TSTP Solution File: SWW294+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW294+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n011.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 12:25:53 EDT 2023

% Result   : Theorem 52.25s 51.25s
% Output   : Proof 52.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWW294+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.11/0.33  % Computer : n011.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May 18 22:28:03 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 52.25/51.25  
% 52.25/51.25  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 52.25/51.25  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.25/51.25  %-----------------------------------------------------
% 52.25/51.25  ncf(matrix, plain, [(51738 ^ _2062237) ^ [] : [v_Q(51730 ^ [], 51734 ^ [])], (51736 ^ _2062237) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, v_pn), 51731 ^ [], c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 51734 ^ []))], (51733 ^ _2062237) ^ [] : [-(v_P(51730 ^ [], 51731 ^ []))], !, (10228 ^ _778908) ^ [_950752, _950754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950752)), _950754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _950752), hAPP(c_Int_Onat, _950754))))], (34282 ^ _778908) ^ [_1405660, _1405662, _1405664, _1405666, _1405668, _1405670] : [-(hBOOL(hAPP(hAPP(c_member(_1405660), _1405662), _1405664))), -(hAPP(c_Set_Oimage(_1405660, _1405666, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1405660, _1405666), _1405668), _1405662), _1405670)), _1405664) = hAPP(c_Set_Oimage(_1405660, _1405666, _1405668), _1405664))], (42143 ^ _778908) ^ [] : [-(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))))], (5865 ^ _778908) ^ [_872306, _872308, _872310, _872312, _872314] : [c_Com_Ocom_OAss(_872306, _872308) = c_Com_Ocom_OCall(_872310, _872312, _872314)], (2060 ^ _778908) ^ [_809490, _809492, _809494, _809496, _809498, _809500, _809502, _809504] : [-(c_Com_Ovname_Ovname__case(_809504, _809500, _809496, _809492) = c_Com_Ovname_Ovname__case(_809502, _809498, _809494, _809490)), _809504 = _809502, _809500 = _809498, _809496 = _809494, _809492 = _809490], (41070 ^ _778908) ^ [_1558844, _1558846, _1558848, _1558850, _1558852, _1558854, _1558856, _1558858] : [c_Finite__Set_Ofolding__image__simple(_1558844, _1558846, _1558848, _1558850, _1558852, _1558854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558846), _1558856)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558846), _1558858)), 41084 ^ _778908 : [(41087 ^ _778908) ^ [] : [hAPP(_1558852, 41083 ^ [_1558844, _1558846, _1558848, _1558850, _1558852, _1558854, _1558856, _1558858]) = _1558850], (41085 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558846), 41083 ^ [_1558844, _1558846, _1558848, _1558850, _1558852, _1558854, _1558856, _1558858]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1558846, tc_HOL_Obool)), _1558856), _1558858))))]], -(hAPP(_1558854, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1558846, tc_HOL_Obool)), _1558856), _1558858)) = hAPP(hAPP(_1558848, hAPP(_1558854, _1558856)), hAPP(_1558854, _1558858)))], (11244 ^ _778908) ^ [_966981, _966983, _966985, _966987, _966989] : [class_Groups_Oordered__ab__semigroup__add(_966981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966981), _966983), _966985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966981), _966987), _966989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966981), _966983), _966987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966981), _966985), _966989))))], (1232 ^ _778908) ^ [_797182, _797184] : [-(class_Groups_Oabs__if(_797182)), _797184 = _797182, class_Groups_Oabs__if(_797184)], (28727 ^ _778908) ^ [_1289693, _1289695, _1289697] : [class_Orderings_Olinorder(_1289693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289693), _1289695), _1289697)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289693, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1289693, _1289695, _1289697)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1289693), _1289697)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1289693), _1289695))], (42977 ^ _778908) ^ [_1612584, _1612586, _1612588, _1612590, _1612592, _1612594, _1612596, _1612598] : [class_Groups_Ocomm__monoid__add(_1612584), c_Fun_Oinj__on(_1612586, _1612588, _1612590, _1612592), _1612594 = hAPP(c_Set_Oimage(_1612586, _1612588, _1612590), _1612592), 42991 ^ _778908 : [(42994 ^ _778908) ^ [] : [hAPP(_1612596, 42990 ^ [_1612584, _1612586, _1612588, _1612590, _1612592, _1612594, _1612596, _1612598]) = hAPP(_1612598, hAPP(_1612590, 42990 ^ [_1612584, _1612586, _1612588, _1612590, _1612592, _1612594, _1612596, _1612598]))], (42992 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612586), 42990 ^ [_1612584, _1612586, _1612588, _1612590, _1612592, _1612594, _1612596, _1612598]), _1612592)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1612588, _1612584), _1612598), _1612594) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1612586, _1612584), _1612596), _1612592))], (50889 ^ _778908) ^ [_1801646, _1801648] : [hBOOL(hAPP(c_List_Odistinct(_1801646), _1801648)), -(hBOOL(hAPP(c_List_Odistinct(_1801646), hAPP(c_List_Orev(_1801646), _1801648))))], (26809 ^ _778908) ^ [_1251671, _1251673] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251673), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251671)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251671)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251673))))], (30784 ^ _778908) ^ [] : [-(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))))], (35564 ^ _778908) ^ [_1433910, _1433912, _1433914] : [hBOOL(hAPP(c_Predicate_OPowp(_1433910, hAPP(hAPP(c_COMBC(_1433910, tc_fun(_1433910, tc_HOL_Obool), tc_HOL_Obool), c_member(_1433910)), _1433912)), _1433914)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1433910, tc_HOL_Obool)), _1433914), hAPP(c_Set_OPow(_1433910), _1433912))))], (41750 ^ _778908) ^ [_1581437, _1581439] : [41751 ^ _778908 : [(41752 ^ _778908) ^ [_1581501, _1581503] : [_1581439 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1581437, _1581501), 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)), _1581503)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1581437), _1581439)))], (11687 ^ _778908) ^ [_974591, _974593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _974591), _974593))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _974591), _974593)), -(_974591 = _974593)], (7104 ^ _778908) ^ [_897689, _897691] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_897689)), hAPP(c_Option_Ooption_OSome(_897689), _897691)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48518 ^ _778908) ^ [_1748151, _1748153, _1748155] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1748151, tc_HOL_Obool)), hAPP(c_List_Oset(_1748151), hAPP(hAPP(c_List_Otake(_1748151), _1748153), _1748155))), hAPP(c_List_Oset(_1748151), _1748155))))], (42204 ^ _778908) ^ [_1593557, _1593559, _1593561] : [-(hAPP(c_Set_Oimage(tc_prod(_1593557, _1593559), _1593559, c_Product__Type_Osnd(_1593557, _1593559)), _1593561) = hAPP(c_Relation_ORange(_1593557, _1593559), _1593561))], (41255 ^ _778908) ^ [_1562962, _1562964, _1562966] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562962, tc_HOL_Obool)), _1562964), _1562966) = hAPP(c_Set_OCollect(_1562962), hAPP(hAPP(c_COMBS(_1562962, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562962), c_fconj), hAPP(hAPP(c_COMBC(_1562962, tc_fun(_1562962, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562962)), _1562964))), hAPP(hAPP(c_COMBC(_1562962, tc_fun(_1562962, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562962)), _1562966))))], (30098 ^ _778908) ^ [_1317955, _1317957, _1317959, _1317961] : [c_Orderings_Obot__class_Obot(tc_fun(_1317955, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1317957, tc_fun(_1317955, tc_HOL_Obool)), _1317959), _1317961), 30101 ^ _778908 : [(30102 ^ _778908) ^ [_1318071] : [hBOOL(hAPP(hAPP(c_member(_1317957), _1318071), _1317959)), -(hAPP(_1317961, _1318071) = c_Orderings_Obot__class_Obot(tc_fun(_1317955, tc_HOL_Obool)))]]], (5464 ^ _778908) ^ [_863336, _863338] : [_863338 = _863336, -(c_Groups_Oone__class_Oone(_863338) = c_Groups_Oone__class_Oone(_863336))], (13240 ^ _778908) ^ [_1002092, _1002094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1002092)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1002094)))), 13243 ^ _778908 : [(13246 ^ _778908) ^ [] : [-(_1002094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13244 ^ _778908) ^ [] : [-(_1002092 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (30184 ^ _778908) ^ [_1319710, _1319712, _1319714, _1319716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1319710, _1319712)), c_Sum__Type_OPlus(_1319710, _1319712, _1319714, _1319716))), 30187 ^ _778908 : [(30190 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1319712), _1319716)))], (30188 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1319710), _1319714)))]]], (41133 ^ _778908) ^ [_1560242, _1560244, _1560246] : [-(hBOOL(hAPP(_1560242, _1560244))), -(hAPP(c_Set_OCollect(_1560246), hAPP(hAPP(c_COMBS(_1560246, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560246), c_fconj), hAPP(c_fequal, _1560244))), _1560242)) = c_Orderings_Obot__class_Obot(tc_fun(_1560246, tc_HOL_Obool)))], (8070 ^ _778908) ^ [_913933] : [8071 ^ _778908 : [(8072 ^ _778908) ^ [_913975] : [_913933 = hAPP(c_Nat_OSuc, _913975)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _913933)))], (35546 ^ _778908) ^ [_1433562, _1433564, _1433566, _1433568, _1433570] : [c_Finite__Set_Ofolding__one__idem(_1433562, _1433564, _1433566), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433562), _1433568)), -(_1433570 = c_Orderings_Obot__class_Obot(tc_fun(_1433562, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433562, tc_HOL_Obool)), _1433570), _1433568)), -(hAPP(hAPP(_1433564, hAPP(_1433566, _1433570)), hAPP(_1433566, _1433568)) = hAPP(_1433566, _1433568))], (34764 ^ _778908) ^ [_1415541, _1415543, _1415545, _1415547, _1415549] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1415541)), hAPP(c_Set_Oimage(_1415543, tc_Option_Ooption(_1415541), _1415545), c_Orderings_Otop__class_Otop(tc_fun(_1415543, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1415541)), hAPP(c_Set_Oimage(_1415543, tc_Option_Ooption(_1415541), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1415543, tc_Option_Ooption(_1415541)), _1415545), _1415547), hAPP(c_Option_Ooption_OSome(_1415541), _1415549))), c_Orderings_Otop__class_Otop(tc_fun(_1415543, tc_HOL_Obool))))))], (2446 ^ _778908) ^ [_815841, _815843, _815845, _815847, _815849, _815851, _815853, _815855] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_815855, _815851, _815847, _815843) = c_Nat_Osemiring__1__class_Oof__nat__aux(_815853, _815849, _815845, _815841)), _815855 = _815853, _815851 = _815849, _815847 = _815845, _815843 = _815841], (19551 ^ _778908) ^ [_1115640, _1115642] : [class_Int_Onumber__ring(_1115640), class_Int_Oring__char__0(_1115640), 19558 ^ _778908 : [(19565 ^ _778908) ^ [] : [c_Int_Oiszero(_1115640, hAPP(c_Int_Onumber__class_Onumber__of(_1115640), _1115642)), -(c_Int_Oiszero(_1115640, hAPP(c_Int_Onumber__class_Onumber__of(_1115640), c_Int_OBit0(_1115642))))], (19559 ^ _778908) ^ [] : [c_Int_Oiszero(_1115640, hAPP(c_Int_Onumber__class_Onumber__of(_1115640), c_Int_OBit0(_1115642))), -(c_Int_Oiszero(_1115640, hAPP(c_Int_Onumber__class_Onumber__of(_1115640), _1115642)))]]], (22458 ^ _778908) ^ [_1167846, _1167848] : [-(c_Divides_Odivmod__nat(_1167846, _1167848) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1167846), _1167848)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1167846, _1167848)))], (3526 ^ _778908) ^ [_833137, _833139] : [_833139 = _833137, -(c_Hoare__Mirabelle_Otriple_Otriple(_833139) = c_Hoare__Mirabelle_Otriple_Otriple(_833137))], (35919 ^ _778908) ^ [_1442960, _1442962, _1442964, _1442966, _1442968, _1442970, _1442972, _1442974] : [c_Finite__Set_Ofolding(_1442960, _1442962, _1442964, _1442966), -(hAPP(c_Fun_Ocomp(_1442962, _1442962, _1442968, hAPP(_1442964, _1442970)), hAPP(c_Fun_Ocomp(_1442962, _1442962, _1442968, hAPP(_1442964, _1442972)), _1442974)) = hAPP(c_Fun_Ocomp(_1442962, _1442962, _1442968, hAPP(_1442964, _1442972)), hAPP(c_Fun_Ocomp(_1442962, _1442962, _1442968, hAPP(_1442964, _1442970)), _1442974)))], (25155 ^ _778908) ^ [_1221198, _1221200, _1221202, _1221204, _1221206] : [hBOOL(hAPP(_1221198, hAPP(hAPP(c_Product__Type_OPair(_1221200, _1221202), _1221204), _1221206))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1221200, _1221202, tc_HOL_Obool, _1221198), _1221204), _1221206)))], (11993 ^ _778908) ^ [_979954, _979956, _979958, _979960, _979962] : [class_Rings_Oordered__semiring(_979954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979954), _979956), _979958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979954), _979960), _979962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979954), c_Groups_Ozero__class_Ozero(_979954)), _979956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979954), c_Groups_Ozero__class_Ozero(_979954)), _979960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979954), _979956), _979960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979954), _979958), _979962))))], (51123 ^ _778908) ^ [_1807989, _1807991] : [class_Lattices_Obounded__lattice(_1807989), -(class_Lattices_Obounded__lattice(tc_fun(_1807991, _1807989)))], (42334 ^ _778908) ^ [_1596750, _1596752, _1596754] : [_1596754 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1596750, _1596752), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1596750, _1596752), _1596754) = c_Orderings_Obot__class_Obot(tc_fun(_1596750, tc_HOL_Obool)))], (44995 ^ _778908) ^ [_1662501, _1662503, _1662505, _1662507, _1662509, _1662511] : [c_Relation_Osingle__valued(_1662501, _1662503, hAPP(c_Relation_Oconverse(_1662503, _1662501), _1662505)), -(_1662507 = c_Orderings_Obot__class_Obot(tc_fun(_1662509, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1662503, _1662501, _1662505), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662509, tc_fun(_1662503, tc_HOL_Obool)), _1662507), _1662511)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662509, tc_fun(_1662501, tc_HOL_Obool)), _1662507), hAPP(hAPP(c_COMBB(tc_fun(_1662503, tc_HOL_Obool), tc_fun(_1662501, tc_HOL_Obool), _1662509), c_Relation_OImage(_1662503, _1662501, _1662505)), _1662511)))], (47148 ^ _778908) ^ [_1715161, _1715163, _1715165, _1715167] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1715161), tc_List_Olist(_1715161), c_List_Olistrel(_1715161, _1715163)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1715161)), hAPP(hAPP(c_List_Olist_OCons(_1715161), _1715165), _1715167)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1715161), tc_HOL_Obool)))) = c_List_Oset__Cons(_1715161, hAPP(c_Relation_OImage(_1715161, _1715161, _1715163), hAPP(hAPP(c_Set_Oinsert(_1715161), _1715165), c_Orderings_Obot__class_Obot(tc_fun(_1715161, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1715161), tc_List_Olist(_1715161), c_List_Olistrel(_1715161, _1715163)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1715161)), _1715167), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1715161), tc_HOL_Obool))))))], (6451 ^ _778908) ^ [_883102, _883104, _883106, _883108, _883110] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_883102, _883104), _883106, _883108, _883110), 6455 ^ _778908 : [(6458 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_883104, 6454 ^ [_883102, _883104, _883106, _883108, _883110], _883108, _883110))], (6456 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_883102, _883106, _883108, 6454 ^ [_883102, _883104, _883106, _883108, _883110]))]]], (35785 ^ _778908) ^ [_1439345, _1439347, _1439349, _1439351, _1439353] : [hBOOL(hAPP(hAPP(c_member(_1439345), _1439347), hAPP(c_Relation_OImage(_1439349, _1439345, _1439351), hAPP(hAPP(c_Set_Oinsert(_1439349), _1439353), c_Orderings_Obot__class_Obot(tc_fun(_1439349, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1439349, _1439345)), hAPP(hAPP(c_Product__Type_OPair(_1439349, _1439345), _1439353), _1439347)), _1439351)))], (25867 ^ _778908) ^ [_1233294, _1233296, _1233298] : [class_Rings_Ocomm__semiring__1(_1233294), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233294), _1233296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233294), _1233296), _1233298))))], (50907 ^ _778908) ^ [_1802012, _1802014] : [-(hAPP(c_List_Orev(_1802012), hAPP(c_List_Orev(_1802012), _1802014)) = _1802014)], (39430 ^ _778908) ^ [_1520309, _1520311, _1520313, _1520315, _1520317, _1520319] : [c_Fun_Oinj__on(_1520309, _1520311, _1520313, _1520315), hBOOL(hAPP(hAPP(c_member(_1520311), _1520317), hAPP(c_Set_Oimage(_1520309, _1520311, _1520313), _1520315))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520309, tc_HOL_Obool)), _1520315), _1520319)), -(hBOOL(hAPP(hAPP(c_member(_1520309), hAPP(c_Fun_Othe__inv__into(_1520309, _1520311, _1520315, _1520313), _1520317)), _1520319)))], (4962 ^ _778908) ^ [_855665, _855667, _855669, _855671] : [-(c_Product__Type_OPair(_855671, _855667) = c_Product__Type_OPair(_855669, _855665)), _855671 = _855669, _855667 = _855665], (51327 ^ _778908) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (17327 ^ _778908) ^ [_1078175, _1078177, _1078179, _1078181] : [class_Rings_Olinordered__semidom(_1078175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078177), _1078179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078175), c_Groups_Ozero__class_Ozero(_1078175)), _1078181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078175), _1078181), c_Groups_Oone__class_Oone(_1078175))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078175), hAPP(hAPP(c_Power_Opower__class_Opower(_1078175), _1078181), _1078179)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078175), _1078181), _1078177))))], (24431 ^ _778908) ^ [_1206323, _1206325, _1206327, _1206329] : [class_Orderings_Olinorder(_1206323), 24434 ^ _778908 : [(24443 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206323), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206323), _1206325), _1206327)), _1206329))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206323), _1206325), _1206329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206323), _1206327), _1206329))], (24435 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206323), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206323), _1206325), _1206327)), _1206329)), 24438 ^ _778908 : [(24441 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206323), _1206327), _1206329)))], (24439 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206323), _1206325), _1206329)))]]]]], (23455 ^ _778908) ^ [_1187725, _1187727] : [-(_1187725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187727, _1187725), c_Divides_Odivmod__int(_1187727, _1187725))))], (31792 ^ _778908) ^ [_1353786, _1353788, _1353790, _1353792] : [hBOOL(hAPP(hAPP(c_member(_1353788), _1353792), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353786, tc_fun(_1353788, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1353786, tc_HOL_Obool))), _1353790))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353786, tc_fun(_1353788, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1353786, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1353788, tc_HOL_Obool), tc_fun(_1353788, tc_HOL_Obool), _1353786), hAPP(c_COMBC(_1353788, tc_fun(_1353788, tc_HOL_Obool), tc_HOL_Obool), c_member(_1353788))), _1353790)), _1353792)))], (34822 ^ _778908) ^ [_1416892, _1416894, _1416896] : [34824 ^ _778908 : [(34827 ^ _778908) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1416896, 34823 ^ [_1416892, _1416894, _1416896]))], (34825 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416892), 34823 ^ [_1416892, _1416894, _1416896]), _1416894)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416892, tc_Int_Oint), _1416896), _1416894) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416892, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1416892), c_Int_Onat), _1416896)), _1416894)))], (43678 ^ _778908) ^ [_1630301, _1630303, _1630305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630301, _1630301)), _1630303), c_Transitive__Closure_Ortrancl(_1630301, _1630305))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630301, _1630301)), _1630303), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630301, _1630301), tc_HOL_Obool), 43681 ^ [_1630301, _1630303, _1630305]), _1630305))))], (49952 ^ _778908) ^ [_1781809, _1781811, _1781813, _1781815] : [-(hAPP(c_List_Ofilter(_1781809, _1781811), hAPP(c_List_Ofilter(_1781809, _1781813), _1781815)) = hAPP(c_List_Ofilter(_1781809, hAPP(hAPP(c_COMBS(_1781809, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1781809), c_fconj), _1781813)), _1781811)), _1781815))], (51329 ^ _778908) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (41382 ^ _778908) ^ [_1567666, _1567668] : [-(hAPP(c_Set_OPow(_1567666), _1567668) = hAPP(c_Set_OCollect(tc_fun(_1567666, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1567666, tc_HOL_Obool), tc_fun(_1567666, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1567666, tc_HOL_Obool))), _1567668)))], (49678 ^ _778908) ^ [_1775887, _1775889, _1775891, _1775893] : [49681 ^ _778908 : [(49686 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775887, _1775887)), hAPP(hAPP(c_Product__Type_OPair(_1775887, _1775887), 49680 ^ [_1775887, _1775889, _1775891, _1775893]), 49679 ^ [_1775887, _1775889, _1775891, _1775893])), _1775889))], (49684 ^ _778908) ^ [] : [49679 ^ [_1775887, _1775889, _1775891, _1775893] = 49680 ^ [_1775887, _1775889, _1775891, _1775893]], (49682 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775887, _1775887)), hAPP(hAPP(c_Product__Type_OPair(_1775887, _1775887), 49679 ^ [_1775887, _1775889, _1775891, _1775893]), 49680 ^ [_1775887, _1775889, _1775891, _1775893])), _1775889))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1775887), tc_List_Olist(_1775887))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1775887), tc_List_Olist(_1775887)), _1775891), _1775893)), c_List_Olexord(_1775887, _1775889)))), -(_1775891 = _1775893), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1775887), tc_List_Olist(_1775887))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1775887), tc_List_Olist(_1775887)), _1775893), _1775891)), c_List_Olexord(_1775887, _1775889))))], (30538 ^ _778908) ^ [_1325844, _1325846, _1325848, _1325850, _1325852] : [_1325844 = c_Orderings_Obot__class_Obot(tc_fun(_1325846, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1325846, tc_fun(_1325848, tc_HOL_Obool)), _1325844), hAPP(hAPP(c_COMBC(_1325846, tc_fun(_1325848, tc_HOL_Obool), tc_fun(_1325848, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325848, tc_HOL_Obool), tc_fun(tc_fun(_1325848, tc_HOL_Obool), tc_fun(_1325848, tc_HOL_Obool)), _1325846), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325848, tc_HOL_Obool))), _1325850)), _1325852)) = c_Orderings_Obot__class_Obot(tc_fun(_1325848, tc_HOL_Obool)))], (48146 ^ _778908) ^ [_1739474, _1739476, _1739478, _1739480, _1739482, _1739484] : [hAPP(hAPP(c_List_Olist_OCons(_1739474), _1739476), _1739478) = _1739480, _1739482 = hAPP(hAPP(c_List_Oappend(_1739474), _1739478), _1739484), -(hAPP(hAPP(c_List_Olist_OCons(_1739474), _1739476), _1739482) = hAPP(hAPP(c_List_Oappend(_1739474), _1739480), _1739484))], (23853 ^ _778908) ^ [_1194636] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1194636), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41201 ^ _778908) ^ [_1561688, _1561690, _1561692] : [hBOOL(hAPP(hAPP(c_member(_1561688), _1561690), hAPP(c_Set_OCollect(_1561688), _1561692))), -(hBOOL(hAPP(_1561692, _1561690)))], (11971 ^ _778908) ^ [_979531, _979533, _979535, _979537, _979539] : [class_Rings_Oordered__semiring(_979531), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979531), _979533), _979535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979531), _979537), _979539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979531), c_Groups_Ozero__class_Ozero(_979531)), _979535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979531), c_Groups_Ozero__class_Ozero(_979531)), _979537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979531), _979533), _979537)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979531), _979535), _979539))))], (32881 ^ _778908) ^ [_1377731, _1377733, _1377735] : [class_Rings_Osemiring__1(_1377731), hBOOL(hAPP(hAPP(c_member(_1377731), _1377733), c_Nat_Osemiring__1__class_ONats(_1377731))), hBOOL(hAPP(hAPP(c_member(_1377731), _1377735), c_Nat_Osemiring__1__class_ONats(_1377731))), -(hBOOL(hAPP(hAPP(c_member(_1377731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377731), _1377733), _1377735)), c_Nat_Osemiring__1__class_ONats(_1377731))))], (35710 ^ _778908) ^ [_1437311, _1437313, _1437315, _1437317, _1437319, _1437321, _1437323] : [-(hAPP(c_Fun_Ocomp(_1437311, _1437313, _1437315, _1437317), hAPP(c_Fun_Ocomp(_1437319, _1437311, _1437315, _1437321), _1437323)) = hAPP(c_Fun_Ocomp(_1437319, _1437313, _1437315, hAPP(c_Fun_Ocomp(_1437311, _1437313, _1437319, _1437317), _1437321)), _1437323))], (43572 ^ _778908) ^ [_1627488, _1627490, _1627492, _1627494, _1627496] : [-(hAPP(c_Relation_Oconverse(_1627488, _1627490), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1627492, tc_fun(tc_prod(_1627488, _1627490), tc_HOL_Obool)), _1627494), _1627496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1627492, tc_fun(tc_prod(_1627490, _1627488), tc_HOL_Obool)), _1627494), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1627488, _1627490), tc_HOL_Obool), tc_fun(tc_prod(_1627490, _1627488), tc_HOL_Obool), _1627492), c_Relation_Oconverse(_1627488, _1627490)), _1627496)))], (39866 ^ _778908) ^ [_1530856, _1530858, _1530860, _1530862, _1530864] : [class_Groups_Oab__semigroup__mult(_1530856), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530856, _1530856, c_Groups_Otimes__class_Otimes(_1530856), _1530858, _1530860), _1530862)), -(hBOOL(hAPP(hAPP(c_member(_1530856), _1530858), _1530860))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530856, _1530856, c_Groups_Otimes__class_Otimes(_1530856), _1530864, hAPP(hAPP(c_Set_Oinsert(_1530856), _1530858), _1530860)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1530856), _1530864), _1530862))))], (47276 ^ _778908) ^ [_1719152, _1719154] : [-(c_Random_Oselect__weight(_1719152, _1719154) = 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(_1719152, 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, _1719152), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1719152)), _1719154)))), hAPP(hAPP(c_COMBB(_1719152, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1719152, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1719152, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1719152, _1719154))))], (9926 ^ _778908) ^ [_945505, _945507, _945509] : [class_Rings_Olinordered__ring__strict(_945505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945505), _945507), c_Groups_Ozero__class_Ozero(_945505))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945505), _945509), c_Groups_Ozero__class_Ozero(_945505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945505), c_Groups_Ozero__class_Ozero(_945505)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945505), _945507), _945509))))], (24413 ^ _778908) ^ [_1205846, _1205848, _1205850, _1205852] : [class_Orderings_Olinorder(_1205846), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205846), _1205848), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205846), _1205850), _1205852)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205846), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205846), _1205848), _1205850)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205846), _1205848), _1205852)))], (36774 ^ _778908) ^ [_1461818, _1461820, _1461822, _1461824] : [class_Lattices_Osemilattice__inf(_1461818), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461818), _1461820), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461818), _1461822), _1461824)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461818), _1461822), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461818), _1461820), _1461824)))], (5835 ^ _778908) ^ [] : [-(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))], (36580 ^ _778908) ^ [_1457200, _1457202] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457200, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1457200, tc_HOL_Obool))), _1457202) = _1457202)], (42244 ^ _778908) ^ [_1595070, _1595072, _1595074, _1595076, _1595078] : [hBOOL(hAPP(hAPP(_1595070, _1595072), _1595074)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1595076, _1595078, _1595070), _1595074)))], (42471 ^ _778908) ^ [_1600515, _1600517] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1600515, _1600515)), _1600517)), 42474 ^ _778908 : [(42481 ^ _778908) ^ [] : [c_Wellfounded_Oacyclic(_1600515, _1600517), -(c_Wellfounded_Owf(_1600515, _1600517))], (42475 ^ _778908) ^ [] : [c_Wellfounded_Owf(_1600515, _1600517), -(c_Wellfounded_Oacyclic(_1600515, _1600517))]]], (13188 ^ _778908) ^ [_1001224, _1001226] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1001224) = _1001226), _1001224 = hAPP(c_Int_Onat, _1001226), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001226))], (10996 ^ _778908) ^ [_963291, _963293, _963295] : [class_Orderings_Oorder(_963291), 10999 ^ _778908 : [(11000 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963291), _963293), _963295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963291), _963293), _963295))), -(_963293 = _963295)], (11010 ^ _778908) ^ [] : [11011 ^ _778908 : [(11014 ^ _778908) ^ [] : [_963293 = _963295], (11012 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963291), _963293), _963295))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963291), _963293), _963295)))]]], (37324 ^ _778908) ^ [_1474718, _1474720, _1474722] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474718), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474718, tc_HOL_Obool)), _1474720), _1474722))), -(hAPP(c_Finite__Set_Ocard(_1474718), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474718, tc_HOL_Obool)), _1474720), _1474722)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474718), _1474720)), hAPP(c_Finite__Set_Ocard(_1474718), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474718, tc_HOL_Obool)), _1474720), _1474722))))], (48646 ^ _778908) ^ [_1751351, _1751353, _1751355, _1751357, _1751359, _1751361] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751351), tc_List_Olist(_1751351))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751351), tc_List_Olist(_1751351)), hAPP(hAPP(c_List_Oappend(_1751351), _1751353), hAPP(hAPP(c_List_Olist_OCons(_1751351), _1751355), c_List_Olist_ONil(_1751351)))), hAPP(hAPP(c_List_Oappend(_1751351), _1751357), hAPP(hAPP(c_List_Olist_OCons(_1751351), _1751359), c_List_Olist_ONil(_1751351))))), c_List_Olistrel1(_1751351, _1751361)))), 48647 ^ _778908 : [(48654 ^ _778908) ^ [] : [_1751353 = _1751357, hBOOL(hAPP(hAPP(c_member(tc_prod(_1751351, _1751351)), hAPP(hAPP(c_Product__Type_OPair(_1751351, _1751351), _1751355), _1751359)), _1751361))], (48648 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751351), tc_List_Olist(_1751351))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751351), tc_List_Olist(_1751351)), _1751353), _1751357)), c_List_Olistrel1(_1751351, _1751361))), _1751355 = _1751359]]], (35074 ^ _778908) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (17459 ^ _778908) ^ [_1080465, _1080467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1080465)), -(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), _1080465), _1080467))))], (43421 ^ _778908) ^ [_1623791, _1623793, _1623795, _1623797] : [-(c_Wellfounded_Owf(_1623791, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1623791, _1623791)), hAPP(hAPP(c_Product__Type_OPair(_1623791, _1623791), _1623793), _1623795)), _1623797))), c_Wellfounded_Owf(_1623791, _1623797), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623791, _1623791)), hAPP(hAPP(c_Product__Type_OPair(_1623791, _1623791), _1623795), _1623793)), c_Transitive__Closure_Ortrancl(_1623791, _1623797))))], (46212 ^ _778908) ^ [_1690548, _1690550, _1690552, _1690554, _1690556, _1690558] : [-(hAPP(hAPP(c_Option_Omap(_1690548, _1690550), _1690552), hAPP(hAPP(c_Option_Omap(_1690554, _1690548), _1690556), _1690558)) = hAPP(hAPP(c_Option_Omap(_1690554, _1690550), hAPP(c_Fun_Ocomp(_1690548, _1690550, _1690554, _1690552), _1690556)), _1690558))], (39822 ^ _778908) ^ [_1529516, _1529518, _1529520] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1529516, hAPP(hAPP(c_COMBC(_1529516, tc_fun(tc_prod(_1529516, _1529516), tc_HOL_Obool), tc_fun(_1529516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529516, tc_fun(tc_fun(tc_prod(_1529516, _1529516), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529516, _1529516), tc_HOL_Obool), tc_fun(_1529516, tc_HOL_Obool)), _1529516), c_COMBC(_1529516, tc_fun(tc_prod(_1529516, _1529516), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529516, tc_prod(_1529516, _1529516)), tc_fun(_1529516, tc_fun(tc_fun(tc_prod(_1529516, _1529516), tc_HOL_Obool), tc_HOL_Obool)), _1529516), hAPP(c_COMBB(tc_prod(_1529516, _1529516), tc_fun(tc_fun(tc_prod(_1529516, _1529516), tc_HOL_Obool), tc_HOL_Obool), _1529516), c_member(tc_prod(_1529516, _1529516)))), c_Product__Type_OPair(_1529516, _1529516)))), _1529518)), _1529520)), -(hBOOL(hAPP(hAPP(c_member(_1529516), _1529520), c_Wellfounded_Oacc(_1529516, _1529518))))], (47803 ^ _778908) ^ [_1731090, _1731092, _1731094, _1731096] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731090), tc_List_Olist(_1731090))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731090), tc_List_Olist(_1731090)), _1731092), _1731094)), c_List_Olistrel(_1731090, _1731096))), 47806 ^ _778908 : [(47809 ^ _778908) ^ [_1731319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731319), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731090)), _1731092))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1731090, _1731090)), hAPP(hAPP(c_Product__Type_OPair(_1731090, _1731090), hAPP(hAPP(c_List_Onth(_1731090), _1731092), _1731319)), hAPP(hAPP(c_List_Onth(_1731090), _1731094), _1731319))), _1731096)))], (47807 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731090)), _1731092) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731090)), _1731094))]]], (35688 ^ _778908) ^ [_1436690, _1436692, _1436694, _1436696, _1436698] : [-(hAPP(c_Relation_OImage(_1436690, _1436692, _1436694), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436690, tc_HOL_Obool)), _1436696), _1436698)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436692, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1436690, _1436692, _1436694), _1436696)), hAPP(c_Relation_OImage(_1436690, _1436692, _1436694), _1436698)))], (6278 ^ _778908) ^ [_880074, _880076, _880078, _880080, _880082, _880084] : [-(c_Com_Ocom_OCond(_880074, _880076, _880078) = c_Com_Ocom_OCond(_880080, _880082, _880084)), _880074 = _880080, _880076 = _880082, _880078 = _880084], (17573 ^ _778908) ^ [_1082585, _1082587, _1082589] : [class_Rings_Olinordered__semidom(_1082585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082585), c_Groups_Ozero__class_Ozero(_1082585)), _1082587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082585), c_Groups_Ozero__class_Ozero(_1082585)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082585), _1082587), _1082589))))], (21285 ^ _778908) ^ [_1146636, _1146638, _1146640, _1146642, _1146644] : [class_Fields_Ofield(_1146636), -(_1146638 = c_Groups_Ozero__class_Ozero(_1146636)), -(_1146640 = c_Groups_Ozero__class_Ozero(_1146636)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1146636), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146636), _1146642), _1146638)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146636), _1146644), _1146640)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1146636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146636), _1146642), _1146640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146636), _1146644), _1146638))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146636), _1146638), _1146640)))], (5951 ^ _778908) ^ [_873934] : [hAPP(c_Com_Ocom_OBODY, _873934) = c_Com_Ocom_OSKIP], (19043 ^ _778908) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (7062 ^ _778908) ^ [_897073, _897075] : [-(_897073 = c_Option_Ooption_ONone(_897075)), -(_897073 = hAPP(c_Option_Ooption_OSome(_897075), 7065 ^ [_897073, _897075]))], (9310 ^ _778908) ^ [_934630, _934632] : [class_Groups_Olinordered__ab__group__add(_934630), 9313 ^ _778908 : [(9320 ^ _778908) ^ [] : [_934632 = c_Groups_Ozero__class_Ozero(_934630), -(_934632 = hAPP(c_Groups_Ouminus__class_Ouminus(_934630), _934632))], (9314 ^ _778908) ^ [] : [_934632 = hAPP(c_Groups_Ouminus__class_Ouminus(_934630), _934632), -(_934632 = c_Groups_Ozero__class_Ozero(_934630))]]], (12477 ^ _778908) ^ [_988673, _988675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988673), _988675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988673)), _988675)))], (13132 ^ _778908) ^ [_1000364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1000364)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1000364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26341 ^ _778908) ^ [_1242751, _1242753, _1242755] : [class_Divides_Osemiring__div(_1242751), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242751), _1242753), _1242755)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242751), _1242753), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242751), _1242755), _1242753)) = _1242755)], (16344 ^ _778908) ^ [_1059633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059633)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059633), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1059633)], (9702 ^ _778908) ^ [_941494, _941496, _941498] : [class_Groups_Ogroup__add(_941494), 9705 ^ _778908 : [(9712 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941494), _941496), _941498) = c_Groups_Ozero__class_Ozero(_941494), -(_941496 = hAPP(c_Groups_Ouminus__class_Ouminus(_941494), _941498))], (9706 ^ _778908) ^ [] : [_941496 = hAPP(c_Groups_Ouminus__class_Ouminus(_941494), _941498), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941494), _941496), _941498) = c_Groups_Ozero__class_Ozero(_941494))]]], (46181 ^ _778908) ^ [_1689604, _1689606, _1689608, _1689610, _1689612] : [-(c_Map_Omap__of(_1689604, _1689606, hAPP(hAPP(c_List_Omap(tc_prod(_1689604, _1689608), tc_prod(_1689604, _1689606)), hAPP(c_Product__Type_Oprod_Oprod__case(_1689604, _1689608, tc_prod(_1689604, _1689606)), hAPP(hAPP(c_COMBC(_1689604, tc_fun(_1689608, _1689606), tc_fun(_1689608, tc_prod(_1689604, _1689606))), hAPP(hAPP(c_COMBB(tc_fun(_1689606, tc_prod(_1689604, _1689606)), tc_fun(tc_fun(_1689608, _1689606), tc_fun(_1689608, tc_prod(_1689604, _1689606))), _1689604), c_COMBB(_1689606, tc_prod(_1689604, _1689606), _1689608)), c_Product__Type_OPair(_1689604, _1689606))), _1689610))), _1689612)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1689608), tc_Option_Ooption(_1689606), _1689604, hAPP(c_Option_Omap(_1689608, _1689606), _1689610)), c_Map_Omap__of(_1689604, _1689608, _1689612)))], (5222 ^ _778908) ^ [_859705, _859707] : [_859707 = _859705, -(c_Finite__Set_Ofinite(_859707) = c_Finite__Set_Ofinite(_859705))], (41698 ^ _778908) ^ [_1580458, _1580460] : [-(c_Product__Type_Oapsnd(_1580458, _1580458, _1580460, c_Fun_Oid(_1580458)) = c_Fun_Oid(tc_prod(_1580460, _1580458)))], (48164 ^ _778908) ^ [_1739883, _1739885, _1739887, _1739889, _1739891] : [-(hAPP(hAPP(c_List_Omap(_1739883, _1739885), _1739887), hAPP(hAPP(c_List_Oappend(_1739883), _1739889), _1739891)) = hAPP(hAPP(c_List_Oappend(_1739885), hAPP(hAPP(c_List_Omap(_1739883, _1739885), _1739887), _1739889)), hAPP(hAPP(c_List_Omap(_1739883, _1739885), _1739887), _1739891)))], (30648 ^ _778908) ^ [_1328127, _1328129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1328127), _1328129))), 30651 ^ _778908 : [(30654 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1328127), _1328129)))], (30652 ^ _778908) ^ [] : [_1328129 = c_Orderings_Obot__class_Obot(tc_fun(_1328127, tc_HOL_Obool))]]], (19689 ^ _778908) ^ [_1118137] : [class_Int_Onumber__ring(_1118137), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118137), c_Groups_Oone__class_Oone(_1118137)), c_Groups_Oone__class_Oone(_1118137)) = hAPP(c_Int_Onumber__class_Onumber__of(_1118137), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (36822 ^ _778908) ^ [_1462840, _1462842, _1462844] : [class_Lattices_Osemilattice__inf(_1462840), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462840), _1462842), _1462844) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462840), _1462844), _1462842))], (30382 ^ _778908) ^ [_1323097, _1323099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323097, tc_HOL_Obool)), _1323099), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323097, tc_HOL_Obool)), _1323099))), -(_1323099 = c_Orderings_Obot__class_Obot(tc_fun(_1323097, tc_HOL_Obool)))], (23411 ^ _778908) ^ [_1187088, _1187090, _1187092] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187088, _1187088), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187090), _1187092))), -(_1187088 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1187092 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (49145 ^ _778908) ^ [_1764699, _1764701] : [-(_1764699 = c_List_Olist_ONil(_1764701)), -(hBOOL(hAPP(hAPP(c_member(_1764701), hAPP(c_List_Ohd(_1764701), _1764699)), hAPP(c_List_Oset(_1764701), _1764699))))], (28201 ^ _778908) ^ [_1279612, _1279614, _1279616] : [class_Lattices_Olattice(_1279612), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279612), _1279614), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279612), _1279614), _1279616)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279612), _1279614), _1279616))], (14160 ^ _778908) ^ [_1018569, _1018571] : [class_Lattices_Oab__semigroup__idem__mult(_1018569), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018569), _1018571), _1018571) = _1018571)], (664 ^ _778908) ^ [_789192, _789194, _789196, _789198, _789200, _789202] : [-(c_Hoare__Mirabelle_Otriple__valid(_789200, _789196, _789192)), c_Hoare__Mirabelle_Otriple__valid(_789202, _789198, _789194), _789202 = _789200, _789198 = _789196, _789194 = _789192], (7488 ^ _778908) ^ [_904045, _904047, _904049] : [class_Rings_Ocomm__semiring__1(_904045), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904045), _904047), _904049) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904045), _904049), _904047))], (13975 ^ _778908) ^ [_1015211, _1015213, _1015215, _1015217] : [class_Divides_Osemiring__div(_1015211), -(c_Divides_Odiv__class_Omod(_1015211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015211), _1015213), _1015215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015211), _1015213), _1015217)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015211), _1015213), c_Divides_Odiv__class_Omod(_1015211, _1015215, _1015217)))], (35819 ^ _778908) ^ [] : [-(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))))))], (41446 ^ _778908) ^ [_1569341, _1569343, _1569345] : [class_Orderings_Olinorder(_1569341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1569341), _1569343)), -(_1569343 = c_Orderings_Obot__class_Obot(tc_fun(_1569341, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1569341), _1569345)), -(_1569345 = c_Orderings_Obot__class_Obot(tc_fun(_1569341, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1569341), c_Big__Operators_Olattice_OSup__fin(_1569341, c_Orderings_Oord__class_Omax(_1569341), _1569343)), c_Big__Operators_Olattice_OSup__fin(_1569341, c_Orderings_Oord__class_Omax(_1569341), _1569345)) = c_Big__Operators_Olattice_OSup__fin(_1569341, c_Orderings_Oord__class_Omax(_1569341), hAPP(c_Set_OCollect(_1569341), hAPP(hAPP(c_COMBB(tc_fun(_1569341, tc_HOL_Obool), tc_HOL_Obool, _1569341), c_HOL_OEx(_1569341)), hAPP(hAPP(c_COMBB(tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool)), tc_fun(_1569341, tc_HOL_Obool), _1569341), hAPP(c_COMBB(tc_fun(_1569341, tc_HOL_Obool), tc_HOL_Obool, _1569341), c_HOL_OEx(_1569341))), hAPP(hAPP(c_COMBC(_1569341, tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool)), tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1569341, tc_fun(tc_fun(_1569341, tc_HOL_Obool), tc_fun(_1569341, tc_HOL_Obool))), tc_fun(tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool)), tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool))), _1569341), c_COMBS(_1569341, tc_fun(_1569341, tc_HOL_Obool), tc_fun(_1569341, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1569341, tc_fun(_1569341, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1569341, tc_fun(tc_fun(_1569341, tc_HOL_Obool), tc_fun(_1569341, tc_HOL_Obool))), _1569341), hAPP(c_COMBB(tc_fun(_1569341, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1569341, tc_HOL_Obool), tc_fun(_1569341, tc_HOL_Obool)), _1569341), c_COMBS(_1569341, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool)), tc_fun(_1569341, tc_fun(_1569341, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1569341), hAPP(c_COMBB(tc_fun(_1569341, tc_HOL_Obool), tc_fun(_1569341, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1569341), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569341), c_fconj))), hAPP(hAPP(c_COMBC(_1569341, tc_fun(_1569341, tc_fun(_1569341, _1569341)), tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1569341, _1569341), tc_fun(_1569341, tc_HOL_Obool)), tc_fun(tc_fun(_1569341, tc_fun(_1569341, _1569341)), tc_fun(_1569341, tc_fun(_1569341, tc_HOL_Obool))), _1569341), c_COMBB(tc_fun(_1569341, _1569341), tc_fun(_1569341, tc_HOL_Obool), _1569341)), hAPP(hAPP(c_COMBB(tc_fun(_1569341, tc_HOL_Obool), tc_fun(tc_fun(_1569341, _1569341), tc_fun(_1569341, tc_HOL_Obool)), _1569341), c_COMBB(_1569341, tc_HOL_Obool, _1569341)), c_fequal))), c_Orderings_Oord__class_Omin(_1569341)))))), hAPP(hAPP(c_COMBC(_1569341, tc_fun(_1569341, tc_HOL_Obool), tc_fun(_1569341, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1569341, tc_HOL_Obool), tc_fun(_1569341, tc_HOL_Obool)), _1569341), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569341)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569341), c_fconj), hAPP(hAPP(c_COMBC(_1569341, tc_fun(_1569341, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569341)), _1569343)))), hAPP(hAPP(c_COMBC(_1569341, tc_fun(_1569341, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569341)), _1569345))))))))], (29042 ^ _778908) ^ [_1296834, _1296836, _1296838, _1296840, _1296842, _1296844] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296834, tc_fun(_1296836, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1296838, _1296834, _1296840), _1296842)), _1296844) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296838, tc_fun(_1296836, tc_HOL_Obool)), _1296842), hAPP(hAPP(c_COMBB(_1296834, tc_fun(_1296836, tc_HOL_Obool), _1296838), _1296844), _1296840)))], (30770 ^ _778908) ^ [_1330817, _1330819] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1330817), _1330819)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1330819, _1330817) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (200 ^ _778908) ^ [_781760, _781762, _781764, _781766, _781768, _781770, _781772, _781774] : [-(c_Orderings_Oorder_Omono(_781772, _781768, _781764, _781760)), c_Orderings_Oorder_Omono(_781774, _781770, _781766, _781762), _781774 = _781772, _781770 = _781768, _781766 = _781764, _781762 = _781760], (35277 ^ _778908) ^ [_1427777, _1427779, _1427781] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1427777, _1427777)), _1427779), c_Relation_OId__on(_1427777, _1427781))), 35281 ^ _778908 : [(35284 ^ _778908) ^ [] : [-(_1427779 = hAPP(hAPP(c_Product__Type_OPair(_1427777, _1427777), 35280 ^ [_1427777, _1427779, _1427781]), 35280 ^ [_1427777, _1427779, _1427781]))], (35282 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1427777), 35280 ^ [_1427777, _1427779, _1427781]), _1427781)))]]], (6069 ^ _778908) ^ [_876097, _876099, _876101, _876103, _876105, _876107] : [hBOOL(hAPP(_876097, _876099)), c_Natural_Oevaln(_876101, _876099, _876103, _876105), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_876097, _876101, _876107), _876099, _876103, _876105))], (42082 ^ _778908) ^ [_1590644, _1590646] : [c_FunDef_Oreduction__pair(_1590644, _1590646), 42085 ^ _778908 : [(42088 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1590644, _1590644, _1590644), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool), tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool)), _1590646)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool), tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool)), _1590646))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool), tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool)), _1590646))))], (42086 ^ _778908) ^ [] : [-(c_Wellfounded_Owf(_1590644, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool), tc_fun(tc_prod(_1590644, _1590644), tc_HOL_Obool)), _1590646)))]]], (3088 ^ _778908) ^ [_826216, _826218, _826220, _826222] : [-(c_Quickcheck_Obeyond(_826222, _826218) = c_Quickcheck_Obeyond(_826220, _826216)), _826222 = _826220, _826218 = _826216], (19925 ^ _778908) ^ [_1122061, _1122063, _1122065] : [class_Rings_Olinordered__semidom(_1122061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122061), hAPP(hAPP(c_Power_Opower__class_Opower(_1122061), _1122063), 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(_1122061), _1122065), 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(_1122061), c_Groups_Ozero__class_Ozero(_1122061)), _1122065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122061), _1122063), _1122065)))], (49392 ^ _778908) ^ [_1769592, _1769594, _1769596] : [class_Orderings_Olinorder(_1769592), -(c_Big__Operators_Olinorder__class_OMax(_1769592, hAPP(c_List_Oset(_1769592), hAPP(hAPP(c_List_Olist_OCons(_1769592), _1769594), _1769596))) = hAPP(c_List_Ofoldl(_1769592, _1769592, c_Orderings_Oord__class_Omax(_1769592), _1769594), _1769596))], (47022 ^ _778908) ^ [_1712146, _1712148, _1712150, _1712152, _1712154] : [hAPP(hAPP(c_List_Olist_OCons(_1712146), _1712148), _1712150) = hAPP(hAPP(c_List_Olist_OCons(_1712146), _1712152), _1712154), 47025 ^ _778908 : [(47028 ^ _778908) ^ [] : [-(_1712150 = _1712154)], (47026 ^ _778908) ^ [] : [-(_1712148 = _1712152)]]], (43051 ^ _778908) ^ [_1614119, _1614121] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1614119, _1614119)), c_Transitive__Closure_Otrancl(_1614119, _1614121))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1614119, _1614119)), _1614121)))], (16595 ^ _778908) ^ [_1064089] : [class_Groups_Oordered__ab__group__add__abs(_1064089), -(hAPP(c_Groups_Oabs__class_Oabs(_1064089), c_Groups_Ozero__class_Ozero(_1064089)) = c_Groups_Ozero__class_Ozero(_1064089))], (24827 ^ _778908) ^ [_1213952, _1213954] : [hAPP(c_Code__Numeral_Onat__of, _1213952) = hAPP(c_Code__Numeral_Onat__of, _1213954), -(_1213952 = _1213954)], (49721 ^ _778908) ^ [_1776909, _1776911, _1776913] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776909)), _1776911), c_List_Olists(_1776909, _1776913)))), 49722 ^ _778908 : [(49725 ^ _778908) ^ [_1777037, _1777039] : [_1776911 = hAPP(hAPP(c_List_Olist_OCons(_1776909), _1777039), _1777037), hBOOL(hAPP(hAPP(c_member(_1776909), _1777039), _1776913)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776909)), _1777037), c_List_Olists(_1776909, _1776913)))], (49723 ^ _778908) ^ [] : [_1776911 = c_List_Olist_ONil(_1776909)]]], (36254 ^ _778908) ^ [_1450824, _1450826, _1450828, _1450830, _1450832] : [c_Equiv__Relations_Oequiv(_1450824, _1450826, _1450828), hBOOL(hAPP(hAPP(c_member(tc_prod(_1450824, _1450824)), hAPP(hAPP(c_Product__Type_OPair(_1450824, _1450824), _1450830), _1450832)), _1450828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1450824, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1450824, _1450824, _1450828), hAPP(hAPP(c_Set_Oinsert(_1450824), _1450830), c_Orderings_Obot__class_Obot(tc_fun(_1450824, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1450824, _1450824, _1450828), hAPP(hAPP(c_Set_Oinsert(_1450824), _1450832), c_Orderings_Obot__class_Obot(tc_fun(_1450824, tc_HOL_Obool)))))))], (40947 ^ _778908) ^ [_1556570, _1556572, _1556574] : [class_Lattices_Oab__semigroup__idem__mult(_1556570), hAPP(_1556572, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1556570), 40952 ^ [_1556570, _1556572, _1556574]), 40953 ^ [_1556570, _1556572, _1556574])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1556570), hAPP(_1556572, 40952 ^ [_1556570, _1556572, _1556574])), hAPP(_1556572, 40953 ^ [_1556570, _1556572, _1556574])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556570), _1556574)), -(_1556574 = c_Orderings_Obot__class_Obot(tc_fun(_1556570, tc_HOL_Obool))), -(hAPP(_1556572, hAPP(c_Finite__Set_Ofold1(_1556570, c_Groups_Otimes__class_Otimes(_1556570)), _1556574)) = hAPP(c_Finite__Set_Ofold1(_1556570, c_Groups_Otimes__class_Otimes(_1556570)), hAPP(c_Set_Oimage(_1556570, _1556570, _1556572), _1556574)))], (47559 ^ _778908) ^ [_1724760, _1724762] : [-(c_List_Oset__Cons(_1724760, _1724762, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1724760)), c_List_Olist_ONil(_1724760)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1724760), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1724760, tc_List_Olist(_1724760), hAPP(hAPP(c_COMBC(_1724760, tc_List_Olist(_1724760), tc_List_Olist(_1724760)), c_List_Olist_OCons(_1724760)), c_List_Olist_ONil(_1724760))), _1724762))], (6007 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (25791 ^ _778908) ^ [_1231924, _1231926] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231924), _1231926)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231924)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231926))))], (35686 ^ _778908) ^ [_1436646, _1436648, _1436650] : [-(hAPP(c_Relation_OImage(_1436646, _1436648, _1436650), c_Orderings_Obot__class_Obot(tc_fun(_1436646, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1436648, tc_HOL_Obool)))], (48387 ^ _778908) ^ [_1744544, _1744546, _1744548, _1744550, _1744552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744544), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744546)), _1744548))), -(hAPP(hAPP(c_List_Olist__update(_1744546, hAPP(hAPP(c_List_Oappend(_1744546), _1744548), _1744550)), _1744544), _1744552) = hAPP(hAPP(c_List_Oappend(_1744546), hAPP(hAPP(c_List_Olist__update(_1744546, _1744548), _1744544), _1744552)), _1744550))], (10503 ^ _778908) ^ [_955318, _955320, _955322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955318), _955320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955318), _955322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955320), _955322))))], (12449 ^ _778908) ^ [_988219, _988221] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988219)), _988221) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988219), _988221)))], (25205 ^ _778908) ^ [_1222136, _1222138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1222136)), 25208 ^ _778908 : [(25215 ^ _778908) ^ [] : [_1222138 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1222136), _1222138)), _1222136)))], (25209 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1222136), _1222138)), _1222136)), -(_1222138 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (44897 ^ _778908) ^ [_1659966, _1659968, _1659970, _1659972, _1659974] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659966, tc_fun(_1659968, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659966, tc_HOL_Obool)), _1659970), _1659972)), _1659974) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659968, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659966, tc_fun(_1659968, tc_HOL_Obool)), _1659970), _1659974)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659966, tc_fun(_1659968, tc_HOL_Obool)), _1659972), _1659974)))], (34804 ^ _778908) ^ [_1416515, _1416517, _1416519, _1416521, _1416523, _1416525, _1416527] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1416515, tc_Option_Ooption(_1416517)), _1416519), _1416521), hAPP(c_Option_Ooption_OSome(_1416517), _1416523)), _1416525) = hAPP(c_Option_Ooption_OSome(_1416517), _1416527)), 34805 ^ _778908 : [(34812 ^ _778908) ^ [] : [-(_1416525 = _1416521), hAPP(_1416519, _1416525) = hAPP(c_Option_Ooption_OSome(_1416517), _1416527)], (34806 ^ _778908) ^ [] : [_1416525 = _1416521, _1416523 = _1416527]]], (11679 ^ _778908) ^ [_974464, _974466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _974464), _974466)), 11682 ^ _778908 : [(11685 ^ _778908) ^ [] : [_974464 = _974466], (11683 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _974464), _974466)))]]], (15218 ^ _778908) ^ [_1037572, _1037574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037574)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1037572, _1037574)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1037572), hAPP(c_Int_Onat, _1037574)))], (51595 ^ _778908) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (22291 ^ _778908) ^ [_1165168, _1165170] : [-(c_Random_Olog(_1165168, _1165170) = 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(_1165168, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1165170), _1165168)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1165168), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1165170), _1165168)))], (27655 ^ _778908) ^ [_1268865, _1268867, _1268869, _1268871, _1268873] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268865, tc_HOL_Obool)), _1268867), hAPP(c_Set_Oimage(_1268869, _1268865, _1268871), _1268873)))), 27656 ^ _778908 : [(27657 ^ _778908) ^ [_1268945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268869, tc_HOL_Obool)), _1268945), _1268873)), _1268867 = hAPP(c_Set_Oimage(_1268869, _1268865, _1268871), _1268945)]]], (4122 ^ _778908) ^ [_842425, _842427] : [_842427 = _842425, -(c_HOL_OAll(_842427) = c_HOL_OAll(_842425))], (23685 ^ _778908) ^ [_1191719, _1191721] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1191719)), hAPP(c_Nat_OSuc, _1191721)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1191719), _1191721)))], (22941 ^ _778908) ^ [_1177882, _1177884, _1177886] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1177882, _1177884), _1177886)), 22944 ^ _778908 : [(22945 ^ _778908) ^ [_1177967] : [hBOOL(hAPP(hAPP(_1177884, _1177967), _1177886)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1177882, _1177884), _1177967)))]]], (13248 ^ _778908) ^ [_1002219, _1002221] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1002219)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1002221))))), _1002219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1002221 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44376 ^ _778908) ^ [_1646385, _1646387, _1646389] : [class_Orderings_Olinorder(_1646385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646385), _1646387)), -(hBOOL(hAPP(hAPP(c_member(_1646385), _1646389), _1646387))), -(c_Big__Operators_Olinorder__class_OMax(_1646385, hAPP(hAPP(c_Set_Oinsert(_1646385), _1646389), _1646387)) = hAPP(hAPP(c_Finite__Set_Ofold(_1646385, _1646385, c_Orderings_Oord__class_Omax(_1646385)), _1646389), _1646387))], (18501 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (1842 ^ _778908) ^ [_804807, _804809, _804811, _804813] : [-(v_P(_804811, _804807)), v_P(_804813, _804809), _804813 = _804811, _804809 = _804807], (34857 ^ _778908) ^ [_1417735, _1417737, _1417739, _1417741, _1417743] : [-(hBOOL(hAPP(hAPP(c_member(_1417735), _1417737), _1417739))), -(hAPP(c_Map_Orestrict__map(_1417735, _1417741, _1417743, _1417739), _1417737) = c_Option_Ooption_ONone(_1417741))], (18497 ^ _778908) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7396 ^ _778908) ^ [_902453] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _902453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _902453)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40899 ^ _778908) ^ [_1555625, _1555627, _1555629] : [class_Orderings_Olinorder(_1555625), -(_1555627 = c_Orderings_Obot__class_Obot(tc_fun(_1555625, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555625, tc_HOL_Obool)), _1555627), _1555629)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555625), _1555629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1555625), hAPP(c_Finite__Set_Ofold1(_1555625, c_Orderings_Oord__class_Omin(_1555625)), _1555629)), hAPP(c_Finite__Set_Ofold1(_1555625, c_Orderings_Oord__class_Omin(_1555625)), _1555627))))], (31798 ^ _778908) ^ [_1354011, _1354013, _1354015, _1354017, _1354019] : [hBOOL(hAPP(hAPP(c_member(_1354011), _1354013), _1354015)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354017, tc_HOL_Obool)), hAPP(_1354019, _1354013)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354011, tc_fun(_1354017, tc_HOL_Obool)), _1354015), _1354019)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354011, tc_fun(_1354017, tc_HOL_Obool)), _1354015), _1354019))], (29588 ^ _778908) ^ [] : [-(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))], (24737 ^ _778908) ^ [_1211974, _1211976, _1211978, _1211980, _1211982, _1211984] : [hAPP(c_Product__Type_Oapfst(_1211974, _1211976, _1211978, _1211980), _1211982) = hAPP(c_Product__Type_Oapfst(_1211974, _1211976, _1211978, _1211984), _1211982), -(hAPP(_1211980, hAPP(c_Product__Type_Ofst(_1211974, _1211978), _1211982)) = hAPP(_1211984, hAPP(c_Product__Type_Ofst(_1211974, _1211978), _1211982)))], (29384 ^ _778908) ^ [_1303973, _1303975, _1303977, _1303979, _1303981] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303973, tc_fun(_1303975, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1303973), _1303977), _1303979)), _1303981) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1303975, tc_HOL_Obool)), hAPP(_1303981, _1303977)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303973, tc_fun(_1303975, tc_HOL_Obool)), _1303979), _1303981)))], (40058 ^ _778908) ^ [_1535578, _1535580, _1535582, _1535584, _1535586, _1535588] : [hBOOL(hAPP(hAPP(c_member(_1535578), _1535580), _1535582)), hBOOL(hAPP(hAPP(c_member(_1535584), _1535586), hAPP(_1535588, _1535580))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1535578, _1535584)), hAPP(hAPP(c_Product__Type_OPair(_1535578, _1535584), _1535580), _1535586)), hAPP(hAPP(c_Product__Type_OSigma(_1535578, _1535584), _1535582), _1535588))))], (24833 ^ _778908) ^ [_1214037, _1214039] : [_1214037 = _1214039, -(hAPP(c_Code__Numeral_Onat__of, _1214037) = hAPP(c_Code__Numeral_Onat__of, _1214039))], (46092 ^ _778908) ^ [_1687642] : [-(hAPP(c_List_Omap(_1687642, _1687642), c_COMBI(_1687642)) = c_Fun_Oid(tc_List_Olist(_1687642)))], (45724 ^ _778908) ^ [_1679297, _1679299, _1679301, _1679303, _1679305, _1679307, _1679309, _1679311] : [c_Finite__Set_Ofolding__image__simple__idem(_1679297, _1679299, _1679301, _1679303, _1679305, _1679307), hBOOL(hAPP(c_Finite__Set_Ofinite(_1679299), _1679309)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1679299), _1679311)), -(hAPP(_1679307, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1679299, tc_HOL_Obool)), _1679309), _1679311)) = hAPP(hAPP(_1679301, hAPP(_1679307, _1679309)), hAPP(_1679307, _1679311)))], (31163 ^ _778908) ^ [_1338662, _1338664] : [hBOOL(hAPP(hAPP(c_member(_1338662), _1338664), c_Orderings_Obot__class_Obot(tc_fun(_1338662, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1338662, tc_HOL_Obool)), _1338664)))], (51379 ^ _778908) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (39594 ^ _778908) ^ [_1524212, _1524214, _1524216, _1524218, _1524220] : [c_Fun_Oinj__on(_1524212, _1524214, _1524216, _1524218), hBOOL(hAPP(hAPP(c_member(_1524212), _1524220), _1524218)), -(hAPP(c_Fun_Othe__inv__into(_1524212, _1524214, _1524218, _1524216), hAPP(_1524216, _1524220)) = _1524220)], (35510 ^ _778908) ^ [_1432807, _1432809, _1432811, _1432813] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1432807, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432809, tc_fun(tc_fun(_1432807, tc_HOL_Obool), tc_HOL_Obool)), _1432811), hAPP(hAPP(c_COMBB(tc_fun(_1432807, tc_HOL_Obool), tc_fun(tc_fun(_1432807, tc_HOL_Obool), tc_HOL_Obool), _1432809), c_Set_OPow(_1432807)), _1432813))), hAPP(c_Set_OPow(_1432807), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432809, tc_fun(_1432807, tc_HOL_Obool)), _1432811), _1432813)))))], (12527 ^ _778908) ^ [_989568] : [-(hAPP(c_Nat_OSuc, _989568) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _989568))], (48249 ^ _778908) ^ [_1741818, _1741820, _1741822, _1741824, _1741826, _1741828] : [-(c_List_Ofoldr(_1741818, _1741820, _1741822, hAPP(hAPP(c_List_Oappend(_1741818), _1741824), _1741826), _1741828) = c_List_Ofoldr(_1741818, _1741820, _1741822, _1741824, c_List_Ofoldr(_1741818, _1741820, _1741822, _1741826, _1741828)))], (10278 ^ _778908) ^ [_951673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _951673), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_951673 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 10281 ^ [_951673]))))], (35773 ^ _778908) ^ [_1438964, _1438966, _1438968, _1438970, _1438972] : [-(hBOOL(hAPP(hAPP(c_member(_1438964), _1438966), hAPP(c_Relation_OImage(_1438968, _1438964, _1438970), _1438972)))), 35774 ^ _778908 : [(35775 ^ _778908) ^ [_1439050] : [hBOOL(hAPP(hAPP(c_member(_1438968), _1439050), _1438972)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1438968, _1438964)), hAPP(hAPP(c_Product__Type_OPair(_1438968, _1438964), _1439050), _1438966)), _1438970))]]], (30492 ^ _778908) ^ [_1325059, _1325061] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325061, _1325059) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325059), _1325061)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325061), _1325059)))], (26737 ^ _778908) ^ [_1250397, _1250399, _1250401, _1250403, _1250405] : [class_Divides_Osemiring__div(_1250397), -(_1250399 = c_Groups_Ozero__class_Ozero(_1250397)), -(_1250401 = c_Groups_Ozero__class_Ozero(_1250397)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250397), _1250399), _1250403)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250397), _1250401), _1250405)), 26756 ^ _778908 : [(26763 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250397), _1250403), _1250401) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250397), _1250399), _1250405), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250397), _1250403), _1250399) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250397), _1250405), _1250401))], (26757 ^ _778908) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250397), _1250403), _1250399) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250397), _1250405), _1250401), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250397), _1250403), _1250401) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250397), _1250399), _1250405))]]], (1142 ^ _778908) ^ [_796057, _796059] : [-(class_Groups_Oab__group__add(_796057)), _796059 = _796057, class_Groups_Oab__group__add(_796059)], (50824 ^ _778908) ^ [_1800336, _1800338] : [c_List_Oconcat(_1800336, _1800338) = c_List_Olist_ONil(_1800336), 50827 ^ _778908 : [(50828 ^ _778908) ^ [_1800427] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1800336)), _1800427), hAPP(c_List_Oset(tc_List_Olist(_1800336)), _1800338))), -(_1800427 = c_List_Olist_ONil(_1800336))]]], (27628 ^ _778908) ^ [_1268335, _1268337] : [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)), _1268335)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1268335), _1268337)))], (4048 ^ _778908) ^ [_841332, _841334, _841336, _841338] : [-(c_Relation_OId__on(_841338, _841334) = c_Relation_OId__on(_841336, _841332)), _841338 = _841336, _841334 = _841332], (24969 ^ _778908) ^ [_1216724, _1216726, _1216728] : [-(c_Nitpick_Oplus__frac(_1216724, _1216726, _1216728) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1216724), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1216724), _1216726), hAPP(c_Nitpick_Odenom(_1216724), _1216728))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1216724), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1216724), tc_Int_Oint), c_Nitpick_Ofrac(_1216724)), 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(_1216724), _1216726))), 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(_1216724), _1216726))))), 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(_1216724), _1216728))), 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(_1216724), _1216728)))))), c_COMBI(tc_Int_Oint))))], (19069 ^ _778908) ^ [_1107348] : [class_Int_Onumber__ring(_1107348), -(hAPP(c_Int_Onumber__class_Onumber__of(_1107348), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1107348))], (51693 ^ _778908) ^ [_1814060, _1814062] : [hBOOL(_1814060), -(hBOOL(hAPP(hAPP(c_fdisj, _1814062), _1814060)))], (6158 ^ _778908) ^ [_877714, _877716, _877718, _877720] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_877714, _877716)), _877718), _877720))), 6159 ^ _778908 : [(6160 ^ _778908) ^ [_877782] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877714), _877718), _877782)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877716), _877782), _877720))]]], (15212 ^ _778908) ^ [_1037465, _1037467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1037465)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037465), _1037467)), _1037465) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10016 ^ _778908) ^ [_947201] : [class_Rings_Olinordered__semidom(_947201), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947201), c_Groups_Ozero__class_Ozero(_947201)), c_Groups_Oone__class_Oone(_947201))))], (9174 ^ _778908) ^ [_932511, _932513] : [class_Groups_Ocomm__monoid__mult(_932511), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932511), _932513), c_Groups_Oone__class_Oone(_932511)) = _932513)], (43494 ^ _778908) ^ [_1625660, _1625662] : [-(c_Transitive__Closure_Ortrancl(_1625660, hAPP(c_Relation_Oconverse(_1625660, _1625660), _1625662)) = hAPP(c_Relation_Oconverse(_1625660, _1625660), c_Transitive__Closure_Ortrancl(_1625660, _1625662)))], (24961 ^ _778908) ^ [_1216487, _1216489, _1216491, _1216493, _1216495, _1216497] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1216487, _1216489, _1216491, _1216493, _1216495), hAPP(c_Sum__Type_OInr(_1216491, _1216487), _1216497)) = hAPP(_1216495, _1216497))], (9602 ^ _778908) ^ [_939819] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939819)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939819))], (29566 ^ _778908) ^ [_1307706, _1307708, _1307710, _1307712] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307706), _1307708)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307710), hAPP(c_Set_Oimage(_1307706, _1307710, _1307712), _1307708))))], (44510 ^ _778908) ^ [_1648973, _1648975, _1648977, _1648979, _1648981, _1648983] : [c_Finite__Set_Ofun__left__comm(_1648973, _1648975, _1648977), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648973), _1648979)), -(hBOOL(hAPP(hAPP(c_member(_1648973), _1648981), _1648979))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1648973, _1648975, _1648977), _1648983), hAPP(hAPP(c_Set_Oinsert(_1648973), _1648981), _1648979)) = hAPP(hAPP(c_Finite__Set_Ofold(_1648973, _1648975, _1648977), hAPP(hAPP(_1648977, _1648981), _1648983)), _1648979))], (47577 ^ _778908) ^ [_1725053, _1725055, _1725057, _1725059, _1725061] : [_1725053 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Lazy__Sequence_Oanamorph(_1725055, _1725057, _1725059, _1725053), _1725061) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725057), _1725055), c_List_Olist_ONil(_1725057)), _1725061))], (51223 ^ _778908) ^ [_1809303, _1809305] : [class_Groups_Ominus(_1809303), -(class_Groups_Ominus(tc_fun(_1809305, _1809303)))], (36378 ^ _778908) ^ [_1453573, _1453575, _1453577] : [class_Lattices_Osemilattice__inf(_1453573), 36381 ^ _778908 : [(36388 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453573), _1453575), _1453577) = _1453575, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453573), _1453575), _1453577)))], (36382 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453573), _1453575), _1453577)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453573), _1453575), _1453577) = _1453575)]]], (16845 ^ _778908) ^ [_1068695, _1068697, _1068699] : [class_Groups_Oordered__ab__group__add__abs(_1068695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068695), hAPP(c_Groups_Oabs__class_Oabs(_1068695), _1068697)), _1068699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068695), hAPP(c_Groups_Ouminus__class_Ouminus(_1068695), _1068697)), _1068699)))], (34770 ^ _778908) ^ [_1415738, _1415740, _1415742, _1415744, _1415746, _1415748] : [-(hBOOL(hAPP(hAPP(c_member(_1415738), _1415740), _1415742))), -(hAPP(c_Set_Oimage(_1415738, tc_Option_Ooption(_1415744), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1415738, tc_Option_Ooption(_1415744)), _1415746), _1415740), hAPP(c_Option_Ooption_OSome(_1415744), _1415748))), _1415742) = hAPP(c_Set_Oimage(_1415738, tc_Option_Ooption(_1415744), _1415746), _1415742))], (19045 ^ _778908) ^ [_1106914, _1106916] : [class_Int_Onumber__ring(_1106914), -(hAPP(c_Int_Onumber__class_Onumber__of(_1106914), c_Int_OBit1(_1106916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106914), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106914), c_Groups_Oone__class_Oone(_1106914)), hAPP(c_Int_Onumber__class_Onumber__of(_1106914), _1106916))), hAPP(c_Int_Onumber__class_Onumber__of(_1106914), _1106916)))], (50066 ^ _778908) ^ [_1784994, _1784996] : [-(c_List_Otranspose(_1784994, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1784994)), c_List_Olist_ONil(_1784994)), _1784996)) = c_List_Otranspose(_1784994, _1784996))], (43996 ^ _778908) ^ [_1638379, _1638381, _1638383, _1638385, _1638387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638379, _1638379)), hAPP(hAPP(c_Product__Type_OPair(_1638379, _1638379), _1638381), _1638383)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638379, _1638379), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1638385)), _1638387))), 44000 ^ _778908 : [(44003 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638379, _1638379)), hAPP(hAPP(c_Product__Type_OPair(_1638379, _1638379), 43999 ^ [_1638379, _1638381, _1638383, _1638385, _1638387]), _1638383)), _1638387)))], (44001 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638379, _1638379)), hAPP(hAPP(c_Product__Type_OPair(_1638379, _1638379), _1638381), 43999 ^ [_1638379, _1638381, _1638383, _1638385, _1638387])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638379, _1638379), tc_HOL_Obool), _1638385), _1638387))))]]], (7536 ^ _778908) ^ [_905101, _905103, _905105, _905107] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_905101, _905103)), _905105), _905107)), 7541 ^ _778908 : [(7544 ^ _778908) ^ [] : [hBOOL(hAPP(_905101, _905105))], (7542 ^ _778908) ^ [] : [-(_905107 = _905105)]], 7545 ^ _778908 : [(7551 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_905101, _905103)), 7547 ^ [_905101, _905103, _905105, _905107]), _905107)))], (7549 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_905103), _905105), 7547 ^ [_905101, _905103, _905105, _905107])))], (7546 ^ _778908) ^ [] : [-(hBOOL(hAPP(_905101, _905105)))]]], (47366 ^ _778908) ^ [_1721274] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1721274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 47369 ^ _778908 : [(47370 ^ _778908) ^ [_1721349] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1721349), hAPP(c_List_Oset(tc_Nat_Onat), _1721274))), -(_1721349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44005 ^ _778908) ^ [_1638691, _1638693, _1638695, _1638697, _1638699] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638691, _1638691)), hAPP(hAPP(c_Product__Type_OPair(_1638691, _1638691), _1638693), _1638695)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638691, _1638691), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1638697)), _1638699))), 44009 ^ _778908 : [(44012 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638691, _1638691)), hAPP(hAPP(c_Product__Type_OPair(_1638691, _1638691), 44008 ^ [_1638691, _1638693, _1638695, _1638697, _1638699]), _1638695)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638691, _1638691), tc_HOL_Obool), _1638697), _1638699))))], (44010 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638691, _1638691)), hAPP(hAPP(c_Product__Type_OPair(_1638691, _1638691), _1638693), 44008 ^ [_1638691, _1638693, _1638695, _1638697, _1638699])), _1638699)))]]], (43725 ^ _778908) ^ [_1631455, _1631457, _1631459] : [c_Relation_Ototal__on(_1631455, _1631457, _1631459), -(c_Relation_Ototal__on(_1631455, _1631457, hAPP(c_Relation_Oconverse(_1631455, _1631455), _1631459)))], (25221 ^ _778908) ^ [_1222379, _1222381] : [-(_1222379 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25224 ^ _778908 : [(25231 ^ _778908) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1222381) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222379), _1222381)), _1222379)))], (25225 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222379), _1222381)), _1222379)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1222381) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (37930 ^ _778908) ^ [_1489141, _1489143, _1489145, _1489147, _1489149] : [class_Fields_Ofield(_1489141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1489143), _1489145)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1489143), _1489147)), 37944 ^ _778908 : [(37947 ^ _778908) ^ [] : [-(hAPP(_1489149, 37943 ^ [_1489141, _1489143, _1489145, _1489147, _1489149]) = c_Groups_Ozero__class_Ozero(_1489141))], (37945 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489143), 37943 ^ [_1489141, _1489143, _1489145, _1489147, _1489149]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489143, tc_HOL_Obool)), _1489145), _1489147))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1489143, _1489141), _1489149), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1489143, tc_HOL_Obool)), _1489145), _1489147)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1489141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1489141), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1489143, _1489141), _1489149), _1489145)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1489143, _1489141), _1489149), _1489147))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1489143, _1489141), _1489149), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489143, tc_HOL_Obool)), _1489145), _1489147))))], (6861 ^ _778908) ^ [_891764, _891766, _891768, _891770] : [c_Com_Ocom_OAss(_891764, _891766) = c_Com_Ocom_OWhile(_891768, _891770)], (12427 ^ _778908) ^ [_987778, _987780] : [-(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), _987778), _987780)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987780))], (3162 ^ _778908) ^ [_827355, _827357] : [_827357 = _827355, -(c_Divides_Odiv__class_Odiv(_827357) = c_Divides_Odiv__class_Odiv(_827355))], (6633 ^ _778908) ^ [_887721, _887723] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_887721, _887723))), -(hBOOL(hAPP(c_Com_OWT, _887723)))], (18513 ^ _778908) ^ [] : [c_Int_OMin = c_Int_OPls], (18833 ^ _778908) ^ [_1103373, _1103375] : [class_Int_Onumber__ring(_1103373), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103373), hAPP(c_Int_Onumber__class_Onumber__of(_1103373), _1103375)), c_Groups_Oone__class_Oone(_1103373)) = hAPP(c_Int_Onumber__class_Onumber__of(_1103373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1103375), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (20707 ^ _778908) ^ [_1136334, _1136336, _1136338, _1136340] : [class_Rings_Odivision__ring(_1136334), -(_1136336 = c_Groups_Ozero__class_Ozero(_1136334)), 20714 ^ _778908 : [(20721 ^ _778908) ^ [] : [_1136338 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136334), _1136340), _1136336), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136334), _1136338), _1136336) = _1136340)], (20715 ^ _778908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136334), _1136338), _1136336) = _1136340, -(_1136338 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136334), _1136340), _1136336))]]], (19913 ^ _778908) ^ [_1121783, _1121785, _1121787] : [class_Rings_Ocomm__semiring__1(_1121783), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121783), _1121785), 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)))), _1121787)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121783), hAPP(hAPP(c_Power_Opower__class_Opower(_1121783), _1121785), _1121787)), hAPP(hAPP(c_Power_Opower__class_Opower(_1121783), _1121785), _1121787)))], (48502 ^ _778908) ^ [_1747773, _1747775] : [-(hAPP(hAPP(c_List_Otake(_1747773), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1747775) = c_List_Olist_ONil(_1747773))], (39382 ^ _778908) ^ [] : [-(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))))], (2378 ^ _778908) ^ [_814787, _814789, _814791, _814793] : [-(c_Nat__Transfer_Otsub(_814793, _814789) = c_Nat__Transfer_Otsub(_814791, _814787)), _814793 = _814791, _814789 = _814787], (51453 ^ _778908) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (18403 ^ _778908) ^ [_1096679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096679), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096679)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (29630 ^ _778908) ^ [_1308786] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1308786)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1308786), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308786), c_Orderings_Otop__class_Otop(tc_fun(_1308786, tc_HOL_Obool)))))], (23773 ^ _778908) ^ [_1193267, _1193269, _1193271] : [class_Orderings_Olinorder(_1193267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193267), _1193269), _1193271)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193267), _1193269), _1193271) = _1193269)], (39174 ^ _778908) ^ [_1514374, _1514376, _1514378, _1514380] : [class_Groups_Ocomm__monoid__mult(_1514374), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514376), _1514378)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514376, _1514374), _1514380), _1514378) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1514374, _1514376, c_Groups_Otimes__class_Otimes(_1514374)), _1514380), c_Groups_Oone__class_Oone(_1514374)), _1514378))], (16939 ^ _778908) ^ [_1070313, _1070315, _1070317, _1070319] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070313), hAPP(c_Int_Onumber__class_Onumber__of(_1070313), _1070315)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070313), _1070317), _1070319)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070313), hAPP(c_Int_Onumber__class_Onumber__of(_1070313), _1070315)), _1070317)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070313), hAPP(c_Int_Onumber__class_Onumber__of(_1070313), _1070315)), _1070319))), class_Int_Onumber(_1070313), class_Rings_Osemiring(_1070313)], (45045 ^ _778908) ^ [_1663504, _1663506, _1663508, _1663510] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1663504, tc_HOL_Obool)), _1663506), _1663508)), hBOOL(hAPP(hAPP(c_member(_1663504), _1663510), _1663506)), -(hBOOL(hAPP(hAPP(c_member(_1663504), _1663510), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663504, tc_HOL_Obool), _1663508))))], (51635 ^ _778908) ^ [_1813274, _1813276, _1813278, _1813280, _1813282, _1813284] : [-(hAPP(hAPP(hAPP(c_COMBS(_1813274, _1813276, _1813278), _1813280), _1813282), _1813284) = hAPP(hAPP(_1813280, _1813284), hAPP(_1813282, _1813284)))], (3988 ^ _778908) ^ [_840422, _840424, _840426, _840428, _840430, _840432] : [-(c_Predicate_ODomainP(_840432, _840428, _840424) = c_Predicate_ODomainP(_840430, _840426, _840422)), _840432 = _840430, _840428 = _840426, _840424 = _840422], (32138 ^ _778908) ^ [_1362452, _1362454, _1362456] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362452), _1362454)), hBOOL(hAPP(hAPP(c_member(_1362452), _1362456), _1362454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1362452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362452, tc_HOL_Obool)), _1362454), hAPP(hAPP(c_Set_Oinsert(_1362452), _1362456), c_Orderings_Obot__class_Obot(tc_fun(_1362452, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1362452), _1362454))))], (25173 ^ _778908) ^ [_1221573, _1221575, _1221577, _1221579, _1221581, _1221583] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1221573, _1221575, _1221577, _1221579), _1221581), _1221583) = hAPP(_1221579, hAPP(hAPP(c_Product__Type_OPair(_1221573, _1221575), _1221581), _1221583)))], (29694 ^ _778908) ^ [_1310063, _1310065, _1310067] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310063), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310063, tc_HOL_Obool)), _1310065), _1310067)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310063), _1310065)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310063), _1310067))], (18397 ^ _778908) ^ [_1096554, _1096556] : [class_Int_Onumber__ring(_1096554), -(hAPP(c_Int_Onumber__class_Onumber__of(_1096554), c_Int_Osucc(_1096556)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096554), c_Groups_Oone__class_Oone(_1096554)), hAPP(c_Int_Onumber__class_Onumber__of(_1096554), _1096556)))], (51347 ^ _778908) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (47880 ^ _778908) ^ [_1733210, _1733212, _1733214, _1733216, _1733218, _1733220] : [-(_1733210 = _1733212), -(hAPP(hAPP(c_List_Olist__update(_1733214, hAPP(hAPP(c_List_Olist__update(_1733214, _1733216), _1733210), _1733218)), _1733212), _1733220) = hAPP(hAPP(c_List_Olist__update(_1733214, hAPP(hAPP(c_List_Olist__update(_1733214, _1733216), _1733212), _1733220)), _1733210), _1733218))], (15610 ^ _778908) ^ [_1044598, _1044600, _1044602] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044598), _1044600)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044598), _1044602)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044600), _1044602))], (2872 ^ _778908) ^ [_822594, _822596, _822598, _822600, _822602, _822604, _822606, _822608] : [-(c_New__DSequence_Oneg__decr__bind(_822608, _822604, _822600, _822596) = c_New__DSequence_Oneg__decr__bind(_822606, _822602, _822598, _822594)), _822608 = _822606, _822604 = _822602, _822600 = _822598, _822596 = _822594], (45251 ^ _778908) ^ [_1667947, _1667949, _1667951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1667947, tc_HOL_Obool), tc_HOL_Obool)), _1667949), _1667951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667947, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667947, tc_HOL_Obool), _1667949)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667947, tc_HOL_Obool), _1667951))))], (11038 ^ _778908) ^ [_963829, _963831, _963833] : [class_Orderings_Olinorder(_963829), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963829), _963831), _963833))), 11045 ^ _778908 : [(11052 ^ _778908) ^ [] : [_963831 = _963833, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963829), _963831), _963833)))], (11046 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963829), _963831), _963833)), -(_963831 = _963833)]]], (22988 ^ _778908) ^ [_1178749, _1178751, _1178753, _1178755] : [-(hAPP(c_Nat_Onat_Onat__rec(_1178749, _1178751, _1178753), hAPP(c_Nat_OSuc, _1178755)) = hAPP(hAPP(_1178753, _1178755), hAPP(c_Nat_Onat_Onat__rec(_1178749, _1178751, _1178753), _1178755)))], (30150 ^ _778908) ^ [_1319172, _1319174] : [class_Lattices_Obounded__lattice__bot(_1319172), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1319172), c_Orderings_Obot__class_Obot(_1319172)), _1319174) = _1319174)], (43073 ^ _778908) ^ [_1614612, _1614614, _1614616, _1614618, _1614620] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614612, _1614612)), hAPP(hAPP(c_Product__Type_OPair(_1614612, _1614612), _1614614), _1614616)), c_Transitive__Closure_Otrancl(_1614612, _1614618))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614612, _1614612)), hAPP(hAPP(c_Product__Type_OPair(_1614612, _1614612), _1614616), _1614620)), _1614618)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614612, _1614612)), hAPP(hAPP(c_Product__Type_OPair(_1614612, _1614612), _1614614), _1614620)), c_Transitive__Closure_Otrancl(_1614612, _1614618))))], (49895 ^ _778908) ^ [_1780753, _1780755, _1780757] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780753)), hAPP(c_List_Ofilter(_1780753, _1780755), _1780757))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780753)), hAPP(c_List_Ofilter(_1780753, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1780753), c_fNot), _1780755)), _1780757))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780753)), _1780757))], (23271 ^ _778908) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (5458 ^ _778908) ^ [_863251, _863253] : [_863253 = _863251, -(c_Groups_Ominus__class_Ominus(_863253) = c_Groups_Ominus__class_Ominus(_863251))], (13963 ^ _778908) ^ [_1014933, _1014935, _1014937, _1014939] : [class_Divides_Osemiring__div(_1014933), -(c_Divides_Odiv__class_Omod(_1014933, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014933), c_Divides_Odiv__class_Omod(_1014933, _1014935, _1014937)), _1014939), _1014937) = c_Divides_Odiv__class_Omod(_1014933, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014933), _1014935), _1014939), _1014937))], (26175 ^ _778908) ^ [_1239704, _1239706] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239704), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1239706)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239704)), _1239706)))], (36728 ^ _778908) ^ [_1460739, _1460741, _1460743, _1460745] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460739, tc_HOL_Obool)), _1460741), _1460743), _1460745)), -(hBOOL(hAPP(_1460743, _1460745)))], (49571 ^ _778908) ^ [_1774175, _1774177, _1774179, _1774181] : [-(_1774175 = c_List_Olist_ONil(_1774177)), 49574 ^ _778908 : [(49581 ^ _778908) ^ [] : [-(_1774179 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774177)), _1774175)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1774177, hAPP(hAPP(c_List_Olist__update(_1774177, _1774175), _1774179), _1774181)) = c_List_Olast(_1774177, _1774175))], (49575 ^ _778908) ^ [] : [_1774179 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774177)), _1774175)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1774177, hAPP(hAPP(c_List_Olist__update(_1774177, _1774175), _1774179), _1774181)) = _1774181)]]], (15698 ^ _778908) ^ [_1046313, _1046315, _1046317] : [-(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, _1046313, _1046315)), _1046317), _1046315) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046313), _1046317), _1046315))], (48231 ^ _778908) ^ [_1741437, _1741439, _1741441, _1741443] : [_1741439 = _1741443, -(hAPP(hAPP(c_List_Oappend(_1741437), _1741439), _1741441) = hAPP(hAPP(c_List_Oappend(_1741437), _1741443), _1741441))], (5080 ^ _778908) ^ [_857496, _857498] : [_857498 = _857496, -(c_Option_Ooption_OSome(_857498) = c_Option_Ooption_OSome(_857496))], (28207 ^ _778908) ^ [_1279737, _1279739, _1279741] : [class_Lattices_Osemilattice__sup(_1279737), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279737), _1279739), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279737), _1279739), _1279741)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279737), _1279739), _1279741))], (24719 ^ _778908) ^ [_1211499, _1211501, _1211503, _1211505] : [class_Orderings_Olinorder(_1211499), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211499), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211499), _1211501), _1211503)), _1211505) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211499), _1211501), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211499), _1211503), _1211505)))], (7404 ^ _778908) ^ [_902605, _902607] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_902605, _902607)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _902607)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11366 ^ _778908) ^ [_969073] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969073) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30000 ^ _778908) ^ [_1316065, _1316067] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316065, tc_HOL_Obool)), _1316067), c_Orderings_Obot__class_Obot(tc_fun(_1316065, tc_HOL_Obool))) = _1316067)], (13682 ^ _778908) ^ [_1009558, _1009560, _1009562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1009558)), 13685 ^ _778908 : [(13692 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009560), _1009562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009558), _1009560)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009558), _1009562))))], (13686 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009558), _1009560)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009558), _1009562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009560), _1009562)))]]], (11392 ^ _778908) ^ [_969525] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969525)))], (8861 ^ _778908) ^ [_926711] : [-(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, _926711)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16060 ^ _778908) ^ [_1053379, _1053381, _1053383, _1053385, _1053387, _1053389] : [class_Rings_Oordered__ring(_1053379), 16063 ^ _778908 : [(16070 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053379), _1053385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053379), _1053387), _1053381)), _1053383)), _1053389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053379), _1053381), _1053383)), _1053385)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053379), _1053387), _1053383)), _1053389))))], (16064 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053379), _1053381), _1053383)), _1053385)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053379), _1053387), _1053383)), _1053389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053379), _1053385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053379), _1053387), _1053381)), _1053383)), _1053389))))]]], (35327 ^ _778908) ^ [_1428830, _1428832, _1428834, _1428836, _1428838] : [class_Groups_Ocomm__monoid__mult(_1428830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428832), _1428834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428832, tc_HOL_Obool)), _1428836), _1428834)), 35341 ^ _778908 : [(35344 ^ _778908) ^ [] : [hAPP(_1428838, 35340 ^ [_1428830, _1428832, _1428834, _1428836, _1428838]) = c_Groups_Oone__class_Oone(_1428830)], (35342 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1428832), 35340 ^ [_1428830, _1428832, _1428834, _1428836, _1428838]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428832, tc_HOL_Obool)), _1428834), _1428836))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1428832, _1428830), _1428838), _1428834) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1428832, _1428830), _1428838), _1428836))], (51069 ^ _778908) ^ [_1806501, _1806503] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1806501), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1806501))), _1806503))), 51072 ^ _778908 : [(51079 ^ _778908) ^ [] : [-(_1806503 = c_List_Olist_ONil(tc_List_Olist(_1806501))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1806501))), c_List_Otranspose(_1806501, _1806503)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806501)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1806501)), _1806503), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51073 ^ _778908) ^ [] : [_1806503 = c_List_Olist_ONil(tc_List_Olist(_1806501)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1806501))), c_List_Otranspose(_1806501, _1806503)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3460 ^ _778908) ^ [_832080, _832082, _832084, _832086, _832088, _832090, _832092, _832094] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_832094, _832090, _832086, _832082) = c_Hoare__Mirabelle_Otriple_Otriple__case(_832092, _832088, _832084, _832080)), _832094 = _832092, _832090 = _832088, _832086 = _832084, _832082 = _832080], (33321 ^ _778908) ^ [_1386816, _1386818, _1386820, _1386822, _1386824] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1386816, _1386818, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1386816), _1386820), _1386822), _1386824)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50084 ^ _778908) ^ [_1785736, _1785738, _1785740, _1785742, _1785744] : [class_Orderings_Olinorder(_1785736), hBOOL(hAPP(hAPP(c_member(_1785738), _1785740), hAPP(c_List_Oset(_1785738), _1785742))), c_List_Olinorder__class_Osorted(_1785736, hAPP(hAPP(c_List_Omap(_1785738, _1785736), _1785744), _1785742)), hAPP(c_List_Ohd(_1785738), hAPP(c_List_Ofilter(_1785738, hAPP(hAPP(c_COMBB(_1785736, tc_HOL_Obool, _1785738), hAPP(c_fequal, hAPP(_1785744, _1785740))), _1785744)), _1785742)) = _1785740, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1785738, _1785736, _1785744), _1785740), c_List_Oremove1(_1785738, _1785740, _1785742)) = _1785742)], (11779 ^ _778908) ^ [_976145, _976147] : [class_Rings_Olinordered__idom(_976145), 11782 ^ _778908 : [(11789 ^ _778908) ^ [] : [_976147 = c_Groups_Ozero__class_Ozero(_976145), -(c_Groups_Osgn__class_Osgn(_976145, _976147) = c_Groups_Ozero__class_Ozero(_976145))], (11783 ^ _778908) ^ [] : [c_Groups_Osgn__class_Osgn(_976145, _976147) = c_Groups_Ozero__class_Ozero(_976145), -(_976147 = c_Groups_Ozero__class_Ozero(_976145))]]], (51575 ^ _778908) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (11604 ^ _778908) ^ [_973006, _973008] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973006), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973006), _973008))))], (43528 ^ _778908) ^ [_1626400, _1626402, _1626404] : [-(hAPP(c_Relation_Oconverse(_1626400, _1626402), hAPP(c_Relation_Oconverse(_1626402, _1626400), _1626404)) = _1626404)], (33283 ^ _778908) ^ [_1386109, _1386111, _1386113] : [class_Lattices_Olattice(_1386109), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386109), _1386111)), -(hBOOL(hAPP(hAPP(c_member(_1386109), _1386113), _1386111))), -(_1386111 = c_Orderings_Obot__class_Obot(tc_fun(_1386109, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1386109, hAPP(hAPP(c_Set_Oinsert(_1386109), _1386113), _1386111)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1386109), _1386113), c_Big__Operators_Olattice__class_OSup__fin(_1386109, _1386111)))], (46956 ^ _778908) ^ [_1709947, _1709949, _1709951, _1709953] : [c_List_Olistrelp(_1709947, hAPP(hAPP(c_COMBC(_1709947, tc_fun(tc_prod(_1709947, _1709947), tc_HOL_Obool), tc_fun(_1709947, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1709947, tc_fun(tc_fun(tc_prod(_1709947, _1709947), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1709947, _1709947), tc_HOL_Obool), tc_fun(_1709947, tc_HOL_Obool)), _1709947), c_COMBC(_1709947, tc_fun(tc_prod(_1709947, _1709947), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1709947, tc_prod(_1709947, _1709947)), tc_fun(_1709947, tc_fun(tc_fun(tc_prod(_1709947, _1709947), tc_HOL_Obool), tc_HOL_Obool)), _1709947), hAPP(c_COMBB(tc_prod(_1709947, _1709947), tc_fun(tc_fun(tc_prod(_1709947, _1709947), tc_HOL_Obool), tc_HOL_Obool), _1709947), c_member(tc_prod(_1709947, _1709947)))), c_Product__Type_OPair(_1709947, _1709947)))), _1709949), _1709951, _1709953), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709947), tc_List_Olist(_1709947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709947), tc_List_Olist(_1709947)), _1709951), _1709953)), c_List_Olistrel(_1709947, _1709949))))], (6851 ^ _778908) ^ [_891494, _891496, _891498] : [c_Com_Ocom_OWhile(_891494, _891496) = hAPP(c_Com_Ocom_OBODY, _891498)], (14603 ^ _778908) ^ [_1026826] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1026826, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33865 ^ _778908) ^ [_1397292, _1397294, _1397296, _1397298, _1397300] : [c_Hoare__Mirabelle_Otriple__valid(_1397292, _1397294, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1397292), _1397296), _1397298), _1397300)), 33868 ^ _778908 : [(33869 ^ _778908) ^ [_1397413, _1397415] : [hBOOL(hAPP(hAPP(_1397296, _1397415), _1397413)), 33872 ^ _778908 : [(33873 ^ _778908) ^ [_1397503] : [c_Natural_Oevaln(_1397298, _1397413, _1397294, _1397503), -(hBOOL(hAPP(hAPP(_1397300, _1397415), _1397503)))]]]]], (9102 ^ _778908) ^ [_931046, _931048, _931050, _931052] : [class_Rings_Ocomm__semiring__1(_931046), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931046), _931048), _931050)), _931052) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931046), _931048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931046), _931050), _931052)))], (10854 ^ _778908) ^ [_961051, _961053, _961055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961051), _961053)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961051), _961055))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961053), _961055)))], (50029 ^ _778908) ^ [_1784113, _1784115, _1784117, _1784119, _1784121, _1784123] : [hAPP(c_Map_Omap__of(_1784113, _1784115, _1784117), _1784119) = hAPP(c_Option_Ooption_OSome(_1784115), _1784121), hBOOL(hAPP(hAPP(_1784123, _1784119), _1784121)), -(hAPP(c_Map_Omap__of(_1784113, _1784115, hAPP(c_List_Ofilter(tc_prod(_1784113, _1784115), hAPP(c_Product__Type_Oprod_Oprod__case(_1784113, _1784115, tc_HOL_Obool), _1784123)), _1784117)), _1784119) = hAPP(c_Option_Ooption_OSome(_1784115), _1784121))], (28737 ^ _778908) ^ [_1289888, _1289890, _1289892] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1289888, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1289890)), _1289892) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289888, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1289888, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1289890)), _1289892)), hAPP(_1289892, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16769 ^ _778908) ^ [_1067185, _1067187] : [class_Groups_Oordered__ab__group__add__abs(_1067185), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067185), c_Groups_Ozero__class_Ozero(_1067185)), hAPP(c_Groups_Oabs__class_Oabs(_1067185), _1067187))))], (23112 ^ _778908) ^ [_1180949, _1180951] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180949))), 23115 ^ _778908 : [(23122 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180951))), -(c_Divides_Odivmod__int(_1180949, _1180951) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180949), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180951))))], (23116 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180951)), -(c_Divides_Odivmod__int(_1180949, _1180951) = c_Divides_OnegDivAlg(_1180949, _1180951))]]], (9062 ^ _778908) ^ [_930301] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930301), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _930301)], (34688 ^ _778908) ^ [_1413906, _1413908, _1413910, _1413912, _1413914] : [class_Groups_Ocomm__monoid__mult(_1413906), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413908), _1413910)), -(hBOOL(hAPP(hAPP(c_member(_1413908), _1413912), _1413910))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413908, _1413906), _1413914), hAPP(hAPP(c_Set_Oinsert(_1413908), _1413912), _1413910)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413906), hAPP(_1413914, _1413912)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413908, _1413906), _1413914), _1413910)))], (19879 ^ _778908) ^ [_1121360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121360), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1121360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1121360 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50297 ^ _778908) ^ [_1789616, _1789618, _1789620] : [class_Orderings_Olinorder(_1789616), 50300 ^ _778908 : [(50319 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1789616, hAPP(hAPP(c_List_Oappend(_1789616), _1789618), _1789620))), c_List_Olinorder__class_Osorted(_1789616, _1789618), c_List_Olinorder__class_Osorted(_1789616, _1789620), 50329 ^ _778908 : [(50335 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789616), 50328 ^ [_1789616, _1789618, _1789620]), 50331 ^ [_1789616, _1789618, _1789620]))], (50333 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789616), 50331 ^ [_1789616, _1789618, _1789620]), hAPP(c_List_Oset(_1789616), _1789620))))], (50330 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789616), 50328 ^ [_1789616, _1789618, _1789620]), hAPP(c_List_Oset(_1789616), _1789618))))]]], (50301 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1789616, hAPP(hAPP(c_List_Oappend(_1789616), _1789618), _1789620)), 50304 ^ _778908 : [(50309 ^ _778908) ^ [_1789852] : [hBOOL(hAPP(hAPP(c_member(_1789616), _1789852), hAPP(c_List_Oset(_1789616), _1789618))), 50312 ^ _778908 : [(50313 ^ _778908) ^ [_1789962] : [hBOOL(hAPP(hAPP(c_member(_1789616), _1789962), hAPP(c_List_Oset(_1789616), _1789620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789616), _1789852), _1789962)))]]], (50307 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1789616, _1789620))], (50305 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1789616, _1789618))]]]]], (51559 ^ _778908) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (7266 ^ _778908) ^ [_900464, _900466] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _900464)), _900466) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900464), _900466)))], (18645 ^ _778908) ^ [_1100263, _1100265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100263)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100265)))), 18648 ^ _778908 : [(18651 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1100265))], (18649 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100263), _1100265)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100263), _1100265))], (37180 ^ _778908) ^ [_1471374, _1471376, _1471378] : [class_Orderings_Oorder(_1471374), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471374, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1471374, _1471376), _1471378)), hAPP(c_SetInterval_Oord__class_OatLeast(_1471374), _1471378)) = c_Orderings_Obot__class_Obot(tc_fun(_1471374, tc_HOL_Obool)))], (11374 ^ _778908) ^ [_969228, _969230, _969232] : [_969230 = _969232, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969228)), _969230) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969228)), _969232))], (17933 ^ _778908) ^ [_1089153] : [class_Power_Opower(_1089153), -(c_Power_Opower__class_Opower(_1089153) = c_Power_Opower_Opower(_1089153, c_Groups_Oone__class_Oone(_1089153), c_Groups_Otimes__class_Otimes(_1089153)))], (31109 ^ _778908) ^ [_1337533, _1337535, _1337537, _1337539] : [hBOOL(hAPP(hAPP(c_member(_1337533), _1337535), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337533, tc_HOL_Obool)), _1337537), _1337539))), 31112 ^ _778908 : [(31115 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1337533), _1337535), _1337539))], (31113 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337533), _1337535), _1337537)))]]], (36336 ^ _778908) ^ [_1452781, _1452783, _1452785, _1452787] : [hBOOL(hAPP(hAPP(c_member(_1452781), _1452783), _1452785)), hBOOL(hAPP(hAPP(c_member(_1452781), _1452783), _1452787)), -(hBOOL(hAPP(hAPP(c_member(_1452781), _1452783), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452781, tc_HOL_Obool)), _1452785), _1452787))))], (25817 ^ _778908) ^ [_1232393, _1232395, _1232397, _1232399] : [class_Rings_Odvd(_1232393), _1232395 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232393), _1232397), _1232399), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232393), _1232397), _1232395)))], (45596 ^ _778908) ^ [_1676289, _1676291, _1676293, _1676295, _1676297, _1676299, _1676301] : [c_Finite__Set_Ofun__left__comm(_1676289, _1676291, _1676293), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1676289, _1676291, _1676293, _1676295, hAPP(hAPP(c_Set_Oinsert(_1676289), _1676297), _1676299)), _1676301)), -(hBOOL(hAPP(hAPP(c_member(_1676289), _1676297), _1676299))), 45608 ^ _778908 : [(45611 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1676289, _1676291, _1676293, _1676295, _1676299), 45607 ^ [_1676289, _1676291, _1676293, _1676295, _1676297, _1676299, _1676301])))], (45609 ^ _778908) ^ [] : [-(_1676301 = hAPP(hAPP(_1676293, _1676297), 45607 ^ [_1676289, _1676291, _1676293, _1676295, _1676297, _1676299, _1676301]))]]], (51171 ^ _778908) ^ [_1808621, _1808623] : [class_Orderings_Opreorder(_1808621), -(class_Orderings_Opreorder(tc_fun(_1808623, _1808621)))], (31960 ^ _778908) ^ [_1358529, _1358531, _1358533, _1358535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1358529, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1358529, tc_HOL_Obool)), _1358531), hAPP(hAPP(c_Set_Oinsert(_1358529), _1358533), c_Orderings_Obot__class_Obot(tc_fun(_1358529, tc_HOL_Obool))))), _1358535)), hBOOL(hAPP(hAPP(c_member(_1358529), _1358533), _1358531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1358529, tc_HOL_Obool)), _1358531), hAPP(hAPP(c_Set_Oinsert(_1358529), _1358533), _1358535))))], (37076 ^ _778908) ^ [_1469000, _1469002, _1469004] : [class_Lattices_Olattice(_1469000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469000), _1469002)), hBOOL(hAPP(hAPP(c_member(_1469000), _1469004), _1469002)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1469000), _1469004), c_Big__Operators_Olattice__class_OSup__fin(_1469000, _1469002)) = _1469004)], (33051 ^ _778908) ^ [_1381437, _1381439, _1381441, _1381443, _1381445, _1381447, _1381449] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1381437), _1381439), _1381441), _1381443) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1381437), _1381445), _1381447), _1381449), 33054 ^ _778908 : [(33059 ^ _778908) ^ [] : [-(_1381443 = _1381449)], (33057 ^ _778908) ^ [] : [-(_1381441 = _1381447)], (33055 ^ _778908) ^ [] : [-(_1381439 = _1381445)]]], (37490 ^ _778908) ^ [_1478417, _1478419, _1478421, _1478423, _1478425] : [class_Groups_Ocomm__monoid__mult(_1478417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478419), _1478421)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478419), _1478423)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478419, tc_HOL_Obool)), _1478421), _1478423) = c_Orderings_Obot__class_Obot(tc_fun(_1478419, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478419, _1478417), _1478425), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478419, tc_HOL_Obool)), _1478421), _1478423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1478417), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478419, _1478417), _1478425), _1478421)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478419, _1478417), _1478425), _1478423)))], (28854 ^ _778908) ^ [_1292116, _1292118] : [class_Orderings_Olinorder(_1292116), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1292116, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1292116), _1292118)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1292116), _1292118))], (17725 ^ _778908) ^ [_1085309, _1085311, _1085313, _1085315] : [class_Rings_Olinordered__semidom(_1085309), hAPP(hAPP(c_Power_Opower__class_Opower(_1085309), _1085311), hAPP(c_Nat_OSuc, _1085313)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1085309), _1085315), hAPP(c_Nat_OSuc, _1085313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085309), c_Groups_Ozero__class_Ozero(_1085309)), _1085311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085309), c_Groups_Ozero__class_Ozero(_1085309)), _1085315)), -(_1085311 = _1085315)], (15842 ^ _778908) ^ [_1049243, _1049245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049243), _1049245)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049243), _1049245)))], (30954 ^ _778908) ^ [_1334309, _1334311, _1334313] : [-(hBOOL(hAPP(hAPP(c_member(_1334309), _1334311), _1334313))), -(hBOOL(hAPP(hAPP(c_member(_1334309), _1334311), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1334309, tc_HOL_Obool)), _1334313))))], (33543 ^ _778908) ^ [_1390755, _1390757, _1390759] : [class_Orderings_Olinorder(_1390755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390755, tc_HOL_Obool)), _1390757), _1390759)), -(_1390757 = c_Orderings_Obot__class_Obot(tc_fun(_1390755, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390755), _1390759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390755), c_Big__Operators_Olinorder__class_OMin(_1390755, _1390759)), c_Big__Operators_Olinorder__class_OMin(_1390755, _1390757))))], (4802 ^ _778908) ^ [_853217, _853219] : [_853219 = _853217, -(c_Orderings_Oord__class_Omin(_853219) = c_Orderings_Oord__class_Omin(_853217))], (47417 ^ _778908) ^ [_1722195, _1722197] : [-(c_List_Olistrelp(_1722195, _1722197, c_List_Olist_ONil(_1722195), c_List_Olist_ONil(_1722195)))], (16571 ^ _778908) ^ [_1063680, _1063682] : [class_Groups_Oordered__ab__group__add__abs(_1063680), -(hAPP(c_Groups_Oabs__class_Oabs(_1063680), hAPP(c_Groups_Oabs__class_Oabs(_1063680), _1063682)) = hAPP(c_Groups_Oabs__class_Oabs(_1063680), _1063682))], (12451 ^ _778908) ^ [_988265, _988267] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988265), hAPP(c_Nat_OSuc, _988267)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _988265), _988267)))], (18511 ^ _778908) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (50947 ^ _778908) ^ [_1802866, _1802868, _1802870] : [-(hAPP(c_List_Orev(_1802866), hAPP(c_List_Ofilter(_1802866, _1802868), _1802870)) = hAPP(c_List_Ofilter(_1802866, _1802868), hAPP(c_List_Orev(_1802866), _1802870)))], (34887 ^ _778908) ^ [_1418312, _1418314] : [-(c_Map_Oran(_1418312, _1418314, hAPP(c_COMBK(tc_Option_Ooption(_1418314), _1418312), c_Option_Ooption_ONone(_1418314))) = c_Orderings_Obot__class_Obot(tc_fun(_1418314, tc_HOL_Obool)))], (7615 ^ _778908) ^ [_906404, _906406, _906408, _906410, _906412, _906414] : [c_Nitpick_Opair__box_OPairBox(_906404, _906406, _906408, _906410) = c_Nitpick_Opair__box_OPairBox(_906404, _906406, _906412, _906414), 7618 ^ _778908 : [(7621 ^ _778908) ^ [] : [-(_906410 = _906414)], (7619 ^ _778908) ^ [] : [-(_906408 = _906412)]]], (22814 ^ _778908) ^ [_1174826, _1174828, _1174830, _1174832] : [-(c_Nat_Onat_Onat__case(_1174826, _1174828, _1174830, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174832)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1174826), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1174832))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1174826, _1174826), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1174826, tc_fun(_1174826, _1174826)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1174826, tc_fun(_1174826, _1174826)), tc_Int_Oint), c_If(_1174826)), c_Nat__Numeral_Oneg)), _1174828)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1174826, tc_Int_Oint), _1174830), c_Int_Onat))))], (42865 ^ _778908) ^ [_1610105, _1610107, _1610109, _1610111] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1610105, tc_HOL_Obool), tc_fun(_1610105, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1610105, tc_HOL_Obool), tc_fun(_1610105, tc_HOL_Obool)), _1610107), _1610109)), c_Wellfounded_Omax__ext(_1610105, _1610111)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610105), _1610107)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610105), _1610109)), -(_1610109 = c_Orderings_Obot__class_Obot(tc_fun(_1610105, tc_HOL_Obool))), 42879 ^ _778908 : [(42882 ^ _778908) ^ [_1610510] : [hBOOL(hAPP(hAPP(c_member(_1610105), _1610510), _1610109)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1610105, _1610105)), hAPP(hAPP(c_Product__Type_OPair(_1610105, _1610105), 42878 ^ [_1610105, _1610107, _1610109, _1610111]), _1610510)), _1610111))], (42880 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1610105), 42878 ^ [_1610105, _1610107, _1610109, _1610111]), _1610107)))]]], (36354 ^ _778908) ^ [_1453145, _1453147, _1453149] : [class_Lattices_Olattice(_1453145), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453145), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453145), _1453147), _1453149)), _1453147)))], (24257 ^ _778908) ^ [_1202697, _1202699] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1202697)), hAPP(c_Nat_OSuc, _1202699)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1202697))), 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)), _1202699)))))], (42776 ^ _778908) ^ [_1607985, _1607987] : [42778 ^ _778908 : [(42781 ^ _778908) ^ [] : [42777 ^ [_1607985, _1607987] = c_Orderings_Obot__class_Obot(tc_fun(_1607985, tc_HOL_Obool))], (42779 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607985, tc_HOL_Obool)), 42777 ^ [_1607985, _1607987]), hAPP(c_Relation_OImage(_1607985, _1607985, _1607987), 42777 ^ [_1607985, _1607987]))))]], -(c_Wellfounded_Owf(_1607985, _1607987))], (10204 ^ _778908) ^ [_950330, _950332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _950330)), hAPP(c_Int_Onat, _950332))), 10207 ^ _778908 : [(10210 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _950330), _950332)))], (10208 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950332)))]]], (22394 ^ _778908) ^ [_1166762, _1166764, _1166766, _1166768] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1166762, _1166764, _1166766, c_Code__Numeral_OSuc__code__numeral(_1166768)) = hAPP(hAPP(_1166766, _1166768), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1166762, _1166764, _1166766, _1166768)))], (49119 ^ _778908) ^ [_1764360, _1764362, _1764364, _1764366] : [-(_1764360 = c_List_Olist_ONil(_1764362)), -(hAPP(c_List_Ohd(_1764364), hAPP(hAPP(c_List_Omap(_1764362, _1764364), _1764366), _1764360)) = hAPP(_1764366, hAPP(c_List_Ohd(_1764362), _1764360)))], (30354 ^ _778908) ^ [_1322629, _1322631, _1322633, _1322635] : [class_Orderings_Oorder(_1322629), 30357 ^ _778908 : [(30366 ^ _778908) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1322629, _1322631, _1322633) = hAPP(hAPP(c_Set_Oinsert(_1322629), _1322635), c_Orderings_Obot__class_Obot(tc_fun(_1322629, tc_HOL_Obool)))), _1322631 = _1322633, _1322633 = _1322635], (30358 ^ _778908) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1322629, _1322631, _1322633) = hAPP(hAPP(c_Set_Oinsert(_1322629), _1322635), c_Orderings_Obot__class_Obot(tc_fun(_1322629, tc_HOL_Obool))), 30361 ^ _778908 : [(30364 ^ _778908) ^ [] : [-(_1322633 = _1322635)], (30362 ^ _778908) ^ [] : [-(_1322631 = _1322633)]]]]], (17705 ^ _778908) ^ [_1084901, _1084903, _1084905] : [class_Rings_Olinordered__idom(_1084901), -(hAPP(c_Groups_Oabs__class_Oabs(_1084901), hAPP(hAPP(c_Power_Opower__class_Opower(_1084901), hAPP(c_Groups_Ouminus__class_Ouminus(_1084901), _1084903)), _1084905)) = hAPP(c_Groups_Oabs__class_Oabs(_1084901), hAPP(hAPP(c_Power_Opower__class_Opower(_1084901), _1084903), _1084905)))], (40600 ^ _778908) ^ [_1550375, _1550377, _1550379] : [-(hAPP(c_Finite__Set_Ofold1(_1550375, _1550377), _1550379) = c_HOL_OThe(_1550375, c_Finite__Set_Ofold1Set(_1550375, _1550377, _1550379)))], (35026 ^ _778908) ^ [_1421236, _1421238, _1421240, _1421242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1421236), _1421238)), -(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), _1421236), _1421240)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1421238), _1421242))), c_FunDef_Opair__leq)))], (51437 ^ _778908) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (45222 ^ _778908) ^ [_1667382, _1667384, _1667386] : [class_Complete__Lattice_Ocomplete__lattice(_1667382), 45225 ^ _778908 : [(45226 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1667382), _1667384), c_Complete__Lattice_OInf__class_OInf(_1667382, _1667386))), 45229 ^ _778908 : [(45230 ^ _778908) ^ [_1667540] : [hBOOL(hAPP(hAPP(c_member(_1667382), _1667540), _1667386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1667382), _1667384), _1667540)))]]], (45236 ^ _778908) ^ [] : [45238 ^ _778908 : [(45241 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1667382), _1667384), 45237 ^ [_1667382, _1667384, _1667386]))], (45239 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1667382), 45237 ^ [_1667382, _1667384, _1667386]), _1667386)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1667382), _1667384), c_Complete__Lattice_OInf__class_OInf(_1667382, _1667386))))]]], (30918 ^ _778908) ^ [_1333629, _1333631, _1333633, _1333635] : [hBOOL(hAPP(hAPP(c_member(_1333629), _1333631), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333629, tc_HOL_Obool)), _1333633), _1333635))), -(hBOOL(hAPP(hAPP(c_member(_1333629), _1333631), _1333633))), -(hBOOL(hAPP(hAPP(c_member(_1333629), _1333631), _1333635)))], (3592 ^ _778908) ^ [_834148, _834150, _834152, _834154, _834156, _834158, _834160, _834162] : [-(c_Random__Sequence_Obind(_834162, _834158, _834154, _834150) = c_Random__Sequence_Obind(_834160, _834156, _834152, _834148)), _834162 = _834160, _834158 = _834156, _834154 = _834152, _834150 = _834148], (16210 ^ _778908) ^ [_1056762, _1056764, _1056766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1056762), _1056764)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1056764), _1056762))), _1056766) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1056764)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1056762), _1056766)))], (30678 ^ _778908) ^ [_1328709, _1328711] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1328709), _1328711))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1328709), hAPP(c_Nat_OSuc, _1328711)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (50164 ^ _778908) ^ [_1787278, _1787280, _1787282, _1787284] : [-(c_List_Oupt(_1787278, _1787280) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1787282), _1787284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787278), _1787280)), _1787278 = _1787282, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1787278), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1787280) = _1787284], (44280 ^ _778908) ^ [_1644624, _1644626, _1644628] : [class_Orderings_Olinorder(_1644624), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644624), _1644626)), -(c_Big__Operators_Olattice_OSup__fin(_1644624, c_Orderings_Oord__class_Omax(_1644624), hAPP(hAPP(c_Set_Oinsert(_1644624), _1644628), _1644626)) = hAPP(hAPP(c_Finite__Set_Ofold(_1644624, _1644624, c_Orderings_Oord__class_Omax(_1644624)), _1644628), _1644626))], (11268 ^ _778908) ^ [_967447, _967449, _967451, _967453] : [class_Groups_Oordered__ab__semigroup__add(_967447), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967447), _967449), _967451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967447), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967447), _967449), _967453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967447), _967451), _967453))))], (20237 ^ _778908) ^ [_1128290, _1128292, _1128294] : [class_Fields_Ofield__inverse__zero(_1128290), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1128290), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128290), _1128292), _1128294)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128290), _1128292), hAPP(c_Groups_Ouminus__class_Ouminus(_1128290), _1128294)))], (19153 ^ _778908) ^ [_1108569, _1108571] : [class_Int_Onumber__ring(_1108569), class_Rings_Olinordered__idom(_1108569), 19160 ^ _778908 : [(19167 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108571), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108569), hAPP(c_Int_Onumber__class_Onumber__of(_1108569), _1108571)), c_Groups_Oone__class_Oone(_1108569))))], (19161 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108569), hAPP(c_Int_Onumber__class_Onumber__of(_1108569), _1108571)), c_Groups_Oone__class_Oone(_1108569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108571), c_Int_OBit1(c_Int_OPls))))]]], (8894 ^ _778908) ^ [_927301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _927301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _927301)))], (48464 ^ _778908) ^ [_1747001, _1747003, _1747005, _1747007] : [-(hAPP(hAPP(c_List_Otake(_1747001), _1747003), hAPP(hAPP(c_List_Oappend(_1747001), _1747005), _1747007)) = hAPP(hAPP(c_List_Oappend(_1747001), hAPP(hAPP(c_List_Otake(_1747001), _1747003), _1747005)), hAPP(hAPP(c_List_Otake(_1747001), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1747003), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747001)), _1747005))), _1747007)))], (6516 ^ _778908) ^ [_884413, _884415, _884417, _884419, _884421, _884423] : [c_Com_Ocom_OCond(_884413, _884415, _884417) = c_Com_Ocom_OCall(_884419, _884421, _884423)], (31554 ^ _778908) ^ [_1348368, _1348370, _1348372, _1348374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348368, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1348368), _1348370), _1348372)), _1348374)), 31557 ^ _778908 : [(31560 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348368, tc_HOL_Obool)), _1348372), _1348374)))], (31558 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1348368), _1348370), _1348374)))]]], (48979 ^ _778908) ^ [_1760682, _1760684, _1760686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760682)), _1760684)), _1760686)), -(hAPP(hAPP(c_List_Odrop(_1760682), _1760686), _1760684) = c_List_Olist_ONil(_1760682))], (43935 ^ _778908) ^ [_1636777, _1636779, _1636781] : [43938 ^ _778908 : [(43944 ^ _778908) ^ [] : [43937 ^ [_1636777, _1636779, _1636781] = 43940 ^ [_1636777, _1636779, _1636781]], (43942 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636777, _1636779)), hAPP(hAPP(c_Product__Type_OPair(_1636777, _1636779), 43936 ^ [_1636777, _1636779, _1636781]), 43940 ^ [_1636777, _1636779, _1636781])), _1636781)))], (43939 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636777, _1636779)), hAPP(hAPP(c_Product__Type_OPair(_1636777, _1636779), 43936 ^ [_1636777, _1636779, _1636781]), 43937 ^ [_1636777, _1636779, _1636781])), _1636781)))]], -(c_Relation_Osingle__valued(_1636777, _1636779, _1636781))], (44390 ^ _778908) ^ [_1646599, _1646601, _1646603] : [class_Orderings_Olinorder(_1646599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646599), _1646601)), -(hBOOL(hAPP(hAPP(c_member(_1646599), _1646603), _1646601))), -(c_Big__Operators_Olattice_OInf__fin(_1646599, c_Orderings_Oord__class_Omin(_1646599), hAPP(hAPP(c_Set_Oinsert(_1646599), _1646603), _1646601)) = hAPP(hAPP(c_Finite__Set_Ofold(_1646599, _1646599, c_Orderings_Oord__class_Omin(_1646599)), _1646603), _1646601))], (9680 ^ _778908) ^ [_941123, _941125, _941127] : [class_Groups_Ogroup__add(_941123), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941123), _941125), _941127) = c_Groups_Ozero__class_Ozero(_941123), -(hAPP(c_Groups_Ouminus__class_Ouminus(_941123), _941125) = _941127)], (44837 ^ _778908) ^ [_1657650, _1657652, _1657654, _1657656, _1657658, _1657660] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1657652, _1657654)), hAPP(hAPP(c_Product__Type_OPair(_1657652, _1657654), _1657658), _1657660)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657650, tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1657650, tc_HOL_Obool))), _1657656))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657650, tc_fun(_1657652, tc_fun(_1657654, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1657650, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool), tc_fun(_1657652, tc_fun(_1657654, tc_HOL_Obool)), _1657650), hAPP(c_COMBC(_1657652, tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool), tc_fun(_1657654, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1657654, tc_fun(tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool), tc_fun(_1657654, tc_HOL_Obool)), _1657652), c_COMBC(_1657654, tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1657654, tc_prod(_1657652, _1657654)), tc_fun(_1657654, tc_fun(tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool), tc_HOL_Obool)), _1657652), hAPP(c_COMBB(tc_prod(_1657652, _1657654), tc_fun(tc_fun(tc_prod(_1657652, _1657654), tc_HOL_Obool), tc_HOL_Obool), _1657654), c_member(tc_prod(_1657652, _1657654)))), c_Product__Type_OPair(_1657652, _1657654))))), _1657656)), _1657658), _1657660)))], (11018 ^ _778908) ^ [_963589, _963591, _963593] : [class_Orderings_Olinorder(_963589), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963589), _963591), _963593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963589), _963593), _963591)))], (36041 ^ _778908) ^ [_1446043, _1446045, _1446047] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446043), _1446045), _1446047) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446043, tc_HOL_Obool), tc_HOL_Obool)), -(_1446045 = c_Orderings_Obot__class_Obot(tc_fun(_1446043, tc_HOL_Obool)))], (22540 ^ _778908) ^ [_1169576, _1169578] : [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(_1169578))), 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)), _1169576))))), -(hAPP(c_Nat_OSuc, _1169576) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169578))], (44164 ^ _778908) ^ [_1642430, _1642432, _1642434, _1642436] : [class_Lattices_Osemilattice__sup(_1642430), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642430), _1642432)), hBOOL(hAPP(hAPP(c_member(_1642430), _1642434), _1642432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1642430), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1642430), _1642434), _1642436)), hAPP(hAPP(c_Finite__Set_Ofold(_1642430, _1642430, c_Lattices_Osemilattice__sup__class_Osup(_1642430)), _1642436), _1642432))))], (14591 ^ _778908) ^ [_1026653, _1026655, _1026657] : [_1026653 = 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), _1026653), _1026655)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026653), _1026657)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30078 ^ _778908) ^ [_1317625, _1317627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1317625, tc_HOL_Obool)), _1317627), c_Orderings_Obot__class_Obot(tc_fun(_1317625, tc_HOL_Obool))))], (35390 ^ _778908) ^ [_1430183, _1430185] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1430183), _1430185)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1430183, tc_HOL_Obool)), hAPP(c_Set_OPow(_1430183), _1430185)) = 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(_1430183), _1430185)))], (34365 ^ _778908) ^ [_1407574, _1407576, _1407578, _1407580] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407574), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407576, tc_Nat_Onat), _1407578), _1407580)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407576, _1407574), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1407574, _1407576), c_Nat_Osemiring__1__class_Oof__nat(_1407574)), _1407578)), _1407580)), class_Groups_Ocomm__monoid__mult(_1407574), class_Rings_Osemiring__1(_1407574)], (29068 ^ _778908) ^ [_1297571, _1297573, _1297575] : [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), _1297571), _1297573))), -(hBOOL(hAPP(hAPP(_1297575, _1297571), _1297573))), 29075 ^ _778908 : [(29078 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29073 ^ [_1297571, _1297573, _1297575]), 29074 ^ [_1297571, _1297573, _1297575])), -(hBOOL(hAPP(hAPP(_1297575, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29073 ^ [_1297571, _1297573, _1297575]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 29074 ^ [_1297571, _1297573, _1297575])))], (29084 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1297575, 29073 ^ [_1297571, _1297573, _1297575]), 29074 ^ [_1297571, _1297573, _1297575]))], (29076 ^ _778908) ^ [] : [-(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), 29073 ^ [_1297571, _1297573, _1297575]), 29074 ^ [_1297571, _1297573, _1297575]))))]]], (13006 ^ _778908) ^ [_998160, _998162, _998164] : [class_Rings_Olinordered__ring(_998160), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998160), c_Groups_Ozero__class_Ozero(_998160)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998160), _998162), _998162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998160), _998164), _998164)))))], (37540 ^ _778908) ^ [_1479459, _1479461, _1479463] : [class_Lattices_Olattice(_1479459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479459), _1479461)), -(_1479461 = c_Orderings_Obot__class_Obot(tc_fun(_1479459, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479459), _1479463)), -(_1479463 = c_Orderings_Obot__class_Obot(tc_fun(_1479459, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479459, tc_HOL_Obool)), _1479461), _1479463) = c_Orderings_Obot__class_Obot(tc_fun(_1479459, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1479459, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479459, tc_HOL_Obool)), _1479461), _1479463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1479459), c_Big__Operators_Olattice__class_OSup__fin(_1479459, _1479461)), c_Big__Operators_Olattice__class_OSup__fin(_1479459, _1479463)))], (1702 ^ _778908) ^ [_803057, _803059] : [-(class_Groups_Omonoid__add(_803057)), _803059 = _803057, class_Groups_Omonoid__add(_803059)], (29614 ^ _778908) ^ [_1308514, _1308516, _1308518] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308514), _1308516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308514, tc_HOL_Obool)), _1308518), _1308516)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308514), _1308518)))], (39763 ^ _778908) ^ [_1528234, _1528236, _1528238] : [c_Map_Odom(_1528234, _1528236, _1528238) = c_Orderings_Obot__class_Obot(tc_fun(_1528234, tc_HOL_Obool)), -(_1528238 = hAPP(c_COMBK(tc_Option_Ooption(_1528236), _1528234), c_Option_Ooption_ONone(_1528236)))], (3952 ^ _778908) ^ [_839890, _839892, _839894, _839896] : [-(c_New__DSequence_Oneg__single(_839896, _839892) = c_New__DSequence_Oneg__single(_839894, _839890)), _839896 = _839894, _839892 = _839890], (15774 ^ _778908) ^ [_1047748, _1047750, _1047752, _1047754, _1047756, _1047758] : [class_Rings_Oring(_1047748), 15777 ^ _778908 : [(15784 ^ _778908) ^ [] : [_1047754 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047748), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047748), _1047756), _1047750)), _1047752)), _1047758), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047748), _1047750), _1047752)), _1047754) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047748), _1047756), _1047752)), _1047758))], (15778 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047748), _1047750), _1047752)), _1047754) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047748), _1047756), _1047752)), _1047758), -(_1047754 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047748), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047748), _1047756), _1047750)), _1047752)), _1047758))]]], (32198 ^ _778908) ^ [_1363849, _1363851, _1363853] : [32200 ^ _778908 : [(32203 ^ _778908) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1363853, 32199 ^ [_1363849, _1363851, _1363853]))], (32201 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1363849), 32199 ^ [_1363849, _1363851, _1363853]), _1363851)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363849, tc_Int_Oint), _1363853), _1363851) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363849, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1363849), c_Int_Onat), _1363853)), _1363851)))], (18489 ^ _778908) ^ [_1098021, _1098023] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098021), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098021)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098023)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1098021), _1098023)))], (49849 ^ _778908) ^ [_1779676, _1779678, _1779680, _1779682] : [hAPP(hAPP(c_List_Oappend(_1779676), _1779678), hAPP(hAPP(c_List_Olist_OCons(_1779676), _1779680), c_List_Olist_ONil(_1779676))) = _1779682, 49852 ^ _778908 : [(49857 ^ _778908) ^ [] : [-(c_List_Olast(_1779676, _1779682) = _1779680)], (49855 ^ _778908) ^ [] : [-(c_List_Obutlast(_1779676, _1779682) = _1779678)], (49853 ^ _778908) ^ [] : [_1779682 = c_List_Olist_ONil(_1779676)]]], (25715 ^ _778908) ^ [_1230577, _1230579, _1230581, _1230583] : [class_Divides_Osemiring__div(_1230577), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230577), _1230579), _1230581)), 25722 ^ _778908 : [(25729 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230577), _1230579), _1230583)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230577), _1230579), c_Divides_Odiv__class_Omod(_1230577, _1230583, _1230581))))], (25723 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230577), _1230579), c_Divides_Odiv__class_Omod(_1230577, _1230583, _1230581))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230577), _1230579), _1230583)))]]], (23911 ^ _778908) ^ [_1195838, _1195840, _1195842, _1195844] : [class_Orderings_Olinorder(_1195838), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195838), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195838), _1195840), _1195842)), _1195844) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195838), _1195840), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195838), _1195842), _1195844)))], (7613 ^ _778908) ^ [_906346] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906346), hAPP(c_Nat_OSuc, _906346))))], (39476 ^ _778908) ^ [_1521443, _1521445, _1521447, _1521449, _1521451] : [hBOOL(hAPP(hAPP(c_member(_1521447), hAPP(_1521449, _1521445)), _1521451)), -(hBOOL(hAPP(hAPP(c_member(_1521443), _1521445), hAPP(c_Set_Ovimage(_1521443, _1521447, _1521449), _1521451))))], (10311 ^ _778908) ^ [_952183, _952185] : [class_Rings_Olinordered__idom(_952183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952183), _952185), c_Groups_Ozero__class_Ozero(_952183))), -(c_Groups_Osgn__class_Osgn(_952183, _952185) = hAPP(c_Groups_Ouminus__class_Ouminus(_952183), c_Groups_Oone__class_Oone(_952183)))], (47433 ^ _778908) ^ [_1722462, _1722464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1722462), _1722464)), -(c_List_Oupto(_1722464, _1722462) = c_List_Olist_ONil(tc_Int_Oint))], (15690 ^ _778908) ^ [_1046085, _1046087, _1046089] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046085), _1046087)), _1046089) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046085), _1046089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046087), _1046089)))], (27384 ^ _778908) ^ [_1263134, _1263136, _1263138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263134)), 27387 ^ _778908 : [(27388 ^ _778908) ^ [_1263268] : [27390 ^ _778908 : [(27396 ^ _778908) ^ [] : [-(_1263268 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27392 ^ [_1263134, _1263136, _1263138, _1263268]), 27389 ^ [_1263134, _1263136, _1263138, _1263268]))], (27394 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27392 ^ [_1263134, _1263136, _1263138, _1263268]), _1263136)))], (27391 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27389 ^ [_1263134, _1263136, _1263138, _1263268]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1263134))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1263268), _1263138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1263268), _1263134)), _1263138)))]]], (24877 ^ _778908) ^ [_1214789, _1214791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1214789)), hAPP(c_Code__Numeral_Onat__of, _1214791))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1214789), _1214791)))], (18735 ^ _778908) ^ [_1101712, _1101714] : [class_Int_Onumber__ring(_1101712), class_Rings_Olinordered__idom(_1101712), 18742 ^ _778908 : [(18749 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1101714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101712), c_Groups_Ozero__class_Ozero(_1101712)), hAPP(c_Int_Onumber__class_Onumber__of(_1101712), _1101714))))], (18743 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101712), c_Groups_Ozero__class_Ozero(_1101712)), hAPP(c_Int_Onumber__class_Onumber__of(_1101712), _1101714))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1101714)))]]], (46489 ^ _778908) ^ [_1696954, _1696956, _1696958] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1696954, tc_HOL_Obool)), hAPP(c_List_Oset(_1696954), c_List_Oremove1(_1696954, _1696956, _1696958))), hAPP(c_List_Oset(_1696954), _1696958))))], (49975 ^ _778908) ^ [_1782263, _1782265] : [-(hAPP(c_List_Ofilter(_1782263, _1782265), c_List_Olist_ONil(_1782263)) = c_List_Olist_ONil(_1782263))], (5208 ^ _778908) ^ [_859484, _859486, _859488, _859490, _859492, _859494] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_859494, _859490, _859486) = c_SetInterval_Oord__class_OgreaterThanLessThan(_859492, _859488, _859484)), _859494 = _859492, _859490 = _859488, _859486 = _859484], (8001 ^ _778908) ^ [_912726, _912728, _912730] : [class_Groups_Oordered__comm__monoid__add(_912726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912726), c_Groups_Ozero__class_Ozero(_912726)), _912728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912726), c_Groups_Ozero__class_Ozero(_912726)), _912730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912726), c_Groups_Ozero__class_Ozero(_912726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_912726), _912728), _912730))))], (44114 ^ _778908) ^ [_1641337, _1641339, _1641341, _1641343] : [class_Orderings_Olinorder(_1641337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641337), _1641339)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1641337, _1641337, c_Orderings_Oord__class_Omax(_1641337)), _1641341), hAPP(hAPP(c_Set_Oinsert(_1641337), _1641343), _1641339)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1641337), _1641343), hAPP(hAPP(c_Finite__Set_Ofold(_1641337, _1641337, c_Orderings_Oord__class_Omax(_1641337)), _1641341), _1641339)))], (49891 ^ _778908) ^ [_1780638, _1780640, _1780642] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780638)), hAPP(c_List_Ofilter(_1780638, _1780640), _1780642))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780638)), _1780642))))], (6897 ^ _778908) ^ [_892654, _892656, _892658, _892660, _892662] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_892654, _892656, _892658)), _892660), _892662)), 6901 ^ _778908 : [(6904 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_892658), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892660), c_Com_Ovname_OLoc(_892654)), hAPP(_892656, _892660))), 6900 ^ [_892654, _892656, _892658, _892660, _892662])))], (6902 ^ _778908) ^ [] : [-(_892662 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6900 ^ [_892654, _892656, _892658, _892660, _892662]), c_Com_Ovname_OLoc(_892654)), hAPP(hAPP(c_Natural_Ogetlocs, _892660), _892654)))]]], (43606 ^ _778908) ^ [_1628340, _1628342, _1628344, _1628346] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628340, _1628340)), hAPP(hAPP(c_Product__Type_OPair(_1628340, _1628340), _1628342), _1628344)), hAPP(c_Relation_Oconverse(_1628340, _1628340), c_Transitive__Closure_Otrancl(_1628340, _1628346)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628340, _1628340)), hAPP(hAPP(c_Product__Type_OPair(_1628340, _1628340), _1628342), _1628344)), c_Transitive__Closure_Otrancl(_1628340, hAPP(c_Relation_Oconverse(_1628340, _1628340), _1628346)))))], (48281 ^ _778908) ^ [_1742538, _1742540, _1742542] : [_1742542 = c_List_Olist_ONil(_1742538), -(hAPP(hAPP(c_List_Oappend(_1742538), _1742540), _1742542) = _1742540)], (46349 ^ _778908) ^ [] : [46351 ^ _778908 : [(46354 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 46350 ^ []))], (46352 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 46350 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (44334 ^ _778908) ^ [_1645743, _1645745, _1645747] : [class_Lattices_Olattice(_1645743), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645743), _1645745)), -(hBOOL(hAPP(hAPP(c_member(_1645743), _1645747), _1645745))), -(c_Big__Operators_Olattice__class_OSup__fin(_1645743, hAPP(hAPP(c_Set_Oinsert(_1645743), _1645747), _1645745)) = hAPP(hAPP(c_Finite__Set_Ofold(_1645743, _1645743, c_Lattices_Osemilattice__sup__class_Osup(_1645743)), _1645747), _1645745))], (13502 ^ _778908) ^ [_1006497, _1006499, _1006501, _1006503, _1006505, _1006507] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006497), _1006499)), _1006501) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006503), _1006505)), _1006507), 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), _1006503), _1006505)), _1006507))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006507), _1006503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006503), _1006497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006499), _1006505)))], (45129 ^ _778908) ^ [_1665689, _1665691, _1665693] : [c_Equiv__Relations_Oequiv(_1665689, _1665691, _1665693), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665689, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1665689), _1665691), _1665693)) = _1665691)], (7524 ^ _778908) ^ [_904903, _904905, _904907, _904909] : [class_Rings_Osemiring__1(_904903), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_904903, _904905, hAPP(c_Nat_OSuc, _904907), _904909) = c_Nat_Osemiring__1__class_Oof__nat__aux(_904903, _904905, _904907, hAPP(_904905, _904909)))], (28124 ^ _778908) ^ [_1277798, _1277800, _1277802, _1277804] : [28138 ^ _778908 : [(28141 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1277804, 28137 ^ [_1277798, _1277800, _1277802, _1277804])))], (28139 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277798), 28137 ^ [_1277798, _1277800, _1277802, _1277804]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277798, tc_HOL_Obool)), _1277800), _1277802))))]], 28125 ^ _778908 : [(28132 ^ _778908) ^ [_1278007] : [hBOOL(hAPP(hAPP(c_member(_1277798), _1278007), _1277802)), hBOOL(hAPP(_1277804, _1278007))], (28126 ^ _778908) ^ [_1277911] : [hBOOL(hAPP(hAPP(c_member(_1277798), _1277911), _1277800)), hBOOL(hAPP(_1277804, _1277911))]]], (48673 ^ _778908) ^ [_1752138, _1752140, _1752142, _1752144] : [hBOOL(hAPP(hAPP(c_member(_1752138), _1752140), c_Wellfounded_Oacc(_1752138, _1752142))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752138)), _1752144), c_Wellfounded_Oacc(tc_List_Olist(_1752138), c_List_Olistrel1(_1752138, _1752142)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1752138)), hAPP(hAPP(c_List_Olist_OCons(_1752138), _1752140), _1752144)), c_Wellfounded_Oacc(tc_List_Olist(_1752138), c_List_Olistrel1(_1752138, _1752142)))))], (48036 ^ _778908) ^ [_1736730, _1736732, _1736734, _1736736] : [-(hAPP(hAPP(c_List_Onth(_1736730), hAPP(hAPP(c_List_Oappend(_1736730), _1736732), hAPP(hAPP(c_List_Olist_OCons(_1736730), _1736734), _1736736))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736730)), _1736732)) = _1736734)], (43869 ^ _778908) ^ [_1635147, _1635149, _1635151, _1635153, _1635155] : [c_Relation_Osingle__valued(_1635147, _1635149, hAPP(c_Relation_Oconverse(_1635149, _1635147), _1635151)), -(hAPP(c_Relation_OImage(_1635149, _1635147, _1635151), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635149, tc_HOL_Obool)), _1635153), _1635155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635147, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1635149, _1635147, _1635151), _1635153)), hAPP(c_Relation_OImage(_1635149, _1635147, _1635151), _1635155)))], (7414 ^ _778908) ^ [_902827, _902829, _902831] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_902827, _902829, _902831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_902831)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19245 ^ _778908) ^ [_1110229, _1110231] : [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), _1110229))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1110231)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1110229))) = 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), _1110231), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1110229)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15564 ^ _778908) ^ [_1043843] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1043843) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41424 ^ _778908) ^ [_1568909] : [-(c_Int_Oint__ge__less__than(_1568909) = 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), _1568909)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (18589 ^ _778908) ^ [_1099395] : [-(c_Int_Opred(_1099395) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1099395), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19007 ^ _778908) ^ [_1106341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1106341))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1106341)))], (31042 ^ _778908) ^ [_1336127, _1336129] : [hBOOL(hAPP(hAPP(c_member(_1336127), _1336129), c_Orderings_Obot__class_Obot(tc_fun(_1336127, tc_HOL_Obool))))], (25143 ^ _778908) ^ [_1220929, _1220931] : [-(c_Divides_Odivmod__nat(_1220929, _1220931) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1220929, _1220931)))], (24851 ^ _778908) ^ [_1214319] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1214319)) = _1214319)], (23557 ^ _778908) ^ [_1189253, _1189255, _1189257, _1189259] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189253, _1189255), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189257), _1189259))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1189253), _1189255), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1189259), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1189257)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1189257)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1189259), 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), _1189255), _1189259))))))], (28149 ^ _778908) ^ [_1278407, _1278409, _1278411] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278407, tc_HOL_Obool)), _1278409), _1278411) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278407, tc_HOL_Obool)), _1278411), _1278409))], (8534 ^ _778908) ^ [_922008, _922010, _922012, _922014] : [class_Orderings_Oorder(_922008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922008), _922010), _922012)), _922010 = _922014, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922008), _922014), _922012)))], (19503 ^ _778908) ^ [_1114823, _1114825] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1114823)), c_Int_OBit0(_1114825)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1114823), _1114825)))], (49065 ^ _778908) ^ [_1762912, _1762914, _1762916, _1762918] : [-(hAPP(c_List_Orotate1(_1762912), c_List_Olist_ONil(_1762912)) = c_List_Olist_ONil(_1762912))], (9802 ^ _778908) ^ [_943213, _943215, _943217, _943219] : [class_Rings_Olinordered__ring__strict(_943213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943213), c_Groups_Ozero__class_Ozero(_943213)), _943215)), 9809 ^ _778908 : [(9816 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943213), _943217), _943219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943213), _943215), _943217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943213), _943215), _943219))))], (9810 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943213), _943215), _943217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943213), _943215), _943219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943213), _943217), _943219)))]]], (22342 ^ _778908) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (17407 ^ _778908) ^ [_1079694] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079694)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1079694)))], (42221 ^ _778908) ^ [_1594012, _1594014, _1594016, _1594018] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1594012, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1594014, _1594012), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594014, _1594012), tc_HOL_Obool)), _1594016), _1594018))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1594012, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1594014, _1594012), _1594016)), hAPP(c_Relation_ORange(_1594014, _1594012), _1594018)))))], (31504 ^ _778908) ^ [_1347309, _1347311, _1347313, _1347315, _1347317] : [-(hBOOL(hAPP(hAPP(c_member(_1347309), _1347311), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1347313, tc_fun(_1347309, tc_HOL_Obool)), _1347315), _1347317)))), 31505 ^ _778908 : [(31506 ^ _778908) ^ [_1347391] : [hBOOL(hAPP(hAPP(c_member(_1347313), _1347391), _1347315)), hBOOL(hAPP(hAPP(c_member(_1347309), _1347311), hAPP(_1347317, _1347391)))]]], (30298 ^ _778908) ^ [_1321768, _1321770, _1321772] : [class_Orderings_Oorder(_1321768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321768), _1321770), _1321772)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321768, _1321772), _1321770) = c_Orderings_Obot__class_Obot(tc_fun(_1321768, tc_HOL_Obool)))], (43049 ^ _778908) ^ [_1614064, _1614066] : [-(hAPP(c_Relation_ORange(_1614064, _1614064), c_Transitive__Closure_Otrancl(_1614064, _1614066)) = hAPP(c_Relation_ORange(_1614064, _1614064), _1614066))], (29877 ^ _778908) ^ [_1313627, _1313629, _1313631] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313627), _1313629))), 29880 ^ _778908 : [(29887 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313631), _1313629))), -(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)), _1313627)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1313631), _1313629)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29881 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313631), _1313629)), -(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)), _1313627)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1313631), _1313629)) = 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))))]]], (27938 ^ _778908) ^ [_1274167, _1274169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1274167), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1274169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1274169), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1274167))))), -(_1274167 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1274169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1274169), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1274167))))], (48985 ^ _778908) ^ [_1760805, _1760807, _1760809, _1760811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1760805), _1760807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1760809, tc_HOL_Obool)), hAPP(c_List_Oset(_1760809), hAPP(hAPP(c_List_Odrop(_1760809), _1760807), _1760811))), hAPP(c_List_Oset(_1760809), hAPP(hAPP(c_List_Odrop(_1760809), _1760805), _1760811)))))], (13937 ^ _778908) ^ [_1014432, _1014434, _1014436] : [class_Divides_Osemiring__div(_1014432), -(c_Divides_Odiv__class_Omod(_1014432, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014432), _1014434), _1014436), _1014434) = c_Divides_Odiv__class_Omod(_1014432, _1014436, _1014434))], (20143 ^ _778908) ^ [_1126347, _1126349] : [class_Fields_Olinordered__field__inverse__zero(_1126347), class_Int_Onumber__ring(_1126347), 20150 ^ _778908 : [(20157 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126347), c_Groups_Ozero__class_Ozero(_1126347)), _1126349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126347), c_Groups_Ozero__class_Ozero(_1126347)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126347), _1126349), hAPP(c_Int_Onumber__class_Onumber__of(_1126347), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20151 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126347), c_Groups_Ozero__class_Ozero(_1126347)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126347), _1126349), hAPP(c_Int_Onumber__class_Onumber__of(_1126347), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126347), c_Groups_Ozero__class_Ozero(_1126347)), _1126349)))]]], (49658 ^ _778908) ^ [_1775597, _1775599] : [-(_1775597 = c_List_Olist_ONil(_1775599)), -(hBOOL(hAPP(hAPP(c_member(_1775599), c_List_Olast(_1775599, _1775597)), hAPP(c_List_Oset(_1775599), _1775597))))], (12554 ^ _778908) ^ [_989988] : [12555 ^ _778908 : [(12556 ^ _778908) ^ [_990045] : [hBOOL(hAPP(_989988, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _990045)))]], 12558 ^ _778908 : [(12561 ^ _778908) ^ [] : [-(hBOOL(hAPP(_989988, 12557 ^ [_989988])))], (12559 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12557 ^ [_989988])))]]], (17163 ^ _778908) ^ [_1075111, _1075113, _1075115] : [class_Groups_Oordered__ab__group__add__abs(_1075111), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075111), hAPP(c_Groups_Oabs__class_Oabs(_1075111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075111), _1075113), _1075115))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075111), hAPP(c_Groups_Oabs__class_Oabs(_1075111), _1075113)), hAPP(c_Groups_Oabs__class_Oabs(_1075111), _1075115)))))], (10359 ^ _778908) ^ [_952884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952884)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _952884)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _952884)))], (18505 ^ _778908) ^ [_1098192] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1098192) = _1098192)], (34658 ^ _778908) ^ [_1413169, _1413171, _1413173, _1413175, _1413177] : [class_Groups_Ocomm__monoid__mult(_1413169), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413171), _1413173)), 34665 ^ _778908 : [(34672 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413171), _1413175), _1413173))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413171, _1413169), hAPP(hAPP(c_COMBC(_1413171, _1413169, _1413169), hAPP(hAPP(c_COMBS(_1413171, _1413169, tc_fun(_1413169, _1413169)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413169, tc_fun(_1413169, _1413169)), _1413171), c_If(_1413169)), hAPP(hAPP(c_COMBC(_1413171, _1413171, tc_HOL_Obool), c_fequal), _1413175))), _1413177)), c_Groups_Oone__class_Oone(_1413169))), _1413173) = c_Groups_Oone__class_Oone(_1413169))], (34666 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1413171), _1413175), _1413173)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413171, _1413169), hAPP(hAPP(c_COMBC(_1413171, _1413169, _1413169), hAPP(hAPP(c_COMBS(_1413171, _1413169, tc_fun(_1413169, _1413169)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413169, tc_fun(_1413169, _1413169)), _1413171), c_If(_1413169)), hAPP(hAPP(c_COMBC(_1413171, _1413171, tc_HOL_Obool), c_fequal), _1413175))), _1413177)), c_Groups_Oone__class_Oone(_1413169))), _1413173) = hAPP(_1413177, _1413175))]]], (32054 ^ _778908) ^ [_1360496, _1360498, _1360500, _1360502] : [hBOOL(hAPP(hAPP(c_member(_1360496), _1360498), _1360500)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360496, tc_Nat_Onat), _1360502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360496, tc_HOL_Obool)), _1360500), hAPP(hAPP(c_Set_Oinsert(_1360496), _1360498), c_Orderings_Obot__class_Obot(tc_fun(_1360496, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360496, tc_Nat_Onat), _1360502), _1360500)), hAPP(_1360502, _1360498)))], (13700 ^ _778908) ^ [_1009859, _1009861, _1009863] : [class_Lattices_Oboolean__algebra(_1009859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009859), _1009861), _1009863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009859), hAPP(c_Groups_Ouminus__class_Ouminus(_1009859), _1009863)), hAPP(c_Groups_Ouminus__class_Ouminus(_1009859), _1009861))))], (47744 ^ _778908) ^ [_1729690, _1729692, _1729694] : [hBOOL(hAPP(hAPP(c_member(_1729690), _1729692), hAPP(c_List_Oset(_1729690), _1729694))), 47748 ^ _778908 : [(47751 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1729690), _1729694), 47747 ^ [_1729690, _1729692, _1729694]) = _1729692)], (47749 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47747 ^ [_1729690, _1729692, _1729694]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729690)), _1729694))))]]], (50971 ^ _778908) ^ [_1803486, _1803488, _1803490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1803486), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803488)), _1803490))), -(hAPP(hAPP(c_List_Onth(_1803488), hAPP(c_List_Orev(_1803488), _1803490)), _1803486) = hAPP(hAPP(c_List_Onth(_1803488), _1803490), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803488)), _1803490)), hAPP(c_Nat_OSuc, _1803486))))], (18855 ^ _778908) ^ [_1103796, _1103798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1103796)), c_Int_OBit1(_1103798))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103796), _1103798)))], (51455 ^ _778908) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (31748 ^ _778908) ^ [_1351897, _1351899, _1351901, _1351903, _1351905, _1351907] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1351897, tc_fun(_1351899, tc_fun(_1351901, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1351897, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool), tc_fun(_1351899, tc_fun(_1351901, tc_HOL_Obool)), _1351897), hAPP(c_COMBC(_1351899, tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool), tc_fun(_1351901, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1351901, tc_fun(tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool), tc_fun(_1351901, tc_HOL_Obool)), _1351899), c_COMBC(_1351901, tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1351901, tc_prod(_1351899, _1351901)), tc_fun(_1351901, tc_fun(tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool), tc_HOL_Obool)), _1351899), hAPP(c_COMBB(tc_prod(_1351899, _1351901), tc_fun(tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool), tc_HOL_Obool), _1351901), c_member(tc_prod(_1351899, _1351901)))), c_Product__Type_OPair(_1351899, _1351901))))), _1351903)), _1351905), _1351907)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1351899, _1351901)), hAPP(hAPP(c_Product__Type_OPair(_1351899, _1351901), _1351905), _1351907)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1351897, tc_fun(tc_prod(_1351899, _1351901), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1351897, tc_HOL_Obool))), _1351903))))], (37985 ^ _778908) ^ [] : [-(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))], (40254 ^ _778908) ^ [_1541061, _1541063, _1541065, _1541067] : [-(_1541061 = c_Orderings_Obot__class_Obot(tc_fun(_1541063, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1541065, _1541063), _1541065, c_Product__Type_Ofst(_1541065, _1541063)), hAPP(hAPP(c_Product__Type_OSigma(_1541065, _1541063), _1541067), hAPP(c_COMBK(tc_fun(_1541063, tc_HOL_Obool), _1541065), _1541061))) = _1541067)], (2768 ^ _778908) ^ [_820874, _820876] : [_820876 = _820874, -(c_Lazy__Sequence_Ohit__bound(_820876) = c_Lazy__Sequence_Ohit__bound(_820874))], (51439 ^ _778908) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (50445 ^ _778908) ^ [_1792086, _1792088] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1792086, _1792088)))], (39374 ^ _778908) ^ [_1519154] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1519154))], (31726 ^ _778908) ^ [_1351513, _1351515, _1351517, _1351519, _1351521] : [class_Complete__Lattice_Ocomplete__lattice(_1351513), hBOOL(hAPP(hAPP(c_member(_1351515), _1351517), _1351519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351513), hAPP(_1351521, _1351517)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1351515, _1351513), _1351519), _1351521))))], (35231 ^ _778908) ^ [_1426802] : [-(c_Relation_OId__on(_1426802, c_Orderings_Obot__class_Obot(tc_fun(_1426802, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1426802, _1426802), tc_HOL_Obool)))], (51313 ^ _778908) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (43165 ^ _778908) ^ [_1617730, _1617732] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1617730, _1617730), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1617730, _1617732)), c_Relation_OId(_1617730)) = c_Transitive__Closure_Ortrancl(_1617730, _1617732))], (45925 ^ _778908) ^ [_1683347, _1683349, _1683351, _1683353, _1683355] : [-(hAPP(c_Map_Omap__add(_1683347, _1683349, _1683351, _1683353), _1683355) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1683349), _1683349, hAPP(_1683351, _1683355), c_Option_Ooption_OSome(_1683349)), hAPP(_1683353, _1683355)))], (49247 ^ _778908) ^ [_1766563, _1766565, _1766567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766563)), _1766565)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1766563, _1766567), _1766565) = _1766565)], (47527 ^ _778908) ^ [_1724216, _1724218] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1724216), _1724218))), -(c_List_Oupto(_1724216, _1724218) = c_List_Olist_ONil(tc_Int_Oint))], (30842 ^ _778908) ^ [_1332111, _1332113, _1332115, _1332117, _1332119, _1332121, _1332123, _1332125] : [c_Finite__Set_Ofolding__image__simple(_1332111, _1332113, _1332115, _1332117, _1332119, _1332121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332113), _1332123)), -(hAPP(_1332121, hAPP(hAPP(c_Set_Oinsert(_1332113), _1332125), _1332123)) = hAPP(hAPP(_1332115, hAPP(_1332119, _1332125)), hAPP(_1332121, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332113, tc_HOL_Obool)), _1332123), hAPP(hAPP(c_Set_Oinsert(_1332113), _1332125), c_Orderings_Obot__class_Obot(tc_fun(_1332113, tc_HOL_Obool)))))))], (35690 ^ _778908) ^ [_1436764, _1436766, _1436768, _1436770, _1436772, _1436774] : [-(hAPP(c_Relation_OImage(_1436764, _1436766, _1436768), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1436770, tc_fun(_1436764, tc_HOL_Obool)), _1436772), _1436774)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1436770, tc_fun(_1436766, tc_HOL_Obool)), _1436772), hAPP(hAPP(c_COMBB(tc_fun(_1436764, tc_HOL_Obool), tc_fun(_1436766, tc_HOL_Obool), _1436770), c_Relation_OImage(_1436764, _1436766, _1436768)), _1436774)))], (47551 ^ _778908) ^ [_1724625, _1724627] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724625)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724627)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724625), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724627)) = c_List_Olist_ONil(tc_Int_Oint))], (24259 ^ _778908) ^ [_1202754, _1202756, _1202758, _1202760, _1202762] : [-(c_Product__Type_Oprod_Oprod__size(_1202754, _1202756, _1202758, _1202760, _1202762) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1202758, hAPP(c_Product__Type_Ofst(_1202754, _1202756), _1202762))), hAPP(_1202760, hAPP(c_Product__Type_Osnd(_1202754, _1202756), _1202762)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50443 ^ _778908) ^ [_1792058, _1792060] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1792058, _1792060)))], (37210 ^ _778908) ^ [_1472045, _1472047, _1472049, _1472051] : [class_Orderings_Oorder(_1472045), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472045, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1472045, _1472047, _1472049)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1472045, _1472049, _1472051)) = c_Orderings_Obot__class_Obot(tc_fun(_1472045, tc_HOL_Obool)))], (50861 ^ _778908) ^ [_1801042, _1801044] : [_1801044 = c_List_Olist_ONil(_1801042), -(c_List_Olist_ONil(_1801042) = hAPP(c_List_Orev(_1801042), _1801044))], (51715 ^ _778908) ^ [_1814281, _1814283] : [hBOOL(_1814281), -(hBOOL(hAPP(hAPP(c_fimplies, _1814283), _1814281)))], (18549 ^ _778908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (7891 ^ _778908) ^ [_910744, _910746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910744), _910746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _910744)), hAPP(c_Nat_OSuc, _910746))))], (44023 ^ _778908) ^ [_1639311, _1639313, _1639315, _1639317] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1639311, _1639311)), hAPP(hAPP(c_Product__Type_OPair(_1639311, _1639311), _1639313), _1639315)), c_Transitive__Closure_Otrancl(_1639311, _1639317))), 44027 ^ _778908 : [(44030 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639311, _1639311)), hAPP(hAPP(c_Product__Type_OPair(_1639311, _1639311), 44026 ^ [_1639311, _1639313, _1639315, _1639317]), _1639315)), _1639317)))], (44028 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639311, _1639311)), hAPP(hAPP(c_Product__Type_OPair(_1639311, _1639311), _1639313), 44026 ^ [_1639311, _1639313, _1639315, _1639317])), c_Transitive__Closure_Ortrancl(_1639311, _1639317))))]]], (39376 ^ _778908) ^ [_1519179, _1519181] : [-(c_Fun_Oinj__on(_1519179, tc_Option_Ooption(_1519179), c_Option_Ooption_OSome(_1519179), _1519181))], (22281 ^ _778908) ^ [_1164992, _1164994, _1164996] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1164992, _1164994, _1164996, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1164994)], (36780 ^ _778908) ^ [_1461961, _1461963, _1461965, _1461967] : [class_Lattices_Olattice(_1461961), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461961), _1461963), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461961), _1461965), _1461967)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461961), _1461965), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461961), _1461963), _1461967)))], (50955 ^ _778908) ^ [_1802958, _1802960] : [-(_1802958 = c_List_Olist_ONil(_1802960)), -(c_List_Olast(_1802960, hAPP(c_List_Orev(_1802960), _1802958)) = hAPP(c_List_Ohd(_1802960), _1802958))], (1802 ^ _778908) ^ [_804307, _804309] : [-(class_Int_Onumber(_804307)), _804309 = _804307, class_Int_Onumber(_804309)], (20319 ^ _778908) ^ [_1129657, _1129659, _1129661] : [class_Fields_Olinordered__field__inverse__zero(_1129657), 20322 ^ _778908 : [(20337 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), c_Groups_Ozero__class_Ozero(_1129657)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129657), _1129659), _1129661)))), 20338 ^ _778908 : [(20345 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), _1129659), c_Groups_Ozero__class_Ozero(_1129657))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), _1129661), c_Groups_Ozero__class_Ozero(_1129657)))], (20339 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), c_Groups_Ozero__class_Ozero(_1129657)), _1129659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), c_Groups_Ozero__class_Ozero(_1129657)), _1129661))]]], (20323 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), c_Groups_Ozero__class_Ozero(_1129657)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129657), _1129659), _1129661))), 20328 ^ _778908 : [(20331 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), c_Groups_Ozero__class_Ozero(_1129657)), _1129661)))], (20329 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), c_Groups_Ozero__class_Ozero(_1129657)), _1129659)))]], 20332 ^ _778908 : [(20335 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), _1129661), c_Groups_Ozero__class_Ozero(_1129657))))], (20333 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129657), _1129659), c_Groups_Ozero__class_Ozero(_1129657))))]]]]], (37372 ^ _778908) ^ [_1475877, _1475879] : [class_Orderings_Oorder(_1475877), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475877, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1475877), _1475879)), hAPP(c_SetInterval_Oord__class_OatLeast(_1475877), _1475879)) = hAPP(hAPP(c_Set_Oinsert(_1475877), _1475879), c_Orderings_Obot__class_Obot(tc_fun(_1475877, tc_HOL_Obool))))], (1782 ^ _778908) ^ [_804057, _804059] : [-(class_Power_Opower(_804057)), _804059 = _804057, class_Power_Opower(_804059)], (15904 ^ _778908) ^ [_1050376, _1050378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050376), _1050378))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050378), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050376), _1050378)) = _1050376)], (46569 ^ _778908) ^ [_1698797, _1698799, _1698801, _1698803, _1698805, _1698807] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1698797, _1698799)), hAPP(hAPP(c_Product__Type_OPair(_1698797, _1698799), _1698801), _1698803)), hAPP(c_List_Oset(tc_prod(_1698797, _1698799)), hAPP(hAPP(c_List_Ozip(_1698797, _1698799), _1698805), _1698807)))), 46572 ^ _778908 : [(46575 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1698799), _1698803), hAPP(c_List_Oset(_1698799), _1698807))))], (46573 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1698797), _1698801), hAPP(c_List_Oset(_1698797), _1698805))))]]], (35306 ^ _778908) ^ [_1428379, _1428381, _1428383, _1428385, _1428387] : [class_Groups_Ocomm__monoid__mult(_1428379), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428381), _1428383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428381, tc_HOL_Obool)), _1428385), _1428383)), 35320 ^ _778908 : [(35323 ^ _778908) ^ [] : [hAPP(_1428387, 35319 ^ [_1428379, _1428381, _1428383, _1428385, _1428387]) = c_Groups_Oone__class_Oone(_1428379)], (35321 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1428381), 35319 ^ [_1428379, _1428381, _1428383, _1428385, _1428387]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428381, tc_HOL_Obool)), _1428383), _1428385))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1428381, _1428379), _1428387), _1428385) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1428381, _1428379), _1428387), _1428383))], (27791 ^ _778908) ^ [_1271697, _1271699, _1271701, _1271703] : [class_Rings_Osemiring__1(_1271697), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1271699, _1271697), hAPP(c_COMBK(_1271697, _1271699), _1271701)), _1271703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271697), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1271697), hAPP(c_Finite__Set_Ocard(_1271699), _1271703))), _1271701))], (6845 ^ _778908) ^ [_891386, _891388] : [hBOOL(hAPP(c_Com_OWT, _891388)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_891386, _891388))))], (13174 ^ _778908) ^ [_1001003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001003)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1001003)) = _1001003)], (15622 ^ _778908) ^ [_1044859, _1044861, _1044863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044859), _1044861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044859), _1044863)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044861), _1044863))))], (44747 ^ _778908) ^ [_1654752, _1654754, _1654756, _1654758, _1654760, _1654762] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654752, tc_fun(_1654754, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1654756, _1654752, _1654758), _1654760)), _1654762) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654756, tc_fun(_1654754, tc_HOL_Obool)), _1654760), hAPP(hAPP(c_COMBB(_1654752, tc_fun(_1654754, tc_HOL_Obool), _1654756), _1654762), _1654758)))], (19663 ^ _778908) ^ [_1117625, _1117627] : [class_Int_Onumber__ring(_1117625), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117625), c_Groups_Oone__class_Oone(_1117625)), c_Groups_Oone__class_Oone(_1117625))), hAPP(c_Int_Onumber__class_Onumber__of(_1117625), _1117627)) = hAPP(c_Int_Onumber__class_Onumber__of(_1117625), c_Int_OBit0(_1117627)))], (28830 ^ _778908) ^ [_1291681] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1291681)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1291681))], (35249 ^ _778908) ^ [_1427203, _1427205, _1427207, _1427209] : [_1427203 = _1427205, hBOOL(hAPP(hAPP(c_member(_1427207), _1427203), _1427209)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1427207, _1427207)), hAPP(hAPP(c_Product__Type_OPair(_1427207, _1427207), _1427203), _1427205)), c_Relation_OId__on(_1427207, _1427209))))], (12029 ^ _778908) ^ [_980646, _980648, _980650, _980652] : [class_Rings_Oordered__ring(_980646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980646), _980648), _980650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980646), _980652), c_Groups_Ozero__class_Ozero(_980646))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980646), _980650), _980652)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980646), _980648), _980652))))], (7206 ^ _778908) ^ [_899482, _899484, _899486] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899482), _899484) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899482), _899486), -(_899484 = _899486)], (41888 ^ _778908) ^ [_1586857, _1586859] : [c_Wellfounded_Owf(_1586857, _1586859), -(c_Wellfounded_Owf(_1586857, hAPP(hAPP(c_Relation_Orel__comp(_1586857, _1586857, _1586857), _1586859), _1586859)))], (29223 ^ _778908) ^ [_1301075, _1301077] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1301075, _1301077))))], (48093 ^ _778908) ^ [_1738214, _1738216, _1738218, _1738220, _1738222] : [-(hAPP(hAPP(c_List_Olist_OCons(_1738214), _1738216), _1738218) = hAPP(hAPP(c_List_Oappend(_1738214), _1738220), _1738222)), 48094 ^ _778908 : [(48101 ^ _778908) ^ [_1738397] : [hAPP(hAPP(c_List_Olist_OCons(_1738214), _1738216), _1738397) = _1738220, _1738218 = hAPP(hAPP(c_List_Oappend(_1738214), _1738397), _1738222)], (48095 ^ _778908) ^ [] : [_1738220 = c_List_Olist_ONil(_1738214), hAPP(hAPP(c_List_Olist_OCons(_1738214), _1738216), _1738218) = _1738222]]], (48747 ^ _778908) ^ [_1754409, _1754411, _1754413, _1754415] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754409), tc_List_Olist(_1754409))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754409), tc_List_Olist(_1754409)), _1754411), _1754413)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1754409), tc_List_Olist(_1754409)), c_List_Olistrel1(_1754409, _1754415)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754409), tc_List_Olist(_1754409))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754409), tc_List_Olist(_1754409)), _1754411), _1754413)), c_List_Olistrel1(_1754409, hAPP(c_Relation_Oconverse(_1754409, _1754409), _1754415)))))], (38626 ^ _778908) ^ [_1503255, _1503257, _1503259, _1503261] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503255), hAPP(c_Set_Oimage(_1503257, _1503255, _1503259), _1503261))), c_Fun_Oinj__on(_1503257, _1503255, _1503259, _1503261), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1503257), _1503261)))], (37440 ^ _778908) ^ [_1477266, _1477268, _1477270, _1477272, _1477274] : [class_Groups_Ocomm__monoid__add(_1477266), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477268), _1477270)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477268), _1477272)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1477268, tc_HOL_Obool)), _1477270), _1477272) = c_Orderings_Obot__class_Obot(tc_fun(_1477268, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477268, _1477266), _1477274), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477268, tc_HOL_Obool)), _1477270), _1477272)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1477266), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477268, _1477266), _1477274), _1477270)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477268, _1477266), _1477274), _1477272)))], (43911 ^ _778908) ^ [_1636223, _1636225] : [-(c_Relation_Osingle__valued(_1636223, _1636223, c_Relation_OId__on(_1636223, _1636225)))], (51585 ^ _778908) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (6258 ^ _778908) ^ [_879749, _879751, _879753, _879755] : [-(c_Com_Ocom_OSemi(_879749, _879751) = c_Com_Ocom_OSemi(_879753, _879755)), _879749 = _879753, _879751 = _879755], (26463 ^ _778908) ^ [_1244967, _1244969, _1244971] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244967), _1244969)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244967), _1244971))), -(_1244967 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244969), _1244971)))], (15260 ^ _778908) ^ [_1038307, _1038309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1038307)), -(c_SMT_Oz3div(_1038309, _1038307) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038309), _1038307))], (8851 ^ _778908) ^ [_926518, _926520, _926522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _926518), _926520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _926522)), -(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), _926522)), _926518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926522)), _926520))))], (8966 ^ _778908) ^ [_928724, _928726, _928728] : [class_Rings_Oring(_928724), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928724), hAPP(c_Groups_Ouminus__class_Ouminus(_928724), _928726)), _928728) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928724), _928726), hAPP(c_Groups_Ouminus__class_Ouminus(_928724), _928728)))], (26169 ^ _778908) ^ [_1239593, _1239595] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239593)), _1239595)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239593), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1239595)))))], (33329 ^ _778908) ^ [_1387000, _1387002, _1387004, _1387006, _1387008, _1387010] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_1387000, _1387002, _1387004, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1387000), _1387006), _1387008), _1387010)) = hAPP(hAPP(hAPP(_1387004, _1387006), _1387008), _1387010))], (13162 ^ _778908) ^ [_1000839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1000839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000839)))], (18595 ^ _778908) ^ [_1099491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099491), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099491)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5294 ^ _778908) ^ [_860785, _860787, _860789, _860791] : [-(c_Product__Type_Osnd(_860791, _860787) = c_Product__Type_Osnd(_860789, _860785)), _860791 = _860789, _860787 = _860785], (42219 ^ _778908) ^ [_1593941, _1593943, _1593945, _1593947, _1593949] : [-(hAPP(c_Relation_ORange(_1593941, _1593943), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593941, _1593943)), hAPP(hAPP(c_Product__Type_OPair(_1593941, _1593943), _1593945), _1593947)), _1593949)) = hAPP(hAPP(c_Set_Oinsert(_1593943), _1593947), hAPP(c_Relation_ORange(_1593941, _1593943), _1593949)))], (6168 ^ _778908) ^ [_877956, _877958, _877960, _877962, _877964] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_877956, _877958, _877960)), _877962), _877964)), 6173 ^ _778908 : [(6176 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877958), _877962), _877964)))], (6174 ^ _778908) ^ [] : [-(hBOOL(hAPP(_877956, _877962)))]], 6177 ^ _778908 : [(6180 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877960), _877962), _877964)))], (6178 ^ _778908) ^ [] : [hBOOL(hAPP(_877956, _877962))]]], (45982 ^ _778908) ^ [_1684999, _1685001, _1685003] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1684999), _1685001))), -(c_Smallcheck_Osmall_H(_1685003, _1684999, _1685001) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1685003, _1684999, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1685001), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1685003, _1685001)))], (11140 ^ _778908) ^ [_965311, _965313, _965315] : [class_Orderings_Oorder(_965311), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965311), _965313), _965315)), -(_965313 = _965315), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965311), _965313), _965315)))], (48925 ^ _778908) ^ [_1759587, _1759589] : [-(hAPP(c_List_Oset(_1759587), hAPP(c_List_Orotate1(_1759587), _1759589)) = hAPP(c_List_Oset(_1759587), _1759589))], (800 ^ _778908) ^ [_791200, _791202, _791204, _791206, _791208, _791210] : [-(c_Relation_Osingle__valued(_791208, _791204, _791200)), c_Relation_Osingle__valued(_791210, _791206, _791202), _791210 = _791208, _791206 = _791204, _791202 = _791200], (31355 ^ _778908) ^ [_1344579, _1344581, _1344583] : [hBOOL(hAPP(hAPP(c_member(_1344579), _1344581), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1344579, tc_HOL_Obool)), _1344583))), hBOOL(hAPP(hAPP(c_member(_1344579), _1344581), _1344583))], (7530 ^ _778908) ^ [_905014, _905016, _905018] : [class_Rings_Osemiring__1(_905014), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_905014, _905016, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _905018) = _905018)], (37138 ^ _778908) ^ [_1470385, _1470387, _1470389, _1470391] : [class_Orderings_Oorder(_1470385), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470385, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1470385, _1470387, _1470389)), c_SetInterval_Oord__class_OatLeastAtMost(_1470385, _1470389, _1470391)) = c_Orderings_Obot__class_Obot(tc_fun(_1470385, tc_HOL_Obool)))], (8650 ^ _778908) ^ [_923613, _923615, _923617] : [class_Orderings_Olinorder(_923613), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923613), _923615), _923617))), -(_923615 = _923617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923613), _923617), _923615)))], (43139 ^ _778908) ^ [_1616846, _1616848, _1616850, _1616852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616846, _1616846)), hAPP(hAPP(c_Product__Type_OPair(_1616846, _1616846), _1616850), _1616852)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616846, _1616846), tc_HOL_Obool)), _1616848), c_Relation_OId(_1616846)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1616846, tc_fun(_1616846, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1616846, tc_fun(tc_prod(_1616846, _1616846), tc_HOL_Obool), tc_fun(_1616846, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616846, tc_fun(tc_fun(tc_prod(_1616846, _1616846), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1616846, _1616846), tc_HOL_Obool), tc_fun(_1616846, tc_HOL_Obool)), _1616846), c_COMBC(_1616846, tc_fun(tc_prod(_1616846, _1616846), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616846, tc_prod(_1616846, _1616846)), tc_fun(_1616846, tc_fun(tc_fun(tc_prod(_1616846, _1616846), tc_HOL_Obool), tc_HOL_Obool)), _1616846), hAPP(c_COMBB(tc_prod(_1616846, _1616846), tc_fun(tc_fun(tc_prod(_1616846, _1616846), tc_HOL_Obool), tc_HOL_Obool), _1616846), c_member(tc_prod(_1616846, _1616846)))), c_Product__Type_OPair(_1616846, _1616846)))), _1616848)), c_fequal), _1616850), _1616852)))], (26061 ^ _778908) ^ [_1236792] : [_1236792 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236792), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (32845 ^ _778908) ^ [_1377123, _1377125] : [class_Int_Onumber__ring(_1377123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1377125)), -(hBOOL(hAPP(hAPP(c_member(_1377123), hAPP(c_Int_Onumber__class_Onumber__of(_1377123), _1377125)), c_Nat_Osemiring__1__class_ONats(_1377123))))], (8113 ^ _778908) ^ [_914645, _914647] : [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), _914645), _914647))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _914645))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _914647)))], (32148 ^ _778908) ^ [_1362685, _1362687, _1362689, _1362691] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362685), _1362687)), hBOOL(hAPP(hAPP(c_member(_1362685), _1362689), _1362687)), hBOOL(hAPP(hAPP(c_member(_1362685), _1362691), _1362687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1362685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362685, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362685, tc_HOL_Obool)), _1362687), hAPP(hAPP(c_Set_Oinsert(_1362685), _1362689), c_Orderings_Obot__class_Obot(tc_fun(_1362685, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1362685), _1362691), c_Orderings_Obot__class_Obot(tc_fun(_1362685, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1362685), _1362687))))], (50373 ^ _778908) ^ [_1791022, _1791024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1791022), _1791024))), -(c_List_Oupt(_1791022, _1791024) = c_List_Olist_ONil(tc_Nat_Onat))], (37036 ^ _778908) ^ [_1468147, _1468149, _1468151] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468147, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468147, tc_HOL_Obool)), _1468149), _1468151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468147, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468147, tc_HOL_Obool)), _1468149)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468147, tc_HOL_Obool)), _1468151)))], (41846 ^ _778908) ^ [_1586107, _1586109, _1586111] : [c_Wellfounded_Owf(_1586107, _1586109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586107, _1586107), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1586107, _1586107, _1586107), _1586109), _1586111)), _1586109)), -(c_FunDef_Oreduction__pair(_1586107, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1586107, _1586107), tc_HOL_Obool), tc_fun(tc_prod(_1586107, _1586107), tc_HOL_Obool)), _1586109), _1586111)))], (1442 ^ _778908) ^ [_799807, _799809] : [-(class_Rings_Olinordered__comm__semiring__strict(_799807)), _799809 = _799807, class_Rings_Olinordered__comm__semiring__strict(_799809)], (16775 ^ _778908) ^ [_1067288, _1067290] : [class_Groups_Oordered__ab__group__add__abs(_1067288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067288), hAPP(c_Groups_Oabs__class_Oabs(_1067288), _1067290)), c_Groups_Ozero__class_Ozero(_1067288)))], (7023 ^ _778908) ^ [_896307, _896309, _896311, _896313, _896315, _896317] : [c_Natural_Oevaln(c_Com_Ocom_OCall(_896307, _896309, _896311), _896313, _896315, _896317), 7027 ^ _778908 : [(7030 ^ _778908) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _896309), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896313), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_896311, _896313)), _896315, 7026 ^ [_896307, _896309, _896311, _896313, _896315, _896317]))], (7028 ^ _778908) ^ [] : [-(_896317 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7026 ^ [_896307, _896309, _896311, _896313, _896315, _896317]), hAPP(c_Natural_Ogetlocs, _896313))), _896307), hAPP(hAPP(c_Natural_Ogetlocs, 7026 ^ [_896307, _896309, _896311, _896313, _896315, _896317]), c_Com_ORes)))]]], (7983 ^ _778908) ^ [_912387, _912389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912387), _912389)), _912389))], (29624 ^ _778908) ^ [_1308683] : [class_Finite__Set_Ofinite(_1308683), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308683), c_Orderings_Otop__class_Otop(tc_fun(_1308683, tc_HOL_Obool)))))], (7412 ^ _778908) ^ [_902784, _902786, _902788] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_902784, _902786, _902788)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _902788)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24065 ^ _778908) ^ [_1198920, _1198922, _1198924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198920, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1198920, tc_HOL_Obool)), _1198922), _1198924)), _1198922)))], (43145 ^ _778908) ^ [_1617273, _1617275, _1617277] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617273, _1617273)), _1617275), _1617277)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617273, _1617273)), _1617275), c_Transitive__Closure_Ortrancl(_1617273, _1617277))))], (17681 ^ _778908) ^ [_1084389, _1084391, _1084393] : [class_Groups_Omonoid__mult(_1084389), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084389), _1084391), hAPP(c_Nat_OSuc, _1084393)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084389), hAPP(hAPP(c_Power_Opower__class_Opower(_1084389), _1084391), _1084393)), _1084391))], (25915 ^ _778908) ^ [_1234102, _1234104, _1234106] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234102), _1234104)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234102), _1234106)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234102), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1234104), _1234106))))], (35853 ^ _778908) ^ [_1441355, _1441357, _1441359, _1441361, _1441363, _1441365, _1441367] : [c_Hoare__Mirabelle_Ohoare__derivs(_1441355, _1441357, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1441355)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1441355), c_Hoare__Mirabelle_Opeek__and(_1441355, _1441359, _1441361)), _1441363), _1441365)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1441355), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1441355, _1441357, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1441355)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1441355), c_Hoare__Mirabelle_Opeek__and(_1441355, _1441359, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1441361))), _1441367), _1441365)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1441355), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1441355, _1441357, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1441355)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1441355), _1441359), c_Com_Ocom_OCond(_1441361, _1441363, _1441367)), _1441365)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1441355), tc_HOL_Obool)))))], (46719 ^ _778908) ^ [_1702736, _1702738, _1702740, _1702742, _1702744] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702736)), _1702738) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702740)), _1702742), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702736)), _1702744) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702740)), _1702742), hBOOL(hAPP(c_List_Odistinct(_1702740), _1702742)), c_Map_Omap__of(_1702740, _1702736, hAPP(hAPP(c_List_Ozip(_1702740, _1702736), _1702742), _1702738)) = c_Map_Omap__of(_1702740, _1702736, hAPP(hAPP(c_List_Ozip(_1702740, _1702736), _1702742), _1702744)), -(_1702738 = _1702744)], (5184 ^ _778908) ^ [_859114, _859116, _859118, _859120] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_859120, _859116) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_859118, _859114)), _859120 = _859118, _859116 = _859114], (25453 ^ _778908) ^ [_1226372, _1226374] : [_1226372 = _1226374, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226372), _1226374)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226374), _1226372)))], (50834 ^ _778908) ^ [_1800542, _1800544] : [50836 ^ _778908 : [(50839 ^ _778908) ^ [] : [50835 ^ [_1800542, _1800544] = c_List_Olist_ONil(_1800542)], (50837 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1800542)), 50835 ^ [_1800542, _1800544]), hAPP(c_List_Oset(tc_List_Olist(_1800542)), _1800544))))]], -(c_List_Oconcat(_1800542, _1800544) = c_List_Olist_ONil(_1800542))], (43891 ^ _778908) ^ [_1635889, _1635891, _1635893, _1635895, _1635897] : [c_Relation_Osingle__valued(_1635889, _1635891, _1635893), c_Relation_Osingle__valued(_1635891, _1635895, _1635897), -(c_Relation_Osingle__valued(_1635889, _1635895, hAPP(hAPP(c_Relation_Orel__comp(_1635889, _1635891, _1635895), _1635893), _1635897)))], (48060 ^ _778908) ^ [_1737505, _1737507, _1737509, _1737511, _1737513] : [hAPP(hAPP(c_List_Oappend(_1737505), _1737507), hAPP(hAPP(c_List_Olist_OCons(_1737505), _1737509), c_List_Olist_ONil(_1737505))) = hAPP(hAPP(c_List_Oappend(_1737505), _1737511), hAPP(hAPP(c_List_Olist_OCons(_1737505), _1737513), c_List_Olist_ONil(_1737505))), 48063 ^ _778908 : [(48066 ^ _778908) ^ [] : [-(_1737509 = _1737513)], (48064 ^ _778908) ^ [] : [-(_1737507 = _1737511)]]], (29396 ^ _778908) ^ [_1304317] : [-(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)), _1304317))))], (41696 ^ _778908) ^ [_1580421, _1580423] : [-(c_Product__Type_Oapfst(_1580421, _1580421, _1580423, c_Fun_Oid(_1580421)) = c_Fun_Oid(tc_prod(_1580421, _1580423)))], (10176 ^ _778908) ^ [_949820, _949822, _949824] : [class_Rings_Oring__1(_949820), -(hAPP(c_Int_Oring__1__class_Oof__int(_949820), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _949822), _949824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949820), hAPP(c_Int_Oring__1__class_Oof__int(_949820), _949822)), hAPP(c_Int_Oring__1__class_Oof__int(_949820), _949824)))], (24783 ^ _778908) ^ [_1213067, _1213069, _1213071] : [class_Groups_Olinordered__ab__group__add(_1213067), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1213067), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213067), _1213069), _1213071)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213067), hAPP(c_Groups_Ouminus__class_Ouminus(_1213067), _1213069)), hAPP(c_Groups_Ouminus__class_Ouminus(_1213067), _1213071)))], (34966 ^ _778908) ^ [_1420183, _1420185, _1420187, _1420189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1420183), _1420185)), -(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), _1420183), _1420187)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1420185), _1420189))), c_FunDef_Opair__less)))], (8506 ^ _778908) ^ [_921542, _921544, _921546, _921548] : [class_Orderings_Oorder(_921542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921542), _921544), _921546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921542), _921548), _921544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921542), _921548), _921546)))], (27799 ^ _778908) ^ [_1271874, _1271876] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1271874), _1271876)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1271876), _1271874)))], (38786 ^ _778908) ^ [_1506443, _1506445, _1506447, _1506449] : [c_Fun_Oinj__on(_1506443, _1506445, _1506447, c_Orderings_Otop__class_Otop(tc_fun(_1506443, tc_HOL_Obool))), 38789 ^ _778908 : [(38803 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1506445), _1506449), hAPP(c_Set_Oimage(_1506443, _1506445, _1506447), c_Orderings_Otop__class_Otop(tc_fun(_1506443, tc_HOL_Obool)))))), 38804 ^ _778908 : [(38805 ^ _778908) ^ [_1506846] : [_1506449 = hAPP(_1506447, _1506846), 38809 ^ _778908 : [(38812 ^ _778908) ^ [] : [38808 ^ [_1506443, _1506445, _1506447, _1506449, _1506846] = _1506846], (38810 ^ _778908) ^ [] : [-(_1506449 = hAPP(_1506447, 38808 ^ [_1506443, _1506445, _1506447, _1506449, _1506846]))]]]]], (38790 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1506445), _1506449), hAPP(c_Set_Oimage(_1506443, _1506445, _1506447), c_Orderings_Otop__class_Otop(tc_fun(_1506443, tc_HOL_Obool))))), 38794 ^ _778908 : [(38797 ^ _778908) ^ [_1506708] : [_1506449 = hAPP(_1506447, _1506708), -(_1506708 = 38793 ^ [_1506443, _1506445, _1506447, _1506449])], (38795 ^ _778908) ^ [] : [-(_1506449 = hAPP(_1506447, 38793 ^ [_1506443, _1506445, _1506447, _1506449]))]]]]], (45738 ^ _778908) ^ [_1679590, _1679592] : [-(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)))), _1679590)) = 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)))), _1679592))), 45740 ^ _778908 : [(45743 ^ _778908) ^ [] : [45744 ^ _778908 : [(45747 ^ _778908) ^ [] : [hBOOL(hAPP(_1679592, 45739 ^ [_1679590, _1679592]))], (45745 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1679590, 45739 ^ [_1679590, _1679592])))]], 45748 ^ _778908 : [(45751 ^ _778908) ^ [] : [hBOOL(hAPP(_1679590, 45739 ^ [_1679590, _1679592]))], (45749 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1679592, 45739 ^ [_1679590, _1679592])))]]], (45741 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 45739 ^ [_1679590, _1679592])))]]], (14561 ^ _778908) ^ [_1026116, _1026118] : [class_Divides_Osemiring__div(_1026116), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1026116), _1026118), c_Groups_Oone__class_Oone(_1026116)) = _1026118)], (51085 ^ _778908) ^ [_1806811, _1806813, _1806815] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1806811), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1806811))), _1806813))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1806815), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1806811))), _1806813))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1806811))), hAPP(c_List_Ofilter(tc_List_Olist(_1806811), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1806811)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1806815)), c_Nat_Osize__class_Osize(tc_List_Olist(_1806811)))), c_List_Otranspose(_1806811, _1806813))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806811)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1806811)), _1806813), _1806815)))], (7843 ^ _778908) ^ [_910017, _910019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910017), _910019)), -(hAPP(c_Nat_OSuc, _910017) = _910019), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _910017)), _910019)))], (24799 ^ _778908) ^ [_1213455, _1213457] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1213455), hAPP(c_Nat_OSuc, _1213457)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1213457), 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)), _1213457)), _1213455))], (23563 ^ _778908) ^ [_1189480, _1189482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189482), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189480, _1189482) = 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), _1189480), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1189482)))))], (45452 ^ _778908) ^ [_1672894, _1672896, _1672898] : [class_Complete__Lattice_Ocomplete__lattice(_1672894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1672894), _1672896)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1672894), _1672898), c_Complete__Lattice_OInf__class_OInf(_1672894, _1672896)) = hAPP(hAPP(c_Finite__Set_Ofold(_1672894, _1672894, c_Lattices_Osemilattice__inf__class_Oinf(_1672894)), _1672898), _1672896))], (40068 ^ _778908) ^ [_1535813, _1535815, _1535817, _1535819, _1535821] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535813, _1535815), _1535817), hAPP(hAPP(c_COMBS(_1535813, tc_fun(_1535815, tc_HOL_Obool), tc_fun(_1535815, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535815, tc_HOL_Obool), tc_fun(tc_fun(_1535815, tc_HOL_Obool), tc_fun(_1535815, tc_HOL_Obool)), _1535813), c_Groups_Ominus__class_Ominus(tc_fun(_1535815, tc_HOL_Obool))), _1535819)), _1535821)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535813, _1535815), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535813, _1535815), _1535817), _1535819)), hAPP(hAPP(c_Product__Type_OSigma(_1535813, _1535815), _1535817), _1535821)))], (7671 ^ _778908) ^ [_907105, _907107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907105), _907107)), _907105 = _907107], (51607 ^ _778908) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (19413 ^ _778908) ^ [_1113224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113224)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113224), c_Int_OPls)))], (11522 ^ _778908) ^ [] : [-(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))))], (1342 ^ _778908) ^ [_798557, _798559] : [-(class_Lattices_Odistrib__lattice(_798557)), _798559 = _798557, class_Lattices_Odistrib__lattice(_798559)], (33978 ^ _778908) ^ [_1399789, _1399791, _1399793] : [class_Orderings_Olinorder(_1399789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399789), _1399791)), hBOOL(hAPP(hAPP(c_member(_1399789), _1399793), _1399791)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1399789), _1399793), c_Big__Operators_Olattice_OSup__fin(_1399789, c_Orderings_Oord__class_Omax(_1399789), _1399791)) = c_Big__Operators_Olattice_OSup__fin(_1399789, c_Orderings_Oord__class_Omax(_1399789), _1399791))], (6611 ^ _778908) ^ [_887111, _887113, _887115, _887117, _887119, _887121] : [-(c_Natural_Oevaln(c_Com_Ocom_OLocal(_887111, _887113, _887115), _887117, _887119, hAPP(hAPP(hAPP(c_Natural_Oupdate, _887121), c_Com_Ovname_OLoc(_887111)), hAPP(hAPP(c_Natural_Ogetlocs, _887117), _887111)))), 6612 ^ _778908 : [(6613 ^ _778908) ^ [_887232] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _887121), c_Com_Ovname_OLoc(_887111)), hAPP(hAPP(c_Natural_Ogetlocs, _887117), _887111)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _887232), c_Com_Ovname_OLoc(_887111)), hAPP(hAPP(c_Natural_Ogetlocs, _887117), _887111)), c_Natural_Oevaln(_887115, hAPP(hAPP(hAPP(c_Natural_Oupdate, _887117), c_Com_Ovname_OLoc(_887111)), hAPP(_887113, _887117)), _887119, _887232)]]], (36884 ^ _778908) ^ [_1463930, _1463932, _1463934, _1463936] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463930, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463930, tc_HOL_Obool)), _1463932), _1463934)), _1463936) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463930, tc_HOL_Obool)), _1463932), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463930, tc_HOL_Obool)), _1463934), _1463936)))], (25585 ^ _778908) ^ [_1228452, _1228454] : [_1228452 = _1228454, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228452), _1228454)))], (34403 ^ _778908) ^ [_1408477, _1408479, _1408481, _1408483, _1408485, _1408487] : [_1408477 = _1408479, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408481, _1408483), _1408485), _1408479), _1408487), _1408477) = _1408487)], (47040 ^ _778908) ^ [_1712473, _1712475, _1712477] : [hAPP(hAPP(c_List_Olist_OCons(_1712473), _1712475), _1712477) = _1712477], (46222 ^ _778908) ^ [_1690948] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1690948)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1690948), tc_HOL_Obool))))], (24389 ^ _778908) ^ [_1205253, _1205255] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1205253)), hAPP(c_Nat_OSuc, _1205255)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1205253))), 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, _1205255))), 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)), _1205255)))))], (16675 ^ _778908) ^ [_1065648, _1065650] : [class_Rings_Ocomm__semiring__1(_1065648), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1065648), _1065650), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1065650)], (4482 ^ _778908) ^ [_848245, _848247, _848249, _848251, _848253, _848255, _848257, _848259] : [-(c_Lazy__Sequence_Oanamorph(_848259, _848255, _848251, _848247) = c_Lazy__Sequence_Oanamorph(_848257, _848253, _848249, _848245)), _848259 = _848257, _848255 = _848253, _848251 = _848249, _848247 = _848245], (35446 ^ _778908) ^ [_1431329, _1431331, _1431333] : [-(hAPP(c_Set_OPow(_1431329), hAPP(hAPP(c_Set_Oinsert(_1431329), _1431331), _1431333)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1431329, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1431329), _1431333)), hAPP(c_Set_Oimage(tc_fun(_1431329, tc_HOL_Obool), tc_fun(_1431329, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1431329), _1431331)), hAPP(c_Set_OPow(_1431329), _1431333))))], (44635 ^ _778908) ^ [_1652054] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652054, tc_HOL_Obool) = c_Set_OBall(_1652054))], (25659 ^ _778908) ^ [_1229668, _1229670] : [-(_1229668 = _1229670), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229668), _1229670)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229670), _1229668))], (50047 ^ _778908) ^ [_1784589, _1784591] : [c_List_Otranspose(_1784589, _1784591) = c_List_Olist_ONil(tc_List_Olist(_1784589)), 50050 ^ _778908 : [(50051 ^ _778908) ^ [_1784684] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1784589)), _1784684), hAPP(c_List_Oset(tc_List_Olist(_1784589)), _1784591))), -(_1784684 = c_List_Olist_ONil(_1784589))]]], (8482 ^ _778908) ^ [_921247, _921249, _921251] : [class_Orderings_Olinorder(_921247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921247), _921249), _921251))), -(_921249 = _921251), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921247), _921251), _921249)))], (15368 ^ _778908) ^ [_1040304, _1040306, _1040308, _1040310, _1040312] : [class_Groups_Oab__group__add(_1040304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040304), _1040306), _1040308) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040304), _1040310), _1040312), 15375 ^ _778908 : [(15382 ^ _778908) ^ [] : [_1040310 = _1040312, -(_1040306 = _1040308)], (15376 ^ _778908) ^ [] : [_1040306 = _1040308, -(_1040310 = _1040312)]]], (39309 ^ _778908) ^ [_1517810, _1517812] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517810), _1517812)), -(hAPP(c_Finite__Set_Ocard(_1517810), _1517812) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1517810, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1517810), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1517812))], (33429 ^ _778908) ^ [_1388951, _1388953] : [class_Orderings_Olinorder(_1388951), -(c_Big__Operators_Olinorder__class_OMin(_1388951, hAPP(hAPP(c_Set_Oinsert(_1388951), _1388953), c_Orderings_Obot__class_Obot(tc_fun(_1388951, tc_HOL_Obool)))) = _1388953)], (41143 ^ _778908) ^ [_1560416, _1560418, _1560420] : [-(hAPP(hAPP(c_Set_Oinsert(_1560416), _1560418), _1560420) = hAPP(c_Set_OCollect(_1560416), hAPP(hAPP(c_COMBS(_1560416, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560416), c_fdisj), hAPP(hAPP(c_COMBC(_1560416, _1560416, tc_HOL_Obool), c_fequal), _1560418))), hAPP(hAPP(c_COMBC(_1560416, tc_fun(_1560416, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560416)), _1560420))))], (49873 ^ _778908) ^ [_1780111, _1780113] : [-(_1780111 = c_List_Olist_ONil(_1780113)), -(hAPP(hAPP(c_List_Oappend(_1780113), c_List_Obutlast(_1780113, _1780111)), hAPP(hAPP(c_List_Olist_OCons(_1780113), c_List_Olast(_1780113, _1780111)), c_List_Olist_ONil(_1780113))) = _1780111)], (26621 ^ _778908) ^ [_1247738, _1247740] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1247738)), _1247740))), 26624 ^ _778908 : [(26627 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1247738), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247740)))], (26625 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247738)))]], 26628 ^ _778908 : [(26631 ^ _778908) ^ [] : [_1247740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26629 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247738))]]], (2 ^ _778908) ^ [_778935] : [-(_778935 = _778935)], (43275 ^ _778908) ^ [_1620460, _1620462] : [-(hAPP(c_Relation_OImage(_1620460, _1620460, c_Relation_OId(_1620460)), _1620462) = _1620462)], (46263 ^ _778908) ^ [_1691794, _1691796, _1691798, _1691800, _1691802] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1691794), tc_Option_Ooption(_1691796), _1691798, hAPP(c_Option_Omap(_1691794, _1691796), _1691800)), hAPP(c_COMBK(tc_Option_Ooption(_1691794), _1691798), c_Option_Ooption_ONone(_1691794))), _1691802) = c_Option_Ooption_ONone(_1691796))], (26321 ^ _778908) ^ [_1242361, _1242363, _1242365] : [class_Divides_Osemiring__div(_1242361), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242361), _1242363), _1242365)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242361), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242361), _1242365), _1242363)), _1242363) = _1242365)], (38506 ^ _778908) ^ [_1501135, _1501137] : [class_Groups_Oordered__ab__group__add(_1501135), -(c_Fun_Oinj__on(_1501135, _1501135, c_Groups_Ouminus__class_Ouminus(_1501135), _1501137))], (41064 ^ _778908) ^ [_1558765] : [class_Orderings_Olinorder(_1558765), -(c_Finite__Set_Ofun__left__comm__idem(_1558765, _1558765, c_Orderings_Oord__class_Omax(_1558765)))], (47196 ^ _778908) ^ [_1717012, _1717014, _1717016, _1717018] : [hBOOL(hAPP(hAPP(c_member(_1717012), _1717014), hAPP(c_List_Oset(_1717012), c_List_Osublist(_1717012, _1717016, _1717018)))), -(hBOOL(hAPP(hAPP(c_member(_1717012), _1717014), hAPP(c_List_Oset(_1717012), _1717016))))], (17211 ^ _778908) ^ [_1075959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1075959)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1075959 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8556 ^ _778908) ^ [_922367, _922369] : [_922367 = _922369, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922367) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922369))], (19099 ^ _778908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (36816 ^ _778908) ^ [_1462731, _1462733, _1462735] : [class_Lattices_Olattice(_1462731), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462731), _1462733), _1462735) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462731), _1462735), _1462733))], (132 ^ _778908) ^ [_780744, _780746] : [-(class_Rings_Oinverse(_780744)), _780746 = _780744, class_Rings_Oinverse(_780746)], (3878 ^ _778908) ^ [_838735, _838737] : [_838737 = _838735, -(c_New__Random__Sequence_Opos__single(_838737) = c_New__Random__Sequence_Opos__single(_838735))], (13698 ^ _778908) ^ [] : [-(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))))], (30454 ^ _778908) ^ [_1324249, _1324251, _1324253, _1324255] : [_1324249 = c_Orderings_Obot__class_Obot(tc_fun(_1324251, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1324251, _1324253, hAPP(c_COMBK(_1324253, _1324251), _1324255)), _1324249) = c_Orderings_Obot__class_Obot(tc_fun(_1324253, tc_HOL_Obool)))], (48901 ^ _778908) ^ [_1758966, _1758968, _1758970, _1758972] : [-(hAPP(hAPP(c_List_Odrop(_1758966), _1758968), hAPP(hAPP(c_List_Oappend(_1758966), _1758970), _1758972)) = hAPP(hAPP(c_List_Oappend(_1758966), hAPP(hAPP(c_List_Odrop(_1758966), _1758968), _1758970)), hAPP(hAPP(c_List_Odrop(_1758966), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1758968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758966)), _1758970))), _1758972)))], (6877 ^ _778908) ^ [_892193, _892195] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_892193, _892195)], (22344 ^ _778908) ^ [_1165921, _1165923] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1165921), _1165923) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1165921), _1165923))], (50387 ^ _778908) ^ [_1791222, _1791224] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1791222), _1791224) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1791222, _1791224)))], (3004 ^ _778908) ^ [_824842, _824844] : [_824844 = _824842, -(c_New__DSequence_Opos__empty(_824844) = c_New__DSequence_Opos__empty(_824842))], (4758 ^ _778908) ^ [_852549, _852551, _852553, _852555] : [-(c_Big__Operators_Olattice__class_OInf__fin(_852555, _852551) = c_Big__Operators_Olattice__class_OInf__fin(_852553, _852549)), _852555 = _852553, _852551 = _852549], (50122 ^ _778908) ^ [_1786505, _1786507, _1786509, _1786511, _1786513] : [class_Orderings_Olinorder(_1786505), -(c_List_Olinorder__class_Osorted(_1786505, hAPP(hAPP(c_List_Omap(_1786507, _1786505), _1786509), hAPP(c_List_Ofilter(_1786507, hAPP(hAPP(c_COMBC(_1786507, _1786505, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1786505, tc_fun(_1786505, tc_HOL_Obool), _1786507), c_fequal), _1786509)), hAPP(_1786511, _1786513))), _1786513))))], (23491 ^ _778908) ^ [_1188141, _1188143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188141), 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)), _1188143)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1188141, _1188143), c_Divides_OnegDivAlg(_1188141, _1188143))))], (41237 ^ _778908) ^ [_1562592, _1562594, _1562596, _1562598] : [hBOOL(hAPP(hAPP(c_member(_1562592), _1562594), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562592, tc_HOL_Obool)), _1562596), hAPP(c_Set_OCollect(_1562592), _1562598)))), 41240 ^ _778908 : [(41243 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1562598, _1562594)))], (41241 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562592), _1562594), _1562596)))]]], (5706 ^ _778908) ^ [_867015, _867017, _867019, _867021] : [-(c_COMBK(_867021, _867017) = c_COMBK(_867019, _867015)), _867021 = _867019, _867017 = _867015], (18545 ^ _778908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (50735 ^ _778908) ^ [_1798025, _1798027] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1798025)), c_List_Otranspose__rel(_1798025)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1798025)), c_List_Olist_ONil(_1798025)), _1798027))), -(c_List_Otranspose(_1798025, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1798025)), c_List_Olist_ONil(_1798025)), _1798027)) = c_List_Otranspose(_1798025, _1798027))], (26873 ^ _778908) ^ [_1252774, _1252776, _1252778, _1252780] : [class_Orderings_Oorder(_1252774), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1252774, 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)))), _1252776), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252774), hAPP(_1252776, _1252778)), hAPP(_1252776, _1252780)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252778), _1252780)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252780), _1252778)))], (48574 ^ _778908) ^ [_1749577, _1749579, _1749581, _1749583] : [-(hAPP(hAPP(c_List_Otake(_1749577), _1749579), hAPP(hAPP(c_List_Olist_OCons(_1749577), _1749581), _1749583)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1749577), c_List_Olist_ONil(_1749577), hAPP(hAPP(c_COMBB(tc_List_Olist(_1749577), tc_List_Olist(_1749577), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1749577), _1749581)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1749577), tc_List_Olist(_1749577)), c_List_Otake(_1749577)), _1749583)), _1749579))], (28487 ^ _778908) ^ [_1284899, _1284901, _1284903] : [class_Lattices_Osemilattice__sup(_1284899), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284899), _1284901), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284899), _1284903), _1284901))))], (37971 ^ _778908) ^ [_1490031, _1490033, _1490035, _1490037, _1490039, _1490041] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490031, tc_fun(_1490033, tc_HOL_Obool))), _1490035), _1490037), _1490039), _1490041)), -(hBOOL(hAPP(hAPP(_1490037, _1490039), _1490041)))], (42188 ^ _778908) ^ [_1593209, _1593211, _1593213] : [_1593213 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1593209, _1593211), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1593209, _1593211), _1593213) = c_Orderings_Obot__class_Obot(tc_fun(_1593211, tc_HOL_Obool)))], (12401 ^ _778908) ^ [_987308, _987310, _987312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987308), _987310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987308), _987312))), 12404 ^ _778908 : [(12407 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987310), _987312)))], (12405 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987308)))]]], (38112 ^ _778908) ^ [_1493197, _1493199] : [class_Lattices_Olattice(_1493197), -(c_Big__Operators_Olattice__class_OInf__fin(_1493197, hAPP(hAPP(c_Set_Oinsert(_1493197), _1493199), c_Orderings_Obot__class_Obot(tc_fun(_1493197, tc_HOL_Obool)))) = _1493199)], (36904 ^ _778908) ^ [_1464929, _1464931, _1464933, _1464935] : [class_Lattices_Olattice(_1464929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1464929), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1464929), _1464931), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1464929), _1464933), _1464935))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1464929), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1464929), _1464931), _1464933)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1464929), _1464931), _1464935)))))], (6746 ^ _778908) ^ [_889540, _889542, _889544, _889546] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_889540, _889542), _889544, _889546, _889544), hBOOL(hAPP(_889540, _889544)), 6754 ^ _778908 : [(6757 ^ _778908) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_889540, _889542), 6753 ^ [_889540, _889542, _889544, _889546], _889546, _889544))], (6755 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_889542, _889544, _889546, 6753 ^ [_889540, _889542, _889544, _889546]))]]], (26113 ^ _778908) ^ [_1238314, _1238316, _1238318, _1238320, _1238322] : [class_Groups_Oab__group__add(_1238314), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238316, _1238314), hAPP(hAPP(c_COMBS(_1238316, _1238314, _1238314), hAPP(hAPP(c_COMBB(_1238314, tc_fun(_1238314, _1238314), _1238316), c_Groups_Ominus__class_Ominus(_1238314)), _1238318)), _1238320)), _1238322) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1238314), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238316, _1238314), _1238318), _1238322)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238316, _1238314), _1238320), _1238322)))], (31245 ^ _778908) ^ [_1342595, _1342597, _1342599, _1342601] : [hBOOL(hAPP(hAPP(c_member(_1342595), _1342597), _1342599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1342595, tc_HOL_Obool)), _1342599), _1342601)), -(hBOOL(hAPP(hAPP(c_member(_1342595), _1342597), _1342601)))], (51491 ^ _778908) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (19395 ^ _778908) ^ [_1112927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112927), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1112927)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49966 ^ _778908) ^ [_1782146, _1782148, _1782150] : [49968 ^ _778908 : [(49971 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1782148, 49967 ^ [_1782146, _1782148, _1782150])))], (49969 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1782146), 49967 ^ [_1782146, _1782148, _1782150]), hAPP(c_List_Oset(_1782146), _1782150))))]], -(hAPP(c_List_Ofilter(_1782146, _1782148), _1782150) = c_List_Olist_ONil(_1782146))], (31754 ^ _778908) ^ [_1352380, _1352382, _1352384, _1352386, _1352388, _1352390] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1352382, _1352384)), hAPP(hAPP(c_Product__Type_OPair(_1352382, _1352384), _1352388), _1352390)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1352380, tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1352380, tc_HOL_Obool))), _1352386))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1352380, tc_fun(_1352382, tc_fun(_1352384, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1352380, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool), tc_fun(_1352382, tc_fun(_1352384, tc_HOL_Obool)), _1352380), hAPP(c_COMBC(_1352382, tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool), tc_fun(_1352384, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1352384, tc_fun(tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool), tc_fun(_1352384, tc_HOL_Obool)), _1352382), c_COMBC(_1352384, tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1352384, tc_prod(_1352382, _1352384)), tc_fun(_1352384, tc_fun(tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool), tc_HOL_Obool)), _1352382), hAPP(c_COMBB(tc_prod(_1352382, _1352384), tc_fun(tc_fun(tc_prod(_1352382, _1352384), tc_HOL_Obool), tc_HOL_Obool), _1352384), c_member(tc_prod(_1352382, _1352384)))), c_Product__Type_OPair(_1352382, _1352384))))), _1352386)), _1352388), _1352390)))], (48919 ^ _778908) ^ [_1759442, _1759444, _1759446, _1759448] : [hBOOL(hAPP(hAPP(c_member(_1759442), _1759444), hAPP(c_List_Oset(_1759442), hAPP(hAPP(c_List_Odrop(_1759442), _1759446), _1759448)))), -(hBOOL(hAPP(hAPP(c_member(_1759442), _1759444), hAPP(c_List_Oset(_1759442), _1759448))))], (19345 ^ _778908) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (15330 ^ _778908) ^ [_1039492, _1039494, _1039496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1039492)), 15336 ^ _778908 : [(15339 ^ _778908) ^ [] : [hBOOL(hAPP(_1039494, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 15335 ^ [_1039492, _1039494, _1039496]), _1039492)))], (15337 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1039494, 15335 ^ [_1039492, _1039494, _1039496])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1039496)), 15344 ^ _778908 : [(15345 ^ _778908) ^ [_1039781] : [hBOOL(hAPP(_1039494, _1039781)), -(hBOOL(hAPP(_1039494, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1039781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1039496), _1039492)))))]]], (36310 ^ _778908) ^ [_1452290, _1452292, _1452294, _1452296] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452290, tc_HOL_Obool)), _1452292), _1452294), _1452296)), 36313 ^ _778908 : [(36316 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1452294, _1452296)))], (36314 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1452292, _1452296)))]]], (8168 ^ _778908) ^ [_915635, _915637, _915639, _915641] : [hAPP(c_Sum__Type_OInr(_915635, _915637), _915639) = hAPP(c_Sum__Type_OInl(_915637, _915635), _915641)], (25349 ^ _778908) ^ [_1224672, _1224674] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224672), _1224674)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224674), _1224672))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224674), _1224672)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224672), _1224674)))], (3804 ^ _778908) ^ [_837526, _837528] : [_837528 = _837526, -(c_Int_Oint__ge__less__than2(_837528) = c_Int_Oint__ge__less__than2(_837526))], (43231 ^ _778908) ^ [_1619300, _1619302] : [-(c_Transitive__Closure_Ortrancl(_1619300, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619300, _1619300), tc_HOL_Obool)), _1619302), c_Relation_OId(_1619300))) = c_Transitive__Closure_Ortrancl(_1619300, _1619302))], (15570 ^ _778908) ^ [_1043969, _1043971, _1043973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043969), _1043971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043969), _1043973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043973), _1043971)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043973), _1043969))))], (17049 ^ _778908) ^ [_1072590, _1072592, _1072594, _1072596] : [class_Int_Onumber__ring(_1072590), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072590), hAPP(c_Int_Onumber__class_Onumber__of(_1072590), _1072592)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072590), hAPP(c_Int_Onumber__class_Onumber__of(_1072590), _1072594)), _1072596)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072590), hAPP(c_Int_Onumber__class_Onumber__of(_1072590), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072592), _1072594))), _1072596))], (40326 ^ _778908) ^ [_1543445, _1543447, _1543449, _1543451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543445), _1543447)), 40332 ^ _778908 : [(40335 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543449), hAPP(_1543451, 40331 ^ [_1543445, _1543447, _1543449, _1543451])))], (40333 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543445), 40331 ^ [_1543445, _1543447, _1543449, _1543451]), _1543447)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1543445, _1543449)), hAPP(hAPP(c_Product__Type_OSigma(_1543445, _1543449), _1543447), _1543451))))], (46641 ^ _778908) ^ [_1701049, _1701051, _1701053, _1701055] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1701049, _1701051))), hAPP(hAPP(c_List_Ozip(_1701049, _1701051), _1701053), _1701055)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701049)), _1701053)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701051)), _1701055)))], (19407 ^ _778908) ^ [_1113123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1113123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1113123))))], (41834 ^ _778908) ^ [_1584855, _1584857, _1584859, _1584861, _1584863, _1584865, _1584867] : [c_Predicate_Opred__comp(_1584855, _1584857, _1584859, hAPP(hAPP(c_COMBC(_1584855, tc_fun(tc_prod(_1584855, _1584857), tc_HOL_Obool), tc_fun(_1584857, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584857, tc_fun(tc_fun(tc_prod(_1584855, _1584857), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584855, _1584857), tc_HOL_Obool), tc_fun(_1584857, tc_HOL_Obool)), _1584855), c_COMBC(_1584857, tc_fun(tc_prod(_1584855, _1584857), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584857, tc_prod(_1584855, _1584857)), tc_fun(_1584857, tc_fun(tc_fun(tc_prod(_1584855, _1584857), tc_HOL_Obool), tc_HOL_Obool)), _1584855), hAPP(c_COMBB(tc_prod(_1584855, _1584857), tc_fun(tc_fun(tc_prod(_1584855, _1584857), tc_HOL_Obool), tc_HOL_Obool), _1584857), c_member(tc_prod(_1584855, _1584857)))), c_Product__Type_OPair(_1584855, _1584857)))), _1584861), hAPP(hAPP(c_COMBC(_1584857, tc_fun(tc_prod(_1584857, _1584859), tc_HOL_Obool), tc_fun(_1584859, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584859, tc_fun(tc_fun(tc_prod(_1584857, _1584859), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584857, _1584859), tc_HOL_Obool), tc_fun(_1584859, tc_HOL_Obool)), _1584857), c_COMBC(_1584859, tc_fun(tc_prod(_1584857, _1584859), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584859, tc_prod(_1584857, _1584859)), tc_fun(_1584859, tc_fun(tc_fun(tc_prod(_1584857, _1584859), tc_HOL_Obool), tc_HOL_Obool)), _1584857), hAPP(c_COMBB(tc_prod(_1584857, _1584859), tc_fun(tc_fun(tc_prod(_1584857, _1584859), tc_HOL_Obool), tc_HOL_Obool), _1584859), c_member(tc_prod(_1584857, _1584859)))), c_Product__Type_OPair(_1584857, _1584859)))), _1584863), _1584865, _1584867), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584855, _1584859)), hAPP(hAPP(c_Product__Type_OPair(_1584855, _1584859), _1584865), _1584867)), hAPP(hAPP(c_Relation_Orel__comp(_1584855, _1584857, _1584859), _1584861), _1584863))))], (47509 ^ _778908) ^ [_1723834, _1723836] : [-(_1723836 = c_List_Olist_ONil(_1723834)), -(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(_1723834)), _1723836))))], (12501 ^ _778908) ^ [_989113, _989115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989113), hAPP(c_Nat_OSuc, _989115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989113), _989115)))], (42424 ^ _778908) ^ [_1599733, _1599735, _1599737, _1599739] : [hBOOL(hAPP(c_Predicate_ODomainP(_1599733, _1599735, _1599737), _1599739)), -(hBOOL(hAPP(hAPP(_1599737, _1599739), 42427 ^ [_1599733, _1599735, _1599737, _1599739])))], (30806 ^ _778908) ^ [_1331342, _1331344] : [_1331344 = c_Option_Ooption_ONone(_1331342), -(c_Option_Oset(_1331342, _1331344) = c_Orderings_Obot__class_Obot(tc_fun(_1331342, tc_HOL_Obool)))], (23617 ^ _778908) ^ [_1190328, _1190330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190328), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1190330), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190328, _1190330) = 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), _1190328), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1190330)))))], (29771 ^ _778908) ^ [_1311562, _1311564] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311562), c_Orderings_Otop__class_Otop(tc_fun(_1311562, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1311562), _1311564) = hAPP(c_Finite__Set_Ocard(_1311562), c_Orderings_Otop__class_Otop(tc_fun(_1311562, tc_HOL_Obool))), -(_1311564 = c_Orderings_Otop__class_Otop(tc_fun(_1311562, tc_HOL_Obool)))], (3108 ^ _778908) ^ [_826514, _826516, _826518, _826520] : [-(c_Divides_Odivmod__nat__rel(_826520, _826516) = c_Divides_Odivmod__nat__rel(_826518, _826514)), _826520 = _826518, _826516 = _826514], (19237 ^ _778908) ^ [_1110014, _1110016] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1110014)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110016)) = 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)))), _1110014)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110016)))], (50116 ^ _778908) ^ [_1786390, _1786392, _1786394] : [class_Orderings_Olinorder(_1786390), -(c_List_Olinorder__class_Osorted(_1786390, hAPP(c_List_Ofilter(_1786390, hAPP(hAPP(c_COMBC(_1786390, _1786390, tc_HOL_Obool), c_fequal), hAPP(_1786392, _1786394))), _1786394)))], (47210 ^ _778908) ^ [_1717323, _1717325, _1717327] : [-(c_Random_Oselect__weight(_1717323, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1717323)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1717323), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1717325)), _1717327)) = c_Random_Oselect__weight(_1717323, _1717327))], (10256 ^ _778908) ^ [_951238, _951240, _951242] : [class_Rings_Olinordered__ring(_951238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951238), _951240), _951240)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951238), _951242), _951242))), c_Groups_Ozero__class_Ozero(_951238)))], (24999 ^ _778908) ^ [_1217296, _1217298, _1217300, _1217302, _1217304, _1217306] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1217296, _1217298, _1217300), _1217302), hAPP(hAPP(c_Product__Type_OPair(_1217296, _1217298), _1217304), _1217306)) = hAPP(hAPP(_1217302, _1217304), _1217306))], (7268 ^ _778908) ^ [_900507, _900509] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900507), hAPP(c_Nat_OSuc, _900509)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900507), _900509)))], (29092 ^ _778908) ^ [_1298128, _1298130] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298128, tc_HOL_Obool)), _1298130), c_Orderings_Otop__class_Otop(tc_fun(_1298128, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1298128, tc_HOL_Obool)))], (19109 ^ _778908) ^ [_1107932] : [class_Int_Onumber__ring(_1107932), c_Int_Oiszero(_1107932, hAPP(c_Int_Onumber__class_Onumber__of(_1107932), c_Int_OBit1(c_Int_OPls)))], (26825 ^ _778908) ^ [_1251945, _1251947, _1251949] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251945), _1251947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251945), _1251949))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1251945)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1251947), _1251949)))], (32581 ^ _778908) ^ [_1371571, _1371573, _1371575, _1371577, _1371579] : [c_Finite__Set_Ofolding__one(_1371571, _1371573, _1371575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371571), _1371577)), hBOOL(hAPP(hAPP(c_member(_1371571), _1371579), _1371577)), 32592 ^ _778908 : [(32599 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371571, tc_HOL_Obool)), _1371577), hAPP(hAPP(c_Set_Oinsert(_1371571), _1371579), c_Orderings_Obot__class_Obot(tc_fun(_1371571, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371571, tc_HOL_Obool))), -(hAPP(_1371575, _1371577) = hAPP(hAPP(_1371573, _1371579), hAPP(_1371575, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371571, tc_HOL_Obool)), _1371577), hAPP(hAPP(c_Set_Oinsert(_1371571), _1371579), c_Orderings_Obot__class_Obot(tc_fun(_1371571, tc_HOL_Obool)))))))], (32593 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371571, tc_HOL_Obool)), _1371577), hAPP(hAPP(c_Set_Oinsert(_1371571), _1371579), c_Orderings_Obot__class_Obot(tc_fun(_1371571, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371571, tc_HOL_Obool)), -(hAPP(_1371575, _1371577) = _1371579)]]], (48484 ^ _778908) ^ [_1747518, _1747520, _1747522] : [hAPP(hAPP(c_List_Otake(_1747518), _1747520), _1747522) = c_List_Olist_ONil(_1747518), -(_1747520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1747522 = c_List_Olist_ONil(_1747518))], (29209 ^ _778908) ^ [_1300862, _1300864] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1300862, _1300864))))], (7096 ^ _778908) ^ [_897544, _897546, _897548] : [_897546 = _897548, -(hAPP(c_Option_Ooption_OSome(_897544), _897546) = hAPP(c_Option_Ooption_OSome(_897544), _897548))], (42753 ^ _778908) ^ [_1607492, _1607494] : [hBOOL(hAPP(_1607492, c_Hilbert__Choice_OEps(_1607494, _1607492))), -(hBOOL(hAPP(_1607492, 42756 ^ [_1607492, _1607494])))], (25985 ^ _778908) ^ [_1235352, _1235354] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235352), _1235354)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235354), _1235352))))], (45191 ^ _778908) ^ [_1666754, _1666756] : [-(hAPP(c_Relation_OField(_1666754), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1666754, _1666754), tc_HOL_Obool), _1666756)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1666754, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1666754, _1666754), tc_HOL_Obool), tc_fun(_1666754, tc_HOL_Obool), c_Relation_OField(_1666754)), _1666756)))], (43759 ^ _778908) ^ [_1632379, _1632381, _1632383] : [-(hAPP(hAPP(c_Nat_Ocompow(_1632379, _1632379), hAPP(c_Nat_OSuc, _1632381)), _1632383) = hAPP(c_Fun_Ocomp(_1632379, _1632379, _1632379, _1632383), hAPP(hAPP(c_Nat_Ocompow(_1632379, _1632379), _1632381), _1632383)))], (16032 ^ _778908) ^ [_1052795, _1052797, _1052799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052795), _1052797)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052799), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052797), _1052795)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052799), _1052795)), _1052797))], (47266 ^ _778908) ^ [_1718975, _1718977] : [class_Groups_Ocomm__monoid__add(_1718975), hBOOL(hAPP(c_List_Odistinct(_1718975), _1718977)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1718975), _1718977) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1718975, _1718975), c_COMBI(_1718975)), hAPP(c_List_Oset(_1718975), _1718977)))], (33037 ^ _778908) ^ [_1381080, _1381082, _1381084, _1381086, _1381088] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1381080, _1381082, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1381080)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1381080), hAPP(hAPP(c_COMBC(_1381080, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1381080), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1381084)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1381086)), _1381088))), c_Com_Ocom_OAss(_1381086, _1381088)), _1381084)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1381080), tc_HOL_Obool)))))], (18667 ^ _778908) ^ [_1100618, _1100620] : [18668 ^ _778908 : [(18671 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100618), c_Int_OPls))], (18669 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100618), _1100620))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100618)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100620))))], (28271 ^ _778908) ^ [_1280932, _1280934, _1280936] : [class_Orderings_Olinorder(_1280932), 28274 ^ _778908 : [(28281 ^ _778908) ^ [] : [_1280934 = _1280936, -(hAPP(c_SetInterval_Oord__class_OatMost(_1280932), _1280934) = hAPP(c_SetInterval_Oord__class_OatMost(_1280932), _1280936))], (28275 ^ _778908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1280932), _1280934) = hAPP(c_SetInterval_Oord__class_OatMost(_1280932), _1280936), -(_1280934 = _1280936)]]], (9576 ^ _778908) ^ [_939124, _939126, _939128, _939130] : [class_Rings_Ocomm__semiring__1(_939124), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939124), _939126), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939124), _939128), _939130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939124), _939126), _939128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939124), _939126), _939130)))], (7817 ^ _778908) ^ [_909627, _909629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909627)), _909629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909627), _909629)))], (22358 ^ _778908) ^ [_1166150] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1166150)], (15038 ^ _778908) ^ [_1033911, _1033913, _1033915] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033911), _1033913)), _1033915) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033911), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033913), _1033915))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033911), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1033913, _1033915))), _1033915)))], (11470 ^ _778908) ^ [_970907, _970909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970907), hAPP(c_Nat_OSuc, _970909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970907), _970909))), -(_970907 = hAPP(c_Nat_OSuc, _970909))], (8382 ^ _778908) ^ [_919367] : [class_Rings_Osemiring__1(_919367), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919367), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_919367))], (29142 ^ _778908) ^ [] : [-(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)))], (51249 ^ _778908) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (29263 ^ _778908) ^ [_1301939, _1301941, _1301943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301939, tc_HOL_Obool)), _1301941), hAPP(hAPP(c_Set_Oinsert(_1301939), _1301943), _1301941))))], (18499 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (30778 ^ _778908) ^ [_1330955, _1330957] : [-(c_Option_Oset(_1330955, hAPP(c_Option_Ooption_OSome(_1330955), _1330957)) = hAPP(hAPP(c_Set_Oinsert(_1330955), _1330957), c_Orderings_Obot__class_Obot(tc_fun(_1330955, tc_HOL_Obool))))], (26447 ^ _778908) ^ [_1244690, _1244692, _1244694] : [-(_1244690 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26450 ^ _778908 : [(26457 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244690), _1244692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244690), _1244694))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244692), _1244694)))], (26451 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244692), _1244694)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244690), _1244692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244690), _1244694))))]]], (50256 ^ _778908) ^ [_1788913, _1788915] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1788913), _1788915))), -(c_List_Oupt(_1788913, hAPP(c_Nat_OSuc, _1788915)) = c_List_Olist_ONil(tc_Nat_Onat))], (29704 ^ _778908) ^ [_1310244, _1310246, _1310248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310244), _1310246)), 29707 ^ _778908 : [(29714 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310244), _1310248)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310244, tc_HOL_Obool)), _1310248), _1310246))))], (29708 