438788), hAPP(hAPP(c_Product__Type_OPair(_1438786, _1438788), _1438790), _1438792)) = _1438792)], (37205 ^ _776541) ^ [_1484649, _1484651, _1484653] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484649, _1484649)), _1484651), c_Relation_OId__on(_1484649, _1484653))), 37209 ^ _776541 : [(37212 ^ _776541) ^ [] : [-(_1484651 = hAPP(hAPP(c_Product__Type_OPair(_1484649, _1484649), 37208 ^ [_1484649, _1484651, _1484653]), 37208 ^ [_1484649, _1484651, _1484653]))], (37210 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484649), 37208 ^ [_1484649, _1484651, _1484653]), _1484653)))]]], (5204 ^ _776541) ^ [_855958, _855960, _855962, _855964] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_855964, _855960) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_855962, _855958)), _855964 = _855962, _855960 = _855958], (1904 ^ _776541) ^ [_803205, _803207] : [-(class_HOL_Oequal(_803205)), _803207 = _803205, class_HOL_Oequal(_803207)], (22221 ^ _776541) ^ [_1179580, _1179582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179580), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179582), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179580), _1179582))), -(_1179580 = _1179582)], (52007 ^ _776541) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (35580 ^ _776541) ^ [_1440540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1440540)), 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), _1440540)) = 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), _1440540))))))], (18978 ^ _776541) ^ [_1118380, _1118382] : [18986 ^ _776541 : [(18989 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1118382, 18985 ^ [_1118380, _1118382])))], (18987 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 18985 ^ [_1118380, _1118382]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1118380))))]], 18979 ^ _776541 : [(18980 ^ _776541) ^ [_1118449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118449), _1118380)), hBOOL(hAPP(_1118382, _1118449))]]], (39611 ^ _776541) ^ [_1544800, _1544802] : [c_Relation_Orefl__on(_1544800, c_Orderings_Otop__class_Otop(tc_fun(_1544800, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544800, _1544800)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544800, _1544800, tc_HOL_Obool), _1544802))), -(c_Predicate_Oreflp(_1544800, _1544802))], (45736 ^ _776541) ^ [_1694183, _1694185, _1694187, _1694189, _1694191] : [c_Finite__Set_Ofun__left__comm(_1694183, _1694185, _1694187), -(hAPP(hAPP(c_Finite__Set_Ofold(_1694183, _1694185, _1694187), _1694189), hAPP(c_List_Oset(_1694183), _1694191)) = hAPP(c_List_Ofoldl(_1694185, _1694183, hAPP(c_COMBC(_1694183, _1694185, _1694185), _1694187), _1694189), c_List_Oremdups(_1694183, _1694191)))], (22069 ^ _776541) ^ [_1176676, _1176678, _1176680, _1176682] : [class_Fields_Ofield(_1176676), -(_1176678 = c_Groups_Ozero__class_Ozero(_1176676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1176680), _1176682)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1176676), _1176678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1176682), _1176680)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176676), hAPP(hAPP(c_Power_Opower__class_Opower(_1176676), _1176678), _1176682)), hAPP(hAPP(c_Power_Opower__class_Opower(_1176676), _1176678), _1176680)))], (45275 ^ _776541) ^ [_1683189, _1683191] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1683189), _1683191) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1683189, 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)))), _1683191))))], (27022 ^ _776541) ^ [_1263297] : [c_Nat__Transfer_Ois__nat(_1263297), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263297)))], (17571 ^ _776541) ^ [_1092993, _1092995, _1092997] : [class_Groups_Oordered__ab__group__add(_1092993), 17574 ^ _776541 : [(17581 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092993), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092993), _1092995), _1092997)), c_Groups_Ozero__class_Ozero(_1092993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092993), _1092995), _1092997)))], (17575 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092993), _1092995), _1092997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092993), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092993), _1092995), _1092997)), c_Groups_Ozero__class_Ozero(_1092993))))]]], (33809 ^ _776541) ^ [_1402677, _1402679, _1402681, _1402683, _1402685] : [_1402677 = c_Orderings_Obot__class_Obot(tc_fun(_1402679, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1402679, tc_fun(_1402681, tc_HOL_Obool)), _1402677), hAPP(hAPP(c_COMBB(tc_fun(_1402681, tc_HOL_Obool), tc_fun(_1402681, tc_HOL_Obool), _1402679), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402681, tc_HOL_Obool)), _1402683)), _1402685)) = c_Orderings_Otop__class_Otop(tc_fun(_1402681, tc_HOL_Obool)))], (47058 ^ _776541) ^ [_1722466, _1722468, _1722470] : [hAPP(c_List_Orev(_1722466), _1722468) = hAPP(c_List_Orev(_1722466), _1722470), -(_1722468 = _1722470)], (41204 ^ _776541) ^ [_1584964, _1584966, _1584968] : [hAPP(hAPP(c_Relation_Orel__comp(_1584964, _1584964, _1584964), hAPP(c_Relation_Oconverse(_1584964, _1584964), _1584966)), _1584966) = _1584966, hAPP(c_Relation_ODomain(_1584964, _1584964), _1584966) = _1584968, -(c_Equiv__Relations_Oequiv(_1584964, _1584968, _1584966))], (37824 ^ _776541) ^ [_1497541] : [class_Nat_Osemiring__char__0(_1497541), -(c_Fun_Oinj__on(tc_Nat_Onat, _1497541, c_Nat_Osemiring__1__class_Oof__nat(_1497541), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (25919 ^ _776541) ^ [_1245301] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245301, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52417 ^ _776541) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (33675 ^ _776541) ^ [_1398631, _1398633, _1398635, _1398637] : [class_Rings_Osemiring__1(_1398631), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1398631), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398633, tc_Nat_Onat), _1398635), _1398637)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398633, _1398631), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1398631, _1398633), c_Nat_Osemiring__1__class_Oof__nat(_1398631)), _1398635)), _1398637))], (49371 ^ _776541) ^ [_1773311, _1773313, _1773315, _1773317] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1773311, tc_fun(_1773313, tc_HOL_Obool)), _1773315), _1773317) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1773313, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1773313, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773311, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1773313, tc_HOL_Obool)), c_HOL_OEx(_1773311)), hAPP(hAPP(c_COMBB(tc_fun(_1773311, tc_HOL_Obool), tc_fun(_1773311, tc_HOL_Obool), tc_fun(_1773313, tc_HOL_Obool)), hAPP(c_COMBS(_1773311, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1773311), c_fconj), hAPP(hAPP(c_COMBC(_1773311, tc_fun(_1773311, tc_HOL_Obool), tc_HOL_Obool), c_member(_1773311)), _1773315)))), hAPP(hAPP(c_COMBC(tc_fun(_1773313, tc_HOL_Obool), tc_fun(_1773311, tc_fun(_1773313, tc_HOL_Obool)), tc_fun(_1773311, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773313, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1773311, tc_fun(_1773313, tc_HOL_Obool)), tc_fun(_1773311, tc_HOL_Obool)), tc_fun(_1773313, tc_HOL_Obool)), c_COMBB(tc_fun(_1773313, tc_HOL_Obool), tc_HOL_Obool, _1773311)), c_fequal)), _1773317))))))], (4368 ^ _776541) ^ [_842740, _842742, _842744, _842746, _842748, _842750, _842752, _842754] : [-(c_Lazy__Sequence_Oproduct(_842754, _842750, _842746, _842742) = c_Lazy__Sequence_Oproduct(_842752, _842748, _842744, _842740)), _842754 = _842752, _842750 = _842748, _842746 = _842744, _842742 = _842740], (45267 ^ _776541) ^ [_1683100, _1683102] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1683100, _1683102) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1683100), hAPP(c_Code__Numeral_Onat__of, _1683102))))], (13638 ^ _776541) ^ [_1019340, _1019342, _1019344, _1019346, _1019348] : [class_Groups_Oordered__ab__semigroup__add(_1019340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019340), _1019342), _1019344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019340), _1019346), _1019348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019340), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019340), _1019342), _1019346)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019340), _1019344), _1019348))))], (34604 ^ _776541) ^ [_1421100] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1421100) = 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)))], (37822 ^ _776541) ^ [_1497516] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1497516))], (52259 ^ _776541) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (48862 ^ _776541) ^ [_1761525, _1761527, _1761529, _1761531, _1761533] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1761525, _1761527, _1761529, _1761531, _1761533) = c_Option_Ooption_Ooption__case(_1761525, tc_prod(_1761527, tc_Lazy__Sequence_Olazy__sequence(_1761527)), _1761529, hAPP(c_Product__Type_Oprod_Oprod__case(_1761527, tc_Lazy__Sequence_Olazy__sequence(_1761527), _1761525), _1761531), hAPP(c_Lazy__Sequence_Oyield(_1761527), _1761533)))], (31395 ^ _776541) ^ [_1340264] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1340264) = c_Orderings_Oord__class_Omax(_1340264)), class_Lattices_Osemilattice__sup(_1340264), class_Orderings_Olinorder(_1340264)], (43476 ^ _776541) ^ [_1643523, _1643525, _1643527, _1643529, _1643531, _1643533] : [hAPP(hAPP(c_List_Oappend(_1643523), _1643525), _1643527) = _1643529, _1643531 = hAPP(hAPP(c_List_Oappend(_1643523), _1643527), _1643533), -(hAPP(hAPP(c_List_Oappend(_1643523), _1643525), _1643531) = hAPP(hAPP(c_List_Oappend(_1643523), _1643529), _1643533))], (46213 ^ _776541) ^ [_1705585, _1705587, _1705589, _1705591] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1705585, tc_Nat_Onat), _1705585), c_Product__Type_Ofst(_1705585, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1705585, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1705585, tc_Nat_Onat)), _1705587), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1705585, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1705585, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1705585, tc_Nat_Onat), _1705589), _1705591))) = hAPP(hAPP(c_List_Omap(tc_prod(_1705585, tc_Nat_Onat), _1705585), c_Product__Type_Ofst(_1705585, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1705585, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1705585, tc_Nat_Onat)), _1705587), c_Product__Type_Osnd(_1705585, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1705585, tc_Nat_Onat), _1705589), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1705591)))))], (23357 ^ _776541) ^ [_1199787, _1199789, _1199791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199787)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199789), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199791)), 23367 ^ _776541 : [(23373 ^ _776541) ^ [] : [-(_1199789 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23369 ^ [_1199787, _1199789, _1199791]), 23366 ^ [_1199787, _1199789, _1199791]))], (23371 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23369 ^ [_1199787, _1199789, _1199791]), _1199791)))], (23368 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23366 ^ [_1199787, _1199789, _1199791]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1199787))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199789), _1199787) = _1199789)], (28129 ^ _776541) ^ [_1281705, _1281707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1281705)), _1281707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1281705), _1281707)))], (30468 ^ _776541) ^ [_1323166, _1323168, _1323170] : [class_Orderings_Olinorder(_1323166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323166), _1323168)), -(_1323168 = c_Orderings_Obot__class_Obot(tc_fun(_1323166, tc_HOL_Obool))), 30479 ^ _776541 : [(30489 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323166), hAPP(c_Finite__Set_Ofold1(_1323166, c_Orderings_Oord__class_Omin(_1323166)), _1323168)), _1323170))), 30490 ^ _776541 : [(30491 ^ _776541) ^ [_1323555] : [hBOOL(hAPP(hAPP(c_member(_1323166), _1323555), _1323168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323166), _1323555), _1323170))]]], (30480 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323166), hAPP(c_Finite__Set_Ofold1(_1323166, c_Orderings_Oord__class_Omin(_1323166)), _1323168)), _1323170)), 30484 ^ _776541 : [(30487 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323166), 30483 ^ [_1323166, _1323168, _1323170]), _1323170)))], (30485 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323166), 30483 ^ [_1323166, _1323168, _1323170]), _1323168)))]]]]], (43583 ^ _776541) ^ [_1645942, _1645944] : [-(hAPP(hAPP(c_List_Oappend(_1645942), _1645944), c_List_Olist_ONil(_1645942)) = _1645944)], (48762 ^ _776541) ^ [_1759209, _1759211] : [class_Lazy__Sequence_Osmall__lazy(_1759209), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1759209), _1759211) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1759209), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1759209)), c_List_Olist_ONil(_1759209)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759209))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1759211)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1759209, tc_List_Olist(_1759209)), tc_List_Olist(_1759209), c_Lazy__Sequence_Oproduct(_1759209, tc_List_Olist(_1759209), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1759209, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1759211), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1759209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1759211), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1759209, tc_List_Olist(_1759209), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759209))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1759209), tc_List_Olist(_1759209)), tc_fun(tc_List_Olist(_1759209), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759209))), _1759209), hAPP(c_COMBB(tc_List_Olist(_1759209), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759209)), tc_List_Olist(_1759209)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1759209)))), c_List_Olist_OCons(_1759209))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1759209)))))], (48492 ^ _776541) ^ [_1753656, _1753658, _1753660] : [-(c_Predicate_Oconversep(_1753656, _1753658, c_Predicate_Oconversep(_1753658, _1753656, _1753660)) = _1753660)], (28679 ^ _776541) ^ [_1290735, _1290737] : [class_Int_Onumber__ring(_1290735), class_Rings_Olinordered__idom(_1290735), 28686 ^ _776541 : [(28693 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1290737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290735), c_Groups_Oone__class_Oone(_1290735)), hAPP(c_Int_Onumber__class_Onumber__of(_1290735), _1290737))))], (28687 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290735), c_Groups_Oone__class_Oone(_1290735)), hAPP(c_Int_Onumber__class_Onumber__of(_1290735), _1290737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1290737)))]]], (17229 ^ _776541) ^ [_1086703, _1086705, _1086707] : [class_Groups_Oordered__comm__monoid__add(_1086703), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086703), _1086705), c_Groups_Ozero__class_Ozero(_1086703))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086703), _1086707), c_Groups_Ozero__class_Ozero(_1086703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086703), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086703), _1086705), _1086707)), c_Groups_Ozero__class_Ozero(_1086703))))], (8429 ^ _776541) ^ [_921307, _921309] : [class_Lattices_Osemilattice__inf(_921307), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921307), _921309), _921309) = _921309)], (36438 ^ _776541) ^ [_1464810, _1464812] : [-(c_FunDef_Orp__inv__image(_1464810, _1464812) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool), tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool), tc_fun(tc_fun(_1464812, _1464810), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool), tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool), tc_fun(tc_fun(_1464812, _1464810), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)), tc_fun(tc_fun(_1464812, _1464810), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool), tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool), tc_fun(tc_fun(_1464812, _1464810), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool))))), tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)), tc_fun(tc_fun(_1464812, _1464810), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool))), tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)), tc_fun(tc_fun(_1464812, _1464810), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)))), tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool)), c_COMBS(tc_fun(_1464812, _1464810), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)), tc_fun(tc_fun(_1464812, _1464810), tc_fun(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)))), tc_fun(tc_prod(_1464810, _1464810), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool))), tc_fun(_1464812, _1464810)), c_Product__Type_OPair(tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool), tc_fun(tc_prod(_1464812, _1464812), tc_HOL_Obool)))), c_Relation_Oinv__image(_1464810, _1464812))))), c_Relation_Oinv__image(_1464810, _1464812))))], (43627 ^ _776541) ^ [_1646733, _1646735, _1646737] : [hAPP(hAPP(c_List_Oappend(_1646733), _1646735), _1646737) = _1646735, -(_1646737 = c_List_Olist_ONil(_1646733))], (38784 ^ _776541) ^ [_1522062, _1522064, _1522066, _1522068] : [-(hAPP(c_Relation_ODomain(_1522062, _1522064), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1522062, _1522064), tc_HOL_Obool)), _1522066), _1522068)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1522062, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1522062, _1522064), _1522066)), hAPP(c_Relation_ODomain(_1522062, _1522064), _1522068)))], (50159 ^ _776541) ^ [_1790138, _1790140, _1790142] : [hAPP(c_Set_Oimage(_1790138, _1790140, _1790142), c_Orderings_Otop__class_Otop(tc_fun(_1790138, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790140, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1790138, _1790140, _1790140, _1790142), c_Hilbert__Choice_Oinv__into(_1790138, _1790140, c_Orderings_Otop__class_Otop(tc_fun(_1790138, tc_HOL_Obool)), _1790142)) = c_Fun_Oid(_1790140))], (30634 ^ _776541) ^ [_1326224, _1326226] : [class_Orderings_Olinorder(_1326224), -(c_Big__Operators_Olattice_OInf__fin(_1326224, c_Orderings_Oord__class_Omin(_1326224), hAPP(hAPP(c_Set_Oinsert(_1326224), _1326226), c_Orderings_Obot__class_Obot(tc_fun(_1326224, tc_HOL_Obool)))) = _1326226)], (38869 ^ _776541) ^ [_1524036, _1524038, _1524040, _1524042] : [38870 ^ _776541 : [(38871 ^ _776541) ^ [_1524111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524036, _1524040)), hAPP(hAPP(c_Product__Type_OPair(_1524036, _1524040), _1524038), _1524111)), _1524042))]], -(hBOOL(hAPP(hAPP(c_member(_1524036), _1524038), hAPP(c_Relation_ODomain(_1524036, _1524040), _1524042))))], (34624 ^ _776541) ^ [_1421494, _1421496] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1421494), hAPP(c_Nat_OSuc, _1421496)) = 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)), _1421496)), _1421494))], (26080 ^ _776541) ^ [_1247889, _1247891] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1247889), _1247891) = 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)), _1247889)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1247891))))], (46077 ^ _776541) ^ [_1701981, _1701983, _1701985, _1701987] : [-(hAPP(c_List_Ofilter(_1701981, _1701983), c_List_Oremove1(_1701981, _1701985, _1701987)) = c_List_Oremove1(_1701981, _1701985, hAPP(c_List_Ofilter(_1701981, _1701983), _1701987)))], (52221 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (18804 ^ _776541) ^ [_1115318, _1115320] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1115318), _1115320)))), -(_1115320 = c_Orderings_Obot__class_Obot(tc_fun(_1115318, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115318), _1115320))], (42537 ^ _776541) ^ [_1623061, _1623063, _1623065, _1623067, _1623069, _1623071] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623061, _1623063)), hAPP(hAPP(c_Product__Type_OPair(_1623061, _1623063), _1623065), _1623067)), hAPP(c_List_Oset(tc_prod(_1623061, _1623063)), hAPP(hAPP(c_List_Ozip(_1623061, _1623063), _1623069), _1623071)))), 42540 ^ _776541 : [(42543 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623063), _1623067), hAPP(c_List_Oset(_1623063), _1623071))))], (42541 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623061), _1623065), hAPP(c_List_Oset(_1623061), _1623069))))]]], (4346 ^ _776541) ^ [_842351, _842353, _842355, _842357, _842359, _842361, _842363, _842365, _842367, _842369] : [-(c_Predicate_Opred__comp(_842369, _842365, _842361, _842357, _842353) = c_Predicate_Opred__comp(_842367, _842363, _842359, _842355, _842351)), _842369 = _842367, _842365 = _842363, _842361 = _842359, _842357 = _842355, _842353 = _842351], (50908 ^ _776541) ^ [_1807629] : [-(c_Lazy__Sequence_Oflat(_1807629, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1807629))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1807629))], (46136 ^ _776541) ^ [_1703164, _1703166, _1703168, _1703170, _1703172] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703164)), hAPP(c_List_Ofilter(_1703164, _1703166), hAPP(hAPP(c_List_Omap(_1703168, _1703164), _1703170), _1703172))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703168)), hAPP(c_List_Ofilter(_1703168, hAPP(c_Fun_Ocomp(_1703164, tc_HOL_Obool, _1703168, _1703166), _1703170)), _1703172)))], (9986 ^ _776541) ^ [_947424, _947426, _947428, _947430, _947432] : [class_Orderings_Oorder(_947424), 9989 ^ _776541 : [(10002 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947424, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_947424, _947426, _947428)), c_SetInterval_Oord__class_OatLeastAtMost(_947424, _947430, _947432)))), 10003 ^ _776541 : [(10006 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947424), _947430), _947426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947424), _947428), _947432))], (10004 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947424), _947426), _947428)))]]], (9990 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947424, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_947424, _947426, _947428)), c_SetInterval_Oord__class_OatLeastAtMost(_947424, _947430, _947432))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947424), _947426), _947428)), 9997 ^ _776541 : [(10000 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947424), _947428), _947432)))], (9998 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947424), _947430), _947426)))]]]]], (23553 ^ _776541) ^ [_1203499, _1203501] : [class_Int_Onumber__ring(_1203499), 23556 ^ _776541 : [(23563 ^ _776541) ^ [] : [-(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), _1203501)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203499), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203501)) = c_Groups_Ozero__class_Ozero(_1203499))], (23557 ^ _776541) ^ [] : [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), _1203501))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203499), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203501)) = hAPP(c_Int_Onumber__class_Onumber__of(_1203499), _1203501))]]], (18174 ^ _776541) ^ [_1103254] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1103254) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1103254))], (43142 ^ _776541) ^ [_1636038, _1636040, _1636042] : [-(hAPP(hAPP(c_List_Olist__update(_1636038, c_List_Olist_ONil(_1636038)), _1636040), _1636042) = c_List_Olist_ONil(_1636038))], (16138 ^ _776541) ^ [_1068217, _1068219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068217)), _1068219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068217), _1068219)))], (50969 ^ _776541) ^ [_1808776] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808776), _1808776)))], (52197 ^ _776541) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (17289 ^ _776541) ^ [_1087779, _1087781, _1087783, _1087785] : [class_Rings_Olinordered__ring__strict(_1087779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087779), _1087781), _1087783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087779), _1087785), c_Groups_Ozero__class_Ozero(_1087779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087779), _1087785), _1087783)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087779), _1087785), _1087781))))], (38505 ^ _776541) ^ [_1514685, _1514687, _1514689, _1514691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514685, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514685, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1514687, _1514685), _1514689)), hAPP(c_Relation_ORange(_1514687, _1514685), _1514691))), hAPP(c_Relation_ORange(_1514687, _1514685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1514687, _1514685), tc_HOL_Obool)), _1514689), _1514691)))))], (19797 ^ _776541) ^ [_1133827, _1133829, _1133831, _1133833] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1133827), _1133829)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133831), _1133833)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1133827, _1133831)), c_Sum__Type_OPlus(_1133827, _1133831, _1133829, _1133833))))], (22647 ^ _776541) ^ [_1186879, _1186881] : [class_Power_Opower(_1186879), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186879), _1186881), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1186879))], (31735 ^ _776541) ^ [_1346675, _1346677, _1346679, _1346681, _1346683] : [class_Orderings_Olinorder(_1346675), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346675, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1346675, _1346677, _1346679)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1346675, _1346681, _1346683)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1346675, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346675), _1346677), _1346681), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346675), _1346679), _1346683)))], (1664 ^ _776541) ^ [_800205, _800207] : [-(class_Rings_Ono__zero__divisors(_800205)), _800207 = _800205, class_Rings_Ono__zero__divisors(_800207)], (36094 ^ _776541) ^ [_1456268, _1456270, _1456272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456268, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1456268, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36095 ^ [_1456268, _1456270, _1456272])), _1456270)), _1456272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456268, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1456268, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1456270)), _1456272)))], (26809 ^ _776541) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (16352 ^ _776541) ^ [_1071558] : [class_Rings_Ozero__neq__one(_1071558), c_Groups_Ozero__class_Ozero(_1071558) = c_Groups_Oone__class_Oone(_1071558)], (29251 ^ _776541) ^ [_1300823, _1300825] : [class_Rings_Oring__1__no__zero__divisors(_1300823), 29254 ^ _776541 : [(29261 ^ _776541) ^ [] : [_1300825 = c_Groups_Ozero__class_Ozero(_1300823), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300823), _1300825), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1300823))], (29255 ^ _776541) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1300823), _1300825), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1300823), -(_1300825 = c_Groups_Ozero__class_Ozero(_1300823))]]], (31158 ^ _776541) ^ [_1335748, _1335750] : [class_Orderings_Olinorder(_1335748), -(c_Big__Operators_Olinorder__class_OMax(_1335748, hAPP(hAPP(c_Set_Oinsert(_1335748), _1335750), c_Orderings_Obot__class_Obot(tc_fun(_1335748, tc_HOL_Obool)))) = _1335750)], (9590 ^ _776541) ^ [_941003, _941005, _941007] : [class_Orderings_Olinorder(_941003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941003), _941005), _941007)), 9597 ^ _776541 : [(9604 ^ _776541) ^ [] : [_941005 = _941007, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941003), _941005), _941007))], (9598 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941003), _941005), _941007))), -(_941005 = _941007)]]], (52173 ^ _776541) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52405 ^ _776541) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52087 ^ _776541) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (26667 ^ _776541) ^ [_1257847, _1257849] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257847)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257847)), _1257849) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257847)), _1257849)))], (8163 ^ _776541) ^ [_915848, _915850, _915852] : [class_Orderings_Olinorder(_915848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915848), _915850), _915852)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915848, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_915848), _915850)), c_SetInterval_Oord__class_OgreaterThanAtMost(_915848, _915850, _915852)) = hAPP(c_SetInterval_Oord__class_OatMost(_915848), _915852))], (28517 ^ _776541) ^ [_1288288, _1288290] : [c_Int_Oiszero(_1288288, hAPP(c_Int_Onumber__class_Onumber__of(_1288288), c_Int_OBit1(_1288290))), class_Int_Onumber__ring(_1288288), class_Int_Oring__char__0(_1288288)], (49295 ^ _776541) ^ [_1771830, _1771832] : [-(c_Relation_Otrans(_1771830, c_Transitive__Closure_Otrancl(_1771830, _1771832)))], (41502 ^ _776541) ^ [_1592191, _1592193] : [-(c_Transitive__Closure_Ortrancl(_1592191, _1592193) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1592191, _1592191), 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(_1592191, _1592191), tc_HOL_Obool), tc_fun(tc_prod(_1592191, _1592191), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1592191, _1592191), tc_HOL_Obool)), _1592193)))], (43609 ^ _776541) ^ [_1646423, _1646425, _1646427] : [hAPP(hAPP(c_List_Oappend(_1646423), _1646425), _1646427) = c_List_Olist_ONil(_1646423), 43612 ^ _776541 : [(43615 ^ _776541) ^ [] : [-(_1646427 = c_List_Olist_ONil(_1646423))], (43613 ^ _776541) ^ [] : [-(_1646425 = c_List_Olist_ONil(_1646423))]]], (41492 ^ _776541) ^ [_1591941, _1591943, _1591945] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591941, _1591941)), _1591943), c_Transitive__Closure_Otrancl(_1591941, _1591945)))), 41493 ^ _776541 : [(41494 ^ _776541) ^ [_1592020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1592020)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591941, _1591941)), _1591943), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591941, _1591941), tc_HOL_Obool), _1592020), _1591945)))]]], (36602 ^ _776541) ^ [_1470102, _1470104] : [-(hAPP(c_Relation_OField(_1470102), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1470102, _1470102), tc_HOL_Obool), _1470104)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1470102, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1470102, _1470102), tc_HOL_Obool), tc_fun(_1470102, tc_HOL_Obool), c_Relation_OField(_1470102)), _1470104)))], (5739 ^ _776541) ^ [_867010, _867012] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867010, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867010)), tc_HOL_Obool)), hAPP(c_Hoare__Mirabelle_ORep__triple(_867010), _867012)), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867010, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867010)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867010)))))], (2746 ^ _776541) ^ [_817153, _817155] : [_817155 = _817153, -(c_Set_OBall(_817155) = c_Set_OBall(_817153))], (4770 ^ _776541) ^ [_849139, _849141, _849143, _849145, _849147, _849149] : [-(c_Relation_OImage(_849149, _849145, _849141) = c_Relation_OImage(_849147, _849143, _849139)), _849149 = _849147, _849145 = _849143, _849141 = _849139], (7061 ^ _776541) ^ [_891488, _891490, _891492] : [class_Orderings_Oorder(_891488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891488), _891490), _891492)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_891488, _891492, _891490) = c_Orderings_Obot__class_Obot(tc_fun(_891488, tc_HOL_Obool)))], (42729 ^ _776541) ^ [_1627517, _1627519, _1627521, _1627523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627517), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627519)), _1627521))), -(hAPP(hAPP(c_List_Onth(_1627519), hAPP(hAPP(c_List_Olist__update(_1627519, _1627521), _1627517), _1627523)), _1627517) = _1627523)], (43366 ^ _776541) ^ [_1641094, _1641096, _1641098, _1641100, _1641102] : [hAPP(hAPP(c_List_Oappend(_1641094), _1641096), _1641098) = hAPP(hAPP(c_List_Olist_OCons(_1641094), _1641100), _1641102), 43371 ^ _776541 : [(43374 ^ _776541) ^ [] : [-(_1641098 = hAPP(hAPP(c_List_Olist_OCons(_1641094), _1641100), _1641102))], (43372 ^ _776541) ^ [] : [-(_1641096 = c_List_Olist_ONil(_1641094))]], 43376 ^ _776541 : [(43379 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1641094), 43375 ^ [_1641094, _1641096, _1641098, _1641100, _1641102]), _1641098) = _1641102)], (43377 ^ _776541) ^ [] : [-(_1641096 = hAPP(hAPP(c_List_Olist_OCons(_1641094), _1641100), 43375 ^ [_1641094, _1641096, _1641098, _1641100, _1641102]))]]], (41158 ^ _776541) ^ [_1583575, _1583577, _1583579] : [-(hAPP(c_Relation_ODomain(_1583575, _1583577), hAPP(c_Relation_Oconverse(_1583577, _1583575), _1583579)) = hAPP(c_Relation_ORange(_1583577, _1583575), _1583579))], (2398 ^ _776541) ^ [_811643, _811645, _811647, _811649, _811651, _811653, _811655, _811657, _811659, _811661] : [-(c_Nitpick_Opair__box_Opair__box__case(_811661, _811657, _811653, _811649, _811645) = c_Nitpick_Opair__box_Opair__box__case(_811659, _811655, _811651, _811647, _811643)), _811661 = _811659, _811657 = _811655, _811653 = _811651, _811649 = _811647, _811645 = _811643], (26262 ^ _776541) ^ [_1250890] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1250890)))), -(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), _1250890)) = 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), _1250890))))], (44124 ^ _776541) ^ [_1659077, _1659079] : [-(_1659077 = c_List_Olist_ONil(_1659079)), -(hBOOL(hAPP(hAPP(c_member(_1659079), hAPP(c_List_Ohd(_1659079), _1659077)), hAPP(c_List_Oset(_1659079), _1659077))))], (35880 ^ _776541) ^ [_1447866, _1447868, _1447870] : [class_Orderings_Olinorder(_1447866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447866), _1447868)), -(_1447868 = c_Orderings_Obot__class_Obot(tc_fun(_1447866, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1447866), _1447870), c_Big__Operators_Olattice_OInf__fin(_1447866, c_Orderings_Oord__class_Omin(_1447866), _1447868)) = c_Big__Operators_Olattice_OInf__fin(_1447866, c_Orderings_Oord__class_Omin(_1447866), hAPP(c_Set_OCollect(_1447866), hAPP(hAPP(c_COMBB(tc_fun(_1447866, tc_HOL_Obool), tc_HOL_Obool, _1447866), c_HOL_OEx(_1447866)), hAPP(hAPP(c_COMBC(_1447866, tc_fun(_1447866, tc_HOL_Obool), tc_fun(_1447866, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447866, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1447866, tc_HOL_Obool), tc_fun(_1447866, tc_HOL_Obool)), _1447866), c_COMBS(_1447866, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447866, tc_HOL_Obool), tc_fun(_1447866, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1447866), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1447866), c_fconj)), hAPP(hAPP(c_COMBC(_1447866, tc_fun(_1447866, _1447866), tc_fun(_1447866, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447866, tc_HOL_Obool), tc_fun(tc_fun(_1447866, _1447866), tc_fun(_1447866, tc_HOL_Obool)), _1447866), c_COMBB(_1447866, tc_HOL_Obool, _1447866)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1447866), _1447870))))), hAPP(hAPP(c_COMBC(_1447866, tc_fun(_1447866, tc_HOL_Obool), tc_HOL_Obool), c_member(_1447866)), _1447868))))))], (6097 ^ _776541) ^ [_874187, _874189, _874191, _874193, _874195, _874197] : [hBOOL(hAPP(hAPP(c_member(_874187), _874189), c_SetInterval_Oord_OatLeastLessThan(_874187, _874191, _874193, _874195, _874197))), 6100 ^ _776541 : [(6103 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_874193, _874189), _874197)))], (6101 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_874191, _874195), _874189)))]]], (28407 ^ _776541) ^ [_1286463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1286463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1286463))))], (38632 ^ _776541) ^ [_1518560, _1518562, _1518564, _1518566] : [c_Fun_Oinj__on(_1518560, _1518562, _1518564, c_Orderings_Otop__class_Otop(tc_fun(_1518560, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518560, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1518560, _1518562, _1518564), hAPP(hAPP(c_Set_Oinsert(_1518562), _1518566), c_Orderings_Obot__class_Obot(tc_fun(_1518562, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1518560), c_HOL_OThe(_1518560, hAPP(hAPP(c_COMBC(_1518560, _1518562, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1518562, tc_fun(_1518562, tc_HOL_Obool), _1518560), c_fequal), _1518564)), _1518566))), c_Orderings_Obot__class_Obot(tc_fun(_1518560, tc_HOL_Obool))))))], (28481 ^ _776541) ^ [_1287685] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1287685))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1287685)))))], (29621 ^ _776541) ^ [_1307459] : [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, _1307459, 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, _1307459, 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))], (16148 ^ _776541) ^ [_1068438, _1068440, _1068442] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068438)), _1068440) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068438)), _1068442), -(_1068440 = _1068442)], (52471 ^ _776541) ^ [_1831078, _1831080, _1831082, _1831084, _1831086, _1831088] : [-(hAPP(hAPP(hAPP(c_COMBS(_1831078, _1831080, _1831082), _1831084), _1831086), _1831088) = hAPP(hAPP(_1831084, _1831088), hAPP(_1831086, _1831088)))], (20 ^ _776541) ^ [_776801, _776803, _776805, _776807, _776809, _776811, _776813, _776815, _776817, _776819, _776821, _776823] : [-(c_Nitpick_Ofold__graph_H(_776821, _776817, _776813, _776809, _776805, _776801)), c_Nitpick_Ofold__graph_H(_776823, _776819, _776815, _776811, _776807, _776803), _776823 = _776821, _776819 = _776817, _776815 = _776813, _776811 = _776809, _776807 = _776805, _776803 = _776801], (17837 ^ _776541) ^ [_1097500, _1097502, _1097504] : [class_Groups_Ocomm__monoid__add(_1097500), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097502, _1097500), _1097504), c_Orderings_Obot__class_Obot(tc_fun(_1097502, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1097500))], (10092 ^ _776541) ^ [_949250, _949252, _949254, _949256] : [class_Orderings_Oorder(_949250), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949250, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949250, _949252, _949254)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949250, _949254, _949256)) = c_Orderings_Obot__class_Obot(tc_fun(_949250, tc_HOL_Obool)))], (44493 ^ _776541) ^ [_1666545, _1666547, _1666549, _1666551, _1666553] : [class_Orderings_Olinorder(_1666545), hBOOL(hAPP(c_List_Odistinct(_1666547), _1666549)), -(hBOOL(hAPP(c_List_Odistinct(_1666547), c_List_Olinorder__class_Oinsort__insert__key(_1666547, _1666545, _1666551, _1666553, _1666549))))], (48903 ^ _776541) ^ [_1762415, _1762417, _1762419, _1762421] : [48904 ^ _776541 : [(48907 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762415), _1762419), _1762421))], (48905 ^ _776541) ^ [] : [_1762417 = _1762421]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1762415), hAPP(hAPP(c_List_Olist_OCons(_1762415), _1762417), _1762419)), _1762421)))], (3306 ^ _776541) ^ [_825891, _825893] : [_825893 = _825891, -(c_Random_Orange(_825893) = c_Random_Orange(_825891))], (30668 ^ _776541) ^ [_1326752, _1326754] : [class_Orderings_Olinorder(_1326752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326752), _1326754)), -(c_Big__Operators_Olattice_OInf__fin(_1326752, c_Orderings_Oord__class_Omin(_1326752), _1326754) = hAPP(c_Finite__Set_Ofold1(_1326752, c_Orderings_Oord__class_Omin(_1326752)), _1326754))], (39886 ^ _776541) ^ [_1552682, _1552684, _1552686, _1552688, _1552690, _1552692] : [-(hAPP(hAPP(c_Fun_Ocomp(_1552682, _1552684, _1552686, hAPP(c_COMBK(_1552684, _1552682), _1552688)), _1552690), _1552692) = _1552688)], (33100 ^ _776541) ^ [_1381638, _1381640, _1381642, _1381644, _1381646] : [hBOOL(hAPP(hAPP(c_member(_1381638), _1381640), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381642, tc_fun(_1381638, tc_HOL_Obool)), _1381644), _1381646))), 33104 ^ _776541 : [(33107 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381638), _1381640), hAPP(_1381646, 33103 ^ [_1381638, _1381640, _1381642, _1381644, _1381646]))))], (33105 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381642), 33103 ^ [_1381638, _1381640, _1381642, _1381644, _1381646]), _1381644)))]]], (13652 ^ _776541) ^ [_1019611, _1019613, _1019615, _1019617] : [class_Groups_Oordered__ab__semigroup__add(_1019611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019611), _1019613), _1019615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019611), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019611), _1019617), _1019613)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019611), _1019617), _1019615))))], (33765 ^ _776541) ^ [_1401373, _1401375, _1401377, _1401379, _1401381] : [class_Groups_Ocomm__monoid__mult(_1401373), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401375), _1401377)), 33772 ^ _776541 : [(33779 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401375), _1401379), _1401377))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401375, _1401373), hAPP(hAPP(c_COMBC(_1401375, _1401373, _1401373), hAPP(hAPP(c_COMBS(_1401375, _1401373, tc_fun(_1401373, _1401373)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401373, tc_fun(_1401373, _1401373)), _1401375), c_If(_1401373)), hAPP(c_fequal, _1401379))), _1401381)), c_Groups_Oone__class_Oone(_1401373))), _1401377) = c_Groups_Oone__class_Oone(_1401373))], (33773 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1401375), _1401379), _1401377)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401375, _1401373), hAPP(hAPP(c_COMBC(_1401375, _1401373, _1401373), hAPP(hAPP(c_COMBS(_1401375, _1401373, tc_fun(_1401373, _1401373)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401373, tc_fun(_1401373, _1401373)), _1401375), c_If(_1401373)), hAPP(c_fequal, _1401379))), _1401381)), c_Groups_Oone__class_Oone(_1401373))), _1401377) = hAPP(_1401381, _1401379))]]], (18111 ^ _776541) ^ [_1102199, _1102201] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102199), _1102201) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102199), _1102201)))], (51931 ^ _776541) ^ [_1825580, _1825582] : [class_Orderings_Oord(_1825580), -(class_Orderings_Oord(tc_fun(_1825582, _1825580)))], (42403 ^ _776541) ^ [_1618294, _1618296, _1618298, _1618300, _1618302] : [hBOOL(hAPP(hAPP(c_member(_1618294), _1618296), hAPP(c_List_Oset(_1618294), _1618298))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1618300), hAPP(_1618302, _1618296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1618300), c_List_Olist_Olist__size(_1618294, _1618302, _1618298))))], (11214 ^ _776541) ^ [_971121, _971123, _971125, _971127] : [-(hBOOL(hAPP(hAPP(c_member(_971121), hAPP(_971123, _971125)), hAPP(c_Set_Oimage(_971127, _971121, _971123), c_Orderings_Otop__class_Otop(tc_fun(_971127, tc_HOL_Obool))))))], (49496 ^ _776541) ^ [_1776893, _1776895] : [c_Equiv__Relations_Oequivp(_1776893, _1776895), 49499 ^ _776541 : [(49504 ^ _776541) ^ [] : [-(c_Predicate_Otransp(_1776893, _1776895))], (49502 ^ _776541) ^ [] : [-(c_Predicate_Osymp(_1776893, _1776895))], (49500 ^ _776541) ^ [] : [-(c_Predicate_Oreflp(_1776893, _1776895))]]], (4522 ^ _776541) ^ [_845229, _845231] : [_845231 = _845229, -(c_List_Olist_OCons(_845231) = c_List_Olist_OCons(_845229))], (19601 ^ _776541) ^ [_1130684] : [class_Groups_Osgn__if(_1130684), -(c_Groups_Osgn__class_Osgn(_1130684, c_Groups_Ozero__class_Ozero(_1130684)) = c_Groups_Ozero__class_Ozero(_1130684))], (39037 ^ _776541) ^ [_1528268, _1528270, _1528272, _1528274, _1528276, _1528278] : [hBOOL(hAPP(hAPP(c_member(_1528268), _1528270), _1528272)), hBOOL(hAPP(hAPP(c_member(_1528274), _1528276), hAPP(_1528278, _1528270))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528268, _1528274)), hAPP(hAPP(c_Product__Type_OPair(_1528268, _1528274), _1528270), _1528276)), hAPP(hAPP(c_Product__Type_OSigma(_1528268, _1528274), _1528272), _1528278))))], (23982 ^ _776541) ^ [_1210830, _1210832, _1210834, _1210836] : [class_Divides_Osemiring__div(_1210830), -(_1210832 = c_Groups_Ozero__class_Ozero(_1210830)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210830), _1210834), _1210832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210830), _1210836), _1210832)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210830), _1210834), _1210836))], (15678 ^ _776541) ^ [_1060828] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060828)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1060828)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060828)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (12017 ^ _776541) ^ [_987759, _987761, _987763, _987765, _987767, _987769] : [c_Finite__Set_Ofolding__image__simple(_987759, _987761, _987763, _987765, _987767, _987769), -(hAPP(_987769, c_Orderings_Obot__class_Obot(tc_fun(_987761, tc_HOL_Obool))) = _987765)], (12105 ^ _776541) ^ [_989182, _989184] : [class_Complete__Lattice_Ocomplete__lattice(_989182), hBOOL(hAPP(c_Finite__Set_Ofinite(_989182), _989184)), -(_989184 = c_Orderings_Obot__class_Obot(tc_fun(_989182, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_989182, _989184) = c_Complete__Lattice_OInf__class_OInf(_989182, _989184))], (2138 ^ _776541) ^ [_807563, _807565] : [_807565 = _807563, -(c_Int_Oring__1__class_OInts(_807565) = c_Int_Oring__1__class_OInts(_807563))], (37951 ^ _776541) ^ [_1501309, _1501311, _1501313, _1501315, _1501317, _1501319, _1501321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501309, _1501311), tc_HOL_Obool)), _1501313), _1501315)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501311, _1501317), tc_HOL_Obool)), _1501319), _1501321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501309, _1501317), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501309, _1501311, _1501317), _1501313), _1501319)), hAPP(hAPP(c_Relation_Orel__comp(_1501309, _1501311, _1501317), _1501315), _1501321))))], (7098 ^ _776541) ^ [_892144] : [-(hBOOL(hAPP(hAPP(c_member(_892144), 7096 ^ [_892144]), c_Orderings_Otop__class_Otop(tc_fun(_892144, tc_HOL_Obool)))))], (10345 ^ _776541) ^ [_954225, _954227, _954229] : [class_Lattices_Oboolean__algebra(_954225), 10348 ^ _776541 : [(10355 ^ _776541) ^ [] : [_954227 = _954229, -(hAPP(c_Groups_Ouminus__class_Ouminus(_954225), _954227) = hAPP(c_Groups_Ouminus__class_Ouminus(_954225), _954229))], (10349 ^ _776541) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_954225), _954227) = hAPP(c_Groups_Ouminus__class_Ouminus(_954225), _954229), -(_954227 = _954229)]]], (33356 ^ _776541) ^ [_1388804, _1388806, _1388808, _1388810, _1388812, _1388814] : [class_Complete__Lattice_Ocomplete__lattice(_1388804), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388806, _1388804), _1388808), hAPP(hAPP(c_COMBB(tc_fun(_1388810, _1388804), _1388804, _1388806), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388810, _1388804), _1388812)), _1388814)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388810, _1388804), _1388812), hAPP(hAPP(c_COMBB(tc_fun(_1388806, _1388804), _1388804, _1388810), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388806, _1388804), _1388808)), hAPP(c_COMBC(_1388806, _1388810, _1388804), _1388814))))], (48075 ^ _776541) ^ [_1744906, _1744908] : [c_List_Olist__ex(_1744906, _1744908, c_List_Olist_ONil(_1744906))], (52317 ^ _776541) ^ [_1829415, _1829417] : [-(class_HOL_Oequal(tc_Nitpick_Opair__box(_1829415, _1829417)))], (45509 ^ _776541) ^ [_1689057, _1689059, _1689061] : [c_List_Olist__all2(_1689061, _1689061, c_fequal, _1689057, _1689059), -(_1689057 = _1689059)], (2300 ^ _776541) ^ [_810048, _810050] : [_810050 = _810048, -(c_Int_Opred(_810050) = c_Int_Opred(_810048))], (35024 ^ _776541) ^ [_1430157, _1430159, _1430161, _1430163] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430157, _1430159), _1430161)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430157, _1430159), _1430163)), -(_1430161 = _1430163)], (26795 ^ _776541) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (2460 ^ _776541) ^ [_812652, _812654, _812656, _812658] : [-(c_Divides_Odivmod__int__rel(_812658, _812654) = c_Divides_Odivmod__int__rel(_812656, _812652)), _812658 = _812656, _812654 = _812652], (1134 ^ _776541) ^ [_793580, _793582] : [-(class_Rings_Olinordered__ring__strict(_793580)), _793582 = _793580, class_Rings_Olinordered__ring__strict(_793582)], (29289 ^ _776541) ^ [_1301399] : [class_Rings_Osemiring__1(_1301399), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301399), c_Groups_Oone__class_Oone(_1301399)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1301399))], (2866 ^ _776541) ^ [_819051, _819053, _819055, _819057] : [-(c_Relation_ORange(_819057, _819053) = c_Relation_ORange(_819055, _819051)), _819057 = _819055, _819053 = _819051], (38674 ^ _776541) ^ [_1519511, _1519513, _1519515, _1519517, _1519519, _1519521] : [-(hAPP(c_Set_Ovimage(_1519511, _1519513, _1519515), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519517, tc_fun(_1519513, tc_HOL_Obool)), _1519519), _1519521)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519517, tc_fun(_1519511, tc_HOL_Obool)), _1519519), hAPP(hAPP(c_COMBB(tc_fun(_1519513, tc_HOL_Obool), tc_fun(_1519511, tc_HOL_Obool), _1519517), c_Set_Ovimage(_1519511, _1519513, _1519515)), _1519521)))], (52121 ^ _776541) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (35630 ^ _776541) ^ [_1441567, _1441569, _1441571, _1441573, _1441575] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441567, _1441569, _1441571), _1441573), _1441575) = hAPP(hAPP(_1441573, hAPP(c_Product__Type_Ofst(_1441567, _1441569), _1441575)), hAPP(c_Product__Type_Osnd(_1441567, _1441569), _1441575)))], (32005 ^ _776541) ^ [_1351650, _1351652] : [class_Orderings_Olinorder(_1351650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351650), _1351652)), -(c_Big__Operators_Olattice_OSup__fin(_1351650, c_Orderings_Oord__class_Omax(_1351650), _1351652) = hAPP(c_Finite__Set_Ofold1(_1351650, c_Orderings_Oord__class_Omax(_1351650)), _1351652))], (45104 ^ _776541) ^ [_1679795, _1679797, _1679799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1679795), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1679797), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1679797)), _1679799)))), -(hBOOL(hAPP(hAPP(c_member(_1679797), hAPP(c_Random_Opick(_1679797, _1679799), _1679795)), hAPP(c_List_Oset(_1679797), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1679797), _1679797), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1679797)), _1679799)))))], (46160 ^ _776541) ^ [_1703825, _1703827, _1703829, _1703831] : [hBOOL(hAPP(hAPP(c_member(_1703825), _1703827), hAPP(c_List_Oset(_1703825), _1703829))), -(hBOOL(hAPP(_1703831, _1703827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703825)), hAPP(c_List_Ofilter(_1703825, _1703831), _1703829))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703825)), _1703829))))], (51977 ^ _776541) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (19141 ^ _776541) ^ [_1121398, _1121400] : [class_Groups_Olinordered__ab__group__add(_1121398), 19144 ^ _776541 : [(19151 ^ _776541) ^ [] : [_1121400 = c_Groups_Ozero__class_Ozero(_1121398), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121398), _1121400), _1121400) = c_Groups_Ozero__class_Ozero(_1121398))], (19145 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121398), _1121400), _1121400) = c_Groups_Ozero__class_Ozero(_1121398), -(_1121400 = c_Groups_Ozero__class_Ozero(_1121398))]]], (7662 ^ _776541) ^ [_904083, _904085, _904087, _904089] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904083, tc_HOL_Obool)), _904085), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904083, tc_HOL_Obool)), _904087), _904089)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904083, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904083, tc_HOL_Obool)), _904085), _904087)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904083, tc_HOL_Obool)), _904085), _904089)))], (2150 ^ _776541) ^ [_807733, _807735, _807737, _807739] : [-(c_Nitpick_Onat__lcm(_807739, _807735) = c_Nitpick_Onat__lcm(_807737, _807733)), _807739 = _807737, _807735 = _807733], (33451 ^ _776541) ^ [_1391518, _1391520, _1391522, _1391524] : [-(hAPP(c_Finite__Set_Ofold__image(_1391518, _1391520, _1391522), _1391524) = c_Finite__Set_Ofold(_1391520, _1391518, hAPP(hAPP(c_COMBB(_1391518, tc_fun(_1391518, _1391518), _1391520), _1391522), _1391524)))], (50566 ^ _776541) ^ [_1798599, _1798601, _1798603, _1798605, _1798607, _1798609, _1798611] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1798599, tc_HOL_Obool)), _1798601), _1798603) = c_Orderings_Obot__class_Obot(tc_fun(_1798599, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1798605, tc_HOL_Obool)), _1798607), _1798609) = c_Orderings_Obot__class_Obot(tc_fun(_1798605, tc_HOL_Obool)), c_Fun_Obij__betw(_1798599, _1798605, _1798611, _1798601, _1798607), c_Fun_Obij__betw(_1798599, _1798605, _1798611, _1798603, _1798609), -(c_Fun_Obij__betw(_1798599, _1798605, _1798611, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798599, tc_HOL_Obool)), _1798601), _1798603), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798605, tc_HOL_Obool)), _1798607), _1798609)))], (13704 ^ _776541) ^ [_1020615, _1020617, _1020619, _1020621] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020615), _1020617), _1020619)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020615), _1020617), _1020621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020615), _1020619), _1020621)))], (35467 ^ _776541) ^ [_1438101, _1438103, _1438105, _1438107] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1438101, _1438101)), hAPP(hAPP(c_Product__Type_OPair(_1438101, _1438101), _1438103), _1438105)), hAPP(c_Wellfounded_Omeasure(_1438101), _1438107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1438107, _1438103)), hAPP(_1438107, _1438105))))], (39966 ^ _776541) ^ [_1554595, _1554597, _1554599, _1554601, _1554603, _1554605, _1554607, _1554609] : [class_Groups_Ocomm__monoid__mult(_1554595), c_Fun_Oinj__on(_1554597, _1554599, _1554601, _1554603), _1554605 = hAPP(c_Set_Oimage(_1554597, _1554599, _1554601), _1554603), _1554607 = hAPP(c_Fun_Ocomp(_1554599, _1554595, _1554597, _1554609), _1554601), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554599, _1554595), _1554609), _1554605) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554597, _1554595), _1554607), _1554603))], (2614 ^ _776541) ^ [_815101, _815103] : [_815103 = _815101, -(c_Nitpick_Ozero__frac(_815103) = c_Nitpick_Ozero__frac(_815101))], (25610 ^ _776541) ^ [_1239870, _1239872, _1239874] : [hBOOL(hAPP(_1239870, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239872, _1239874))), 25613 ^ _776541 : [(25638 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239874), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25641 ^ _776541 : [(25642 ^ _776541) ^ [_1240492, _1240494] : [-(hBOOL(hAPP(_1239870, _1240492))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239874), _1240492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1240492), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1239872 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239874), _1240494)), _1240492)]]], (25620 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239874)), 25623 ^ _776541 : [(25624 ^ _776541) ^ [_1240200, _1240202] : [-(hBOOL(hAPP(_1239870, _1240200))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240200), _1239874)), _1239872 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239874), _1240202)), _1240200)]]], (25614 ^ _776541) ^ [] : [_1239874 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1239870, _1239872)))]]], (15542 ^ _776541) ^ [_1058057, _1058059, _1058061, _1058063, _1058065] : [class_Groups_Ocomm__monoid__mult(_1058057), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058059), _1058061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1058059, tc_HOL_Obool)), _1058063), _1058061)), 15556 ^ _776541 : [(15559 ^ _776541) ^ [] : [hAPP(_1058065, 15555 ^ [_1058057, _1058059, _1058061, _1058063, _1058065]) = c_Groups_Oone__class_Oone(_1058057)], (15557 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1058059), 15555 ^ [_1058057, _1058059, _1058061, _1058063, _1058065]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058059, tc_HOL_Obool)), _1058061), _1058063))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058059, _1058057), _1058065), _1058061) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058059, _1058057), _1058065), _1058063))], (51273 ^ _776541) ^ [_1814655, _1814657, _1814659] : [class_Rings_Ocomm__semiring__1(_1814655), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814655), _1814657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814655), _1814659), _1814657))))], (22307 ^ _776541) ^ [_1180948, _1180950, _1180952] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180948), _1180950)), _1180952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180950), _1180952)))], (23077 ^ _776541) ^ [_1194653, _1194655] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1194653), _1194655)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194653)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194655))))], (36559 ^ _776541) ^ [_1468947, _1468949, _1468951, _1468953] : [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), _1468947), _1468949)), 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), _1468951), _1468953)), 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), _1468947), _1468953)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468951), _1468949))))], (45702 ^ _776541) ^ [_1693360, _1693362, _1693364] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693360))), c_Enum_On__lists(_1693360, _1693362, _1693364)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693360)), _1693364)), _1693362))], (39339 ^ _776541) ^ [_1538176, _1538178] : [-(hAPP(c_Fun_Oid(_1538176), _1538178) = _1538178)], (15156 ^ _776541) ^ [_1050096, _1050098] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050096), _1050098) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 15159 ^ _776541 : [(15162 ^ _776541) ^ [] : [-(_1050098 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15160 ^ _776541) ^ [] : [-(_1050096 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (27190 ^ _776541) ^ [_1265848, _1265850] : [c_Nat__Transfer_Onat__set(_1265848), c_Nat__Transfer_Onat__set(_1265850), 27197 ^ _776541 : [(27204 ^ _776541) ^ [] : [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), _1265848)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265850))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265848), _1265850)))], (27198 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265848), _1265850)), -(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), _1265848)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265850))))]]], (40837 ^ _776541) ^ [_1575982, _1575984] : [-(hAPP(c_Relation_ODomain(_1575982, _1575982), c_Transitive__Closure_Ortrancl(_1575982, _1575984)) = c_Orderings_Otop__class_Otop(tc_fun(_1575982, tc_HOL_Obool)))], (43944 ^ _776541) ^ [_1654727, _1654729, _1654731] : [hAPP(hAPP(c_List_Odrop(_1654727), _1654729), _1654731) = c_List_Olist_ONil(_1654727), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654727)), _1654731)), _1654729)))], (36118 ^ _776541) ^ [_1457237, _1457239, _1457241, _1457243, _1457245, _1457247, _1457249, _1457251] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1457237, _1457239), tc_prod(_1457237, _1457239))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1457237, _1457239), tc_prod(_1457237, _1457239)), hAPP(hAPP(c_Product__Type_OPair(_1457237, _1457239), _1457241), _1457243)), hAPP(hAPP(c_Product__Type_OPair(_1457237, _1457239), _1457245), _1457247))), c_Wellfounded_Olex__prod(_1457237, _1457239, _1457249, _1457251))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457237, _1457237)), hAPP(hAPP(c_Product__Type_OPair(_1457237, _1457237), _1457241), _1457245)), _1457249))), 36125 ^ _776541 : [(36128 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457239, _1457239)), hAPP(hAPP(c_Product__Type_OPair(_1457239, _1457239), _1457243), _1457247)), _1457251)))], (36126 ^ _776541) ^ [] : [-(_1457241 = _1457245)]]], (16488 ^ _776541) ^ [_1073461, _1073463] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1073461), _1073463)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1073461)), hAPP(c_Nat_OSuc, _1073463)))], (50224 ^ _776541) ^ [_1791910] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1791910), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1791910 = hAPP(c_Code__Numeral_Onat__of, 50227 ^ [_1791910]))], (40054 ^ _776541) ^ [_1556481, _1556483, _1556485, _1556487, _1556489, _1556491, _1556493, _1556495] : [c_Finite__Set_Ofolding__image(_1556481, _1556483, _1556485, _1556487, _1556489), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556483), _1556491)), c_Fun_Oinj__on(_1556483, _1556483, _1556493, _1556491), -(hAPP(hAPP(_1556489, _1556495), hAPP(c_Set_Oimage(_1556483, _1556483, _1556493), _1556491)) = hAPP(hAPP(_1556489, hAPP(c_Fun_Ocomp(_1556483, _1556481, _1556483, _1556495), _1556493)), _1556491))], (23717 ^ _776541) ^ [_1206108] : [-(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), _1206108))))], (44142 ^ _776541) ^ [_1659242, _1659244, _1659246] : [-(_1659242 = c_List_Olist_ONil(_1659244)), -(hAPP(c_List_Ohd(_1659244), hAPP(c_List_Orotate(_1659244, _1659246), _1659242)) = hAPP(hAPP(c_List_Onth(_1659244), _1659242), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1659246, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659244)), _1659242))))], (36440 ^ _776541) ^ [_1465338, _1465340] : [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)), _1465338), 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)), _1465340), 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)), _1465338), _1465340)), c_Int_Ointrel)))], (48207 ^ _776541) ^ [_1747668, _1747670, _1747672, _1747674] : [c_List_Olist__all(_1747668, _1747670, hAPP(hAPP(c_List_Oappend(_1747668), _1747672), _1747674)), 48210 ^ _776541 : [(48213 ^ _776541) ^ [] : [-(c_List_Olist__all(_1747668, _1747670, _1747674))], (48211 ^ _776541) ^ [] : [-(c_List_Olist__all(_1747668, _1747670, _1747672))]]], (46150 ^ _776541) ^ [_1703426, _1703428, _1703430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703428))), c_List_Otranspose(_1703428, _1703430)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1703428)), c_List_Otranspose(_1703428, _1703430)), _1703426) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1703428), _1703428), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703428), tc_Nat_Onat, _1703428), c_List_Onth(_1703428)), _1703426)), hAPP(c_List_Ofilter(tc_List_Olist(_1703428), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1703428)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703426)), c_Nat_Osize__class_Osize(tc_List_Olist(_1703428)))), _1703430)))], (48738 ^ _776541) ^ [_1758816, _1758818, _1758820] : [-(hAPP(hAPP(c_List_Oappend(_1758816), c_List_Oreplicate(_1758816, _1758818, _1758820)), hAPP(hAPP(c_List_Olist_OCons(_1758816), _1758820), c_List_Olist_ONil(_1758816))) = hAPP(hAPP(c_List_Olist_OCons(_1758816), _1758820), c_List_Oreplicate(_1758816, _1758818, _1758820)))], (13838 ^ _776541) ^ [_1023366, _1023368, _1023370, _1023372, _1023374] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1023366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023366), _1023368), _1023370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023366), _1023372), _1023374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023366), _1023368), _1023372)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023366), _1023370), _1023374))))], (37870 ^ _776541) ^ [_1498374, _1498376, _1498378, _1498380] : [c_Fun_Oinj__on(_1498374, _1498376, _1498378, _1498380), -(c_Fun_Oinj__on(_1498376, _1498374, c_Fun_Othe__inv__into(_1498374, _1498376, _1498380, _1498378), hAPP(c_Set_Oimage(_1498374, _1498376, _1498378), _1498380)))], (6844 ^ _776541) ^ [_887444, _887446, _887448] : [6846 ^ _776541 : [(6849 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_887444), 6845 ^ [_887444, _887446, _887448]), _887448))], (6847 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887444), 6845 ^ [_887444, _887446, _887448]), _887446)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887444, tc_HOL_Obool)), _887446), _887448)))], (50863 ^ _776541) ^ [_1806379, _1806381, _1806383, _1806385] : [50866 ^ _776541 : [(50869 ^ _776541) ^ [] : [hAPP(_1806383, 50864 ^ [_1806379, _1806381, _1806383, _1806385]) = hAPP(_1806383, 50865 ^ [_1806379, _1806381, _1806383, _1806385])], (50867 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1806379, _1806379)), hAPP(hAPP(c_Product__Type_OPair(_1806379, _1806379), 50864 ^ [_1806379, _1806381, _1806383, _1806385]), 50865 ^ [_1806379, _1806381, _1806383, _1806385])), _1806381)))]], -(c_Equiv__Relations_Ocongruent(_1806379, _1806385, _1806381, _1806383))], (48584 ^ _776541) ^ [_1756052, _1756054, _1756056, _1756058] : [-(hAPP(hAPP(c_List_Odrop(_1756052), _1756054), c_List_Oreplicate(_1756052, _1756056, _1756058)) = c_List_Oreplicate(_1756052, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1756056), _1756054), _1756058))], (41542 ^ _776541) ^ [_1593174, _1593176, _1593178, _1593180, _1593182] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593174, _1593174)), hAPP(hAPP(c_Product__Type_OPair(_1593174, _1593174), _1593176), _1593178)), c_Transitive__Closure_Ortrancl(_1593174, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593174, _1593174), tc_HOL_Obool)), _1593180), _1593182)))), 41548 ^ _776541 : [(41554 ^ _776541) ^ [] : [41547 ^ [_1593174, _1593176, _1593178, _1593180, _1593182] = 41550 ^ [_1593174, _1593176, _1593178, _1593180, _1593182]], (41552 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593174, _1593174)), hAPP(hAPP(c_Product__Type_OPair(_1593174, _1593174), 41547 ^ [_1593174, _1593176, _1593178, _1593180, _1593182]), 41550 ^ [_1593174, _1593176, _1593178, _1593180, _1593182])), _1593182)))], (41549 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593174, _1593174)), hAPP(hAPP(c_Product__Type_OPair(_1593174, _1593174), _1593176), 41547 ^ [_1593174, _1593176, _1593178, _1593180, _1593182])), c_Transitive__Closure_Ortrancl(_1593174, _1593180))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593174, _1593174)), hAPP(hAPP(c_Product__Type_OPair(_1593174, _1593174), _1593176), _1593178)), c_Transitive__Closure_Ortrancl(_1593174, _1593180))))], (7476 ^ _776541) ^ [_899639, _899641, _899643, _899645] : [hBOOL(hAPP(hAPP(c_member(_899639), _899641), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899639, tc_HOL_Obool)), _899643), _899645))), -(hBOOL(hAPP(hAPP(c_member(_899639), _899641), _899643))), -(hBOOL(hAPP(hAPP(c_member(_899639), _899641), _899645)))], (48868 ^ _776541) ^ [_1761669, _1761671, _1761673, _1761675, _1761677] : [48870 ^ _776541 : [(48873 ^ _776541) ^ [] : [c_Relation_Orefl__on(_1761673, hAPP(_1761675, 48869 ^ [_1761669, _1761671, _1761673, _1761675, _1761677]), hAPP(_1761677, 48869 ^ [_1761669, _1761671, _1761673, _1761675, _1761677]))], (48871 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761669), 48869 ^ [_1761669, _1761671, _1761673, _1761675, _1761677]), _1761671)))]], -(c_Relation_Orefl__on(_1761673, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1761669, tc_fun(_1761673, tc_HOL_Obool)), _1761671), _1761675), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1761669, tc_fun(tc_prod(_1761673, _1761673), tc_HOL_Obool)), _1761671), _1761677)))], (31072 ^ _776541) ^ [_1334209, _1334211, _1334213] : [class_Orderings_Olinorder(_1334209), hAPP(_1334211, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334209), 31077 ^ [_1334209, _1334211, _1334213]), 31078 ^ [_1334209, _1334211, _1334213])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334209), hAPP(_1334211, 31077 ^ [_1334209, _1334211, _1334213])), hAPP(_1334211, 31078 ^ [_1334209, _1334211, _1334213])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334209), _1334213)), -(_1334213 = c_Orderings_Obot__class_Obot(tc_fun(_1334209, tc_HOL_Obool))), -(hAPP(_1334211, c_Big__Operators_Olinorder__class_OMin(_1334209, _1334213)) = c_Big__Operators_Olinorder__class_OMin(_1334209, hAPP(c_Set_Oimage(_1334209, _1334209, _1334211), _1334213)))], (10098 ^ _776541) ^ [_949377, _949379, _949381, _949383] : [class_Orderings_Oorder(_949377), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949377, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_949377, _949379, _949381)), c_SetInterval_Oord__class_OatLeastAtMost(_949377, _949381, _949383)) = c_Orderings_Obot__class_Obot(tc_fun(_949377, tc_HOL_Obool)))], (2544 ^ _776541) ^ [_814026, _814028, _814030, _814032] : [-(c_FunDef_Orp__inv__image(_814032, _814028) = c_FunDef_Orp__inv__image(_814030, _814026)), _814032 = _814030, _814028 = _814026], (36092 ^ _776541) ^ [] : [-(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))], (17627 ^ _776541) ^ [_1093992] : [class_Rings_Olinordered__semidom(_1093992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093992), c_Groups_Oone__class_Oone(_1093992)), c_Groups_Ozero__class_Ozero(_1093992)))], (32830 ^ _776541) ^ [_1373383, _1373385, _1373387, _1373389, _1373391] : [32832 ^ _776541 : [(32835 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373383, tc_HOL_Obool)), _1373385), hAPP(_1373391, 32831 ^ [_1373383, _1373385, _1373387, _1373389, _1373391])))], (32833 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373387), 32831 ^ [_1373383, _1373385, _1373387, _1373389, _1373391]), _1373389)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373383, tc_HOL_Obool)), _1373385), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1373387, tc_fun(_1373383, tc_HOL_Obool)), _1373389), _1373391))))], (8315 ^ _776541) ^ [_918988, _918990, _918992] : [class_Lattices_Olattice(_918988), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918988), _918990), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918988), _918990), _918992)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918988), _918990), _918992))], (32986 ^ _776541) ^ [_1378584, _1378586, _1378588] : [-(hAPP(hAPP(c_Set_Oinsert(_1378584), _1378586), _1378588) = hAPP(c_Set_OCollect(_1378584), hAPP(hAPP(c_COMBS(_1378584, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378584), c_fdisj), hAPP(hAPP(c_COMBC(_1378584, _1378584, tc_HOL_Obool), c_fequal), _1378586))), hAPP(hAPP(c_COMBC(_1378584, tc_fun(_1378584, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378584)), _1378588))))], (13488 ^ _776541) ^ [_1016491, _1016493, _1016495, _1016497, _1016499, _1016501, _1016503, _1016505] : [c_Finite__Set_Ofolding__image__simple__idem(_1016491, _1016493, _1016495, _1016497, _1016499, _1016501), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016493), _1016503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016493, tc_HOL_Obool)), _1016505), _1016503)), -(hAPP(hAPP(_1016495, hAPP(_1016501, _1016505)), hAPP(_1016501, _1016503)) = hAPP(_1016501, _1016503))], (15075 ^ _776541) ^ [_1048767, _1048769] : [class_Rings_Ocomm__semiring__1(_1048767), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048767), _1048769), c_Groups_Oone__class_Oone(_1048767)) = _1048769)], (22329 ^ _776541) ^ [_1181259, _1181261, _1181263] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181259), _1181261)), _1181263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181259), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181261), _1181263)))], (3086 ^ _776541) ^ [_822441, _822443, _822445, _822447] : [-(c_Nitpick_Ocard_H(_822447, _822443) = c_Nitpick_Ocard_H(_822445, _822441)), _822447 = _822445, _822443 = _822441], (43034 ^ _776541) ^ [_1634210, _1634212, _1634214] : [c_List_Olist_ONil(_1634210) = hAPP(hAPP(c_List_Olist_OCons(_1634210), _1634212), _1634214)], (17497 ^ _776541) ^ [_1091671, _1091673, _1091675, _1091677] : [class_Rings_Olinordered__ring__strict(_1091671), 17500 ^ _776541 : [(17515 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091671), _1091673), _1091675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091671), _1091673), _1091677)))), 17516 ^ _776541 : [(17523 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), _1091673), c_Groups_Ozero__class_Ozero(_1091671))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), _1091677), _1091675))], (17517 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), c_Groups_Ozero__class_Ozero(_1091671)), _1091673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), _1091675), _1091677))]]], (17501 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091671), _1091673), _1091675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091671), _1091673), _1091677))), 17506 ^ _776541 : [(17509 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), _1091675), _1091677)))], (17507 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), c_Groups_Ozero__class_Ozero(_1091671)), _1091673)))]], 17510 ^ _776541 : [(17513 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), _1091677), _1091675)))], (17511 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091671), _1091673), c_Groups_Ozero__class_Ozero(_1091671))))]]]]], (16116 ^ _776541) ^ [_1067879, _1067881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067879), _1067881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067879)), hAPP(c_Nat_OSuc, _1067881))))], (48690 ^ _776541) ^ [_1757962, _1757964] : [-(c_List_Oconcat(_1757962, c_List_Oreplicate(tc_List_Olist(_1757962), _1757964, c_List_Olist_ONil(_1757962))) = c_List_Olist_ONil(_1757962))], (44960 ^ _776541) ^ [_1676827, _1676829, _1676831] : [c_Fun_Oinj__on(tc_List_Olist(_1676827), tc_List_Olist(_1676829), hAPP(c_List_Omap(_1676827, _1676829), _1676831), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676827), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1676827, _1676829, _1676831, c_Orderings_Otop__class_Otop(tc_fun(_1676827, tc_HOL_Obool))))], (50463 ^ _776541) ^ [_1796768, _1796770, _1796772, _1796774, _1796776, _1796778, _1796780] : [c_Fun_Obij__betw(_1796768, _1796770, _1796772, _1796774, _1796776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1796768, tc_HOL_Obool)), _1796778), _1796774)), hAPP(c_Set_Oimage(_1796768, _1796770, _1796772), _1796778) = _1796780, -(c_Fun_Obij__betw(_1796768, _1796770, _1796772, _1796778, _1796780))], (22175 ^ _776541) ^ [_1178707, _1178709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178707), _1178709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178707)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178709))))], (43938 ^ _776541) ^ [_1654546, _1654548, _1654550, _1654552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1654546), _1654548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654550, tc_HOL_Obool)), hAPP(c_List_Oset(_1654550), hAPP(hAPP(c_List_Odrop(_1654550), _1654548), _1654552))), hAPP(c_List_Oset(_1654550), hAPP(hAPP(c_List_Odrop(_1654550), _1654546), _1654552)))))], (43673 ^ _776541) ^ [_1647549, _1647551, _1647553, _1647555] : [-(hAPP(hAPP(c_List_Otake(_1647549), _1647551), hAPP(hAPP(c_List_Oappend(_1647549), _1647553), _1647555)) = hAPP(hAPP(c_List_Oappend(_1647549), hAPP(hAPP(c_List_Otake(_1647549), _1647551), _1647553)), hAPP(hAPP(c_List_Otake(_1647549), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1647551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647549)), _1647553))), _1647555)))], (24535 ^ _776541) ^ [_1220335, _1220337, _1220339] : [hBOOL(hAPP(_1220335, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1220337), _1220339)))), 24538 ^ _776541 : [(24545 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220337), _1220339)), -(hBOOL(hAPP(_1220335, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24539 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220339), _1220337)), -(hBOOL(hAPP(_1220335, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220337)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220339)))))]]], (34678 ^ _776541) ^ [_1422578, _1422580, _1422582, _1422584, _1422586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1422578, _1422580)), hAPP(hAPP(c_Product__Type_OPair(_1422578, _1422580), _1422584), _1422586)), _1422582)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1422578, _1422580, _1422582), _1422584), _1422586)))], (6484 ^ _776541) ^ [_881318, _881320] : [c_Orderings_Obot__class_Obot(tc_fun(_881318, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_881318), _881320), 6487 ^ _776541 : [(6488 ^ _776541) ^ [_881403] : [hBOOL(hAPP(_881320, _881403))]]], (48566 ^ _776541) ^ [_1755710, _1755712, _1755714] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755710)), c_List_Oreplicate(_1755710, _1755712, _1755714)) = _1755712)], (29795 ^ _776541) ^ [_1310759, _1310761, _1310763] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1310759, _1310761, _1310763, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1310761)], (47052 ^ _776541) ^ [_1722331, _1722333, _1722335, _1722337, _1722339] : [c_List_Olist__all2(_1722331, _1722333, _1722335, _1722337, _1722339), -(c_List_Olist__all2(_1722331, _1722333, _1722335, hAPP(c_List_Orev(_1722331), _1722337), hAPP(c_List_Orev(_1722333), _1722339)))], (43270 ^ _776541) ^ [_1638608, _1638610, _1638612] : [hBOOL(hAPP(hAPP(c_member(_1638608), _1638610), hAPP(c_List_Oset(_1638608), _1638612))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638608)), c_List_Oremove1(_1638608, _1638610, _1638612)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638608)), _1638612)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9796 ^ _776541) ^ [_944323, _944325, _944327] : [9797 ^ _776541 : [(9800 ^ _776541) ^ [] : [_944325 = _944327], (9798 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944323, tc_HOL_Obool)), _944325), _944327))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944323, tc_HOL_Obool)), _944325), _944327)))], (32964 ^ _776541) ^ [_1377745, _1377747, _1377749, _1377751, _1377753] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377745, tc_fun(_1377747, tc_HOL_Obool)), _1377749), hAPP(hAPP(c_COMBB(tc_fun(_1377747, tc_HOL_Obool), tc_fun(_1377747, tc_HOL_Obool), _1377745), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377747, tc_HOL_Obool)), _1377751)), _1377753)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377747, tc_HOL_Obool)), _1377751), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377745, tc_fun(_1377747, tc_HOL_Obool)), _1377749), _1377753)))], (41389 ^ _776541) ^ [_1589279, _1589281, _1589283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589279, _1589279)), _1589281), c_Transitive__Closure_Ortrancl(_1589279, _1589283))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589279, _1589279)), _1589281), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1589279, _1589279), 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(_1589279, _1589279), tc_HOL_Obool), tc_fun(tc_prod(_1589279, _1589279), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1589279, _1589279), tc_HOL_Obool)), _1589283)))))], (39794 ^ _776541) ^ [_1550286, _1550288] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1550286, tc_HOL_Obool), _1550288) = hAPP(c_Set_OCollect(_1550286), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1550286, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1550286), c_HOL_OAll(tc_fun(_1550286, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1550286, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1550286, tc_HOL_Obool), tc_HOL_Obool), _1550286), hAPP(c_COMBS(tc_fun(_1550286, 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(_1550286, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1550286, tc_HOL_Obool), tc_fun(tc_fun(_1550286, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1550286, tc_HOL_Obool))), _1550288)))), c_member(_1550286)))))], (23173 ^ _776541) ^ [_1196286] : [class_Power_Opower(_1196286), -(c_Power_Opower__class_Opower(_1196286) = c_Power_Opower_Opower(_1196286, c_Groups_Oone__class_Oone(_1196286), c_Groups_Otimes__class_Otimes(_1196286)))], (36812 ^ _776541) ^ [_1475045, _1475047, _1475049, _1475051, _1475053, _1475055, _1475057] : [c_Equiv__Relations_Oequiv(_1475045, _1475047, _1475049), hBOOL(hAPP(hAPP(c_member(tc_fun(_1475045, tc_HOL_Obool)), _1475051), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475045), _1475047), _1475049))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1475045, tc_HOL_Obool)), _1475053), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475045), _1475047), _1475049))), hBOOL(hAPP(hAPP(c_member(_1475045), _1475055), _1475051)), hBOOL(hAPP(hAPP(c_member(_1475045), _1475057), _1475053)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475045, _1475045)), hAPP(hAPP(c_Product__Type_OPair(_1475045, _1475045), _1475055), _1475057)), _1475049)), -(_1475051 = _1475053)], (46970 ^ _776541) ^ [_1720591, _1720593, _1720595] : [hAPP(c_List_Orev(_1720591), _1720593) = hAPP(hAPP(c_List_Olist_OCons(_1720591), _1720595), c_List_Olist_ONil(_1720591)), -(_1720593 = hAPP(hAPP(c_List_Olist_OCons(_1720591), _1720595), c_List_Olist_ONil(_1720591)))], (22231 ^ _776541) ^ [_1179698, _1179700] : [22232 ^ _776541 : [(22235 ^ _776541) ^ [] : [_1179698 = _1179700], (22233 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179698), _1179700))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179698), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179700), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (8441 ^ _776541) ^ [_921489, _921491, _921493, _921495] : [class_Lattices_Osemilattice__sup(_921489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921489), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921489), _921491), _921493)), _921495)), 8448 ^ _776541 : [(8451 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921489), _921493), _921495)))], (8449 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921489), _921491), _921495)))]]], (52453 ^ _776541) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (2678 ^ _776541) ^ [_816107, _816109, _816111, _816113] : [-(c_Divides_Odivmod__nat(_816113, _816109) = c_Divides_Odivmod__nat(_816111, _816107)), _816113 = _816111, _816109 = _816107], (26194 ^ _776541) ^ [_1249772] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249772))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1249772)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40841 ^ _776541) ^ [_1576055, _1576057] : [-(hAPP(c_Relation_OImage(_1576055, _1576055, c_Relation_OId(_1576055)), _1576057) = _1576057)], (4900 ^ _776541) ^ [_851218, _851220, _851222, _851224] : [-(c_Relation_OId__on(_851224, _851220) = c_Relation_OId__on(_851222, _851218)), _851224 = _851222, _851220 = _851218], (48866 ^ _776541) ^ [_1761620, _1761622, _1761624, _1761626, _1761628, _1761630] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1761620, _1761622, _1761624, _1761626, c_Lazy__Sequence_Olazy__sequence_OInsert(_1761622, _1761628, _1761630)) = hAPP(hAPP(_1761626, _1761628), _1761630))], (1164 ^ _776541) ^ [_793955, _793957] : [-(class_Groups_Oordered__ab__group__add(_793955)), _793957 = _793955, class_Groups_Oordered__ab__group__add(_793957)], (29075 ^ _776541) ^ [_1297729] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1297729))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1297729)))], (1554 ^ _776541) ^ [_798830, _798832] : [-(class_Groups_Oordered__comm__monoid__add(_798830)), _798832 = _798830, class_Groups_Oordered__comm__monoid__add(_798832)], (37937 ^ _776541) ^ [_1500706, _1500708, _1500710, _1500712, _1500714, _1500716, _1500718] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500706, _1500708, _1500710), _1500712), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500714, tc_fun(tc_prod(_1500708, _1500710), tc_HOL_Obool)), _1500716), _1500718)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500714, tc_fun(tc_prod(_1500706, _1500710), tc_HOL_Obool)), _1500716), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1500708, _1500710), tc_HOL_Obool), tc_fun(tc_prod(_1500706, _1500710), tc_HOL_Obool), _1500714), hAPP(c_Relation_Orel__comp(_1500706, _1500708, _1500710), _1500712)), _1500718)))], (52219 ^ _776541) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (13204 ^ _776541) ^ [_1010275] : [class_Lattices_Oab__semigroup__idem__mult(_1010275), -(c_Finite__Set_Ofun__left__comm__idem(_1010275, _1010275, c_Groups_Otimes__class_Otimes(_1010275)))], (36434 ^ _776541) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (52255 ^ _776541) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52423 ^ _776541) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (42473 ^ _776541) ^ [_1620171, _1620173, _1620175] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1620171), _1620173)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1620171)), hAPP(c_Set_OCollect(tc_List_Olist(_1620171)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1620171), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1620171)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1620171), tc_fun(_1620171, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1620171, tc_HOL_Obool), tc_fun(tc_fun(_1620171, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1620171)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1620171, tc_HOL_Obool))), c_List_Oset(_1620171))), _1620173))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1620171), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1620171)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1620171)))), _1620175))))))], (26340 ^ _776541) ^ [_1252054, _1252056] : [-(hAPP(c_Int_Onat, _1252054) = _1252056), 26343 ^ _776541 : [(26346 ^ _776541) ^ [] : [_1252054 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252056)], (26344 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252054)))]], 26347 ^ _776541 : [(26350 ^ _776541) ^ [] : [_1252056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26348 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252054))]]], (32566 ^ _776541) ^ [_1365569, _1365571, _1365573, _1365575] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365569, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1365569, tc_fun(_1365569, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365569)), _1365571)), hAPP(hAPP(c_COMBC(_1365569, tc_fun(_1365569, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365569)), _1365573)), _1365575)), -(hBOOL(hAPP(hAPP(c_member(_1365569), _1365575), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365569, tc_HOL_Obool)), _1365571), _1365573))))], (39026 ^ _776541) ^ [_1528086, _1528088] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1528086), c_Int_OInteg)), hBOOL(hAPP(_1528088, hAPP(c_Int_ORep__Integ, 39031 ^ [_1528086, _1528088]))), -(hBOOL(hAPP(_1528088, _1528086)))], (29677 ^ _776541) ^ [_1308589, _1308591] : [class_Int_Onumber__ring(_1308589), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1308589), hAPP(c_Int_Onumber__class_Onumber__of(_1308589), 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)))), _1308591))) = hAPP(c_Int_Onumber__class_Onumber__of(_1308589), c_Int_OMin))], (48061 ^ _776541) ^ [_1744575, _1744577, _1744579] : [hBOOL(hAPP(hAPP(c_member(_1744575), _1744577), hAPP(c_List_Oset(_1744575), _1744579))), -(_1744579 = hAPP(hAPP(c_List_Oappend(_1744575), 48064 ^ [_1744575, _1744577, _1744579]), hAPP(hAPP(c_List_Olist_OCons(_1744575), _1744577), 48065 ^ [_1744575, _1744577, _1744579])))], (22309 ^ _776541) ^ [_1180995, _1180997] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180995), _1180997))), -(_1180995 = _1180997), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180997), _1180995)))], (43549 ^ _776541) ^ [_1645165, _1645167, _1645169] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645165)), hAPP(hAPP(c_List_Oappend(_1645165), _1645167), _1645169)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645165)), _1645167)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645165)), _1645169)))], (29503 ^ _776541) ^ [_1305003, _1305005, _1305007] : [class_Rings_Oring__1(_1305003), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1305003), hAPP(c_Groups_Ouminus__class_Ouminus(_1305003), _1305005)), 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)))), _1305007)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1305003), _1305005), 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)))), _1305007)))], (6644 ^ _776541) ^ [_884090, _884092, _884094, _884096] : [class_Orderings_Opreorder(_884090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884090), _884092), _884094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884090), _884094), _884096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884090), _884092), _884096)))], (47613 ^ _776541) ^ [_1734042, _1734044, _1734046] : [-(c_List_Omaps(_1734042, _1734044, _1734046, c_List_Olist_ONil(_1734042)) = c_List_Olist_ONil(_1734044))], (36496 ^ _776541) ^ [_1467169, _1467171, _1467173, _1467175, _1467177, _1467179] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1467175, _1467175)), hAPP(hAPP(c_Product__Type_OPair(_1467175, _1467175), hAPP(_1467179, _1467171)), hAPP(_1467179, _1467173))), _1467177)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1467169, _1467169)), hAPP(hAPP(c_Product__Type_OPair(_1467169, _1467169), _1467171), _1467173)), hAPP(hAPP(c_Relation_Oinv__image(_1467175, _1467169), _1467177), _1467179))))], (22183 ^ _776541) ^ [_1178859, _1178861] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178859), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1178861) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1178859, _1178861))], (34047 ^ _776541) ^ [_1408591] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1408591) = 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), _1408591), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (48456 ^ _776541) ^ [_1752763, _1752765, _1752767] : [-(hAPP(c_New__DSequence_Oneg__single(_1752763, _1752765), _1752767) = c_Lazy__Sequence_Ohb__single(_1752763, _1752765))], (47593 ^ _776541) ^ [_1733642, _1733644, _1733646] : [hBOOL(hAPP(c_List_Odistinct(_1733642), _1733644)), -(hBOOL(hAPP(c_List_Odistinct(_1733642), c_List_Oinsert(_1733642, _1733646, _1733644))))], (8044 ^ _776541) ^ [_913172, _913174, _913176, _913178] : [-(hBOOL(hAPP(hAPP(c_member(_913172), _913174), _913176))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913172, tc_HOL_Obool)), _913176), hAPP(hAPP(c_Set_Oinsert(_913172), _913174), _913178)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913172, tc_HOL_Obool)), _913176), _913178))], (51199 ^ _776541) ^ [_1813326, _1813328, _1813330] : [class_Divides_Osemiring__div(_1813326), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813326), _1813328), _1813330)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813326), _1813328), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813326), _1813330), _1813328)) = _1813330)], (1040 ^ _776541) ^ [_792241, _792243, _792245, _792247, _792249, _792251] : [-(c_List_Oall__interval__nat(_792249, _792245, _792241)), c_List_Oall__interval__nat(_792251, _792247, _792243), _792251 = _792249, _792247 = _792245, _792243 = _792241], (30720 ^ _776541) ^ [_1327624, _1327626, _1327628] : [class_Orderings_Olinorder(_1327624), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327624), _1327626)), -(_1327626 = c_Orderings_Obot__class_Obot(tc_fun(_1327624, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327624), _1327628)), -(_1327628 = c_Orderings_Obot__class_Obot(tc_fun(_1327624, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1327624, c_Orderings_Oord__class_Omin(_1327624), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327624, tc_HOL_Obool)), _1327626), _1327628)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1327624), c_Big__Operators_Olattice_OInf__fin(_1327624, c_Orderings_Oord__class_Omin(_1327624), _1327626)), c_Big__Operators_Olattice_OInf__fin(_1327624, c_Orderings_Oord__class_Omin(_1327624), _1327628)))], (25307 ^ _776541) ^ [_1234554, _1234556, _1234558] : [-(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), _1234554), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234556), _1234554))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234556, _1234554))), _1234558) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1234556), _1234558))], (8879 ^ _776541) ^ [_929410, _929412, _929414, _929416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929410, tc_HOL_Obool)), _929412), hAPP(hAPP(c_Set_Oinsert(_929410), _929414), _929416))), 8882 ^ _776541 : [(8889 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929410), _929414), _929416))), 8892 ^ _776541 : [(8899 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929410), _929414), _929412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929410, tc_HOL_Obool)), _929412), _929416)))], (8893 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929410), _929414), _929412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929410, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929410, tc_HOL_Obool)), _929412), hAPP(hAPP(c_Set_Oinsert(_929410), _929414), c_Orderings_Obot__class_Obot(tc_fun(_929410, tc_HOL_Obool))))), _929416)))]]], (8883 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929410), _929414), _929416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929410, tc_HOL_Obool)), _929412), _929416)))]]], (20955 ^ _776541) ^ [_1154948, _1154950, _1154952, _1154954] : [class_Fields_Olinordered__field(_1154948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154948), c_Groups_Ozero__class_Ozero(_1154948)), _1154950)), 20962 ^ _776541 : [(20969 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154948), _1154952), _1154950)), _1154954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154948), _1154952), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154948), _1154954), _1154950))))], (20963 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154948), _1154952), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154948), _1154954), _1154950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154948), _1154952), _1154950)), _1154954)))]]], (5434 ^ _776541) ^ [_859551, _859553, _859555, _859557, _859559, _859561] : [-(c_SetInterval_Oord_OlessThan(_859561, _859557, _859553) = c_SetInterval_Oord_OlessThan(_859559, _859555, _859551)), _859561 = _859559, _859557 = _859555, _859553 = _859551], (36033 ^ _776541) ^ [_1454008, _1454010, _1454012] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1454008, tc_HOL_Obool), tc_fun(_1454008, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1454008, tc_HOL_Obool), tc_fun(_1454008, tc_HOL_Obool)), _1454010), _1454012)), c_Wellfounded_Ofinite__psubset(_1454008)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1454008, tc_HOL_Obool)), _1454010), _1454012)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454008), _1454012))], (23003 ^ _776541) ^ [_1193294, _1193296, _1193298] : [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), _1193294), _1193296)), _1193298)), 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)), _1193298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193296), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23083 ^ _776541) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (1384 ^ _776541) ^ [_796705, _796707] : [-(class_Lattices_Osemilattice__sup(_796705)), _796707 = _796705, class_Lattices_Osemilattice__sup(_796707)], (41102 ^ _776541) ^ [_1582504, _1582506, _1582508, _1582510] : [-(hAPP(c_Relation_Oconverse(_1582504, _1582506), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1582504, _1582506), tc_HOL_Obool)), _1582508), _1582510)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1582506, _1582504), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1582504, _1582506), _1582508)), hAPP(c_Relation_Oconverse(_1582504, _1582506), _1582510)))], (38810 ^ _776541) ^ [_1522746, _1522748, _1522750, _1522752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522746), hAPP(c_Set_Ovimage(_1522746, _1522748, _1522750), _1522752))), hAPP(c_Set_Oimage(_1522746, _1522748, _1522750), c_Orderings_Otop__class_Otop(tc_fun(_1522746, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522748, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522748), _1522752)))], (43140 ^ _776541) ^ [_1635998, _1636000, _1636002] : [-(hAPP(hAPP(c_List_Olist__update(_1635998, c_List_Olist_ONil(_1635998)), _1636000), _1636002) = c_List_Olist_ONil(_1635998))], (38917 ^ _776541) ^ [_1525018, _1525020] : [-(hAPP(c_Relation_OField(_1525018), _1525020) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525018, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525018, _1525018), _1525020)), hAPP(c_Relation_ORange(_1525018, _1525018), _1525020)))], (33903 ^ _776541) ^ [_1404893, _1404895, _1404897] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404893), _1404895), _1404897) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1404893), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1404893, tc_Int_Oint), _1404895), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1404897))), class_Groups_Ocomm__monoid__add(_1404893), class_Groups_Ocomm__monoid__mult(_1404893)], (3648 ^ _776541) ^ [_831198, _831200, _831202, _831204] : [-(c_List_Olist__update(_831204, _831200) = c_List_Olist__update(_831202, _831198)), _831204 = _831202, _831200 = _831198], (39469 ^ _776541) ^ [_1541438, _1541440] : [-(c_Product__Type_Omap__pair(_1541438, _1541438, _1541440, _1541440, c_Fun_Oid(_1541438), c_Fun_Oid(_1541440)) = c_Fun_Oid(tc_prod(_1541438, _1541440)))], (26821 ^ _776541) ^ [_1260041, _1260043] : [c_Nat__Transfer_Ois__nat(_1260041), c_Nat__Transfer_Ois__nat(_1260043), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1260041, _1260043)))], (10719 ^ _776541) ^ [_961259, _961261, _961263] : [class_Orderings_Oorder(_961259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961259), _961261), _961263)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961259, _961263), _961261) = c_Orderings_Obot__class_Obot(tc_fun(_961259, tc_HOL_Obool)))], (1084 ^ _776541) ^ [_792955, _792957] : [-(class_Lattices_Obounded__lattice(_792955)), _792957 = _792955, class_Lattices_Obounded__lattice(_792957)], (45900 ^ _776541) ^ [_1697315, _1697317, _1697319, _1697321] : [class_Orderings_Olinorder(_1697315), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697317)), c_List_Olinorder__class_Osort__key(_1697317, _1697315, _1697319, _1697321)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697317)), _1697321))], (13124 ^ _776541) ^ [_1008459, _1008461, _1008463, _1008465, _1008467, _1008469] : [c_Finite__Set_Ofun__left__comm__idem(_1008459, _1008461, _1008463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008459), _1008465)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1008459, _1008461, _1008463), _1008467), hAPP(hAPP(c_Set_Oinsert(_1008459), _1008469), _1008465)) = hAPP(hAPP(c_Finite__Set_Ofold(_1008459, _1008461, _1008463), hAPP(hAPP(_1008463, _1008469), _1008467)), _1008465))], (40360 ^ _776541) ^ [_1563499, _1563501, _1563503] : [hBOOL(hAPP(_1563499, _1563501)), -(hBOOL(hAPP(_1563499, c_Hilbert__Choice_OEps(_1563503, _1563499))))], (23797 ^ _776541) ^ [_1207575, _1207577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207575)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207577))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207575), _1207577)))], (17387 ^ _776541) ^ [_1089634, _1089636, _1089638, _1089640] : [class_Rings_Olinordered__ring__strict(_1089634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089634), _1089636), c_Groups_Ozero__class_Ozero(_1089634))), 17394 ^ _776541 : [(17401 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089634), _1089640), _1089638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089634), _1089636), _1089638)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089634), _1089636), _1089640))))], (17395 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089634), _1089636), _1089638)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089634), _1089636), _1089640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089634), _1089640), _1089638)))]]], (44136 ^ _776541) ^ [_1659175, _1659177] : [-(_1659175 = c_List_Olist_ONil(_1659177)), -(hAPP(c_List_Orotate1(_1659177), _1659175) = hAPP(hAPP(c_List_Oappend(_1659177), hAPP(c_List_Otl(_1659177), _1659175)), hAPP(hAPP(c_List_Olist_OCons(_1659177), hAPP(c_List_Ohd(_1659177), _1659175)), c_List_Olist_ONil(_1659177))))], (16428 ^ _776541) ^ [_1072647, _1072649, _1072651, _1072653, _1072655] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1072647, _1072649, _1072651), _1072653), _1072655), c_Orderings_Obot__class_Obot(tc_fun(_1072649, tc_HOL_Obool))) = _1072655)], (48454 ^ _776541) ^ [_1752646, _1752648, _1752650, _1752652, _1752654, _1752656, _1752658] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1752646, _1752648, _1752650, _1752652), _1752654), _1752656), _1752658) = c_New__DSequence_Opos__bind(_1752646, _1752648, hAPP(hAPP(hAPP(_1752650, _1752654), _1752656), _1752658), hAPP(hAPP(c_COMBC(_1752646, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1752648))), hAPP(hAPP(c_COMBC(_1752646, 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(_1752648)))), hAPP(hAPP(c_COMBC(_1752646, 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(_1752648))))), _1752652), _1752654)), _1752656)), _1752658)))], (1254 ^ _776541) ^ [_795080, _795082] : [-(class_Rings_Ocomm__ring(_795080)), _795082 = _795080, class_Rings_Ocomm__ring(_795082)], (36221 ^ _776541) ^ [_1459879, _1459881, _1459883, _1459885, _1459887, _1459889] : [hAPP(_1459885, hAPP(c_Product__Type_Ofst(_1459879, _1459883), _1459887)) = hAPP(_1459889, hAPP(c_Product__Type_Ofst(_1459879, _1459883), _1459887)), -(hAPP(c_Product__Type_Oapfst(_1459879, _1459881, _1459883, _1459885), _1459887) = hAPP(c_Product__Type_Oapfst(_1459879, _1459881, _1459883, _1459889), _1459887))], (41686 ^ _776541) ^ [_1597372, _1597374] : [-(c_Nitpick_Ouminus__frac(_1597372, _1597374) = c_Nitpick_OAbs__Frac(_1597372, 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(_1597372), _1597374))), hAPP(c_Nitpick_Odenom(_1597372), _1597374))))], (48372 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50779 ^ _776541) ^ [_1802950, _1802952, _1802954, _1802956, _1802958, _1802960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802950, tc_HOL_Obool)), _1802952), _1802954)), 50785 ^ _776541 : [(50788 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802956, tc_HOL_Obool)), hAPP(_1802958, 50784 ^ [_1802950, _1802952, _1802954, _1802956, _1802958, _1802960])), hAPP(_1802960, 50784 ^ [_1802950, _1802952, _1802954, _1802956, _1802958, _1802960])))], (50786 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802950), 50784 ^ [_1802950, _1802952, _1802954, _1802956, _1802958, _1802960]), _1802954)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802956, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1802950, tc_fun(_1802956, tc_HOL_Obool)), _1802954), _1802958)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1802950, tc_fun(_1802956, tc_HOL_Obool)), _1802954), _1802960))))], (45955 ^ _776541) ^ [_1698404, _1698406] : [45957 ^ _776541 : [(45960 ^ _776541) ^ [] : [45956 ^ [_1698404, _1698406] = c_List_Olist_ONil(_1698404)], (45958 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698404)), 45956 ^ [_1698404, _1698406]), hAPP(c_List_Oset(tc_List_Olist(_1698404)), _1698406))))]], -(c_List_Oconcat(_1698404, _1698406) = c_List_Olist_ONil(_1698404))], (33885 ^ _776541) ^ [_1404448] : [-(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)))), _1404448)) = 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), _1404448), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (25355 ^ _776541) ^ [_1235297] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235297), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1235297))], (46590 ^ _776541) ^ [_1713195] : [class_Orderings_Olinorder(_1713195), -(c_List_Olinorder__class_Osorted(_1713195, c_List_Olist_ONil(_1713195)))], (38734 ^ _776541) ^ [_1521013, _1521015, _1521017] : [c_Wellfounded_Oacyclic(_1521013, _1521015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521013, _1521013), tc_HOL_Obool)), _1521017), _1521015)), -(c_Wellfounded_Oacyclic(_1521013, _1521017))], (44801 ^ _776541) ^ [_1672621, _1672623, _1672625] : [class_Groups_Omonoid__add(_1672621), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672621), hAPP(hAPP(c_List_Omap(_1672623, _1672621), hAPP(c_COMBK(_1672621, _1672623), c_Groups_Ozero__class_Ozero(_1672621))), _1672625)) = c_Groups_Ozero__class_Ozero(_1672621))], (5933 ^ _776541) ^ [_870921, _870923, _870925] : [hBOOL(hAPP(hAPP(c_member(_870921), _870923), hAPP(c_fequal, _870925))), -(_870923 = _870925)], (45383 ^ _776541) ^ [_1686054, _1686056, _1686058] : [hBOOL(hAPP(c_List_Olistsp(_1686054, _1686056), _1686058)), 45386 ^ _776541 : [(45387 ^ _776541) ^ [_1686143] : [hBOOL(hAPP(hAPP(c_member(_1686054), _1686143), hAPP(c_List_Oset(_1686054), _1686058))), -(hBOOL(hAPP(_1686056, _1686143)))]]], (38606 ^ _776541) ^ [_1518036, _1518038, _1518040, _1518042] : [hBOOL(hAPP(hAPP(c_member(_1518036), _1518038), hAPP(c_Relation_ORange(_1518040, _1518036), _1518042))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1518040, _1518036)), hAPP(hAPP(c_Product__Type_OPair(_1518040, _1518036), 38609 ^ [_1518036, _1518038, _1518040, _1518042]), _1518038)), _1518042)))], (15698 ^ _776541) ^ [_1061229] : [hAPP(c_Nat_OSuc, _1061229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45363 ^ _776541) ^ [_1685573, _1685575, _1685577] : [-(c_List_Olistsp(_1685573, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1685573, tc_HOL_Obool)), _1685575), _1685577)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1685573), tc_HOL_Obool)), c_List_Olistsp(_1685573, _1685575)), c_List_Olistsp(_1685573, _1685577)))], (6420 ^ _776541) ^ [_880238, _880240, _880242, _880244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880238, tc_HOL_Obool)), _880240), _880242)), hBOOL(hAPP(hAPP(c_member(_880238), _880244), _880240)), -(hBOOL(hAPP(hAPP(c_member(_880238), _880244), _880242)))], (48768 ^ _776541) ^ [_1759570, _1759572] : [-(c_Predicate_Opred__comp(_1759570, _1759570, _1759570, c_fequal, c_Predicate_Opred__comp(_1759570, _1759570, _1759570, _1759572, c_fequal)) = _1759572)], (18404 ^ _776541) ^ [_1107642, _1107644, _1107646, _1107648, _1107650] : [class_Rings_Olinordered__semiring__strict(_1107642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107642), _1107644), _1107646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107642), _1107648), _1107650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107642), c_Groups_Ozero__class_Ozero(_1107642)), _1107644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107642), c_Groups_Ozero__class_Ozero(_1107642)), _1107648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107642), _1107644), _1107648)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107642), _1107646), _1107650))))], (42491 ^ _776541) ^ [_1621224, _1621226, _1621228, _1621230] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621224), tc_List_Olist(_1621224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621224), tc_List_Olist(_1621224)), _1621226), _1621228)), c_List_Olistrel(_1621224, _1621230)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621224)), _1621226) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621224)), _1621228), 42497 ^ _776541 : [(42500 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1621224, _1621224, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1621224, tc_fun(tc_prod(_1621224, _1621224), tc_HOL_Obool), tc_fun(_1621224, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1621224, tc_fun(tc_fun(tc_prod(_1621224, _1621224), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1621224, _1621224), tc_HOL_Obool), tc_fun(_1621224, tc_HOL_Obool)), _1621224), c_COMBC(_1621224, tc_fun(tc_prod(_1621224, _1621224), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1621224, tc_prod(_1621224, _1621224)), tc_fun(_1621224, tc_fun(tc_fun(tc_prod(_1621224, _1621224), tc_HOL_Obool), tc_HOL_Obool)), _1621224), hAPP(c_COMBB(tc_prod(_1621224, _1621224), tc_fun(tc_fun(tc_prod(_1621224, _1621224), tc_HOL_Obool), tc_HOL_Obool), _1621224), c_member(tc_prod(_1621224, _1621224)))), c_Product__Type_OPair(_1621224, _1621224)))), _1621230)), 42496 ^ [_1621224, _1621226, _1621228, _1621230]))], (42498 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621224, _1621224)), 42496 ^ [_1621224, _1621226, _1621228, _1621230]), hAPP(c_List_Oset(tc_prod(_1621224, _1621224)), hAPP(hAPP(c_List_Ozip(_1621224, _1621224), _1621226), _1621228)))))]]], (34816 ^ _776541) ^ [_1426175, _1426177, _1426179] : [hBOOL(hAPP(_1426175, hAPP(hAPP(c_Product__Type_OPair(_1426177, _1426179), 34817 ^ [_1426175, _1426177, _1426179]), 34818 ^ [_1426175, _1426177, _1426179]))), 34821 ^ _776541 : [(34822 ^ _776541) ^ [_1426322] : [-(hBOOL(hAPP(_1426175, _1426322)))]]], (620 ^ _776541) ^ [_785909, _785911, _785913, _785915] : [-(c_List_Olinorder__class_Osorted(_785913, _785909)), c_List_Olinorder__class_Osorted(_785915, _785911), _785915 = _785913, _785911 = _785909], (12407 ^ _776541) ^ [_994507, _994509, _994511] : [class_Lattices_Olattice(_994507), hBOOL(hAPP(c_Finite__Set_Ofinite(_994507), _994509)), -(_994509 = c_Orderings_Obot__class_Obot(tc_fun(_994507, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_994507), _994511)), -(_994511 = c_Orderings_Obot__class_Obot(tc_fun(_994507, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994507, tc_HOL_Obool)), _994509), _994511) = c_Orderings_Obot__class_Obot(tc_fun(_994507, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_994507, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_994507, tc_HOL_Obool)), _994509), _994511)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994507), c_Big__Operators_Olattice__class_OInf__fin(_994507, _994509)), c_Big__Operators_Olattice__class_OInf__fin(_994507, _994511)))], (47860 ^ _776541) ^ [_1740100, _1740102, _1740104, _1740106, _1740108] : [hAPP(c_List_Ofilter(_1740100, _1740102), _1740104) = hAPP(hAPP(c_List_Olist_OCons(_1740100), _1740106), _1740108), 47865 ^ _776541 : [(47874 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1740102, _1740106)))], (47876 ^ _776541) ^ [] : [-(_1740108 = hAPP(c_List_Ofilter(_1740100, _1740102), 47864 ^ [_1740100, _1740102, _1740104, _1740106, _1740108]))], (47868 ^ _776541) ^ [_1740414] : [hBOOL(hAPP(hAPP(c_member(_1740100), _1740414), hAPP(c_List_Oset(_1740100), 47863 ^ [_1740100, _1740102, _1740104, _1740106, _1740108]))), hBOOL(hAPP(_1740102, _1740414))], (47866 ^ _776541) ^ [] : [-(_1740104 = hAPP(hAPP(c_List_Oappend(_1740100), 47863 ^ [_1740100, _1740102, _1740104, _1740106, _1740108]), hAPP(hAPP(c_List_Olist_OCons(_1740100), _1740106), 47864 ^ [_1740100, _1740102, _1740104, _1740106, _1740108])))]]], (38040 ^ _776541) ^ [_1505033, _1505035, _1505037] : [c_Wellfounded_Owf(_1505033, _1505035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1505033, _1505033), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1505033, _1505033, _1505033), _1505035), _1505037)), _1505035)), -(c_FunDef_Oreduction__pair(_1505033, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1505033, _1505033), tc_HOL_Obool), tc_fun(tc_prod(_1505033, _1505033), tc_HOL_Obool)), _1505035), _1505037)))], (25197 ^ _776541) ^ [_1232743, _1232745] : [class_Int_Onumber__ring(_1232743), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232743), _1232745), hAPP(c_Int_Onumber__class_Onumber__of(_1232743), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1232743), _1232745))], (33651 ^ _776541) ^ [_1398093, _1398095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398093), hAPP(c_Set_OCollect(_1398093), _1398095))), 33654 ^ _776541 : [(33661 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398093), c_Orderings_Otop__class_Otop(tc_fun(_1398093, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1398093), hAPP(c_Set_OCollect(_1398093), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1398093), c_fNot), _1398095)))))], (33655 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398093), hAPP(c_Set_OCollect(_1398093), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1398093), c_fNot), _1398095)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1398093), c_Orderings_Otop__class_Otop(tc_fun(_1398093, tc_HOL_Obool)))))]]], (29091 ^ _776541) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (39367 ^ _776541) ^ [_1538695, _1538697, _1538699, _1538701, _1538703, _1538705] : [class_Groups_Ocomm__monoid__mult(_1538695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538697), _1538699)), 39377 ^ _776541 : [(39380 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538701), hAPP(_1538703, 39376 ^ [_1538695, _1538697, _1538699, _1538701, _1538703, _1538705])))], (39378 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538697), 39376 ^ [_1538695, _1538697, _1538699, _1538701, _1538703, _1538705]), _1538699)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538697, _1538695), hAPP(hAPP(c_COMBS(_1538697, tc_fun(_1538701, tc_HOL_Obool), _1538695), hAPP(hAPP(c_COMBB(tc_fun(_1538701, _1538695), tc_fun(tc_fun(_1538701, tc_HOL_Obool), _1538695), _1538697), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538701, _1538695)), _1538705)), _1538703)), _1538699) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1538697, _1538701), _1538695), hAPP(c_Product__Type_Oprod_Oprod__case(_1538697, _1538701, _1538695), _1538705)), hAPP(hAPP(c_Product__Type_OSigma(_1538697, _1538701), _1538699), _1538703)))], (51285 ^ _776541) ^ [_1814869, _1814871, _1814873, _1814875] : [class_Rings_Oidom(_1814869), 51288 ^ _776541 : [(51289 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814869), _1814871), _1814873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814869), _1814871), _1814875))), -(_1814871 = c_Groups_Ozero__class_Ozero(_1814869)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814869), _1814873), _1814875)))], (51299 ^ _776541) ^ [] : [51300 ^ _776541 : [(51303 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814869), _1814873), _1814875))], (51301 ^ _776541) ^ [] : [_1814871 = c_Groups_Ozero__class_Ozero(_1814869)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814869), _1814871), _1814873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814869), _1814871), _1814875))))]]], (40584 ^ _776541) ^ [_1569018, _1569020] : [c_Wellfounded_Oacyclic(_1569018, _1569020), 40587 ^ _776541 : [(40588 ^ _776541) ^ [_1569103] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569018, _1569018)), hAPP(hAPP(c_Product__Type_OPair(_1569018, _1569018), _1569103), _1569103)), c_Transitive__Closure_Otrancl(_1569018, _1569020)))]]], (47363 ^ _776541) ^ [_1728930, _1728932, _1728934] : [-(hAPP(hAPP(c_List_Oappend(_1728930), c_List_OtakeWhile(_1728930, _1728932, _1728934)), c_List_OdropWhile(_1728930, _1728932, _1728934)) = _1728934)], (46199 ^ _776541) ^ [_1704741, _1704743] : [-(c_List_Oconcat(tc_List_Olist(_1704741), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704741), tc_List_Olist(tc_List_Olist(_1704741))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1704741)), _1704741, c_List_Olist_ONil(tc_List_Olist(_1704741)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1704741), tc_List_Olist(tc_List_Olist(_1704741))), _1704741), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704741), tc_List_Olist(tc_List_Olist(_1704741)), tc_List_Olist(tc_List_Olist(_1704741))), c_List_Olist_OCons(tc_List_Olist(_1704741))), c_List_Olist_ONil(tc_List_Olist(_1704741)))))), _1704743)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704741), tc_List_Olist(_1704741)), c_List_Otl(_1704741)), hAPP(c_List_Ofilter(tc_List_Olist(_1704741), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1704741)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704741), tc_List_Olist(_1704741), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1704741)))), _1704743)))], (30006 ^ _776541) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (6404 ^ _776541) ^ [_879942, _879944, _879946] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_879942, tc_HOL_Obool)), _879944), _879946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879942, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_879942, tc_HOL_Obool), _879946)), _879944)))], (688 ^ _776541) ^ [_786917, _786919, _786921, _786923, _786925, _786927] : [-(c_List_Oall__interval__int(_786925, _786921, _786917)), c_List_Oall__interval__int(_786927, _786923, _786919), _786927 = _786925, _786923 = _786921, _786919 = _786917], (12746 ^ _776541) ^ [_1001384, _1001386, _1001388] : [class_Complete__Lattice_Ocomplete__lattice(_1001384), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001384), _1001386)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1001384), _1001388), c_Complete__Lattice_OInf__class_OInf(_1001384, _1001386)) = hAPP(hAPP(c_Finite__Set_Ofold(_1001384, _1001384, c_Lattices_Osemilattice__inf__class_Oinf(_1001384)), _1001388), _1001386))], (8082 ^ _776541) ^ [_913934, _913936, _913938] : [-(hAPP(hAPP(c_Set_Oinsert(_913934), _913936), _913938) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913934, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913934), _913936), c_Orderings_Obot__class_Obot(tc_fun(_913934, tc_HOL_Obool)))), _913938))], (37775 ^ _776541) ^ [_1496428, _1496430, _1496432, _1496434, _1496436, _1496438, _1496440, _1496442] : [c_Fun_Oinj__on(_1496428, _1496430, _1496432, _1496434), 37781 ^ _776541 : [(37784 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496428, tc_HOL_Obool)), hAPP(_1496440, 37780 ^ [_1496428, _1496430, _1496432, _1496434, _1496436, _1496438, _1496440, _1496442])), _1496434))], (37782 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1496436), 37780 ^ [_1496428, _1496430, _1496432, _1496434, _1496436, _1496438, _1496440, _1496442]), _1496438)))]], hBOOL(hAPP(hAPP(c_member(_1496436), _1496442), _1496438)), -(hAPP(c_Set_Oimage(_1496428, _1496430, _1496432), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1496436, tc_fun(_1496428, tc_HOL_Obool)), _1496438), _1496440)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1496436, tc_fun(_1496430, tc_HOL_Obool)), _1496438), hAPP(hAPP(c_COMBB(tc_fun(_1496428, tc_HOL_Obool), tc_fun(_1496430, tc_HOL_Obool), _1496436), c_Set_Oimage(_1496428, _1496430, _1496432)), _1496440)))], (22481 ^ _776541) ^ [_1183866, _1183868, _1183870] : [class_Rings_Oring__1__no__zero__divisors(_1183866), -(_1183868 = c_Groups_Ozero__class_Ozero(_1183866)), hAPP(hAPP(c_Power_Opower__class_Opower(_1183866), _1183868), _1183870) = c_Groups_Ozero__class_Ozero(_1183866)], (200 ^ _776541) ^ [_779813, _779815] : [-(class_Rings_Odivision__ring(_779813)), _779815 = _779813, class_Rings_Odivision__ring(_779815)], (45251 ^ _776541) ^ [_1682794, _1682796] : [-(c_Code__Numeral_Onat__of__aux(_1682794, _1682796) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682794)), _1682796))], (41653 ^ _776541) ^ [_1596460, _1596462, _1596464, _1596466, _1596468, _1596470] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596460, _1596462)), _1596464), hAPP(hAPP(c_Relation_Orel__comp(_1596460, _1596466, _1596462), _1596468), _1596470))), 41659 ^ _776541 : [(41664 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596466, _1596462)), hAPP(hAPP(c_Product__Type_OPair(_1596466, _1596462), 41657 ^ [_1596460, _1596462, _1596464, _1596466, _1596468, _1596470]), 41658 ^ [_1596460, _1596462, _1596464, _1596466, _1596468, _1596470])), _1596470)))], (41662 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596460, _1596466)), hAPP(hAPP(c_Product__Type_OPair(_1596460, _1596466), 41656 ^ [_1596460, _1596462, _1596464, _1596466, _1596468, _1596470]), 41657 ^ [_1596460, _1596462, _1596464, _1596466, _1596468, _1596470])), _1596468)))], (41660 ^ _776541) ^ [] : [-(_1596464 = hAPP(hAPP(c_Product__Type_OPair(_1596460, _1596462), 41656 ^ [_1596460, _1596462, _1596464, _1596466, _1596468, _1596470]), 41658 ^ [_1596460, _1596462, _1596464, _1596466, _1596468, _1596470]))]]], (50928 ^ _776541) ^ [_1807963, _1807965, _1807967] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1807963), _1807965, _1807967)), -(c_List_Olist__ex(tc_Nat_Onat, _1807963, c_List_Oupt(_1807965, _1807967)))], (11106 ^ _776541) ^ [_968620, _968622, _968624, _968626, _968628] : [hBOOL(hAPP(hAPP(c_member(_968620), _968622), hAPP(c_Set_Oimage(_968624, _968620, _968626), _968628))), 11110 ^ _776541 : [(11113 ^ _776541) ^ [] : [-(_968622 = hAPP(_968626, 11109 ^ [_968620, _968622, _968624, _968626, _968628]))], (11111 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968624), 11109 ^ [_968620, _968622, _968624, _968626, _968628]), _968628)))]]], (38007 ^ _776541) ^ [_1502745, _1502747, _1502749] : [38009 ^ _776541 : [(38012 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1502745), 38008 ^ [_1502745, _1502747, _1502749]), c_Wellfounded_Oacc(_1502745, _1502749)))], (38010 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1502745, _1502745)), hAPP(hAPP(c_Product__Type_OPair(_1502745, _1502745), 38008 ^ [_1502745, _1502747, _1502749]), _1502747)), _1502749)))]], -(hBOOL(hAPP(hAPP(c_member(_1502745), _1502747), c_Wellfounded_Oacc(_1502745, _1502749))))], (1948 ^ _776541) ^ [_803773, _803775, _803777, _803779] : [-(v_Q_H(_803777, _803773)), v_Q_H(_803779, _803775), _803779 = _803777, _803775 = _803773], (33068 ^ _776541) ^ [_1380767, _1380769, _1380771] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380767, tc_Nat_Onat), _1380769), _1380771)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380767, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1380767), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1380769)), _1380771))], (8327 ^ _776541) ^ [_919238, _919240, _919242] : [class_Lattices_Osemilattice__sup(_919238), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919238), _919240), _919242) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919238), _919242), _919240))], (36770 ^ _776541) ^ [_1474140, _1474142, _1474144, _1474146, _1474148] : [c_Equiv__Relations_Oequiv(_1474140, _1474142, _1474144), hBOOL(hAPP(hAPP(c_member(tc_prod(_1474140, _1474140)), hAPP(hAPP(c_Product__Type_OPair(_1474140, _1474140), _1474146), _1474148)), _1474144)), -(hAPP(c_Relation_OImage(_1474140, _1474140, _1474144), hAPP(hAPP(c_Set_Oinsert(_1474140), _1474146), c_Orderings_Obot__class_Obot(tc_fun(_1474140, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1474140, _1474140, _1474144), hAPP(hAPP(c_Set_Oinsert(_1474140), _1474148), c_Orderings_Obot__class_Obot(tc_fun(_1474140, tc_HOL_Obool)))))], (28319 ^ _776541) ^ [_1284890, _1284892] : [_1284890 = _1284892, -(c_Int_OBit1(_1284890) = c_Int_OBit1(_1284892))], (43082 ^ _776541) ^ [_1634995, _1634997] : [-(c_List_Oremove1(_1634995, _1634997, c_List_Olist_ONil(_1634995)) = c_List_Olist_ONil(_1634995))], (33018 ^ _776541) ^ [_1379366, _1379368, _1379370, _1379372, _1379374, _1379376] : [hBOOL(hAPP(hAPP(c_member(_1379366), _1379368), _1379370)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379366, tc_fun(_1379372, tc_HOL_Obool)), _1379370), hAPP(hAPP(c_COMBB(tc_fun(_1379372, tc_HOL_Obool), tc_fun(_1379372, tc_HOL_Obool), _1379366), hAPP(c_Set_Oinsert(_1379372), _1379374)), _1379376)) = hAPP(hAPP(c_Set_Oinsert(_1379372), _1379374), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379366, tc_fun(_1379372, tc_HOL_Obool)), _1379370), _1379376)))], (23898 ^ _776541) ^ [_1209408, _1209410, _1209412] : [class_Rings_Olinordered__semidom(_1209408), 23901 ^ _776541 : [(23908 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209410), _1209412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209408), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209408), _1209410)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209408), _1209412))))], (23902 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209408), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209408), _1209410)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209408), _1209412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209410), _1209412)))]]], (28969 ^ _776541) ^ [_1295860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295860), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1295860)), c_Int_OPls)))], (7041 ^ _776541) ^ [_891070, _891072, _891074, _891076, _891078] : [class_Complete__Lattice_Ocomplete__lattice(_891070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891072, tc_HOL_Obool)), _891074), _891076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891070), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891072, _891070), _891076), _891078)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891072, _891070), _891074), _891078))))], (31255 ^ _776541) ^ [_1337446, _1337448, _1337450] : [class_Orderings_Olinorder(_1337446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337446), _1337448)), -(hBOOL(hAPP(hAPP(c_member(_1337446), _1337450), _1337448))), -(c_Big__Operators_Olinorder__class_OMax(_1337446, hAPP(hAPP(c_Set_Oinsert(_1337446), _1337450), _1337448)) = hAPP(hAPP(c_Finite__Set_Ofold(_1337446, _1337446, c_Orderings_Oord__class_Omax(_1337446)), _1337450), _1337448))], (14314 ^ _776541) ^ [_1034594, _1034596, _1034598, _1034600, _1034602] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1034594), 14317 ^ _776541 : [(14318 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034596), _1034598)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034600), _1034602)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034596), _1034602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034600), _1034598)), -(_1034596 = _1034600), -(_1034598 = _1034602)], (14328 ^ _776541) ^ [] : [14329 ^ _776541 : [(14332 ^ _776541) ^ [] : [_1034598 = _1034602], (14330 ^ _776541) ^ [] : [_1034596 = _1034600]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034596), _1034598)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034600), _1034602)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034596), _1034602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034594), _1034600), _1034598)))]]], (28301 ^ _776541) ^ [_1284638] : [c_Int_OBit1(_1284638) = c_Int_OMin, -(_1284638 = c_Int_OMin)], (27419 ^ _776541) ^ [_1269653, _1269655] : [class_Groups_Oordered__ab__group__add__abs(_1269653), 27422 ^ _776541 : [(27429 ^ _776541) ^ [] : [-(_1269655 = c_Groups_Ozero__class_Ozero(_1269653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269653), c_Groups_Ozero__class_Ozero(_1269653)), hAPP(c_Groups_Oabs__class_Oabs(_1269653), _1269655))))], (27423 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269653), c_Groups_Ozero__class_Ozero(_1269653)), hAPP(c_Groups_Oabs__class_Oabs(_1269653), _1269655))), _1269655 = c_Groups_Ozero__class_Ozero(_1269653)]]], (34711 ^ _776541) ^ [_1423337, _1423339, _1423341, _1423343, _1423345] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423337, _1423339, _1423341), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423343)), _1423345)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1423337), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1423343))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423337, _1423337), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1423337, tc_fun(_1423337, _1423337)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1423337, tc_fun(_1423337, _1423337)), tc_Int_Oint), c_If(_1423337)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1423337, _1423339, _1423341), _1423345))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423337, _1423337), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1423337, _1423337), tc_Int_Oint), _1423341), 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)), _1423345))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1423337, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1423337, _1423339, _1423341)), 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)), _1423345))))))], (7542 ^ _776541) ^ [_900921, _900923, _900925, _900927] : [hBOOL(hAPP(_900921, _900923)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900925, tc_HOL_Obool)), _900927), _900921), _900923)))], (25071 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8076 ^ _776541) ^ [_913813, _913815, _913817] : [class_Complete__Lattice_Ocomplete__lattice(_913813), -(c_Complete__Lattice_OSup__class_OSup(_913813, hAPP(hAPP(c_Set_Oinsert(_913813), _913815), _913817)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913813), _913815), c_Complete__Lattice_OSup__class_OSup(_913813, _913817)))], (45800 ^ _776541) ^ [_1695497, _1695499, _1695501, _1695503] : [-(_1695497 = _1695499), -(hAPP(c_List_OremoveAll(_1695501, _1695497), hAPP(hAPP(c_List_Olist_OCons(_1695501), _1695499), _1695503)) = hAPP(hAPP(c_List_Olist_OCons(_1695501), _1695499), hAPP(c_List_OremoveAll(_1695501, _1695497), _1695503)))], (1774 ^ _776541) ^ [_801580, _801582] : [-(class_Groups_Omonoid__add(_801580)), _801582 = _801580, class_Groups_Omonoid__add(_801582)], (45046 ^ _776541) ^ [_1678666, _1678668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678666), _1678668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1678666)), hAPP(c_Code__Numeral_Oof__nat, _1678668))))], (42250 ^ _776541) ^ [_1614382, _1614384, _1614386, _1614388] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1614384), hAPP(hAPP(c_List_Olist_OCons(_1614384), _1614386), _1614388)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614382)) = _1614386)], (48462 ^ _776541) ^ [_1752910, _1752912, _1752914] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752910)), c_List_Osplice(_1752910, _1752912, _1752914)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752910)), _1752912)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752910)), _1752914)))], (20753 ^ _776541) ^ [_1151228, _1151230, _1151232, _1151234] : [class_Fields_Ofield(_1151228), -(_1151230 = c_Groups_Ozero__class_Ozero(_1151228)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151228), _1151232), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151228), _1151234), _1151230)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151228), _1151230), _1151232)), _1151234)), _1151230))], (44529 ^ _776541) ^ [_1667207, _1667209, _1667211] : [class_Orderings_Olinorder(_1667207), -(hBOOL(hAPP(hAPP(c_member(_1667207), _1667209), hAPP(c_List_Oset(_1667207), _1667211)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1667207, _1667207, c_COMBI(_1667207), _1667209, _1667211) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1667207, _1667207, c_COMBI(_1667207)), _1667209), _1667211))], (27122 ^ _776541) ^ [_1264815, _1264817] : [class_Rings_Olinordered__idom(_1264815), 27125 ^ _776541 : [(27132 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264817), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264815), hAPP(c_Int_Oring__1__class_Oof__int(_1264815), _1264817)), c_Groups_Ozero__class_Ozero(_1264815))))], (27126 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264815), hAPP(c_Int_Oring__1__class_Oof__int(_1264815), _1264817)), c_Groups_Ozero__class_Ozero(_1264815))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264817), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (27809 ^ _776541) ^ [_1276576, _1276578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276576)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276578))), 27812 ^ _776541 : [(27813 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276576), _1276578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1276578)))], (27819 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276576), _1276578)))]]], (22687 ^ _776541) ^ [_1187595, _1187597] : [22688 ^ _776541 : [(22691 ^ _776541) ^ [] : [_1187595 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22689 ^ _776541) ^ [] : [_1187597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187595), _1187597) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22325 ^ _776541) ^ [_1181171, _1181173] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181171), _1181173) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181173), _1181171))], (32712 ^ _776541) ^ [_1370834, _1370836] : [-(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), _1370834)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1370836))))))], (4284 ^ _776541) ^ [_841428, _841430, _841432, _841434] : [-(c_List_Ofilter(_841434, _841430) = c_List_Ofilter(_841432, _841428)), _841434 = _841432, _841430 = _841428], (11125 ^ _776541) ^ [_969022, _969024, _969026, _969028, _969030] : [hBOOL(hAPP(hAPP(c_member(_969022), _969024), _969026)), -(hBOOL(hAPP(hAPP(c_member(_969028), hAPP(_969030, _969024)), hAPP(c_Set_Oimage(_969022, _969028, _969030), _969026))))], (7846 ^ _776541) ^ [_908616, _908618] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908616, tc_HOL_Obool)), _908618), c_Orderings_Obot__class_Obot(tc_fun(_908616, tc_HOL_Obool))) = _908618)], (47228 ^ _776541) ^ [_1726026, _1726028, _1726030] : [c_List_OtakeWhile(_1726026, _1726028, _1726030) = _1726030, 47231 ^ _776541 : [(47232 ^ _776541) ^ [_1726113] : [hBOOL(hAPP(hAPP(c_member(_1726026), _1726113), hAPP(c_List_Oset(_1726026), _1726030))), -(hBOOL(hAPP(_1726028, _1726113)))]]], (31164 ^ _776541) ^ [_1335855, _1335857, _1335859] : [class_Orderings_Olinorder(_1335855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335855), _1335857)), hBOOL(hAPP(hAPP(c_member(_1335855), _1335859), _1335857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335855), _1335859), c_Big__Operators_Olinorder__class_OMax(_1335855, _1335857))))], (22197 ^ _776541) ^ [_1179114, _1179116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179114), _1179116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179116), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (31693 ^ _776541) ^ [_1345728, _1345730, _1345732, _1345734] : [class_Orderings_Olinorder(_1345728), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345728), _1345730)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1345728, _1345728, c_Orderings_Oord__class_Omax(_1345728)), _1345732), hAPP(hAPP(c_Set_Oinsert(_1345728), _1345734), _1345730)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345728), _1345734), hAPP(hAPP(c_Finite__Set_Ofold(_1345728, _1345728, c_Orderings_Oord__class_Omax(_1345728)), _1345732), _1345730)))], (28547 ^ _776541) ^ [_1288793] : [class_Int_Onumber__ring(_1288793), -(c_Groups_Oone__class_Oone(_1288793) = hAPP(c_Int_Onumber__class_Onumber__of(_1288793), c_Int_OBit1(c_Int_OPls)))], (27939 ^ _776541) ^ [_1278731, _1278733] : [class_Int_Onumber__ring(_1278731), class_Rings_Olinordered__idom(_1278731), 27946 ^ _776541 : [(27953 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1278733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278731), c_Groups_Ozero__class_Ozero(_1278731)), hAPP(c_Int_Onumber__class_Onumber__of(_1278731), _1278733))))], (27947 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278731), c_Groups_Ozero__class_Ozero(_1278731)), hAPP(c_Int_Onumber__class_Onumber__of(_1278731), _1278733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1278733)))]]], (38570 ^ _776541) ^ [_1516435, _1516437] : [c_Wellfounded_OwfP(_1516435, hAPP(hAPP(c_COMBC(_1516435, tc_fun(tc_prod(_1516435, _1516435), tc_HOL_Obool), tc_fun(_1516435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516435, tc_fun(tc_fun(tc_prod(_1516435, _1516435), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516435, _1516435), tc_HOL_Obool), tc_fun(_1516435, tc_HOL_Obool)), _1516435), c_COMBC(_1516435, tc_fun(tc_prod(_1516435, _1516435), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516435, tc_prod(_1516435, _1516435)), tc_fun(_1516435, tc_fun(tc_fun(tc_prod(_1516435, _1516435), tc_HOL_Obool), tc_HOL_Obool)), _1516435), hAPP(c_COMBB(tc_prod(_1516435, _1516435), tc_fun(tc_fun(tc_prod(_1516435, _1516435), tc_HOL_Obool), tc_HOL_Obool), _1516435), c_member(tc_prod(_1516435, _1516435)))), c_Product__Type_OPair(_1516435, _1516435)))), _1516437)), -(c_Wellfounded_Owf(_1516435, _1516437))], (28419 ^ _776541) ^ [_1286659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286659), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286659)), c_Int_OPls)))], (45792 ^ _776541) ^ [_1695304, _1695306, _1695308, _1695310] : [-(hAPP(c_List_OremoveAll(_1695304, _1695306), hAPP(hAPP(c_List_Oappend(_1695304), _1695308), _1695310)) = hAPP(hAPP(c_List_Oappend(_1695304), hAPP(c_List_OremoveAll(_1695304, _1695306), _1695308)), hAPP(c_List_OremoveAll(_1695304, _1695306), _1695310)))], (9458 ^ _776541) ^ [_939054, _939056, _939058] : [class_Orderings_Opreorder(_939054), 9461 ^ _776541 : [(9470 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939054), _939056), _939058))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939054), _939056), _939058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939054), _939058), _939056)))], (9462 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939054), _939056), _939058)), 9465 ^ _776541 : [(9468 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939054), _939058), _939056))], (9466 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939054), _939056), _939058)))]]]]], (34791 ^ _776541) ^ [_1425661, _1425663, _1425665, _1425667, _1425669, _1425671, _1425673] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425661, _1425663, tc_fun(_1425665, tc_HOL_Obool)), _1425667), hAPP(hAPP(c_Product__Type_OPair(_1425661, _1425663), _1425669), _1425671)), _1425673)), -(hBOOL(hAPP(hAPP(hAPP(_1425667, _1425669), _1425671), _1425673)))], (52389 ^ _776541) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (4426 ^ _776541) ^ [_843747, _843749] : [_843749 = _843747, -(c_Lazy__Sequence_Oempty(_843749) = c_Lazy__Sequence_Oempty(_843747))], (52123 ^ _776541) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (29843 ^ _776541) ^ [_1311614] : [c_Code__Numeral_OSuc__code__numeral(_1311614) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (26246 ^ _776541) ^ [_1250594, _1250596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250594)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250594), _1250596)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1250594)), hAPP(c_Int_Onat, _1250596)))], (19460 ^ _776541) ^ [_1127928, _1127930] : [-(hBOOL(hAPP(_1127928, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1127928, _1127930)), 19468 ^ _776541 : [(19471 ^ _776541) ^ [_1128166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128166), 19467 ^ [_1127928, _1127930])), hBOOL(hAPP(_1127928, _1128166))], (19477 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1127928, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19467 ^ [_1127928, _1127930]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (19469 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19467 ^ [_1127928, _1127930]), _1127930)))]]], (38919 ^ _776541) ^ [_1525092, _1525094, _1525096, _1525098, _1525100, _1525102] : [hBOOL(hAPP(hAPP(c_member(_1525092), _1525094), _1525096)), 38922 ^ _776541 : [(38929 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525092), _1525098), _1525096))), -(hAPP(c_Set_Ovimage(_1525100, _1525092, hAPP(hAPP(c_COMBC(_1525100, _1525092, _1525092), hAPP(hAPP(c_COMBC(_1525100, _1525092, tc_fun(_1525092, _1525092)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525092, tc_fun(_1525092, _1525092)), _1525100), c_If(_1525092)), hAPP(hAPP(c_COMBC(_1525100, tc_fun(_1525100, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525100)), _1525102))), _1525094)), _1525098)), _1525096) = _1525102)], (38923 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1525092), _1525098), _1525096)), -(hAPP(c_Set_Ovimage(_1525100, _1525092, hAPP(hAPP(c_COMBC(_1525100, _1525092, _1525092), hAPP(hAPP(c_COMBC(_1525100, _1525092, tc_fun(_1525092, _1525092)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525092, tc_fun(_1525092, _1525092)), _1525100), c_If(_1525092)), hAPP(hAPP(c_COMBC(_1525100, tc_fun(_1525100, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525100)), _1525102))), _1525094)), _1525098)), _1525096) = c_Orderings_Otop__class_Otop(tc_fun(_1525100, tc_HOL_Obool)))]]], (37913 ^ _776541) ^ [_1499283, _1499285, _1499287] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1499283, hAPP(hAPP(c_COMBC(_1499283, tc_fun(tc_prod(_1499283, _1499283), tc_HOL_Obool), tc_fun(_1499283, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499283, tc_fun(tc_fun(tc_prod(_1499283, _1499283), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499283, _1499283), tc_HOL_Obool), tc_fun(_1499283, tc_HOL_Obool)), _1499283), c_COMBC(_1499283, tc_fun(tc_prod(_1499283, _1499283), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499283, tc_prod(_1499283, _1499283)), tc_fun(_1499283, tc_fun(tc_fun(tc_prod(_1499283, _1499283), tc_HOL_Obool), tc_HOL_Obool)), _1499283), hAPP(c_COMBB(tc_prod(_1499283, _1499283), tc_fun(tc_fun(tc_prod(_1499283, _1499283), tc_HOL_Obool), tc_HOL_Obool), _1499283), c_member(tc_prod(_1499283, _1499283)))), c_Product__Type_OPair(_1499283, _1499283)))), _1499285)), _1499287)), -(hBOOL(hAPP(hAPP(c_member(_1499283), _1499287), c_Wellfounded_Oacc(_1499283, _1499285))))], (45243 ^ _776541) ^ [_1682654, _1682656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682654)), hAPP(c_Code__Numeral_Onat__of, _1682656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1682654), _1682656)))], (33973 ^ _776541) ^ [_1406963, _1406965, _1406967, _1406969] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406963), _1406965)), -(hAPP(c_Set_Oimage(_1406963, _1406967, _1406969), _1406965) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1406967, tc_HOL_Obool), _1406963, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406967, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1406963, tc_fun(_1406967, tc_HOL_Obool), tc_fun(_1406967, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1406967, tc_fun(tc_fun(_1406967, tc_HOL_Obool), tc_fun(_1406967, tc_HOL_Obool)), _1406963), c_Set_Oinsert(_1406967)), _1406969)), c_Orderings_Obot__class_Obot(tc_fun(_1406967, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1406967, tc_HOL_Obool))), _1406965))], (11169 ^ _776541) ^ [_969952, _969954, _969956, _969958, _969960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969952, tc_HOL_Obool)), _969954), _969956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969958, tc_HOL_Obool)), hAPP(c_Set_Oimage(_969952, _969958, _969960), _969954)), hAPP(c_Set_Oimage(_969952, _969958, _969960), _969956))))], (38613 ^ _776541) ^ [_1518201, _1518203, _1518205, _1518207, _1518209] : [hBOOL(hAPP(hAPP(_1518201, _1518203), _1518205)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1518207, _1518209, _1518201), _1518205)))], (45710 ^ _776541) ^ [_1693548, _1693550, _1693552, _1693554, _1693556] : [45712 ^ _776541 : [(45715 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1693548, _1693550, tc_HOL_Obool), _1693556), 45711 ^ [_1693548, _1693550, _1693552, _1693554, _1693556]))], (45713 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1693548, _1693550)), 45711 ^ [_1693548, _1693550, _1693552, _1693554, _1693556]), hAPP(c_List_Oset(tc_prod(_1693548, _1693550)), hAPP(hAPP(c_List_Ozip(_1693548, _1693550), _1693552), _1693554)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693548)), _1693552) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693550)), _1693554), -(c_List_Olist__all2(_1693548, _1693550, _1693556, _1693552, _1693554))], (47343 ^ _776541) ^ [_1728342, _1728344, _1728346] : [hBOOL(hAPP(c_List_Odistinct(_1728342), _1728344)), hBOOL(hAPP(hAPP(c_member(_1728342), _1728346), hAPP(c_List_Oset(_1728342), _1728344))), -(c_List_OtakeWhile(_1728342, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728342), c_fNot), hAPP(hAPP(c_COMBC(_1728342, _1728342, tc_HOL_Obool), c_fequal), _1728346)), hAPP(c_List_Orev(_1728342), _1728344)) = hAPP(c_List_Orev(_1728342), hAPP(c_List_Otl(_1728342), c_List_OdropWhile(_1728342, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728342), c_fNot), hAPP(hAPP(c_COMBC(_1728342, _1728342, tc_HOL_Obool), c_fequal), _1728346)), _1728344))))], (11258 ^ _776541) ^ [_972088, _972090, _972092] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_972088, _972090, c_Orderings_Obot__class_Obot(tc_fun(_972088, tc_HOL_Obool))), _972092))], (17001 ^ _776541) ^ [_1082541, _1082543, _1082545, _1082547] : [class_Rings_Oordered__ring(_1082541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082541), _1082543), _1082545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082541), _1082547), c_Groups_Ozero__class_Ozero(_1082541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082541), _1082547), _1082545)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082541), _1082547), _1082543))))], (23609 ^ _776541) ^ [_1204414, _1204416] : [class_Divides_Osemiring__div(_1204414), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204414), _1204416), c_Groups_Oone__class_Oone(_1204414)) = _1204416)], (42875 ^ _776541) ^ [_1630754, _1630756, _1630758, _1630760] : [hBOOL(hAPP(c_List_Odistinct(_1630754), _1630756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630758), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630754)), _1630756))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630760), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630754)), _1630756))), 42886 ^ _776541 : [(42893 ^ _776541) ^ [] : [_1630758 = _1630760, -(hAPP(hAPP(c_List_Onth(_1630754), _1630756), _1630758) = hAPP(hAPP(c_List_Onth(_1630754), _1630756), _1630760))], (42887 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Onth(_1630754), _1630756), _1630758) = hAPP(hAPP(c_List_Onth(_1630754), _1630756), _1630760), -(_1630758 = _1630760)]]], (30968 ^ _776541) ^ [_1332075, _1332077, _1332079] : [class_Orderings_Olinorder(_1332075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332075), _1332077)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332075), _1332079)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332075, tc_HOL_Obool)), _1332077), _1332079) = c_Orderings_Obot__class_Obot(tc_fun(_1332075, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332075), c_Big__Operators_Olinorder__class_OMin(_1332075, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332075, tc_HOL_Obool)), _1332077), _1332079))), c_Big__Operators_Olinorder__class_OMin(_1332075, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332075, tc_HOL_Obool)), _1332077), _1332079))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332075), c_Big__Operators_Olinorder__class_OMin(_1332075, _1332077)), c_Big__Operators_Olinorder__class_OMin(_1332075, _1332079)))], (7268 ^ _776541) ^ [_895238, _895240, _895242, _895244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895238, tc_HOL_Obool)), _895240), _895242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895238, tc_HOL_Obool)), _895240), hAPP(hAPP(c_Set_Oinsert(_895238), _895244), _895242))))], (39149 ^ _776541) ^ [_1531770, _1531772, _1531774, _1531776, _1531778] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531770, _1531772), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1531770, tc_HOL_Obool)), _1531774), _1531776)), hAPP(c_COMBK(tc_fun(_1531772, tc_HOL_Obool), _1531770), _1531778)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1531770, _1531772), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531770, _1531772), _1531774), hAPP(c_COMBK(tc_fun(_1531772, tc_HOL_Obool), _1531770), _1531778))), hAPP(hAPP(c_Product__Type_OSigma(_1531770, _1531772), _1531776), hAPP(c_COMBK(tc_fun(_1531772, tc_HOL_Obool), _1531770), _1531778))))], (6031 ^ _776541) ^ [_872843, _872845, _872847, _872849] : [hBOOL(hAPP(hAPP(c_member(_872843), _872845), c_SetInterval_Oord_OgreaterThan(_872843, _872847, _872849))), -(hBOOL(hAPP(hAPP(_872847, _872849), _872845)))], (15676 ^ _776541) ^ [_1060796] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060796)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1060796))], (1564 ^ _776541) ^ [_798955, _798957] : [-(class_Groups_Ocancel__ab__semigroup__add(_798955)), _798957 = _798955, class_Groups_Ocancel__ab__semigroup__add(_798957)], (33475 ^ _776541) ^ [_1392161, _1392163, _1392165, _1392167, _1392169] : [class_Fields_Ofield__inverse__zero(_1392161), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392163), _1392165)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392163, _1392161), hAPP(hAPP(c_COMBS(_1392163, _1392161, _1392161), hAPP(hAPP(c_COMBB(_1392161, tc_fun(_1392161, _1392161), _1392163), c_Rings_Oinverse__class_Odivide(_1392161)), _1392167)), _1392169)), _1392165) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392161), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392163, _1392161), _1392167), _1392165)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392163, _1392161), _1392169), _1392165)))], (43912 ^ _776541) ^ [_1654011, _1654013, _1654015] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654011)), hAPP(hAPP(c_List_Odrop(_1654011), _1654013), _1654015)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654011)), _1654015)), _1654013))], (8729 ^ _776541) ^ [_926533, _926535, _926537] : [class_Lattices_Osemilattice__inf(_926533), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926533), _926535), _926537)), _926537)))], (48235 ^ _776541) ^ [_1748081, _1748083] : [-(c_FunDef_Ois__measure(_1748081, _1748083))], (36736 ^ _776541) ^ [_1473506, _1473508, _1473510] : [c_Equiv__Relations_Oequiv(_1473506, _1473508, _1473510), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1473506, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473506), _1473508), _1473510)) = _1473508)], (49267 ^ _776541) ^ [_1771403, _1771405] : [c_Relation_Otrans(_1771403, _1771405), -(c_Relation_Otrans(_1771403, hAPP(c_Relation_Oconverse(_1771403, _1771403), _1771405)))], (2290 ^ _776541) ^ [_809899, _809901, _809903, _809905] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_809905, _809901) = c_Code__Numeral_Odiv__mod__code__numeral(_809903, _809899)), _809905 = _809903, _809901 = _809899], (39824 ^ _776541) ^ [_1551401, _1551403, _1551405, _1551407, _1551409] : [hAPP(c_Set_Oimage(_1551401, _1551403, _1551405), c_Orderings_Otop__class_Otop(tc_fun(_1551401, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551403, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1551403, _1551407, _1551409), c_Orderings_Otop__class_Otop(tc_fun(_1551403, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551407, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1551401, _1551407, hAPP(c_Fun_Ocomp(_1551403, _1551407, _1551401, _1551409), _1551405)), c_Orderings_Otop__class_Otop(tc_fun(_1551401, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551407, tc_HOL_Obool)))], (19098 ^ _776541) ^ [_1120658, _1120660, _1120662, _1120664, _1120666, _1120668, _1120670] : [c_Big__Operators_Ocomm__monoid__big(_1120658, _1120660, _1120662, _1120664, _1120666), 19101 ^ _776541 : [(19108 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1120660), _1120668))), -(hAPP(hAPP(_1120666, _1120670), _1120668) = _1120664)], (19102 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1120660), _1120668)), -(hAPP(hAPP(_1120666, _1120670), _1120668) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1120658, _1120660, _1120662), _1120670), _1120664), _1120668))]]], (4062 ^ _776541) ^ [_837971, _837973, _837975, _837977, _837979, _837981, _837983, _837985] : [-(c_New__Random__Sequence_Oneg__map(_837985, _837981, _837977, _837973) = c_New__Random__Sequence_Oneg__map(_837983, _837979, _837975, _837971)), _837985 = _837983, _837981 = _837979, _837977 = _837975, _837973 = _837971], (25141 ^ _776541) ^ [_1231663, _1231665, _1231667] : [class_Divides_Osemiring__div(_1231663), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231663), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231663), _1231665), _1231667)), _1231667)), c_Divides_Odiv__class_Omod(_1231663, _1231665, _1231667)) = _1231665)], (31555 ^ _776541) ^ [_1343074, _1343076, _1343078, _1343080] : [class_Orderings_Olinorder(_1343074), 31558 ^ _776541 : [(31559 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343074), _1343076), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343074), _1343078), _1343080))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343074), _1343076), _1343078))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343074), _1343076), _1343080)))], (31569 ^ _776541) ^ [] : [31570 ^ _776541 : [(31573 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343074), _1343076), _1343080))], (31571 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343074), _1343076), _1343078))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343074), _1343076), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343074), _1343078), _1343080))))]]], (16781 ^ _776541) ^ [_1078481, _1078483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078481), _1078483)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078483)), _1078481) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1078483), _1078481)))], (32268 ^ _776541) ^ [_1356676, _1356678, _1356680] : [-(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), _1356676)), 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))), _1356678))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1356680))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1356680)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356676), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356676), 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), _1356680), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1356678)))))], (28817 ^ _776541) ^ [_1293165, _1293167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293165)), c_Int_OBit0(_1293167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293165), _1293167)))], (52037 ^ _776541) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (9720 ^ _776541) ^ [_942948, _942950, _942952, _942954] : [class_Lattices_Osemilattice__sup(_942948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942948), _942950), _942952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942948), _942950), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942948), _942952), _942954))))], (24361 ^ _776541) ^ [_1217131, _1217133, _1217135] : [class_Divides_Osemiring__div(_1217131), -(_1217133 = c_Groups_Ozero__class_Ozero(_1217131)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217131), _1217135), _1217133)), _1217133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217131), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217131), _1217135), _1217133)), c_Groups_Oone__class_Oone(_1217131)))], (47138 ^ _776541) ^ [_1724139, _1724141, _1724143, _1724145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724139), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724141)), _1724143))), -(hAPP(c_List_Orev(_1724141), hAPP(hAPP(c_List_Olist__update(_1724141, _1724143), _1724139), _1724145)) = hAPP(hAPP(c_List_Olist__update(_1724141, hAPP(c_List_Orev(_1724141), _1724143)), 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(_1724141)), _1724143)), _1724139)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1724145))], (48042 ^ _776541) ^ [_1744167, _1744169, _1744171] : [c_List_Olist__ex(_1744167, _1744169, _1744171), 48046 ^ _776541 : [(48049 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1744169, hAPP(hAPP(c_List_Onth(_1744167), _1744171), 48045 ^ [_1744167, _1744169, _1744171]))))], (48047 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48045 ^ [_1744167, _1744169, _1744171]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744167)), _1744171))))]]], (17781 ^ _776541) ^ [_1096584, _1096586, _1096588] : [class_Groups_Ogroup__add(_1096584), 17784 ^ _776541 : [(17791 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096584), _1096586), _1096588) = c_Groups_Ozero__class_Ozero(_1096584), -(_1096586 = hAPP(c_Groups_Ouminus__class_Ouminus(_1096584), _1096588))], (17785 ^ _776541) ^ [] : [_1096586 = hAPP(c_Groups_Ouminus__class_Ouminus(_1096584), _1096588), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096584), _1096586), _1096588) = c_Groups_Ozero__class_Ozero(_1096584))]]], (12485 ^ _776541) ^ [_995974, _995976] : [class_Lattices_Olattice(_995974), hBOOL(hAPP(c_Finite__Set_Ofinite(_995974), _995976)), -(_995976 = c_Orderings_Obot__class_Obot(tc_fun(_995974, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_995974), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_995974), 12498 ^ [_995974, _995976]), 12499 ^ [_995974, _995976])), hAPP(hAPP(c_Set_Oinsert(_995974), 12498 ^ [_995974, _995976]), hAPP(hAPP(c_Set_Oinsert(_995974), 12499 ^ [_995974, _995976]), c_Orderings_Obot__class_Obot(tc_fun(_995974, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_995974), c_Big__Operators_Olattice__class_OSup__fin(_995974, _995976)), _995976)))], (41086 ^ _776541) ^ [_1582050, _1582052, _1582054, _1582056, _1582058] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582050, _1582052)), hAPP(hAPP(c_Product__Type_OPair(_1582050, _1582052), _1582054), _1582056)), hAPP(c_Relation_Oconverse(_1582052, _1582050), _1582058))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582052, _1582050)), hAPP(hAPP(c_Product__Type_OPair(_1582052, _1582050), _1582056), _1582054)), _1582058)))], (8339 ^ _776541) ^ [_919456, _919458, _919460] : [class_Lattices_Osemilattice__sup(_919456), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919456), _919458), _919460) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919456), _919460), _919458))], (12756 ^ _776541) ^ [_1001569, _1001571, _1001573, _1001575, _1001577] : [c_Finite__Set_Ofun__left__comm(_1001569, _1001571, _1001573), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001569), _1001575)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1001569, _1001571, _1001573, _1001577, _1001575), hAPP(hAPP(c_Finite__Set_Ofold(_1001569, _1001571, _1001573), _1001577), _1001575))))], (8557 ^ _776541) ^ [_923541, _923543, _923545] : [class_Lattices_Osemilattice__sup(_923541), 8560 ^ _776541 : [(8567 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923541), _923543), _923545) = _923545, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923541), _923543), _923545)))], (8561 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923541), _923543), _923545)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923541), _923543), _923545) = _923545)]]], (27677 ^ _776541) ^ [_1274430, _1274432] : [class_Groups_Oordered__ab__group__add__abs(_1274430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274430), _1274432), c_Groups_Ozero__class_Ozero(_1274430))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274430), _1274432) = hAPP(c_Groups_Ouminus__class_Ouminus(_1274430), _1274432))], (21051 ^ _776541) ^ [_1156958, _1156960, _1156962] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1156958), _1156960)), 21057 ^ _776541 : [(21060 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1156962, 21056 ^ [_1156958, _1156960, _1156962])))], (21058 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1156958), 21056 ^ [_1156958, _1156960, _1156962]), _1156960)))]], -(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(_1156958, tc_Nat_Onat), _1156962), _1156960))))], (47676 ^ _776541) ^ [_1735796, _1735798, _1735800, _1735802, _1735804] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1735796, _1735796)), hAPP(hAPP(c_Product__Type_OPair(_1735796, _1735796), _1735798), _1735800)), c_List_Omeasures(_1735796, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1735796, tc_Nat_Onat)), _1735802), _1735804))))), 47677 ^ _776541 : [(47680 ^ _776541) ^ [] : [hAPP(_1735802, _1735798) = hAPP(_1735802, _1735800), hBOOL(hAPP(hAPP(c_member(tc_prod(_1735796, _1735796)), hAPP(hAPP(c_Product__Type_OPair(_1735796, _1735796), _1735798), _1735800)), c_List_Omeasures(_1735796, _1735804)))], (47678 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1735802, _1735798)), hAPP(_1735802, _1735800)))]]], (33687 ^ _776541) ^ [_1399086, _1399088, _1399090, _1399092] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1399086), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399088, tc_Nat_Onat), _1399090), _1399092)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399088, _1399086), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1399086, _1399088), c_Nat_Osemiring__1__class_Oof__nat(_1399086)), _1399090)), _1399092)), class_Groups_Ocomm__monoid__mult(_1399086), class_Rings_Osemiring__1(_1399086)], (34560 ^ _776541) ^ [_1420184, _1420186, _1420188, _1420190, _1420192, _1420194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420184, tc_fun(_1420186, tc_HOL_Obool))), _1420188), _1420190)), hBOOL(hAPP(hAPP(_1420188, _1420192), _1420194)), -(hBOOL(hAPP(hAPP(_1420190, _1420192), _1420194)))], (28013 ^ _776541) ^ [_1279944, _1279946, _1279948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279944), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279946)), _1279948)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18644 ^ _776541) ^ [_1112166, _1112168, _1112170] : [18645 ^ _776541 : [(18648 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112166), _1112170))], (18646 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1112168)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112166), _1112168)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112170), _1112168))))], (16957 ^ _776541) ^ [_1081695, _1081697, _1081699, _1081701, _1081703] : [class_Rings_Oordered__semiring(_1081695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081695), _1081697), _1081699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081695), _1081701), _1081703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081695), c_Groups_Ozero__class_Ozero(_1081695)), _1081699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081695), c_Groups_Ozero__class_Ozero(_1081695)), _1081701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081695), _1081697), _1081701)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081695), _1081699), _1081703))))], (48594 ^ _776541) ^ [_1756237, _1756239, _1756241, _1756243] : [48596 ^ _776541 : [(48599 ^ _776541) ^ [] : [hBOOL(hAPP(_1756243, 48595 ^ [_1756237, _1756239, _1756241, _1756243]))], (48597 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756237), 48595 ^ [_1756237, _1756239, _1756241, _1756243]), hAPP(c_List_Oset(_1756237), c_List_Oreplicate(_1756237, _1756239, _1756241)))))]], -(hBOOL(hAPP(_1756243, _1756241))), -(_1756239 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47809 ^ _776541) ^ [_1738966, _1738968] : [class_Orderings_Olinorder(_1738966), hBOOL(hAPP(c_Finite__Set_Ofinite(_1738966), _1738968)), 47817 ^ _776541 : [(47820 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1738966, 47816 ^ [_1738966, _1738968]))], (47822 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1738966), 47816 ^ [_1738966, _1738968])))], (47824 ^ _776541) ^ [_1739292] : [-(_1739292 = 47816 ^ [_1738966, _1738968]), hAPP(c_List_Oset(_1738966), _1739292) = _1738968, c_List_Olinorder__class_Osorted(_1738966, _1739292), hBOOL(hAPP(c_List_Odistinct(_1738966), _1739292))], (47818 ^ _776541) ^ [] : [-(hAPP(c_List_Oset(_1738966), 47816 ^ [_1738966, _1738968]) = _1738968)]]], (44214 ^ _776541) ^ [_1660624, _1660626, _1660628] : [-(hAPP(c_List_Otl(_1660624), hAPP(hAPP(c_List_Oappend(_1660624), _1660626), _1660628)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1660624), _1660624, hAPP(c_List_Otl(_1660624), _1660628), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1660624), tc_List_Olist(_1660624)), _1660624), hAPP(hAPP(c_COMBC(tc_List_Olist(_1660624), tc_List_Olist(_1660624), tc_List_Olist(_1660624)), c_List_Oappend(_1660624)), _1660628))), _1660626))], (25455 ^ _776541) ^ [_1237021, _1237023] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237021), hAPP(c_Int_Onumber__class_Onumber__of(_1237021), c_Int_OMin)), _1237023) = hAPP(c_Groups_Ouminus__class_Ouminus(_1237021), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237021), c_Groups_Oone__class_Oone(_1237021)), _1237023))), class_Fields_Ofield__inverse__zero(_1237021), class_Int_Onumber__ring(_1237021)], (44625 ^ _776541) ^ [_1668790, _1668792, _1668794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668790), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668792)), _1668794))), -(c_List_Olast(_1668792, hAPP(hAPP(c_List_Odrop(_1668792), _1668790), _1668794)) = c_List_Olast(_1668792, _1668794))], (47579 ^ _776541) ^ [_1733479, _1733481, _1733483] : [-(hBOOL(hAPP(hAPP(c_member(_1733479), _1733481), hAPP(c_List_Oset(_1733479), _1733483)))), -(c_List_Oinsert(_1733479, _1733481, _1733483) = hAPP(hAPP(c_List_Olist_OCons(_1733479), _1733481), _1733483))], (44998 ^ _776541) ^ [_1677694, _1677696, _1677698, _1677700] : [class_Groups_Ocomm__monoid__add(_1677694), 45001 ^ _776541 : [(45008 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1677696), _1677698))), -(c_Nitpick_Osetsum_H(_1677696, _1677694, _1677700, _1677698) = c_Groups_Ozero__class_Ozero(_1677694))], (45002 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1677696), _1677698)), -(c_Nitpick_Osetsum_H(_1677696, _1677694, _1677700, _1677698) = hAPP(c_List_Omonoid__add__class_Olistsum(_1677694), hAPP(hAPP(c_List_Omap(_1677696, _1677694), _1677700), c_Hilbert__Choice_OEps(tc_List_Olist(_1677696), hAPP(hAPP(c_COMBS(tc_List_Olist(_1677696), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1677696)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677696), tc_fun(_1677696, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1677696, tc_HOL_Obool), tc_fun(tc_fun(_1677696, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1677696)), c_fequal), c_List_Oset(_1677696))), _1677698))), c_List_Odistinct(_1677696))))))]]], (4568 ^ _776541) ^ [_845918, _845920] : [_845920 = _845918, -(c_Nat_Osize__class_Osize(_845920) = c_Nat_Osize__class_Osize(_845918))], (41857 ^ _776541) ^ [_1602836, _1602838, _1602840, _1602842] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602836), tc_List_Olist(_1602836))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602836), tc_List_Olist(_1602836)), _1602838), _1602840)), c_List_Olex(_1602836, _1602842)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602836), tc_List_Olist(_1602836))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602836), tc_List_Olist(_1602836)), _1602838), _1602840)), c_List_Olexord(_1602836, _1602842))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602836)), _1602838) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602836)), _1602840)], (21073 ^ _776541) ^ [_1157401, _1157403, _1157405] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1157401, tc_HOL_Obool)), _1157403)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1157401), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1157401, tc_HOL_Obool), _1157403))), 21083 ^ _776541 : [(21086 ^ _776541) ^ [] : [hAPP(c_Finite__Set_Ocard(_1157401), 21082 ^ [_1157401, _1157403, _1157405]) = _1157405], (21084 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1157401, tc_HOL_Obool)), 21082 ^ [_1157401, _1157403, _1157405]), _1157403)))]], 21090 ^ _776541 : [(21094 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1157401, tc_HOL_Obool)), 21092 ^ [_1157401, _1157403, _1157405]), _1157403)))], (21096 ^ _776541) ^ [] : [21089 ^ [_1157401, _1157403, _1157405] = 21092 ^ [_1157401, _1157403, _1157405]], (21098 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1157401, tc_HOL_Obool)), 21089 ^ [_1157401, _1157403, _1157405]), 21092 ^ [_1157401, _1157403, _1157405]) = c_Orderings_Obot__class_Obot(tc_fun(_1157401, tc_HOL_Obool))], (21091 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1157401, tc_HOL_Obool)), 21089 ^ [_1157401, _1157403, _1157405]), _1157403)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157405), hAPP(c_Finite__Set_Ocard(tc_fun(_1157401, tc_HOL_Obool)), _1157403)) = hAPP(c_Finite__Set_Ocard(_1157401), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1157401, tc_HOL_Obool), _1157403)))], (46170 ^ _776541) ^ [_1703999, _1704001, _1704003] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1703999, tc_HOL_Obool)), hAPP(c_List_Oset(_1703999), _1704001)), hAPP(hAPP(c_Set_Oinsert(_1703999), _1704003), c_Orderings_Obot__class_Obot(tc_fun(_1703999, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1703999), hAPP(c_List_Ofilter(_1703999, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1703999), c_fNot), hAPP(hAPP(c_COMBC(_1703999, _1703999, tc_HOL_Obool), c_fequal), _1704003))), _1704001)))], (33669 ^ _776541) ^ [_1398460, _1398462, _1398464, _1398466] : [class_Groups_Ocomm__monoid__add(_1398460), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1398460), _1398462), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1398464)), hAPP(c_Nat_OSuc, _1398466))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1398460), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1398460, tc_Nat_Onat), _1398462), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1398464), _1398466)))], (39253 ^ _776541) ^ [_1534521, _1534523, _1534525, _1534527] : [_1534521 = c_Orderings_Obot__class_Obot(tc_fun(_1534523, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1534523, _1534525), _1534525, c_Product__Type_Osnd(_1534523, _1534525)), hAPP(hAPP(c_Product__Type_OSigma(_1534523, _1534525), _1534521), hAPP(c_COMBK(tc_fun(_1534525, tc_HOL_Obool), _1534523), _1534527))) = c_Orderings_Obot__class_Obot(tc_fun(_1534525, tc_HOL_Obool)))], (35525 ^ _776541) ^ [_1439352] : [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), _1439352))), -(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), _1439352)) = 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), _1439352))))], (3686 ^ _776541) ^ [_831821, _831823, _831825, _831827] : [-(c_List_Otranspose(_831827, _831823) = c_List_Otranspose(_831825, _831821)), _831827 = _831825, _831823 = _831821], (45263 ^ _776541) ^ [_1683008, _1683010] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1683008), _1683010) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1683008)), hAPP(c_Code__Numeral_Onat__of, _1683010))))], (46249 ^ _776541) ^ [_1706715, _1706717] : [class_Groups_Omonoid__add(_1706715), -(hAPP(c_List_Ofoldl(_1706715, _1706715, c_Groups_Oplus__class_Oplus(_1706715), c_Groups_Ozero__class_Ozero(_1706715)), _1706717) = c_List_Ofoldr(_1706715, _1706715, c_Groups_Oplus__class_Oplus(_1706715), _1706717, c_Groups_Ozero__class_Ozero(_1706715)))], (7440 ^ _776541) ^ [_899038, _899040, _899042, _899044] : [7441 ^ _776541 : [(7444 ^ _776541) ^ [] : [hBOOL(hAPP(_899042, _899040))], (7442 ^ _776541) ^ [] : [hBOOL(hAPP(_899038, _899040))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899044, tc_HOL_Obool)), _899042), _899038), _899040)))], (40721 ^ _776541) ^ [_1573088, _1573090, _1573092, _1573094] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573088, _1573088)), hAPP(hAPP(c_Product__Type_OPair(_1573088, _1573088), _1573090), _1573092)), c_Transitive__Closure_Otrancl(_1573088, _1573094))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573088, _1573088)), hAPP(hAPP(c_Product__Type_OPair(_1573088, _1573088), _1573090), _1573092)), c_Transitive__Closure_Ortrancl(_1573088, _1573094))))], (10361 ^ _776541) ^ [_954466, _954468, _954470] : [class_Lattices_Oboolean__algebra(_954466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954466), _954468), _954470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954466), hAPP(c_Groups_Ouminus__class_Ouminus(_954466), _954470)), hAPP(c_Groups_Ouminus__class_Ouminus(_954466), _954468))))], (47434 ^ _776541) ^ [_1730266, _1730268, _1730270, _1730272, _1730274] : [c_List_OdropWhile(_1730266, _1730268, _1730270) = hAPP(hAPP(c_List_Olist_OCons(_1730266), _1730272), _1730274), 47437 ^ _776541 : [(47440 ^ _776541) ^ [] : [hBOOL(hAPP(_1730268, _1730272))], (47438 ^ _776541) ^ [] : [-(_1730270 = hAPP(hAPP(c_List_Oappend(_1730266), c_List_OtakeWhile(_1730266, _1730268, _1730270)), hAPP(hAPP(c_List_Olist_OCons(_1730266), _1730272), _1730274)))]]], (40727 ^ _776541) ^ [_1573257, _1573259] : [-(c_Transitive__Closure_Ortrancl(_1573257, c_Transitive__Closure_Otrancl(_1573257, _1573259)) = c_Transitive__Closure_Ortrancl(_1573257, _1573259))], (44435 ^ _776541) ^ [_1665198, _1665200, _1665202] : [class_Orderings_Olinorder(_1665198), -(c_Big__Operators_Olinorder__class_OMin(_1665198, hAPP(c_List_Oset(_1665198), hAPP(hAPP(c_List_Olist_OCons(_1665198), _1665200), _1665202))) = hAPP(c_List_Ofoldl(_1665198, _1665198, c_Orderings_Oord__class_Omin(_1665198), _1665200), _1665202))], (8515 ^ _776541) ^ [_922803, _922805, _922807, _922809] : [class_Lattices_Osemilattice__sup(_922803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922803), _922805), _922807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922803), _922805), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922803), _922809), _922807))))], (30076 ^ _776541) ^ [_1316028, _1316030, _1316032, _1316034] : [class_Orderings_Olinorder(_1316028), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316028), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316028), _1316030), _1316032)), _1316034) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316028), _1316030), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316028), _1316032), _1316034)))], (6376 ^ _776541) ^ [_879410, _879412] : [_879412 = c_Orderings_Obot__class_Obot(tc_fun(_879410, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879410, tc_HOL_Obool)), _879412), c_Orderings_Obot__class_Obot(tc_fun(_879410, tc_HOL_Obool)))))], (42479 ^ _776541) ^ [_1620495, _1620497, _1620499, _1620501] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1620495), tc_List_Olist(_1620495))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1620495), tc_List_Olist(_1620495)), _1620497), _1620499)), c_List_Olistrel(_1620495, _1620501))), 42482 ^ _776541 : [(42485 ^ _776541) ^ [_1620831] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620495, _1620495)), _1620831), hAPP(c_List_Oset(tc_prod(_1620495, _1620495)), hAPP(hAPP(c_List_Ozip(_1620495, _1620495), _1620497), _1620499)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1620495, _1620495, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1620495, tc_fun(tc_prod(_1620495, _1620495), tc_HOL_Obool), tc_fun(_1620495, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1620495, tc_fun(tc_fun(tc_prod(_1620495, _1620495), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1620495, _1620495), tc_HOL_Obool), tc_fun(_1620495, tc_HOL_Obool)), _1620495), c_COMBC(_1620495, tc_fun(tc_prod(_1620495, _1620495), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1620495, tc_prod(_1620495, _1620495)), tc_fun(_1620495, tc_fun(tc_fun(tc_prod(_1620495, _1620495), tc_HOL_Obool), tc_HOL_Obool)), _1620495), hAPP(c_COMBB(tc_prod(_1620495, _1620495), tc_fun(tc_fun(tc_prod(_1620495, _1620495), tc_HOL_Obool), tc_HOL_Obool), _1620495), c_member(tc_prod(_1620495, _1620495)))), c_Product__Type_OPair(_1620495, _1620495)))), _1620501)), _1620831)))], (42483 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620495)), _1620497) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620495)), _1620499))]]], (16242 ^ _776541) ^ [_1069890, _1069892, _1069894] : [class_Rings_Ono__zero__divisors(_1069890), -(_1069892 = c_Groups_Ozero__class_Ozero(_1069890)), -(_1069894 = c_Groups_Ozero__class_Ozero(_1069890)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069890), _1069892), _1069894) = c_Groups_Ozero__class_Ozero(_1069890)], (48164 ^ _776541) ^ [_1746634, _1746636, _1746638] : [hBOOL(hAPP(hAPP(c_member(_1746634), _1746636), hAPP(c_List_Oset(_1746634), _1746638))), 48169 ^ _776541 : [(48172 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1746634), _1746636), hAPP(c_List_Oset(_1746634), 48168 ^ [_1746634, _1746636, _1746638])))], (48170 ^ _776541) ^ [] : [-(_1746638 = hAPP(hAPP(c_List_Oappend(_1746634), 48167 ^ [_1746634, _1746636, _1746638]), hAPP(hAPP(c_List_Olist_OCons(_1746634), _1746636), 48168 ^ [_1746634, _1746636, _1746638])))]]], (36725 ^ _776541) ^ [_1473260, _1473262, _1473264, _1473266] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1473260, tc_HOL_Obool)), _1473262), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473260), _1473264), _1473266))), 36729 ^ _776541 : [(36732 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473260), 36728 ^ [_1473260, _1473262, _1473264, _1473266]), _1473264)))], (36730 ^ _776541) ^ [] : [-(_1473262 = hAPP(c_Relation_OImage(_1473260, _1473260, _1473266), hAPP(hAPP(c_Set_Oinsert(_1473260), 36728 ^ [_1473260, _1473262, _1473264, _1473266]), c_Orderings_Obot__class_Obot(tc_fun(_1473260, tc_HOL_Obool)))))]]], (16875 ^ _776541) ^ [_1080182, _1080184, _1080186, _1080188] : [class_Groups_Oordered__comm__monoid__add(_1080182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080182), c_Groups_Ozero__class_Ozero(_1080182)), _1080184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080182), _1080186), _1080188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080182), _1080186), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080182), _1080184), _1080188))))], (26044 ^ _776541) ^ [_1247315, _1247317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247315), _1247317)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247317, _1247315) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247317), _1247315), _1247315))], (50592 ^ _776541) ^ [_1799191, _1799193, _1799195] : [-(c_Fun_Obij__betw(_1799191, _1799193, _1799195, c_Orderings_Otop__class_Otop(tc_fun(_1799191, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799193, tc_HOL_Obool)))), c_Fun_Oinj__on(_1799191, _1799193, _1799195, c_Orderings_Otop__class_Otop(tc_fun(_1799191, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1799191, _1799193, _1799195), c_Orderings_Otop__class_Otop(tc_fun(_1799191, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799193, tc_HOL_Obool))], (42821 ^ _776541) ^ [_1629681, _1629683, _1629685] : [hBOOL(hAPP(c_List_Odistinct(_1629681), _1629683)), -(hBOOL(hAPP(c_List_Odistinct(_1629681), hAPP(hAPP(c_List_Otake(_1629681), _1629685), _1629683))))], (38951 ^ _776541) ^ [_1526088, _1526090, _1526092] : [-(hAPP(c_Relation_ODomain(_1526088, _1526090), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1526088, _1526090), tc_HOL_Obool), _1526092)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1526088, _1526090), tc_HOL_Obool), tc_fun(_1526088, tc_HOL_Obool)), _1526092), c_Relation_ODomain(_1526088, _1526090)))], (10607 ^ _776541) ^ [_958934, _958936, _958938, _958940, _958942] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_958934, _958936, _958938, _958940, c_Orderings_Obot__class_Obot(tc_fun(_958934, tc_HOL_Obool))), _958942)), -(_958942 = _958940)], (4104 ^ _776541) ^ [_838658, _838660, _838662, _838664, _838666, _838668, _838670, _838672] : [-(c_New__DSequence_Opos__bind(_838672, _838668, _838664, _838660) = c_New__DSequence_Opos__bind(_838670, _838666, _838662, _838658)), _838672 = _838670, _838668 = _838666, _838664 = _838662, _838660 = _838658], (30392 ^ _776541) ^ [_1321801, _1321803, _1321805] : [class_Orderings_Olinorder(_1321801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321801), _1321803)), hBOOL(hAPP(hAPP(c_member(_1321801), _1321805), _1321803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321801), hAPP(c_Finite__Set_Ofold1(_1321801, c_Orderings_Oord__class_Omin(_1321801)), _1321803)), _1321805)))], (37844 ^ _776541) ^ [_1497879, _1497881, _1497883, _1497885, _1497887, _1497889] : [c_Fun_Oinj__on(_1497879, _1497881, _1497883, _1497885), hAPP(_1497883, _1497887) = _1497889, hBOOL(hAPP(hAPP(c_member(_1497879), _1497887), _1497885)), -(hAPP(c_Fun_Othe__inv__into(_1497879, _1497881, _1497885, _1497883), _1497889) = _1497887)], (8681 ^ _776541) ^ [_925718, _925720, _925722, _925724] : [class_Lattices_Osemilattice__inf(_925718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925718), _925720), _925722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925718), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925718), _925720), _925724)), _925722)))], (47283 ^ _776541) ^ [_1727137, _1727139, _1727141] : [hBOOL(hAPP(c_List_Odistinct(_1727137), _1727139)), -(hBOOL(hAPP(c_List_Odistinct(_1727137), c_List_OtakeWhile(_1727137, _1727141, _1727139))))], (15584 ^ _776541) ^ [_1058959, _1058961, _1058963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1058959), _1058961)), hBOOL(hAPP(hAPP(c_member(_1058959), _1058963), _1058961)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1058959), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058959, tc_HOL_Obool)), _1058961), hAPP(hAPP(c_Set_Oinsert(_1058959), _1058963), c_Orderings_Obot__class_Obot(tc_fun(_1058959, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1058959), _1058961))], (42359 ^ _776541) ^ [_1617246, _1617248, _1617250, _1617252] : [-(hAPP(hAPP(c_List_Otake(_1617246), _1617248), hAPP(hAPP(c_List_Otake(_1617246), _1617250), _1617252)) = hAPP(hAPP(c_List_Otake(_1617246), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1617248), _1617250)), _1617252))], (43924 ^ _776541) ^ [_1654306, _1654308] : [-(hAPP(hAPP(c_List_Odrop(_1654306), _1654308), c_List_Olist_ONil(_1654306)) = c_List_Olist_ONil(_1654306))], (22357 ^ _776541) ^ [] : [-(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))], (27633 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (47110 ^ _776541) ^ [_1723558, _1723560] : [-(_1723558 = c_List_Olist_ONil(_1723560)), -(c_List_Olast(_1723560, hAPP(c_List_Orev(_1723560), _1723558)) = hAPP(c_List_Ohd(_1723560), _1723558))], (32450 ^ _776541) ^ [_1360695, _1360697, _1360699, _1360701, _1360703] : [_1360695 = c_Orderings_Obot__class_Obot(tc_fun(_1360697, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360697, tc_fun(_1360699, tc_HOL_Obool)), _1360695), hAPP(hAPP(c_COMBC(_1360697, tc_fun(_1360699, tc_HOL_Obool), tc_fun(_1360699, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360699, tc_HOL_Obool), tc_fun(tc_fun(_1360699, tc_HOL_Obool), tc_fun(_1360699, tc_HOL_Obool)), _1360697), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360699, tc_HOL_Obool))), _1360701)), _1360703)) = c_Orderings_Obot__class_Obot(tc_fun(_1360699, tc_HOL_Obool)))], (23667 ^ _776541) ^ [_1205415, _1205417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205415), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23670 ^ _776541 : [(23677 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205417), _1205415)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23671 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205417), _1205415)), 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)), _1205417)))]]], (32502 ^ _776541) ^ [_1363254, _1363256, _1363258, _1363260, _1363262] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363254, tc_fun(_1363256, tc_HOL_Obool)), _1363258), hAPP(hAPP(c_COMBS(_1363254, tc_fun(_1363256, tc_HOL_Obool), tc_fun(_1363256, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363256, tc_HOL_Obool), tc_fun(tc_fun(_1363256, tc_HOL_Obool), tc_fun(_1363256, tc_HOL_Obool)), _1363254), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363256, tc_HOL_Obool))), _1363260)), _1363262)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363256, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363254, tc_fun(_1363256, tc_HOL_Obool)), _1363258), _1363260)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363254, tc_fun(_1363256, tc_HOL_Obool)), _1363258), _1363262)))], (38915 ^ _776541) ^ [_1524936, _1524938, _1524940, _1524942] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524936, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1524936, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524936, _1524938), _1524940)), hAPP(c_Relation_ODomain(_1524936, _1524938), _1524942))), hAPP(c_Relation_ODomain(_1524936, _1524938), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1524936, _1524938), tc_HOL_Obool)), _1524940), _1524942)))))], (40576 ^ _776541) ^ [_1568902, _1568904] : [c_Wellfounded_Owf(_1568902, _1568904), -(c_Wellfounded_Owf(_1568902, c_Transitive__Closure_Otrancl(_1568902, _1568904)))], (7928 ^ _776541) ^ [_910470, _910472, _910474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910470, tc_HOL_Obool)), _910472), _910474)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910470, tc_HOL_Obool)), _910474), _910472) = _910474)], (11260 ^ _776541) ^ [_972126, _972128, _972130, _972132] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_972126, _972128, _972130), _972132)), _972130 = c_Orderings_Obot__class_Obot(tc_fun(_972126, tc_HOL_Obool))], (44727 ^ _776541) ^ [_1670743] : [-(hAPP(c_List_Omap(_1670743, _1670743), c_Fun_Oid(_1670743)) = c_Fun_Oid(tc_List_Olist(_1670743)))], (37876 ^ _776541) ^ [_1498487, _1498489] : [-(c_Fun_Oinj__on(tc_fun(_1498487, _1498489), tc_fun(tc_prod(_1498487, _1498489), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1498487, _1498489), tc_HOL_Obool), tc_fun(tc_prod(_1498487, _1498489), tc_HOL_Obool), tc_fun(_1498487, _1498489)), c_Set_OCollect(tc_prod(_1498487, _1498489))), hAPP(hAPP(c_COMBB(tc_fun(_1498487, tc_fun(_1498489, tc_HOL_Obool)), tc_fun(tc_prod(_1498487, _1498489), tc_HOL_Obool), tc_fun(_1498487, _1498489)), c_Product__Type_Oprod_Oprod__case(_1498487, _1498489, tc_HOL_Obool)), hAPP(c_COMBB(_1498489, tc_fun(_1498489, tc_HOL_Obool), _1498487), hAPP(c_COMBC(_1498489, _1498489, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1498487, _1498489), tc_HOL_Obool))))], (25357 ^ _776541) ^ [_1235329] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235329))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32358 ^ _776541) ^ [_1358598, _1358600, _1358602, _1358604] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1358602), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358598, tc_fun(_1358602, tc_HOL_Obool)), _1358600), _1358604)))), 32359 ^ _776541 : [(32360 ^ _776541) ^ [_1358672] : [hBOOL(hAPP(hAPP(c_member(_1358598), _1358672), _1358600)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358602), hAPP(_1358604, _1358672)))]]], (25291 ^ _776541) ^ [_1234282, _1234284] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234282, _1234284) = 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), _1234282), _1234284) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30366 ^ _776541) ^ [_1321248, _1321250, _1321252, _1321254] : [class_Orderings_Olinorder(_1321248), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321248, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1321248, _1321250, _1321252)), hAPP(c_SetInterval_Oord__class_OatMost(_1321248), _1321254)) = c_SetInterval_Oord__class_OatLeastAtMost(_1321248, _1321250, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321248), _1321252), _1321254)))], (11469 ^ _776541) ^ [_976873, _976875, _976877] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976873), _976875)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976873), hAPP(hAPP(c_Set_Oinsert(_976873), _976877), _976875))))], (41727 ^ _776541) ^ [_1598180, _1598182] : [-(c_List_Olenlex(_1598180, _1598182) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1598180)), tc_List_Olist(_1598180)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1598180), c_Wellfounded_Oless__than, c_List_Olex(_1598180, _1598182))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1598180), tc_List_Olist(_1598180), tc_prod(tc_Nat_Onat, tc_List_Olist(_1598180))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1598180), tc_prod(tc_Nat_Onat, tc_List_Olist(_1598180))), tc_List_Olist(_1598180)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1598180))), c_Nat_Osize__class_Osize(tc_List_Olist(_1598180)))), c_COMBI(tc_List_Olist(_1598180)))))], (32015 ^ _776541) ^ [_1351813, _1351815, _1351817] : [class_Orderings_Olinorder(_1351813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351813), _1351815)), -(_1351815 = c_Orderings_Obot__class_Obot(tc_fun(_1351813, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1351813, c_Orderings_Oord__class_Omax(_1351813), hAPP(hAPP(c_Set_Oinsert(_1351813), _1351817), _1351815)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351813), _1351817), c_Big__Operators_Olattice_OSup__fin(_1351813, c_Orderings_Oord__class_Omax(_1351813), _1351815)))], (10707 ^ _776541) ^ [_961037, _961039] : [class_Orderings_Olinorder(_961037), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961037, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_961037), _961039)) = hAPP(c_SetInterval_Oord__class_OlessThan(_961037), _961039))], (10829 ^ _776541) ^ [_963229, _963231, _963233] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963229, tc_HOL_Obool)), _963231), _963233) = c_Orderings_Obot__class_Obot(tc_fun(_963229, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963229, tc_HOL_Obool)), _963231), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_963229, tc_HOL_Obool)), _963233))))], (7956 ^ _776541) ^ [_911066, _911068] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911066, tc_HOL_Obool)), _911068), c_Orderings_Otop__class_Otop(tc_fun(_911066, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_911066, tc_HOL_Obool)))], (26140 ^ _776541) ^ [_1248894, _1248896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1248894)), hAPP(c_Int_Onat, _1248896))), 26143 ^ _776541 : [(26146 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248894), _1248896)))], (26144 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248896)))]]], (45086 ^ _776541) ^ [_1679406, _1679408, _1679410] : [-(hAPP(hAPP(c_List_Ozip(_1679406, _1679408), hAPP(hAPP(c_List_Omap(tc_prod(_1679406, _1679408), _1679406), c_Product__Type_Ofst(_1679406, _1679408)), _1679410)), hAPP(hAPP(c_List_Omap(tc_prod(_1679406, _1679408), _1679408), c_Product__Type_Osnd(_1679406, _1679408)), _1679410)) = _1679410)], (38181 ^ _776541) ^ [_1507744, _1507746, _1507748] : [c_Wellfounded_Owf(_1507744, _1507746), -(c_Wellfounded_Owf(_1507744, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1507744, _1507744), tc_HOL_Obool)), _1507746), _1507748)))], (16444 ^ _776541) ^ [_1072862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072862), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29059 ^ _776541) ^ [_1297449] : [-(c_Int_Opred(c_Int_OBit0(_1297449)) = c_Int_OBit1(c_Int_Opred(_1297449)))], (20975 ^ _776541) ^ [_1155329, _1155331, _1155333, _1155335] : [class_Fields_Olinordered__field(_1155329), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155329), c_Groups_Ozero__class_Ozero(_1155329)), _1155331)), 20982 ^ _776541 : [(20989 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155329), _1155333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155329), _1155335), _1155331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155329), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155329), _1155333), _1155331)), _1155335)))], (20983 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155329), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155329), _1155333), _1155331)), _1155335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155329), _1155333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155329), _1155335), _1155331))))]]], (32528 ^ _776541) ^ [_1364432, _1364434, _1364436, _1364438, _1364440] : [hBOOL(hAPP(hAPP(c_member(_1364432), _1364434), _1364436)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364438, tc_HOL_Obool)), hAPP(_1364440, _1364434)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364432, tc_fun(_1364438, tc_HOL_Obool)), _1364436), _1364440)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364432, tc_fun(_1364438, tc_HOL_Obool)), _1364436), _1364440))], (32674 ^ _776541) ^ [_1369954, _1369956] : [-(hAPP(c_Finite__Set_Ocard(_1369954), _1369956) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369954, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1369954), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1369956))], (32972 ^ _776541) ^ [_1378143, _1378145, _1378147, _1378149, _1378151] : [class_Groups_Ominus(_1378143), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378145, _1378143)), _1378147), _1378149), _1378151) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1378143), hAPP(_1378147, _1378151)), hAPP(_1378149, _1378151)))], (33060 ^ _776541) ^ [_1380515, _1380517, _1380519, _1380521, _1380523, _1380525] : [-(hAPP(c_Set_Oimage(_1380515, _1380517, _1380519), hAPP(c_Set_Oimage(_1380521, _1380515, _1380523), _1380525)) = hAPP(c_Set_Oimage(_1380521, _1380517, hAPP(hAPP(c_COMBB(_1380515, _1380517, _1380521), _1380519), _1380523)), _1380525))], (2726 ^ _776541) ^ [_816847, _816849, _816851, _816853, _816855, _816857] : [-(c_Partial__Function_Oflat__lub(_816857, _816853, _816849) = c_Partial__Function_Oflat__lub(_816855, _816851, _816847)), _816857 = _816855, _816853 = _816851, _816849 = _816847], (37598 ^ _776541) ^ [_1492278, _1492280, _1492282, _1492284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492278), _1492280)), hAPP(c_Finite__Set_Ocard(_1492282), hAPP(c_Set_Oimage(_1492278, _1492282, _1492284), _1492280)) = hAPP(c_Finite__Set_Ocard(_1492278), _1492280), -(c_Fun_Oinj__on(_1492278, _1492282, _1492284, _1492280))], (33054 ^ _776541) ^ [_1380277, _1380279, _1380281, _1380283, _1380285, _1380287] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380277, tc_fun(_1380279, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380281, _1380277, _1380283), _1380285)), _1380287) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380281, tc_fun(_1380279, tc_HOL_Obool)), _1380285), hAPP(hAPP(c_COMBB(_1380277, tc_fun(_1380279, tc_HOL_Obool), _1380281), _1380287), _1380283)))], (37536 ^ _776541) ^ [_1490940, _1490942] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490940), c_Orderings_Otop__class_Otop(tc_fun(_1490940, tc_HOL_Obool)))), c_Fun_Oinj__on(_1490940, _1490940, _1490942, c_Orderings_Otop__class_Otop(tc_fun(_1490940, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1490940, _1490940, _1490942), c_Orderings_Otop__class_Otop(tc_fun(_1490940, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1490940, tc_HOL_Obool)))], (18105 ^ _776541) ^ [_1102085, _1102087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102085), _1102087)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102085), _1102087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26967 ^ _776541) ^ [_1262306] : [class_Rings_Oring__1(_1262306), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262306), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1262306))], (14598 ^ _776541) ^ [_1039702, _1039704, _1039706] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039702), _1039704)), _1039706) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039704), _1039706)))], (31333 ^ _776541) ^ [_1338996, _1338998] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1338996)), hAPP(c_Nat_OSuc, _1338998)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1338996), _1338998)))], (19701 ^ _776541) ^ [_1132316, _1132318] : [class_Rings_Odivision__ring(_1132316), -(_1132318 = c_Groups_Ozero__class_Ozero(_1132316)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132316), _1132318), _1132318) = c_Groups_Oone__class_Oone(_1132316))], (14206 ^ _776541) ^ [_1032051, _1032053, _1032055, _1032057] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032051), _1032053)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032055), _1032053)), _1032057)) = 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), _1032051), _1032055)), _1032053)), _1032057))], (5310 ^ _776541) ^ [_857595, _857597, _857599, _857601, _857603, _857605] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_857605, _857601, _857597) = c_Lazy__Sequence_Olazy__sequence_OInsert(_857603, _857599, _857595)), _857605 = _857603, _857601 = _857599, _857597 = _857595], (43466 ^ _776541) ^ [_1643296, _1643298, _1643300, _1643302] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643296)), hAPP(hAPP(c_List_Oappend(_1643296), _1643298), _1643300)), c_List_Olists(_1643296, _1643302)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643296)), _1643298), c_List_Olists(_1643296, _1643302))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643296)), _1643300), c_List_Olists(_1643296, _1643302)))], (21939 ^ _776541) ^ [_1174164, _1174166, _1174168, _1174170] : [class_Fields_Olinordered__field__inverse__zero(_1174164), class_Int_Onumber(_1174164), 21946 ^ _776541 : [(21947 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174164), _1174168), _1174170))), 21950 ^ _776541 : [(21957 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), c_Groups_Ozero__class_Ozero(_1174164)), _1174170))), 21960 ^ _776541 : [(21967 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), _1174170), c_Groups_Ozero__class_Ozero(_1174164)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), c_Groups_Ozero__class_Ozero(_1174164))))], (21961 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), _1174170), c_Groups_Ozero__class_Ozero(_1174164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), _1174168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), _1174170))))]]], (21951 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), c_Groups_Ozero__class_Ozero(_1174164)), _1174170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), _1174170)), _1174168)))]]], (21973 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174164), _1174168), _1174170)))), 21976 ^ _776541 : [(21979 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), _1174170)), _1174168))], (21977 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), c_Groups_Ozero__class_Ozero(_1174164)), _1174170)))]], 21980 ^ _776541 : [(21983 ^ _776541) ^ [] : [21984 ^ _776541 : [(21987 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), _1174168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), _1174170)))], (21985 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), _1174170), c_Groups_Ozero__class_Ozero(_1174164))))]], 21988 ^ _776541 : [(21991 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174164), hAPP(c_Int_Onumber__class_Onumber__of(_1174164), _1174166)), c_Groups_Ozero__class_Ozero(_1174164)))], (21989 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), _1174170), c_Groups_Ozero__class_Ozero(_1174164)))]]], (21981 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174164), c_Groups_Ozero__class_Ozero(_1174164)), _1174170))]]]]], (2280 ^ _776541) ^ [_809750, _809752, _809754, _809756] : [-(c_Orderings_Oord_Omin(_809756, _809752) = c_Orderings_Oord_Omin(_809754, _809750)), _809756 = _809754, _809752 = _809750], (43228 ^ _776541) ^ [_1637779, _1637781, _1637783] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1637779)), -(c_List_Osublist(_1637781, hAPP(hAPP(c_List_Olist_OCons(_1637781), _1637783), c_List_Olist_ONil(_1637781)), _1637779) = hAPP(hAPP(c_List_Olist_OCons(_1637781), _1637783), c_List_Olist_ONil(_1637781)))], (9522 ^ _776541) ^ [_939949, _939951, _939953] : [class_Orderings_Olinorder(_939949), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939949), _939951), _939953))), 9529 ^ _776541 : [(9536 ^ _776541) ^ [] : [_939951 = _939953, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939949), _939951), _939953)))], (9530 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939949), _939951), _939953)), -(_939951 = _939953)]]], (25353 ^ _776541) ^ [_1235250, _1235252] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235250, _1235252) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235250), _1235252)), _1235252)))], (8173 ^ _776541) ^ [_916043, _916045, _916047] : [class_Orderings_Oorder(_916043), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916043, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_916043), _916045)), c_SetInterval_Oord__class_OgreaterThanAtMost(_916043, _916045, _916047)) = c_Orderings_Obot__class_Obot(tc_fun(_916043, tc_HOL_Obool)))], (17209 ^ _776541) ^ [_1086341, _1086343] : [class_Rings_Olinordered__ring(_1086341), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086341), c_Groups_Ozero__class_Ozero(_1086341)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086341), _1086343), _1086343))))], (24583 ^ _776541) ^ [_1221161, _1221163, _1221165, _1221167, _1221169] : [class_Groups_Oordered__ab__semigroup__add(_1221161), class_Rings_Osemiring__1(_1221161), 24593 ^ _776541 : [(24596 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221161), hAPP(_1221167, 24592 ^ [_1221161, _1221163, _1221165, _1221167, _1221169])), _1221169))], (24594 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1221163), 24592 ^ [_1221161, _1221163, _1221165, _1221167, _1221169]), _1221165)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221161), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221163, _1221161), _1221167), _1221165)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221161), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1221161), hAPP(c_Finite__Set_Ocard(_1221163), _1221165))), _1221169))))], (2500 ^ _776541) ^ [_813248, _813250, _813252, _813254, _813256, _813258, _813260, _813262, _813264, _813266] : [-(c_Product__Type_Oprod_Oprod__size(_813266, _813262, _813258, _813254, _813250) = c_Product__Type_Oprod_Oprod__size(_813264, _813260, _813256, _813252, _813248)), _813266 = _813264, _813262 = _813260, _813258 = _813256, _813254 = _813252, _813250 = _813248], (35450 ^ _776541) ^ [_1437600, _1437602] : [-(c_Divides_Odivmod__int__rel(_1437600, _1437602) = 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, _1437600))), 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), _1437602)))))), 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)), _1437602))), 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)), _1437602))))), 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)), _1437602)))), 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), _1437602))), 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))))))))], (42321 ^ _776541) ^ [_1616425, _1616427, _1616429, _1616431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1616425), _1616427)), -(hAPP(hAPP(c_List_Onth(_1616429), hAPP(hAPP(c_List_Otake(_1616429), _1616427), _1616431)), _1616425) = hAPP(hAPP(c_List_Onth(_1616429), _1616431), _1616425))], (41236 ^ _776541) ^ [_1585718, _1585720, _1585722] : [c_Relation_Ototal__on(_1585718, _1585720, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1585718, _1585718), tc_HOL_Obool)), _1585722), c_Relation_OId(_1585718))), -(c_Relation_Ototal__on(_1585718, _1585720, _1585722))], (26553 ^ _776541) ^ [_1255820, _1255822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1255820)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1255820), _1255822)), _1255820) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (44274 ^ _776541) ^ [_1661852, _1661854, _1661856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1661852), _1661854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1661852), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1661854), _1661856))))], (41118 ^ _776541) ^ [_1582885, _1582887] : [c_Wellfounded_Oacyclic(_1582885, hAPP(c_Relation_Oconverse(_1582885, _1582885), _1582887)), -(c_Wellfounded_Oacyclic(_1582885, _1582887))], (33310 ^ _776541) ^ [_1387544, _1387546, _1387548, _1387550, _1387552] : [class_Rings_Osemiring__0(_1387544), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387544), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387546, _1387544), _1387548), _1387550)), _1387552) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387546, _1387544), hAPP(hAPP(c_COMBC(_1387546, _1387544, _1387544), hAPP(hAPP(c_COMBB(_1387544, tc_fun(_1387544, _1387544), _1387546), c_Groups_Otimes__class_Otimes(_1387544)), _1387548)), _1387552)), _1387550))], (7051 ^ _776541) ^ [_891279, _891281, _891283, _891285, _891287] : [class_Complete__Lattice_Ocomplete__lattice(_891279), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891281, tc_HOL_Obool)), _891283), _891285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891279), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891281, _891279), _891283), _891287)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891281, _891279), _891285), _891287))))], (32648 ^ _776541) ^ [_1369300, _1369302, _1369304, _1369306] : [hBOOL(hAPP(hAPP(c_member(_1369300), _1369302), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369300, tc_HOL_Obool)), _1369304), hAPP(c_Set_OCollect(_1369300), _1369306)))), 32651 ^ _776541 : [(32654 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1369306, _1369302)))], (32652 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1369300), _1369302), _1369304)))]]], (11196 ^ _776541) ^ [_970650, _970652, _970654, _970656, _970658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970650, tc_HOL_Obool)), hAPP(c_Set_Oimage(_970652, _970650, _970654), _970656)), _970658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_970650, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_970652, tc_HOL_Obool), tc_fun(_970650, tc_HOL_Obool), c_Set_Oimage(_970652, _970650, _970654)), hAPP(c_Set_OPow(_970652), _970656))), hAPP(c_Set_OPow(_970650), _970658))))], (35953 ^ _776541) ^ [_1450625, _1450627, _1450629] : [class_Lattices_Odistrib__lattice(_1450625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450625), _1450627)), -(_1450627 = c_Orderings_Obot__class_Obot(tc_fun(_1450625, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1450625), _1450629), c_Big__Operators_Olattice__class_OInf__fin(_1450625, _1450627)) = c_Big__Operators_Olattice__class_OInf__fin(_1450625, hAPP(c_Set_OCollect(_1450625), hAPP(hAPP(c_COMBB(tc_fun(_1450625, tc_HOL_Obool), tc_HOL_Obool, _1450625), c_HOL_OEx(_1450625)), hAPP(hAPP(c_COMBC(_1450625, tc_fun(_1450625, tc_HOL_Obool), tc_fun(_1450625, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450625, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1450625, tc_HOL_Obool), tc_fun(_1450625, tc_HOL_Obool)), _1450625), c_COMBS(_1450625, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450625, tc_HOL_Obool), tc_fun(_1450625, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1450625), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1450625), c_fconj)), hAPP(hAPP(c_COMBC(_1450625, tc_fun(_1450625, _1450625), tc_fun(_1450625, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450625, tc_HOL_Obool), tc_fun(tc_fun(_1450625, _1450625), tc_fun(_1450625, tc_HOL_Obool)), _1450625), c_COMBB(_1450625, tc_HOL_Obool, _1450625)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1450625), _1450629))))), hAPP(hAPP(c_COMBC(_1450625, tc_fun(_1450625, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450625)), _1450627))))))], (14923 ^ _776541) ^ [_1045736, _1045738, _1045740] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045736), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045738), _1045740)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045736), _1045738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045736), _1045740)))], (49107 ^ _776541) ^ [_1766978, _1766980, _1766982, _1766984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1766978), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1766980, _1766982, _1766978, _1766984) = 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(_1766980)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1766980)))], (8363 ^ _776541) ^ [_919890, _919892, _919894, _919896] : [class_Lattices_Olattice(_919890), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919890), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919890), _919892), _919894)), _919896) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919890), _919892), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919890), _919894), _919896)))], (32029 ^ _776541) ^ [_1352033, _1352035, _1352037] : [class_Orderings_Olinorder(_1352033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352033), _1352035)), -(_1352037 = c_Orderings_Obot__class_Obot(tc_fun(_1352033, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1352033, tc_HOL_Obool)), _1352037), _1352035)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352033), c_Big__Operators_Olattice_OSup__fin(_1352033, c_Orderings_Oord__class_Omax(_1352033), _1352037)), c_Big__Operators_Olattice_OSup__fin(_1352033, c_Orderings_Oord__class_Omax(_1352033), _1352035)) = c_Big__Operators_Olattice_OSup__fin(_1352033, c_Orderings_Oord__class_Omax(_1352033), _1352035))], (42551 ^ _776541) ^ [_1623477, _1623479, _1623481, _1623483, _1623485, _1623487] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623477, _1623479)), hAPP(hAPP(c_Product__Type_OPair(_1623477, _1623479), _1623481), _1623483)), hAPP(c_List_Oset(tc_prod(_1623477, _1623479)), hAPP(hAPP(c_List_Ozip(_1623477, _1623479), _1623485), _1623487)))), -(hBOOL(hAPP(hAPP(c_member(_1623477), _1623481), hAPP(c_List_Oset(_1623477), _1623485))))], (38600 ^ _776541) ^ [_1517927, _1517929, _1517931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517927, tc_HOL_Obool)), _1517929), hAPP(hAPP(c_Set_Oinsert(_1517927), _1517931), c_Orderings_Obot__class_Obot(tc_fun(_1517927, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1517927, _1517931, _1517929) = c_HOL_OThe(_1517927, hAPP(hAPP(c_COMBC(_1517927, tc_fun(_1517927, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517927)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1517927, tc_HOL_Obool)), _1517929), hAPP(hAPP(c_Set_Oinsert(_1517927), _1517931), c_Orderings_Obot__class_Obot(tc_fun(_1517927, tc_HOL_Obool)))))))], (10301 ^ _776541) ^ [_953531, _953533, _953535] : [class_Groups_Ogroup__add(_953531), 10304 ^ _776541 : [(10311 ^ _776541) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_953531), _953535) = _953533, -(hAPP(c_Groups_Ouminus__class_Ouminus(_953531), _953533) = _953535)], (10305 ^ _776541) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_953531), _953533) = _953535, -(hAPP(c_Groups_Ouminus__class_Ouminus(_953531), _953535) = _953533)]]], (46207 ^ _776541) ^ [_1705426, _1705428] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1705426)), c_List_Otranspose__rel(_1705426)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1705426)), c_List_Olist_ONil(_1705426)), _1705428))), -(c_List_Otranspose(_1705426, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1705426)), c_List_Olist_ONil(_1705426)), _1705428)) = c_List_Otranspose(_1705426, _1705428))], (25893 ^ _776541) ^ [_1244927, _1244929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244929)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244927, _1244929)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1244927), hAPP(c_Int_Onat, _1244929)))], (24295 ^ _776541) ^ [_1215934, _1215936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215934)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215936))))), _1215934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1215936 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7698 ^ _776541) ^ [_905098, _905100, _905102, _905104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905098, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905098, tc_HOL_Obool)), _905100), _905102)), _905104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905098, tc_HOL_Obool)), _905100), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905098, tc_HOL_Obool)), _905102), _905104))))], (24577 ^ _776541) ^ [_1221106, _1221108] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221106))), -(c_SMT_Oz3div(_1221108, _1221106) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221108), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1221106))))], (47615 ^ _776541) ^ [_1734078, _1734080, _1734082, _1734084, _1734086] : [-(c_List_Omaps(_1734078, _1734080, _1734082, hAPP(hAPP(c_List_Olist_OCons(_1734078), _1734084), _1734086)) = hAPP(hAPP(c_List_Oappend(_1734080), hAPP(_1734082, _1734084)), c_List_Omaps(_1734078, _1734080, _1734082, _1734086)))], (48336 ^ _776541) ^ [_1750044, _1750046, _1750048, _1750050] : [c_List_Olist__ex1(_1750044, _1750046, hAPP(hAPP(c_List_Olist_OCons(_1750044), _1750048), _1750050)), 48339 ^ _776541 : [(48346 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1750046, _1750048))), -(c_List_Olist__ex1(_1750044, _1750046, _1750050))], (48340 ^ _776541) ^ [] : [hBOOL(hAPP(_1750046, _1750048)), -(c_List_Olist__all(_1750044, hAPP(hAPP(c_COMBS(_1750044, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1750044), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750044), c_fNot), _1750046))), hAPP(c_fequal, _1750048)), _1750050))]]], (32468 ^ _776541) ^ [_1361216, _1361218, _1361220, _1361222, _1361224] : [-(_1361216 = c_Orderings_Obot__class_Obot(tc_fun(_1361218, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361218, tc_fun(_1361220, tc_HOL_Obool)), _1361216), hAPP(hAPP(c_COMBB(tc_fun(_1361220, tc_HOL_Obool), tc_fun(_1361220, tc_HOL_Obool), _1361218), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361220, tc_HOL_Obool)), _1361222)), _1361224)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361220, tc_HOL_Obool)), _1361222), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361218, tc_fun(_1361220, tc_HOL_Obool)), _1361216), _1361224)))], (23715 ^ _776541) ^ [_1206080] : [-(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), _1206080))))], (46538 ^ _776541) ^ [_1712309, _1712311, _1712313] : [class_Orderings_Olinorder(_1712309), 46541 ^ _776541 : [(46548 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1712309, _1712313), -(c_List_Olinorder__class_Osorted(_1712309, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712309, _1712309, c_COMBI(_1712309)), _1712311), _1712313)))], (46542 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1712309, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712309, _1712309, c_COMBI(_1712309)), _1712311), _1712313)), -(c_List_Olinorder__class_Osorted(_1712309, _1712313))]]], (5954 ^ _776541) ^ [_871293, _871295, _871297, _871299, _871301, _871303, _871305] : [c_Typedef_Otype__definition(_871293, _871295, _871297, _871299, _871301), 5960 ^ _776541 : [(5963 ^ _776541) ^ [] : [hBOOL(hAPP(_871303, hAPP(_871299, 5959 ^ [_871293, _871295, _871297, _871299, _871301, _871303, _871305])))], (5961 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_871295), 5959 ^ [_871293, _871295, _871297, _871299, _871301, _871303, _871305]), _871301)))]], -(hBOOL(hAPP(_871303, _871305)))], (37939 ^ _776541) ^ [_1500810, _1500812, _1500814, _1500816, _1500818, _1500820, _1500822] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500810, _1500812, _1500814), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500816, tc_fun(tc_prod(_1500810, _1500812), tc_HOL_Obool)), _1500818), _1500820)), _1500822) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500816, tc_fun(tc_prod(_1500810, _1500814), tc_HOL_Obool)), _1500818), hAPP(hAPP(c_COMBC(_1500816, tc_fun(tc_prod(_1500812, _1500814), tc_HOL_Obool), tc_fun(tc_prod(_1500810, _1500814), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1500810, _1500812), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1500812, _1500814), tc_HOL_Obool), tc_fun(tc_prod(_1500810, _1500814), tc_HOL_Obool)), _1500816), c_Relation_Orel__comp(_1500810, _1500812, _1500814)), _1500820)), _1500822)))], (23809 ^ _776541) ^ [_1207791, _1207793] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207791)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207793)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207791), _1207793)))], (3848 ^ _776541) ^ [_834336, _834338] : [_834338 = _834336, -(c_List_Odistinct(_834338) = c_List_Odistinct(_834336))], (52289 ^ _776541) ^ [_1829061, _1829063] : [-(class_Enum_Oenum(tc_sum(_1829061, _1829063))), class_Enum_Oenum(_1829061), class_Enum_Oenum(_1829063)], (26058 ^ _776541) ^ [_1247588, _1247590] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247588, _1247590) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247588), _1247590)), _1247590)))], (17359 ^ _776541) ^ [_1089124, _1089126, _1089128] : [class_Rings_Olinordered__ring__strict(_1089124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089124), _1089126), c_Groups_Ozero__class_Ozero(_1089124))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089124), _1089128), c_Groups_Ozero__class_Ozero(_1089124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089124), c_Groups_Ozero__class_Ozero(_1089124)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089124), _1089126), _1089128))))], (39121 ^ _776541) ^ [_1530841, _1530843, _1530845, _1530847] : [-(hAPP(c_Set_Oimage(tc_prod(_1530841, _1530843), tc_prod(_1530843, _1530841), hAPP(c_Product__Type_Oprod_Oprod__case(_1530841, _1530843, tc_prod(_1530843, _1530841)), hAPP(c_COMBC(_1530843, _1530841, tc_prod(_1530843, _1530841)), c_Product__Type_OPair(_1530843, _1530841)))), hAPP(hAPP(c_Product__Type_OSigma(_1530841, _1530843), _1530845), hAPP(c_COMBK(tc_fun(_1530843, tc_HOL_Obool), _1530841), _1530847))) = hAPP(hAPP(c_Product__Type_OSigma(_1530843, _1530841), _1530847), hAPP(c_COMBK(tc_fun(_1530841, tc_HOL_Obool), _1530843), _1530845)))], (11872 ^ _776541) ^ [_984935, _984937, _984939] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_984935), _984937)), hBOOL(hAPP(_984939, _984937)), 11883 ^ _776541 : [(11886 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_984935), 11881 ^ [_984935, _984937, _984939]), 11882 ^ [_984935, _984937, _984939])))], (11888 ^ _776541) ^ [] : [-(hBOOL(hAPP(_984939, 11882 ^ [_984935, _984937, _984939])))], (11890 ^ _776541) ^ [] : [hBOOL(hAPP(_984939, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984935, tc_HOL_Obool)), 11882 ^ [_984935, _984937, _984939]), hAPP(hAPP(c_Set_Oinsert(_984935), 11881 ^ [_984935, _984937, _984939]), c_Orderings_Obot__class_Obot(tc_fun(_984935, tc_HOL_Obool))))))], (11884 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_984935), 11882 ^ [_984935, _984937, _984939])))]], -(hBOOL(hAPP(_984939, c_Orderings_Obot__class_Obot(tc_fun(_984935, tc_HOL_Obool)))))], (38786 ^ _776541) ^ [_1522134, _1522136, _1522138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522134, _1522136)), _1522138)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522134), hAPP(c_Relation_ODomain(_1522134, _1522136), _1522138))))], (47132 ^ _776541) ^ [_1723962, _1723964, _1723966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723962), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723964)), _1723966))), -(hAPP(hAPP(c_List_Onth(_1723964), hAPP(c_List_Orev(_1723964), _1723966)), _1723962) = hAPP(hAPP(c_List_Onth(_1723964), _1723966), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723964)), _1723966)), hAPP(c_Nat_OSuc, _1723962))))], (5516 ^ _776541) ^ [_860826, _860828] : [_860828 = _860826, -(c_Divides_Odiv__class_Odiv(_860828) = c_Divides_Odiv__class_Odiv(_860826))], (24704 ^ _776541) ^ [_1223506, _1223508] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223506) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223508), -(_1223506 = _1223508)], (24844 ^ _776541) ^ [_1226112, _1226114, _1226116, _1226118] : [class_Divides_Osemiring__div(_1226112), -(c_Divides_Odiv__class_Omod(_1226112, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226112), _1226114), _1226116), _1226118) = c_Divides_Odiv__class_Omod(_1226112, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226112), c_Divides_Odiv__class_Omod(_1226112, _1226114, _1226118)), c_Divides_Odiv__class_Omod(_1226112, _1226116, _1226118)), _1226118))], (25046 ^ _776541) ^ [_1230030, _1230032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230030), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230030), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230032, _1230030))))], (51307 ^ _776541) ^ [_1815227, _1815229, _1815231, _1815233] : [class_Rings_Oidom(_1815227), 51310 ^ _776541 : [(51311 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815227), _1815229), _1815231)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815227), _1815233), _1815231))), -(_1815231 = c_Groups_Ozero__class_Ozero(_1815227)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815227), _1815229), _1815233)))], (51321 ^ _776541) ^ [] : [51322 ^ _776541 : [(51325 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815227), _1815229), _1815233))], (51323 ^ _776541) ^ [] : [_1815231 = c_Groups_Ozero__class_Ozero(_1815227)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815227), _1815229), _1815231)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815227), _1815233), _1815231))))]]], (18830 ^ _776541) ^ [_1115756, _1115758, _1115760, _1115762] : [class_Groups_Ocomm__monoid__mult(_1115756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115758), _1115760)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1115758, _1115756), _1115762), _1115760) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1115756, _1115758, c_Groups_Otimes__class_Otimes(_1115756)), _1115762), c_Groups_Oone__class_Oone(_1115756)), _1115760))], (39173 ^ _776541) ^ [_1532485, _1532487, _1532489, _1532491, _1532493, _1532495] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532485, _1532487)), hAPP(hAPP(c_Product__Type_OPair(_1532485, _1532487), _1532489), _1532491)), hAPP(hAPP(c_Product__Type_OSigma(_1532485, _1532487), _1532493), _1532495))), -(hBOOL(hAPP(hAPP(c_member(_1532485), _1532489), _1532493)))], (29897 ^ _776541) ^ [_1312583, _1312585, _1312587] : [class_Divides_Osemiring__div(_1312583), -(_1312585 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312583), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1312583), _1312585), _1312587)), _1312587)), c_Divides_Odiv__class_Omod(_1312583, _1312585, _1312587)))], (41130 ^ _776541) ^ [_1583079, _1583081, _1583083] : [c_Relation_Orefl__on(_1583079, _1583081, hAPP(c_Relation_Oconverse(_1583079, _1583079), _1583083)), -(c_Relation_Orefl__on(_1583079, _1583081, _1583083))], (49143 ^ _776541) ^ [_1768224, _1768226, _1768228, _1768230, _1768232] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768224), tc_List_Olist(_1768224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768224), tc_List_Olist(_1768224)), _1768226), _1768228)), c_List_Olexord(_1768224, _1768230))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768224), tc_List_Olist(_1768224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768224), tc_List_Olist(_1768224)), _1768228), _1768232)), c_List_Olexord(_1768224, _1768230))), c_Relation_Otrans(_1768224, _1768230), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768224), tc_List_Olist(_1768224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768224), tc_List_Olist(_1768224)), _1768226), _1768232)), c_List_Olexord(_1768224, _1768230))))], (35668 ^ _776541) ^ [_1442360, _1442362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1442360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1442362), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1442360), _1442362) = 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), _1442360), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1442362)))))], (34001 ^ _776541) ^ [_1407750, _1407752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1407750), _1407752)), -(hAPP(c_Finite__Set_Ocard(_1407750), _1407752) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1407750, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1407750), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407752))], (38750 ^ _776541) ^ [_1521249, _1521251, _1521253, _1521255] : [-(hAPP(c_Set_Ovimage(_1521249, _1521251, _1521253), hAPP(c_Set_OCollect(_1521251), _1521255)) = hAPP(c_Set_OCollect(_1521249), hAPP(hAPP(c_COMBB(_1521251, tc_HOL_Obool, _1521249), _1521255), _1521253)))], (29303 ^ _776541) ^ [_1301648] : [-(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)))), _1301648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301648), _1301648))], (38848 ^ _776541) ^ [_1523575, _1523577, _1523579, _1523581] : [hBOOL(hAPP(hAPP(c_member(_1523575), _1523577), _1523579)), -(hAPP(c_Set_Ovimage(_1523581, _1523575, hAPP(c_COMBK(_1523575, _1523581), _1523577)), _1523579) = c_Orderings_Otop__class_Otop(tc_fun(_1523581, tc_HOL_Obool)))], (5993 ^ _776541) ^ [] : [c_HOL_Oinduct__false], (48923 ^ _776541) ^ [_1762848, _1762850, _1762852] : [c_List_Olist__ex1(_1762848, _1762850, _1762852), 48927 ^ _776541 : [(48932 ^ _776541) ^ [_1763094] : [-(_1763094 = 48926 ^ [_1762848, _1762850, _1762852]), hBOOL(hAPP(hAPP(c_member(_1762848), _1763094), hAPP(c_List_Oset(_1762848), _1762852))), hBOOL(hAPP(_1762850, _1763094))], (48930 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1762850, 48926 ^ [_1762848, _1762850, _1762852])))], (48928 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762848), 48926 ^ [_1762848, _1762850, _1762852]), hAPP(c_List_Oset(_1762848), _1762852))))]]], (43036 ^ _776541) ^ [_1634262, _1634264, _1634266] : [hAPP(hAPP(c_List_Olist_OCons(_1634262), _1634264), _1634266) = c_List_Olist_ONil(_1634262)], (5807 ^ _776541) ^ [_868487, _868489, _868491, _868493, _868495, _868497] : [c_Typedef_Otype__definition(_868487, _868489, _868491, _868493, _868495), hBOOL(hAPP(hAPP(c_member(_868489), _868497), _868495)), -(hAPP(_868491, hAPP(_868493, _868497)) = _868497)], (28797 ^ _776541) ^ [_1292883] : [_1292883 = c_Int_OPls, -(c_Int_OBit0(_1292883) = c_Int_OPls)], (44972 ^ _776541) ^ [_1677087, _1677089, _1677091, _1677093] : [class_Groups_Ocomm__monoid__add(_1677087), hBOOL(hAPP(c_List_Odistinct(_1677089), _1677091)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677087), hAPP(hAPP(c_List_Omap(_1677089, _1677087), _1677093), _1677091)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1677089, _1677087), _1677093), hAPP(c_List_Oset(_1677089), _1677091)))], (24371 ^ _776541) ^ [_1217307] : [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), _1217307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217307)))], (19030 ^ _776541) ^ [_1119390, _1119392] : [19038 ^ _776541 : [(19041 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1119392, 19037 ^ [_1119390, _1119392])))], (19039 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19037 ^ [_1119390, _1119392]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119390))))]], 19031 ^ _776541 : [(19032 ^ _776541) ^ [_1119458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119458), _1119390)), hBOOL(hAPP(_1119392, _1119458))]]], (33667 ^ _776541) ^ [_1398402, _1398404, _1398406] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398402, tc_Nat_Onat), _1398404), _1398406) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398402, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1398402), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1398404)), _1398406)))], (47452 ^ _776541) ^ [_1730661, _1730663, _1730665] : [-(c_List_OdropWhile(_1730661, _1730663, _1730665) = hAPP(hAPP(c_List_Odrop(_1730661), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730661)), c_List_OtakeWhile(_1730661, _1730663, _1730665))), _1730665))], (43833 ^ _776541) ^ [_1651945, _1651947, _1651949, _1651951] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651945), tc_List_Olist(_1651945))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651945), tc_List_Olist(_1651945)), _1651947), _1651949)), c_List_Olistrel1(_1651945, _1651951))), 43838 ^ _776541 : [(43845 ^ _776541) ^ [] : [-(_1651949 = hAPP(hAPP(c_List_Oappend(_1651945), 43840 ^ [_1651945, _1651947, _1651949, _1651951]), hAPP(hAPP(c_List_Olist_OCons(_1651945), 43837 ^ [_1651945, _1651947, _1651949, _1651951]), 43841 ^ [_1651945, _1651947, _1651949, _1651951])))], (43843 ^ _776541) ^ [] : [-(_1651947 = hAPP(hAPP(c_List_Oappend(_1651945), 43840 ^ [_1651945, _1651947, _1651949, _1651951]), hAPP(hAPP(c_List_Olist_OCons(_1651945), 43836 ^ [_1651945, _1651947, _1651949, _1651951]), 43841 ^ [_1651945, _1651947, _1651949, _1651951])))], (43839 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651945, _1651945)), hAPP(hAPP(c_Product__Type_OPair(_1651945, _1651945), 43836 ^ [_1651945, _1651947, _1651949, _1651951]), 43837 ^ [_1651945, _1651947, _1651949, _1651951])), _1651951)))]]], (25233 ^ _776541) ^ [_1233376, _1233378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233376), _1233378)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233376, _1233378) = _1233376)], (48782 ^ _776541) ^ [_1759816, _1759818, _1759820] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1759816)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1759816, _1759818, _1759820)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1759816)), _1759820)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21279 ^ _776541) ^ [_1161606, _1161608, _1161610] : [class_Int_Onumber__ring(_1161606), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161606), hAPP(c_Int_Onumber__class_Onumber__of(_1161606), _1161608)), hAPP(c_Int_Onumber__class_Onumber__of(_1161606), _1161610)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1161608), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161610))))], (27383 ^ _776541) ^ [_1269090, _1269092] : [class_Groups_Oordered__ab__group__add__abs(_1269090), 27386 ^ _776541 : [(27393 ^ _776541) ^ [] : [_1269092 = c_Groups_Ozero__class_Ozero(_1269090), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269090), hAPP(c_Groups_Oabs__class_Oabs(_1269090), _1269092)), c_Groups_Ozero__class_Ozero(_1269090))))], (27387 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269090), hAPP(c_Groups_Oabs__class_Oabs(_1269090), _1269092)), c_Groups_Ozero__class_Ozero(_1269090))), -(_1269092 = c_Groups_Ozero__class_Ozero(_1269090))]]], (38550 ^ _776541) ^ [_1515877, _1515879, _1515881, _1515883, _1515885] : [-(hAPP(c_Fun_Othe__inv__into(_1515877, _1515879, _1515881, _1515883), _1515885) = c_HOL_OThe(_1515877, hAPP(hAPP(c_COMBS(_1515877, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515877), c_fconj), hAPP(hAPP(c_COMBC(_1515877, tc_fun(_1515877, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515877)), _1515881))), hAPP(hAPP(c_COMBC(_1515877, _1515879, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1515879, tc_fun(_1515879, tc_HOL_Obool), _1515877), c_fequal), _1515883)), _1515885))))], (51395 ^ _776541) ^ [_1816833, _1816835, _1816837, _1816839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816833, _1816835)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816837, _1816839))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816833), _1816835)), 51402 ^ _776541 : [(51405 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816835), _1816839)))], (51403 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816837), _1816833)))]]], (34123 ^ _776541) ^ [_1410560, _1410562] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410560) = hAPP(c_Nat_OSuc, _1410562), -(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(_1410560))), 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)), _1410562))))))], (28791 ^ _776541) ^ [_1292808] : [c_Int_OBit0(_1292808) = c_Int_OPls, -(_1292808 = c_Int_OPls)], (5945 ^ _776541) ^ [_871117, _871119, _871121, _871123, _871125, _871127] : [c_Typedef_Otype__definition(_871117, _871119, _871121, _871123, _871125), 5949 ^ _776541 : [(5952 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_871119), 5948 ^ [_871117, _871119, _871121, _871123, _871125, _871127]), _871125)))], (5950 ^ _776541) ^ [] : [-(_871127 = hAPP(_871123, 5948 ^ [_871117, _871119, _871121, _871123, _871125, _871127]))]]], (52299 ^ _776541) ^ [_1829190, _1829192] : [-(class_Nat_Osize(tc_sum(_1829190, _1829192)))], (10413 ^ _776541) ^ [_955390, _955392, _955394] : [class_Groups_Oordered__ab__group__add(_955390), 10416 ^ _776541 : [(10423 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955390), hAPP(c_Groups_Ouminus__class_Ouminus(_955390), _955394)), _955392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955390), hAPP(c_Groups_Ouminus__class_Ouminus(_955390), _955392)), _955394)))], (10417 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955390), hAPP(c_Groups_Ouminus__class_Ouminus(_955390), _955392)), _955394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955390), hAPP(c_Groups_Ouminus__class_Ouminus(_955390), _955394)), _955392)))]]], (8713 ^ _776541) ^ [_926277, _926279, _926281] : [class_Lattices_Osemilattice__inf(_926277), 8716 ^ _776541 : [(8723 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926277), _926279), _926281) = _926279, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926277), _926279), _926281)))], (8717 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926277), _926279), _926281)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926277), _926279), _926281) = _926279)]]], (22149 ^ _776541) ^ [_1178180, _1178182] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178180)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178182)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178180), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178182))))], (5737 ^ _776541) ^ [_866975, _866977] : [-(hAPP(c_Hoare__Mirabelle_OAbs__triple(_866975), hAPP(c_Hoare__Mirabelle_ORep__triple(_866975), _866977)) = _866977)], (38069 ^ _776541) ^ [_1505675, _1505677, _1505679, _1505681] : [-(c_Wellfounded_Omax__extp(_1505675, _1505677, _1505679, _1505681)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505675), _1505679)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505675), _1505681)), -(_1505681 = c_Orderings_Obot__class_Obot(tc_fun(_1505675, tc_HOL_Obool))), 38083 ^ _776541 : [(38086 ^ _776541) ^ [_1506020] : [hBOOL(hAPP(hAPP(c_member(_1505675), _1506020), _1505681)), hBOOL(hAPP(hAPP(_1505677, 38082 ^ [_1505675, _1505677, _1505679, _1505681]), _1506020))], (38084 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505675), 38082 ^ [_1505675, _1505677, _1505679, _1505681]), _1505679)))]]], (33298 ^ _776541) ^ [_1387004, _1387006, _1387008, _1387010, _1387012] : [class_Groups_Ocomm__monoid__mult(_1387004), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387006, _1387004), hAPP(hAPP(c_COMBS(_1387006, _1387004, _1387004), hAPP(hAPP(c_COMBB(_1387004, tc_fun(_1387004, _1387004), _1387006), c_Groups_Otimes__class_Otimes(_1387004)), _1387008)), _1387010)), _1387012) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387004), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387006, _1387004), _1387008), _1387012)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387006, _1387004), _1387010), _1387012)))], (29473 ^ _776541) ^ [] : [-(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))))], (36624 ^ _776541) ^ [_1470807, _1470809, _1470811, _1470813, _1470815] : [hBOOL(hAPP(hAPP(c_member(_1470807), _1470809), hAPP(c_Relation_OImage(_1470811, _1470807, _1470813), _1470815))), 36628 ^ _776541 : [(36631 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1470811), 36627 ^ [_1470807, _1470809, _1470811, _1470813, _1470815]), _1470815)))], (36629 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1470811, _1470807)), hAPP(hAPP(c_Product__Type_OPair(_1470811, _1470807), 36627 ^ [_1470807, _1470809, _1470811, _1470813, _1470815]), _1470809)), _1470813)))]]], (17849 ^ _776541) ^ [_1097718, _1097720, _1097722, _1097724] : [class_Groups_Ocomm__monoid__add(_1097718), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1097720), _1097722))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097720, _1097718), _1097724), _1097722) = c_Groups_Ozero__class_Ozero(_1097718))], (16278 ^ _776541) ^ [_1070408, _1070410] : [class_Rings_Omult__zero(_1070408), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070408), _1070410), c_Groups_Ozero__class_Ozero(_1070408)) = c_Groups_Ozero__class_Ozero(_1070408))], (52407 ^ _776541) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (15648 ^ _776541) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27531 ^ _776541) ^ [_1271818, _1271820, _1271822] : [class_Rings_Olinordered__idom(_1271818), 27534 ^ _776541 : [(27543 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271818), hAPP(c_Groups_Oabs__class_Oabs(_1271818), _1271820)), _1271822))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271818), _1271820), _1271822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271818), hAPP(c_Groups_Ouminus__class_Ouminus(_1271818), _1271820)), _1271822))], (27535 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271818), hAPP(c_Groups_Oabs__class_Oabs(_1271818), _1271820)), _1271822)), 27538 ^ _776541 : [(27541 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271818), hAPP(c_Groups_Ouminus__class_Ouminus(_1271818), _1271820)), _1271822)))], (27539 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271818), _1271820), _1271822)))]]]]], (7908 ^ _776541) ^ [_910006, _910008, _910010, _910012, _910014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910006, tc_HOL_Obool)), _910008), _910010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910006, tc_HOL_Obool)), _910012), _910014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910006, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910006, tc_HOL_Obool)), _910008), _910012)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910006, tc_HOL_Obool)), _910010), _910014))))], (28287 ^ _776541) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (52179 ^ _776541) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (32946 ^ _776541) ^ [_1377359, _1377361, _1377363, _1377365, _1377367] : [-(_1377359 = c_Orderings_Obot__class_Obot(tc_fun(_1377361, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377363, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377361, tc_fun(_1377363, tc_HOL_Obool)), _1377359), _1377365)), _1377367) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377361, tc_fun(_1377363, tc_HOL_Obool)), _1377359), hAPP(hAPP(c_COMBC(_1377361, tc_fun(_1377363, tc_HOL_Obool), tc_fun(_1377363, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377363, tc_HOL_Obool), tc_fun(tc_fun(_1377363, tc_HOL_Obool), tc_fun(_1377363, tc_HOL_Obool)), _1377361), c_Groups_Ominus__class_Ominus(tc_fun(_1377363, tc_HOL_Obool))), _1377365)), _1377367)))], (6469 ^ _776541) ^ [_881093, _881095] : [-(_881095 = c_Orderings_Obot__class_Obot(tc_fun(_881093, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_881093), 6472 ^ [_881093, _881095]), _881095)))], (12648 ^ _776541) ^ [_999463, _999465, _999467] : [class_Lattices_Oab__semigroup__idem__mult(_999463), hBOOL(hAPP(c_Finite__Set_Ofinite(_999463), _999465)), -(hAPP(c_Finite__Set_Ofold1(_999463, c_Groups_Otimes__class_Otimes(_999463)), hAPP(hAPP(c_Set_Oinsert(_999463), _999467), _999465)) = hAPP(hAPP(c_Finite__Set_Ofold(_999463, _999463, c_Groups_Otimes__class_Otimes(_999463)), _999467), _999465))], (27243 ^ _776541) ^ [_1266730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266730), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1266730)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31137 ^ _776541) ^ [_1335376, _1335378, _1335380] : [class_Orderings_Olinorder(_1335376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335376), _1335378)), 31147 ^ _776541 : [(31150 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335376), _1335380), 31146 ^ [_1335376, _1335378, _1335380]))], (31148 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335376), 31146 ^ [_1335376, _1335378, _1335380]), _1335378)))]], hBOOL(hAPP(hAPP(c_member(_1335376), _1335380), _1335378)), -(c_Big__Operators_Olinorder__class_OMin(_1335376, _1335378) = _1335380)], (46225 ^ _776541) ^ [_1705981, _1705983] : [-(c_List_Ofoldr(tc_List_Olist(_1705981), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1705981)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1705981))), c_List_Otranspose(_1705981, _1705983), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705981))), hAPP(c_List_Ofilter(tc_List_Olist(_1705981), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1705981)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705981), tc_List_Olist(_1705981), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1705981)))), _1705983)))], (38953 ^ _776541) ^ [_1526151, _1526153, _1526155] : [-(hAPP(c_Relation_ODomain(_1526151, _1526153), hAPP(c_Set_OCollect(tc_prod(_1526151, _1526153)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526151, _1526153, tc_HOL_Obool), _1526155))) = hAPP(c_Set_OCollect(_1526151), hAPP(hAPP(c_COMBB(tc_fun(_1526153, tc_HOL_Obool), tc_HOL_Obool, _1526151), c_HOL_OEx(_1526153)), _1526155)))], (38470 ^ _776541) ^ [_1514124, _1514126] : [c_Wellfounded_OwfP(_1514124, _1514126), 38473 ^ _776541 : [(38474 ^ _776541) ^ [_1514188] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1514124, _1514126), _1514188)))]]], (23595 ^ _776541) ^ [_1204173, _1204175] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204173), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204175)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204173)), _1204175))], (20295 ^ _776541) ^ [_1142808, _1142810, _1142812, _1142814] : [class_Fields_Ofield__inverse__zero(_1142808), 20298 ^ _776541 : [(20299 ^ _776541) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142808), _1142810), _1142812) = _1142814, 20302 ^ _776541 : [(20309 ^ _776541) ^ [] : [_1142812 = c_Groups_Ozero__class_Ozero(_1142808), -(_1142814 = c_Groups_Ozero__class_Ozero(_1142808))], (20303 ^ _776541) ^ [] : [-(_1142812 = c_Groups_Ozero__class_Ozero(_1142808)), -(_1142810 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142808), _1142814), _1142812))]]], (20315 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142808), _1142810), _1142812) = _1142814), 20318 ^ _776541 : [(20321 ^ _776541) ^ [] : [_1142810 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142808), _1142814), _1142812)], (20319 ^ _776541) ^ [] : [_1142812 = c_Groups_Ozero__class_Ozero(_1142808)]], 20322 ^ _776541 : [(20325 ^ _776541) ^ [] : [_1142814 = c_Groups_Ozero__class_Ozero(_1142808)], (20323 ^ _776541) ^ [] : [-(_1142812 = c_Groups_Ozero__class_Ozero(_1142808))]]]]], (36514 ^ _776541) ^ [_1467705, _1467707, _1467709, _1467711, _1467713] : [hBOOL(hAPP(hAPP(c_member(_1467705), _1467707), hAPP(c_Relation_OImage(_1467709, _1467705, _1467711), _1467713))), 36518 ^ _776541 : [(36521 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1467709, _1467705)), hAPP(hAPP(c_Product__Type_OPair(_1467709, _1467705), 36517 ^ [_1467705, _1467707, _1467709, _1467711, _1467713]), _1467707)), _1467711)))], (36519 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1467709), 36517 ^ [_1467705, _1467707, _1467709, _1467711, _1467713]), _1467713)))]]], (49080 ^ _776541) ^ [_1766493, _1766495, _1766497] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1766493), _1766495, _1766497)), -(c_List_Olist__ex(tc_Int_Oint, _1766493, c_List_Oupto(_1766495, _1766497)))], (7494 ^ _776541) ^ [_899984, _899986, _899988, _899990] : [hBOOL(hAPP(hAPP(c_member(_899984), _899986), _899988)), hBOOL(hAPP(hAPP(c_member(_899984), _899986), _899990)), -(hBOOL(hAPP(hAPP(c_member(_899984), _899986), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_899984, tc_HOL_Obool)), _899988), _899990))))], (43346 ^ _776541) ^ [_1640455] : [class_Orderings_Olinorder(_1640455), -(c_List_Olinorder__class_Osorted__list__of__set(_1640455, c_Orderings_Obot__class_Obot(tc_fun(_1640455, tc_HOL_Obool))) = c_List_Olist_ONil(_1640455))], (13606 ^ _776541) ^ [_1018682, _1018684, _1018686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1018682), _1018684)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1018682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018684), _1018686)) = 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, _1018682), _1018684)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1018684), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018684), _1018686))))], (12119 ^ _776541) ^ [_989354, _989356, _989358, _989360, _989362] : [c_Finite__Set_Ofolding__one__idem(_989354, _989356, _989358), hBOOL(hAPP(c_Finite__Set_Ofinite(_989354), _989360)), hBOOL(hAPP(hAPP(c_member(_989354), _989362), _989360)), -(hAPP(hAPP(_989356, _989362), hAPP(_989358, _989360)) = hAPP(_989358, _989360))], (6346 ^ _776541) ^ [_878849, _878851, _878853] : [_878849 = _878851, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878853, tc_HOL_Obool)), _878849), _878851)))], (17015 ^ _776541) ^ [_1082810, _1082812, _1082814, _1082816] : [class_Rings_Oordered__ring(_1082810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082810), _1082812), _1082814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082810), _1082816), c_Groups_Ozero__class_Ozero(_1082810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082810), _1082814), _1082816)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082810), _1082812), _1082816))))], (39998 ^ _776541) ^ [_1555219, _1555221, _1555223, _1555225, _1555227] : [class_Groups_Ocomm__monoid__mult(_1555219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555221), _1555223)), c_Fun_Oinj__on(_1555221, _1555221, _1555225, _1555223), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555221, _1555219), _1555227), hAPP(c_Set_Oimage(_1555221, _1555221, _1555225), _1555223)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555221, _1555219), hAPP(c_Fun_Ocomp(_1555221, _1555219, _1555221, _1555227), _1555225)), _1555223))], (44825 ^ _776541) ^ [_1673217, _1673219, _1673221, _1673223, _1673225] : [44827 ^ _776541 : [(44830 ^ _776541) ^ [] : [hAPP(_1673221, 44826 ^ [_1673217, _1673219, _1673221, _1673223, _1673225]) = hAPP(_1673225, 44826 ^ [_1673217, _1673219, _1673221, _1673223, _1673225])], (44828 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673217), 44826 ^ [_1673217, _1673219, _1673221, _1673223, _1673225]), hAPP(c_List_Oset(_1673217), _1673223))))]], -(hAPP(hAPP(c_List_Omap(_1673217, _1673219), _1673221), _1673223) = hAPP(hAPP(c_List_Omap(_1673217, _1673219), _1673225), _1673223))], (22537 ^ _776541) ^ [_1184996, _1184998, _1185000, _1185002] : [class_Rings_Olinordered__semidom(_1184996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184996), _1184998), _1185000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184996), c_Groups_Ozero__class_Ozero(_1184996)), _1184998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184996), hAPP(hAPP(c_Power_Opower__class_Opower(_1184996), _1184998), _1185002)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184996), _1185000), _1185002))))], (7992 ^ _776541) ^ [_911864, _911866, _911868] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911864, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911864, tc_HOL_Obool)), _911866), _911868)), _911868)))], (16602 ^ _776541) ^ [_1075174] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1075174)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1075174)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1075174)))], (52103 ^ _776541) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (40987 ^ _776541) ^ [_1579386, _1579388, _1579390, _1579392] : [-(c_Wellfounded_Owf(_1579386, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579386, _1579386)), hAPP(hAPP(c_Product__Type_OPair(_1579386, _1579386), _1579388), _1579390)), _1579392))), c_Wellfounded_Owf(_1579386, _1579392), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579386, _1579386)), hAPP(hAPP(c_Product__Type_OPair(_1579386, _1579386), _1579390), _1579388)), c_Transitive__Closure_Ortrancl(_1579386, _1579392))))], (7780 ^ _776541) ^ [_907215, _907217, _907219, _907221] : [hBOOL(hAPP(hAPP(c_member(_907215), _907217), _907219)), -(hBOOL(hAPP(hAPP(c_member(_907215), _907217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907215, tc_HOL_Obool)), _907219), _907221))))], (44815 ^ _776541) ^ [_1672973, _1672975, _1672977, _1672979, _1672981] : [hAPP(hAPP(c_List_Omap(_1672973, _1672975), _1672977), _1672979) = hAPP(hAPP(c_List_Omap(_1672973, _1672975), _1672981), _1672979), 44818 ^ _776541 : [(44819 ^ _776541) ^ [_1673096] : [hBOOL(hAPP(hAPP(c_member(_1672973), _1673096), hAPP(c_List_Oset(_1672973), _1672979))), -(hAPP(_1672977, _1673096) = hAPP(_1672981, _1673096))]]], (17831 ^ _776541) ^ [_1097448, _1097450] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1097448), _1097450))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1097448), hAPP(c_Nat_OSuc, _1097450)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (21309 ^ _776541) ^ [_1162243, _1162245] : [class_Rings_Ocomm__semiring__1(_1162243), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1162243), _1162245), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1162245)], (2876 ^ _776541) ^ [_819200, _819202, _819204, _819206] : [-(c_Relation_ODomain(_819206, _819202) = c_Relation_ODomain(_819204, _819200)), _819206 = _819204, _819202 = _819200], (33439 ^ _776541) ^ [_1391187, _1391189, _1391191, _1391193, _1391195, _1391197] : [-(_1391187 = _1391189), -(hAPP(c_Fun_Ofun__upd(_1391191, _1391193, _1391195, _1391189, _1391197), _1391187) = hAPP(_1391195, _1391187))], (5982 ^ _776541) ^ [_871868, _871870, _871872, _871874, _871876, _871878] : [c_Typedef_Otype__definition(_871868, _871870, _871872, _871874, _871876), hBOOL(hAPP(hAPP(c_member(_871870), _871878), _871876)), -(_871878 = hAPP(_871872, 5989 ^ [_871868, _871870, _871872, _871874, _871876, _871878]))], (16506 ^ _776541) ^ [_1073738] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073738), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1073738)], (18710 ^ _776541) ^ [_1113445, _1113447, _1113449] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1113445), _1113447)), 18713 ^ _776541 : [(18720 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113445), _1113449), _1113447))), -(hAPP(c_Finite__Set_Ocard(_1113445), hAPP(hAPP(c_Set_Oinsert(_1113445), _1113449), _1113447)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1113445), _1113447)))], (18714 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1113445), _1113449), _1113447)), -(hAPP(c_Finite__Set_Ocard(_1113445), hAPP(hAPP(c_Set_Oinsert(_1113445), _1113449), _1113447)) = hAPP(c_Finite__Set_Ocard(_1113445), _1113447))]]], (42827 ^ _776541) ^ [_1629792, _1629794, _1629796] : [hBOOL(hAPP(c_List_Odistinct(_1629792), _1629794)), -(hBOOL(hAPP(c_List_Odistinct(_1629792), c_List_Osublist(_1629792, _1629794, _1629796))))], (8074 ^ _776541) ^ [_913767, _913769] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913767, tc_HOL_Obool)), _913769), c_Orderings_Otop__class_Otop(tc_fun(_913767, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_913767, tc_HOL_Obool)))], (48025 ^ _776541) ^ [_1743833, _1743835, _1743837] : [class_Orderings_Olinorder(_1743833), 48031 ^ _776541 : [(48034 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743833), _1743837), 48030 ^ [_1743833, _1743835, _1743837]))], (48032 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743833), 48030 ^ [_1743833, _1743835, _1743837]), hAPP(c_List_Oset(_1743833), _1743835))))]], c_List_Olinorder__class_Osorted(_1743833, _1743835), -(c_List_Olinorder__class_Osorted(_1743833, hAPP(hAPP(c_List_Olist_OCons(_1743833), _1743837), _1743835)))], (42809 ^ _776541) ^ [_1629433, _1629435, _1629437, _1629439] : [hBOOL(hAPP(c_List_Odistinct(_1629433), _1629435)), -(hBOOL(hAPP(hAPP(c_member(_1629433), _1629437), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1629433, tc_HOL_Obool)), hAPP(c_List_Oset(_1629433), _1629435)), hAPP(hAPP(c_Set_Oinsert(_1629433), hAPP(hAPP(c_List_Onth(_1629433), _1629435), _1629439)), c_Orderings_Obot__class_Obot(tc_fun(_1629433, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1629433), hAPP(hAPP(c_List_Olist__update(_1629433, _1629435), _1629439), _1629437))))], (32590 ^ _776541) ^ [_1366830, _1366832, _1366834, _1366836, _1366838, _1366840] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1366830, _1366832)), hAPP(hAPP(c_Product__Type_OPair(_1366830, _1366832), _1366838), _1366840)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool)), _1366834), _1366836))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366830, tc_fun(_1366832, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1366830, tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_fun(_1366832, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366832, tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_fun(_1366832, tc_HOL_Obool)), _1366830), c_COMBC(_1366832, tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366832, tc_prod(_1366830, _1366832)), tc_fun(_1366832, tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool)), _1366830), hAPP(c_COMBB(tc_prod(_1366830, _1366832), tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool), _1366832), c_member(tc_prod(_1366830, _1366832)))), c_Product__Type_OPair(_1366830, _1366832)))), _1366834)), hAPP(hAPP(c_COMBC(_1366830, tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_fun(_1366832, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366832, tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_fun(_1366832, tc_HOL_Obool)), _1366830), c_COMBC(_1366832, tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366832, tc_prod(_1366830, _1366832)), tc_fun(_1366832, tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool)), _1366830), hAPP(c_COMBB(tc_prod(_1366830, _1366832), tc_fun(tc_fun(tc_prod(_1366830, _1366832), tc_HOL_Obool), tc_HOL_Obool), _1366832), c_member(tc_prod(_1366830, _1366832)))), c_Product__Type_OPair(_1366830, _1366832)))), _1366836)), _1366838), _1366840)))], (34719 ^ _776541) ^ [_1423604, _1423606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1423604), _1423606)), -(c_Divides_Odivmod__nat(_1423604, _1423606) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1423604))], (29903 ^ _776541) ^ [_1312716, _1312718, _1312720, _1312722] : [class_Rings_Olinordered__semidom(_1312716), 29909 ^ _776541 : [(29912 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312716), c_Groups_Ozero__class_Ozero(_1312716)), hAPP(_1312722, 29908 ^ [_1312716, _1312718, _1312720, _1312722])))], (29910 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312718), 29908 ^ [_1312716, _1312718, _1312720, _1312722]), _1312720)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312716), c_Groups_Ozero__class_Ozero(_1312716)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1312718, _1312716), _1312722), _1312720))))], (48740 ^ _776541) ^ [_1758877, _1758879, _1758881] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1758877), hAPP(c_COMBK(_1758877, tc_Nat_Onat), _1758879)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1758881)) = c_List_Oreplicate(_1758877, _1758881, _1758879))], (8197 ^ _776541) ^ [_916597, _916599, _916601, _916603] : [class_Lattices_Olattice(_916597), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916597), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916597), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916597), _916599), _916601)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916597), _916599), _916603))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916597), _916599), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916597), _916601), _916603)))))], (15442 ^ _776541) ^ [_1055734, _1055736, _1055738] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055734), _1055736)), -(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(_1055734), _1055738)), hAPP(c_Finite__Set_Ocard(_1055734), _1055736))), hAPP(c_Finite__Set_Ocard(_1055734), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055734, tc_HOL_Obool)), _1055738), _1055736)))))], (50 ^ _776541) ^ [_777346, _777348, _777350, _777352, _777354, _777356] : [-(c_Finite__Set_Ofolding__one__idem(_777354, _777350, _777346)), c_Finite__Set_Ofolding__one__idem(_777356, _777352, _777348), _777356 = _777354, _777352 = _777350, _777348 = _777346], (6961 ^ _776541) ^ [_889505, _889507] : [hAPP(c_Set_OPow(_889505), _889507) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_889505, tc_HOL_Obool), tc_HOL_Obool))], (37416 ^ _776541) ^ [_1488588, _1488590, _1488592, _1488594] : [c_Fun_Oinj__on(_1488588, _1488590, _1488592, _1488594), -(hAPP(c_Finite__Set_Ocard(_1488590), hAPP(c_Set_Oimage(_1488588, _1488590, _1488592), _1488594)) = hAPP(c_Finite__Set_Ocard(_1488588), _1488594))], (52319 ^ _776541) ^ [_1829442, _1829444] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1829442, _1829444)))], (35135 ^ _776541) ^ [_1432283, _1432285, _1432287] : [35137 ^ _776541 : [(35140 ^ _776541) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1432283, _1432285), 35136 ^ [_1432283, _1432285, _1432287]))], (35138 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1432285, 35136 ^ [_1432283, _1432285, _1432287]), _1432287)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1432283, _1432285), _1432287)))], (52361 ^ _776541) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (2376 ^ _776541) ^ [_811254, _811256, _811258, _811260, _811262, _811264, _811266, _811268, _811270, _811272] : [-(c_Nitpick_Opair__box_Opair__box__rec(_811272, _811268, _811264, _811260, _811256) = c_Nitpick_Opair__box_Opair__box__rec(_811270, _811266, _811262, _811258, _811254)), _811272 = _811270, _811268 = _811266, _811264 = _811262, _811260 = _811258, _811256 = _811254], (52067 ^ _776541) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (7970 ^ _776541) ^ [_911403, _911405, _911407, _911409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911403, tc_HOL_Obool)), _911405), _911407)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911403, tc_HOL_Obool)), _911405), _911409)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911403, tc_HOL_Obool)), _911405), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911403, tc_HOL_Obool)), _911407), _911409))))], (32508 ^ _776541) ^ [_1363554, _1363556, _1363558, _1363560, _1363562] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363554, tc_fun(_1363556, tc_HOL_Obool)), _1363558), hAPP(hAPP(c_COMBC(_1363554, tc_fun(_1363556, tc_HOL_Obool), tc_fun(_1363556, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363556, tc_HOL_Obool), tc_fun(tc_fun(_1363556, tc_HOL_Obool), tc_fun(_1363556, tc_HOL_Obool)), _1363554), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363556, tc_HOL_Obool))), _1363560)), _1363562)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363556, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363554, tc_fun(_1363556, tc_HOL_Obool)), _1363558), _1363560)), _1363562))], (12920 ^ _776541) ^ [_1004468, _1004470, _1004472] : [class_Lattices_Osemilattice__inf(_1004468), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004468), _1004470)), -(_1004470 = c_Orderings_Obot__class_Obot(tc_fun(_1004468, tc_HOL_Obool))), 12931 ^ _776541 : [(12932 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004468), _1004472), hAPP(c_Finite__Set_Ofold1(_1004468, c_Lattices_Osemilattice__inf__class_Oinf(_1004468)), _1004470))), 12935 ^ _776541 : [(12936 ^ _776541) ^ [_1004761] : [hBOOL(hAPP(hAPP(c_member(_1004468), _1004761), _1004470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004468), _1004472), _1004761)))]]], (12942 ^ _776541) ^ [] : [12944 ^ _776541 : [(12947 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004468), _1004472), 12943 ^ [_1004468, _1004470, _1004472]))], (12945 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004468), 12943 ^ [_1004468, _1004470, _1004472]), _1004470)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004468), _1004472), hAPP(c_Finite__Set_Ofold1(_1004468, c_Lattices_Osemilattice__inf__class_Oinf(_1004468)), _1004470))))]]], (29053 ^ _776541) ^ [_1297348] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297348))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297348)))))], (38138 ^ _776541) ^ [_1506921, _1506923] : [c_Wellfounded_Owf(_1506921, _1506923), -(c_Wellfounded_Owf(tc_fun(_1506921, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1506921, _1506923)))], (41402 ^ _776541) ^ [_1589558, _1589560, _1589562] : [c_Relation_Osingle__valued(_1589558, _1589558, _1589560), -(c_Relation_Osingle__valued(_1589558, _1589558, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589558, _1589558), tc_HOL_Obool), _1589562), _1589560)))], (29627 ^ _776541) ^ [_1307550] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1307550, 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, _1307550, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (50016 ^ _776541) ^ [_1786858, _1786860, _1786862] : [hAPP(_1786862, hAPP(c_Hilbert__Choice_Oinv__into(_1786858, _1786860, c_Orderings_Otop__class_Otop(tc_fun(_1786858, tc_HOL_Obool)), _1786862), 50017 ^ [_1786858, _1786860, _1786862])) = 50017 ^ [_1786858, _1786860, _1786862], -(hAPP(c_Set_Oimage(_1786858, _1786860, _1786862), c_Orderings_Otop__class_Otop(tc_fun(_1786858, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1786860, tc_HOL_Obool)))], (47333 ^ _776541) ^ [_1728190] : [c_List_Onat__list(_1728190), -(c_List_Oembed__list(c_List_Oreturn__list(_1728190)) = _1728190)], (28731 ^ _776541) ^ [_1291602, _1291604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1291602)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1291604)), _1291602) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1291604), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1291602), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (35473 ^ _776541) ^ [_1438248, _1438250, _1438252, _1438254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1438254, _1438250)), hAPP(_1438254, _1438252))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1438248, _1438248)), hAPP(hAPP(c_Product__Type_OPair(_1438248, _1438248), _1438250), _1438252)), hAPP(c_Wellfounded_Omeasure(_1438248), _1438254))))], (32512 ^ _776541) ^ [_1363753, _1363755, _1363757, _1363759, _1363761] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363753, tc_HOL_Obool)), _1363755), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363757, tc_fun(_1363753, tc_HOL_Obool)), _1363759), _1363761)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363757, tc_fun(_1363753, tc_HOL_Obool)), _1363759), hAPP(hAPP(c_COMBB(tc_fun(_1363753, tc_HOL_Obool), tc_fun(_1363753, tc_HOL_Obool), _1363757), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363753, tc_HOL_Obool)), _1363755)), _1363761)))], (52101 ^ _776541) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (22779 ^ _776541) ^ [_1189251, _1189253, _1189255] : [class_Rings_Olinordered__semidom(_1189251), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189251), c_Groups_Oone__class_Oone(_1189251)), _1189253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189251), c_Groups_Oone__class_Oone(_1189251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189251), _1189253), hAPP(hAPP(c_Power_Opower__class_Opower(_1189251), _1189253), _1189255)))))], (31335 ^ _776541) ^ [_1339042, _1339044] : [class_Orderings_Olinorder(_1339042), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339042), _1339044), _1339044) = _1339044)], (49159 ^ _776541) ^ [_1768621, _1768623, _1768625, _1768627] : [c_Relation_Otrans(_1768621, _1768623), c_Relation_Otrans(_1768625, _1768627), -(c_Relation_Otrans(tc_prod(_1768621, _1768625), c_Wellfounded_Olex__prod(_1768621, _1768625, _1768623, _1768627)))], (39333 ^ _776541) ^ [_1538072, _1538074] : [-(c_Product__Type_Oapfst(_1538072, _1538072, _1538074, c_Fun_Oid(_1538072)) = c_Fun_Oid(tc_prod(_1538072, _1538074)))], (8084 ^ _776541) ^ [_913993, _913995, _913997] : [class_Complete__Lattice_Ocomplete__lattice(_913993), -(c_Complete__Lattice_OInf__class_OInf(_913993, hAPP(hAPP(c_Set_Oinsert(_913993), _913995), _913997)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_913993), _913995), c_Complete__Lattice_OInf__class_OInf(_913993, _913997)))], (51057 ^ _776541) ^ [_1810485, _1810487, _1810489, _1810491] : [class_Rings_Ocomm__ring(_1810485), class_Rings_Odvd(_1810485), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810485), _1810487), _1810489)), 51068 ^ _776541 : [(51075 ^ _776541) ^ [_1810911, _1810913] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810485), _1810487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1810485), _1810913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1810485), _1810911), _1810489))), _1810491))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810485), _1810487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810485), _1810913), _1810491))))], (51069 ^ _776541) ^ [_1810738, _1810740] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810485), _1810487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810485), _1810740), _1810491))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810485), _1810487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1810485), _1810740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1810485), _1810738), _1810489))), _1810491))))]]], (29321 ^ _776541) ^ [_1301964, _1301966] : [class_Rings_Olinordered__idom(_1301964), -(hAPP(c_Groups_Oabs__class_Oabs(_1301964), hAPP(hAPP(c_Power_Opower__class_Opower(_1301964), _1301966), 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(_1301964), _1301966), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (3868 ^ _776541) ^ [_834642, _834644, _834646, _834648, _834650, _834652] : [-(c_List_Olinorder__class_Oinsort__key(_834652, _834648, _834644) = c_List_Olinorder__class_Oinsort__key(_834650, _834646, _834642)), _834652 = _834650, _834648 = _834646, _834644 = _834642], (12029 ^ _776541) ^ [_987975, _987977] : [class_Lattices_Olattice(_987975), -(c_Big__Operators_Olattice__class_OSup__fin(_987975, hAPP(hAPP(c_Set_Oinsert(_987975), _987977), c_Orderings_Obot__class_Obot(tc_fun(_987975, tc_HOL_Obool)))) = _987977)], (31353 ^ _776541) ^ [_1339333, _1339335, _1339337] : [class_Orderings_Olinorder(_1339333), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339333), _1339335), _1339337) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339333), _1339337), _1339335))], (12305 ^ _776541) ^ [_992394, _992396, _992398] : [class_Lattices_Olattice(_992394), hBOOL(hAPP(c_Finite__Set_Ofinite(_992394), _992396)), 12312 ^ _776541 : [(12319 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992394, tc_HOL_Obool)), _992396), hAPP(hAPP(c_Set_Oinsert(_992394), _992398), c_Orderings_Obot__class_Obot(tc_fun(_992394, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992394, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_992394, hAPP(hAPP(c_Set_Oinsert(_992394), _992398), _992396)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_992394), _992398), c_Big__Operators_Olattice__class_OSup__fin(_992394, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992394, tc_HOL_Obool)), _992396), hAPP(hAPP(c_Set_Oinsert(_992394), _992398), c_Orderings_Obot__class_Obot(tc_fun(_992394, tc_HOL_Obool)))))))], (12313 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992394, tc_HOL_Obool)), _992396), hAPP(hAPP(c_Set_Oinsert(_992394), _992398), c_Orderings_Obot__class_Obot(tc_fun(_992394, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992394, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_992394, hAPP(hAPP(c_Set_Oinsert(_992394), _992398), _992396)) = _992398)]]], (7656 ^ _776541) ^ [_903831, _903833, _903835, _903837] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903831, tc_HOL_Obool)), _903833), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903831, tc_HOL_Obool)), _903835), _903837)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903831, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903831, tc_HOL_Obool)), _903833), _903835)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903831, tc_HOL_Obool)), _903833), _903837)))], (13053 ^ _776541) ^ [_1006858, _1006860] : [class_Groups_Oab__semigroup__mult(_1006858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006858), _1006860)), -(_1006860 = c_Orderings_Obot__class_Obot(tc_fun(_1006858, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1006858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006858), 13066 ^ [_1006858, _1006860]), 13067 ^ [_1006858, _1006860])), hAPP(hAPP(c_Set_Oinsert(_1006858), 13066 ^ [_1006858, _1006860]), hAPP(hAPP(c_Set_Oinsert(_1006858), 13067 ^ [_1006858, _1006860]), c_Orderings_Obot__class_Obot(tc_fun(_1006858, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1006858), hAPP(c_Finite__Set_Ofold1(_1006858, c_Groups_Otimes__class_Otimes(_1006858)), _1006860)), _1006860)))], (15838 ^ _776541) ^ [_1063351, _1063353] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063351), _1063353) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 15839 ^ _776541 : [(15846 ^ _776541) ^ [] : [_1063351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1063353 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15840 ^ _776541) ^ [] : [_1063351 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063353 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (38290 ^ _776541) ^ [_1509980, _1509982, _1509984] : [c_Wellfounded_Owf(_1509980, _1509982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509980, tc_HOL_Obool)), _1509984), hAPP(c_Relation_OImage(_1509980, _1509980, _1509982), _1509984))), -(_1509984 = c_Orderings_Obot__class_Obot(tc_fun(_1509980, tc_HOL_Obool)))], (35288 ^ _776541) ^ [_1434961, _1434963, _1434965] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1434961, _1434961), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1434963), _1434965))), -(_1434961 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1434965 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33523 ^ _776541) ^ [] : [-(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)))], (2320 ^ _776541) ^ [_810354, _810356, _810358, _810360, _810362, _810364, _810366, _810368] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_810368, _810364, _810360, _810356) = c_Nat_Osemiring__1__class_Oof__nat__aux(_810366, _810362, _810358, _810354)), _810368 = _810366, _810364 = _810362, _810360 = _810358, _810356 = _810354], (51647 ^ _776541) ^ [_1821288] : [_1821288 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821288), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (47410 ^ _776541) ^ [_1729836, _1729838, _1729840, _1729842] : [-(hBOOL(hAPP(_1729836, _1729838))), -(c_List_OdropWhile(_1729840, _1729836, hAPP(hAPP(c_List_Olist_OCons(_1729840), _1729838), _1729842)) = hAPP(hAPP(c_List_Olist_OCons(_1729840), _1729838), _1729842))], (15093 ^ _776541) ^ [_1049052, _1049054] : [class_Groups_Omonoid__mult(_1049052), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049052), _1049054), c_Groups_Oone__class_Oone(_1049052)) = _1049054)], (38875 ^ _776541) ^ [_1524196, _1524198, _1524200, _1524202, _1524204] : [-(hAPP(c_Relation_ODomain(_1524196, _1524198), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1524196, _1524198)), hAPP(hAPP(c_Product__Type_OPair(_1524196, _1524198), _1524200), _1524202)), _1524204)) = hAPP(hAPP(c_Set_Oinsert(_1524196), _1524200), hAPP(c_Relation_ODomain(_1524196, _1524198), _1524204)))], (41431 ^ _776541) ^ [_1590237, _1590239, _1590241] : [41432 ^ _776541 : [(41433 ^ _776541) ^ [_1590313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590237, _1590237)), _1590239), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590237, _1590237), tc_HOL_Obool), _1590313), _1590241)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590237, _1590237)), _1590239), c_Transitive__Closure_Ortrancl(_1590237, _1590241))))], (39145 ^ _776541) ^ [_1531596, _1531598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531596, _1531596), tc_HOL_Obool)), c_Relation_OId__on(_1531596, _1531598)), hAPP(hAPP(c_Product__Type_OSigma(_1531596, _1531596), _1531598), hAPP(c_COMBK(tc_fun(_1531596, tc_HOL_Obool), _1531596), _1531598)))))], (7414 ^ _776541) ^ [_898441, _898443, _898445] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_898441, tc_HOL_Obool)), _898443), _898445) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_898441, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898441, tc_HOL_Obool)), _898443), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898441, tc_HOL_Obool)), _898445), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_898441, tc_HOL_Obool), tc_HOL_Obool))))))], (44052 ^ _776541) ^ [_1657385, _1657387, _1657389, _1657391] : [-(hAPP(c_List_Orotate1(_1657387), hAPP(hAPP(c_List_Olist_OCons(_1657387), _1657389), _1657391)) = hAPP(hAPP(c_List_Oappend(_1657387), _1657391), hAPP(hAPP(c_List_Olist_OCons(_1657387), _1657389), c_List_Olist_ONil(_1657387))))], (42970 ^ _776541) ^ [_1632981, _1632983, _1632985] : [hBOOL(hAPP(c_List_Odistinct(_1632981), _1632983)), -(hAPP(c_List_Oset(_1632981), c_List_Oremove1(_1632981, _1632985, _1632983)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1632981, tc_HOL_Obool)), hAPP(c_List_Oset(_1632981), _1632983)), hAPP(hAPP(c_Set_Oinsert(_1632981), _1632985), c_Orderings_Obot__class_Obot(tc_fun(_1632981, tc_HOL_Obool)))))], (51855 ^ _776541) ^ [_1824582, _1824584] : [class_Complete__Lattice_Ocomplete__lattice(_1824582), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1824584, _1824582)))], (35632 ^ _776541) ^ [_1441626, _1441628] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1441626), _1441628) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1441626, _1441628)))], (14536 ^ _776541) ^ [_1038719, _1038721, _1038723] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038719), _1038721) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038719), _1038723), -(_1038721 = _1038723)], (11272 ^ _776541) ^ [_972365, _972367, _972369] : [class_Groups_Oordered__ab__group__add(_972365), -(hAPP(c_Set_Oimage(_972365, _972365, c_Groups_Ouminus__class_Ouminus(_972365)), c_SetInterval_Oord__class_OgreaterThanAtMost(_972365, _972367, _972369)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_972365, hAPP(c_Groups_Ouminus__class_Ouminus(_972365), _972369)), hAPP(c_Groups_Ouminus__class_Ouminus(_972365), _972367)))], (32774 ^ _776541) ^ [_1372113, _1372115, _1372117, _1372119, _1372121] : [class_Complete__Lattice_Ocomplete__lattice(_1372113), 32777 ^ _776541 : [(32778 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372113), _1372115), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372117, _1372113), _1372119), _1372121))), 32781 ^ _776541 : [(32782 ^ _776541) ^ [_1372294] : [hBOOL(hAPP(hAPP(c_member(_1372117), _1372294), _1372119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372113), _1372115), hAPP(_1372121, _1372294))))]]], (32788 ^ _776541) ^ [] : [32790 ^ _776541 : [(32793 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372113), _1372115), hAPP(_1372121, 32789 ^ [_1372113, _1372115, _1372117, _1372119, _1372121])))], (32791 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372117), 32789 ^ [_1372113, _1372115, _1372117, _1372119, _1372121]), _1372119)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372113), _1372115), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372117, _1372113), _1372119), _1372121))))]]], (26991 ^ _776541) ^ [_1262740, _1262742] : [class_Rings_Oring__1(_1262740), -(hBOOL(hAPP(hAPP(c_member(_1262740), hAPP(c_Int_Oring__1__class_Oof__int(_1262740), _1262742)), c_Int_Oring__1__class_OInts(_1262740))))], (51279 ^ _776541) ^ [_1814762, _1814764, _1814766] : [class_Rings_Ocomm__semiring__1(_1814762), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814762), _1814764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814762), _1814764), _1814766))))], (41116 ^ _776541) ^ [_1582833, _1582835] : [-(hAPP(c_Relation_Oconverse(_1582833, _1582833), c_Relation_OId__on(_1582833, _1582835)) = c_Relation_OId__on(_1582833, _1582835))], (28963 ^ _776541) ^ [_1295765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1295765)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295765), c_Int_OPls)))], (15448 ^ _776541) ^ [_1055895, _1055897, _1055899] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055895), _1055897)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1055895, tc_HOL_Obool)), _1055899), _1055897)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055895), _1055899)), hAPP(c_Finite__Set_Ocard(_1055895), _1055897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1055895, tc_HOL_Obool)), _1055899), _1055897)))], (30028 ^ _776541) ^ [_1315040, _1315042] : [class_Orderings_Olinorder(_1315040), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315040), _1315042), _1315042) = _1315042)], (33807 ^ _776541) ^ [_1402511, _1402513, _1402515, _1402517, _1402519, _1402521] : [-(hAPP(c_Set_Oimage(_1402511, _1402513, hAPP(hAPP(c_COMBS(_1402511, _1402513, _1402513), hAPP(hAPP(c_COMBS(_1402511, _1402513, tc_fun(_1402513, _1402513)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1402513, tc_fun(_1402513, _1402513)), _1402511), c_If(_1402513)), _1402515)), _1402517)), _1402519)), _1402521) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402513, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1402511, _1402513, _1402517), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402511, tc_HOL_Obool)), _1402521), hAPP(c_Set_OCollect(_1402511), _1402515)))), hAPP(c_Set_Oimage(_1402511, _1402513, _1402519), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402511, tc_HOL_Obool)), _1402521), hAPP(c_Set_OCollect(_1402511), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1402511), c_fNot), _1402515))))))], (14847 ^ _776541) ^ [_1044308, _1044310, _1044312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044308), _1044310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044308), _1044312)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044310), _1044308)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044312), _1044308)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044310), _1044312))], (33937 ^ _776541) ^ [_1405671, _1405673, _1405675] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1405671, tc_HOL_Obool)), _1405675), hAPP(c_Set_OPow(_1405671), _1405673))), -(hBOOL(hAPP(c_Predicate_OPowp(_1405671, hAPP(hAPP(c_COMBC(_1405671, tc_fun(_1405671, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405671)), _1405673)), _1405675)))], (29934 ^ _776541) ^ [_1313280, _1313282] : [-(_1313280 = _1313282), -(c_Random_Oinc__shift(_1313280, _1313282) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1313282), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (49050 ^ _776541) ^ [_1765962] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1765962)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1765962)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1684 ^ _776541) ^ [_800455, _800457] : [-(class_Rings_Ocomm__semiring__1(_800455)), _800457 = _800455, class_Rings_Ocomm__semiring__1(_800457)], (44002 ^ _776541) ^ [_1656078, _1656080, _1656082, _1656084, _1656086] : [hAPP(hAPP(c_List_Oappend(_1656078), _1656080), _1656082) = hAPP(hAPP(c_List_Oappend(_1656078), _1656084), _1656086), 44005 ^ _776541 : [(44014 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656080)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656084)))), 44017 ^ _776541 : [(44020 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1656078), hAPP(hAPP(c_List_Odrop(_1656078), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656084)), _1656080)), _1656082) = _1656086)], (44018 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1656078), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656084)), _1656080) = _1656084)]]], (44006 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656080)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656084))), 44009 ^ _776541 : [(44012 ^ _776541) ^ [] : [-(_1656082 = hAPP(hAPP(c_List_Oappend(_1656078), hAPP(hAPP(c_List_Odrop(_1656078), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656080)), _1656084)), _1656086))], (44010 ^ _776541) ^ [] : [-(_1656080 = hAPP(hAPP(c_List_Otake(_1656078), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656078)), _1656080)), _1656084))]]]]], (18135 ^ _776541) ^ [_1102535, _1102537, _1102539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102535), _1102537)), 18138 ^ _776541 : [(18139 ^ _776541) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102535, tc_Nat_Onat), _1102539), _1102537) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18142 ^ _776541 : [(18143 ^ _776541) ^ [_1102697] : [hBOOL(hAPP(hAPP(c_member(_1102535), _1102697), _1102537)), -(hAPP(_1102539, _1102697) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18149 ^ _776541) ^ [] : [18151 ^ _776541 : [(18154 ^ _776541) ^ [] : [hAPP(_1102539, 18150 ^ [_1102535, _1102537, _1102539]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18152 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1102535), 18150 ^ [_1102535, _1102537, _1102539]), _1102537)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102535, tc_Nat_Onat), _1102539), _1102537) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46093 ^ _776541) ^ [_1702290, _1702292, _1702294] : [-(c_List_Opartition(_1702290, _1702292, _1702294) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702290), tc_List_Olist(_1702290)), hAPP(c_List_Ofilter(_1702290, _1702292), _1702294)), hAPP(c_List_Ofilter(_1702290, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1702290, c_fNot), _1702292)), _1702294)))], (18974 ^ _776541) ^ [_1118287] : [-(hAPP(c_Nat_OSuc, _1118287) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118287), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (26218 ^ _776541) ^ [_1250093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250093)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1250093)) = _1250093)], (3734 ^ _776541) ^ [_832523, _832525, _832527, _832529, _832531, _832533] : [-(c_List_Oinsert(_832533, _832529, _832525) = c_List_Oinsert(_832531, _832527, _832523)), _832533 = _832531, _832529 = _832527, _832525 = _832523], (45680 ^ _776541) ^ [_1693005, _1693007] : [-(c_Enum_Oenum__the(_1693005, _1693007) = c_HOL_OThe(_1693005, _1693007))], (36320 ^ _776541) ^ [_1462691] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462691)), -(_1462691 = 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))), _1462691)), c_FunDef_Omax__strict)))], (49616 ^ _776541) ^ [_1779162, _1779164] : [49619 ^ _776541 : [(49624 ^ _776541) ^ [] : [49617 ^ [_1779162, _1779164] = 49618 ^ [_1779162, _1779164]], (49622 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779162, _1779162)), hAPP(hAPP(c_Product__Type_OPair(_1779162, _1779162), 49618 ^ [_1779162, _1779164]), 49617 ^ [_1779162, _1779164])), _1779164)))], (49620 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779162, _1779162)), hAPP(hAPP(c_Product__Type_OPair(_1779162, _1779162), 49617 ^ [_1779162, _1779164]), 49618 ^ [_1779162, _1779164])), _1779164)))]], -(c_Relation_Oantisym(_1779162, _1779164))], (8597 ^ _776541) ^ [_924225, _924227, _924229, _924231] : [class_Lattices_Osemilattice__inf(_924225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924225), _924227), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924225), _924229), _924231))), 8604 ^ _776541 : [(8607 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924225), _924227), _924231)))], (8605 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924225), _924227), _924229)))]]], (25109 ^ _776541) ^ [_1231021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231021)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1231021))], (7342 ^ _776541) ^ [_896785, _896787] : [class_Complete__Lattice_Ocomplete__lattice(_896785), -(c_Complete__Lattice_OSup__class_OSup(_896785, hAPP(hAPP(c_Set_Oinsert(_896785), _896787), c_Orderings_Obot__class_Obot(tc_fun(_896785, tc_HOL_Obool)))) = _896787)], (29475 ^ _776541) ^ [_1304549, _1304551] : [class_Rings_Oring__1__no__zero__divisors(_1304549), 29478 ^ _776541 : [(29479 ^ _776541) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1304549), _1304551), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1304549), -(_1304551 = c_Groups_Oone__class_Oone(_1304549)), -(_1304551 = hAPP(c_Groups_Ouminus__class_Ouminus(_1304549), c_Groups_Oone__class_Oone(_1304549)))], (29489 ^ _776541) ^ [] : [29490 ^ _776541 : [(29493 ^ _776541) ^ [] : [_1304551 = hAPP(c_Groups_Ouminus__class_Ouminus(_1304549), c_Groups_Oone__class_Oone(_1304549))], (29491 ^ _776541) ^ [] : [_1304551 = c_Groups_Oone__class_Oone(_1304549)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1304549), _1304551), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1304549))]]], (33827 ^ _776541) ^ [_1403099, _1403101, _1403103] : [class_Int_Onumber__ring(_1403099), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1403099), _1403101), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1403103))) = hAPP(hAPP(c_HOL_OLet(_1403099, _1403099), hAPP(hAPP(c_Power_Opower__class_Opower(_1403099), _1403101), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403103))), hAPP(hAPP(c_COMBS(_1403099, _1403099, _1403099), c_Groups_Otimes__class_Otimes(_1403099)), c_COMBI(_1403099))))], (49736 ^ _776541) ^ [_1781694] : [-(c_Relation_Osym(_1781694, c_Relation_OId(_1781694)))], (49183 ^ _776541) ^ [_1769231, _1769233] : [49186 ^ _776541 : [(49192 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769231, _1769231)), hAPP(hAPP(c_Product__Type_OPair(_1769231, _1769231), 49184 ^ [_1769231, _1769233]), 49188 ^ [_1769231, _1769233])), _1769233))], (49190 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769231, _1769231)), hAPP(hAPP(c_Product__Type_OPair(_1769231, _1769231), 49185 ^ [_1769231, _1769233]), 49188 ^ [_1769231, _1769233])), _1769233)))], (49187 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769231, _1769231)), hAPP(hAPP(c_Product__Type_OPair(_1769231, _1769231), 49184 ^ [_1769231, _1769233]), 49185 ^ [_1769231, _1769233])), _1769233)))]], -(c_Relation_Otrans(_1769231, _1769233))], (47642 ^ _776541) ^ [_1734855, _1734857, _1734859, _1734861, _1734863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1734855, _1734857)), hAPP(_1734855, _1734859))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1734861, _1734861)), hAPP(hAPP(c_Product__Type_OPair(_1734861, _1734861), _1734857), _1734859)), c_List_Omeasures(_1734861, _1734863))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734861, _1734861)), hAPP(hAPP(c_Product__Type_OPair(_1734861, _1734861), _1734857), _1734859)), c_List_Omeasures(_1734861, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1734861, tc_Nat_Onat)), _1734855), _1734863)))))], (38935 ^ _776541) ^ [_1525583, _1525585, _1525587, _1525589, _1525591, _1525593] : [-(hBOOL(hAPP(hAPP(c_member(_1525583), _1525585), _1525587))), 38938 ^ _776541 : [(38945 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525583), _1525589), _1525587))), -(hAPP(c_Set_Ovimage(_1525591, _1525583, hAPP(hAPP(c_COMBC(_1525591, _1525583, _1525583), hAPP(hAPP(c_COMBC(_1525591, _1525583, tc_fun(_1525583, _1525583)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525583, tc_fun(_1525583, _1525583)), _1525591), c_If(_1525583)), hAPP(hAPP(c_COMBC(_1525591, tc_fun(_1525591, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525591)), _1525593))), _1525585)), _1525589)), _1525587) = c_Orderings_Obot__class_Obot(tc_fun(_1525591, tc_HOL_Obool)))], (38939 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1525583), _1525589), _1525587)), -(hAPP(c_Set_Ovimage(_1525591, _1525583, hAPP(hAPP(c_COMBC(_1525591, _1525583, _1525583), hAPP(hAPP(c_COMBC(_1525591, _1525583, tc_fun(_1525583, _1525583)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525583, tc_fun(_1525583, _1525583)), _1525591), c_If(_1525583)), hAPP(hAPP(c_COMBC(_1525591, tc_fun(_1525591, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525591)), _1525593))), _1525585)), _1525589)), _1525587) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1525591, tc_HOL_Obool)), _1525593))]]], (23573 ^ _776541) ^ [_1203820, _1203822] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203820), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203822)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1203820), _1203822)))], (23683 ^ _776541) ^ [_1205671, _1205673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205671), 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)), _1205673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205671), _1205673)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32578 ^ _776541) ^ [_1365973, _1365975, _1365977, _1365979, _1365981] : [hBOOL(hAPP(hAPP(c_member(_1365973), _1365975), _1365977)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365979, tc_HOL_Obool)), hAPP(_1365981, _1365975)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365973, tc_fun(_1365979, tc_HOL_Obool)), _1365977), _1365981)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365973, tc_fun(_1365979, tc_HOL_Obool)), _1365977), _1365981))], (10705 ^ _776541) ^ [_960980, _960982, _960984] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960980, tc_HOL_Obool)), _960982), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960980, tc_HOL_Obool)), _960984)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960980, tc_HOL_Obool)), _960982), _960984))], (8345 ^ _776541) ^ [_919565, _919567] : [class_Lattices_Osemilattice__sup(_919565), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919565), _919567), _919567) = _919567)], (36402 ^ _776541) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (30244 ^ _776541) ^ [_1319038, _1319040, _1319042, _1319044] : [class_Orderings_Olinorder(_1319038), 30247 ^ _776541 : [(30248 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319038), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319038), _1319040), _1319042)), _1319044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319038), _1319040), _1319044))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319038), _1319042), _1319044)))], (30258 ^ _776541) ^ [] : [30259 ^ _776541 : [(30262 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319038), _1319042), _1319044))], (30260 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319038), _1319040), _1319044))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319038), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319038), _1319040), _1319042)), _1319044)))]]], (52191 ^ _776541) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (16608 ^ _776541) ^ [] : [-(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)))], (50261 ^ _776541) ^ [_1792450, _1792452, _1792454, _1792456, _1792458, _1792460] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1792450, _1792452, _1792454, _1792456, c_Lazy__Sequence_Olazy__sequence_OInsert(_1792452, _1792458, _1792460)) = hAPP(hAPP(hAPP(_1792456, _1792458), _1792460), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1792450, _1792452, _1792454, _1792456, _1792460)))], (30238 ^ _776541) ^ [_1318931, _1318933, _1318935] : [class_Orderings_Olinorder(_1318931), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318931), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318931), _1318933), _1318935)), _1318933)))], (12465 ^ _776541) ^ [_995530, _995532] : [class_Lattices_Olattice(_995530), hBOOL(hAPP(c_Finite__Set_Ofinite(_995530), _995532)), -(_995532 = c_Orderings_Obot__class_Obot(tc_fun(_995530, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_995530), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_995530), 12478 ^ [_995530, _995532]), 12479 ^ [_995530, _995532])), hAPP(hAPP(c_Set_Oinsert(_995530), 12478 ^ [_995530, _995532]), hAPP(hAPP(c_Set_Oinsert(_995530), 12479 ^ [_995530, _995532]), c_Orderings_Obot__class_Obot(tc_fun(_995530, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_995530), c_Big__Operators_Olattice__class_OInf__fin(_995530, _995532)), _995532)))], (7658 ^ _776541) ^ [_903915, _903917, _903919, _903921] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903915, tc_HOL_Obool)), _903917), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903915, tc_HOL_Obool)), _903919), _903921)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903915, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903915, tc_HOL_Obool)), _903917), _903919)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903915, tc_HOL_Obool)), _903917), _903921)))], (52449 ^ _776541) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52015 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (44717 ^ _776541) ^ [_1670409, _1670411, _1670413, _1670415, _1670417] : [-(c_List_Olist_Olist__size(_1670409, _1670411, hAPP(hAPP(c_List_Omap(_1670413, _1670409), _1670415), _1670417)) = c_List_Olist_Olist__size(_1670413, hAPP(c_Fun_Ocomp(_1670409, tc_Nat_Onat, _1670413, _1670411), _1670415), _1670417))], (15718 ^ _776541) ^ [_1061551, _1061553] : [hAPP(c_Nat_OSuc, _1061551) = hAPP(c_Nat_OSuc, _1061553), -(_1061551 = _1061553)], (68 ^ _776541) ^ [_777615, _777617, _777619, _777621, _777623, _777625] : [-(c_Finite__Set_Ofolding__one(_777623, _777619, _777615)), c_Finite__Set_Ofolding__one(_777625, _777621, _777617), _777625 = _777623, _777621 = _777619, _777617 = _777615], (40639 ^ _776541) ^ [_1570195, _1570197, _1570199, _1570201, _1570203] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570195, _1570195)), hAPP(hAPP(c_Product__Type_OPair(_1570195, _1570195), _1570197), _1570199)), _1570201)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570195, _1570195)), hAPP(hAPP(c_Product__Type_OPair(_1570195, _1570195), _1570199), _1570203)), c_Transitive__Closure_Otrancl(_1570195, _1570201))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570195, _1570195)), hAPP(hAPP(c_Product__Type_OPair(_1570195, _1570195), _1570197), _1570203)), c_Transitive__Closure_Otrancl(_1570195, _1570201))))], (30530 ^ _776541) ^ [_1324294] : [class_Orderings_Oord(_1324294), -(c_Orderings_Oord__class_Omin(_1324294) = c_Orderings_Oord_Omin(_1324294, c_Orderings_Oord__class_Oless__eq(_1324294)))], (24716 ^ _776541) ^ [_1223697, _1223699] : [_1223697 = _1223699, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223697) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223699))], (45752 ^ _776541) ^ [_1694607, _1694609] : [c_List_Oremdups(_1694607, _1694609) = _1694609, -(hBOOL(hAPP(c_List_Odistinct(_1694607), _1694609)))], (41877 ^ _776541) ^ [_1603484, _1603486, _1603488, _1603490] : [-(c_List_Olist_Olist__size(_1603484, _1603486, hAPP(hAPP(c_List_Olist_OCons(_1603484), _1603488), _1603490)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1603486, _1603488)), c_List_Olist_Olist__size(_1603484, _1603486, _1603490))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28607 ^ _776541) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (35144 ^ _776541) ^ [_1432469, _1432471, _1432473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432469, tc_fun(_1432469, tc_HOL_Obool))), _1432471), _1432473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432469, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1432469, _1432473)), c_Wellfounded_Oaccp(_1432469, _1432471))))], (8062 ^ _776541) ^ [_913523, _913525, _913527, _913529] : [hBOOL(hAPP(hAPP(c_member(_913523), _913525), _913527)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913523, tc_HOL_Obool)), _913527), hAPP(hAPP(c_Set_Oinsert(_913523), _913525), _913529)) = hAPP(hAPP(c_Set_Oinsert(_913523), _913525), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913523, tc_HOL_Obool)), _913527), _913529)))], (45158 ^ _776541) ^ [_1680896, _1680898, _1680900] : [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, _1680896), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1680896)), _1680898)))), -(hBOOL(hAPP(hAPP(c_member(_1680896), hAPP(c_Product__Type_Ofst(_1680896, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1680896, _1680898), _1680900))), hAPP(c_List_Oset(_1680896), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1680896), _1680896), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1680896)), _1680898)))))], (35056 ^ _776541) ^ [_1430714, _1430716, _1430718, _1430720, _1430722, _1430724, _1430726] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430714, _1430716), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430718), _1430720))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430722, _1430716), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430724), _1430726))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1430716)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430714), _1430722), _1430716), 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), _1430718), _1430724)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430720), _1430726)), _1430716))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430720), _1430726), _1430716)))))], (36472 ^ _776541) ^ [_1466397, _1466399, _1466401, _1466403, _1466405] : [-(hAPP(c_Relation_OImage(_1466397, _1466399, _1466401), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466397, tc_HOL_Obool)), _1466403), _1466405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466399, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466397, _1466399, _1466401), _1466403)), hAPP(c_Relation_OImage(_1466397, _1466399, _1466401), _1466405)))], (47259 ^ _776541) ^ [_1726725, _1726727, _1726729, _1726731, _1726733] : [-(c_List_OtakeWhile(_1726725, _1726727, hAPP(hAPP(c_List_Omap(_1726729, _1726725), _1726731), _1726733)) = hAPP(hAPP(c_List_Omap(_1726729, _1726725), _1726731), c_List_OtakeWhile(_1726729, hAPP(c_Fun_Ocomp(_1726725, tc_HOL_Obool, _1726729, _1726727), _1726731), _1726733)))], (41757 ^ _776541) ^ [_1599696, _1599698, _1599700] : [hAPP(hAPP(c_List_Olist_OCons(_1599696), _1599698), _1599700) = _1599700], (39493 ^ _776541) ^ [_1542094, _1542096, _1542098, _1542100, _1542102, _1542104, _1542106, _1542108] : [c_Fun_Oinj__on(_1542094, _1542096, _1542098, _1542100), c_Fun_Oinj__on(_1542102, _1542104, _1542106, _1542108), -(c_Fun_Oinj__on(tc_prod(_1542094, _1542102), tc_prod(_1542096, _1542104), c_Product__Type_Omap__pair(_1542094, _1542096, _1542102, _1542104, _1542098, _1542106), hAPP(hAPP(c_Product__Type_OSigma(_1542094, _1542102), _1542100), hAPP(c_COMBK(tc_fun(_1542102, tc_HOL_Obool), _1542094), _1542108))))], (35440 ^ _776541) ^ [_1437378, _1437380, _1437382, _1437384, _1437386] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1437378, _1437380), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1437382), _1437384))), -(_1437380 = 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), _1437386), _1437378), _1437380), 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), _1437386), _1437382)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1437386), _1437384)), _1437380))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1437386), _1437384), _1437380)))))], (35072 ^ _776541) ^ [_1431125, _1431127, _1431129, _1431131, _1431133, _1431135] : [-(c_Nitpick_Opair__box_Opair__box__case(_1431125, _1431127, _1431129, _1431131, c_Nitpick_Opair__box_OPairBox(_1431125, _1431127, _1431133, _1431135)) = hAPP(hAPP(_1431131, _1431133), _1431135))], (3418 ^ _776541) ^ [_827575, _827577, _827579, _827581, _827583, _827585] : [-(c_Finite__Set_Ofold(_827585, _827581, _827577) = c_Finite__Set_Ofold(_827583, _827579, _827575)), _827585 = _827583, _827581 = _827579, _827577 = _827575], (41899 ^ _776541) ^ [_1604039, _1604041, _1604043, _1604045, _1604047] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604039), tc_List_Olist(_1604039))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604039), tc_List_Olist(_1604039)), _1604041), _1604043)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1604039), c_List_Olistrel1(_1604039, _1604045)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604039), tc_List_Olist(_1604039))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604039), tc_List_Olist(_1604039)), hAPP(hAPP(c_List_Olist_OCons(_1604039), _1604047), _1604041)), hAPP(hAPP(c_List_Olist_OCons(_1604039), _1604047), _1604043))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1604039), c_List_Olistrel1(_1604039, _1604045)))))], (24838 ^ _776541) ^ [_1225977, _1225979, _1225981, _1225983] : [class_Divides_Osemiring__div(_1225977), -(c_Divides_Odiv__class_Omod(_1225977, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225977), _1225979), _1225981), _1225983) = c_Divides_Odiv__class_Omod(_1225977, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225977), c_Divides_Odiv__class_Omod(_1225977, _1225979, _1225983)), _1225981), _1225983))], (50584 ^ _776541) ^ [_1799016, _1799018, _1799020] : [c_Fun_Obij__betw(_1799016, _1799018, _1799020, c_Orderings_Otop__class_Otop(tc_fun(_1799016, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799018, tc_HOL_Obool))), 50587 ^ _776541 : [(50590 ^ _776541) ^ [] : [-(hAPP(c_Set_Oimage(_1799016, _1799018, _1799020), c_Orderings_Otop__class_Otop(tc_fun(_1799016, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799018, tc_HOL_Obool)))], (50588 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1799016, _1799018, _1799020, c_Orderings_Otop__class_Otop(tc_fun(_1799016, tc_HOL_Obool))))]]], (4142 ^ _776541) ^ [_839257, _839259, _839261, _839263, _839265, _839267, _839269, _839271] : [-(c_New__Random__Sequence_Opos__map(_839271, _839267, _839263, _839259) = c_New__Random__Sequence_Opos__map(_839269, _839265, _839261, _839257)), _839271 = _839269, _839267 = _839265, _839263 = _839261, _839259 = _839257], (42143 ^ _776541) ^ [_1611623, _1611625, _1611627, _1611629] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611623)), hAPP(hAPP(c_List_Olist_OCons(_1611623), _1611625), _1611627)), c_List_Olists(_1611623, _1611629))), 42146 ^ _776541 : [(42149 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611623)), _1611627), c_List_Olists(_1611623, _1611629))))], (42147 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611623), _1611625), _1611629)))]]], (29585 ^ _776541) ^ [_1306670, _1306672, _1306674] : [class_Rings_Olinordered__idom(_1306670), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306670), c_Groups_Ozero__class_Ozero(_1306670)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306670), _1306672), 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)))), _1306674)))))], (49788 ^ _776541) ^ [_1782498, _1782500, _1782502] : [c_Equiv__Relations_Oequiv(_1782498, _1782500, _1782502), 49791 ^ _776541 : [(49796 ^ _776541) ^ [] : [-(c_Relation_Otrans(_1782498, _1782502))], (49794 ^ _776541) ^ [] : [-(c_Relation_Osym(_1782498, _1782502))], (49792 ^ _776541) ^ [] : [-(c_Relation_Orefl__on(_1782498, _1782500, _1782502))]]], (34842 ^ _776541) ^ [_1426706, _1426708, _1426710, _1426712, _1426714, _1426716] : [hAPP(hAPP(c_Product__Type_OPair(_1426706, _1426708), _1426710), _1426712) = hAPP(hAPP(c_Product__Type_OPair(_1426706, _1426708), _1426714), _1426716), 34845 ^ _776541 : [(34848 ^ _776541) ^ [] : [-(_1426712 = _1426716)], (34846 ^ _776541) ^ [] : [-(_1426710 = _1426714)]]], (47046 ^ _776541) ^ [_1722220, _1722222, _1722224, _1722226, _1722228] : [c_List_Olist__all2(_1722220, _1722222, _1722224, hAPP(c_List_Orev(_1722220), _1722226), hAPP(c_List_Orev(_1722222), _1722228)), -(c_List_Olist__all2(_1722220, _1722222, _1722224, _1722226, _1722228))], (19573 ^ _776541) ^ [_1130234, _1130236] : [class_Rings_Odivision__ring(_1130234), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130234), _1130236), c_Groups_Oone__class_Oone(_1130234)) = _1130236)], (32490 ^ _776541) ^ [_1361934, _1361936, _1361938, _1361940, _1361942, _1361944] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361934, tc_fun(_1361936, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1361934, tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_fun(_1361936, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361936, tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_fun(_1361936, tc_HOL_Obool)), _1361934), c_COMBC(_1361936, tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361936, tc_prod(_1361934, _1361936)), tc_fun(_1361936, tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool)), _1361934), hAPP(c_COMBB(tc_prod(_1361934, _1361936), tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool), _1361936), c_member(tc_prod(_1361934, _1361936)))), c_Product__Type_OPair(_1361934, _1361936)))), _1361938)), hAPP(hAPP(c_COMBC(_1361934, tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_fun(_1361936, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361936, tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_fun(_1361936, tc_HOL_Obool)), _1361934), c_COMBC(_1361936, tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361936, tc_prod(_1361934, _1361936)), tc_fun(_1361936, tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool)), _1361934), hAPP(c_COMBB(tc_prod(_1361934, _1361936), tc_fun(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool), tc_HOL_Obool), _1361936), c_member(tc_prod(_1361934, _1361936)))), c_Product__Type_OPair(_1361934, _1361936)))), _1361940)), _1361942), _1361944)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361934, _1361936)), hAPP(hAPP(c_Product__Type_OPair(_1361934, _1361936), _1361942), _1361944)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1361934, _1361936), tc_HOL_Obool)), _1361938), _1361940))))], (34117 ^ _776541) ^ [_1410416, _1410418] : [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(_1410418))), 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)), _1410416))))), -(hAPP(c_Nat_OSuc, _1410416) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410418))], (6672 ^ _776541) ^ [_884536, _884538, _884540, _884542] : [class_Orderings_Oorder(_884536), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884536), _884538), _884540)), _884538 = _884542, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884536), _884542), _884540)))], (52135 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (39259 ^ _776541) ^ [_1534678, _1534680, _1534682, _1534684] : [-(_1534678 = c_Orderings_Obot__class_Obot(tc_fun(_1534680, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1534680, _1534682), _1534682, c_Product__Type_Osnd(_1534680, _1534682)), hAPP(hAPP(c_Product__Type_OSigma(_1534680, _1534682), _1534678), hAPP(c_COMBK(tc_fun(_1534682, tc_HOL_Obool), _1534680), _1534684))) = _1534684)], (36699 ^ _776541) ^ [_1472519, _1472521, _1472523] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472519), hAPP(hAPP(c_Set_Oinsert(_1472519), _1472521), c_Orderings_Obot__class_Obot(tc_fun(_1472519, tc_HOL_Obool)))), _1472523) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1472519, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472519, _1472519, _1472523), hAPP(hAPP(c_Set_Oinsert(_1472519), _1472521), c_Orderings_Obot__class_Obot(tc_fun(_1472519, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1472519, tc_HOL_Obool), tc_HOL_Obool))))], (46217 ^ _776541) ^ [_1705791, _1705793] : [-(c_Random_Oselect__weight(_1705791, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1705791), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1705791, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1705791, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1705791)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1705793)) = c_Random_Oselect__weight(_1705791, _1705793))], (32636 ^ _776541) ^ [_1368745, _1368747, _1368749, _1368751, _1368753, _1368755, _1368757] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368745, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368747, tc_fun(_1368745, tc_HOL_Obool)), _1368749), _1368751)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368753, tc_fun(_1368745, tc_HOL_Obool)), _1368755), _1368757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368747, tc_fun(_1368745, tc_HOL_Obool)), _1368749), hAPP(hAPP(c_COMBB(tc_fun(_1368753, tc_fun(_1368745, tc_HOL_Obool)), tc_fun(_1368745, tc_HOL_Obool), _1368747), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368753, tc_fun(_1368745, tc_HOL_Obool)), _1368755)), hAPP(hAPP(c_COMBC(_1368747, tc_fun(_1368753, tc_fun(_1368745, tc_HOL_Obool)), tc_fun(_1368753, tc_fun(_1368745, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368745, tc_HOL_Obool), tc_fun(_1368745, tc_HOL_Obool)), tc_fun(tc_fun(_1368753, tc_fun(_1368745, tc_HOL_Obool)), tc_fun(_1368753, tc_fun(_1368745, tc_HOL_Obool))), _1368747), c_COMBB(tc_fun(_1368745, tc_HOL_Obool), tc_fun(_1368745, tc_HOL_Obool), _1368753)), hAPP(hAPP(c_COMBB(tc_fun(_1368745, tc_HOL_Obool), tc_fun(tc_fun(_1368745, tc_HOL_Obool), tc_fun(_1368745, tc_HOL_Obool)), _1368747), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368745, tc_HOL_Obool))), _1368751))), _1368757))))], (23811 ^ _776541) ^ [_1207837, _1207839, _1207841] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207837)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207839)), _1207841)) = 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), _1207837), _1207839))), _1207841))], (33014 ^ _776541) ^ [_1379267, _1379269] : [-(hAPP(c_Set_OCollect(_1379267), hAPP(hAPP(c_COMBC(_1379267, _1379267, tc_HOL_Obool), c_fequal), _1379269)) = hAPP(hAPP(c_Set_Oinsert(_1379267), _1379269), c_Orderings_Obot__class_Obot(tc_fun(_1379267, tc_HOL_Obool))))], (4262 ^ _776541) ^ [_841109, _841111, _841113, _841115] : [-(c_List_Ozip(_841115, _841111) = c_List_Ozip(_841113, _841109)), _841115 = _841113, _841111 = _841109], (34512 ^ _776541) ^ [_1418985, _1418987, _1418989, _1418991, _1418993, _1418995, _1418997] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418985, tc_fun(_1418987, tc_fun(_1418989, tc_HOL_Obool))), _1418991), _1418993), _1418995), _1418997)), 34515 ^ _776541 : [(34516 ^ _776541) ^ [_1419113] : [hBOOL(hAPP(hAPP(c_member(_1418985), _1419113), _1418991)), -(hBOOL(hAPP(hAPP(hAPP(_1418993, _1419113), _1418995), _1418997)))]]], (3540 ^ _776541) ^ [_829462, _829464, _829466, _829468, _829470, _829472] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_829472, _829468, _829464) = c_SetInterval_Oord__class_OgreaterThanAtMost(_829470, _829466, _829462)), _829472 = _829470, _829468 = _829466, _829464 = _829462], (50085 ^ _776541) ^ [_1788361, _1788363, _1788365, _1788367, _1788369] : [c_Fun_Oinj__on(_1788361, _1788363, _1788365, c_Orderings_Otop__class_Otop(tc_fun(_1788361, tc_HOL_Obool))), hAPP(_1788365, _1788367) = _1788369, -(hAPP(c_Hilbert__Choice_Oinv__into(_1788361, _1788363, c_Orderings_Otop__class_Otop(tc_fun(_1788361, tc_HOL_Obool)), _1788365), _1788369) = _1788367)], (6616 ^ _776541) ^ [_883644, _883646, _883648, _883650] : [class_Orderings_Oorder(_883644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883644), _883646), _883648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883644), _883650), _883646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883644), _883650), _883648)))], (32820 ^ _776541) ^ [_1373125, _1373127, _1373129, _1373131, _1373133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373125, tc_HOL_Obool)), _1373127), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1373129, tc_fun(_1373125, tc_HOL_Obool)), _1373131), _1373133))), 32823 ^ _776541 : [(32824 ^ _776541) ^ [_1373258] : [hBOOL(hAPP(hAPP(c_member(_1373129), _1373258), _1373131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373125, tc_HOL_Obool)), _1373127), hAPP(_1373133, _1373258))))]]], (34692 ^ _776541) ^ [_1422898, _1422900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1422898, _1422898)), hAPP(hAPP(c_Product__Type_OPair(_1422898, _1422898), 34693 ^ [_1422898, _1422900]), 34693 ^ [_1422898, _1422900])), _1422900)), -(c_Nitpick_Orefl_H(_1422898, _1422900))], (35096 ^ _776541) ^ [_1431522, _1431524, _1431526, _1431528] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1431522, _1431524), _1431526)), hBOOL(hAPP(hAPP(_1431524, _1431528), _1431526)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1431522, _1431524), _1431528)))], (16548 ^ _776541) ^ [_1074352, _1074354, _1074356] : [16549 ^ _776541 : [(16552 ^ _776541) ^ [] : [_1074352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16550 ^ _776541) ^ [] : [_1074354 = _1074356]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074352), _1074354) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074352), _1074356))], (3712 ^ _776541) ^ [_832204, _832206] : [_832206 = _832204, -(c_List_Oembed__list(_832206) = c_List_Oembed__list(_832204))], (29315 ^ _776541) ^ [_1301847, _1301849] : [class_Rings_Olinordered__idom(_1301847), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301847), hAPP(c_Groups_Oabs__class_Oabs(_1301847), _1301849)), 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(_1301847), _1301849), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29665 ^ _776541) ^ [_1308347, _1308349] : [class_Rings_Oring__1(_1308347), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1308347), hAPP(c_Groups_Ouminus__class_Ouminus(_1308347), c_Groups_Oone__class_Oone(_1308347))), 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)))), _1308349))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1308347), c_Groups_Oone__class_Oone(_1308347)))], (16076 ^ _776541) ^ [_1067234, _1067236] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067234), hAPP(c_Nat_OSuc, _1067236)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067234), _1067236)))], (20445 ^ _776541) ^ [_1145431, _1145433, _1145435, _1145437, _1145439] : [class_Fields_Olinordered__field(_1145431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145431), c_Groups_Ozero__class_Ozero(_1145431)), _1145433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145431), _1145433), _1145435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145431), c_Groups_Ozero__class_Ozero(_1145431)), _1145437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145431), _1145437), _1145439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145431), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145431), _1145433), _1145439)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145431), _1145435), _1145437))))], (4998 ^ _776541) ^ [_852743, _852745] : [_852745 = _852743, -(c_Set_OCollect(_852745) = c_Set_OCollect(_852743))], (43298 ^ _776541) ^ [_1639073, _1639075, _1639077] : [-(_1639073 = c_List_Olist_ONil(_1639075)), -(hBOOL(hAPP(hAPP(c_member(_1639075), hAPP(c_Product__Type_Ofst(_1639075, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1639075, _1639073), _1639077))), hAPP(c_List_Oset(_1639075), _1639073))))], (14198 ^ _776541) ^ [_1031930, _1031932] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1031930, _1031932))))], (14242 ^ _776541) ^ [_1032776, _1032778, _1032780, _1032782] : [class_Rings_Ocomm__semiring__1(_1032776), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032776), _1032778), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032776), _1032780), _1032782)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032776), _1032778), _1032780)), _1032782))], (5004 ^ _776541) ^ [_852828, _852830] : [_852830 = _852828, -(c_Groups_Ouminus__class_Ouminus(_852830) = c_Groups_Ouminus__class_Ouminus(_852828))], (46235 ^ _776541) ^ [_1706402, _1706404, _1706406] : [class_Groups_Oab__semigroup__add(_1706402), -(c_List_Ofoldr(_1706402, _1706402, c_Groups_Oplus__class_Oplus(_1706402), _1706404, _1706406) = hAPP(c_List_Ofoldl(_1706402, _1706402, c_Groups_Oplus__class_Oplus(_1706402), _1706406), _1706404))], (45189 ^ _776541) ^ [_1681764] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1681764)) = _1681764)], (38462 ^ _776541) ^ [_1513924] : [-(c_Wellfounded_OwfP(_1513924, hAPP(c_COMBK(tc_fun(_1513924, tc_HOL_Obool), _1513924), hAPP(c_COMBK(tc_HOL_Obool, _1513924), c_fFalse))))], (3776 ^ _776541) ^ [_833194, _833196, _833198, _833200] : [-(c_List_Omeasures(_833200, _833196) = c_List_Omeasures(_833198, _833194)), _833200 = _833198, _833196 = _833194], (17603 ^ _776541) ^ [_1093559, _1093561, _1093563, _1093565, _1093567, _1093569] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1093559), -(_1093561 = c_Groups_Ozero__class_Ozero(_1093559)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093559), _1093563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093559), _1093561), _1093567)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093559), _1093565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093559), _1093561), _1093569)), _1093563 = _1093565, -(_1093567 = _1093569)], (40821 ^ _776541) ^ [_1575600, _1575602, _1575604, _1575606, _1575608] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575600, _1575600)), hAPP(hAPP(c_Product__Type_OPair(_1575600, _1575600), _1575602), _1575604)), c_Transitive__Closure_Ortrancl(_1575600, _1575606))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575600, _1575600)), hAPP(hAPP(c_Product__Type_OPair(_1575600, _1575600), _1575604), _1575608)), c_Transitive__Closure_Ortrancl(_1575600, _1575606))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575600, _1575600)), hAPP(hAPP(c_Product__Type_OPair(_1575600, _1575600), _1575602), _1575608)), c_Transitive__Closure_Ortrancl(_1575600, _1575606))))], (45945 ^ _776541) ^ [_1698198, _1698200] : [c_List_Oconcat(_1698198, _1698200) = c_List_Olist_ONil(_1698198), 45948 ^ _776541 : [(45949 ^ _776541) ^ [_1698289] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698198)), _1698289), hAPP(c_List_Oset(tc_List_Olist(_1698198)), _1698200))), -(_1698289 = c_List_Olist_ONil(_1698198))]]], (42465 ^ _776541) ^ [_1619742, _1619744] : [-(hAPP(c_List_Oset(_1619742), _1619744) = hAPP(c_Set_OCollect(_1619742), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1619742), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1619742, 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)), _1619742), 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)), _1619742), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1619742, tc_fun(tc_Nat_Onat, _1619742), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619742, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1619742), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1619742), c_COMBB(_1619742, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1619742), _1619744))))), 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(_1619742)), _1619744))))))], (30406 ^ _776541) ^ [_1322038, _1322040, _1322042] : [class_Orderings_Olinorder(_1322038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322038), _1322040)), -(_1322040 = c_Orderings_Obot__class_Obot(tc_fun(_1322038, tc_HOL_Obool))), 30417 ^ _776541 : [(30418 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322038), _1322042), hAPP(c_Finite__Set_Ofold1(_1322038, c_Orderings_Oord__class_Omin(_1322038)), _1322040))), 30421 ^ _776541 : [(30422 ^ _776541) ^ [_1322331] : [hBOOL(hAPP(hAPP(c_member(_1322038), _1322331), _1322040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322038), _1322042), _1322331)))]]], (30428 ^ _776541) ^ [] : [30430 ^ _776541 : [(30433 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322038), _1322042), 30429 ^ [_1322038, _1322040, _1322042]))], (30431 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322038), 30429 ^ [_1322038, _1322040, _1322042]), _1322040)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322038), _1322042), hAPP(c_Finite__Set_Ofold1(_1322038, c_Orderings_Oord__class_Omin(_1322038)), _1322040))))]]], (37358 ^ _776541) ^ [_1487565, _1487567, _1487569, _1487571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487565), hAPP(c_Set_Oimage(_1487567, _1487565, _1487569), _1487571))), c_Fun_Oinj__on(_1487567, _1487565, _1487569, _1487571), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1487567), _1487571)))], (1834 ^ _776541) ^ [_802330, _802332] : [-(class_Orderings_Oord(_802330)), _802332 = _802330, class_Orderings_Oord(_802332)], (15240 ^ _776541) ^ [_1051624, _1051626] : [class_Rings_Oring__1__no__zero__divisors(_1051624), 15243 ^ _776541 : [(15244 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051624), _1051626), _1051626) = c_Groups_Oone__class_Oone(_1051624), -(_1051626 = c_Groups_Oone__class_Oone(_1051624)), -(_1051626 = hAPP(c_Groups_Ouminus__class_Ouminus(_1051624), c_Groups_Oone__class_Oone(_1051624)))], (15254 ^ _776541) ^ [] : [15255 ^ _776541 : [(15258 ^ _776541) ^ [] : [_1051626 = hAPP(c_Groups_Ouminus__class_Ouminus(_1051624), c_Groups_Oone__class_Oone(_1051624))], (15256 ^ _776541) ^ [] : [_1051626 = c_Groups_Oone__class_Oone(_1051624)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051624), _1051626), _1051626) = c_Groups_Oone__class_Oone(_1051624))]]], (48237 ^ _776541) ^ [_1748124, _1748126, _1748128] : [c_List_Olist__all(_1748124, _1748126, _1748128), 48240 ^ _776541 : [(48241 ^ _776541) ^ [_1748205] : [hBOOL(hAPP(hAPP(c_member(_1748124), _1748205), hAPP(c_List_Oset(_1748124), _1748128))), -(hBOOL(hAPP(_1748126, _1748205)))]]], (44912 ^ _776541) ^ [_1675784, _1675786, _1675788, _1675790, _1675792, _1675794] : [-(hBOOL(hAPP(hAPP(c_member(_1675784), _1675786), hAPP(c_List_Oset(_1675784), _1675788)))), -(hAPP(hAPP(c_List_Omap(_1675784, _1675790), c_Fun_Ofun__upd(_1675784, _1675790, _1675792, _1675786, _1675794)), _1675788) = hAPP(hAPP(c_List_Omap(_1675784, _1675790), _1675792), _1675788))], (48370 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27441 ^ _776541) ^ [_1269972, _1269974, _1269976] : [class_Groups_Oordered__ab__group__add__abs(_1269972), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269972), hAPP(c_Groups_Oabs__class_Oabs(_1269972), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269972), _1269974), _1269976))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269972), hAPP(c_Groups_Oabs__class_Oabs(_1269972), _1269974)), hAPP(c_Groups_Oabs__class_Oabs(_1269972), _1269976)))))], (44328 ^ _776541) ^ [_1663046, _1663048, _1663050, _1663052, _1663054, _1663056] : [class_Orderings_Olinorder(_1663046), 44331 ^ _776541 : [(44338 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1663046), hAPP(_1663048, _1663050)), hAPP(_1663048, _1663052)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663054, _1663046, _1663048), _1663050), hAPP(hAPP(c_List_Olist_OCons(_1663054), _1663052), _1663056)) = hAPP(hAPP(c_List_Olist_OCons(_1663054), _1663052), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663054, _1663046, _1663048), _1663050), _1663056)))], (44332 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1663046), hAPP(_1663048, _1663050)), hAPP(_1663048, _1663052))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663054, _1663046, _1663048), _1663050), hAPP(hAPP(c_List_Olist_OCons(_1663054), _1663052), _1663056)) = hAPP(hAPP(c_List_Olist_OCons(_1663054), _1663050), hAPP(hAPP(c_List_Olist_OCons(_1663054), _1663052), _1663056)))]]], (15105 ^ _776541) ^ [_1049242, _1049244] : [class_Groups_Omonoid__mult(_1049242), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049242), c_Groups_Oone__class_Oone(_1049242)), _1049244) = _1049244)], (46148 ^ _776541) ^ [_1703383, _1703385] : [-(c_List_Otranspose(_1703383, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1703383)), c_List_Olist_ONil(_1703383)), _1703385)) = c_List_Otranspose(_1703383, _1703385))], (17477 ^ _776541) ^ [_1091290, _1091292, _1091294, _1091296] : [class_Rings_Olinordered__ring__strict(_1091290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091290), c_Groups_Ozero__class_Ozero(_1091290)), _1091292)), 17484 ^ _776541 : [(17491 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091290), _1091294), _1091296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091290), _1091292), _1091294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091290), _1091292), _1091296))))], (17485 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091290), _1091292), _1091294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091290), _1091292), _1091296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091290), _1091294), _1091296)))]]], (14644 ^ _776541) ^ [_1040647, _1040649, _1040651, _1040653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040647), _1040649)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040651), _1040649) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040647), _1040653), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040651), _1040653)))], (10641 ^ _776541) ^ [_959547] : [class_Lattices_Oboolean__algebra(_959547), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959547), c_Orderings_Obot__class_Obot(_959547)) = c_Orderings_Otop__class_Otop(_959547))], (46795 ^ _776541) ^ [_1716891, _1716893, _1716895] : [class_Orderings_Olinorder(_1716891), 46798 ^ _776541 : [(46811 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1716891, hAPP(hAPP(c_List_Olist_OCons(_1716891), _1716893), _1716895))), 46815 ^ _776541 : [(46818 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716891), _1716893), 46814 ^ [_1716891, _1716893, _1716895]))], (46816 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1716891), 46814 ^ [_1716891, _1716893, _1716895]), hAPP(c_List_Oset(_1716891), _1716895))))]], c_List_Olinorder__class_Osorted(_1716891, _1716895)], (46799 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1716891, hAPP(hAPP(c_List_Olist_OCons(_1716891), _1716893), _1716895)), 46802 ^ _776541 : [(46803 ^ _776541) ^ [_1717059] : [hBOOL(hAPP(hAPP(c_member(_1716891), _1717059), hAPP(c_List_Oset(_1716891), _1716895))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716891), _1716893), _1717059)))], (46809 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1716891, _1716895))]]]]], (8255 ^ _776541) ^ [_917698, _917700] : [class_Lattices_Obounded__lattice__top(_917698), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917698), c_Orderings_Otop__class_Otop(_917698)), _917700) = c_Orderings_Otop__class_Otop(_917698))], (39329 ^ _776541) ^ [_1538009, _1538011] : [-(hAPP(c_Set_Ovimage(_1538009, _1538009, c_Fun_Oid(_1538009)), _1538011) = _1538011)], (47255 ^ _776541) ^ [_1726577, _1726579, _1726581, _1726583, _1726585] : [-(hAPP(hAPP(c_List_Ozip(_1726577, _1726579), c_List_OtakeWhile(_1726577, _1726581, _1726583)), _1726585) = c_List_OtakeWhile(tc_prod(_1726577, _1726579), hAPP(c_Fun_Ocomp(_1726577, tc_HOL_Obool, tc_prod(_1726577, _1726579), _1726581), c_Product__Type_Ofst(_1726577, _1726579)), hAPP(hAPP(c_List_Ozip(_1726577, _1726579), _1726583), _1726585)))], (21591 ^ _776541) ^ [_1167461, _1167463, _1167465, _1167467] : [class_Fields_Olinordered__field__inverse__zero(_1167461), class_Int_Onumber(_1167461), 21598 ^ _776541 : [(21599 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), _1167463), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167461), _1167465), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)))), 21602 ^ _776541 : [(21609 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), c_Groups_Ozero__class_Ozero(_1167461)), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)))), 21612 ^ _776541 : [(21619 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)), c_Groups_Ozero__class_Ozero(_1167461)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), _1167463), c_Groups_Ozero__class_Ozero(_1167461))))], (21613 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)), c_Groups_Ozero__class_Ozero(_1167461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), _1167465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167461), _1167463), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)))))]]], (21603 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), c_Groups_Ozero__class_Ozero(_1167461)), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167461), _1167463), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467))), _1167465)))]]], (21625 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), _1167463), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167461), _1167465), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467))))), 21628 ^ _776541 : [(21631 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167461), _1167463), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467))), _1167465))], (21629 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), c_Groups_Ozero__class_Ozero(_1167461)), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467))))]], 21632 ^ _776541 : [(21635 ^ _776541) ^ [] : [21636 ^ _776541 : [(21639 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), _1167465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167461), _1167463), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467))))], (21637 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)), c_Groups_Ozero__class_Ozero(_1167461))))]], 21640 ^ _776541 : [(21643 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), _1167463), c_Groups_Ozero__class_Ozero(_1167461)))], (21641 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)), c_Groups_Ozero__class_Ozero(_1167461)))]]], (21633 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167461), c_Groups_Ozero__class_Ozero(_1167461)), hAPP(c_Int_Onumber__class_Onumber__of(_1167461), _1167467)))]]]]], (21217 ^ _776541) ^ [_1160238, _1160240, _1160242] : [class_Int_Onumber__ring(_1160238), class_Rings_Olinordered__idom(_1160238), 21224 ^ _776541 : [(21231 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160240), _1160242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160238), hAPP(c_Int_Onumber__class_Onumber__of(_1160238), _1160240)), hAPP(c_Int_Onumber__class_Onumber__of(_1160238), _1160242))))], (21225 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160238), hAPP(c_Int_Onumber__class_Onumber__of(_1160238), _1160240)), hAPP(c_Int_Onumber__class_Onumber__of(_1160238), _1160242))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160240), _1160242)))]]], (31741 ^ _776541) ^ [_1346834, _1346836, _1346838, _1346840] : [class_Orderings_Olinorder(_1346834), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346834, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1346834, _1346836, _1346838)), hAPP(c_SetInterval_Oord__class_OatLeast(_1346834), _1346840)) = c_SetInterval_Oord__class_OatLeastAtMost(_1346834, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346834), _1346836), _1346840), _1346838))], (28815 ^ _776541) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (41917 ^ _776541) ^ [_1604708, _1604710, _1604712, _1604714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604708), tc_List_Olist(_1604708))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604708), tc_List_Olist(_1604708)), _1604710), _1604712)), c_List_Olistrel1(_1604708, _1604714))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604708)), _1604710) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604708)), _1604712))], (25883 ^ _776541) ^ [_1244756, _1244758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244758)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1244756), hAPP(c_Int_Onat, _1244758)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244756, _1244758)))], (46620 ^ _776541) ^ [_1713597, _1713599, _1713601] : [class_Orderings_Olinorder(_1713597), c_List_Olinorder__class_Osorted(_1713597, _1713599), hBOOL(hAPP(c_List_Odistinct(_1713597), _1713599)), c_List_Olinorder__class_Osorted(_1713597, _1713601), hBOOL(hAPP(c_List_Odistinct(_1713597), _1713601)), hAPP(c_List_Oset(_1713597), _1713599) = hAPP(c_List_Oset(_1713597), _1713601), -(_1713599 = _1713601)], (38808 ^ _776541) ^ [_1522662, _1522664, _1522666, _1522668, _1522670] : [-(hAPP(c_Set_Ovimage(_1522662, _1522664, _1522666), hAPP(hAPP(c_Set_Oinsert(_1522664), _1522668), _1522670)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1522662, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522662, _1522664, _1522666), hAPP(hAPP(c_Set_Oinsert(_1522664), _1522668), c_Orderings_Obot__class_Obot(tc_fun(_1522664, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1522662, _1522664, _1522666), _1522670)))], (14678 ^ _776541) ^ [_1041186, _1041188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041186), _1041188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041186), _1041188)))], (39239 ^ _776541) ^ [_1534131, _1534133, _1534135, _1534137] : [-(hAPP(c_Set_OCollect(tc_prod(_1534131, _1534133)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534131, _1534133, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1534131, tc_fun(_1534133, tc_HOL_Obool), tc_fun(_1534133, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534133, tc_HOL_Obool), tc_fun(_1534133, tc_HOL_Obool)), _1534131), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534133)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534131), c_fconj), _1534135))), _1534137))) = hAPP(hAPP(c_Product__Type_OSigma(_1534131, _1534133), hAPP(c_Set_OCollect(_1534131), _1534135)), hAPP(hAPP(c_COMBB(tc_fun(_1534133, tc_HOL_Obool), tc_fun(_1534133, tc_HOL_Obool), _1534131), c_Set_OCollect(_1534133)), _1534137)))], (4830 ^ _776541) ^ [_850065, _850067, _850069, _850071] : [-(c_Complete__Lattice_OSup__class_OSup(_850071, _850067) = c_Complete__Lattice_OSup__class_OSup(_850069, _850065)), _850071 = _850069, _850067 = _850065], (26186 ^ _776541) ^ [_1249628, _1249630, _1249632] : [-(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), _1249628), _1249630)), _1249632)), _1249630) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1249632), _1249630))], (50957 ^ _776541) ^ [_1808550, _1808552, _1808554, _1808556, _1808558] : [-(c_New__DSequence_Opos__map(_1808550, _1808552, _1808554, _1808556, _1808558) = c_Lazy__Sequence_Omap(_1808550, _1808552, _1808554, hAPP(_1808556, _1808558)))], (33419 ^ _776541) ^ [_1390384, _1390386, _1390388, _1390390, _1390392, _1390394] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390384, tc_fun(_1390386, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390388, tc_fun(_1390384, tc_HOL_Obool)), _1390390), _1390392)), _1390394) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390388, tc_fun(_1390386, tc_HOL_Obool)), _1390390), hAPP(hAPP(c_COMBC(_1390388, tc_fun(_1390384, tc_fun(_1390386, tc_HOL_Obool)), tc_fun(_1390386, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390384, tc_HOL_Obool), tc_fun(tc_fun(_1390384, tc_fun(_1390386, tc_HOL_Obool)), tc_fun(_1390386, tc_HOL_Obool)), _1390388), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390384, tc_fun(_1390386, tc_HOL_Obool))), _1390392)), _1390394)))], (7644 ^ _776541) ^ [_903408, _903410, _903412, _903414] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903408, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903408, tc_HOL_Obool)), _903410), _903412)), _903414) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903408, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903408, tc_HOL_Obool)), _903410), _903414)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903408, tc_HOL_Obool)), _903412), _903414)))], (720 ^ _776541) ^ [_787379, _787381, _787383, _787385, _787387, _787389, _787391, _787393] : [-(c_Wellfounded_Omax__extp(_787391, _787387, _787383, _787379)), c_Wellfounded_Omax__extp(_787393, _787389, _787385, _787381), _787393 = _787391, _787389 = _787387, _787385 = _787383, _787381 = _787379], (6105 ^ _776541) ^ [_874340, _874342, _874344, _874346, _874348, _874350] : [-(hBOOL(hAPP(hAPP(c_member(_874340), _874342), c_SetInterval_Oord_OatLeastLessThan(_874340, _874344, _874346, _874348, _874350)))), hBOOL(hAPP(hAPP(_874344, _874348), _874342)), hBOOL(hAPP(hAPP(_874346, _874342), _874350))], (13724 ^ _776541) ^ [_1021005, _1021007, _1021009, _1021011, _1021013] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1021005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021005), _1021007), _1021009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021005), _1021011), _1021013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021005), _1021007), _1021011)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021005), _1021009), _1021013))))], (52091 ^ _776541) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (39343 ^ _776541) ^ [_1538224] : [-(hAPP(c_Set_Oimage(_1538224, _1538224, c_Fun_Oid(_1538224)), c_Orderings_Otop__class_Otop(tc_fun(_1538224, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1538224, tc_HOL_Obool)))], (44447 ^ _776541) ^ [_1665456, _1665458, _1665460] : [class_Orderings_Olinorder(_1665456), -(c_Big__Operators_Olattice_OInf__fin(_1665456, c_Orderings_Oord__class_Omin(_1665456), hAPP(c_List_Oset(_1665456), hAPP(hAPP(c_List_Olist_OCons(_1665456), _1665458), _1665460))) = hAPP(c_List_Ofoldl(_1665456, _1665456, c_Orderings_Oord__class_Omin(_1665456), _1665458), _1665460))], (52057 ^ _776541) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (33503 ^ _776541) ^ [_1392929, _1392931, _1392933, _1392935, _1392937] : [-(_1392929 = c_Orderings_Obot__class_Obot(tc_fun(_1392931, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1392933), _1392935), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392931, tc_fun(_1392933, tc_HOL_Obool)), _1392929), _1392937)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392931, tc_fun(_1392933, tc_HOL_Obool)), _1392929), hAPP(hAPP(c_COMBB(tc_fun(_1392933, tc_HOL_Obool), tc_fun(_1392933, tc_HOL_Obool), _1392931), hAPP(c_Set_Oinsert(_1392933), _1392935)), _1392937)))], (27347 ^ _776541) ^ [_1268535, _1268537, _1268539] : [class_Rings_Olinordered__idom(_1268535), -(hAPP(c_Groups_Oabs__class_Oabs(_1268535), hAPP(hAPP(c_Power_Opower__class_Opower(_1268535), _1268537), _1268539)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1268535), hAPP(c_Groups_Oabs__class_Oabs(_1268535), _1268537)), _1268539))], (45237 ^ _776541) ^ [_1682549, _1682551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1682549), _1682551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682549)), hAPP(c_Code__Numeral_Onat__of, _1682551))))], (22605 ^ _776541) ^ [_1186123, _1186125] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1186123), c_Groups_Ozero__class_Ozero(_1186123)), hAPP(c_Nat_OSuc, _1186125)) = c_Groups_Ozero__class_Ozero(_1186123)), class_Power_Opower(_1186123), class_Rings_Osemiring__0(_1186123)], (36410 ^ _776541) ^ [_1464179, _1464181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1464179), _1464181)), -(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), _1464179), _1464181)), c_Wellfounded_Oless__than)))], (50767 ^ _776541) ^ [_1802625, _1802627, _1802629] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802625, _1802625)), hAPP(hAPP(c_Product__Type_OPair(_1802625, _1802625), hAPP(_1802627, hAPP(c_Nat_OSuc, 50768 ^ [_1802625, _1802627, _1802629]))), hAPP(_1802627, 50768 ^ [_1802625, _1802627, _1802629]))), c_Transitive__Closure_Ortrancl(_1802625, _1802629))), c_Wellfounded_Owf(_1802625, c_Transitive__Closure_Otrancl(_1802625, _1802629)), 50776 ^ _776541 : [(50777 ^ _776541) ^ [_1802891] : [-(hAPP(_1802627, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50775 ^ [_1802625, _1802627, _1802629]), _1802891)) = hAPP(_1802627, 50775 ^ [_1802625, _1802627, _1802629]))]]], (41066 ^ _776541) ^ [_1581423, _1581425, _1581427, _1581429, _1581431] : [-(hAPP(c_Relation_Oconverse(_1581423, _1581425), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1581427, tc_fun(tc_prod(_1581423, _1581425), tc_HOL_Obool)), _1581429), _1581431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1581427, tc_fun(tc_prod(_1581425, _1581423), tc_HOL_Obool)), _1581429), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1581423, _1581425), tc_HOL_Obool), tc_fun(tc_prod(_1581425, _1581423), tc_HOL_Obool), _1581427), c_Relation_Oconverse(_1581423, _1581425)), _1581431)))], (42677 ^ _776541) ^ [_1626226, _1626228, _1626230] : [-(hAPP(hAPP(c_List_Olist__update(_1626226, _1626228), _1626230), hAPP(hAPP(c_List_Onth(_1626226), _1626228), _1626230)) = _1626228)], (43896 ^ _776541) ^ [_1653567, _1653569, _1653571] : [-(c_List_Obutlast(_1653567, hAPP(hAPP(c_List_Odrop(_1653567), _1653569), _1653571)) = hAPP(hAPP(c_List_Odrop(_1653567), _1653569), c_List_Obutlast(_1653567, _1653571)))], (1534 ^ _776541) ^ [_798580, _798582] : [-(class_Rings_Olinordered__semiring__strict(_798580)), _798582 = _798580, class_Rings_Olinordered__semiring__strict(_798582)], (5672 ^ _776541) ^ [_865950, _865952] : [hAPP(_865950, 5673 ^ [_865950, _865952]) = hAPP(_865952, 5673 ^ [_865950, _865952]), -(_865950 = _865952)], (44870 ^ _776541) ^ [_1674582, _1674584, _1674586, _1674588, _1674590, _1674592] : [-(hAPP(hAPP(c_List_Ozip(_1674582, _1674584), hAPP(hAPP(c_List_Omap(_1674586, _1674582), _1674588), _1674590)), _1674592) = hAPP(hAPP(c_List_Omap(tc_prod(_1674586, _1674584), tc_prod(_1674582, _1674584)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674586, _1674584, tc_prod(_1674582, _1674584)), hAPP(hAPP(c_COMBB(_1674582, tc_fun(_1674584, tc_prod(_1674582, _1674584)), _1674586), c_Product__Type_OPair(_1674582, _1674584)), _1674588))), hAPP(hAPP(c_List_Ozip(_1674586, _1674584), _1674590), _1674592)))], (38544 ^ _776541) ^ [_1515717, _1515719, _1515721, _1515723] : [38545 ^ _776541 : [(38546 ^ _776541) ^ [_1515792] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515721, _1515717)), hAPP(hAPP(c_Product__Type_OPair(_1515721, _1515717), _1515792), _1515719)), _1515723))]], -(hBOOL(hAPP(hAPP(c_member(_1515717), _1515719), hAPP(c_Relation_ORange(_1515721, _1515717), _1515723))))], (22737 ^ _776541) ^ [_1188432, _1188434, _1188436, _1188438] : [class_Rings_Olinordered__semidom(_1188432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188432), hAPP(hAPP(c_Power_Opower__class_Opower(_1188432), _1188434), hAPP(c_Nat_OSuc, _1188436))), hAPP(hAPP(c_Power_Opower__class_Opower(_1188432), _1188438), hAPP(c_Nat_OSuc, _1188436)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188432), c_Groups_Ozero__class_Ozero(_1188432)), _1188438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188432), _1188434), _1188438)))], (45968 ^ _776541) ^ [_1698711, _1698713] : [-(hAPP(c_List_Oset(_1698711), c_List_Oconcat(_1698711, _1698713)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1698711), tc_fun(_1698711, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1698711)), _1698713)), c_List_Oset(_1698711)))], (15636 ^ _776541) ^ [_1060179] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060179)))], (47070 ^ _776541) ^ [_1722680, _1722682, _1722684] : [hAPP(c_List_Orev(_1722680), _1722682) = _1722684, -(_1722682 = hAPP(c_List_Orev(_1722680), _1722684))], (42709 ^ _776541) ^ [_1627031, _1627033, _1627035, _1627037] : [-(hAPP(hAPP(c_List_Olist__update(_1627031, hAPP(hAPP(c_List_Olist_OCons(_1627031), _1627033), _1627035)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1627037) = hAPP(hAPP(c_List_Olist_OCons(_1627031), _1627037), _1627035))], (26857 ^ _776541) ^ [_1260521, _1260523] : [c_Nat__Transfer_Ois__nat(_1260521), c_Nat__Transfer_Onat__set(_1260523), 26864 ^ _776541 : [(26871 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1260521)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1260523))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1260521), _1260523)))], (26865 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1260521), _1260523)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1260521)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1260523))))]]], (26457 ^ _776541) ^ [_1254002, _1254004, _1254006] : [-(hBOOL(hAPP(_1254002, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1254004, _1254006)))), 26460 ^ _776541 : [(26463 ^ _776541) ^ [] : [hBOOL(hAPP(_1254002, _1254004))], (26461 ^ _776541) ^ [] : [-(_1254006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 26464 ^ _776541 : [(26469 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26467 ^ [_1254002, _1254004, _1254006]), _1254006)))], (26471 ^ _776541) ^ [] : [-(_1254004 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1254006), 26466 ^ [_1254002, _1254004, _1254006])), 26467 ^ [_1254002, _1254004, _1254006]))], (26473 ^ _776541) ^ [] : [hBOOL(hAPP(_1254002, 26467 ^ [_1254002, _1254004, _1254006]))], (26465 ^ _776541) ^ [] : [_1254006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (22751 ^ _776541) ^ [_1188713, _1188715, _1188717, _1188719] : [class_Rings_Olinordered__semidom(_1188713), hAPP(hAPP(c_Power_Opower__class_Opower(_1188713), _1188715), hAPP(c_Nat_OSuc, _1188717)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1188713), _1188719), hAPP(c_Nat_OSuc, _1188717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188713), c_Groups_Ozero__class_Ozero(_1188713)), _1188715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188713), c_Groups_Ozero__class_Ozero(_1188713)), _1188719)), -(_1188715 = _1188719)], (23569 ^ _776541) ^ [_1203739, _1203741] : [-(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), _1203739))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203741))))], (17967 ^ _776541) ^ [_1099705] : [-(hAPP(c_Finite__Set_Ocard(_1099705), c_Orderings_Obot__class_Obot(tc_fun(_1099705, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30164 ^ _776541) ^ [_1317669, _1317671, _1317673] : [class_Orderings_Olinorder(_1317669), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317669), _1317671), _1317673)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317669), _1317671), _1317673) = _1317671)], (33370 ^ _776541) ^ [_1389254, _1389256, _1389258, _1389260] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1389254, tc_HOL_Obool), tc_fun(_1389256, tc_HOL_Obool)), _1389258), hAPP(hAPP(c_COMBC(tc_fun(_1389254, tc_HOL_Obool), tc_fun(_1389254, tc_fun(_1389256, tc_HOL_Obool)), tc_fun(_1389256, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389254, tc_fun(_1389256, tc_HOL_Obool))), _1389260)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389254, tc_fun(_1389256, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1389254, tc_HOL_Obool), _1389258)), _1389260))], (23888 ^ _776541) ^ [_1209233, _1209235, _1209237] : [class_Rings_Olinordered__semidom(_1209233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209235), _1209237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209233), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209233), _1209235)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209233), _1209237))))], (906 ^ _776541) ^ [_790150, _790152, _790154, _790156, _790158, _790160] : [-(c_Relation_Orefl__on(_790158, _790154, _790150)), c_Relation_Orefl__on(_790160, _790156, _790152), _790160 = _790158, _790156 = _790154, _790152 = _790150], (31945 ^ _776541) ^ [_1350550, _1350552] : [class_Orderings_Olinorder(_1350550), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350550), _1350552)), -(_1350552 = c_Orderings_Obot__class_Obot(tc_fun(_1350550, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350550), c_Big__Operators_Olattice_OInf__fin(_1350550, c_Orderings_Oord__class_Omin(_1350550), _1350552)), c_Big__Operators_Olattice_OSup__fin(_1350550, c_Orderings_Oord__class_Omax(_1350550), _1350552))))], (4198 ^ _776541) ^ [_840165, _840167, _840169, _840171] : [-(c_New__DSequence_Opos__single(_840171, _840167) = c_New__DSequence_Opos__single(_840169, _840165)), _840171 = _840169, _840167 = _840165], (49218 ^ _776541) ^ [_1770230, _1770232] : [-(hBOOL(hAPP(_1770232, 49225 ^ [_1770230, _1770232]))), 49219 ^ _776541 : [(49220 ^ _776541) ^ [_1770291] : [hBOOL(hAPP(hAPP(c_member(_1770230), _1770291), c_Orderings_Otop__class_Otop(tc_fun(_1770230, tc_HOL_Obool)))), hBOOL(hAPP(_1770232, _1770291))]]], (14272 ^ _776541) ^ [_1033491, _1033493, _1033495, _1033497] : [class_Rings_Ocomm__semiring__1(_1033491), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033491), _1033493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033491), _1033495), _1033497)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033491), _1033495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033491), _1033493), _1033497)))], (17991 ^ _776541) ^ [_1100052, _1100054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100054), _1100052)), -(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), _1100052), _1100054))))], (35074 ^ _776541) ^ [_1431175, _1431177] : [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), _1431175), _1431177))), 35077 ^ _776541 : [(35086 ^ _776541) ^ [] : [-(c_Divides_OnegDivAlg(_1431175, _1431177) = hAPP(c_Divides_Oadjust(_1431177), c_Divides_OnegDivAlg(_1431175, 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)))), _1431177)))), -(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), _1431175), _1431177)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431177), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35078 ^ _776541) ^ [] : [35079 ^ _776541 : [(35082 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431177), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35080 ^ _776541) ^ [] : [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), _1431175), _1431177)))]], -(c_Divides_OnegDivAlg(_1431175, _1431177) = 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), _1431175), _1431177)))]]], (43705 ^ _776541) ^ [_1648398, _1648400, _1648402, _1648404, _1648406, _1648408] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648398), tc_List_Olist(_1648398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648398), tc_List_Olist(_1648398)), hAPP(hAPP(c_List_Oappend(_1648398), _1648400), _1648406)), hAPP(hAPP(c_List_Oappend(_1648398), _1648402), _1648408))), c_List_Olistrel1(_1648398, _1648404)))), 43706 ^ _776541 : [(43713 ^ _776541) ^ [] : [_1648400 = _1648402, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648398), tc_List_Olist(_1648398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648398), tc_List_Olist(_1648398)), _1648406), _1648408)), c_List_Olistrel1(_1648398, _1648404)))], (43707 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648398), tc_List_Olist(_1648398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648398), tc_List_Olist(_1648398)), _1648400), _1648402)), c_List_Olistrel1(_1648398, _1648404))), _1648406 = _1648408]]], (31791 ^ _776541) ^ [_1347752, _1347754, _1347756] : [class_Orderings_Olinorder(_1347752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347752), _1347754)), -(_1347756 = c_Orderings_Obot__class_Obot(tc_fun(_1347752, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1347752, tc_HOL_Obool)), _1347756), _1347754)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347752), c_Big__Operators_Olinorder__class_OMax(_1347752, _1347756)), c_Big__Operators_Olinorder__class_OMax(_1347752, _1347754)) = c_Big__Operators_Olinorder__class_OMax(_1347752, _1347754))], (14975 ^ _776541) ^ [_1046701, _1046703, _1046705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046701), _1046703)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046703), _1046705)), _1046701) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046703), _1046701)), _1046705))], (31893 ^ _776541) ^ [_1349542, _1349544, _1349546] : [class_Orderings_Olinorder(_1349542), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349542), _1349544)), -(_1349544 = c_Orderings_Obot__class_Obot(tc_fun(_1349542, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349542), _1349546)), -(_1349546 = c_Orderings_Obot__class_Obot(tc_fun(_1349542, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349542, tc_HOL_Obool)), _1349544), _1349546) = c_Orderings_Obot__class_Obot(tc_fun(_1349542, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1349542, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349542, tc_HOL_Obool)), _1349544), _1349546)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349542), c_Big__Operators_Olinorder__class_OMax(_1349542, _1349544)), c_Big__Operators_Olinorder__class_OMax(_1349542, _1349546)))], (34956 ^ _776541) ^ [_1428716, _1428718] : [-(c_Divides_Opdivmod(_1428716, _1428718) = 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), _1428716)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428718))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428716), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428718))))], (24260 ^ _776541) ^ [_1215334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215334)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1215334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18942 ^ _776541) ^ [_1117722, _1117724, _1117726] : [class_Rings_Olinordered__ring(_1117722), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117722), c_Groups_Ozero__class_Ozero(_1117722)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117722), _1117724), _1117724)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117722), _1117726), _1117726)))))], (3120 ^ _776541) ^ [_822960, _822962, _822964, _822966] : [-(c_List_Olistrel1(_822966, _822962) = c_List_Olistrel1(_822964, _822960)), _822966 = _822964, _822962 = _822960], (39463 ^ _776541) ^ [_1541311, _1541313] : [-(c_Product__Type_Omap__pair(_1541311, _1541311, _1541313, _1541313, c_COMBI(_1541311), c_COMBI(_1541313)) = c_Fun_Oid(tc_prod(_1541311, _1541313)))], (11580 ^ _776541) ^ [_979044, _979046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979044), c_Complete__Lattice_OSup__class_OSup(tc_fun(_979044, tc_HOL_Obool), _979046))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979044, tc_HOL_Obool)), _979046)))], (38425 ^ _776541) ^ [_1513158] : [-(c_Nitpick_Ozero__frac(_1513158) = c_Nitpick_OAbs__Frac(_1513158, 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))))], (6630 ^ _776541) ^ [_883877, _883879, _883881] : [class_Orderings_Oorder(_883877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883877), _883879), _883881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883877), _883881), _883879)), -(_883881 = _883879)], (51563 ^ _776541) ^ [_1819851, _1819853, _1819855, _1819857] : [class_Divides_Osemiring__div(_1819851), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819851), _1819853), _1819855)), -(c_Divides_Odiv__class_Omod(_1819851, c_Divides_Odiv__class_Omod(_1819851, _1819857, _1819855), _1819853) = c_Divides_Odiv__class_Omod(_1819851, _1819857, _1819853))], (24174 ^ _776541) ^ [_1213837, _1213839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213837), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24177 ^ _776541 : [(24184 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213839), 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), _1213839), _1213837))))], (24178 ^ _776541) ^ [] : [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), _1213839), _1213837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213839), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (5871 ^ _776541) ^ [_869873, _869875, _869877, _869879, _869881, _869883] : [c_Typedef_Otype__definition(_869873, _869875, _869877, _869879, _869881), -(hAPP(_869879, hAPP(_869877, _869883)) = _869883)], (7158 ^ _776541) ^ [_893169, _893171, _893173] : [class_Orderings_Olinorder(_893169), 7161 ^ _776541 : [(7168 ^ _776541) ^ [] : [_893171 = _893173, -(hAPP(c_SetInterval_Oord__class_OlessThan(_893169), _893171) = hAPP(c_SetInterval_Oord__class_OlessThan(_893169), _893173))], (7162 ^ _776541) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_893169), _893171) = hAPP(c_SetInterval_Oord__class_OlessThan(_893169), _893173), -(_893171 = _893173)]]], (41867 ^ _776541) ^ [_1603123, _1603125, _1603127, _1603129, _1603131, _1603133] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603123, _1603123)), hAPP(hAPP(c_Product__Type_OPair(_1603123, _1603123), _1603125), _1603127)), c_Transitive__Closure_Ortrancl(_1603123, _1603129))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603123), tc_List_Olist(_1603123))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603123), tc_List_Olist(_1603123)), _1603131), _1603133)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603123), c_List_Olistrel1(_1603123, _1603129)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603123), tc_List_Olist(_1603123))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603123), tc_List_Olist(_1603123)), hAPP(hAPP(c_List_Olist_OCons(_1603123), _1603125), _1603131)), hAPP(hAPP(c_List_Olist_OCons(_1603123), _1603127), _1603133))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603123), c_List_Olistrel1(_1603123, _1603129)))))], (42869 ^ _776541) ^ [_1630635, _1630637] : [hAPP(c_Finite__Set_Ocard(_1630635), hAPP(c_List_Oset(_1630635), _1630637)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630635)), _1630637), -(hBOOL(hAPP(c_List_Odistinct(_1630635), _1630637)))], (40603 ^ _776541) ^ [_1569383, _1569385] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569383, _1569383), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569383, _1569385)), hAPP(hAPP(c_Product__Type_OSigma(_1569383, _1569383), hAPP(c_Relation_OField(_1569383), _1569385)), hAPP(c_COMBK(tc_fun(_1569383, tc_HOL_Obool), _1569383), hAPP(c_Relation_OField(_1569383), _1569385))))))], (38096 ^ _776541) ^ [_1506206, _1506208, _1506210, _1506212, _1506214, _1506216, _1506218, _1506220] : [hBOOL(hAPP(hAPP(_1506206, _1506208), _1506210)), hBOOL(hAPP(hAPP(_1506212, _1506210), _1506214)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1506216, _1506218, _1506220, _1506206, _1506212), _1506208), _1506214)))], (44314 ^ _776541) ^ [_1662711, _1662713, _1662715, _1662717, _1662719] : [class_Orderings_Olinorder(_1662711), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662713)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662713, _1662711, _1662715), _1662717), _1662719)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662713)), _1662719)))], (38489 ^ _776541) ^ [_1514423, _1514425] : [-(c_HOL_OThe(_1514423, hAPP(hAPP(c_COMBC(_1514423, _1514423, tc_HOL_Obool), c_fequal), _1514425)) = _1514425)], (47475 ^ _776541) ^ [_1731289, _1731291] : [class_Orderings_Olinorder(_1731289), 47482 ^ _776541 : [(47487 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1731289), hAPP(hAPP(c_List_Onth(_1731289), _1731291), 47480 ^ [_1731289, _1731291])), hAPP(hAPP(c_List_Onth(_1731289), _1731291), 47481 ^ [_1731289, _1731291])))], (47485 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47481 ^ [_1731289, _1731291]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731289)), _1731291))))], (47483 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47480 ^ [_1731289, _1731291]), 47481 ^ [_1731289, _1731291])))]], -(c_List_Olinorder__class_Osorted(_1731289, _1731291))], (11958 ^ _776541) ^ [_986470, _986472, _986474, _986476, _986478] : [hAPP(_986474, _986476) = _986478, -(c_Fun_Ofun__upd(_986470, _986472, _986474, _986476, _986478) = _986474)], (51465 ^ _776541) ^ [_1818111, _1818113] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818111), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1818113))), 51468 ^ _776541 : [(51471 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818111), _1818113))], (51469 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818113), _1818111)))]]], (23834 ^ _776541) ^ [_1208294, _1208296] : [class_Rings_Olinordered__semidom(_1208294), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208294), c_Groups_Ozero__class_Ozero(_1208294)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208294), _1208296))))], (28487 ^ _776541) ^ [_1287795] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1287795)))], (50612 ^ _776541) ^ [_1799607, _1799609, _1799611, _1799613] : [-(c_Product__Type_Ocurry(_1799607, _1799609, _1799611, hAPP(c_Product__Type_Oprod_Oprod__case(_1799607, _1799609, _1799611), _1799613)) = _1799613)], (36352 ^ _776541) ^ [_1463237, _1463239, _1463241, _1463243] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1463237), _1463239)), 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)), _1463241), _1463237)), 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)), _1463243), _1463239)), 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)), _1463241), _1463243)), _1463239)), c_FunDef_Omax__weak)))], (15524 ^ _776541) ^ [_1057614, _1057616, _1057618, _1057620, _1057622] : [class_Groups_Ocomm__monoid__mult(_1057614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057616), _1057618)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057616), _1057620)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057616, tc_HOL_Obool)), _1057618), _1057620) = c_Orderings_Obot__class_Obot(tc_fun(_1057616, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057614, _1057616, c_Groups_Otimes__class_Otimes(_1057614)), _1057622), c_Groups_Oone__class_Oone(_1057614)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1057616, tc_HOL_Obool)), _1057618), _1057620)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057614), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057614, _1057616, c_Groups_Otimes__class_Otimes(_1057614)), _1057622), c_Groups_Oone__class_Oone(_1057614)), _1057618)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057614, _1057616, c_Groups_Otimes__class_Otimes(_1057614)), _1057622), c_Groups_Oone__class_Oone(_1057614)), _1057620)))], (33865 ^ _776541) ^ [_1403986, _1403988, _1403990, _1403992, _1403994] : [class_Complete__Lattice_Ocomplete__lattice(_1403986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403988), _1403990)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1403986), _1403992), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403988, _1403986), _1403990), _1403994)) = hAPP(hAPP(c_Finite__Set_Ofold(_1403988, _1403986, hAPP(hAPP(c_COMBB(_1403986, tc_fun(_1403986, _1403986), _1403988), c_Lattices_Osemilattice__sup__class_Osup(_1403986)), _1403994)), _1403992), _1403990))], (47032 ^ _776541) ^ [_1721904, _1721906] : [-(hAPP(c_List_Oset(_1721904), hAPP(c_List_Orev(_1721904), _1721906)) = hAPP(c_List_Oset(_1721904), _1721906))], (3282 ^ _776541) ^ [_825521, _825523, _825525, _825527, _825529, _825531] : [-(c_List_Olist_Olist__size(_825531, _825527, _825523) = c_List_Olist_Olist__size(_825529, _825525, _825521)), _825531 = _825529, _825527 = _825525, _825523 = _825521], (47992 ^ _776541) ^ [_1743108, _1743110, _1743112] : [class_Enum_Oenum(_1743108), class_Enum_Oenum(_1743110), 47999 ^ _776541 : [(48006 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1743110), hAPP(hAPP(c_COMBB(tc_fun(_1743108, tc_HOL_Obool), tc_HOL_Obool, _1743110), c_Enum_Oenum__class_Oenum__all(_1743108)), hAPP(hAPP(c_COMBB(tc_fun(_1743108, tc_prod(_1743110, _1743108)), tc_fun(_1743108, tc_HOL_Obool), _1743110), hAPP(c_COMBB(tc_prod(_1743110, _1743108), tc_HOL_Obool, _1743108), _1743112)), c_Product__Type_OPair(_1743110, _1743108))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1743110, _1743108)), _1743112)))], (48000 ^ _776541) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1743110, _1743108)), _1743112)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1743110), hAPP(hAPP(c_COMBB(tc_fun(_1743108, tc_HOL_Obool), tc_HOL_Obool, _1743110), c_Enum_Oenum__class_Oenum__all(_1743108)), hAPP(hAPP(c_COMBB(tc_fun(_1743108, tc_prod(_1743110, _1743108)), tc_fun(_1743108, tc_HOL_Obool), _1743110), hAPP(c_COMBB(tc_prod(_1743110, _1743108), tc_HOL_Obool, _1743108), _1743112)), c_Product__Type_OPair(_1743110, _1743108))))))]]], (43956 ^ _776541) ^ [_1654971, _1654973, _1654975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654971)), _1654973)), _1654975)), -(hAPP(hAPP(c_List_Odrop(_1654971), _1654975), _1654973) = c_List_Olist_ONil(_1654971))], (41445 ^ _776541) ^ [_1590616, _1590618, _1590620, _1590622] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590616, _1590616), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1590618), _1590620)), _1590622) = hAPP(hAPP(c_Relation_Orel__comp(_1590616, _1590616, _1590616), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590616, _1590616), tc_HOL_Obool), _1590618), _1590622)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590616, _1590616), tc_HOL_Obool), _1590620), _1590622)))], (29940 ^ _776541) ^ [_1313327, _1313329, _1313331, _1313333] : [class_Rings_Olinordered__semidom(_1313327), 29946 ^ _776541 : [(29949 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313327), c_Groups_Ozero__class_Ozero(_1313327)), hAPP(_1313333, 29945 ^ [_1313327, _1313329, _1313331, _1313333])))], (29947 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313329), 29945 ^ [_1313327, _1313329, _1313331, _1313333]), _1313331)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313327), c_Groups_Ozero__class_Ozero(_1313327)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1313329, _1313327), _1313333), _1313331))))], (27503 ^ _776541) ^ [_1271331, _1271333, _1271335] : [class_Groups_Oordered__ab__group__add__abs(_1271331), 27506 ^ _776541 : [(27515 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271331), hAPP(c_Groups_Oabs__class_Oabs(_1271331), _1271333)), _1271335))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271331), _1271333), _1271335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271331), hAPP(c_Groups_Ouminus__class_Ouminus(_1271331), _1271333)), _1271335))], (27507 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271331), hAPP(c_Groups_Oabs__class_Oabs(_1271331), _1271333)), _1271335)), 27510 ^ _776541 : [(27513 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271331), hAPP(c_Groups_Ouminus__class_Ouminus(_1271331), _1271333)), _1271335)))], (27511 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271331), _1271333), _1271335)))]]]]], (1784 ^ _776541) ^ [_801705, _801707] : [-(class_Rings_Osemiring__1(_801705)), _801707 = _801705, class_Rings_Osemiring__1(_801707)], (48784 ^ _776541) ^ [_1759867, _1759869, _1759871, _1759873] : [-(c_Lazy__Sequence_Oappend(_1759867, c_Lazy__Sequence_Olazy__sequence_OInsert(_1759867, _1759869, _1759871), _1759873) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1759867, _1759869, c_Lazy__Sequence_Oappend(_1759867, _1759871, _1759873)))], (10273 ^ _776541) ^ [_953135, _953137, _953139] : [-(hBOOL(hAPP(hAPP(c_member(_953135), _953137), _953139))), -(hBOOL(hAPP(hAPP(c_member(_953135), _953137), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_953135, tc_HOL_Obool)), _953139))))], (1464 ^ _776541) ^ [_797705, _797707] : [-(class_Lazy__Sequence_Osmall__lazy(_797705)), _797707 = _797705, class_Lazy__Sequence_Osmall__lazy(_797707)], (25720 ^ _776541) ^ [_1241971, _1241973, _1241975, _1241977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241973), _1241975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1241975), 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), _1241973), _1241971)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241973), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241977, _1241971))), _1241975))))], (2044 ^ _776541) ^ [_806056, _806058, _806060, _806062, _806064, _806066, _806068, _806070, _806072, _806074] : [-(c_SetInterval_Oord_OatLeastLessThan(_806074, _806070, _806066, _806062, _806058) = c_SetInterval_Oord_OatLeastLessThan(_806072, _806068, _806064, _806060, _806056)), _806074 = _806072, _806070 = _806068, _806066 = _806064, _806062 = _806060, _806058 = _806056], (18616 ^ _776541) ^ [_1111632, _1111634, _1111636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111632), _1111634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111632), _1111636))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111634), _1111636)))], (49273 ^ _776541) ^ [_1771494, _1771496, _1771498] : [hBOOL(hAPP(hAPP(c_member(_1771496), _1771494), c_Orderings_Obot__class_Obot(tc_fun(_1771496, tc_HOL_Obool)))), hBOOL(hAPP(_1771498, _1771494))], (24525 ^ _776541) ^ [_1220170, _1220172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1220170, _1220172))))], (26052 ^ _776541) ^ [_1247462] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247462)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247462))], (49350 ^ _776541) ^ [_1772777, _1772779, _1772781] : [-(c_List_Olist__ex(_1772777, _1772781, _1772779)), 49351 ^ _776541 : [(49352 ^ _776541) ^ [_1772834] : [hBOOL(hAPP(hAPP(c_member(_1772777), _1772834), hAPP(c_List_Oset(_1772777), _1772779))), hBOOL(hAPP(_1772781, _1772834))]]], (50638 ^ _776541) ^ [_1800197, _1800199] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800197), _1800199)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1800197, 50641 ^ [_1800197, _1800199], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1800197), _1800199)), _1800199))], (51983 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (9154 ^ _776541) ^ [_934666, _934668, _934670] : [class_Orderings_Opreorder(_934666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934666), _934668), _934670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934666), _934670), _934668))], (10803 ^ _776541) ^ [_962655, _962657, _962659, _962661, _962663, _962665, _962667] : [-(hBOOL(hAPP(hAPP(c_member(_962655), _962657), _962659))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_962655, _962661, _962663, _962665, _962659), _962667)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_962655, _962661, _962663, _962665, hAPP(hAPP(c_Set_Oinsert(_962655), _962657), _962659)), hAPP(hAPP(_962663, _962657), _962667))))], (45682 ^ _776541) ^ [_1693036, _1693038, _1693040] : [hBOOL(hAPP(c_List_Odistinct(_1693036), _1693038)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1693036)), c_Enum_On__lists(_1693036, _1693040, _1693038))))], (48452 ^ _776541) ^ [_1752598, _1752600, _1752602, _1752604, _1752606] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1752598), _1752600), _1752602), _1752604), _1752606) = c_New__DSequence_Oneg__single(_1752598, _1752600))], (44723 ^ _776541) ^ [_1670601, _1670603, _1670605, _1670607, _1670609] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1670601), tc_List_Olist(_1670603), tc_List_Olist(_1670605), hAPP(c_List_Omap(_1670601, _1670603), _1670607)), hAPP(c_List_Omap(_1670605, _1670601), _1670609)) = hAPP(c_List_Omap(_1670605, _1670603), hAPP(c_Fun_Ocomp(_1670601, _1670603, _1670605, _1670607), _1670609)))], (48215 ^ _776541) ^ [_1747793, _1747795, _1747797, _1747799] : [-(c_List_Olist__all(_1747793, _1747795, hAPP(hAPP(c_List_Oappend(_1747793), _1747797), _1747799))), c_List_Olist__all(_1747793, _1747795, _1747797), c_List_Olist__all(_1747793, _1747795, _1747799)], (33396 ^ _776541) ^ [_1389778, _1389780] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1389778, tc_HOL_Obool), _1389780) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1389778, tc_HOL_Obool), tc_fun(_1389778, tc_HOL_Obool)), _1389780), c_COMBI(tc_fun(_1389778, tc_HOL_Obool))))], (31777 ^ _776541) ^ [_1347544, _1347546, _1347548] : [class_Orderings_Olinorder(_1347544), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347544), _1347546)), -(_1347546 = c_Orderings_Obot__class_Obot(tc_fun(_1347544, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1347544, hAPP(hAPP(c_Set_Oinsert(_1347544), _1347548), _1347546)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347544), _1347548), c_Big__Operators_Olinorder__class_OMax(_1347544, _1347546)))], (22255 ^ _776541) ^ [_1180176, _1180178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180176), _1180178)), 22258 ^ _776541 : [(22261 ^ _776541) ^ [] : [_1180176 = _1180178], (22259 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180176), _1180178)))]]], (2144 ^ _776541) ^ [_807648, _807650] : [_807650 = _807648, -(c_Nat_Osemiring__1__class_ONats(_807650) = c_Nat_Osemiring__1__class_ONats(_807648))], (39894 ^ _776541) ^ [_1552849, _1552851, _1552853, _1552855, _1552857] : [c_Finite__Set_Ofun__left__comm(_1552849, _1552851, _1552853), -(hAPP(c_Fun_Ocomp(_1552851, _1552851, _1552851, hAPP(_1552853, _1552855)), hAPP(_1552853, _1552857)) = hAPP(c_Fun_Ocomp(_1552851, _1552851, _1552851, hAPP(_1552853, _1552857)), hAPP(_1552853, _1552855)))], (50922 ^ _776541) ^ [_1807873, _1807875, _1807877] : [c_List_Olist__ex(tc_Nat_Onat, _1807873, c_List_Oupt(_1807875, _1807877)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1807873), _1807875, _1807877)], (17949 ^ _776541) ^ [_1099454, _1099456] : [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), _1099454), _1099456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099456)))], (8024 ^ _776541) ^ [_912678, _912680, _912682, _912684] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912678, tc_HOL_Obool)), _912680), hAPP(hAPP(c_Set_Oinsert(_912678), _912682), _912684)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912678, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912678, tc_HOL_Obool)), _912680), _912684)), hAPP(hAPP(c_Set_Oinsert(_912678), _912682), c_Orderings_Obot__class_Obot(tc_fun(_912678, tc_HOL_Obool)))))], (41424 ^ _776541) ^ [_1590078, _1590080, _1590082] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590078, _1590078)), _1590080), c_Transitive__Closure_Ortrancl(_1590078, _1590082))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590078, _1590078)), _1590080), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590078, _1590078), tc_HOL_Obool), 41427 ^ [_1590078, _1590080, _1590082]), _1590082))))], (12682 ^ _776541) ^ [_1000101, _1000103, _1000105, _1000107] : [_1000101 = c_Finite__Set_Ofold1(_1000103, _1000105), -(hAPP(_1000101, hAPP(hAPP(c_Set_Oinsert(_1000103), _1000107), c_Orderings_Obot__class_Obot(tc_fun(_1000103, tc_HOL_Obool)))) = _1000107)], (24164 ^ _776541) ^ [_1213682, _1213684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213682), _1213684)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213682), _1213684) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52421 ^ _776541) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (15700 ^ _776541) ^ [_1061264] : [hAPP(c_Nat_OSuc, _1061264) = _1061264], (4554 ^ _776541) ^ [_845697, _845699, _845701, _845703, _845705, _845707] : [-(c_FunDef_OTHE__default(_845707, _845703, _845699) = c_FunDef_OTHE__default(_845705, _845701, _845697)), _845707 = _845705, _845703 = _845701, _845699 = _845697], (35823 ^ _776541) ^ [_1445501, _1445503, _1445505, _1445507, _1445509, _1445511] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445501), _1445503)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445505), _1445507)), 35833 ^ _776541 : [(35836 ^ _776541) ^ [] : [hAPP(c_Finite__Set_Ocard(_1445501), hAPP(c_Set_OCollect(_1445501), hAPP(hAPP(c_COMBS(_1445501, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1445501), c_fconj), hAPP(hAPP(c_COMBC(_1445501, tc_fun(_1445501, tc_HOL_Obool), tc_HOL_Obool), c_member(_1445501)), _1445503))), hAPP(hAPP(c_COMBC(_1445501, _1445505, tc_HOL_Obool), _1445509), 35832 ^ [_1445501, _1445503, _1445505, _1445507, _1445509, _1445511])))) = _1445511], (35834 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1445505), 35832 ^ [_1445501, _1445503, _1445505, _1445507, _1445509, _1445511]), _1445507)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1445501, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1445505, tc_HOL_Obool), tc_Nat_Onat, _1445501), c_Finite__Set_Ocard(_1445505)), hAPP(hAPP(c_COMBB(tc_fun(_1445505, tc_HOL_Obool), tc_fun(_1445505, tc_HOL_Obool), _1445501), c_Set_OCollect(_1445505)), hAPP(hAPP(c_COMBB(tc_fun(_1445505, tc_HOL_Obool), tc_fun(_1445505, tc_HOL_Obool), _1445501), hAPP(c_COMBS(_1445505, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1445505), c_fconj), hAPP(hAPP(c_COMBC(_1445505, tc_fun(_1445505, tc_HOL_Obool), tc_HOL_Obool), c_member(_1445505)), _1445507)))), _1445509)))), _1445503) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1445511), hAPP(c_Finite__Set_Ocard(_1445505), _1445507)))], (15316 ^ _776541) ^ [_1052864, _1052866, _1052868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052864), _1052866)), -(hAPP(c_Finite__Set_Ocard(_1052864), hAPP(hAPP(c_Set_Oinsert(_1052864), _1052868), _1052866)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1052864), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052864, tc_HOL_Obool)), _1052866), hAPP(hAPP(c_Set_Oinsert(_1052864), _1052868), c_Orderings_Obot__class_Obot(tc_fun(_1052864, tc_HOL_Obool)))))))], (3696 ^ _776541) ^ [_831970, _831972, _831974, _831976] : [-(c_List_Obutlast(_831976, _831972) = c_List_Obutlast(_831974, _831970)), _831976 = _831974, _831972 = _831970], (7810 ^ _776541) ^ [_907868, _907870, _907872, _907874] : [hBOOL(hAPP(hAPP(c_member(_907868), _907870), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907868, tc_HOL_Obool)), _907872), _907874))), -(hBOOL(hAPP(hAPP(c_member(_907868), _907870), _907872)))], (48490 ^ _776541) ^ [_1753629] : [-(c_Predicate_Oconversep(_1753629, _1753629, c_fequal) = c_fequal)], (6977 ^ _776541) ^ [_889860, _889862, _889864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889860, tc_HOL_Obool)), _889862), _889864)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_889860, tc_HOL_Obool)), _889862), hAPP(c_Set_OPow(_889860), _889864))))], (9312 ^ _776541) ^ [_936707, _936709, _936711, _936713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936707, tc_HOL_Obool)), _936709), _936711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936707, tc_HOL_Obool)), _936711), _936713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936707, tc_HOL_Obool)), _936709), _936713)))], (11060 ^ _776541) ^ [_967761, _967763, _967765] : [class_Rings_Oring(_967761), -(hAPP(c_Groups_Ouminus__class_Ouminus(_967761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967761), _967763), _967765)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967761), _967763), hAPP(c_Groups_Ouminus__class_Ouminus(_967761), _967765)))], (24036 ^ _776541) ^ [_1211724] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1211724)), -(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)), _1211724))))], (28527 ^ _776541) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (50343 ^ _776541) ^ [_1794385, _1794387, _1794389, _1794391, _1794393] : [c_Fun_Obij__betw(_1794385, _1794387, _1794389, c_Orderings_Otop__class_Otop(tc_fun(_1794385, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794387, tc_HOL_Obool))), c_Fun_Obij__betw(_1794387, _1794391, _1794393, c_Orderings_Otop__class_Otop(tc_fun(_1794387, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794391, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1794385, _1794391, hAPP(c_Fun_Ocomp(_1794387, _1794391, _1794385, _1794393), _1794389), c_Orderings_Otop__class_Otop(tc_fun(_1794385, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794391, tc_HOL_Obool))))], (43617 ^ _776541) ^ [_1646552, _1646554, _1646556] : [-(hAPP(hAPP(c_List_Oappend(_1646552), _1646554), _1646556) = c_List_Olist_ONil(_1646552)), _1646554 = c_List_Olist_ONil(_1646552), _1646556 = c_List_Olist_ONil(_1646552)], (50184 ^ _776541) ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778] : [class_Groups_Ocomm__monoid__mult(_1790768), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790770), _1790772)), 50194 ^ _776541 : [(50197 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1790774), hAPP(_1790776, 50193 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778])))], (50195 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790770), 50193 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778]), _1790772)))]], 50201 ^ _776541 : [(50205 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790770), 50203 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778]), _1790772)))], (50207 ^ _776541) ^ [] : [50200 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778] = 50203 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778]], (50209 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1790774, tc_HOL_Obool)), hAPP(_1790776, 50200 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778])), hAPP(_1790776, 50203 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778])) = c_Orderings_Obot__class_Obot(tc_fun(_1790774, tc_HOL_Obool))], (50202 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790770), 50200 ^ [_1790768, _1790770, _1790772, _1790774, _1790776, _1790778]), _1790772)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1790768, _1790774, c_Groups_Otimes__class_Otimes(_1790768)), _1790778), c_Groups_Oone__class_Oone(_1790768)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1790770, tc_fun(_1790774, tc_HOL_Obool)), _1790772), _1790776)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1790768, _1790770, c_Groups_Otimes__class_Otimes(_1790768)), hAPP(hAPP(c_COMBB(tc_fun(_1790774, tc_HOL_Obool), _1790768, _1790770), hAPP(hAPP(c_Finite__Set_Ofold__image(_1790768, _1790774, c_Groups_Otimes__class_Otimes(_1790768)), _1790778), c_Groups_Oone__class_Oone(_1790768))), _1790776)), c_Groups_Oone__class_Oone(_1790768)), _1790772))], (28775 ^ _776541) ^ [_1292440, _1292442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1292440), 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)))), _1292442)), 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)))), _1292440)) = 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), _1292442), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1292440))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (52093 ^ _776541) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (27058 ^ _776541) ^ [_1263821] : [c_Nat__Transfer_Onat__set(_1263821), -(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), _1263821)) = _1263821)], (33212 ^ _776541) ^ [_1385213, _1385215, _1385217] : [class_Orderings_Obot(_1385213), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1385215, _1385213)), _1385217) = c_Orderings_Obot__class_Obot(_1385213))], (38732 ^ _776541) ^ [_1520969, _1520971, _1520973] : [-(hAPP(c_Set_Ovimage(_1520969, _1520971, _1520973), c_Orderings_Otop__class_Otop(tc_fun(_1520971, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1520969, tc_HOL_Obool)))], (8000 ^ _776541) ^ [_912042, _912044, _912046] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_912042, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_912042, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_912042), _912044)), hAPP(c_Set_OPow(_912042), _912046))), hAPP(c_Set_OPow(_912042), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912042, tc_HOL_Obool)), _912044), _912046)))))], (4744 ^ _776541) ^ [_848756, _848758] : [_848758 = _848756, -(c_Random__Sequence_Osingle(_848758) = c_Random__Sequence_Osingle(_848756))], (12716 ^ _776541) ^ [_1000753, _1000755, _1000757, _1000759] : [class_Lattices_Osemilattice__sup(_1000753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000753), _1000755)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1000753, _1000753, c_Lattices_Osemilattice__sup__class_Osup(_1000753)), _1000757), hAPP(hAPP(c_Set_Oinsert(_1000753), _1000759), _1000755)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1000753), _1000759), hAPP(hAPP(c_Finite__Set_Ofold(_1000753, _1000753, c_Lattices_Osemilattice__sup__class_Osup(_1000753)), _1000757), _1000755)))], (43248 ^ _776541) ^ [_1638138, _1638140, _1638142, _1638144] : [-(_1638138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1638140), _1638138), hAPP(hAPP(c_List_Olist_OCons(_1638140), _1638142), _1638144)) = hAPP(hAPP(c_List_Olist_OCons(_1638140), _1638142), hAPP(hAPP(c_List_Otake(_1638140), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1638138), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1638144)))], (50457 ^ _776541) ^ [_1796629, _1796631, _1796633] : [c_Fun_Obij__betw(_1796629, _1796631, _1796633, c_Orderings_Otop__class_Otop(tc_fun(_1796629, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1796631, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1796629, _1796631, _1796633), c_Orderings_Otop__class_Otop(tc_fun(_1796629, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1796631, tc_HOL_Obool)))], (28499 ^ _776541) ^ [_1287991] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1287991)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287991))))], (44465 ^ _776541) ^ [_1665897, _1665899, _1665901, _1665903] : [class_Complete__Lattice_Ocomplete__lattice(_1665897), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665899, _1665897), hAPP(c_List_Oset(_1665899), _1665901)), _1665903) = hAPP(c_List_Ofoldl(_1665897, _1665899, hAPP(c_COMBC(_1665899, _1665897, _1665897), hAPP(hAPP(c_COMBB(_1665897, tc_fun(_1665897, _1665897), _1665899), c_Lattices_Osemilattice__inf__class_Oinf(_1665897)), _1665903)), c_Orderings_Otop__class_Otop(_1665897)), _1665901))], (16166 ^ _776541) ^ [_1068761, _1068763] : [class_Groups_Ocomm__monoid__add(_1068761), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068761), c_Groups_Ozero__class_Ozero(_1068761)), _1068763) = _1068763)], (788 ^ _776541) ^ [_788387, _788389, _788391, _788393] : [-(c_Relation_Otrans(_788391, _788387)), c_Relation_Otrans(_788393, _788389), _788393 = _788391, _788389 = _788387], (45696 ^ _776541) ^ [_1693312, _1693314] : [-(_1693312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1693314, _1693312, c_List_Olist_ONil(_1693314)) = c_List_Olist_ONil(tc_List_Olist(_1693314)))], (21249 ^ _776541) ^ [_1160863, _1160865, _1160867] : [class_Int_Onumber__ring(_1160863), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160863), hAPP(c_Int_Onumber__class_Onumber__of(_1160863), _1160865)), hAPP(c_Int_Onumber__class_Onumber__of(_1160863), _1160867)) = hAPP(c_Int_Onumber__class_Onumber__of(_1160863), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1160865), _1160867)))], (41412 ^ _776541) ^ [_1589786, _1589788, _1589790] : [c_Wellfounded_Owf(_1589786, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589786, _1589786), tc_HOL_Obool), _1589788), _1589790)), -(c_Wellfounded_Owf(_1589786, _1589790))], (40234 ^ _776541) ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580] : [class_Groups_Ocomm__monoid__add(_1560570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560572), _1560574)), 40244 ^ _776541 : [(40245 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560572), 40243 ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580]), _1560574)))], (40250 ^ _776541) ^ [] : [40243 ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580] = 40246 ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580]], (40254 ^ _776541) ^ [] : [hAPP(_1560578, hAPP(_1560576, 40243 ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580])) = c_Groups_Ozero__class_Ozero(_1560570)], (40252 ^ _776541) ^ [] : [-(hAPP(_1560576, 40243 ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580]) = hAPP(_1560576, 40246 ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580]))], (40248 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560572), 40246 ^ [_1560570, _1560572, _1560574, _1560576, _1560578, _1560580]), _1560574)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560580, _1560570), _1560578), hAPP(c_Set_Oimage(_1560572, _1560580, _1560576), _1560574)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560572, _1560570), hAPP(c_Fun_Ocomp(_1560580, _1560570, _1560572, _1560578), _1560576)), _1560574))], (50632 ^ _776541) ^ [_1800042, _1800044, _1800046, _1800048] : [c_Fun_Obij__betw(_1800042, _1800044, _1800046, c_Orderings_Otop__class_Otop(tc_fun(_1800042, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800044, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1800042, _1800044, _1800046), _1800048) = hAPP(c_Set_Oimage(_1800044, _1800042, c_Hilbert__Choice_Oinv__into(_1800042, _1800044, c_Orderings_Otop__class_Otop(tc_fun(_1800042, tc_HOL_Obool)), _1800046)), _1800048))], (13182 ^ _776541) ^ [_1009802, _1009804, _1009806, _1009808, _1009810] : [c_Finite__Set_Ofun__left__comm__idem(_1009802, _1009804, _1009806), -(hAPP(hAPP(_1009806, _1009808), hAPP(hAPP(_1009806, _1009808), _1009810)) = hAPP(hAPP(_1009806, _1009808), _1009810))], (34061 ^ _776541) ^ [_1408835, _1408837] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408835)), -(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)), _1408835))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1408837))))) = 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)), _1408835))), 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, _1408837))))))], (24896 ^ _776541) ^ [_1227242, _1227244, _1227246, _1227248] : [class_Divides_Oring__div(_1227242), -(c_Divides_Odiv__class_Omod(_1227242, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227242), _1227244), _1227246), _1227248) = c_Divides_Odiv__class_Omod(_1227242, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227242), c_Divides_Odiv__class_Omod(_1227242, _1227244, _1227248)), c_Divides_Odiv__class_Omod(_1227242, _1227246, _1227248)), _1227248))], (41214 ^ _776541) ^ [_1585143, _1585145] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1585143, _1585143)), _1585145)), c_Wellfounded_Oacyclic(_1585143, _1585145), -(c_Wellfounded_Owf(_1585143, hAPP(c_Relation_Oconverse(_1585143, _1585143), _1585145)))], (48556 ^ _776541) ^ [_1755480, _1755482, _1755484, _1755486] : [-(c_Lazy__Sequence_Oproduct(_1755480, _1755482, _1755484, _1755486) = hAPP(c_Lazy__Sequence_Obind(_1755480, tc_prod(_1755480, _1755482), _1755484), hAPP(hAPP(c_COMBB(tc_fun(_1755482, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755480, _1755482))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755480, _1755482)), _1755480), c_Lazy__Sequence_Obind(_1755482, tc_prod(_1755480, _1755482), _1755486)), hAPP(hAPP(c_COMBB(tc_fun(_1755482, tc_prod(_1755480, _1755482)), tc_fun(_1755482, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755480, _1755482))), _1755480), hAPP(c_COMBB(tc_prod(_1755480, _1755482), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755480, _1755482)), _1755482), c_Lazy__Sequence_Osingle(tc_prod(_1755480, _1755482)))), c_Product__Type_OPair(_1755480, _1755482)))))], (14174 ^ _776541) ^ [_1031340, _1031342, _1031344, _1031346, _1031348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031340), _1031342)), 14177 ^ _776541 : [(14184 ^ _776541) ^ [] : [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), _1031342), _1031340)), _1031344)), _1031346) = _1031348, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031342), _1031344)), _1031346) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031340), _1031344)), _1031348))], (14178 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031342), _1031344)), _1031346) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031340), _1031344)), _1031348), -(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), _1031342), _1031340)), _1031344)), _1031346) = _1031348)]]], (40623 ^ _776541) ^ [_1569821, _1569823] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569821, _1569821)), _1569823)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569821, _1569821)), c_Transitive__Closure_Otrancl(_1569821, _1569823))))], (4432 ^ _776541) ^ [_843832, _843834] : [_843834 = _843832, -(c_Lazy__Sequence_Osingle(_843834) = c_Lazy__Sequence_Osingle(_843832))], (32368 ^ _776541) ^ [_1358826, _1358828, _1358830] : [hBOOL(hAPP(_1358826, _1358828)), -(hBOOL(hAPP(hAPP(c_member(_1358830), _1358828), hAPP(c_Set_OCollect(_1358830), _1358826))))], (52439 ^ _776541) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (34970 ^ _776541) ^ [_1428929, _1428931] : [_1428929 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1428929, _1428931) = 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)))], (41674 ^ _776541) ^ [_1597133, _1597135, _1597137] : [-(c_Nitpick_Oof__frac(_1597135, _1597133, _1597137) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1597133), hAPP(c_Int_Oring__1__class_Oof__int(_1597133), hAPP(c_Nitpick_Onum(_1597135), _1597137))), hAPP(c_Int_Oring__1__class_Oof__int(_1597133), hAPP(c_Nitpick_Odenom(_1597135), _1597137)))), class_Rings_Oinverse(_1597133), class_Rings_Oring__1(_1597133)], (17621 ^ _776541) ^ [_1093897] : [class_Rings_Olinordered__semidom(_1093897), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093897), c_Groups_Ozero__class_Ozero(_1093897)), c_Groups_Oone__class_Oone(_1093897))))], (1324 ^ _776541) ^ [_795955, _795957] : [-(class_Rings_Oidom(_795955)), _795957 = _795955, class_Rings_Oidom(_795957)], (26158 ^ _776541) ^ [_1249196, _1249198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1249196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249198, _1249196)), _1249196)))], (40871 ^ _776541) ^ [_1576704, _1576706, _1576708, _1576710] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576704, _1576704)), hAPP(hAPP(c_Product__Type_OPair(_1576704, _1576704), _1576706), _1576708)), c_Transitive__Closure_Ortrancl(_1576704, _1576710)))), 40872 ^ _776541 : [(40875 ^ _776541) ^ [] : [-(_1576706 = _1576708), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576704, _1576704)), hAPP(hAPP(c_Product__Type_OPair(_1576704, _1576704), _1576706), _1576708)), c_Transitive__Closure_Otrancl(_1576704, _1576710)))], (40873 ^ _776541) ^ [] : [_1576706 = _1576708]]], (8905 ^ _776541) ^ [_929937, _929939, _929941, _929943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929937, tc_HOL_Obool)), _929939), hAPP(hAPP(c_Set_Oinsert(_929937), _929941), _929943)))), 8908 ^ _776541 : [(8911 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929937, tc_HOL_Obool)), _929939), _929943))], (8909 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929937), _929941), _929943)))]], 8912 ^ _776541 : [(8915 ^ _776541) ^ [] : [8916 ^ _776541 : [(8919 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929937, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929937, tc_HOL_Obool)), _929939), hAPP(hAPP(c_Set_Oinsert(_929937), _929941), c_Orderings_Obot__class_Obot(tc_fun(_929937, tc_HOL_Obool))))), _929943))], (8917 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929937), _929941), _929939)))]], 8920 ^ _776541 : [(8923 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929937, tc_HOL_Obool)), _929939), _929943))], (8921 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929937), _929941), _929939))]]], (8913 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929937), _929941), _929943))]]], (28491 ^ _776541) ^ [_1287861] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1287861)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1287861))))], (33354 ^ _776541) ^ [_1388753, _1388755] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1388753, tc_HOL_Obool), _1388755) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1388753, tc_HOL_Obool), tc_fun(_1388753, tc_HOL_Obool)), _1388755), c_COMBI(tc_fun(_1388753, tc_HOL_Obool))))], (30372 ^ _776541) ^ [_1321391, _1321393, _1321395, _1321397] : [class_Orderings_Olinorder(_1321391), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321391, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1321391), _1321393)), c_SetInterval_Oord__class_OatLeastAtMost(_1321391, _1321395, _1321397)) = c_SetInterval_Oord__class_OatLeastAtMost(_1321391, _1321395, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321391), _1321393), _1321397)))], (52033 ^ _776541) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (37516 ^ _776541) ^ [_1490566, _1490568, _1490570] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490566), _1490568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490566, tc_HOL_Obool)), _1490568), hAPP(c_Set_Oimage(_1490566, _1490566, _1490570), _1490568))), -(c_Fun_Oinj__on(_1490566, _1490566, _1490570, _1490568))], (25129 ^ _776541) ^ [_1231329, _1231331, _1231333, _1231335] : [class_Divides_Osemiring__div(_1231329), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231329), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231329), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231329), _1231331), _1231333)), _1231333)), c_Divides_Odiv__class_Omod(_1231329, _1231331, _1231333))), _1231335) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231329), _1231331), _1231335))], (14817 ^ _776541) ^ [_1043716, _1043718, _1043720] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043716), _1043718)), _1043720) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043716), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043718), _1043720)))], (6079 ^ _776541) ^ [_873814, _873816, _873818, _873820, _873822, _873824] : [hBOOL(hAPP(hAPP(c_member(_873814), _873816), c_SetInterval_Oord_OgreaterThanAtMost(_873814, _873818, _873820, _873822, _873824))), 6082 ^ _776541 : [(6085 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_873818, _873816), _873824)))], (6083 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_873820, _873822), _873816)))]]], (41666 ^ _776541) ^ [_1596838, _1596840, _1596842] : [-(c_Nitpick_Oplus__frac(_1596838, _1596840, _1596842) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1596838), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1596838), _1596840), hAPP(c_Nitpick_Odenom(_1596838), _1596842))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1596838), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1596838), tc_Int_Oint), c_Nitpick_Ofrac(_1596838)), 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(_1596838), _1596840))), 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(_1596838), _1596840))))), 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(_1596838), _1596842))), 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(_1596838), _1596842)))))), c_COMBI(tc_Int_Oint))))], (52065 ^ _776541) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (28865 ^ _776541) ^ [_1294042, _1294044] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1294042)), c_Int_OBit0(_1294044)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1294042), _1294044)))], (46115 ^ _776541) ^ [_1702789, _1702791] : [-(hAPP(c_List_Ofilter(_1702789, _1702791), c_List_Olist_ONil(_1702789)) = c_List_Olist_ONil(_1702789))], (19787 ^ _776541) ^ [_1133648, _1133650, _1133652, _1133654] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1133648, _1133650)), c_Sum__Type_OPlus(_1133648, _1133650, _1133652, _1133654)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133648), _1133652)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133650), _1133654))], (44942 ^ _776541) ^ [_1676364, _1676366, _1676368, _1676370] : [class_Groups_Oab__group__add(_1676364), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1676364), hAPP(c_List_Omonoid__add__class_Olistsum(_1676364), hAPP(hAPP(c_List_Omap(_1676366, _1676364), _1676368), _1676370))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1676364), hAPP(hAPP(c_List_Omap(_1676366, _1676364), hAPP(c_Fun_Ocomp(_1676364, _1676364, _1676366, c_Groups_Ouminus__class_Ouminus(_1676364)), _1676368)), _1676370)))], (38209 ^ _776541) ^ [_1508181, _1508183, _1508185, _1508187] : [c_Wellfounded_Owf(_1508181, _1508183), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508181, _1508181)), hAPP(hAPP(c_Product__Type_OPair(_1508181, _1508181), _1508185), _1508187)), _1508183)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508181, _1508181)), hAPP(hAPP(c_Product__Type_OPair(_1508181, _1508181), _1508187), _1508185)), _1508183))], (21417 ^ _776541) ^ [_1164620, _1164622, _1164624] : [class_Int_Onumber__ring(_1164620), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164620), hAPP(c_Groups_Ouminus__class_Ouminus(_1164620), hAPP(c_Int_Onumber__class_Onumber__of(_1164620), _1164622))), _1164624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164620), hAPP(c_Int_Onumber__class_Onumber__of(_1164620), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1164622))), _1164624))], (1004 ^ _776541) ^ [_791703, _791705, _791707, _791709, _791711, _791713] : [-(c_List_Olist__all(_791711, _791707, _791703)), c_List_Olist__all(_791713, _791709, _791705), _791713 = _791711, _791709 = _791707, _791705 = _791703], (44184 ^ _776541) ^ [_1660070, _1660072, _1660074] : [hAPP(c_List_Orotate(_1660070, _1660072), _1660074) = c_List_Olist_ONil(_1660070), -(_1660074 = c_List_Olist_ONil(_1660070))], (25309 ^ _776541) ^ [_1234615, _1234617, _1234619] : [-(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), _1234615), _1234617)), _1234617)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234615, _1234617))), _1234619) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1234615), _1234619))], (44174 ^ _776541) ^ [_1659844] : [-(c_List_Orotate(_1659844, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1659844)))], (41684 ^ _776541) ^ [_1597326, _1597328] : [-(c_Nitpick_Oinverse__frac(_1597326, _1597328) = hAPP(hAPP(c_Nitpick_Ofrac(_1597326), hAPP(c_Nitpick_Odenom(_1597326), _1597328)), hAPP(c_Nitpick_Onum(_1597326), _1597328)))], (44926 ^ _776541) ^ [_1676036, _1676038, _1676040, _1676042] : [-(hBOOL(hAPP(c_List_Odistinct(_1676036), hAPP(hAPP(c_List_Omap(_1676038, _1676036), _1676040), _1676042)))), hBOOL(hAPP(c_List_Odistinct(_1676038), _1676042)), c_Fun_Oinj__on(_1676038, _1676036, _1676040, hAPP(c_List_Oset(_1676038), _1676042))], (10703 ^ _776541) ^ [_960923, _960925, _960927] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960923, tc_HOL_Obool)), _960925), _960927) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960923, tc_HOL_Obool)), _960925), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960923, tc_HOL_Obool)), _960927)))], (34095 ^ _776541) ^ [_1409628, _1409630, _1409632, _1409634, _1409636, _1409638] : [class_Groups_Ocomm__monoid__add(_1409628), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409630), _1409632)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409630, _1409628), hAPP(hAPP(c_COMBS(_1409630, _1409628, _1409628), hAPP(hAPP(c_COMBS(_1409630, _1409628, tc_fun(_1409628, _1409628)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409628, tc_fun(_1409628, _1409628)), _1409630), c_If(_1409628)), _1409634)), _1409636)), _1409638)), _1409632) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409628), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409630, _1409628), _1409636), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409630, tc_HOL_Obool)), _1409632), hAPP(c_Set_OCollect(_1409630), _1409634)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409630, _1409628), _1409638), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409630, tc_HOL_Obool)), _1409632), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1409630, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1409630), _1409634))))))], (6478 ^ _776541) ^ [_881199, _881201, _881203] : [_881199 = c_Orderings_Obot__class_Obot(tc_fun(_881201, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_881201), _881203), _881199))], (45134 ^ _776541) ^ [_1680496] : [-(_1680496 = 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)), _1680496)))], (340 ^ _776541) ^ [_781653, _781655, _781657, _781659, _781661, _781663, _781665, _781667] : [-(c_Finite__Set_Ofolding(_781665, _781661, _781657, _781653)), c_Finite__Set_Ofolding(_781667, _781663, _781659, _781655), _781667 = _781665, _781663 = _781661, _781659 = _781657, _781655 = _781653], (44200 ^ _776541) ^ [_1660354, _1660356, _1660358] : [-(_1660354 = c_List_Olist_ONil(_1660356)), -(hAPP(c_List_Otl(_1660356), hAPP(hAPP(c_List_Oappend(_1660356), _1660354), _1660358)) = hAPP(hAPP(c_List_Oappend(_1660356), hAPP(c_List_Otl(_1660356), _1660354)), _1660358))], (29095 ^ _776541) ^ [_1298059] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1298059)))], (52047 ^ _776541) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (10713 ^ _776541) ^ [_961148, _961150] : [class_Orderings_Olinorder(_961148), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961148, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_961148), _961150)) = hAPP(c_SetInterval_Oord__class_OatLeast(_961148), _961150))], (22669 ^ _776541) ^ [_1187307, _1187309, _1187311] : [class_Fields_Ofield__inverse__zero(_1187307), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187307), c_Groups_Oone__class_Oone(_1187307)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187307), _1187309), _1187311)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1187307), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187307), c_Groups_Oone__class_Oone(_1187307)), _1187309)), _1187311))], (50445 ^ _776541) ^ [_1796393, _1796395, _1796397, _1796399] : [c_Fun_Oinj__on(_1796393, _1796395, _1796397, _1796399), -(c_Fun_Obij__betw(_1796393, _1796395, _1796397, _1796399, hAPP(c_Set_Oimage(_1796393, _1796395, _1796397), _1796399)))], (25052 ^ _776541) ^ [_1230135, _1230137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230137, _1230135)), _1230135)))], (15334 ^ _776541) ^ [_1053308, _1053310, _1053312] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053308), _1053310)), hBOOL(hAPP(hAPP(c_member(_1053308), _1053312), _1053310)), -(hAPP(c_Finite__Set_Ocard(_1053308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053308, tc_HOL_Obool)), _1053310), hAPP(hAPP(c_Set_Oinsert(_1053308), _1053312), c_Orderings_Obot__class_Obot(tc_fun(_1053308, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1053308), _1053310)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13882 ^ _776541) ^ [_1024305, _1024307, _1024309, _1024311, _1024313, _1024315] : [class_Rings_Oring(_1024305), 13885 ^ _776541 : [(13892 ^ _776541) ^ [] : [_1024311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024305), _1024313), _1024307)), _1024309)), _1024315), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024305), _1024307), _1024309)), _1024311) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024305), _1024313), _1024309)), _1024315))], (13886 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024305), _1024307), _1024309)), _1024311) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024305), _1024313), _1024309)), _1024315), -(_1024311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024305), _1024313), _1024307)), _1024309)), _1024315))]]], (41558 ^ _776541) ^ [_1593733, _1593735, _1593737, _1593739, _1593741] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593733, _1593733)), hAPP(hAPP(c_Product__Type_OPair(_1593733, _1593733), _1593735), _1593737)), c_Transitive__Closure_Ortrancl(_1593733, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593733, _1593733), tc_HOL_Obool)), _1593739), _1593741)))), 41564 ^ _776541 : [(41570 ^ _776541) ^ [] : [41566 ^ [_1593733, _1593735, _1593737, _1593739, _1593741] = 41563 ^ [_1593733, _1593735, _1593737, _1593739, _1593741]], (41568 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593733, _1593733)), hAPP(hAPP(c_Product__Type_OPair(_1593733, _1593733), 41566 ^ [_1593733, _1593735, _1593737, _1593739, _1593741]), 41563 ^ [_1593733, _1593735, _1593737, _1593739, _1593741])), _1593741)))], (41565 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593733, _1593733)), hAPP(hAPP(c_Product__Type_OPair(_1593733, _1593733), 41563 ^ [_1593733, _1593735, _1593737, _1593739, _1593741]), _1593737)), c_Transitive__Closure_Ortrancl(_1593733, _1593739))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593733, _1593733)), hAPP(hAPP(c_Product__Type_OPair(_1593733, _1593733), _1593735), _1593737)), c_Transitive__Closure_Ortrancl(_1593733, _1593739))))], (43397 ^ _776541) ^ [_1641758, _1641760, _1641762, _1641764, _1641766] : [hAPP(hAPP(c_List_Olist_OCons(_1641758), _1641760), _1641762) = hAPP(hAPP(c_List_Oappend(_1641758), _1641764), _1641766), 43402 ^ _776541 : [(43405 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1641758), _1641760), _1641762) = _1641766)], (43403 ^ _776541) ^ [] : [-(_1641764 = c_List_Olist_ONil(_1641758))]], 43407 ^ _776541 : [(43410 ^ _776541) ^ [] : [-(_1641762 = hAPP(hAPP(c_List_Oappend(_1641758), 43406 ^ [_1641758, _1641760, _1641762, _1641764, _1641766]), _1641766))], (43408 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1641758), _1641760), 43406 ^ [_1641758, _1641760, _1641762, _1641764, _1641766]) = _1641764)]]], (27769 ^ _776541) ^ [_1275913, _1275915] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1275913), _1275915))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275913))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275915))))], (48450 ^ _776541) ^ [_1752533, _1752535, _1752537, _1752539] : [-(c_New__Random__Sequence_Oneg__map(_1752533, _1752535, _1752537, _1752539) = c_New__Random__Sequence_Oneg__bind(_1752533, _1752535, _1752539, hAPP(c_Fun_Ocomp(_1752535, 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(_1752535)))))), _1752533, c_New__Random__Sequence_Oneg__single(_1752535)), _1752537)))], (51015 ^ _776541) ^ [_1809539, _1809541, _1809543, _1809545, _1809547] : [class_Groups_Ocomm__monoid__mult(_1809539), class_Rings_Odvd(_1809539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1809541), _1809543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809541, tc_HOL_Obool)), _1809545), _1809543)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809539), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1809541, _1809539), _1809547), _1809545)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1809541, _1809539), _1809547), _1809543))))], (26567 ^ _776541) ^ [_1256085, _1256087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256085)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1256085), _1256087)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1256085)), _1256087))], (44749 ^ _776541) ^ [_1671253, _1671255] : [-(hAPP(hAPP(c_List_Omap(_1671253, _1671253), c_COMBI(_1671253)), _1671255) = _1671255)], (44741 ^ _776541) ^ [_1671012, _1671014, _1671016, _1671018, _1671020] : [-(hAPP(hAPP(c_List_Omap(_1671012, _1671014), _1671016), hAPP(hAPP(c_List_Olist_OCons(_1671012), _1671018), _1671020)) = hAPP(hAPP(c_List_Olist_OCons(_1671014), hAPP(_1671016, _1671018)), hAPP(hAPP(c_List_Omap(_1671012, _1671014), _1671016), _1671020)))], (2842 ^ _776541) ^ [_818665, _818667, _818669, _818671, _818673, _818675, _818677, _818679] : [-(c_Random_Oiterate(_818679, _818675, _818671, _818667) = c_Random_Oiterate(_818677, _818673, _818669, _818665)), _818679 = _818677, _818675 = _818673, _818671 = _818669, _818667 = _818665], (29209 ^ _776541) ^ [_1300044, _1300046] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1300044)), c_Int_OBit1(_1300046)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1300044), c_Int_Osucc(_1300046))))], (33763 ^ _776541) ^ [] : [-(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)))], (38686 ^ _776541) ^ [_1519894, _1519896, _1519898, _1519900, _1519902] : [hBOOL(hAPP(hAPP(c_member(_1519894), hAPP(_1519896, _1519898)), _1519900)), -(hBOOL(hAPP(hAPP(c_member(_1519902), _1519898), hAPP(c_Set_Ovimage(_1519902, _1519894, _1519896), _1519900))))], (5522 ^ _776541) ^ [_860911, _860913] : [_860913 = _860911, -(c_Groups_Oone__class_Oone(_860913) = c_Groups_Oone__class_Oone(_860911))], (29127 ^ _776541) ^ [_1298599, _1298601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298599)), c_Int_OBit1(_1298601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298599), _1298601)))], (14965 ^ _776541) ^ [_1046514, _1046516, _1046518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046514), _1046516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046518), _1046514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046514), _1046518)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046516), _1046518))))], (45854 ^ _776541) ^ [_1696364, _1696366, _1696368] : [hBOOL(hAPP(hAPP(c_member(_1696364), _1696366), hAPP(c_List_Oset(_1696364), _1696368))), -(c_List_Oremdups(_1696364, hAPP(hAPP(c_List_Olist_OCons(_1696364), _1696366), _1696368)) = c_List_Oremdups(_1696364, _1696368))], (50678 ^ _776541) ^ [_1800923, _1800925, _1800927, _1800929, _1800931] : [50680 ^ _776541 : [(50683 ^ _776541) ^ [] : [c_Relation_Orefl__on(_1800927, hAPP(_1800929, 50679 ^ [_1800923, _1800925, _1800927, _1800929, _1800931]), hAPP(_1800931, 50679 ^ [_1800923, _1800925, _1800927, _1800929, _1800931]))], (50681 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800923), 50679 ^ [_1800923, _1800925, _1800927, _1800929, _1800931]), _1800925)))]], -(c_Relation_Orefl__on(_1800927, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1800923, tc_fun(_1800927, tc_HOL_Obool)), _1800925), _1800929), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1800923, tc_fun(tc_prod(_1800927, _1800927), tc_HOL_Obool)), _1800925), _1800931)))], (3528 ^ _776541) ^ [_829292, _829294] : [_829294 = _829292, -(c_Int_Onumber__class_Onumber__of(_829294) = c_Int_Onumber__class_Onumber__of(_829292))], (41365 ^ _776541) ^ [_1588706, _1588708, _1588710, _1588712, _1588714] : [c_Relation_Osingle__valued(_1588706, _1588706, _1588708), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588706, _1588706)), hAPP(hAPP(c_Product__Type_OPair(_1588706, _1588706), _1588710), _1588712)), c_Transitive__Closure_Ortrancl(_1588706, _1588708))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588706, _1588706)), hAPP(hAPP(c_Product__Type_OPair(_1588706, _1588706), _1588710), _1588714)), c_Transitive__Closure_Ortrancl(_1588706, _1588708))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588706, _1588706)), hAPP(hAPP(c_Product__Type_OPair(_1588706, _1588706), _1588712), _1588714)), c_Transitive__Closure_Ortrancl(_1588706, _1588708)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588706, _1588706)), hAPP(hAPP(c_Product__Type_OPair(_1588706, _1588706), _1588714), _1588712)), c_Transitive__Closure_Ortrancl(_1588706, _1588708))))], (38328 ^ _776541) ^ [_1510829, _1510831] : [-(c_FunDef_Oreduction__pair(_1510829, _1510831)), c_Wellfounded_Owf(_1510829, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool), tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool)), _1510831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510829, _1510829, _1510829), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool), tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool)), _1510831)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool), tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool)), _1510831))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool), tc_fun(tc_prod(_1510829, _1510829), tc_HOL_Obool)), _1510831)))], (42299 ^ _776541) ^ [_1615804, _1615806, _1615808] : [-(hAPP(c_List_Oset(_1615804), c_List_Osublist(_1615804, _1615806, _1615808)) = hAPP(c_Set_OCollect(_1615804), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1615804), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1615804, 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)), _1615804), 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)), _1615804), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1615804, tc_fun(tc_Nat_Onat, _1615804), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615804, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1615804), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1615804), c_COMBB(_1615804, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1615804), _1615806))))), 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(_1615804)), _1615806)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1615808))))))], (43044 ^ _776541) ^ [_1634413, _1634415, _1634417, _1634419] : [-(_1634413 = _1634415), -(c_List_Oremove1(_1634417, _1634413, hAPP(hAPP(c_List_Olist_OCons(_1634417), _1634415), _1634419)) = hAPP(hAPP(c_List_Olist_OCons(_1634417), _1634415), c_List_Oremove1(_1634417, _1634413, _1634419)))], (11115 ^ _776541) ^ [_968804, _968806, _968808, _968810, _968812] : [-(hBOOL(hAPP(hAPP(c_member(_968804), _968806), hAPP(c_Set_Oimage(_968808, _968804, _968810), _968812)))), 11116 ^ _776541 : [(11117 ^ _776541) ^ [_968874] : [hBOOL(hAPP(hAPP(c_member(_968808), _968874), _968812)), _968806 = hAPP(_968810, _968874)]]], (19378 ^ _776541) ^ [_1126398, _1126400] : [class_Rings_Oring__1(_1126398), hBOOL(hAPP(hAPP(c_member(_1126398), _1126400), c_Int_Oring__1__class_OInts(_1126398))), -(hBOOL(hAPP(hAPP(c_member(_1126398), hAPP(c_Groups_Ouminus__class_Ouminus(_1126398), _1126400)), c_Int_Oring__1__class_OInts(_1126398))))], (47064 ^ _776541) ^ [_1722561, _1722563, _1722565] : [_1722563 = _1722565, -(hAPP(c_List_Orev(_1722561), _1722563) = hAPP(c_List_Orev(_1722561), _1722565))], (38533 ^ _776541) ^ [_1515355, _1515357, _1515359] : [-(c_HOL_OThe(tc_prod(_1515355, _1515357), _1515359) = c_HOL_OThe(tc_prod(_1515355, _1515357), hAPP(c_Product__Type_Oprod_Oprod__case(_1515355, _1515357, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1515357, tc_prod(_1515355, _1515357)), tc_fun(_1515357, tc_HOL_Obool), _1515355), hAPP(c_COMBB(tc_prod(_1515355, _1515357), tc_HOL_Obool, _1515357), _1515359)), c_Product__Type_OPair(_1515355, _1515357)))))], (22185 ^ _776541) ^ [_1178900, _1178902] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178900), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1178902) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1178900, _1178902))], (35414 ^ _776541) ^ [_1436916, _1436918, _1436920, _1436922] : [_1436916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1436918), _1436920)), _1436922), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436916, _1436918), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436920), _1436922)))), 35421 ^ _776541 : [(35424 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436922), _1436918))], (35422 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436918)))]], 35429 ^ _776541 : [(35432 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436918), _1436922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436922), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35430 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436918))]]], (6007 ^ _776541) ^ [_872353, _872355, _872357, _872359] : [hBOOL(hAPP(hAPP(c_member(_872353), _872355), c_SetInterval_Oord_OatLeast(_872353, _872357, _872359))), -(hBOOL(hAPP(hAPP(_872357, _872359), _872355)))], (49720 ^ _776541) ^ [_1781450, _1781452] : [c_Relation_Osym(_1781450, _1781452), -(c_Relation_Osym(_1781450, c_Transitive__Closure_Otrancl(_1781450, _1781452)))], (45808 ^ _776541) ^ [_1695612, _1695614] : [c_List_Olist_ONil(_1695612) = c_List_Oremdups(_1695612, _1695614), -(_1695614 = c_List_Olist_ONil(_1695612))], (23571 ^ _776541) ^ [_1203778, _1203780] : [-(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, _1203778)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203780))))], (23593 ^ _776541) ^ [_1204130, _1204132] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204130)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204132)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204130), _1204132))], (5398 ^ _776541) ^ [_858995, _858997] : [_858997 = _858995, -(c_Groups_Oplus__class_Oplus(_858997) = c_Groups_Oplus__class_Oplus(_858995))], (10249 ^ _776541) ^ [_952705, _952707, _952709] : [class_Lattices_Oboolean__algebra(_952705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952705), _952707), _952709) = c_Orderings_Obot__class_Obot(_952705), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952705), _952707), _952709) = c_Orderings_Otop__class_Otop(_952705), -(hAPP(c_Groups_Ouminus__class_Ouminus(_952705), _952707) = _952709)], (22615 ^ _776541) ^ [_1186278, _1186280, _1186282, _1186284] : [class_Rings_Olinordered__semidom(_1186278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186278), c_Groups_Oone__class_Oone(_1186278)), _1186280)), 22622 ^ _776541 : [(22629 ^ _776541) ^ [] : [_1186282 = _1186284, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186278), _1186280), _1186282) = hAPP(hAPP(c_Power_Opower__class_Opower(_1186278), _1186280), _1186284))], (22623 ^ _776541) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1186278), _1186280), _1186282) = hAPP(hAPP(c_Power_Opower__class_Opower(_1186278), _1186280), _1186284), -(_1186282 = _1186284)]]], (27891 ^ _776541) ^ [_1277976, _1277978] : [27892 ^ _776541 : [(27895 ^ _776541) ^ [] : [_1277978 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27893 ^ _776541) ^ [] : [-(_1277976 = 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), _1277976)), _1277978))))], (31052 ^ _776541) ^ [_1333794, _1333796, _1333798] : [class_Orderings_Olinorder(_1333794), hAPP(_1333796, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333794), 31057 ^ [_1333794, _1333796, _1333798]), 31058 ^ [_1333794, _1333796, _1333798])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333794), hAPP(_1333796, 31057 ^ [_1333794, _1333796, _1333798])), hAPP(_1333796, 31058 ^ [_1333794, _1333796, _1333798])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333794), _1333798)), -(_1333798 = c_Orderings_Obot__class_Obot(tc_fun(_1333794, tc_HOL_Obool))), -(hAPP(_1333796, c_Big__Operators_Olattice_OInf__fin(_1333794, c_Orderings_Oord__class_Omin(_1333794), _1333798)) = c_Big__Operators_Olattice_OInf__fin(_1333794, c_Orderings_Oord__class_Omin(_1333794), hAPP(c_Set_Oimage(_1333794, _1333794, _1333796), _1333798)))], (1434 ^ _776541) ^ [_797330, _797332] : [-(class_Orderings_Otop(_797330)), _797332 = _797330, class_Orderings_Otop(_797332)], (43188 ^ _776541) ^ [_1636881, _1636883] : [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(_1636881)), _1636883))), _1636883 = c_List_Olist_ONil(_1636881)], (33445 ^ _776541) ^ [_1391245, _1391247, _1391249, _1391251, _1391253, _1391255] : [class_Groups_Ocomm__monoid__add(_1391245), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391247, _1391245), hAPP(hAPP(c_COMBC(_1391247, tc_fun(_1391249, tc_HOL_Obool), _1391245), hAPP(hAPP(c_COMBB(tc_fun(_1391249, _1391245), tc_fun(tc_fun(_1391249, tc_HOL_Obool), _1391245), _1391247), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391249, _1391245)), _1391251)), _1391253)), _1391255) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391249, _1391245), hAPP(hAPP(c_COMBC(_1391249, tc_fun(_1391247, tc_HOL_Obool), _1391245), hAPP(hAPP(c_COMBB(tc_fun(_1391247, _1391245), tc_fun(tc_fun(_1391247, tc_HOL_Obool), _1391245), _1391249), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391247, _1391245)), hAPP(c_COMBC(_1391247, _1391249, _1391245), _1391251))), _1391255)), _1391253))], (18524 ^ _776541) ^ [_1109896] : [class_Rings_Olinordered__semidom(_1109896), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109896), c_Groups_Ozero__class_Ozero(_1109896)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109896), c_Groups_Oone__class_Oone(_1109896)), c_Groups_Oone__class_Oone(_1109896)))))], (44423 ^ _776541) ^ [_1664940, _1664942, _1664944] : [class_Lattices_Olattice(_1664940), -(c_Big__Operators_Olattice__class_OSup__fin(_1664940, hAPP(c_List_Oset(_1664940), hAPP(hAPP(c_List_Olist_OCons(_1664940), _1664942), _1664944))) = hAPP(c_List_Ofoldl(_1664940, _1664940, c_Lattices_Osemilattice__sup__class_Osup(_1664940), _1664942), _1664944))], (23615 ^ _776541) ^ [_1204509] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1204509) = 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)), _1204509)))], (33455 ^ _776541) ^ [_1391661, _1391663, _1391665, _1391667] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391661, tc_fun(_1391663, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1391661, tc_HOL_Obool), _1391665)), _1391667) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1391661, tc_HOL_Obool), tc_fun(_1391663, tc_HOL_Obool)), _1391665), hAPP(hAPP(c_COMBC(tc_fun(_1391661, tc_HOL_Obool), tc_fun(_1391661, tc_fun(_1391663, tc_HOL_Obool)), tc_fun(_1391663, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391661, tc_fun(_1391663, tc_HOL_Obool))), _1391667)))], (38802 ^ _776541) ^ [_1522517, _1522519, _1522521, _1522523, _1522525] : [hAPP(_1522523, _1522519) = _1522525, -(hBOOL(hAPP(hAPP(c_member(_1522517), _1522519), hAPP(c_Set_Ovimage(_1522517, _1522521, _1522523), hAPP(hAPP(c_Set_Oinsert(_1522521), _1522525), c_Orderings_Obot__class_Obot(tc_fun(_1522521, tc_HOL_Obool)))))))], (12690 ^ _776541) ^ [_1000266, _1000268, _1000270, _1000272, _1000274, _1000276] : [c_Finite__Set_Ofun__left__comm(_1000266, _1000268, _1000270), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1000266, _1000268, _1000270, _1000272, _1000274), _1000276)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1000266, _1000268, _1000270), _1000272), _1000274) = _1000276)], (28763 ^ _776541) ^ [_1292211, _1292213] : [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), _1292211))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1292213)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1292211))) = 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), _1292213), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292211)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30314 ^ _776541) ^ [_1320253, _1320255, _1320257, _1320259] : [class_Orderings_Olinorder(_1320253), 30317 ^ _776541 : [(30326 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320253), _1320255), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320253), _1320257), _1320259)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320253), _1320255), _1320257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320253), _1320255), _1320259))], (30318 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320253), _1320255), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320253), _1320257), _1320259))), 30321 ^ _776541 : [(30324 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320253), _1320255), _1320259)))], (30322 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320253), _1320255), _1320257)))]]]]], (18736 ^ _776541) ^ [_1113897, _1113899, _1113901, _1113903, _1113905, _1113907] : [class_Rings_Olinordered__semiring__1(_1113897), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113897), _1113899), _1113901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113897), _1113903), _1113901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113897), c_Groups_Ozero__class_Ozero(_1113897)), _1113905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113897), c_Groups_Ozero__class_Ozero(_1113897)), _1113907)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113897), _1113905), _1113907) = c_Groups_Oone__class_Oone(_1113897), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113897), _1113905), _1113899)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113897), _1113907), _1113903))), _1113901)))], (19388 ^ _776541) ^ [_1126571, _1126573] : [class_Int_Oring__char__0(_1126571), hBOOL(hAPP(hAPP(c_member(_1126571), _1126573), c_Int_Oring__1__class_OInts(_1126571))), 19395 ^ _776541 : [(19402 ^ _776541) ^ [] : [_1126573 = c_Groups_Ozero__class_Ozero(_1126571), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126571), _1126573), _1126573) = c_Groups_Ozero__class_Ozero(_1126571))], (19396 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126571), _1126573), _1126573) = c_Groups_Ozero__class_Ozero(_1126571), -(_1126573 = c_Groups_Ozero__class_Ozero(_1126571))]]], (38754 ^ _776541) ^ [_1521349, _1521351, _1521353, _1521355] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521349, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1521351, _1521349, _1521353), hAPP(c_Set_Ovimage(_1521351, _1521349, _1521353), _1521355))), _1521355)))], (10745 ^ _776541) ^ [_961651, _961653, _961655] : [class_Orderings_Oorder(_961651), 10748 ^ _776541 : [(10755 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961651), _961653), _961655))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961651, _961653), _961655) = c_Orderings_Obot__class_Obot(tc_fun(_961651, tc_HOL_Obool)))], (10749 ^ _776541) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961651, _961653), _961655) = c_Orderings_Obot__class_Obot(tc_fun(_961651, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961651), _961653), _961655))]]], (6013 ^ _776541) ^ [_872462, _872464, _872466, _872468] : [hBOOL(hAPP(hAPP(_872466, _872468), _872464)), -(hBOOL(hAPP(hAPP(c_member(_872462), _872464), c_SetInterval_Oord_OatLeast(_872462, _872466, _872468))))], (5582 ^ _776541) ^ [_861783, _861785, _861787, _861789] : [-(tc_prod(_861789, _861785) = tc_prod(_861787, _861783)), _861789 = _861787, _861785 = _861783], (18071 ^ _776541) ^ [_1101512, _1101514, _1101516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101512)), 18074 ^ _776541 : [(18081 ^ _776541) ^ [] : [_1101514 = _1101516, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101512), _1101514) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101512), _1101516))], (18075 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101512), _1101514) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101512), _1101516), -(_1101514 = _1101516)]]], (30356 ^ _776541) ^ [_1321025, _1321027, _1321029, _1321031] : [class_Orderings_Olinorder(_1321025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321025), _1321027)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1321025, _1321025, c_Orderings_Oord__class_Omin(_1321025)), _1321029), hAPP(hAPP(c_Set_Oinsert(_1321025), _1321031), _1321027)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321025), _1321031), hAPP(hAPP(c_Finite__Set_Ofold(_1321025, _1321025, c_Orderings_Oord__class_Omin(_1321025)), _1321029), _1321027)))], (38830 ^ _776541) ^ [_1523190, _1523192, _1523194, _1523196] : [-(hAPP(c_Set_Oimage(_1523190, _1523192, _1523194), hAPP(c_Set_Ovimage(_1523190, _1523192, _1523194), _1523196)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523192, tc_HOL_Obool)), _1523196), hAPP(c_Set_Oimage(_1523190, _1523192, _1523194), c_Orderings_Otop__class_Otop(tc_fun(_1523190, tc_HOL_Obool)))))], (6232 ^ _776541) ^ [_876698] : [class_Complete__Lattice_Ocomplete__lattice(_876698), -(c_Complete__Lattice_OInf__class_OInf(_876698, c_Orderings_Obot__class_Obot(tc_fun(_876698, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_876698))], (36577 ^ _776541) ^ [_1469553, _1469555, _1469557, _1469559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469553), _1469559)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469557), _1469555))), -(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), _1469553), _1469555)), 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), _1469557), _1469559)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (41759 ^ _776541) ^ [_1599755, _1599757, _1599759, _1599761, _1599763] : [hAPP(hAPP(c_List_Olist_OCons(_1599755), _1599757), _1599759) = hAPP(hAPP(c_List_Olist_OCons(_1599755), _1599761), _1599763), 41762 ^ _776541 : [(41765 ^ _776541) ^ [] : [-(_1599759 = _1599763)], (41763 ^ _776541) ^ [] : [-(_1599757 = _1599761)]]], (24140 ^ _776541) ^ [_1213278, _1213280, _1213282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213280), _1213282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213278), _1213282)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213278), _1213280))))], (40090 ^ _776541) ^ [_1557289, _1557291, _1557293, _1557295, _1557297, _1557299, _1557301, _1557303] : [c_Finite__Set_Ofolding(_1557289, _1557291, _1557293, _1557295), -(hAPP(c_Fun_Ocomp(_1557291, _1557291, _1557297, hAPP(_1557293, _1557299)), hAPP(c_Fun_Ocomp(_1557291, _1557291, _1557297, hAPP(_1557293, _1557301)), _1557303)) = hAPP(c_Fun_Ocomp(_1557291, _1557291, _1557297, hAPP(_1557293, _1557301)), hAPP(c_Fun_Ocomp(_1557291, _1557291, _1557297, hAPP(_1557293, _1557299)), _1557303)))], (45964 ^ _776541) ^ [_1698595, _1698597, _1698599, _1698601] : [-(hAPP(hAPP(c_List_Omap(_1698595, _1698597), _1698599), c_List_Oconcat(_1698595, _1698601)) = c_List_Oconcat(_1698597, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698595), tc_List_Olist(_1698597)), hAPP(c_List_Omap(_1698595, _1698597), _1698599)), _1698601)))], (14825 ^ _776541) ^ [_1043898, _1043900, _1043902] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043898), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043900), _1043902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043898), _1043900)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043898), _1043902)))], (28659 ^ _776541) ^ [_1290421, _1290423] : [class_Int_Onumber__ring(_1290421), class_Rings_Olinordered__idom(_1290421), 28666 ^ _776541 : [(28673 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290423), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290421), hAPP(c_Int_Onumber__class_Onumber__of(_1290421), _1290423)), c_Groups_Oone__class_Oone(_1290421))))], (28667 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290421), hAPP(c_Int_Onumber__class_Onumber__of(_1290421), _1290423)), c_Groups_Oone__class_Oone(_1290421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290423), c_Int_OBit1(c_Int_OPls))))]]], (38034 ^ _776541) ^ [_1504392, _1504394, _1504396, _1504398, _1504400, _1504402, _1504404] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504392, _1504396)), hAPP(hAPP(c_Product__Type_OPair(_1504392, _1504396), _1504402), _1504404)), hAPP(hAPP(c_Relation_Orel__comp(_1504392, _1504394, _1504396), _1504398), _1504400))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1504392, _1504394, _1504396, hAPP(hAPP(c_COMBC(_1504392, tc_fun(tc_prod(_1504392, _1504394), tc_HOL_Obool), tc_fun(_1504394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504394, tc_fun(tc_fun(tc_prod(_1504392, _1504394), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504392, _1504394), tc_HOL_Obool), tc_fun(_1504394, tc_HOL_Obool)), _1504392), c_COMBC(_1504394, tc_fun(tc_prod(_1504392, _1504394), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504394, tc_prod(_1504392, _1504394)), tc_fun(_1504394, tc_fun(tc_fun(tc_prod(_1504392, _1504394), tc_HOL_Obool), tc_HOL_Obool)), _1504392), hAPP(c_COMBB(tc_prod(_1504392, _1504394), tc_fun(tc_fun(tc_prod(_1504392, _1504394), tc_HOL_Obool), tc_HOL_Obool), _1504394), c_member(tc_prod(_1504392, _1504394)))), c_Product__Type_OPair(_1504392, _1504394)))), _1504398), hAPP(hAPP(c_COMBC(_1504394, tc_fun(tc_prod(_1504394, _1504396), tc_HOL_Obool), tc_fun(_1504396, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504396, tc_fun(tc_fun(tc_prod(_1504394, _1504396), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504394, _1504396), tc_HOL_Obool), tc_fun(_1504396, tc_HOL_Obool)), _1504394), c_COMBC(_1504396, tc_fun(tc_prod(_1504394, _1504396), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504396, tc_prod(_1504394, _1504396)), tc_fun(_1504396, tc_fun(tc_fun(tc_prod(_1504394, _1504396), tc_HOL_Obool), tc_HOL_Obool)), _1504394), hAPP(c_COMBB(tc_prod(_1504394, _1504396), tc_fun(tc_fun(tc_prod(_1504394, _1504396), tc_HOL_Obool), tc_HOL_Obool), _1504396), c_member(tc_prod(_1504394, _1504396)))), c_Product__Type_OPair(_1504394, _1504396)))), _1504400)), _1504402), _1504404)))], (4640 ^ _776541) ^ [_847076, _847078, _847080, _847082, _847084, _847086, _847088, _847090] : [-(c_Random__Sequence_ORandom(_847090, _847086, _847082, _847078) = c_Random__Sequence_ORandom(_847088, _847084, _847080, _847076)), _847090 = _847088, _847086 = _847084, _847082 = _847080, _847078 = _847076], (46900 ^ _776541) ^ [_1718930, _1718932, _1718934, _1718936, _1718938] : [class_Orderings_Olinorder(_1718930), c_Fun_Oinj__on(_1718932, _1718930, _1718934, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1718932, tc_HOL_Obool)), hAPP(c_List_Oset(_1718932), _1718936)), hAPP(c_List_Oset(_1718932), _1718938))), c_List_Olinorder__class_Osorted(_1718930, hAPP(hAPP(c_List_Omap(_1718932, _1718930), _1718934), _1718936)), hBOOL(hAPP(c_List_Odistinct(_1718930), hAPP(hAPP(c_List_Omap(_1718932, _1718930), _1718934), _1718936))), c_List_Olinorder__class_Osorted(_1718930, hAPP(hAPP(c_List_Omap(_1718932, _1718930), _1718934), _1718938)), hBOOL(hAPP(c_List_Odistinct(_1718930), hAPP(hAPP(c_List_Omap(_1718932, _1718930), _1718934), _1718938))), hAPP(c_List_Oset(_1718932), _1718936) = hAPP(c_List_Oset(_1718932), _1718938), -(_1718936 = _1718938)], (7100 ^ _776541) ^ [_892184, _892186, _892188, _892190] : [class_Orderings_Oord(_892184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892184), hAPP(_892186, 7105 ^ [_892184, _892186, _892188, _892190])), hAPP(_892188, 7105 ^ [_892184, _892186, _892188, _892190]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892190, _892184)), _892186), _892188)))], (38531 ^ _776541) ^ [_1515309, _1515311, _1515313] : [-(hAPP(c_Set_Oimage(tc_prod(_1515309, _1515311), _1515311, c_Product__Type_Osnd(_1515309, _1515311)), _1515313) = hAPP(c_Relation_ORange(_1515309, _1515311), _1515313))], (14190 ^ _776541) ^ [_1031701, _1031703, _1031705, _1031707, _1031709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031701), _1031703)), -(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), _1031703), _1031705)), _1031707)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031701), _1031705)), _1031709)) = 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), _1031703), _1031701)), _1031705)), _1031707)), _1031709))], (39310 ^ _776541) ^ [_1537418, _1537420, _1537422, _1537424, _1537426, _1537428] : [class_Groups_Ocomm__monoid__mult(_1537418), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537420), _1537422)), 39320 ^ _776541 : [(39323 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1537424), hAPP(_1537426, 39319 ^ [_1537418, _1537420, _1537422, _1537424, _1537426, _1537428])))], (39321 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537420), 39319 ^ [_1537418, _1537420, _1537422, _1537424, _1537426, _1537428]), _1537422)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1537418, _1537420, c_Groups_Otimes__class_Otimes(_1537418)), hAPP(hAPP(c_COMBS(_1537420, tc_fun(_1537424, tc_HOL_Obool), _1537418), hAPP(hAPP(c_COMBC(_1537420, _1537418, tc_fun(tc_fun(_1537424, tc_HOL_Obool), _1537418)), hAPP(hAPP(c_COMBB(tc_fun(_1537424, _1537418), tc_fun(_1537418, tc_fun(tc_fun(_1537424, tc_HOL_Obool), _1537418)), _1537420), c_Finite__Set_Ofold__image(_1537418, _1537424, c_Groups_Otimes__class_Otimes(_1537418))), _1537428)), c_Groups_Oone__class_Oone(_1537418))), _1537426)), c_Groups_Oone__class_Oone(_1537418)), _1537422) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1537418, tc_prod(_1537420, _1537424), c_Groups_Otimes__class_Otimes(_1537418)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537420, _1537424, _1537418), _1537428)), c_Groups_Oone__class_Oone(_1537418)), hAPP(hAPP(c_Product__Type_OSigma(_1537420, _1537424), _1537422), _1537426)))], (40843 ^ _776541) ^ [_1576089, _1576091, _1576093] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1576089, _1576089, _1576091), c_Relation_OId(_1576089)), _1576093) = _1576093)], (18248 ^ _776541) ^ [_1104672, _1104674, _1104676] : [class_Groups_Oordered__comm__monoid__add(_1104672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104672), c_Groups_Ozero__class_Ozero(_1104672)), _1104674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104672), c_Groups_Ozero__class_Ozero(_1104672)), _1104676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104672), c_Groups_Ozero__class_Ozero(_1104672)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104672), _1104674), _1104676))))], (22111 ^ _776541) ^ [_1177466, _1177468, _1177470, _1177472] : [class_Rings_Olinordered__semidom(_1177466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177466), c_Groups_Oone__class_Oone(_1177466)), _1177468)), 22118 ^ _776541 : [(22125 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177470), _1177472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177466), hAPP(hAPP(c_Power_Opower__class_Opower(_1177466), _1177468), _1177470)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177466), _1177468), _1177472))))], (22119 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177466), hAPP(hAPP(c_Power_Opower__class_Opower(_1177466), _1177468), _1177470)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177466), _1177468), _1177472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177470), _1177472)))]]], (9372 ^ _776541) ^ [_937790, _937792, _937794, _937796] : [class_Orderings_Oord(_937790), 9375 ^ _776541 : [(9384 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937792, _937790)), _937794), _937796))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937792, _937790)), _937794), _937796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937792, _937790)), _937796), _937794)))], (9376 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937792, _937790)), _937794), _937796)), 9379 ^ _776541 : [(9382 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937792, _937790)), _937796), _937794))], (9380 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937792, _937790)), _937794), _937796)))]]]]], (29916 ^ _776541) ^ [_1313024, _1313026, _1313028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1313024), _1313026)), -(c_Random_Ominus__shift(_1313028, _1313024, _1313026) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1313028), _1313024)), _1313026))], (42001 ^ _776541) ^ [_1607281, _1607283] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607281), tc_List_Olist(_1607281)), tc_HOL_Obool)), c_List_Olistrel(_1607281, _1607283)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607281), c_List_Olistrel1(_1607281, _1607283)))))], (46365 ^ _776541) ^ [_1709008, _1709010, _1709012, _1709014] : [c_List_Oupt(_1709008, _1709010) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1709012), _1709014), 46368 ^ _776541 : [(46373 ^ _776541) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709008), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1709010) = _1709014)], (46371 ^ _776541) ^ [] : [-(_1709008 = _1709012)], (46369 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709008), _1709010)))]]], (43204 ^ _776541) ^ [_1637166, _1637168, _1637170] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637166), tc_List_Olist(_1637166))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637166), tc_List_Olist(_1637166)), c_List_Olist_ONil(_1637166)), _1637168)), c_List_Olistrel1(_1637166, _1637170)))], (28577 ^ _776541) ^ [_1289270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1289270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1289270))))], (29295 ^ _776541) ^ [_1301496, _1301498] : [class_Rings_Oring__1(_1301496), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301496), hAPP(c_Groups_Ouminus__class_Ouminus(_1301496), _1301498)), 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(_1301496), _1301498), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (23085 ^ _776541) ^ [_1194788] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1194788), _1194788)))], (32404 ^ _776541) ^ [_1359589] : [-(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)), _1359589)))))], (33585 ^ _776541) ^ [_1394775, _1394777, _1394779] : [class_Groups_Ocomm__monoid__add(_1394775), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1394777, _1394775), hAPP(c_COMBK(_1394775, _1394777), c_Groups_Ozero__class_Ozero(_1394775))), _1394779) = c_Groups_Ozero__class_Ozero(_1394775))], (26961 ^ _776541) ^ [_1262171, _1262173, _1262175] : [class_Rings_Oring__1(_1262171), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1262173), _1262175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262171), hAPP(c_Int_Oring__1__class_Oof__int(_1262171), _1262173)), hAPP(c_Int_Oring__1__class_Oof__int(_1262171), _1262175)))], (51985 ^ _776541) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (802 ^ _776541) ^ [_788580, _788582, _788584, _788586] : [-(c_Relation_Osym(_788584, _788580)), c_Relation_Osym(_788586, _788582), _788586 = _788584, _788582 = _788580], (15324 ^ _776541) ^ [_1053079, _1053081, _1053083] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053079), _1053081)), hBOOL(hAPP(hAPP(c_member(_1053079), _1053083), _1053081)), -(hAPP(c_Finite__Set_Ocard(_1053079), _1053081) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1053079), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053079, tc_HOL_Obool)), _1053081), hAPP(hAPP(c_Set_Oinsert(_1053079), _1053083), c_Orderings_Obot__class_Obot(tc_fun(_1053079, tc_HOL_Obool)))))))], (42504 ^ _776541) ^ [_1621962, _1621964, _1621966, _1621968] : [-(hAPP(c_List_Oset(tc_prod(_1621962, _1621964)), hAPP(hAPP(c_List_Ozip(_1621962, _1621964), _1621966), _1621968)) = hAPP(c_Set_OCollect(tc_prod(_1621962, _1621964)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1621962, _1621964)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1621962, _1621964), 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(_1621962, _1621964)), 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(_1621962, _1621964)), 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(_1621962, _1621964), tc_fun(tc_Nat_Onat, tc_prod(_1621962, _1621964)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1621962, _1621964), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1621962, _1621964)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1621962, _1621964)), c_COMBB(tc_prod(_1621962, _1621964), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1621964, tc_prod(_1621962, _1621964)), hAPP(hAPP(c_COMBB(_1621962, tc_fun(_1621964, tc_prod(_1621962, _1621964)), tc_Nat_Onat), c_Product__Type_OPair(_1621962, _1621964)), hAPP(c_List_Onth(_1621962), _1621966))), hAPP(c_List_Onth(_1621964), _1621968)))))), 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(_1621962)), _1621966)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621964)), _1621968)))))))], (4320 ^ _776541) ^ [_841960, _841962, _841964, _841966, _841968, _841970] : [-(c_List_Oreplicate(_841970, _841966, _841962) = c_List_Oreplicate(_841968, _841964, _841960)), _841970 = _841968, _841966 = _841964, _841962 = _841960], (43214 ^ _776541) ^ [_1637506, _1637508, _1637510, _1637512] : [-(hAPP(hAPP(c_List_Otake(_1637506), _1637508), hAPP(hAPP(c_List_Olist_OCons(_1637506), _1637510), _1637512)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1637506), c_List_Olist_ONil(_1637506), hAPP(hAPP(c_COMBB(tc_List_Olist(_1637506), tc_List_Olist(_1637506), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1637506), _1637510)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1637506), tc_List_Olist(_1637506)), c_List_Otake(_1637506)), _1637512)), _1637508))], (42205 ^ _776541) ^ [_1613363] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1613363)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1613363), tc_HOL_Obool))))], (2902 ^ _776541) ^ [_819583, _819585, _819587, _819589, _819591, _819593] : [-(c_Product__Type_Ointernal__split(_819593, _819589, _819585) = c_Product__Type_Ointernal__split(_819591, _819587, _819583)), _819593 = _819591, _819589 = _819587, _819585 = _819583], (44866 ^ _776541) ^ [_1674258, _1674260, _1674262, _1674264, _1674266, _1674268, _1674270, _1674272] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674258, _1674260), _1674262), _1674264), hAPP(hAPP(c_List_Ozip(_1674258, _1674260), _1674266), hAPP(hAPP(c_List_Omap(_1674268, _1674260), _1674270), _1674272))) = hAPP(hAPP(c_List_Omap(tc_prod(_1674258, _1674268), _1674262), hAPP(c_Product__Type_Oprod_Oprod__case(_1674258, _1674268, _1674262), hAPP(hAPP(c_COMBB(tc_fun(_1674268, tc_prod(_1674258, _1674260)), tc_fun(_1674268, _1674262), _1674258), hAPP(c_COMBB(tc_prod(_1674258, _1674260), _1674262, _1674268), _1674264)), hAPP(hAPP(c_COMBC(_1674258, tc_fun(_1674268, _1674260), tc_fun(_1674268, tc_prod(_1674258, _1674260))), hAPP(hAPP(c_COMBB(tc_fun(_1674260, tc_prod(_1674258, _1674260)), tc_fun(tc_fun(_1674268, _1674260), tc_fun(_1674268, tc_prod(_1674258, _1674260))), _1674258), c_COMBB(_1674260, tc_prod(_1674258, _1674260), _1674268)), c_Product__Type_OPair(_1674258, _1674260))), _1674270)))), hAPP(hAPP(c_List_Ozip(_1674258, _1674268), _1674266), _1674272)))], (11860 ^ _776541) ^ [_984665, _984667, _984669, _984671, _984673, _984675] : [hBOOL(hAPP(hAPP(c_member(_984665), _984667), _984669)), -(hAPP(c_Set_Oimage(_984665, _984671, c_Fun_Ofun__upd(_984665, _984671, _984673, _984667, _984675)), _984669) = hAPP(hAPP(c_Set_Oinsert(_984671), _984675), hAPP(c_Set_Oimage(_984665, _984671, _984673), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984665, tc_HOL_Obool)), _984669), hAPP(hAPP(c_Set_Oinsert(_984665), _984667), c_Orderings_Obot__class_Obot(tc_fun(_984665, tc_HOL_Obool)))))))], (26418 ^ _776541) ^ [_1253288, _1253290] : [-(hBOOL(hAPP(_1253288, hAPP(c_Int_Onat, _1253290)))), 26422 ^ _776541 : [(26425 ^ _776541) ^ [] : [hBOOL(hAPP(_1253288, 26421 ^ [_1253288, _1253290]))], (26423 ^ _776541) ^ [] : [-(_1253290 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 26421 ^ [_1253288, _1253290]))]], 26426 ^ _776541 : [(26429 ^ _776541) ^ [] : [hBOOL(hAPP(_1253288, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26427 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253290), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (17449 ^ _776541) ^ [_1090780, _1090782, _1090784] : [class_Rings_Olinordered__semiring__strict(_1090780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090780), c_Groups_Ozero__class_Ozero(_1090780)), _1090782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090780), _1090784), c_Groups_Ozero__class_Ozero(_1090780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090780), _1090782), _1090784)), c_Groups_Ozero__class_Ozero(_1090780))))], (26118 ^ _776541) ^ [_1248527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248527), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1248527) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45652 ^ _776541) ^ [_1692192, _1692194, _1692196, _1692198] : [hBOOL(hAPP(c_List_Odistinct(_1692192), _1692194)), hBOOL(hAPP(c_List_Odistinct(_1692196), _1692198)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1692192, _1692196)), c_Enum_Oproduct(_1692192, _1692196, _1692194, _1692198))))], (16154 ^ _776541) ^ [_1068549, _1068551, _1068553] : [_1068551 = _1068553, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068549)), _1068551) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068549)), _1068553))], (2066 ^ _776541) ^ [_806445, _806447, _806449, _806451, _806453, _806455, _806457, _806459] : [-(c_Sum__Type_OPlus(_806459, _806455, _806451, _806447) = c_Sum__Type_OPlus(_806457, _806453, _806449, _806445)), _806459 = _806457, _806455 = _806453, _806451 = _806449, _806447 = _806445], (19967 ^ _776541) ^ [_1136885, _1136887, _1136889, _1136891] : [class_Fields_Olinordered__field(_1136885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136885), c_Groups_Ozero__class_Ozero(_1136885)), _1136887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136885), _1136889), _1136887)), _1136891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136885), _1136889), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136885), _1136891), _1136887))))], (22809 ^ _776541) ^ [_1189724, _1189726, _1189728] : [class_Rings_Olinordered__semidom(_1189724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189724), c_Groups_Oone__class_Oone(_1189724)), _1189726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189724), c_Groups_Oone__class_Oone(_1189724)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189724), _1189726), hAPP(c_Nat_OSuc, _1189728)))))], (43234 ^ _776541) ^ [_1637904, _1637906, _1637908] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1637904))), -(c_List_Osublist(_1637906, hAPP(hAPP(c_List_Olist_OCons(_1637906), _1637908), c_List_Olist_ONil(_1637906)), _1637904) = c_List_Olist_ONil(_1637906))], (16576 ^ _776541) ^ [_1074766] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1074766) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25465 ^ _776541) ^ [_1237202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237202)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1237202) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18158 ^ _776541) ^ [_1102955] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1102955)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1102955))], (52105 ^ _776541) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (23822 ^ _776541) ^ [_1208071, _1208073] : [23823 ^ _776541 : [(23824 ^ _776541) ^ [_1208124] : [_1208073 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1208071), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208124))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1208071), _1208073)))], (1514 ^ _776541) ^ [_798330, _798332] : [-(class_Rings_Olinordered__comm__semiring__strict(_798330)), _798332 = _798330, class_Rings_Olinordered__comm__semiring__strict(_798332)], (8609 ^ _776541) ^ [_924448, _924450, _924452, _924454, _924456] : [class_Lattices_Osemilattice__inf(_924448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924448), _924450), _924452)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924448), _924454), _924456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924448), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924448), _924450), _924454)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924448), _924452), _924456))))], (26955 ^ _776541) ^ [_1262070, _1262072] : [class_Int_Onumber__ring(_1262070), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262070), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262072)) = hAPP(c_Int_Onumber__class_Onumber__of(_1262070), _1262072))], (36233 ^ _776541) ^ [_1460214, _1460216, _1460218, _1460220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1460214), _1460216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1460218), _1460220)), -(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), _1460214), _1460218)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1460216), _1460220))), c_FunDef_Opair__less)))], (30378 ^ _776541) ^ [_1321534, _1321536, _1321538, _1321540] : [class_Orderings_Olinorder(_1321534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321534), _1321536)), hBOOL(hAPP(hAPP(c_member(_1321534), _1321538), _1321536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321534), hAPP(hAPP(c_Finite__Set_Ofold(_1321534, _1321534, c_Orderings_Oord__class_Omin(_1321534)), _1321540), _1321536)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321534), _1321538), _1321540))))], (42027 ^ _776541) ^ [_1608088, _1608090, _1608092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1608088, _1608088), tc_HOL_Obool)), _1608090), _1608092)), c_Relation_Orefl__on(_1608088, c_Orderings_Otop__class_Otop(tc_fun(_1608088, tc_HOL_Obool)), _1608092), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1608088), tc_List_Olist(_1608088)), tc_HOL_Obool)), c_List_Olistrel1(_1608088, _1608090)), c_List_Olistrel(_1608088, _1608092))))], (47585 ^ _776541) ^ [_1733539, _1733541, _1733543] : [-(hBOOL(hAPP(hAPP(c_member(_1733539), _1733541), hAPP(c_List_Oset(_1733539), _1733543)))), -(c_List_Oinsert(_1733539, _1733541, _1733543) = hAPP(hAPP(c_List_Olist_OCons(_1733539), _1733541), _1733543))], (37140 ^ _776541) ^ [_1482769, _1482771, _1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789] : [c_Equiv__Relations_Oequiv(_1482769, _1482771, _1482773), c_Equiv__Relations_Oequiv(_1482775, _1482777, _1482779), c_Equiv__Relations_Ocongruent2(_1482769, _1482775, tc_fun(_1482781, tc_HOL_Obool), _1482773, _1482779, _1482783), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482769, tc_HOL_Obool)), _1482785), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482769), _1482771), _1482773))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482775, tc_HOL_Obool)), _1482787), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482775), _1482777), _1482779))), 37162 ^ _776541 : [(37168 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1482781, tc_HOL_Obool)), hAPP(hAPP(_1482783, 37161 ^ [_1482769, _1482771, _1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789]), 37164 ^ [_1482769, _1482771, _1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789])), _1482789))], (37166 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482775), 37164 ^ [_1482769, _1482771, _1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789]), _1482777)))], (37163 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482769), 37161 ^ [_1482769, _1482771, _1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789]), _1482771)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1482781, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482769, tc_fun(_1482781, tc_HOL_Obool)), _1482785), hAPP(hAPP(c_COMBB(tc_fun(_1482775, tc_fun(_1482781, tc_HOL_Obool)), tc_fun(_1482781, tc_HOL_Obool), _1482769), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482775, tc_fun(_1482781, tc_HOL_Obool)), _1482787)), _1482783))), _1482789)))], (6069 ^ _776541) ^ [_873600, _873602, _873604, _873606, _873608] : [-(hBOOL(hAPP(hAPP(c_member(_873600), _873602), c_SetInterval_Oord_OgreaterThanLessThan(_873600, _873604, _873606, _873608)))), hBOOL(hAPP(hAPP(_873604, _873606), _873602)), hBOOL(hAPP(hAPP(_873604, _873602), _873608))], (11918 ^ _776541) ^ [_985863, _985865, _985867, _985869, _985871] : [hAPP(_985863, _985865) = _985867, -(c_Fun_Ofun__upd(_985869, _985871, _985863, _985865, _985867) = _985863)], (14827 ^ _776541) ^ [_1043955, _1043957, _1043959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043955), _1043957)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043955), _1043959)), 14834 ^ _776541 : [(14841 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043957), _1043959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043957), _1043955)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043959), _1043955))))], (14835 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043957), _1043955)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043959), _1043955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043957), _1043959)))]]], (16080 ^ _776541) ^ [_1067326, _1067328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067326), _1067328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067328)), _1067326)))], (30916 ^ _776541) ^ [_1331148, _1331150, _1331152] : [class_Orderings_Olinorder(_1331148), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331148), _1331150)), -(hBOOL(hAPP(hAPP(c_member(_1331148), _1331152), _1331150))), -(c_Big__Operators_Olattice_OInf__fin(_1331148, c_Orderings_Oord__class_Omin(_1331148), hAPP(hAPP(c_Set_Oinsert(_1331148), _1331152), _1331150)) = hAPP(hAPP(c_Finite__Set_Ofold(_1331148, _1331148, c_Orderings_Oord__class_Omin(_1331148)), _1331152), _1331150))], (49774 ^ _776541) ^ [_1782289, _1782291, _1782293] : [c_Relation_Orefl__on(_1782289, _1782291, _1782293), c_Relation_Osym(_1782289, _1782293), c_Relation_Otrans(_1782289, _1782293), -(c_Equiv__Relations_Oequiv(_1782289, _1782291, _1782293))], (43565 ^ _776541) ^ [_1645650, _1645652, _1645654] : [c_List_Olist_ONil(_1645650) = hAPP(hAPP(c_List_Oappend(_1645650), _1645652), _1645654), 43568 ^ _776541 : [(43571 ^ _776541) ^ [] : [-(_1645654 = c_List_Olist_ONil(_1645650))], (43569 ^ _776541) ^ [] : [-(_1645652 = c_List_Olist_ONil(_1645650))]]], (50035 ^ _776541) ^ [_1787368, _1787370, _1787372, _1787374, _1787376, _1787378] : [hAPP(c_Hilbert__Choice_Oinv__into(_1787368, _1787370, _1787372, _1787374), _1787376) = hAPP(c_Hilbert__Choice_Oinv__into(_1787368, _1787370, _1787372, _1787374), _1787378), hBOOL(hAPP(hAPP(c_member(_1787370), _1787376), hAPP(c_Set_Oimage(_1787368, _1787370, _1787374), _1787372))), hBOOL(hAPP(hAPP(c_member(_1787370), _1787378), hAPP(c_Set_Oimage(_1787368, _1787370, _1787374), _1787372))), -(_1787376 = _1787378)], (38710 ^ _776541) ^ [_1520440, _1520442] : [-(hAPP(c_Set_Ovimage(_1520440, _1520440, c_COMBI(_1520440)), _1520442) = _1520442)], (14793 ^ _776541) ^ [_1043244, _1043246] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043244), _1043246))))], (4080 ^ _776541) ^ [_838272, _838274, _838276, _838278, _838280, _838282, _838284, _838286] : [-(c_New__Random__Sequence_Oneg__bind(_838286, _838282, _838278, _838274) = c_New__Random__Sequence_Oneg__bind(_838284, _838280, _838276, _838272)), _838286 = _838284, _838282 = _838280, _838278 = _838276, _838274 = _838272], (27757 ^ _776541) ^ [_1275778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275778), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275778) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1275778))], (42775 ^ _776541) ^ [_1628435, _1628437, _1628439, _1628441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628437)), _1628439))), -(hBOOL(hAPP(hAPP(c_member(_1628437), _1628441), hAPP(c_List_Oset(_1628437), hAPP(hAPP(c_List_Olist__update(_1628437, _1628439), _1628435), _1628441)))))], (7986 ^ _776541) ^ [_911743, _911745, _911747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911743, tc_HOL_Obool)), _911745), _911747)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911743, tc_HOL_Obool)), _911745), _911747) = _911745)], (27623 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (51517 ^ _776541) ^ [_1819103, _1819105, _1819107] : [class_Divides_Osemiring__div(_1819103), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819103), _1819105), _1819107)), -(c_Divides_Odiv__class_Omod(_1819103, _1819107, _1819105) = c_Groups_Ozero__class_Ozero(_1819103))], (42234 ^ _776541) ^ [_1614075, _1614077, _1614079] : [-(hAPP(hAPP(c_List_Onth(_1614075), hAPP(hAPP(c_List_Olist_OCons(_1614075), _1614077), _1614079)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1614077)], (17825 ^ _776541) ^ [_1097325, _1097327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1097325), _1097327)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1097325), hAPP(c_Nat_OSuc, _1097327)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1097327), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1097325), _1097327)))], (41694 ^ _776541) ^ [_1597551, _1597553, _1597555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597551), c_Nitpick_Oplus__frac(_1597551, _1597553, c_Nitpick_Ouminus__frac(_1597551, _1597555)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1597551, _1597553, _1597555))], (40611 ^ _776541) ^ [_1569577] : [-(c_Transitive__Closure_Otrancl(_1569577, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569577, _1569577), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569577, _1569577), tc_HOL_Obool)))], (25040 ^ _776541) ^ [_1229931, _1229933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1229931, _1229933)), _1229931)))], (42365 ^ _776541) ^ [_1617400, _1617402] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1617400), hAPP(c_List_Oset(_1617400), _1617402))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617400)), _1617402))))], (13932 ^ _776541) ^ [_1025498, _1025500, _1025502, _1025504, _1025506, _1025508] : [class_Rings_Oordered__ring(_1025498), 13935 ^ _776541 : [(13942 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025498), _1025504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025498), _1025506), _1025500)), _1025502)), _1025508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025498), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025498), _1025500), _1025502)), _1025504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025498), _1025506), _1025502)), _1025508))))], (13936 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025498), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025498), _1025500), _1025502)), _1025504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025498), _1025506), _1025502)), _1025508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025498), _1025504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025498), _1025506), _1025500)), _1025502)), _1025508))))]]], (50687 ^ _776541) ^ [_1801191, _1801193, _1801195] : [c_Equiv__Relations_Oequivp(_1801191, _1801193), 50690 ^ _776541 : [(50691 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1801195, 50698 ^ [_1801191, _1801193, _1801195]))), 50692 ^ _776541 : [(50693 ^ _776541) ^ [_1801313] : [hBOOL(hAPP(hAPP(c_member(_1801191), _1801313), c_Quotient_ORespects(_1801191, _1801193))), hBOOL(hAPP(_1801195, _1801313))]]], (50702 ^ _776541) ^ [] : [50703 ^ _776541 : [(50704 ^ _776541) ^ [_1801480] : [hBOOL(hAPP(_1801195, _1801480))]], 50706 ^ _776541 : [(50709 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1801195, 50705 ^ [_1801191, _1801193, _1801195])))], (50707 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801191), 50705 ^ [_1801191, _1801193, _1801195]), c_Quotient_ORespects(_1801191, _1801193))))]]]]], (51189 ^ _776541) ^ [_1813113, _1813115, _1813117, _1813119] : [class_Divides_Osemiring__div(_1813113), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813113), _1813115), _1813117)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813113), _1813119), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813113), _1813117), _1813115)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813113), _1813119), _1813117)), _1813115))], (25828 ^ _776541) ^ [_1243824, _1243826] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1243824))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243824)), _1243826)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1243826))], (6061 ^ _776541) ^ [_873451, _873453, _873455, _873457, _873459] : [hBOOL(hAPP(hAPP(c_member(_873451), _873453), c_SetInterval_Oord_OgreaterThanLessThan(_873451, _873455, _873457, _873459))), 6064 ^ _776541 : [(6067 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_873455, _873453), _873459)))], (6065 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_873455, _873457), _873453)))]]], (43817 ^ _776541) ^ [_1651477, _1651479, _1651481, _1651483, _1651485, _1651487] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651477), tc_List_Olist(_1651477))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651477), tc_List_Olist(_1651477)), hAPP(hAPP(c_List_Oappend(_1651477), _1651479), hAPP(hAPP(c_List_Olist_OCons(_1651477), _1651481), c_List_Olist_ONil(_1651477)))), hAPP(hAPP(c_List_Oappend(_1651477), _1651483), hAPP(hAPP(c_List_Olist_OCons(_1651477), _1651485), c_List_Olist_ONil(_1651477))))), c_List_Olistrel1(_1651477, _1651487)))), 43818 ^ _776541 : [(43825 ^ _776541) ^ [] : [_1651479 = _1651483, hBOOL(hAPP(hAPP(c_member(tc_prod(_1651477, _1651477)), hAPP(hAPP(c_Product__Type_OPair(_1651477, _1651477), _1651481), _1651485)), _1651487))], (43819 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651477), tc_List_Olist(_1651477))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651477), tc_List_Olist(_1651477)), _1651479), _1651483)), c_List_Olistrel1(_1651477, _1651487))), _1651481 = _1651485]]], (6174 ^ _776541) ^ [_875655, _875657, _875659, _875661] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_875655, tc_HOL_Obool)), _875657), _875659)), hBOOL(hAPP(hAPP(c_member(_875655), _875661), _875657)), -(hBOOL(hAPP(hAPP(c_member(_875655), _875661), c_Complete__Lattice_OSup__class_OSup(tc_fun(_875655, tc_HOL_Obool), _875659))))], (48518 ^ _776541) ^ [_1754179, _1754181, _1754183, _1754185, _1754187] : [hBOOL(hAPP(hAPP(_1754179, _1754181), _1754183)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754185, _1754187, _1754179), _1754183), _1754181)))], (40659 ^ _776541) ^ [_1570729, _1570731, _1570733, _1570735, _1570737] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570729, _1570729)), hAPP(hAPP(c_Product__Type_OPair(_1570729, _1570729), _1570731), _1570733)), c_Transitive__Closure_Otrancl(_1570729, _1570735))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570729, _1570729)), hAPP(hAPP(c_Product__Type_OPair(_1570729, _1570729), _1570733), _1570737)), c_Transitive__Closure_Otrancl(_1570729, _1570735))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570729, _1570729)), hAPP(hAPP(c_Product__Type_OPair(_1570729, _1570729), _1570731), _1570737)), c_Transitive__Closure_Otrancl(_1570729, _1570735))))], (51807 ^ _776541) ^ [_1823881, _1823883, _1823885] : [_1823881 = _1823883, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823883), _1823885)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823881), _1823885)))], (47144 ^ _776541) ^ [_1724338, _1724340, _1724342, _1724344] : [class_Orderings_Olinorder(_1724338), c_List_Olinorder__class_Osorted(_1724338, hAPP(c_List_Orev(_1724338), _1724340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724342), _1724344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724344), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724338)), _1724340))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1724338), hAPP(hAPP(c_List_Onth(_1724338), _1724340), _1724344)), hAPP(hAPP(c_List_Onth(_1724338), _1724340), _1724342))))], (47323 ^ _776541) ^ [_1727943, _1727945, _1727947, _1727949, _1727951] : [class_Orderings_Olinorder(_1727943), c_List_Olinorder__class_Osorted(_1727943, hAPP(c_List_Orev(_1727943), hAPP(hAPP(c_List_Omap(_1727945, _1727943), _1727947), _1727949))), -(hAPP(c_List_Ofilter(_1727945, hAPP(hAPP(c_COMBB(_1727943, tc_HOL_Obool, _1727945), hAPP(c_Orderings_Oord__class_Oless(_1727943), _1727951)), _1727947)), _1727949) = c_List_OtakeWhile(_1727945, hAPP(hAPP(c_COMBB(_1727943, tc_HOL_Obool, _1727945), hAPP(c_Orderings_Oord__class_Oless(_1727943), _1727951)), _1727947), _1727949))], (7292 ^ _776541) ^ [_895782, _895784, _895786] : [hBOOL(hAPP(hAPP(c_member(_895782), _895784), hAPP(hAPP(c_Set_Oinsert(_895782), _895786), c_Orderings_Obot__class_Obot(tc_fun(_895782, tc_HOL_Obool))))), -(_895784 = _895786)], (43671 ^ _776541) ^ [_1647483, _1647485, _1647487, _1647489] : [-(hAPP(hAPP(c_List_Onth(_1647483), hAPP(hAPP(c_List_Oappend(_1647483), _1647485), _1647487)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647483)), _1647485)), _1647489)) = hAPP(hAPP(c_List_Onth(_1647483), _1647487), _1647489))], (49588 ^ _776541) ^ [_1778553, _1778555, _1778557, _1778559] : [c_Relation_Oantisym(_1778553, _1778555), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778553, _1778553)), hAPP(hAPP(c_Product__Type_OPair(_1778553, _1778553), _1778557), _1778559)), _1778555)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778553, _1778553)), hAPP(hAPP(c_Product__Type_OPair(_1778553, _1778553), _1778559), _1778557)), _1778555)), -(_1778557 = _1778559)], (32382 ^ _776541) ^ [_1359144, _1359146, _1359148, _1359150, _1359152, _1359154] : [hBOOL(hAPP(hAPP(c_member(_1359144), _1359146), _1359148)), hBOOL(hAPP(hAPP(c_member(_1359150), _1359152), hAPP(_1359154, _1359146))), -(hBOOL(hAPP(hAPP(c_member(_1359150), _1359152), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359144, tc_fun(_1359150, tc_HOL_Obool)), _1359148), _1359154))))], (28957 ^ _776541) ^ [_1295646, _1295648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295646), _1295648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295646)), c_Int_OBit1(_1295648))))], (39868 ^ _776541) ^ [_1552324, _1552326, _1552328, _1552330, _1552332, _1552334] : [c_Fun_Oinj__on(_1552324, _1552326, hAPP(c_Fun_Ocomp(_1552328, _1552326, _1552324, _1552330), _1552332), _1552334), -(c_Fun_Oinj__on(_1552324, _1552328, _1552332, _1552334))], (49448 ^ _776541) ^ [_1776249, _1776251] : [c_Equiv__Relations_Oequivp(_1776249, _1776251), 49451 ^ _776541 : [(49456 ^ _776541) ^ [] : [-(c_Predicate_Otransp(_1776249, _1776251))], (49454 ^ _776541) ^ [] : [-(c_Predicate_Osymp(_1776249, _1776251))], (49452 ^ _776541) ^ [] : [-(c_Predicate_Oreflp(_1776249, _1776251))]]], (31999 ^ _776541) ^ [_1351537, _1351539] : [class_Orderings_Olinorder(_1351537), -(c_Big__Operators_Olattice_OSup__fin(_1351537, c_Orderings_Oord__class_Omax(_1351537), hAPP(hAPP(c_Set_Oinsert(_1351537), _1351539), c_Orderings_Obot__class_Obot(tc_fun(_1351537, tc_HOL_Obool)))) = _1351539)], (25279 ^ _776541) ^ [_1234121, _1234123] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234121, _1234123) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234121, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234123)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28835 ^ _776541) ^ [_1293489, _1293491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293489), _1293491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293489)), c_Int_OBit0(_1293491))))], (32111 ^ _776541) ^ [_1353407, _1353409, _1353411] : [class_Orderings_Olinorder(_1353407), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353407), _1353409)), 32118 ^ _776541 : [(32125 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353407, tc_HOL_Obool)), _1353409), hAPP(hAPP(c_Set_Oinsert(_1353407), _1353411), c_Orderings_Obot__class_Obot(tc_fun(_1353407, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353407, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1353407, c_Orderings_Oord__class_Omax(_1353407), hAPP(hAPP(c_Set_Oinsert(_1353407), _1353411), _1353409)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353407), _1353411), c_Big__Operators_Olattice_OSup__fin(_1353407, c_Orderings_Oord__class_Omax(_1353407), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353407, tc_HOL_Obool)), _1353409), hAPP(hAPP(c_Set_Oinsert(_1353407), _1353411), c_Orderings_Obot__class_Obot(tc_fun(_1353407, tc_HOL_Obool)))))))], (32119 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353407, tc_HOL_Obool)), _1353409), hAPP(hAPP(c_Set_Oinsert(_1353407), _1353411), c_Orderings_Obot__class_Obot(tc_fun(_1353407, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353407, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1353407, c_Orderings_Oord__class_Omax(_1353407), hAPP(hAPP(c_Set_Oinsert(_1353407), _1353411), _1353409)) = _1353411)]]], (11638 ^ _776541) ^ [_980119] : [class_Finite__Set_Ofinite(_980119), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980119), c_Orderings_Otop__class_Otop(tc_fun(_980119, tc_HOL_Obool)))))], (45868 ^ _776541) ^ [_1696608, _1696610, _1696612, _1696614, _1696616] : [c_Fun_Oinj__on(_1696608, _1696610, _1696612, c_Orderings_Otop__class_Otop(tc_fun(_1696608, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1696608, _1696610), _1696612), hAPP(c_List_OremoveAll(_1696608, _1696614), _1696616)) = hAPP(c_List_OremoveAll(_1696610, hAPP(_1696612, _1696614)), hAPP(hAPP(c_List_Omap(_1696608, _1696610), _1696612), _1696616)))], (8369 ^ _776541) ^ [_920033, _920035, _920037, _920039] : [class_Lattices_Osemilattice__inf(_920033), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920033), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920033), _920035), _920037)), _920039) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920033), _920035), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920033), _920037), _920039)))], (52437 ^ _776541) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (44519 ^ _776541) ^ [_1667012, _1667014, _1667016, _1667018, _1667020] : [class_Orderings_Olinorder(_1667012), hBOOL(hAPP(hAPP(c_member(_1667012), hAPP(_1667014, _1667016)), hAPP(c_Set_Oimage(_1667018, _1667012, _1667014), hAPP(c_List_Oset(_1667018), _1667020)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1667018, _1667012, _1667014, _1667016, _1667020) = _1667020)], (44575 ^ _776541) ^ [_1668138, _1668140, _1668142] : [-(_1668138 = c_List_Olist_ONil(_1668140)), -(c_List_Olast(_1668140, hAPP(hAPP(c_List_Olist_OCons(_1668140), _1668142), _1668138)) = c_List_Olast(_1668140, _1668138))], (3984 ^ _776541) ^ [_836682, _836684, _836686, _836688, _836690, _836692, _836694, _836696] : [-(c_New__DSequence_Opos__decr__bind(_836696, _836692, _836688, _836684) = c_New__DSequence_Opos__decr__bind(_836694, _836690, _836686, _836682)), _836696 = _836694, _836692 = _836690, _836688 = _836686, _836684 = _836682], (38320 ^ _776541) ^ [_1510540, _1510542] : [c_FunDef_Oreduction__pair(_1510540, _1510542), 38323 ^ _776541 : [(38326 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510540, _1510540, _1510540), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool), tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool)), _1510542)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool), tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool)), _1510542))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool), tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool)), _1510542))))], (38324 ^ _776541) ^ [] : [-(c_Wellfounded_Owf(_1510540, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool), tc_fun(tc_prod(_1510540, _1510540), tc_HOL_Obool)), _1510542)))]]], (49640 ^ _776541) ^ [_1779714, _1779716] : [c_Wellfounded_Oacyclic(_1779714, _1779716), -(c_Relation_Oantisym(_1779714, c_Transitive__Closure_Ortrancl(_1779714, _1779716)))], (29705 ^ _776541) ^ [_1309147, _1309149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309147), 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)))), _1309149))), 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)))), _1309147)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309149), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1309147))], (33833 ^ _776541) ^ [_1403270, _1403272, _1403274, _1403276, _1403278] : [class_Groups_Ocomm__monoid__mult(_1403270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403272), _1403274)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403270, _1403272, c_Groups_Otimes__class_Otimes(_1403270)), hAPP(hAPP(c_COMBS(_1403272, _1403270, _1403270), hAPP(hAPP(c_COMBB(_1403270, tc_fun(_1403270, _1403270), _1403272), c_Groups_Otimes__class_Otimes(_1403270)), _1403276)), _1403278)), c_Groups_Oone__class_Oone(_1403270)), _1403274) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403270), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403270, _1403272, c_Groups_Otimes__class_Otimes(_1403270)), _1403276), c_Groups_Oone__class_Oone(_1403270)), _1403274)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403270, _1403272, c_Groups_Otimes__class_Otimes(_1403270)), _1403278), c_Groups_Oone__class_Oone(_1403270)), _1403274)))], (20585 ^ _776541) ^ [_1148113, _1148115, _1148117, _1148119] : [class_Fields_Olinordered__field(_1148113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148113), c_Groups_Ozero__class_Ozero(_1148113)), _1148115)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148113), _1148117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148113), _1148119), _1148115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148113), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148113), _1148117), _1148115)), _1148119)))], (32714 ^ _776541) ^ [_1370876, _1370878, _1370880, _1370882, _1370884] : [class_Complete__Lattice_Ocomplete__lattice(_1370876), class_Orderings_Olinorder(_1370876), 32721 ^ _776541 : [(32731 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370878, _1370876), _1370880), _1370882)), _1370884))), 32732 ^ _776541 : [(32733 ^ _776541) ^ [_1371224] : [hBOOL(hAPP(hAPP(c_member(_1370878), _1371224), _1370880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370876), hAPP(_1370882, _1371224)), _1370884))]]], (32722 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370878, _1370876), _1370880), _1370882)), _1370884)), 32726 ^ _776541 : [(32729 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370876), hAPP(_1370882, 32725 ^ [_1370876, _1370878, _1370880, _1370882, _1370884])), _1370884)))], (32727 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370878), 32725 ^ [_1370876, _1370878, _1370880, _1370882, _1370884]), _1370880)))]]]]], (50887 ^ _776541) ^ [_1807201, _1807203, _1807205] : [-(c_Lazy__Sequence_Oflat(_1807201, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1807201), _1807203, _1807205)) = c_Lazy__Sequence_Oappend(_1807201, _1807203, c_Lazy__Sequence_Oflat(_1807201, _1807205)))], (34862 ^ _776541) ^ [_1427151, _1427153] : [34863 ^ _776541 : [(34866 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1427153), _1427151))], (34864 ^ _776541) ^ [] : [_1427151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1427153, _1427151) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1427153))], (16464 ^ _776541) ^ [_1073114, _1073116] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073114), _1073116) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 16467 ^ _776541 : [(16470 ^ _776541) ^ [] : [-(_1073116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16468 ^ _776541) ^ [] : [-(_1073114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9306 ^ _776541) ^ [_936617, _936619] : [class_Orderings_Opreorder(_936617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936617), _936619), _936619))], (35408 ^ _776541) ^ [_1436689, _1436691, _1436693, _1436695] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436689, _1436691), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436693), _1436695))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436689), _1436691), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1436695), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436693)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436693)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1436695), 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), _1436691), _1436695))))))], (45422 ^ _776541) ^ [_1686911, _1686913, _1686915, _1686917, _1686919] : [-(c_Enum_Oproduct(_1686911, _1686913, hAPP(hAPP(c_List_Olist_OCons(_1686911), _1686915), _1686917), _1686919) = hAPP(hAPP(c_List_Oappend(tc_prod(_1686911, _1686913)), hAPP(hAPP(c_List_Omap(_1686913, tc_prod(_1686911, _1686913)), hAPP(c_Product__Type_OPair(_1686911, _1686913), _1686915)), _1686919)), c_Enum_Oproduct(_1686911, _1686913, _1686917, _1686919)))], (33593 ^ _776541) ^ [_1394929, _1394931, _1394933, _1394935] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394929, tc_fun(_1394931, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1394929, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1394931, tc_HOL_Obool), tc_fun(_1394931, tc_HOL_Obool), _1394929), hAPP(c_COMBC(_1394931, tc_fun(_1394931, tc_HOL_Obool), tc_HOL_Obool), c_member(_1394931))), _1394933)), _1394935)), -(hBOOL(hAPP(hAPP(c_member(_1394931), _1394935), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394929, tc_fun(_1394931, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1394929, tc_HOL_Obool))), _1394933))))], (26997 ^ _776541) ^ [_1262843, _1262845, _1262847] : [class_Rings_Oring__1(_1262843), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262843), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1262845), _1262847)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1262843), hAPP(c_Int_Oring__1__class_Oof__int(_1262843), _1262845)), _1262847))], (6019 ^ _776541) ^ [_872598, _872600, _872602, _872604] : [hBOOL(hAPP(hAPP(c_member(_872598), _872600), c_SetInterval_Oord_OlessThan(_872598, _872602, _872604))), -(hBOOL(hAPP(hAPP(_872602, _872600), _872604)))], (52209 ^ _776541) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (1814 ^ _776541) ^ [_802080, _802082] : [-(class_Orderings_Oorder(_802080)), _802082 = _802080, class_Orderings_Oorder(_802082)], (38517 ^ _776541) ^ [_1515005, _1515007, _1515009] : [_1515009 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1515005, _1515007), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1515005, _1515007), _1515009) = c_Orderings_Obot__class_Obot(tc_fun(_1515007, tc_HOL_Obool)))], (42705 ^ _776541) ^ [_1626866, _1626868, _1626870, _1626872, _1626874] : [-(hAPP(hAPP(c_List_Olist__update(_1626866, hAPP(hAPP(c_List_Olist_OCons(_1626866), _1626868), _1626870)), _1626872), _1626874) = c_Nat_Onat_Onat__case(tc_List_Olist(_1626866), hAPP(hAPP(c_List_Olist_OCons(_1626866), _1626874), _1626870), hAPP(hAPP(c_COMBB(tc_List_Olist(_1626866), tc_List_Olist(_1626866), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1626866), _1626868)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1626866, tc_List_Olist(_1626866)), c_List_Olist__update(_1626866, _1626870)), _1626874)), _1626872))], (24924 ^ _776541) ^ [_1227842, _1227844, _1227846] : [class_Divides_Oring__div(_1227842), -(c_Divides_Odiv__class_Omod(_1227842, hAPP(c_Groups_Ouminus__class_Ouminus(_1227842), _1227844), _1227846) = c_Divides_Odiv__class_Omod(_1227842, hAPP(c_Groups_Ouminus__class_Ouminus(_1227842), c_Divides_Odiv__class_Omod(_1227842, _1227844, _1227846)), _1227846))], (4812 ^ _776541) ^ [_849810, _849812] : [_849812 = _849810, -(c_Wellfounded_Ofinite__psubset(_849812) = c_Wellfounded_Ofinite__psubset(_849810))], (4278 ^ _776541) ^ [_841343, _841345] : [_841345 = _841343, -(c_List_Onth(_841345) = c_List_Onth(_841343))], (52185 ^ _776541) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (22461 ^ _776541) ^ [_1183566] : [-(_1183566 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22464 ^ _776541 : [(22471 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183566))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1183566) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22465 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183566)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1183566) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (11155 ^ _776541) ^ [_969660, _969662, _969664, _969666] : [c_Orderings_Obot__class_Obot(tc_fun(_969660, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_969662, _969660, _969664), _969666), -(_969666 = c_Orderings_Obot__class_Obot(tc_fun(_969662, tc_HOL_Obool)))], (34785 ^ _776541) ^ [_1425532, _1425534, _1425536, _1425538, _1425540] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425532, _1425534, tc_HOL_Obool), _1425536), hAPP(hAPP(c_Product__Type_OPair(_1425532, _1425534), _1425538), _1425540))), -(hBOOL(hAPP(hAPP(_1425536, _1425538), _1425540)))], (40935 ^ _776541) ^ [_1578312] : [-(hAPP(c_Relation_ODomain(_1578312, _1578312), c_Relation_OId(_1578312)) = c_Orderings_Otop__class_Otop(tc_fun(_1578312, tc_HOL_Obool)))], (34025 ^ _776541) ^ [_1408241, _1408243] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1408241)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1408243)), hAPP(c_Int_Onat, _1408241)) = hAPP(c_Int_Onat, _1408243))], (38744 ^ _776541) ^ [_1521172, _1521174] : [c_Wellfounded_Owf(_1521172, _1521174), -(c_Wellfounded_Oacyclic(_1521172, _1521174))], (25873 ^ _776541) ^ [_1244504, _1244506, _1244508] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244504), _1244506)), _1244508) = 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), _1244504), _1244508)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244506), _1244508))), 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, _1244504, _1244508)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244506, _1244508))), _1244508)))], (19763 ^ _776541) ^ [_1133216, _1133218] : [class_Rings_Olinordered__idom(_1133216), 19766 ^ _776541 : [(19773 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133216), c_Groups_Ozero__class_Ozero(_1133216)), _1133218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133216), c_Groups_Ozero__class_Ozero(_1133216)), c_Groups_Osgn__class_Osgn(_1133216, _1133218))))], (19767 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133216), c_Groups_Ozero__class_Ozero(_1133216)), c_Groups_Osgn__class_Osgn(_1133216, _1133218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133216), c_Groups_Ozero__class_Ozero(_1133216)), _1133218)))]]], (44078 ^ _776541) ^ [_1657998, _1658000, _1658002, _1658004, _1658006] : [-(hAPP(hAPP(c_List_Ozip(_1657998, _1658000), hAPP(hAPP(c_List_Oappend(_1657998), _1658002), _1658004)), _1658006) = hAPP(hAPP(c_List_Oappend(tc_prod(_1657998, _1658000)), hAPP(hAPP(c_List_Ozip(_1657998, _1658000), _1658002), hAPP(hAPP(c_List_Otake(_1658000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657998)), _1658002)), _1658006))), hAPP(hAPP(c_List_Ozip(_1657998, _1658000), _1658004), hAPP(hAPP(c_List_Odrop(_1658000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657998)), _1658002)), _1658006))))], (35022 ^ _776541) ^ [_1430115, _1430117, _1430119, _1430121] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1430115, _1430117)), c_Nitpick_Opair__box_OPairBox(_1430115, _1430117, _1430119, _1430121)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15714 ^ _776541) ^ [_1061490] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1061490)], (27170 ^ _776541) ^ [_1265545, _1265547] : [c_Nat__Transfer_Onat__set(_1265545), c_Nat__Transfer_Onat__set(_1265547), 27177 ^ _776541 : [(27184 ^ _776541) ^ [] : [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), _1265545)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265545), _1265547)))], (27178 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265545), _1265547)), -(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), _1265545)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265547))))]]], (34582 ^ _776541) ^ [_1420629, _1420631, _1420633, _1420635, _1420637, _1420639] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420629, tc_fun(_1420631, tc_HOL_Obool))), _1420633), _1420635), _1420637), _1420639)), -(hBOOL(hAPP(hAPP(_1420635, _1420637), _1420639)))], (50213 ^ _776541) ^ [_1791728, _1791730] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1791728), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1791730, hAPP(c_Code__Numeral_Onat__of, 50218 ^ [_1791728, _1791730]))), -(hBOOL(hAPP(_1791730, _1791728)))], (13300 ^ _776541) ^ [_1012284, _1012286, _1012288, _1012290, _1012292] : [class_Groups_Oab__group__add(_1012284), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012286), _1012288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012286, tc_HOL_Obool)), _1012290), _1012288)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012286, _1012284), _1012292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012286, tc_HOL_Obool)), _1012288), _1012290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012284), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012286, _1012284), _1012292), _1012288)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012286, _1012284), _1012292), _1012290)))], (3514 ^ _776541) ^ [_829071, _829073, _829075, _829077, _829079, _829081] : [-(c_List_Osublist(_829081, _829077, _829073) = c_List_Osublist(_829079, _829075, _829071)), _829081 = _829079, _829077 = _829075, _829073 = _829071], (14120 ^ _776541) ^ [_1029996, _1029998, _1030000, _1030002, _1030004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029996), _1029998)), 14123 ^ _776541 : [(14130 ^ _776541) ^ [] : [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), _1029998), _1029996)), _1030000)), _1030002)), _1030004)), -(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), _1029998), _1030000)), _1030002)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029996), _1030000)), _1030004))))], (14124 ^ _776541) ^ [] : [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), _1029998), _1030000)), _1030002)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029996), _1030000)), _1030004))), -(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), _1029998), _1029996)), _1030000)), _1030002)), _1030004)))]]], (26014 ^ _776541) ^ [_1246814, _1246816] : [26015 ^ _776541 : [(26016 ^ _776541) ^ [_1246863] : [_1246814 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246816), _1246863)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246814, _1246816) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23181 ^ _776541) ^ [_1196403, _1196405, _1196407, _1196409] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1196403, _1196405, _1196407), _1196409), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1196405)], (35811 ^ _776541) ^ [_1445303, _1445305] : [_1445303 = _1445305, -(hAPP(c_Int_ORep__Integ, _1445303) = hAPP(c_Int_ORep__Integ, _1445305))], (16636 ^ _776541) ^ [_1075750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1075750)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075750), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1075750)], (6796 ^ _776541) ^ [_886439, _886441, _886443] : [6798 ^ _776541 : [(6801 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886439, tc_HOL_Obool)), 6797 ^ [_886439, _886441, _886443]), _886443))], (6799 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_886439, tc_HOL_Obool)), 6797 ^ [_886439, _886441, _886443]), _886441)))]], -(_886441 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_886439, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886439, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_886439, tc_HOL_Obool), _886441)), _886443)))], (42679 ^ _776541) ^ [_1626285, _1626287, _1626289, _1626291] : [_1626285 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626287)), _1626289)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1626287, hAPP(hAPP(c_List_Olist__update(_1626287, _1626289), _1626285), _1626291)) = c_List_Obutlast(_1626287, _1626289))], (31451 ^ _776541) ^ [_1341295, _1341297, _1341299, _1341301] : [class_Orderings_Olinorder(_1341295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341295), _1341297), _1341299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341295), _1341301), _1341299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341295), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341295), _1341297), _1341301)), _1341299)))], (48911 ^ _776541) ^ [_1762598, _1762600, _1762602] : [hBOOL(hAPP(hAPP(c_member(_1762598), _1762600), hAPP(c_List_Oset(_1762598), _1762602))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1762598), _1762602), _1762600)))], (52117 ^ _776541) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (46413 ^ _776541) ^ [_1709888, _1709890] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1709888), hAPP(c_List_Onth(_1709888), _1709890)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709888)), _1709890))) = _1709890)], (47182 ^ _776541) ^ [_1724989, _1724991] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1724989), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1724989))), _1724991))), 47185 ^ _776541 : [(47192 ^ _776541) ^ [] : [-(_1724991 = c_List_Olist_ONil(tc_List_Olist(_1724989))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1724989))), c_List_Otranspose(_1724989, _1724991)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724989)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1724989)), _1724991), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47186 ^ _776541) ^ [] : [_1724991 = c_List_Olist_ONil(tc_List_Olist(_1724989)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1724989))), c_List_Otranspose(_1724989, _1724991)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (416 ^ _776541) ^ [_782821, _782823, _782825, _782827, _782829, _782831] : [-(c_Relation_Osingle__valued(_782829, _782825, _782821)), c_Relation_Osingle__valued(_782831, _782827, _782823), _782831 = _782829, _782827 = _782825, _782823 = _782821], (48458 ^ _776541) ^ [_1752799, _1752801, _1752803, _1752805] : [-(c_New__Random__Sequence_Opos__map(_1752799, _1752801, _1752803, _1752805) = c_New__Random__Sequence_Opos__bind(_1752799, _1752801, _1752805, hAPP(c_Fun_Ocomp(_1752801, 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(_1752801))))), _1752799, c_New__Random__Sequence_Opos__single(_1752801)), _1752803)))], (48466 ^ _776541) ^ [_1753039, _1753041] : [-(c_List_Osplice(_1753039, _1753041, c_List_Olist_ONil(_1753039)) = _1753041)], (48512 ^ _776541) ^ [_1754066, _1754068, _1754070, _1754072, _1754074] : [hBOOL(hAPP(hAPP(_1754070, _1754074), _1754072)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754066, _1754068, _1754070), _1754072), _1754074)))], (39834 ^ _776541) ^ [_1551660, _1551662, _1551664, _1551666, _1551668, _1551670] : [-(hAPP(c_Set_Oimage(_1551660, _1551662, hAPP(c_Fun_Ocomp(_1551664, _1551662, _1551660, _1551666), _1551668)), _1551670) = hAPP(c_Set_Oimage(_1551664, _1551662, _1551666), hAPP(c_Set_Oimage(_1551660, _1551664, _1551668), _1551670)))], (52441 ^ _776541) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (20599 ^ _776541) ^ [_1148382, _1148384, _1148386, _1148388] : [class_Fields_Olinordered__field(_1148382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148382), c_Groups_Ozero__class_Ozero(_1148382)), _1148384)), 20606 ^ _776541 : [(20613 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148382), _1148386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148382), _1148388), _1148384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148382), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148382), _1148386), _1148384)), _1148388)))], (20607 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148382), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148382), _1148386), _1148384)), _1148388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148382), _1148386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148382), _1148388), _1148384))))]]], (1962 ^ _776541) ^ [_803962, _803964, _803966, _803968] : [-(v_Q(_803966, _803962)), v_Q(_803968, _803964), _803968 = _803966, _803964 = _803962], (6330 ^ _776541) ^ [_878553, _878555, _878557, _878559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878553, tc_HOL_Obool)), _878555), _878557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878553, tc_HOL_Obool)), _878557), _878559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878553, tc_HOL_Obool)), _878555), _878559)))], (45152 ^ _776541) ^ [_1680753, _1680755, _1680757, _1680759] : [class_Groups_Ocomm__monoid__add(_1680753), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1680753), _1680755), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1680757, _1680759))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1680753), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1680753), _1680755), c_List_Oupto(_1680757, _1680759))))], (27687 ^ _776541) ^ [_1274595, _1274597] : [class_Groups_Oordered__ab__group__add__abs(_1274595), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274595), hAPP(c_Groups_Ouminus__class_Ouminus(_1274595), hAPP(c_Groups_Oabs__class_Oabs(_1274595), _1274597))), c_Groups_Ozero__class_Ozero(_1274595))))], (15176 ^ _776541) ^ [_1050379, _1050381, _1050383] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050379), _1050381)), -(hBOOL(hAPP(hAPP(c_member(_1050379), _1050383), _1050381))), -(hAPP(c_Finite__Set_Ocard(_1050379), hAPP(hAPP(c_Set_Oinsert(_1050379), _1050383), _1050381)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1050379), _1050381)))], (28737 ^ _776541) ^ [_1291734, _1291736] : [_1291734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1291736, _1291734) = _1291736)], (30194 ^ _776541) ^ [_1318188, _1318190, _1318192, _1318194] : [class_Orderings_Olinorder(_1318188), 30197 ^ _776541 : [(30206 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318188), _1318190), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318188), _1318192), _1318194)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318188), _1318190), _1318192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318188), _1318190), _1318194))], (30198 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318188), _1318190), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318188), _1318192), _1318194))), 30201 ^ _776541 : [(30204 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318188), _1318190), _1318194)))], (30202 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318188), _1318190), _1318192)))]]]]], (46101 ^ _776541) ^ [_1702556, _1702558, _1702560, _1702562] : [hBOOL(hAPP(_1702556, _1702558)), -(hAPP(c_List_Ofilter(_1702560, _1702556), hAPP(hAPP(c_List_Olist_OCons(_1702560), _1702558), _1702562)) = hAPP(hAPP(c_List_Olist_OCons(_1702560), _1702558), hAPP(c_List_Ofilter(_1702560, _1702556), _1702562)))], (52019 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (27003 ^ _776541) ^ [_1262980] : [c_Nat__Transfer_Onat__set(_1262980), 27006 ^ _776541 : [(27007 ^ _776541) ^ [_1263046] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1263046), _1262980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263046)))]]], (39900 ^ _776541) ^ [_1552990, _1552992, _1552994, _1552996, _1552998, _1553000, _1553002, _1553004] : [hAPP(c_Fun_Ocomp(_1552990, _1552992, _1552994, _1552996), _1552998) = hAPP(c_Fun_Ocomp(_1553000, _1552992, _1552994, _1553002), _1553004), 39903 ^ _776541 : [(39904 ^ _776541) ^ [_1553105] : [-(hAPP(_1552996, hAPP(_1552998, _1553105)) = hAPP(_1553002, hAPP(_1553004, _1553105)))]]], (52309 ^ _776541) ^ [_1829316] : [class_Enum_Oenum(_1829316), -(class_Enum_Oenum(tc_Option_Ooption(_1829316)))], (47216 ^ _776541) ^ [_1725819, _1725821, _1725823] : [class_Orderings_Olinorder(_1725819), c_List_Olinorder__class_Osorted(_1725819, _1725821), -(c_List_Olinorder__class_Osorted(_1725819, c_List_OtakeWhile(_1725819, _1725823, _1725821)))], (28875 ^ _776541) ^ [_1294212, _1294214] : [_1294212 = _1294214, -(c_Int_OBit0(_1294212) = c_Int_OBit0(_1294214))], (52231 ^ _776541) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (34727 ^ _776541) ^ [_1423747, _1423749, _1423751, _1423753] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423747, _1423749, _1423751), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423753)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1423747), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1423753))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423747, _1423747), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1423747, tc_fun(_1423747, _1423747)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1423747, tc_fun(_1423747, _1423747)), tc_Int_Oint), c_If(_1423747)), c_Nat__Numeral_Oneg)), _1423749)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423747, _1423747), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1423747, _1423747), tc_Int_Oint), _1423751), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1423747, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1423747, _1423749, _1423751)), c_Int_Onat)))))], (17679 ^ _776541) ^ [_1094853, _1094855] : [class_Groups_Oordered__ab__group__add(_1094853), 17682 ^ _776541 : [(17689 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094853), c_Groups_Ozero__class_Ozero(_1094853)), _1094855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094853), hAPP(c_Groups_Ouminus__class_Ouminus(_1094853), _1094855)), c_Groups_Ozero__class_Ozero(_1094853))))], (17683 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094853), hAPP(c_Groups_Ouminus__class_Ouminus(_1094853), _1094855)), c_Groups_Ozero__class_Ozero(_1094853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094853), c_Groups_Ozero__class_Ozero(_1094853)), _1094855)))]]], (23962 ^ _776541) ^ [_1210574, _1210576, _1210578] : [class_Divides_Osemiring__div(_1210574), -(_1210576 = c_Groups_Ozero__class_Ozero(_1210574)), 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_1533505), _1533511)), _1533509)))], (32504 ^ _776541) ^ [_1363375, _1363377, _1363379, _1363381, _1363383] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363375, tc_fun(_1363377, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363375, tc_HOL_Obool)), _1363379), _1363381)), _1363383) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363377, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363375, tc_fun(_1363377, tc_HOL_Obool)), _1363379), _1363383)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363375, tc_fun(_1363377, tc_HOL_Obool)), _1363381), _1363383)))], (24048 ^ _776541) ^ [] : [-(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))))], (18488 ^ _776541) ^ [_1109250, _1109252, _1109254] : [class_Rings_Olinordered__idom(_1109250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109250), c_Groups_Ozero__class_Ozero(_1109250)), _1109252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109250), c_Groups_Ozero__class_Ozero(_1109250)), _1109254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109250), _1109254), c_Groups_Oone__class_Oone(_1109250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109250), _1109254), _1109252)), _1109252)))], (51997 ^ _776541) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (12219 ^ _776541) ^ [_990994, _990996, _990998] : [class_Lattices_Olattice(_990994), hBOOL(hAPP(c_Finite__Set_Ofinite(_990994), _990996)), -(_990996 = c_Orderings_Obot__class_Obot(tc_fun(_990994, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_990994), _990998)), -(_990998 = c_Orderings_Obot__class_Obot(tc_fun(_990994, tc_HOL_Obool))), 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923161), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923161), _923163), _923165)), _923167)), 8542 ^ _776541 : [(8545 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923161), _923165), _923167)))], (8543 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923161), _923163), _923167)))]]]]], (29785 ^ _776541) ^ [_1310670, _1310672] : [-(_1310670 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1310670, _1310672) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1310670), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1310672)))], (5016 ^ _776541) ^ [_852998, _853000, _853002, _853004, _853006, _853008, _853010, _853012] : [-(c_Fun_Othe__inv__into(_853012, _853008, _853004, _853000) = c_Fun_Othe__inv__into(_853010, _853006, _853002, _852998)), _853012 = _853010, _853008 = _853006, _853004 = _853002, _853000 = _852998], (50421 ^ _776541) ^ [_1795980, _1795982, _1795984, _1795986, _1795988] : [c_Fun_Obij__betw(_1795980, _1795982, _1795984, _1795986, _1795988), -(c_Fun_Oinj__on(_1795980, _1795982, _1795984, _1795986))], (43757 ^ _776541) ^ [_1649759, _1649761, _1649763, _1649765] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649761)), _1649763)))), -(hAPP(hAPP(c_List_Onth(_1649761), hAPP(hAPP(c_List_Oappend(_1649761), _1649763), _1649765)), _1649759) = hAPP(hAPP(c_List_Onth(_1649761), _1649765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649761)), _1649763))))], (49688 ^ _776541) ^ [_1780968, _1780970] : [c_Relation_Osym(_1780968, hAPP(c_Relation_Oconverse(_1780968, _1780968), _1780970)), -(c_Relation_Osym(_1780968, _1780970))], (20691 ^ _776541) ^ [_1150097, _1150099, _1150101, _1150103] : [class_Fields_Olinordered__field__inverse__zero(_1150097), 20694 ^ _776541 : [(20695 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150099), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150097), _1150101), _1150103))), 20698 ^ _776541 : [(20705 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), c_Groups_Ozero__class_Ozero(_1150097)), _1150103))), 20708 ^ _776541 : [(20715 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150103), c_Groups_Ozero__class_Ozero(_1150097)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150099), c_Groups_Ozero__class_Ozero(_1150097))))], (20709 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150103), c_Groups_Ozero__class_Ozero(_1150097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150097), _1150099), _1150103))))]]], (20699 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), c_Groups_Ozero__class_Ozero(_1150097)), _1150103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150097), _1150099), _1150103)), _1150101)))]]], (20721 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150099), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150097), _1150101), _1150103)))), 20724 ^ _776541 : [(20727 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150097), _1150099), _1150103)), _1150101))], (20725 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), c_Groups_Ozero__class_Ozero(_1150097)), _1150103)))]], 20728 ^ _776541 : [(20731 ^ _776541) ^ [] : [20732 ^ _776541 : [(20735 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150097), _1150099), _1150103)))], (20733 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150103), c_Groups_Ozero__class_Ozero(_1150097))))]], 20736 ^ _776541 : [(20739 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150099), c_Groups_Ozero__class_Ozero(_1150097)))], (20737 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), _1150103), c_Groups_Ozero__class_Ozero(_1150097)))]]], (20729 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150097), c_Groups_Ozero__class_Ozero(_1150097)), _1150103))]]]]], (33685 ^ _776541) ^ [_1398991, _1398993, _1398995, _1398997] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1398991, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398993, tc_fun(tc_fun(_1398991, tc_HOL_Obool), tc_HOL_Obool)), _1398995), hAPP(hAPP(c_COMBB(tc_fun(_1398991, tc_HOL_Obool), tc_fun(tc_fun(_1398991, tc_HOL_Obool), tc_HOL_Obool), _1398993), 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013662, _1013660), _1013666), _1013664)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013662, _1013660), _1013668), _1013664))))], (9750 ^ _776541) ^ [_943485, _943487, _943489, _943491] : [class_Lattices_Osemilattice__inf(_943485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943485), _943487), _943489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943485), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_943485), _943491), _943487)), _943489)))], (42853 ^ _776541) ^ [_1630322, _1630324, _1630326] : [-(hBOOL(hAPP(c_List_Odistinct(_1630322), hAPP(hAPP(c_List_Olist_OCons(_1630322), _1630324), _1630326)))), -(hBOOL(hAPP(hAPP(c_member(_1630322), _1630324), hAPP(c_List_Oset(_1630322), _1630326)))), hBOOL(hAPP(c_List_Odistinct(_1630322), _1630326))], (1022 ^ _776541) ^ [_791972, _791974, _791976, _791978, _791980, _791982] : [-(c_List_Olist__ex(_791980, _791976, _791972)), c_List_Olist__ex(_791982, _791978, _791974), _791982 = _791980, _791978 = _791976, _791974 = _791972], (27599 ^ _776541) ^ [_1272970, _1272972] : [class_Rings_Olinordered__idom(_1272970), -(hAPP(c_Groups_Oabs__class_Oabs(_1272970), _1272972) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272970), _1272972), c_Groups_Osgn__class_Osgn(_1272970, _1272972)))], (41150 ^ _776541) ^ [_1583417, _1583419, _1583421] : [c_Equiv__Relations_Oequiv(_1583417, _1583419, _1583421), -(hAPP(hAPP(c_Relation_Orel__comp(_1583417, _1583417, _1583417), hAPP(c_Relation_Oconverse(_1583417, _1583417), _1583421)), _1583421) = _1583421)], (38692 ^ _776541) ^ [_1520025, _1520027, _1520029, _1520031, _1520033] : [hBOOL(hAPP(hAPP(c_member(_1520025), _1520027), hAPP(c_Set_Ovimage(_1520025, _1520029, _1520031), _1520033))), -(hBOOL(hAPP(hAPP(c_member(_1520029), hAPP(_1520031, _1520027)), _1520033)))], (44539 ^ _776541) ^ [_1667381, _1667383, _1667385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667381), tc_List_Olist(_1667381))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667381), tc_List_Olist(_1667381)), c_List_Olist_ONil(_1667381)), _1667383)), c_List_Olexord(_1667381, _1667385))), -(_1667383 = hAPP(hAPP(c_List_Olist_OCons(_1667381), 44542 ^ [_1667381, _1667383, _1667385]), 44543 ^ [_1667381, _1667383, _1667385]))], (52395 ^ _776541) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (49744 ^ _776541) ^ [_1781802, _1781804, _1781806] : [c_Relation_Osym(_1781802, _1781804), c_Relation_Osym(_1781802, _1781806), -(c_Relation_Osym(_1781802, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1781802, _1781802), tc_HOL_Obool)), _1781804), _1781806)))], (38108 ^ _776541) ^ [_1506432, _1506434, _1506436, _1506438] : [c_Wellfounded_Owf(_1506432, _1506434), -(c_Wellfounded_Owf(_1506436, hAPP(hAPP(c_Relation_Oinv__image(_1506432, _1506436), _1506434), _1506438)))], (34550 ^ _776541) ^ [_1419993, _1419995, _1419997, _1419999, _1420001, _1420003] : [hBOOL(hAPP(hAPP(_1419993, _1419995), _1419997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419999, tc_fun(_1420001, tc_HOL_Obool))), _1419993), _1420003)), -(hBOOL(hAPP(hAPP(_1420003, _1419995), _1419997)))], (26775 ^ _776541) ^ [_1259437, _1259439] : [c_Nat__Transfer_Onat__set(_1259437), c_Nat__Transfer_Onat__set(_1259439), 26782 ^ _776541 : [(26789 ^ _776541) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259437) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259439), -(_1259437 = _1259439)], (26783 ^ _776541) ^ [] : [_1259437 = _1259439, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259437) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259439))]]], (1654 ^ _776541) ^ [_800080, _800082] : [-(class_Rings_Oordered__semiring(_800080)), _800082 = _800080, class_Rings_Oordered__semiring(_800082)], (36202 ^ _776541) ^ [_1459260, _1459262, _1459264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1459260, 36203 ^ [_1459260, _1459262, _1459264])), hAPP(_1459262, 36203 ^ [_1459260, _1459262, _1459264]))), -(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), _1459262), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459264))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1459260), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459264))) = 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)), _1459262)), _1459260)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459264)))], (10823 ^ _776541) ^ [_963076, _963078, _963080, _963082] : [class_Orderings_Oorder(_963076), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963076, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963076, _963078), _963080)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963076, _963080), _963082)) = c_Orderings_Obot__class_Obot(tc_fun(_963076, tc_HOL_Obool)))], (23972 ^ _776541) ^ [_1210702, _1210704, _1210706] : [class_Divides_Osemiring__div(_1210702), -(_1210704 = c_Groups_Ozero__class_Ozero(_1210702)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210702), _1210704), _1210706)), _1210704) = _1210706)], (36142 ^ _776541) ^ [_1457937, _1457939, _1457941, _1457943, _1457945, _1457947, _1457949] : [hBOOL(hAPP(_1457937, _1457939)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1457941, _1457941)), hAPP(hAPP(c_Product__Type_OPair(_1457941, _1457941), _1457943), _1457945)), hAPP(_1457947, _1457939))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1457949, _1457941), tc_prod(_1457949, _1457941))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1457949, _1457941), tc_prod(_1457949, _1457941)), hAPP(hAPP(c_Product__Type_OPair(_1457949, _1457941), _1457939), _1457943)), hAPP(hAPP(c_Product__Type_OPair(_1457949, _1457941), _1457939), _1457945))), c_Recdef_Osame__fst(_1457949, _1457941, _1457937, _1457947))))], (43132 ^ _776541) ^ [_1635864, _1635866] : [_1635866 = c_List_Olist_ONil(_1635864), -(hAPP(c_List_Oset(_1635864), _1635866) = c_Orderings_Obot__class_Obot(tc_fun(_1635864, tc_HOL_Obool)))], (3810 ^ _776541) ^ [_833729, _833731, _833733, _833735, _833737, _833739, _833741, _833743] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_833743, _833739, _833735, _833731) = c_New__Random__Sequence_Opos__not__random__dseq(_833741, _833737, _833733, _833729)), _833743 = _833741, _833739 = _833737, _833735 = _833733, _833731 = _833729], (36620 ^ _776541) ^ [_1470527, _1470529] : [-(c_Relation_OId__on(_1470527, _1470529) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470527, tc_fun(tc_prod(_1470527, _1470527), tc_HOL_Obool)), _1470529), hAPP(hAPP(c_COMBC(_1470527, tc_fun(tc_prod(_1470527, _1470527), tc_HOL_Obool), tc_fun(tc_prod(_1470527, _1470527), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1470527, _1470527), tc_fun(tc_fun(tc_prod(_1470527, _1470527), tc_HOL_Obool), tc_fun(tc_prod(_1470527, _1470527), tc_HOL_Obool)), _1470527), c_Set_Oinsert(tc_prod(_1470527, _1470527))), hAPP(hAPP(c_COMBS(_1470527, _1470527, tc_prod(_1470527, _1470527)), c_Product__Type_OPair(_1470527, _1470527)), c_COMBI(_1470527)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1470527, _1470527), tc_HOL_Obool)))))], (9204 ^ _776541) ^ [_935438, _935440, _935442] : [class_Orderings_Oorder(_935438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935438), _935440), _935442)), _935440 = _935442], (46201 ^ _776541) ^ [_1704893, _1704895, _1704897, _1704899] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1704893)), c_List_Otranspose__rel(_1704893)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704893)), hAPP(hAPP(c_List_Olist_OCons(_1704893), _1704895), _1704897)), _1704899))), -(c_List_Otranspose(_1704893, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704893)), hAPP(hAPP(c_List_Olist_OCons(_1704893), _1704895), _1704897)), _1704899)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704893)), hAPP(hAPP(c_List_Olist_OCons(_1704893), _1704895), c_List_Oconcat(_1704893, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704893), tc_List_Olist(_1704893)), c_List_Olist_Olist__case(tc_List_Olist(_1704893), _1704893, c_List_Olist_ONil(_1704893), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704893), tc_fun(tc_List_Olist(_1704893), tc_List_Olist(_1704893)), _1704893), c_COMBK(tc_List_Olist(_1704893), tc_List_Olist(_1704893))), hAPP(hAPP(c_COMBC(_1704893, tc_List_Olist(_1704893), tc_List_Olist(_1704893)), c_List_Olist_OCons(_1704893)), c_List_Olist_ONil(_1704893))))), _1704899)))), c_List_Otranspose(_1704893, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704893)), _1704897), c_List_Oconcat(tc_List_Olist(_1704893), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704893), tc_List_Olist(tc_List_Olist(_1704893))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1704893)), _1704893, c_List_Olist_ONil(tc_List_Olist(_1704893)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1704893), tc_List_Olist(tc_List_Olist(_1704893))), _1704893), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704893), tc_List_Olist(tc_List_Olist(_1704893)), tc_List_Olist(tc_List_Olist(_1704893))), c_List_Olist_OCons(tc_List_Olist(_1704893))), c_List_Olist_ONil(tc_List_Olist(_1704893)))))), _1704899))))))], (26647 ^ _776541) ^ [_1257490, _1257492] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1257490, _1257492)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1257492), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1257490), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (15416 ^ _776541) ^ [_1055057, _1055059, _1055061] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055057), _1055059)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055057), _1055061)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055057), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055057, tc_HOL_Obool)), _1055059), _1055061))), hAPP(c_Finite__Set_Ocard(_1055057), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055057, tc_HOL_Obool)), _1055059), _1055061))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055057), _1055059)), hAPP(c_Finite__Set_Ocard(_1055057), _1055061)))], (34992 ^ _776541) ^ [_1429319, _1429321, _1429323, _1429325] : [-(c_Nitpick_Oprod(_1429319, _1429321, _1429323, _1429325) = hAPP(c_Set_OCollect(tc_prod(_1429319, _1429321)), hAPP(c_Product__Type_Oprod_Oprod__case(_1429319, _1429321, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1429319, tc_fun(_1429321, tc_HOL_Obool), tc_fun(_1429321, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1429321, tc_HOL_Obool), tc_fun(_1429321, tc_HOL_Obool)), _1429319), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1429321)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1429319), c_fconj), hAPP(hAPP(c_COMBC(_1429319, tc_fun(_1429319, tc_HOL_Obool), tc_HOL_Obool), c_member(_1429319)), _1429323)))), hAPP(hAPP(c_COMBC(_1429321, tc_fun(_1429321, tc_HOL_Obool), tc_HOL_Obool), c_member(_1429321)), _1429325)))))], (34421 ^ _776541) ^ [_1417234] : [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), _1417234))), 34424 ^ _776541 : [(34431 ^ _776541) ^ [] : [-(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), _1417234)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417234)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417234)), 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), _1417234)))))], (34425 ^ _776541) ^ [] : [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), _1417234))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417234)) = 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)))]]], (7904 ^ _776541) ^ [_909864, _909866, _909868, _909870] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909864, tc_HOL_Obool)), _909866), hAPP(hAPP(c_Set_Oinsert(_909864), _909868), _909870)) = hAPP(hAPP(c_Set_Oinsert(_909864), _909868), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909864, tc_HOL_Obool)), _909866), _909870)))], (16644 ^ _776541) ^ [_1075865, _1075867, _1075869, _1075871] : [class_Groups_Ocomm__monoid__add(_1075865), 16647 ^ _776541 : [(16654 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1075867), _1075869))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1075865), _1075871), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075869), hAPP(c_Nat_OSuc, _1075867))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075865), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1075865), _1075871), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075869), _1075867))), hAPP(_1075871, _1075867)))], (16648 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1075867), _1075869)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1075865), _1075871), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075869), hAPP(c_Nat_OSuc, _1075867))) = c_Groups_Ozero__class_Ozero(_1075865))]]], (31855 ^ _776541) ^ [_1348835, _1348837, _1348839] : [class_Orderings_Olinorder(_1348835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348835), _1348837)), -(hBOOL(hAPP(hAPP(c_member(_1348835), _1348839), _1348837))), -(_1348837 = c_Orderings_Obot__class_Obot(tc_fun(_1348835, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1348835, hAPP(hAPP(c_Set_Oinsert(_1348835), _1348839), _1348837)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348835), _1348839), c_Big__Operators_Olinorder__class_OMax(_1348835, _1348837)))], (9102 ^ _776541) ^ [_933849, _933851, _933853, _933855] : [class_Orderings_Oord(_933849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933849), _933851), _933853)), _933853 = _933855, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933849), _933851), _933855)))], (22839 ^ _776541) ^ [_1190288, _1190290, _1190292, _1190294] : [class_Rings_Olinordered__semidom(_1190288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190288), c_Groups_Oone__class_Oone(_1190288)), _1190290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190288), hAPP(hAPP(c_Power_Opower__class_Opower(_1190288), _1190290), _1190292)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190288), _1190290), _1190294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190292), _1190294)))], (43669 ^ _776541) ^ [_1647423, _1647425, _1647427, _1647429] : [-(hAPP(hAPP(c_List_Onth(_1647423), hAPP(hAPP(c_List_Oappend(_1647423), _1647425), hAPP(hAPP(c_List_Olist_OCons(_1647423), _1647427), _1647429))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647423)), _1647425)) = _1647427)], (48205 ^ _776541) ^ [_1747619, _1747621] : [-(c_List_Olist__all(_1747619, _1747621, c_List_Olist_ONil(_1747619)))], (16660 ^ _776541) ^ [_1076195, _1076197] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076195), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076195), _1076197)))))], (29139 ^ _776541) ^ [_1298822, _1298824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298822)), c_Int_OBit1(_1298824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298822), _1298824)))], (4 ^ _776541) ^ [_776591, _776593] : [_776593 = _776591, -(_776591 = _776593)], (22327 ^ _776541) ^ [_1181208, _1181210, _1181212] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181208), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181210), _1181212)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181208), _1181212)))], (33875 ^ _776541) ^ [_1404217, _1404219, _1404221, _1404223, _1404225] : [class_Complete__Lattice_Ocomplete__lattice(_1404217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404219), _1404221)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404217), _1404223), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404219, _1404217), _1404221), _1404225)) = hAPP(hAPP(c_Finite__Set_Ofold(_1404219, _1404217, hAPP(hAPP(c_COMBB(_1404217, tc_fun(_1404217, _1404217), _1404219), c_Lattices_Osemilattice__inf__class_Oinf(_1404217)), _1404225)), _1404223), _1404221))], (15134 ^ _776541) ^ [_1049757] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1049757) = _1049757)], (1364 ^ _776541) ^ [_796455, _796457] : [-(class_Lattices_Obounded__lattice__top(_796455)), _796457 = _796455, class_Lattices_Obounded__lattice__top(_796457)], (34638 ^ _776541) ^ [_1421759, _1421761, _1421763, _1421765] : [-(c_Nat_Onat_Onat__case(_1421759, _1421761, _1421763, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421765)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1421759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1421765))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1421759, _1421759), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1421759, tc_fun(_1421759, _1421759)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1421759, tc_fun(_1421759, _1421759)), tc_Int_Oint), c_If(_1421759)), c_Nat__Numeral_Oneg)), _1421761)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1421759, tc_Int_Oint), _1421763), c_Int_Onat))))], (4386 ^ _776541) ^ [_843041, _843043, _843045, _843047, _843049, _843051, _843053, _843055, _843057, _843059, _843061, _843063] : [-(c_New__Random__Sequence_Opos__union(_843063, _843059, _843055, _843051, _843047, _843043) = c_New__Random__Sequence_Opos__union(_843061, _843057, _843053, _843049, _843045, _843041)), _843063 = _843061, _843059 = _843057, _843055 = _843053, _843051 = _843049, _843047 = _843045, _843043 = _843041], (2230 ^ _776541) ^ [_808957, _808959, _808961, _808963, _808965, _808967, _808969, _808971, _808973, _808975] : [-(c_Nitpick_Opair__box_Opair__box__size(_808975, _808971, _808967, _808963, _808959) = c_Nitpick_Opair__box_Opair__box__size(_808973, _808969, _808965, _808961, _808957)), _808975 = _808973, _808971 = _808969, _808967 = _808965, _808963 = _808961, _808959 = _808957], (33330 ^ _776541) ^ [_1388060, _1388062, _1388064, _1388066] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1388060, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388062, tc_fun(_1388060, tc_HOL_Obool)), _1388064), _1388066)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388062, tc_fun(_1388060, tc_HOL_Obool)), _1388064), hAPP(hAPP(c_COMBB(tc_fun(_1388060, tc_HOL_Obool), tc_fun(_1388060, tc_HOL_Obool), _1388062), c_Groups_Ouminus__class_Ouminus(tc_fun(_1388060, tc_HOL_Obool))), _1388066)))], (41015 ^ _776541) ^ [_1580054, _1580056] : [-(c_Relation_Orefl__on(_1580054, c_Orderings_Otop__class_Otop(tc_fun(_1580054, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1580054, _1580054), tc_HOL_Obool)), _1580056), c_Relation_OId(_1580054))))], (19069 ^ _776541) ^ [_1120121, _1120123] : [19071 ^ _776541 : [(19074 ^ _776541) ^ [] : [hBOOL(hAPP(_1120123, 19070 ^ [_1120121, _1120123]))], (19072 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19070 ^ [_1120121, _1120123]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1120121))))]], 19075 ^ _776541 : [(19076 ^ _776541) ^ [_1120274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120274), _1120121)), -(hBOOL(hAPP(_1120123, _1120274)))]]], (27735 ^ _776541) ^ [_1275435] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1275435), hAPP(c_Int_Onumber__class_Onumber__of(_1275435), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1275435)), class_Int_Onumber__ring(_1275435), class_Rings_Olinordered__idom(_1275435)], (16212 ^ _776541) ^ [_1069477, _1069479, _1069481] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1069477), 16215 ^ _776541 : [(16222 ^ _776541) ^ [] : [_1069481 = c_Groups_Ozero__class_Ozero(_1069477), -(_1069479 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069477), _1069479), _1069481))], (16216 ^ _776541) ^ [] : [_1069479 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069477), _1069479), _1069481), -(_1069481 = c_Groups_Ozero__class_Ozero(_1069477))]]], (42219 ^ _776541) ^ [_1613704, _1613706, _1613708] : [-(_1613704 = _1613706), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613708)), _1613704) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613708)), _1613706), 42225 ^ _776541 : [(42228 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Onth(_1613708), _1613704), 42224 ^ [_1613704, _1613706, _1613708]) = hAPP(hAPP(c_List_Onth(_1613708), _1613706), 42224 ^ [_1613704, _1613706, _1613708])], (42226 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42224 ^ [_1613704, _1613706, _1613708]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613708)), _1613704))))]]], (46095 ^ _776541) ^ [_1702354, _1702356, _1702358] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1702354), tc_List_Olist(_1702354)), c_List_Opartition(_1702354, _1702356, _1702358)) = hAPP(c_List_Ofilter(_1702354, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1702354, c_fNot), _1702356)), _1702358))], (45666 ^ _776541) ^ [_1692498, _1692500] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1692498))), c_Enum_Osublists(_1692498, _1692500)) = 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(_1692498)), _1692500)))], (13628 ^ _776541) ^ [_1019145, _1019147, _1019149, _1019151] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1019145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019145), _1019147), _1019149)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019145), _1019151), _1019149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019145), _1019147), _1019151)))], (14278 ^ _776541) ^ [_1033634, _1033636, _1033638, _1033640] : [class_Rings_Ocomm__semiring__1(_1033634), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033634), _1033636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033634), _1033638), _1033640)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033634), _1033636), _1033638)), _1033640))], (18346 ^ _776541) ^ [_1106527, _1106529, _1106531, _1106533] : [class_Rings_Olinordered__semiring(_1106527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106527), _1106529), _1106531)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106527), _1106533), _1106531))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106527), c_Groups_Ozero__class_Ozero(_1106527)), _1106531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106527), _1106529), _1106533)))], (44166 ^ _776541) ^ [_1659682, _1659684, _1659686] : [hBOOL(hAPP(c_List_Odistinct(_1659682), _1659686)), -(hBOOL(hAPP(c_List_Odistinct(_1659682), hAPP(c_List_Orotate(_1659682, _1659684), _1659686))))], (13518 ^ _776541) ^ [_1017142] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1017142)), 13522 ^ _776541 : [(13523 ^ _776541) ^ [_1017222] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1017222), _1017142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1017222), 13521 ^ [_1017142])))]]], (38638 ^ _776541) ^ [_1518793, _1518795] : [c_Wellfounded_OwfP(_1518793, _1518795), -(c_Wellfounded_Oacyclic(_1518793, hAPP(c_Set_OCollect(tc_prod(_1518793, _1518793)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518793, _1518793, tc_HOL_Obool), _1518795))))], (44104 ^ _776541) ^ [_1658802, _1658804, _1658806] : [-(hAPP(c_List_Ohd(_1658802), hAPP(hAPP(c_List_Olist_OCons(_1658802), _1658804), _1658806)) = _1658804)], (33843 ^ _776541) ^ [_1403585] : [class_Orderings_Olinorder(_1403585), -(c_Orderings_Oord_Omax(_1403585, hAPP(c_COMBC(_1403585, _1403585, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1403585))) = c_Orderings_Oord__class_Omin(_1403585))], (27367 ^ _776541) ^ [_1268874] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1268874), c_Int_OPls) = _1268874)], (30064 ^ _776541) ^ [_1315742, _1315744, _1315746, _1315748] : [class_Orderings_Olinorder(_1315742), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315742), _1315744), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315742), _1315746), _1315748)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315742), _1315746), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315742), _1315744), _1315748)))], (5370 ^ _776541) ^ [_858591, _858593] : [_858593 = _858591, -(c_Orderings_Oord__class_Oless(_858593) = c_Orderings_Oord__class_Oless(_858591))], (7900 ^ _776541) ^ [_909749, _909751, _909753] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909749, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909749, tc_HOL_Obool)), _909751), _909753)), _909751)))], (6476 ^ _776541) ^ [_881162, _881164] : [hBOOL(hAPP(hAPP(c_member(_881162), _881164), c_Orderings_Obot__class_Obot(tc_fun(_881162, tc_HOL_Obool))))], (15390 ^ _776541) ^ [_1054476, _1054478, _1054480, _1054482] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054476), _1054478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054480), hAPP(c_Set_Oimage(_1054476, _1054480, _1054482), _1054478))), hAPP(c_Finite__Set_Ocard(_1054476), _1054478))))], (24962 ^ _776541) ^ [_1228607, _1228609] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228607), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228609)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228607, _1228609)))], (6909 ^ _776541) ^ [_888694, _888696, _888698] : [class_Orderings_Olinorder(_888694), 6912 ^ _776541 : [(6919 ^ _776541) ^ [] : [_888696 = _888698, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_888694), _888696) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_888694), _888698))], (6913 ^ _776541) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_888694), _888696) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_888694), _888698), -(_888696 = _888698)]]], (48247 ^ _776541) ^ [_1748314, _1748316, _1748318] : [48249 ^ _776541 : [(48252 ^ _776541) ^ [] : [hBOOL(hAPP(_1748316, 48248 ^ [_1748314, _1748316, _1748318]))], (48250 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748314), 48248 ^ [_1748314, _1748316, _1748318]), hAPP(c_List_Oset(_1748314), _1748318))))]], -(c_List_Olist__all(_1748314, _1748316, _1748318))], (43312 ^ _776541) ^ [_1639482, _1639484, _1639486] : [-(c_List_Olistset(_1639482, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1639482, tc_HOL_Obool)), _1639484), _1639486)) = c_List_Oset__Cons(_1639482, _1639484, c_List_Olistset(_1639482, _1639486)))], (28135 ^ _776541) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (50055 ^ _776541) ^ [_1787802, _1787804, _1787806, _1787808, _1787810] : [hBOOL(hAPP(hAPP(c_member(_1787802), _1787804), hAPP(c_Set_Oimage(_1787806, _1787802, _1787808), _1787810))), -(hAPP(_1787808, hAPP(c_Hilbert__Choice_Oinv__into(_1787806, _1787802, _1787810, _1787808), _1787804)) = _1787804)], (7946 ^ _776541) ^ [_910847, _910849, _910851] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910847, tc_HOL_Obool)), _910849), _910851) = _910851, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910847, tc_HOL_Obool)), _910849), _910851)))], (6714 ^ _776541) ^ [_885193, _885195, _885197, _885199] : [class_Orderings_Oord(_885193), _885195 = _885197, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885193), _885197), _885199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885193), _885195), _885199)))], (50323 ^ _776541) ^ [_1793996, _1793998, _1794000, _1794002, _1794004, _1794006, _1794008, _1794010] : [c_Fun_Obij__betw(_1793996, _1793998, _1794000, _1794002, _1794004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1793996, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1794006, _1793996, _1794008), _1794010)), _1794002)), 50330 ^ _776541 : [(50337 ^ _776541) ^ [] : [c_Fun_Obij__betw(_1794006, _1793998, hAPP(c_Fun_Ocomp(_1793996, _1793998, _1794006, _1794000), _1794008), _1794010, _1794004), -(c_Fun_Obij__betw(_1794006, _1793996, _1794008, _1794010, _1794002))], (50331 ^ _776541) ^ [] : [c_Fun_Obij__betw(_1794006, _1793996, _1794008, _1794010, _1794002), -(c_Fun_Obij__betw(_1794006, _1793998, hAPP(c_Fun_Ocomp(_1793996, _1793998, _1794006, _1794000), _1794008), _1794010, _1794004))]]], (46172 ^ _776541) ^ [_1704086, _1704088, _1704090] : [hBOOL(hAPP(c_List_Odistinct(_1704086), _1704088)), -(hAPP(c_List_Ofilter(_1704086, hAPP(hAPP(c_COMBC(_1704086, tc_fun(_1704086, tc_HOL_Obool), tc_HOL_Obool), c_member(_1704086)), hAPP(c_List_Oset(_1704086), c_List_Osublist(_1704086, _1704088, _1704090)))), _1704088) = c_List_Osublist(_1704086, _1704088, _1704090))], (4438 ^ _776541) ^ [_843917, _843919, _843921, _843923] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_843923, _843919) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_843921, _843917)), _843923 = _843921, _843919 = _843917], (34713 ^ _776541) ^ [_1423489, _1423491, _1423493] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423489, _1423491, _1423493), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1423491)], (38507 ^ _776541) ^ [_1514767, _1514769, _1514771] : [-(hAPP(c_Relation_ORange(_1514767, _1514769), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1514767, _1514769), tc_HOL_Obool), _1514771)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1514767, _1514769), tc_HOL_Obool), tc_fun(_1514769, tc_HOL_Obool)), _1514771), c_Relation_ORange(_1514767, _1514769)))], (44751 ^ _776541) ^ [_1671289, _1671291, _1671293, _1671295, _1671297] : [c_Fun_Oinj__on(_1671289, _1671291, _1671293, c_Orderings_Otop__class_Otop(tc_fun(_1671289, tc_HOL_Obool))), 44754 ^ _776541 : [(44761 ^ _776541) ^ [] : [_1671295 = _1671297, -(hAPP(hAPP(c_List_Omap(_1671289, _1671291), _1671293), _1671295) = hAPP(hAPP(c_List_Omap(_1671289, _1671291), _1671293), _1671297))], (44755 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Omap(_1671289, _1671291), _1671293), _1671295) = hAPP(hAPP(c_List_Omap(_1671289, _1671291), _1671293), _1671297), -(_1671295 = _1671297)]]], (24068 ^ _776541) ^ [_1212164, _1212166] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1212164), _1212166) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24069 ^ _776541 : [(24078 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212164), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212166), _1212164))], (24072 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212164), _1212166))], (24070 ^ _776541) ^ [] : [_1212166 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (29689 ^ _776541) ^ [_1308819, _1308821] : [class_Rings_Osemiring__1(_1308819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308821)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1308819), 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)))), _1308821))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1308819), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1308819), hAPP(c_Int_Onat, _1308821))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1308819), hAPP(c_Int_Onat, _1308821))))], (5482 ^ _776541) ^ [_860299, _860301, _860303, _860305, _860307, _860309] : [-(c_SetInterval_Oord_OatMost(_860309, _860305, _860301) = c_SetInterval_Oord_OatMost(_860307, _860303, _860299)), _860309 = _860307, _860305 = _860303, _860301 = _860299], (86 ^ _776541) ^ [_777884, _777886, _777888, _777890, _777892, _777894] : [-(c_Big__Operators_Osemilattice__big(_777892, _777888, _777884)), c_Big__Operators_Osemilattice__big(_777894, _777890, _777886), _777894 = _777892, _777890 = _777888, _777886 = _777884], (2570 ^ _776541) ^ [_814409, _814411, _814413, _814415, _814417, _814419] : [-(c_Wellfounded_Omlex__prod(_814419, _814415, _814411) = c_Wellfounded_Omlex__prod(_814417, _814413, _814409)), _814419 = _814417, _814415 = _814413, _814411 = _814409], (18318 ^ _776541) ^ [_1105989, _1105991, _1105993, _1105995] : [class_Rings_Olinordered__semiring(_1105989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105989), _1105991), _1105993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105989), _1105991), _1105995))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105989), c_Groups_Ozero__class_Ozero(_1105989)), _1105991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105989), _1105993), _1105995)))], (39357 ^ _776541) ^ [_1538502, _1538504, _1538506, _1538508] : [class_Groups_Ocomm__monoid__mult(_1538502), c_Fun_Oinj__on(_1538504, _1538502, _1538506, _1538508), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538504, _1538502), _1538506), _1538508) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538502, _1538502), c_Fun_Oid(_1538502)), hAPP(c_Set_Oimage(_1538504, _1538502, _1538506), _1538508)))], (35652 ^ _776541) ^ [_1442084, _1442086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1442084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1442086)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1442084), _1442086) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1442084, _1442086)))], (41021 ^ _776541) ^ [_1580286, _1580288] : [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), _1580286), _1580288)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1580286), _1580288)))], (33749 ^ _776541) ^ [_1400662, _1400664, _1400666, _1400668, _1400670, _1400672, _1400674] : [class_Groups_Ocomm__monoid__add(_1400662), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400664), _1400666)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400668), _1400670)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400664, _1400662), hAPP(hAPP(c_COMBS(_1400664, tc_fun(_1400668, tc_HOL_Obool), _1400662), hAPP(hAPP(c_COMBB(tc_fun(_1400668, _1400662), tc_fun(tc_fun(_1400668, tc_HOL_Obool), _1400662), _1400664), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400668, _1400662)), _1400672)), hAPP(hAPP(c_COMBB(tc_fun(_1400668, tc_HOL_Obool), tc_fun(_1400668, tc_HOL_Obool), _1400664), c_Set_OCollect(_1400668)), hAPP(hAPP(c_COMBB(tc_fun(_1400668, tc_HOL_Obool), tc_fun(_1400668, tc_HOL_Obool), _1400664), hAPP(c_COMBS(_1400668, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1400668), c_fconj), hAPP(hAPP(c_COMBC(_1400668, tc_fun(_1400668, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400668)), _1400670)))), _1400674)))), _1400666) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400668, _1400662), hAPP(hAPP(c_COMBS(_1400668, tc_fun(_1400664, tc_HOL_Obool), _1400662), hAPP(hAPP(c_COMBB(tc_fun(_1400664, _1400662), tc_fun(tc_fun(_1400664, tc_HOL_Obool), _1400662), _1400668), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400664, _1400662)), hAPP(c_COMBC(_1400664, _1400668, _1400662), _1400672))), hAPP(hAPP(c_COMBB(tc_fun(_1400664, tc_HOL_Obool), tc_fun(_1400664, tc_HOL_Obool), _1400668), c_Set_OCollect(_1400664)), hAPP(hAPP(c_COMBB(tc_fun(_1400664, tc_HOL_Obool), tc_fun(_1400664, tc_HOL_Obool), _1400668), hAPP(c_COMBS(_1400664, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1400664), c_fconj), hAPP(hAPP(c_COMBC(_1400664, tc_fun(_1400664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400664)), _1400666)))), hAPP(c_COMBC(_1400664, _1400668, tc_HOL_Obool), _1400674))))), _1400670))], (52071 ^ _776541) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (12147 ^ _776541) ^ [_989809, _989811, _989813] : [class_Lattices_Olattice(_989809), hBOOL(hAPP(c_Finite__Set_Ofinite(_989809), _989811)), -(_989811 = c_Orderings_Obot__class_Obot(tc_fun(_989809, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_989809, hAPP(hAPP(c_Set_Oinsert(_989809), _989813), _989811)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_989809), _989813), c_Big__Operators_Olattice__class_OInf__fin(_989809, _989811)))], (45269 ^ _776541) ^ [_1683138] : [-(_1683138 = 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, _1683138)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1683138))))], (8387 ^ _776541) ^ [_920462, _920464, _920466, _920468] : [class_Lattices_Osemilattice__inf(_920462), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920462), _920464), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920462), _920466), _920468)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920462), _920466), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920462), _920464), _920468)))], (5156 ^ _776541) ^ [_855210, _855212, _855214, _855216] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855216, _855212) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855214, _855210)), _855216 = _855214, _855212 = _855210], (32534 ^ _776541) ^ [_1364605, _1364607, _1364609] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364605, tc_HOL_Obool)), _1364607), _1364609) = hAPP(c_Set_OCollect(_1364605), hAPP(hAPP(c_COMBS(_1364605, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364605), c_fdisj), hAPP(hAPP(c_COMBC(_1364605, tc_fun(_1364605, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364605)), _1364607))), hAPP(hAPP(c_COMBC(_1364605, tc_fun(_1364605, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364605)), _1364609))))], (22301 ^ _776541) ^ [_1180839] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180839)) = _1180839)], (18023 ^ _776541) ^ [_1100617, _1100619, _1100621] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100617), _1100619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100617), _1100621)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100619), _1100621))], (4310 ^ _776541) ^ [_841811, _841813, _841815, _841817] : [-(c_List_Omap(_841817, _841813) = c_List_Omap(_841815, _841811)), _841817 = _841815, _841813 = _841811], (48804 ^ _776541) ^ [_1760216, _1760218, _1760220, _1760222, _1760224, _1760226] : [-(c_New__Random__Sequence_Opos__union(_1760216, _1760218, _1760220, _1760222, _1760224, _1760226) = c_New__DSequence_Opos__union(_1760216, hAPP(hAPP(hAPP(_1760218, _1760222), _1760224), _1760226), hAPP(hAPP(hAPP(_1760220, _1760222), _1760224), _1760226)))], (51897 ^ _776541) ^ [_1825135, _1825137] : [class_Orderings_Opreorder(_1825135), -(class_Orderings_Opreorder(tc_fun(_1825137, _1825135)))], (13447 ^ _776541) ^ [_1015569, _1015571, _1015573, _1015575, _1015577, _1015579, _1015581, _1015583] : [class_Groups_Ocomm__monoid__add(_1015569), class_Orderings_Oord(_1015571), _1015573 = _1015575, _1015577 = _1015579, 13465 ^ _776541 : [(13470 ^ _776541) ^ [] : [hAPP(_1015581, 13464 ^ [_1015569, _1015571, _1015573, _1015575, _1015577, _1015579, _1015581, _1015583]) = hAPP(_1015583, 13464 ^ [_1015569, _1015571, _1015573, _1015575, _1015577, _1015579, _1015581, _1015583])], (13468 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015571), 13464 ^ [_1015569, _1015571, _1015573, _1015575, _1015577, _1015579, _1015581, _1015583]), _1015579)))], (13466 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015571), _1015575), 13464 ^ [_1015569, _1015571, _1015573, _1015575, _1015577, _1015579, _1015581, _1015583])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1015571, _1015569), _1015581), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1015571, _1015573), _1015577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1015571, _1015569), _1015583), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1015571, _1015575), _1015579)))], (48136 ^ _776541) ^ [_1745915, _1745917, _1745919, _1745921] : [48137 ^ _776541 : [(48140 ^ _776541) ^ [] : [c_List_Olist__ex(_1745915, _1745917, _1745921)], (48138 ^ _776541) ^ [] : [hBOOL(hAPP(_1745917, _1745919))]], -(c_List_Olist__ex(_1745915, _1745917, hAPP(hAPP(c_List_Olist_OCons(_1745915), _1745919), _1745921)))], (22853 ^ _776541) ^ [_1190553, _1190555, _1190557, _1190559] : [class_Rings_Olinordered__semidom(_1190553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190555), _1190557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190553), c_Groups_Oone__class_Oone(_1190553)), _1190559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190553), hAPP(hAPP(c_Power_Opower__class_Opower(_1190553), _1190559), _1190555)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190553), _1190559), _1190557))))], (46739 ^ _776541) ^ [_1715754, _1715756, _1715758] : [class_Orderings_Olinorder(_1715754), 46742 ^ _776541 : [(46761 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715754, hAPP(hAPP(c_List_Oappend(_1715754), _1715756), _1715758))), c_List_Olinorder__class_Osorted(_1715754, _1715756), c_List_Olinorder__class_Osorted(_1715754, _1715758), 46771 ^ _776541 : [(46777 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715754), 46770 ^ [_1715754, _1715756, _1715758]), 46773 ^ [_1715754, _1715756, _1715758]))], (46775 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715754), 46773 ^ [_1715754, _1715756, _1715758]), hAPP(c_List_Oset(_1715754), _1715758))))], (46772 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715754), 46770 ^ [_1715754, _1715756, _1715758]), hAPP(c_List_Oset(_1715754), _1715756))))]]], (46743 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1715754, hAPP(hAPP(c_List_Oappend(_1715754), _1715756), _1715758)), 46746 ^ _776541 : [(46751 ^ _776541) ^ [_1715990] : [hBOOL(hAPP(hAPP(c_member(_1715754), _1715990), hAPP(c_List_Oset(_1715754), _1715756))), 46754 ^ _776541 : [(46755 ^ _776541) ^ [_1716100] : [hBOOL(hAPP(hAPP(c_member(_1715754), _1716100), hAPP(c_List_Oset(_1715754), _1715758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715754), _1715990), _1716100)))]]], (46749 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715754, _1715758))], (46747 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715754, _1715756))]]]]], (46261 ^ _776541) ^ [_1707203, _1707205] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1707203, _1707205)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1707203), _1707205))], (34503 ^ _776541) ^ [_1418732, _1418734, _1418736, _1418738, _1418740] : [34505 ^ _776541 : [(34508 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1418738, 34504 ^ [_1418732, _1418734, _1418736, _1418738, _1418740]), _1418740))], (34506 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418732), 34504 ^ [_1418732, _1418734, _1418736, _1418738, _1418740]), _1418736)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418732, tc_fun(_1418734, tc_HOL_Obool)), _1418736), _1418738), _1418740)))], (24868 ^ _776541) ^ [_1226676, _1226678, _1226680, _1226682, _1226684, _1226686] : [class_Divides_Osemiring__div(_1226676), c_Divides_Odiv__class_Omod(_1226676, _1226678, _1226680) = c_Divides_Odiv__class_Omod(_1226676, _1226682, _1226680), c_Divides_Odiv__class_Omod(_1226676, _1226684, _1226680) = c_Divides_Odiv__class_Omod(_1226676, _1226686, _1226680), -(c_Divides_Odiv__class_Omod(_1226676, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226676), _1226678), _1226684), _1226680) = c_Divides_Odiv__class_Omod(_1226676, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226676), _1226682), _1226686), _1226680))], (8129 ^ _776541) ^ [_915055, _915057, _915059] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_915055, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_915055, tc_HOL_Obool)), _915057), _915059)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915055, tc_HOL_Obool)), _915057), c_Complete__Lattice_OSup__class_OSup(tc_fun(_915055, tc_HOL_Obool), _915059)))], (28361 ^ _776541) ^ [_1285661, _1285663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285661)), c_Int_OBit1(_1285663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285661), _1285663)))], (37878 ^ _776541) ^ [_1498607, _1498609, _1498611, _1498613, _1498615] : [c_Fun_Oinj__on(_1498607, _1498609, _1498611, _1498613), hBOOL(hAPP(hAPP(c_member(_1498609), _1498615), hAPP(c_Set_Oimage(_1498607, _1498609, _1498611), _1498613))), -(hAPP(_1498611, hAPP(c_Fun_Othe__inv__into(_1498607, _1498609, _1498613, _1498611), _1498615)) = _1498615)], (14230 ^ _776541) ^ [_1032524, _1032526, _1032528] : [class_Rings_Ocomm__semiring__1(_1032524), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032524), _1032526), _1032528) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032524), _1032528), _1032526))], (23934 ^ _776541) ^ [_1209998, _1210000, _1210002] : [class_Rings_Osemiring__1(_1209998), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1210000), _1210002)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209998), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209998), _1210000)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209998), _1210002)))], (30010 ^ _776541) ^ [_1314769] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1314769), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14032 ^ _776541) ^ [_1027969, _1027971, _1027973, _1027975, _1027977, _1027979, _1027981, _1027983] : [c_Finite__Set_Ofolding__image__simple__idem(_1027969, _1027971, _1027973, _1027975, _1027977, _1027979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027971), _1027981)), hBOOL(hAPP(hAPP(c_member(_1027971), _1027983), _1027981)), -(hAPP(hAPP(_1027973, hAPP(_1027977, _1027983)), hAPP(_1027979, _1027981)) = hAPP(_1027979, _1027981))], (34570 ^ _776541) ^ [_1420375, _1420377, _1420379] : [_1420375 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1420377, _1420377), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1420377, _1420377), tc_HOL_Obool)), _1420375), _1420379)))], (21703 ^ _776541) ^ [_1169644, _1169646, _1169648, _1169650] : [class_Fields_Olinordered__field__inverse__zero(_1169644), class_Int_Onumber(_1169644), 21710 ^ _776541 : [(21711 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169644), _1169646), _1169648)), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650))), 21714 ^ _776541 : [(21721 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), c_Groups_Ozero__class_Ozero(_1169644)), _1169648))), 21724 ^ _776541 : [(21731 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), _1169648), c_Groups_Ozero__class_Ozero(_1169644)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), c_Groups_Ozero__class_Ozero(_1169644)), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650))))], (21725 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), _1169648), c_Groups_Ozero__class_Ozero(_1169644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169644), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650)), _1169648)), _1169646)))]]], (21715 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), c_Groups_Ozero__class_Ozero(_1169644)), _1169648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), _1169646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169644), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650)), _1169648))))]]], (21737 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169644), _1169646), _1169648)), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650)))), 21740 ^ _776541 : [(21743 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), _1169646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169644), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650)), _1169648)))], (21741 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), c_Groups_Ozero__class_Ozero(_1169644)), _1169648)))]], 21744 ^ _776541 : [(21747 ^ _776541) ^ [] : [21748 ^ _776541 : [(21751 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169644), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650)), _1169648)), _1169646))], (21749 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), _1169648), c_Groups_Ozero__class_Ozero(_1169644))))]], 21752 ^ _776541 : [(21755 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), c_Groups_Ozero__class_Ozero(_1169644)), hAPP(c_Int_Onumber__class_Onumber__of(_1169644), _1169650)))], (21753 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), _1169648), c_Groups_Ozero__class_Ozero(_1169644)))]]], (21745 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169644), c_Groups_Ozero__class_Ozero(_1169644)), _1169648))]]]]], (24600 ^ _776541) ^ [_1221551, _1221553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1221551), _1221553)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221551), _1221553) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (10939 ^ _776541) ^ [_965475, _965477] : [_965475 = c_Orderings_Obot__class_Obot(tc_fun(_965477, tc_HOL_Obool)), 10940 ^ _776541 : [(10941 ^ _776541) ^ [_965544, _965546] : [_965475 = hAPP(hAPP(c_Set_Oinsert(_965477), _965546), _965544), -(hBOOL(hAPP(hAPP(c_member(_965477), _965546), _965544)))]]], (50049 ^ _776541) ^ [_1787661, _1787663, _1787665, _1787667, _1787669] : [hBOOL(hAPP(hAPP(c_member(_1787661), _1787663), hAPP(c_Set_Oimage(_1787665, _1787661, _1787667), _1787669))), -(hBOOL(hAPP(hAPP(c_member(_1787665), hAPP(c_Hilbert__Choice_Oinv__into(_1787665, _1787661, _1787669, _1787667), _1787663)), _1787669)))], (20007 ^ _776541) ^ [_1137729, _1137731, _1137733] : [class_Fields_Ofield__inverse__zero(_1137729), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1137729), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137729), _1137731), _1137733)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137729), _1137731), hAPP(c_Groups_Ouminus__class_Ouminus(_1137729), _1137733)))], (2470 ^ _776541) ^ [_812801, _812803, _812805, _812807] : [-(c_Divides_Odivmod__int(_812807, _812803) = c_Divides_Odivmod__int(_812805, _812801)), _812807 = _812805, _812803 = _812801], (11322 ^ _776541) ^ [_973443, _973445, _973447] : [hAPP(c_Set_Oimage(_973445, tc_fun(_973445, tc_HOL_Obool), _973443), _973447) = hAPP(c_Set_OPow(_973445), _973447)], (22245 ^ _776541) ^ [_1179970, _1179972, _1179974, _1179976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179970), _1179972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179974), _1179976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179970), _1179974)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179972), _1179976))))], (50971 ^ _776541) ^ [_1808804, _1808806] : [class_Rings_Ocomm__semiring__1(_1808804), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808804), _1808806), c_Groups_Ozero__class_Ozero(_1808804))))], (13618 ^ _776541) ^ [_1018950, _1018952, _1018954, _1018956] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1018950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018950), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018950), _1018952), _1018954)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018950), _1018952), _1018956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018950), _1018954), _1018956)))], (34773 ^ _776541) ^ [_1425232, _1425234, _1425236, _1425238, _1425240] : [hBOOL(hAPP(hAPP(_1425232, _1425234), _1425236)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425238, _1425240, tc_HOL_Obool), _1425232), hAPP(hAPP(c_Product__Type_OPair(_1425238, _1425240), _1425234), _1425236))))], (48808 ^ _776541) ^ [_1760347, _1760349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760347), _1760349)), -(c_Lazy__Sequence_Osmall__lazy_H(_1760347, _1760349) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (7980 ^ _776541) ^ [_911622, _911624, _911626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911622, tc_HOL_Obool)), _911624), _911626)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911622, tc_HOL_Obool)), _911626), _911624) = _911624)], (39852 ^ _776541) ^ [_1552014, _1552016, _1552018, _1552020, _1552022, _1552024] : [c_Fun_Oinj__on(_1552014, _1552016, _1552018, _1552020), c_Fun_Oinj__on(_1552016, _1552022, _1552024, hAPP(c_Set_Oimage(_1552014, _1552016, _1552018), _1552020)), -(c_Fun_Oinj__on(_1552014, _1552022, hAPP(c_Fun_Ocomp(_1552016, _1552022, _1552014, _1552024), _1552018), _1552020))], (10683 ^ _776541) ^ [_960385] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960385, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_960385, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_960385, tc_HOL_Obool)))], (14622 ^ _776541) ^ [_1040222, _1040224, _1040226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040222), _1040224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040222), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040226), _1040224))))], (34179 ^ _776541) ^ [_1411818, _1411820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1411818)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411820))), -(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(_1411820))), 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), _1411818)), c_Int_Onat))))))], (23337 ^ _776541) ^ [_1199448, _1199450, _1199452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199448)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1199450), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199452)), 23347 ^ _776541 : [(23353 ^ _776541) ^ [] : [-(_1199450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23349 ^ [_1199448, _1199450, _1199452]), 23346 ^ [_1199448, _1199450, _1199452]))], (23351 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23349 ^ [_1199448, _1199450, _1199452]), _1199452)))], (23348 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23346 ^ [_1199448, _1199450, _1199452]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1199448))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1199450), _1199448) = _1199450)], (43591 ^ _776541) ^ [_1646090, _1646092, _1646094] : [_1646094 = c_List_Olist_ONil(_1646092), -(_1646090 = hAPP(hAPP(c_List_Oappend(_1646092), _1646090), _1646094))], (14710 ^ _776541) ^ [_1041683, _1041685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041683), _1041685))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041683), _1041685)), -(_1041683 = _1041685)], (49835 ^ _776541) ^ [_1783214, _1783216] : [-(c_Equiv__Relations_Opart__equivp(_1783214, _1783216)), 49838 ^ _776541 : [(49839 ^ _776541) ^ [_1783291] : [hBOOL(hAPP(hAPP(_1783216, _1783291), _1783291))]], c_Predicate_Osymp(_1783214, _1783216), c_Predicate_Otransp(_1783214, _1783216)], (44795 ^ _776541) ^ [_1672418, _1672420, _1672422, _1672424, _1672426] : [class_Rings_Osemiring__0(_1672418), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672418), hAPP(hAPP(c_List_Omap(_1672420, _1672418), hAPP(hAPP(c_COMBC(_1672420, _1672418, _1672418), hAPP(hAPP(c_COMBB(_1672418, tc_fun(_1672418, _1672418), _1672420), c_Groups_Otimes__class_Otimes(_1672418)), _1672422)), _1672424)), _1672426)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1672418), hAPP(c_List_Omonoid__add__class_Olistsum(_1672418), hAPP(hAPP(c_List_Omap(_1672420, _1672418), _1672422), _1672426))), _1672424))], (10529 ^ _776541) ^ [_957535, _957537, _957539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957535, tc_HOL_Obool)), _957539), _957537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957535, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957535, tc_HOL_Obool)), _957537)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957535, tc_HOL_Obool)), _957539))))], (28213 ^ _776541) ^ [_1283118] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1283118) = 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(_1283118)))))], (24776 ^ _776541) ^ [_1224658, _1224660, _1224662] : [class_Divides_Osemiring__div(_1224658), -(c_Divides_Odiv__class_Omod(_1224658, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224658), _1224660), _1224662), _1224662) = c_Divides_Odiv__class_Omod(_1224658, _1224660, _1224662))], (14899 ^ _776541) ^ [_1045259] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045259), _1045259)))))], (14762 ^ _776541) ^ [_1042635, _1042637, _1042639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042635), _1042637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042637), _1042639))))], (10861 ^ _776541) ^ [_963921, _963923, _963925] : [class_Orderings_Olinorder(_963921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963921), _963923), _963925)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963921, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_963921), _963923)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963921, _963923), _963925)) = hAPP(c_SetInterval_Oord__class_OlessThan(_963921), _963925))], (49762 ^ _776541) ^ [_1782107, _1782109] : [-(c_Relation_Osym(_1782107, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1782107, _1782107), tc_HOL_Obool)), _1782109), hAPP(c_Relation_Oconverse(_1782107, _1782107), _1782109))))], (35008 ^ _776541) ^ [_1429808, _1429810, _1429812, _1429814, _1429816] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1429808, _1429810), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1429812), _1429814))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429816)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1429808, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429810), _1429816)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1429812), _1429816)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429810), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1429812, _1429816))), _1429814)))))], (35696 ^ _776541) ^ [_1442966, _1442968, _1442970, _1442972, _1442974, _1442976] : [hBOOL(hAPP(_1442966, _1442968)), hBOOL(hAPP(_1442970, _1442972)), 35703 ^ _776541 : [(35706 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1442970, hAPP(c_Product__Type_Osnd(_1442974, _1442976), hAPP(hAPP(c_Product__Type_OPair(_1442974, _1442976), _1442968), _1442972)))))], (35704 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1442966, hAPP(c_Product__Type_Ofst(_1442974, _1442976), hAPP(hAPP(c_Product__Type_OPair(_1442974, _1442976), _1442968), _1442972)))))]]], (3012 ^ _776541) ^ [_821254, _821256] : [_821256 = _821254, -(c_Nitpick_Onum(_821256) = c_Nitpick_Onum(_821254))], (33639 ^ _776541) ^ [_1397649, _1397651, _1397653, _1397655] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397649, tc_fun(_1397651, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397649, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1397651, tc_HOL_Obool), tc_fun(_1397651, tc_HOL_Obool), _1397649), hAPP(c_COMBC(_1397651, tc_fun(_1397651, tc_HOL_Obool), tc_HOL_Obool), c_member(_1397651))), _1397653)), _1397655)), -(hBOOL(hAPP(hAPP(c_member(_1397651), _1397655), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397649, tc_fun(_1397651, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397649, tc_HOL_Obool))), _1397653))))], (15476 ^ _776541) ^ [_1056459, _1056461, _1056463] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056459), _1056461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1056459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056459, tc_HOL_Obool)), _1056461), hAPP(hAPP(c_Set_Oinsert(_1056459), _1056463), c_Orderings_Obot__class_Obot(tc_fun(_1056459, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1056459), _1056461))))], (33036 ^ _776541) ^ [_1379780, _1379782, _1379784, _1379786] : [class_Fields_Olinordered__field(_1379780), -(hAPP(c_Groups_Oabs__class_Oabs(_1379780), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379782, _1379780), _1379784), _1379786)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379782, _1379780), hAPP(hAPP(c_COMBB(_1379780, _1379780, _1379782), c_Groups_Oabs__class_Oabs(_1379780)), _1379784)), _1379786))], (13015 ^ _776541) ^ [_1006123, _1006125, _1006127, _1006129, _1006131, _1006133] : [c_Finite__Set_Ofun__left__comm(_1006123, _1006125, _1006127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006123), _1006129)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1006123, _1006125, _1006127), _1006131), hAPP(hAPP(c_Set_Oinsert(_1006123), _1006133), _1006129)) = hAPP(hAPP(_1006127, _1006133), hAPP(hAPP(c_Finite__Set_Ofold(_1006123, _1006125, _1006127), _1006131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006123, tc_HOL_Obool)), _1006129), hAPP(hAPP(c_Set_Oinsert(_1006123), _1006133), c_Orderings_Obot__class_Obot(tc_fun(_1006123, tc_HOL_Obool)))))))], (49738 ^ _776541) ^ [_1781719, _1781721] : [c_Relation_Osym(_1781719, _1781721), -(c_Relation_Osym(_1781719, c_Transitive__Closure_Ortrancl(_1781719, _1781721)))], (41418 ^ _776541) ^ [_1589889, _1589891, _1589893, _1589895] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1589889, _1589891), tc_fun(_1589889, _1589891)), _1589893), c_Fun_Ocomp(_1589891, _1589891, _1589889, _1589895)) = c_Fun_Ocomp(_1589891, _1589891, _1589889, hAPP(hAPP(c_Nat_Ocompow(_1589891, _1589891), _1589893), _1589895)))], (24234 ^ _776541) ^ [_1214845, _1214847, _1214849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214845), _1214847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214849), 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), _1214847), _1214849)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214845), _1214849))))], (50241 ^ _776541) ^ [_1792182] : [-(_1792182 = hAPP(c_Code__Numeral_Oof__nat, 50239 ^ [_1792182]))], (14756 ^ _776541) ^ [_1042524, _1042526, _1042528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042524), _1042526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042528), _1042526))))], (14152 ^ _776541) ^ [_1030748, _1030750, _1030752, _1030754, _1030756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030748), _1030750)), -(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), _1030748), _1030752)), _1030754)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030750), _1030752)), _1030756)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030754), 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), _1030750), _1030748)), _1030752)), _1030756)))], (46081 ^ _776541) ^ [_1702097, _1702099, _1702101, _1702103, _1702105, _1702107] : [class_Orderings_Olinorder(_1702097), -(hBOOL(hAPP(_1702099, _1702101))), -(hAPP(c_List_Ofilter(_1702103, _1702099), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1702103, _1702097, _1702105), _1702101), _1702107)) = hAPP(c_List_Ofilter(_1702103, _1702099), _1702107))], (15222 ^ _776541) ^ [_1051233, _1051235, _1051237] : [class_Rings_Ocomm__semiring__1(_1051233), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051233), _1051235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051233), _1051237), _1051235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051233), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051233), _1051237), c_Groups_Oone__class_Oone(_1051233))), _1051235))], (25852 ^ _776541) ^ [_1244150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244150)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244150) = 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, _1244150))))], (41096 ^ _776541) ^ [_1582365, _1582367] : [-(hAPP(c_Relation_OField(_1582365), hAPP(c_Relation_Oconverse(_1582365, _1582365), _1582367)) = hAPP(c_Relation_OField(_1582365), _1582367))], (34289 ^ _776541) ^ [_1414525, _1414527] : [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), _1414525))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414527), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1414525))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414527), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414525))), 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), _1414527))), c_COMBI(tc_Int_Oint))))], (44358 ^ _776541) ^ [_1663726, _1663728] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663726), _1663728) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44361 ^ _776541 : [(44364 ^ _776541) ^ [_1663840] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1663840), hAPP(c_List_Oset(tc_Nat_Onat), _1663728))), -(_1663840 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44362 ^ _776541) ^ [] : [-(_1663726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22381 ^ _776541) ^ [_1182305] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182305) = _1182305)], (33697 ^ _776541) ^ [_1399289, _1399291, _1399293] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399289, tc_Nat_Onat), _1399291), _1399293) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399289, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1399289), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1399291)), _1399293)))], (41973 ^ _776541) ^ [_1606523, _1606525, _1606527, _1606529] : [41976 ^ _776541 : [(41981 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606523, _1606523)), hAPP(hAPP(c_Product__Type_OPair(_1606523, _1606523), 41975 ^ [_1606523, _1606525, _1606527, _1606529]), 41974 ^ [_1606523, _1606525, _1606527, _1606529])), _1606525))], (41979 ^ _776541) ^ [] : [41974 ^ [_1606523, _1606525, _1606527, _1606529] = 41975 ^ [_1606523, _1606525, _1606527, _1606529]], (41977 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606523, _1606523)), hAPP(hAPP(c_Product__Type_OPair(_1606523, _1606523), 41974 ^ [_1606523, _1606525, _1606527, _1606529]), 41975 ^ [_1606523, _1606525, _1606527, _1606529])), _1606525))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606523), tc_List_Olist(_1606523))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606523), tc_List_Olist(_1606523)), _1606527), _1606529)), c_List_Olexord(_1606523, _1606525)))), -(_1606527 = _1606529), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606523), tc_List_Olist(_1606523))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606523), tc_List_Olist(_1606523)), _1606529), _1606527)), c_List_Olexord(_1606523, _1606525))))], (36177 ^ _776541) ^ [_1458740, _1458742, _1458744, _1458746, _1458748, _1458750] : [class_Groups_Oordered__ab__group__add(_1458740), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458742), _1458744)), 36187 ^ _776541 : [(36190 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458740), c_Groups_Ozero__class_Ozero(_1458740)), hAPP(_1458746, 36186 ^ [_1458740, _1458742, _1458744, _1458746, _1458748, _1458750])))], (36188 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458742), 36186 ^ [_1458740, _1458742, _1458744, _1458746, _1458748, _1458750]), _1458744)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458742, _1458740), _1458746), _1458744) = _1458748, hBOOL(hAPP(hAPP(c_member(_1458742), _1458750), _1458744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458740), hAPP(_1458746, _1458750)), _1458748)))], (47130 ^ _776541) ^ [_1723889, _1723891, _1723893] : [-(hAPP(c_List_Orotate(_1723889, _1723891), hAPP(c_List_Orev(_1723889), _1723893)) = hAPP(c_List_Orev(_1723889), hAPP(c_List_Orotate(_1723889, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723889)), _1723893)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1723891, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723889)), _1723893)))), _1723893)))], (33963 ^ _776541) ^ [_1406552, _1406554, _1406556, _1406558, _1406560, _1406562] : [class_Groups_Ocomm__monoid__add(_1406552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406554), _1406556)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406554, _1406552), _1406558), _1406556) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406560, _1406552), hAPP(hAPP(c_COMBB(tc_fun(_1406554, tc_HOL_Obool), _1406552, _1406560), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406554, _1406552), _1406558)), hAPP(hAPP(c_COMBB(tc_fun(_1406554, tc_HOL_Obool), tc_fun(_1406554, tc_HOL_Obool), _1406560), c_Set_OCollect(_1406554)), hAPP(hAPP(c_COMBB(tc_fun(_1406554, tc_HOL_Obool), tc_fun(_1406554, tc_HOL_Obool), _1406560), hAPP(c_COMBS(_1406554, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1406554), c_fconj), hAPP(hAPP(c_COMBC(_1406554, tc_fun(_1406554, tc_HOL_Obool), tc_HOL_Obool), c_member(_1406554)), _1406556)))), hAPP(c_COMBC(_1406554, _1406560, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1406560, tc_fun(_1406560, tc_HOL_Obool), _1406554), c_fequal), _1406562)))))), hAPP(c_Set_Oimage(_1406554, _1406560, _1406562), _1406556)))], (24274 ^ _776541) ^ [_1215547, _1215549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215547), _1215549)), -(_1215549 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215547), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 24277 ^ [_1215547, _1215549]))))], (29033 ^ _776541) ^ [_1297016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1297016))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1297016)))], (14939 ^ _776541) ^ [_1046036, _1046038, _1046040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046036), _1046040)), _1046038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046036), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046038), _1046040))))], (47838 ^ _776541) ^ [_1739523, _1739525, _1739527, _1739529] : [47840 ^ _776541 : [(47843 ^ _776541) ^ [] : [hBOOL(hAPP(_1739527, 47839 ^ [_1739523, _1739525, _1739527, _1739529]))], (47841 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739523), 47839 ^ [_1739523, _1739525, _1739527, _1739529]), hAPP(c_List_Oset(_1739523), _1739525))))]], -(c_List_OtakeWhile(_1739523, _1739527, hAPP(hAPP(c_List_Oappend(_1739523), _1739525), _1739529)) = hAPP(hAPP(c_List_Oappend(_1739523), _1739525), c_List_OtakeWhile(_1739523, _1739527, _1739529)))], (52145 ^ _776541) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52237 ^ _776541) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (8579 ^ _776541) ^ [_923904, _923906, _923908] : [class_Lattices_Olattice(_923904), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923904), _923906), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923904), _923908), _923906))))], (28927 ^ _776541) ^ [_1295111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295111)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295111), c_Int_OPls)))], (28535 ^ _776541) ^ [_1288591, _1288593] : [class_Int_Onumber__ring(_1288591), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288591), hAPP(c_Int_Onumber__class_Onumber__of(_1288591), c_Int_OBit1(c_Int_OPls))), _1288593) = _1288593)], (51455 ^ _776541) ^ [_1817924, _1817926] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1817924), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1817926)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817924), _1817926)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817926), _1817924)))], (22375 ^ _776541) ^ [_1182194, _1182196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1182194), _1182196)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182194), _1182196)))], (36227 ^ _776541) ^ [_1460034, _1460036, _1460038, _1460040, _1460042, _1460044] : [-(hAPP(c_Product__Type_Oapfst(_1460034, _1460036, _1460038, _1460040), hAPP(hAPP(c_Product__Type_OPair(_1460034, _1460038), _1460042), _1460044)) = hAPP(hAPP(c_Product__Type_OPair(_1460036, _1460038), hAPP(_1460040, _1460042)), _1460044))], (25065 ^ _776541) ^ [_1230354, _1230356] : [25066 ^ _776541 : [(25067 ^ _776541) ^ [_1230403] : [_1230354 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230356), _1230403)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230354, _1230356) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28493 ^ _776541) ^ [_1287908] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287908))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1287908)))], (47289 ^ _776541) ^ [_1727240] : [-(c_List_Oreturn__list(_1727240) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1727240))], (24966 ^ _776541) ^ [_1228692, _1228694, _1228696] : [-(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, _1228692, _1228694)), _1228696), _1228694) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1228692), _1228696), _1228694))], (36661 ^ _776541) ^ [_1471687] : [-(c_Relation_OId__on(_1471687, c_Orderings_Obot__class_Obot(tc_fun(_1471687, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1471687, _1471687), tc_HOL_Obool)))], (30640 ^ _776541) ^ [_1326337, _1326339] : [class_Orderings_Olinorder(_1326337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326337), _1326339)), -(_1326339 = c_Orderings_Obot__class_Obot(tc_fun(_1326337, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1326337), c_Big__Operators_Olinorder__class_OMin(_1326337, _1326339)), _1326339)))], (14084 ^ _776541) ^ [_1029125, _1029127, _1029129, _1029131, _1029133] : [class_Groups_Oab__group__add(_1029125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029127), _1029129)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029127), _1029131)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029127, _1029125), _1029133), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029127, tc_HOL_Obool)), _1029129), _1029131)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029125), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029125), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029127, _1029125), _1029133), _1029129)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029127, _1029125), _1029133), _1029131))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029127, _1029125), _1029133), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1029127, tc_HOL_Obool)), _1029129), _1029131))))], (14248 ^ _776541) ^ [_1032919, _1032921, _1032923, _1032925] : [class_Rings_Ocomm__semiring__1(_1032919), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032919), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032919), _1032921), _1032923)), _1032925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032919), _1032921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032919), _1032923), _1032925)))], (48806 ^ _776541) ^ [_1760278, _1760280, _1760282, _1760284] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760278, _1760280), c_Lazy__Sequence_Olazy__sequence_OInsert(_1760278, _1760282, _1760284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1760280, _1760282)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760278, _1760280), _1760284))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5662 ^ _776541) ^ [_862995, _862997, _862999, _863001] : [-(hAPP(_863001, _862997) = hAPP(_862999, _862995)), _863001 = _862999, _862997 = _862995], (51617 ^ _776541) ^ [_1820748, _1820750, _1820752, _1820754] : [class_Divides_Osemiring__div(_1820748), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820748), _1820750), _1820752)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820748), _1820750), _1820754)), 51628 ^ _776541 : [(51635 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820748), _1820752), _1820754)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820748), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820748), _1820752), _1820750)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820748), _1820754), _1820750))))], (51629 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820748), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820748), _1820752), _1820750)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820748), _1820754), _1820750))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820748), _1820752), _1820754)))]]], (15047 ^ _776541) ^ [_1048241, _1048243, _1048245, _1048247, _1048249] : [class_Groups_Ocomm__monoid__add(_1048241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048243), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048245), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1048241), _1048247), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1048243, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048245), _1048249))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048241), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1048241), _1048247), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1048243, _1048245))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1048241), _1048247), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048245), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048245), _1048249)))))], (28823 ^ _776541) ^ [_1293266, _1293268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293266), _1293268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293266)), c_Int_OBit0(_1293268))))], (48488 ^ _776541) ^ [_1753560, _1753562, _1753564, _1753566] : [-(c_Predicate_Oconversep(_1753560, _1753562, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1753560, tc_fun(_1753562, tc_HOL_Obool))), _1753564), _1753566)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1753562, tc_fun(_1753560, tc_HOL_Obool))), c_Predicate_Oconversep(_1753560, _1753562, _1753564)), c_Predicate_Oconversep(_1753560, _1753562, _1753566)))], (37680 ^ _776541) ^ [_1494040, _1494042, _1494044, _1494046, _1494048] : [c_Fun_Oinj__on(_1494040, _1494042, _1494044, hAPP(hAPP(c_Set_Oinsert(_1494040), _1494046), _1494048)), 37683 ^ _776541 : [(37686 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1494042), hAPP(_1494044, _1494046)), hAPP(c_Set_Oimage(_1494040, _1494042, _1494044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494040, tc_HOL_Obool)), _1494048), hAPP(hAPP(c_Set_Oinsert(_1494040), _1494046), c_Orderings_Obot__class_Obot(tc_fun(_1494040, tc_HOL_Obool)))))))], (37684 ^ _776541) ^ [] : [-(c_Fun_Oinj__on(_1494040, _1494042, _1494044, _1494048))]]], (42059 ^ _776541) ^ [_1609249, _1609251, _1609253, _1609255] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609249), tc_List_Olist(_1609249))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609249), tc_List_Olist(_1609249)), _1609253), _1609255)), c_List_Olistrel(_1609249, _1609251))), -(c_List_Olistrelp(_1609249, hAPP(hAPP(c_COMBC(_1609249, tc_fun(tc_prod(_1609249, _1609249), tc_HOL_Obool), tc_fun(_1609249, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609249, tc_fun(tc_fun(tc_prod(_1609249, _1609249), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1609249, _1609249), tc_HOL_Obool), tc_fun(_1609249, tc_HOL_Obool)), _1609249), c_COMBC(_1609249, tc_fun(tc_prod(_1609249, _1609249), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609249, tc_prod(_1609249, _1609249)), tc_fun(_1609249, tc_fun(tc_fun(tc_prod(_1609249, _1609249), tc_HOL_Obool), tc_HOL_Obool)), _1609249), hAPP(c_COMBB(tc_prod(_1609249, _1609249), tc_fun(tc_fun(tc_prod(_1609249, _1609249), tc_HOL_Obool), tc_HOL_Obool), _1609249), c_member(tc_prod(_1609249, _1609249)))), c_Product__Type_OPair(_1609249, _1609249)))), _1609251), _1609253, _1609255))], (28235 ^ _776541) ^ [_1283498, _1283500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1283498)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1283500)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1283498)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1283500), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1283498))))], (12658 ^ _776541) ^ [_999658, _999660, _999662] : [class_Groups_Oab__semigroup__mult(_999658), hBOOL(hAPP(c_Finite__Set_Ofinite(_999658), _999660)), -(hBOOL(hAPP(hAPP(c_member(_999658), _999662), _999660))), -(hAPP(c_Finite__Set_Ofold1(_999658, c_Groups_Otimes__class_Otimes(_999658)), hAPP(hAPP(c_Set_Oinsert(_999658), _999662), _999660)) = hAPP(hAPP(c_Finite__Set_Ofold(_999658, _999658, c_Groups_Otimes__class_Otimes(_999658)), _999662), _999660))], (29311 ^ _776541) ^ [] : [-(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)))))], (40739 ^ _776541) ^ [_1573501, _1573503] : [-(c_Transitive__Closure_Ortrancl(_1573501, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1573501, _1573501), tc_HOL_Obool)), _1573503), c_Relation_OId(_1573501))) = c_Transitive__Closure_Ortrancl(_1573501, _1573503))], (15380 ^ _776541) ^ [_1054285, _1054287, _1054289] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054285), _1054287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1054285, tc_HOL_Obool)), _1054289), _1054287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054285), _1054289)), hAPP(c_Finite__Set_Ocard(_1054285), _1054287))))], (45436 ^ _776541) ^ [_1687338, _1687340, _1687342, _1687344, _1687346] : [-(c_List_Olist__all2(_1687338, _1687340, _1687342, _1687344, _1687346)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687338)), _1687344) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687340)), _1687346), 45442 ^ _776541 : [(45445 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687338, _1687340, tc_HOL_Obool), _1687342), 45441 ^ [_1687338, _1687340, _1687342, _1687344, _1687346]))], (45443 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1687338, _1687340)), 45441 ^ [_1687338, _1687340, _1687342, _1687344, _1687346]), hAPP(c_List_Oset(tc_prod(_1687338, _1687340)), hAPP(hAPP(c_List_Ozip(_1687338, _1687340), _1687344), _1687346)))))]]], (7668 ^ _776541) ^ [_904324, _904326, _904328, _904330] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904324, tc_HOL_Obool)), _904326), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904324, tc_HOL_Obool)), _904328), _904330)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904324, tc_HOL_Obool)), _904328), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904324, tc_HOL_Obool)), _904326), _904330)))], (42917 ^ _776541) ^ [_1631664, _1631666] : [42919 ^ _776541 : [(42923 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42921 ^ [_1631664, _1631666]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631664)), _1631666))))], (42925 ^ _776541) ^ [] : [42918 ^ [_1631664, _1631666] = 42921 ^ [_1631664, _1631666]], (42927 ^ _776541) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1631664), _1631666), 42918 ^ [_1631664, _1631666]) = hAPP(hAPP(c_List_Onth(_1631664), _1631666), 42921 ^ [_1631664, _1631666]))], (42920 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42918 ^ [_1631664, _1631666]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631664)), _1631666))))]], -(hBOOL(hAPP(c_List_Odistinct(_1631664), _1631666)))], (46291 ^ _776541) ^ [_1707646, _1707648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707646), _1707648)), -(c_List_Oupt(_1707646, _1707648) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1707646), c_List_Oupt(hAPP(c_Nat_OSuc, _1707646), _1707648)))], (7150 ^ _776541) ^ [_893024, _893026, _893028, _893030] : [7151 ^ _776541 : [(7154 ^ _776541) ^ [] : [hBOOL(hAPP(_893028, _893030))], (7152 ^ _776541) ^ [] : [_893026 = _893030]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_893024), _893026), _893028), _893030)))], (13774 ^ _776541) ^ [_1021973, _1021975, _1021977, _1021979] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1021973), 13777 ^ _776541 : [(13784 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021973), _1021975), _1021979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021973), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021973), _1021975), _1021977)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021973), _1021979), _1021977))))], (13778 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021973), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021973), _1021975), _1021977)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021973), _1021979), _1021977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021973), _1021975), _1021979)))]]], (28505 ^ _776541) ^ [_1288092] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1288092)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1288092), c_Int_OMin)))], (49550 ^ _776541) ^ [_1777958, _1777960] : [c_Relation_Otrans(_1777958, _1777960), c_Relation_Oantisym(_1777958, _1777960), -(c_Relation_Otrans(_1777958, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1777958, _1777958), tc_HOL_Obool)), _1777960), c_Relation_OId(_1777958))))], (37432 ^ _776541) ^ [_1488920, _1488922, _1488924, _1488926] : [c_Fun_Oinj__on(_1488920, _1488922, _1488924, c_Orderings_Otop__class_Otop(tc_fun(_1488920, tc_HOL_Obool))), 37435 ^ _776541 : [(37449 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488922), _1488926), hAPP(c_Set_Oimage(_1488920, _1488922, _1488924), c_Orderings_Otop__class_Otop(tc_fun(_1488920, tc_HOL_Obool)))))), 37450 ^ _776541 : [(37451 ^ _776541) ^ [_1489323] : [_1488926 = hAPP(_1488924, _1489323), 37455 ^ _776541 : [(37458 ^ _776541) ^ [] : [37454 ^ [_1488920, _1488922, _1488924, _1488926, _1489323] = _1489323], (37456 ^ _776541) ^ [] : [-(_1488926 = hAPP(_1488924, 37454 ^ [_1488920, _1488922, _1488924, _1488926, _1489323]))]]]]], (37436 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1488922), _1488926), hAPP(c_Set_Oimage(_1488920, _1488922, _1488924), c_Orderings_Otop__class_Otop(tc_fun(_1488920, tc_HOL_Obool))))), 37440 ^ _776541 : [(37443 ^ _776541) ^ [_1489185] : [_1488926 = hAPP(_1488924, _1489185), -(_1489185 = 37439 ^ [_1488920, _1488922, _1488924, _1488926])], (37441 ^ _776541) ^ [] : [-(_1488926 = hAPP(_1488924, 37439 ^ [_1488920, _1488922, _1488924, _1488926]))]]]]], (30058 ^ _776541) ^ [_1315599, _1315601, _1315603, _1315605] : [class_Orderings_Olinorder(_1315599), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315599), _1315601), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315599), _1315603), _1315605)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315599), _1315603), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315599), _1315601), _1315605)))], (17633 ^ _776541) ^ [_1094088] : [class_Rings_Olinordered__semidom(_1094088), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094088), c_Groups_Ozero__class_Ozero(_1094088)), c_Groups_Oone__class_Oone(_1094088))))], (52501 ^ _776541) ^ [_1831464, _1831466] : [hBOOL(_1831464), hBOOL(_1831466), -(hBOOL(hAPP(hAPP(c_fconj, _1831464), _1831466)))], (28183 ^ _776541) ^ [_1282604] : [class_Int_Onumber__ring(_1282604), c_Int_Oiszero(_1282604, hAPP(c_Int_Onumber__class_Onumber__of(_1282604), c_Int_OMin))], (5634 ^ _776541) ^ [_862557, _862559, _862561, _862563, _862565, _862567] : [-(c_COMBC(_862567, _862563, _862559) = c_COMBC(_862565, _862561, _862557)), _862567 = _862565, _862563 = _862561, _862559 = _862557], (31505 ^ _776541) ^ [_1342224, _1342226, _1342228, _1342230] : [class_Orderings_Olinorder(_1342224), 31508 ^ _776541 : [(31517 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342224), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342224), _1342226), _1342228)), _1342230))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342224), _1342226), _1342230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342224), _1342228), _1342230))], (31509 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342224), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342224), _1342226), _1342228)), _1342230)), 31512 ^ _776541 : [(31515 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342224), _1342228), _1342230)))], (31513 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342224), _1342226), _1342230)))]]]]], (26847 ^ _776541) ^ [_1260392, _1260394] : [c_Nat__Transfer_Ois__nat(_1260392), c_Nat__Transfer_Ois__nat(_1260394), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1260392, _1260394)))], (2790 ^ _776541) ^ [_817829, _817831] : [_817831 = _817829, -(c_HOL_OAll(_817831) = c_HOL_OAll(_817829))], (51663 ^ _776541) ^ [_1821570, _1821572] : [class_Rings_Ocomm__semiring__1(_1821570), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821570), _1821572), _1821572)))], (49648 ^ _776541) ^ [_1780010, _1780012] : [c_Relation_Osym(_1780010, _1780012), c_Relation_Otrans(_1780010, _1780012), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1780010, _1780010), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1780010, _1780010, _1780010), hAPP(c_Relation_Oconverse(_1780010, _1780010), _1780012)), _1780012)), _1780012)))], (30046 ^ _776541) ^ [_1315349, _1315351, _1315353] : [class_Orderings_Olinorder(_1315349), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315349), _1315351), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315349), _1315351), _1315353)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315349), _1315351), _1315353))], (52227 ^ _776541) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (34606 ^ _776541) ^ [_1421126, _1421128] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421126)), _1421128) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1421126), 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), _1421126)), _1421128))], (15608 ^ _776541) ^ [_1059613, _1059615, _1059617, _1059619, _1059621, _1059623] : [class_Rings_Olinordered__semiring__1__strict(_1059613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059613), _1059615), _1059617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059613), _1059619), _1059617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059613), c_Groups_Ozero__class_Ozero(_1059613)), _1059621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059613), c_Groups_Ozero__class_Ozero(_1059613)), _1059623)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059613), _1059621), _1059623) = c_Groups_Oone__class_Oone(_1059613), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059613), _1059621), _1059615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059613), _1059623), _1059619))), _1059617)))], (14410 ^ _776541) ^ [_1036691, _1036693, _1036695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036691), _1036693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036695), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036693), _1036695)), _1036691))))], (7792 ^ _776541) ^ [_907498, _907500, _907502, _907504] : [hBOOL(hAPP(hAPP(c_member(_907498), _907500), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907498, tc_HOL_Obool)), _907502), _907504))), 7795 ^ _776541 : [(7798 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907498), _907500), _907504)))], (7796 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907498), _907500), _907502)))]]], (31371 ^ _776541) ^ [_1339692, _1339694, _1339696, _1339698] : [class_Orderings_Olinorder(_1339692), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339692), _1339694), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339692), _1339696), _1339698)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339692), _1339696), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339692), _1339694), _1339698)))], (48570 ^ _776541) ^ [_1755803, _1755805, _1755807, _1755809] : [-(hAPP(hAPP(c_List_Oappend(_1755803), c_List_Oreplicate(_1755803, _1755805, _1755807)), hAPP(hAPP(c_List_Olist_OCons(_1755803), _1755807), _1755809)) = hAPP(hAPP(c_List_Olist_OCons(_1755803), _1755807), hAPP(hAPP(c_List_Oappend(_1755803), c_List_Oreplicate(_1755803, _1755805, _1755807)), _1755809)))], (18117 ^ _776541) ^ [_1102294, _1102296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102294), _1102296)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102294), _1102296) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25877 ^ _776541) ^ [_1244621, _1244623, _1244625] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244621, _1244623)), _1244625) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244621), _1244625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244623), _1244625)))], (45836 ^ _776541) ^ [_1696078, _1696080, _1696082] : [hBOOL(hAPP(c_List_Odistinct(_1696078), _1696080)), -(c_List_Oremove1(_1696078, _1696082, c_List_Oremdups(_1696078, _1696080)) = c_List_Oremdups(_1696078, c_List_Oremove1(_1696078, _1696082, _1696080)))], (40088 ^ _776541) ^ [_1557214, _1557216, _1557218, _1557220, _1557222, _1557224] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557214, tc_fun(_1557216, tc_HOL_Obool)), _1557218), hAPP(c_Fun_Ocomp(_1557220, tc_fun(_1557216, tc_HOL_Obool), _1557214, _1557222), _1557224)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557220, tc_fun(_1557216, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1557214, _1557220, _1557224), _1557218)), _1557222))], (5833 ^ _776541) ^ [_869035, _869037] : [-(_869035 = hAPP(c_Hoare__Mirabelle_OAbs__triple(_869037), 5831 ^ [_869035, _869037]))], (11866 ^ _776541) ^ [_984862, _984864, _984866, _984868, _984870, _984872] : [-(hBOOL(hAPP(hAPP(c_member(_984862), _984864), _984866))), -(hAPP(c_Set_Oimage(_984862, _984868, c_Fun_Ofun__upd(_984862, _984868, _984870, _984864, _984872)), _984866) = hAPP(c_Set_Oimage(_984862, _984868, _984870), _984866))], (37172 ^ _776541) ^ [_1483771, _1483773, _1483775, _1483777, _1483779, _1483781, _1483783] : [c_Equiv__Relations_Oequiv(_1483771, _1483773, _1483775), c_Equiv__Relations_Ocongruent(_1483771, tc_fun(_1483777, tc_HOL_Obool), _1483775, _1483779), hBOOL(hAPP(hAPP(c_member(tc_fun(_1483771, tc_HOL_Obool)), _1483781), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483771), _1483773), _1483775))), 37186 ^ _776541 : [(37189 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1483777, tc_HOL_Obool)), hAPP(_1483779, 37185 ^ [_1483771, _1483773, _1483775, _1483777, _1483779, _1483781, _1483783])), _1483783))], (37187 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483771), 37185 ^ [_1483771, _1483773, _1483775, _1483777, _1483779, _1483781, _1483783]), _1483773)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1483777, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1483771, tc_fun(_1483777, tc_HOL_Obool)), _1483781), _1483779)), _1483783)))], (39956 ^ _776541) ^ [_1554382, _1554384, _1554386, _1554388, _1554390, _1554392] : [class_Groups_Ocomm__monoid__mult(_1554382), c_Fun_Oinj__on(_1554384, _1554386, _1554388, _1554390), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554386, _1554382), _1554392), hAPP(c_Set_Oimage(_1554384, _1554386, _1554388), _1554390)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554384, _1554382), hAPP(c_Fun_Ocomp(_1554386, _1554382, _1554384, _1554392), _1554388)), _1554390))], (33917 ^ _776541) ^ [_1405263, _1405265, _1405267] : [class_Groups_Ocomm__monoid__add(_1405263), class_Groups_Ocomm__monoid__mult(_1405263), c_Nat__Transfer_Onat__set(_1405265), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1405263), _1405267), _1405265) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1405263), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1405263, tc_Nat_Onat), _1405267), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1405265)))], (51147 ^ _776541) ^ [_1812239, _1812241, _1812243] : [51148 ^ _776541 : [(51151 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812241), _1812243))], (51149 ^ _776541) ^ [] : [_1812239 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1812239), _1812241)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1812239), _1812243))))], (43721 ^ _776541) ^ [_1648846, _1648848, _1648850, _1648852, _1648854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648846), tc_List_Olist(_1648846))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648846), tc_List_Olist(_1648846)), _1648848), _1648850)), c_List_Olexord(_1648846, _1648852))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648846), tc_List_Olist(_1648846))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648846), tc_List_Olist(_1648846)), hAPP(hAPP(c_List_Oappend(_1648846), _1648854), _1648848)), hAPP(hAPP(c_List_Oappend(_1648846), _1648854), _1648850))), c_List_Olexord(_1648846, _1648852))))], (37384 ^ _776541) ^ [_1487993, _1487995, _1487997, _1487999, _1488001] : [c_Fun_Oinj__on(_1487993, _1487995, _1487997, c_Orderings_Otop__class_Otop(tc_fun(_1487993, tc_HOL_Obool))), hAPP(_1487997, _1487999) = hAPP(_1487997, _1488001), -(_1487999 = _1488001)], (24266 ^ _776541) ^ [_1215421] : [_1215421 = 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), _1215421)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16078 ^ _776541) ^ [_1067286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067286)), _1067286))], (20001 ^ _776541) ^ [_1137600, _1137602, _1137604] : [class_Fields_Ofield__inverse__zero(_1137600), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137600), hAPP(c_Groups_Ouminus__class_Ouminus(_1137600), _1137602)), hAPP(c_Groups_Ouminus__class_Ouminus(_1137600), _1137604)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137600), _1137602), _1137604))], (46197 ^ _776541) ^ [_1704661, _1704663, _1704665] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704661)), hAPP(c_List_Ofilter(_1704661, _1704663), _1704665)) = 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(_1704661)), _1704665)))), hAPP(hAPP(c_COMBB(_1704661, tc_HOL_Obool, tc_Nat_Onat), _1704663), hAPP(c_List_Onth(_1704661), _1704665))))))], (47787 ^ _776541) ^ [_1738390, _1738392, _1738394, _1738396] : [47789 ^ _776541 : [(47792 ^ _776541) ^ [] : [hBOOL(hAPP(_1738394, 47788 ^ [_1738390, _1738392, _1738394, _1738396]))], (47790 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738390), 47788 ^ [_1738390, _1738392, _1738394, _1738396]), hAPP(c_List_Oset(_1738390), _1738392))))]], -(c_List_OdropWhile(_1738390, _1738394, hAPP(hAPP(c_List_Oappend(_1738390), _1738392), _1738396)) = c_List_OdropWhile(_1738390, _1738394, _1738396))], (33050 ^ _776541) ^ [_1380159, _1380161, _1380163, _1380165] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1380159, tc_HOL_Obool), hAPP(c_Set_Oimage(_1380161, tc_fun(_1380159, tc_HOL_Obool), _1380163), _1380165)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380161, tc_fun(_1380159, tc_HOL_Obool)), _1380165), _1380163))], (33390 ^ _776541) ^ [_1389665, _1389667, _1389669, _1389671, _1389673] : [c_Finite__Set_Ofun__left__comm(_1389665, _1389667, _1389669), -(c_Finite__Set_Ofun__left__comm(_1389671, _1389667, hAPP(hAPP(c_COMBB(_1389665, tc_fun(_1389667, _1389667), _1389671), _1389669), _1389673)))], (27763 ^ _776541) ^ [_1275869] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275869), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275869) = _1275869)], (40649 ^ _776541) ^ [_1570462, _1570464, _1570466, _1570468, _1570470] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570462, _1570462)), hAPP(hAPP(c_Product__Type_OPair(_1570462, _1570462), _1570464), _1570466)), c_Transitive__Closure_Otrancl(_1570462, _1570468))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570462, _1570462)), hAPP(hAPP(c_Product__Type_OPair(_1570462, _1570462), _1570466), _1570470)), _1570468)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570462, _1570462)), hAPP(hAPP(c_Product__Type_OPair(_1570462, _1570462), _1570464), _1570470)), c_Transitive__Closure_Otrancl(_1570462, _1570468))))], (10541 ^ _776541) ^ [_957839, _957841, _957843, _957845, _957847] : [class_Orderings_Olinorder(_957839), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957839), _957841), _957843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957839), _957845), _957847)), 10552 ^ _776541 : [(10561 ^ _776541) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957839, _957841), _957843) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957839, _957845), _957847)), _957841 = _957845, _957843 = _957847], (10553 ^ _776541) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957839, _957841), _957843) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957839, _957845), _957847), 10556 ^ _776541 : [(10559 ^ _776541) ^ [] : [-(_957843 = _957847)], (10557 ^ _776541) ^ [] : [-(_957841 = _957845)]]]]], (43984 ^ _776541) ^ [_1655682, _1655684, _1655686, _1655688] : [_1655682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1655684), _1655682), hAPP(hAPP(c_List_Olist_OCons(_1655684), _1655686), _1655688)) = hAPP(hAPP(c_List_Olist_OCons(_1655684), _1655686), _1655688))], (26637 ^ _776541) ^ [_1257335, _1257337] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257335)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257335)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257337)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257335)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257337))))], (52379 ^ _776541) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52445 ^ _776541) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (50717 ^ _776541) ^ [_1801702, _1801704, _1801706] : [hBOOL(hAPP(hAPP(_1801704, _1801706), _1801706)), -(hBOOL(hAPP(c_Quotient_ORespects(_1801702, _1801704), _1801706)))], (43240 ^ _776541) ^ [_1637962] : [-(c_List_Olists(_1637962, c_Orderings_Obot__class_Obot(tc_fun(_1637962, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1637962)), c_List_Olist_ONil(_1637962)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1637962), tc_HOL_Obool))))], (40731 ^ _776541) ^ [_1573325, _1573327] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573325, _1573325), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1573325, _1573327)), c_Relation_OId(_1573325)) = c_Transitive__Closure_Ortrancl(_1573325, _1573327))], (11628 ^ _776541) ^ [_979950, _979952, _979954] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979950), _979952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979950, tc_HOL_Obool)), _979954), _979952)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979950), _979954)))], (8145 ^ _776541) ^ [_915407, _915409, _915411] : [class_Complete__Lattice_Ocomplete__lattice(_915407), -(c_Complete__Lattice_OSup__class_OSup(_915407, hAPP(hAPP(c_Set_Oinsert(_915407), _915409), hAPP(hAPP(c_Set_Oinsert(_915407), _915411), c_Orderings_Obot__class_Obot(tc_fun(_915407, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915407), _915409), _915411))], (2196 ^ _776541) ^ [_808438, _808440, _808442, _808444] : [-(c_Random_Olog(_808444, _808440) = c_Random_Olog(_808442, _808438)), _808444 = _808442, _808440 = _808438], (47777 ^ _776541) ^ [_1737933, _1737935, _1737937, _1737939, _1737941] : [47778 ^ _776541 : [(47781 ^ _776541) ^ [] : [hBOOL(hAPP(_1737941, hAPP(hAPP(c_List_Ozip(_1737933, _1737937), hAPP(hAPP(c_List_Otake(_1737933), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737933)), _1737935)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939))), _1737935)), hAPP(hAPP(c_List_Otake(_1737937), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737933)), _1737935)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939))), _1737939))))], (47779 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737933)), hAPP(hAPP(c_List_Otake(_1737933), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737933)), _1737935)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939))), _1737935)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), hAPP(hAPP(c_List_Otake(_1737937), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737933)), _1737935)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939))), _1737939)))]], -(hBOOL(hAPP(_1737941, hAPP(hAPP(c_List_Ozip(_1737933, _1737937), _1737935), _1737939))))], (21355 ^ _776541) ^ [_1163147, _1163149, _1163151] : [class_Rings_Ocomm__semiring__1(_1163147), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1163147), _1163149), hAPP(c_Nat_OSuc, _1163151)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163147), _1163149), hAPP(hAPP(c_Power_Opower__class_Opower(_1163147), _1163149), _1163151)))], (24948 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (9638 ^ _776541) ^ [_941605, _941607, _941609] : [class_Orderings_Oorder(_941605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941605), _941607), _941609)), -(_941609 = _941607), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941605), _941607), _941609)))], (28611 ^ _776541) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (24489 ^ _776541) ^ [_1219456, _1219458, _1219460] : [-(hBOOL(hAPP(_1219456, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1219458), _1219460)))), 24492 ^ _776541 : [(24495 ^ _776541) ^ [] : [hBOOL(hAPP(_1219456, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24493 ^ _776541) ^ [] : [-(_1219460 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 24498 ^ _776541 : [(24499 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219460)))], (24505 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24501 ^ [_1219456, _1219458, _1219460]), _1219460)))], (24509 ^ _776541) ^ [] : [hBOOL(hAPP(_1219456, 24500 ^ [_1219456, _1219458, _1219460]))], (24507 ^ _776541) ^ [] : [-(_1219458 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219460), 24500 ^ [_1219456, _1219458, _1219460])), 24501 ^ [_1219456, _1219458, _1219460]))], (24503 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24501 ^ [_1219456, _1219458, _1219460])))]], 24510 ^ _776541 : [(24511 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219460), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24517 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24513 ^ [_1219456, _1219458, _1219460]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24521 ^ _776541) ^ [] : [hBOOL(hAPP(_1219456, 24512 ^ [_1219456, _1219458, _1219460]))], (24519 ^ _776541) ^ [] : [-(_1219458 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219460), 24512 ^ [_1219456, _1219458, _1219460])), 24513 ^ [_1219456, _1219458, _1219460]))], (24515 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219460), 24513 ^ [_1219456, _1219458, _1219460])))]]], (49285 ^ _776541) ^ [_1771687, _1771689] : [c_Relation_Otrans(_1771687, _1771689), -(c_Relation_Otrans(tc_List_Olist(_1771687), c_List_Olexord(_1771687, _1771689)))], (8351 ^ _776541) ^ [_919656, _919658] : [class_Lattices_Osemilattice__sup(_919656), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919656), _919658), _919658) = _919658)], (48368 ^ _776541) ^ [_1750658, _1750660] : [c_List_Olist__ex1(_1750658, _1750660, c_List_Olist_ONil(_1750658))], (52375 ^ _776541) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (43663 ^ _776541) ^ [_1647359, _1647361, _1647363] : [-(_1647359 = c_List_Olist_ONil(_1647361)), -(c_List_Obutlast(_1647361, hAPP(hAPP(c_List_Oappend(_1647361), _1647363), _1647359)) = hAPP(hAPP(c_List_Oappend(_1647361), _1647363), c_List_Obutlast(_1647361, _1647359)))], (21405 ^ _776541) ^ [_1164370, _1164372] : [class_Rings_Ocomm__semiring__1(_1164370), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1164370), _1164372), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1164370))], (39467 ^ _776541) ^ [_1541395, _1541397, _1541399, _1541401] : [-(c_Product__Type_Oapsnd(_1541395, _1541397, _1541399, _1541401) = c_Product__Type_Omap__pair(_1541399, _1541399, _1541395, _1541397, c_Fun_Oid(_1541399), _1541401))], (10130 ^ _776541) ^ [_950023, _950025, _950027] : [class_Orderings_Olinorder(_950023), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950023), _950025), _950027)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_950023, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_950023), _950025)), c_SetInterval_Oord__class_OgreaterThanLessThan(_950023, _950025, _950027)) = hAPP(c_SetInterval_Oord__class_OlessThan(_950023), _950027))], (36734 ^ _776541) ^ [] : [-(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))], (33322 ^ _776541) ^ [_1387890, _1387892] : [-(hAPP(c_Set_OCollect(_1387890), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1387890), c_fNot), _1387892)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1387890, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1387890), _1387892)))], (41327 ^ _776541) ^ [_1587635, _1587637, _1587639] : [c_Relation_Ototal__on(_1587635, _1587637, _1587639), 41330 ^ _776541 : [(41331 ^ _776541) ^ [_1587779] : [hBOOL(hAPP(hAPP(c_member(_1587635), _1587779), _1587637)), 41334 ^ _776541 : [(41335 ^ _776541) ^ [_1587919] : [hBOOL(hAPP(hAPP(c_member(_1587635), _1587919), _1587637)), -(_1587779 = _1587919), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587635, _1587635)), hAPP(hAPP(c_Product__Type_OPair(_1587635, _1587635), _1587779), _1587919)), _1587639))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587635, _1587635)), hAPP(hAPP(c_Product__Type_OPair(_1587635, _1587635), _1587919), _1587779)), _1587639)))]]]]], (48436 ^ _776541) ^ [_1751992, _1751994, _1751996, _1751998, _1752000, _1752002, _1752004] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1751992, _1751994, _1751996, _1751998, _1752000, _1752002, _1752004) = c_New__DSequence_Oneg__decr__bind(_1751992, _1751994, hAPP(hAPP(hAPP(_1751996, _1752000), _1752002), _1752004), hAPP(hAPP(c_COMBC(_1751992, 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(_1751994)))), hAPP(hAPP(c_COMBC(_1751992, 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(_1751994))))), hAPP(hAPP(c_COMBC(_1751992, 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(_1751994)))))), _1751998), _1752000)), _1752002)), _1752004)))], (24800 ^ _776541) ^ [_1225146, _1225148, _1225150, _1225152] : [class_Divides_Osemiring__div(_1225146), -(c_Divides_Odiv__class_Omod(_1225146, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225146), _1225148), _1225150), _1225152) = c_Divides_Odiv__class_Omod(_1225146, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225146), c_Divides_Odiv__class_Omod(_1225146, _1225148, _1225152)), c_Divides_Odiv__class_Omod(_1225146, _1225150, _1225152)), _1225152))], (8109 ^ _776541) ^ [_914663, _914665, _914667, _914669] : [class_Orderings_Olinorder(_914663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914663), _914665), _914667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914663), _914667), _914669)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914663, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914663, _914665, _914667)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914663, _914667, _914669)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_914663, _914665, _914669))], (45521 ^ _776541) ^ [_1689303, _1689305, _1689307, _1689309, _1689311, _1689313, _1689315] : [c_List_Olist__all2(_1689303, _1689305, _1689307, hAPP(hAPP(c_List_Olist_OCons(_1689303), _1689309), _1689311), hAPP(hAPP(c_List_Olist_OCons(_1689305), _1689313), _1689315)), 45524 ^ _776541 : [(45527 ^ _776541) ^ [] : [-(c_List_Olist__all2(_1689303, _1689305, _1689307, _1689311, _1689315))], (45525 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1689307, _1689309), _1689313)))]]], (7800 ^ _776541) ^ [_907665, _907667, _907669, _907671] : [-(hBOOL(hAPP(hAPP(c_member(_907665), _907667), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907665, tc_HOL_Obool)), _907669), _907671)))), hBOOL(hAPP(hAPP(c_member(_907665), _907667), _907669)), hBOOL(hAPP(hAPP(c_member(_907665), _907667), _907671))], (25778 ^ _776541) ^ [_1242966, _1242968, _1242970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242966)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242968, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242970), _1242966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242970), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1242968), _1242970), _1242966))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242968, _1242970)))], (21411 ^ _776541) ^ [_1164465, _1164467, _1164469, _1164471] : [class_Rings_Ocomm__semiring__1(_1164465), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164465), hAPP(hAPP(c_Power_Opower__class_Opower(_1164465), _1164467), _1164469)), hAPP(hAPP(c_Power_Opower__class_Opower(_1164465), _1164467), _1164471)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1164465), _1164467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164469), _1164471)))], (30092 ^ _776541) ^ [_1316300, _1316302, _1316304] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1316300), _1316302)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1316304), _1316302)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1316300), _1316304)), _1316302))], (8399 ^ _776541) ^ [_920730, _920732, _920734] : [class_Lattices_Olattice(_920730), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920730), _920732), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920730), _920732), _920734)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920730), _920732), _920734))], (36598 ^ _776541) ^ [_1469960] : [-(_1469960 = 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), 36595 ^ [_1469960]), 36596 ^ [_1469960])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (6198 ^ _776541) ^ [_876123, _876125, _876127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876123, tc_HOL_Obool)), _876125), _876127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876123, tc_HOL_Obool)), _876127), _876125)), -(_876125 = _876127)], (41047 ^ _776541) ^ [_1580776, _1580778, _1580780] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580776, _1580776), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1580776, _1580776), _1580778)), c_Transitive__Closure_Ortrancl(_1580776, _1580778)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1580776, _1580776), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580776, _1580776)), hAPP(hAPP(c_Product__Type_OPair(_1580776, _1580776), _1580780), _1580780)), c_Transitive__Closure_Otrancl(_1580776, _1580778)))], (2348 ^ _776541) ^ [_810804, _810806, _810808, _810810] : [-(c_Divides_Opdivmod(_810810, _810806) = c_Divides_Opdivmod(_810808, _810804)), _810810 = _810808, _810806 = _810804], (13814 ^ _776541) ^ [_1022850, _1022852, _1022854] : [class_Groups_Oab__group__add(_1022850), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1022850), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022850), _1022852), _1022854)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022850), hAPP(c_Groups_Ouminus__class_Ouminus(_1022850), _1022852)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022850), _1022854)))], (52143 ^ _776541) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (42767 ^ _776541) ^ [_1628246, _1628248, _1628250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628246), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628248)), _1628250))), -(hAPP(hAPP(c_List_Otake(_1628248), _1628246), c_List_Obutlast(_1628248, _1628250)) = hAPP(hAPP(c_List_Otake(_1628248), _1628246), _1628250))], (40699 ^ _776541) ^ [_1572020, _1572022, _1572024, _1572026] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572020, tc_fun(_1572020, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1572020, tc_fun(tc_prod(_1572020, _1572020), tc_HOL_Obool), tc_fun(_1572020, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572020, tc_fun(tc_fun(tc_prod(_1572020, _1572020), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1572020, _1572020), tc_HOL_Obool), tc_fun(_1572020, tc_HOL_Obool)), _1572020), c_COMBC(_1572020, tc_fun(tc_prod(_1572020, _1572020), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572020, tc_prod(_1572020, _1572020)), tc_fun(_1572020, tc_fun(tc_fun(tc_prod(_1572020, _1572020), tc_HOL_Obool), tc_HOL_Obool)), _1572020), hAPP(c_COMBB(tc_prod(_1572020, _1572020), tc_fun(tc_fun(tc_prod(_1572020, _1572020), tc_HOL_Obool), tc_HOL_Obool), _1572020), c_member(tc_prod(_1572020, _1572020)))), c_Product__Type_OPair(_1572020, _1572020)))), _1572022)), c_fequal), _1572024), _1572026)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572020, _1572020)), hAPP(hAPP(c_Product__Type_OPair(_1572020, _1572020), _1572024), _1572026)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572020, _1572020), tc_HOL_Obool)), _1572022), c_Relation_OId(_1572020)))))], (15268 ^ _776541) ^ [_1052078, _1052080] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1052078), _1052080)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052080), _1052078))], (52211 ^ _776541) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (26613 ^ _776541) ^ [_1256858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256858)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1256858)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1256858)))], (16566 ^ _776541) ^ [_1074608, _1074610] : [16567 ^ _776541 : [(16570 ^ _776541) ^ [] : [_1074610 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16568 ^ _776541) ^ [] : [_1074608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074608), _1074610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25588 ^ _776541) ^ [_1239389, _1239391, _1239393] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239389))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239389)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239391)), _1239393)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239391)), _1239393))], (10236 ^ _776541) ^ [_952425, _952427, _952429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_952425, tc_HOL_Obool)), _952427), _952429)), -(hBOOL(hAPP(hAPP(c_member(_952425), 10239 ^ [_952425, _952427, _952429]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952425, tc_HOL_Obool)), _952429), _952427))))], (14604 ^ _776541) ^ [_1039867, _1039869, _1039871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039867), _1039869)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039867), _1039871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039869), _1039871)))], (29453 ^ _776541) ^ [_1304246, _1304248] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1304246), hAPP(c_Int_Onumber__class_Onumber__of(_1304246), _1304248)), 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(_1304246), hAPP(c_Int_Onumber__class_Onumber__of(_1304246), _1304248)), hAPP(c_Int_Onumber__class_Onumber__of(_1304246), _1304248))), class_Groups_Omonoid__mult(_1304246), class_Int_Onumber(_1304246)], (26643 ^ _776541) ^ [_1257405, _1257407] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1257405, _1257407)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1257407), _1257405)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (47022 ^ _776541) ^ [_1721617, _1721619, _1721621, _1721623] : [-(hAPP(c_List_Orev(_1721617), hAPP(hAPP(c_List_Omap(_1721619, _1721617), _1721621), _1721623)) = hAPP(hAPP(c_List_Omap(_1721619, _1721617), _1721621), hAPP(c_List_Orev(_1721619), _1721623)))], (15638 ^ _776541) ^ [_1060204] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1060204))))], (33138 ^ _776541) ^ [_1382628, _1382630, _1382632] : [hAPP(hAPP(c_COMBC(_1382628, tc_fun(_1382628, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382628)), _1382630) = hAPP(hAPP(c_COMBC(_1382628, tc_fun(_1382628, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382628)), _1382632), -(_1382630 = _1382632)], (33052 ^ _776541) ^ [_1380216, _1380218, _1380220, _1380222] : [-(hAPP(c_Set_Oimage(_1380216, _1380218, _1380220), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1380216, tc_HOL_Obool), _1380222)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1380216, tc_HOL_Obool), tc_fun(_1380218, tc_HOL_Obool)), _1380222), c_Set_Oimage(_1380216, _1380218, _1380220)))], (12786 ^ _776541) ^ [_1002106, _1002108] : [class_Lattices_Olattice(_1002106), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002106), _1002108)), -(c_Big__Operators_Olattice__class_OInf__fin(_1002106, _1002108) = hAPP(c_Finite__Set_Ofold1(_1002106, c_Lattices_Osemilattice__inf__class_Oinf(_1002106)), _1002108))], (26184 ^ _776541) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19829 ^ _776541) ^ [_1134385, _1134387] : [class_Rings_Olinordered__idom(_1134385), 19832 ^ _776541 : [(19839 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134385), c_Groups_Ozero__class_Ozero(_1134385)), _1134387)), -(c_Groups_Osgn__class_Osgn(_1134385, _1134387) = c_Groups_Oone__class_Oone(_1134385))], (19833 ^ _776541) ^ [] : [c_Groups_Osgn__class_Osgn(_1134385, _1134387) = c_Groups_Oone__class_Oone(_1134385), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134385), c_Groups_Ozero__class_Ozero(_1134385)), _1134387)))]]], (2944 ^ _776541) ^ [_820246, _820248] : [_820248 = _820246, -(c_Rings_Oinverse__class_Odivide(_820248) = c_Rings_Oinverse__class_Odivide(_820246))], (3312 ^ _776541) ^ [_825976, _825978, _825980, _825982] : [-(c_Code__Numeral_Onat__of__aux(_825982, _825978) = c_Code__Numeral_Onat__of__aux(_825980, _825976)), _825982 = _825980, _825978 = _825976], (48710 ^ _776541) ^ [_1758303, _1758305, _1758307] : [_1758305 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1758303) = c_List_Oreplicate(_1758303, _1758305, _1758307))], (51501 ^ _776541) ^ [_1818767, _1818769] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818767), _1818769)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818767), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818769))))], (41174 ^ _776541) ^ [_1584027, _1584029, _1584031, _1584033] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584027, _1584027)), hAPP(hAPP(c_Product__Type_OPair(_1584027, _1584027), _1584029), _1584031)), c_Transitive__Closure_Otrancl(_1584027, hAPP(c_Relation_Oconverse(_1584027, _1584027), _1584033)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584027, _1584027)), hAPP(hAPP(c_Product__Type_OPair(_1584027, _1584027), _1584029), _1584031)), hAPP(c_Relation_Oconverse(_1584027, _1584027), c_Transitive__Closure_Otrancl(_1584027, _1584033)))))], (18180 ^ _776541) ^ [_1103358, _1103360, _1103362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103358), _1103360)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103360), _1103358))), _1103362) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103360)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1103358), _1103362)))], (46156 ^ _776541) ^ [_1703669, _1703671, _1703673, _1703675] : [-(c_List_Otranspose(_1703669, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1703671), tc_List_Olist(_1703669)), hAPP(c_List_Omap(_1703671, _1703669), _1703673)), _1703675)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1703671), tc_List_Olist(_1703669)), hAPP(c_List_Omap(_1703671, _1703669), _1703673)), c_List_Otranspose(_1703671, _1703675)))], (35106 ^ _776541) ^ [_1431707, _1431709, _1431711] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1431707, _1431709), _1431711)), 35109 ^ _776541 : [(35110 ^ _776541) ^ [_1431792] : [hBOOL(hAPP(hAPP(_1431709, _1431792), _1431711)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1431707, _1431709), _1431792)))]]], (29509 ^ _776541) ^ [_1305134, _1305136, _1305138] : [class_Rings_Olinordered__semidom(_1305134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305134), hAPP(hAPP(c_Power_Opower__class_Opower(_1305134), _1305136), 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(_1305134), _1305138), 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(_1305134), c_Groups_Ozero__class_Ozero(_1305134)), _1305138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305134), _1305136), _1305138)))], (29185 ^ _776541) ^ [_1299636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1299636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1299636))))], (3894 ^ _776541) ^ [_835033, _835035] : [_835035 = _835033, -(c_Nat_Osemiring__1__class_Oof__nat(_835035) = c_Nat_Osemiring__1__class_Oof__nat(_835033))], (11600 ^ _776541) ^ [_979436, _979438, _979440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979436), hAPP(hAPP(c_Set_Oinsert(_979436), _979438), _979440))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979436), _979440)))], (50540 ^ _776541) ^ [_1798080, _1798082, _1798084, _1798086, _1798088] : [c_Fun_Obij__betw(_1798080, _1798082, _1798084, _1798086, _1798088), -(hAPP(c_Finite__Set_Ocard(_1798080), _1798086) = hAPP(c_Finite__Set_Ocard(_1798082), _1798088))], (9680 ^ _776541) ^ [_942245, _942247, _942249, _942251] : [class_Orderings_Opreorder(_942245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942245), _942247), _942249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942245), _942249), _942251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942245), _942247), _942251)))], (50552 ^ _776541) ^ [_1798294, _1798296, _1798298, _1798300, _1798302, _1798304, _1798306] : [c_Fun_Obij__betw(_1798294, _1798296, _1798298, _1798300, _1798302), c_Fun_Obij__betw(_1798294, _1798296, _1798298, _1798304, _1798306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1798296, tc_HOL_Obool)), _1798302), _1798306) = c_Orderings_Obot__class_Obot(tc_fun(_1798296, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1798294, _1798296, _1798298, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798294, tc_HOL_Obool)), _1798300), _1798304), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798296, tc_HOL_Obool)), _1798302), _1798306)))], (52343 ^ _776541) ^ [_1829754, _1829756] : [-(class_Enum_Oenum(tc_prod(_1829754, _1829756))), class_Enum_Oenum(_1829754), class_Enum_Oenum(_1829756)], (36571 ^ _776541) ^ [_1469360, _1469362, _1469364, _1469366] : [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), _1469360), _1469362)), 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), _1469364), _1469366)), 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), _1469360), _1469366)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469364), _1469362))))], (4682 ^ _776541) ^ [_847763, _847765, _847767, _847769, _847771, _847773] : [-(c_Random__Sequence_Oempty(_847773, _847769, _847765) = c_Random__Sequence_Oempty(_847771, _847767, _847763)), _847773 = _847771, _847769 = _847767, _847765 = _847763], (27275 ^ _776541) ^ [_1267186, _1267188, _1267190] : [class_Groups_Oordered__ab__group__add__abs(_1267186), -(hAPP(c_Groups_Oabs__class_Oabs(_1267186), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1267186), hAPP(c_Groups_Oabs__class_Oabs(_1267186), _1267188)), hAPP(c_Groups_Oabs__class_Oabs(_1267186), _1267190))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1267186), hAPP(c_Groups_Oabs__class_Oabs(_1267186), _1267188)), hAPP(c_Groups_Oabs__class_Oabs(_1267186), _1267190)))], (15234 ^ _776541) ^ [_1051509, _1051511] : [class_Rings_Ocomm__ring__1(_1051509), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1051509), _1051511) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051509), hAPP(c_Groups_Ouminus__class_Ouminus(_1051509), c_Groups_Oone__class_Oone(_1051509))), _1051511))], (3900 ^ _776541) ^ [_835118, _835120] : [_835120 = _835118, -(c_Lazy__Sequence_Ohit__bound(_835120) = c_Lazy__Sequence_Ohit__bound(_835118))], (5534 ^ _776541) ^ [_861081, _861083] : [_861083 = _861081, -(c_Rings_Odvd__class_Odvd(_861083) = c_Rings_Odvd__class_Odvd(_861081))], (25030 ^ _776541) ^ [_1229782, _1229784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229784)), -(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, _1229782, _1229784))))], (45317 ^ _776541) ^ [_1684707, _1684709, _1684711, _1684713] : [hBOOL(hAPP(c_List_Olistsp(_1684707, _1684709), hAPP(hAPP(c_List_Oappend(_1684707), _1684711), _1684713))), 45320 ^ _776541 : [(45323 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1684707, _1684709), _1684713)))], (45321 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1684707, _1684709), _1684711)))]]], (11216 ^ _776541) ^ [_971172, _971174, _971176, _971178, _971180] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971172, tc_HOL_Obool)), hAPP(c_Set_Oimage(_971174, _971172, _971176), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971174, tc_HOL_Obool)), _971178), _971180))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971172, tc_HOL_Obool)), hAPP(c_Set_Oimage(_971174, _971172, _971176), _971178)), hAPP(c_Set_Oimage(_971174, _971172, _971176), _971180)))))], (44954 ^ _776541) ^ [_1676678, _1676680, _1676682] : [c_Fun_Oinj__on(tc_List_Olist(_1676678), tc_List_Olist(_1676680), hAPP(c_List_Omap(_1676678, _1676680), _1676682), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676678), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1676678, _1676680, _1676682, c_Orderings_Otop__class_Otop(tc_fun(_1676678, tc_HOL_Obool))))], (29205 ^ _776541) ^ [_1299966] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1299966)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1299966)))], (7704 ^ _776541) ^ [_905259, _905261, _905263, _905265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905259, tc_HOL_Obool)), _905261), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905259, tc_HOL_Obool)), _905263), _905265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905259, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905259, tc_HOL_Obool)), _905261), _905263)), _905265)))], (24383 ^ _776541) ^ [_1217483, _1217485, _1217487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217483), _1217485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217487)), -(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), _1217487)), _1217483)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217487)), _1217485))))], (21345 ^ _776541) ^ [_1162904, _1162906, _1162908, _1162910] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162904), hAPP(c_Int_Onumber__class_Onumber__of(_1162904), _1162906)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162904), _1162908), _1162910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162904), hAPP(c_Int_Onumber__class_Onumber__of(_1162904), _1162906)), _1162908)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162904), hAPP(c_Int_Onumber__class_Onumber__of(_1162904), _1162906)), _1162910))), class_Int_Onumber(_1162904), class_Rings_Osemiring(_1162904)], (52369 ^ _776541) ^ [_1830036] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1830036)))], (24782 ^ _776541) ^ [_1224767, _1224769, _1224771] : [class_Divides_Osemiring__div(_1224767), -(c_Divides_Odiv__class_Omod(_1224767, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224767), _1224769), _1224771), _1224769) = c_Divides_Odiv__class_Omod(_1224767, _1224771, _1224769))], (10589 ^ _776541) ^ [_958627, _958629, _958631, _958633, _958635] : [class_Orderings_Olinorder(_958627), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958627, _958629), _958631) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958627, _958633), _958635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958627), _958629), _958631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958627), _958633), _958635)), -(_958631 = _958635)], (28999 ^ _776541) ^ [_1296383, _1296385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296383)), c_Int_OBit0(_1296385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296383), _1296385)))], (48718 ^ _776541) ^ [_1758427, _1758429, _1758431, _1758433, _1758435] : [-(hAPP(hAPP(c_List_Omap(_1758427, _1758429), _1758431), c_List_Oreplicate(_1758427, _1758433, _1758435)) = c_List_Oreplicate(_1758429, _1758433, hAPP(_1758431, _1758435)))], (22515 ^ _776541) ^ [_1184563, _1184565, _1184567, _1184569] : [class_Fields_Ofield__inverse__zero(_1184563), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184563), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184563), _1184565), _1184567)), _1184569) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184563), hAPP(hAPP(c_Power_Opower__class_Opower(_1184563), _1184565), _1184569)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184563), _1184567), _1184569)))], (52079 ^ _776541) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (14987 ^ _776541) ^ [_1046975, _1046977, _1046979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046975), _1046977)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046979), _1046977)), _1046975) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046979), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046977), _1046975)))], (7660 ^ _776541) ^ [_903999, _904001, _904003, _904005] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903999, tc_HOL_Obool)), _904001), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903999, tc_HOL_Obool)), _904003), _904005)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903999, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903999, tc_HOL_Obool)), _904001), _904003)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903999, tc_HOL_Obool)), _904001), _904005)))], (18852 ^ _776541) ^ [_1116245, _1116247] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1116245, _1116247)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1116245, _1116247), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1116247), c_Orderings_Otop__class_Otop(tc_fun(_1116247, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1116245), c_Orderings_Otop__class_Otop(tc_fun(_1116245, tc_HOL_Obool)))))], (51419 ^ _776541) ^ [_1817286, _1817288, _1817290] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1817288), _1817290))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817286), _1817288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1817290), _1817288)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817286), _1817290)))], (6037 ^ _776541) ^ [_872952, _872954, _872956, _872958] : [hBOOL(hAPP(hAPP(_872956, _872958), _872954)), -(hBOOL(hAPP(hAPP(c_member(_872952), _872954), c_SetInterval_Oord_OgreaterThan(_872952, _872956, _872958))))], (52377 ^ _776541) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (47341 ^ _776541) ^ [_1728314] : [-(c_List_Oembed__list(_1728314) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1728314))], (48184 ^ _776541) ^ [_1747179, _1747181, _1747183] : [c_List_Olist__all(_1747179, _1747181, _1747183), 48187 ^ _776541 : [(48188 ^ _776541) ^ [_1747268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747268), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747179)), _1747183))), -(hBOOL(hAPP(_1747181, hAPP(hAPP(c_List_Onth(_1747179), _1747183), _1747268))))]]], (30834 ^ _776541) ^ [_1329544, _1329546, _1329548] : [class_Orderings_Olinorder(_1329544), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329544), _1329546)), -(hBOOL(hAPP(hAPP(c_member(_1329544), _1329548), _1329546))), -(_1329546 = c_Orderings_Obot__class_Obot(tc_fun(_1329544, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1329544, c_Orderings_Oord__class_Omin(_1329544), hAPP(hAPP(c_Set_Oinsert(_1329544), _1329548), _1329546)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329544), _1329548), c_Big__Operators_Olattice_OInf__fin(_1329544, c_Orderings_Oord__class_Omin(_1329544), _1329546)))], (26713 ^ _776541) ^ [_1258554, _1258556] : [c_Nat__Transfer_Ois__nat(_1258554), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1258554, _1258556)))], (21273 ^ _776541) ^ [_1161437, _1161439, _1161441, _1161443] : [class_Int_Onumber__ring(_1161437), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161437), hAPP(c_Int_Onumber__class_Onumber__of(_1161437), _1161439)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161437), hAPP(c_Int_Onumber__class_Onumber__of(_1161437), _1161441)), _1161443)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161437), hAPP(c_Int_Onumber__class_Onumber__of(_1161437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1161439), _1161441))), _1161443))], (4272 ^ _776541) ^ [_841258, _841260] : [_841260 = _841258, -(c_Orderings_Oord__class_Omin(_841260) = c_Orderings_Oord__class_Omin(_841258))], (32548 ^ _776541) ^ [_1365126, _1365128, _1365130, _1365132, _1365134] : [-(_1365126 = c_Orderings_Obot__class_Obot(tc_fun(_1365128, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365128, tc_fun(_1365130, tc_HOL_Obool)), _1365126), hAPP(hAPP(c_COMBC(_1365128, tc_fun(_1365130, tc_HOL_Obool), tc_fun(_1365130, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1365130, tc_HOL_Obool), tc_fun(tc_fun(_1365130, tc_HOL_Obool), tc_fun(_1365130, tc_HOL_Obool)), _1365128), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365130, tc_HOL_Obool))), _1365132)), _1365134)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365130, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365128, tc_fun(_1365130, tc_HOL_Obool)), _1365126), _1365132)), _1365134))], (30034 ^ _776541) ^ [_1315131, _1315133, _1315135] : [class_Orderings_Olinorder(_1315131), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315131), _1315133), _1315135) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315131), _1315135), _1315133))], (19043 ^ _776541) ^ [_1119618, _1119620] : [19051 ^ _776541 : [(19054 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1119620, 19050 ^ [_1119618, _1119620])))], (19052 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19050 ^ [_1119618, _1119620]), _1119618)))]], 19044 ^ _776541 : [(19045 ^ _776541) ^ [_1119686] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1119686), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119618))), hBOOL(hAPP(_1119620, _1119686))]]], (7710 ^ _776541) ^ [_905447, _905449, _905451, _905453] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905447, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905447, tc_HOL_Obool)), _905449), _905451)), _905453) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905447, tc_HOL_Obool)), _905449), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905447, tc_HOL_Obool)), _905451), _905453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905447, tc_HOL_Obool)), _905453), _905449)))], (14889 ^ _776541) ^ [_1045066, _1045068, _1045070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045066), _1045068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045070), _1045068)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045070), _1045066))))], (52203 ^ _776541) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (6360 ^ _776541) ^ [_879107, _879109, _879111] : [-(_879107 = _879109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879111, tc_HOL_Obool)), _879107), _879109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879111, tc_HOL_Obool)), _879109), _879107))], (5715 ^ _776541) ^ [_866666, _866668, _866670] : [class_HOL_Oequal(_866666), 5718 ^ _776541 : [(5725 ^ _776541) ^ [] : [_866668 = _866670, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_866666), _866668), _866670)))], (5719 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_866666), _866668), _866670)), -(_866668 = _866670)]]], (10635 ^ _776541) ^ [_959456] : [class_Lattices_Oboolean__algebra(_959456), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959456), c_Orderings_Otop__class_Otop(_959456)) = c_Orderings_Obot__class_Obot(_959456))], (24244 ^ _776541) ^ [_1215032, _1215034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1215034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215032), _1215034)), _1215032)))], (47226 ^ _776541) ^ [_1725958, _1725960, _1725962] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725958)), c_List_OtakeWhile(_1725958, _1725960, _1725962))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725958)), _1725962))))], (41672 ^ _776541) ^ [_1597062, _1597064, _1597066] : [-(c_Nitpick_Otimes__frac(_1597062, _1597064, _1597066) = hAPP(hAPP(c_Nitpick_Ofrac(_1597062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597062), _1597064)), hAPP(c_Nitpick_Onum(_1597062), _1597066))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1597062), _1597064)), hAPP(c_Nitpick_Odenom(_1597062), _1597066))))], (49900 ^ _776541) ^ [_1784297, _1784299] : [-(c_Equiv__Relations_Opart__equivp(_1784297, _1784299)), 49903 ^ _776541 : [(49904 ^ _776541) ^ [_1784417] : [hBOOL(hAPP(hAPP(_1784299, _1784417), _1784417))]], 49921 ^ _776541 : [(49924 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1784299, 49906 ^ [_1784297, _1784299]), 49906 ^ [_1784297, _1784299])))], (49926 ^ _776541) ^ [] : [-(hAPP(_1784299, 49905 ^ [_1784297, _1784299]) = hAPP(_1784299, 49906 ^ [_1784297, _1784299]))], (49928 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1784299, 49905 ^ [_1784297, _1784299]), 49906 ^ [_1784297, _1784299]))], (49922 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1784299, 49905 ^ [_1784297, _1784299]), 49905 ^ [_1784297, _1784299])))]], 49909 ^ _776541 : [(49912 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(_1784299, 49905 ^ [_1784297, _1784299]), 49905 ^ [_1784297, _1784299])), hBOOL(hAPP(hAPP(_1784299, 49906 ^ [_1784297, _1784299]), 49906 ^ [_1784297, _1784299])), hAPP(_1784299, 49905 ^ [_1784297, _1784299]) = hAPP(_1784299, 49906 ^ [_1784297, _1784299])], (49910 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1784299, 49905 ^ [_1784297, _1784299]), 49906 ^ [_1784297, _1784299])))]]], (10 ^ _776541) ^ [_776664, _776666, _776668] : [-(_776668 = _776664), _776668 = _776666, _776666 = _776664], (44856 ^ _776541) ^ [_1673943, _1673945, _1673947, _1673949] : [_1673949 = c_List_Olist_ONil(_1673943), -(hAPP(hAPP(c_List_Omap(_1673943, _1673945), _1673947), _1673949) = c_List_Olist_ONil(_1673945))], (41160 ^ _776541) ^ [_1583620, _1583622, _1583624] : [-(hAPP(c_Relation_ORange(_1583620, _1583622), _1583624) = hAPP(c_Relation_ODomain(_1583622, _1583620), hAPP(c_Relation_Oconverse(_1583620, _1583622), _1583624)))], (32628 ^ _776541) ^ [_1368347, _1368349, _1368351, _1368353, _1368355] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368347, tc_fun(_1368349, tc_HOL_Obool)), _1368351), hAPP(hAPP(c_COMBC(_1368347, tc_fun(_1368349, tc_HOL_Obool), tc_fun(_1368349, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368349, tc_HOL_Obool), tc_fun(tc_fun(_1368349, tc_HOL_Obool), tc_fun(_1368349, tc_HOL_Obool)), _1368347), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368349, tc_HOL_Obool))), _1368353)), _1368355)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368349, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368347, tc_fun(_1368349, tc_HOL_Obool)), _1368351), _1368353)), _1368355))], (26064 ^ _776541) ^ [_1247695, _1247697] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247695), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247697)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247695, _1247697)))], (38440 ^ _776541) ^ [_1513446] : [-(c_Nitpick_Oone__frac(_1513446) = c_Nitpick_OAbs__Frac(_1513446, 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))))], (39285 ^ _776541) ^ [_1535770, _1535772, _1535774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535770), _1535772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535770, _1535770), tc_HOL_Obool)), _1535774), hAPP(hAPP(c_Product__Type_OSigma(_1535770, _1535770), _1535772), hAPP(c_COMBK(tc_fun(_1535770, tc_HOL_Obool), _1535770), _1535772)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1535770, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1535770), _1535772), _1535774))))], (29409 ^ _776541) ^ [_1303537, _1303539] : [class_Rings_Olinordered__idom(_1303537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303537), hAPP(hAPP(c_Power_Opower__class_Opower(_1303537), _1303539), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1303537)))], (19114 ^ _776541) ^ [_1120926, _1120928, _1120930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1120926), _1120928)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120926), _1120930)), 19124 ^ _776541 : [(19127 ^ _776541) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19125 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1120926), 19123 ^ [_1120926, _1120928, _1120930]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1120926, tc_HOL_Obool)), _1120928), _1120930))))]], -(hAPP(c_Finite__Set_Ocard(_1120926), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1120926, tc_HOL_Obool)), _1120928), _1120930)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1120926), _1120928)), hAPP(c_Finite__Set_Ocard(_1120926), _1120930)))], (5556 ^ _776541) ^ [_861400, _861402, _861404, _861406] : [-(tc_sum(_861406, _861402) = tc_sum(_861404, _861400)), _861406 = _861404, _861402 = _861400], (37830 ^ _776541) ^ [] : [-(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))))], (40831 ^ _776541) ^ [_1575873, _1575875] : [-(c_Transitive__Closure_Ortrancl(_1575873, c_Transitive__Closure_Ortrancl(_1575873, _1575875)) = c_Transitive__Closure_Ortrancl(_1575873, _1575875))], (40520 ^ _776541) ^ [_1567302, _1567304, _1567306, _1567308, _1567310] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1567302, _1567304, _1567302, _1567306), hAPP(c_Product__Type_OPair(_1567304, _1567302), _1567308)), _1567310) = hAPP(_1567310, _1567308))], (38860 ^ _776541) ^ [_1523767, _1523769, _1523771, _1523773] : [-(hAPP(c_Set_Ovimage(_1523767, _1523769, _1523771), _1523773) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523769, tc_fun(_1523767, tc_HOL_Obool)), _1523773), hAPP(hAPP(c_COMBB(tc_fun(_1523769, tc_HOL_Obool), tc_fun(_1523767, tc_HOL_Obool), _1523769), c_Set_Ovimage(_1523767, _1523769, _1523771)), hAPP(hAPP(c_COMBC(_1523769, tc_fun(_1523769, tc_HOL_Obool), tc_fun(_1523769, tc_HOL_Obool)), c_Set_Oinsert(_1523769)), c_Orderings_Obot__class_Obot(tc_fun(_1523769, tc_HOL_Obool))))))], (29671 ^ _776541) ^ [_1308478, _1308480] : [class_Int_Onumber__ring(_1308478), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1308478), hAPP(c_Int_Onumber__class_Onumber__of(_1308478), 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)))), _1308480)) = c_Groups_Oone__class_Oone(_1308478))], (39143 ^ _776541) ^ [_1531513, _1531515, _1531517, _1531519, _1531521] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531513, _1531515), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531513, tc_HOL_Obool)), _1531517), _1531519)), _1531521) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1531513, _1531515), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531513, _1531515), _1531517), _1531521)), hAPP(hAPP(c_Product__Type_OSigma(_1531513, _1531515), _1531519), _1531521)))], (28425 ^ _776541) ^ [_1286760] : [-(c_Int_OBit1(_1286760) = 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)), _1286760)), _1286760))], (52107 ^ _776541) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (49506 ^ _776541) ^ [_1777045, _1777047, _1777049, _1777051] : [c_Wellfounded_Omax__extp(_1777045, _1777047, _1777049, _1777051), 49509 ^ _776541 : [(49512 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1777045), _1777051)))], (49514 ^ _776541) ^ [] : [_1777051 = c_Orderings_Obot__class_Obot(tc_fun(_1777045, tc_HOL_Obool))], (49516 ^ _776541) ^ [_1777261] : [hBOOL(hAPP(hAPP(c_member(_1777045), _1777261), _1777049)), 49520 ^ _776541 : [(49523 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1777047, _1777261), 49519 ^ [_1777045, _1777047, _1777049, _1777051, _1777261])))], (49521 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777045), 49519 ^ [_1777045, _1777047, _1777049, _1777051, _1777261]), _1777051)))]]], (49510 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1777045), _1777049)))]]], (33459 ^ _776541) ^ [_1391809, _1391811, _1391813, _1391815] : [class_Rings_Oring__1(_1391809), -(hAPP(c_Int_Oring__1__class_Oof__int(_1391809), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391811, tc_Int_Oint), _1391813), _1391815)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391811, _1391809), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1391809, _1391811), c_Int_Oring__1__class_Oof__int(_1391809)), _1391813)), _1391815))], (48530 ^ _776541) ^ [_1754419, _1754421, _1754423] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754419, _1754419, hAPP(hAPP(c_COMBB(tc_fun(_1754419, tc_HOL_Obool), tc_fun(_1754419, tc_HOL_Obool), _1754419), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754419), c_fNot)), c_fequal)), _1754421), _1754423)), _1754421 = _1754423], (33206 ^ _776541) ^ [_1384960, _1384962, _1384964, _1384966, _1384968] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384960, tc_fun(_1384962, tc_HOL_Obool)), _1384964), hAPP(hAPP(c_COMBB(tc_fun(_1384962, tc_HOL_Obool), tc_fun(_1384962, tc_HOL_Obool), _1384960), hAPP(c_Set_Oinsert(_1384962), _1384966)), _1384968)) = hAPP(hAPP(c_Set_Oinsert(_1384962), _1384966), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384960, tc_fun(_1384962, tc_HOL_Obool)), _1384964), _1384968)))], (29089 ^ _776541) ^ [_1297959, _1297961] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1297959)), c_Int_OBit1(_1297961)))], (3574 ^ _776541) ^ [_829989, _829991, _829993, _829995, _829997, _829999, _830001, _830003] : [-(c_List_Olinorder__class_Osort__key(_830003, _829999, _829995, _829991) = c_List_Olinorder__class_Osort__key(_830001, _829997, _829993, _829989)), _830003 = _830001, _829999 = _829997, _829995 = _829993, _829991 = _829989], (45794 ^ _776541) ^ [_1695382, _1695384, _1695386, _1695388] : [_1695382 = _1695384, -(hAPP(c_List_OremoveAll(_1695386, _1695382), hAPP(hAPP(c_List_Olist_OCons(_1695386), _1695384), _1695388)) = hAPP(c_List_OremoveAll(_1695386, _1695382), _1695388))], (9436 ^ _776541) ^ [_938718, _938720, _938722] : [class_Orderings_Oorder(_938718), 9439 ^ _776541 : [(9448 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938718), _938720), _938722))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938718), _938720), _938722)), -(_938720 = _938722)], (9440 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938718), _938720), _938722)), 9443 ^ _776541 : [(9446 ^ _776541) ^ [] : [_938720 = _938722], (9444 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938718), _938720), _938722)))]]]]], (29157 ^ _776541) ^ [_1299146, _1299148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299146), _1299148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299146)), c_Int_OBit0(_1299148))))], (7996 ^ _776541) ^ [_911960, _911962] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911960, tc_HOL_Obool)), _911962), c_Orderings_Otop__class_Otop(tc_fun(_911960, tc_HOL_Obool))) = _911962)], (12091 ^ _776541) ^ [_989010, _989012] : [class_Complete__Lattice_Ocomplete__lattice(_989010), hBOOL(hAPP(c_Finite__Set_Ofinite(_989010), _989012)), -(_989012 = c_Orderings_Obot__class_Obot(tc_fun(_989010, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_989010, _989012) = c_Complete__Lattice_OSup__class_OSup(_989010, _989012))], (37195 ^ _776541) ^ [_1484300, _1484302, _1484304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1484300), _1484302)), c_Fun_Oinj__on(_1484300, tc_fun(tc_fun(_1484300, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1484300, tc_fun(tc_prod(_1484300, _1484300), tc_HOL_Obool), tc_fun(tc_fun(_1484300, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484300, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1484300, _1484300), tc_HOL_Obool), tc_fun(tc_fun(_1484300, tc_HOL_Obool), tc_HOL_Obool)), _1484300), c_Equiv__Relations_Oquotient(_1484300)), hAPP(hAPP(c_COMBC(_1484300, tc_fun(_1484300, tc_HOL_Obool), tc_fun(_1484300, tc_HOL_Obool)), c_Set_Oinsert(_1484300)), c_Orderings_Obot__class_Obot(tc_fun(_1484300, tc_HOL_Obool))))), _1484304), _1484302), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1484300, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1484300), _1484302), _1484304)) = hAPP(c_Finite__Set_Ocard(_1484300), _1484302))], (43058 ^ _776541) ^ [_1634627, _1634629, _1634631] : [hAPP(hAPP(c_List_Otake(_1634627), _1634629), _1634631) = c_List_Olist_ONil(_1634627), -(_1634629 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1634631 = c_List_Olist_ONil(_1634627))], (48877 ^ _776541) ^ [_1761955, _1761957, _1761959] : [hBOOL(hAPP(hAPP(c_List_Omember(_1761955), _1761957), _1761959)), -(hBOOL(hAPP(hAPP(c_member(_1761955), _1761959), hAPP(c_List_Oset(_1761955), _1761957))))], (39796 ^ _776541) ^ [_1550414, _1550416, _1550418, _1550420, _1550422, _1550424] : [39799 ^ _776541 : [(39802 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550420), _1550422), hAPP(hAPP(_1550424, 39797 ^ [_1550414, _1550416, _1550418, _1550420, _1550422, _1550424]), 39798 ^ [_1550414, _1550416, _1550418, _1550420, _1550422, _1550424])))], (39800 ^ _776541) ^ [] : [-(_1550414 = hAPP(hAPP(c_Product__Type_OPair(_1550416, _1550418), 39797 ^ [_1550414, _1550416, _1550418, _1550420, _1550422, _1550424]), 39798 ^ [_1550414, _1550416, _1550418, _1550420, _1550422, _1550424]))]], -(hBOOL(hAPP(hAPP(c_member(_1550420), _1550422), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550416, _1550418, tc_fun(_1550420, tc_HOL_Obool)), _1550424), _1550414))))], (47697 ^ _776541) ^ [_1736488, _1736490, _1736492, _1736494] : [class_Orderings_Oorder(_1736488), class_Enum_Oenum(_1736490), 47704 ^ _776541 : [(47713 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1736490, _1736488)), _1736492), _1736494))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736490, _1736488)), _1736492), _1736494)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1736490), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1736490), c_fNot), hAPP(hAPP(c_COMBS(_1736490, _1736488, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736488, tc_fun(_1736488, tc_HOL_Obool), _1736490), c_fequal), _1736492)), _1736494))))], (47705 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1736490, _1736488)), _1736492), _1736494)), 47708 ^ _776541 : [(47711 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1736490), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1736490), c_fNot), hAPP(hAPP(c_COMBS(_1736490, _1736488, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736488, tc_fun(_1736488, tc_HOL_Obool), _1736490), c_fequal), _1736492)), _1736494)))))], (47709 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736490, _1736488)), _1736492), _1736494)))]]]]], (52235 ^ _776541) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (42009 ^ _776541) ^ [_1607503, _1607505, _1607507, _1607509, _1607511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607503), tc_List_Olist(_1607503))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607503), tc_List_Olist(_1607503)), _1607505), _1607507)), c_List_Olistrel(_1607503, c_Transitive__Closure_Ortrancl(_1607503, _1607509)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607503), tc_List_Olist(_1607503))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607503), tc_List_Olist(_1607503)), _1607507), _1607511)), c_List_Olistrel(_1607503, c_Transitive__Closure_Ortrancl(_1607503, _1607509)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607503), tc_List_Olist(_1607503))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607503), tc_List_Olist(_1607503)), _1607505), _1607511)), c_List_Olistrel(_1607503, c_Transitive__Closure_Ortrancl(_1607503, _1607509)))))], (29327 ^ _776541) ^ [] : [-(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))))], (4616 ^ _776541) ^ [_846690, _846692] : [_846692 = _846690, -(c_Code__Numeral_OSuc__code__numeral(_846692) = c_Code__Numeral_OSuc__code__numeral(_846690))], (43639 ^ _776541) ^ [_1646947, _1646949, _1646951] : [hAPP(hAPP(c_List_Oappend(_1646947), _1646949), _1646951) = _1646951, -(_1646949 = c_List_Olist_ONil(_1646947))], (49121 ^ _776541) ^ [_1767520, _1767522, _1767524] : [-(c_Random__Sequence_Oempty(_1767520, _1767522, _1767524) = 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(_1767520)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1767520)))], (52199 ^ _776541) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (8972 ^ _776541) ^ [_931504, _931506, _931508] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_931504, tc_HOL_Obool)), _931506), _931508))), 8978 ^ _776541 : [(8982 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_931504, tc_HOL_Obool)), 8980 ^ [_931504, _931506, _931508]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_931504, tc_HOL_Obool)), _931506), _931508))))], (8984 ^ _776541) ^ [] : [8977 ^ [_931504, _931506, _931508] = 8980 ^ [_931504, _931506, _931508]], (8986 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931504, tc_HOL_Obool)), 8977 ^ [_931504, _931506, _931508]), 8980 ^ [_931504, _931506, _931508]) = c_Orderings_Obot__class_Obot(tc_fun(_931504, tc_HOL_Obool))], (8979 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_931504, tc_HOL_Obool)), 8977 ^ [_931504, _931506, _931508]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_931504, tc_HOL_Obool)), _931506), _931508))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931504, tc_HOL_Obool)), _931506), c_Complete__Lattice_OSup__class_OSup(tc_fun(_931504, tc_HOL_Obool), _931508)) = c_Orderings_Obot__class_Obot(tc_fun(_931504, tc_HOL_Obool)))], (4240 ^ _776541) ^ [_840790, _840792] : [_840792 = _840790, -(c_List_Ohd(_840792) = c_List_Ohd(_840790))], (52025 ^ _776541) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (9116 ^ _776541) ^ [_934068, _934070, _934072, _934074] : [class_Orderings_Oorder(_934068), _934070 = _934072, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934068), _934074), _934072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934068), _934074), _934070)))], (26541 ^ _776541) ^ [_1255589, _1255591] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1255589), _1255591) = 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)), _1255589)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1255591))))], (29633 ^ _776541) ^ [_1307647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1307647)), -(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), _1307647), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (42819 ^ _776541) ^ [_1629651, _1629653] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1629651, _1629653))))], (28389 ^ _776541) ^ [_1286172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286172)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286172), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23377 ^ _776541) ^ [_1200126, _1200128, _1200130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200126)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1200128), _1200130)), 23384 ^ _776541 : [(23385 ^ _776541) ^ [_1200322] : [23387 ^ _776541 : [(23393 ^ _776541) ^ [] : [-(_1200322 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23389 ^ [_1200126, _1200128, _1200130, _1200322]), 23386 ^ [_1200126, _1200128, _1200130, _1200322]))], (23391 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23389 ^ [_1200126, _1200128, _1200130, _1200322]), _1200130)))], (23388 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23386 ^ [_1200126, _1200128, _1200130, _1200322]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1200126))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200322), _1200128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200322), _1200126)), _1200128)))]]], (40765 ^ _776541) ^ [_1574213, _1574215, _1574217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574213, _1574213), tc_HOL_Obool)), _1574215), c_Transitive__Closure_Ortrancl(_1574213, _1574217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574213, _1574213), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574213, _1574215)), c_Transitive__Closure_Ortrancl(_1574213, _1574217))))], (52085 ^ _776541) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (48393 ^ _776541) ^ [_1751173, _1751175, _1751177] : [-(c_List_Olist__ex1(_1751173, _1751175, _1751177)), 48394 ^ _776541 : [(48395 ^ _776541) ^ [_1751267] : [hBOOL(hAPP(hAPP(c_member(_1751173), _1751267), hAPP(c_List_Oset(_1751173), _1751177))), hBOOL(hAPP(_1751175, _1751267)), 48403 ^ _776541 : [(48408 ^ _776541) ^ [] : [48402 ^ [_1751173, _1751175, _1751177, _1751267] = _1751267], (48406 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1751175, 48402 ^ [_1751173, _1751175, _1751177, _1751267])))], (48404 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751173), 48402 ^ [_1751173, _1751175, _1751177, _1751267]), hAPP(c_List_Oset(_1751173), _1751177))))]]]]], (32288 ^ _776541) ^ [_1357089, _1357091, _1357093, _1357095, _1357097, _1357099, _1357101, _1357103] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357089, tc_fun(_1357091, tc_fun(_1357093, tc_HOL_Obool))), _1357095), _1357097), _1357099), _1357101)), -(hBOOL(hAPP(hAPP(hAPP(_1357097, _1357103), _1357099), _1357101))), hBOOL(hAPP(hAPP(c_member(_1357089), _1357103), _1357095))], (11840 ^ _776541) ^ [_984158, _984160, _984162, _984164] : [c_Finite__Set_Ofolding__one(_984158, _984160, _984162), hBOOL(hAPP(c_Finite__Set_Ofinite(_984158), _984164)), -(_984164 = c_Orderings_Obot__class_Obot(tc_fun(_984158, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_984158), hAPP(hAPP(_984160, 11853 ^ [_984158, _984160, _984162, _984164]), 11854 ^ [_984158, _984160, _984162, _984164])), hAPP(hAPP(c_Set_Oinsert(_984158), 11853 ^ [_984158, _984160, _984162, _984164]), hAPP(hAPP(c_Set_Oinsert(_984158), 11854 ^ [_984158, _984160, _984162, _984164]), c_Orderings_Obot__class_Obot(tc_fun(_984158, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_984158), hAPP(_984162, _984164)), _984164)))], (28137 ^ _776541) ^ [_1281826] : [-(c_Int_Opred(_1281826) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1281826), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33539 ^ _776541) ^ [_1393682, _1393684, _1393686, _1393688] : [c_Orderings_Otop__class_Otop(tc_fun(_1393682, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393684, tc_fun(_1393682, tc_HOL_Obool)), _1393686), _1393688), 33542 ^ _776541 : [(33543 ^ _776541) ^ [_1393798] : [hBOOL(hAPP(hAPP(c_member(_1393684), _1393798), _1393686)), -(hAPP(_1393688, _1393798) = c_Orderings_Otop__class_Otop(tc_fun(_1393682, tc_HOL_Obool)))]]], (11475 ^ _776541) ^ [_976984, _976986, _976988, _976990] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976984), _976986)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976988), hAPP(c_Set_Oimage(_976984, _976988, _976990), _976986))))], (45842 ^ _776541) ^ [_1696189, _1696191, _1696193] : [-(hBOOL(hAPP(hAPP(c_member(_1696189), _1696191), hAPP(c_List_Oset(_1696189), _1696193)))), -(hAPP(c_List_OremoveAll(_1696189, _1696191), _1696193) = _1696193)], (26575 ^ _776541) ^ [_1256238, _1256240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256240)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1256238)), hAPP(c_Int_Onat, _1256240)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1256238, _1256240)))], (28463 ^ _776541) ^ [_1287406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1287406)))], (38270 ^ _776541) ^ [_1509456, _1509458, _1509460] : [c_Wellfounded_Owf(_1509456, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509456, _1509456), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509456, _1509456), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509456, _1509456, _1509456), _1509458), _1509458)), hAPP(hAPP(c_Relation_Orel__comp(_1509456, _1509456, _1509456), _1509460), _1509458))), _1509460)), -(c_Wellfounded_Owf(_1509456, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509456, _1509456), tc_HOL_Obool)), _1509458), _1509460)))], (51955 ^ _776541) ^ [_1825896, _1825898] : [-(class_HOL_Oequal(tc_fun(_1825896, _1825898))), class_Enum_Oenum(_1825896), class_HOL_Oequal(_1825898)], (17029 ^ _776541) ^ [_1083079, _1083081, _1083083, _1083085] : [class_Rings_Oordered__comm__semiring(_1083079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083079), _1083081), _1083083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083079), c_Groups_Ozero__class_Ozero(_1083079)), _1083085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083079), _1083085), _1083081)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083079), _1083085), _1083083))))], (49634 ^ _776541) ^ [_1779603, _1779605] : [c_Relation_Oantisym(_1779603, _1779605), -(c_Relation_Oantisym(_1779603, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779603, _1779603), tc_HOL_Obool)), _1779605), c_Relation_OId(_1779603))))], (4696 ^ _776541) ^ [_847984, _847986] : [_847986 = _847984, -(c_DSequence_Oempty(_847986) = c_DSequence_Oempty(_847984))], (13001 ^ _776541) ^ [_1005909, _1005911, _1005913] : [class_Lattices_Olattice(_1005909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005909), _1005911)), -(hBOOL(hAPP(hAPP(c_member(_1005909), _1005913), _1005911))), -(c_Big__Operators_Olattice__class_OInf__fin(_1005909, hAPP(hAPP(c_Set_Oinsert(_1005909), _1005913), _1005911)) = hAPP(hAPP(c_Finite__Set_Ofold(_1005909, _1005909, c_Lattices_Osemilattice__inf__class_Oinf(_1005909)), _1005913), _1005911))], (7081 ^ _776541) ^ [_891814, _891816, _891818] : [7083 ^ _776541 : [(7086 ^ _776541) ^ [] : [hBOOL(hAPP(_891816, 7082 ^ [_891814, _891816, _891818]))], (7084 ^ _776541) ^ [] : [-(hBOOL(hAPP(_891814, 7082 ^ [_891814, _891816, _891818])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891818, tc_HOL_Obool)), hAPP(c_Set_OCollect(_891818), _891814)), hAPP(c_Set_OCollect(_891818), _891816))))], (50477 ^ _776541) ^ [_1797025] : [-(c_Fun_Obij__betw(_1797025, _1797025, c_Fun_Oid(_1797025), c_Orderings_Otop__class_Otop(tc_fun(_1797025, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797025, tc_HOL_Obool))))], (21181 ^ _776541) ^ [_1159666, _1159668, _1159670] : [class_Int_Onumber(_1159666), 21184 ^ _776541 : [(21191 ^ _776541) ^ [] : [_1159670 = hAPP(c_Int_Onumber__class_Onumber__of(_1159666), _1159668), -(hAPP(c_Int_Onumber__class_Onumber__of(_1159666), _1159668) = _1159670)], (21185 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1159666), _1159668) = _1159670, -(_1159670 = hAPP(c_Int_Onumber__class_Onumber__of(_1159666), _1159668))]]], (19408 ^ _776541) ^ [_1126882, _1126884] : [class_Int_Oring__char__0(_1126882), hBOOL(hAPP(hAPP(c_member(_1126882), _1126884), c_Int_Oring__1__class_OInts(_1126882))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126882), c_Groups_Oone__class_Oone(_1126882)), _1126884)), _1126884) = c_Groups_Ozero__class_Ozero(_1126882)], (1444 ^ _776541) ^ [_797455, _797457] : [-(class_Orderings_Obot(_797455)), _797457 = _797455, class_Orderings_Obot(_797457)], (5835 ^ _776541) ^ [_869069, _869071] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869071, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869071)), tc_HOL_Obool)), 5831 ^ [_869069, _869071]), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869071, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869071)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_869071)))))], (36416 ^ _776541) ^ [_1464311, _1464313, _1464315, _1464317] : [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), _1464311), _1464313)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1464315), _1464317))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464311), _1464317) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464315), _1464313))], (39779 ^ _776541) ^ [_1549846, _1549848, _1549850] : [c_Wellfounded_OwfP(_1549846, hAPP(_1549848, 39780 ^ [_1549846, _1549848, _1549850])), 39787 ^ _776541 : [(39790 ^ _776541) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549846, tc_HOL_Obool)), c_Predicate_ODomainP(_1549846, _1549846, hAPP(_1549848, 39785 ^ [_1549846, _1549848, _1549850]))), c_Predicate_ORangeP(_1549846, _1549846, hAPP(_1549848, 39786 ^ [_1549846, _1549848, _1549850]))) = c_Orderings_Obot__class_Obot(tc_fun(_1549846, tc_HOL_Obool))], (39788 ^ _776541) ^ [] : [hAPP(_1549848, 39785 ^ [_1549846, _1549848, _1549850]) = hAPP(_1549848, 39786 ^ [_1549846, _1549848, _1549850])]], -(c_Wellfounded_OwfP(_1549846, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549850, tc_fun(_1549846, tc_fun(_1549846, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1549850, tc_HOL_Obool))), _1549848)))], (10226 ^ _776541) ^ [_952170, _952172, _952174, _952176, _952178, _952180, _952182] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_952170, _952172, _952174, _952176, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952170, tc_HOL_Obool)), _952178), hAPP(hAPP(c_Set_Oinsert(_952170), _952180), c_Orderings_Obot__class_Obot(tc_fun(_952170, tc_HOL_Obool))))), _952182)), hBOOL(hAPP(hAPP(c_member(_952170), _952180), _952178)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_952170, _952172, _952174, _952176, _952178), hAPP(hAPP(_952174, _952180), _952182))))], (38493 ^ _776541) ^ [_1514492, _1514494] : [-(hAPP(c_Relation_ORange(_1514492, _1514492), c_Relation_OId__on(_1514492, _1514494)) = _1514494)], (43504 ^ _776541) ^ [_1644107, _1644109, _1644111, _1644113] : [_1644111 = _1644113, -(hAPP(hAPP(c_List_Oappend(_1644107), _1644109), _1644111) = hAPP(hAPP(c_List_Oappend(_1644107), _1644109), _1644113))], (29993 ^ _776541) ^ [_1314436, _1314438, _1314440] : [class_Fields_Olinordered__field(_1314436), 29999 ^ _776541 : [(30002 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314436), _1314438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1314436), _1314440), 29998 ^ [_1314436, _1314438, _1314440])))], (30000 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314436), c_Groups_Ozero__class_Ozero(_1314436)), 29998 ^ [_1314436, _1314438, _1314440])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314436), _1314438), _1314440)))], (29791 ^ _776541) ^ [] : [-(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))], (23617 ^ _776541) ^ [_1204556, _1204558] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1204556), _1204558)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204556)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204558))))], (2480 ^ _776541) ^ [_812950, _812952, _812954, _812956] : [-(c_Divides_OnegDivAlg(_812956, _812952) = c_Divides_OnegDivAlg(_812954, _812950)), _812956 = _812954, _812952 = _812950], (12951 ^ _776541) ^ [_1005046, _1005048, _1005050] : [class_Lattices_Oab__semigroup__idem__mult(_1005046), -(_1005048 = c_Orderings_Obot__class_Obot(tc_fun(_1005046, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005046), _1005048)), -(hAPP(c_Finite__Set_Ofold1(_1005046, c_Groups_Otimes__class_Otimes(_1005046)), hAPP(hAPP(c_Set_Oinsert(_1005046), _1005050), _1005048)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005046), _1005050), hAPP(c_Finite__Set_Ofold1(_1005046, c_Groups_Otimes__class_Otimes(_1005046)), _1005048)))], (13662 ^ _776541) ^ [_1019806, _1019808, _1019810, _1019812] : [class_Groups_Oordered__ab__semigroup__add(_1019806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019806), _1019808), _1019810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019806), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019806), _1019808), _1019812)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019806), _1019810), _1019812))))], (14284 ^ _776541) ^ [_1033777, _1033779, _1033781, _1033783] : [class_Rings_Ocomm__semiring__1(_1033777), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033777), _1033779), _1033781)), _1033783) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033777), _1033779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033777), _1033781), _1033783)))], (32426 ^ _776541) ^ [_1360158, _1360160, _1360162, _1360164, _1360166] : [_1360158 = c_Orderings_Obot__class_Obot(tc_fun(_1360160, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360162, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360160, tc_fun(_1360162, tc_HOL_Obool)), _1360158), _1360164)), _1360166) = _1360166)], (43727 ^ _776541) ^ [_1649099, _1649101, _1649103] : [hBOOL(hAPP(c_List_Odistinct(_1649099), hAPP(hAPP(c_List_Oappend(_1649099), _1649101), _1649103))), 43730 ^ _776541 : [(43735 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1649099, tc_HOL_Obool)), hAPP(c_List_Oset(_1649099), _1649101)), hAPP(c_List_Oset(_1649099), _1649103)) = c_Orderings_Obot__class_Obot(tc_fun(_1649099, tc_HOL_Obool)))], (43733 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1649099), _1649103)))], (43731 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1649099), _1649101)))]]], (38412 ^ _776541) ^ [_1512912, _1512914] : [-(hAPP(c_List_Olexn(_1512912, _1512914), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1512912), tc_List_Olist(_1512912)), tc_HOL_Obool)))], (15724 ^ _776541) ^ [] : [-(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))))], (15136 ^ _776541) ^ [_1049798, _1049800] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049798), _1049800), 15139 ^ _776541 : [(15142 ^ _776541) ^ [] : [-(_1049800 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15140 ^ _776541) ^ [] : [-(_1049798 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (16588 ^ _776541) ^ [_1074922, _1074924, _1074926] : [16589 ^ _776541 : [(16592 ^ _776541) ^ [] : [_1074924 = _1074926], (16590 ^ _776541) ^ [] : [_1074922 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074922), _1074924) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074922), _1074926))], (48506 ^ _776541) ^ [_1753959, _1753961, _1753963, _1753965, _1753967] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1753959, _1753961, _1753963), _1753965), _1753967)), -(hBOOL(hAPP(hAPP(_1753963, _1753967), _1753965)))], (1194 ^ _776541) ^ [_794330, _794332] : [-(class_Rings_Olinordered__idom(_794330)), _794332 = _794330, class_Rings_Olinordered__idom(_794332)], (27164 ^ _776541) ^ [_1265454] : [c_Nat__Transfer_Onat__set(_1265454), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1265454) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265454)))], (49123 ^ _776541) ^ [_1767569, _1767571, _1767573, _1767575] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1767569), _1767571), _1767573), _1767575) = 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(_1767569)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1767569), _1767571)))], (8811 ^ _776541) ^ [_927994, _927996, _927998, _928000] : [class_Lattices_Odistrib__lattice(_927994), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927994), _927996), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927994), _927998), _928000)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927994), _927996), _927998)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927994), _927996), _928000)))], (43860 ^ _776541) ^ [_1652763, _1652765, _1652767, _1652769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652763), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652765)), _1652767))), -(hAPP(hAPP(c_List_Olist__update(_1652765, _1652767), _1652763), _1652769) = hAPP(hAPP(c_List_Oappend(_1652765), hAPP(hAPP(c_List_Otake(_1652765), _1652763), _1652767)), hAPP(hAPP(c_List_Olist_OCons(_1652765), _1652769), hAPP(hAPP(c_List_Odrop(_1652765), hAPP(c_Nat_OSuc, _1652763)), _1652767))))], (26288 ^ _776541) ^ [_1251273, _1251275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251273)), 26291 ^ _776541 : [(26298 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251273), _1251275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251273)), hAPP(c_Int_Onat, _1251275))))], (26292 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251273)), hAPP(c_Int_Onat, _1251275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251273), _1251275)))]]], (27997 ^ _776541) ^ [_1279659, _1279661] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279659), c_Int_OPls))), 28000 ^ _776541 : [(28007 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279661), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279659)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279661)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1279659), _1279661)))], (28001 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279661), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279659)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279661)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279659))]]], (3680 ^ _776541) ^ [_831736, _831738] : [_831738 = _831736, -(c_Orderings_Oord__class_Omax(_831738) = c_Orderings_Oord__class_Omax(_831736))], (14815 ^ _776541) ^ [_1043665, _1043667, _1043669] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043665), _1043667)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043665), _1043669)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043667), _1043669))], (27028 ^ _776541) ^ [_1263370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263370)), -(c_Nat__Transfer_Ois__nat(_1263370))], (42996 ^ _776541) ^ [_1633557, _1633559, _1633561] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633557), tc_List_Olist(_1633557))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633557), tc_List_Olist(_1633557)), c_List_Olist_ONil(_1633557)), _1633559)), c_List_Olistrel(_1633557, _1633561))), -(_1633559 = c_List_Olist_ONil(_1633557))], (19855 ^ _776541) ^ [_1134843, _1134845] : [class_Groups_Osgn__if(_1134843), 19858 ^ _776541 : [(19865 ^ _776541) ^ [] : [-(_1134845 = c_Groups_Ozero__class_Ozero(_1134843)), 19868 ^ _776541 : [(19875 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134843), c_Groups_Ozero__class_Ozero(_1134843)), _1134845))), -(c_Groups_Osgn__class_Osgn(_1134843, _1134845) = hAPP(c_Groups_Ouminus__class_Ouminus(_1134843), c_Groups_Oone__class_Oone(_1134843)))], (19869 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134843), c_Groups_Ozero__class_Ozero(_1134843)), _1134845)), -(c_Groups_Osgn__class_Osgn(_1134843, _1134845) = c_Groups_Oone__class_Oone(_1134843))]]], (19859 ^ _776541) ^ [] : [_1134845 = c_Groups_Ozero__class_Ozero(_1134843), -(c_Groups_Osgn__class_Osgn(_1134843, _1134845) = c_Groups_Ozero__class_Ozero(_1134843))]]], (34037 ^ _776541) ^ [_1408410, _1408412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408410), 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)), _1408412)), -(c_Divides_OnegDivAlg(_1408410, _1408412) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1408410), _1408412)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1408410, _1408412)))], (28529 ^ _776541) ^ [_1288446, _1288448] : [class_Int_Onumber__ring(_1288446), -(hAPP(c_Int_Onumber__class_Onumber__of(_1288446), c_Int_OBit1(_1288448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288446), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288446), c_Groups_Oone__class_Oone(_1288446)), hAPP(c_Int_Onumber__class_Onumber__of(_1288446), _1288448))), hAPP(c_Int_Onumber__class_Onumber__of(_1288446), _1288448)))], (46107 ^ _776541) ^ [_1702691, _1702693, _1702695, _1702697] : [-(hBOOL(hAPP(_1702691, _1702693))), -(hAPP(c_List_Ofilter(_1702695, _1702691), hAPP(hAPP(c_List_Olist_OCons(_1702695), _1702693), _1702697)) = hAPP(c_List_Ofilter(_1702695, _1702691), _1702697))], (47460 ^ _776541) ^ [_1730898, _1730900, _1730902, _1730904, _1730906] : [class_Groups_Omonoid__add(_1730898), 47466 ^ _776541 : [(47471 ^ _776541) ^ [] : [hAPP(_1730906, 47465 ^ [_1730898, _1730900, _1730902, _1730904, _1730906]) = c_Groups_Ozero__class_Ozero(_1730898)], (47469 ^ _776541) ^ [] : [hBOOL(hAPP(_1730904, 47465 ^ [_1730898, _1730900, _1730902, _1730904, _1730906]))], (47467 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730900), 47465 ^ [_1730898, _1730900, _1730902, _1730904, _1730906]), hAPP(c_List_Oset(_1730900), _1730902))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1730898), hAPP(hAPP(c_List_Omap(_1730900, _1730898), _1730906), hAPP(c_List_Ofilter(_1730900, _1730904), _1730902))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1730898), hAPP(hAPP(c_List_Omap(_1730900, _1730898), _1730906), _1730902)))], (5741 ^ _776541) ^ [_867084] : [-(c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(_867084), tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867084, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867084)), tc_HOL_Obool), c_Hoare__Mirabelle_ORep__triple(_867084), c_Hoare__Mirabelle_OAbs__triple(_867084), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867084, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867084)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867084))))], (3076 ^ _776541) ^ [_822292, _822294, _822296, _822298] : [-(c_Wellfounded_Oacc(_822298, _822294) = c_Wellfounded_Oacc(_822296, _822292)), _822298 = _822296, _822294 = _822292], (45894 ^ _776541) ^ [_1697206, _1697208, _1697210, _1697212] : [class_Orderings_Olinorder(_1697206), -(hAPP(c_List_Oset(_1697208), c_List_Olinorder__class_Osort__key(_1697208, _1697206, _1697210, _1697212)) = hAPP(c_List_Oset(_1697208), _1697212))], (3096 ^ _776541) ^ [_822590, _822592, _822594, _822596, _822598, _822600] : [-(c_List_Oset__Cons(_822600, _822596, _822592) = c_List_Oset__Cons(_822598, _822594, _822590)), _822600 = _822598, _822596 = _822594, _822592 = _822590], (13324 ^ _776541) ^ [_1012870, _1012872, _1012874, _1012876, _1012878] : [class_Groups_Ocomm__monoid__mult(_1012870), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012872), _1012874)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012872), _1012876)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1012872, tc_HOL_Obool)), _1012874), _1012876) = c_Orderings_Obot__class_Obot(tc_fun(_1012872, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012872, _1012870), _1012878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012872, tc_HOL_Obool)), _1012874), _1012876)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012870), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012872, _1012870), _1012878), _1012874)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012872, _1012870), _1012878), _1012876)))], (37316 ^ _776541) ^ [_1486851, _1486853, _1486855, _1486857, _1486859, _1486861] : [c_Fun_Oinj__on(_1486851, _1486853, _1486855, _1486857), hBOOL(hAPP(hAPP(c_member(_1486851), _1486859), _1486857)), hBOOL(hAPP(hAPP(c_member(_1486851), _1486861), _1486857)), 37327 ^ _776541 : [(37334 ^ _776541) ^ [] : [_1486859 = _1486861, -(hAPP(_1486855, _1486859) = hAPP(_1486855, _1486861))], (37328 ^ _776541) ^ [] : [hAPP(_1486855, _1486859) = hAPP(_1486855, _1486861), -(_1486859 = _1486861)]]], (14925 ^ _776541) ^ [_1045793, _1045795, _1045797] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045793), _1045795)), _1045797) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045793), _1045797)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045795), _1045797)))], (44777 ^ _776541) ^ [_1671773, _1671775, _1671777, _1671779, _1671781] : [class_Groups_Oab__group__add(_1671773), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671773), hAPP(hAPP(c_List_Omap(_1671775, _1671773), hAPP(hAPP(c_COMBS(_1671775, _1671773, _1671773), hAPP(hAPP(c_COMBB(_1671773, tc_fun(_1671773, _1671773), _1671775), c_Groups_Ominus__class_Ominus(_1671773)), _1671777)), _1671779)), _1671781)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1671773), hAPP(c_List_Omonoid__add__class_Olistsum(_1671773), hAPP(hAPP(c_List_Omap(_1671775, _1671773), _1671777), _1671781))), hAPP(c_List_Omonoid__add__class_Olistsum(_1671773), hAPP(hAPP(c_List_Omap(_1671775, _1671773), _1671779), _1671781))))], (8151 ^ _776541) ^ [_915548, _915550, _915552] : [class_Complete__Lattice_Ocomplete__lattice(_915548), -(c_Complete__Lattice_OInf__class_OInf(_915548, hAPP(hAPP(c_Set_Oinsert(_915548), _915550), hAPP(hAPP(c_Set_Oinsert(_915548), _915552), c_Orderings_Obot__class_Obot(tc_fun(_915548, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_915548), _915550), _915552))], (46568 ^ _776541) ^ [_1712809, _1712811, _1712813, _1712815] : [class_Orderings_Olinorder(_1712809), 46571 ^ _776541 : [(46580 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1712809, hAPP(hAPP(c_List_Olist_OCons(_1712809), _1712811), hAPP(hAPP(c_List_Olist_OCons(_1712809), _1712813), _1712815)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712809), _1712811), _1712813)), c_List_Olinorder__class_Osorted(_1712809, hAPP(hAPP(c_List_Olist_OCons(_1712809), _1712813), _1712815))], (46572 ^ _776541) ^ [] : [c_List_Olinorder__class_Osorted(_1712809, hAPP(hAPP(c_List_Olist_OCons(_1712809), _1712811), hAPP(hAPP(c_List_Olist_OCons(_1712809), _1712813), _1712815))), 46575 ^ _776541 : [(46578 ^ _776541) ^ [] : [-(c_List_Olinorder__class_Osorted(_1712809, hAPP(hAPP(c_List_Olist_OCons(_1712809), _1712813), _1712815)))], (46576 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712809), _1712811), _1712813)))]]]]], (1614 ^ _776541) ^ [_799580, _799582] : [-(class_Rings_Olinordered__semidom(_799580)), _799582 = _799580, class_Rings_Olinordered__semidom(_799582)], (25956 ^ _776541) ^ [_1245867] : [-(hBOOL(hAPP(_1245867, 25963 ^ [_1245867]))), 25957 ^ _776541 : [(25958 ^ _776541) ^ [_1245919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245919)), hBOOL(hAPP(_1245867, hAPP(c_Int_Onat, _1245919)))]]], (22305 ^ _776541) ^ [_1180911, _1180913] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180911), _1180913) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180913), _1180911))], (37048 ^ _776541) ^ [_1480562] : [-(c_Equiv__Relations_Oequivp(_1480562, c_fequal))], (9262 ^ _776541) ^ [_936109, _936111, _936113] : [class_Orderings_Olinorder(_936109), 9265 ^ _776541 : [(9266 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936109), _936111), _936113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936109), _936113), _936111))), -(_936111 = _936113)], (9276 ^ _776541) ^ [] : [9277 ^ _776541 : [(9280 ^ _776541) ^ [] : [_936111 = _936113], (9278 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936109), _936113), _936111))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936109), _936111), _936113))]]], (38165 ^ _776541) ^ [_1507478, _1507480, _1507482] : [c_Wellfounded_Owf(_1507478, _1507480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507478, _1507478), tc_HOL_Obool)), _1507482), _1507480)), -(c_Wellfounded_Owf(_1507478, _1507482))], (19418 ^ _776541) ^ [_1127083, _1127085, _1127087, _1127089] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1127083, _1127087)), c_Sum__Type_OPlus(_1127083, _1127087, _1127085, _1127089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1127083), _1127085)), hAPP(c_Finite__Set_Ocard(_1127087), _1127089))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127083), _1127085)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127087), _1127089))], (30022 ^ _776541) ^ [_1314949, _1314951] : [class_Orderings_Olinorder(_1314949), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314949), _1314951), _1314951) = _1314951)], (32149 ^ _776541) ^ [_1354267, _1354269, _1354271] : [class_Orderings_Olinorder(_1354267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354267), _1354269)), -(_1354269 = c_Orderings_Obot__class_Obot(tc_fun(_1354267, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354267), _1354271)), -(_1354271 = c_Orderings_Obot__class_Obot(tc_fun(_1354267, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354267, tc_HOL_Obool)), _1354269), _1354271) = c_Orderings_Obot__class_Obot(tc_fun(_1354267, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1354267, c_Orderings_Oord__class_Omax(_1354267), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354267, tc_HOL_Obool)), _1354269), _1354271)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354267), c_Big__Operators_Olattice_OSup__fin(_1354267, c_Orderings_Oord__class_Omax(_1354267), _1354269)), c_Big__Operators_Olattice_OSup__fin(_1354267, c_Orderings_Oord__class_Omax(_1354267), _1354271)))], (24974 ^ _776541) ^ [_1228809, _1228811, _1228813] : [class_Divides_Osemiring__div(_1228809), -(c_Divides_Odiv__class_Omod(_1228809, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228809), _1228811), _1228813), _1228811) = c_Groups_Ozero__class_Ozero(_1228809))], (45970 ^ _776541) ^ [_1698767, _1698769, _1698771, _1698773, _1698775] : [class_Orderings_Olinorder(_1698767), -(c_List_Olinorder__class_Osort__key(_1698769, _1698767, _1698771, hAPP(hAPP(c_List_Olist_OCons(_1698769), _1698773), _1698775)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698769, _1698767, _1698771), _1698773), c_List_Olinorder__class_Osort__key(_1698769, _1698767, _1698771, _1698775)))], (44834 ^ _776541) ^ [_1673474, _1673476, _1673478, _1673480, _1673482, _1673484] : [-(hAPP(hAPP(c_List_Omap(_1673474, _1673476), _1673478), hAPP(hAPP(c_List_Olist__update(_1673474, _1673480), _1673482), _1673484)) = hAPP(hAPP(c_List_Olist__update(_1673476, hAPP(hAPP(c_List_Omap(_1673474, _1673476), _1673478), _1673480)), _1673482), hAPP(_1673478, _1673484)))], (23161 ^ _776541) ^ [] : [-(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))))], (25251 ^ _776541) ^ [_1233664, _1233666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233664)), -(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, _1233666, _1233664))))], (41777 ^ _776541) ^ [_1600067, _1600069, _1600071] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600067)), hAPP(hAPP(c_List_Olist_OCons(_1600067), _1600069), _1600071)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600067)), _1600071)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34886 ^ _776541) ^ [_1427548, _1427550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427548)), 34889 ^ _776541 : [(34896 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427550))), 34899 ^ _776541 : [(34906 ^ _776541) ^ [] : [-(_1427548 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1427548, _1427550) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427548), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427550))))], (34900 ^ _776541) ^ [] : [_1427548 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1427548, _1427550) = 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)))]]], (34890 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427550)), -(c_Divides_Odivmod__int(_1427548, _1427550) = c_Divides_OposDivAlg(_1427548, _1427550))]]], (36428 ^ _776541) ^ [_1464611, _1464613, _1464615, _1464617] : [c_FunDef_Oreduction__pair(_1464611, _1464613), -(c_FunDef_Oreduction__pair(_1464615, hAPP(hAPP(c_FunDef_Orp__inv__image(_1464611, _1464615), _1464613), _1464617)))], (27671 ^ _776541) ^ [_1274209, _1274211, _1274213, _1274215, _1274217] : [class_Groups_Oordered__ab__group__add__abs(_1274209), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274209), hAPP(c_Groups_Oabs__class_Oabs(_1274209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274209), _1274211), _1274213)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274209), _1274215), _1274217)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274209), hAPP(c_Groups_Oabs__class_Oabs(_1274209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274209), _1274211), _1274215))), hAPP(c_Groups_Oabs__class_Oabs(_1274209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274209), _1274213), _1274217))))))], (15886 ^ _776541) ^ [_1064101, _1064103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064103)), -(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), _1064103), _1064101))))], (50899 ^ _776541) ^ [_1807449, _1807451, _1807453] : [50901 ^ _776541 : [(50904 ^ _776541) ^ [] : [hBOOL(hAPP(_1807449, 50900 ^ [_1807449, _1807451, _1807453]))], (50902 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50900 ^ [_1807449, _1807451, _1807453]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1807451), _1807453))))]], -(c_List_Oall__interval__nat(_1807449, _1807451, _1807453))], (42783 ^ _776541) ^ [_1628652, _1628654, _1628656, _1628658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628652), tc_List_Olist(_1628652))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628652), tc_List_Olist(_1628652)), _1628654), _1628656)), c_List_Olistrel1(_1628652, _1628658))), 42788 ^ _776541 : [(42793 ^ _776541) ^ [] : [-(_1628656 = hAPP(hAPP(c_List_Olist__update(_1628652, _1628654), 42787 ^ [_1628652, _1628654, _1628656, _1628658]), 42786 ^ [_1628652, _1628654, _1628656, _1628658]))], (42791 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42787 ^ [_1628652, _1628654, _1628656, _1628658]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628652)), _1628654))))], (42789 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628652, _1628652)), hAPP(hAPP(c_Product__Type_OPair(_1628652, _1628652), hAPP(hAPP(c_List_Onth(_1628652), _1628654), 42787 ^ [_1628652, _1628654, _1628656, _1628658])), 42786 ^ [_1628652, _1628654, _1628656, _1628658])), _1628658)))]]], (42357 ^ _776541) ^ [_1617191, _1617193, _1617195] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617191)), hAPP(hAPP(c_List_Otake(_1617191), _1617193), _1617195)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617191)), _1617195)), _1617193))], (21815 ^ _776541) ^ [_1171836, _1171838] : [_1171836 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1171838), _1171836) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6510 ^ _776541) ^ [_881663, _881665] : [class_Orderings_Opreorder(_881663), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881663), _881665), _881665)))], (48544 ^ _776541) ^ [_1754708, _1754710, _1754712, _1754714, _1754716] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754708, _1754710, hAPP(hAPP(c_COMBC(_1754708, tc_fun(tc_prod(_1754708, _1754710), tc_HOL_Obool), tc_fun(_1754710, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1754710, tc_fun(tc_fun(tc_prod(_1754708, _1754710), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1754708, _1754710), tc_HOL_Obool), tc_fun(_1754710, tc_HOL_Obool)), _1754708), c_COMBC(_1754710, tc_fun(tc_prod(_1754708, _1754710), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1754710, tc_prod(_1754708, _1754710)), tc_fun(_1754710, tc_fun(tc_fun(tc_prod(_1754708, _1754710), tc_HOL_Obool), tc_HOL_Obool)), _1754708), hAPP(c_COMBB(tc_prod(_1754708, _1754710), tc_fun(tc_fun(tc_prod(_1754708, _1754710), tc_HOL_Obool), tc_HOL_Obool), _1754710), c_member(tc_prod(_1754708, _1754710)))), c_Product__Type_OPair(_1754708, _1754710)))), _1754712)), _1754714), _1754716)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1754710, _1754708)), hAPP(hAPP(c_Product__Type_OPair(_1754710, _1754708), _1754714), _1754716)), hAPP(c_Relation_Oconverse(_1754708, _1754710), _1754712))))], (37949 ^ _776541) ^ [_1501234, _1501236, _1501238, _1501240, _1501242, _1501244, _1501246] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1501234, _1501236, _1501238), hAPP(hAPP(c_Relation_Orel__comp(_1501234, _1501240, _1501236), _1501242), _1501244)), _1501246) = hAPP(hAPP(c_Relation_Orel__comp(_1501234, _1501240, _1501238), _1501242), hAPP(hAPP(c_Relation_Orel__comp(_1501240, _1501236, _1501238), _1501244), _1501246)))], (7522 ^ _776541) ^ [_900520, _900522, _900524, _900526] : [hBOOL(hAPP(hAPP(c_member(_900520), _900522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900520, tc_HOL_Obool)), _900524), _900526))), 7525 ^ _776541 : [(7528 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900520), _900522), _900526))], (7526 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900520), _900522), _900524)))]]], (44094 ^ _776541) ^ [_1658603, _1658605, _1658607] : [-(_1658603 = c_List_Olist_ONil(_1658605)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658607), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658605)), _1658603))), -(hAPP(c_List_Ohd(_1658605), hAPP(hAPP(c_List_Odrop(_1658605), _1658607), _1658603)) = hAPP(hAPP(c_List_Onth(_1658605), _1658603), _1658607))], (39217 ^ _776541) ^ [_1533682, _1533684, _1533686, _1533688] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1533682, _1533684)), hAPP(hAPP(c_Product__Type_OSigma(_1533682, _1533684), _1533686), hAPP(c_COMBK(tc_fun(_1533684, tc_HOL_Obool), _1533682), _1533688)))), -(_1533688 = c_Orderings_Obot__class_Obot(tc_fun(_1533684, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533682), _1533686)))], (21155 ^ _776541) ^ [_1159244, _1159246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1159244), _1159246)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1159244, tc_HOL_Obool)), hAPP(c_Set_OPow(_1159244), _1159246)) = 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(_1159244), _1159246)))], (46930 ^ _776541) ^ [_1719513, _1719515, _1719517] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719513), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719513))), _1719515))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719517), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719513))), _1719515))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719513), _1719513), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719513), tc_Nat_Onat, _1719513), c_List_Onth(_1719513)), _1719517)), hAPP(c_List_Ofilter(tc_List_Olist(_1719513), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1719513)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719517)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719513)))), c_List_Otranspose(_1719513, _1719515))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719513)), _1719515), _1719517))], (42593 ^ _776541) ^ [_1624584] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1624584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42596 ^ _776541 : [(42597 ^ _776541) ^ [_1624659] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1624659), hAPP(c_List_Oset(tc_Nat_Onat), _1624584))), -(_1624659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44262 ^ _776541) ^ [_1661637, _1661639, _1661641, _1661643, _1661645] : [class_Orderings_Olinorder(_1661637), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661639, _1661637, _1661641), _1661643), _1661645) = c_List_Olist_ONil(_1661639)], (31347 ^ _776541) ^ [_1339224, _1339226, _1339228] : [class_Orderings_Olinorder(_1339224), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339224), _1339226), _1339228) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339224), _1339228), _1339226))], (16438 ^ _776541) ^ [_1072771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072771)), _1072771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3296 ^ _776541) ^ [_825742, _825744, _825746, _825748] : [-(c_Random_Oselect(_825748, _825744) = c_Random_Oselect(_825746, _825742)), _825748 = _825746, _825744 = _825742], (7025 ^ _776541) ^ [_890778, _890780, _890782] : [class_Orderings_Olinorder(_890778), 7028 ^ _776541 : [(7035 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890778), _890780), _890782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890778, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_890778), _890780)), hAPP(c_SetInterval_Oord__class_OlessThan(_890778), _890782))))], (7029 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890778, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_890778), _890780)), hAPP(c_SetInterval_Oord__class_OlessThan(_890778), _890782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890778), _890780), _890782)))]]], (48942 ^ _776541) ^ [_1763281, _1763283, _1763285] : [-(c_List_Olist__ex1(_1763281, _1763283, _1763285)), 48943 ^ _776541 : [(48944 ^ _776541) ^ [_1763375] : [hBOOL(hAPP(hAPP(c_member(_1763281), _1763375), hAPP(c_List_Oset(_1763281), _1763285))), hBOOL(hAPP(_1763283, _1763375)), 48952 ^ _776541 : [(48957 ^ _776541) ^ [] : [48951 ^ [_1763281, _1763283, _1763285, _1763375] = _1763375], (48955 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1763283, 48951 ^ [_1763281, _1763283, _1763285, _1763375])))], (48953 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763281), 48951 ^ [_1763281, _1763283, _1763285, _1763375]), hAPP(c_List_Oset(_1763281), _1763285))))]]]]], (32298 ^ _776541) ^ [_1357316, _1357318, _1357320, _1357322, _1357324, _1357326, _1357328, _1357330] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357316, tc_fun(_1357318, tc_fun(_1357320, tc_HOL_Obool))), _1357322), _1357324), _1357326), _1357328)), hBOOL(hAPP(hAPP(c_member(_1357316), _1357330), _1357322)), -(hBOOL(hAPP(hAPP(hAPP(_1357324, _1357330), _1357326), _1357328)))], (42622 ^ _776541) ^ [_1625099, _1625101, _1625103] : [class_Groups_Omonoid__add(_1625099), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1625099), hAPP(hAPP(c_List_Olist_OCons(_1625099), _1625101), _1625103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1625099), _1625101), hAPP(c_List_Omonoid__add__class_Olistsum(_1625099), _1625103)))], (29277 ^ _776541) ^ [_1301207, _1301209] : [class_Groups_Omonoid__mult(_1301207), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301207), _1301209), 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(_1301207), _1301209), _1301209))], (23163 ^ _776541) ^ [_1196133, _1196135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196135)), -(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), _1196133), _1196135))))], (31543 ^ _776541) ^ [_1342860, _1342862, _1342864] : [class_Orderings_Olinorder(_1342860), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342860), _1342862), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342860), _1342864), _1342862))))], (7244 ^ _776541) ^ [_894746, _894748, _894750, _894752, _894754] : [-(hAPP(hAPP(c_Set_Oinsert(_894746), _894748), hAPP(hAPP(c_Set_Oinsert(_894746), _894750), c_Orderings_Obot__class_Obot(tc_fun(_894746, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_894746), _894752), hAPP(hAPP(c_Set_Oinsert(_894746), _894754), c_Orderings_Obot__class_Obot(tc_fun(_894746, tc_HOL_Obool))))), 7245 ^ _776541 : [(7252 ^ _776541) ^ [] : [_894748 = _894754, _894750 = _894752], (7246 ^ _776541) ^ [] : [_894748 = _894752, _894750 = _894754]]], (12776 ^ _776541) ^ [_1001949, _1001951] : [class_Lattices_Olattice(_1001949), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001949), _1001951)), -(c_Big__Operators_Olattice__class_OSup__fin(_1001949, _1001951) = hAPP(c_Finite__Set_Ofold1(_1001949, c_Lattices_Osemilattice__sup__class_Osup(_1001949)), _1001951))], (42311 ^ _776541) ^ [_1616156, _1616158, _1616160, _1616162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1616156), _1616158)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616160, tc_HOL_Obool)), hAPP(c_List_Oset(_1616160), hAPP(hAPP(c_List_Otake(_1616160), _1616156), _1616162))), hAPP(c_List_Oset(_1616160), hAPP(hAPP(c_List_Otake(_1616160), _1616158), _1616162)))))], (20027 ^ _776541) ^ [_1138127, _1138129, _1138131, _1138133] : [class_Fields_Olinordered__field__inverse__zero(_1138127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138127), _1138129), _1138131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138127), c_Groups_Ozero__class_Ozero(_1138127)), _1138133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138127), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138127), _1138129), _1138133)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138127), _1138131), _1138133))))], (4184 ^ _776541) ^ [_839944, _839946, _839948, _839950, _839952, _839954] : [-(c_List_Osplice(_839954, _839950, _839946) = c_List_Osplice(_839952, _839948, _839944)), _839954 = _839952, _839950 = _839948, _839946 = _839944], (16030 ^ _776541) ^ [_1066525, _1066527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066525), _1066527)), -(hAPP(c_Nat_OSuc, _1066525) = _1066527), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1066525)), _1066527)))], (40224 ^ _776541) ^ [_1560315, _1560317, _1560319, _1560321, _1560323, _1560325] : [c_Finite__Set_Ofolding(_1560315, _1560317, _1560319, _1560321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560315), _1560323)), -(hAPP(_1560321, hAPP(hAPP(c_Set_Oinsert(_1560315), _1560325), _1560323)) = hAPP(c_Fun_Ocomp(_1560317, _1560317, _1560317, hAPP(_1560321, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1560315, tc_HOL_Obool)), _1560323), hAPP(hAPP(c_Set_Oinsert(_1560315), _1560325), c_Orderings_Obot__class_Obot(tc_fun(_1560315, tc_HOL_Obool)))))), hAPP(_1560319, _1560325)))], (20467 ^ _776541) ^ [_1145854, _1145856, _1145858] : [class_Fields_Olinordered__field(_1145854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145854), _1145856), c_Groups_Ozero__class_Ozero(_1145854))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145854), c_Groups_Ozero__class_Ozero(_1145854)), _1145858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145854), _1145856), _1145858)), c_Groups_Ozero__class_Ozero(_1145854))))], (28383 ^ _776541) ^ [_1286053, _1286055] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1286053), _1286055)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1286053)), c_Int_OBit1(_1286055))))], (13596 ^ _776541) ^ [_1018515, _1018517, _1018519, _1018521] : [class_Groups_Ocancel__semigroup__add(_1018515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018515), _1018517), _1018519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018515), _1018521), _1018519), -(_1018517 = _1018521)], (28613 ^ _776541) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (24968 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (29849 ^ _776541) ^ [_1311712] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1311712)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1311712)], (33699 ^ _776541) ^ [_1399347, _1399349, _1399351] : [-(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)), _1399347)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1399349), _1399351)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399349), _1399347)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399351), _1399347)))], (28149 ^ _776541) ^ [_1281999] : [class_Rings_Osemiring__1(_1281999), -(hBOOL(hAPP(hAPP(c_member(_1281999), c_Groups_Ozero__class_Ozero(_1281999)), c_Nat_Osemiring__1__class_ONats(_1281999))))], (38237 ^ _776541) ^ [_1508752] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1508752)))], (48542 ^ _776541) ^ [_1754629, _1754631, _1754633, _1754635, _1754637] : [-(c_Predicate_Oconversep(_1754629, _1754631, c_Predicate_Opred__comp(_1754629, _1754633, _1754631, _1754635, _1754637)) = c_Predicate_Opred__comp(_1754631, _1754633, _1754629, c_Predicate_Oconversep(_1754633, _1754631, _1754637), c_Predicate_Oconversep(_1754629, _1754633, _1754635)))], (46359 ^ _776541) ^ [_1708929, _1708931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708929)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708931)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708929), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708931)) = c_List_Olist_ONil(tc_Nat_Onat))], (48468 ^ _776541) ^ [_1753070, _1753072] : [-(c_List_Osplice(_1753070, c_List_Olist_ONil(_1753070), _1753072) = _1753072)], (41410 ^ _776541) ^ [_1589724, _1589726, _1589728, _1589730] : [-(hAPP(hAPP(c_Nat_Ocompow(_1589724, _1589724), _1589726), hAPP(hAPP(c_Nat_Ocompow(_1589724, _1589724), _1589728), _1589730)) = hAPP(hAPP(c_Nat_Ocompow(_1589724, _1589724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1589728), _1589726)), _1589730))], (52411 ^ _776541) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (26370 ^ _776541) ^ [_1252485, _1252487] : [-(_1252485 = hAPP(c_Int_Onat, _1252487)), 26373 ^ _776541 : [(26376 ^ _776541) ^ [] : [_1252487 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252485)], (26374 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252487)))]], 26377 ^ _776541 : [(26380 ^ _776541) ^ [] : [_1252485 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26378 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252487))]]], (13916 ^ _776541) ^ [_1025059, _1025061, _1025063, _1025065, _1025067, _1025069] : [class_Rings_Oordered__ring(_1025059), 13919 ^ _776541 : [(13926 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025059), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025059), _1025061), _1025067)), _1025063)), _1025065)), _1025069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025059), _1025061), _1025063)), _1025065)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025059), _1025067), _1025063)), _1025069))))], (13920 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025059), _1025061), _1025063)), _1025065)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025059), _1025067), _1025063)), _1025069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025059), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025059), _1025061), _1025067)), _1025063)), _1025065)), _1025069)))]]], (43498 ^ _776541) ^ [_1643998, _1644000, _1644002, _1644004] : [hAPP(hAPP(c_List_Oappend(_1643998), _1644000), _1644002) = hAPP(hAPP(c_List_Oappend(_1643998), _1644000), _1644004), -(_1644002 = _1644004)], (29093 ^ _776541) ^ [_1298020] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1298020)), c_Int_OMin))], (15563 ^ _776541) ^ [_1058508, _1058510, _1058512, _1058514, _1058516] : [class_Groups_Ocomm__monoid__mult(_1058508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058510), _1058512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1058510, tc_HOL_Obool)), _1058514), _1058512)), 15577 ^ _776541 : [(15580 ^ _776541) ^ [] : [hAPP(_1058516, 15576 ^ [_1058508, _1058510, _1058512, _1058514, _1058516]) = c_Groups_Oone__class_Oone(_1058508)], (15578 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1058510), 15576 ^ [_1058508, _1058510, _1058512, _1058514, _1058516]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058510, tc_HOL_Obool)), _1058512), _1058514))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058510, _1058508), _1058516), _1058514) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058510, _1058508), _1058516), _1058512))], (38792 ^ _776541) ^ [_1522247, _1522249, _1522251] : [-(hAPP(c_Set_Oimage(tc_prod(_1522247, _1522249), _1522247, c_Product__Type_Ofst(_1522247, _1522249)), _1522251) = hAPP(c_Relation_ODomain(_1522247, _1522249), _1522251))], (41897 ^ _776541) ^ [_1603983, _1603985] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1603983), tc_List_Olist(_1603983)), tc_HOL_Obool)), c_List_Olistrel1(_1603983, c_Transitive__Closure_Ortrancl(_1603983, _1603985))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603983), c_List_Olistrel1(_1603983, _1603985)))))], (20401 ^ _776541) ^ [_1144585, _1144587, _1144589, _1144591, _1144593] : [class_Fields_Olinordered__field(_1144585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), c_Groups_Ozero__class_Ozero(_1144585)), _1144587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144585), _1144587), _1144589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), c_Groups_Ozero__class_Ozero(_1144585)), _1144591)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), _1144591), _1144593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144585), _1144587), _1144593)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144585), _1144589), _1144591))))], (44180 ^ _776541) ^ [_1659977, _1659979, _1659981] : [-(hAPP(c_List_Oset(_1659977), hAPP(c_List_Orotate(_1659977, _1659979), _1659981)) = hAPP(c_List_Oset(_1659977), _1659981))], (51999 ^ _776541) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (44411 ^ _776541) ^ [_1664710, _1664712] : [class_Complete__Lattice_Ocomplete__lattice(_1664710), -(c_Complete__Lattice_OSup__class_OSup(_1664710, hAPP(c_List_Oset(_1664710), _1664712)) = hAPP(c_List_Ofoldl(_1664710, _1664710, c_Lattices_Osemilattice__sup__class_Osup(_1664710), c_Orderings_Obot__class_Obot(_1664710)), _1664712))], (31377 ^ _776541) ^ [_1339835, _1339837, _1339839, _1339841] : [class_Orderings_Olinorder(_1339835), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339835), _1339837), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339835), _1339839), _1339841)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339835), _1339839), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339835), _1339837), _1339841)))], (41027 ^ _776541) ^ [_1580391, _1580393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1580391), _1580393)), -(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), _1580391), _1580393)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (30140 ^ _776541) ^ [_1317259, _1317261, _1317263, _1317265] : [class_Orderings_Olinorder(_1317259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317259), _1317261), _1317263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317259), _1317261), _1317265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317259), _1317261), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317259), _1317263), _1317265))))], (36583 ^ _776541) ^ [_1469767, _1469769] : [c_Relation_Oirrefl(_1469767, _1469769), 36586 ^ _776541 : [(36587 ^ _776541) ^ [_1469849] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1469767, _1469767)), hAPP(hAPP(c_Product__Type_OPair(_1469767, _1469767), _1469849), _1469849)), _1469769))]]], (21036 ^ _776541) ^ [_1156609, _1156611, _1156613] : [class_Fields_Olinordered__field__inverse__zero(_1156609), 21042 ^ _776541 : [(21047 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156609), 21041 ^ [_1156609, _1156611, _1156613]), _1156611)), _1156613))], (21045 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156609), 21041 ^ [_1156609, _1156611, _1156613]), c_Groups_Oone__class_Oone(_1156609))))], (21043 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156609), c_Groups_Ozero__class_Ozero(_1156609)), 21041 ^ [_1156609, _1156611, _1156613])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156609), _1156611), _1156613)))], (44711 ^ _776541) ^ [_1670349, _1670351, _1670353, _1670355] : [-(_1670349 = c_List_Olist_ONil(_1670351)), -(c_List_Olast(_1670353, hAPP(hAPP(c_List_Omap(_1670351, _1670353), _1670355), _1670349)) = hAPP(_1670355, c_List_Olast(_1670351, _1670349)))], (1844 ^ _776541) ^ [_802455, _802457] : [-(class_Groups_Ominus(_802455)), _802457 = _802455, class_Groups_Ominus(_802457)], (30742 ^ _776541) ^ [_1327991, _1327993, _1327995] : [class_Orderings_Olinorder(_1327991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327991, tc_HOL_Obool)), _1327993), _1327995)), -(_1327993 = c_Orderings_Obot__class_Obot(tc_fun(_1327991, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327991), _1327995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327991), c_Big__Operators_Olinorder__class_OMin(_1327991, _1327995)), c_Big__Operators_Olinorder__class_OMin(_1327991, _1327993))))], (17759 ^ _776541) ^ [_1096211, _1096213] : [class_Rings_Olinordered__idom(_1096211), 17762 ^ _776541 : [(17769 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096211), _1096213), c_Groups_Ozero__class_Ozero(_1096211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096211), _1096213), hAPP(c_Groups_Ouminus__class_Ouminus(_1096211), _1096213))))], (17763 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096211), _1096213), hAPP(c_Groups_Ouminus__class_Ouminus(_1096211), _1096213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096211), _1096213), c_Groups_Ozero__class_Ozero(_1096211))))]]], (5052 ^ _776541) ^ [_853554, _853556, _853558, _853560, _853562, _853564] : [-(c_Product__Type_Oprod_Oprod__case(_853564, _853560, _853556) = c_Product__Type_Oprod_Oprod__case(_853562, _853558, _853554)), _853564 = _853562, _853560 = _853558, _853556 = _853554], (39930 ^ _776541) ^ [_1553758, _1553760, _1553762, _1553764, _1553766, _1553768, _1553770] : [-(hAPP(c_Product__Type_Oapsnd(_1553758, _1553760, _1553762, _1553764), hAPP(c_Product__Type_Oapsnd(_1553766, _1553758, _1553762, _1553768), _1553770)) = hAPP(c_Product__Type_Oapsnd(_1553766, _1553760, _1553762, hAPP(c_Fun_Ocomp(_1553758, _1553760, _1553766, _1553764), _1553768)), _1553770))], (10877 ^ _776541) ^ [_964251, _964253, _964255, _964257] : [class_Orderings_Oorder(_964251), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964251, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964251, _964253, _964255)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964251, _964255), _964257)) = c_Orderings_Obot__class_Obot(tc_fun(_964251, tc_HOL_Obool)))], (6384 ^ _776541) ^ [_879564, _879566] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879564, tc_HOL_Obool)), _879566), c_Orderings_Otop__class_Otop(tc_fun(_879564, tc_HOL_Obool)))))], (49824 ^ _776541) ^ [_1783062, _1783064] : [c_Equiv__Relations_Opart__equivp(_1783062, _1783064), 49828 ^ _776541 : [(49833 ^ _776541) ^ [] : [-(c_Predicate_Otransp(_1783062, _1783064))], (49831 ^ _776541) ^ [] : [-(c_Predicate_Osymp(_1783062, _1783064))], (49829 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1783064, 49827 ^ [_1783062, _1783064]), 49827 ^ [_1783062, _1783064])))]]], (45038 ^ _776541) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (27751 ^ _776541) ^ [_1275679] : [_1275679 = 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), _1275679)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (36504 ^ _776541) ^ [_1467456, _1467458, _1467460, _1467462, _1467464, _1467466] : [hBOOL(hAPP(hAPP(c_member(_1467456), _1467458), _1467460)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1467456, _1467462)), hAPP(hAPP(c_Product__Type_OPair(_1467456, _1467462), _1467458), _1467464)), _1467466)), -(hBOOL(hAPP(hAPP(c_member(_1467462), _1467464), hAPP(c_Relation_OImage(_1467456, _1467462, _1467466), _1467460))))], (4942 ^ _776541) ^ [_851835, _851837, _851839, _851841] : [-(c_Hilbert__Choice_OEps(_851841, _851837) = c_Hilbert__Choice_OEps(_851839, _851835)), _851841 = _851839, _851837 = _851835], (37648 ^ _776541) ^ [_1493344, _1493346, _1493348, _1493350, _1493352, _1493354] : [c_Fun_Oinj__on(_1493344, _1493346, _1493348, _1493350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493346, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493344, _1493346, _1493348), _1493350)), _1493352)), c_Fun_Oinj__on(_1493346, _1493344, _1493354, _1493352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493344, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493346, _1493344, _1493354), _1493352)), _1493350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493344), _1493350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493346), _1493352)), -(hAPP(c_Finite__Set_Ocard(_1493344), _1493350) = hAPP(c_Finite__Set_Ocard(_1493346), _1493352))], (50271 ^ _776541) ^ [_1792745, _1792747, _1792749, _1792751, _1792753] : [hBOOL(hAPP(_1792745, hAPP(hAPP(c_Product__Type_OPair(_1792747, _1792749), _1792751), _1792753))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1792747, _1792749, tc_HOL_Obool, _1792745), _1792751), _1792753)))], (39643 ^ _776541) ^ [_1545732, _1545734, _1545736] : [c_Predicate_Oreflp(_1545732, _1545734), -(hBOOL(hAPP(hAPP(_1545734, _1545736), _1545736)))], (41437 ^ _776541) ^ [_1590401, _1590403, _1590405, _1590407] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590401, _1590401)), _1590403), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590401, _1590401), tc_HOL_Obool), _1590405), _1590407))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590401, _1590401)), _1590403), c_Transitive__Closure_Ortrancl(_1590401, _1590407))))], (33070 ^ _776541) ^ [_1380825, _1380827, _1380829, _1380831, _1380833, _1380835] : [hBOOL(hAPP(hAPP(c_member(_1380825), _1380827), _1380829)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380825, tc_fun(_1380831, tc_HOL_Obool)), _1380829), hAPP(hAPP(c_COMBB(tc_fun(_1380831, tc_HOL_Obool), tc_fun(_1380831, tc_HOL_Obool), _1380825), hAPP(c_Set_Oinsert(_1380831), _1380833)), _1380835)) = hAPP(hAPP(c_Set_Oinsert(_1380831), _1380833), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380825, tc_fun(_1380831, tc_HOL_Obool)), _1380829), _1380835)))], (48592 ^ _776541) ^ [_1756144, _1756146, _1756148, _1756150, _1756152, _1756154] : [-(hAPP(hAPP(c_List_Ozip(_1756144, _1756146), c_List_Oreplicate(_1756144, _1756148, _1756150)), c_List_Oreplicate(_1756146, _1756152, _1756154)) = c_List_Oreplicate(tc_prod(_1756144, _1756146), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1756148), _1756152), hAPP(hAPP(c_Product__Type_OPair(_1756144, _1756146), _1756150), _1756154)))], (50101 ^ _776541) ^ [_1788675, _1788677, _1788679, _1788681, _1788683] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1788675, _1788677, _1788679, _1788681), _1788683) = c_Hilbert__Choice_OEps(_1788675, hAPP(hAPP(c_COMBS(_1788675, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1788675), c_fconj), hAPP(hAPP(c_COMBC(_1788675, tc_fun(_1788675, tc_HOL_Obool), tc_HOL_Obool), c_member(_1788675)), _1788679))), hAPP(hAPP(c_COMBC(_1788675, _1788677, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1788677, tc_fun(_1788677, tc_HOL_Obool), _1788675), c_fequal), _1788681)), _1788683))))], (52073 ^ _776541) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (10511 ^ _776541) ^ [_957189, _957191, _957193] : [-(hBOOL(hAPP(hAPP(c_member(_957189), _957191), _957193))), -(hBOOL(hAPP(hAPP(c_member(_957189), _957191), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957189, tc_HOL_Obool)), _957193))))], (42614 ^ _776541) ^ [_1624943, _1624945] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1624943, _1624945)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1624943, _1624945))], (48256 ^ _776541) ^ [_1748496, _1748498, _1748500] : [c_FunDef_Ois__measure(_1748496, _1748498), -(c_FunDef_Ois__measure(tc_prod(_1748500, _1748496), hAPP(hAPP(c_COMBB(_1748496, tc_Nat_Onat, tc_prod(_1748500, _1748496)), _1748498), c_Product__Type_Osnd(_1748500, _1748496))))], (40068 ^ _776541) ^ [_1556770, _1556772, _1556774, _1556776, _1556778, _1556780] : [c_Finite__Set_Ofolding(_1556770, _1556772, _1556774, _1556776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556770), _1556778)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556770), _1556780)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1556770, tc_HOL_Obool)), _1556778), _1556780) = c_Orderings_Obot__class_Obot(tc_fun(_1556770, tc_HOL_Obool)), -(hAPP(_1556776, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1556770, tc_HOL_Obool)), _1556778), _1556780)) = hAPP(c_Fun_Ocomp(_1556772, _1556772, _1556772, hAPP(_1556776, _1556778)), hAPP(_1556776, _1556780)))], (30232 ^ _776541) ^ [_1318824, _1318826, _1318828] : [class_Orderings_Olinorder(_1318824), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318824), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318824), _1318826), _1318828)), _1318828)))], (41005 ^ _776541) ^ [_1579828, _1579830, _1579832, _1579834] : [-(c_Wellfounded_Oacyclic(_1579828, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579828, _1579828)), hAPP(hAPP(c_Product__Type_OPair(_1579828, _1579828), _1579830), _1579832)), _1579834))), c_Wellfounded_Oacyclic(_1579828, _1579834), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579828, _1579828)), hAPP(hAPP(c_Product__Type_OPair(_1579828, _1579828), _1579832), _1579830)), c_Transitive__Closure_Ortrancl(_1579828, _1579834))))], (28743 ^ _776541) ^ [_1291811, _1291813] : [-(_1291811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1291813, _1291811) = c_Nitpick_Onat__gcd(_1291811, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1291813, _1291811)))], (33785 ^ _776541) ^ [_1401883, _1401885, _1401887, _1401889, _1401891] : [class_Groups_Ocomm__monoid__mult(_1401883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401885), _1401887)), 33792 ^ _776541 : [(33799 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401885), _1401889), _1401887))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401885, _1401883), hAPP(hAPP(c_COMBC(_1401885, _1401883, _1401883), hAPP(hAPP(c_COMBS(_1401885, _1401883, tc_fun(_1401883, _1401883)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401883, tc_fun(_1401883, _1401883)), _1401885), c_If(_1401883)), hAPP(hAPP(c_COMBC(_1401885, _1401885, tc_HOL_Obool), c_fequal), _1401889))), _1401891)), c_Groups_Oone__class_Oone(_1401883))), _1401887) = c_Groups_Oone__class_Oone(_1401883))], (33793 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1401885), _1401889), _1401887)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401885, _1401883), hAPP(hAPP(c_COMBC(_1401885, _1401883, _1401883), hAPP(hAPP(c_COMBS(_1401885, _1401883, tc_fun(_1401883, _1401883)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401883, tc_fun(_1401883, _1401883)), _1401885), c_If(_1401883)), hAPP(hAPP(c_COMBC(_1401885, _1401885, tc_HOL_Obool), c_fequal), _1401889))), _1401891)), c_Groups_Oone__class_Oone(_1401883))), _1401887) = hAPP(_1401891, _1401889))]]], (18585 ^ _776541) ^ [_1111029, _1111031, _1111033] : [hBOOL(hAPP(_1111029, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1111031), _1111033))), 18588 ^ _776541 : [(18595 ^ _776541) ^ [_1111220] : [_1111031 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111033), _1111220), -(hBOOL(hAPP(_1111029, _1111220)))], (18589 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111031), _1111033)), -(hBOOL(hAPP(_1111029, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (52111 ^ _776541) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (5709 ^ _776541) ^ [_866577, _866579] : [class_HOL_Oequal(_866577), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_866577), _866579), _866579)))], (44876 ^ _776541) ^ [_1674914, _1674916, _1674918, _1674920, _1674922] : [-(hAPP(c_List_Orotate(_1674914, _1674916), hAPP(hAPP(c_List_Omap(_1674918, _1674914), _1674920), _1674922)) = hAPP(hAPP(c_List_Omap(_1674918, _1674914), _1674920), hAPP(c_List_Orotate(_1674918, _1674916), _1674922)))], (30292 ^ _776541) ^ [_1319904, _1319906, _1319908, _1319910] : [class_Orderings_Olinorder(_1319904), 30295 ^ _776541 : [(30296 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319904), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319904), _1319906), _1319908)), _1319910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319904), _1319906), _1319910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319904), _1319908), _1319910)))], (30306 ^ _776541) ^ [] : [30307 ^ _776541 : [(30310 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319904), _1319908), _1319910))], (30308 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319904), _1319906), _1319910))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319904), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319904), _1319906), _1319908)), _1319910)))]]], (41825 ^ _776541) ^ [_1601864, _1601866, _1601868, _1601870, _1601872, _1601874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601864), tc_List_Olist(_1601864))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601864), tc_List_Olist(_1601864)), hAPP(hAPP(c_List_Olist_OCons(_1601864), _1601866), _1601868)), hAPP(hAPP(c_List_Olist_OCons(_1601864), _1601870), _1601872))), c_List_Olexord(_1601864, _1601874))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601864, _1601864)), hAPP(hAPP(c_Product__Type_OPair(_1601864, _1601864), _1601866), _1601870)), _1601874))), 41832 ^ _776541 : [(41835 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601864), tc_List_Olist(_1601864))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601864), tc_List_Olist(_1601864)), _1601868), _1601872)), c_List_Olexord(_1601864, _1601874))))], (41833 ^ _776541) ^ [] : [-(_1601866 = _1601870)]]], (43791 ^ _776541) ^ [_1650598, _1650600, _1650602, _1650604, _1650606, _1650608, _1650610] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650598, _1650598)), hAPP(hAPP(c_Product__Type_OPair(_1650598, _1650598), _1650600), _1650602)), _1650604)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650598), tc_List_Olist(_1650598))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650598), tc_List_Olist(_1650598)), hAPP(hAPP(c_List_Oappend(_1650598), _1650606), hAPP(hAPP(c_List_Olist_OCons(_1650598), _1650600), _1650608))), hAPP(hAPP(c_List_Oappend(_1650598), _1650606), hAPP(hAPP(c_List_Olist_OCons(_1650598), _1650602), _1650610)))), c_List_Olexord(_1650598, _1650604))))], (22341 ^ _776541) ^ [_1181550, _1181552, _1181554] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181550), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181552), _1181554)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181550), _1181552)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181550), _1181554)))], (39414 ^ _776541) ^ [_1539986, _1539988, _1539990, _1539992] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539986), _1539988)), 39420 ^ _776541 : [(39423 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539990), hAPP(_1539992, 39419 ^ [_1539986, _1539988, _1539990, _1539992])))], (39421 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539986), 39419 ^ [_1539986, _1539988, _1539990, _1539992]), _1539988)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539986, _1539990)), hAPP(hAPP(c_Product__Type_OSigma(_1539986, _1539990), _1539988), _1539992))))], (24571 ^ _776541) ^ [_1221013, _1221015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221013)), -(c_SMT_Oz3div(_1221015, _1221013) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221015), _1221013))], (46554 ^ _776541) ^ [_1712556, _1712558, _1712560, _1712562] : [class_Orderings_Olinorder(_1712556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712556), _1712558), _1712560)), c_List_Olinorder__class_Osorted(_1712556, hAPP(hAPP(c_List_Olist_OCons(_1712556), _1712560), _1712562)), -(c_List_Olinorder__class_Osorted(_1712556, hAPP(hAPP(c_List_Olist_OCons(_1712556), _1712558), hAPP(hAPP(c_List_Olist_OCons(_1712556), _1712560), _1712562))))], (40613 ^ _776541) ^ [_1569619, _1569621] : [-(hAPP(c_Relation_ODomain(_1569619, _1569619), c_Transitive__Closure_Otrancl(_1569619, _1569621)) = hAPP(c_Relation_ODomain(_1569619, _1569619), _1569621))], (23575 ^ _776541) ^ [_1203863, _1203865, _1203867] : [class_Nat_Osemiring__char__0(_1203863), 23578 ^ _776541 : [(23585 ^ _776541) ^ [] : [_1203865 = _1203867, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203863), _1203865) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203863), _1203867))], (23579 ^ _776541) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203863), _1203865) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203863), _1203867), -(_1203865 = _1203867)]]], (35268 ^ _776541) ^ [_1434620, _1434622, _1434624, _1434626, _1434628] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1434620, _1434622), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1434624), _1434626))), -(_1434622 = 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)), _1434628)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1434620, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1434622), _1434628)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1434624), _1434628)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1434622), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1434624, _1434628))), _1434626)))))], (12834 ^ _776541) ^ [_1002966, _1002968] : [class_Complete__Lattice_Ocomplete__lattice(_1002966), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002966), _1002968)), -(c_Complete__Lattice_OInf__class_OInf(_1002966, _1002968) = hAPP(hAPP(c_Finite__Set_Ofold(_1002966, _1002966, c_Lattices_Osemilattice__inf__class_Oinf(_1002966)), c_Orderings_Otop__class_Otop(_1002966)), _1002968))], (4458 ^ _776541) ^ [_844215, _844217, _844219, _844221] : [-(c_Wellfounded_Oaccp(_844221, _844217) = c_Wellfounded_Oaccp(_844219, _844215)), _844221 = _844219, _844217 = _844215], (3398 ^ _776541) ^ [_827277, _827279, _827281, _827283] : [-(c_Enum_Osublists(_827283, _827279) = c_Enum_Osublists(_827281, _827277)), _827283 = _827281, _827279 = _827277], (31673 ^ _776541) ^ [_1345234, _1345236, _1345238, _1345240] : [class_Orderings_Olinorder(_1345234), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345234), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345234), _1345236), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345234), _1345238), _1345240))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345234), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345234), _1345236), _1345238)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345234), _1345236), _1345240)))))], (12003 ^ _776541) ^ [_987573, _987575] : [class_Lattices_Olattice(_987573), hBOOL(hAPP(c_Finite__Set_Ofinite(_987573), _987575)), -(_987575 = c_Orderings_Obot__class_Obot(tc_fun(_987573, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987573), c_Big__Operators_Olattice__class_OInf__fin(_987573, _987575)), c_Big__Operators_Olattice__class_OSup__fin(_987573, _987575))))], (33417 ^ _776541) ^ [_1390265, _1390267, _1390269, _1390271, _1390273, _1390275] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390265, tc_fun(_1390267, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390269, tc_fun(_1390265, tc_HOL_Obool)), _1390271), _1390273)), _1390275) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390269, tc_fun(_1390267, tc_HOL_Obool)), _1390271), hAPP(hAPP(c_COMBC(_1390269, tc_fun(_1390265, tc_fun(_1390267, tc_HOL_Obool)), tc_fun(_1390267, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390265, tc_HOL_Obool), tc_fun(tc_fun(_1390265, tc_fun(_1390267, tc_HOL_Obool)), tc_fun(_1390267, tc_HOL_Obool)), _1390269), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390265, tc_fun(_1390267, tc_HOL_Obool))), _1390273)), _1390275)))], (48572 ^ _776541) ^ [_1755872, _1755874, _1755876] : [-(c_List_Oreplicate(_1755872, hAPP(c_Nat_OSuc, _1755874), _1755876) = hAPP(hAPP(c_List_Olist_OCons(_1755872), _1755876), c_List_Oreplicate(_1755872, _1755874, _1755876)))], (47034 ^ _776541) ^ [_1721968, _1721970, _1721972, _1721974, _1721976] : [c_List_Olist__all2(_1721968, _1721970, _1721972, hAPP(c_List_Orev(_1721968), _1721974), _1721976), -(c_List_Olist__all2(_1721968, _1721970, _1721972, _1721974, hAPP(c_List_Orev(_1721970), _1721976)))], (32047 ^ _776541) ^ [_1352365, _1352367, _1352369] : [class_Orderings_Olinorder(_1352365), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352365), _1352367)), hBOOL(hAPP(hAPP(c_member(_1352365), _1352369), _1352367)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1352365), _1352369), c_Big__Operators_Olattice_OSup__fin(_1352365, c_Orderings_Oord__class_Omax(_1352365), _1352367)) = _1352369)], (49307 ^ _776541) ^ [_1771994, _1771996, _1771998] : [c_Relation_Otrans(_1771994, _1771996), c_Relation_Otrans(_1771994, _1771998), -(c_Relation_Otrans(_1771994, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1771994, _1771994), tc_HOL_Obool)), _1771996), _1771998)))], (48174 ^ _776541) ^ [_1746889, _1746891, _1746893] : [-(hBOOL(hAPP(hAPP(c_member(_1746889), _1746891), hAPP(c_List_Oset(_1746889), _1746893)))), 48175 ^ _776541 : [(48176 ^ _776541) ^ [_1746978, _1746980] : [_1746893 = hAPP(hAPP(c_List_Oappend(_1746889), _1746980), hAPP(hAPP(c_List_Olist_OCons(_1746889), _1746891), _1746978)), -(hBOOL(hAPP(hAPP(c_member(_1746889), _1746891), hAPP(c_List_Oset(_1746889), _1746978))))]]], (15992 ^ _776541) ^ [_1065931, _1065933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065931), _1065933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065931)), hAPP(c_Nat_OSuc, _1065933))))], (11290 ^ _776541) ^ [_972746, _972748] : [class_Groups_Oordered__ab__group__add(_972746), -(hAPP(c_Set_Oimage(_972746, _972746, c_Groups_Ouminus__class_Ouminus(_972746)), hAPP(c_SetInterval_Oord__class_OatLeast(_972746), _972748)) = hAPP(c_SetInterval_Oord__class_OatMost(_972746), hAPP(c_Groups_Ouminus__class_Ouminus(_972746), _972748)))], (43446 ^ _776541) ^ [_1642814, _1642816, _1642818, _1642820] : [-(hAPP(hAPP(c_List_Oappend(_1642814), hAPP(hAPP(c_List_Olist_OCons(_1642814), _1642816), _1642818)), _1642820) = hAPP(hAPP(c_List_Olist_OCons(_1642814), _1642816), hAPP(hAPP(c_List_Oappend(_1642814), _1642818), _1642820)))], (32984 ^ _776541) ^ [_1378481, _1378483, _1378485] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378481, tc_HOL_Obool)), _1378483), _1378485) = hAPP(c_Set_OCollect(_1378481), hAPP(hAPP(c_COMBS(_1378481, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378481), c_fconj), hAPP(hAPP(c_COMBC(_1378481, tc_fun(_1378481, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378481)), _1378483))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1378481), c_fNot), hAPP(hAPP(c_COMBC(_1378481, tc_fun(_1378481, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378481)), _1378485)))))], (30052 ^ _776541) ^ [_1315474, _1315476, _1315478] : [class_Orderings_Olinorder(_1315474), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315474), _1315476), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315474), _1315476), _1315478)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315474), _1315476), _1315478))], (21883 ^ _776541) ^ [_1173095, _1173097, _1173099, _1173101] : [class_Fields_Olinordered__field__inverse__zero(_1173095), class_Int_Onumber(_1173095), 21890 ^ _776541 : [(21891 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173095), 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tc_List_Olist(_1599204))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1599204)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1599204), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1599204)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1599204)))), hAPP(c_Nat_OSuc, _1599208))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1599204), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1599204)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1599204)))), hAPP(c_Nat_OSuc, _1599208)))))))], (13504 ^ _776541) ^ [_1016807, _1016809, _1016811, _1016813, _1016815] : [class_Groups_Ocomm__monoid__add(_1016807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016809), _1016811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016811), _1016813)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016807), 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[_1111321, _1111323, _1111325]))], (18610 ^ _776541) ^ [] : [-(_1111323 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111325), 18608 ^ [_1111321, _1111323, _1111325]))]]], (19500 ^ _776541) ^ [_1128769, _1128771, _1128773, _1128775, _1128777] : [class_Groups_Ocomm__monoid__add(_1128769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128771), _1128773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128771, tc_HOL_Obool)), _1128775), _1128773)), 19514 ^ _776541 : [(19517 ^ _776541) ^ [] : [hAPP(_1128777, 19513 ^ [_1128769, _1128771, _1128773, _1128775, _1128777]) = c_Groups_Ozero__class_Ozero(_1128769)], (19515 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1128771), 19513 ^ [_1128769, _1128771, _1128773, _1128775, _1128777]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1128771, tc_HOL_Obool)), _1128773), _1128775))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128771, _1128769), _1128777), _1128775) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128771, _1128769), _1128777), _1128773))], (51885 ^ _776541) ^ [_1824977, _1824979] : [class_Lattices_Odistrib__lattice(_1824977), -(class_Lattices_Odistrib__lattice(tc_fun(_1824979, _1824977)))], (3554 ^ _776541) ^ [_829683, _829685, _829687, _829689, _829691, _829693] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_829693, _829689, _829685) = c_SetInterval_Oord__class_OgreaterThanLessThan(_829691, _829687, _829683)), _829693 = _829691, _829689 = _829687, _829685 = _829683], (30930 ^ _776541) ^ [_1331368, _1331370, _1331372] : [class_Orderings_Olinorder(_1331368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331368), _1331370)), -(hBOOL(hAPP(hAPP(c_member(_1331368), _1331372), _1331370))), -(_1331370 = c_Orderings_Obot__class_Obot(tc_fun(_1331368, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1331368, hAPP(hAPP(c_Set_Oinsert(_1331368), _1331372), _1331370)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331368), _1331372), c_Big__Operators_Olinorder__class_OMin(_1331368, _1331370)))], (11534 ^ _776541) ^ [_978141, _978143] : [class_Finite__Set_Ofinite(_978141), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_978141), _978143)))], (20811 ^ _776541) ^ [_1152256, _1152258, _1152260, _1152262] : [class_Fields_Ofield(_1152256), -(_1152258 = c_Groups_Ozero__class_Ozero(_1152256)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152256), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152256), _1152260), _1152258)), _1152262) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152256), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152256), _1152260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152256), _1152258), _1152262))), _1152258))], (15017 ^ _776541) ^ [_1047542, _1047544, _1047546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047542), _1047544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047546), _1047544))))], (36980 ^ _776541) ^ [_1479118, _1479120] : [c_Equiv__Relations_Oequivp(_1479118, hAPP(hAPP(c_COMBC(_1479118, tc_fun(tc_prod(_1479118, _1479118), tc_HOL_Obool), tc_fun(_1479118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479118, tc_fun(tc_fun(tc_prod(_1479118, _1479118), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1479118, _1479118), tc_HOL_Obool), tc_fun(_1479118, tc_HOL_Obool)), _1479118), c_COMBC(_1479118, tc_fun(tc_prod(_1479118, _1479118), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479118, tc_prod(_1479118, _1479118)), tc_fun(_1479118, tc_fun(tc_fun(tc_prod(_1479118, _1479118), tc_HOL_Obool), tc_HOL_Obool)), _1479118), hAPP(c_COMBB(tc_prod(_1479118, _1479118), tc_fun(tc_fun(tc_prod(_1479118, _1479118), tc_HOL_Obool), tc_HOL_Obool), _1479118), c_member(tc_prod(_1479118, _1479118)))), c_Product__Type_OPair(_1479118, _1479118)))), _1479120)), -(c_Equiv__Relations_Oequiv(_1479118, c_Orderings_Otop__class_Otop(tc_fun(_1479118, tc_HOL_Obool)), _1479120))], (41610 ^ _776541) ^ [_1595484, _1595486, _1595488, _1595490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595484, _1595484)), hAPP(hAPP(c_Product__Type_OPair(_1595484, _1595484), _1595486), _1595488)), c_Transitive__Closure_Otrancl(_1595484, _1595490))), 41614 ^ _776541 : [(41617 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595484, _1595484)), hAPP(hAPP(c_Product__Type_OPair(_1595484, _1595484), 41613 ^ [_1595484, _1595486, _1595488, _1595490]), _1595488)), _1595490)))], (41615 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595484, _1595484)), hAPP(hAPP(c_Product__Type_OPair(_1595484, _1595484), _1595486), 41613 ^ [_1595484, _1595486, _1595488, _1595490])), c_Transitive__Closure_Ortrancl(_1595484, _1595490))))]]], (51949 ^ _776541) ^ [_1825817, _1825819] : [class_Groups_Ominus(_1825817), -(class_Groups_Ominus(tc_fun(_1825819, _1825817)))], (48327 ^ _776541) ^ [_1749841, _1749843, _1749845] : [48329 ^ _776541 : [(48332 ^ _776541) ^ [] : [hBOOL(hAPP(_1749843, 48328 ^ [_1749841, _1749843, _1749845]))], (48330 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749841), 48328 ^ [_1749841, _1749843, _1749845]), hAPP(c_List_Oset(_1749841), _1749845))))]], -(c_List_Olist__all(_1749841, _1749843, _1749845))], (8393 ^ _776541) ^ [_920605, _920607, _920609] : [class_Lattices_Osemilattice__inf(_920605), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920605), _920607), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920605), _920607), _920609)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920605), _920607), _920609))], (10285 ^ _776541) ^ [_953290, _953292, _953294] : [class_Groups_Ogroup__add(_953290), 10288 ^ _776541 : [(10295 ^ _776541) ^ [] : [_953294 = hAPP(c_Groups_Ouminus__class_Ouminus(_953290), _953292), -(_953292 = hAPP(c_Groups_Ouminus__class_Ouminus(_953290), _953294))], (10289 ^ _776541) ^ [] : [_953292 = hAPP(c_Groups_Ouminus__class_Ouminus(_953290), _953294), -(_953294 = hAPP(c_Groups_Ouminus__class_Ouminus(_953290), _953292))]]], (30112 ^ _776541) ^ [_1316739, _1316741, _1316743, _1316745, _1316747] : [class_Orderings_Olinorder(_1316739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316739), _1316741), _1316743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316739), _1316745), _1316747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316739), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316739), _1316741), _1316745)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316739), _1316743), _1316747))))], (47611 ^ _776541) ^ [_1733994, _1733996, _1733998, _1734000] : [-(c_List_Omaps(_1733994, _1733996, _1733998, _1734000) = c_List_Oconcat(_1733996, hAPP(hAPP(c_List_Omap(_1733994, tc_List_Olist(_1733996)), _1733998), _1734000)))], (6184 ^ _776541) ^ [_875864, _875866] : [hBOOL(hAPP(hAPP(c_member(_875864), _875866), c_Orderings_Obot__class_Obot(tc_fun(_875864, tc_HOL_Obool))))], (44072 ^ _776541) ^ [_1657887, _1657889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657887)), _1657889)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1657887), _1657889) = _1657889)], (38698 ^ _776541) ^ [_1520180, _1520182, _1520184, _1520186, _1520188] : [hBOOL(hAPP(hAPP(c_member(_1520180), _1520182), hAPP(c_Set_Ovimage(_1520180, _1520184, _1520186), _1520188))), -(hBOOL(hAPP(hAPP(c_member(_1520184), hAPP(_1520186, _1520182)), _1520188)))], (566 ^ _776541) ^ [_785070, _785072, _785074, _785076, _785078, _785080] : [-(c_Finite__Set_Ofun__left__comm(_785078, _785074, _785070)), c_Finite__Set_Ofun__left__comm(_785080, _785076, _785072), _785080 = _785078, _785076 = _785074, _785072 = _785070], (39097 ^ _776541) ^ [_1529837, _1529839, _1529841] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1529837, _1529839), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529837, _1529839), c_Orderings_Otop__class_Otop(tc_fun(_1529837, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1529839, tc_HOL_Obool), _1529837), _1529841))) = hAPP(hAPP(c_Product__Type_OSigma(_1529837, _1529839), c_Orderings_Otop__class_Otop(tc_fun(_1529837, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1529839, tc_HOL_Obool), _1529837), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529839, tc_HOL_Obool)), _1529841))))], (35332 ^ _776541) ^ [_1435598, _1435600] : [-(_1435598 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435600, _1435598), c_Divides_Odivmod__int(_1435600, _1435598))))], (34880 ^ _776541) ^ [_1427347, _1427349, _1427351, _1427353] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1427347, _1427349, _1427351), hAPP(hAPP(c_COMBB(tc_fun(_1427349, tc_prod(_1427347, _1427349)), tc_fun(_1427349, _1427351), _1427347), hAPP(c_COMBB(tc_prod(_1427347, _1427349), _1427351, _1427349), _1427353)), c_Product__Type_OPair(_1427347, _1427349))) = _1427353)], (11131 ^ _776541) ^ [_969153, _969155, _969157, _969159, _969161, _969163] : [hBOOL(hAPP(hAPP(c_member(_969153), _969155), _969157)), _969159 = hAPP(_969161, _969155), -(hBOOL(hAPP(hAPP(c_member(_969163), _969159), hAPP(c_Set_Oimage(_969153, _969163, _969161), _969157))))], (11556 ^ _776541) ^ [_978546] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_978546), c_Orderings_Otop__class_Otop(tc_fun(_978546, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_978546)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_978546), tc_HOL_Obool)))))], (6410 ^ _776541) ^ [_880073, _880075, _880077] : [class_Complete__Lattice_Ocomplete__lattice(_880073), hBOOL(hAPP(hAPP(c_member(_880073), _880075), _880077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880073), c_Complete__Lattice_OInf__class_OInf(_880073, _880077)), _880075)))], (10523 ^ _776541) ^ [_957388, _957390, _957392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957388, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957388, tc_HOL_Obool)), _957390)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957388, tc_HOL_Obool)), _957392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957388, tc_HOL_Obool)), _957392), _957390)))], (23940 ^ _776541) ^ [_1210133, _1210135, _1210137] : [class_Rings_Osemiring__1(_1210133), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210135), _1210137)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210133), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210133), _1210135)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210133), _1210137)))], (44308 ^ _776541) ^ [_1662620] : [class_Orderings_Olinorder(_1662620), -(c_Finite__Set_Ofun__left__comm(_1662620, tc_List_Olist(_1662620), c_List_Olinorder__class_Oinsort__key(_1662620, _1662620, c_COMBI(_1662620))))], (51873 ^ _776541) ^ [_1824819, _1824821] : [class_Lattices_Olattice(_1824819), -(class_Lattices_Osemilattice__sup(tc_fun(_1824821, _1824819)))], (7724 ^ _776541) ^ [_905893, _905895, _905897] : [-(hAPP(c_Set_OPow(_905893), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905893, tc_HOL_Obool)), _905895), _905897)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_905893, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_905893), _905895)), hAPP(c_Set_OPow(_905893), _905897)))], (16556 ^ _776541) ^ [_1074510, _1074512] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074510), _1074512) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1074510 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1074512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6087 ^ _776541) ^ [_873967, _873969, _873971, _873973, _873975, _873977] : [-(hBOOL(hAPP(hAPP(c_member(_873967), _873969), c_SetInterval_Oord_OgreaterThanAtMost(_873967, _873971, _873973, _873975, _873977)))), hBOOL(hAPP(hAPP(_873973, _873975), _873969)), hBOOL(hAPP(hAPP(_873971, _873969), _873977))], (42361 ^ _776541) ^ [_1617305, _1617307, _1617309] : [-(hAPP(c_List_Oset(_1617305), hAPP(hAPP(c_List_Olist_OCons(_1617305), _1617307), _1617309)) = hAPP(hAPP(c_Set_Oinsert(_1617305), _1617307), hAPP(c_List_Oset(_1617305), _1617309)))], (41718 ^ _776541) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18051 ^ _776541) ^ [_1101150, _1101152, _1101154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101150), _1101152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101150), _1101154)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101152), _1101154))))], (24942 ^ _776541) ^ [_1228200] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1228200) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43900 ^ _776541) ^ [_1653665, _1653667, _1653669, _1653671] : [-(hAPP(hAPP(c_List_Odrop(_1653665), _1653667), hAPP(hAPP(c_List_Otake(_1653665), _1653669), _1653671)) = hAPP(hAPP(c_List_Otake(_1653665), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1653669), _1653667)), hAPP(hAPP(c_List_Odrop(_1653665), _1653667), _1653671)))], (48494 ^ _776541) ^ [_1753715, _1753717, _1753719, _1753721, _1753723] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1753715, _1753717, _1753719), _1753721), _1753723)), -(hBOOL(hAPP(hAPP(_1753719, _1753723), _1753721)))], (45491 ^ _776541) ^ [_1688744, _1688746, _1688748, _1688750] : [_1688750 = c_List_Olist_ONil(_1688746), -(c_List_Olist__all2(_1688744, _1688746, _1688748, c_List_Olist_ONil(_1688744), _1688750))], (26270 ^ _776541) ^ [_1250979] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1250979), c_Int_OMin) = c_Int_Osucc(_1250979))], (52147 ^ _776541) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (29329 ^ _776541) ^ [_1302099] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1302099)), 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, _1302099, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (37260 ^ _776541) ^ [_1485631, _1485633, _1485635, _1485637, _1485639] : [c_Fun_Oinj__on(_1485631, _1485633, _1485635, _1485637), -(c_Fun_Oinj__on(_1485631, _1485633, _1485635, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485631, tc_HOL_Obool)), _1485637), _1485639)))], (34856 ^ _776541) ^ [_1426982, _1426984] : [-(c_Divides_Odivmod__int(_1426982, _1426984) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1426982), _1426984)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1426982, _1426984)))], (34976 ^ _776541) ^ [_1429007, _1429009] : [-(_1429007 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34979 ^ _776541 : [(34986 ^ _776541) ^ [] : [-(_1429009 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1429007, _1429009) = 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, _1429009))), 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, _1429007)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1429009))), c_Divides_Opdivmod(_1429007, _1429009)), 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), _1429009))))), c_Divides_Opdivmod(_1429007, _1429009)))))], (34980 ^ _776541) ^ [] : [_1429009 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1429007, _1429009) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1429007))]]], (50761 ^ _776541) ^ [_1802506, _1802508, _1802510, _1802512, _1802514] : [hBOOL(hAPP(hAPP(c_member(_1802506), _1802508), _1802510)), -(hAPP(c_Quotient_OBabs(_1802506, _1802512, _1802510, _1802514), _1802508) = hAPP(_1802514, _1802508))], (39914 ^ _776541) ^ [_1553341, _1553343, _1553345, _1553347, _1553349, _1553351, _1553353] : [-(hAPP(c_Fun_Ocomp(_1553341, _1553343, _1553345, _1553347), hAPP(c_Fun_Ocomp(_1553349, _1553341, _1553345, _1553351), _1553353)) = hAPP(c_Fun_Ocomp(_1553349, _1553343, _1553345, hAPP(c_Fun_Ocomp(_1553341, _1553343, _1553349, _1553347), _1553351)), _1553353))], (11421 ^ _776541) ^ [_975858, _975860, _975862, _975864, _975866] : [c_Finite__Set_Ofolding__one(_975858, _975860, _975862), hBOOL(hAPP(c_Finite__Set_Ofinite(_975858), _975864)), -(_975864 = c_Orderings_Obot__class_Obot(tc_fun(_975858, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_975858), _975866)), -(_975866 = c_Orderings_Obot__class_Obot(tc_fun(_975858, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975858, tc_HOL_Obool)), _975864), _975866) = c_Orderings_Obot__class_Obot(tc_fun(_975858, tc_HOL_Obool)), -(hAPP(_975862, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_975858, tc_HOL_Obool)), _975864), _975866)) = hAPP(hAPP(_975860, hAPP(_975862, _975864)), hAPP(_975862, _975866)))], (32624 ^ _776541) ^ [_1368174, _1368176, _1368178] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368174, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1368174, tc_HOL_Obool), _1368176)), _1368178) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1368174, tc_HOL_Obool), tc_fun(_1368174, tc_HOL_Obool)), _1368176), hAPP(hAPP(c_COMBC(tc_fun(_1368174, tc_HOL_Obool), tc_fun(_1368174, tc_HOL_Obool), tc_fun(_1368174, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368174, tc_HOL_Obool))), _1368178)))], (28377 ^ _776541) ^ [_1285952, _1285954] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1285952)), c_Int_OBit1(_1285954))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1285952), _1285954)))], (33485 ^ _776541) ^ [_1392428, _1392430] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1392428, tc_HOL_Obool)), _1392430) = hAPP(c_Set_OCollect(_1392428), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1392428), c_fNot), hAPP(hAPP(c_COMBC(_1392428, tc_fun(_1392428, tc_HOL_Obool), tc_HOL_Obool), c_member(_1392428)), _1392430))))], (38126 ^ _776541) ^ [_1506729, _1506731] : [c_Wellfounded_Owf(_1506729, _1506731), -(c_Wellfounded_Owf(_1506729, hAPP(hAPP(c_Relation_Orel__comp(_1506729, _1506729, _1506729), _1506731), _1506731)))], (34247 ^ _776541) ^ [_1413471, _1413473, _1413475, _1413477, _1413479, _1413481] : [class_Groups_Ocomm__monoid__mult(_1413471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413473), _1413475)), 34254 ^ _776541 : [(34261 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413473), _1413477), _1413475))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413473, _1413471), hAPP(hAPP(c_COMBC(_1413473, _1413471, _1413471), hAPP(hAPP(c_COMBS(_1413473, _1413471, tc_fun(_1413471, _1413471)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413471, tc_fun(_1413471, _1413471)), _1413473), c_If(_1413471)), hAPP(hAPP(c_COMBC(_1413473, _1413473, tc_HOL_Obool), c_fequal), _1413477))), _1413479)), _1413481)), _1413475) = hAPP(hAPP(c_Power_Opower__class_Opower(_1413471), _1413481), hAPP(c_Finite__Set_Ocard(_1413473), _1413475)))], (34255 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1413473), _1413477), _1413475)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413473, _1413471), hAPP(hAPP(c_COMBC(_1413473, _1413471, _1413471), hAPP(hAPP(c_COMBS(_1413473, _1413471, tc_fun(_1413471, _1413471)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413471, tc_fun(_1413471, _1413471)), _1413473), c_If(_1413471)), hAPP(hAPP(c_COMBC(_1413473, _1413473, tc_HOL_Obool), c_fequal), _1413477))), _1413479)), _1413481)), _1413475) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413471), hAPP(_1413479, _1413477)), hAPP(hAPP(c_Power_Opower__class_Opower(_1413471), _1413481), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1413473), _1413475)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (21026 ^ _776541) ^ [_1156424, _1156426, _1156428, _1156430] : [-(c_Sum__Type_OPlus(_1156424, _1156426, _1156428, _1156430) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1156424, _1156426), tc_HOL_Obool))), _1156428 = c_Orderings_Obot__class_Obot(tc_fun(_1156424, tc_HOL_Obool)), _1156430 = c_Orderings_Obot__class_Obot(tc_fun(_1156426, tc_HOL_Obool))], (44240 ^ _776541) ^ [_1661199, _1661201] : [class_Lattices_Oab__semigroup__idem__mult(_1661199), -(_1661201 = c_List_Olist_ONil(_1661199)), -(hAPP(c_Finite__Set_Ofold1(_1661199, c_Groups_Otimes__class_Otimes(_1661199)), hAPP(c_List_Oset(_1661199), _1661201)) = hAPP(c_List_Ofoldl(_1661199, _1661199, c_Groups_Otimes__class_Otimes(_1661199), hAPP(c_List_Ohd(_1661199), _1661201)), hAPP(c_List_Otl(_1661199), _1661201)))], (22083 ^ _776541) ^ [_1176960, _1176962, _1176964] : [class_Rings_Olinordered__semidom(_1176960), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176960), c_Groups_Oone__class_Oone(_1176960)), _1176962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176960), c_Groups_Oone__class_Oone(_1176960)), hAPP(hAPP(c_Power_Opower__class_Opower(_1176960), _1176962), _1176964))))], (1764 ^ _776541) ^ [_801455, _801457] : [-(class_Groups_Omonoid__mult(_801455)), _801457 = _801455, class_Groups_Omonoid__mult(_801457)], (36701 ^ _776541) ^ [_1472606, _1472608, _1472610, _1472612, _1472614, _1472616] : [c_Equiv__Relations_Oequiv(_1472606, _1472608, _1472610), hBOOL(hAPP(hAPP(c_member(_1472606), _1472612), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472606, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472606, _1472606, _1472610), hAPP(hAPP(c_Set_Oinsert(_1472606), _1472614), c_Orderings_Obot__class_Obot(tc_fun(_1472606, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1472606, _1472606, _1472610), hAPP(hAPP(c_Set_Oinsert(_1472606), _1472616), c_Orderings_Obot__class_Obot(tc_fun(_1472606, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472606, _1472606)), hAPP(hAPP(c_Product__Type_OPair(_1472606, _1472606), _1472614), _1472616)), _1472610)))], (52331 ^ _776541) ^ [_1829598, _1829600] : [-(class_Finite__Set_Ofinite(tc_prod(_1829598, _1829600))), class_Finite__Set_Ofinite(_1829598), class_Finite__Set_Ofinite(_1829600)], (28915 ^ _776541) ^ [_1294927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1294927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1294927)))], (39862 ^ _776541) ^ [_1552201, _1552203, _1552205, _1552207, _1552209, _1552211] : [c_Fun_Oinj__on(_1552201, _1552203, hAPP(c_Fun_Ocomp(_1552205, _1552203, _1552201, _1552207), _1552209), _1552211), -(c_Fun_Oinj__on(_1552205, _1552203, _1552207, hAPP(c_Set_Oimage(_1552201, _1552205, _1552209), _1552211)))], (43683 ^ _776541) ^ [_1647900, _1647902, _1647904, _1647906] : [hBOOL(hAPP(hAPP(c_member(_1647900), _1647902), hAPP(c_List_Oset(_1647900), _1647904))), -(c_List_Oremove1(_1647900, _1647902, hAPP(hAPP(c_List_Oappend(_1647900), _1647904), _1647906)) = hAPP(hAPP(c_List_Oappend(_1647900), c_List_Oremove1(_1647900, _1647902, _1647904)), _1647906))], (13399 ^ _776541) ^ [_1014516, _1014518, _1014520, _1014522, _1014524] : [class_Groups_Ocomm__monoid__add(_1014516), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014518), _1014520)), hBOOL(hAPP(hAPP(c_member(_1014518), _1014522), _1014520)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014518, _1014516), _1014524), _1014520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014516), hAPP(_1014524, _1014522)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014518, _1014516), _1014524), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014518, tc_HOL_Obool)), _1014520), hAPP(hAPP(c_Set_Oinsert(_1014518), _1014522), c_Orderings_Obot__class_Obot(tc_fun(_1014518, tc_HOL_Obool)))))))], (25445 ^ _776541) ^ [_1236846, _1236848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236846), _1236848)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236846, _1236848) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236846), _1236848))], (52307 ^ _776541) ^ [_1829292] : [-(class_HOL_Oequal(tc_Option_Ooption(_1829292)))], (16689 ^ _776541) ^ [_1076755, _1076757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076755), hAPP(c_Nat_OSuc, _1076757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076755), _1076757)))], (3264 ^ _776541) ^ [_825220, _825222, _825224, _825226, _825228, _825230, _825232, _825234] : [-(c_Nitpick_Osetsum_H(_825234, _825230, _825226, _825222) = c_Nitpick_Osetsum_H(_825232, _825228, _825224, _825220)), _825234 = _825232, _825230 = _825228, _825226 = _825224, _825222 = _825220], (10202 ^ _776541) ^ [_951688, _951690, _951692] : [class_Orderings_Olinorder(_951688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951688), _951690), _951692)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951688, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951688, _951690), _951692)), hAPP(hAPP(c_Set_Oinsert(_951688), _951692), c_Orderings_Obot__class_Obot(tc_fun(_951688, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_951688, _951690, _951692))], (32249 ^ _776541) ^ [_1356250, _1356252, _1356254, _1356256] : [class_Orderings_Olinorder(_1356250), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356250), _1356252)), 32259 ^ _776541 : [(32262 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356250), 32258 ^ [_1356250, _1356252, _1356254, _1356256]), _1356254))], (32260 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356250), 32258 ^ [_1356250, _1356252, _1356254, _1356256]), _1356252)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356250), hAPP(hAPP(c_Finite__Set_Ofold(_1356250, _1356250, c_Orderings_Oord__class_Omax(_1356250)), _1356256), _1356252)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356250), _1356254), _1356256))))], (39553 ^ _776541) ^ [_1543658] : [-(c_Relation_Orefl__on(_1543658, c_Orderings_Obot__class_Obot(tc_fun(_1543658, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543658, _1543658), tc_HOL_Obool))))], (14780 ^ _776541) ^ [_1043023, _1043025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043023), _1043025)), -(_1043025 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043023), 14783 ^ [_1043023, _1043025]))], (24190 ^ _776541) ^ [_1214093, _1214095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214093), 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)), _1214095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214093), _1214095)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33617 ^ _776541) ^ [_1396399, _1396401, _1396403, _1396405, _1396407, _1396409] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396399, tc_fun(_1396401, tc_fun(_1396403, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1396399, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool), tc_fun(_1396401, tc_fun(_1396403, tc_HOL_Obool)), _1396399), hAPP(c_COMBC(_1396401, tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool), tc_fun(_1396403, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396403, tc_fun(tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool), tc_fun(_1396403, tc_HOL_Obool)), _1396401), c_COMBC(_1396403, tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396403, tc_prod(_1396401, _1396403)), tc_fun(_1396403, tc_fun(tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool), tc_HOL_Obool)), _1396401), hAPP(c_COMBB(tc_prod(_1396401, _1396403), tc_fun(tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool), tc_HOL_Obool), _1396403), c_member(tc_prod(_1396401, _1396403)))), c_Product__Type_OPair(_1396401, _1396403))))), _1396405)), _1396407), _1396409)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1396401, _1396403)), hAPP(hAPP(c_Product__Type_OPair(_1396401, _1396403), _1396407), _1396409)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396399, tc_fun(tc_prod(_1396401, _1396403), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396399, tc_HOL_Obool))), _1396405))))], (34832 ^ _776541) ^ [_1426523, _1426525, _1426527, _1426529, _1426531, _1426533] : [-(hAPP(hAPP(c_Product__Type_OPair(_1426523, _1426525), _1426527), _1426529) = hAPP(hAPP(c_Product__Type_OPair(_1426523, _1426525), _1426531), _1426533)), _1426527 = _1426531, _1426529 = _1426533], (1224 ^ _776541) ^ [_794705, _794707] : [-(class_Rings_Ocomm__ring__1(_794705)), _794707 = _794705, class_Rings_Ocomm__ring__1(_794707)], (51587 ^ _776541) ^ [_1820265, _1820267, _1820269, _1820271] : [class_Divides_Osemiring__div(_1820265), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820265), _1820267), c_Divides_Odiv__class_Omod(_1820265, _1820269, _1820271))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820265), _1820267), _1820271)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820265), _1820267), _1820269)))], (28615 ^ _776541) ^ [_1289784] : [class_Int_Onumber__ring(_1289784), c_Int_Oiszero(_1289784, hAPP(c_Int_Onumber__class_Onumber__of(_1289784), c_Int_OBit1(c_Int_OPls)))], (43150 ^ _776541) ^ [_1636202, _1636204, _1636206, _1636208] : [_1636204 = c_List_Olist_ONil(_1636202), -(hAPP(hAPP(c_List_Olist__update(_1636202, _1636204), _1636206), _1636208) = c_List_Olist_ONil(_1636202))], (35925 ^ _776541) ^ [_1449653, _1449655, _1449657] : [class_Groups_Olinordered__ab__semigroup__add(_1449653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1449653), _1449655)), -(_1449655 = c_Orderings_Obot__class_Obot(tc_fun(_1449653, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1449653), _1449657), c_Big__Operators_Olinorder__class_OMax(_1449653, _1449655)) = c_Big__Operators_Olinorder__class_OMax(_1449653, hAPP(c_Set_OCollect(_1449653), hAPP(hAPP(c_COMBB(tc_fun(_1449653, tc_HOL_Obool), tc_HOL_Obool, _1449653), c_HOL_OEx(_1449653)), hAPP(hAPP(c_COMBC(_1449653, tc_fun(_1449653, tc_HOL_Obool), tc_fun(_1449653, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449653, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1449653, tc_HOL_Obool), tc_fun(_1449653, tc_HOL_Obool)), _1449653), c_COMBS(_1449653, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449653, tc_HOL_Obool), tc_fun(_1449653, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1449653), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1449653), c_fconj)), hAPP(hAPP(c_COMBC(_1449653, tc_fun(_1449653, _1449653), tc_fun(_1449653, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449653, tc_HOL_Obool), tc_fun(tc_fun(_1449653, _1449653), tc_fun(_1449653, tc_HOL_Obool)), _1449653), c_COMBB(_1449653, tc_HOL_Obool, _1449653)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1449653), _1449657))))), hAPP(hAPP(c_COMBC(_1449653, tc_fun(_1449653, tc_HOL_Obool), tc_HOL_Obool), c_member(_1449653)), _1449655))))))], (36081 ^ _776541) ^ [_1455890, _1455892, _1455894, _1455896, _1455898, _1455900] : [-(c_Product__Type_Oprod_Oprod__rec(_1455890, _1455892, _1455894, _1455896, hAPP(hAPP(c_Product__Type_OPair(_1455890, _1455892), _1455898), _1455900)) = hAPP(hAPP(_1455896, _1455898), _1455900))], (39075 ^ _776541) ^ [_1529311, _1529313, _1529315] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529311, _1529313), _1529315), hAPP(c_COMBK(tc_fun(_1529313, tc_HOL_Obool), _1529311), c_Orderings_Obot__class_Obot(tc_fun(_1529313, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529311, _1529313), tc_HOL_Obool)))], (17819 ^ _776541) ^ [_1097211, _1097213] : [class_Groups_Ogroup__add(_1097211), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097211), c_Groups_Ozero__class_Ozero(_1097211)), _1097213) = hAPP(c_Groups_Ouminus__class_Ouminus(_1097211), _1097213))], (16831 ^ _776541) ^ [_1079456, _1079458, _1079460] : [class_Groups_Oordered__comm__monoid__add(_1079456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079456), c_Groups_Ozero__class_Ozero(_1079456)), _1079458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079456), c_Groups_Ozero__class_Ozero(_1079456)), _1079460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079456), c_Groups_Ozero__class_Ozero(_1079456)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079456), _1079458), _1079460))))], (12586 ^ _776541) ^ [_998148, _998150, _998152, _998154, _998156, _998158] : [c_Finite__Set_Ofun__left__comm(_998148, _998150, _998152), hBOOL(hAPP(c_Finite__Set_Ofinite(_998148), _998154)), hBOOL(hAPP(hAPP(c_member(_998148), _998156), _998154)), -(hAPP(hAPP(c_Finite__Set_Ofold(_998148, _998150, _998152), _998158), _998154) = hAPP(hAPP(_998152, _998156), hAPP(hAPP(c_Finite__Set_Ofold(_998148, _998150, _998152), _998158), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998148, tc_HOL_Obool)), _998154), hAPP(hAPP(c_Set_Oinsert(_998148), _998156), c_Orderings_Obot__class_Obot(tc_fun(_998148, tc_HOL_Obool)))))))], (50285 ^ _776541) ^ [_1793051, _1793053, _1793055] : [c_Fun_Obij__betw(_1793051, _1793053, _1793055, c_Orderings_Otop__class_Otop(tc_fun(_1793051, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793053, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1793053, _1793051, c_Orderings_Otop__class_Otop(tc_fun(_1793053, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1793051, _1793053, c_Orderings_Otop__class_Otop(tc_fun(_1793051, tc_HOL_Obool)), _1793055)) = _1793055)], (28809 ^ _776541) ^ [_1293051] : [c_Int_OPls = _1293051, -(c_Int_OPls = c_Int_OBit0(_1293051))], (14999 ^ _776541) ^ [_1047223, _1047225, _1047227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047223), _1047225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047223), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047225), _1047227))))], (706 ^ _776541) ^ [_787186, _787188, _787190, _787192] : [-(c_Predicate_Oreflp(_787190, _787186)), c_Predicate_Oreflp(_787192, _787188), _787192 = _787190, _787188 = _787186], (10397 ^ _776541) ^ [_955107, _955109, _955111] : [class_Groups_Oordered__ab__group__add(_955107), 10400 ^ _776541 : [(10407 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955107), _955111), _955109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955107), hAPP(c_Groups_Ouminus__class_Ouminus(_955107), _955109)), hAPP(c_Groups_Ouminus__class_Ouminus(_955107), _955111))))], (10401 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955107), hAPP(c_Groups_Ouminus__class_Ouminus(_955107), _955109)), hAPP(c_Groups_Ouminus__class_Ouminus(_955107), _955111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955107), _955111), _955109)))]]], (34779 ^ _776541) ^ [_1425361, _1425363, _1425365, _1425367, _1425369, _1425371, _1425373] : [hBOOL(hAPP(hAPP(c_member(_1425361), _1425363), hAPP(hAPP(_1425365, _1425367), _1425369))), -(hBOOL(hAPP(hAPP(c_member(_1425361), _1425363), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425371, _1425373, tc_fun(_1425361, tc_HOL_Obool)), _1425365), hAPP(hAPP(c_Product__Type_OPair(_1425371, _1425373), _1425367), _1425369)))))], (36476 ^ _776541) ^ [_1466555, _1466557, _1466559, _1466561, _1466563] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466555, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466557, _1466555, _1466559), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466557, tc_HOL_Obool)), _1466561), _1466563))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466555, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466557, _1466555, _1466559), _1466561)), hAPP(c_Relation_OImage(_1466557, _1466555, _1466559), _1466563)))))], (44848 ^ _776541) ^ [_1673779, _1673781, _1673783] : [-(hAPP(hAPP(c_List_Omap(_1673779, _1673781), _1673783), c_List_Olist_ONil(_1673779)) = c_List_Olist_ONil(_1673781))], (1114 ^ _776541) ^ [_793330, _793332] : [-(class_Groups_Olinordered__ab__group__add(_793330)), _793332 = _793330, class_Groups_Olinordered__ab__group__add(_793332)], (42236 ^ _776541) ^ [_1614118, _1614120, _1614122, _1614124] : [-(hAPP(hAPP(c_List_Onth(_1614118), hAPP(hAPP(c_List_Olist_OCons(_1614118), _1614120), _1614122)), _1614124) = c_Nat_Onat_Onat__case(_1614118, _1614120, hAPP(c_List_Onth(_1614118), _1614122), _1614124))], (33953 ^ _776541) ^ [_1406231, _1406233, _1406235, _1406237, _1406239] : [class_Groups_Ocomm__monoid__add(_1406231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406233), _1406235)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406233, _1406231), _1406237), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406233, tc_HOL_Obool)), _1406235), _1406239)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406233, _1406231), hAPP(hAPP(c_COMBC(_1406233, _1406231, _1406231), hAPP(hAPP(c_COMBS(_1406233, _1406231, tc_fun(_1406231, _1406231)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1406231, tc_fun(_1406231, _1406231)), _1406233), c_If(_1406231)), hAPP(hAPP(c_COMBC(_1406233, tc_fun(_1406233, tc_HOL_Obool), tc_HOL_Obool), c_member(_1406233)), _1406239))), _1406237)), c_Groups_Ozero__class_Ozero(_1406231))), _1406235))], (27587 ^ _776541) ^ [_1272768, _1272770] : [class_Int_Onumber__ring(_1272768), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272768), hAPP(c_Int_Onumber__class_Onumber__of(_1272768), c_Int_OPls)), _1272770) = _1272770)], (28413 ^ _776541) ^ [_1286564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286564)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286564), c_Int_OPls)))], (18626 ^ _776541) ^ [_1111809, _1111811, _1111813] : [18627 ^ _776541 : [(18630 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111811), _1111813))], (18628 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111809)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111809), _1111811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111809), _1111813))))], (32083 ^ _776541) ^ [_1352967, _1352969, _1352971] : [class_Orderings_Olinorder(_1352967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352967), _1352969)), -(c_Big__Operators_Olattice_OSup__fin(_1352967, c_Orderings_Oord__class_Omax(_1352967), hAPP(hAPP(c_Set_Oinsert(_1352967), _1352971), _1352969)) = hAPP(hAPP(c_Finite__Set_Ofold(_1352967, _1352967, c_Orderings_Oord__class_Omax(_1352967)), _1352971), _1352969))], (34347 ^ _776541) ^ [_1415898, _1415900] : [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), _1415898))), 34350 ^ _776541 : [(34357 ^ _776541) ^ [] : [-(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), _1415900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415898))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415900), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415898)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415898)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415900), 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), _1415898)))))], (34351 ^ _776541) ^ [] : [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), _1415900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415898)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415900), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415898)) = 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), _1415900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415898))))]]], (42457 ^ _776541) ^ [_1619521, _1619523, _1619525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619521), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619523)), _1619525))), -(hBOOL(hAPP(hAPP(c_member(_1619523), hAPP(hAPP(c_List_Onth(_1619523), _1619525), _1619521)), hAPP(c_List_Oset(_1619523), _1619525))))], (21197 ^ _776541) ^ [_1159907, _1159909, _1159911] : [class_Int_Onumber__ring(_1159907), class_Rings_Olinordered__idom(_1159907), 21204 ^ _776541 : [(21211 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159909), _1159911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159907), hAPP(c_Int_Onumber__class_Onumber__of(_1159907), _1159909)), hAPP(c_Int_Onumber__class_Onumber__of(_1159907), _1159911))))], (21205 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159907), hAPP(c_Int_Onumber__class_Onumber__of(_1159907), _1159909)), hAPP(c_Int_Onumber__class_Onumber__of(_1159907), _1159911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159909), _1159911)))]]], (10647 ^ _776541) ^ [_959638, _959640, _959642] : [class_Lattices_Oboolean__algebra(_959638), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959638), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959638), _959640), _959642)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959638), hAPP(c_Groups_Ouminus__class_Ouminus(_959638), _959640)), hAPP(c_Groups_Ouminus__class_Ouminus(_959638), _959642)))], (23313 ^ _776541) ^ [_1198998, _1199000, _1199002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198998)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1199000), _1199002)), 23320 ^ _776541 : [(23321 ^ _776541) ^ [_1199188] : [23323 ^ _776541 : [(23329 ^ _776541) ^ [] : [-(_1199188 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23325 ^ [_1198998, _1199000, _1199002, _1199188]), 23322 ^ [_1198998, _1199000, _1199002, _1199188]))], (23327 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23325 ^ [_1198998, _1199000, _1199002, _1199188]), _1199002)))], (23324 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23322 ^ [_1198998, _1199000, _1199002, _1199188]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1198998))))]], -(_1199188 = _1199000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199188), _1198998) = _1199000]]], (49141 ^ _776541) ^ [_1768098, _1768100, _1768102, _1768104] : [-(hAPP(c_Relation_OImage(_1768098, _1768100, hAPP(c_Set_OCollect(tc_prod(_1768098, _1768100)), hAPP(c_Product__Type_Oprod_Oprod__case(_1768098, _1768100, tc_HOL_Obool), _1768102))), _1768104) = hAPP(c_Set_OCollect(_1768100), hAPP(hAPP(c_COMBB(tc_fun(_1768098, tc_HOL_Obool), tc_HOL_Obool, _1768100), c_HOL_OEx(_1768098)), hAPP(hAPP(c_COMBB(tc_fun(_1768098, tc_HOL_Obool), tc_fun(_1768098, tc_HOL_Obool), _1768100), hAPP(c_COMBS(_1768098, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1768098), c_fconj), hAPP(hAPP(c_COMBC(_1768098, tc_fun(_1768098, tc_HOL_Obool), tc_HOL_Obool), c_member(_1768098)), _1768104)))), hAPP(c_COMBC(_1768098, _1768100, tc_HOL_Obool), _1768102)))))], (48684 ^ _776541) ^ [_1757906, _1757908, _1757910, _1757912] : [-(hBOOL(hAPP(_1757906, _1757908))), -(hAPP(c_List_Ofilter(_1757910, _1757906), c_List_Oreplicate(_1757910, _1757912, _1757908)) = c_List_Olist_ONil(_1757910))], (14510 ^ _776541) ^ [_1038338, _1038340] : [-(_1038338 = _1038340), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038338), _1038340))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038340), _1038338)))], (26559 ^ _776541) ^ [_1255927, _1255929] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1255927, _1255929)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1255929), _1255927)))], (21827 ^ _776541) ^ [_1171981, _1171983, _1171985, _1171987] : [class_Fields_Olinordered__field__inverse__zero(_1171981), class_Int_Onumber(_1171981), 21834 ^ _776541 : [(21835 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171981), _1171983), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985))), _1171987)), 21838 ^ _776541 : [(21845 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), c_Groups_Ozero__class_Ozero(_1171981)), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985)))), 21848 ^ _776541 : [(21855 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985)), c_Groups_Ozero__class_Ozero(_1171981)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), c_Groups_Ozero__class_Ozero(_1171981)), _1171987)))], (21849 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985)), c_Groups_Ozero__class_Ozero(_1171981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171981), _1171987), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985))), _1171983)))]]], (21839 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), c_Groups_Ozero__class_Ozero(_1171981)), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), _1171983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171981), _1171987), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985)))))]]], (21861 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171981), _1171983), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985))), _1171987))), 21864 ^ _776541 : [(21867 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), _1171983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171981), _1171987), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985))))], (21865 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), c_Groups_Ozero__class_Ozero(_1171981)), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985))))]], 21868 ^ _776541 : [(21871 ^ _776541) ^ [] : [21872 ^ _776541 : [(21875 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171981), _1171987), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985))), _1171983))], (21873 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985)), c_Groups_Ozero__class_Ozero(_1171981))))]], 21876 ^ _776541 : [(21879 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171981), c_Groups_Ozero__class_Ozero(_1171981)), _1171987))], (21877 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985)), c_Groups_Ozero__class_Ozero(_1171981)))]]], (21869 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171981), c_Groups_Ozero__class_Ozero(_1171981)), hAPP(c_Int_Onumber__class_Onumber__of(_1171981), _1171985)))]]]]], (49798 ^ _776541) ^ [_1782627, _1782629, _1782631] : [-(c_Equiv__Relations_Oequiv(_1782627, _1782629, _1782631)), c_Relation_Orefl__on(_1782627, _1782629, _1782631), c_Relation_Osym(_1782627, _1782631), c_Relation_Otrans(_1782627, _1782631)], (3228 ^ _776541) ^ [_824610, _824612, _824614, _824616, _824618, _824620] : [-(c_Big__Operators_Olattice_OSup__fin(_824620, _824616, _824612) = c_Big__Operators_Olattice_OSup__fin(_824618, _824614, _824610)), _824620 = _824618, _824616 = _824614, _824612 = _824610], (858 ^ _776541) ^ [_789352, _789354, _789356, _789358, _789360, _789362, _789364, _789366] : [-(c_Fun_Oinj__on(_789364, _789360, _789356, _789352)), c_Fun_Oinj__on(_789366, _789362, _789358, _789354), _789366 = _789364, _789362 = _789360, _789358 = _789356, _789354 = _789352], (51701 ^ _776541) ^ [_1822192, _1822194] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822192), _1822194)), 51706 ^ _776541 : [(51709 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822194), _1822192))], (51707 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822192), _1822194)))]], -(_1822192 = _1822194)], (10629 ^ _776541) ^ [_959337, _959339, _959341] : [class_Lattices_Oboolean__algebra(_959337), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959337), _959339), _959341) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959337), _959339), hAPP(c_Groups_Ouminus__class_Ouminus(_959337), _959341)))], (7994 ^ _776541) ^ [_911912, _911914, _911916] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911912, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911912, tc_HOL_Obool)), _911914), _911916)), _911914)))], (46427 ^ _776541) ^ [_1710223, _1710225, _1710227, _1710229, _1710231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1710223), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1710225), _1710227))), -(hAPP(hAPP(c_List_Onth(_1710229), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1710229), _1710231), c_List_Oupt(_1710227, _1710225))), _1710223) = hAPP(_1710231, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710227), _1710223)))], (44082 ^ _776541) ^ [_1658212, _1658214, _1658216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658212), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658214)), _1658216))), -(_1658216 = hAPP(hAPP(c_List_Oappend(_1658214), hAPP(hAPP(c_List_Otake(_1658214), _1658212), _1658216)), hAPP(hAPP(c_List_Olist_OCons(_1658214), hAPP(hAPP(c_List_Onth(_1658214), _1658216), _1658212)), hAPP(hAPP(c_List_Odrop(_1658214), hAPP(c_Nat_OSuc, _1658212)), _1658216))))], (1424 ^ _776541) ^ [_797205, _797207] : [-(class_Lattices_Olattice(_797205)), _797207 = _797205, class_Lattices_Olattice(_797207)], (27369 ^ _776541) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (44022 ^ _776541) ^ [_1656591, _1656593, _1656595, _1656597, _1656599] : [-(hAPP(hAPP(c_List_Oappend(_1656591), _1656593), _1656595) = hAPP(hAPP(c_List_Oappend(_1656591), _1656597), _1656599)), 44025 ^ _776541 : [(44028 ^ _776541) ^ [] : [_1656593 = hAPP(hAPP(c_List_Otake(_1656591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656593)), _1656597), _1656595 = hAPP(hAPP(c_List_Oappend(_1656591), hAPP(hAPP(c_List_Odrop(_1656591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656593)), _1656597)), _1656599)], (44026 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656593)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656597))))]], 44033 ^ _776541 : [(44036 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Otake(_1656591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656597)), _1656593) = _1656597, hAPP(hAPP(c_List_Oappend(_1656591), hAPP(hAPP(c_List_Odrop(_1656591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656597)), _1656593)), _1656595) = _1656599], (44034 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656593)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656591)), _1656597)))]]], (42612 ^ _776541) ^ [_1624908, _1624910] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1624908, _1624910) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1624908, _1624910)))], (11024 ^ _776541) ^ [_967097, _967099, _967101] : [class_Lattices_Oab__semigroup__idem__mult(_967097), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967097), _967099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967097), _967099), _967101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967097), _967099), _967101))], (6370 ^ _776541) ^ [_879297, _879299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879297, tc_HOL_Obool)), _879299), c_Orderings_Obot__class_Obot(tc_fun(_879297, tc_HOL_Obool)))), -(_879299 = c_Orderings_Obot__class_Obot(tc_fun(_879297, tc_HOL_Obool)))], (25967 ^ _776541) ^ [_1246058] : [hBOOL(hAPP(_1246058, 25968 ^ [_1246058])), 25971 ^ _776541 : [(25972 ^ _776541) ^ [_1246152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246152)), -(hBOOL(hAPP(_1246058, hAPP(c_Int_Onat, _1246152))))]]], (47208 ^ _776541) ^ [_1725608, _1725610] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725608), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1725608))), _1725610))), -(c_List_Otranspose(_1725608, c_List_Otranspose(_1725608, _1725610)) = c_List_OtakeWhile(tc_List_Olist(_1725608), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1725608)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1725608), tc_List_Olist(_1725608), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1725608))), _1725610))], (44874 ^ _776541) ^ [_1674857, _1674859, _1674861, _1674863] : [-(hAPP(hAPP(c_List_Omap(_1674857, _1674859), _1674861), hAPP(c_List_Otl(_1674857), _1674863)) = hAPP(c_List_Otl(_1674859), hAPP(hAPP(c_List_Omap(_1674857, _1674859), _1674861), _1674863)))], (33913 ^ _776541) ^ [_1405084, _1405086, _1405088, _1405090, _1405092] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405084, tc_fun(_1405086, tc_HOL_Obool)), _1405088), hAPP(hAPP(c_COMBS(_1405084, tc_fun(_1405086, tc_HOL_Obool), tc_fun(_1405086, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405086, tc_HOL_Obool), tc_fun(tc_fun(_1405086, tc_HOL_Obool), tc_fun(_1405086, tc_HOL_Obool)), _1405084), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405086, tc_HOL_Obool))), _1405090)), _1405092)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405086, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1405086, tc_HOL_Obool), hAPP(c_Set_Oimage(_1405084, tc_fun(_1405086, tc_HOL_Obool), _1405090), _1405088))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1405086, tc_HOL_Obool), hAPP(c_Set_Oimage(_1405084, tc_fun(_1405086, tc_HOL_Obool), _1405092), _1405088))))], (22425 ^ _776541) ^ [_1183054, _1183056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183054), _1183056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1183054), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1183056), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (46448 ^ _776541) ^ [_1710896, _1710898, _1710900, _1710902, _1710904] : [class_Orderings_Olinorder(_1710896), hBOOL(hAPP(hAPP(c_member(_1710898), _1710900), hAPP(c_List_Oset(_1710898), _1710902))), c_List_Olinorder__class_Osorted(_1710896, hAPP(hAPP(c_List_Omap(_1710898, _1710896), _1710904), _1710902)), hAPP(c_List_Ohd(_1710898), hAPP(c_List_Ofilter(_1710898, hAPP(hAPP(c_COMBB(_1710896, tc_HOL_Obool, _1710898), hAPP(c_fequal, hAPP(_1710904, _1710900))), _1710904)), _1710902)) = _1710900, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710898, _1710896, _1710904), _1710900), c_List_Oremove1(_1710898, _1710900, _1710902)) = _1710902)], (26703 ^ _776541) ^ [_1258387, _1258389] : [c_Nat__Transfer_Onat__set(_1258387), c_Nat__Transfer_Onat__set(_1258389), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258387), _1258389) = 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), _1258387)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258389))))], (40771 ^ _776541) ^ [_1574362, _1574364, _1574366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574362, _1574362), tc_HOL_Obool)), _1574364), _1574366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574362, _1574362), tc_HOL_Obool)), _1574366), c_Transitive__Closure_Ortrancl(_1574362, _1574364))), -(c_Transitive__Closure_Ortrancl(_1574362, _1574366) = c_Transitive__Closure_Ortrancl(_1574362, _1574364))], (8411 ^ _776541) ^ [_920980, _920982, _920984] : [class_Lattices_Osemilattice__inf(_920980), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920980), _920982), _920984) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920980), _920984), _920982))], (33257 ^ _776541) ^ [_1386173, _1386175, _1386177, _1386179] : [-(_1386173 = c_Orderings_Obot__class_Obot(tc_fun(_1386175, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386175, tc_fun(_1386177, tc_HOL_Obool)), _1386173), hAPP(c_COMBK(tc_fun(_1386177, tc_HOL_Obool), _1386175), _1386179)) = _1386179)], (19220 ^ _776541) ^ [_1123163, _1123165, _1123167, _1123169, _1123171] : [class_Groups_Ocomm__monoid__add(_1123163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123165), _1123167)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123165), _1123169)), 19234 ^ _776541 : [(19237 ^ _776541) ^ [] : [hAPP(_1123171, 19233 ^ [_1123163, _1123165, _1123167, _1123169, _1123171]) = c_Groups_Ozero__class_Ozero(_1123163)], (19235 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1123165), 19233 ^ [_1123163, _1123165, _1123167, _1123169, _1123171]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1123165, tc_HOL_Obool)), _1123167), _1123169))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1123165, _1123163), _1123171), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1123165, tc_HOL_Obool)), _1123167), _1123169)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123163), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1123165, _1123163), _1123171), _1123167)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1123165, _1123163), _1123171), _1123169)))], (11467 ^ _776541) ^ [_976841] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_976841), c_Orderings_Obot__class_Obot(tc_fun(_976841, tc_HOL_Obool)))))], (34031 ^ _776541) ^ [_1408346, _1408348] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1408346))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1408348)), hAPP(c_Int_Onat, _1408346)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1408348), _1408346)), 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)))], (7666 ^ _776541) ^ [_904251, _904253, _904255, _904257] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904251, tc_HOL_Obool)), _904253), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904251, tc_HOL_Obool)), _904255), _904257)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904251, tc_HOL_Obool)), _904255), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904251, tc_HOL_Obool)), _904253), _904257)))], (48051 ^ _776541) ^ [_1744337, _1744339, _1744341] : [-(c_List_Olist__ex(_1744337, _1744339, _1744341)), 48052 ^ _776541 : [(48053 ^ _776541) ^ [_1744402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744402), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744337)), _1744341))), hBOOL(hAPP(_1744339, hAPP(hAPP(c_List_Onth(_1744337), _1744341), _1744402)))]]], (33985 ^ _776541) ^ [_1407393, _1407395, _1407397, _1407399] : [class_Complete__Lattice_Ocomplete__lattice(_1407393), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407395), _1407397)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407395, _1407393), _1407397), _1407399) = hAPP(hAPP(c_Finite__Set_Ofold(_1407395, _1407393, hAPP(hAPP(c_COMBB(_1407393, tc_fun(_1407393, _1407393), _1407395), c_Lattices_Osemilattice__sup__class_Osup(_1407393)), _1407399)), c_Orderings_Obot__class_Obot(_1407393)), _1407397))], (10671 ^ _776541) ^ [_960141, _960143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960141, tc_HOL_Obool)), _960143), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960141, tc_HOL_Obool)), _960143))), -(_960143 = c_Orderings_Obot__class_Obot(tc_fun(_960141, tc_HOL_Obool)))], (45052 ^ _776541) ^ [_1678777, _1678779] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1678777), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1678779), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45059 ^ _776541 : [(45066 ^ _776541) ^ [] : [_1678777 = _1678779, -(hAPP(c_Code__Numeral_Oof__nat, _1678777) = hAPP(c_Code__Numeral_Oof__nat, _1678779))], (45060 ^ _776541) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1678777) = hAPP(c_Code__Numeral_Oof__nat, _1678779), -(_1678777 = _1678779)]]], (28095 ^ _776541) ^ [_1281227, _1281229] : [class_Rings_Osemiring__1(_1281227), 28098 ^ _776541 : [(28105 ^ _776541) ^ [] : [_1281229 = c_Groups_Ozero__class_Ozero(_1281227), -(c_Int_Oiszero(_1281227, _1281229))], (28099 ^ _776541) ^ [] : [c_Int_Oiszero(_1281227, _1281229), -(_1281229 = c_Groups_Ozero__class_Ozero(_1281227))]]], (45670 ^ _776541) ^ [_1692589, _1692591, _1692593] : [-(c_Enum_Osublists(_1692589, hAPP(hAPP(c_List_Olist_OCons(_1692589), _1692591), _1692593)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1692589)), tc_List_Olist(tc_List_Olist(_1692589))), c_Enum_Osublists(_1692589, _1692593)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1692589)), tc_List_Olist(tc_List_Olist(_1692589)), tc_List_Olist(tc_List_Olist(_1692589))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1692589)), tc_fun(tc_List_Olist(tc_List_Olist(_1692589)), tc_List_Olist(tc_List_Olist(_1692589))), tc_List_Olist(tc_List_Olist(_1692589))), c_List_Oappend(tc_List_Olist(_1692589))), hAPP(c_List_Omap(tc_List_Olist(_1692589), tc_List_Olist(_1692589)), hAPP(c_List_Olist_OCons(_1692589), _1692591)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1692589))))))], (8227 ^ _776541) ^ [_917276, _917278] : [class_Lattices_Obounded__lattice__top(_917276), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917276), _917278), c_Orderings_Otop__class_Otop(_917276)) = _917278)], (33251 ^ _776541) ^ [_1386036, _1386038, _1386040, _1386042] : [_1386036 = c_Orderings_Obot__class_Obot(tc_fun(_1386038, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386038, tc_fun(_1386040, tc_HOL_Obool)), _1386036), hAPP(c_COMBK(tc_fun(_1386040, tc_HOL_Obool), _1386038), _1386042)) = c_Orderings_Obot__class_Obot(tc_fun(_1386040, tc_HOL_Obool)))], (52419 ^ _776541) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (25159 ^ _776541) ^ [_1232062, _1232064, _1232066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1232062), _1232064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232066), _1232064)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232066), _1232062))))], (34473 ^ _776541) ^ [_1418054, _1418056, _1418058, _1418060, _1418062, _1418064] : [hBOOL(hAPP(hAPP(_1418054, _1418056), _1418058)), hBOOL(hAPP(hAPP(_1418060, _1418056), _1418058)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418062, tc_fun(_1418064, tc_HOL_Obool))), _1418054), _1418060), _1418056), _1418058)))], (26104 ^ _776541) ^ [] : [-(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))))], (25363 ^ _776541) ^ [_1235426] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235426))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235426)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26773 ^ _776541) ^ [_1259405] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259405)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259405))], (33218 ^ _776541) ^ [_1385310] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1385310, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1385310), hAPP(c_COMBK(tc_HOL_Obool, _1385310), c_fFalse)))], (27871 ^ _776541) ^ [_1277647, _1277649] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1277647), hAPP(hAPP(c_Power_Opower__class_Opower(_1277647), hAPP(c_Int_Onumber__class_Onumber__of(_1277647), c_Int_OMin)), _1277649)) = c_Groups_Oone__class_Oone(_1277647)), class_Int_Onumber__ring(_1277647), class_Rings_Olinordered__idom(_1277647)], (31305 ^ _776541) ^ [_1338385, _1338387, _1338389, _1338391] : [class_Orderings_Olinorder(_1338385), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338385), _1338387), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338385), _1338389), _1338391)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338385), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338385), _1338387), _1338389)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338385), _1338387), _1338391)))], (45402 ^ _776541) ^ [_1686442, _1686444] : [-(hBOOL(hAPP(c_List_Olistsp(_1686442, _1686444), c_List_Olist_ONil(_1686442))))], (17695 ^ _776541) ^ [_1095127, _1095129] : [class_Groups_Olinordered__ab__group__add(_1095127), 17698 ^ _776541 : [(17705 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095127), c_Groups_Ozero__class_Ozero(_1095127)), _1095129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095127), hAPP(c_Groups_Ouminus__class_Ouminus(_1095127), _1095129)), _1095129)))], (17699 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095127), hAPP(c_Groups_Ouminus__class_Ouminus(_1095127), _1095129)), _1095129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095127), c_Groups_Ozero__class_Ozero(_1095127)), _1095129)))]]], (4890 ^ _776541) ^ [_851069, _851071, _851073, _851075] : [-(c_List_Olistrel(_851075, _851071) = c_List_Olistrel(_851073, _851069)), _851075 = _851073, _851071 = _851069], (25153 ^ _776541) ^ [_1231929, _1231931, _1231933] : [class_Divides_Osemiring__div(_1231929), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231929), c_Divides_Odiv__class_Omod(_1231929, _1231931, _1231933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231929), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231929), _1231931), _1231933)), _1231933)) = _1231931)], (8505 ^ _776541) ^ [_922642, _922644, _922646] : [class_Lattices_Osemilattice__sup(_922642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922642), _922644), _922646)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922642), _922644), _922646) = _922646)], (29735 ^ _776541) ^ [_1309648, _1309650, _1309652] : [29737 ^ _776541 : [(29740 ^ _776541) ^ [] : [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(_1309650, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29736 ^ [_1309648, _1309650, _1309652]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1309650, 29736 ^ [_1309648, _1309650, _1309652])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29738 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29736 ^ [_1309648, _1309650, _1309652]), _1309648)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1309650, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1309652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309652), hAPP(_1309650, _1309648))), 29750 ^ _776541 : [(29753 ^ _776541) ^ [] : [-(hAPP(_1309650, 29749 ^ [_1309648, _1309650, _1309652]) = _1309652)], (29751 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29749 ^ [_1309648, _1309650, _1309652]), _1309648)))]]], (29019 ^ _776541) ^ [_1296753, _1296755] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1296753)), c_Int_OBit0(_1296755)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296753), _1296755)))], (17639 ^ _776541) ^ [_1094183] : [class_Rings_Olinordered__semidom(_1094183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094183), c_Groups_Oone__class_Oone(_1094183)), c_Groups_Ozero__class_Ozero(_1094183)))], (2698 ^ _776541) ^ [_816405, _816407, _816409, _816411, _816413, _816415] : [-(c_Finite__Set_Ofold1Set(_816415, _816411, _816407) = c_Finite__Set_Ofold1Set(_816413, _816409, _816405)), _816415 = _816413, _816411 = _816409, _816407 = _816405], (1264 ^ _776541) ^ [_795205, _795207] : [-(class_Int_Oring__char__0(_795205)), _795207 = _795205, class_Int_Oring__char__0(_795207)], (2108 ^ _776541) ^ [_807116, _807118, _807120, _807122] : [-(c_SMT_Oz3mod(_807122, _807118) = c_SMT_Oz3mod(_807120, _807116)), _807122 = _807120, _807118 = _807116], (43551 ^ _776541) ^ [_1645227, _1645229, _1645231, _1645233, _1645235, _1645237] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645227)), _1645229) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645231)), _1645233), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645227)), _1645235) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645231)), _1645237), -(hAPP(hAPP(c_List_Ozip(_1645227, _1645231), hAPP(hAPP(c_List_Oappend(_1645227), _1645229), _1645235)), hAPP(hAPP(c_List_Oappend(_1645231), _1645233), _1645237)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1645227, _1645231)), hAPP(hAPP(c_List_Ozip(_1645227, _1645231), _1645229), _1645233)), hAPP(hAPP(c_List_Ozip(_1645227, _1645231), _1645235), _1645237)))], (26877 ^ _776541) ^ [_1260824, _1260826] : [class_Int_Oring__char__0(_1260824), 26880 ^ _776541 : [(26887 ^ _776541) ^ [] : [_1260826 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1260824), _1260826) = c_Groups_Ozero__class_Ozero(_1260824))], (26881 ^ _776541) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1260824), _1260826) = c_Groups_Ozero__class_Ozero(_1260824), -(_1260826 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (9954 ^ _776541) ^ [_946986, _946988, _946990] : [class_Orderings_Oorder(_946986), 9957 ^ _776541 : [(9964 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946986), _946988), _946990))), -(c_SetInterval_Oord__class_OatLeastAtMost(_946986, _946988, _946990) = c_Orderings_Obot__class_Obot(tc_fun(_946986, tc_HOL_Obool)))], (9958 ^ _776541) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_946986, _946988, _946990) = c_Orderings_Obot__class_Obot(tc_fun(_946986, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946986), _946988), _946990))]]], (6959 ^ _776541) ^ [_889457, _889459] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_889457, tc_HOL_Obool), hAPP(c_Set_OPow(_889457), _889459)) = _889459)], (26054 ^ _776541) ^ [_1247494, _1247496] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247494), _1247496)), _1247496) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247494), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247494, _1247496)))], (24551 ^ _776541) ^ [_1220624, _1220626, _1220628] : [-(hBOOL(hAPP(_1220624, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1220626), _1220628))))), 24554 ^ _776541 : [(24557 ^ _776541) ^ [] : [hBOOL(hAPP(_1220624, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220626)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220628))))], (24555 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220628), _1220626)))]], 24558 ^ _776541 : [(24561 ^ _776541) ^ [] : [hBOOL(hAPP(_1220624, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24559 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220626), _1220628)))]]], (9410 ^ _776541) ^ [_938391, _938393, _938395] : [class_Orderings_Olinorder(_938391), 9413 ^ _776541 : [(9420 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938391), _938395), _938393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938391), _938393), _938395))], (9414 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938391), _938393), _938395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938391), _938395), _938393)))]]], (16777 ^ _776541) ^ [_1078389, _1078391] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078389)), _1078391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1078391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1078389), _1078391)))], (6322 ^ _776541) ^ [_878404, _878406, _878408] : [_878404 = _878406, 6325 ^ _776541 : [(6328 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878408, tc_HOL_Obool)), _878406), _878404)))], (6326 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878408, tc_HOL_Obool)), _878404), _878406)))]]], (49678 ^ _776541) ^ [_1780740, _1780742, _1780744, _1780746] : [c_Relation_Osym(_1780740, _1780742), hBOOL(hAPP(hAPP(c_member(tc_prod(_1780740, _1780740)), hAPP(hAPP(c_Product__Type_OPair(_1780740, _1780740), _1780744), _1780746)), _1780742)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780740, _1780740)), hAPP(hAPP(c_Product__Type_OPair(_1780740, _1780740), _1780746), _1780744)), _1780742)))], (47878 ^ _776541) ^ [_1740618, _1740620, _1740622, _1740624, _1740626] : [-(hAPP(c_List_Ofilter(_1740618, _1740620), _1740622) = hAPP(hAPP(c_List_Olist_OCons(_1740618), _1740624), _1740626)), 47879 ^ _776541 : [(47880 ^ _776541) ^ [_1740746, _1740748] : [_1740622 = hAPP(hAPP(c_List_Oappend(_1740618), _1740748), hAPP(hAPP(c_List_Olist_OCons(_1740618), _1740624), _1740746)), 47886 ^ _776541 : [(47889 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1740620, 47885 ^ [_1740618, _1740620, _1740622, _1740624, _1740626, _1740746, _1740748])))], (47887 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740618), 47885 ^ [_1740618, _1740620, _1740622, _1740624, _1740626, _1740746, _1740748]), hAPP(c_List_Oset(_1740618), _1740748))))]], hBOOL(hAPP(_1740620, _1740624)), _1740626 = hAPP(c_List_Ofilter(_1740618, _1740620), _1740746)]]], (52529 ^ _776541) ^ [_1831864, _1831866] : [hBOOL(_1831864), -(hBOOL(hAPP(hAPP(c_fdisj, _1831866), _1831864)))], (18874 ^ _776541) ^ [_1116568, _1116570] : [_1116568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116568), _1116570) = _1116570)], (45884 ^ _776541) ^ [_1697015, _1697017] : [-(c_List_Oconcat(_1697015, _1697017) = hAPP(c_List_Ofoldl(tc_List_Olist(_1697015), tc_List_Olist(_1697015), c_List_Oappend(_1697015), c_List_Olist_ONil(_1697015)), _1697017))], (20773 ^ _776541) ^ [_1151584, _1151586, _1151588, _1151590] : [class_Fields_Ofield(_1151584), -(_1151586 = c_Groups_Ozero__class_Ozero(_1151584)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151584), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151584), _1151588), _1151586)), _1151590) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151584), _1151588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151584), _1151586), _1151590))), _1151586))], (48631 ^ _776541) ^ [_1756959, _1756961, _1756963, _1756965] : [48639 ^ _776541 : [(48642 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1756965, 48638 ^ [_1756959, _1756961, _1756963, _1756965])))], (48640 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756959), 48638 ^ [_1756959, _1756961, _1756963, _1756965]), hAPP(c_List_Oset(_1756959), c_List_Oreplicate(_1756959, _1756961, _1756963)))))]], hBOOL(hAPP(_1756965, _1756963)), -(_1756961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10923 ^ _776541) ^ [_965133, _965135, _965137, _965139] : [_965137 = _965139, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_965133, _965135, hAPP(hAPP(c_Set_Oinsert(_965133), _965137), c_Orderings_Obot__class_Obot(tc_fun(_965133, tc_HOL_Obool)))), _965139)))], (28075 ^ _776541) ^ [_1280940] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1280940), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280940)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1280940)))], (27409 ^ _776541) ^ [_1269498, _1269500] : [class_Groups_Oordered__ab__group__add__abs(_1269498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269498), c_Groups_Ozero__class_Ozero(_1269498)), _1269500)), -(hAPP(c_Groups_Oabs__class_Oabs(_1269498), _1269500) = _1269500)], (2338 ^ _776541) ^ [_810655, _810657, _810659, _810661] : [-(c_Groups_Osgn__class_Osgn(_810661, _810657) = c_Groups_Osgn__class_Osgn(_810659, _810655)), _810661 = _810659, _810657 = _810655], (8823 ^ _776541) ^ [_928312, _928314, _928316] : [class_Lattices_Olattice(_928312), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928312), _928314), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928312), _928314), _928316)) = _928314)], (11505 ^ _776541) ^ [_977583, _977585, _977587, _977589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977583), _977585)), 11508 ^ _776541 : [(11509 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977587), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_977583, tc_fun(_977587, tc_HOL_Obool)), _977585), _977589))), 11512 ^ _776541 : [(11513 ^ _776541) ^ [_977767] : [hBOOL(hAPP(hAPP(c_member(_977583), _977767), _977585)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977587), hAPP(_977589, _977767))))]]], (11519 ^ _776541) ^ [] : [11521 ^ _776541 : [(11524 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977587), hAPP(_977589, 11520 ^ [_977583, _977585, _977587, _977589])))], (11522 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977583), 11520 ^ [_977583, _977585, _977587, _977589]), _977585)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977587), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_977583, tc_fun(_977587, tc_HOL_Obool)), _977585), _977589))))]]], (27489 ^ _776541) ^ [_1271084, _1271086, _1271088] : [class_Groups_Oordered__ab__group__add__abs(_1271084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271084), _1271086), _1271088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271084), hAPP(c_Groups_Ouminus__class_Ouminus(_1271084), _1271086)), _1271088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271084), hAPP(c_Groups_Oabs__class_Oabs(_1271084), _1271086)), _1271088)))], (4160 ^ _776541) ^ [_839558, _839560, _839562, _839564, _839566, _839568, _839570, _839572] : [-(c_New__Random__Sequence_Opos__bind(_839572, _839568, _839564, _839560) = c_New__Random__Sequence_Opos__bind(_839570, _839566, _839562, _839558)), _839572 = _839570, _839568 = _839566, _839564 = _839562, _839560 = _839558], (29271 ^ _776541) ^ [_1301100, _1301102] : [class_Rings_Ocomm__semiring__1(_1301100), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301100), _1301102), _1301102) = hAPP(hAPP(c_Power_Opower__class_Opower(_1301100), _1301102), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17743 ^ _776541) ^ [_1095943, _1095945] : [class_Groups_Olinordered__ab__group__add(_1095943), 17746 ^ _776541 : [(17753 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095943), c_Groups_Ozero__class_Ozero(_1095943)), _1095945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095943), hAPP(c_Groups_Ouminus__class_Ouminus(_1095943), _1095945)), _1095945)))], (17747 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095943), hAPP(c_Groups_Ouminus__class_Ouminus(_1095943), _1095945)), _1095945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095943), c_Groups_Ozero__class_Ozero(_1095943)), _1095945)))]]], (10014 ^ _776541) ^ [_947927, _947929, _947931] : [class_Orderings_Oorder(_947927), _947929 = _947931, -(c_SetInterval_Oord__class_OatLeastAtMost(_947927, _947929, _947931) = hAPP(hAPP(c_Set_Oinsert(_947927), _947929), c_Orderings_Obot__class_Obot(tc_fun(_947927, tc_HOL_Obool))))], (5749 ^ _776541) ^ [_867338, _867340, _867342] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867338, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867338)), tc_HOL_Obool)), _867340), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867338, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867338)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867338)))), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867338, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867338)), tc_HOL_Obool)), _867342), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867338, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867338)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867338)))), 5756 ^ _776541 : [(5763 ^ _776541) ^ [] : [_867340 = _867342, -(hAPP(c_Hoare__Mirabelle_OAbs__triple(_867338), _867340) = hAPP(c_Hoare__Mirabelle_OAbs__triple(_867338), _867342))], (5757 ^ _776541) ^ [] : [hAPP(c_Hoare__Mirabelle_OAbs__triple(_867338), _867340) = hAPP(c_Hoare__Mirabelle_OAbs__triple(_867338), _867342), -(_867340 = _867342)]]], (29069 ^ _776541) ^ [_1297616] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1297616), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1297616)), c_Int_OPls)))], (316 ^ _776541) ^ [_781335, _781337] : [-(c_Nitpick_Ounknown(_781335)), _781337 = _781335, c_Nitpick_Ounknown(_781337)], (44250 ^ _776541) ^ [_1661359, _1661361, _1661363] : [class_Orderings_Olinorder(_1661359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1661359), _1661361)), -(c_List_Olinorder__class_Osorted__list__of__set(_1661359, hAPP(hAPP(c_Set_Oinsert(_1661359), _1661363), _1661361)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661359, _1661359, c_COMBI(_1661359)), _1661363), c_List_Olinorder__class_Osorted__list__of__set(_1661359, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661359, tc_HOL_Obool)), _1661361), hAPP(hAPP(c_Set_Oinsert(_1661359), _1661363), c_Orderings_Obot__class_Obot(tc_fun(_1661359, tc_HOL_Obool)))))))], (9812 ^ _776541) ^ [_944649, _944651, _944653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944649, tc_HOL_Obool)), _944651), _944653))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944649, tc_HOL_Obool)), _944651), _944653)), -(_944651 = _944653)], (28275 ^ _776541) ^ [_1284186, _1284188] : [class_Int_Onumber__ring(_1284186), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1284186), hAPP(c_Int_Onumber__class_Onumber__of(_1284186), _1284188)), c_Groups_Oone__class_Oone(_1284186)) = hAPP(c_Int_Onumber__class_Onumber__of(_1284186), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1284188), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (25566 ^ _776541) ^ [_1238976, _1238978] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238976) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238978)), 25569 ^ _776541 : [(25572 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238978)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25570 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238976))))]], 25573 ^ _776541 : [(25576 ^ _776541) ^ [] : [25577 ^ _776541 : [(25580 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238976) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (25578 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238978))))]], 25581 ^ _776541 : [(25584 ^ _776541) ^ [] : [_1238976 = _1238978], (25582 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238978)))]]], (25574 ^ _776541) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238976)))]]], (6352 ^ _776541) ^ [_878966, _878968, _878970] : [_878966 = _878968, 6355 ^ _776541 : [(6358 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878970, tc_HOL_Obool)), _878968), _878966)))], (6356 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878970, tc_HOL_Obool)), _878966), _878968)))]]], (42161 ^ _776541) ^ [_1612021, _1612023, _1612025] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612021)), _1612023), c_List_Olists(_1612021, c_Wellfounded_Oacc(_1612021, _1612025)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612021)), _1612023), c_Wellfounded_Oacc(tc_List_Olist(_1612021), c_List_Olistrel1(_1612021, _1612025)))))], (33168 ^ _776541) ^ [_1384136, _1384138, _1384140] : [hBOOL(hAPP(hAPP(c_member(_1384136), _1384138), hAPP(c_Set_OCollect(_1384136), _1384140))), -(hBOOL(hAPP(_1384140, _1384138)))], (12600 ^ _776541) ^ [_998477, _998479, _998481] : [class_Groups_Oab__semigroup__mult(_998477), hBOOL(hAPP(c_Finite__Set_Ofinite(_998477), _998479)), -(_998479 = c_Orderings_Obot__class_Obot(tc_fun(_998477, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_998477), _998481)), -(_998481 = c_Orderings_Obot__class_Obot(tc_fun(_998477, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998477, tc_HOL_Obool)), _998479), _998481) = c_Orderings_Obot__class_Obot(tc_fun(_998477, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_998477, c_Groups_Otimes__class_Otimes(_998477)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998477, tc_HOL_Obool)), _998479), _998481)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998477), hAPP(c_Finite__Set_Ofold1(_998477, c_Groups_Otimes__class_Otimes(_998477)), _998479)), hAPP(c_Finite__Set_Ofold1(_998477, c_Groups_Otimes__class_Otimes(_998477)), _998481)))], (19779 ^ _776541) ^ [_1133505, _1133507, _1133509, _1133511] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1133505, _1133507)), c_Sum__Type_OPlus(_1133505, _1133507, _1133509, _1133511))), 19782 ^ _776541 : [(19785 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1133507), _1133511)))], (19783 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1133505), _1133509)))]]], (34767 ^ _776541) ^ [_1425103, _1425105, _1425107, _1425109, _1425111] : [hBOOL(hAPP(hAPP(_1425103, _1425105), _1425107)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425109, _1425111, tc_HOL_Obool), _1425103), hAPP(hAPP(c_Product__Type_OPair(_1425109, _1425111), _1425105), _1425107))))], (35326 ^ _776541) ^ [_1435485, _1435487, _1435489] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435485), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435487)), _1435489)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435485, _1435487), hAPP(c_Divides_OnegateSnd, _1435489))))], (25987 ^ _776541) ^ [_1246409, _1246411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246411)), 25994 ^ _776541 : [(26001 ^ _776541) ^ [] : [_1246409 = _1246411, -(hAPP(c_Int_Onat, _1246409) = hAPP(c_Int_Onat, _1246411))], (25995 ^ _776541) ^ [] : [hAPP(c_Int_Onat, _1246409) = hAPP(c_Int_Onat, _1246411), -(_1246409 = _1246411)]]], (49238 ^ _776541) ^ [_1770599, _1770601, _1770603, _1770605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770599), _1770601)), 49241 ^ _776541 : [(49242 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770603), hAPP(c_Set_OCollect(_1770603), hAPP(hAPP(c_COMBB(tc_fun(_1770599, tc_HOL_Obool), tc_HOL_Obool, _1770603), c_HOL_OEx(_1770599)), hAPP(hAPP(c_COMBB(tc_fun(_1770599, tc_HOL_Obool), tc_fun(_1770599, tc_HOL_Obool), _1770603), hAPP(c_COMBS(_1770599, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1770599), c_fconj), hAPP(hAPP(c_COMBC(_1770599, tc_fun(_1770599, tc_HOL_Obool), tc_HOL_Obool), c_member(_1770599)), _1770601)))), _1770605))))), 49245 ^ _776541 : [(49246 ^ _776541) ^ [_1770907] : [hBOOL(hAPP(hAPP(c_member(_1770599), _1770907), _1770601)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1770603), hAPP(c_Set_OCollect(_1770603), hAPP(hAPP(c_COMBC(_1770603, _1770599, tc_HOL_Obool), _1770605), _1770907)))))]]], (49252 ^ _776541) ^ [] : [49254 ^ _776541 : [(49257 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770603), hAPP(c_Set_OCollect(_1770603), hAPP(hAPP(c_COMBC(_1770603, _1770599, tc_HOL_Obool), _1770605), 49253 ^ [_1770599, _1770601, _1770603, _1770605]))))], (49255 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770599), 49253 ^ [_1770599, _1770601, _1770603, _1770605]), _1770601)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1770603), hAPP(c_Set_OCollect(_1770603), hAPP(hAPP(c_COMBB(tc_fun(_1770599, tc_HOL_Obool), tc_HOL_Obool, _1770603), c_HOL_OEx(_1770599)), hAPP(hAPP(c_COMBB(tc_fun(_1770599, tc_HOL_Obool), tc_fun(_1770599, tc_HOL_Obool), _1770603), hAPP(c_COMBS(_1770599, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1770599), c_fconj), hAPP(hAPP(c_COMBC(_1770599, tc_fun(_1770599, tc_HOL_Obool), tc_HOL_Obool), c_member(_1770599)), _1770601)))), _1770605))))))]]], (47381 ^ _776541) ^ [_1729217, _1729219, _1729221] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729217)), c_List_OdropWhile(_1729217, _1729219, _1729221))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729217)), _1729221))))], (42773 ^ _776541) ^ [_1628387, _1628389] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628387)), c_List_Obutlast(_1628387, _1628389)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628387)), _1628389)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (48095 ^ _776541) ^ [_1745228, _1745230, _1745232] : [c_List_Olist__ex(_1745228, _1745230, _1745232), 48099 ^ _776541 : [(48102 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1745230, 48098 ^ [_1745228, _1745230, _1745232])))], (48100 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745228), 48098 ^ [_1745228, _1745230, _1745232]), hAPP(c_List_Oset(_1745228), _1745232))))]]], (28623 ^ _776541) ^ [] : [-(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)))))], (15216 ^ _776541) ^ [_1051088, _1051090, _1051092] : [class_Rings_Ocomm__semiring__1(_1051088), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051088), _1051090), _1051092)), _1051092) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051088), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051088), _1051090), c_Groups_Oone__class_Oone(_1051088))), _1051092))], (44683 ^ _776541) ^ [_1669798, _1669800, _1669802] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669798)), _1669800), c_List_Olists(_1669798, _1669802)))), 44684 ^ _776541 : [(44687 ^ _776541) ^ [_1669926, _1669928] : [_1669800 = hAPP(hAPP(c_List_Olist_OCons(_1669798), _1669928), _1669926), hBOOL(hAPP(hAPP(c_member(_1669798), _1669928), _1669802)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669798)), _1669926), c_List_Olists(_1669798, _1669802)))], (44685 ^ _776541) ^ [] : [_1669800 = c_List_Olist_ONil(_1669798)]]], (26026 ^ _776541) ^ [_1246986, _1246988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246986), _1246988)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246986, _1246988) = _1246986)], (20763 ^ _776541) ^ [_1151406, _1151408, _1151410, _1151412] : [class_Fields_Ofield__inverse__zero(_1151406), -(_1151408 = c_Groups_Ozero__class_Ozero(_1151406)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151406), _1151410), _1151408)), _1151412) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151406), _1151410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151406), _1151412), _1151408))), _1151408))], (16086 ^ _776541) ^ [_1067371, _1067373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067373)), _1067371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067371), _1067373))], (1124 ^ _776541) ^ [_793455, _793457] : [-(class_Rings_Oring__1__no__zero__divisors(_793455)), _793457 = _793455, class_Rings_Oring__1__no__zero__divisors(_793457)], (24102 ^ _776541) ^ [_1212700, _1212702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212700)), 24105 ^ _776541 : [(24112 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212700), _1212702)), -(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), _1212702), _1212700))))], (24106 ^ _776541) ^ [] : [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), _1212702), _1212700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212700), _1212702)))]]], (36229 ^ _776541) ^ [_1460096, _1460098, _1460100, _1460102, _1460104] : [-(hAPP(c_Product__Type_Osnd(_1460096, _1460098), hAPP(c_Product__Type_Oapfst(_1460100, _1460096, _1460098, _1460102), _1460104)) = hAPP(c_Product__Type_Osnd(_1460100, _1460098), _1460104))], (38658 ^ _776541) ^ [_1519171, _1519173, _1519175, _1519177, _1519179, _1519181] : [hAPP(_1519171, _1519173) = _1519175, hBOOL(hAPP(hAPP(c_member(_1519177), _1519175), _1519179)), -(hBOOL(hAPP(hAPP(c_member(_1519181), _1519173), hAPP(c_Set_Ovimage(_1519181, _1519177, _1519171), _1519179))))], (30272 ^ _776541) ^ [_1319546, _1319548, _1319550, _1319552] : [class_Orderings_Olinorder(_1319546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319546), _1319548), _1319550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319546), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319546), _1319552), _1319548)), _1319550)))], (46034 ^ _776541) ^ [_1701104, _1701106, _1701108, _1701110, _1701112] : [class_Orderings_Olinorder(_1701104), -(hAPP(c_List_Ofilter(_1701106, _1701108), c_List_Olinorder__class_Osort__key(_1701106, _1701104, _1701110, _1701112)) = c_List_Olinorder__class_Osort__key(_1701106, _1701104, _1701110, hAPP(c_List_Ofilter(_1701106, _1701108), _1701112)))], (844 ^ _776541) ^ [_789159, _789161, _789163, _789165] : [-(c_Equiv__Relations_Opart__equivp(_789163, _789159)), c_Equiv__Relations_Opart__equivp(_789165, _789161), _789165 = _789163, _789161 = _789159], (52425 ^ _776541) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (42953 ^ _776541) ^ [_1632564, _1632566, _1632568, _1632570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632564), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632566)), _1632568))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632564), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632566)), _1632570))), 42963 ^ _776541 : [(42966 ^ _776541) ^ [] : [hAPP(hAPP(c_List_Onth(_1632566), _1632568), 42962 ^ [_1632564, _1632566, _1632568, _1632570]) = hAPP(hAPP(c_List_Onth(_1632566), _1632570), 42962 ^ [_1632564, _1632566, _1632568, _1632570])], (42964 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42962 ^ [_1632564, _1632566, _1632568, _1632570]), _1632564)))]], -(hAPP(hAPP(c_List_Otake(_1632566), _1632564), _1632568) = hAPP(hAPP(c_List_Otake(_1632566), _1632564), _1632570))], (6440 ^ _776541) ^ [_880608, _880610, _880612, _880614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880608, tc_HOL_Obool)), _880610), _880612)), hBOOL(hAPP(hAPP(c_member(_880608), _880614), _880610)), -(hBOOL(hAPP(hAPP(c_member(_880608), _880614), _880612)))], (25095 ^ _776541) ^ [_1230853] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1230853) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230853))], (19436 ^ _776541) ^ [_1127388, _1127390, _1127392, _1127394, _1127396] : [class_Fields_Ofield(_1127388), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127390), _1127392)), -(hAPP(_1127394, _1127396) = c_Groups_Ozero__class_Ozero(_1127388)), 19447 ^ _776541 : [(19454 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1127390), _1127396), _1127392))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127390, _1127388), _1127394), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127390, tc_HOL_Obool)), _1127392), hAPP(hAPP(c_Set_Oinsert(_1127390), _1127396), c_Orderings_Obot__class_Obot(tc_fun(_1127390, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127390, _1127388), _1127394), _1127392))], (19448 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1127390), _1127396), _1127392)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127390, _1127388), _1127394), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127390, tc_HOL_Obool)), _1127392), hAPP(hAPP(c_Set_Oinsert(_1127390), _1127396), c_Orderings_Obot__class_Obot(tc_fun(_1127390, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127388), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127390, _1127388), _1127394), _1127392)), hAPP(_1127394, _1127396)))]]], (9730 ^ _776541) ^ [_943127, _943129, _943131, _943133] : [class_Lattices_Osemilattice__sup(_943127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943127), _943129), _943131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943127), _943129), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_943127), _943133), _943131))))], (52229 ^ _776541) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (23868 ^ _776541) ^ [_1208879, _1208881] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208879)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208881)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208879), _1208881)))], (39141 ^ _776541) ^ [_1531403, _1531405, _1531407, _1531409, _1531411] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531403, _1531405), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531403, tc_HOL_Obool)), _1531407), _1531409)), hAPP(c_COMBK(tc_fun(_1531405, tc_HOL_Obool), _1531403), _1531411)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1531403, _1531405), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531403, _1531405), _1531407), hAPP(c_COMBK(tc_fun(_1531405, tc_HOL_Obool), _1531403), _1531411))), hAPP(hAPP(c_Product__Type_OSigma(_1531403, _1531405), _1531409), hAPP(c_COMBK(tc_fun(_1531405, tc_HOL_Obool), _1531403), _1531411))))], (32266 ^ _776541) ^ [_1356614, _1356616, _1356618, _1356620, _1356622, _1356624] : [-(c_Nitpick_Opair__box_Opair__box__size(_1356614, _1356616, _1356618, _1356620, c_Nitpick_Opair__box_OPairBox(_1356614, _1356616, _1356622, _1356624)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1356618, _1356622)), hAPP(_1356620, _1356624))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42839 ^ _776541) ^ [_1630016, _1630018, _1630020, _1630022] : [hBOOL(hAPP(c_List_Odistinct(_1630016), _1630018)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1630020, _1630016)), hAPP(hAPP(c_List_Ozip(_1630020, _1630016), _1630022), _1630018))))], (11716 ^ _776541) ^ [_981646, _981648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981646), _981648)), 11719 ^ _776541 : [(11726 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981646), c_Orderings_Otop__class_Otop(tc_fun(_981646, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981646), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_981646, tc_HOL_Obool)), _981648))))], (11720 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981646), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_981646, tc_HOL_Obool)), _981648))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981646), c_Orderings_Otop__class_Otop(tc_fun(_981646, tc_HOL_Obool)))))]]], (43689 ^ _776541) ^ [_1648047, _1648049, _1648051, _1648053] : [-(hBOOL(hAPP(hAPP(c_member(_1648047), _1648049), hAPP(c_List_Oset(_1648047), _1648051)))), -(c_List_Oremove1(_1648047, _1648049, hAPP(hAPP(c_List_Oappend(_1648047), _1648051), _1648053)) = hAPP(hAPP(c_List_Oappend(_1648047), _1648051), c_List_Oremove1(_1648047, _1648049, _1648053)))], (46516 ^ _776541) ^ [_1711987, _1711989, _1711991] : [class_Orderings_Olinorder(_1711987), c_List_Olinorder__class_Osorted(_1711987, _1711989), -(c_List_Olinorder__class_Osorted(_1711987, hAPP(hAPP(c_List_Otake(_1711987), _1711991), _1711989)))], (35034 ^ _776541) ^ [_1430314, _1430316] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430314, _1430316), c_Divides_Odivmod__nat(_1430314, _1430316))))], (7560 ^ _776541) ^ [_901447, _901449, _901451, _901453] : [7562 ^ _776541 : [(7565 ^ _776541) ^ [] : [hBOOL(hAPP(_901453, 7561 ^ [_901447, _901449, _901451, _901453]))], (7563 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901447), 7561 ^ [_901447, _901449, _901451, _901453]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901447, tc_HOL_Obool)), _901449), _901451))))]], 7566 ^ _776541 : [(7573 ^ _776541) ^ [_901764] : [hBOOL(hAPP(hAPP(c_member(_901447), _901764), _901451)), -(hBOOL(hAPP(_901453, _901764)))], (7567 ^ _776541) ^ [_901667] : [hBOOL(hAPP(hAPP(c_member(_901447), _901667), _901449)), -(hBOOL(hAPP(_901453, _901667)))]]], (34850 ^ _776541) ^ [_1426857, _1426859, _1426861, _1426863, _1426865, _1426867] : [_1426857 = _1426859, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1426861, _1426863, _1426865), _1426867), _1426857) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1426861, _1426863, _1426865), _1426867), _1426859))], (34576 ^ _776541) ^ [_1420496, _1420498, _1420500, _1420502, _1420504, _1420506] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420496, tc_fun(_1420498, tc_HOL_Obool))), _1420500), _1420502), _1420504), _1420506)), -(hBOOL(hAPP(hAPP(_1420500, _1420504), _1420506)))], (44906 ^ _776541) ^ [_1675625, _1675627, _1675629, _1675631, _1675633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1675625), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675627)), _1675629))), -(hAPP(hAPP(c_List_Onth(_1675631), hAPP(hAPP(c_List_Omap(_1675627, _1675631), _1675633), _1675629)), _1675625) = hAPP(_1675633, hAPP(hAPP(c_List_Onth(_1675627), _1675629), _1675625)))], (13043 ^ _776541) ^ [_1006693, _1006695, _1006697, _1006699] : [c_Big__Operators_Osemilattice__big(_1006693, _1006695, _1006697), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006693), _1006699)), -(hAPP(_1006697, _1006699) = hAPP(c_Finite__Set_Ofold1(_1006693, _1006695), _1006699))], (28635 ^ _776541) ^ [] : [-(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)))))], (18540 ^ _776541) ^ [_1110181, _1110183] : [18541 ^ _776541 : [(18544 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110181), _1110183)))], (18542 ^ _776541) ^ [] : [_1110183 = c_Orderings_Obot__class_Obot(tc_fun(_1110181, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1110181), _1110183) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48568 ^ _776541) ^ [_1755748, _1755750, _1755752, _1755754] : [-(hAPP(hAPP(c_List_Omap(_1755748, _1755750), hAPP(c_COMBK(_1755750, _1755748), _1755752)), _1755754) = c_List_Oreplicate(_1755750, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755748)), _1755754), _1755752))], (7954 ^ _776541) ^ [_911018, _911020, _911022] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911018, tc_HOL_Obool)), _911020), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911018, tc_HOL_Obool)), _911020), _911022))))], (9780 ^ _776541) ^ [_944058, _944060, _944062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944058, tc_HOL_Obool)), _944060), _944062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944058, tc_HOL_Obool)), _944060), _944062)))], (26807 ^ _776541) ^ [_1259863] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259863)))], (22131 ^ _776541) ^ [_1177841, _1177843, _1177845, _1177847] : [class_Rings_Olinordered__semidom(_1177841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177843), _1177845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177841), c_Groups_Ozero__class_Ozero(_1177841)), _1177847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177841), _1177847), c_Groups_Oone__class_Oone(_1177841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177841), hAPP(hAPP(c_Power_Opower__class_Opower(_1177841), _1177847), _1177845)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177841), _1177847), _1177843))))], (52233 ^ _776541) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (49472 ^ _776541) ^ [_1776555, _1776557] : [c_Predicate_Oreflp(_1776555, _1776557), c_Predicate_Osymp(_1776555, _1776557), c_Predicate_Otransp(_1776555, _1776557), -(c_Equiv__Relations_Oequivp(_1776555, _1776557))], (39697 ^ _776541) ^ [_1547357, _1547359, _1547361] : [hBOOL(hAPP(hAPP(c_member(_1547359), _1547357), c_Orderings_Obot__class_Obot(tc_fun(_1547359, tc_HOL_Obool)))), -(hBOOL(hAPP(_1547361, _1547357)))], (20137 ^ _776541) ^ [_1140114, _1140116, _1140118] : [class_Fields_Olinordered__field(_1140114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140114), _1140116), c_Groups_Ozero__class_Ozero(_1140114))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140114), _1140118), c_Groups_Ozero__class_Ozero(_1140114))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140114), c_Groups_Ozero__class_Ozero(_1140114)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140114), _1140116), _1140118))))], (28207 ^ _776541) ^ [_1283027] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1283027)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1283027) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14492 ^ _776541) ^ [_1038155, _1038157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038155), _1038157)), _1038157 = _1038155], (24938 ^ _776541) ^ [_1228122, _1228124, _1228126] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228124), _1228126)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228122), _1228124)), _1228126))], (34185 ^ _776541) ^ [_1411963, _1411965] : [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(_1411965))), 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), _1411963)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1411963)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411965))))], (41817 ^ _776541) ^ [_1601696, _1601698, _1601700, _1601702] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1601696), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1601698), _1601700)))), -(hAPP(c_Random_Opick(_1601698, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1601698)), _1601700), _1601702)), _1601696) = hAPP(c_Random_Opick(_1601698, _1601702), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1601696), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1601698), _1601700))))], (22635 ^ _776541) ^ [_1186617, _1186619, _1186621] : [class_Groups_Omonoid__mult(_1186617), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186617), _1186619), hAPP(c_Nat_OSuc, _1186621)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186617), hAPP(hAPP(c_Power_Opower__class_Opower(_1186617), _1186619), _1186621)), _1186619))], (224 ^ _776541) ^ [_780131, _780133] : [-(class_Fields_Olinordered__field__inverse__zero(_780131)), _780133 = _780131, class_Fields_Olinordered__field__inverse__zero(_780133)], (32526 ^ _776541) ^ [_1364365, _1364367, _1364369] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364365, tc_HOL_Obool)), _1364367), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1364365, tc_HOL_Obool), _1364369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1364365, tc_HOL_Obool), tc_fun(_1364365, tc_HOL_Obool)), _1364369), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364365, tc_HOL_Obool)), _1364367)))], (43972 ^ _776541) ^ [_1655376, _1655378, _1655380, _1655382] : [-(hAPP(hAPP(c_List_Oappend(_1655376), _1655378), _1655380) = _1655382), _1655378 = hAPP(hAPP(c_List_Otake(_1655376), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655376)), _1655378)), _1655382), _1655380 = hAPP(hAPP(c_List_Odrop(_1655376), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655376)), _1655378)), _1655382)], (23803 ^ _776541) ^ [_1207680, _1207682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207680), _1207682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207680)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207682))))], (27719 ^ _776541) ^ [_1275113, _1275115, _1275117] : [class_Rings_Olinordered__idom(_1275113), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275113), c_Groups_Ozero__class_Ozero(_1275113)), hAPP(hAPP(c_Power_Opower__class_Opower(_1275113), hAPP(c_Groups_Oabs__class_Oabs(_1275113), _1275115)), _1275117))))], (35116 ^ _776541) ^ [_1431893, _1431895, _1431897] : [35118 ^ _776541 : [(35121 ^ _776541) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1431893, _1431895), 35117 ^ [_1431893, _1431895, _1431897]))], (35119 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1431895, 35117 ^ [_1431893, _1431895, _1431897]), _1431897)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1431893, _1431895), _1431897)))], (11403 ^ _776541) ^ [_975502, _975504, _975506, _975508, _975510] : [c_Finite__Set_Ofolding__one(_975502, _975504, _975506), hBOOL(hAPP(c_Finite__Set_Ofinite(_975502), _975508)), hBOOL(hAPP(c_Finite__Set_Ofinite(_975502), _975510)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975502, tc_HOL_Obool)), _975508), _975510) = c_Orderings_Obot__class_Obot(tc_fun(_975502, tc_HOL_Obool))), -(hAPP(hAPP(_975504, hAPP(_975506, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_975502, tc_HOL_Obool)), _975508), _975510))), hAPP(_975506, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975502, tc_HOL_Obool)), _975508), _975510))) = hAPP(hAPP(_975504, hAPP(_975506, _975508)), hAPP(_975506, _975510)))], (27359 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (42339 ^ _776541) ^ [_1616786, _1616788, _1616790, _1616792] : [hBOOL(hAPP(hAPP(c_member(_1616786), _1616788), hAPP(c_List_Oset(_1616786), c_List_Osublist(_1616786, _1616790, _1616792)))), -(hBOOL(hAPP(hAPP(c_member(_1616786), _1616788), hAPP(c_List_Oset(_1616786), _1616790))))], (52193 ^ _776541) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (43898 ^ _776541) ^ [_1653616, _1653618, _1653620] : [-(hAPP(hAPP(c_List_Odrop(_1653616), _1653618), c_List_Obutlast(_1653616, _1653620)) = c_List_Obutlast(_1653616, hAPP(hAPP(c_List_Odrop(_1653616), _1653618), _1653620)))], (35541 ^ _776541) ^ [_1439650, _1439652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439650), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439652), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439650, _1439652) = 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), _1439650), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1439652)))))], (24748 ^ _776541) ^ [_1224247, _1224249] : [class_Divides_Osemiring__div(_1224247), -(c_Divides_Odiv__class_Omod(_1224247, c_Groups_Ozero__class_Ozero(_1224247), _1224249) = c_Groups_Ozero__class_Ozero(_1224247))], (19199 ^ _776541) ^ [_1122668, _1122670, _1122672, _1122674, _1122676] : [class_Groups_Ocomm__monoid__add(_1122668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122670), _1122672)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122670), _1122674)), 19213 ^ _776541 : [(19216 ^ _776541) ^ [] : [hAPP(_1122676, 19212 ^ [_1122668, _1122670, _1122672, _1122674, _1122676]) = c_Groups_Ozero__class_Ozero(_1122668)], (19214 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1122670), 19212 ^ [_1122668, _1122670, _1122672, _1122674, _1122676]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1122670, tc_HOL_Obool)), _1122672), _1122674))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1122670, _1122668), _1122676), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1122670, tc_HOL_Obool)), _1122672), _1122674)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122668), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1122670, _1122668), _1122676), _1122672)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1122670, _1122668), _1122676), _1122674)))], (46466 ^ _776541) ^ [_1711275] : [class_Orderings_Olinorder(_1711275), -(c_List_Olinorder__class_Osorted(_1711275, c_List_Olist_ONil(_1711275)))], (25471 ^ _776541) ^ [_1237287, _1237289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1237287), _1237289)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237289), _1237287) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237289), _1237287)), _1237287)))], (34600 ^ _776541) ^ [_1421028, _1421030, _1421032] : [-(c_Nat_Onat_Onat__case(_1421028, _1421030, _1421032, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1421030)], (40136 ^ _776541) ^ [_1558512, _1558514, _1558516, _1558518, _1558520, _1558522] : [c_Finite__Set_Ofolding(_1558512, _1558514, _1558516, _1558518), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558512), _1558520)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558512), _1558522)), -(hAPP(c_Fun_Ocomp(_1558514, _1558514, _1558514, hAPP(_1558518, _1558522)), hAPP(_1558518, _1558520)) = hAPP(c_Fun_Ocomp(_1558514, _1558514, _1558514, hAPP(_1558518, _1558520)), hAPP(_1558518, _1558522)))], (6748 ^ _776541) ^ [_885712, _885714, _885716] : [class_Orderings_Opreorder(_885712), _885714 = _885716, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885712), _885714), _885716)))], (19358 ^ _776541) ^ [_1126048, _1126050, _1126052] : [class_Rings_Oring__1(_1126048), hBOOL(hAPP(hAPP(c_member(_1126048), _1126050), c_Int_Oring__1__class_OInts(_1126048))), hBOOL(hAPP(hAPP(c_member(_1126048), _1126052), c_Int_Oring__1__class_OInts(_1126048))), -(hBOOL(hAPP(hAPP(c_member(_1126048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126048), _1126050), _1126052)), c_Int_Oring__1__class_OInts(_1126048))))], (1804 ^ _776541) ^ [_801955, _801957] : [-(class_Rings_Omult__zero(_801955)), _801957 = _801955, class_Rings_Omult__zero(_801957)], (44182 ^ _776541) ^ [_1660020] : [-(hAPP(c_List_Otl(_1660020), c_List_Olist_ONil(_1660020)) = c_List_Olist_ONil(_1660020))], (38239 ^ _776541) ^ [_1508777, _1508779, _1508781] : [c_Wellfounded_Owf(_1508777, _1508779), -(hBOOL(hAPP(hAPP(c_member(_1508777), _1508781), c_Wellfounded_Oacc(_1508777, _1508779))))], (24950 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (52061 ^ _776541) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52551 ^ _776541) ^ [_1832085, _1832087] : [hBOOL(_1832085), -(hBOOL(hAPP(hAPP(c_fimplies, _1832087), _1832085)))], (22319 ^ _776541) ^ [_1181048, _1181050, _1181052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181048), _1181050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181048), _1181052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181050), _1181052))))], (18796 ^ _776541) ^ [_1115177, _1115179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1115177), _1115179))), 18799 ^ _776541 : [(18802 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1115177), _1115179)))], (18800 ^ _776541) ^ [] : [_1115179 = c_Orderings_Obot__class_Obot(tc_fun(_1115177, tc_HOL_Obool))]]], (44611 ^ _776541) ^ [_1668637, _1668639, _1668641] : [-(_1668637 = c_List_Olist_ONil(_1668639)), -(c_List_Olast(_1668639, hAPP(hAPP(c_List_Oappend(_1668639), _1668641), _1668637)) = c_List_Olast(_1668639, _1668637))], (39695 ^ _776541) ^ [_1547329] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1547329, tc_HOL_Obool) = c_Set_OBall(_1547329))], (25073 ^ _776541) ^ [_1230483, _1230485] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230483, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230485)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230483, _1230485) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (2740 ^ _776541) ^ [_817068, _817070] : [_817070 = _817068, -(c_Equiv__Relations_Oquotient(_817070) = c_Equiv__Relations_Oquotient(_817068))], (18772 ^ _776541) ^ [_1114659, _1114661, _1114663, _1114665, _1114667, _1114669] : [class_Groups_Oab__semigroup__mult(_1114659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114661), _1114663)), -(hBOOL(hAPP(hAPP(c_member(_1114661), _1114665), _1114663))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1114659, _1114661, c_Groups_Otimes__class_Otimes(_1114659)), _1114667), _1114669), hAPP(hAPP(c_Set_Oinsert(_1114661), _1114665), _1114663)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114659), hAPP(_1114667, _1114665)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1114659, _1114661, c_Groups_Otimes__class_Otimes(_1114659)), _1114667), _1114669), _1114663)))], (27265 ^ _776541) ^ [_1267017, _1267019, _1267021] : [class_Groups_Oordered__ab__group__add__abs(_1267017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267017), hAPP(c_Groups_Oabs__class_Oabs(_1267017), _1267019)), _1267021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267017), _1267019), _1267021)))], (52247 ^ _776541) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (50301 ^ _776541) ^ [_1793393, _1793395, _1793397, _1793399, _1793401] : [c_Fun_Obij__betw(_1793393, _1793395, _1793397, _1793399, _1793401), -(c_Fun_Obij__betw(_1793395, _1793393, c_Hilbert__Choice_Oinv__into(_1793393, _1793395, _1793399, _1793397), _1793401, _1793399))], (40679 ^ _776541) ^ [_1571217, _1571219] : [-(c_Transitive__Closure_Otrancl(_1571217, _1571219) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571217, _1571217), tc_HOL_Obool)), _1571219), hAPP(hAPP(c_Relation_Orel__comp(_1571217, _1571217, _1571217), c_Transitive__Closure_Otrancl(_1571217, _1571219)), _1571219)))], (51357 ^ _776541) ^ [_1816087, _1816089, _1816091, _1816093] : [class_Rings_Ocomm__semiring__1(_1816087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1816089), _1816091)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816087), hAPP(hAPP(c_Power_Opower__class_Opower(_1816087), _1816093), _1816089)), hAPP(hAPP(c_Power_Opower__class_Opower(_1816087), _1816093), _1816091))))], (26497 ^ _776541) ^ [_1254795, _1254797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254797)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1254795)), hAPP(c_Int_Onat, _1254797)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254795), _1254797)))], (26032 ^ _776541) ^ [_1247075, _1247077] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1247075), _1247077))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247075, _1247077) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247075), _1247077), _1247077))], (38404 ^ _776541) ^ [_1512767, _1512769, _1512771] : [c_Wellfounded_Owf(_1512767, _1512769), -(c_Wellfounded_Owf(tc_List_Olist(_1512767), hAPP(c_List_Olexn(_1512767, _1512769), _1512771)))], (10761 ^ _776541) ^ [_961876, _961878] : [class_Orderings_Olinorder(_961876), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961876, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_961876), _961878)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_961876), _961878))], (1454 ^ _776541) ^ [_797580, _797582] : [-(class_Groups_Ouminus(_797580)), _797582 = _797580, class_Groups_Ouminus(_797582)], (45690 ^ _776541) ^ [_1693197, _1693199] : [_1693197 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1693199, _1693197, c_List_Olist_ONil(_1693199)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1693199)), c_List_Olist_ONil(_1693199)), c_List_Olist_ONil(tc_List_Olist(_1693199))))], (52253 ^ _776541) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (6516 ^ _776541) ^ [_881752, _881754, _881756] : [class_Orderings_Otop(_881752), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_881754, _881752)), _881756) = c_Orderings_Otop__class_Otop(_881752))], (2 ^ _776541) ^ [_776568] : [-(_776568 = _776568)], (1174 ^ _776541) ^ [_794080, _794082] : [-(class_Rings_Oordered__ring__abs(_794080)), _794082 = _794080, class_Rings_Oordered__ring__abs(_794082)], (15426 ^ _776541) ^ [_1055314, _1055316, _1055318] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055314), _1055316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1055314, tc_HOL_Obool)), _1055316), _1055318)), -(hAPP(c_Finite__Set_Ocard(_1055314), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055314, tc_HOL_Obool)), _1055318), _1055316)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055314), _1055318)), hAPP(c_Finite__Set_Ocard(_1055314), _1055316)))], (23713 ^ _776541) ^ [] : [-(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)))], (6809 ^ _776541) ^ [_886701, _886703, _886705] : [6811 ^ _776541 : [(6814 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886701, tc_HOL_Obool)), 6810 ^ [_886701, _886703, _886705]), _886705))], (6812 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_886701, tc_HOL_Obool)), 6810 ^ [_886701, _886703, _886705]), _886703)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886701, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_886701, tc_HOL_Obool), _886703)), _886705)))], (8481 ^ _776541) ^ [_922232, _922234, _922236, _922238] : [class_Lattices_Osemilattice__sup(_922232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922232), _922234), _922236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922232), _922238), _922236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922232), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922232), _922234), _922238)), _922236)))], (17127 ^ _776541) ^ [_1084906, _1084908, _1084910] : [class_Rings_Oordered__cancel__semiring(_1084906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084906), c_Groups_Ozero__class_Ozero(_1084906)), _1084908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084906), c_Groups_Ozero__class_Ozero(_1084906)), _1084910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084906), c_Groups_Ozero__class_Ozero(_1084906)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084906), _1084908), _1084910))))], (36639 ^ _776541) ^ [_1471166, _1471168, _1471170] : [_1471168 = c_Orderings_Obot__class_Obot(tc_fun(_1471166, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471166), _1471168), _1471170) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471166, tc_HOL_Obool), tc_HOL_Obool)))], (40559 ^ _776541) ^ [_1568426, _1568428] : [-(c_Wellfounded_Owf(_1568426, _1568428)), 40562 ^ _776541 : [(40565 ^ _776541) ^ [_1568646] : [hBOOL(hAPP(hAPP(c_member(_1568426), _1568646), 40560 ^ [_1568426, _1568428])), 40569 ^ _776541 : [(40572 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568426), 40568 ^ [_1568426, _1568428, _1568646]), 40560 ^ [_1568426, _1568428])))], (40570 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568426, _1568426)), hAPP(hAPP(c_Product__Type_OPair(_1568426, _1568426), 40568 ^ [_1568426, _1568428, _1568646]), _1568646)), _1568428)))]]], (40563 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568426), 40561 ^ [_1568426, _1568428]), 40560 ^ [_1568426, _1568428])))]]], (3372 ^ _776541) ^ [_826894, _826896, _826898, _826900] : [-(c_Product__Type_OSigma(_826900, _826896) = c_Product__Type_OSigma(_826898, _826894)), _826900 = _826898, _826896 = _826894], (39327 ^ _776541) ^ [_1537975, _1537977] : [-(hAPP(c_Set_Oimage(_1537975, _1537975, c_Fun_Oid(_1537975)), _1537977) = _1537977)], (49849 ^ _776541) ^ [_1783420, _1783422] : [49850 ^ _776541 : [(49851 ^ _776541) ^ [_1783476] : [hBOOL(hAPP(hAPP(_1783420, _1783476), _1783476))]], c_Predicate_Osymp(_1783422, _1783420), c_Predicate_Otransp(_1783422, _1783420), -(c_Equiv__Relations_Opart__equivp(_1783422, _1783420))], (1374 ^ _776541) ^ [_796580, _796582] : [-(class_Lattices_Obounded__lattice__bot(_796580)), _796582 = _796580, class_Lattices_Obounded__lattice__bot(_796582)], (45449 ^ _776541) ^ [_1687709, _1687711, _1687713, _1687715, _1687717, _1687719, _1687721] : [c_List_Olist__all2(_1687709, _1687711, _1687713, hAPP(hAPP(c_List_Omap(_1687715, _1687709), _1687717), _1687719), _1687721), -(c_List_Olist__all2(_1687715, _1687711, hAPP(hAPP(c_COMBB(_1687709, tc_fun(_1687711, tc_HOL_Obool), _1687715), _1687713), _1687717), _1687719, _1687721))], (39459 ^ _776541) ^ [_1541199, _1541201, _1541203, _1541205, _1541207, _1541209, _1541211, _1541213] : [-(hAPP(c_Product__Type_Omap__pair(_1541199, _1541201, _1541203, _1541205, _1541207, _1541209), hAPP(hAPP(c_Product__Type_OPair(_1541199, _1541203), _1541211), _1541213)) = hAPP(hAPP(c_Product__Type_OPair(_1541201, _1541205), hAPP(_1541207, _1541211)), hAPP(_1541209, _1541213)))], (6001 ^ _776541) ^ [_872217, _872219, _872221, _872223] : [hBOOL(hAPP(hAPP(_872221, _872219), _872223)), -(hBOOL(hAPP(hAPP(c_member(_872217), _872219), c_SetInterval_Oord_OatMost(_872217, _872221, _872223))))], (48069 ^ _776541) ^ [_1744734, _1744736, _1744738] : [48070 ^ _776541 : [(48071 ^ _776541) ^ [_1744811, _1744813] : [_1744738 = hAPP(hAPP(c_List_Oappend(_1744734), _1744813), hAPP(hAPP(c_List_Olist_OCons(_1744734), _1744736), _1744811))]], -(hBOOL(hAPP(hAPP(c_member(_1744734), _1744736), hAPP(c_List_Oset(_1744734), _1744738))))], (7940 ^ _776541) ^ [_910730, _910732, _910734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910730, tc_HOL_Obool)), _910732), _910734)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910730, tc_HOL_Obool)), _910732), _910734) = _910734)], (34797 ^ _776541) ^ [_1425812, _1425814, _1425816] : [class_Rings_Osemiring__1(_1425812), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1425812, _1425814, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1425816) = _1425816)], (15781 ^ _776541) ^ [_1062536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062536)), -(_1062536 = hAPP(c_Nat_OSuc, 15784 ^ [_1062536]))], (48126 ^ _776541) ^ [_1745801, _1745803, _1745805, _1745807] : [c_List_Olist__ex(_1745801, _1745803, hAPP(hAPP(c_List_Olist_OCons(_1745801), _1745805), _1745807)), -(hBOOL(hAPP(_1745803, _1745805))), -(c_List_Olist__ex(_1745801, _1745803, _1745807))], (23651 ^ _776541) ^ [_1205156, _1205158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205156)), 23654 ^ _776541 : [(23661 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205158), 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), _1205158), _1205156)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23655 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205158), _1205156)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205158), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (45579 ^ _776541) ^ [_1690484, _1690486, _1690488, _1690490, _1690492] : [c_List_Olist__all2(_1690484, _1690486, _1690488, _1690490, _1690492), 45582 ^ _776541 : [(45585 ^ _776541) ^ [_1690647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690647), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690484)), _1690490))), -(hBOOL(hAPP(hAPP(_1690488, hAPP(hAPP(c_List_Onth(_1690484), _1690490), _1690647)), hAPP(hAPP(c_List_Onth(_1690486), _1690492), _1690647))))], (45583 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690484)), _1690490) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690486)), _1690492))]]], (35894 ^ _776541) ^ [_1448364, _1448366, _1448368, _1448370] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448364), hAPP(c_Set_OCollect(_1448364), _1448366))), 35897 ^ _776541 : [(35898 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448368), hAPP(c_Set_OCollect(_1448368), hAPP(hAPP(c_COMBB(tc_fun(_1448364, tc_HOL_Obool), tc_HOL_Obool, _1448368), c_HOL_OEx(_1448364)), hAPP(hAPP(c_COMBB(tc_fun(_1448364, tc_HOL_Obool), tc_fun(_1448364, tc_HOL_Obool), _1448368), hAPP(c_COMBS(_1448364, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1448364), c_fconj), _1448366))), _1448370))))), 35901 ^ _776541 : [(35902 ^ _776541) ^ [_1448647] : [hBOOL(hAPP(_1448366, _1448647)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448368), hAPP(c_Set_OCollect(_1448368), hAPP(hAPP(c_COMBC(_1448368, _1448364, tc_HOL_Obool), _1448370), _1448647)))))]]], (35908 ^ _776541) ^ [] : [35910 ^ _776541 : [(35913 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448368), hAPP(c_Set_OCollect(_1448368), hAPP(hAPP(c_COMBC(_1448368, _1448364, tc_HOL_Obool), _1448370), 35909 ^ [_1448364, _1448366, _1448368, _1448370]))))], (35911 ^ _776541) ^ [] : [-(hBOOL(hAPP(_1448366, 35909 ^ [_1448364, _1448366, _1448368, _1448370])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448368), hAPP(c_Set_OCollect(_1448368), hAPP(hAPP(c_COMBB(tc_fun(_1448364, tc_HOL_Obool), tc_HOL_Obool, _1448368), c_HOL_OEx(_1448364)), hAPP(hAPP(c_COMBB(tc_fun(_1448364, tc_HOL_Obool), tc_fun(_1448364, tc_HOL_Obool), _1448368), hAPP(c_COMBS(_1448364, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1448364), c_fconj), _1448366))), _1448370))))))]]], (28829 ^ _776541) ^ [_1293388, _1293390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293388)), c_Int_OBit0(_1293390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293388), _1293390)))], (37792 ^ _776541) ^ [_1496917, _1496919, _1496921, _1496923, _1496925, _1496927] : [c_Fun_Oinj__on(_1496917, _1496919, _1496921, _1496923), hBOOL(hAPP(hAPP(c_member(_1496919), _1496925), hAPP(c_Set_Oimage(_1496917, _1496919, _1496921), _1496923))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496917, tc_HOL_Obool)), _1496923), _1496927)), -(hBOOL(hAPP(hAPP(c_member(_1496917), hAPP(c_Fun_Othe__inv__into(_1496917, _1496919, _1496923, _1496921), _1496925)), _1496927)))], (11324 ^ _776541) ^ [_973485, _973487, _973489, _973491, _973493] : [c_Finite__Set_Ofolding__one(_973485, _973487, _973489), hBOOL(hAPP(c_Finite__Set_Ofinite(_973485), _973491)), hBOOL(hAPP(hAPP(c_member(_973485), _973493), _973491)), 11335 ^ _776541 : [(11342 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973485, tc_HOL_Obool)), _973491), hAPP(hAPP(c_Set_Oinsert(_973485), _973493), c_Orderings_Obot__class_Obot(tc_fun(_973485, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_973485, tc_HOL_Obool))), -(hAPP(_973489, _973491) = hAPP(hAPP(_973487, _973493), hAPP(_973489, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973485, tc_HOL_Obool)), _973491), hAPP(hAPP(c_Set_Oinsert(_973485), _973493), c_Orderings_Obot__class_Obot(tc_fun(_973485, tc_HOL_Obool)))))))], (11336 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973485, tc_HOL_Obool)), _973491), hAPP(hAPP(c_Set_Oinsert(_973485), _973493), c_Orderings_Obot__class_Obot(tc_fun(_973485, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_973485, tc_HOL_Obool)), -(hAPP(_973489, _973491) = _973493)]]], (39067 ^ _776541) ^ [_1528995, _1528997, _1528999, _1529001] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1528995, _1528997)), hAPP(hAPP(c_Product__Type_OSigma(_1528995, _1528997), _1528999), hAPP(c_COMBK(tc_fun(_1528997, tc_HOL_Obool), _1528995), _1529001))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1528995), _1528999)), hAPP(c_Finite__Set_Ocard(_1528997), _1529001)))], (39345 ^ _776541) ^ [_1538266, _1538268] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1538266, _1538268, tc_prod(_1538266, _1538268)), c_Product__Type_OPair(_1538266, _1538268)) = c_Fun_Oid(tc_prod(_1538266, _1538268)))], (45325 ^ _776541) ^ [_1684856, _1684858, _1684860, _1684862] : [-(hBOOL(hAPP(c_List_Olistsp(_1684856, _1684858), hAPP(hAPP(c_List_Oappend(_1684856), _1684860), _1684862)))), hBOOL(hAPP(c_List_Olistsp(_1684856, _1684858), _1684860)), hBOOL(hAPP(c_List_Olistsp(_1684856, _1684858), _1684862))], (45978 ^ _776541) ^ [_1698958, _1698960] : [class_Orderings_Olinorder(_1698958), -(c_List_Olinorder__class_Osort__key(_1698958, _1698958, c_COMBI(_1698958), _1698960) = hAPP(c_List_Ofoldl(tc_List_Olist(_1698958), _1698958, hAPP(c_COMBC(_1698958, tc_List_Olist(_1698958), tc_List_Olist(_1698958)), c_List_Olinorder__class_Oinsort__key(_1698958, _1698958, c_COMBI(_1698958))), c_List_Olist_ONil(_1698958)), _1698960))], (26282 ^ _776541) ^ [_1251182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1251182))))], (19661 ^ _776541) ^ [_1131686, _1131688, _1131690, _1131692] : [class_Rings_Odivision__ring(_1131686), -(_1131688 = c_Groups_Ozero__class_Ozero(_1131686)), 19668 ^ _776541 : [(19675 ^ _776541) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131686), _1131690), _1131688) = _1131692, -(_1131690 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131686), _1131692), _1131688))], (19669 ^ _776541) ^ [] : [_1131690 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131686), _1131692), _1131688), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131686), _1131690), _1131688) = _1131692)]]], (52321 ^ _776541) ^ [_1829469, _1829471] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1829469, _1829471))), class_Lazy__Sequence_Osmall__lazy(_1829469), class_Lazy__Sequence_Osmall__lazy(_1829471)], (47605 ^ _776541) ^ [_1733856, _1733858, _1733860] : [-(hAPP(c_List_Oset(_1733856), c_List_Oinsert(_1733856, _1733858, _1733860)) = hAPP(hAPP(c_Set_Oinsert(_1733856), _1733858), hAPP(c_List_Oset(_1733856), _1733860)))], (38356 ^ _776541) ^ [_1511551, _1511553] : [c_Wellfounded_Owf(_1511551, _1511553), -(c_Wellfounded_Owf(tc_List_Olist(_1511551), c_List_Olenlex(_1511551, _1511553)))], (42423 ^ _776541) ^ [_1618738, _1618740, _1618742] : [42425 ^ _776541 : [(42428 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1618738), 42424 ^ [_1618738, _1618740, _1618742]), _1618742))], (42426 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618738), 42424 ^ [_1618738, _1618740, _1618742]), hAPP(c_List_Oset(_1618738), _1618740))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618738)), _1618740), c_List_Olists(_1618738, _1618742))))], (23235 ^ _776541) ^ [_1197488, _1197490, _1197492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197488)), 23238 ^ _776541 : [(23239 ^ _776541) ^ [_1197622] : [23241 ^ _776541 : [(23247 ^ _776541) ^ [] : [-(_1197622 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23243 ^ [_1197488, _1197490, _1197492, _1197622]), 23240 ^ [_1197488, _1197490, _1197492, _1197622]))], (23245 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23243 ^ [_1197488, _1197490, _1197492, _1197622]), _1197490)))], (23242 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23240 ^ [_1197488, _1197490, _1197492, _1197622]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1197488))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197622), _1197492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197622), _1197488)), _1197492)))]]], (39267 ^ _776541) ^ [_1534909, _1534911, _1534913, _1534915] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534909), _1534911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534909, _1534909), tc_HOL_Obool)), _1534913), hAPP(hAPP(c_Product__Type_OSigma(_1534909, _1534909), _1534911), hAPP(c_COMBK(tc_fun(_1534909, tc_HOL_Obool), _1534909), _1534911)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1534909, tc_HOL_Obool)), _1534915), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1534909), _1534911), _1534913))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1534909), _1534915)))], (22401 ^ _776541) ^ [_1182669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182669)), -(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)), _1182669))))], (47517 ^ _776541) ^ [_1732185, _1732187, _1732189, _1732191] : [47519 ^ _776541 : [(47522 ^ _776541) ^ [] : [hBOOL(hAPP(_1732187, hAPP(hAPP(c_List_Onth(_1732189), _1732191), 47518 ^ [_1732185, _1732187, _1732189, _1732191])))], (47520 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47518 ^ [_1732185, _1732187, _1732189, _1732191]), _1732185)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1732185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732189)), _1732191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1732185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732189)), c_List_OtakeWhile(_1732189, _1732187, _1732191)))))], (9144 ^ _776541) ^ [_934506, _934508, _934510] : [class_Orderings_Oorder(_934506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934506), _934508), _934510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934506), _934510), _934508))], (15744 ^ _776541) ^ [_1061942, _1061944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1061942), hAPP(c_Nat_OSuc, _1061944))), -(_1061942 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15752 ^ _776541 : [(15755 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15751 ^ [_1061942, _1061944]), _1061944)))], (15753 ^ _776541) ^ [] : [-(_1061942 = hAPP(c_Nat_OSuc, 15751 ^ [_1061942, _1061944]))]]], (16364 ^ _776541) ^ [_1071731, _1071733] : [class_Groups_Ogroup__add(_1071731), 16367 ^ _776541 : [(16374 ^ _776541) ^ [] : [c_Groups_Ozero__class_Ozero(_1071731) = _1071733, -(c_Groups_Ozero__class_Ozero(_1071731) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071731), _1071733))], (16368 ^ _776541) ^ [] : [c_Groups_Ozero__class_Ozero(_1071731) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071731), _1071733), -(c_Groups_Ozero__class_Ozero(_1071731) = _1071733)]]], (50959 ^ _776541) ^ [_1808595, _1808597, _1808599] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1808595), _1808597)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1808595), _1808599))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1808595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1808597), _1808599)))], (52429 ^ _776541) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (7918 ^ _776541) ^ [_910251, _910253, _910255, _910257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910251, tc_HOL_Obool)), _910253), _910255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910251, tc_HOL_Obool)), _910257), _910255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910251, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910251, tc_HOL_Obool)), _910253), _910257)), _910255)))], (40491 ^ _776541) ^ [_1566668, _1566670, _1566672, _1566674, _1566676] : [-(_1566668 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1566670, _1566672, _1566668, _1566674), _1566676) = hAPP(hAPP(c_Product__Type_Oscomp(_1566672, _1566670, _1566672, tc_prod(_1566670, _1566672)), hAPP(_1566674, _1566676)), c_Random_Oiterate(_1566670, _1566672, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1566668), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1566674)))], (462 ^ _776541) ^ [_783484, _783486, _783488, _783490, _783492, _783494] : [-(c_Nitpick_Oless__eq__frac(_783492, _783488, _783484)), c_Nitpick_Oless__eq__frac(_783494, _783490, _783486), _783494 = _783492, _783490 = _783488, _783486 = _783484], (3174 ^ _776541) ^ [_823793, _823795, _823797, _823799] : [-(c_Big__Operators_Olattice__class_OSup__fin(_823799, _823795) = c_Big__Operators_Olattice__class_OSup__fin(_823797, _823793)), _823799 = _823797, _823795 = _823793], (34049 ^ _776541) ^ [_1408622, _1408624] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408622))), -(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)), _1408622))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1408624)))) = 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)), _1408622))), 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, _1408624))))))], (38132 ^ _776541) ^ [_1506822, _1506824] : [c_Wellfounded_Owf(_1506822, hAPP(hAPP(c_Relation_Orel__comp(_1506822, _1506822, _1506822), _1506824), _1506824)), -(c_Wellfounded_Owf(_1506822, _1506824))], (35479 ^ _776541) ^ [_1438401, _1438403, _1438405, _1438407, _1438409] : [-(hAPP(c_Product__Type_Osnd(_1438401, _1438403), hAPP(c_Product__Type_Oapsnd(_1438405, _1438403, _1438401, _1438407), _1438409)) = hAPP(_1438407, hAPP(c_Product__Type_Osnd(_1438401, _1438405), _1438409)))], (22359 ^ _776541) ^ [_1181893, _1181895, _1181897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181893), _1181895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181897), _1181893)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181897), _1181895))))], (1624 ^ _776541) ^ [_799705, _799707] : [-(class_Groups_Oab__semigroup__mult(_799705)), _799707 = _799705, class_Groups_Oab__semigroup__mult(_799707)], (10855 ^ _776541) ^ [_963790, _963792, _963794, _963796] : [class_Orderings_Oorder(_963790), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963790, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963790, _963792), _963794)), c_SetInterval_Oord__class_OatLeastAtMost(_963790, _963794, _963796)) = c_Orderings_Obot__class_Obot(tc_fun(_963790, tc_HOL_Obool)))], (18920 ^ _776541) ^ [_1117326, _1117328, _1117330] : [class_Rings_Olinordered__ring__strict(_1117326), 18923 ^ _776541 : [(18932 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117326), _1117328), _1117328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117326), _1117330), _1117330))), c_Groups_Ozero__class_Ozero(_1117326)))), _1117328 = c_Groups_Ozero__class_Ozero(_1117326), _1117330 = c_Groups_Ozero__class_Ozero(_1117326)], (18924 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117326), _1117328), _1117328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117326), _1117330), _1117330))), c_Groups_Ozero__class_Ozero(_1117326))), 18927 ^ _776541 : [(18930 ^ _776541) ^ [] : [-(_1117330 = c_Groups_Ozero__class_Ozero(_1117326))], (18928 ^ _776541) ^ [] : [-(_1117328 = c_Groups_Ozero__class_Ozero(_1117326))]]]]], (7023 ^ _776541) ^ [_890721] : [-(hAPP(c_Set_OPow(_890721), c_Orderings_Obot__class_Obot(tc_fun(_890721, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_890721, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_890721, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_890721, tc_HOL_Obool), tc_HOL_Obool))))], (28367 ^ _776541) ^ [_1285762, _1285764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285762), _1285764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285762)), c_Int_OBit1(_1285764))))], (44783 ^ _776541) ^ [_1672004, _1672006, _1672008, _1672010, _1672012] : [class_Groups_Ocomm__monoid__add(_1672004), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672004), hAPP(hAPP(c_List_Omap(_1672006, _1672004), hAPP(hAPP(c_COMBS(_1672006, _1672004, _1672004), hAPP(hAPP(c_COMBB(_1672004, tc_fun(_1672004, _1672004), _1672006), c_Groups_Oplus__class_Oplus(_1672004)), _1672008)), _1672010)), _1672012)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672004), hAPP(c_List_Omonoid__add__class_Olistsum(_1672004), hAPP(hAPP(c_List_Omap(_1672006, _1672004), _1672008), _1672012))), hAPP(c_List_Omonoid__add__class_Olistsum(_1672004), hAPP(hAPP(c_List_Omap(_1672006, _1672004), _1672010), _1672012))))], (44842 ^ _776541) ^ [_1673670, _1673672, _1673674, _1673676] : [_1673676 = c_List_Olist_ONil(_1673672), -(c_List_Olist_ONil(_1673670) = hAPP(hAPP(c_List_Omap(_1673672, _1673670), _1673674), _1673676))], (37340 ^ _776541) ^ [_1487252, _1487254, _1487256, _1487258, _1487260, _1487262] : [c_Fun_Oinj__on(_1487252, _1487254, _1487256, _1487258), -(_1487260 = _1487262), hBOOL(hAPP(hAPP(c_member(_1487252), _1487260), _1487258)), hBOOL(hAPP(hAPP(c_member(_1487252), _1487262), _1487258)), hAPP(_1487256, _1487260) = hAPP(_1487256, _1487262)], (20797 ^ _776541) ^ [_1152009, _1152011, _1152013, _1152015, _1152017] : [class_Fields_Ofield(_1152009), -(_1152011 = c_Groups_Ozero__class_Ozero(_1152009)), -(_1152013 = c_Groups_Ozero__class_Ozero(_1152009)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152009), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152009), _1152015), _1152011)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152009), _1152017), _1152013)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152009), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152009), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152009), _1152015), _1152013)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152009), _1152017), _1152011))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152009), _1152011), _1152013)))], (10505 ^ _776541) ^ [_957071, _957073, _957075] : [hBOOL(hAPP(hAPP(c_member(_957071), _957073), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957071, tc_HOL_Obool)), _957075))), hBOOL(hAPP(hAPP(c_member(_957071), _957073), _957075))], (28939 ^ _776541) ^ [_1295322, _1295324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295322)), c_Int_OBit1(_1295324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295322), _1295324)))], (24944 ^ _776541) ^ [_1228227, _1228229] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228227), _1228229)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228227)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228229)))], (39457 ^ _776541) ^ [_1541139, _1541141, _1541143, _1541145, _1541147, _1541149, _1541151] : [-(hAPP(c_Product__Type_Osnd(_1541139, _1541141), hAPP(c_Product__Type_Omap__pair(_1541143, _1541139, _1541145, _1541141, _1541147, _1541149), _1541151)) = hAPP(_1541149, hAPP(c_Product__Type_Osnd(_1541143, _1541145), _1541151)))], (38716 ^ _776541) ^ [_1520632, _1520634, _1520636, _1520638] : [-(hAPP(c_Set_Ovimage(_1520632, _1520634, _1520636), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1520634, tc_HOL_Obool)), _1520638)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1520632, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1520632, _1520634, _1520636), _1520638)))], (16498 ^ _776541) ^ [_1073625] : [_1073625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073625), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6563 ^ _776541) ^ [_882607, _882609, _882611, _882613, _882615] : [class_Orderings_Oord(_882607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882609, _882607)), _882611), _882613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882607), hAPP(_882611, _882615)), hAPP(_882613, _882615))))], (4802 ^ _776541) ^ [_849661, _849663, _849665, _849667] : [-(c_List_Olexord(_849667, _849663) = c_List_Olexord(_849665, _849661)), _849667 = _849665, _849663 = _849661], (18726 ^ _776541) ^ [_1113739, _1113741, _1113743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1113739), _1113741)), -(hBOOL(hAPP(hAPP(c_member(_1113739), _1113743), _1113741))), -(hAPP(c_Finite__Set_Ocard(_1113739), hAPP(hAPP(c_Set_Oinsert(_1113739), _1113743), _1113741)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1113739), _1113741)))], (254 ^ _776541) ^ [_780506, _780508] : [-(class_Fields_Ofield(_780506)), _780508 = _780506, class_Fields_Ofield(_780508)], (20551 ^ _776541) ^ [_1147463, _1147465, _1147467, _1147469] : [class_Fields_Olinordered__field(_1147463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147463), _1147465), c_Groups_Ozero__class_Ozero(_1147463))), 20558 ^ _776541 : [(20565 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147463), _1147469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147463), _1147467), _1147465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147463), _1147467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147463), _1147469), _1147465))))], (20559 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147463), _1147467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147463), _1147469), _1147465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147463), _1147469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147463), _1147467), _1147465))))]]], (15154 ^ _776541) ^ [_1050052] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050052), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1050052)], (47658 ^ _776541) ^ [_1735322, _1735324, _1735326, _1735328, _1735330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1735322, _1735324)), hAPP(_1735322, _1735326))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1735328, _1735328)), hAPP(hAPP(c_Product__Type_OPair(_1735328, _1735328), _1735324), _1735326)), c_List_Omeasures(_1735328, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1735328, tc_Nat_Onat)), _1735322), _1735330)))))], (23183 ^ _776541) ^ [_1196442, _1196444, _1196446, _1196448, _1196450] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1196442, _1196444, _1196446), _1196448), hAPP(c_Nat_OSuc, _1196450)) = hAPP(hAPP(_1196446, _1196448), hAPP(hAPP(c_Power_Opower_Opower(_1196442, _1196444, _1196446), _1196448), _1196450)))], (13790 ^ _776541) ^ [_1022280, _1022282, _1022284, _1022286, _1022288] : [class_Rings_Osemiring(_1022280), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022280), _1022282), _1022284)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022280), _1022286), _1022284)), _1022288)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022280), _1022282), _1022286)), _1022284)), _1022288))], (4664 ^ _776541) ^ [_847462, _847464, _847466, _847468, _847470, _847472, _847474, _847476] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_847476, _847472, _847468, _847464) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_847474, _847470, _847466, _847462)), _847476 = _847474, _847472 = _847470, _847468 = _847466, _847464 = _847462], (41019 ^ _776541) ^ [_1580230, _1580232] : [-(c_Relation_Oirrefl(_1580230, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1580230, _1580230), tc_HOL_Obool)), _1580232), c_Relation_OId(_1580230))))], (43847 ^ _776541) ^ [_1652350, _1652352, _1652354, _1652356, _1652358] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652350), tc_List_Olist(_1652350))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652350), tc_List_Olist(_1652350)), hAPP(hAPP(c_List_Oappend(_1652350), _1652352), _1652354)), hAPP(hAPP(c_List_Oappend(_1652350), _1652352), _1652356))), c_List_Olexord(_1652350, _1652358))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652350, _1652350)), hAPP(hAPP(c_Product__Type_OPair(_1652350, _1652350), 43852 ^ [_1652350, _1652352, _1652354, _1652356, _1652358]), 43852 ^ [_1652350, _1652352, _1652354, _1652356, _1652358])), _1652358))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652350), tc_List_Olist(_1652350))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652350), tc_List_Olist(_1652350)), _1652354), _1652356)), c_List_Olexord(_1652350, _1652358))))], (38456 ^ _776541) ^ [_1513815, _1513817] : [c_Wellfounded_Owf(_1513815, hAPP(c_Set_OCollect(tc_prod(_1513815, _1513815)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513815, _1513815, tc_HOL_Obool), _1513817))), -(c_Wellfounded_OwfP(_1513815, _1513817))], (49056 ^ _776541) ^ [_1766073, _1766075, _1766077] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1766073, _1766075, _1766077) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766073)], (38016 ^ _776541) ^ [_1502985, _1502987, _1502989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502985, _1502985), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1502985, _1502985, _1502985), _1502987), _1502989)), _1502987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1502985, tc_HOL_Obool), tc_fun(_1502985, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1502985, tc_HOL_Obool), tc_fun(_1502985, tc_HOL_Obool), tc_fun(_1502985, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1502985, _1502987)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1502985, tc_HOL_Obool), tc_fun(_1502985, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1502985, _1502989)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1502985, tc_HOL_Obool), tc_fun(_1502985, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1502985, tc_HOL_Obool), tc_fun(_1502985, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1502985, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1502985, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1502985, tc_HOL_Obool), tc_fun(_1502985, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1502985, _1502987))))], (45529 ^ _776541) ^ [_1689466, _1689468, _1689470, _1689472, _1689474, _1689476, _1689478] : [-(c_List_Olist__all2(_1689466, _1689468, _1689470, hAPP(hAPP(c_List_Olist_OCons(_1689466), _1689472), _1689474), hAPP(hAPP(c_List_Olist_OCons(_1689468), _1689476), _1689478))), hBOOL(hAPP(hAPP(_1689470, _1689472), _1689476)), c_List_Olist__all2(_1689466, _1689468, _1689470, _1689474, _1689478)], (14907 ^ _776541) ^ [_1045422, _1045424, _1045426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045422), _1045424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045426), _1045422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045426), _1045424))))], (45539 ^ _776541) ^ [_1689671, _1689673, _1689675, _1689677, _1689679, _1689681, _1689683] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689671)), _1689673) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689675)), _1689677), 45542 ^ _776541 : [(45551 ^ _776541) ^ [] : [-(c_List_Olist__all2(_1689671, _1689675, _1689679, hAPP(hAPP(c_List_Oappend(_1689671), _1689673), _1689681), hAPP(hAPP(c_List_Oappend(_1689675), _1689677), _1689683))), c_List_Olist__all2(_1689671, _1689675, _1689679, _1689673, _1689677), c_List_Olist__all2(_1689671, _1689675, _1689679, _1689681, _1689683)], (45543 ^ _776541) ^ [] : [c_List_Olist__all2(_1689671, _1689675, _1689679, hAPP(hAPP(c_List_Oappend(_1689671), _1689673), _1689681), hAPP(hAPP(c_List_Oappend(_1689675), _1689677), _1689683)), 45546 ^ _776541 : [(45549 ^ _776541) ^ [] : [-(c_List_Olist__all2(_1689671, _1689675, _1689679, _1689681, _1689683))], (45547 ^ _776541) ^ [] : [-(c_List_Olist__all2(_1689671, _1689675, _1689679, _1689673, _1689677))]]]]], (2762 ^ _776541) ^ [_817387, _817389, _817391, _817393, _817395, _817397] : [-(c_Predicate_ODomainP(_817397, _817393, _817389) = c_Predicate_ODomainP(_817395, _817391, _817387)), _817397 = _817395, _817393 = _817391, _817389 = _817387], (26745 ^ _776541) ^ [_1259011, _1259013] : [c_Nat__Transfer_Onat__set(_1259011), c_Nat__Transfer_Onat__set(_1259013), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1259011), _1259013)))], (18332 ^ _776541) ^ [_1106258, _1106260, _1106262, _1106264] : [class_Rings_Olinordered__semiring__strict(_1106258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106258), _1106260), _1106262)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106258), _1106264), _1106262))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106258), c_Groups_Ozero__class_Ozero(_1106258)), _1106262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106258), _1106260), _1106264)))], (3110 ^ _776541) ^ [_822811, _822813, _822815, _822817] : [-(c_List_Olistset(_822817, _822813) = c_List_Olistset(_822815, _822811)), _822817 = _822815, _822813 = _822811], (44453 ^ _776541) ^ [_1665591, _1665593, _1665595] : [class_Orderings_Olinorder(_1665591), -(c_Big__Operators_Olattice_OSup__fin(_1665591, c_Orderings_Oord__class_Omax(_1665591), hAPP(c_List_Oset(_1665591), hAPP(hAPP(c_List_Olist_OCons(_1665591), _1665593), _1665595))) = hAPP(c_List_Ofoldl(_1665591, _1665591, c_Orderings_Oord__class_Omax(_1665591), _1665593), _1665595))], (15322 ^ _776541) ^ [_1053041, _1053043] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1053041, _1053043)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053043), _1053041))], (31365 ^ _776541) ^ [_1339567, _1339569, _1339571] : [class_Orderings_Olinorder(_1339567), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339567), _1339569), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339567), _1339569), _1339571)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339567), _1339569), _1339571))], (43020 ^ _776541) ^ [_1633986] : [-(c_List_Obutlast(_1633986, c_List_Olist_ONil(_1633986)) = c_List_Olist_ONil(_1633986))], (25784 ^ _776541) ^ [_1243120, _1243122] : [-(_1243120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25787 ^ _776541 : [(25794 ^ _776541) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243122, _1243120) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243122), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243120)) = 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), _1243122), _1243120))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25788 ^ _776541) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243122, _1243120) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243122), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243120)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243122), _1243120)))]]], (36215 ^ _776541) ^ [_1459730, _1459732, _1459734, _1459736, _1459738, _1459740] : [hAPP(c_Product__Type_Oapfst(_1459730, _1459732, _1459734, _1459736), _1459738) = hAPP(c_Product__Type_Oapfst(_1459730, _1459732, _1459734, _1459740), _1459738), -(hAPP(_1459736, hAPP(c_Product__Type_Ofst(_1459730, _1459734), _1459738)) = hAPP(_1459740, hAPP(c_Product__Type_Ofst(_1459730, _1459734), _1459738)))], (14927 ^ _776541) ^ [_1045846, _1045848] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045846), _1045848))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045848), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045846), _1045848)) = _1045846)], (47422 ^ _776541) ^ [_1730003, _1730005, _1730007, _1730009, _1730011] : [-(c_List_OdropWhile(_1730003, _1730005, hAPP(hAPP(c_List_Omap(_1730007, _1730003), _1730009), _1730011)) = hAPP(hAPP(c_List_Omap(_1730007, _1730003), _1730009), c_List_OdropWhile(_1730007, hAPP(c_Fun_Ocomp(_1730003, tc_HOL_Obool, _1730007, _1730005), _1730009), _1730011)))], (11654 ^ _776541) ^ [_980407, _980409, _980411] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980407), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980407, tc_HOL_Obool)), _980409), _980411))), 11657 ^ _776541 : [(11660 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_980407), _980411)))], (11658 ^ _776541) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_980407), _980409)))]]], (39155 ^ _776541) ^ [_1532051, _1532053, _1532055, _1532057, _1532059, _1532061] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532051, _1532053)), hAPP(hAPP(c_Product__Type_OPair(_1532051, _1532053), _1532055), _1532057)), hAPP(hAPP(c_Product__Type_OSigma(_1532051, _1532053), _1532059), _1532061))), 39158 ^ _776541 : [(39161 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532053), _1532057), hAPP(_1532061, _1532055))))], (39159 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532051), _1532055), _1532059)))]]], (23597 ^ _776541) ^ [_1204216, _1204218] : [class_Divides_Osemiring__div(_1204216), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204216), c_Groups_Ozero__class_Ozero(_1204216)), _1204218) = c_Groups_Ozero__class_Ozero(_1204216))], (17071 ^ _776541) ^ [_1083886, _1083888, _1083890] : [class_Rings_Oordered__ring(_1083886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083886), _1083888), c_Groups_Ozero__class_Ozero(_1083886))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083886), _1083890), c_Groups_Ozero__class_Ozero(_1083886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083886), c_Groups_Ozero__class_Ozero(_1083886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083886), _1083888), _1083890))))], (40102 ^ _776541) ^ [_1557615, _1557617, _1557619, _1557621, _1557623, _1557625, _1557627, _1557629, _1557631, _1557633, _1557635] : [c_Finite__Set_Ofolding(_1557615, _1557617, _1557619, _1557621), -(hAPP(c_Fun_Ocomp(_1557623, _1557625, _1557627, _1557629), hAPP(c_Fun_Ocomp(_1557631, _1557623, _1557627, _1557633), _1557635)) = hAPP(c_Fun_Ocomp(_1557631, _1557625, _1557627, hAPP(c_Fun_Ocomp(_1557623, _1557625, _1557631, _1557629), _1557633)), _1557635))], (34491 ^ _776541) ^ [_1418448, _1418450, _1418452, _1418454] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1418448, tc_fun(_1418450, tc_HOL_Obool))), _1418452), _1418454))], (11481 ^ _776541) ^ [_977095, _977097, _977099] : [11482 ^ _776541 : [(11485 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977095), _977099))], (11483 ^ _776541) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977095), _977097))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977095), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977095, tc_HOL_Obool)), _977097), _977099))))], (26573 ^ _776541) ^ [_1256202] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1256202) = 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), _1256202))))], (3130 ^ _776541) ^ [_823109, _823111, _823113, _823115, _823117, _823119, _823121, _823123] : [-(c_Nat_Onat_Onat__case(_823123, _823119, _823115, _823111) = c_Nat_Onat_Onat__case(_823121, _823117, _823113, _823109)), _823123 = _823121, _823119 = _823117, _823115 = _823113, _823111 = _823109], (47092 ^ _776541) ^ [_1723060, _1723062, _1723064, _1723066, _1723068] : [-(c_List_Ofoldr(_1723060, _1723062, _1723064, _1723066, _1723068) = hAPP(c_List_Ofoldl(_1723062, _1723060, hAPP(c_COMBC(_1723060, _1723062, _1723062), _1723064), _1723068), hAPP(c_List_Orev(_1723060), _1723066)))], (40735 ^ _776541) ^ [_1573419, _1573421] : [-(c_Transitive__Closure_Otrancl(_1573419, _1573421) = hAPP(hAPP(c_Relation_Orel__comp(_1573419, _1573419, _1573419), c_Transitive__Closure_Ortrancl(_1573419, _1573421)), _1573421))], (22769 ^ _776541) ^ [_1189040, _1189042, _1189044] : [class_Rings_Olinordered__semidom(_1189040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189040), c_Groups_Oone__class_Oone(_1189040)), _1189042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189040), hAPP(hAPP(c_Power_Opower__class_Opower(_1189040), _1189042), _1189044)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189040), _1189042), hAPP(hAPP(c_Power_Opower__class_Opower(_1189040), _1189042), _1189044)))))], (15650 ^ _776541) ^ [_1060390, _1060392, _1060394] : [class_Groups_Ocomm__monoid__add(_1060390), hAPP(_1060392, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1060390), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1060390), _1060392), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1060394)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1060390), _1060392), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060394)))], (288 ^ _776541) ^ [_780949, _780951, _780953, _780955] : [-(c_FunDef_Oreduction__pair(_780953, _780949)), c_FunDef_Oreduction__pair(_780955, _780951), _780955 = _780953, _780951 = _780949], (38554 ^ _776541) ^ [_1516027, _1516029, _1516031, _1516033, _1516035] : [-(hAPP(c_Relation_ORange(_1516027, _1516029), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1516027, _1516029)), hAPP(hAPP(c_Product__Type_OPair(_1516027, _1516029), _1516031), _1516033)), _1516035)) = hAPP(hAPP(c_Set_Oinsert(_1516029), _1516033), hAPP(c_Relation_ORange(_1516027, _1516029), _1516035)))], (1864 ^ _776541) ^ [_802705, _802707] : [-(class_Groups_Ozero(_802705)), _802707 = _802705, class_Groups_Ozero(_802707)], (21515 ^ _776541) ^ [_1166256, _1166258, _1166260, _1166262] : [class_Fields_Ofield__inverse__zero(_1166256), class_Int_Onumber(_1166256), 21522 ^ _776541 : [(21523 ^ _776541) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166256), _1166258), _1166260) = hAPP(c_Int_Onumber__class_Onumber__of(_1166256), _1166262), 21526 ^ _776541 : [(21533 ^ _776541) ^ [] : [_1166260 = c_Groups_Ozero__class_Ozero(_1166256), -(hAPP(c_Int_Onumber__class_Onumber__of(_1166256), _1166262) = c_Groups_Ozero__class_Ozero(_1166256))], (21527 ^ _776541) ^ [] : [-(_1166260 = c_Groups_Ozero__class_Ozero(_1166256)), -(_1166258 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166256), hAPP(c_Int_Onumber__class_Onumber__of(_1166256), _1166262)), _1166260))]]], (21539 ^ _776541) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166256), _1166258), _1166260) = hAPP(c_Int_Onumber__class_Onumber__of(_1166256), _1166262)), 21542 ^ _776541 : [(21545 ^ _776541) ^ [] : [_1166258 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166256), hAPP(c_Int_Onumber__class_Onumber__of(_1166256), _1166262)), _1166260)], (21543 ^ _776541) ^ [] : [_1166260 = c_Groups_Ozero__class_Ozero(_1166256)]], 21546 ^ _776541 : [(21549 ^ _776541) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1166256), _1166262) = c_Groups_Ozero__class_Ozero(_1166256)], (21547 ^ _776541) ^ [] : [-(_1166260 = c_Groups_Ozero__class_Ozero(_1166256))]]]]], (6240 ^ _776541) ^ [_876833] : [class_Complete__Lattice_Ocomplete__lattice(_876833), -(c_Complete__Lattice_OInf__class_OInf(_876833, c_Orderings_Otop__class_Otop(tc_fun(_876833, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_876833))], (22333 ^ _776541) ^ [_1181367, _1181369, _1181371] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181367), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181369), _1181371)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181367), _1181369)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181367), _1181371)))], (44172 ^ _776541) ^ [_1659791, _1659793, _1659795, _1659797] : [-(hAPP(c_List_Orotate(_1659791, _1659793), hAPP(c_List_Orotate(_1659791, _1659795), _1659797)) = hAPP(c_List_Orotate(_1659791, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659793), _1659795)), _1659797))], (32520 ^ _776541) ^ [_1364228, _1364230, _1364232, _1364234, _1364236] : [class_Lattices_Olattice(_1364228), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364230, _1364228)), _1364232), _1364234), _1364236) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1364228), hAPP(_1364232, _1364236)), hAPP(_1364234, _1364236)))], (41286 ^ _776541) ^ [_1586572, _1586574, _1586576, _1586578, _1586580, _1586582] : [c_Relation_Osingle__valued(_1586572, _1586574, _1586576), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586572, _1586574)), hAPP(hAPP(c_Product__Type_OPair(_1586572, _1586574), _1586578), _1586580)), _1586576)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586572, _1586574)), hAPP(hAPP(c_Product__Type_OPair(_1586572, _1586574), _1586578), _1586582)), _1586576)), -(_1586580 = _1586582)], (15688 ^ _776541) ^ [_1061042] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1061042)) = 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), _1061042))))], (5679 ^ _776541) ^ [_866094, _866096, _866098] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(_866094)), _866096), _866098)), -(_866096 = _866098)], (28699 ^ _776541) ^ [_1291040, _1291042] : [class_Int_Onumber__ring(_1291040), class_Rings_Olinordered__idom(_1291040), 28706 ^ _776541 : [(28713 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1291042), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291040), hAPP(c_Int_Onumber__class_Onumber__of(_1291040), _1291042)), c_Groups_Oone__class_Oone(_1291040))))], (28707 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291040), hAPP(c_Int_Onumber__class_Onumber__of(_1291040), _1291042)), c_Groups_Oone__class_Oone(_1291040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1291042), c_Int_OBit1(c_Int_OPls))))]]], (20123 ^ _776541) ^ [_1139845, _1139847, _1139849, _1139851] : [class_Fields_Olinordered__field(_1139845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139845), _1139847), _1139849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139845), c_Groups_Ozero__class_Ozero(_1139845)), _1139851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139845), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139845), _1139847), _1139851)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139845), _1139849), _1139851))))], (49576 ^ _776541) ^ [_1778377, _1778379] : [c_Relation_Oantisym(_1778377, hAPP(c_Relation_Oconverse(_1778377, _1778377), _1778379)), -(c_Relation_Oantisym(_1778377, _1778379))], (45758 ^ _776541) ^ [_1694694, _1694696] : [hBOOL(hAPP(c_List_Odistinct(_1694694), _1694696)), -(c_List_Oremdups(_1694694, _1694696) = _1694696)], (50095 ^ _776541) ^ [_1788548, _1788550, _1788552, _1788554] : [c_Fun_Oinj__on(_1788548, _1788550, _1788552, c_Orderings_Otop__class_Otop(tc_fun(_1788548, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1788548, _1788550, c_Orderings_Otop__class_Otop(tc_fun(_1788548, tc_HOL_Obool)), _1788552), hAPP(_1788552, _1788554)) = _1788554)], (12518 ^ _776541) ^ [_996677, _996679, _996681] : [class_Lattices_Olattice(_996677), hAPP(_996679, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996677), 12523 ^ [_996677, _996679, _996681]), 12524 ^ [_996677, _996679, _996681])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996677), hAPP(_996679, 12523 ^ [_996677, _996679, _996681])), hAPP(_996679, 12524 ^ [_996677, _996679, _996681])), hBOOL(hAPP(c_Finite__Set_Ofinite(_996677), _996681)), -(_996681 = c_Orderings_Obot__class_Obot(tc_fun(_996677, tc_HOL_Obool))), -(hAPP(_996679, c_Big__Operators_Olattice__class_OInf__fin(_996677, _996681)) = c_Big__Operators_Olattice__class_OInf__fin(_996677, hAPP(c_Set_Oimage(_996677, _996677, _996679), _996681)))], (14897 ^ _776541) ^ [_1045225] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045225), _1045225))))], (42087 ^ _776541) ^ [_1610243, _1610245, _1610247, _1610249, _1610251, _1610253] : [c_List_Olistrelp(_1610243, _1610245, hAPP(hAPP(c_List_Olist_OCons(_1610243), _1610247), _1610249), hAPP(hAPP(c_List_Olist_OCons(_1610243), _1610251), _1610253)), 42090 ^ _776541 : [(42093 ^ _776541) ^ [] : [-(c_List_Olistrelp(_1610243, _1610245, _1610249, _1610253))], (42091 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(_1610245, _1610247), _1610251)))]]], (10767 ^ _776541) ^ [_961987, _961989] : [class_Orderings_Olinorder(_961987), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961987, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_961987), _961989)) = hAPP(c_SetInterval_Oord__class_OatMost(_961987), _961989))], (12864 ^ _776541) ^ [_1003505, _1003507, _1003509, _1003511, _1003513, _1003515] : [c_Finite__Set_Ofun__left__comm(_1003505, _1003507, _1003509), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003505), _1003511)), -(hBOOL(hAPP(hAPP(c_member(_1003505), _1003513), _1003511))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1003505, _1003507, _1003509), _1003515), hAPP(hAPP(c_Set_Oinsert(_1003505), _1003513), _1003511)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003505, _1003507, _1003509), hAPP(hAPP(_1003509, _1003513), _1003515)), _1003511))], (21119 ^ _776541) ^ [_1158524, _1158526] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1158524), _1158526)), 21125 ^ _776541 : [(21128 ^ _776541) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21126 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1158524), 21124 ^ [_1158524, _1158526]), _1158526)))]], -(hAPP(c_Finite__Set_Ocard(_1158524), _1158526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36890 ^ _776541) ^ [_1476730, _1476732, _1476734, _1476736, _1476738] : [hAPP(c_Relation_OImage(_1476730, _1476730, _1476732), hAPP(hAPP(c_Set_Oinsert(_1476730), _1476734), c_Orderings_Obot__class_Obot(tc_fun(_1476730, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1476730, _1476730, _1476732), hAPP(hAPP(c_Set_Oinsert(_1476730), _1476736), c_Orderings_Obot__class_Obot(tc_fun(_1476730, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1476730, _1476738, _1476732), hBOOL(hAPP(hAPP(c_member(_1476730), _1476736), _1476738)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476730, _1476730)), hAPP(hAPP(c_Product__Type_OPair(_1476730, _1476730), _1476734), _1476736)), _1476732)))], (49818 ^ _776541) ^ [_1782938, _1782940] : [c_Relation_Osym(_1782938, hAPP(c_Set_OCollect(tc_prod(_1782938, _1782938)), hAPP(c_Product__Type_Oprod_Oprod__case(_1782938, _1782938, tc_HOL_Obool), _1782940))), -(c_Predicate_Osymp(_1782938, _1782940))], (38511 ^ _776541) ^ [_1514892, _1514894, _1514896] : [hAPP(c_Relation_ORange(_1514892, _1514894), _1514896) = c_Orderings_Obot__class_Obot(tc_fun(_1514894, tc_HOL_Obool)), -(_1514896 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514892, _1514894), tc_HOL_Obool)))], (14594 ^ _776541) ^ [_1039614, _1039616, _1039618] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039614), _1039616)), _1039618) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039614), _1039618)), _1039616))], (49340 ^ _776541) ^ [_1772563, _1772565, _1772567] : [-(c_List_Olist__ex(_1772563, _1772565, _1772567)), 49341 ^ _776541 : [(49342 ^ _776541) ^ [_1772620] : [hBOOL(hAPP(hAPP(c_member(_1772563), _1772620), hAPP(c_List_Oset(_1772563), _1772567))), hBOOL(hAPP(_1772565, _1772620))]]], (27627 ^ _776541) ^ [] : [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)], (43178 ^ _776541) ^ [_1636730, _1636732, _1636734] : [-(hBOOL(hAPP(hAPP(c_member(_1636730), _1636732), hAPP(c_List_Oset(_1636730), _1636734)))), -(c_List_Oremove1(_1636730, _1636732, _1636734) = _1636734)], (40026 ^ _776541) ^ [_1555857, _1555859, _1555861, _1555863, _1555865, _1555867, _1555869] : [class_Groups_Oab__semigroup__mult(_1555857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555859), _1555861)), c_Fun_Oinj__on(_1555859, _1555863, _1555865, _1555861), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1555857, _1555863, c_Groups_Otimes__class_Otimes(_1555857)), _1555867), _1555869), hAPP(c_Set_Oimage(_1555859, _1555863, _1555865), _1555861)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1555857, _1555859, c_Groups_Otimes__class_Otimes(_1555857)), hAPP(c_Fun_Ocomp(_1555863, _1555857, _1555859, _1555867), _1555865)), _1555869), _1555861))], (33427 ^ _776541) ^ [_1390860, _1390862, _1390864, _1390866, _1390868, _1390870] : [class_Complete__Lattice_Ocomplete__lattice(_1390860), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390862, _1390860), _1390864), hAPP(hAPP(c_COMBB(tc_fun(_1390866, _1390860), _1390860, _1390862), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390866, _1390860), _1390868)), _1390870)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390866, _1390860), _1390868), hAPP(hAPP(c_COMBB(tc_fun(_1390862, _1390860), _1390860, _1390866), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390862, _1390860), _1390864)), hAPP(c_COMBC(_1390862, _1390866, _1390860), _1390870))))], (2004 ^ _776541) ^ [_805366, _805368, _805370, _805372, _805374, _805376, _805378, _805380] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_805380, _805376, _805372, _805368) = c_SetInterval_Oord_OgreaterThanLessThan(_805378, _805374, _805370, _805366)), _805380 = _805378, _805376 = _805374, _805372 = _805370, _805368 = _805366], (39283 ^ _776541) ^ [_1535490, _1535492, _1535494, _1535496] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535490, _1535492), _1535494), _1535496) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535490, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool)), _1535494), hAPP(hAPP(c_COMBS(_1535490, tc_fun(_1535492, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool)), tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535492, tc_HOL_Obool), tc_fun(tc_fun(_1535492, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool)), tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool)), _1535490), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535492, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool))), _1535496)), hAPP(hAPP(c_COMBC(_1535490, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool), tc_fun(_1535492, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535492, tc_fun(tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool), tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool), tc_fun(_1535492, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool))), _1535490), c_COMBC(_1535492, tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool), tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535492, tc_prod(_1535490, _1535492)), tc_fun(_1535492, tc_fun(tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool), tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool))), _1535490), hAPP(c_COMBB(tc_prod(_1535490, _1535492), tc_fun(tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool), tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool)), _1535492), c_Set_Oinsert(tc_prod(_1535490, _1535492)))), c_Product__Type_OPair(_1535490, _1535492)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1535490, _1535492), tc_HOL_Obool))))))], (39932 ^ _776541) ^ [_1553825, _1553827, _1553829, _1553831, _1553833, _1553835, _1553837] : [-(hAPP(c_Product__Type_Oapfst(_1553825, _1553827, _1553829, _1553831), hAPP(c_Product__Type_Oapfst(_1553833, _1553825, _1553829, _1553835), _1553837)) = hAPP(c_Product__Type_Oapfst(_1553833, _1553827, _1553829, hAPP(c_Fun_Ocomp(_1553825, _1553827, _1553833, _1553831), _1553835)), _1553837))], (16779 ^ _776541) ^ [_1078435, _1078437] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1078435), hAPP(c_Nat_OSuc, _1078437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1078435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1078435), _1078437)))], (36711 ^ _776541) ^ [_1472907, _1472909, _1472911, _1472913, _1472915] : [c_Equiv__Relations_Oequiv(_1472907, _1472909, _1472911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472907, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472907, _1472907, _1472911), hAPP(hAPP(c_Set_Oinsert(_1472907), _1472913), c_Orderings_Obot__class_Obot(tc_fun(_1472907, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1472907, _1472907, _1472911), hAPP(hAPP(c_Set_Oinsert(_1472907), _1472915), c_Orderings_Obot__class_Obot(tc_fun(_1472907, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1472907), _1472913), _1472909)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472907, _1472907)), hAPP(hAPP(c_Product__Type_OPair(_1472907, _1472907), _1472915), _1472913)), _1472911)))], (44721 ^ _776541) ^ [_1670533, _1670535, _1670537, _1670539, _1670541, _1670543] : [-(hAPP(hAPP(c_List_Omap(_1670533, _1670535), _1670537), hAPP(hAPP(c_List_Omap(_1670539, _1670533), _1670541), _1670543)) = hAPP(hAPP(c_List_Omap(_1670539, _1670535), hAPP(c_Fun_Ocomp(_1670533, _1670535, _1670539, _1670537), _1670541)), _1670543))], (29615 ^ _776541) ^ [_1307370, _1307372] : [-(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), _1307370)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1307372))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1307370))) = 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), _1307372)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1307370)))], (41849 ^ _776541) ^ [_1602585, _1602587, _1602589, _1602591] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602585), tc_List_Olist(_1602585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602585), tc_List_Olist(_1602585)), _1602587), _1602589)), c_List_Olex(_1602585, _1602591))), 41852 ^ _776541 : [(41855 ^ _776541) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602585)), _1602587) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602585)), _1602589))], (41853 ^ _776541) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602585), tc_List_Olist(_1602585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602585), tc_List_Olist(_1602585)), _1602587), _1602589)), c_List_Olexord(_1602585, _1602591))))]]], (33457 ^ _776541) ^ [_1391751, _1391753, _1391755] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391751, tc_Nat_Onat), _1391753), _1391755)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391751, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1391751), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1391753)), _1391755))], (22653 ^ _776541) ^ [_1186974, _1186976, _1186978, _1186980] : [class_Groups_Omonoid__mult(_1186974), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186974), _1186976), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1186978), _1186980)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186974), hAPP(hAPP(c_Power_Opower__class_Opower(_1186974), _1186976), _1186978)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186974), _1186976), _1186980)))], (42711 ^ _776541) ^ [_1627085, _1627087, _1627089] : [hBOOL(hAPP(hAPP(c_member(_1627085), _1627087), hAPP(c_List_Oset(_1627085), c_List_Obutlast(_1627085, _1627089)))), -(hBOOL(hAPP(hAPP(c_member(_1627085), _1627087), hAPP(c_List_Oset(_1627085), _1627089))))], (28719 ^ _776541) ^ [_1291354, _1291356] : [class_Int_Onumber__ring(_1291354), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1291354), hAPP(c_Int_Onumber__class_Onumber__of(_1291354), _1291356)), c_Groups_Oone__class_Oone(_1291354)) = hAPP(c_Int_Onumber__class_Onumber__of(_1291354), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1291356), c_Int_OBit1(c_Int_OPls))))], (33815 ^ _776541) ^ [_1402846, _1402848, _1402850, _1402852, _1402854] : [-(_1402846 = c_Orderings_Obot__class_Obot(tc_fun(_1402848, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1402848, tc_fun(_1402850, tc_HOL_Obool)), _1402846), hAPP(hAPP(c_COMBB(tc_fun(_1402850, tc_HOL_Obool), tc_fun(_1402850, tc_HOL_Obool), _1402848), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402850, tc_HOL_Obool)), _1402852)), _1402854)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402850, tc_HOL_Obool)), _1402852), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402848, tc_fun(_1402850, tc_HOL_Obool)), _1402846), _1402854)))], (17273 ^ _776541) ^ [_1087496, _1087498] : [class_Groups_Olinordered__ab__group__add(_1087496), 17276 ^ _776541 : [(17283 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087496), c_Groups_Ozero__class_Ozero(_1087496)), _1087498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087496), c_Groups_Ozero__class_Ozero(_1087496)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087496), _1087498), _1087498))))], (17277 ^ _776541) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087496), c_Groups_Ozero__class_Ozero(_1087496)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087496), _1087498), _1087498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087496), c_Groups_Ozero__class_Ozero(_1087496)), _1087498)))]]]], input).
% 45.01/44.00  ncf('1',plain,[v_P(52572 ^ [], 52573 ^ []), -(v_Q_H(52572 ^ [], 52576 ^ []))],start(52578 ^ 0,bind([[_2080006], [52572 ^ []]]))).
% 45.01/44.00  ncf('1.1',plain,[-(v_P(52572 ^ [], 52573 ^ []))],extension(52575 ^ 1)).
% 45.01/44.00  ncf('1.2',plain,[v_Q_H(52572 ^ [], 52576 ^ []), -(v_Q(52572 ^ [], 52576 ^ []))],extension(52567 ^ 1,bind([[_1832307, _1832309], [52576 ^ [], 52572 ^ []]]))).
% 45.01/44.00  ncf('1.2.1',plain,[v_Q(52572 ^ [], 52576 ^ [])],extension(52584 ^ 2)).
% 45.01/44.00  %-----------------------------------------------------
% 45.01/44.00  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------