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310244, tc_HOL_Obool)), _1310248), _1310246))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310244), _1310248)))]]], (19717 ^ _778908) ^ [] : [-(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))))], (22480 ^ _778908) ^ [_1168417, _1168419] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1168417))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1168419)), hAPP(c_Int_Onat, _1168417)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1168419), _1168417)), 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)))], (5412 ^ _778908) ^ [_862562, _862564] : [_862564 = _862562, -(c_member(_862564) = c_member(_862562))], (40442 ^ _778908) ^ [_1546709, _1546711, _1546713, _1546715, _1546717, _1546719] : [-(c_Product__Type_Omap__pair(_1546709, _1546711, _1546713, _1546715, _1546717, _1546719) = hAPP(c_Product__Type_Oprod_Oprod__case(_1546709, _1546713, tc_prod(_1546711, _1546715)), hAPP(hAPP(c_COMBC(_1546709, tc_fun(_1546713, _1546715), tc_fun(_1546713, tc_prod(_1546711, _1546715))), hAPP(hAPP(c_COMBB(tc_fun(_1546715, tc_prod(_1546711, _1546715)), tc_fun(tc_fun(_1546713, _1546715), tc_fun(_1546713, tc_prod(_1546711, _1546715))), _1546709), c_COMBB(_1546715, tc_prod(_1546711, _1546715), _1546713)), hAPP(hAPP(c_COMBB(_1546711, tc_fun(_1546715, tc_prod(_1546711, _1546715)), _1546709), c_Product__Type_OPair(_1546711, _1546715)), _1546717))), _1546719)))], (38578 ^ _778908) ^ [_1502360, _1502362, _1502364, _1502366, _1502368] : [c_Fun_Oinj__on(_1502360, _1502362, _1502364, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502360, tc_HOL_Obool)), _1502366), _1502368)), 38581 ^ _778908 : [(38588 ^ _778908) ^ [] : [_1502366 = _1502368, -(hAPP(c_Set_Oimage(_1502360, _1502362, _1502364), _1502366) = hAPP(c_Set_Oimage(_1502360, _1502362, _1502364), _1502368))], (38582 ^ _778908) ^ [] : [hAPP(c_Set_Oimage(_1502360, _1502362, _1502364), _1502366) = hAPP(c_Set_Oimage(_1502360, _1502362, _1502364), _1502368), -(_1502366 = _1502368)]]], (10731 ^ _778908) ^ [_958933, _958935, _958937] : [class_Orderings_Oorder(_958933), 10734 ^ _778908 : [(10743 ^ _778908) ^ [] : [-(_958935 = _958937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958933), _958935), _958937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958933), _958937), _958935))], (10735 ^ _778908) ^ [] : [_958935 = _958937, 10738 ^ _778908 : [(10741 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958933), _958937), _958935)))], (10739 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958933), _958935), _958937)))]]]]], (25405 ^ _778908) ^ [_1225597, _1225599] : [_1225597 = _1225599, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225597), _1225599)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225599), _1225597)))], (50765 ^ _778908) ^ [_1798922, _1798924, _1798926] : [-(hAPP(c_List_Orev(_1798922), hAPP(hAPP(c_List_Olist_OCons(_1798922), _1798924), _1798926)) = hAPP(hAPP(c_List_Oappend(_1798922), hAPP(c_List_Orev(_1798922), _1798926)), hAPP(hAPP(c_List_Olist_OCons(_1798922), _1798924), c_List_Olist_ONil(_1798922))))], (31586 ^ _778908) ^ [_1349090, _1349092, _1349094, _1349096] : [hBOOL(hAPP(hAPP(c_member(_1349090), _1349092), _1349094)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349090, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1349090), _1349092), _1349096)), _1349094) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349090, tc_HOL_Obool)), _1349096), _1349094))], (41840 ^ _778908) ^ [_1585478, _1585480, _1585482, _1585484, _1585486, _1585488, _1585490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585478, _1585482)), hAPP(hAPP(c_Product__Type_OPair(_1585478, _1585482), _1585488), _1585490)), hAPP(hAPP(c_Relation_Orel__comp(_1585478, _1585480, _1585482), _1585484), _1585486))), -(c_Predicate_Opred__comp(_1585478, _1585480, _1585482, hAPP(hAPP(c_COMBC(_1585478, tc_fun(tc_prod(_1585478, _1585480), tc_HOL_Obool), tc_fun(_1585480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585480, tc_fun(tc_fun(tc_prod(_1585478, _1585480), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585478, _1585480), tc_HOL_Obool), tc_fun(_1585480, tc_HOL_Obool)), _1585478), c_COMBC(_1585480, tc_fun(tc_prod(_1585478, _1585480), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585480, tc_prod(_1585478, _1585480)), tc_fun(_1585480, tc_fun(tc_fun(tc_prod(_1585478, _1585480), tc_HOL_Obool), tc_HOL_Obool)), _1585478), hAPP(c_COMBB(tc_prod(_1585478, _1585480), tc_fun(tc_fun(tc_prod(_1585478, _1585480), tc_HOL_Obool), tc_HOL_Obool), _1585480), c_member(tc_prod(_1585478, _1585480)))), c_Product__Type_OPair(_1585478, _1585480)))), _1585484), hAPP(hAPP(c_COMBC(_1585480, tc_fun(tc_prod(_1585480, _1585482), tc_HOL_Obool), tc_fun(_1585482, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585482, tc_fun(tc_fun(tc_prod(_1585480, _1585482), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585480, _1585482), tc_HOL_Obool), tc_fun(_1585482, tc_HOL_Obool)), _1585480), c_COMBC(_1585482, tc_fun(tc_prod(_1585480, _1585482), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585482, tc_prod(_1585480, _1585482)), tc_fun(_1585482, tc_fun(tc_fun(tc_prod(_1585480, _1585482), tc_HOL_Obool), tc_HOL_Obool)), _1585480), hAPP(c_COMBB(tc_prod(_1585480, _1585482), tc_fun(tc_fun(tc_prod(_1585480, _1585482), tc_HOL_Obool), tc_HOL_Obool), _1585482), c_member(tc_prod(_1585480, _1585482)))), c_Product__Type_OPair(_1585480, _1585482)))), _1585486), _1585488, _1585490))], (8335 ^ _778908) ^ [_918493, _918495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _918493), _918495)), -(_918495 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918493), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 8338 ^ [_918493, _918495]))))], (1272 ^ _778908) ^ [_797682, _797684] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_797682)), _797684 = _797682, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_797684)], (6131 ^ _778908) ^ [_877211, _877213, _877215, _877217, _877219] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877211), _877213), _877215)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877217), _877215), _877219)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_877211, _877217)), _877213), _877219)))], (10144 ^ _778908) ^ [_949317, _949319] : [class_Int_Oring__char__0(_949317), 10147 ^ _778908 : [(10154 ^ _778908) ^ [] : [_949319 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_949317), _949319) = c_Groups_Ozero__class_Ozero(_949317))], (10148 ^ _778908) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_949317), _949319) = c_Groups_Ozero__class_Ozero(_949317), -(_949319 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (24523 ^ _778908) ^ [_1207918, _1207920, _1207922, _1207924] : [class_Orderings_Olinorder(_1207918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207918), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207918), _1207920), _1207922)), _1207924)), 24530 ^ _778908 : [(24533 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207918), _1207922), _1207924)))], (24531 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207918), _1207920), _1207924)))]]], (32775 ^ _778908) ^ [_1375810, _1375812, _1375814, _1375816, _1375818, _1375820] : [-(hBOOL(hAPP(hAPP(c_member(_1375810), _1375812), c_SetInterval_Oord_OgreaterThanAtMost(_1375810, _1375814, _1375816, _1375818, _1375820)))), hBOOL(hAPP(hAPP(_1375816, _1375818), _1375812)), hBOOL(hAPP(hAPP(_1375814, _1375812), _1375820))], (51431 ^ _778908) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (3762 ^ _778908) ^ [_836901, _836903] : [_836903 = _836901, -(c_Wellfounded_Omeasure(_836903) = c_Wellfounded_Omeasure(_836901))], (23991 ^ _778908) ^ [_1197328, _1197330, _1197332, _1197334, _1197336] : [hAPP(c_Product__Type_Ofst(_1197328, _1197330), hAPP(hAPP(c_Product__Type_OPair(_1197328, _1197330), _1197332), _1197334)) = _1197336, -(_1197332 = _1197336)], (1482 ^ _778908) ^ [_800307, _800309] : [-(class_Groups_Oordered__comm__monoid__add(_800307)), _800309 = _800307, class_Groups_Oordered__comm__monoid__add(_800309)], (9072 ^ _778908) ^ [_930476, _930478, _930480, _930482] : [class_Rings_Ocomm__semiring__1(_930476), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930476), _930478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930476), _930480), _930482)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930476), _930480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930476), _930478), _930482)))], (48779 ^ _778908) ^ [_1755459, _1755461, _1755463, _1755465, _1755467, _1755469] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755459), tc_List_Olist(_1755459))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755459), tc_List_Olist(_1755459)), hAPP(hAPP(c_List_Olist_OCons(_1755459), _1755461), _1755463)), hAPP(hAPP(c_List_Olist_OCons(_1755459), _1755465), _1755467))), c_List_Olistrel1(_1755459, _1755469)))), 48780 ^ _778908 : [(48787 ^ _778908) ^ [] : [_1755461 = _1755465, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755459), tc_List_Olist(_1755459))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755459), tc_List_Olist(_1755459)), _1755463), _1755467)), c_List_Olistrel1(_1755459, _1755469)))], (48781 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1755459, _1755459)), hAPP(hAPP(c_Product__Type_OPair(_1755459, _1755459), _1755461), _1755465)), _1755469)), _1755463 = _1755467]]], (44551 ^ _778908) ^ [_1649824, _1649826, _1649828, _1649830, _1649832, _1649834] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649824, tc_fun(_1649826, tc_HOL_Obool)), _1649828), _1649830), _1649832)), -(hBOOL(hAPP(hAPP(_1649830, _1649834), _1649832))), hBOOL(hAPP(hAPP(c_member(_1649824), _1649834), _1649828))], (50757 ^ _778908) ^ [_1798638, _1798640] : [-(c_List_Oconcat(_1798638, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798638), tc_List_Olist(_1798638)), c_List_Olist_Olist__case(tc_List_Olist(_1798638), _1798638, c_List_Olist_ONil(_1798638), hAPP(hAPP(c_COMBB(tc_List_Olist(_1798638), tc_fun(tc_List_Olist(_1798638), tc_List_Olist(_1798638)), _1798638), c_COMBK(tc_List_Olist(_1798638), tc_List_Olist(_1798638))), hAPP(hAPP(c_COMBC(_1798638, tc_List_Olist(_1798638), tc_List_Olist(_1798638)), c_List_Olist_OCons(_1798638)), c_List_Olist_ONil(_1798638))))), _1798640)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798638), _1798638), c_List_Ohd(_1798638)), hAPP(c_List_Ofilter(tc_List_Olist(_1798638), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1798638)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1798638), tc_List_Olist(_1798638), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1798638)))), _1798640)))], (51625 ^ _778908) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (44881 ^ _778908) ^ [_1659099, _1659101, _1659103, _1659105, _1659107, _1659109] : [-(hAPP(c_Set_Ovimage(_1659099, _1659101, _1659103), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659105, tc_fun(_1659101, tc_HOL_Obool)), _1659107), _1659109)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659105, tc_fun(_1659099, tc_HOL_Obool)), _1659107), hAPP(hAPP(c_COMBB(tc_fun(_1659101, tc_HOL_Obool), tc_fun(_1659099, tc_HOL_Obool), _1659105), c_Set_Ovimage(_1659099, _1659101, _1659103)), _1659109)))], (8978 ^ _778908) ^ [_928982, _928984] : [class_Rings_Oring__1__no__zero__divisors(_928982), 8981 ^ _778908 : [(8982 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928982), _928984), _928984) = c_Groups_Oone__class_Oone(_928982), -(_928984 = c_Groups_Oone__class_Oone(_928982)), -(_928984 = hAPP(c_Groups_Ouminus__class_Ouminus(_928982), c_Groups_Oone__class_Oone(_928982)))], (8992 ^ _778908) ^ [] : [8993 ^ _778908 : [(8996 ^ _778908) ^ [] : [_928984 = hAPP(c_Groups_Ouminus__class_Ouminus(_928982), c_Groups_Oone__class_Oone(_928982))], (8994 ^ _778908) ^ [] : [_928984 = c_Groups_Oone__class_Oone(_928982)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928982), _928984), _928984) = c_Groups_Oone__class_Oone(_928982))]]], (21791 ^ _778908) ^ [_1155602, _1155604, _1155606, _1155608] : [class_Fields_Olinordered__field__inverse__zero(_1155602), class_Int_Onumber(_1155602), 21798 ^ _778908 : [(21799 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), _1155604), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155602), _1155606), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)))), 21802 ^ _778908 : [(21809 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), c_Groups_Ozero__class_Ozero(_1155602)), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)))), 21812 ^ _778908 : [(21819 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)), c_Groups_Ozero__class_Ozero(_1155602)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), _1155604), c_Groups_Ozero__class_Ozero(_1155602))))], (21813 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)), c_Groups_Ozero__class_Ozero(_1155602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), _1155606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155602), _1155604), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)))))]]], (21803 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), c_Groups_Ozero__class_Ozero(_1155602)), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155602), _1155604), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608))), _1155606)))]]], (21825 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), _1155604), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155602), _1155606), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608))))), 21828 ^ _778908 : [(21831 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155602), _1155604), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608))), _1155606))], (21829 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), c_Groups_Ozero__class_Ozero(_1155602)), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608))))]], 21832 ^ _778908 : [(21835 ^ _778908) ^ [] : [21836 ^ _778908 : [(21839 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), _1155606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155602), _1155604), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608))))], (21837 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)), c_Groups_Ozero__class_Ozero(_1155602))))]], 21840 ^ _778908 : [(21843 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), _1155604), c_Groups_Ozero__class_Ozero(_1155602)))], (21841 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)), c_Groups_Ozero__class_Ozero(_1155602)))]]], (21833 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155602), c_Groups_Ozero__class_Ozero(_1155602)), hAPP(c_Int_Onumber__class_Onumber__of(_1155602), _1155608)))]]]]], (31050 ^ _778908) ^ [_1336268, _1336270, _1336272, _1336274, _1336276, _1336278] : [hBOOL(hAPP(hAPP(c_member(_1336268), _1336270), _1336272)), _1336274 = hAPP(_1336276, _1336270), -(hBOOL(hAPP(hAPP(c_member(_1336278), _1336274), hAPP(c_Set_Oimage(_1336268, _1336278, _1336276), _1336272))))], (5793 ^ _778908) ^ [_871219, _871221] : [class_Groups_Ozero(_871219), 5796 ^ _778908 : [(5803 ^ _778908) ^ [] : [_871221 = c_Groups_Ozero__class_Ozero(_871219), -(c_Groups_Ozero__class_Ozero(_871219) = _871221)], (5797 ^ _778908) ^ [] : [c_Groups_Ozero__class_Ozero(_871219) = _871221, -(_871221 = c_Groups_Ozero__class_Ozero(_871219))]]], (25997 ^ _778908) ^ [_1235612, _1235614, _1235616, _1235618] : [class_Rings_Ocomm__ring__1(_1235612), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235612), _1235614), _1235616)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235612), _1235614), _1235618)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235612), _1235614), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1235612), _1235616), _1235618))))], (25075 ^ _778908) ^ [_1219127, _1219129, _1219131, _1219133] : [hBOOL(hAPP(_1219127, _1219129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219131, tc_HOL_Obool)), _1219127), _1219133)), -(hBOOL(hAPP(_1219133, _1219129)))], (8414 ^ _778908) ^ [_919906, _919908, _919910] : [class_Rings_Olinordered__semidom(_919906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919906), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919906), _919908)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919906), _919910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919908), _919910)))], (44887 ^ _778908) ^ [_1659478, _1659480, _1659482, _1659484, _1659486] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659478, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659480, tc_fun(_1659478, tc_HOL_Obool)), _1659482), _1659484)), _1659486) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659480, tc_fun(_1659478, tc_HOL_Obool)), _1659482), hAPP(hAPP(c_COMBC(_1659480, tc_fun(_1659478, tc_HOL_Obool), tc_fun(_1659478, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659478, tc_HOL_Obool), tc_fun(tc_fun(_1659478, tc_HOL_Obool), tc_fun(_1659478, tc_HOL_Obool)), _1659480), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659478, tc_HOL_Obool))), _1659484)), _1659486)))], (17091 ^ _778908) ^ [_1073565, _1073567] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1073565), _1073567)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1073565) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (27290 ^ _778908) ^ [_1261121, _1261123, _1261125, _1261127] : [class_Orderings_Olinorder(_1261121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261121), _1261123), _1261125)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261121, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1261121, _1261123), _1261127)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1261121, _1261123), _1261125)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1261121, _1261125), _1261127))], (28225 ^ _778908) ^ [_1280080, _1280082, _1280084] : [class_Lattices_Osemilattice__sup(_1280080), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280080), _1280082), _1280084) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280080), _1280084), _1280082))], (18657 ^ _778908) ^ [_1100488, _1100490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100488)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100488), _1100490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100488), c_Int_OPls)))], (33469 ^ _778908) ^ [_1389619, _1389621] : [class_Orderings_Olinorder(_1389619), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389619), _1389621)), -(_1389621 = c_Orderings_Obot__class_Obot(tc_fun(_1389619, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1389619), c_Big__Operators_Olinorder__class_OMin(_1389619, _1389621)), _1389621)))], (28493 ^ _778908) ^ [_1285006, _1285008, _1285010] : [class_Lattices_Olattice(_1285006), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285006), _1285008), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285006), _1285010), _1285008))))], (15266 ^ _778908) ^ [_1038400, _1038402] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1038400))), -(c_SMT_Oz3div(_1038402, _1038400) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038402), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1038400))))], (17235 ^ _778908) ^ [_1076405] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076405), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1076405) = _1076405)], (31060 ^ _778908) ^ [_1336461, _1336463, _1336465, _1336467, _1336469] : [hBOOL(hAPP(hAPP(c_member(_1336461), _1336463), _1336465)), -(hBOOL(hAPP(hAPP(c_member(_1336467), hAPP(_1336469, _1336463)), hAPP(c_Set_Oimage(_1336461, _1336467, _1336469), _1336465))))], (27596 ^ _778908) ^ [_1267650, _1267652, _1267654] : [class_Groups_Oordered__ab__group__add(_1267650), -(hAPP(c_Set_Oimage(_1267650, _1267650, c_Groups_Ouminus__class_Ouminus(_1267650)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1267650, _1267652, _1267654)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1267650, hAPP(c_Groups_Ouminus__class_Ouminus(_1267650), _1267654)), hAPP(c_Groups_Ouminus__class_Ouminus(_1267650), _1267652)))], (7082 ^ _778908) ^ [_897281, _897283] : [_897281 = c_Option_Ooption_ONone(_897283), 7085 ^ _778908 : [(7086 ^ _778908) ^ [_897353] : [_897281 = hAPP(c_Option_Ooption_OSome(_897283), _897353)]]], (30119 ^ _778908) ^ [_1318487, _1318489, _1318491, _1318493] : [_1318487 = c_Orderings_Obot__class_Obot(tc_fun(_1318489, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318489, tc_fun(_1318491, tc_HOL_Obool)), _1318487), hAPP(c_COMBK(tc_fun(_1318491, tc_HOL_Obool), _1318489), _1318493)) = c_Orderings_Obot__class_Obot(tc_fun(_1318491, tc_HOL_Obool)))], (35635 ^ _778908) ^ [_1435554, _1435556] : [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)), _1435554), 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)), _1435556), 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)), _1435554), _1435556)), c_Int_Ointrel)))], (27739 ^ _778908) ^ [_1270720, _1270722] : [class_Groups_Oordered__ab__group__add(_1270720), -(hAPP(c_Set_Oimage(_1270720, _1270720, c_Groups_Ouminus__class_Ouminus(_1270720)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1270720), _1270722)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1270720), hAPP(c_Groups_Ouminus__class_Ouminus(_1270720), _1270722)))], (46006 ^ _778908) ^ [_1685399, _1685401, _1685403, _1685405] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1685401, _1685399)), _1685403), _1685405) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1685401), hAPP(hAPP(c_COMBC(_1685401, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1685399, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1685401), c_Smallcheck_Osmall__class_Osmall(_1685399)), hAPP(hAPP(c_COMBB(tc_fun(_1685399, tc_prod(_1685401, _1685399)), tc_fun(_1685399, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1685401), hAPP(c_COMBB(tc_prod(_1685401, _1685399), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1685399), _1685403)), c_Product__Type_OPair(_1685401, _1685399)))), _1685405)), _1685405)), class_Smallcheck_Osmall(_1685399), class_Smallcheck_Osmall(_1685401)], (30710 ^ _778908) ^ [_1329384, _1329386, _1329388] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329384), _1329386)), -(hAPP(c_Finite__Set_Ocard(_1329384), hAPP(hAPP(c_Set_Oinsert(_1329384), _1329388), _1329386)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1329384), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329384, tc_HOL_Obool)), _1329386), hAPP(hAPP(c_Set_Oinsert(_1329384), _1329388), c_Orderings_Obot__class_Obot(tc_fun(_1329384, tc_HOL_Obool)))))))], (5056 ^ _778908) ^ [_857110, _857112, _857114, _857116, _857118, _857120, _857122, _857124] : [-(c_List_Omap__filter(_857124, _857120, _857116, _857112) = c_List_Omap__filter(_857122, _857118, _857114, _857110)), _857124 = _857122, _857120 = _857118, _857116 = _857114, _857112 = _857110], (37096 ^ _778908) ^ [_1469390, _1469392, _1469394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469390, tc_HOL_Obool)), _1469392), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1469390, tc_HOL_Obool)), _1469394))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469390, tc_HOL_Obool)), _1469392), _1469394) = c_Orderings_Obot__class_Obot(tc_fun(_1469390, tc_HOL_Obool)))], (27805 ^ _778908) ^ [_1271998, _1272000] : [-(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)), _1271998)), 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), _1272000), _1271998))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1271998), _1272000))], (44917 ^ _778908) ^ [_1660654, _1660656, _1660658, _1660660, _1660662] : [-(_1660654 = c_Orderings_Obot__class_Obot(tc_fun(_1660656, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660656, tc_fun(_1660658, tc_HOL_Obool)), _1660654), hAPP(hAPP(c_COMBC(_1660656, tc_fun(_1660658, tc_HOL_Obool), tc_fun(_1660658, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1660658, tc_HOL_Obool), tc_fun(tc_fun(_1660658, tc_HOL_Obool), tc_fun(_1660658, tc_HOL_Obool)), _1660656), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660658, tc_HOL_Obool))), _1660660)), _1660662)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660658, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660656, tc_fun(_1660658, tc_HOL_Obool)), _1660654), _1660660)), _1660662))], (35120 ^ _778908) ^ [_1423761, _1423763, _1423765, _1423767] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423761), _1423767) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423765), _1423763), -(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), _1423761), _1423763)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1423765), _1423767))), c_Int_Ointrel)))], (50015 ^ _778908) ^ [_1783260, _1783262, _1783264] : [hBOOL(hAPP(c_List_Odistinct(_1783260), _1783262)), -(hAPP(c_List_Ofilter(_1783260, hAPP(hAPP(c_COMBC(_1783260, tc_fun(_1783260, tc_HOL_Obool), tc_HOL_Obool), c_member(_1783260)), hAPP(c_List_Oset(_1783260), c_List_Osublist(_1783260, _1783262, _1783264)))), _1783262) = c_List_Osublist(_1783260, _1783262, _1783264))], (28601 ^ _778908) ^ [_1287202, _1287204, _1287206] : [class_Orderings_Oorder(_1287202), 28604 ^ _778908 : [(28611 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287202), _1287204), _1287206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287202, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287202), _1287204)), hAPP(c_SetInterval_Oord__class_OatMost(_1287202), _1287206))))], (28605 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287202, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1287202), _1287204)), hAPP(c_SetInterval_Oord__class_OatMost(_1287202), _1287206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287202), _1287204), _1287206)))]]], (18259 ^ _778908) ^ [_1094584, _1094586] : [class_Rings_Osemiring__1(_1094584), 18262 ^ _778908 : [(18269 ^ _778908) ^ [] : [_1094586 = c_Groups_Ozero__class_Ozero(_1094584), -(c_Int_Oiszero(_1094584, _1094586))], (18263 ^ _778908) ^ [] : [c_Int_Oiszero(_1094584, _1094586), -(_1094586 = c_Groups_Ozero__class_Ozero(_1094584))]]], (36840 ^ _778908) ^ [_1463131, _1463133, _1463135, _1463137, _1463139] : [class_Lattices_Olattice(_1463131), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463133, _1463131)), _1463135), _1463137), _1463139) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463131), hAPP(_1463135, _1463139)), hAPP(_1463137, _1463139)))], (47601 ^ _778908) ^ [_1726084, _1726086] : [-(c_Random_Oselect(_1726084, _1726086) = 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(_1726084, 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(_1726084)), _1726086)))), hAPP(hAPP(c_COMBB(_1726084, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1726084, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1726084, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1726084, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1726084), _1726086)), c_Code__Numeral_Onat__of))))], (14521 ^ _778908) ^ [_1025354, _1025356, _1025358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025354), _1025356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025354), _1025358)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025356), _1025358))))], (26381 ^ _778908) ^ [_1243513, _1243515, _1243517, _1243519, _1243521] : [class_Rings_Ocomm__semiring__1(_1243513), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243513), _1243515), _1243517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243519), _1243521)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243513), hAPP(hAPP(c_Power_Opower__class_Opower(_1243513), _1243515), _1243519)), hAPP(hAPP(c_Power_Opower__class_Opower(_1243513), _1243517), _1243521))))], (8250 ^ _778908) ^ [_917132, _917134, _917136, _917138, _917140] : [-(hAPP(c_Sum__Type_OSuml(_917132, _917134, _917136, _917138), hAPP(c_Sum__Type_OInl(_917132, _917136), _917140)) = hAPP(_917138, _917140))], (41020 ^ _778908) ^ [_1558069, _1558071, _1558073, _1558075] : [c_Finite__Set_Ofun__left__comm__idem(_1558069, _1558071, _1558073), -(hAPP(c_Fun_Ocomp(_1558071, _1558071, _1558071, hAPP(_1558073, _1558075)), hAPP(_1558073, _1558075)) = hAPP(_1558073, _1558075))], (15410 ^ _778908) ^ [_1041088, _1041090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041088), _1041090)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1041090)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1041088)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041090), _1041088)))], (38890 ^ _778908) ^ [_1508465, _1508467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508465), c_Orderings_Otop__class_Otop(tc_fun(_1508465, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1508465, _1508465, _1508467), c_Orderings_Otop__class_Otop(tc_fun(_1508465, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1508465, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1508465, _1508465, _1508467, c_Orderings_Otop__class_Otop(tc_fun(_1508465, tc_HOL_Obool))))], (41426 ^ _778908) ^ [_1568955] : [-(c_Int_Oint__ge__less__than2(_1568955) = 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), _1568955)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (39753 ^ _778908) ^ [_1527988, _1527990, _1527992, _1527994, _1527996] : [hAPP(_1527988, _1527990) = hAPP(c_Option_Ooption_OSome(_1527992), _1527994), -(hAPP(hAPP(c_Set_Oinsert(_1527996), _1527990), c_Map_Odom(_1527996, _1527992, _1527988)) = c_Map_Odom(_1527996, _1527992, _1527988))], (51611 ^ _778908) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (5272 ^ _778908) ^ [_860466, _860468] : [_860468 = _860466, -(c_Lattices_Osemilattice__sup__class_Osup(_860468) = c_Lattices_Osemilattice__sup__class_Osup(_860466))], (25161 ^ _778908) ^ [_1221323, _1221325, _1221327, _1221329, _1221331] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1221323, _1221325, tc_HOL_Obool, _1221327), _1221329), _1221331)), -(hBOOL(hAPP(_1221327, hAPP(hAPP(c_Product__Type_OPair(_1221323, _1221325), _1221329), _1221331))))], (41440 ^ _778908) ^ [_1569252, _1569254, _1569256] : [c_Predicate_Oreflp(_1569252, _1569254), -(hBOOL(hAPP(hAPP(_1569254, _1569256), _1569256)))], (47924 ^ _778908) ^ [_1734228, _1734230, _1734232, _1734234, _1734236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734228), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734230)), _1734232))), 47927 ^ _778908 : [(47934 ^ _778908) ^ [] : [-(_1734228 = _1734234), -(hAPP(hAPP(c_List_Onth(_1734230), hAPP(hAPP(c_List_Olist__update(_1734230, _1734232), _1734228), _1734236)), _1734234) = hAPP(hAPP(c_List_Onth(_1734230), _1734232), _1734234))], (47928 ^ _778908) ^ [] : [_1734228 = _1734234, -(hAPP(hAPP(c_List_Onth(_1734230), hAPP(hAPP(c_List_Olist__update(_1734230, _1734232), _1734228), _1734236)), _1734234) = _1734236)]]], (30642 ^ _778908) ^ [_1327947, _1327949, _1327951, _1327953] : [-(c_Sum__Type_OPlus(_1327947, _1327949, _1327951, _1327953) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(_1327947, _1327949), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1327947, tc_sum(_1327947, _1327949), c_Sum__Type_OInl(_1327947, _1327949)), _1327951)), hAPP(c_Set_Oimage(_1327949, tc_sum(_1327947, _1327949), c_Sum__Type_OInr(_1327949, _1327947)), _1327953)))], (4246 ^ _778908) ^ [_844387, _844389, _844391, _844393, _844395, _844397] : [-(c_Smallcheck_Osmall_H(_844397, _844393, _844389) = c_Smallcheck_Osmall_H(_844395, _844391, _844387)), _844397 = _844395, _844393 = _844391, _844389 = _844387], (29158 ^ _778908) ^ [_1299440, _1299442, _1299444, _1299446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1299440, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299440, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29159 ^ [_1299440, _1299442, _1299444, _1299446])), _1299442)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299440, 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), 29159 ^ [_1299440, _1299442, _1299444, _1299446]), _1299444))), _1299446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1299440, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299440, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1299442)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299440, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1299446))))], (20645 ^ _778908) ^ [_1135263, _1135265, _1135267, _1135269] : [class_Fields_Ofield__inverse__zero(_1135263), -(_1135265 = c_Groups_Ozero__class_Ozero(_1135263)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135263), _1135265), _1135267)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135263), _1135265), _1135269)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135263), _1135267), _1135269))], (24029 ^ _778908) ^ [_1198082, _1198084, _1198086] : [class_Int_Onumber(_1198082), class_Orderings_Oord(_1198082), 24036 ^ _778908 : [(24043 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198082), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198084)), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198086)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198082), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198084)), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198086)) = hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198086))], (24037 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198082), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198084)), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198086))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198082), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198084)), hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198086)) = hAPP(c_Int_Onumber__class_Onumber__of(_1198082), _1198084))]]], (15090 ^ _778908) ^ [_1034923, _1034925, _1034927] : [class_Divides_Osemiring__div(_1034923), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034923), _1034925), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034923), _1034927), _1034925))), c_Divides_Odiv__class_Omod(_1034923, _1034927, _1034925)) = _1034927)], (29144 ^ _778908) ^ [_1299134, _1299136] : [class_Lattices_Oboolean__algebra(_1299134), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299134), _1299136), hAPP(c_Groups_Ouminus__class_Ouminus(_1299134), _1299136)) = c_Orderings_Otop__class_Otop(_1299134))], (44911 ^ _778908) ^ [_1660447, _1660449, _1660451, _1660453, _1660455] : [_1660447 = c_Orderings_Obot__class_Obot(tc_fun(_1660449, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660449, tc_fun(_1660451, tc_HOL_Obool)), _1660447), hAPP(hAPP(c_COMBC(_1660449, tc_fun(_1660451, tc_HOL_Obool), tc_fun(_1660451, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1660451, tc_HOL_Obool), tc_fun(tc_fun(_1660451, tc_HOL_Obool), tc_fun(_1660451, tc_HOL_Obool)), _1660449), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660451, tc_HOL_Obool))), _1660453)), _1660455)) = c_Orderings_Otop__class_Otop(tc_fun(_1660451, tc_HOL_Obool)))], (35512 ^ _778908) ^ [_1432902, _1432904, _1432906, _1432908, _1432910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432902, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1432904, _1432902, _1432906), _1432908)), _1432910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1432902, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1432904, tc_HOL_Obool), tc_fun(_1432902, tc_HOL_Obool), c_Set_Oimage(_1432904, _1432902, _1432906)), hAPP(c_Set_OPow(_1432904), _1432908))), hAPP(c_Set_OPow(_1432902), _1432910))))], (2428 ^ _778908) ^ [_815540, _815542, _815544, _815546, _815548, _815550, _815552, _815554] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_815554, _815550, _815546, _815542) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_815552, _815548, _815544, _815540)), _815554 = _815552, _815550 = _815548, _815546 = _815544, _815542 = _815540], (18415 ^ _778908) ^ [_1096837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096837), 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), _1096837)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20727 ^ _778908) ^ [_1136662, _1136664, _1136666, _1136668] : [class_Rings_Odivision__ring(_1136662), -(_1136664 = c_Groups_Ozero__class_Ozero(_1136662)), 20734 ^ _778908 : [(20741 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136662), _1136666), _1136664) = _1136668, -(_1136666 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136662), _1136668), _1136664))], (20735 ^ _778908) ^ [] : [_1136666 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136662), _1136668), _1136664), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136662), _1136666), _1136664) = _1136668)]]], (25051 ^ _778908) ^ [_1218563, _1218565, _1218567, _1218569, _1218571, _1218573, _1218575] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1218563, _1218565, _1218567, _1218569), _1218571), _1218573), _1218575) = c_New__DSequence_Oneg__bind(_1218563, _1218565, hAPP(hAPP(hAPP(_1218567, _1218571), _1218573), _1218575), hAPP(hAPP(c_COMBC(_1218563, 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(_1218565)))), hAPP(hAPP(c_COMBC(_1218563, 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(_1218565))))), hAPP(hAPP(c_COMBC(_1218563, 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(_1218565)))))), _1218569), _1218571)), _1218573)), _1218575)))], (9610 ^ _778908) ^ [_939948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _939948)), -(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, _939948))))], (45823 ^ _778908) ^ [_1681381, _1681383, _1681385, _1681387, _1681389, _1681391] : [-(hBOOL(hAPP(hAPP(c_member(_1681381), _1681383), c_Map_Odom(_1681381, _1681385, _1681387)))), -(c_Map_Omap__add(_1681381, _1681385, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1681381, tc_Option_Ooption(_1681385)), _1681389), _1681383), hAPP(c_Option_Ooption_OSome(_1681385), _1681391)), _1681387) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1681381, tc_Option_Ooption(_1681385)), c_Map_Omap__add(_1681381, _1681385, _1681389, _1681387)), _1681383), hAPP(c_Option_Ooption_OSome(_1681385), _1681391)))], (23421 ^ _778908) ^ [_1187204, _1187206, _1187208, _1187210, _1187212, _1187214] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187204, _1187206), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187208), _1187210))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187204, _1187206), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187212), _1187214))), -(_1187206 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1187208 = _1187212)], (50489 ^ _778908) ^ [_1792758, _1792760, _1792762, _1792764, _1792766] : [class_Orderings_Olinorder(_1792758), 50492 ^ _778908 : [(50499 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1792758, hAPP(hAPP(c_List_Omap(_1792760, _1792758), _1792762), _1792766)), -(c_List_Olinorder__class_Osorted(_1792758, hAPP(hAPP(c_List_Omap(_1792760, _1792758), _1792762), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1792760, _1792758, _1792762), _1792764), _1792766))))], (50493 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1792758, hAPP(hAPP(c_List_Omap(_1792760, _1792758), _1792762), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1792760, _1792758, _1792762), _1792764), _1792766))), -(c_List_Olinorder__class_Osorted(_1792758, hAPP(hAPP(c_List_Omap(_1792760, _1792758), _1792762), _1792766)))]]], (6602 ^ _778908) ^ [_886823, _886825, _886827, _886829, _886831, _886833] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_886823, _886825, _886827), _886829, _886831, hAPP(hAPP(hAPP(c_Natural_Oupdate, _886833), c_Com_Ovname_OLoc(_886823)), hAPP(hAPP(c_Natural_Ogetlocs, _886829), _886823))), 6606 ^ _778908 : [(6609 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_886827, hAPP(hAPP(hAPP(c_Natural_Oupdate, _886829), c_Com_Ovname_OLoc(_886823)), hAPP(_886825, _886829)), _886831, 6605 ^ [_886823, _886825, _886827, _886829, _886831, _886833]))], (6607 ^ _778908) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _886833), c_Com_Ovname_OLoc(_886823)), hAPP(hAPP(c_Natural_Ogetlocs, _886829), _886823)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6605 ^ [_886823, _886825, _886827, _886829, _886831, _886833]), c_Com_Ovname_OLoc(_886823)), hAPP(hAPP(c_Natural_Ogetlocs, _886829), _886823)))]]], (40222 ^ _778908) ^ [_1540380, _1540382, _1540384, _1540386, _1540388, _1540390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1540380, _1540382), tc_HOL_Obool)), _1540384), hAPP(hAPP(c_Product__Type_OSigma(_1540380, _1540382), _1540386), hAPP(c_COMBK(tc_fun(_1540382, tc_HOL_Obool), _1540380), _1540388)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1540382, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1540380, _1540382, _1540384), _1540390)), _1540388)))], (37120 ^ _778908) ^ [_1470000, _1470002, _1470004] : [class_Orderings_Oorder(_1470000), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470000, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1470000), _1470002)), c_SetInterval_Oord__class_OatLeastAtMost(_1470000, _1470002, _1470004)) = c_Orderings_Obot__class_Obot(tc_fun(_1470000, tc_HOL_Obool)))], (4190 ^ _778908) ^ [_843503, _843505, _843507, _843509, _843511, _843513] : [-(c_Relation_Orel__comp(_843513, _843509, _843505) = c_Relation_Orel__comp(_843511, _843507, _843503)), _843513 = _843511, _843509 = _843507, _843505 = _843503], (19263 ^ _778908) ^ [_1110599, _1110601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110599)), -(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)))), _1110601))), 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)))), _1110599)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1110601), _1110599))], (17345 ^ _778908) ^ [_1078514, _1078516, _1078518, _1078520] : [class_Rings_Olinordered__semidom(_1078514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078516), _1078518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078514), c_Groups_Ozero__class_Ozero(_1078514)), _1078520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078514), _1078520), c_Groups_Oone__class_Oone(_1078514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078514), hAPP(hAPP(c_Power_Opower__class_Opower(_1078514), _1078520), _1078518)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078514), _1078520), _1078516))))], (50357 ^ _778908) ^ [_1790755, _1790757, _1790759] : [class_Orderings_Olinorder(_1790755), c_List_Olinorder__class_Osorted(_1790755, _1790757), -(c_List_Olinorder__class_Osorted(_1790755, c_List_Olinorder__class_Oinsort__insert__key(_1790755, _1790755, c_COMBI(_1790755), _1790759, _1790757)))], (40440 ^ _778908) ^ [_1546638, _1546640, _1546642, _1546644, _1546646, _1546648, _1546650, _1546652] : [-(hAPP(c_Product__Type_Omap__pair(_1546638, _1546640, _1546642, _1546644, _1546646, _1546648), hAPP(hAPP(c_Product__Type_OPair(_1546638, _1546642), _1546650), _1546652)) = hAPP(hAPP(c_Product__Type_OPair(_1546640, _1546644), hAPP(_1546646, _1546650)), hAPP(_1546648, _1546652)))], (31223 ^ _778908) ^ [_1342006, _1342008, _1342010, _1342012] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342006, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1342006, tc_fun(_1342006, tc_HOL_Obool), tc_HOL_Obool), c_member(_1342006)), _1342008)), hAPP(hAPP(c_COMBC(_1342006, tc_fun(_1342006, tc_HOL_Obool), tc_HOL_Obool), c_member(_1342006)), _1342010)), _1342012)), -(hBOOL(hAPP(hAPP(c_member(_1342006), _1342012), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342006, tc_HOL_Obool)), _1342008), _1342010))))], (48725 ^ _778908) ^ [_1753711, _1753713, _1753715, _1753717, _1753719, _1753721] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753711), tc_List_Olist(_1753711))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753711), tc_List_Olist(_1753711)), hAPP(hAPP(c_List_Oappend(_1753711), _1753713), _1753719)), hAPP(hAPP(c_List_Oappend(_1753711), _1753715), _1753721))), c_List_Olistrel1(_1753711, _1753717)))), 48726 ^ _778908 : [(48733 ^ _778908) ^ [] : [_1753713 = _1753715, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753711), tc_List_Olist(_1753711))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753711), tc_List_Olist(_1753711)), _1753719), _1753721)), c_List_Olistrel1(_1753711, _1753717)))], (48727 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753711), tc_List_Olist(_1753711))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753711), tc_List_Olist(_1753711)), _1753713), _1753715)), c_List_Olistrel1(_1753711, _1753717))), _1753719 = _1753721]]], (42517 ^ _778908) ^ [_1601197, _1601199, _1601201, _1601203, _1601205] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1601197), _1601199), _1601201), _1601203), _1601205) = c_New__DSequence_Oneg__single(_1601197, _1601199))], (9648 ^ _778908) ^ [_940587, _940589] : [class_Groups_Olinordered__ab__group__add(_940587), 9651 ^ _778908 : [(9658 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940587), c_Groups_Ozero__class_Ozero(_940587)), _940589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940587), hAPP(c_Groups_Ouminus__class_Ouminus(_940587), _940589)), _940589)))], (9652 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940587), hAPP(c_Groups_Ouminus__class_Ouminus(_940587), _940589)), _940589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940587), c_Groups_Ozero__class_Ozero(_940587)), _940589)))]]], (28439 ^ _778908) ^ [_1284084, _1284086, _1284088, _1284090] : [class_Lattices_Osemilattice__sup(_1284084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284084), _1284086), _1284088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284084), _1284086), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284084), _1284088), _1284090))))], (43737 ^ _778908) ^ [_1631695, _1631697, _1631699] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631695, _1631695)), hAPP(hAPP(c_Product__Type_OPair(_1631695, _1631695), _1631697), _1631697)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631695, _1631695), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1631699))))], (15028 ^ _778908) ^ [_1033680, _1033682, _1033684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033680)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033684), _1033680)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033682), _1033684)), _1033680))], (6583 ^ _778908) ^ [_886113, _886115, _886117, _886119, _886121] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_886113, _886115, _886117)), _886119), hAPP(hAPP(hAPP(c_Natural_Oupdate, _886121), c_Com_Ovname_OLoc(_886113)), hAPP(hAPP(c_Natural_Ogetlocs, _886119), _886113)))), 6587 ^ _778908 : [(6590 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886117), hAPP(hAPP(hAPP(c_Natural_Oupdate, _886119), c_Com_Ovname_OLoc(_886113)), hAPP(_886115, _886119))), 6586 ^ [_886113, _886115, _886117, _886119, _886121])))], (6588 ^ _778908) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _886121), c_Com_Ovname_OLoc(_886113)), hAPP(hAPP(c_Natural_Ogetlocs, _886119), _886113)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6586 ^ [_886113, _886115, _886117, _886119, _886121]), c_Com_Ovname_OLoc(_886113)), hAPP(hAPP(c_Natural_Ogetlocs, _886119), _886113)))]]], (30156 ^ _778908) ^ [_1319267, _1319269] : [class_Lattices_Obounded__lattice__bot(_1319267), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1319267), _1319269), c_Orderings_Obot__class_Obot(_1319267)) = _1319269)], (34597 ^ _778908) ^ [_1411890, _1411892, _1411894] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1411890), _1411892)), 34600 ^ _778908 : [(34601 ^ _778908) ^ [] : [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(_1411890, tc_Nat_Onat), _1411894), _1411892))), 34604 ^ _778908 : [(34605 ^ _778908) ^ [_1412058] : [hBOOL(hAPP(hAPP(c_member(_1411890), _1412058), _1411892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1411894, _1412058))))]]], (34611 ^ _778908) ^ [] : [34613 ^ _778908 : [(34616 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1411894, 34612 ^ [_1411890, _1411892, _1411894])))], (34614 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411890), 34612 ^ [_1411890, _1411892, _1411894]), _1411892)))]], -(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(_1411890, tc_Nat_Onat), _1411894), _1411892))))]]], (1222 ^ _778908) ^ [_797057, _797059] : [-(class_Groups_Osgn__if(_797057)), _797059 = _797057, class_Groups_Osgn__if(_797059)], (39795 ^ _778908) ^ [_1528952, _1528954, _1528956, _1528958, _1528960] : [class_Groups_Oab__semigroup__mult(_1528952), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1528952, _1528952, c_Groups_Otimes__class_Otimes(_1528952), _1528954, _1528956), _1528958)), hBOOL(hAPP(hAPP(c_member(_1528952), _1528960), _1528956)), -(hBOOL(hAPP(hAPP(c_member(_1528952), _1528954), _1528956))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1528952, _1528952, c_Groups_Otimes__class_Otimes(_1528952), _1528960, hAPP(hAPP(c_Set_Oinsert(_1528952), _1528954), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1528952, tc_HOL_Obool)), _1528956), hAPP(hAPP(c_Set_Oinsert(_1528952), _1528960), c_Orderings_Obot__class_Obot(tc_fun(_1528952, tc_HOL_Obool)))))), _1528958)))], (40766 ^ _778908) ^ [_1553269, _1553271, _1553273] : [class_Orderings_Olinorder(_1553269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553269), _1553271)), -(_1553271 = c_Orderings_Obot__class_Obot(tc_fun(_1553269, tc_HOL_Obool))), 40777 ^ _778908 : [(40787 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553269), hAPP(c_Finite__Set_Ofold1(_1553269, c_Orderings_Oord__class_Omin(_1553269)), _1553271)), _1553273))), 40788 ^ _778908 : [(40789 ^ _778908) ^ [_1553658] : [hBOOL(hAPP(hAPP(c_member(_1553269), _1553658), _1553271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553269), _1553658), _1553273))]]], (40778 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553269), hAPP(c_Finite__Set_Ofold1(_1553269, c_Orderings_Oord__class_Omin(_1553269)), _1553271)), _1553273)), 40782 ^ _778908 : [(40785 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553269), 40781 ^ [_1553269, _1553271, _1553273]), _1553273)))], (40783 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553269), 40781 ^ [_1553269, _1553271, _1553273]), _1553271)))]]]]], (42356 ^ _778908) ^ [_1597249, _1597251, _1597253] : [-(hAPP(c_Set_Oimage(tc_prod(_1597249, _1597251), _1597249, c_Product__Type_Ofst(_1597249, _1597251)), _1597253) = hAPP(c_Relation_ODomain(_1597249, _1597251), _1597253))], (23959 ^ _778908) ^ [_1196719, _1196721, _1196723, _1196725] : [class_Orderings_Olinorder(_1196719), 23962 ^ _778908 : [(23963 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196719), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196719), _1196721), _1196723)), _1196725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196719), _1196721), _1196725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196719), _1196723), _1196725)))], (23973 ^ _778908) ^ [] : [23974 ^ _778908 : [(23977 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196719), _1196723), _1196725))], (23975 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196719), _1196721), _1196725))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196719), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196719), _1196721), _1196723)), _1196725)))]]], (8176 ^ _778908) ^ [_915853, _915855, _915857] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_915853, _915855)), hAPP(c_Sum__Type_OInl(_915853, _915855), _915857)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10649 ^ _778908) ^ [_957646, _957648, _957650, _957652] : [class_Orderings_Oord(_957646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957646), _957648), _957650)), _957650 = _957652, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957646), _957648), _957652)))], (22608 ^ _778908) ^ [_1171008, _1171010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1171008)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1171010))), -(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(_1171010))), 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), _1171008)), c_Int_Onat))))))], (51205 ^ _778908) ^ [_1809066, _1809068] : [class_Orderings_Oord(_1809066), -(class_Orderings_Oord(tc_fun(_1809068, _1809066)))], (19599 ^ _778908) ^ [_1116477, _1116479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116477), _1116479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1116477)), c_Int_OBit0(_1116479))))], (21511 ^ _778908) ^ [_1150435, _1150437] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150435), _1150437), hAPP(c_Int_Onumber__class_Onumber__of(_1150435), c_Int_OBit1(c_Int_OPls))) = _1150437), class_Fields_Ofield(_1150435), class_Int_Onumber__ring(_1150435)], (7310 ^ _778908) ^ [_901186, _901188] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901186), _901188), 7315 ^ _778908 : [(7318 ^ _778908) ^ [] : [-(_901188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7316 ^ _778908) ^ [] : [-(_901186 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7319 ^ _778908 : [(7322 ^ _778908) ^ [] : [-(_901188 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7320 ^ _778908) ^ [] : [-(_901186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49416 ^ _778908) ^ [_1770162, _1770164, _1770166, _1770168] : [class_Complete__Lattice_Ocomplete__lattice(_1770162), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1770164, _1770162), hAPP(c_List_Oset(_1770164), _1770166)), _1770168) = hAPP(c_List_Ofoldl(_1770162, _1770164, hAPP(c_COMBC(_1770164, _1770162, _1770162), hAPP(hAPP(c_COMBB(_1770162, tc_fun(_1770162, _1770162), _1770164), c_Lattices_Osemilattice__inf__class_Oinf(_1770162)), _1770168)), c_Orderings_Otop__class_Otop(_1770162)), _1770166))], (40434 ^ _778908) ^ [_1546477, _1546479, _1546481] : [-(hAPP(c_Product__Type_Omap__pair(_1546477, _1546477, _1546479, _1546479, c_COMBI(_1546477), c_COMBI(_1546479)), _1546481) = _1546481)], (35570 ^ _778908) ^ [_1434055, _1434057, _1434059] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1434055, tc_HOL_Obool)), _1434059), hAPP(c_Set_OPow(_1434055), _1434057))), -(hBOOL(hAPP(c_Predicate_OPowp(_1434055, hAPP(hAPP(c_COMBC(_1434055, tc_fun(_1434055, tc_HOL_Obool), tc_HOL_Obool), c_member(_1434055)), _1434057)), _1434059)))], (1918 ^ _778908) ^ [_806679, _806681, _806683, _806685, _806687, _806689] : [-(c_String_Ochar_Ochar__case(_806689, _806685, _806681) = c_String_Ochar_Ochar__case(_806687, _806683, _806679)), _806689 = _806687, _806685 = _806683, _806681 = _806679], (25415 ^ _778908) ^ [_1225750, _1225752] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225750), _1225752)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225752), _1225750))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225752), _1225750)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225750), _1225752)))], (48967 ^ _778908) ^ [_1760438, _1760440, _1760442] : [hAPP(hAPP(c_List_Odrop(_1760438), _1760440), _1760442) = c_List_Olist_ONil(_1760438), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760438)), _1760442)), _1760440)))], (26553 ^ _778908) ^ [_1246593, _1246595, _1246597] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1246595), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246593), _1246597))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246593, _1246595) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246597, _1246595))], (14718 ^ _778908) ^ [_1028684, _1028686, _1028688, _1028690] : [class_Divides_Osemiring__div(_1028684), -(_1028686 = c_Groups_Ozero__class_Ozero(_1028684)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028684), _1028688), _1028686)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028684), _1028690), _1028686)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028684), _1028688), _1028690))], (3488 ^ _778908) ^ [_832530, _832532] : [_832532 = _832530, -(c_Power_Opower__class_Opower(_832532) = c_Power_Opower__class_Opower(_832530))], (41682 ^ _778908) ^ [_1580149, _1580151, _1580153] : [-(hAPP(c_Fun_Ocomp(_1580149, _1580149, _1580151, c_Fun_Oid(_1580149)), _1580153) = _1580153)], (32006 ^ _778908) ^ [_1359415, _1359417, _1359419, _1359421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359415, tc_HOL_Obool)), _1359417), hAPP(hAPP(c_Set_Oinsert(_1359415), _1359419), _1359421))), 32009 ^ _778908 : [(32016 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359415), _1359419), _1359421))), 32019 ^ _778908 : [(32026 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359415), _1359419), _1359417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1359415, tc_HOL_Obool)), _1359417), _1359421)))], (32020 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1359415), _1359419), _1359417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359415, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359415, tc_HOL_Obool)), _1359417), hAPP(hAPP(c_Set_Oinsert(_1359415), _1359419), c_Orderings_Obot__class_Obot(tc_fun(_1359415, tc_HOL_Obool))))), _1359421)))]]], (32010 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1359415), _1359419), _1359421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359415, tc_HOL_Obool)), _1359417), _1359421)))]]], (32449 ^ _778908) ^ [_1368942, _1368944, _1368946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368942)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1368944), _1368946)), 32456 ^ _778908 : [(32457 ^ _778908) ^ [_1369132] : [32459 ^ _778908 : [(32465 ^ _778908) ^ [] : [-(_1369132 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32461 ^ [_1368942, _1368944, _1368946, _1369132]), 32458 ^ [_1368942, _1368944, _1368946, _1369132]))], (32463 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32461 ^ [_1368942, _1368944, _1368946, _1369132]), _1368946)))], (32460 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32458 ^ [_1368942, _1368944, _1368946, _1369132]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1368942))))]], -(_1369132 = _1368944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1369132), _1368942) = _1368944]]], (14019 ^ _778908) ^ [_1016129, _1016131, _1016133] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016129), _1016131), _1016133) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016129), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016131, _1016133)), _1016133))], (19117 ^ _778908) ^ [] : [-(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)))], (31980 ^ _778908) ^ [_1358942, _1358944, _1358946] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358942), _1358944)), 31983 ^ _778908 : [(31990 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358942), _1358946), _1358944))), -(hAPP(c_Finite__Set_Ocard(_1358942), hAPP(hAPP(c_Set_Oinsert(_1358942), _1358946), _1358944)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1358942), _1358944)))], (31984 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1358942), _1358946), _1358944)), -(hAPP(c_Finite__Set_Ocard(_1358942), hAPP(hAPP(c_Set_Oinsert(_1358942), _1358946), _1358944)) = hAPP(c_Finite__Set_Ocard(_1358942), _1358944))]]], (36278 ^ _778908) ^ [_1451406, _1451408, _1451410, _1451412, _1451414, _1451416, _1451418, _1451420, _1451422, _1451424] : [c_Equiv__Relations_Oequiv(_1451406, _1451408, _1451410), c_Equiv__Relations_Oequiv(_1451412, _1451414, _1451416), c_Equiv__Relations_Ocongruent2(_1451406, _1451412, tc_fun(_1451418, tc_HOL_Obool), _1451410, _1451416, _1451420), hBOOL(hAPP(hAPP(c_member(_1451406), _1451422), _1451408)), hBOOL(hAPP(hAPP(c_member(_1451412), _1451424), _1451414)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451406, tc_fun(_1451418, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1451406, _1451406, _1451410), hAPP(hAPP(c_Set_Oinsert(_1451406), _1451422), c_Orderings_Obot__class_Obot(tc_fun(_1451406, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1451412, tc_fun(_1451418, tc_HOL_Obool)), tc_fun(_1451418, tc_HOL_Obool), _1451406), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451412, tc_fun(_1451418, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1451412, _1451412, _1451416), hAPP(hAPP(c_Set_Oinsert(_1451412), _1451424), c_Orderings_Obot__class_Obot(tc_fun(_1451412, tc_HOL_Obool)))))), _1451420)) = hAPP(hAPP(_1451420, _1451422), _1451424))], (32684 ^ _778908) ^ [_1373748, _1373750, _1373752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373748, tc_HOL_Obool)), _1373750), hAPP(hAPP(c_Set_Oinsert(_1373748), _1373752), c_Orderings_Obot__class_Obot(tc_fun(_1373748, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1373748, _1373752, _1373750) = _1373752)], (45388 ^ _778908) ^ [_1671511] : [class_Complete__Lattice_Ocomplete__lattice(_1671511), -(c_Complete__Lattice_OInf__class_OInf(_1671511, c_Orderings_Obot__class_Obot(tc_fun(_1671511, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1671511))], (16585 ^ _778908) ^ [_1063920, _1063922, _1063924] : [class_Groups_Oordered__ab__group__add__abs(_1063920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063920), hAPP(c_Groups_Oabs__class_Oabs(_1063920), _1063922)), _1063924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063920), _1063922), _1063924)))], (3010 ^ _778908) ^ [_824927, _824929, _824931, _824933, _824935, _824937, _824939, _824941] : [-(c_New__DSequence_Oneg__bind(_824941, _824937, _824933, _824929) = c_New__DSequence_Oneg__bind(_824939, _824935, _824931, _824927)), _824941 = _824939, _824937 = _824935, _824933 = _824931, _824929 = _824927], (46452 ^ _778908) ^ [_1696217, _1696219] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1696217, _1696219) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1696217), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1696219), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (41822 ^ _778908) ^ [_1584083, _1584085, _1584087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584083, _1584083), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584083, _1584083, _1584083), _1584085), _1584087)), _1584085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1584083, tc_HOL_Obool), tc_fun(_1584083, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1584083, tc_HOL_Obool), tc_fun(_1584083, tc_HOL_Obool), tc_fun(_1584083, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1584083, _1584085)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1584083, tc_HOL_Obool), tc_fun(_1584083, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1584083, _1584087)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1584083, tc_HOL_Obool), tc_fun(_1584083, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1584083, tc_HOL_Obool), tc_fun(_1584083, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1584083, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1584083, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1584083, tc_HOL_Obool), tc_fun(_1584083, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1584083, _1584085))))], (49241 ^ _778908) ^ [_1766450, _1766452, _1766454] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1766450, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766452)), _1766454)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1766452, _1766450), _1766454) = _1766454)], (5674 ^ _778908) ^ [_866547, _866549, _866551, _866553] : [-(tc_sum(_866553, _866549) = tc_sum(_866551, _866547)), _866553 = _866551, _866549 = _866547], (10044 ^ _778908) ^ [_947671, _947673, _947675, _947677, _947679, _947681] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_947671), -(_947673 = c_Groups_Ozero__class_Ozero(_947671)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947671), _947675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947671), _947673), _947679)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947671), _947677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947671), _947673), _947681)), _947675 = _947677, -(_947679 = _947681)], (22554 ^ _778908) ^ [_1169871, _1169873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169871), _1169873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1169871)), hAPP(c_Code__Numeral_Oof__nat, _1169873))))], (26351 ^ _778908) ^ [_1242928, _1242930, _1242932] : [class_Divides_Oring__div(_1242928), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242928), _1242930), _1242932)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242928), hAPP(c_Groups_Ouminus__class_Ouminus(_1242928), _1242932)), _1242930) = hAPP(c_Groups_Ouminus__class_Ouminus(_1242928), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242928), _1242932), _1242930)))], (51349 ^ _778908) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (10100 ^ _778908) ^ [] : [-(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))))], (10182 ^ _778908) ^ [_949955, _949957] : [class_Rings_Oring__1(_949955), -(hAPP(c_Int_Oring__1__class_Oof__int(_949955), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _949957)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_949955), _949957))], (6228 ^ _778908) ^ [_879082, _879084, _879086, _879088] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_879082), _879084), _879086)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_879082), _879084), _879088)), -(_879088 = _879086)], (39552 ^ _778908) ^ [_1523301, _1523303, _1523305, _1523307, _1523309] : [hAPP(c_Set_Oimage(_1523301, _1523303, _1523305), c_Orderings_Otop__class_Otop(tc_fun(_1523301, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1523303, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523301, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1523301, _1523303, _1523305), _1523307)), _1523309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523303, tc_HOL_Obool)), _1523307), hAPP(c_Set_Oimage(_1523301, _1523303, _1523305), _1523309))))], (42611 ^ _778908) ^ [_1604281] : [-(_1604281 = hAPP(c_Int_OAbs__Integ, 42609 ^ [_1604281]))], (41396 ^ _778908) ^ [_1567907, _1567909, _1567911, _1567913] : [-(c_Fun_Ooverride__on(_1567907, _1567909, _1567911, _1567913, c_Orderings_Obot__class_Obot(tc_fun(_1567907, tc_HOL_Obool))) = _1567911)], (51273 ^ _778908) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (32969 ^ _778908) ^ [_1379600, _1379602, _1379604] : [class_Lattices_Olattice(_1379600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379600), _1379602)), hBOOL(hAPP(hAPP(c_member(_1379600), _1379604), _1379602)), 32980 ^ _778908 : [(32987 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379600, tc_HOL_Obool)), _1379602), hAPP(hAPP(c_Set_Oinsert(_1379600), _1379604), c_Orderings_Obot__class_Obot(tc_fun(_1379600, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1379600, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1379600, _1379602) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1379600), _1379604), c_Big__Operators_Olattice__class_OSup__fin(_1379600, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379600, tc_HOL_Obool)), _1379602), hAPP(hAPP(c_Set_Oinsert(_1379600), _1379604), c_Orderings_Obot__class_Obot(tc_fun(_1379600, tc_HOL_Obool)))))))], (32981 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379600, tc_HOL_Obool)), _1379602), hAPP(hAPP(c_Set_Oinsert(_1379600), _1379604), c_Orderings_Obot__class_Obot(tc_fun(_1379600, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1379600, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1379600, _1379602) = _1379604)]]], (29861 ^ _778908) ^ [_1313303, _1313305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1313303, _1313305)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1313303, _1313305), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1313305), c_Orderings_Otop__class_Otop(tc_fun(_1313305, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1313303), c_Orderings_Otop__class_Otop(tc_fun(_1313303, tc_HOL_Obool)))))], (28920 ^ _778908) ^ [_1293546, _1293548, _1293550, _1293552, _1293554] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293546, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293548, tc_fun(_1293546, tc_HOL_Obool)), _1293550), _1293552)), _1293554) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293548, tc_fun(_1293546, tc_HOL_Obool)), _1293550), hAPP(hAPP(c_COMBC(_1293548, tc_fun(_1293546, tc_HOL_Obool), tc_fun(_1293546, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293546, tc_HOL_Obool), tc_fun(tc_fun(_1293546, tc_HOL_Obool), tc_fun(_1293546, tc_HOL_Obool)), _1293548), c_Groups_Ominus__class_Ominus(tc_fun(_1293546, tc_HOL_Obool))), _1293552)), _1293554)))], (50963 ^ _778908) ^ [_1803055, _1803057, _1803059] : [-(hAPP(c_List_Orev(_1803055), hAPP(hAPP(c_List_Odrop(_1803055), _1803057), _1803059)) = hAPP(hAPP(c_List_Otake(_1803055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803055)), _1803059)), _1803057)), hAPP(c_List_Orev(_1803055), _1803059)))], (16014 ^ _778908) ^ [_1052410, _1052412, _1052414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052410), _1052412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052412), _1052414)), _1052410))))], (18257 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (36628 ^ _778908) ^ [_1458499, _1458501, _1458503, _1458505] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458499, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458499, tc_HOL_Obool)), _1458501), _1458503)), _1458505) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458499, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458499, tc_HOL_Obool)), _1458501), _1458505)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458499, tc_HOL_Obool)), _1458503), _1458505)))], (48576 ^ _778908) ^ [_1749681, _1749683, _1749685, _1749687] : [_1749681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1749683), _1749681), hAPP(hAPP(c_List_Olist_OCons(_1749683), _1749685), _1749687)) = c_List_Olist_ONil(_1749683))], (9616 ^ _778908) ^ [_940039, _940041] : [class_Groups_Oordered__ab__group__add(_940039), 9619 ^ _778908 : [(9626 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940039), _940041), c_Groups_Ozero__class_Ozero(_940039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940039), c_Groups_Ozero__class_Ozero(_940039)), hAPP(c_Groups_Ouminus__class_Ouminus(_940039), _940041))))], (9620 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940039), c_Groups_Ozero__class_Ozero(_940039)), hAPP(c_Groups_Ouminus__class_Ouminus(_940039), _940041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940039), _940041), c_Groups_Ozero__class_Ozero(_940039))))]]], (22326 ^ _778908) ^ [_1165707, _1165709] : [_1165707 = _1165709, -(c_Random_Oinc__shift(_1165707, _1165709) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (100 ^ _778908) ^ [_780266, _780268] : [-(class_Fields_Olinordered__field__inverse__zero(_780266)), _780268 = _780266, class_Fields_Olinordered__field__inverse__zero(_780268)], (19225 ^ _778908) ^ [_1109750, _1109752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1109750)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1109752)), _1109750) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109750), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (4134 ^ _778908) ^ [_842595, _842597, _842599, _842601] : [-(c_Relation_ODomain(_842601, _842597) = c_Relation_ODomain(_842599, _842595)), _842601 = _842599, _842597 = _842595], (40164 ^ _778908) ^ [_1538842, _1538844] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1538842, _1538844), c_Orderings_Otop__class_Otop(tc_fun(_1538842, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1538844, tc_HOL_Obool), _1538842), c_Orderings_Otop__class_Otop(tc_fun(_1538844, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1538842, _1538844), tc_HOL_Obool)))], (10974 ^ _778908) ^ [_962934, _962936, _962938] : [class_Orderings_Opreorder(_962934), 10977 ^ _778908 : [(10986 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962934), _962936), _962938))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962934), _962936), _962938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962934), _962938), _962936)))], (10978 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962934), _962936), _962938)), 10981 ^ _778908 : [(10984 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962934), _962938), _962936))], (10982 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962934), _962936), _962938)))]]]]], (35712 ^ _778908) ^ [_1437378, _1437380, _1437382, _1437384, _1437386, _1437388, _1437390] : [-(hAPP(c_Product__Type_Oapfst(_1437378, _1437380, _1437382, _1437384), hAPP(c_Product__Type_Oapfst(_1437386, _1437378, _1437382, _1437388), _1437390)) = hAPP(c_Product__Type_Oapfst(_1437386, _1437380, _1437382, hAPP(c_Fun_Ocomp(_1437378, _1437380, _1437386, _1437384), _1437388)), _1437390))], (13260 ^ _778908) ^ [_1002412, _1002414, _1002416, _1002418, _1002420, _1002422] : [class_Rings_Olinordered__semiring__1(_1002412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002412), _1002414), _1002416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002412), _1002418), _1002416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002412), c_Groups_Ozero__class_Ozero(_1002412)), _1002420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002412), c_Groups_Ozero__class_Ozero(_1002412)), _1002422)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002412), _1002420), _1002422) = c_Groups_Oone__class_Oone(_1002412), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002412), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002412), _1002420), _1002414)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002412), _1002422), _1002418))), _1002416)))], (41802 ^ _778908) ^ [_1583451, _1583453, _1583455, _1583457] : [hAPP(hAPP(c_Relation_Orel__comp(_1583451, _1583451, _1583451), _1583453), _1583455) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583451, _1583451), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1583451, _1583451, _1583451), _1583457), _1583455) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583451, _1583451), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1583451, _1583451, _1583451), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583451, _1583451), tc_HOL_Obool)), _1583453), _1583457)), _1583455) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583451, _1583451), tc_HOL_Obool)))], (51619 ^ _778908) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (36120 ^ _778908) ^ [_1447901, _1447903, _1447905, _1447907, _1447909] : [c_Equiv__Relations_Oequiv(_1447901, _1447903, _1447905), hBOOL(hAPP(hAPP(c_member(tc_prod(_1447901, _1447901)), hAPP(hAPP(c_Product__Type_OPair(_1447901, _1447901), _1447907), _1447909)), _1447905)), -(hAPP(c_Relation_OImage(_1447901, _1447901, _1447905), hAPP(hAPP(c_Set_Oinsert(_1447901), _1447907), c_Orderings_Obot__class_Obot(tc_fun(_1447901, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1447901, _1447901, _1447905), hAPP(hAPP(c_Set_Oinsert(_1447901), _1447909), c_Orderings_Obot__class_Obot(tc_fun(_1447901, tc_HOL_Obool)))))], (25053 ^ _778908) ^ [_1218686, _1218688, _1218690, _1218692, _1218694] : [-(hAPP(c_New__DSequence_Opos__bind(_1218686, _1218688, _1218690, _1218692), _1218694) = c_Lazy__Sequence_Obind(_1218686, _1218688, hAPP(_1218690, _1218694), hAPP(hAPP(c_COMBC(_1218686, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1218688)), _1218692), _1218694)))], (30218 ^ _778908) ^ [_1320322, _1320324, _1320326, _1320328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1320322, _1320324)), c_Sum__Type_OPlus(_1320322, _1320324, _1320326, _1320328))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1320324), _1320328)))], (34865 ^ _778908) ^ [_1417878, _1417880, _1417882, _1417884, _1417886] : [hBOOL(hAPP(hAPP(c_member(_1417878), _1417880), _1417882)), -(hAPP(c_Map_Orestrict__map(_1417878, _1417884, _1417886, _1417882), _1417880) = hAPP(_1417886, _1417880))], (37724 ^ _778908) ^ [_1482948, _1482950, _1482952] : [class_Orderings_Olinorder(_1482948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482948), _1482950)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482948), _1482952)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482948, tc_HOL_Obool)), _1482950), _1482952) = c_Orderings_Obot__class_Obot(tc_fun(_1482948, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1482948), c_Big__Operators_Olattice_OSup__fin(_1482948, c_Orderings_Oord__class_Omax(_1482948), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482948, tc_HOL_Obool)), _1482950), _1482952))), c_Big__Operators_Olattice_OSup__fin(_1482948, c_Orderings_Oord__class_Omax(_1482948), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482948, tc_HOL_Obool)), _1482950), _1482952))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1482948), c_Big__Operators_Olattice_OSup__fin(_1482948, c_Orderings_Oord__class_Omax(_1482948), _1482950)), c_Big__Operators_Olattice_OSup__fin(_1482948, c_Orderings_Oord__class_Omax(_1482948), _1482952)))], (3396 ^ _778908) ^ [_831082, _831084, _831086, _831088, _831090, _831092] : [-(c_Com_Ocom_OLocal(_831092, _831088, _831084) = c_Com_Ocom_OLocal(_831090, _831086, _831082)), _831092 = _831090, _831088 = _831086, _831084 = _831082], (19531 ^ _778908) ^ [_1115301, _1115303] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115301))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115303))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115301)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115303)))], (27240 ^ _778908) ^ [_1260104, _1260106, _1260108, _1260110, _1260112] : [class_Orderings_Olinorder(_1260104), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1260104, _1260106), _1260108) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1260104, _1260110), _1260112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260104), _1260106), _1260108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260104), _1260110), _1260112)), -(_1260108 = _1260112)], (8174 ^ _778908) ^ [_915812, _915814, _915816, _915818] : [hAPP(c_Sum__Type_OInl(_915812, _915814), _915816) = hAPP(c_Sum__Type_OInr(_915814, _915812), _915818)], (5126 ^ _778908) ^ [_858185, _858187, _858189, _858191] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_858191, _858187) = c_SetInterval_Oord__class_OatLeastLessThan(_858189, _858185)), _858191 = _858189, _858187 = _858185], (10128 ^ _778908) ^ [_949091, _949093] : [class_Int_Oring__char__0(_949091), 10131 ^ _778908 : [(10138 ^ _778908) ^ [] : [_949093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_949091) = hAPP(c_Int_Oring__1__class_Oof__int(_949091), _949093))], (10132 ^ _778908) ^ [] : [c_Groups_Ozero__class_Ozero(_949091) = hAPP(c_Int_Oring__1__class_Oof__int(_949091), _949093), -(_949093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (38050 ^ _778908) ^ [_1491831, _1491833, _1491835, _1491837, _1491839] : [class_Groups_Ocomm__monoid__add(_1491831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491833), _1491835)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491833), _1491837)), 38064 ^ _778908 : [(38067 ^ _778908) ^ [] : [hAPP(_1491839, 38063 ^ [_1491831, _1491833, _1491835, _1491837, _1491839]) = c_Groups_Ozero__class_Ozero(_1491831)], (38065 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491833), 38063 ^ [_1491831, _1491833, _1491835, _1491837, _1491839]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491833, tc_HOL_Obool)), _1491835), _1491837))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491833, _1491831), _1491839), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491833, tc_HOL_Obool)), _1491835), _1491837)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1491831), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491833, _1491831), _1491839), _1491835)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491833, _1491831), _1491839), _1491837)))], (41934 ^ _778908) ^ [_1587843, _1587845] : [hBOOL(hAPP(hAPP(c_member(_1587843), 41935 ^ [_1587843, _1587845]), c_Wellfounded_Oacc(_1587843, _1587845))), -(c_Wellfounded_Owf(_1587843, _1587845))], (48558 ^ _778908) ^ [_1749182, _1749184, _1749186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749182)), _1749184)), _1749186)), -(hAPP(hAPP(c_List_Otake(_1749182), _1749186), _1749184) = _1749184)], (27877 ^ _778908) ^ [_1273189, _1273191] : [c_Nat__Transfer_Onat__set(_1273189), c_Nat__Transfer_Onat__set(_1273191), 27884 ^ _778908 : [(27891 ^ _778908) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1273189) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1273191), -(_1273189 = _1273191)], (27885 ^ _778908) ^ [] : [_1273189 = _1273191, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1273189) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1273191))]]], (9262 ^ _778908) ^ [_933956] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933956))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15606 ^ _778908) ^ [_1044510, _1044512] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044510), _1044512)), _1044510) = _1044512)], (43862 ^ _778908) ^ [_1635075, _1635077] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635075, _1635075)), hAPP(hAPP(c_Product__Type_OPair(_1635075, _1635075), 43863 ^ [_1635075, _1635077]), 43863 ^ [_1635075, _1635077])), c_Transitive__Closure_Otrancl(_1635075, _1635077)))), -(c_Wellfounded_Oacyclic(_1635075, _1635077))], (36896 ^ _778908) ^ [_1464437, _1464439, _1464441, _1464443, _1464445] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464437, tc_HOL_Obool)), _1464439), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464441, tc_fun(_1464437, tc_HOL_Obool)), _1464443), _1464445)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464441, tc_fun(_1464437, tc_HOL_Obool)), _1464443), hAPP(hAPP(c_COMBB(tc_fun(_1464437, tc_HOL_Obool), tc_fun(_1464437, tc_HOL_Obool), _1464441), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464437, tc_HOL_Obool)), _1464439)), _1464445)))], (22986 ^ _778908) ^ [_1178715, _1178717, _1178719] : [-(hAPP(c_Nat_Onat_Onat__rec(_1178715, _1178717, _1178719), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1178717)], (22932 ^ _778908) ^ [_1177678, _1177680, _1177682] : [22934 ^ _778908 : [(22937 ^ _778908) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1177678, _1177680), 22933 ^ [_1177678, _1177680, _1177682]))], (22935 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1177680, 22933 ^ [_1177678, _1177680, _1177682]), _1177682)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1177678, _1177680), _1177682)))], (32192 ^ _778908) ^ [_1363708, _1363710, _1363712, _1363714, _1363716] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1363708, _1363710)), hAPP(hAPP(c_Product__Type_OPair(_1363708, _1363710), _1363714), _1363716)), _1363712)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1363708, _1363710, _1363712), _1363714), _1363716)))], (42198 ^ _778908) ^ [_1593444, _1593446, _1593448] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1593444, _1593446)), _1593448)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1593446), hAPP(c_Relation_ORange(_1593444, _1593446), _1593448))))], (9554 ^ _778908) ^ [_938706, _938708, _938710, _938712, _938714] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_938706), 9557 ^ _778908 : [(9558 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938708), _938712)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938710), _938714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938708), _938714)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938710), _938712)), -(_938708 = _938710), -(_938712 = _938714)], (9568 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938708), _938712)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938710), _938714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938708), _938714)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938706), _938710), _938712))), 9571 ^ _778908 : [(9574 ^ _778908) ^ [] : [_938712 = _938714], (9572 ^ _778908) ^ [] : [_938708 = _938710]]]]], (51565 ^ _778908) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51545 ^ _778908) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (35813 ^ _778908) ^ [] : [-(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))], (9266 ^ _778908) ^ [_934006, _934008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934006)), 9269 ^ _778908 : [(9278 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _934006), _934008) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _934006 = c_Groups_Oone__class_Oone(tc_Int_Oint), _934008 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (9270 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _934006), _934008) = c_Groups_Oone__class_Oone(tc_Int_Oint), 9273 ^ _778908 : [(9276 ^ _778908) ^ [] : [-(_934008 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9274 ^ _778908) ^ [] : [-(_934006 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (23511 ^ _778908) ^ [_1188459, _1188461] : [-(_1188459 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1188461, _1188459), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188461), _1188459)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1188461, _1188459)))))], (50467 ^ _778908) ^ [_1792401, _1792403] : [class_Orderings_Olinorder(_1792401), c_List_Olinorder__class_Osorted(_1792401, _1792403), -(c_List_Olinorder__class_Osorted(_1792401, hAPP(c_List_Otl(_1792401), _1792403)))], (10459 ^ _778908) ^ [_954637] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _954637) = _954637)], (24067 ^ _778908) ^ [_1198968, _1198970, _1198972, _1198974, _1198976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198968, tc_HOL_Obool)), _1198970), _1198972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198968, tc_HOL_Obool)), _1198974), _1198976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198968, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1198968, tc_HOL_Obool)), _1198970), _1198976)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1198968, tc_HOL_Obool)), _1198972), _1198974))))], (51423 ^ _778908) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (36226 ^ _778908) ^ [_1450224, _1450226, _1450228, _1450230, _1450232] : [c_Equiv__Relations_Oequiv(_1450224, _1450226, _1450228), 36229 ^ _778908 : [(36240 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450224, _1450224)), hAPP(hAPP(c_Product__Type_OPair(_1450224, _1450224), _1450230), _1450232)), _1450228))), hAPP(c_Relation_OImage(_1450224, _1450224, _1450228), hAPP(hAPP(c_Set_Oinsert(_1450224), _1450230), c_Orderings_Obot__class_Obot(tc_fun(_1450224, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450224, _1450224, _1450228), hAPP(hAPP(c_Set_Oinsert(_1450224), _1450232), c_Orderings_Obot__class_Obot(tc_fun(_1450224, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1450224), _1450230), _1450226)), hBOOL(hAPP(hAPP(c_member(_1450224), _1450232), _1450226))], (36230 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450224, _1450224)), hAPP(hAPP(c_Product__Type_OPair(_1450224, _1450224), _1450230), _1450232)), _1450228)), 36233 ^ _778908 : [(36238 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450224), _1450232), _1450226)))], (36236 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450224), _1450230), _1450226)))], (36234 ^ _778908) ^ [] : [-(hAPP(c_Relation_OImage(_1450224, _1450224, _1450228), hAPP(hAPP(c_Set_Oinsert(_1450224), _1450230), c_Orderings_Obot__class_Obot(tc_fun(_1450224, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1450224, _1450224, _1450228), hAPP(hAPP(c_Set_Oinsert(_1450224), _1450232), c_Orderings_Obot__class_Obot(tc_fun(_1450224, tc_HOL_Obool)))))]]]]], (20567 ^ _778908) ^ [_1134113, _1134115, _1134117, _1134119] : [class_Fields_Ofield__inverse__zero(_1134113), 20570 ^ _778908 : [(20571 ^ _778908) ^ [] : [_1134115 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134113), _1134117), _1134119), 20574 ^ _778908 : [(20581 ^ _778908) ^ [] : [_1134119 = c_Groups_Ozero__class_Ozero(_1134113), -(_1134115 = c_Groups_Ozero__class_Ozero(_1134113))], (20575 ^ _778908) ^ [] : [-(_1134119 = c_Groups_Ozero__class_Ozero(_1134113)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134113), _1134115), _1134119) = _1134117)]]], (20587 ^ _778908) ^ [] : [-(_1134115 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134113), _1134117), _1134119)), 20590 ^ _778908 : [(20593 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134113), _1134115), _1134119) = _1134117], (20591 ^ _778908) ^ [] : [_1134119 = c_Groups_Ozero__class_Ozero(_1134113)]], 20594 ^ _778908 : [(20597 ^ _778908) ^ [] : [_1134115 = c_Groups_Ozero__class_Ozero(_1134113)], (20595 ^ _778908) ^ [] : [-(_1134119 = c_Groups_Ozero__class_Ozero(_1134113))]]]]], (43691 ^ _778908) ^ [_1630624, _1630626, _1630628, _1630630] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630624, _1630624)), _1630626), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630624, _1630624), tc_HOL_Obool), _1630628), _1630630))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630624, _1630624)), _1630626), c_Transitive__Closure_Ortrancl(_1630624, _1630630))))], (7118 ^ _778908) ^ [_897942] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _897942)], (14539 ^ _778908) ^ [_1025692, _1025694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025692, _1025694)), _1025692)))], (37168 ^ _778908) ^ [_1471088, _1471090, _1471092, _1471094] : [class_Orderings_Olinorder(_1471088), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471088, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1471088), _1471090)), c_SetInterval_Oord__class_OatLeastAtMost(_1471088, _1471092, _1471094)) = c_SetInterval_Oord__class_OatLeastAtMost(_1471088, _1471092, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1471088), _1471090), _1471094)))], (23289 ^ _778908) ^ [_1184421, _1184423, _1184425, _1184427] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1184421, _1184423, _1184425), hAPP(hAPP(c_COMBB(tc_fun(_1184423, tc_prod(_1184421, _1184423)), tc_fun(_1184423, _1184425), _1184421), hAPP(c_COMBB(tc_prod(_1184421, _1184423), _1184425, _1184423), _1184427)), c_Product__Type_OPair(_1184421, _1184423))) = _1184427)], (7374 ^ _778908) ^ [_902103, _902105] : [hAPP(c_Nat_OSuc, _902103) = hAPP(c_Nat_OSuc, _902105), -(_902103 = _902105)], (160 ^ _778908) ^ [_781138, _781140, _781142, _781144, _781146, _781148] : [-(c_Nitpick_Oless__eq__frac(_781146, _781142, _781138)), c_Nitpick_Oless__eq__frac(_781148, _781144, _781140), _781148 = _781146, _781144 = _781142, _781140 = _781138], (22746 ^ _778908) ^ [_1173623, _1173625, _1173627, _1173629, _1173631] : [-(c_Nat_Onat_Onat__case(_1173623, _1173625, _1173627, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173629)), _1173631)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1173623), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1173629))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1173623, _1173623), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1173623, tc_fun(_1173623, _1173623)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1173623, tc_fun(_1173623, _1173623)), tc_Int_Oint), c_If(_1173623)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1173623, _1173625, _1173627, _1173631))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1173623, tc_Int_Oint), _1173627), 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)), _1173631)))))], (29753 ^ _778908) ^ [_1311209, _1311211, _1311213, _1311215] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1311209, tc_HOL_Obool)), _1311211), hAPP(hAPP(c_Set_Oinsert(_1311209), _1311213), _1311215)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1311209, tc_HOL_Obool)), _1311211), _1311215))))], (41786 ^ _778908) ^ [_1582887, _1582889, _1582891, _1582893] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582887, _1582889, _1582891), _1582893), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582889, _1582891), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582887, _1582891), tc_HOL_Obool)))], (22658 ^ _778908) ^ [_1172096, _1172098] : [-(c_Divides_OnegDivAlg(_1172096, _1172098) = hAPP(c_Divides_Oadjust(_1172098), c_Divides_OnegDivAlg(_1172096, 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)))), _1172098)))), -(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), _1172096), _1172098)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1172098), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6679 ^ _778908) ^ [_888412, _888414, _888416, _888418] : [c_Com_Ocom_OWhile(_888412, _888414) = c_Com_Ocom_OWhile(_888416, _888418), 6682 ^ _778908 : [(6685 ^ _778908) ^ [] : [-(_888414 = _888418)], (6683 ^ _778908) ^ [] : [-(_888412 = _888416)]]], (29574 ^ _778908) ^ [_1307841] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1307841), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1307841)), c_Option_Ooption_ONone(_1307841)), hAPP(c_Set_Oimage(_1307841, tc_Option_Ooption(_1307841), c_Option_Ooption_OSome(_1307841)), c_Orderings_Otop__class_Otop(tc_fun(_1307841, tc_HOL_Obool)))))], (38160 ^ _778908) ^ [_1493976, _1493978, _1493980] : [class_Lattices_Olattice(_1493976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493976), _1493978)), -(_1493980 = c_Orderings_Obot__class_Obot(tc_fun(_1493976, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493976, tc_HOL_Obool)), _1493980), _1493978)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493976), c_Big__Operators_Olattice__class_OInf__fin(_1493976, _1493980)), c_Big__Operators_Olattice__class_OInf__fin(_1493976, _1493978)) = c_Big__Operators_Olattice__class_OInf__fin(_1493976, _1493978))], (26593 ^ _778908) ^ [_1247289] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1247289) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1247289), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (22832 ^ _778908) ^ [_1175168, _1175170] : [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), _1175168))), 22835 ^ _778908 : [(22842 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175168)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175170), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175168)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175168)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175170), 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), _1175168)))))], (22836 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175168))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175170), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175168)) = 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), _1175170)))]]], (26297 ^ _778908) ^ [_1241827, _1241829, _1241831, _1241833, _1241835] : [class_Divides_Osemiring__div(_1241827), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241827), _1241829), _1241831)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241827), _1241833), _1241835)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241827), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241827), _1241831), _1241829)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241827), _1241835), _1241833)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241827), _1241831), _1241835)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241827), _1241829), _1241833)))], (30776 ^ _778908) ^ [_1330914, _1330916] : [-(c_Set_Othe__elem(_1330914, hAPP(hAPP(c_Set_Oinsert(_1330914), _1330916), c_Orderings_Obot__class_Obot(tc_fun(_1330914, tc_HOL_Obool)))) = _1330916)], (22578 ^ _778908) ^ [_1170274, _1170276] : [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(_1170274))), 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)), _1170276)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170274)), hAPP(c_Nat_OSuc, _1170276))))], (5939 ^ _778908) ^ [_873652, _873654] : [-(hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar), hAPP(hAPP(c_String_Ochar_OChar, _873652), _873654)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11328 ^ _778908) ^ [_968547, _968549, _968551] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968547), _968549) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968547), _968551), -(_968549 = _968551), -(_968547 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30502 ^ _778908) ^ [_1325236, _1325238] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325236, _1325238) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325236), _1325238))], (35835 ^ _778908) ^ [_1440743, _1440745, _1440747, _1440749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440743), _1440749)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440747), _1440745))), -(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), _1440743), _1440745)), 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), _1440747), _1440749)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (50897 ^ _778908) ^ [_1801805, _1801807, _1801809] : [-(hAPP(c_List_Orev(_1801805), hAPP(hAPP(c_List_Oappend(_1801805), _1801807), _1801809)) = hAPP(hAPP(c_List_Oappend(_1801805), hAPP(c_List_Orev(_1801805), _1801809)), hAPP(c_List_Orev(_1801805), _1801807)))], (26973 ^ _778908) ^ [_1254786, _1254788, _1254790, _1254792] : [class_Groups_Ocomm__monoid__add(_1254786), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254786), _1254788), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1254790), hAPP(c_Nat_OSuc, _1254792))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254786), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1254786, tc_Nat_Onat), _1254788), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1254790, _1254792)))], (29759 ^ _778908) ^ [_1311362, _1311364, _1311366, _1311368] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311362), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1311362, tc_HOL_Obool)), _1311364), _1311368))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311362), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1311362, tc_HOL_Obool)), _1311364), hAPP(hAPP(c_Set_Oinsert(_1311362), _1311366), _1311368)))))], (35418 ^ _778908) ^ [_1430835, _1430837, _1430839, _1430841, _1430843] : [c_Finite__Set_Ofolding__one__idem(_1430835, _1430837, _1430839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430835), _1430841)), -(_1430841 = c_Orderings_Obot__class_Obot(tc_fun(_1430835, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430835), _1430843)), -(_1430843 = c_Orderings_Obot__class_Obot(tc_fun(_1430835, tc_HOL_Obool))), -(hAPP(_1430839, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430835, tc_HOL_Obool)), _1430841), _1430843)) = hAPP(hAPP(_1430837, hAPP(_1430839, _1430841)), hAPP(_1430839, _1430843)))], (8364 ^ _778908) ^ [_919087] : [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), _919087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919087)))], (35791 ^ _778908) ^ [_1439516, _1439518, _1439520, _1439522, _1439524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1439520, _1439516)), hAPP(hAPP(c_Product__Type_OPair(_1439520, _1439516), _1439524), _1439518)), _1439522)), -(hBOOL(hAPP(hAPP(c_member(_1439516), _1439518), hAPP(c_Relation_OImage(_1439520, _1439516, _1439522), hAPP(hAPP(c_Set_Oinsert(_1439520), _1439524), c_Orderings_Obot__class_Obot(tc_fun(_1439520, tc_HOL_Obool)))))))], (39813 ^ _778908) ^ [_1529296, _1529298, _1529300, _1529302, _1529304] : [hBOOL(hAPP(hAPP(c_member(_1529296), _1529298), c_Map_Oran(_1529300, _1529296, c_Map_Orestrict__map(_1529300, _1529296, _1529302, _1529304)))), 39817 ^ _778908 : [(39820 ^ _778908) ^ [] : [-(hAPP(_1529302, 39816 ^ [_1529296, _1529298, _1529300, _1529302, _1529304]) = hAPP(c_Option_Ooption_OSome(_1529296), _1529298))], (39818 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1529300), 39816 ^ [_1529296, _1529298, _1529300, _1529302, _1529304]), _1529304)))]]], (20499 ^ _778908) ^ [_1132933, _1132935, _1132937] : [class_Fields_Olinordered__field__inverse__zero(_1132933), 20502 ^ _778908 : [(20517 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132933), _1132935), _1132937)), c_Groups_Ozero__class_Ozero(_1132933)))), 20518 ^ _778908 : [(20525 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), _1132935), c_Groups_Ozero__class_Ozero(_1132933))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), c_Groups_Ozero__class_Ozero(_1132933)), _1132937))], (20519 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), c_Groups_Ozero__class_Ozero(_1132933)), _1132935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), _1132937), c_Groups_Ozero__class_Ozero(_1132933)))]]], (20503 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132933), _1132935), _1132937)), c_Groups_Ozero__class_Ozero(_1132933))), 20508 ^ _778908 : [(20511 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), _1132937), c_Groups_Ozero__class_Ozero(_1132933))))], (20509 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), c_Groups_Ozero__class_Ozero(_1132933)), _1132935)))]], 20512 ^ _778908 : [(20515 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), c_Groups_Ozero__class_Ozero(_1132933)), _1132937)))], (20513 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132933), _1132935), c_Groups_Ozero__class_Ozero(_1132933))))]]]]], (30344 ^ _778908) ^ [_1322464, _1322466, _1322468] : [class_Orderings_Oorder(_1322464), _1322466 = _1322468, -(c_SetInterval_Oord__class_OatLeastAtMost(_1322464, _1322466, _1322468) = hAPP(hAPP(c_Set_Oinsert(_1322464), _1322466), c_Orderings_Obot__class_Obot(tc_fun(_1322464, tc_HOL_Obool))))], (47455 ^ _778908) ^ [_1722844] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722844)), c_List_Olist_ONil(_1722844)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48444 ^ _778908) ^ [_1746340, _1746342, _1746344, _1746346] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746340), tc_List_Olist(_1746340))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746340), tc_List_Olist(_1746340)), _1746342), _1746344)), c_List_Olexord(_1746340, _1746346)))), 48445 ^ _778908 : [(48452 ^ _778908) ^ [_1746647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746647), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746340)), _1746342)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746340)), _1746344)))), hAPP(hAPP(c_List_Otake(_1746340), _1746647), _1746342) = hAPP(hAPP(c_List_Otake(_1746340), _1746647), _1746344), hBOOL(hAPP(hAPP(c_member(tc_prod(_1746340, _1746340)), hAPP(hAPP(c_Product__Type_OPair(_1746340, _1746340), hAPP(hAPP(c_List_Onth(_1746340), _1746342), _1746647)), hAPP(hAPP(c_List_Onth(_1746340), _1746344), _1746647))), _1746346))], (48446 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746340)), _1746342)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746340)), _1746344))), hAPP(hAPP(c_List_Otake(_1746340), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746340)), _1746342)), _1746344) = _1746342]]], (23893 ^ _778908) ^ [_1195409, _1195411, _1195413, _1195415] : [class_Orderings_Olinorder(_1195409), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195409), _1195411), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195409), _1195413), _1195415)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195409), _1195413), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195409), _1195411), _1195415)))], (33301 ^ _778908) ^ [_1386346, _1386348, _1386350] : [class_Lattices_Olattice(_1386346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386346), _1386348)), 33308 ^ _778908 : [(33315 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386346, tc_HOL_Obool)), _1386348), hAPP(hAPP(c_Set_Oinsert(_1386346), _1386350), c_Orderings_Obot__class_Obot(tc_fun(_1386346, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1386346, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1386346, hAPP(hAPP(c_Set_Oinsert(_1386346), _1386350), _1386348)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1386346), _1386350), c_Big__Operators_Olattice__class_OSup__fin(_1386346, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386346, tc_HOL_Obool)), _1386348), hAPP(hAPP(c_Set_Oinsert(_1386346), _1386350), c_Orderings_Obot__class_Obot(tc_fun(_1386346, tc_HOL_Obool)))))))], (33309 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386346, tc_HOL_Obool)), _1386348), hAPP(hAPP(c_Set_Oinsert(_1386346), _1386350), c_Orderings_Obot__class_Obot(tc_fun(_1386346, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1386346, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1386346, hAPP(hAPP(c_Set_Oinsert(_1386346), _1386350), _1386348)) = _1386350)]]], (35086 ^ _778908) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (45382 ^ _778908) ^ [_1671404, _1671406] : [class_Complete__Lattice_Ocomplete__lattice(_1671404), -(c_Complete__Lattice_OInf__class_OInf(_1671404, hAPP(hAPP(c_Set_Oinsert(_1671404), _1671406), c_Orderings_Obot__class_Obot(tc_fun(_1671404, tc_HOL_Obool)))) = _1671406)], (12127 ^ _778908) ^ [_982487, _982489, _982491] : [class_Rings_Oordered__cancel__semiring(_982487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982487), c_Groups_Ozero__class_Ozero(_982487)), _982489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982487), _982491), c_Groups_Ozero__class_Ozero(_982487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982487), _982489), _982491)), c_Groups_Ozero__class_Ozero(_982487))))], (4890 ^ _778908) ^ [_854593, _854595] : [_854595 = _854593, -(c_Orderings_Otop__class_Otop(_854595) = c_Orderings_Otop__class_Otop(_854593))], (27153 ^ _778908) ^ [_1258559, _1258561] : [27161 ^ _778908 : [(27164 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1258561, 27160 ^ [_1258559, _1258561])))], (27162 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27160 ^ [_1258559, _1258561]), _1258559)))]], 27154 ^ _778908 : [(27155 ^ _778908) ^ [_1258627] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1258627), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258559))), hBOOL(hAPP(_1258561, _1258627))]]], (51465 ^ _778908) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (16332 ^ _778908) ^ [_1059490, _1059492] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059490), _1059492))), -(c_Nat__Transfer_Otsub(_1059492, _1059490) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (1642 ^ _778908) ^ [_802307, _802309] : [-(class_Rings_Ocomm__semiring(_802307)), _802309 = _802307, class_Rings_Ocomm__semiring(_802309)], (30980 ^ _778908) ^ [_1334783, _1334785, _1334787, _1334789, _1334791, _1334793, _1334795] : [hBOOL(hAPP(hAPP(c_member(_1334783), _1334785), hAPP(hAPP(_1334787, _1334789), _1334791))), -(hBOOL(hAPP(hAPP(c_member(_1334783), _1334785), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1334793, _1334795, tc_fun(_1334783, tc_HOL_Obool)), _1334787), hAPP(hAPP(c_Product__Type_OPair(_1334793, _1334795), _1334789), _1334791)))))], (37186 ^ _778908) ^ [_1471505, _1471507, _1471509] : [class_Orderings_Oorder(_1471505), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471505, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1471505, _1471507, _1471509)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1471505), _1471509)) = c_Orderings_Obot__class_Obot(tc_fun(_1471505, tc_HOL_Obool)))], (19051 ^ _778908) ^ [_1107059, _1107061] : [class_Int_Onumber__ring(_1107059), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107059), hAPP(c_Int_Onumber__class_Onumber__of(_1107059), c_Int_OBit1(c_Int_OPls))), _1107061) = _1107061)], (51339 ^ _778908) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (40307 ^ _778908) ^ [_1542802, _1542804, _1542806, _1542808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542804, _1542802), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1542802, tc_prod(_1542804, _1542802), 40303 ^ [_1542802, _1542804, _1542806, _1542808]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542804, tc_fun(_1542802, tc_HOL_Obool)), _1542806), _1542808))), hAPP(hAPP(c_Product__Type_OSigma(_1542804, _1542802), _1542806), _1542808))))], (49386 ^ _778908) ^ [_1769463, _1769465, _1769467] : [class_Orderings_Olinorder(_1769463), -(c_Big__Operators_Olinorder__class_OMin(_1769463, hAPP(c_List_Oset(_1769463), hAPP(hAPP(c_List_Olist_OCons(_1769463), _1769465), _1769467))) = hAPP(c_List_Ofoldl(_1769463, _1769463, c_Orderings_Oord__class_Omin(_1769463), _1769465), _1769467))], (15400 ^ _778908) ^ [_1040889, _1040891, _1040893] : [class_Rings_Oring__1(_1040889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040891), _1040893)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1040889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040893), _1040891)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040889), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1040889), _1040893)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1040889), _1040891)))], (11795 ^ _778908) ^ [_976371] : [class_Groups_Osgn__if(_976371), -(c_Groups_Osgn__class_Osgn(_976371, c_Groups_Ozero__class_Ozero(_976371)) = c_Groups_Ozero__class_Ozero(_976371))], (5867 ^ _778908) ^ [_872359, _872361, _872363] : [c_Com_Ocom_OCall(_872359, _872361, _872363) = c_Com_Ocom_OSKIP], (12419 ^ _778908) ^ [_987655, _987657] : [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), _987655), _987657))), 12422 ^ _778908 : [(12425 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987657)))], (12423 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987655)))]]], (41782 ^ _778908) ^ [_1582741, _1582743, _1582745, _1582747, _1582749, _1582751] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582741, _1582743, _1582745), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582741, _1582743), tc_HOL_Obool)), _1582747), _1582749)), _1582751) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582741, _1582745), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1582741, _1582743, _1582745), _1582747), _1582751)), hAPP(hAPP(c_Relation_Orel__comp(_1582741, _1582743, _1582745), _1582749), _1582751)))], (17927 ^ _778908) ^ [_1089095] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089095)))), -(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), _1089095)) = 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), _1089095))))], (35243 ^ _778908) ^ [_1427094, _1427096] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1427094, _1427094)), _1427096)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1427094), hAPP(c_Relation_OField(_1427094), _1427096))))], (48610 ^ _778908) ^ [_1750353, _1750355, _1750357, _1750359] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1750353) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1750355), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1750353)), hAPP(hAPP(c_List_Olist_OCons(_1750355), _1750357), _1750359)) = hAPP(hAPP(c_List_Olist_OCons(_1750355), _1750357), hAPP(hAPP(c_List_Otake(_1750355), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1750353)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1750359)))], (34439 ^ _778908) ^ [_1409041, _1409043, _1409045, _1409047, _1409049, _1409051] : [-(_1409041 = _1409043), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1409045, _1409047), _1409049), _1409043), _1409051), _1409041) = hAPP(_1409049, _1409041))], (6939 ^ _778908) ^ [_893584] : [-(hAPP(c_Com_Obody, _893584) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _893584))))], (23673 ^ _778908) ^ [_1191465, _1191467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191465), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1191467), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1191465), _1191467) = 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), _1191465), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1191467)))))], (23783 ^ _778908) ^ [_1193428, _1193430, _1193432, _1193434] : [class_Orderings_Olinorder(_1193428), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193428), _1193430), _1193432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193428), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193428), _1193434), _1193430)), _1193432)))], (29781 ^ _778908) ^ [_1311749, _1311751] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311749), _1311751)), 29784 ^ _778908 : [(29791 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311749), c_Orderings_Otop__class_Otop(tc_fun(_1311749, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311749), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1311749, tc_HOL_Obool)), _1311751))))], (29785 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311749), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1311749, tc_HOL_Obool)), _1311751))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311749), c_Orderings_Otop__class_Otop(tc_fun(_1311749, tc_HOL_Obool)))))]]], (9054 ^ _778908) ^ [_930180] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _930180) = _930180)], (14059 ^ _778908) ^ [_1016913, _1016915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016913, _1016915)), _1016913)))], (25979 ^ _778908) ^ [_1235247, _1235249] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1235249), _1235247))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235247), _1235249)))], (30514 ^ _778908) ^ [_1325391, _1325393] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325391, _1325393), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325391), _1325393))], (31572 ^ _778908) ^ [_1348750, _1348752, _1348754, _1348756, _1348758] : [hBOOL(hAPP(hAPP(c_member(_1348750), _1348752), _1348754)), -(hAPP(hAPP(c_Set_Oinsert(_1348756), hAPP(_1348758, _1348752)), hAPP(c_Set_Oimage(_1348750, _1348756, _1348758), _1348754)) = hAPP(c_Set_Oimage(_1348750, _1348756, _1348758), _1348754))], (23389 ^ _778908) ^ [_1186660, _1186662, _1186664, _1186666, _1186668, _1186670] : [hAPP(c_Product__Type_Oapsnd(_1186660, _1186662, _1186664, _1186666), _1186668) = hAPP(c_Product__Type_Oapsnd(_1186660, _1186662, _1186664, _1186670), _1186668), -(hAPP(_1186666, hAPP(c_Product__Type_Osnd(_1186664, _1186660), _1186668)) = hAPP(_1186670, hAPP(c_Product__Type_Osnd(_1186664, _1186660), _1186668)))], (35229 ^ _778908) ^ [_1426708, _1426710] : [-(c_Relation_OId__on(_1426708, _1426710) = hAPP(c_Product__Type_Oprod_Oprod__case(_1426708, _1426708, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1426708, tc_HOL_Obool, tc_fun(_1426708, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1426708, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1426708, tc_HOL_Obool)), _1426708), c_COMBC(_1426708, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1426708, tc_HOL_Obool), tc_fun(_1426708, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1426708), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1426708), c_fconj)), c_fequal))), _1426710)))], (32636 ^ _778908) ^ [_1372818, _1372820, _1372822, _1372824] : [-(c_Nitpick_Ofold__graph_H(_1372818, _1372820, _1372822, _1372824, c_Orderings_Obot__class_Obot(tc_fun(_1372818, tc_HOL_Obool)), _1372824))], (49472 ^ _778908) ^ [_1771729, _1771731, _1771733] : [c_Equiv__Relations_Oequiv(_1771729, _1771731, _1771733), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1771729), c_List_Olists(_1771729, _1771731), c_List_Olistrel(_1771729, _1771733)))], (42515 ^ _778908) ^ [_1601132, _1601134, _1601136, _1601138] : [-(c_New__Random__Sequence_Oneg__map(_1601132, _1601134, _1601136, _1601138) = c_New__Random__Sequence_Oneg__bind(_1601132, _1601134, _1601138, hAPP(c_Fun_Ocomp(_1601134, 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(_1601134)))))), _1601132, c_New__Random__Sequence_Oneg__single(_1601134)), _1601136)))], (26361 ^ _778908) ^ [_1243125, _1243127, _1243129] : [class_Divides_Oring__div(_1243125), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243125), _1243127), _1243129)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243125), _1243129), hAPP(c_Groups_Ouminus__class_Ouminus(_1243125), _1243127)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1243125), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243125), _1243129), _1243127)))], (51593 ^ _778908) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (1202 ^ _778908) ^ [_796807, _796809] : [-(class_Int_Oring__char__0(_796807)), _796809 = _796807, class_Int_Oring__char__0(_796809)], (11580 ^ _778908) ^ [_972594, _972596] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972594), _972596))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972594), _972596)), -(_972594 = _972596)], (46237 ^ _778908) ^ [_1691258, _1691260, _1691262, _1691264, _1691266] : [-(hAPP(hAPP(c_Option_Omap(_1691258, _1691260), _1691262), _1691264) = hAPP(c_Option_Ooption_OSome(_1691260), _1691266)), 46238 ^ _778908 : [(46239 ^ _778908) ^ [_1691326] : [_1691264 = hAPP(c_Option_Ooption_OSome(_1691258), _1691326), hAPP(_1691262, _1691326) = _1691266]]], (2348 ^ _778908) ^ [_814332, _814334, _814336, _814338] : [-(c_Nitpick_Onat__lcm(_814338, _814334) = c_Nitpick_Onat__lcm(_814336, _814332)), _814338 = _814336, _814334 = _814332], (33199 ^ _778908) ^ [_1384741, _1384743] : [class_Int_Oring__char__0(_1384741), hBOOL(hAPP(hAPP(c_member(_1384741), _1384743), c_Int_Oring__1__class_OInts(_1384741))), 33206 ^ _778908 : [(33213 ^ _778908) ^ [] : [_1384743 = c_Groups_Ozero__class_Ozero(_1384741), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384741), _1384743), _1384743) = c_Groups_Ozero__class_Ozero(_1384741))], (33207 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384741), _1384743), _1384743) = c_Groups_Ozero__class_Ozero(_1384741), -(_1384743 = c_Groups_Ozero__class_Ozero(_1384741))]]], (19761 ^ _778908) ^ [] : [-(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)))))], (18547 ^ _778908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6985 ^ _778908) ^ [_894734, _894736, _894738, _894740, _894742, _894744] : [-(c_Natural_Oevaln(c_Com_Ocom_OCall(_894734, _894736, _894738), _894740, _894742, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894744), hAPP(c_Natural_Ogetlocs, _894740))), _894734), hAPP(hAPP(c_Natural_Ogetlocs, _894744), c_Com_ORes)))), 6986 ^ _778908 : [(6987 ^ _778908) ^ [_894883] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894744), hAPP(c_Natural_Ogetlocs, _894740))), _894734), hAPP(hAPP(c_Natural_Ogetlocs, _894744), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894883), hAPP(c_Natural_Ogetlocs, _894740))), _894734), hAPP(hAPP(c_Natural_Ogetlocs, _894883), c_Com_ORes)), c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _894736), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894740), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_894738, _894740)), _894742, _894883)]]], (7585 ^ _778908) ^ [_905941] : [-(_905941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_905941 = hAPP(c_Nat_OSuc, 7588 ^ [_905941]))], (1522 ^ _778908) ^ [_800807, _800809] : [-(class_Groups_Ocancel__semigroup__add(_800807)), _800809 = _800807, class_Groups_Ocancel__semigroup__add(_800809)], (48510 ^ _778908) ^ [_1747985, _1747987, _1747989, _1747991, _1747993, _1747995] : [-(c_Map_Omap__add(_1747985, _1747987, _1747989, c_Map_Omap__upds(_1747985, _1747987, _1747991, _1747993, _1747995)) = c_Map_Omap__upds(_1747985, _1747987, c_Map_Omap__add(_1747985, _1747987, _1747989, _1747991), _1747993, _1747995))], (47278 ^ _778908) ^ [_1719236, _1719238, _1719240, _1719242] : [class_Groups_Ocomm__monoid__add(_1719236), hBOOL(hAPP(c_List_Odistinct(_1719238), _1719240)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1719236), hAPP(hAPP(c_List_Omap(_1719238, _1719236), _1719242), _1719240)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1719238, _1719236), _1719242), hAPP(c_List_Oset(_1719238), _1719240)))], (3532 ^ _778908) ^ [_833222, _833224, _833226, _833228] : [-(c_Com_Ocom_OWhile(_833228, _833224) = c_Com_Ocom_OWhile(_833226, _833222)), _833228 = _833226, _833224 = _833222], (47599 ^ _778908) ^ [_1726045, _1726047, _1726049, _1726051] : [-(hAPP(c_List_Olist_Olist__case(_1726045, _1726047, _1726049, _1726051), c_List_Olist_ONil(_1726047)) = _1726049)], (35694 ^ _778908) ^ [_1436910, _1436912, _1436914, _1436916, _1436918, _1436920] : [-(hAPP(hAPP(c_Fun_Ocomp(_1436910, _1436912, _1436914, _1436916), _1436918), _1436920) = hAPP(_1436916, hAPP(_1436918, _1436920)))], (19327 ^ _778908) ^ [_1111795, _1111797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111795), _1111797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1111795)), c_Int_OBit0(_1111797))))], (38816 ^ _778908) ^ [_1507074, _1507076, _1507078, _1507080, _1507082] : [c_Fun_Oinj__on(_1507074, _1507076, _1507078, c_Orderings_Otop__class_Otop(tc_fun(_1507074, tc_HOL_Obool))), 38819 ^ _778908 : [(38826 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1507074), _1507080), _1507082)), -(hBOOL(hAPP(hAPP(c_member(_1507076), hAPP(_1507078, _1507080)), hAPP(c_Set_Oimage(_1507074, _1507076, _1507078), _1507082))))], (38820 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1507076), hAPP(_1507078, _1507080)), hAPP(c_Set_Oimage(_1507074, _1507076, _1507078), _1507082))), -(hBOOL(hAPP(hAPP(c_member(_1507074), _1507080), _1507082)))]]], (7977 ^ _778908) ^ [_912250, _912252, _912254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912252), _912254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912250), _912252)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912250), _912254))))], (1904 ^ _778908) ^ [_806458, _806460, _806462, _806464, _806466, _806468] : [-(c_String_Ochar_Ochar__rec(_806468, _806464, _806460) = c_String_Ochar_Ochar__rec(_806466, _806462, _806458)), _806468 = _806466, _806464 = _806462, _806460 = _806458], (8270 ^ _778908) ^ [_917481, _917483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917481), _917483)), -(_917483 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _917481), 8273 ^ [_917481, _917483])))], (14700 ^ _778908) ^ [_1028308, _1028310, _1028312] : [-(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), _1028308), _1028310)), _1028312), _1028310) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028312, _1028310))], (17249 ^ _778908) ^ [_1076649, _1076651, _1076653] : [class_Int_Onumber__ring(_1076649), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1076649), hAPP(c_Int_Onumber__class_Onumber__of(_1076649), _1076651)), hAPP(c_Int_Onumber__class_Onumber__of(_1076649), _1076653)) = hAPP(c_Int_Onumber__class_Onumber__of(_1076649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1076651), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076653))))], (20061 ^ _778908) ^ [_1124884, _1124886, _1124888] : [class_Rings_Olinordered__idom(_1124884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124884), c_Groups_Ozero__class_Ozero(_1124884)), hAPP(hAPP(c_Power_Opower__class_Opower(_1124884), _1124886), 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)))), _1124888))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124884), c_Groups_Ozero__class_Ozero(_1124884)), _1124886)))], (43357 ^ _778908) ^ [_1622451, _1622453, _1622455, _1622457] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622451, _1622451)), hAPP(hAPP(c_Product__Type_OPair(_1622451, _1622451), _1622453), _1622455)), c_Transitive__Closure_Ortrancl(_1622451, _1622457)))), 43358 ^ _778908 : [(43361 ^ _778908) ^ [] : [-(_1622453 = _1622455), hBOOL(hAPP(hAPP(c_member(tc_prod(_1622451, _1622451)), hAPP(hAPP(c_Product__Type_OPair(_1622451, _1622451), _1622453), _1622455)), c_Transitive__Closure_Otrancl(_1622451, _1622457)))], (43359 ^ _778908) ^ [] : [_1622453 = _1622455]]], (22265 ^ _778908) ^ [_1164826, _1164828] : [_1164826 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1164826, _1164828) = _1164828)], (10635 ^ _778908) ^ [_957427, _957429, _957431, _957433] : [class_Orderings_Oorder(_957427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957427), _957429), _957431)), _957429 = _957433, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957427), _957433), _957431)))], (43676 ^ _778908) ^ [_1630244, _1630246] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630244, _1630244), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1630246) = c_Relation_OId(_1630244))], (7240 ^ _778908) ^ [_900078, _900080] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900078), _900080) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 7243 ^ _778908 : [(7246 ^ _778908) ^ [] : [-(_900080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7244 ^ _778908) ^ [] : [-(_900078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49672 ^ _778908) ^ [_1775825, _1775827] : [-(_1775825 = c_List_Olist_ONil(_1775827)), -(c_List_Olast(_1775827, _1775825) = hAPP(hAPP(c_List_Onth(_1775827), _1775825), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775827)), _1775825)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (28961 ^ _778908) ^ [_1294711, _1294713, _1294715, _1294717, _1294719, _1294721] : [class_Complete__Lattice_Ocomplete__lattice(_1294711), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294713, _1294711), _1294715), hAPP(hAPP(c_COMBB(tc_fun(_1294717, _1294711), _1294711, _1294713), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294717, _1294711), _1294719)), _1294721)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294717, _1294711), _1294719), hAPP(hAPP(c_COMBB(tc_fun(_1294713, _1294711), _1294711, _1294717), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294713, _1294711), _1294715)), hAPP(c_COMBC(_1294713, _1294717, _1294711), _1294721))))], (48929 ^ _778908) ^ [_1759682, _1759684, _1759686] : [hBOOL(hAPP(c_List_Odistinct(_1759682), _1759684)), -(hBOOL(hAPP(c_List_Odistinct(_1759682), hAPP(hAPP(c_List_Odrop(_1759682), _1759686), _1759684))))], (37396 ^ _778908) ^ [_1476409, _1476411, _1476413, _1476415, _1476417] : [c_Finite__Set_Ofolding__one(_1476409, _1476411, _1476413), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476409), _1476415)), -(_1476415 = c_Orderings_Obot__class_Obot(tc_fun(_1476409, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476409), _1476417)), -(_1476417 = c_Orderings_Obot__class_Obot(tc_fun(_1476409, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476409, tc_HOL_Obool)), _1476415), _1476417) = c_Orderings_Obot__class_Obot(tc_fun(_1476409, tc_HOL_Obool)), -(hAPP(_1476413, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476409, tc_HOL_Obool)), _1476415), _1476417)) = hAPP(hAPP(_1476411, hAPP(_1476413, _1476415)), hAPP(_1476413, _1476417)))], (8252 ^ _778908) ^ [_917180, _917182, _917184, _917186, _917188] : [-(hAPP(c_Sum__Type_OSumr(_917180, _917182, _917184, _917186), hAPP(c_Sum__Type_OInr(_917180, _917184), _917188)) = hAPP(_917186, _917188))], (20267 ^ _778908) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25515 ^ _778908) ^ [_1227375, _1227377] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227375), _1227377)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227377), _1227375)), -(_1227375 = _1227377)], (51403 ^ _778908) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (600 ^ _778908) ^ [_788252, _788254, _788256, _788258] : [-(c_Nitpick_Owf_H(_788256, _788252)), c_Nitpick_Owf_H(_788258, _788254), _788258 = _788256, _788254 = _788252], (48632 ^ _778908) ^ [_1750941, _1750943, _1750945, _1750947, _1750949, _1750951] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750941), tc_List_Olist(_1750941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750941), tc_List_Olist(_1750941)), hAPP(hAPP(c_List_Oappend(_1750941), _1750943), hAPP(hAPP(c_List_Olist_OCons(_1750941), _1750945), c_List_Olist_ONil(_1750941)))), hAPP(hAPP(c_List_Oappend(_1750941), _1750947), hAPP(hAPP(c_List_Olist_OCons(_1750941), _1750949), c_List_Olist_ONil(_1750941))))), c_List_Olistrel1(_1750941, _1750951))), 48637 ^ _778908 : [(48640 ^ _778908) ^ [] : [-(_1750945 = _1750949)], (48638 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750941), tc_List_Olist(_1750941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750941), tc_List_Olist(_1750941)), _1750943), _1750947)), c_List_Olistrel1(_1750941, _1750951))))]], 48641 ^ _778908 : [(48644 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1750941, _1750941)), hAPP(hAPP(c_Product__Type_OPair(_1750941, _1750941), _1750945), _1750949)), _1750951)))], (48642 ^ _778908) ^ [] : [-(_1750943 = _1750947)]]], (28013 ^ _778908) ^ [_1275560, _1275562, _1275564, _1275566] : [28014 ^ _778908 : [(28017 ^ _778908) ^ [] : [hBOOL(hAPP(_1275564, _1275562))], (28015 ^ _778908) ^ [] : [hBOOL(hAPP(_1275560, _1275562))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275566, tc_HOL_Obool)), _1275564), _1275560), _1275562)))], (30248 ^ _778908) ^ [_1320875, _1320877, _1320879] : [-(hAPP(hAPP(c_Set_Oinsert(_1320875), _1320877), _1320879) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320875, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1320875), _1320877), c_Orderings_Obot__class_Obot(tc_fun(_1320875, tc_HOL_Obool)))), _1320879))], (17743 ^ _778908) ^ [_1085636, _1085638, _1085640, _1085642] : [class_Rings_Olinordered__semidom(_1085636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085636), hAPP(hAPP(c_Power_Opower__class_Opower(_1085636), _1085638), hAPP(c_Nat_OSuc, _1085640))), hAPP(hAPP(c_Power_Opower__class_Opower(_1085636), _1085642), hAPP(c_Nat_OSuc, _1085640)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085636), c_Groups_Ozero__class_Ozero(_1085636)), _1085642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085636), _1085638), _1085642)))], (32361 ^ _778908) ^ [_1367323, _1367325, _1367327, _1367329] : [hBOOL(hAPP(hAPP(c_member(_1367323), _1367325), c_SetInterval_Oord_OlessThan(_1367323, _1367327, _1367329))), -(hBOOL(hAPP(hAPP(_1367327, _1367325), _1367329)))], (39680 ^ _778908) ^ [_1526341, _1526343, _1526345, _1526347, _1526349] : [c_Fun_Oinj__on(_1526341, _1526343, _1526345, _1526347), hBOOL(hAPP(hAPP(c_member(_1526343), _1526349), hAPP(c_Set_Oimage(_1526341, _1526343, _1526345), _1526347))), -(hAPP(_1526345, hAPP(c_Fun_Othe__inv__into(_1526341, _1526343, _1526347, _1526345), _1526349)) = _1526349)], (46609 ^ _778908) ^ [_1699991, _1699993, _1699995, _1699997, _1699999, _1700001] : [-(hAPP(hAPP(c_List_Ozip(_1699991, _1699993), hAPP(hAPP(c_List_Omap(_1699995, _1699991), _1699997), _1699999)), _1700001) = hAPP(hAPP(c_List_Omap(tc_prod(_1699995, _1699993), tc_prod(_1699991, _1699993)), hAPP(c_Product__Type_Oprod_Oprod__case(_1699995, _1699993, tc_prod(_1699991, _1699993)), hAPP(hAPP(c_COMBB(_1699991, tc_fun(_1699993, tc_prod(_1699991, _1699993)), _1699995), c_Product__Type_OPair(_1699991, _1699993)), _1699997))), hAPP(hAPP(c_List_Ozip(_1699995, _1699993), _1699999), _1700001)))], (46331 ^ _778908) ^ [_1693479, _1693481, _1693483, _1693485] : [-(hBOOL(hAPP(hAPP(c_member(_1693479), _1693485), hAPP(c_Set_Oimage(tc_prod(_1693479, _1693481), _1693479, c_Product__Type_Ofst(_1693479, _1693481)), hAPP(c_List_Oset(tc_prod(_1693479, _1693481)), _1693483))))), -(hAPP(c_Map_Omap__of(_1693479, _1693481, _1693483), _1693485) = c_Option_Ooption_ONone(_1693481))], (6788 ^ _778908) ^ [_890302, _890304, _890306, _890308] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_890302, _890304)), _890306), _890308))), 6789 ^ _778908 : [(6796 ^ _778908) ^ [] : [hBOOL(hAPP(_890302, _890306)), 6799 ^ _778908 : [(6800 ^ _778908) ^ [_890521] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890304), _890306), _890521)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_890302, _890304)), _890521), _890308))]]], (6790 ^ _778908) ^ [] : [_890308 = _890306, -(hBOOL(hAPP(_890302, _890306)))]]], (46919 ^ _778908) ^ [_1708469, _1708471, _1708473, _1708475] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708469), tc_List_Olist(_1708469))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708469), tc_List_Olist(_1708469)), _1708471), _1708473)), c_List_Olistrel(_1708469, _1708475)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708469)), _1708471) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708469)), _1708473), 46925 ^ _778908 : [(46928 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1708469, _1708469, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1708469, tc_fun(tc_prod(_1708469, _1708469), tc_HOL_Obool), tc_fun(_1708469, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1708469, tc_fun(tc_fun(tc_prod(_1708469, _1708469), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1708469, _1708469), tc_HOL_Obool), tc_fun(_1708469, tc_HOL_Obool)), _1708469), c_COMBC(_1708469, tc_fun(tc_prod(_1708469, _1708469), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1708469, tc_prod(_1708469, _1708469)), tc_fun(_1708469, tc_fun(tc_fun(tc_prod(_1708469, _1708469), tc_HOL_Obool), tc_HOL_Obool)), _1708469), hAPP(c_COMBB(tc_prod(_1708469, _1708469), tc_fun(tc_fun(tc_prod(_1708469, _1708469), tc_HOL_Obool), tc_HOL_Obool), _1708469), c_member(tc_prod(_1708469, _1708469)))), c_Product__Type_OPair(_1708469, _1708469)))), _1708475)), 46924 ^ [_1708469, _1708471, _1708473, _1708475]))], (46926 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708469, _1708469)), 46924 ^ [_1708469, _1708471, _1708473, _1708475]), hAPP(c_List_Oset(tc_prod(_1708469, _1708469)), hAPP(hAPP(c_List_Ozip(_1708469, _1708469), _1708471), _1708473)))))]]], (43536 ^ _778908) ^ [_1626576, _1626578, _1626580, _1626582, _1626584] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626576, _1626578)), hAPP(hAPP(c_Product__Type_OPair(_1626576, _1626578), _1626580), _1626582)), hAPP(c_Relation_Oconverse(_1626578, _1626576), _1626584))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626578, _1626576)), hAPP(hAPP(c_Product__Type_OPair(_1626578, _1626576), _1626582), _1626580)), _1626584)))], (10942 ^ _778908) ^ [_962480, _962482, _962484] : [class_Orderings_Olinorder(_962480), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962480), _962482), _962484))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962480), _962484), _962482)))], (34427 ^ _778908) ^ [_1408798, _1408800, _1408802, _1408804, _1408806] : [hAPP(_1408798, _1408800) = _1408802, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408804, _1408806), _1408798), _1408800), _1408802) = _1408798)], (10553 ^ _778908) ^ [_956137, _956139] : [class_Rings_Olinordered__idom(_956137), -(c_Groups_Osgn__class_Osgn(_956137, c_Groups_Osgn__class_Osgn(_956137, _956139)) = c_Groups_Osgn__class_Osgn(_956137, _956139))], (48526 ^ _778908) ^ [_1748369, _1748371, _1748373, _1748375] : [hBOOL(hAPP(hAPP(c_member(_1748369), _1748371), hAPP(c_List_Oset(_1748369), hAPP(hAPP(c_List_Otake(_1748369), _1748373), _1748375)))), -(hBOOL(hAPP(hAPP(c_member(_1748369), _1748371), hAPP(c_List_Oset(_1748369), _1748375))))], (26985 ^ _778908) ^ [_1255132, _1255134, _1255136] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1255132, tc_Nat_Onat), _1255134), _1255136)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1255132, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1255132), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1255134)), _1255136))], (29183 ^ _778908) ^ [_1300312, _1300314, _1300316, _1300318, _1300320] : [c_Typedef_Otype__definition(_1300312, _1300314, _1300316, _1300318, _1300320), -(hAPP(c_Set_Oimage(_1300314, _1300312, _1300318), _1300320) = c_Orderings_Otop__class_Otop(tc_fun(_1300312, tc_HOL_Obool)))], (3884 ^ _778908) ^ [_838820, _838822, _838824, _838826] : [-(c_New__DSequence_Opos__single(_838826, _838822) = c_New__DSequence_Opos__single(_838824, _838820)), _838826 = _838824, _838822 = _838820], (28231 ^ _778908) ^ [_1280189, _1280191] : [class_Lattices_Osemilattice__sup(_1280189), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280189), _1280191), _1280191) = _1280191)], (30028 ^ _778908) ^ [_1316609, _1316611, _1316613, _1316615] : [c_Sum__Type_OPlus(_1316609, _1316611, _1316613, _1316615) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1316609, _1316611), tc_HOL_Obool)), 30031 ^ _778908 : [(30034 ^ _778908) ^ [] : [-(_1316615 = c_Orderings_Obot__class_Obot(tc_fun(_1316611, tc_HOL_Obool)))], (30032 ^ _778908) ^ [] : [-(_1316613 = c_Orderings_Obot__class_Obot(tc_fun(_1316609, tc_HOL_Obool)))]]], (31097 ^ _778908) ^ [_1337249, _1337251, _1337253, _1337255] : [hBOOL(hAPP(hAPP(c_member(_1337249), _1337251), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337249, tc_HOL_Obool)), _1337253), _1337255))), hBOOL(hAPP(hAPP(c_member(_1337249), _1337251), _1337255))], (44971 ^ _778908) ^ [_1661997, _1661999, _1662001, _1662003, _1662005] : [class_Complete__Lattice_Ocomplete__lattice(_1661997), hBOOL(hAPP(hAPP(c_member(_1661999), _1662001), _1662003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1661997), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661999, _1661997), _1662003), _1662005)), hAPP(_1662005, _1662001))))], (33525 ^ _778908) ^ [_1390449, _1390451, _1390453] : [class_Orderings_Olinorder(_1390449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390449, tc_HOL_Obool)), _1390451), _1390453)), -(_1390451 = c_Orderings_Obot__class_Obot(tc_fun(_1390449, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390449), _1390453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390449), c_Big__Operators_Olinorder__class_OMax(_1390449, _1390451)), c_Big__Operators_Olinorder__class_OMax(_1390449, _1390453))))], (34776 ^ _778908) ^ [_1415847, _1415849, _1415851, _1415853, _1415855] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1415847, tc_Option_Ooption(_1415849)), _1415851), _1415853), hAPP(c_Option_Ooption_OSome(_1415849), _1415855)) = hAPP(c_COMBK(tc_Option_Ooption(_1415849), _1415847), c_Option_Ooption_ONone(_1415849))], (2464 ^ _778908) ^ [_816142, _816144, _816146, _816148, _816150, _816152, _816154, _816156] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_816156, _816152, _816148, _816144) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_816154, _816150, _816146, _816142)), _816156 = _816154, _816152 = _816150, _816148 = _816146, _816144 = _816142], (4016 ^ _778908) ^ [_840864, _840866, _840868, _840870] : [-(c_Wellfounded_Omax__ext(_840870, _840866) = c_Wellfounded_Omax__ext(_840868, _840864)), _840870 = _840868, _840866 = _840864], (4870 ^ _778908) ^ [_854295, _854297, _854299, _854301] : [-(c_Product__Type_OSigma(_854301, _854297) = c_Product__Type_OSigma(_854299, _854295)), _854301 = _854299, _854297 = _854295], (15550 ^ _778908) ^ [_1043632, _1043634] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043632), _1043634) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043634), _1043632) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1043632 = _1043634)], (31413 ^ _778908) ^ [_1345605, _1345607, _1345609, _1345611, _1345613, _1345615] : [c_Typedef_Otype__definition(_1345605, _1345607, _1345609, _1345611, _1345613), hBOOL(hAPP(hAPP(c_member(_1345607), _1345615), _1345613)), -(hAPP(_1345609, hAPP(_1345611, _1345615)) = _1345615)], (48883 ^ _778908) ^ [_1758572, _1758574, _1758576, _1758578] : [hAPP(hAPP(c_List_Oappend(_1758572), _1758574), _1758576) = _1758578, 48886 ^ _778908 : [(48889 ^ _778908) ^ [] : [-(_1758576 = hAPP(hAPP(c_List_Odrop(_1758572), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758572)), _1758574)), _1758578))], (48887 ^ _778908) ^ [] : [-(_1758574 = hAPP(hAPP(c_List_Otake(_1758572), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758572)), _1758574)), _1758578))]]], (24577 ^ _778908) ^ [_1208910, _1208912, _1208914] : [class_Orderings_Olinorder(_1208910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208910), _1208912), _1208914)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208910), _1208914), _1208912) = _1208914)], (14968 ^ _778908) ^ [_1032648, _1032650, _1032652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032648), 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)), _1032650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032650), _1032652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1032648), _1032650)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1032648), _1032652))))], (33021 ^ _778908) ^ [_1380810, _1380812, _1380814, _1380816] : [c_Hoare__Mirabelle_Ohoare__derivs(_1380810, _1380812, _1380814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380810), tc_HOL_Obool)), _1380816), _1380814)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1380810, _1380812, _1380816))], (24887 ^ _778908) ^ [_1214966, _1214968] : [class_Orderings_Olinorder(_1214966), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214966), _1214968), _1214968) = _1214968)], (5823 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39226 ^ _778908) ^ [_1515694, _1515696, _1515698, _1515700, _1515702] : [c_Fun_Oinj__on(_1515694, _1515696, _1515698, _1515700), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515696, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1515694, _1515696, _1515698), _1515700)), _1515702)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515696), _1515702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1515694), _1515700)), hAPP(c_Finite__Set_Ocard(_1515696), _1515702))))], (42679 ^ _778908) ^ [_1605784, _1605786, _1605788] : [c_Wellfounded_OwfP(_1605784, hAPP(_1605786, 42680 ^ [_1605784, _1605786, _1605788])), 42687 ^ _778908 : [(42690 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1605784, tc_HOL_Obool)), c_Predicate_ODomainP(_1605784, _1605784, hAPP(_1605786, 42685 ^ [_1605784, _1605786, _1605788]))), c_Predicate_ORangeP(_1605784, _1605784, hAPP(_1605786, 42686 ^ [_1605784, _1605786, _1605788]))) = c_Orderings_Obot__class_Obot(tc_fun(_1605784, tc_HOL_Obool))], (42688 ^ _778908) ^ [] : [hAPP(_1605786, 42685 ^ [_1605784, _1605786, _1605788]) = hAPP(_1605786, 42686 ^ [_1605784, _1605786, _1605788])]], -(c_Wellfounded_OwfP(_1605784, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1605788, tc_fun(_1605784, tc_fun(_1605784, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1605788, tc_HOL_Obool))), _1605786)))], (11278 ^ _778908) ^ [_967642, _967644, _967646, _967648] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_967642), 11281 ^ _778908 : [(11288 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967642), _967646), _967648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967642), _967644), _967646)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967642), _967644), _967648))))], (11282 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967642), _967644), _967646)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967642), _967644), _967648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967642), _967646), _967648)))]]], (17255 ^ _778908) ^ [_1076790, _1076792, _1076794, _1076796] : [class_Int_Onumber__ring(_1076790), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1076790), hAPP(c_Int_Onumber__class_Onumber__of(_1076790), _1076792)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1076790), _1076794), hAPP(c_Int_Onumber__class_Onumber__of(_1076790), _1076796))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1076790), hAPP(c_Int_Onumber__class_Onumber__of(_1076790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1076792), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076796)))), _1076794))], (49843 ^ _778908) ^ [_1779576, _1779578, _1779580, _1779582] : [-(_1779576 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779578)), _1779580)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1779578, hAPP(hAPP(c_List_Olist__update(_1779578, _1779580), _1779576), _1779582)) = hAPP(hAPP(c_List_Olist__update(_1779578, c_List_Obutlast(_1779578, _1779580)), _1779576), _1779582))], (29265 ^ _778908) ^ [_1301996] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1301996)), 29269 ^ _778908 : [(29270 ^ _778908) ^ [_1302076] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1302076), _1301996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1302076), 29268 ^ [_1301996])))]]], (9212 ^ _778908) ^ [_933088, _933090, _933092] : [class_Groups_Ogroup__add(_933088), 9215 ^ _778908 : [(9222 ^ _778908) ^ [] : [_933090 = _933092, -(hAPP(c_Groups_Ouminus__class_Ouminus(_933088), _933090) = hAPP(c_Groups_Ouminus__class_Ouminus(_933088), _933092))], (9216 ^ _778908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_933088), _933090) = hAPP(c_Groups_Ouminus__class_Ouminus(_933088), _933092), -(_933090 = _933092)]]], (30812 ^ _778908) ^ [_1331441] : [-(c_Option_Oset(_1331441, c_Option_Ooption_ONone(_1331441)) = c_Orderings_Obot__class_Obot(tc_fun(_1331441, tc_HOL_Obool)))], (28862 ^ _778908) ^ [_1292309, _1292311, _1292313] : [class_Orderings_Olinorder(_1292309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292309), _1292311), _1292313)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292309, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1292309, _1292311), _1292313)), hAPP(c_SetInterval_Oord__class_OatLeast(_1292309), _1292313)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1292309), _1292311))], (5811 ^ _778908) ^ [_871464] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _871464)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25247 ^ _778908) ^ [_1222834] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1222834)))], (35010 ^ _778908) ^ [_1421081] : [-(_1421081 = 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)), _1421081), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (51449 ^ _778908) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (43749 ^ _778908) ^ [_1632066, _1632068, _1632070, _1632072, _1632074, _1632076] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632066, _1632066)), hAPP(hAPP(c_Product__Type_OPair(_1632066, _1632066), _1632068), _1632070)), _1632072)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1632066, _1632066)), hAPP(hAPP(c_Product__Type_OPair(_1632066, _1632066), _1632070), _1632074)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1632066, _1632066), tc_HOL_Obool), _1632076), _1632072))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632066, _1632066)), hAPP(hAPP(c_Product__Type_OPair(_1632066, _1632066), _1632068), _1632074)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1632066, _1632066), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1632076)), _1632072))))], (6480 ^ _778908) ^ [_883747, _883749, _883751] : [c_Com_Ocom_OLocal(_883747, _883749, _883751) = c_Com_Ocom_OSKIP], (40444 ^ _778908) ^ [_1546832, _1546834, _1546836, _1546838, _1546840, _1546842, _1546844, _1546846, _1546848, _1546850] : [hAPP(c_Set_Oimage(_1546832, _1546834, _1546836), _1546838) = _1546840, hAPP(c_Set_Oimage(_1546842, _1546844, _1546846), _1546848) = _1546850, -(hAPP(c_Set_Oimage(tc_prod(_1546832, _1546842), tc_prod(_1546834, _1546844), c_Product__Type_Omap__pair(_1546832, _1546834, _1546842, _1546844, _1546836, _1546846)), hAPP(hAPP(c_Product__Type_OSigma(_1546832, _1546842), _1546838), hAPP(c_COMBK(tc_fun(_1546842, tc_HOL_Obool), _1546832), _1546848))) = hAPP(hAPP(c_Product__Type_OSigma(_1546834, _1546844), _1546840), hAPP(c_COMBK(tc_fun(_1546844, tc_HOL_Obool), _1546834), _1546850)))], (39775 ^ _778908) ^ [_1528466, _1528468, _1528470] : [-(c_Map_Odom(_1528466, _1528468, hAPP(hAPP(c_COMBB(_1528468, tc_Option_Ooption(_1528468), _1528466), c_Option_Ooption_OSome(_1528468)), _1528470)) = c_Orderings_Otop__class_Otop(tc_fun(_1528466, tc_HOL_Obool)))], (44953 ^ _778908) ^ [_1661611, _1661613, _1661615, _1661617, _1661619] : [-(_1661611 = c_Orderings_Obot__class_Obot(tc_fun(_1661613, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661615, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661613, tc_fun(_1661615, tc_HOL_Obool)), _1661611), _1661617)), _1661619) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661613, tc_fun(_1661615, tc_HOL_Obool)), _1661611), hAPP(hAPP(c_COMBC(_1661613, tc_fun(_1661615, tc_HOL_Obool), tc_fun(_1661615, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1661615, tc_HOL_Obool), tc_fun(tc_fun(_1661615, tc_HOL_Obool), tc_fun(_1661615, tc_HOL_Obool)), _1661613), c_Groups_Ominus__class_Ominus(tc_fun(_1661615, tc_HOL_Obool))), _1661617)), _1661619)))], (35971 ^ _778908) ^ [_1444196, _1444198, _1444200, _1444202, _1444204, _1444206, _1444208, _1444210] : [c_Finite__Set_Ofolding(_1444196, _1444198, _1444200, _1444202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444196), _1444204)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444196), _1444206)), -(hAPP(c_Fun_Ocomp(_1444198, _1444198, _1444208, hAPP(_1444202, _1444206)), hAPP(c_Fun_Ocomp(_1444198, _1444198, _1444208, hAPP(_1444202, _1444204)), _1444210)) = hAPP(c_Fun_Ocomp(_1444198, _1444198, _1444208, hAPP(_1444202, _1444204)), hAPP(c_Fun_Ocomp(_1444198, _1444198, _1444208, hAPP(_1444202, _1444206)), _1444210)))], (6248 ^ _778908) ^ [_879572, _879574, _879576, _879578, _879580, _879582] : [c_Com_Ocom_OLocal(_879572, _879574, _879576) = c_Com_Ocom_OCond(_879578, _879580, _879582)], (39727 ^ _778908) ^ [_1527474, _1527476, _1527478, _1527480] : [39728 ^ _778908 : [(39729 ^ _778908) ^ [_1527563] : [_1527478 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1527474, tc_Option_Ooption(_1527476)), hAPP(c_COMBK(tc_Option_Ooption(_1527476), _1527474), c_Option_Ooption_ONone(_1527476))), _1527480), hAPP(c_Option_Ooption_OSome(_1527476), _1527563))]], -(c_Map_Odom(_1527474, _1527476, _1527478) = hAPP(hAPP(c_Set_Oinsert(_1527474), _1527480), c_Orderings_Obot__class_Obot(tc_fun(_1527474, tc_HOL_Obool))))], (22209 ^ _778908) ^ [_1163703, _1163705, _1163707, _1163709] : [class_Fields_Olinordered__field__inverse__zero(_1163703), class_Int_Onumber(_1163703), 22216 ^ _778908 : [(22217 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), _1163705), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163703), _1163707), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)))), 22220 ^ _778908 : [(22227 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), c_Groups_Ozero__class_Ozero(_1163703)), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)))), 22230 ^ _778908 : [(22237 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)), c_Groups_Ozero__class_Ozero(_1163703)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), _1163705), c_Groups_Ozero__class_Ozero(_1163703))))], (22231 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)), c_Groups_Ozero__class_Ozero(_1163703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), _1163707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163703), _1163705), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)))))]]], (22221 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), c_Groups_Ozero__class_Ozero(_1163703)), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163703), _1163705), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709))), _1163707)))]]], (22243 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), _1163705), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1163703), _1163707), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709))))), 22246 ^ _778908 : [(22249 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163703), _1163705), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709))), _1163707))], (22247 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), c_Groups_Ozero__class_Ozero(_1163703)), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709))))]], 22250 ^ _778908 : [(22253 ^ _778908) ^ [] : [22254 ^ _778908 : [(22257 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), _1163707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163703), _1163705), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709))))], (22255 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)), c_Groups_Ozero__class_Ozero(_1163703))))]], 22258 ^ _778908 : [(22261 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163703), _1163705), c_Groups_Ozero__class_Ozero(_1163703)))], (22259 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)), c_Groups_Ozero__class_Ozero(_1163703)))]]], (22251 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163703), c_Groups_Ozero__class_Ozero(_1163703)), hAPP(c_Int_Onumber__class_Onumber__of(_1163703), _1163709)))]]]]], (47567 ^ _778908) ^ [_1724889, _1724891, _1724893] : [-(_1724889 = c_List_Olist_ONil(_1724891)), -(hBOOL(hAPP(hAPP(c_member(_1724891), hAPP(c_Product__Type_Ofst(_1724891, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1724891, _1724889), _1724893))), hAPP(c_List_Oset(_1724891), _1724889))))], (49368 ^ _778908) ^ [_1769090, _1769092] : [class_Complete__Lattice_Ocomplete__lattice(_1769090), -(c_Complete__Lattice_OInf__class_OInf(_1769090, hAPP(c_List_Oset(_1769090), _1769092)) = hAPP(c_List_Ofoldl(_1769090, _1769090, c_Lattices_Osemilattice__inf__class_Oinf(_1769090), c_Orderings_Otop__class_Otop(_1769090)), _1769092))], (17261 ^ _778908) ^ [_1076965, _1076967, _1076969, _1076971] : [class_Rings_Olinordered__semidom(_1076965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076965), _1076967), _1076969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076965), c_Groups_Ozero__class_Ozero(_1076965)), _1076967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1076971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076965), hAPP(hAPP(c_Power_Opower__class_Opower(_1076965), _1076967), _1076971)), hAPP(hAPP(c_Power_Opower__class_Opower(_1076965), _1076969), _1076971))))], (43369 ^ _778908) ^ [_1622717] : [-(hAPP(c_Relation_ODomain(_1622717, _1622717), c_Relation_OId(_1622717)) = c_Orderings_Otop__class_Otop(tc_fun(_1622717, tc_HOL_Obool)))], (51547 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (39460 ^ _778908) ^ [_1521022, _1521024, _1521026, _1521028, _1521030] : [-(hAPP(c_Set_Ovimage(_1521022, _1521024, _1521026), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521024, tc_HOL_Obool)), _1521028), _1521030)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521022, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521022, _1521024, _1521026), _1521028)), hAPP(c_Set_Ovimage(_1521022, _1521024, _1521026), _1521030)))], (43115 ^ _778908) ^ [_1615677, _1615679, _1615681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615677, _1615677), tc_HOL_Obool)), _1615679), hAPP(hAPP(c_Product__Type_OSigma(_1615677, _1615677), _1615681), hAPP(c_COMBK(tc_fun(_1615677, tc_HOL_Obool), _1615677), _1615681)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615677, _1615677), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1615677, _1615679)), hAPP(hAPP(c_Product__Type_OSigma(_1615677, _1615677), _1615681), hAPP(c_COMBK(tc_fun(_1615677, tc_HOL_Obool), _1615677), _1615681)))))], (12625 ^ _778908) ^ [_991146] : [hBOOL(hAPP(_991146, 12626 ^ [_991146])), 12629 ^ _778908 : [(12630 ^ _778908) ^ [_991240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991240)), -(hBOOL(hAPP(_991146, hAPP(c_Int_Onat, _991240))))]]], (17465 ^ _778908) ^ [_1080562] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080562) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080562)))], (19649 ^ _778908) ^ [_1117380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1117380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1117380))))], (30998 ^ _778908) ^ [_1335278, _1335280, _1335282, _1335284, _1335286] : [hBOOL(hAPP(hAPP(c_member(_1335278), _1335280), _1335282)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1335278, _1335284)), hAPP(c_Sum__Type_OInl(_1335278, _1335284), _1335280)), c_Sum__Type_OPlus(_1335278, _1335284, _1335282, _1335286))))], (41323 ^ _778908) ^ [_1565476, _1565478, _1565480, _1565482, _1565484, _1565486] : [class_Groups_Ocomm__monoid__add(_1565476), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565478), _1565480)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565478, _1565476), _1565482), _1565480) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565484, _1565476), hAPP(hAPP(c_COMBB(tc_fun(_1565478, tc_HOL_Obool), _1565476, _1565484), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565478, _1565476), _1565482)), hAPP(hAPP(c_COMBB(tc_fun(_1565478, tc_HOL_Obool), tc_fun(_1565478, tc_HOL_Obool), _1565484), c_Set_OCollect(_1565478)), hAPP(hAPP(c_COMBB(tc_fun(_1565478, tc_HOL_Obool), tc_fun(_1565478, tc_HOL_Obool), _1565484), hAPP(c_COMBS(_1565478, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565478), c_fconj), hAPP(hAPP(c_COMBC(_1565478, tc_fun(_1565478, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565478)), _1565480)))), hAPP(c_COMBC(_1565478, _1565484, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1565484, tc_fun(_1565484, tc_HOL_Obool), _1565478), c_fequal), _1565486)))))), hAPP(c_Set_Oimage(_1565478, _1565484, _1565486), _1565480)))], (27701 ^ _778908) ^ [_1269862, _1269864, _1269866, _1269868] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1269862, tc_Nat_Onat), _1269864), _1269866) = hAPP(c_Nat_OSuc, _1269868), 27705 ^ _778908 : [(27708 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1269864, 27704 ^ [_1269862, _1269864, _1269866, _1269868]))))], (27706 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1269862), 27704 ^ [_1269862, _1269864, _1269866, _1269868]), _1269866)))]]], (12780 ^ _778908) ^ [_993837, _993839, _993841] : [class_Groups_Oordered__comm__monoid__add(_993837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993837), c_Groups_Ozero__class_Ozero(_993837)), _993839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993837), c_Groups_Ozero__class_Ozero(_993837)), _993841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993837), c_Groups_Ozero__class_Ozero(_993837)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_993837), _993839), _993841))))], (51353 ^ _778908) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (21471 ^ _778908) ^ [_1149649, _1149651, _1149653] : [class_Fields_Olinordered__field(_1149649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149649), _1149651), _1149653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149649), _1149651), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149649), _1149651), _1149653)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149649), c_Groups_Oone__class_Oone(_1149649)), c_Groups_Oone__class_Oone(_1149649))))))], (40513 ^ _778908) ^ [_1548610, _1548612, _1548614, _1548616] : [c_Relation_Orefl__on(_1548610, _1548612, _1548614), hBOOL(hAPP(hAPP(c_member(_1548610), _1548616), _1548612)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548610, _1548610)), hAPP(hAPP(c_Product__Type_OPair(_1548610, _1548610), _1548616), _1548616)), _1548614)))], (6526 ^ _778908) ^ [_884660, _884662, _884664, _884666] : [c_Com_Ocom_OAss(_884660, _884662) = c_Com_Ocom_OSemi(_884664, _884666)], (38418 ^ _778908) ^ [_1499163, _1499165, _1499167, _1499169, _1499171, _1499173] : [c_Finite__Set_Ofolding__idem(_1499163, _1499165, _1499167, _1499169), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499163), _1499171)), hBOOL(hAPP(hAPP(c_member(_1499163), _1499173), _1499171)), -(hAPP(c_Fun_Ocomp(_1499165, _1499165, _1499165, hAPP(_1499169, _1499171)), hAPP(_1499167, _1499173)) = hAPP(_1499169, _1499171))], (51119 ^ _778908) ^ [_1807906, _1807908, _1807910, _1807912, _1807914] : [-(c_List_OtakeWhile(_1807906, _1807908, hAPP(hAPP(c_List_Omap(_1807910, _1807906), _1807912), _1807914)) = hAPP(hAPP(c_List_Omap(_1807910, _1807906), _1807912), c_List_OtakeWhile(_1807910, hAPP(c_Fun_Ocomp(_1807906, tc_HOL_Obool, _1807910, _1807908), _1807912), _1807914)))], (18247 ^ _778908) ^ [_1094427] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1094427), c_Int_OMin) = c_Int_Osucc(_1094427))], (40044 ^ _778908) ^ [_1534988, _1534990, _1534992, _1534994, _1534996] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1534988, _1534990, hAPP(hAPP(c_Set_Oinsert(_1534988), _1534992), _1534994)), _1534996)), 40049 ^ _778908 : [(40054 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1534988), 40047 ^ [_1534988, _1534990, _1534992, _1534994, _1534996]), 40048 ^ [_1534988, _1534990, _1534992, _1534994, _1534996]))], (40052 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1534988, _1534988, _1534990, 40047 ^ [_1534988, _1534990, _1534992, _1534994, _1534996], 40048 ^ [_1534988, _1534990, _1534992, _1534994, _1534996]), _1534996)))], (40050 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1534988), _1534992), _1534994) = hAPP(hAPP(c_Set_Oinsert(_1534988), 40047 ^ [_1534988, _1534990, _1534992, _1534994, _1534996]), 40048 ^ [_1534988, _1534990, _1534992, _1534994, _1534996]))]]], (27608 ^ _778908) ^ [_1267920, _1267922, _1267924, _1267926, _1267928, _1267930] : [-(hAPP(c_Set_Oimage(_1267920, _1267922, _1267924), hAPP(c_Set_Oimage(_1267926, _1267920, _1267928), _1267930)) = hAPP(c_Set_Oimage(_1267926, _1267922, hAPP(hAPP(c_COMBB(_1267920, _1267922, _1267926), _1267924), _1267928)), _1267930))], (51409 ^ _778908) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (48913 ^ _778908) ^ [_1759278, _1759280, _1759282] : [-(hAPP(hAPP(c_List_Odrop(_1759278), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1759278), _1759280), _1759282)) = _1759282)], (51389 ^ _778908) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (24053 ^ _778908) ^ [_1198570, _1198572, _1198574, _1198576, _1198578] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198570, _1198572, _1198574), _1198576), _1198578) = hAPP(hAPP(_1198576, hAPP(c_Product__Type_Ofst(_1198570, _1198572), _1198578)), hAPP(c_Product__Type_Osnd(_1198570, _1198572), _1198578)))], (50670 ^ _778908) ^ [_1796400, _1796402, _1796404, _1796406] : [class_Orderings_Olinorder(_1796400), c_List_Olinorder__class_Osorted(_1796400, _1796402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1796404), _1796406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796406), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796400)), _1796402))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1796400), hAPP(hAPP(c_List_Onth(_1796400), _1796402), _1796404)), hAPP(hAPP(c_List_Onth(_1796400), _1796402), _1796406))))], (43717 ^ _778908) ^ [_1631315, _1631317] : [-(c_Relation_Ototal__on(_1631315, c_Orderings_Obot__class_Obot(tc_fun(_1631315, tc_HOL_Obool)), _1631317))], (47483 ^ _778908) ^ [_1723331, _1723333] : [_1723333 = c_List_Olist_ONil(_1723331), -(hAPP(c_List_Oset(_1723331), _1723333) = c_Orderings_Obot__class_Obot(tc_fun(_1723331, tc_HOL_Obool)))], (23709 ^ _778908) ^ [_1192114, _1192116, _1192118, _1192120] : [class_Orderings_Olinorder(_1192114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192114), _1192116), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192114), _1192118), _1192120))), 23716 ^ _778908 : [(23719 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192114), _1192116), _1192120)))], (23717 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192114), _1192116), _1192118)))]]], (42576 ^ _778908) ^ [_1603224, _1603226, _1603228] : [42578 ^ _778908 : [(42581 ^ _778908) ^ [] : [hBOOL(hAPP(_1603226, 42577 ^ [_1603224, _1603226, _1603228]))], (42579 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603224), 42577 ^ [_1603224, _1603226, _1603228]), _1603228)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1603224, _1603226), _1603228)))], (44862 ^ _778908) ^ [_1658640, _1658642, _1658644, _1658646] : [c_Orderings_Otop__class_Otop(tc_fun(_1658640, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658642, tc_fun(_1658640, tc_HOL_Obool)), _1658644), _1658646), 44865 ^ _778908 : [(44866 ^ _778908) ^ [_1658756] : [hBOOL(hAPP(hAPP(c_member(_1658642), _1658756), _1658644)), -(hAPP(_1658646, _1658756) = c_Orderings_Otop__class_Otop(tc_fun(_1658640, tc_HOL_Obool)))]]], (18011 ^ _778908) ^ [_1090340] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1090340))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1090340)) = _1090340)], (41285 ^ _778908) ^ [_1563837, _1563839, _1563841] : [-(c_Map_Odom(_1563837, _1563839, _1563841) = hAPP(c_Set_OCollect(_1563837), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1563837), c_fNot), hAPP(hAPP(c_COMBC(_1563837, tc_Option_Ooption(_1563839), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1563839), tc_fun(tc_Option_Ooption(_1563839), tc_HOL_Obool), _1563837), c_fequal), _1563841)), c_Option_Ooption_ONone(_1563839)))))], (380 ^ _778908) ^ [_784610, _784612, _784614, _784616] : [-(c_Equiv__Relations_Oequivp(_784614, _784610)), c_Equiv__Relations_Oequivp(_784616, _784612), _784616 = _784614, _784612 = _784610], (42030 ^ _778908) ^ [_1589633, _1589635, _1589637] : [c_Wellfounded_Owf(_1589633, _1589635), -(c_Wellfounded_Owf(_1589633, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1589633, _1589633), tc_HOL_Obool)), _1589637), _1589635)))], (2774 ^ _778908) ^ [_820959, _820961, _820963, _820965, _820967, _820969] : [-(c_Product__Type_Ointernal__split(_820969, _820965, _820961) = c_Product__Type_Ointernal__split(_820967, _820963, _820959)), _820969 = _820967, _820965 = _820963, _820961 = _820959], (43241 ^ _778908) ^ [_1619572, _1619574, _1619576, _1619578, _1619580] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619572, _1619572)), hAPP(hAPP(c_Product__Type_OPair(_1619572, _1619572), _1619574), _1619576)), c_Transitive__Closure_Ortrancl(_1619572, _1619578))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1619572, _1619572)), hAPP(hAPP(c_Product__Type_OPair(_1619572, _1619572), _1619576), _1619580)), c_Transitive__Closure_Ortrancl(_1619572, _1619578))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619572, _1619572)), hAPP(hAPP(c_Product__Type_OPair(_1619572, _1619572), _1619574), _1619580)), c_Transitive__Closure_Ortrancl(_1619572, _1619578))))], (13086 ^ _778908) ^ [_999613, _999615] : [class_Rings_Olinordered__idom(_999613), 13089 ^ _778908 : [(13096 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999613), c_Groups_Ozero__class_Ozero(_999613)), _999615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999613), c_Groups_Ozero__class_Ozero(_999613)), c_Groups_Osgn__class_Osgn(_999613, _999615))))], (13090 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999613), c_Groups_Ozero__class_Ozero(_999613)), c_Groups_Osgn__class_Osgn(_999613, _999615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999613), c_Groups_Ozero__class_Ozero(_999613)), _999615)))]]], (15562 ^ _778908) ^ [_1043814] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043814), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1043814)], (39444 ^ _778908) ^ [_1520596, _1520598, _1520600, _1520602] : [c_Fun_Oinj__on(_1520596, _1520598, _1520600, c_Orderings_Otop__class_Otop(tc_fun(_1520596, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520596, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1520596, _1520598, _1520600), hAPP(hAPP(c_Set_Oinsert(_1520598), _1520602), c_Orderings_Obot__class_Obot(tc_fun(_1520598, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1520596), c_HOL_OThe(_1520596, hAPP(hAPP(c_COMBC(_1520596, _1520598, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1520598, tc_fun(_1520598, tc_HOL_Obool), _1520596), c_fequal), _1520600)), _1520602))), c_Orderings_Obot__class_Obot(tc_fun(_1520596, tc_HOL_Obool))))))], (47489 ^ _778908) ^ [_1723449, _1723451, _1723453] : [hAPP(hAPP(c_List_Olist_OCons(_1723449), _1723451), _1723453) = c_List_Olist_ONil(_1723449)], (45539 ^ _778908) ^ [_1674882, _1674884, _1674886] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1674882, tc_HOL_Obool)), _1674884), _1674886))), 45545 ^ _778908 : [(45549 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1674882, tc_HOL_Obool)), 45547 ^ [_1674882, _1674884, _1674886]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1674882, tc_HOL_Obool)), _1674884), _1674886))))], (45551 ^ _778908) ^ [] : [45544 ^ [_1674882, _1674884, _1674886] = 45547 ^ [_1674882, _1674884, _1674886]], (45553 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1674882, tc_HOL_Obool)), 45544 ^ [_1674882, _1674884, _1674886]), 45547 ^ [_1674882, _1674884, _1674886]) = c_Orderings_Obot__class_Obot(tc_fun(_1674882, tc_HOL_Obool))], (45546 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1674882, tc_HOL_Obool)), 45544 ^ [_1674882, _1674884, _1674886]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1674882, tc_HOL_Obool)), _1674884), _1674886))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1674882, tc_HOL_Obool)), _1674884), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1674882, tc_HOL_Obool), _1674886)) = c_Orderings_Obot__class_Obot(tc_fun(_1674882, tc_HOL_Obool)))], (5897 ^ _778908) ^ [_872884, _872886, _872888, _872890] : [-(hAPP(hAPP(c_String_Ochar_OChar, _872884), _872886) = hAPP(hAPP(c_String_Ochar_OChar, _872888), _872890)), _872884 = _872888, _872886 = _872890], (19275 ^ _778908) ^ [_1110849, _1110851] : [class_Rings_Osemiring__1(_1110849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110851)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110849), 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)))), _1110851))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110849), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110849), hAPP(c_Int_Onat, _1110851))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110849), hAPP(c_Int_Onat, _1110851))))], (31690 ^ _778908) ^ [_1350948, _1350950, _1350952] : [class_Orderings_Oord(_1350948), 31693 ^ _778908 : [(31700 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350948), _1350952), _1350950)), -(hBOOL(hAPP(hAPP(c_member(_1350948), _1350950), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1350948), _1350952))))], (31694 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1350948), _1350950), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1350948), _1350952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350948), _1350952), _1350950)))]]], (14818 ^ _778908) ^ [_1030323, _1030325] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030323), _1030325) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1030325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14827 ^ _778908 : [(14830 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030323), _1030325)))], (14828 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030323)))]], 14831 ^ _778908 : [(14834 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030325), _1030323)))], (14832 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1030323), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23295 ^ _778908) ^ [_1184660, _1184662] : [_1184660 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1184662, _1184660) = 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), _1184662)))], (38484 ^ _778908) ^ [_1500698, _1500700, _1500702] : [class_Lattices_Olattice(_1500698), hAPP(_1500700, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1500698), 38489 ^ [_1500698, _1500700, _1500702]), 38490 ^ [_1500698, _1500700, _1500702])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1500698), hAPP(_1500700, 38489 ^ [_1500698, _1500700, _1500702])), hAPP(_1500700, 38490 ^ [_1500698, _1500700, _1500702])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500698), _1500702)), -(_1500702 = c_Orderings_Obot__class_Obot(tc_fun(_1500698, tc_HOL_Obool))), -(hAPP(_1500700, c_Big__Operators_Olattice__class_OInf__fin(_1500698, _1500702)) = c_Big__Operators_Olattice__class_OInf__fin(_1500698, hAPP(c_Set_Oimage(_1500698, _1500698, _1500700), _1500702)))], (22039 ^ _778908) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (14009 ^ _778908) ^ [_1015954, _1015956, _1015958] : [class_Divides_Oring__div(_1015954), -(c_Divides_Odiv__class_Omod(_1015954, hAPP(c_Groups_Ouminus__class_Ouminus(_1015954), _1015956), _1015958) = c_Divides_Odiv__class_Omod(_1015954, hAPP(c_Groups_Ouminus__class_Ouminus(_1015954), c_Divides_Odiv__class_Omod(_1015954, _1015956, _1015958)), _1015958))], (47611 ^ _778908) ^ [_1726400, _1726402, _1726404] : [-(hAPP(hAPP(c_List_Onth(_1726400), hAPP(hAPP(c_List_Olist_OCons(_1726400), _1726402), _1726404)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1726402)], (51665 ^ _778908) ^ [_1813660, _1813662] : [hBOOL(_1813660), hBOOL(_1813662), -(hBOOL(hAPP(hAPP(c_fconj, _1813660), _1813662)))], (25699 ^ _778908) ^ [_1230293, _1230295] : [class_Rings_Ocomm__semiring__1(_1230293), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230293), _1230295), _1230295)))], (51621 ^ _778908) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (47150 ^ _778908) ^ [_1715284, _1715286, _1715288] : [-(c_List_Oset__Cons(_1715284, _1715286, _1715288) = hAPP(c_Set_OCollect(tc_List_Olist(_1715284)), hAPP(hAPP(c_COMBB(tc_fun(_1715284, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1715284)), c_HOL_OEx(_1715284)), hAPP(hAPP(c_COMBB(tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), tc_fun(_1715284, tc_HOL_Obool), tc_List_Olist(_1715284)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_HOL_Obool, _1715284), c_HOL_OEx(tc_List_Olist(_1715284)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715284), tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1715284, tc_fun(tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool))), tc_fun(tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool))), tc_List_Olist(_1715284)), c_COMBS(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1715284, tc_fun(tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool))), tc_List_Olist(_1715284)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1715284), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), _1715284), c_COMBS(tc_List_Olist(_1715284), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1715284)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_List_Olist(_1715284), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1715284), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1715284)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715284), tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_List_Olist(_1715284))), tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1715284), tc_List_Olist(_1715284)), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), tc_fun(tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_List_Olist(_1715284))), tc_fun(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool))), tc_List_Olist(_1715284)), c_COMBB(tc_fun(tc_List_Olist(_1715284), tc_List_Olist(_1715284)), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), _1715284)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1715284), tc_List_Olist(_1715284)), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), tc_List_Olist(_1715284)), c_COMBB(tc_List_Olist(_1715284), tc_HOL_Obool, tc_List_Olist(_1715284))), c_fequal))), c_List_Olist_OCons(_1715284)))))), hAPP(hAPP(c_COMBC(_1715284, tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool)), _1715284), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1715284))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1715284), c_fconj), hAPP(hAPP(c_COMBC(_1715284, tc_fun(_1715284, tc_HOL_Obool), tc_HOL_Obool), c_member(_1715284)), _1715286)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715284), tc_fun(tc_List_Olist(_1715284), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1715284))), _1715288)))))))], (41167 ^ _778908) ^ [_1561101, _1561103] : [-(hAPP(c_Set_OCollect(_1561101), _1561103) = _1561103)], (51459 ^ _778908) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (24939 ^ _778908) ^ [_1216012, _1216014, _1216016, _1216018, _1216020] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1216012, _1216014, _1216016, hAPP(c_COMBK(_1216014, _1216012), _1216018), hAPP(c_COMBK(_1216014, _1216016), _1216018)), _1216020) = _1216018)], (46255 ^ _778908) ^ [_1691645, _1691647, _1691649, _1691651] : [_1691651 = c_Option_Ooption_ONone(_1691645), -(hAPP(hAPP(c_Option_Omap(_1691645, _1691647), _1691649), _1691651) = c_Option_Ooption_ONone(_1691647))], (30394 ^ _778908) ^ [_1323341] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323341, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1323341, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1323341, tc_HOL_Obool)))], (44446 ^ _778908) ^ [_1647746, _1647748, _1647750, _1647752, _1647754, _1647756, _1647758] : [c_Finite__Set_Ofun__left__comm(_1647746, _1647748, _1647750), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1647746, _1647748, _1647750, _1647752, _1647754), _1647756)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1647746, _1647748, _1647750, _1647752, _1647754), _1647758)), -(_1647758 = _1647756)], (22922 ^ _778908) ^ [_1177492, _1177494, _1177496] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1177492, _1177494), _1177496)), 22925 ^ _778908 : [(22926 ^ _778908) ^ [_1177577] : [hBOOL(hAPP(hAPP(_1177494, _1177577), _1177496)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1177492, _1177494), _1177577)))]]], (5530 ^ _778908) ^ [_864363, _864365, _864367, _864369, _864371, _864373, _864375, _864377] : [-(c_List_Olist_Olist__case(_864377, _864373, _864369, _864365) = c_List_Olist_Olist__case(_864375, _864371, _864367, _864363)), _864377 = _864375, _864373 = _864371, _864369 = _864367, _864365 = _864363], (17279 ^ _778908) ^ [_1077294, _1077296, _1077298] : [class_Rings_Olinordered__semidom(_1077294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077294), c_Groups_Oone__class_Oone(_1077294)), _1077296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1077298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077294), c_Groups_Oone__class_Oone(_1077294)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077294), _1077296), _1077298))))], (43191 ^ _778908) ^ [_1618339, _1618341] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1618339, _1618339, _1618339), _1618341), c_Transitive__Closure_Ortrancl(_1618339, _1618341)) = hAPP(hAPP(c_Relation_Orel__comp(_1618339, _1618339, _1618339), c_Transitive__Closure_Ortrancl(_1618339, _1618341)), _1618341))], (37144 ^ _778908) ^ [_1470512, _1470514, _1470516, _1470518] : [class_Orderings_Oorder(_1470512), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470512, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1470512, _1470514, _1470516)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1470512, _1470516, _1470518)) = c_Orderings_Obot__class_Obot(tc_fun(_1470512, tc_HOL_Obool)))], (42350 ^ _778908) ^ [_1597136, _1597138, _1597140] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1597136, _1597138)), _1597140)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1597136), hAPP(c_Relation_ODomain(_1597136, _1597138), _1597140))))], (50104 ^ _778908) ^ [_1786218] : [class_Orderings_Olinorder(_1786218), -(c_List_Olinorder__class_Osorted(_1786218, c_List_Olist_ONil(_1786218)))], (51307 ^ _778908) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (6709 ^ _778908) ^ [_888885, _888887, _888889, _888891, _888893] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_888885, _888887), _888889, _888891, _888893), 6714 ^ _778908 : [(6717 ^ _778908) ^ [] : [hBOOL(hAPP(_888885, _888889))], (6715 ^ _778908) ^ [] : [-(_888893 = _888889)]], 6718 ^ _778908 : [(6724 ^ _778908) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_888885, _888887), 6720 ^ [_888885, _888887, _888889, _888891, _888893], _888891, _888893))], (6722 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_888887, _888889, _888891, 6720 ^ [_888885, _888887, _888889, _888891, _888893]))], (6719 ^ _778908) ^ [] : [-(hBOOL(hAPP(_888885, _888889)))]]], (8154 ^ _778908) ^ [_915364, _915366, _915368, _915370] : [class_Rings_Olinordered__semidom(_915364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915364), c_Groups_Ozero__class_Ozero(_915364)), _915366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915364), _915368), _915370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915364), _915368), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915364), _915366), _915370))))], (45304 ^ _778908) ^ [_1669464, _1669466, _1669468] : [-(hAPP(c_Relation_ODomain(_1669464, _1669466), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1669464, _1669466), tc_HOL_Obool), _1669468)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1669464, _1669466), tc_HOL_Obool), tc_fun(_1669464, tc_HOL_Obool)), _1669468), c_Relation_ODomain(_1669464, _1669466)))], (26067 ^ _778908) ^ [_1236879, _1236881, _1236883, _1236885, _1236887, _1236889] : [class_Groups_Ocomm__monoid__add(_1236879), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236881, _1236879), hAPP(hAPP(c_COMBC(_1236881, tc_fun(_1236883, tc_HOL_Obool), _1236879), hAPP(hAPP(c_COMBB(tc_fun(_1236883, _1236879), tc_fun(tc_fun(_1236883, tc_HOL_Obool), _1236879), _1236881), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236883, _1236879)), _1236885)), _1236887)), _1236889) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236883, _1236879), hAPP(hAPP(c_COMBC(_1236883, tc_fun(_1236881, tc_HOL_Obool), _1236879), hAPP(hAPP(c_COMBB(tc_fun(_1236881, _1236879), tc_fun(tc_fun(_1236881, tc_HOL_Obool), _1236879), _1236883), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236881, _1236879)), hAPP(c_COMBC(_1236881, _1236883, _1236879), _1236885))), _1236889)), _1236887))], (624 ^ _778908) ^ [_788570, _788572, _788574, _788576, _788578, _788580, _788582, _788584] : [-(c_Equiv__Relations_Ocongruent(_788582, _788578, _788574, _788570)), c_Equiv__Relations_Ocongruent(_788584, _788580, _788576, _788572), _788584 = _788582, _788580 = _788578, _788576 = _788574, _788572 = _788570], (39506 ^ _778908) ^ [_1522141, _1522143, _1522145, _1522147] : [-(hAPP(c_Set_Ovimage(_1522141, _1522143, _1522145), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1522143, tc_HOL_Obool)), _1522147)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1522141, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522141, _1522143, _1522145), _1522147)))], (4058 ^ _778908) ^ [_841481, _841483, _841485, _841487] : [-(c_Transitive__Closure_Otrancl(_841487, _841483) = c_Transitive__Closure_Otrancl(_841485, _841481)), _841487 = _841485, _841483 = _841481], (46850 ^ _778908) ^ [_1706303, _1706305, _1706307, _1706309, _1706311] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706303)), _1706305) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706307)), _1706309), 46853 ^ _778908 : [(46861 ^ _778908) ^ [] : [46862 ^ _778908 : [(46863 ^ _778908) ^ [_1706591] : [hAPP(c_Map_Omap__of(_1706303, _1706307, hAPP(hAPP(c_List_Ozip(_1706303, _1706307), _1706305), _1706309)), _1706311) = hAPP(c_Option_Ooption_OSome(_1706307), _1706591)]], -(hBOOL(hAPP(hAPP(c_member(_1706303), _1706311), hAPP(c_List_Oset(_1706303), _1706305))))], (46854 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1706303), _1706311), hAPP(c_List_Oset(_1706303), _1706305))), -(hAPP(c_Map_Omap__of(_1706303, _1706307, hAPP(hAPP(c_List_Ozip(_1706303, _1706307), _1706305), _1706309)), _1706311) = hAPP(c_Option_Ooption_OSome(_1706307), 46857 ^ [_1706303, _1706305, _1706307, _1706309, _1706311]))]]], (49938 ^ _778908) ^ [_1781599, _1781601, _1781603] : [hBOOL(hAPP(c_List_Odistinct(_1781599), _1781601)), -(hBOOL(hAPP(c_List_Odistinct(_1781599), hAPP(c_List_Ofilter(_1781599, _1781603), _1781601))))], (43171 ^ _778908) ^ [_1617865, _1617867] : [-(c_Transitive__Closure_Otrancl(_1617865, _1617867) = hAPP(hAPP(c_Relation_Orel__comp(_1617865, _1617865, _1617865), c_Transitive__Closure_Ortrancl(_1617865, _1617867)), _1617867))], (45897 ^ _778908) ^ [_1682775, _1682777, _1682779] : [-(c_Map_Omap__add(_1682775, _1682777, _1682779, hAPP(c_COMBK(tc_Option_Ooption(_1682777), _1682775), c_Option_Ooption_ONone(_1682777))) = _1682779)], (21245 ^ _778908) ^ [_1145924, _1145926, _1145928, _1145930] : [class_Fields_Ofield(_1145924), -(_1145926 = c_Groups_Ozero__class_Ozero(_1145924)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145924), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145924), _1145928), _1145926)), _1145930) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145924), _1145928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145924), _1145926), _1145930))), _1145926))], (4128 ^ _778908) ^ [_842510, _842512] : [_842512 = _842510, -(c_Set_OPow(_842512) = c_Set_OPow(_842510))], (13666 ^ _778908) ^ [_1009305, _1009307, _1009309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1009305)), 13669 ^ _778908 : [(13676 ^ _778908) ^ [] : [_1009307 = _1009309, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009305), _1009307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009305), _1009309))], (13670 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009305), _1009307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009305), _1009309), -(_1009307 = _1009309)]]], (9490 ^ _778908) ^ [_937593, _937595, _937597] : [class_Rings_Ono__zero__divisors(_937593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937593), _937595), _937597) = c_Groups_Ozero__class_Ozero(_937593), -(_937595 = c_Groups_Ozero__class_Ozero(_937593)), -(_937597 = c_Groups_Ozero__class_Ozero(_937593))], (46665 ^ _778908) ^ [_1701619, _1701621, _1701623, _1701625, _1701627] : [class_Orderings_Olinorder(_1701619), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701621)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701621, _1701619, _1701623), _1701625), _1701627)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701621)), _1701627)))], (6005 ^ _778908) ^ [_874919, _874921] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_874919, _874921))))], (8960 ^ _778908) ^ [_928595, _928597, _928599] : [class_Rings_Oring(_928595), -(hAPP(c_Groups_Ouminus__class_Ouminus(_928595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928595), _928597), _928599)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928595), hAPP(c_Groups_Ouminus__class_Ouminus(_928595), _928597)), _928599))], (14519 ^ _778908) ^ [_1025318, _1025320] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025318), _1025320)), _1025318)))], (19513 ^ _778908) ^ [_1115016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115016), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1115016)), c_Int_OMin)))], (42145 ^ _778908) ^ [_1592344, _1592346] : [c_Wellfounded_Owf(_1592344, _1592346), -(c_Wellfounded_Owf(tc_List_Olist(_1592344), c_List_Olex(_1592344, _1592346)))], (25363 ^ _778908) ^ [_1224902, _1224904, _1224906] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224902), _1224904)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224904), _1224902))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224904), _1224906)), 25374 ^ _778908 : [(25377 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224906), _1224902))], (25375 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224902), _1224906)))]]], (50873 ^ _778908) ^ [_1801266, _1801268, _1801270, _1801272] : [-(hAPP(c_List_Orev(_1801266), hAPP(hAPP(c_List_Omap(_1801268, _1801266), _1801270), _1801272)) = hAPP(hAPP(c_List_Omap(_1801268, _1801266), _1801270), hAPP(c_List_Orev(_1801268), _1801272)))], (43806 ^ _778908) ^ [_1633514, _1633516, _1633518] : [43808 ^ _778908 : [(43809 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633514), 43807 ^ [_1633514, _1633516, _1633518]), _1633516)))], (43814 ^ _778908) ^ [] : [43807 ^ [_1633514, _1633516, _1633518] = 43810 ^ [_1633514, _1633516, _1633518]], (43818 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633514, _1633514)), hAPP(hAPP(c_Product__Type_OPair(_1633514, _1633514), 43810 ^ [_1633514, _1633516, _1633518]), 43807 ^ [_1633514, _1633516, _1633518])), _1633518))], (43816 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633514, _1633514)), hAPP(hAPP(c_Product__Type_OPair(_1633514, _1633514), 43807 ^ [_1633514, _1633516, _1633518]), 43810 ^ [_1633514, _1633516, _1633518])), _1633518))], (43812 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633514), 43810 ^ [_1633514, _1633516, _1633518]), _1633516)))]], -(c_Relation_Ototal__on(_1633514, _1633516, _1633518))], (22980 ^ _778908) ^ [_1178578, _1178580, _1178582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178578, tc_fun(_1178578, tc_HOL_Obool))), _1178580), _1178582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1178578, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1178578, _1178582)), c_Wellfounded_Oaccp(_1178578, _1178580))))], (39504 ^ _778908) ^ [_1522107, _1522109] : [-(hAPP(c_Set_Ovimage(_1522107, _1522107, c_COMBI(_1522107)), _1522109) = _1522109)], (818 ^ _778908) ^ [_791469, _791471, _791473, _791475] : [-(c_Wellfounded_Owf(_791473, _791469)), c_Wellfounded_Owf(_791475, _791471), _791475 = _791473, _791471 = _791469], (24607 ^ _778908) ^ [_1209411, _1209413, _1209415, _1209417] : [class_Orderings_Olinorder(_1209411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209411), _1209413), _1209415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209411), _1209413), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209411), _1209415), _1209417))))], (42289 ^ _778908) ^ [_1595927] : [-(c_Wellfounded_OwfP(_1595927, hAPP(c_COMBK(tc_fun(_1595927, tc_HOL_Obool), _1595927), hAPP(c_COMBK(tc_HOL_Obool, _1595927), c_fFalse))))], (33075 ^ _778908) ^ [_1381871, _1381873] : [class_Lattices_Olattice(_1381871), -(c_Big__Operators_Olattice__class_OSup__fin(_1381871, hAPP(hAPP(c_Set_Oinsert(_1381871), _1381873), c_Orderings_Obot__class_Obot(tc_fun(_1381871, tc_HOL_Obool)))) = _1381873)], (16304 ^ _778908) ^ [_1059068, _1059070] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059068, _1059070) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059068, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1059070)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059068, _1059070)), _1059070))], (4110 ^ _778908) ^ [_842255, _842257] : [_842257 = _842255, -(c_Equiv__Relations_Oquotient(_842257) = c_Equiv__Relations_Oquotient(_842255))], (36810 ^ _778908) ^ [_1462622, _1462624, _1462626] : [class_Lattices_Osemilattice__inf(_1462622), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462622), _1462624), _1462626) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462622), _1462626), _1462624))], (9110 ^ _778908) ^ [_931240, _931242, _931244, _931246] : [class_Rings_Ocomm__semiring__1(_931240), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931240), _931242), _931244)), _931246) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931240), _931242), _931246)), _931244))], (47595 ^ _778908) ^ [_1725763, _1725765, _1725767, _1725769, _1725771] : [-(hAPP(hAPP(c_List_Ozip(_1725763, _1725765), _1725767), hAPP(hAPP(c_List_Olist_OCons(_1725765), _1725769), _1725771)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1725763, _1725765)), _1725763, c_List_Olist_ONil(tc_prod(_1725763, _1725765)), hAPP(hAPP(c_COMBC(_1725763, tc_fun(tc_List_Olist(_1725763), tc_List_Olist(tc_prod(_1725763, _1725765))), tc_fun(tc_List_Olist(_1725763), tc_List_Olist(tc_prod(_1725763, _1725765)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1725763, _1725765)), tc_List_Olist(tc_prod(_1725763, _1725765))), tc_fun(tc_fun(tc_List_Olist(_1725763), tc_List_Olist(tc_prod(_1725763, _1725765))), tc_fun(tc_List_Olist(_1725763), tc_List_Olist(tc_prod(_1725763, _1725765)))), _1725763), c_COMBB(tc_List_Olist(tc_prod(_1725763, _1725765)), tc_List_Olist(tc_prod(_1725763, _1725765)), tc_List_Olist(_1725763))), hAPP(hAPP(c_COMBB(tc_prod(_1725763, _1725765), tc_fun(tc_List_Olist(tc_prod(_1725763, _1725765)), tc_List_Olist(tc_prod(_1725763, _1725765))), _1725763), c_List_Olist_OCons(tc_prod(_1725763, _1725765))), hAPP(hAPP(c_COMBC(_1725763, _1725765, tc_prod(_1725763, _1725765)), c_Product__Type_OPair(_1725763, _1725765)), _1725769)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1725763), tc_List_Olist(_1725765), tc_List_Olist(tc_prod(_1725763, _1725765))), c_List_Ozip(_1725763, _1725765)), _1725771))), _1725767))], (28297 ^ _778908) ^ [_1281352, _1281354, _1281356, _1281358] : [class_Lattices_Osemilattice__sup(_1281352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281352), _1281354), _1281356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281352), _1281354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281352), _1281358), _1281356))))], (6472 ^ _778908) ^ [_883518, _883520, _883522, _883524, _883526] : [c_Com_Ocom_OLocal(_883518, _883520, _883522) = c_Com_Ocom_OAss(_883524, _883526)], (44687 ^ _778908) ^ [_1653116, _1653118, _1653120, _1653122, _1653124] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653116, tc_fun(_1653118, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1653116), _1653120), _1653122)), _1653124) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1653118, tc_HOL_Obool)), hAPP(_1653124, _1653120)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653116, tc_fun(_1653118, tc_HOL_Obool)), _1653122), _1653124)))], (27679 ^ _778908) ^ [_1269476, _1269478] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1269476), _1269478) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1269476, _1269478))], (43016 ^ _778908) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (696 ^ _778908) ^ [_789654, _789656, _789658, _789660] : [-(c_Relation_Oirrefl(_789658, _789654)), c_Relation_Oirrefl(_789660, _789656), _789660 = _789658, _789656 = _789654], (48257 ^ _778908) ^ [_1742112, _1742114, _1742116] : [_1742112 = _1742114, -(_1742112 = hAPP(hAPP(c_List_Oappend(_1742116), c_List_Olist_ONil(_1742116)), _1742114))], (31343 ^ _778908) ^ [_1344285, _1344287, _1344289] : [hAPP(hAPP(c_COMBC(_1344285, tc_fun(_1344285, tc_HOL_Obool), tc_HOL_Obool), c_member(_1344285)), _1344287) = hAPP(hAPP(c_COMBC(_1344285, tc_fun(_1344285, tc_HOL_Obool), tc_HOL_Obool), c_member(_1344285)), _1344289), -(_1344287 = _1344289)], (35732 ^ _778908) ^ [_1437924, _1437926, _1437928, _1437930, _1437932] : [hAPP(c_Set_Oimage(_1437924, _1437926, _1437928), c_Orderings_Otop__class_Otop(tc_fun(_1437924, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1437926, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1437926, _1437930, _1437932), c_Orderings_Otop__class_Otop(tc_fun(_1437926, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1437930, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1437924, _1437930, hAPP(c_Fun_Ocomp(_1437926, _1437930, _1437924, _1437932), _1437928)), c_Orderings_Otop__class_Otop(tc_fun(_1437924, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1437930, tc_HOL_Obool)))], (23517 ^ _778908) ^ [_1188516, _1188518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188518)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1188516, _1188518), c_Divides_OposDivAlg(_1188516, _1188518))))], (50883 ^ _778908) ^ [_1801547, _1801549] : [hBOOL(hAPP(c_List_Odistinct(_1801547), hAPP(c_List_Orev(_1801547), _1801549))), -(hBOOL(hAPP(c_List_Odistinct(_1801547), _1801549)))], (24475 ^ _778908) ^ [_1207052, _1207054, _1207056, _1207058] : [class_Orderings_Olinorder(_1207052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207052), _1207054), _1207056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207052), _1207054), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207052), _1207056), _1207058))))], (5937 ^ _778908) ^ [_873626] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _873626) = _873626)], (37508 ^ _778908) ^ [_1478812, _1478814, _1478816] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1478812), _1478814)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478812), _1478816)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478812, tc_HOL_Obool)), _1478814), _1478816) = c_Orderings_Obot__class_Obot(tc_fun(_1478812, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1478812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478812, tc_HOL_Obool)), _1478814), _1478816)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1478812), _1478814)), hAPP(c_Finite__Set_Ocard(_1478812), _1478816)))], (19431 ^ _778908) ^ [_1113536, _1113538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113536), _1113538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113536)), c_Int_OBit1(_1113538))))], (43520 ^ _778908) ^ [_1626204, _1626206, _1626208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1626206, _1626204)), _1626208)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1626204, _1626206)), hAPP(c_Relation_Oconverse(_1626206, _1626204), _1626208))))], (14047 ^ _778908) ^ [_1016695, _1016697, _1016699, _1016701] : [class_Divides_Osemiring__div(_1016695), -(c_Divides_Odiv__class_Omod(_1016695, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016695), _1016697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016695), _1016699), _1016701)), _1016699) = c_Divides_Odiv__class_Omod(_1016695, _1016697, _1016699))], (23899 ^ _778908) ^ [_1195552, _1195554, _1195556, _1195558] : [class_Orderings_Olinorder(_1195552), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195552), _1195554), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195552), _1195556), _1195558)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195552), _1195556), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195552), _1195554), _1195558)))], (34096 ^ _778908) ^ [_1401836, _1401838, _1401840] : [class_Orderings_Olinorder(_1401836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401836), _1401838)), -(_1401838 = c_Orderings_Obot__class_Obot(tc_fun(_1401836, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401836), _1401840)), -(_1401840 = c_Orderings_Obot__class_Obot(tc_fun(_1401836, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1401836, c_Orderings_Oord__class_Omin(_1401836), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401836, tc_HOL_Obool)), _1401838), _1401840)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1401836), c_Big__Operators_Olattice_OInf__fin(_1401836, c_Orderings_Oord__class_Omin(_1401836), _1401838)), c_Big__Operators_Olattice_OInf__fin(_1401836, c_Orderings_Oord__class_Omin(_1401836), _1401840)))], (41537 ^ _778908) ^ [_1573444, _1573446, _1573448] : [class_Groups_Olinordered__ab__semigroup__add(_1573444), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573444), _1573446)), -(_1573446 = c_Orderings_Obot__class_Obot(tc_fun(_1573444, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1573444), _1573448), c_Big__Operators_Olinorder__class_OMax(_1573444, _1573446)) = c_Big__Operators_Olinorder__class_OMax(_1573444, hAPP(c_Set_OCollect(_1573444), hAPP(hAPP(c_COMBB(tc_fun(_1573444, tc_HOL_Obool), tc_HOL_Obool, _1573444), c_HOL_OEx(_1573444)), hAPP(hAPP(c_COMBC(_1573444, tc_fun(_1573444, tc_HOL_Obool), tc_fun(_1573444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573444, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1573444, tc_HOL_Obool), tc_fun(_1573444, tc_HOL_Obool)), _1573444), c_COMBS(_1573444, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573444, tc_HOL_Obool), tc_fun(_1573444, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1573444), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573444), c_fconj)), hAPP(hAPP(c_COMBC(_1573444, tc_fun(_1573444, _1573444), tc_fun(_1573444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573444, tc_HOL_Obool), tc_fun(tc_fun(_1573444, _1573444), tc_fun(_1573444, tc_HOL_Obool)), _1573444), c_COMBB(_1573444, tc_HOL_Obool, _1573444)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1573444), _1573448))))), hAPP(hAPP(c_COMBC(_1573444, tc_fun(_1573444, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573444)), _1573446))))))], (22320 ^ _778908) ^ [_1165643, _1165645, _1165647] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1165643), _1165645))), -(c_Random_Ominus__shift(_1165647, _1165643, _1165645) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1165643), _1165645))], (23387 ^ _778908) ^ [_1186579, _1186581, _1186583, _1186585, _1186587] : [-(hAPP(c_Product__Type_Osnd(_1186579, _1186581), hAPP(c_Product__Type_Oapsnd(_1186583, _1186581, _1186579, _1186585), _1186587)) = hAPP(_1186585, hAPP(c_Product__Type_Osnd(_1186579, _1186583), _1186587)))], (47781 ^ _778908) ^ [_1730451, _1730453] : [-(hAPP(c_List_Oset(_1730451), _1730453) = hAPP(c_Set_OCollect(_1730451), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1730451), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1730451, 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)), _1730451), 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)), _1730451), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1730451, tc_fun(tc_Nat_Onat, _1730451), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1730451, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1730451), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1730451), c_COMBB(_1730451, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1730451), _1730453))))), 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(_1730451)), _1730453))))))], (43093 ^ _778908) ^ [_1615146, _1615148, _1615150, _1615152, _1615154] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615146, _1615146)), hAPP(hAPP(c_Product__Type_OPair(_1615146, _1615146), _1615148), _1615150)), _1615152)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615146, _1615146)), hAPP(hAPP(c_Product__Type_OPair(_1615146, _1615146), _1615150), _1615154)), _1615152)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615146, _1615146)), hAPP(hAPP(c_Product__Type_OPair(_1615146, _1615146), _1615148), _1615154)), c_Transitive__Closure_Otrancl(_1615146, _1615152))))], (29803 ^ _778908) ^ [_1312194, _1312196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1312194), _1312196))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1312194), _1312196)))], (7122 ^ _778908) ^ [_897995] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OGlb(_897995)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51319 ^ _778908) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (44048 ^ _778908) ^ [_1639973, _1639975, _1639977] : [class_Orderings_Olinorder(_1639973), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639973), _1639975)), -(hBOOL(hAPP(hAPP(c_member(_1639973), _1639977), _1639975))), -(c_Big__Operators_Olattice_OSup__fin(_1639973, c_Orderings_Oord__class_Omax(_1639973), hAPP(hAPP(c_Set_Oinsert(_1639973), _1639977), _1639975)) = hAPP(hAPP(c_Finite__Set_Ofold(_1639973, _1639973, c_Orderings_Oord__class_Omax(_1639973)), _1639977), _1639975))], (19661 ^ _778908) ^ [_1117580, _1117582] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1117580)), c_Int_OBit1(_1117582)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117580), c_Int_Osucc(_1117582))))], (31211 ^ _778908) ^ [_1341629, _1341631, _1341633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341629, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1341629, tc_fun(_1341629, tc_HOL_Obool), tc_HOL_Obool), c_member(_1341629)), _1341631)), hAPP(hAPP(c_COMBC(_1341629, tc_fun(_1341629, tc_HOL_Obool), tc_HOL_Obool), c_member(_1341629)), _1341633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341629, tc_HOL_Obool)), _1341631), _1341633)))], (29871 ^ _778908) ^ [_1313475, _1313477, _1313479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313475), _1313477)), -(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)), _1313475)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1313479), _1313477)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1313479), _1313475)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1313477), _1313475)))], (32128 ^ _778908) ^ [_1362223, _1362225, _1362227] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362223), _1362225)), hBOOL(hAPP(hAPP(c_member(_1362223), _1362227), _1362225)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1362223), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362223, tc_HOL_Obool)), _1362225), hAPP(hAPP(c_Set_Oinsert(_1362223), _1362227), c_Orderings_Obot__class_Obot(tc_fun(_1362223, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1362223), _1362225))], (18249 ^ _778908) ^ [_1094458] : [class_Int_Onumber__ring(_1094458), c_Int_Oiszero(_1094458, hAPP(c_Int_Onumber__class_Onumber__of(_1094458), c_Int_OMin))], (15096 ^ _778908) ^ [_1035056, _1035058, _1035060] : [class_Divides_Osemiring__div(_1035056), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035056), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1035056), _1035058), _1035060)), _1035060)), c_Divides_Odiv__class_Omod(_1035056, _1035058, _1035060)) = _1035058)], (48156 ^ _778908) ^ [_1739683, _1739685, _1739687, _1739689] : [-(hAPP(hAPP(c_List_Oappend(_1739683), hAPP(hAPP(c_List_Olist_OCons(_1739683), _1739685), _1739687)), _1739689) = hAPP(hAPP(c_List_Olist_OCons(_1739683), _1739685), hAPP(hAPP(c_List_Oappend(_1739683), _1739687), _1739689)))], (15964 ^ _778908) ^ [_1051503, _1051505, _1051507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051503), _1051505)), 15967 ^ _778908 : [(15974 ^ _778908) ^ [] : [_1051505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051507), _1051503), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051505), _1051503) = _1051507)], (15968 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051505), _1051503) = _1051507, -(_1051505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051507), _1051503))]]], (32379 ^ _778908) ^ [_1367677, _1367679, _1367681, _1367683] : [hBOOL(hAPP(hAPP(_1367681, _1367683), _1367679)), -(hBOOL(hAPP(hAPP(c_member(_1367677), _1367679), c_SetInterval_Oord_OgreaterThan(_1367677, _1367681, _1367683))))], (17139 ^ _778908) ^ [_1074495, _1074497, _1074499] : [class_Rings_Oordered__ring__abs(_1074495), -(hAPP(c_Groups_Oabs__class_Oabs(_1074495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074495), _1074497), _1074499)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074495), hAPP(c_Groups_Oabs__class_Oabs(_1074495), _1074497)), hAPP(c_Groups_Oabs__class_Oabs(_1074495), _1074499))), 17146 ^ _778908 : [(17149 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074495), _1074497), c_Groups_Ozero__class_Ozero(_1074495)))], (17147 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074495), c_Groups_Ozero__class_Ozero(_1074495)), _1074497))]], 17150 ^ _778908 : [(17153 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074495), _1074499), c_Groups_Ozero__class_Ozero(_1074495)))], (17151 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074495), c_Groups_Ozero__class_Ozero(_1074495)), _1074499))]]], (25705 ^ _778908) ^ [_1230382, _1230384, _1230386, _1230388] : [class_Rings_Ocomm__semiring__1(_1230382), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230382), _1230384), _1230386)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230382), hAPP(hAPP(c_Power_Opower__class_Opower(_1230382), _1230384), _1230388)), hAPP(hAPP(c_Power_Opower__class_Opower(_1230382), _1230386), _1230388))))], (43175 ^ _778908) ^ [_1617945, _1617947] : [-(hAPP(c_Relation_ORange(_1617945, _1617945), c_Transitive__Closure_Ortrancl(_1617945, _1617947)) = c_Orderings_Otop__class_Otop(tc_fun(_1617945, tc_HOL_Obool)))], (44643 ^ _778908) ^ [_1652233, _1652235, _1652237, _1652239, _1652241] : [-(_1652233 = c_Orderings_Obot__class_Obot(tc_fun(_1652235, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652237, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652235, tc_fun(_1652237, tc_HOL_Obool)), _1652233), _1652239)), _1652241) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652235, tc_fun(_1652237, tc_HOL_Obool)), _1652233), hAPP(hAPP(c_COMBC(_1652235, tc_fun(_1652237, tc_HOL_Obool), tc_fun(_1652237, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1652237, tc_HOL_Obool), tc_fun(tc_fun(_1652237, tc_HOL_Obool), tc_fun(_1652237, tc_HOL_Obool)), _1652235), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652237, tc_HOL_Obool))), _1652239)), _1652241)))], (3568 ^ _778908) ^ [_833762, _833764] : [_833764 = _833762, -(c_Nitpick_ORep__Frac(_833764) = c_Nitpick_ORep__Frac(_833762))], (47801 ^ _778908) ^ [_1730925, _1730927, _1730929] : [-(hAPP(c_List_Oset(_1730925), c_List_Osublist(_1730925, _1730927, _1730929)) = hAPP(c_Set_OCollect(_1730925), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1730925), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1730925, 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)), _1730925), 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)), _1730925), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1730925, tc_fun(tc_Nat_Onat, _1730925), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1730925, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1730925), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1730925), c_COMBB(_1730925, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1730925), _1730927))))), 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(_1730925)), _1730927)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1730929))))))], (43449 ^ _778908) ^ [_1624459, _1624461] : [-(c_Relation_Orefl__on(_1624459, c_Orderings_Otop__class_Otop(tc_fun(_1624459, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1624459, _1624459), tc_HOL_Obool)), _1624461), c_Relation_OId(_1624459))))], (48361 ^ _778908) ^ [_1743992, _1743994, _1743996] : [-(hBOOL(hAPP(c_List_Odistinct(_1743992), hAPP(hAPP(c_List_Oappend(_1743992), _1743994), _1743996)))), hBOOL(hAPP(c_List_Odistinct(_1743992), _1743994)), hBOOL(hAPP(c_List_Odistinct(_1743992), _1743996)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1743992, tc_HOL_Obool)), hAPP(c_List_Oset(_1743992), _1743994)), hAPP(c_List_Oset(_1743992), _1743996)) = c_Orderings_Obot__class_Obot(tc_fun(_1743992, tc_HOL_Obool))], (7572 ^ _778908) ^ [_905767, _905769, _905771, _905773, _905775] : [-(c_Sum__Type_Osum_Osum__size(_905767, _905769, _905771, _905773, hAPP(c_Sum__Type_OInr(_905769, _905767), _905775)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_905773, _905775)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49432 ^ _778908) ^ [_1770532, _1770534, _1770536, _1770538, _1770540] : [hBOOL(hAPP(hAPP(c_member(_1770532), _1770534), hAPP(c_List_Oset(_1770532), _1770536))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1770538), hAPP(_1770540, _1770534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1770538), c_List_Olist_Olist__size(_1770532, _1770540, _1770536))))], (18507 ^ _778908) ^ [_1098218] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1098218) = c_Int_OPls)], (41828 ^ _778908) ^ [_1584454, _1584456, _1584458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584454, _1584454), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584454, _1584454, _1584454), _1584456), _1584458)), _1584456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1584454, tc_HOL_Obool), tc_fun(_1584454, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1584454, tc_HOL_Obool), tc_fun(_1584454, tc_HOL_Obool), tc_fun(_1584454, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1584454, _1584456)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1584454, tc_HOL_Obool), tc_fun(_1584454, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1584454, _1584458)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1584454, tc_HOL_Obool), tc_fun(_1584454, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1584454, tc_HOL_Obool), tc_fun(_1584454, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1584454, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1584454, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1584454, tc_HOL_Obool), tc_fun(_1584454, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1584454, _1584456))))], (50431 ^ _778908) ^ [_1791889, _1791891] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1791889, _1791891))))], (26815 ^ _778908) ^ [_1251792, _1251794] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1251792), _1251794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1251794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1251792), _1251794)))], (49795 ^ _778908) ^ [_1778576, _1778578, _1778580] : [-(_1778576 = c_List_Olist_ONil(_1778578)), -(c_List_Obutlast(_1778578, hAPP(hAPP(c_List_Olist_OCons(_1778578), _1778580), _1778576)) = hAPP(hAPP(c_List_Olist_OCons(_1778578), _1778580), c_List_Obutlast(_1778578, _1778576)))], (35164 ^ _778908) ^ [_1425255, _1425257, _1425259, _1425261, _1425263, _1425265] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1425261, _1425261)), hAPP(hAPP(c_Product__Type_OPair(_1425261, _1425261), hAPP(_1425265, _1425257)), hAPP(_1425265, _1425259))), _1425263)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1425255, _1425255)), hAPP(hAPP(c_Product__Type_OPair(_1425255, _1425255), _1425257), _1425259)), hAPP(hAPP(c_Relation_Oinv__image(_1425261, _1425255), _1425263), _1425265))))], (36982 ^ _778908) ^ [_1466546, _1466548, _1466550, _1466552] : [hBOOL(hAPP(hAPP(c_member(_1466546), _1466548), _1466550)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466546, tc_HOL_Obool)), _1466550), hAPP(hAPP(c_Set_Oinsert(_1466546), _1466548), _1466552)) = hAPP(hAPP(c_Set_Oinsert(_1466546), _1466548), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466546, tc_HOL_Obool)), _1466550), _1466552)))], (41718 ^ _778908) ^ [_1580819, _1580821, _1580823, _1580825] : [-(c_Product__Type_Oapsnd(_1580819, _1580821, _1580823, _1580825) = c_Product__Type_Omap__pair(_1580823, _1580823, _1580819, _1580821, c_Fun_Oid(_1580823), _1580825))], (6198 ^ _778908) ^ [_878531, _878533, _878535, _878537, _878539] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_878531, _878533, _878535)), _878537), _878539)), 6203 ^ _778908 : [(6206 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878533), _878537), _878539)))], (6204 ^ _778908) ^ [] : [-(hBOOL(hAPP(_878531, _878537)))]], 6207 ^ _778908 : [(6210 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878535), _878537), _878539)))], (6208 ^ _778908) ^ [] : [hBOOL(hAPP(_878531, _878537))]]], (40302 ^ _778908) ^ [_1542636, _1542638, _1542640, _1542642, _1542644, _1542646] : [-(hAPP(c_Set_Ovimage(_1542636, tc_prod(_1542638, _1542640), _1542642), hAPP(hAPP(c_Product__Type_OSigma(_1542638, _1542640), _1542644), hAPP(c_COMBK(tc_fun(_1542640, tc_HOL_Obool), _1542638), _1542646))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1542636, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1542636, _1542638, hAPP(c_Fun_Ocomp(tc_prod(_1542638, _1542640), _1542638, _1542636, c_Product__Type_Ofst(_1542638, _1542640)), _1542642)), _1542644)), hAPP(c_Set_Ovimage(_1542636, _1542640, hAPP(c_Fun_Ocomp(tc_prod(_1542638, _1542640), _1542640, _1542636, c_Product__Type_Osnd(_1542638, _1542640)), _1542642)), _1542646)))], (10515 ^ _778908) ^ [_955564, _955566, _955568, _955570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955564), _955566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955568), _955570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955564), _955568)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955566), _955570))))], (20049 ^ _778908) ^ [_1124574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1124574)), -(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), _1124574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (30722 ^ _778908) ^ [_1329726, _1329728, _1329730] : [class_Orderings_Olinorder(_1329726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329726), _1329728), _1329730)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329726, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1329726, _1329728), _1329730)), hAPP(hAPP(c_Set_Oinsert(_1329726), _1329730), c_Orderings_Obot__class_Obot(tc_fun(_1329726, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1329726, _1329728, _1329730))], (45328 ^ _778908) ^ [_1670305, _1670307, _1670309, _1670311] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670305, tc_HOL_Obool), hAPP(c_Set_Oimage(_1670307, tc_fun(_1670305, tc_HOL_Obool), _1670309), _1670311)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670307, tc_fun(_1670305, tc_HOL_Obool)), _1670311), _1670309))], (44733 ^ _778908) ^ [_1654316, _1654318, _1654320, _1654322, _1654324] : [-(hAPP(hAPP(c_Set_Oinsert(_1654316), _1654318), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654320, tc_fun(_1654316, tc_HOL_Obool)), _1654322), _1654324)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654320, tc_fun(_1654316, tc_HOL_Obool)), _1654322), hAPP(hAPP(c_COMBB(tc_fun(_1654316, tc_HOL_Obool), tc_fun(_1654316, tc_HOL_Obool), _1654320), hAPP(c_Set_Oinsert(_1654316), _1654318)), _1654324)))], (44486 ^ _778908) ^ [_1648534, _1648536, _1648538, _1648540, _1648542] : [c_Finite__Set_Ofun__left__comm(_1648534, _1648536, _1648538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648534), _1648540)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1648534, _1648536, _1648538, _1648542, _1648540), hAPP(hAPP(c_Finite__Set_Ofold(_1648534, _1648536, _1648538), _1648542), _1648540))))], (51369 ^ _778908) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (24733 ^ _778908) ^ [_1211831, _1211833, _1211835, _1211837, _1211839, _1211841] : [-(hAPP(c_Product__Type_Oapfst(_1211831, _1211833, _1211835, _1211837), hAPP(hAPP(c_Product__Type_OPair(_1211831, _1211835), _1211839), _1211841)) = hAPP(hAPP(c_Product__Type_OPair(_1211833, _1211835), hAPP(_1211837, _1211839)), _1211841))], (13150 ^ _778908) ^ [_1000643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1000643), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1000643) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1732 ^ _778908) ^ [_803432, _803434] : [-(class_Rings_Omult__zero(_803432)), _803434 = _803432, class_Rings_Omult__zero(_803434)], (41513 ^ _778908) ^ [_1572223, _1572225, _1572227, _1572229] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1572223), hAPP(c_Set_OCollect(_1572223), _1572225))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1572227), hAPP(c_Set_OCollect(_1572227), hAPP(hAPP(c_COMBB(tc_fun(_1572223, tc_HOL_Obool), tc_HOL_Obool, _1572227), c_HOL_OEx(_1572223)), hAPP(hAPP(c_COMBC(_1572227, tc_fun(_1572223, tc_HOL_Obool), tc_fun(_1572223, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572223, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1572223, tc_HOL_Obool), tc_fun(_1572223, tc_HOL_Obool)), _1572227), c_COMBS(_1572223, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572223, tc_HOL_Obool), tc_fun(_1572223, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1572227), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572223), c_fconj)), hAPP(hAPP(c_COMBC(_1572227, tc_fun(_1572223, _1572227), tc_fun(_1572223, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572227, tc_HOL_Obool), tc_fun(tc_fun(_1572223, _1572227), tc_fun(_1572223, tc_HOL_Obool)), _1572227), c_COMBB(_1572227, tc_HOL_Obool, _1572223)), c_fequal)), _1572229)))), _1572225))))))], (42443 ^ _778908) ^ [_1600073, _1600075, _1600077, _1600079] : [-(c_New__Random__Sequence_Opos__map(_1600073, _1600075, _1600077, _1600079) = c_New__Random__Sequence_Opos__bind(_1600073, _1600075, _1600079, hAPP(c_Fun_Ocomp(_1600075, 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(_1600075))))), _1600073, c_New__Random__Sequence_Opos__single(_1600075)), _1600077)))], (3138 ^ _778908) ^ [_826969, _826971] : [_826971 = _826969, -(c_DSequence_Osingle(_826971) = c_DSequence_Osingle(_826969))], (50935 ^ _778908) ^ [_1802532, _1802534, _1802536, _1802538, _1802540] : [-(c_List_Ofoldr(_1802532, _1802534, _1802536, _1802538, _1802540) = hAPP(c_List_Ofoldl(_1802534, _1802532, hAPP(c_COMBC(_1802532, _1802534, _1802534), _1802536), _1802540), hAPP(c_List_Orev(_1802532), _1802538)))], (17797 ^ _778908) ^ [_1086601, _1086603, _1086605] : [class_Rings_Olinordered__semidom(_1086601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086601), c_Groups_Oone__class_Oone(_1086601)), _1086603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086601), c_Groups_Oone__class_Oone(_1086601)), hAPP(hAPP(c_Power_Opower__class_Opower(_1086601), _1086603), hAPP(c_Nat_OSuc, _1086605)))))], (46465 ^ _778908) ^ [_1696513, _1696515] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1696513, _1696515))))], (1772 ^ _778908) ^ [_803932, _803934] : [-(class_Groups_Ominus(_803932)), _803934 = _803932, class_Groups_Ominus(_803934)], (31331 ^ _778908) ^ [_1344071, _1344073, _1344075] : [hBOOL(hAPP(hAPP(c_member(_1344071), _1344073), hAPP(c_fequal, _1344075))), -(_1344073 = _1344075)], (6673 ^ _778908) ^ [_888344, _888346, _888348, _888350] : [-(hBOOL(hAPP(_888344, _888346))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_888344, _888348), _888346, _888350, _888346))], (24267 ^ _778908) ^ [_1202984, _1202986, _1202988, _1202990, _1202992, _1202994] : [hBOOL(hAPP(_1202984, _1202986)), hBOOL(hAPP(_1202988, _1202990)), 24274 ^ _778908 : [(24277 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1202988, hAPP(c_Product__Type_Osnd(_1202992, _1202994), hAPP(hAPP(c_Product__Type_OPair(_1202992, _1202994), _1202986), _1202990)))))], (24275 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1202984, hAPP(c_Product__Type_Ofst(_1202992, _1202994), hAPP(hAPP(c_Product__Type_OPair(_1202992, _1202994), _1202986), _1202990)))))]]], (46096 ^ _778908) ^ [_1687712, _1687714] : [-(hAPP(hAPP(c_List_Omap(_1687712, _1687712), c_COMBI(_1687712)), _1687714) = _1687714)], (41277 ^ _778908) ^ [_1563560, _1563562, _1563564] : [-(hAPP(hAPP(c_Set_Oinsert(_1563560), _1563562), _1563564) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1563560, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1563560), hAPP(hAPP(c_COMBC(_1563560, _1563560, tc_HOL_Obool), c_fequal), _1563562))), _1563564))], (48219 ^ _778908) ^ [_1741192, _1741194, _1741196, _1741198] : [_1741196 = _1741198, -(hAPP(hAPP(c_List_Oappend(_1741192), _1741194), _1741196) = hAPP(hAPP(c_List_Oappend(_1741192), _1741194), _1741198))], (3720 ^ _778908) ^ [_836214, _836216] : [_836216 = _836214, -(c_Int_Oring__1__class_Oof__int(_836216) = c_Int_Oring__1__class_Oof__int(_836214))], (28367 ^ _778908) ^ [_1282814, _1282816, _1282818, _1282820, _1282822] : [class_Lattices_Osemilattice__sup(_1282814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282814), _1282816), _1282818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282814), _1282820), _1282822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282814), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282814), _1282816), _1282820)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282814), _1282818), _1282822))))], (46962 ^ _778908) ^ [_1710324, _1710326, _1710328, _1710330] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710324), tc_List_Olist(_1710324))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710324), tc_List_Olist(_1710324)), _1710328), _1710330)), c_List_Olistrel(_1710324, _1710326))), -(c_List_Olistrelp(_1710324, hAPP(hAPP(c_COMBC(_1710324, tc_fun(tc_prod(_1710324, _1710324), tc_HOL_Obool), tc_fun(_1710324, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1710324, tc_fun(tc_fun(tc_prod(_1710324, _1710324), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1710324, _1710324), tc_HOL_Obool), tc_fun(_1710324, tc_HOL_Obool)), _1710324), c_COMBC(_1710324, tc_fun(tc_prod(_1710324, _1710324), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1710324, tc_prod(_1710324, _1710324)), tc_fun(_1710324, tc_fun(tc_fun(tc_prod(_1710324, _1710324), tc_HOL_Obool), tc_HOL_Obool)), _1710324), hAPP(c_COMBB(tc_prod(_1710324, _1710324), tc_fun(tc_fun(tc_prod(_1710324, _1710324), tc_HOL_Obool), tc_HOL_Obool), _1710324), c_member(tc_prod(_1710324, _1710324)))), c_Product__Type_OPair(_1710324, _1710324)))), _1710326), _1710328, _1710330))], (29112 ^ _778908) ^ [_1298522, _1298524] : [class_Lattices_Obounded__lattice__top(_1298522), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1298522), c_Orderings_Otop__class_Otop(_1298522)), _1298524) = c_Orderings_Otop__class_Otop(_1298522))], (24495 ^ _778908) ^ [_1207410, _1207412, _1207414, _1207416] : [class_Groups_Oordered__ab__group__add(_1207410), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207410), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207410), _1207412), _1207414)), _1207416) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207410), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207410), _1207412), _1207416)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207410), _1207414), _1207416)))], (19631 ^ _778908) ^ [_1117089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1117089)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1117089), c_Int_OMin)))], (40493 ^ _778908) ^ [_1548216, _1548218, _1548220, _1548222, _1548224] : [c_Relation_Orefl__on(_1548216, _1548218, _1548220), c_Relation_Orefl__on(_1548216, _1548222, _1548224), -(c_Relation_Orefl__on(_1548216, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1548216, tc_HOL_Obool)), _1548218), _1548222), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1548216, _1548216), tc_HOL_Obool)), _1548220), _1548224)))], (3436 ^ _778908) ^ [_831694, _831696] : [_831696 = _831694, -(c_Natural_Oevalc(_831696) = c_Natural_Oevalc(_831694))], (7797 ^ _778908) ^ [_909370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909370), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35233 ^ _778908) ^ [_1426841] : [-(hAPP(c_Relation_OField(_1426841), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1426841, _1426841), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1426841, tc_HOL_Obool)))], (43121 ^ _778908) ^ [_1615886, _1615888, _1615890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615886, _1615886), tc_HOL_Obool)), _1615888), _1615890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615886, _1615886), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1615886, _1615886, _1615886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1615886, _1615886), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1615886, _1615888)), _1615890)), _1615888)), _1615890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615886, _1615886), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1615886, _1615888)), _1615890)))], (48721 ^ _778908) ^ [_1753578, _1753580, _1753582] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753578), tc_List_Olist(_1753578))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753578), tc_List_Olist(_1753578)), c_List_Olist_ONil(_1753578)), _1753580)), c_List_Olistrel1(_1753578, _1753582)))], (47316 ^ _778908) ^ [_1720129, _1720131, _1720133] : [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, _1720129), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1720129)), _1720131)))), -(hBOOL(hAPP(hAPP(c_member(_1720129), hAPP(c_Product__Type_Ofst(_1720129, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1720129, _1720131), _1720133))), hAPP(c_List_Oset(_1720129), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1720129), _1720129), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1720129)), _1720131)))))], (30768 ^ _778908) ^ [_1330747, _1330749] : [-(c_Set_Othe__elem(_1330747, _1330749) = c_HOL_OThe(_1330747, hAPP(hAPP(c_COMBB(tc_fun(_1330747, tc_HOL_Obool), tc_HOL_Obool, _1330747), hAPP(c_fequal, _1330749)), hAPP(hAPP(c_COMBC(_1330747, tc_fun(_1330747, tc_HOL_Obool), tc_fun(_1330747, tc_HOL_Obool)), c_Set_Oinsert(_1330747)), c_Orderings_Obot__class_Obot(tc_fun(_1330747, tc_HOL_Obool))))))], (41758 ^ _778908) ^ [_1582021, _1582023, _1582025, _1582027, _1582029, _1582031, _1582033, _1582035] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582021, _1582023)), hAPP(hAPP(c_Product__Type_OPair(_1582021, _1582023), _1582025), _1582027)), _1582029)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582023, _1582031)), hAPP(hAPP(c_Product__Type_OPair(_1582023, _1582031), _1582027), _1582033)), _1582035)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582021, _1582031)), hAPP(hAPP(c_Product__Type_OPair(_1582021, _1582031), _1582025), _1582033)), hAPP(hAPP(c_Relation_Orel__comp(_1582021, _1582023, _1582031), _1582029), _1582035))))], (25147 ^ _778908) ^ [_1221012, _1221014, _1221016, _1221018] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1221012), _1221014), _1221016), _1221018) = 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(_1221012)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1221012), _1221014)))], (44571 ^ _778908) ^ [_1650222, _1650224, _1650226, _1650228, _1650230, _1650232] : [hBOOL(hAPP(hAPP(c_member(_1650222), _1650224), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650226, tc_fun(_1650222, tc_HOL_Obool)), _1650228), _1650230))), -(hBOOL(hAPP(hAPP(c_member(_1650222), _1650224), hAPP(_1650230, _1650232)))), hBOOL(hAPP(hAPP(c_member(_1650226), _1650232), _1650228))], (50565 ^ _778908) ^ [_1794280, _1794282, _1794284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794280), _1794282)), _1794284)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1794280, _1794284)), _1794282) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794280), _1794282))], (20293 ^ _778908) ^ [_1129306, _1129308] : [c_Nat__Transfer_Ois__nat(_1129306), c_Nat__Transfer_Ois__nat(_1129308), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1129306, _1129308)))], (13841 ^ _778908) ^ [_1012564, _1012566, _1012568, _1012570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012566), _1012568)), -(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), _1012568), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012570, _1012564))), _1012566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012568), _1012564))))], (24907 ^ _778908) ^ [_1215283, _1215285] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1215283), _1215285) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1215283)), hAPP(c_Code__Numeral_Onat__of, _1215285))))], (22468 ^ _778908) ^ [_1168112, _1168114, _1168116] : [class_Int_Onumber__ring(_1168112), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1168112), hAPP(c_Int_Onumber__class_Onumber__of(_1168112), _1168114)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1168116))) = hAPP(hAPP(c_HOL_OLet(_1168112, _1168112), hAPP(hAPP(c_Power_Opower__class_Opower(_1168112), hAPP(c_Int_Onumber__class_Onumber__of(_1168112), _1168114)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168116))), hAPP(hAPP(c_COMBS(_1168112, _1168112, _1168112), c_Groups_Otimes__class_Otimes(_1168112)), c_COMBI(_1168112))))], (5164 ^ _778908) ^ [_858808, _858810, _858812, _858814, _858816, _858818] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_858818, _858814, _858810) = c_SetInterval_Oord__class_OatLeastAtMost(_858816, _858812, _858808)), _858818 = _858816, _858814 = _858812, _858810 = _858808], (12229 ^ _778908) ^ [_984286, _984288, _984290, _984292, _984294] : [class_Groups_Oordered__cancel__ab__semigroup__add(_984286), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984286), _984288), _984290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984286), _984292), _984294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984286), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984286), _984288), _984292)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984286), _984290), _984294))))], (23086 ^ _778908) ^ [_1180579, _1180581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180579)), 23089 ^ _778908 : [(23096 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180581))), 23099 ^ _778908 : [(23106 ^ _778908) ^ [] : [-(_1180579 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1180579, _1180581) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180579), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180581))))], (23100 ^ _778908) ^ [] : [_1180579 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1180579, _1180581) = 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)))]]], (23090 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180581)), -(c_Divides_Odivmod__int(_1180579, _1180581) = c_Divides_OposDivAlg(_1180579, _1180581))]]], (8348 ^ _778908) ^ [_918753, _918755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918753)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918753), _918755)))], (39297 ^ _778908) ^ [_1517636, _1517638] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517636), _1517638)), -(hAPP(c_Finite__Set_Ocard(_1517636), _1517638) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1517636, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1517636), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1517638))], (16338 ^ _778908) ^ [_1059536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059536)), -(_1059536 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059536), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (12878 ^ _778908) ^ [_995706, _995708, _995710, _995712, _995714] : [class_Rings_Olinordered__semiring__strict(_995706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995706), _995708), _995710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995706), _995712), _995714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995706), c_Groups_Ozero__class_Ozero(_995706)), _995708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995706), c_Groups_Ozero__class_Ozero(_995706)), _995712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995706), _995708), _995712)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995706), _995710), _995714))))], (23863 ^ _778908) ^ [_1194850, _1194852] : [class_Orderings_Olinorder(_1194850), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194850), _1194852), _1194852) = _1194852)], (23238 ^ _778908) ^ [_1183364, _1183366, _1183368, _1183370, _1183372, _1183374] : [hAPP(hAPP(c_Product__Type_OPair(_1183364, _1183366), _1183368), _1183370) = hAPP(hAPP(c_Product__Type_OPair(_1183364, _1183366), _1183372), _1183374), 23241 ^ _778908 : [(23244 ^ _778908) ^ [] : [-(_1183370 = _1183374)], (23242 ^ _778908) ^ [] : [-(_1183368 = _1183372)]]], (4648 ^ _778908) ^ [_850878, _850880, _850882, _850884] : [-(c_Transitive__Closure_Ortrancl(_850884, _850880) = c_Transitive__Closure_Ortrancl(_850882, _850878)), _850884 = _850882, _850880 = _850878], (51413 ^ _778908) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (18575 ^ _778908) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (2816 ^ _778908) ^ [_821622, _821624, _821626, _821628] : [-(c_Nitpick_Oinverse__frac(_821628, _821624) = c_Nitpick_Oinverse__frac(_821626, _821622)), _821628 = _821626, _821624 = _821622], (7258 ^ _778908) ^ [_900332, _900334] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900332), _900334) = _900332, -(_900334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29138 ^ _778908) ^ [_1299018, _1299020] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299018, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1299018, tc_HOL_Obool)), _1299020)), _1299020) = c_Orderings_Otop__class_Otop(tc_fun(_1299018, tc_HOL_Obool)))], (36590 ^ _778908) ^ [_1457502, _1457504, _1457506, _1457508] : [hBOOL(hAPP(hAPP(c_member(_1457502), _1457508), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457502, tc_HOL_Obool)), _1457504), _1457506))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457502, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1457502, tc_fun(_1457502, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457502)), _1457504)), hAPP(hAPP(c_COMBC(_1457502, tc_fun(_1457502, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457502)), _1457506)), _1457508)))], (51407 ^ _778908) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (50041 ^ _778908) ^ [_1784421, _1784423, _1784425, _1784427, _1784429] : [-(c_List_Omap__filter(_1784421, _1784423, _1784425, hAPP(hAPP(c_List_Olist_OCons(_1784421), _1784427), _1784429)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1784423), _1784423, c_List_Omap__filter(_1784421, _1784423, _1784425, _1784429), hAPP(hAPP(c_COMBC(_1784423, tc_List_Olist(_1784423), tc_List_Olist(_1784423)), c_List_Olist_OCons(_1784423)), c_List_Omap__filter(_1784421, _1784423, _1784425, _1784429))), hAPP(_1784425, _1784427)))], (9288 ^ _778908) ^ [_934307] : [class_Groups_Ogroup__add(_934307), -(hAPP(c_Groups_Ouminus__class_Ouminus(_934307), c_Groups_Ozero__class_Ozero(_934307)) = c_Groups_Ozero__class_Ozero(_934307))], (35730 ^ _778908) ^ [_1437846, _1437848, _1437850, _1437852, _1437854, _1437856, _1437858] : [-(hAPP(c_Fun_Ocomp(_1437846, _1437848, _1437850, _1437852), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1437850, _1437846), _1437854), _1437856), _1437858)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1437850, _1437848), hAPP(c_Fun_Ocomp(_1437846, _1437848, _1437850, _1437852), _1437854)), _1437856), hAPP(_1437852, _1437858)))], (25991 ^ _778908) ^ [_1235463, _1235465, _1235467, _1235469] : [class_Rings_Osemiring__1(_1235463), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1235463), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235465, tc_Nat_Onat), _1235467), _1235469)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1235465, _1235463), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1235463, _1235465), c_Nat_Osemiring__1__class_Oof__nat(_1235463)), _1235467)), _1235469))], (51121 ^ _778908) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (45394 ^ _778908) ^ [_1671604] : [class_Complete__Lattice_Ocomplete__lattice(_1671604), -(c_Complete__Lattice_OInf__class_OInf(_1671604, c_Orderings_Otop__class_Otop(tc_fun(_1671604, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1671604))], (45362 ^ _778908) ^ [_1670954, _1670956] : [class_Complete__Lattice_Ocomplete__lattice(_1670954), -(c_Complete__Lattice_OSup__class_OSup(_1670954, hAPP(hAPP(c_Set_Oinsert(_1670954), _1670956), c_Orderings_Obot__class_Obot(tc_fun(_1670954, tc_HOL_Obool)))) = _1670956)], (1462 ^ _778908) ^ [_800057, _800059] : [-(class_Rings_Olinordered__semiring__strict(_800057)), _800059 = _800057, class_Rings_Olinordered__semiring__strict(_800059)], (51687 ^ _778908) ^ [_1813973, _1813975] : [hBOOL(_1813973), -(hBOOL(hAPP(hAPP(c_fdisj, _1813973), _1813975)))], (25785 ^ _778908) ^ [_1231819, _1231821] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231819)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231821))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231819), _1231821)))], (40622 ^ _778908) ^ [_1550729, _1550731] : [class_Orderings_Olinorder(_1550729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550729), _1550731)), -(c_Big__Operators_Olinorder__class_OMin(_1550729, _1550731) = hAPP(c_Finite__Set_Ofold1(_1550729, c_Orderings_Oord__class_Omin(_1550729)), _1550731))], (43980 ^ _778908) ^ [_1637820, _1637822, _1637824, _1637826, _1637828] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637820, _1637820)), hAPP(hAPP(c_Product__Type_OPair(_1637820, _1637820), _1637822), _1637824)), c_Transitive__Closure_Ortrancl(_1637820, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1637820, _1637820), tc_HOL_Obool)), _1637826), _1637828)))), 43986 ^ _778908 : [(43992 ^ _778908) ^ [] : [43985 ^ [_1637820, _1637822, _1637824, _1637826, _1637828] = 43988 ^ [_1637820, _1637822, _1637824, _1637826, _1637828]], (43990 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637820, _1637820)), hAPP(hAPP(c_Product__Type_OPair(_1637820, _1637820), 43985 ^ [_1637820, _1637822, _1637824, _1637826, _1637828]), 43988 ^ [_1637820, _1637822, _1637824, _1637826, _1637828])), _1637828)))], (43987 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637820, _1637820)), hAPP(hAPP(c_Product__Type_OPair(_1637820, _1637820), _1637822), 43985 ^ [_1637820, _1637822, _1637824, _1637826, _1637828])), c_Transitive__Closure_Ortrancl(_1637820, _1637826))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637820, _1637820)), hAPP(hAPP(c_Product__Type_OPair(_1637820, _1637820), _1637822), _1637824)), c_Transitive__Closure_Ortrancl(_1637820, _1637826))))], (34433 ^ _778908) ^ [_1408932, _1408934, _1408936, _1408938, _1408940, _1408942] : [_1408932 = _1408934, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408936, _1408938), _1408940), _1408934), _1408942), _1408932) = _1408942)], (30058 ^ _778908) ^ [_1317203, _1317205, _1317207, _1317209] : [_1317209 = c_Orderings_Obot__class_Obot(tc_fun(_1317203, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1317203, _1317205, _1317207), _1317209) = c_Orderings_Obot__class_Obot(tc_fun(_1317205, tc_HOL_Obool)))], (24057 ^ _778908) ^ [_1198666, _1198668] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1198666, _1198668) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1198666, _1198668)))], (20899 ^ _778908) ^ [_1139471, _1139473, _1139475, _1139477, _1139479] : [class_Fields_Olinordered__field(_1139471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139471), c_Groups_Ozero__class_Ozero(_1139471)), _1139473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139471), _1139473), _1139475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139471), c_Groups_Ozero__class_Ozero(_1139471)), _1139477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139471), _1139477), _1139479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139471), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139471), _1139473), _1139479)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139471), _1139475), _1139477))))], (43774 ^ _778908) ^ [_1632757, _1632759, _1632761] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632757, _1632757)), _1632759), c_Transitive__Closure_Otrancl(_1632757, _1632761)))), 43775 ^ _778908 : [(43776 ^ _778908) ^ [_1632836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632836)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1632757, _1632757)), _1632759), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1632757, _1632757), tc_HOL_Obool), _1632836), _1632761)))]]], (17513 ^ _778908) ^ [_1081388, _1081390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1081388)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1081388)), _1081390) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1081388), _1081390)))], (34216 ^ _778908) ^ [_1404044, _1404046] : [class_Orderings_Olinorder(_1404044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404044), _1404046)), -(_1404046 = c_Orderings_Obot__class_Obot(tc_fun(_1404044, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1404044), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1404044), 34229 ^ [_1404044, _1404046]), 34230 ^ [_1404044, _1404046])), hAPP(hAPP(c_Set_Oinsert(_1404044), 34229 ^ [_1404044, _1404046]), hAPP(hAPP(c_Set_Oinsert(_1404044), 34230 ^ [_1404044, _1404046]), c_Orderings_Obot__class_Obot(tc_fun(_1404044, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1404044), c_Big__Operators_Olattice_OSup__fin(_1404044, c_Orderings_Oord__class_Omax(_1404044), _1404046)), _1404046)))], (49157 ^ _778908) ^ [_1764797, _1764799] : [-(_1764797 = c_List_Olist_ONil(_1764799)), -(hAPP(c_List_Orotate1(_1764799), _1764797) = hAPP(hAPP(c_List_Oappend(_1764799), hAPP(c_List_Otl(_1764799), _1764797)), hAPP(hAPP(c_List_Olist_OCons(_1764799), hAPP(c_List_Ohd(_1764799), _1764797)), c_List_Olist_ONil(_1764799))))], (20429 ^ _778908) ^ [_1131644, _1131646, _1131648, _1131650] : [class_Fields_Olinordered__field(_1131644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131644), _1131646), _1131648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131644), c_Groups_Ozero__class_Ozero(_1131644)), _1131650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131644), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131644), _1131646), _1131650)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131644), _1131648), _1131650))))], (19617 ^ _778908) ^ [_1116822, _1116824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116822)), c_Int_OBit1(_1116824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116822), _1116824)))], (19333 ^ _778908) ^ [_1111917, _1111919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1111917)), c_Int_OBit0(_1111919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111917), _1111919)))], (4552 ^ _778908) ^ [_849366, _849368] : [_849368 = _849366, -(c_Random_Orange(_849368) = c_Random_Orange(_849366))], (15102 ^ _778908) ^ [_1035189, _1035191, _1035193, _1035195] : [class_Divides_Osemiring__div(_1035189), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035189), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035189), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035189), _1035191), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1035189), _1035193), _1035191))), c_Divides_Odiv__class_Omod(_1035189, _1035193, _1035191))), _1035195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035189), _1035193), _1035195))], (32032 ^ _778908) ^ [_1359942, _1359944, _1359946, _1359948] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359942, tc_HOL_Obool)), _1359944), hAPP(hAPP(c_Set_Oinsert(_1359942), _1359946), _1359948)))), 32035 ^ _778908 : [(32038 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359942, tc_HOL_Obool)), _1359944), _1359948))], (32036 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359942), _1359946), _1359948)))]], 32039 ^ _778908 : [(32042 ^ _778908) ^ [] : [32043 ^ _778908 : [(32046 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1359942, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359942, tc_HOL_Obool)), _1359944), hAPP(hAPP(c_Set_Oinsert(_1359942), _1359946), c_Orderings_Obot__class_Obot(tc_fun(_1359942, tc_HOL_Obool))))), _1359948))], (32044 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359942), _1359946), _1359944)))]], 32047 ^ _778908 : [(32050 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1359942, tc_HOL_Obool)), _1359944), _1359948))], (32048 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1359942), _1359946), _1359944))]]], (32040 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1359942), _1359946), _1359948))]]], (35827 ^ _778908) ^ [_1440491] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1440491) = 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, _1440491)), 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))))))))], (50759 ^ _778908) ^ [_1798781, _1798783] : [-(c_Fun_Oinj__on(tc_List_Olist(_1798781), tc_List_Olist(_1798781), c_List_Orev(_1798781), _1798783))], (15108 ^ _778908) ^ [_1035356, _1035358, _1035360, _1035362] : [class_Divides_Osemiring__div(_1035356), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035356), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1035356), _1035358), _1035360)), _1035360)), c_Divides_Odiv__class_Omod(_1035356, _1035358, _1035360))), _1035362) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035356), _1035358), _1035362))], (47679 ^ _778908) ^ [_1728217, _1728219, _1728221, _1728223] : [hBOOL(hAPP(c_List_Odistinct(_1728217), _1728219)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728221), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728217)), _1728219))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728223), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728217)), _1728219))), 47690 ^ _778908 : [(47697 ^ _778908) ^ [] : [_1728221 = _1728223, -(hAPP(hAPP(c_List_Onth(_1728217), _1728219), _1728221) = hAPP(hAPP(c_List_Onth(_1728217), _1728219), _1728223))], (47691 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Onth(_1728217), _1728219), _1728221) = hAPP(hAPP(c_List_Onth(_1728217), _1728219), _1728223), -(_1728221 = _1728223)]]], (16002 ^ _778908) ^ [_1052162, _1052164, _1052166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052162), _1052164)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052164), _1052162)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052166), _1052164)), _1052162))], (5424 ^ _778908) ^ [_862732, _862734, _862736, _862738] : [-(c_List_Ozip(_862738, _862734) = c_List_Ozip(_862736, _862732)), _862738 = _862736, _862734 = _862732], (34638 ^ _778908) ^ [_1412659, _1412661, _1412663, _1412665, _1412667] : [class_Groups_Ocomm__monoid__mult(_1412659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412661), _1412663)), 34645 ^ _778908 : [(34652 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412661), _1412665), _1412663))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1412661, _1412659), hAPP(hAPP(c_COMBC(_1412661, _1412659, _1412659), hAPP(hAPP(c_COMBS(_1412661, _1412659, tc_fun(_1412659, _1412659)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1412659, tc_fun(_1412659, _1412659)), _1412661), c_If(_1412659)), hAPP(c_fequal, _1412665))), _1412667)), c_Groups_Oone__class_Oone(_1412659))), _1412663) = c_Groups_Oone__class_Oone(_1412659))], (34646 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1412661), _1412665), _1412663)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1412661, _1412659), hAPP(hAPP(c_COMBC(_1412661, _1412659, _1412659), hAPP(hAPP(c_COMBS(_1412661, _1412659, tc_fun(_1412659, _1412659)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1412659, tc_fun(_1412659, _1412659)), _1412661), c_If(_1412659)), hAPP(c_fequal, _1412665))), _1412667)), c_Groups_Oone__class_Oone(_1412659))), _1412663) = hAPP(_1412667, _1412665))]]], (14567 ^ _778908) ^ [_1026211, _1026213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026211)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1026211), _1026213)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1026211)), hAPP(c_Int_Onat, _1026213)))], (39777 ^ _778908) ^ [_1528516, _1528518, _1528520, _1528522, _1528524] : [hAPP(_1528516, _1528518) = c_Option_Ooption_ONone(_1528520), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1528522, tc_HOL_Obool)), c_Map_Odom(_1528522, _1528520, _1528516)), hAPP(hAPP(c_Set_Oinsert(_1528522), _1528518), _1528524)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1528522, tc_HOL_Obool)), c_Map_Odom(_1528522, _1528520, _1528516)), _1528524))], (30410 ^ _778908) ^ [_1323615, _1323617, _1323619] : [class_Orderings_Oorder(_1323615), 30413 ^ _778908 : [(30420 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323615), _1323617), _1323619))), -(c_Orderings_Obot__class_Obot(tc_fun(_1323615, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1323615, _1323617, _1323619))], (30414 ^ _778908) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1323615, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1323615, _1323617, _1323619), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323615), _1323617), _1323619))]]], (19995 ^ _778908) ^ [_1123382, _1123384, _1123386] : [class_Int_Onumber__ring(_1123382), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123382), _1123384), _1123386)), 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(_1123382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123382), hAPP(hAPP(c_Power_Opower__class_Opower(_1123382), _1123384), 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(_1123382), _1123386), 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(_1123382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123382), hAPP(c_Int_Onumber__class_Onumber__of(_1123382), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1123384)), _1123386)))], (5787 ^ _778908) ^ [_871128, _871130] : [_871128 = _871130, -(hAPP(c_Com_Ocom_OBODY, _871128) = hAPP(c_Com_Ocom_OBODY, _871130))], (16699 ^ _778908) ^ [_1066030, _1066032] : [class_Int_Onumber__ring(_1066030), -(hAPP(c_Int_Onumber__class_Onumber__of(_1066030), _1066032) = hAPP(c_Int_Oring__1__class_Oof__int(_1066030), _1066032))], (17553 ^ _778908) ^ [_1082188, _1082190, _1082192, _1082194] : [class_Groups_Omonoid__mult(_1082188), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1082188), _1082190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082192), _1082194)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1082188), hAPP(hAPP(c_Power_Opower__class_Opower(_1082188), _1082190), _1082192)), _1082194))], (24919 ^ _778908) ^ [_1215537, _1215539] : [-(c_Nitpick_Onumber__of__frac(_1215537, _1215539) = c_Nitpick_OAbs__Frac(_1215537, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1215539), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (50339 ^ _778908) ^ [_1790464, _1790466, _1790468] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1790464), c_List_Oupt(_1790466, _1790468)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1790466), _1790464), _1790468))], (13070 ^ _778908) ^ [_999345, _999347] : [class_Rings_Olinordered__idom(_999345), 13073 ^ _778908 : [(13080 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999345), _999347), c_Groups_Ozero__class_Ozero(_999345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999345), c_Groups_Osgn__class_Osgn(_999345, _999347)), c_Groups_Ozero__class_Ozero(_999345))))], (13074 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999345), c_Groups_Osgn__class_Osgn(_999345, _999347)), c_Groups_Ozero__class_Ozero(_999345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999345), _999347), c_Groups_Ozero__class_Ozero(_999345))))]]], (4412 ^ _778908) ^ [_847170, _847172, _847174, _847176] : [-(c_List_Olexn(_847176, _847172) = c_List_Olexn(_847174, _847170)), _847176 = _847174, _847172 = _847170], (9448 ^ _778908) ^ [_936976, _936978] : [class_Rings_Omult__zero(_936976), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936976), _936978), c_Groups_Ozero__class_Ozero(_936976)) = c_Groups_Ozero__class_Ozero(_936976))], (19251 ^ _778908) ^ [_1110376, _1110378] : [-(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), _1110376)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1110378)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1110376))) = 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), _1110378)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1110376)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37010 ^ _778908) ^ [_1467365, _1467367, _1467369, _1467371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467365, tc_HOL_Obool)), _1467371), _1467367)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467365, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467365, tc_HOL_Obool)), _1467367), _1467369)), _1467371) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467365, tc_HOL_Obool)), _1467367), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467365, tc_HOL_Obool)), _1467369), _1467371)))], (12113 ^ _778908) ^ [_982232, _982234, _982236] : [class_Rings_Oordered__cancel__semiring(_982232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982232), c_Groups_Ozero__class_Ozero(_982232)), _982234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982232), _982236), c_Groups_Ozero__class_Ozero(_982232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982232), _982236), _982234)), c_Groups_Ozero__class_Ozero(_982232))))], (47164 ^ _778908) ^ [_1716208, _1716210, _1716212, _1716214, _1716216] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1716208), tc_List_Olist(_1716208))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716208), tc_List_Olist(_1716208)), _1716210), hAPP(hAPP(c_List_Olist_OCons(_1716208), _1716212), _1716214))), c_List_Olistrel(_1716208, _1716216))), 47169 ^ _778908 : [(47174 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1716208), tc_List_Olist(_1716208))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716208), tc_List_Olist(_1716208)), 47168 ^ [_1716208, _1716210, _1716212, _1716214, _1716216]), _1716214)), c_List_Olistrel(_1716208, _1716216))))], (47172 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1716208, _1716208)), hAPP(hAPP(c_Product__Type_OPair(_1716208, _1716208), 47167 ^ [_1716208, _1716210, _1716212, _1716214, _1716216]), _1716212)), _1716216)))], (47170 ^ _778908) ^ [] : [-(_1716210 = hAPP(hAPP(c_List_Olist_OCons(_1716208), 47167 ^ [_1716208, _1716210, _1716212, _1716214, _1716216]), 47168 ^ [_1716208, _1716210, _1716212, _1716214, _1716216]))]]], (41199 ^ _778908) ^ [_1561615, _1561617, _1561619] : [-(hAPP(c_Set_OCollect(_1561615), hAPP(hAPP(c_COMBS(_1561615, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1561615), c_fdisj), _1561617)), _1561619)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1561615, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1561615), _1561617)), hAPP(c_Set_OCollect(_1561615), _1561619)))], (42128 ^ _778908) ^ [_1591846, _1591848] : [c_Wellfounded_Owf(_1591846, _1591848), -(c_Wellfounded_Owf(tc_List_Olist(_1591846), c_List_Olenlex(_1591846, _1591848)))], (14511 ^ _778908) ^ [_1025090, _1025092] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025090), _1025092)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025090)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025092)))], (40491 ^ _778908) ^ [_1548179] : [-(c_Relation_Orefl__on(_1548179, c_Orderings_Obot__class_Obot(tc_fun(_1548179, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1548179, _1548179), tc_HOL_Obool))))], (22590 ^ _778908) ^ [_1170567, _1170569] : [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(_1170569))), 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), _1170567)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1170567)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170569))))], (3168 ^ _778908) ^ [_827440, _827442] : [_827442 = _827440, -(c_Int_OBit0(_827442) = c_Int_OBit0(_827440))], (23152 ^ _778908) ^ [_1181672, _1181674] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1181672), _1181674)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1181672), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181674)))], (47491 ^ _778908) ^ [_1723501, _1723503, _1723505] : [c_List_Olist_ONil(_1723501) = hAPP(hAPP(c_List_Olist_OCons(_1723501), _1723503), _1723505)], (5388 ^ _778908) ^ [_862192, _862194, _862196, _862198] : [-(c_List_Orotate(_862198, _862194) = c_List_Orotate(_862196, _862192)), _862198 = _862196, _862194 = _862192], (7236 ^ _778908) ^ [_900008] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _900008) = _900008)], (30908 ^ _778908) ^ [_1333436, _1333438, _1333440, _1333442, _1333444, _1333446] : [_1333436 = hAPP(_1333438, _1333440), hBOOL(hAPP(hAPP(c_member(_1333442), _1333440), _1333444)), -(hBOOL(hAPP(hAPP(c_member(_1333446), _1333436), hAPP(c_Set_Oimage(_1333442, _1333446, _1333438), _1333444))))], (36498 ^ _778908) ^ [_1455658, _1455660, _1455662, _1455664] : [class_Lattices_Osemilattice__inf(_1455658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455658), _1455660), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455658), _1455662), _1455664))), 36505 ^ _778908 : [(36508 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455658), _1455660), _1455664)))], (36506 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455658), _1455660), _1455662)))]]], (48715 ^ _778908) ^ [_1753384, _1753386, _1753388, _1753390] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753384), tc_List_Olist(_1753384))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753384), tc_List_Olist(_1753384)), _1753386), _1753388)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1753384), c_List_Olistrel1(_1753384, _1753390)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753384)), _1753386) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753384)), _1753388))], (1472 ^ _778908) ^ [_800182, _800184] : [-(class_Groups_Oordered__ab__semigroup__add(_800182)), _800184 = _800182, class_Groups_Oordered__ab__semigroup__add(_800184)], (18377 ^ _778908) ^ [_1096241] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1096241), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096241))], (28261 ^ _778908) ^ [_1280803] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1280803) = c_Orderings_Oord__class_Omax(_1280803)), class_Lattices_Osemilattice__sup(_1280803), class_Orderings_Olinorder(_1280803)], (42501 ^ _778908) ^ [_1600919, _1600921] : [-(c_Nitpick_Owf_H(_1600919, _1600921)), c_Wellfounded_Oacyclic(_1600919, _1600921), 42506 ^ _778908 : [(42509 ^ _778908) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (42507 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1600919, _1600919)), _1600921))]]], (12155 ^ _778908) ^ [_982997, _982999, _983001] : [class_Rings_Olinordered__ring__strict(_982997), 12158 ^ _778908 : [(12173 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982997), _982999), _983001)), c_Groups_Ozero__class_Ozero(_982997)))), 12174 ^ _778908 : [(12181 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), _982999), c_Groups_Ozero__class_Ozero(_982997))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), c_Groups_Ozero__class_Ozero(_982997)), _983001))], (12175 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), c_Groups_Ozero__class_Ozero(_982997)), _982999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), _983001), c_Groups_Ozero__class_Ozero(_982997)))]]], (12159 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982997), _982999), _983001)), c_Groups_Ozero__class_Ozero(_982997))), 12164 ^ _778908 : [(12167 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), _983001), c_Groups_Ozero__class_Ozero(_982997))))], (12165 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), c_Groups_Ozero__class_Ozero(_982997)), _982999)))]], 12168 ^ _778908 : [(12171 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), c_Groups_Ozero__class_Ozero(_982997)), _983001)))], (12169 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982997), _982999), c_Groups_Ozero__class_Ozero(_982997))))]]]]], (9768 ^ _778908) ^ [_942607, _942609, _942611, _942613] : [class_Rings_Olinordered__ring__strict(_942607), 9771 ^ _778908 : [(9786 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942607), _942609), _942611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942607), _942609), _942613)))), 9787 ^ _778908 : [(9794 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), _942609), c_Groups_Ozero__class_Ozero(_942607))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), _942613), _942611))], (9788 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), c_Groups_Ozero__class_Ozero(_942607)), _942609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), _942611), _942613))]]], (9772 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942607), _942609), _942611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942607), _942609), _942613))), 9777 ^ _778908 : [(9780 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), _942611), _942613)))], (9778 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), c_Groups_Ozero__class_Ozero(_942607)), _942609)))]], 9781 ^ _778908 : [(9784 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), _942613), _942611)))], (9782 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942607), _942609), c_Groups_Ozero__class_Ozero(_942607))))]]]]], (38880 ^ _778908) ^ [_1508286, _1508288, _1508290] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508286), _1508288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508286, tc_HOL_Obool)), _1508288), hAPP(c_Set_Oimage(_1508286, _1508286, _1508290), _1508288))), -(c_Fun_Oinj__on(_1508286, _1508286, _1508290, _1508288))], (33039 ^ _778908) ^ [_1381172, _1381174, _1381176, _1381178, _1381180] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1381172, _1381174, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1381172)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1381172), hAPP(hAPP(c_COMBC(_1381172, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1381172), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1381176)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1381178)), _1381180))), c_Com_Ocom_OAss(_1381178, _1381180)), _1381176)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1381172), tc_HOL_Obool)))))], (22360 ^ _778908) ^ [_1166184] : [c_Code__Numeral_OSuc__code__numeral(_1166184) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (42365 ^ _778908) ^ [_1597473, _1597475, _1597477, _1597479] : [42366 ^ _778908 : [(42367 ^ _778908) ^ [_1597548] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597473, _1597477)), hAPP(hAPP(c_Product__Type_OPair(_1597473, _1597477), _1597475), _1597548)), _1597479))]], -(hBOOL(hAPP(hAPP(c_member(_1597473), _1597475), hAPP(c_Relation_ODomain(_1597473, _1597477), _1597479))))], (28973 ^ _778908) ^ [_1295277, _1295279, _1295281, _1295283, _1295285] : [class_Complete__Lattice_Ocomplete__lattice(_1295277), 28976 ^ _778908 : [(28977 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295277), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295279, _1295277), _1295281), _1295283)), _1295285)), 28980 ^ _778908 : [(28981 ^ _778908) ^ [_1295458] : [hBOOL(hAPP(hAPP(c_member(_1295279), _1295458), _1295281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295277), hAPP(_1295283, _1295458)), _1295285)))]]], (28987 ^ _778908) ^ [] : [28989 ^ _778908 : [(28992 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295277), hAPP(_1295283, 28988 ^ [_1295277, _1295279, _1295281, _1295283, _1295285])), _1295285))], (28990 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295279), 28988 ^ [_1295277, _1295279, _1295281, _1295283, _1295285]), _1295281)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295277), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295279, _1295277), _1295281), _1295283)), _1295285)))]]], (19587 ^ _778908) ^ [_1116254, _1116256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116254), _1116256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1116254)), c_Int_OBit0(_1116256))))], (51393 ^ _778908) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (1022 ^ _778908) ^ [_794557, _794559] : [-(class_Lattices_Obounded__lattice(_794557)), _794559 = _794557, class_Lattices_Obounded__lattice(_794559)], (26523 ^ _778908) ^ [_1246056, _1246058, _1246060] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246056), _1246058)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246056), _1246060))), -(_1246056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246058), _1246060)))], (16310 ^ _778908) ^ [_1059136, _1059138] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059136, _1059138) = 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), _1059136), _1059138) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7987 ^ _778908) ^ [_912471, _912473, _912475] : [class_Groups_Oordered__comm__monoid__add(_912471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912471), _912473), c_Groups_Ozero__class_Ozero(_912471))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912471), _912475), c_Groups_Ozero__class_Ozero(_912471))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_912471), _912473), _912475)), c_Groups_Ozero__class_Ozero(_912471))))], (46144 ^ _778908) ^ [_1688712, _1688714, _1688716, _1688718, _1688720] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1688712), tc_List_Olist(_1688714), tc_List_Olist(_1688716), hAPP(c_List_Omap(_1688712, _1688714), _1688718)), hAPP(c_List_Omap(_1688716, _1688712), _1688720)) = hAPP(c_List_Omap(_1688716, _1688714), hAPP(c_Fun_Ocomp(_1688712, _1688714, _1688716, _1688718), _1688720)))], (24107 ^ _778908) ^ [_1199956, _1199958, _1199960] : [_1199956 = _1199958, 24110 ^ _778908 : [(24113 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199960, tc_HOL_Obool)), _1199958), _1199956)))], (24111 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199960, tc_HOL_Obool)), _1199956), _1199958)))]]], (38636 ^ _778908) ^ [_1503426, _1503428, _1503430, _1503432, _1503434] : [c_Fun_Oinj__on(_1503426, _1503428, _1503430, _1503432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503426, tc_HOL_Obool)), _1503434), _1503432)), -(c_Fun_Oinj__on(_1503426, _1503428, _1503430, _1503434))], (3118 ^ _778908) ^ [_826663, _826665, _826667, _826669, _826671, _826673] : [-(c_Random__Sequence_Oempty(_826673, _826669, _826665) = c_Random__Sequence_Oempty(_826671, _826667, _826663)), _826673 = _826671, _826669 = _826667, _826665 = _826663], (28031 ^ _778908) ^ [_1275845, _1275847, _1275849] : [class_Orderings_Olinorder(_1275845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275845), _1275847), _1275849)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275845, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1275845), _1275847)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1275845, _1275847, _1275849)) = hAPP(c_SetInterval_Oord__class_OatMost(_1275845), _1275849))], (4324 ^ _778908) ^ [_845716, _845718, _845720, _845722, _845724, _845726] : [-(c_Map_Oran(_845726, _845722, _845718) = c_Map_Oran(_845724, _845720, _845716)), _845726 = _845724, _845722 = _845720, _845718 = _845716], (48109 ^ _778908) ^ [_1738585, _1738587, _1738589, _1738591, _1738593] : [hAPP(hAPP(c_List_Oappend(_1738585), _1738587), _1738589) = hAPP(hAPP(c_List_Olist_OCons(_1738585), _1738591), _1738593), 48114 ^ _778908 : [(48117 ^ _778908) ^ [] : [-(_1738589 = hAPP(hAPP(c_List_Olist_OCons(_1738585), _1738591), _1738593))], (48115 ^ _778908) ^ [] : [-(_1738587 = c_List_Olist_ONil(_1738585))]], 48119 ^ _778908 : [(48122 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1738585), 48118 ^ [_1738585, _1738587, _1738589, _1738591, _1738593]), _1738589) = _1738593)], (48120 ^ _778908) ^ [] : [-(_1738587 = hAPP(hAPP(c_List_Olist_OCons(_1738585), _1738591), 48118 ^ [_1738585, _1738587, _1738589, _1738591, _1738593]))]]], (31435 ^ _778908) ^ [_1346002, _1346004, _1346006, _1346008] : [hBOOL(hAPP(hAPP(c_member(_1346002), _1346004), _1346006)), -(hBOOL(hAPP(hAPP(c_member(_1346002), _1346004), hAPP(hAPP(c_Set_Oinsert(_1346002), _1346008), _1346006))))], (15084 ^ _778908) ^ [_1034790, _1034792, _1034794] : [class_Divides_Osemiring__div(_1034790), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034790), c_Divides_Odiv__class_Omod(_1034790, _1034792, _1034794)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034790), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034790), _1034792), _1034794)), _1034794)) = _1034792)], (39488 ^ _778908) ^ [_1521707, _1521709, _1521711, _1521713, _1521715] : [hBOOL(hAPP(hAPP(c_member(_1521707), hAPP(_1521709, _1521711)), _1521713)), -(hBOOL(hAPP(hAPP(c_member(_1521715), _1521711), hAPP(c_Set_Ovimage(_1521715, _1521707, _1521709), _1521713))))], (39514 ^ _778908) ^ [_1522331, _1522333, _1522335, _1522337, _1522339] : [hBOOL(hAPP(_1522337, hAPP(_1522335, _1522339))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1522331, _1522333, _1522335), _1522337), _1522339)))], (19655 ^ _778908) ^ [_1117469] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1117469)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1117469)))], (7304 ^ _778908) ^ [_901076, _901078] : [class_Groups_Ocomm__monoid__add(_901076), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901076), _901078), c_Groups_Ozero__class_Ozero(_901076)) = _901078)], (41259 ^ _778908) ^ [_1563148, _1563150, _1563152] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1563148, tc_HOL_Obool)), _1563150), _1563152) = hAPP(c_Set_OCollect(_1563148), hAPP(hAPP(c_COMBS(_1563148, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563148), c_fconj), hAPP(hAPP(c_COMBC(_1563148, tc_fun(_1563148, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563148)), _1563150))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1563148), c_fNot), hAPP(hAPP(c_COMBC(_1563148, tc_fun(_1563148, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563148)), _1563152)))))], (19381 ^ _778908) ^ [_1112676, _1112678] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1112676)), c_Int_OBit0(_1112678)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1112676), _1112678)))], (15592 ^ _778908) ^ [_1044327, _1044329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1044327), _1044329)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044327, _1044329) = _1044327)], (11368 ^ _778908) ^ [_969117, _969119, _969121] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969117)), _969119) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969117)), _969121), -(_969119 = _969121)], (50027 ^ _778908) ^ [_1784016, _1784018] : [-(c_List_Ofoldr(tc_List_Olist(_1784016), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1784016)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1784016))), c_List_Otranspose(_1784016, _1784018), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1784016))), hAPP(c_List_Ofilter(tc_List_Olist(_1784016), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1784016)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1784016), tc_List_Olist(_1784016), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1784016)))), _1784018)))], (17711 ^ _778908) ^ [_1085040, _1085042, _1085044, _1085046] : [class_Rings_Olinordered__semidom(_1085040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085040), hAPP(hAPP(c_Power_Opower__class_Opower(_1085040), _1085042), _1085044)), hAPP(hAPP(c_Power_Opower__class_Opower(_1085040), _1085046), _1085044))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085040), c_Groups_Ozero__class_Ozero(_1085040)), _1085046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085040), _1085042), _1085046)))], (42379 ^ _778908) ^ [_1597921, _1597923] : [c_Wellfounded_Owf(_1597921, _1597923), -(c_Wellfounded_OwfP(_1597921, c_FunDef_Oin__rel(_1597921, _1597921, _1597923)))], (6415 ^ _778908) ^ [_882433, _882435, _882437, _882439] : [hAPP(c_Com_Ocom_OBODY, _882433) = c_Com_Ocom_OLocal(_882435, _882437, _882439)], (41050 ^ _778908) ^ [_1558536, _1558538, _1558540, _1558542, _1558544] : [c_Finite__Set_Ofun__left__comm__idem(_1558536, _1558538, _1558540), -(hAPP(hAPP(_1558540, _1558542), hAPP(hAPP(_1558540, _1558542), _1558544)) = hAPP(hAPP(_1558540, _1558542), _1558544))], (15452 ^ _778908) ^ [_1041813, _1041815, _1041817] : [class_Groups_Oab__group__add(_1041813), 15455 ^ _778908 : [(15462 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041813), _1041815), _1041817) = c_Groups_Ozero__class_Ozero(_1041813), -(_1041815 = _1041817)], (15456 ^ _778908) ^ [] : [_1041815 = _1041817, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041813), _1041815), _1041817) = c_Groups_Ozero__class_Ozero(_1041813))]]], (46267 ^ _778908) ^ [_1691970, _1691972, _1691974, _1691976, _1691978] : [c_Fun_Oinj__on(_1691970, _1691972, _1691974, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1691970, tc_HOL_Obool)), hAPP(c_List_Oset(_1691970), _1691976)), hAPP(c_List_Oset(_1691970), _1691978))), 46270 ^ _778908 : [(46277 ^ _778908) ^ [] : [_1691976 = _1691978, -(hAPP(hAPP(c_List_Omap(_1691970, _1691972), _1691974), _1691976) = hAPP(hAPP(c_List_Omap(_1691970, _1691972), _1691974), _1691978))], (46271 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Omap(_1691970, _1691972), _1691974), _1691976) = hAPP(hAPP(c_List_Omap(_1691970, _1691972), _1691974), _1691978), -(_1691976 = _1691978)]]], (34421 ^ _778908) ^ [_1408736, _1408738, _1408740, _1408742, _1408744, _1408746] : [-(_1408736 = _1408738), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408740, _1408742), _1408744), _1408738), _1408746), _1408736) = hAPP(_1408744, _1408736))], (33087 ^ _778908) ^ [_1382499] : [class_Rings_Oring__1(_1382499), -(hBOOL(hAPP(hAPP(c_member(_1382499), c_Groups_Ozero__class_Ozero(_1382499)), c_Int_Oring__1__class_OInts(_1382499))))], (5570 ^ _778908) ^ [_864983, _864985] : [_864985 = _864983, -(c_Orderings_Oord__class_Oless(_864985) = c_Orderings_Oord__class_Oless(_864983))], (10088 ^ _778908) ^ [_948443, _948445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948443)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948445))))], (41637 ^ _778908) ^ [_1577598, _1577600, _1577602] : [class_Orderings_Olinorder(_1577598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577598), _1577600)), -(_1577600 = c_Orderings_Obot__class_Obot(tc_fun(_1577598, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1577598), _1577602), c_Big__Operators_Olattice_OSup__fin(_1577598, c_Orderings_Oord__class_Omax(_1577598), _1577600)) = c_Big__Operators_Olattice_OSup__fin(_1577598, c_Orderings_Oord__class_Omax(_1577598), hAPP(c_Set_OCollect(_1577598), hAPP(hAPP(c_COMBB(tc_fun(_1577598, tc_HOL_Obool), tc_HOL_Obool, _1577598), c_HOL_OEx(_1577598)), hAPP(hAPP(c_COMBC(_1577598, tc_fun(_1577598, tc_HOL_Obool), tc_fun(_1577598, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577598, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1577598, tc_HOL_Obool), tc_fun(_1577598, tc_HOL_Obool)), _1577598), c_COMBS(_1577598, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577598, tc_HOL_Obool), tc_fun(_1577598, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1577598), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577598), c_fconj)), hAPP(hAPP(c_COMBC(_1577598, tc_fun(_1577598, _1577598), tc_fun(_1577598, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577598, tc_HOL_Obool), tc_fun(tc_fun(_1577598, _1577598), tc_fun(_1577598, tc_HOL_Obool)), _1577598), c_COMBB(_1577598, tc_HOL_Obool, _1577598)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1577598), _1577602))))), hAPP(hAPP(c_COMBC(_1577598, tc_fun(_1577598, tc_HOL_Obool), tc_HOL_Obool), c_member(_1577598)), _1577600))))))], (8246 ^ _778908) ^ [_917034, _917036, _917038, _917040, _917042, _917044] : [-(c_Sum__Type_Osum_Osum__rec(_917034, _917036, _917038, _917040, _917042, hAPP(c_Sum__Type_OInl(_917034, _917038), _917044)) = hAPP(_917040, _917044))], (16298 ^ _778908) ^ [_1058975, _1058977] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1058975, _1058977) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1058975, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1058977)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15018 ^ _778908) ^ [_1033521, _1033523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1033523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033521), _1033523)), _1033521)))], (35702 ^ _778908) ^ [_1437114, _1437116, _1437118, _1437120, _1437122, _1437124, _1437126, _1437128, _1437130] : [hAPP(c_Fun_Ocomp(_1437114, _1437116, _1437118, _1437120), _1437122) = hAPP(c_Fun_Ocomp(_1437124, _1437116, _1437118, _1437126), _1437128), -(hAPP(_1437120, hAPP(_1437122, _1437130)) = hAPP(_1437126, hAPP(_1437128, _1437130)))], (20249 ^ _778908) ^ [_1128548, _1128550, _1128552] : [class_Rings_Odivision__ring(_1128548), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1128548), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128548), _1128550), _1128552)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128548), hAPP(c_Groups_Ouminus__class_Ouminus(_1128548), _1128550)), _1128552))], (31828 ^ _778908) ^ [_1355643, _1355645, _1355647] : [-(hBOOL(hAPP(hAPP(c_member(_1355643), _1355645), _1355647))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355643, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1355643), _1355645), _1355647)), hAPP(hAPP(c_Set_Oinsert(_1355643), _1355645), c_Orderings_Obot__class_Obot(tc_fun(_1355643, tc_HOL_Obool)))) = _1355647)], (7298 ^ _778908) ^ [_900981, _900983] : [class_Groups_Omonoid__add(_900981), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900981), _900983), c_Groups_Ozero__class_Ozero(_900981)) = _900983)], (49235 ^ _778908) ^ [_1766278, _1766280, _1766282] : [-(hAPP(c_List_Otl(_1766278), hAPP(hAPP(c_List_Oappend(_1766278), _1766280), _1766282)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1766278), _1766278, hAPP(c_List_Otl(_1766278), _1766282), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1766278), tc_List_Olist(_1766278)), _1766278), hAPP(hAPP(c_COMBC(tc_List_Olist(_1766278), tc_List_Olist(_1766278), tc_List_Olist(_1766278)), c_List_Oappend(_1766278)), _1766282))), _1766280))], (46148 ^ _778908) ^ [_1688851, _1688853, _1688855, _1688857, _1688859, _1688861] : [-(hAPP(hAPP(c_List_Omap(_1688851, _1688853), _1688855), hAPP(hAPP(c_List_Omap(_1688857, _1688851), _1688859), _1688861)) = hAPP(hAPP(c_List_Omap(_1688857, _1688853), hAPP(c_Fun_Ocomp(_1688851, _1688853, _1688857, _1688855), _1688859)), _1688861))], (30742 ^ _778908) ^ [_1330148, _1330150, _1330152] : [class_Orderings_Olinorder(_1330148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330148), _1330150), _1330152)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330148, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1330148), _1330150), c_Orderings_Obot__class_Obot(tc_fun(_1330148, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330148, _1330150, _1330152)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1330148, _1330150), _1330152))], (51257 ^ _778908) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (35474 ^ _778908) ^ [_1432046, _1432048] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1432046, tc_HOL_Obool)), _1432048), hAPP(c_Set_OPow(_1432046), _1432048))))], (49522 ^ _778908) ^ [_1772877, _1772879, _1772881] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772877)), _1772879), c_List_Olists(_1772877, _1772881))), 49525 ^ _778908 : [(49526 ^ _778908) ^ [_1772985] : [hBOOL(hAPP(hAPP(c_member(_1772877), _1772985), hAPP(c_List_Oset(_1772877), _1772879))), -(hBOOL(hAPP(hAPP(c_member(_1772877), _1772985), _1772881)))]]], (47385 ^ _778908) ^ [_1721598] : [class_Groups_Omonoid__add(_1721598), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1721598), c_List_Olist_ONil(_1721598)) = c_Groups_Ozero__class_Ozero(_1721598))], (6490 ^ _778908) ^ [_883910, _883912] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_883910, _883912)))), hBOOL(hAPP(c_Com_OWT, _883910)), hBOOL(hAPP(c_Com_OWT, _883912))], (20415 ^ _778908) ^ [_1131375, _1131377, _1131379, _1131381] : [class_Fields_Olinordered__field(_1131375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131375), _1131377), _1131379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131375), _1131381), c_Groups_Ozero__class_Ozero(_1131375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131375), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131375), _1131379), _1131381)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131375), _1131377), _1131381))))], (20071 ^ _778908) ^ [_1125079, _1125081, _1125083] : [class_Rings_Olinordered__idom(_1125079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125079), _1125081), c_Groups_Ozero__class_Ozero(_1125079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125079), hAPP(hAPP(c_Power_Opower__class_Opower(_1125079), _1125081), 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)))), _1125083)))), c_Groups_Ozero__class_Ozero(_1125079))))], (1192 ^ _778908) ^ [_796682, _796684] : [-(class_Rings_Ocomm__ring(_796682)), _796684 = _796682, class_Rings_Ocomm__ring(_796684)], (2672 ^ _778908) ^ [_819424, _819426] : [_819426 = _819424, -(c_New__DSequence_Opos__not__seq(_819426) = c_New__DSequence_Opos__not__seq(_819424))], (45344 ^ _778908) ^ [_1670626, _1670628, _1670630] : [class_Complete__Lattice_Ocomplete__lattice(_1670626), hBOOL(hAPP(hAPP(c_member(_1670626), _1670628), _1670630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670626), c_Complete__Lattice_OInf__class_OInf(_1670626, _1670630)), _1670628)))], (39267 ^ _778908) ^ [_1516496, _1516498, _1516500, _1516502] : [c_Fun_Oinj__on(_1516496, tc_fun(tc_fun(_1516496, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1516496, tc_fun(tc_prod(_1516496, _1516496), tc_HOL_Obool), tc_fun(tc_fun(_1516496, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516496, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1516496, _1516496), tc_HOL_Obool), tc_fun(tc_fun(_1516496, tc_HOL_Obool), tc_HOL_Obool)), _1516496), c_Equiv__Relations_Oquotient(_1516496)), hAPP(hAPP(c_COMBC(_1516496, tc_fun(_1516496, tc_HOL_Obool), tc_fun(_1516496, tc_HOL_Obool)), c_Set_Oinsert(_1516496)), c_Orderings_Obot__class_Obot(tc_fun(_1516496, tc_HOL_Obool))))), _1516498), _1516500), hBOOL(hAPP(hAPP(c_member(_1516496), _1516502), _1516500)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1516496), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1516496, tc_HOL_Obool)), _1516500), hAPP(hAPP(c_Set_Oinsert(_1516496), _1516502), c_Orderings_Obot__class_Obot(tc_fun(_1516496, tc_HOL_Obool))))), _1516498) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1516496, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1516496), _1516500), _1516498)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1516496), hAPP(hAPP(c_Set_Oinsert(_1516496), _1516502), c_Orderings_Obot__class_Obot(tc_fun(_1516496, tc_HOL_Obool)))), _1516498)))], (51553 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (23435 ^ _778908) ^ [_1187408, _1187410, _1187412, _1187414, _1187416, _1187418] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187408, _1187410), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187412), _1187414))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187408, _1187410), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187416), _1187418))), -(_1187410 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1187414 = _1187418)], (30342 ^ _778908) ^ [_1322418, _1322420] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322418, tc_HOL_Obool)), _1322420), c_Orderings_Otop__class_Otop(tc_fun(_1322418, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1322418, tc_HOL_Obool)))], (24947 ^ _778908) ^ [_1216187, _1216189, _1216191, _1216193, _1216195, _1216197, _1216199] : [c_Sum__Type_Osum_Osum__case(_1216187, _1216189, _1216191, _1216193, _1216195) = c_Sum__Type_Osum_Osum__case(_1216187, _1216189, _1216191, _1216197, _1216199), 24950 ^ _778908 : [(24953 ^ _778908) ^ [] : [-(_1216195 = _1216199)], (24951 ^ _778908) ^ [] : [-(_1216193 = _1216197)]]], (12453 ^ _778908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7623 ^ _778908) ^ [_906531, _906533, _906535, _906537, _906539, _906541] : [-(c_Nitpick_Opair__box_OPairBox(_906531, _906533, _906535, _906537) = c_Nitpick_Opair__box_OPairBox(_906531, _906533, _906539, _906541)), _906535 = _906539, _906537 = _906541], (49640 ^ _778908) ^ [_1775390, _1775392, _1775394] : [_1775390 = c_List_Olist_ONil(_1775392), -(c_List_Olast(_1775392, hAPP(hAPP(c_List_Olist_OCons(_1775392), _1775394), _1775390)) = _1775394)], (27944 ^ _778908) ^ [_1274314, _1274316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1274314)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1274314, _1274316)))], (51605 ^ _778908) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (46169 ^ _778908) ^ [_1689339, _1689341, _1689343, _1689345, _1689347, _1689349] : [-(c_Map_Omap__comp(_1689339, _1689341, _1689343, _1689345, _1689347, _1689349) = c_Option_Ooption_ONone(_1689341)), 46170 ^ _778908 : [(46173 ^ _778908) ^ [_1689451] : [hAPP(_1689347, _1689349) = hAPP(c_Option_Ooption_OSome(_1689339), _1689451), hAPP(_1689345, _1689451) = c_Option_Ooption_ONone(_1689341)], (46171 ^ _778908) ^ [] : [hAPP(_1689347, _1689349) = c_Option_Ooption_ONone(_1689339)]]], (12301 ^ _778908) ^ [_985561, _985563] : [class_Groups_Oordered__ab__group__add(_985561), 12304 ^ _778908 : [(12311 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985561), c_Groups_Ozero__class_Ozero(_985561)), _985563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985561), hAPP(c_Groups_Ouminus__class_Ouminus(_985561), _985563)), c_Groups_Ozero__class_Ozero(_985561))))], (12305 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985561), hAPP(c_Groups_Ouminus__class_Ouminus(_985561), _985563)), c_Groups_Ozero__class_Ozero(_985561))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985561), c_Groups_Ozero__class_Ozero(_985561)), _985563)))]]], (3416 ^ _778908) ^ [_831388, _831390, _831392, _831394, _831396, _831398] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_831398, _831394, _831390) = c_Hoare__Mirabelle_Otriple_Otriple__size(_831396, _831392, _831388)), _831398 = _831396, _831394 = _831392, _831390 = _831388], (1172 ^ _778908) ^ [_796432, _796434] : [-(class_Groups_Ogroup__add(_796432)), _796434 = _796432, class_Groups_Ogroup__add(_796434)], (17777 ^ _778908) ^ [_1086327, _1086329] : [class_Power_Opower(_1086327), class_Rings_Osemiring__0(_1086327), 17784 ^ _778908 : [(17791 ^ _778908) ^ [] : [-(_1086329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1086327), c_Groups_Ozero__class_Ozero(_1086327)), _1086329) = c_Groups_Ozero__class_Ozero(_1086327))], (17785 ^ _778908) ^ [] : [_1086329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1086327), c_Groups_Ozero__class_Ozero(_1086327)), _1086329) = c_Groups_Oone__class_Oone(_1086327))]]], (15538 ^ _778908) ^ [_1043362, _1043364, _1043366, _1043368] : [class_Divides_Oring__div(_1043362), -(c_Divides_Odiv__class_Omod(_1043362, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043362), _1043364), _1043366), _1043368) = c_Divides_Odiv__class_Omod(_1043362, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043362), c_Divides_Odiv__class_Omod(_1043362, _1043364, _1043368)), _1043366), _1043368))], (21007 ^ _778908) ^ [_1141545, _1141547, _1141549, _1141551] : [class_Fields_Olinordered__field(_1141545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141545), _1141547), c_Groups_Ozero__class_Ozero(_1141545))), 21014 ^ _778908 : [(21021 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141545), _1141551), _1141547)), _1141549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141545), _1141549), _1141547)), _1141551)))], (21015 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141545), _1141549), _1141547)), _1141551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141545), _1141551), _1141547)), _1141549)))]]], (41408 ^ _778908) ^ [_1568233, _1568235, _1568237, _1568239, _1568241, _1568243] : [-(hBOOL(hAPP(hAPP(c_member(_1568233), _1568235), _1568237))), -(hAPP(c_Fun_Ooverride__on(_1568233, _1568239, _1568241, _1568243, _1568237), _1568235) = hAPP(_1568241, _1568235))], (5973 ^ _778908) ^ [_874288, _874290, _874292] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _874288))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_874290, _874288, _874292))))], (31598 ^ _778908) ^ [_1349326, _1349328, _1349330, _1349332] : [hBOOL(hAPP(hAPP(c_member(_1349326), _1349328), _1349330)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349326, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1349326), _1349328), _1349332)), _1349330) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349326, tc_HOL_Obool)), _1349332), _1349330))], (50559 ^ _778908) ^ [_1794137, _1794139, _1794141, _1794143] : [class_Groups_Ocomm__monoid__add(_1794137), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1794137), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1794137), _1794139), c_List_Oupt(_1794141, _1794143))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1794137), _1794139), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1794141, _1794143))))], (45081 ^ _778908) ^ [_1664299, _1664301, _1664303, _1664305] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664299, tc_fun(_1664301, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1664299, tc_HOL_Obool), _1664303)), _1664305) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1664299, tc_HOL_Obool), tc_fun(_1664301, tc_HOL_Obool)), _1664303), hAPP(hAPP(c_COMBC(tc_fun(_1664299, tc_HOL_Obool), tc_fun(_1664299, tc_fun(_1664301, tc_HOL_Obool)), tc_fun(_1664301, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664299, tc_fun(_1664301, tc_HOL_Obool))), _1664305)))], (17993 ^ _778908) ^ [_1090083] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1090083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090083), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6958 ^ _778908) ^ [_893853, _893855, _893857, _893859, _893861] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _893853)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _893855), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_893857, _893855))), _893859)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_893861, _893853, _893857)), _893855), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _893859), hAPP(c_Natural_Ogetlocs, _893855))), _893861), hAPP(hAPP(c_Natural_Ogetlocs, _893859), c_Com_ORes)))))], (45656 ^ _778908) ^ [_1677559, _1677561, _1677563, _1677565] : [class_Lattices_Osemilattice__inf(_1677559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1677559), _1677561)), 45666 ^ _778908 : [(45669 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1677559), _1677563), 45665 ^ [_1677559, _1677561, _1677563, _1677565]))], (45667 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677559), 45665 ^ [_1677559, _1677561, _1677563, _1677565]), _1677561)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1677559), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1677559), _1677563), _1677565)), hAPP(hAPP(c_Finite__Set_Ofold(_1677559, _1677559, c_Lattices_Osemilattice__inf__class_Oinf(_1677559)), _1677565), _1677561))))], (11364 ^ _778908) ^ [_969044] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969044), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6045 ^ _778908) ^ [_875663, _875665, _875667, _875669, _875671, _875673, _875675, _875677, _875679, _875681, _875683] : [-(c_Com_Ocom_Ocom__case(_875663, _875665, _875667, _875669, _875671, _875673, _875675, _875677, _875679, c_Com_Ocom_OSemi(_875681, _875683)) = hAPP(hAPP(_875671, _875681), _875683))], (15872 ^ _778908) ^ [_1049771, _1049773] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049771), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1049771), _1049773)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14023 ^ _778908) ^ [_1016231, _1016233] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016231, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016233)) = 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), _1016231), _1016233)))], (3250 ^ _778908) ^ [_828731, _828733, _828735, _828737, _828739, _828741] : [-(c_SetInterval_Oord_OgreaterThan(_828741, _828737, _828733) = c_SetInterval_Oord_OgreaterThan(_828739, _828735, _828731)), _828741 = _828739, _828737 = _828735, _828733 = _828731], (14260 ^ _778908) ^ [_1020237, _1020239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020237)), -(c_SMT_Oz3mod(_1020239, _1020237) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1020239, _1020237))], (35754 ^ _778908) ^ [_1438499, _1438501, _1438503, _1438505, _1438507, _1438509] : [hBOOL(hAPP(hAPP(c_member(_1438499), _1438501), _1438503)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1438499, _1438505)), hAPP(hAPP(c_Product__Type_OPair(_1438499, _1438505), _1438501), _1438507)), _1438509)), -(hBOOL(hAPP(hAPP(c_member(_1438505), _1438507), hAPP(c_Relation_OImage(_1438499, _1438505, _1438509), _1438503))))], (19637 ^ _778908) ^ [_1117184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1117184), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1117184)), c_Int_OMin)))], (41179 ^ _778908) ^ [_1561378, _1561380] : [-(hBOOL(hAPP(_1561380, 41180 ^ [_1561378, _1561380]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1561378, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1561378), _1561380))], (31674 ^ _778908) ^ [_1350680, _1350682, _1350684] : [class_Orderings_Oord(_1350680), 31677 ^ _778908 : [(31684 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350680), _1350684), _1350682)), -(hBOOL(hAPP(hAPP(c_member(_1350680), _1350682), hAPP(c_SetInterval_Oord__class_OatLeast(_1350680), _1350684))))], (31678 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1350680), _1350682), hAPP(c_SetInterval_Oord__class_OatLeast(_1350680), _1350684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350680), _1350684), _1350682)))]]], (45112 ^ _778908) ^ [_1665131, _1665133, _1665135, _1665137, _1665139, _1665141, _1665143] : [45114 ^ _778908 : [(45117 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1665139, 45113 ^ [_1665131, _1665133, _1665135, _1665137, _1665139, _1665141, _1665143]), _1665141), _1665143))], (45115 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1665131), 45113 ^ [_1665131, _1665133, _1665135, _1665137, _1665139, _1665141, _1665143]), _1665137)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665131, tc_fun(_1665133, tc_fun(_1665135, tc_HOL_Obool))), _1665137), _1665139), _1665141), _1665143)))], (40418 ^ _778908) ^ [_1545837, _1545839, _1545841, _1545843, _1545845, _1545847, _1545849, _1545851, _1545853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545837, _1545839)), hAPP(hAPP(c_Product__Type_OPair(_1545837, _1545839), _1545841), _1545843)), _1545845)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545847, _1545849)), hAPP(hAPP(c_Product__Type_OPair(_1545847, _1545849), hAPP(_1545851, _1545841)), hAPP(_1545853, _1545843))), hAPP(c_Set_Oimage(tc_prod(_1545837, _1545839), tc_prod(_1545847, _1545849), c_Product__Type_Omap__pair(_1545837, _1545847, _1545839, _1545849, _1545851, _1545853)), _1545845))))], (14515 ^ _778908) ^ [_1025182, _1025184, _1025186] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025182), _1025184)), _1025186) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025182), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025184), _1025186))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025182), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025184, _1025186))), _1025186)))], (36372 ^ _778908) ^ [_1453466, _1453468, _1453470] : [class_Lattices_Osemilattice__inf(_1453466), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453466), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453466), _1453468), _1453470)), _1453470)))], (14266 ^ _778908) ^ [_1020326, _1020328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020326))), -(c_SMT_Oz3mod(_1020328, _1020326) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1020328, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1020326)))], (5827 ^ _778908) ^ [_871634] : [-(hAPP(c_Nat_Osize__class_Osize(tc_String_Ochar), _871634) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32405 ^ _778908) ^ [_1368131, _1368133, _1368135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368131)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1368133), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1368135)), 32415 ^ _778908 : [(32421 ^ _778908) ^ [] : [-(_1368133 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32417 ^ [_1368131, _1368133, _1368135]), 32414 ^ [_1368131, _1368133, _1368135]))], (32419 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32417 ^ [_1368131, _1368133, _1368135]), _1368135)))], (32416 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32414 ^ [_1368131, _1368133, _1368135]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1368131))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1368133), _1368131) = _1368133)], (22396 ^ _778908) ^ [_1166809, _1166811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1166809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1166809), _1166811)), -(c_Divides_Odivmod__nat(_1166811, _1166809) = 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), _1166811), _1166809)), _1166809))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166811), _1166809), _1166809)))], (21735 ^ _778908) ^ [_1154503, _1154505, _1154507, _1154509] : [class_Fields_Olinordered__field(_1154503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154503), _1154505), c_Groups_Ozero__class_Ozero(_1154503))), 21742 ^ _778908 : [(21749 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154503), _1154509), _1154505)), _1154507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154503), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154503), _1154507), _1154505)), _1154509)))], (21743 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154503), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154503), _1154507), _1154505)), _1154509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154503), _1154509), _1154505)), _1154507)))]]], (40102 ^ _778908) ^ [_1536857, _1536859, _1536861] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1536857, _1536859), _1536861), hAPP(c_COMBK(tc_fun(_1536859, tc_HOL_Obool), _1536857), c_Orderings_Obot__class_Obot(tc_fun(_1536859, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1536857, _1536859), tc_HOL_Obool)))], (39699 ^ _778908) ^ [_1526760, _1526762, _1526764, _1526766, _1526768, _1526770, _1526772, _1526774] : [class_Groups_Ocomm__monoid__mult(_1526760), c_Fun_Oinj__on(_1526762, _1526764, _1526766, _1526768), _1526770 = hAPP(c_Set_Oimage(_1526762, _1526764, _1526766), _1526768), 39713 ^ _778908 : [(39716 ^ _778908) ^ [] : [hAPP(_1526772, 39712 ^ [_1526760, _1526762, _1526764, _1526766, _1526768, _1526770, _1526772, _1526774]) = hAPP(hAPP(c_Fun_Ocomp(_1526764, _1526760, _1526762, _1526774), _1526766), 39712 ^ [_1526760, _1526762, _1526764, _1526766, _1526768, _1526770, _1526772, _1526774])], (39714 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526762), 39712 ^ [_1526760, _1526762, _1526764, _1526766, _1526768, _1526770, _1526772, _1526774]), _1526768)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526764, _1526760), _1526774), _1526770) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1526762, _1526760), _1526772), _1526768))], (50415 ^ _778908) ^ [_1791642, _1791644, _1791646] : [class_Orderings_Olinorder(_1791642), 50418 ^ _778908 : [(50425 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1791642, _1791646), -(c_List_Olinorder__class_Osorted(_1791642, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1791642, _1791642, c_COMBI(_1791642)), _1791644), _1791646)))], (50419 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1791642, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1791642, _1791642, c_COMBI(_1791642)), _1791644), _1791646)), -(c_List_Olinorder__class_Osorted(_1791642, _1791646))]]], (18275 ^ _778908) ^ [_1094795] : [class_Rings_Osemiring__1(_1094795), -(c_Int_Oiszero(_1094795, c_Groups_Ozero__class_Ozero(_1094795)))], (46311 ^ _778908) ^ [_1692930, _1692932, _1692934, _1692936, _1692938] : [hAPP(c_Map_Omap__of(_1692930, _1692932, _1692934), _1692936) = hAPP(c_Option_Ooption_OSome(_1692932), _1692938), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1692930, _1692932)), hAPP(hAPP(c_Product__Type_OPair(_1692930, _1692932), _1692936), _1692938)), hAPP(c_List_Oset(tc_prod(_1692930, _1692932)), _1692934))))], (51097 ^ _778908) ^ [_1807272, _1807274, _1807276, _1807278] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1807272), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1807272))), _1807274))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1807276), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1807272))), c_List_Otranspose(_1807272, _1807274)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1807278), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1807272))), hAPP(c_List_Ofilter(tc_List_Olist(_1807272), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1807272)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1807276)), c_Nat_Osize__class_Osize(tc_List_Olist(_1807272)))), _1807274)))), -(hAPP(hAPP(c_List_Onth(_1807272), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1807272)), c_List_Otranspose(_1807272, _1807274)), _1807276)), _1807278) = hAPP(hAPP(c_List_Onth(_1807272), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1807272)), _1807274), _1807278)), _1807276))], (38504 ^ _778908) ^ [_1501101, _1501103, _1501105] : [-(c_Fun_Oinj__on(_1501101, _1501103, _1501105, c_Orderings_Obot__class_Obot(tc_fun(_1501101, tc_HOL_Obool))))], (48399 ^ _778908) ^ [_1744831, _1744833, _1744835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744831), tc_List_Olist(_1744831))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744831), tc_List_Olist(_1744831)), _1744833), c_List_Olist_ONil(_1744831))), c_List_Olexord(_1744831, _1744835)))], (16997 ^ _778908) ^ [_1071678, _1071680, _1071682] : [class_Int_Onumber__ring(_1071678), class_Rings_Olinordered__idom(_1071678), 17004 ^ _778908 : [(17011 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071680), _1071682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071678), hAPP(c_Int_Onumber__class_Onumber__of(_1071678), _1071680)), hAPP(c_Int_Onumber__class_Onumber__of(_1071678), _1071682))))], (17005 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071678), hAPP(c_Int_Onumber__class_Onumber__of(_1071678), _1071680)), hAPP(c_Int_Onumber__class_Onumber__of(_1071678), _1071682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071680), _1071682)))]]], (17583 ^ _778908) ^ [_1082768, _1082770, _1082772, _1082774] : [class_Rings_Olinordered__semidom(_1082768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082768), _1082770), _1082772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082768), c_Groups_Ozero__class_Ozero(_1082768)), _1082770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082768), hAPP(hAPP(c_Power_Opower__class_Opower(_1082768), _1082770), _1082774)), hAPP(hAPP(c_Power_Opower__class_Opower(_1082768), _1082772), _1082774))))], (46537 ^ _778908) ^ [_1697851, _1697853, _1697855, _1697857, _1697859] : [hBOOL(hAPP(hAPP(c_member(_1697851), _1697853), hAPP(c_List_Oset(_1697851), _1697855))), -(hAPP(c_Map_Omap__of(_1697851, _1697857, hAPP(hAPP(c_List_Ozip(_1697851, _1697857), _1697855), hAPP(hAPP(c_List_Omap(_1697851, _1697857), _1697859), _1697855))), _1697853) = hAPP(c_Option_Ooption_OSome(_1697857), hAPP(_1697859, _1697853)))], (35060 ^ _778908) ^ [_1421935] : [-(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)), _1421935), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (14025 ^ _778908) ^ [_1016273, _1016275] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016273), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016275)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016273, _1016275)))], (3574 ^ _778908) ^ [_833847, _833849, _833851, _833853, _833855, _833857, _833859, _833861] : [-(c_Random__Sequence_Omap(_833861, _833857, _833853, _833849) = c_Random__Sequence_Omap(_833859, _833855, _833851, _833847)), _833861 = _833859, _833857 = _833855, _833853 = _833851, _833849 = _833847], (39212 ^ _778908) ^ [_1515355, _1515357, _1515359, _1515361, _1515363] : [-(c_Fun_Oinj__on(_1515355, _1515357, _1515359, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1515355, tc_HOL_Obool)), _1515361), _1515363))), c_Fun_Oinj__on(_1515355, _1515357, _1515359, _1515361), c_Fun_Oinj__on(_1515355, _1515357, _1515359, _1515363), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1515357, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1515355, _1515357, _1515359), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1515355, tc_HOL_Obool)), _1515361), _1515363))), hAPP(c_Set_Oimage(_1515355, _1515357, _1515359), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1515355, tc_HOL_Obool)), _1515363), _1515361))) = c_Orderings_Obot__class_Obot(tc_fun(_1515357, tc_HOL_Obool))], (20111 ^ _778908) ^ [_1125828] : [-(_1125828 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 20114 ^ _778908 : [(20121 ^ _778908) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1125828, 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, _1125828) = 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), _1125828), 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)))], (20115 ^ _778908) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1125828, 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, _1125828) = 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), _1125828), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (51461 ^ _778908) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (47104 ^ _778908) ^ [_1713811, _1713813, _1713815] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713811)), hAPP(hAPP(c_List_Olist_OCons(_1713811), _1713813), _1713815)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713811)), _1713815)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14021 ^ _778908) ^ [_1016180, _1016182, _1016184] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016180), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016182, _1016184)), _1016184) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016180), _1016182), _1016184))], (24301 ^ _778908) ^ [_1203651, _1203653, _1203655] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1203651, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1203651, tc_HOL_Obool)), _1203653), _1203655)), _1203655) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1203651, tc_HOL_Obool)), _1203653), _1203655))], (18427 ^ _778908) ^ [_1096980, _1096982] : [class_Int_Onumber__ring(_1096980), 18430 ^ _778908 : [(18437 ^ _778908) ^ [] : [c_Int_Oiszero(_1096980, hAPP(c_Int_Onumber__class_Onumber__of(_1096980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096982)))), -(c_Groups_Ozero__class_Ozero(_1096980) = hAPP(c_Int_Onumber__class_Onumber__of(_1096980), _1096982))], (18431 ^ _778908) ^ [] : [c_Groups_Ozero__class_Ozero(_1096980) = hAPP(c_Int_Onumber__class_Onumber__of(_1096980), _1096982), -(c_Int_Oiszero(_1096980, hAPP(c_Int_Onumber__class_Onumber__of(_1096980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096982)))))]]], (47872 ^ _778908) ^ [_1732937, _1732939, _1732941] : [-(hAPP(hAPP(c_List_Olist__update(_1732937, c_List_Olist_ONil(_1732937)), _1732939), _1732941) = c_List_Olist_ONil(_1732937))], (50718 ^ _778908) ^ [_1797310, _1797312, _1797314, _1797316] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1797310, tc_Nat_Onat), _1797310), c_Product__Type_Ofst(_1797310, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1797310, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1797310, 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(_1797310, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1797310, tc_Nat_Onat))), _1797312)), hAPP(hAPP(c_List_Ozip(_1797310, tc_Nat_Onat), _1797314), c_List_Oupt(_1797316, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1797316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797310)), _1797314)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1797310, tc_Nat_Onat), _1797310), c_Product__Type_Ofst(_1797310, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1797310, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1797310, 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(_1797310, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1797310, 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(_1797310, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1797310, tc_Nat_Onat))), _1797316))), _1797312)), hAPP(hAPP(c_List_Ozip(_1797310, tc_Nat_Onat), _1797314), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797310)), _1797314))))))], (12710 ^ _778908) ^ [_992566, _992568, _992570] : [class_Groups_Oordered__comm__monoid__add(_992566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992566), _992568), c_Groups_Ozero__class_Ozero(_992566))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992566), _992570), c_Groups_Ozero__class_Ozero(_992566))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_992566), _992568), _992570)), c_Groups_Ozero__class_Ozero(_992566))))], (35841 ^ _778908) ^ [_1440963, _1440965, _1440967, _1440969] : [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), _1440963), _1440965)), 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), _1440967), _1440969)), 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), _1440963), _1440969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440967), _1440965))))], (5092 ^ _778908) ^ [_857666, _857668, _857670, _857672, _857674, _857676] : [-(c_List_Osublist(_857676, _857672, _857668) = c_List_Osublist(_857674, _857670, _857666)), _857676 = _857674, _857672 = _857670, _857668 = _857666], (21115 ^ _778908) ^ [_1143607, _1143609, _1143611, _1143613] : [class_Fields_Olinordered__field__inverse__zero(_1143607), 21118 ^ _778908 : [(21119 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143607), _1143609), _1143611)), _1143613)), 21122 ^ _778908 : [(21129 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), c_Groups_Ozero__class_Ozero(_1143607)), _1143611))), 21132 ^ _778908 : [(21139 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), _1143611), c_Groups_Ozero__class_Ozero(_1143607)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), c_Groups_Ozero__class_Ozero(_1143607)), _1143613)))], (21133 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), _1143611), c_Groups_Ozero__class_Ozero(_1143607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143607), _1143613), _1143611)), _1143609)))]]], (21123 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), c_Groups_Ozero__class_Ozero(_1143607)), _1143611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), _1143609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143607), _1143613), _1143611))))]]], (21145 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143607), _1143609), _1143611)), _1143613))), 21148 ^ _778908 : [(21151 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), _1143609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143607), _1143613), _1143611)))], (21149 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), c_Groups_Ozero__class_Ozero(_1143607)), _1143611)))]], 21152 ^ _778908 : [(21155 ^ _778908) ^ [] : [21156 ^ _778908 : [(21159 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143607), _1143613), _1143611)), _1143609))], (21157 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), _1143611), c_Groups_Ozero__class_Ozero(_1143607))))]], 21160 ^ _778908 : [(21163 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), c_Groups_Ozero__class_Ozero(_1143607)), _1143613))], (21161 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), _1143611), c_Groups_Ozero__class_Ozero(_1143607)))]]], (21153 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143607), c_Groups_Ozero__class_Ozero(_1143607)), _1143611))]]]]], (10721 ^ _778908) ^ [_958788, _958790, _958792] : [class_Orderings_Opreorder(_958788), _958790 = _958792, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958788), _958790), _958792)))], (7174 ^ _778908) ^ [_898908, _898910, _898912, _898914] : [class_Groups_Ocancel__ab__semigroup__add(_898908), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898908), _898910), _898912) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898908), _898910), _898914), -(_898912 = _898914)], (19721 ^ _778908) ^ [_1118618, _1118620] : [class_Rings_Ocomm__semiring__1(_1118618), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118618), _1118620), _1118620) = hAPP(hAPP(c_Power_Opower__class_Opower(_1118618), _1118620), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (10890 ^ _778908) ^ [_961747, _961749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _961749)), 10897 ^ _778908 : [(10904 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _961747), _961749)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _961747)), hAPP(c_Int_Onat, _961749))))], (10898 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _961747)), hAPP(c_Int_Onat, _961749))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _961747), _961749)))]]], (11606 ^ _778908) ^ [_973057, _973059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973057), _973059)), -(_973059 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973057), 11609 ^ [_973057, _973059]))], (29982 ^ _778908) ^ [_1315725, _1315727, _1315729] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315725, tc_HOL_Obool)), _1315727), _1315729) = c_Orderings_Obot__class_Obot(tc_fun(_1315725, tc_HOL_Obool)), 29985 ^ _778908 : [(29988 ^ _778908) ^ [] : [-(_1315729 = c_Orderings_Obot__class_Obot(tc_fun(_1315725, tc_HOL_Obool)))], (29986 ^ _778908) ^ [] : [-(_1315727 = c_Orderings_Obot__class_Obot(tc_fun(_1315725, tc_HOL_Obool)))]]], (40582 ^ _778908) ^ [_1550045, _1550047, _1550049] : [-(hAPP(c_Finite__Set_Ofold1(_1550045, _1550047), hAPP(hAPP(c_Set_Oinsert(_1550045), _1550049), c_Orderings_Obot__class_Obot(tc_fun(_1550045, tc_HOL_Obool)))) = _1550049)], (47116 ^ _778908) ^ [_1714201, _1714203, _1714205, _1714207] : [-(c_Map_Omap__of(_1714201, _1714203, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1714201, _1714203)), _1714205), _1714207)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1714201, tc_Option_Ooption(_1714203)), c_Map_Omap__of(_1714201, _1714203, _1714207)), hAPP(c_Product__Type_Ofst(_1714201, _1714203), _1714205)), hAPP(c_Option_Ooption_OSome(_1714203), hAPP(c_Product__Type_Osnd(_1714201, _1714203), _1714205))))], (37016 ^ _778908) ^ [_1467556, _1467558, _1467560] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467556, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467556, tc_HOL_Obool)), _1467558), _1467560)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467556, tc_HOL_Obool)), _1467558), _1467560)) = _1467558)], (28971 ^ _778908) ^ [_1295158, _1295160, _1295162, _1295164, _1295166, _1295168] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295158, tc_fun(_1295160, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295162, tc_fun(_1295158, tc_HOL_Obool)), _1295164), _1295166)), _1295168) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295162, tc_fun(_1295160, tc_HOL_Obool)), _1295164), hAPP(hAPP(c_COMBC(_1295162, tc_fun(_1295158, tc_fun(_1295160, tc_HOL_Obool)), tc_fun(_1295160, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1295158, tc_HOL_Obool), tc_fun(tc_fun(_1295158, tc_fun(_1295160, tc_HOL_Obool)), tc_fun(_1295160, tc_HOL_Obool)), _1295162), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295158, tc_fun(_1295160, tc_HOL_Obool))), _1295166)), _1295168)))], (18983 ^ _778908) ^ [_1105949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1105949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1105949)))], (29088 ^ _778908) ^ [_1298062, _1298064] : [-(hAPP(c_Set_Oimage(_1298062, _1298062, c_COMBI(_1298062)), _1298064) = _1298064)], (28793 ^ _778908) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (43542 ^ _778908) ^ [_1626747, _1626749, _1626751, _1626753, _1626755] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626747, _1626749)), hAPP(hAPP(c_Product__Type_OPair(_1626747, _1626749), _1626751), _1626753)), _1626755)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626749, _1626747)), hAPP(hAPP(c_Product__Type_OPair(_1626749, _1626747), _1626753), _1626751)), hAPP(c_Relation_Oconverse(_1626747, _1626749), _1626755))))], (47132 ^ _778908) ^ [_1714705, _1714707, _1714709, _1714711, _1714713, _1714715] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714705), tc_List_Olist(_1714705))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714705), tc_List_Olist(_1714705)), hAPP(hAPP(c_List_Olist_OCons(_1714705), _1714707), _1714709)), hAPP(hAPP(c_List_Olist_OCons(_1714705), _1714711), _1714713))), c_List_Olex(_1714705, _1714715)))), 47133 ^ _778908 : [(47140 ^ _778908) ^ [] : [_1714707 = _1714711, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714705), tc_List_Olist(_1714705))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714705), tc_List_Olist(_1714705)), _1714709), _1714713)), c_List_Olex(_1714705, _1714715)))], (47134 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1714705, _1714705)), hAPP(hAPP(c_Product__Type_OPair(_1714705, _1714705), _1714707), _1714711)), _1714715)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714705)), _1714709) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714705)), _1714713)]]], (8796 ^ _778908) ^ [_925654, _925656, _925658, _925660] : [class_Orderings_Oord(_925654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925654), _925656), _925658)), _925658 = _925660, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925654), _925656), _925660)))], (7474 ^ _778908) ^ [_903860, _903862] : [c_Option_Ois__none(_903860, _903862), -(_903862 = c_Option_Ooption_ONone(_903860))], (40096 ^ _778908) ^ [_1536612, _1536614, _1536616, _1536618, _1536620, _1536622] : [class_Groups_Ocomm__monoid__add(_1536612), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536614, _1536612), hAPP(hAPP(c_COMBC(_1536614, tc_fun(_1536616, tc_HOL_Obool), _1536612), hAPP(hAPP(c_COMBB(tc_fun(_1536616, _1536612), tc_fun(tc_fun(_1536616, tc_HOL_Obool), _1536612), _1536614), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536616, _1536612)), _1536618)), _1536620)), _1536622) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1536614, _1536616), _1536612), hAPP(c_Product__Type_Oprod_Oprod__case(_1536614, _1536616, _1536612), _1536618)), hAPP(hAPP(c_Product__Type_OSigma(_1536614, _1536616), _1536622), hAPP(c_COMBK(tc_fun(_1536616, tc_HOL_Obool), _1536614), _1536620))))], (24285 ^ _778908) ^ [_1203318, _1203320, _1203322, _1203324, _1203326, _1203328] : [-(c_Product__Type_Oprod_Oprod__rec(_1203318, _1203320, _1203322, _1203324, hAPP(hAPP(c_Product__Type_OPair(_1203318, _1203320), _1203326), _1203328)) = hAPP(hAPP(_1203324, _1203326), _1203328))], (9234 ^ _778908) ^ [_933472, _933474, _933476] : [class_Rings_Osemiring__1(_933472), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_933472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _933474), _933476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933472), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_933472), _933474)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_933472), _933476)))], (24261 ^ _778908) ^ [_1202821, _1202823, _1202825, _1202827, _1202829] : [hBOOL(hAPP(hAPP(_1202821, _1202823), _1202825)), -(hBOOL(hAPP(hAPP(_1202821, hAPP(c_Product__Type_Osnd(_1202827, _1202829), hAPP(hAPP(c_Product__Type_OPair(_1202827, _1202829), _1202825), _1202823))), hAPP(c_Product__Type_Ofst(_1202827, _1202829), hAPP(hAPP(c_Product__Type_OPair(_1202827, _1202829), _1202825), _1202823)))))], (24131 ^ _778908) ^ [_1200371, _1200373, _1200375] : [_1200371 = _1200373, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200375, tc_HOL_Obool)), _1200373), _1200371)))], (40424 ^ _778908) ^ [_1546056, _1546058, _1546060, _1546062, _1546064, _1546066] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1546056, _1546058), _1546056, tc_prod(_1546060, _1546062), c_Product__Type_Ofst(_1546056, _1546058)), c_Product__Type_Omap__pair(_1546060, _1546056, _1546062, _1546058, _1546064, _1546066)) = hAPP(c_Fun_Ocomp(_1546060, _1546056, tc_prod(_1546060, _1546062), _1546064), c_Product__Type_Ofst(_1546060, _1546062)))], (5953 ^ _778908) ^ [_873960, _873962] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _873960, _873962, _873960))], (13710 ^ _778908) ^ [_1010038, _1010040, _1010042] : [class_Lattices_Oboolean__algebra(_1010038), 13713 ^ _778908 : [(13720 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010038), _1010042), _1010040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010038), hAPP(c_Groups_Ouminus__class_Ouminus(_1010038), _1010040)), hAPP(c_Groups_Ouminus__class_Ouminus(_1010038), _1010042))))], (13714 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010038), hAPP(c_Groups_Ouminus__class_Ouminus(_1010038), _1010040)), hAPP(c_Groups_Ouminus__class_Ouminus(_1010038), _1010042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010038), _1010042), _1010040)))]]], (48058 ^ _778908) ^ [_1737402, _1737404, _1737406, _1737408, _1737410] : [-(hAPP(hAPP(c_List_Olist__update(_1737402, hAPP(hAPP(c_List_Oappend(_1737402), _1737404), hAPP(hAPP(c_List_Olist_OCons(_1737402), _1737406), _1737408))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737402)), _1737404)), _1737410) = hAPP(hAPP(c_List_Oappend(_1737402), _1737404), hAPP(hAPP(c_List_Olist_OCons(_1737402), _1737410), _1737408)))], (27140 ^ _778908) ^ [_1258331, _1258333] : [27148 ^ _778908 : [(27151 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1258333, 27147 ^ [_1258331, _1258333])))], (27149 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27147 ^ [_1258331, _1258333]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258331))))]], 27141 ^ _778908 : [(27142 ^ _778908) ^ [_1258399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1258399), _1258331)), hBOOL(hAPP(_1258333, _1258399))]]], (47783 ^ _778908) ^ [_1730592, _1730594, _1730596, _1730598] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730592) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1730594), hAPP(hAPP(c_List_Olist_OCons(_1730594), _1730596), _1730598)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730592)) = _1730596)], (11859 ^ _778908) ^ [_977547, _977549, _977551] : [class_Groups_Oordered__comm__monoid__add(_977547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977547), c_Groups_Ozero__class_Ozero(_977547)), _977549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977547), c_Groups_Ozero__class_Ozero(_977547)), _977551)), 11870 ^ _778908 : [(11879 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977547), _977549), _977551) = c_Groups_Ozero__class_Ozero(_977547)), _977549 = c_Groups_Ozero__class_Ozero(_977547), _977551 = c_Groups_Ozero__class_Ozero(_977547)], (11871 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977547), _977549), _977551) = c_Groups_Ozero__class_Ozero(_977547), 11874 ^ _778908 : [(11877 ^ _778908) ^ [] : [-(_977551 = c_Groups_Ozero__class_Ozero(_977547))], (11875 ^ _778908) ^ [] : [-(_977549 = c_Groups_Ozero__class_Ozero(_977547))]]]]], (41434 ^ _778908) ^ [_1569131, _1569133] : [c_Relation_Orefl__on(_1569131, c_Orderings_Otop__class_Otop(tc_fun(_1569131, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1569131, _1569131)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569131, _1569131, tc_HOL_Obool), _1569133))), -(c_Predicate_Oreflp(_1569131, _1569133))], (6970 ^ _778908) ^ [_894253, _894255, _894257, _894259] : [c_Natural_Oevaln(_894253, _894255, _894257, _894259), -(c_Natural_Oevaln(_894253, _894255, hAPP(c_Nat_OSuc, _894257), _894259))], (21395 ^ _778908) ^ [_1148444, _1148446, _1148448, _1148450] : [class_Fields_Ofield__inverse__zero(_1148444), class_Int_Onumber(_1148444), 21402 ^ _778908 : [(21403 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1148444), _1148446) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148444), _1148448), _1148450), 21406 ^ _778908 : [(21413 ^ _778908) ^ [] : [_1148450 = c_Groups_Ozero__class_Ozero(_1148444), -(hAPP(c_Int_Onumber__class_Onumber__of(_1148444), _1148446) = c_Groups_Ozero__class_Ozero(_1148444))], (21407 ^ _778908) ^ [] : [-(_1148450 = c_Groups_Ozero__class_Ozero(_1148444)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148444), hAPP(c_Int_Onumber__class_Onumber__of(_1148444), _1148446)), _1148450) = _1148448)]]], (21419 ^ _778908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1148444), _1148446) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148444), _1148448), _1148450)), 21422 ^ _778908 : [(21425 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148444), hAPP(c_Int_Onumber__class_Onumber__of(_1148444), _1148446)), _1148450) = _1148448], (21423 ^ _778908) ^ [] : [_1148450 = c_Groups_Ozero__class_Ozero(_1148444)]], 21426 ^ _778908 : [(21429 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1148444), _1148446) = c_Groups_Ozero__class_Ozero(_1148444)], (21427 ^ _778908) ^ [] : [-(_1148450 = c_Groups_Ozero__class_Ozero(_1148444))]]]]], (32300 ^ _778908) ^ [_1366070, _1366072, _1366074, _1366076, _1366078, _1366080] : [hBOOL(hAPP(hAPP(_1366070, _1366072), _1366074)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1366076, tc_fun(_1366078, tc_HOL_Obool))), _1366080), _1366070), _1366072), _1366074)))], (50184 ^ _778908) ^ [_1787656, _1787658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1787656), _1787658)), -(c_List_Oupt(_1787658, _1787656) = c_List_Olist_ONil(tc_Nat_Onat))], (36882 ^ _778908) ^ [_1463846, _1463848, _1463850, _1463852] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463846, tc_HOL_Obool)), _1463848), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463846, tc_HOL_Obool)), _1463850), _1463852)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463846, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463846, tc_HOL_Obool)), _1463848), _1463850)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463846, tc_HOL_Obool)), _1463848), _1463852)))], (31840 ^ _778908) ^ [_1355877, _1355879] : [c_Nat__Transfer_Onat__set(_1355877), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1355879), _1355877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355879)))], (14708 ^ _778908) ^ [_1028522, _1028524, _1028526, _1028528] : [class_Divides_Osemiring__div(_1028522), -(_1028524 = c_Groups_Ozero__class_Ozero(_1028522)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028522), _1028524), _1028526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028522), _1028524), _1028528)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028522), _1028526), _1028528))], (45245 ^ _778908) ^ [_1667816, _1667818, _1667820] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1667816, tc_HOL_Obool)), _1667818), _1667820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667816, tc_HOL_Obool)), _1667818), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1667816, tc_HOL_Obool), _1667820))))], (36027 ^ _778908) ^ [_1445721, _1445723] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445721), c_Orderings_Obot__class_Obot(tc_fun(_1445721, tc_HOL_Obool))), _1445723) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1445721, tc_HOL_Obool), tc_HOL_Obool)))], (21647 ^ _778908) ^ [_1152822, _1152824, _1152826, _1152828] : [class_Fields_Olinordered__field(_1152822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152822), c_Groups_Ozero__class_Ozero(_1152822)), _1152824)), 21654 ^ _778908 : [(21661 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152822), _1152826), _1152824)), _1152828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152822), _1152826), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152822), _1152828), _1152824))))], (21655 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152822), _1152826), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152822), _1152828), _1152824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152822), _1152826), _1152824)), _1152828)))]]], (33251 ^ _778908) ^ [_1385574, _1385576, _1385578] : [class_Lattices_Olattice(_1385574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385574), _1385576)), -(_1385576 = c_Orderings_Obot__class_Obot(tc_fun(_1385574, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385574), _1385578)), -(_1385578 = c_Orderings_Obot__class_Obot(tc_fun(_1385574, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1385574, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385574, tc_HOL_Obool)), _1385576), _1385578)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1385574), c_Big__Operators_Olattice__class_OSup__fin(_1385574, _1385576)), c_Big__Operators_Olattice__class_OSup__fin(_1385574, _1385578)))], (16040 ^ _778908) ^ [_1052972, _1052974] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052972), _1052974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052972), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1052974)))], (28567 ^ _778908) ^ [_1286564, _1286566, _1286568, _1286570] : [class_Orderings_Olinorder(_1286564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286564), _1286566), _1286568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286564), _1286568), _1286570)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286564, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1286564, _1286566, _1286568)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1286564, _1286568, _1286570)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1286564, _1286566, _1286570))], (28559 ^ _778908) ^ [_1286375, _1286377, _1286379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286375, tc_HOL_Obool)), _1286377), _1286379)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286375, tc_HOL_Obool)), _1286377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286375, tc_HOL_Obool)), _1286379), _1286377)) = _1286379)], (39462 ^ _778908) ^ [_1521096, _1521098, _1521100, _1521102] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521096, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1521098, _1521096, _1521100), hAPP(c_Set_Ovimage(_1521098, _1521096, _1521100), _1521102))), _1521102)))], (39929 ^ _778908) ^ [_1532254, _1532256, _1532258, _1532260] : [c_Wellfounded_Omax__extp(_1532254, _1532256, _1532258, _1532260), 39932 ^ _778908 : [(39935 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532254), _1532260)))], (39937 ^ _778908) ^ [] : [_1532260 = c_Orderings_Obot__class_Obot(tc_fun(_1532254, tc_HOL_Obool))], (39939 ^ _778908) ^ [_1532470] : [hBOOL(hAPP(hAPP(c_member(_1532254), _1532470), _1532258)), 39943 ^ _778908 : [(39946 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1532256, _1532470), 39942 ^ [_1532254, _1532256, _1532258, _1532260, _1532470])))], (39944 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532254), 39942 ^ [_1532254, _1532256, _1532258, _1532260, _1532470]), _1532260)))]]], (39933 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532254), _1532258)))]]], (50057 ^ _778908) ^ [_1784799, _1784801] : [50059 ^ _778908 : [(50062 ^ _778908) ^ [] : [50058 ^ [_1784799, _1784801] = c_List_Olist_ONil(_1784799)], (50060 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1784799)), 50058 ^ [_1784799, _1784801]), hAPP(c_List_Oset(tc_List_Olist(_1784799)), _1784801))))]], -(c_List_Otranspose(_1784799, _1784801) = c_List_Olist_ONil(tc_List_Olist(_1784799)))], (24839 ^ _778908) ^ [_1214143, _1214145] : [hAPP(c_Code__Numeral_Onat__of, _1214143) = hAPP(c_Code__Numeral_Onat__of, _1214145), -(_1214143 = _1214145)], (7276 ^ _778908) ^ [_900645, _900647] : [class_Groups_Ocomm__monoid__add(_900645), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900645), c_Groups_Ozero__class_Ozero(_900645)), _900647) = _900647)], (17945 ^ _778908) ^ [_1089360, _1089362] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089360)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089360)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089362)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089360)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089362))))], (8200 ^ _778908) ^ [_916202, _916204, _916206, _916208] : [hAPP(c_Sum__Type_OInr(_916202, _916204), _916206) = hAPP(c_Sum__Type_OInr(_916202, _916204), _916208), -(_916206 = _916208)], (41213 ^ _778908) ^ [_1561920, _1561922, _1561924] : [hBOOL(hAPP(hAPP(c_member(_1561920), _1561922), hAPP(c_Set_OCollect(_1561920), _1561924))), -(hBOOL(hAPP(_1561924, _1561922)))], (6542 ^ _778908) ^ [_885126, _885128, _885130, _885132, _885134, _885136, _885138, _885140, _885142, _885144, _885146] : [-(c_Com_Ocom_Ocom__rec(_885126, _885128, _885130, _885132, _885134, _885136, _885138, _885140, _885142, c_Com_Ocom_OSemi(_885144, _885146)) = hAPP(hAPP(hAPP(hAPP(_885134, _885144), _885146), c_Com_Ocom_Ocom__rec(_885126, _885128, _885130, _885132, _885134, _885136, _885138, _885140, _885142, _885144)), c_Com_Ocom_Ocom__rec(_885126, _885128, _885130, _885132, _885134, _885136, _885138, _885140, _885142, _885146)))], (27610 ^ _778908) ^ [_1267999, _1268001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1267999), _1268001)), -(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)), _1267999)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268001))))], (28928 ^ _778908) ^ [_1293830, _1293832, _1293834, _1293836, _1293838] : [28930 ^ _778908 : [(28933 ^ _778908) ^ [] : [hBOOL(hAPP(_1293838, 28929 ^ [_1293830, _1293832, _1293834, _1293836, _1293838]))], (28931 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1293830), 28929 ^ [_1293830, _1293832, _1293834, _1293836, _1293838]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293832, tc_fun(_1293830, tc_HOL_Obool)), _1293834), _1293836))))]], 28934 ^ _778908 : [(28935 ^ _778908) ^ [_1294052] : [hBOOL(hAPP(hAPP(c_member(_1293832), _1294052), _1293834)), 28938 ^ _778908 : [(28939 ^ _778908) ^ [_1294149] : [hBOOL(hAPP(hAPP(c_member(_1293830), _1294149), hAPP(_1293836, _1294052))), -(hBOOL(hAPP(_1293838, _1294149)))]]]]], (26541 ^ _778908) ^ [_1246351, _1246353] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1246351), _1246353)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1246351), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1246353), _1246351)) = _1246353)], (28159 ^ _778908) ^ [_1278629, _1278631, _1278633, _1278635] : [class_Lattices_Osemilattice__sup(_1278629), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278629), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278629), _1278631), _1278633)), _1278635) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278629), _1278631), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278629), _1278633), _1278635)))], (18841 ^ _778908) ^ [_1103549, _1103551] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1103549)))), _1103551) = 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)))), _1103549)), _1103551))], (41303 ^ _778908) ^ [_1564649, _1564651, _1564653, _1564655, _1564657, _1564659] : [-(hAPP(c_Set_Oimage(_1564649, _1564651, hAPP(hAPP(c_COMBS(_1564649, _1564651, _1564651), hAPP(hAPP(c_COMBS(_1564649, _1564651, tc_fun(_1564651, _1564651)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1564651, tc_fun(_1564651, _1564651)), _1564649), c_If(_1564651)), _1564653)), _1564655)), _1564657)), _1564659) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564651, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1564649, _1564651, _1564655), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1564649, tc_HOL_Obool)), _1564659), hAPP(c_Set_OCollect(_1564649), _1564653)))), hAPP(c_Set_Oimage(_1564649, _1564651, _1564657), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1564649, tc_HOL_Obool)), _1564659), hAPP(c_Set_OCollect(_1564649), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564649), c_fNot), _1564653))))))], (1622 ^ _778908) ^ [_802057, _802059] : [-(class_Groups_Osemigroup__add(_802057)), _802059 = _802057, class_Groups_Osemigroup__add(_802059)], (44786 ^ _778908) ^ [_1655984, _1655986, _1655988, _1655990, _1655992] : [class_Complete__Lattice_Ocomplete__lattice(_1655984), class_Orderings_Olinorder(_1655984), 44793 ^ _778908 : [(44803 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655984), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655986, _1655984), _1655988), _1655990)), _1655992))), 44804 ^ _778908 : [(44805 ^ _778908) ^ [_1656332] : [hBOOL(hAPP(hAPP(c_member(_1655986), _1656332), _1655988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655984), hAPP(_1655990, _1656332)), _1655992))]]], (44794 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655984), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655986, _1655984), _1655988), _1655990)), _1655992)), 44798 ^ _778908 : [(44801 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655984), hAPP(_1655990, 44797 ^ [_1655984, _1655986, _1655988, _1655990, _1655992])), _1655992)))], (44799 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655986), 44797 ^ [_1655984, _1655986, _1655988, _1655990, _1655992]), _1655988)))]]]]], (23887 ^ _778908) ^ [_1195284, _1195286, _1195288] : [class_Orderings_Olinorder(_1195284), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195284), _1195286), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195284), _1195286), _1195288)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195284), _1195286), _1195288))], (30936 ^ _778908) ^ [_1333974, _1333976, _1333978, _1333980] : [hBOOL(hAPP(hAPP(c_member(_1333974), _1333976), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333974, tc_HOL_Obool)), _1333978), _1333980))), 30939 ^ _778908 : [(30942 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333974), _1333976), _1333980))], (30940 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333974), _1333976), _1333978)))]]], (16517 ^ _778908) ^ [_1062870, _1062872] : [-(_1062870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1062872, _1062870) = c_Nitpick_Onat__gcd(_1062870, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062872, _1062870)))], (51277 ^ _778908) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (14854 ^ _778908) ^ [_1030849, _1030851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030849)), 14857 ^ _778908 : [(14864 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030851)), -(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), _1030851), _1030849))))], (14858 ^ _778908) ^ [] : [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), _1030851), _1030849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030851)))]]], (9196 ^ _778908) ^ [_932847, _932849, _932851] : [class_Groups_Ogroup__add(_932847), 9199 ^ _778908 : [(9206 ^ _778908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_932847), _932851) = _932849, -(hAPP(c_Groups_Ouminus__class_Ouminus(_932847), _932849) = _932851)], (9200 ^ _778908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_932847), _932849) = _932851, -(hAPP(c_Groups_Ouminus__class_Ouminus(_932847), _932851) = _932849)]]], (42194 ^ _778908) ^ [_1593328, _1593330] : [-(hAPP(c_Relation_ORange(_1593328, _1593330), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1593328, _1593330), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1593330, tc_HOL_Obool)))], (29942 ^ _778908) ^ [_1314879, _1314881, _1314883] : [c_Orderings_Obot__class_Obot(tc_fun(_1314879, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1314879), _1314881), _1314883)], (13993 ^ _778908) ^ [_1015632, _1015634, _1015636, _1015638] : [class_Divides_Osemiring__div(_1015632), -(c_Divides_Odiv__class_Omod(_1015632, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015632), _1015634), _1015636), _1015638) = c_Divides_Odiv__class_Omod(_1015632, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015632), _1015634), c_Divides_Odiv__class_Omod(_1015632, _1015636, _1015638)), _1015638))], (24669 ^ _778908) ^ [_1210469] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210469) = _1210469)], (5965 ^ _778908) ^ [_874142, _874144, _874146, _874148] : [-(c_String_Ochar_Ochar__case(_874142, _874144, hAPP(hAPP(c_String_Ochar_OChar, _874146), _874148)) = hAPP(hAPP(_874144, _874146), _874148))], (49496 ^ _778908) ^ [_1772267, _1772269, _1772271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1772267, tc_HOL_Obool)), _1772269), _1772271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1772267), tc_HOL_Obool)), c_List_Olists(_1772267, _1772269)), c_List_Olists(_1772267, _1772271))))], (7811 ^ _778908) ^ [_909518, _909520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909518)), hAPP(c_Nat_OSuc, _909520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909518), _909520)))], (44631 ^ _778908) ^ [_1651830, _1651832, _1651834, _1651836, _1651838] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1651830, tc_fun(_1651832, tc_HOL_Obool)), _1651834), hAPP(hAPP(c_COMBB(tc_fun(_1651832, tc_HOL_Obool), tc_fun(_1651832, tc_HOL_Obool), _1651830), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1651832, tc_HOL_Obool)), _1651836)), _1651838)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1651832, tc_HOL_Obool)), _1651836), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651830, tc_fun(_1651832, tc_HOL_Obool)), _1651834), _1651838)))], (23847 ^ _778908) ^ [_1194529, _1194531, _1194533] : [class_Orderings_Olinorder(_1194529), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194529), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194529), _1194531), _1194533)), _1194531)))], (4348 ^ _778908) ^ [_846086, _846088, _846090, _846092] : [-(c_Relation_Oinv__image(_846092, _846088) = c_Relation_Oinv__image(_846090, _846086)), _846092 = _846090, _846088 = _846086], (18919 ^ _778908) ^ [_1104921] : [c_Int_OMin = c_Int_OBit1(_1104921), -(c_Int_OMin = _1104921)], (36666 ^ _778908) ^ [_1459580, _1459582, _1459584] : [class_Lattices_Olattice(_1459580), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459580), _1459582), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1459580), _1459582), _1459584)) = _1459582)], (41918 ^ _778908) ^ [] : [-(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)))))], (30266 ^ _778908) ^ [_1321153, _1321155, _1321157] : [class_Orderings_Oorder(_1321153), 30269 ^ _778908 : [(30276 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321153), _1321155), _1321157))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1321153, _1321155, _1321157) = c_Orderings_Obot__class_Obot(tc_fun(_1321153, tc_HOL_Obool)))], (30270 ^ _778908) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1321153, _1321155, _1321157) = c_Orderings_Obot__class_Obot(tc_fun(_1321153, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321153), _1321155), _1321157))]]], (43574 ^ _778908) ^ [_1627580, _1627582, _1627584] : [c_Equiv__Relations_Oequiv(_1627580, _1627582, _1627584), -(hAPP(hAPP(c_Relation_Orel__comp(_1627580, _1627580, _1627580), hAPP(c_Relation_Oconverse(_1627580, _1627580), _1627584)), _1627584) = _1627584)], (39524 ^ _778908) ^ [_1522590, _1522592, _1522594] : [-(hAPP(c_Set_Ovimage(_1522590, _1522592, _1522594), c_Orderings_Otop__class_Otop(tc_fun(_1522592, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522590, tc_HOL_Obool)))], (36996 ^ _778908) ^ [_1466972, _1466974, _1466976] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466972, tc_HOL_Obool)), _1466974), _1466976) = c_Orderings_Obot__class_Obot(tc_fun(_1466972, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1466972, tc_HOL_Obool)), _1466974), _1466976) = _1466974)], (50547 ^ _778908) ^ [_1793875, _1793877] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1793875), hAPP(c_List_Onth(_1793875), _1793877)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793875)), _1793877))) = _1793877)], (5931 ^ _778908) ^ [_873444, _873446, _873448, _873450, _873452, _873454, _873456, _873458, _873460] : [-(c_Com_Ocom_Ocom__case(_873444, _873446, _873448, _873450, _873452, _873454, _873456, _873458, _873460, c_Com_Ocom_OSKIP) = _873446)], (6500 ^ _778908) ^ [_884059, _884061] : [hBOOL(hAPP(c_Com_OWT, _884059)), hBOOL(hAPP(c_Com_OWT, _884061)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_884059, _884061))))], (19571 ^ _778908) ^ [_1115933] : [-(c_Int_Osucc(c_Int_OBit1(_1115933)) = c_Int_OBit0(c_Int_Osucc(_1115933)))], (51361 ^ _778908) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (22998 ^ _778908) ^ [_1178929, _1178931, _1178933, _1178935] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1178929, _1178931), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1178933), _1178935))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1178929, _1178931) = _1178935)], (40090 ^ _778908) ^ [_1536474, _1536476, _1536478] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1536474, _1536476), c_Orderings_Obot__class_Obot(tc_fun(_1536474, tc_HOL_Obool))), _1536478) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1536474, _1536476), tc_HOL_Obool)))], (51633 ^ _778908) ^ [_1813222, _1813224, _1813226, _1813228, _1813230, _1813232] : [-(hAPP(hAPP(hAPP(c_COMBC(_1813222, _1813224, _1813226), _1813228), _1813230), _1813232) = hAPP(hAPP(_1813228, _1813232), _1813230))], (33323 ^ _778908) ^ [_1386862] : [-(c_Hoare__Mirabelle_OMGT(_1386862) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _1386862), c_Natural_Oevalc(_1386862)))], (39036 ^ _778908) ^ [_1511551, _1511553, _1511555, _1511557, _1511559, _1511561] : [class_Groups_Ocomm__monoid__mult(_1511551), c_Fun_Oinj__on(_1511553, _1511555, _1511557, _1511559), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1511555, _1511551), _1511561), hAPP(c_Set_Oimage(_1511553, _1511555, _1511557), _1511559)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1511553, _1511551), hAPP(c_Fun_Ocomp(_1511555, _1511551, _1511553, _1511561), _1511557)), _1511559))], (42846 ^ _778908) ^ [_1609599, _1609601, _1609603, _1609605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1609599, tc_HOL_Obool), tc_fun(_1609599, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1609599, tc_HOL_Obool), tc_fun(_1609599, tc_HOL_Obool)), _1609601), _1609603)), c_Wellfounded_Omax__ext(_1609599, _1609605))), 42849 ^ _778908 : [(42852 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1609599), _1609603)))], (42854 ^ _778908) ^ [] : [_1609603 = c_Orderings_Obot__class_Obot(tc_fun(_1609599, tc_HOL_Obool))], (42856 ^ _778908) ^ [_1609893] : [hBOOL(hAPP(hAPP(c_member(_1609599), _1609893), _1609601)), 42860 ^ _778908 : [(42863 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609599, _1609599)), hAPP(hAPP(c_Product__Type_OPair(_1609599, _1609599), _1609893), 42859 ^ [_1609599, _1609601, _1609603, _1609605, _1609893])), _1609605)))], (42861 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609599), 42859 ^ [_1609599, _1609601, _1609603, _1609605, _1609893]), _1609603)))]]], (42850 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1609599), _1609601)))]]], (22283 ^ _778908) ^ [_1165033, _1165035] : [22284 ^ _778908 : [(22287 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1165035), _1165033))], (22285 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1165033), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1165033, _1165035) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (22029 ^ _778908) ^ [_1160252, _1160254] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160252), hAPP(c_Int_Onumber__class_Onumber__of(_1160252), c_Int_OMin)), _1160254) = hAPP(c_Groups_Ouminus__class_Ouminus(_1160252), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160252), c_Groups_Oone__class_Oone(_1160252)), _1160254))), class_Fields_Ofield__inverse__zero(_1160252), class_Int_Onumber__ring(_1160252)], (45368 ^ _778908) ^ [_1671061, _1671063, _1671065] : [class_Complete__Lattice_Ocomplete__lattice(_1671061), -(c_Complete__Lattice_OSup__class_OSup(_1671061, hAPP(hAPP(c_Set_Oinsert(_1671061), _1671063), _1671065)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1671061), _1671063), c_Complete__Lattice_OSup__class_OSup(_1671061, _1671065)))], (33147 ^ _778908) ^ [_1383557, _1383559] : [class_Rings_Oring__1(_1383557), hBOOL(hAPP(hAPP(c_member(_1383557), _1383559), c_Int_Oring__1__class_OInts(_1383557))), -(hBOOL(hAPP(hAPP(c_member(_1383557), hAPP(c_Groups_Ouminus__class_Ouminus(_1383557), _1383559)), c_Int_Oring__1__class_OInts(_1383557))))], (31337 ^ _778908) ^ [_1344166, _1344168, _1344170] : [_1344168 = _1344170, -(hBOOL(hAPP(hAPP(c_member(_1344166), _1344168), hAPP(c_fequal, _1344170))))], (15898 ^ _778908) ^ [_1050255, _1050257, _1050259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050255), _1050259)), _1050257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050257), _1050259))))], (36456 ^ _778908) ^ [_1454889, _1454891, _1454893, _1454895] : [class_Lattices_Osemilattice__inf(_1454889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454889), _1454891), _1454893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454889), _1454891), _1454895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454889), _1454891), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454889), _1454893), _1454895))))], (43824 ^ _778908) ^ [_1634167] : [-(c_Nat_Ofunpow(_1634167) = c_Nat_Ocompow(_1634167, _1634167))], (24987 ^ _778908) ^ [_1217119, _1217121, _1217123, _1217125, _1217127] : [_1217119 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1217121, _1217123, _1217125, _1217127), _1217119) = c_Lazy__Sequence_Ohit__bound(_1217123))], (17419 ^ _778908) ^ [_1079842, _1079844] : [17420 ^ _778908 : [(17423 ^ _778908) ^ [] : [_1079842 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17421 ^ _778908) ^ [] : [_1079844 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1079842), _1079844) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19783 ^ _778908) ^ [_1119698, _1119700] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1119698)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1119700))) = 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), _1119698), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119700))))], (43612 ^ _778908) ^ [_1628533, _1628535, _1628537, _1628539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628533, _1628533)), hAPP(hAPP(c_Product__Type_OPair(_1628533, _1628533), _1628535), _1628537)), c_Transitive__Closure_Otrancl(_1628533, hAPP(c_Relation_Oconverse(_1628533, _1628533), _1628539)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628533, _1628533)), hAPP(hAPP(c_Product__Type_OPair(_1628533, _1628533), _1628535), _1628537)), hAPP(c_Relation_Oconverse(_1628533, _1628533), c_Transitive__Closure_Otrancl(_1628533, _1628539)))))], (8170 ^ _778908) ^ [_915694, _915696, _915698, _915700] : [hAPP(c_Sum__Type_OInr(_915694, _915696), _915698) = hAPP(c_Sum__Type_OInl(_915696, _915694), _915700)], (47322 ^ _778908) ^ [_1720326, _1720328, _1720330, _1720332] : [class_Groups_Ocomm__monoid__add(_1720326), 47325 ^ _778908 : [(47332 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1720328), _1720330))), -(c_Nitpick_Osetsum_H(_1720328, _1720326, _1720332, _1720330) = c_Groups_Ozero__class_Ozero(_1720326))], (47326 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1720328), _1720330)), -(c_Nitpick_Osetsum_H(_1720328, _1720326, _1720332, _1720330) = hAPP(c_List_Omonoid__add__class_Olistsum(_1720326), hAPP(hAPP(c_List_Omap(_1720328, _1720326), _1720332), c_Hilbert__Choice_OEps(tc_List_Olist(_1720328), hAPP(hAPP(c_COMBS(tc_List_Olist(_1720328), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1720328)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720328), tc_fun(_1720328, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1720328, tc_HOL_Obool), tc_fun(tc_fun(_1720328, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1720328)), c_fequal), c_List_Oset(_1720328))), _1720330))), c_List_Odistinct(_1720328))))))]]], (40386 ^ _778908) ^ [_1545023, _1545025, _1545027, _1545029, _1545031] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545023, _1545025)), _1545027), hAPP(hAPP(c_Product__Type_OSigma(_1545023, _1545025), _1545029), _1545031))), 40390 ^ _778908 : [(40396 ^ _778908) ^ [] : [-(_1545027 = hAPP(hAPP(c_Product__Type_OPair(_1545023, _1545025), 40389 ^ [_1545023, _1545025, _1545027, _1545029, _1545031]), 40392 ^ [_1545023, _1545025, _1545027, _1545029, _1545031]))], (40394 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545025), 40392 ^ [_1545023, _1545025, _1545027, _1545029, _1545031]), hAPP(_1545031, 40389 ^ [_1545023, _1545025, _1545027, _1545029, _1545031]))))], (40391 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545023), 40389 ^ [_1545023, _1545025, _1545027, _1545029, _1545031]), _1545029)))]]], (50043 ^ _778908) ^ [_1784504] : [-(c_List_Otranspose(_1784504, c_List_Olist_ONil(tc_List_Olist(_1784504))) = c_List_Olist_ONil(tc_List_Olist(_1784504)))], (49380 ^ _778908) ^ [_1769334, _1769336, _1769338] : [class_Lattices_Olattice(_1769334), -(c_Big__Operators_Olattice__class_OInf__fin(_1769334, hAPP(c_List_Oset(_1769334), hAPP(hAPP(c_List_Olist_OCons(_1769334), _1769336), _1769338))) = hAPP(c_List_Ofoldl(_1769334, _1769334, c_Lattices_Osemilattice__inf__class_Oinf(_1769334), _1769336), _1769338))], (4686 ^ _778908) ^ [_851477, _851479] : [_851479 = _851477, -(c_List_Orotate1(_851479) = c_List_Orotate1(_851477))], (3894 ^ _778908) ^ [_838969, _838971, _838973, _838975] : [-(c_Lazy__Sequence_Osingle(_838975, _838971) = c_Lazy__Sequence_Osingle(_838973, _838969)), _838975 = _838973, _838971 = _838969], (46623 ^ _778908) ^ [_1700505, _1700507, _1700509, _1700511, _1700513, _1700515, _1700517, _1700519] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700505)), _1700507) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700509)), _1700511), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700505)), _1700513) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700509)), _1700511), -(hBOOL(hAPP(hAPP(c_member(_1700509), _1700515), hAPP(c_List_Oset(_1700509), _1700511)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1700509, tc_Option_Ooption(_1700505)), c_Map_Omap__of(_1700509, _1700505, hAPP(hAPP(c_List_Ozip(_1700509, _1700505), _1700511), _1700507))), _1700515), hAPP(c_Option_Ooption_OSome(_1700505), _1700517)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1700509, tc_Option_Ooption(_1700505)), c_Map_Omap__of(_1700509, _1700505, hAPP(hAPP(c_List_Ozip(_1700509, _1700505), _1700511), _1700513))), _1700515), hAPP(c_Option_Ooption_OSome(_1700505), _1700519)), -(c_Map_Omap__of(_1700509, _1700505, hAPP(hAPP(c_List_Ozip(_1700509, _1700505), _1700511), _1700507)) = c_Map_Omap__of(_1700509, _1700505, hAPP(hAPP(c_List_Ozip(_1700509, _1700505), _1700511), _1700513)))], (13368 ^ _778908) ^ [_1004153, _1004155] : [-(_1004153 = hAPP(c_Int_Onat, _1004155)), 13371 ^ _778908 : [(13374 ^ _778908) ^ [] : [_1004155 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1004153)], (13372 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004155)))]], 13375 ^ _778908 : [(13378 ^ _778908) ^ [] : [_1004153 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13376 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004155))]]], (16987 ^ _778908) ^ [_1071435, _1071437, _1071439, _1071441] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071435), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071435), _1071437), _1071439)), hAPP(c_Int_Onumber__class_Onumber__of(_1071435), _1071441)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071435), _1071437), hAPP(c_Int_Onumber__class_Onumber__of(_1071435), _1071441))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071435), _1071439), hAPP(c_Int_Onumber__class_Onumber__of(_1071435), _1071441)))), class_Int_Onumber(_1071435), class_Rings_Oring(_1071435)], (39789 ^ _778908) ^ [_1528876, _1528878, _1528880, _1528882, _1528884] : [-(_1528876 = c_Option_Ooption_ONone(_1528878)), -(c_Map_Odom(_1528880, _1528878, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1528880, tc_Option_Ooption(_1528878)), _1528882), _1528884), _1528876)) = hAPP(hAPP(c_Set_Oinsert(_1528880), _1528884), c_Map_Odom(_1528880, _1528878, _1528882)))], (50072 ^ _778908) ^ [_1785243, _1785245] : [-(c_Random_Opick(_1785243, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1785243), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1785243, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1785243, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1785243)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1785245)) = c_Random_Opick(_1785243, _1785245))], (19737 ^ _778908) ^ [_1118885] : [-(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)))), _1118885) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1118885)))], (10457 ^ _778908) ^ [_954597] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954597), _954597)))))], (17157 ^ _778908) ^ [_1074890, _1074892, _1074894, _1074896, _1074898] : [class_Groups_Oordered__ab__group__add__abs(_1074890), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074890), hAPP(c_Groups_Oabs__class_Oabs(_1074890), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074890), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074890), _1074892), _1074894)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074890), _1074896), _1074898)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074890), hAPP(c_Groups_Oabs__class_Oabs(_1074890), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074890), _1074892), _1074896))), hAPP(c_Groups_Oabs__class_Oabs(_1074890), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074890), _1074894), _1074898))))))], (28165 ^ _778908) ^ [_1278772, _1278774, _1278776, _1278778] : [class_Lattices_Olattice(_1278772), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278772), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278772), _1278774), _1278776)), _1278778) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278772), _1278774), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278772), _1278776), _1278778)))], (50341 ^ _778908) ^ [_1790509, _1790511, _1790513] : [class_Orderings_Olinorder(_1790509), c_List_Olinorder__class_Osorted(_1790509, _1790511), -(c_List_Olinorder__class_Osorted(_1790509, hAPP(hAPP(c_List_Odrop(_1790509), _1790513), _1790511)))], (8354 ^ _778908) ^ [_918858, _918860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918858), _918860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918858)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918860))))], (39900 ^ _778908) ^ [_1531582, _1531584, _1531586] : [39902 ^ _778908 : [(39905 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1531582), 39901 ^ [_1531582, _1531584, _1531586]), c_Wellfounded_Oacc(_1531582, _1531586)))], (39903 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531582, _1531582)), hAPP(hAPP(c_Product__Type_OPair(_1531582, _1531582), 39901 ^ [_1531582, _1531584, _1531586]), _1531584)), _1531586)))]], -(hBOOL(hAPP(hAPP(c_member(_1531582), _1531584), c_Wellfounded_Oacc(_1531582, _1531586))))], (41169 ^ _778908) ^ [_1561131, _1561133, _1561135] : [-(hAPP(hAPP(c_Set_Oinsert(_1561131), _1561133), hAPP(c_Set_OCollect(_1561131), _1561135)) = hAPP(c_Set_OCollect(_1561131), hAPP(hAPP(c_COMBS(_1561131, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1561131), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1561131), c_fNot), hAPP(hAPP(c_COMBC(_1561131, _1561131, tc_HOL_Obool), c_fequal), _1561133)))), _1561135)))], (22951 ^ _778908) ^ [_1178068, _1178070, _1178072] : [22953 ^ _778908 : [(22956 ^ _778908) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1178068, _1178070), 22952 ^ [_1178068, _1178070, _1178072]))], (22954 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1178070, 22952 ^ [_1178068, _1178070, _1178072]), _1178072)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1178068, _1178070), _1178072)))], (25627 ^ _778908) ^ [_1229149, _1229151] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229149), _1229151)), 25632 ^ _778908 : [(25635 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229151), _1229149))], (25633 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229149), _1229151)))]], -(_1229149 = _1229151)], (29321 ^ _778908) ^ [_1303006] : [c_Nat__Transfer_Onat__set(_1303006), 29324 ^ _778908 : [(29331 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1303006))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1303006)))], (29325 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1303006)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1303006))))]]], (36714 ^ _778908) ^ [_1460472, _1460474, _1460476, _1460478] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460472, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1460472), _1460474), _1460476)), hAPP(hAPP(c_Set_Oinsert(_1460472), _1460474), _1460478)) = hAPP(hAPP(c_Set_Oinsert(_1460472), _1460474), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460472, tc_HOL_Obool)), _1460476), _1460478)))], (12563 ^ _778908) ^ [_990149] : [12565 ^ _778908 : [(12568 ^ _778908) ^ [] : [hBOOL(hAPP(_990149, 12564 ^ [_990149]))], (12566 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12564 ^ [_990149])))]], 12569 ^ _778908 : [(12570 ^ _778908) ^ [_990276] : [-(hBOOL(hAPP(_990149, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _990276))))]]], (19129 ^ _778908) ^ [] : [-(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)))))], (41989 ^ _778908) ^ [_1588888] : [-(c_Wellfounded_Owf(tc_fun(_1588888, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1588888)))], (46214 ^ _778908) ^ [_1690616, _1690618, _1690620, _1690622, _1690624, _1690626] : [-(hAPP(hAPP(c_Option_Omap(_1690616, _1690618), _1690620), hAPP(hAPP(c_Option_Omap(_1690622, _1690616), _1690624), _1690626)) = hAPP(hAPP(c_Option_Omap(_1690622, _1690618), hAPP(c_Fun_Ocomp(_1690616, _1690618, _1690622, _1690620), _1690624)), _1690626))], (18675 ^ _778908) ^ [_1100779, _1100781] : [class_Int_Onumber__ring(_1100779), class_Rings_Olinordered__idom(_1100779), 18682 ^ _778908 : [(18689 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1100781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100779), c_Groups_Ozero__class_Ozero(_1100779)), hAPP(c_Int_Onumber__class_Onumber__of(_1100779), _1100781))))], (18683 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100779), c_Groups_Ozero__class_Ozero(_1100779)), hAPP(c_Int_Onumber__class_Onumber__of(_1100779), _1100781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1100781)))]]], (30036 ^ _778908) ^ [_1316758, _1316760, _1316762, _1316764] : [-(c_Sum__Type_OPlus(_1316758, _1316760, _1316762, _1316764) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1316758, _1316760), tc_HOL_Obool))), _1316762 = c_Orderings_Obot__class_Obot(tc_fun(_1316758, tc_HOL_Obool)), _1316764 = c_Orderings_Obot__class_Obot(tc_fun(_1316760, tc_HOL_Obool))], (23405 ^ _778908) ^ [_1187049] : [-(_1187049 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1187049), 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)))))], (28143 ^ _778908) ^ [_1278201, _1278203, _1278205, _1278207] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278201, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278201, tc_HOL_Obool)), _1278203), _1278205)), _1278207) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278201, tc_HOL_Obool)), _1278203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278201, tc_HOL_Obool)), _1278205), _1278207)))], (710 ^ _778908) ^ [_789847, _789849, _789851, _789853, _789855, _789857] : [-(c_Relation_Ototal__on(_789855, _789851, _789847)), c_Relation_Ototal__on(_789857, _789853, _789849), _789857 = _789855, _789853 = _789851, _789849 = _789847], (24883 ^ _778908) ^ [_1214900] : [-(hAPP(c_Code__Numeral_Onat__of, _1214900) = c_Code__Numeral_Onat__of__aux(_1214900, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1672 ^ _778908) ^ [_802682, _802684] : [-(class_Orderings_Opreorder(_802682)), _802684 = _802682, class_Orderings_Opreorder(_802684)], (30788 ^ _778908) ^ [_1331082, _1331084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331082), _1331084)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1331084, _1331082) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (12706 ^ _778908) ^ [] : [-(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)))], (14688 ^ _778908) ^ [_1028108, _1028110] : [14689 ^ _778908 : [(14690 ^ _778908) ^ [_1028157] : [_1028108 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028110), _1028157)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028108, _1028110) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5418 ^ _778908) ^ [_862647, _862649] : [_862649 = _862647, -(c_List_Oset(_862649) = c_List_Oset(_862647))], (48935 ^ _778908) ^ [_1759808, _1759810] : [hBOOL(hAPP(c_List_Odistinct(_1759808), hAPP(c_List_Orotate1(_1759808), _1759810))), -(hBOOL(hAPP(c_List_Odistinct(_1759808), _1759810)))], (23981 ^ _778908) ^ [_1197068, _1197070, _1197072, _1197074] : [class_Groups_Oordered__ab__group__add(_1197068), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1197068), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197068), _1197070), _1197072)), _1197074) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1197068), _1197070), _1197074)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1197068), _1197072), _1197074)))], (36742 ^ _778908) ^ [_1461034, _1461036, _1461038, _1461040] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461034, tc_HOL_Obool)), _1461036), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461034, tc_HOL_Obool)), _1461038), _1461040)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461034, tc_HOL_Obool)), _1461038), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461034, tc_HOL_Obool)), _1461036), _1461040)))], (44741 ^ _778908) ^ [_1654547, _1654549, _1654551, _1654553, _1654555, _1654557] : [hBOOL(hAPP(hAPP(c_member(_1654547), _1654549), _1654551)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654547, tc_fun(_1654553, tc_HOL_Obool)), _1654551), hAPP(hAPP(c_COMBB(tc_fun(_1654553, tc_HOL_Obool), tc_fun(_1654553, tc_HOL_Obool), _1654547), hAPP(c_Set_Oinsert(_1654553), _1654555)), _1654557)) = hAPP(hAPP(c_Set_Oinsert(_1654553), _1654555), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654547, tc_fun(_1654553, tc_HOL_Obool)), _1654551), _1654557)))], (11737 ^ _778908) ^ [_975451, _975453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975453)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _975451)), hAPP(c_Int_Onat, _975453)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _975451), _975453)))], (14390 ^ _778908) ^ [_1022613, _1022615, _1022617] : [hBOOL(hAPP(_1022613, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022615), _1022617))), 14393 ^ _778908 : [(14418 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022617), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14421 ^ _778908 : [(14422 ^ _778908) ^ [_1023277] : [-(hBOOL(hAPP(_1022613, _1023277))), 14423 ^ _778908 : [(14424 ^ _778908) ^ [_1023351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022617), _1023351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023351), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1022615 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022617), _1023277)), _1023351)]]]]], (14400 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022617)), 14403 ^ _778908 : [(14404 ^ _778908) ^ [_1022947] : [-(hBOOL(hAPP(_1022613, _1022947))), 14405 ^ _778908 : [(14406 ^ _778908) ^ [_1023018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023018), _1022617)), _1022615 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022617), _1022947)), _1023018)]]]]], (14394 ^ _778908) ^ [] : [_1022617 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1022613, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (18631 ^ _778908) ^ [] : [-(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))))], (18557 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (50070 ^ _778908) ^ [_1785180, _1785182] : [-(c_Random_Oselect__weight(_1785180, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1785180), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1785180, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1785180, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1785180)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1785182)) = c_Random_Oselect__weight(_1785180, _1785182))], (45005 ^ _778908) ^ [_1662727, _1662729, _1662731, _1662733, _1662735] : [class_Complete__Lattice_Ocomplete__lattice(_1662727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1662729), _1662731)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1662727), _1662733), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662729, _1662727), _1662731), _1662735)) = hAPP(hAPP(c_Finite__Set_Ofold(_1662729, _1662727, hAPP(hAPP(c_COMBB(_1662727, tc_fun(_1662727, _1662727), _1662729), c_Lattices_Osemilattice__inf__class_Oinf(_1662727)), _1662735)), _1662733), _1662731))], (13144 ^ _778908) ^ [_1000556] : [hAPP(c_Int_Onat, _1000556) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1000556), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35016 ^ _778908) ^ [_1421126] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1421126)), -(_1421126 = 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))), _1421126)), c_FunDef_Omax__strict)))], (38316 ^ _778908) ^ [_1496801, _1496803, _1496805, _1496807, _1496809, _1496811] : [c_Finite__Set_Ofolding__idem(_1496801, _1496803, _1496805, _1496807), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496801), _1496809)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496801), _1496811)), -(hAPP(_1496807, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496801, tc_HOL_Obool)), _1496809), _1496811)) = hAPP(c_Fun_Ocomp(_1496803, _1496803, _1496803, hAPP(_1496807, _1496809)), hAPP(_1496807, _1496811)))], (7124 ^ _778908) ^ [_898023, _898025, _898027] : [-(c_Option_Ooption_Ooption__size(_898023, _898025, hAPP(c_Option_Ooption_OSome(_898023), _898027)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_898025, _898027)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47910 ^ _778908) ^ [_1733832, _1733834, _1733836, _1733838, _1733840] : [-(hAPP(hAPP(c_List_Olist__update(_1733832, hAPP(hAPP(c_List_Olist_OCons(_1733832), _1733834), _1733836)), _1733838), _1733840) = c_Nat_Onat_Onat__case(tc_List_Olist(_1733832), hAPP(hAPP(c_List_Olist_OCons(_1733832), _1733840), _1733836), hAPP(hAPP(c_COMBB(tc_List_Olist(_1733832), tc_List_Olist(_1733832), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1733832), _1733834)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1733832, tc_List_Olist(_1733832)), c_List_Olist__update(_1733832, _1733836)), _1733840)), _1733838))], (8580 ^ _778908) ^ [_922788] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922788), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _922788)], (42155 ^ _778908) ^ [_1592499, _1592501, _1592503] : [c_Wellfounded_Owf(_1592499, _1592501), -(c_Wellfounded_Owf(tc_List_Olist(_1592499), hAPP(c_List_Olexn(_1592499, _1592501), _1592503)))], (16058 ^ _778908) ^ [_1053336, _1053338] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053336), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053338)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053336), _1053338)))], (28631 ^ _778908) ^ [_1287763, _1287765, _1287767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1287763), _1287765)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1287763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287765), _1287767)) = 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, _1287763), _1287765)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1287765), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287765), _1287767))))], (18767 ^ _778908) ^ [_1102214, _1102216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102214), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102214)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102216)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102216))], (16869 ^ _778908) ^ [_1069121, _1069123, _1069125] : [class_Groups_Oordered__ab__group__add__abs(_1069121), 16872 ^ _778908 : [(16881 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069121), hAPP(c_Groups_Oabs__class_Oabs(_1069121), _1069123)), _1069125))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069121), _1069123), _1069125)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069121), hAPP(c_Groups_Ouminus__class_Ouminus(_1069121), _1069123)), _1069125))], (16873 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069121), hAPP(c_Groups_Oabs__class_Oabs(_1069121), _1069123)), _1069125)), 16876 ^ _778908 : [(16879 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069121), hAPP(c_Groups_Ouminus__class_Ouminus(_1069121), _1069123)), _1069125)))], (16877 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069121), _1069123), _1069125)))]]]]], (6895 ^ _778908) ^ [_892627] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(_892627)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36892 ^ _778908) ^ [_1464238, _1464240, _1464242, _1464244, _1464246] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464238, tc_fun(_1464240, tc_HOL_Obool)), _1464242), hAPP(hAPP(c_COMBB(tc_fun(_1464240, tc_HOL_Obool), tc_fun(_1464240, tc_HOL_Obool), _1464238), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464240, tc_HOL_Obool)), _1464244)), _1464246)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464240, tc_HOL_Obool)), _1464244), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464238, tc_fun(_1464240, tc_HOL_Obool)), _1464242), _1464246)))], (16511 ^ _778908) ^ [_1062793, _1062795] : [_1062793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1062795, _1062793) = _1062795)], (11464 ^ _778908) ^ [_970786, _970788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970788)), _970786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970786), _970788))], (31578 ^ _778908) ^ [_1348897, _1348899, _1348901, _1348903, _1348905] : [_1348897 = hAPP(_1348899, _1348901), -(hBOOL(hAPP(hAPP(c_member(_1348903), _1348897), hAPP(c_Set_Oimage(_1348905, _1348903, _1348899), c_Orderings_Otop__class_Otop(tc_fun(_1348905, tc_HOL_Obool))))))], (20693 ^ _778908) ^ [_1136104, _1136106, _1136108, _1136110] : [class_Rings_Odivision__ring(_1136104), -(_1136106 = c_Groups_Ozero__class_Ozero(_1136104)), _1136108 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136104), _1136110), _1136106), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136104), _1136108), _1136106) = _1136110)], (46108 ^ _778908) ^ [_1687939, _1687941, _1687943] : [c_Fun_Oinj__on(tc_List_Olist(_1687939), tc_List_Olist(_1687941), hAPP(c_List_Omap(_1687939, _1687941), _1687943), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1687939), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1687939, _1687941, _1687943, c_Orderings_Otop__class_Otop(tc_fun(_1687939, tc_HOL_Obool))))], (9342 ^ _778908) ^ [_935088, _935090] : [class_Groups_Olinordered__ab__group__add(_935088), 9345 ^ _778908 : [(9352 ^ _778908) ^ [] : [_935090 = c_Groups_Ozero__class_Ozero(_935088), -(hAPP(c_Groups_Ouminus__class_Ouminus(_935088), _935090) = _935090)], (9346 ^ _778908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_935088), _935090) = _935090, -(_935090 = c_Groups_Ozero__class_Ozero(_935088))]]], (1856 ^ _778908) ^ [_805000, _805002, _805004, _805006, _805008, _805010, _805012, _805014] : [-(c_Natural_Oevaln(_805012, _805008, _805004, _805000)), c_Natural_Oevaln(_805014, _805010, _805006, _805002), _805014 = _805012, _805010 = _805008, _805006 = _805004, _805002 = _805000], (24713 ^ _778908) ^ [_1211356, _1211358, _1211360, _1211362] : [class_Orderings_Olinorder(_1211356), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211356), _1211358), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211356), _1211360), _1211362)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211356), _1211360), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211356), _1211358), _1211362)))], (39406 ^ _778908) ^ [_1519818, _1519820, _1519822, _1519824, _1519826, _1519828, _1519830] : [c_Big__Operators_Ocomm__monoid__big(_1519818, _1519820, _1519822, _1519824, _1519826), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1519820), _1519828))), -(hAPP(hAPP(_1519826, _1519830), _1519828) = _1519824)], (47956 ^ _778908) ^ [_1734818, _1734820, _1734822, _1734824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734818), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734820)), _1734822))), -(hAPP(hAPP(c_List_Onth(_1734820), hAPP(hAPP(c_List_Olist__update(_1734820, _1734822), _1734818), _1734824)), _1734818) = _1734824)], (48247 ^ _778908) ^ [_1741761, _1741763, _1741765, _1741767] : [-(c_Map_Omap__of(_1741761, _1741763, hAPP(hAPP(c_List_Oappend(tc_prod(_1741761, _1741763)), _1741765), _1741767)) = c_Map_Omap__add(_1741761, _1741763, c_Map_Omap__of(_1741761, _1741763, _1741767), c_Map_Omap__of(_1741761, _1741763, _1741765)))], (19455 ^ _778908) ^ [_1113961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1113961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1113961))))], (29825 ^ _778908) ^ [_1312617, _1312619, _1312621] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312617), _1312619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312617, tc_HOL_Obool)), _1312621), _1312619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312617), _1312619)), hAPP(c_Finite__Set_Ocard(_1312617), _1312621))), -(_1312621 = _1312619)], (37794 ^ _778908) ^ [_1484522, _1484524, _1484526, _1484528, _1484530, _1484532, _1484534, _1484536, _1484538] : [c_Equiv__Relations_Oequiv(_1484522, _1484524, _1484526), c_Equiv__Relations_Oequiv(_1484528, _1484530, _1484532), c_Equiv__Relations_Ocongruent2(_1484522, _1484528, tc_fun(_1484534, tc_HOL_Obool), _1484526, _1484532, _1484536), hBOOL(hAPP(hAPP(c_member(_1484528), _1484538), _1484530)), -(c_Equiv__Relations_Ocongruent(_1484522, tc_fun(_1484534, tc_HOL_Obool), _1484526, hAPP(hAPP(c_COMBB(tc_fun(_1484528, tc_fun(_1484534, tc_HOL_Obool)), tc_fun(_1484534, tc_HOL_Obool), _1484522), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484528, tc_fun(_1484534, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1484528, _1484528, _1484532), hAPP(hAPP(c_Set_Oinsert(_1484528), _1484538), c_Orderings_Obot__class_Obot(tc_fun(_1484528, tc_HOL_Obool)))))), _1484536)))], (35070 ^ _778908) ^ [] : [-(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)))))], (48540 ^ _778908) ^ [_1748643, _1748645, _1748647, _1748649] : [-(hAPP(hAPP(c_List_Otake(_1748643), hAPP(c_Nat_OSuc, _1748645)), hAPP(hAPP(c_List_Olist_OCons(_1748643), _1748647), _1748649)) = hAPP(hAPP(c_List_Olist_OCons(_1748643), _1748647), hAPP(hAPP(c_List_Otake(_1748643), _1748645), _1748649)))], (19285 ^ _778908) ^ [_1111065, _1111067] : [c_Int_OBit0(_1111065) = c_Int_OBit0(_1111067), -(_1111065 = _1111067)], (9518 ^ _778908) ^ [_937947] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _937947)) = _937947)], (24221 ^ _778908) ^ [_1202069, _1202071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202069), 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)), _1202071)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202069), _1202071) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1202069, _1202071)))], (11516 ^ _778908) ^ [_971632, _971634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _971632)), _971634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971632), _971634)))], (49944 ^ _778908) ^ [_1781702, _1781704, _1781706, _1781708] : [-(hBOOL(hAPP(_1781702, _1781704))), -(c_List_Oremove1(_1781706, _1781704, hAPP(c_List_Ofilter(_1781706, _1781702), _1781708)) = hAPP(c_List_Ofilter(_1781706, _1781702), _1781708))], (48723 ^ _778908) ^ [_1753652, _1753654, _1753656] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753652), tc_List_Olist(_1753652))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753652), tc_List_Olist(_1753652)), _1753654), c_List_Olist_ONil(_1753652))), c_List_Olistrel1(_1753652, _1753656)))], (45324 ^ _778908) ^ [_1670174, _1670176, _1670178] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670174, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1670174, tc_HOL_Obool), tc_HOL_Obool)), _1670176), _1670178)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1670174, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670174, tc_HOL_Obool), _1670176)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670174, tc_HOL_Obool), _1670178)))], (1932 ^ _778908) ^ [_806900, _806902, _806904, _806906, _806908, _806910, _806912, _806914, _806916, _806918, _806920, _806922, _806924, _806926, _806928, _806930, _806932, _806934, _806936, _806938] : [-(c_Com_Ocom_Ocom__rec(_806938, _806934, _806930, _806926, _806922, _806918, _806914, _806910, _806906, _806902) = c_Com_Ocom_Ocom__rec(_806936, _806932, _806928, _806924, _806920, _806916, _806912, _806908, _806904, _806900)), _806938 = _806936, _806934 = _806932, _806930 = _806928, _806926 = _806924, _806922 = _806920, _806918 = _806916, _806914 = _806912, _806910 = _806908, _806906 = _806904, _806902 = _806900], (22153 ^ _778908) ^ [_1162634, _1162636, _1162638, _1162640] : [class_Fields_Olinordered__field__inverse__zero(_1162634), class_Int_Onumber(_1162634), 22160 ^ _778908 : [(22161 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162634), _1162638), _1162640))), 22164 ^ _778908 : [(22171 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), c_Groups_Ozero__class_Ozero(_1162634)), _1162640))), 22174 ^ _778908 : [(22181 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), _1162640), c_Groups_Ozero__class_Ozero(_1162634)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), c_Groups_Ozero__class_Ozero(_1162634))))], (22175 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), _1162640), c_Groups_Ozero__class_Ozero(_1162634))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), _1162638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), _1162640))))]]], (22165 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), c_Groups_Ozero__class_Ozero(_1162634)), _1162640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), _1162640)), _1162638)))]]], (22187 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162634), _1162638), _1162640)))), 22190 ^ _778908 : [(22193 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), _1162640)), _1162638))], (22191 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), c_Groups_Ozero__class_Ozero(_1162634)), _1162640)))]], 22194 ^ _778908 : [(22197 ^ _778908) ^ [] : [22198 ^ _778908 : [(22201 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), _1162638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), _1162640)))], (22199 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), _1162640), c_Groups_Ozero__class_Ozero(_1162634))))]], 22202 ^ _778908 : [(22205 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162634), hAPP(c_Int_Onumber__class_Onumber__of(_1162634), _1162636)), c_Groups_Ozero__class_Ozero(_1162634)))], (22203 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), _1162640), c_Groups_Ozero__class_Ozero(_1162634)))]]], (22195 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162634), c_Groups_Ozero__class_Ozero(_1162634)), _1162640))]]]]], (42615 ^ _778908) ^ [_1604344, _1604346] : [42617 ^ _778908 : [(42620 ^ _778908) ^ [] : [hBOOL(hAPP(_1604344, hAPP(c_Int_OAbs__Integ, 42616 ^ [_1604344, _1604346])))], (42618 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42616 ^ [_1604344, _1604346]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1604344, _1604346)))], (51385 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (26851 ^ _778908) ^ [_1252408, _1252410] : [-(_1252408 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252410), _1252408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1252410)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1252408))))], (41947 ^ _778908) ^ [_1588094, _1588096, _1588098, _1588100] : [c_Wellfounded_Owf(_1588094, _1588096), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588094, _1588094)), hAPP(hAPP(c_Product__Type_OPair(_1588094, _1588094), _1588098), _1588100)), _1588096)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588094, _1588094)), hAPP(hAPP(c_Product__Type_OPair(_1588094, _1588094), _1588100), _1588098)), _1588096))], (41227 ^ _778908) ^ [_1562177, _1562179] : [-(hAPP(c_Set_OCollect(_1562177), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1562177), c_fNot), _1562179)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1562177, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1562177), _1562179)))], (24207 ^ _778908) ^ [_1201782, _1201784, _1201786, _1201788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201782, tc_HOL_Obool)), _1201784), _1201786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201782, tc_HOL_Obool)), _1201786), _1201788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201782, tc_HOL_Obool)), _1201784), _1201788)))], (5907 ^ _778908) ^ [_873074, _873076, _873078, _873080, _873082, _873084] : [c_Com_Ocom_OCall(_873074, _873076, _873078) = c_Com_Ocom_OCall(_873080, _873082, _873084), 5910 ^ _778908 : [(5915 ^ _778908) ^ [] : [-(_873078 = _873084)], (5913 ^ _778908) ^ [] : [-(_873076 = _873082)], (5911 ^ _778908) ^ [] : [-(_873074 = _873080)]]], (46561 ^ _778908) ^ [_1698343, _1698345] : [-(hAPP(hAPP(c_List_Ozip(_1698343, _1698343), _1698345), _1698345) = hAPP(hAPP(c_List_Omap(_1698343, tc_prod(_1698343, _1698343)), hAPP(hAPP(c_COMBS(_1698343, _1698343, tc_prod(_1698343, _1698343)), c_Product__Type_OPair(_1698343, _1698343)), c_COMBI(_1698343))), _1698345))], (42237 ^ _778908) ^ [_1594905, _1594907, _1594909, _1594911] : [hBOOL(hAPP(hAPP(c_member(_1594905), _1594907), hAPP(c_Relation_ORange(_1594909, _1594905), _1594911))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594909, _1594905)), hAPP(hAPP(c_Product__Type_OPair(_1594909, _1594905), 42240 ^ [_1594905, _1594907, _1594909, _1594911]), _1594907)), _1594911)))], (26945 ^ _778908) ^ [_1254283, _1254285, _1254287, _1254289, _1254291] : [class_Orderings_Oorder(_1254283), 26948 ^ _778908 : [(26961 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254283, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1254283, _1254285, _1254287)), c_SetInterval_Oord__class_OatLeastAtMost(_1254283, _1254289, _1254291)))), 26962 ^ _778908 : [(26965 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254283), _1254289), _1254285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254283), _1254287), _1254291))], (26963 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254283), _1254285), _1254287)))]]], (26949 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254283, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1254283, _1254285, _1254287)), c_SetInterval_Oord__class_OatLeastAtMost(_1254283, _1254289, _1254291))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254283), _1254285), _1254287)), 26956 ^ _778908 : [(26959 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254283), _1254287), _1254291)))], (26957 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254283), _1254289), _1254285)))]]]]], (15634 ^ _778908) ^ [_1045093, _1045095, _1045097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045093), _1045095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045093), _1045097)), 15641 ^ _778908 : [(15648 ^ _778908) ^ [] : [_1045095 = _1045097, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045095), _1045093) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045097), _1045093))], (15642 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045095), _1045093) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045097), _1045093), -(_1045095 = _1045097)]]], (24289 ^ _778908) ^ [_1203431, _1203433, _1203435] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203431, tc_HOL_Obool)), _1203433) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203431, tc_HOL_Obool)), _1203435), -(_1203433 = _1203435)], (13338 ^ _778908) ^ [_1003722, _1003724] : [-(hAPP(c_Int_Onat, _1003722) = _1003724), 13341 ^ _778908 : [(13344 ^ _778908) ^ [] : [_1003722 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1003724)], (13342 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003722)))]], 13345 ^ _778908 : [(13348 ^ _778908) ^ [] : [_1003724 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13346 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003722))]]], (12257 ^ _778908) ^ [_984828] : [class_Rings_Olinordered__semidom(_984828), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984828), c_Groups_Ozero__class_Ozero(_984828)), c_Groups_Oone__class_Oone(_984828))))], (36632 ^ _778908) ^ [_1458667, _1458669, _1458671, _1458673] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458667, tc_HOL_Obool)), _1458669), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458667, tc_HOL_Obool)), _1458671), _1458673)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458667, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458667, tc_HOL_Obool)), _1458669), _1458671)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458667, tc_HOL_Obool)), _1458669), _1458673)))], (11917 ^ _778908) ^ [_978524, _978526, _978528] : [class_Groups_Oordered__comm__monoid__add(_978524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978524), _978526), c_Groups_Ozero__class_Ozero(_978524))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978524), _978528), c_Groups_Ozero__class_Ozero(_978524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978524), _978526), _978528)), c_Groups_Ozero__class_Ozero(_978524))))], (1392 ^ _778908) ^ [_799182, _799184] : [-(class_Groups_Ouminus(_799182)), _799184 = _799182, class_Groups_Ouminus(_799184)], (20485 ^ _778908) ^ [_1132678, _1132680, _1132682] : [class_Fields_Olinordered__field(_1132678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132678), c_Groups_Ozero__class_Ozero(_1132678)), _1132680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132678), c_Groups_Ozero__class_Ozero(_1132678)), _1132682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132678), c_Groups_Ozero__class_Ozero(_1132678)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132678), _1132680), _1132682))))], (47403 ^ _778908) ^ [_1721922, _1721924, _1721926] : [-(hAPP(hAPP(c_List_Omap(_1721922, _1721924), _1721926), c_List_Olist_ONil(_1721922)) = c_List_Olist_ONil(_1721924))], (15892 ^ _778908) ^ [_1050136, _1050138, _1050140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050136), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050138), _1050140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050136), _1050140)), _1050138)))], (36366 ^ _778908) ^ [_1453359, _1453361, _1453363] : [class_Lattices_Olattice(_1453359), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453359), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453359), _1453361), _1453363)), _1453363)))], (26495 ^ _778908) ^ [_1245579, _1245581, _1245583] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245579), _1245581)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245579), _1245583)))))], (25049 ^ _778908) ^ [_1218527, _1218529, _1218531, _1218533] : [-(c_New__Random__Sequence_Opos__empty(_1218527, _1218529, _1218531, _1218533) = c_New__DSequence_Opos__empty(_1218527))], (19659 ^ _778908) ^ [_1117535, _1117537] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1117535)), c_Int_OBit1(_1117537)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1117535)), _1117537)))], (33926 ^ _778908) ^ [_1398820, _1398822, _1398824] : [class_Orderings_Olinorder(_1398820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398820), _1398822)), hBOOL(hAPP(hAPP(c_member(_1398820), _1398824), _1398822)), 33937 ^ _778908 : [(33944 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398820, tc_HOL_Obool)), _1398822), hAPP(hAPP(c_Set_Oinsert(_1398820), _1398824), c_Orderings_Obot__class_Obot(tc_fun(_1398820, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1398820, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1398820, c_Orderings_Oord__class_Omin(_1398820), _1398822) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1398820), _1398824), c_Big__Operators_Olattice_OInf__fin(_1398820, c_Orderings_Oord__class_Omin(_1398820), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398820, tc_HOL_Obool)), _1398822), hAPP(hAPP(c_Set_Oinsert(_1398820), _1398824), c_Orderings_Obot__class_Obot(tc_fun(_1398820, tc_HOL_Obool)))))))], (33938 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398820, tc_HOL_Obool)), _1398822), hAPP(hAPP(c_Set_Oinsert(_1398820), _1398824), c_Orderings_Obot__class_Obot(tc_fun(_1398820, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1398820, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1398820, c_Orderings_Oord__class_Omin(_1398820), _1398822) = _1398824)]]], (23937 ^ _778908) ^ [_1196339, _1196341, _1196343, _1196345] : [class_Orderings_Olinorder(_1196339), 23940 ^ _778908 : [(23949 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196339), _1196341), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196339), _1196343), _1196345)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196339), _1196341), _1196343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196339), _1196341), _1196345))], (23941 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196339), _1196341), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196339), _1196343), _1196345))), 23944 ^ _778908 : [(23947 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196339), _1196341), _1196345)))], (23945 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196339), _1196341), _1196343)))]]]]], (46189 ^ _778908) ^ [_1689934, _1689936] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1689934), hAPP(c_List_Oset(_1689934), _1689936))))], (30852 ^ _778908) ^ [_1332374, _1332376, _1332378, _1332380] : [_1332374 = _1332376, 30857 ^ _778908 : [(30860 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332378), _1332380), _1332376)))], (30858 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332378), _1332380), _1332374)))]], 30861 ^ _778908 : [(30864 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332378), _1332380), _1332376))], (30862 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332378), _1332380), _1332374))]]], (32809 ^ _778908) ^ [_1376441, _1376443] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1376441, _1376443), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376441), _1376443)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376443), _1376441)))], (43566 ^ _778908) ^ [_1627391, _1627393, _1627395] : [c_Relation_Orefl__on(_1627391, _1627393, _1627395), -(c_Relation_Orefl__on(_1627391, _1627393, hAPP(c_Relation_Oconverse(_1627391, _1627391), _1627395)))], (40428 ^ _778908) ^ [_1546198, _1546200, _1546202, _1546204, _1546206, _1546208, _1546210, _1546212, _1546214, _1546216] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1546198, _1546200), tc_prod(_1546202, _1546204), tc_prod(_1546206, _1546208), c_Product__Type_Omap__pair(_1546198, _1546202, _1546200, _1546204, _1546210, _1546212)), c_Product__Type_Omap__pair(_1546206, _1546198, _1546208, _1546200, _1546214, _1546216)) = c_Product__Type_Omap__pair(_1546206, _1546202, _1546208, _1546204, hAPP(c_Fun_Ocomp(_1546198, _1546202, _1546206, _1546210), _1546214), hAPP(c_Fun_Ocomp(_1546200, _1546204, _1546208, _1546212), _1546216)))], (19093 ^ _778908) ^ [_1107726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107726), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107726)), c_Int_OPls)))], (29094 ^ _778908) ^ [_1298174, _1298176] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298174, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1298174, tc_HOL_Obool))), _1298176) = c_Orderings_Otop__class_Otop(tc_fun(_1298174, tc_HOL_Obool)))], (51271 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (41756 ^ _778908) ^ [_1581573, _1581575, _1581577, _1581579, _1581581] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1581573, _1581575, _1581577), _1581579), _1581581) = hAPP(c_Set_OCollect(tc_prod(_1581573, _1581577)), hAPP(c_Product__Type_Oprod_Oprod__case(_1581573, _1581577, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1581577, tc_fun(_1581575, tc_HOL_Obool)), tc_fun(_1581577, tc_HOL_Obool), _1581573), hAPP(c_COMBB(tc_fun(_1581575, tc_HOL_Obool), tc_HOL_Obool, _1581577), c_HOL_OEx(_1581575))), hAPP(hAPP(c_COMBC(_1581573, tc_fun(_1581577, tc_fun(_1581575, tc_HOL_Obool)), tc_fun(_1581577, tc_fun(_1581575, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1581575, tc_HOL_Obool), tc_fun(_1581575, tc_HOL_Obool)), tc_fun(tc_fun(_1581577, tc_fun(_1581575, tc_HOL_Obool)), tc_fun(_1581577, tc_fun(_1581575, tc_HOL_Obool))), _1581573), c_COMBB(tc_fun(_1581575, tc_HOL_Obool), tc_fun(_1581575, tc_HOL_Obool), _1581577)), hAPP(hAPP(c_COMBB(tc_fun(_1581575, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1581575, tc_HOL_Obool), tc_fun(_1581575, tc_HOL_Obool)), _1581573), c_COMBS(_1581575, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581575, tc_HOL_Obool), tc_fun(_1581575, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1581573), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1581575), c_fconj)), hAPP(hAPP(c_COMBC(_1581573, tc_fun(tc_prod(_1581573, _1581575), tc_HOL_Obool), tc_fun(_1581575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581575, tc_fun(tc_fun(tc_prod(_1581573, _1581575), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1581573, _1581575), tc_HOL_Obool), tc_fun(_1581575, tc_HOL_Obool)), _1581573), c_COMBC(_1581575, tc_fun(tc_prod(_1581573, _1581575), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581575, tc_prod(_1581573, _1581575)), tc_fun(_1581575, tc_fun(tc_fun(tc_prod(_1581573, _1581575), tc_HOL_Obool), tc_HOL_Obool)), _1581573), hAPP(c_COMBB(tc_prod(_1581573, _1581575), tc_fun(tc_fun(tc_prod(_1581573, _1581575), tc_HOL_Obool), tc_HOL_Obool), _1581575), c_member(tc_prod(_1581573, _1581575)))), c_Product__Type_OPair(_1581573, _1581575)))), _1581579))))), hAPP(hAPP(c_COMBC(_1581577, tc_fun(tc_prod(_1581575, _1581577), tc_HOL_Obool), tc_fun(_1581575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581575, tc_fun(tc_fun(tc_prod(_1581575, _1581577), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1581575, _1581577), tc_HOL_Obool), tc_fun(_1581575, tc_HOL_Obool)), _1581577), c_COMBC(_1581575, tc_fun(tc_prod(_1581575, _1581577), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581575, tc_prod(_1581575, _1581577)), tc_fun(_1581575, tc_fun(tc_fun(tc_prod(_1581575, _1581577), tc_HOL_Obool), tc_HOL_Obool)), _1581577), hAPP(c_COMBB(tc_prod(_1581575, _1581577), tc_fun(tc_fun(tc_prod(_1581575, _1581577), tc_HOL_Obool), tc_HOL_Obool), _1581575), c_member(tc_prod(_1581575, _1581577)))), hAPP(c_COMBC(_1581575, _1581577, tc_prod(_1581575, _1581577)), c_Product__Type_OPair(_1581575, _1581577))))), _1581581))))))], (29136 ^ _778908) ^ [_1298969, _1298971] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298969, tc_HOL_Obool)), _1298971), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298969, tc_HOL_Obool)), _1298971)) = c_Orderings_Otop__class_Otop(tc_fun(_1298969, tc_HOL_Obool)))], (27570 ^ _778908) ^ [_1267068, _1267070, _1267072, _1267074] : [class_Groups_Ocomm__monoid__add(_1267068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1267070), _1267072)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1267068), _1267074), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1267070, _1267072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1267068), hAPP(_1267074, _1267070)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1267068), _1267074), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1267070, _1267072))))], (33855 ^ _778908) ^ [_1397039, _1397041, _1397043] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1397039, tc_HOL_Obool), tc_fun(_1397039, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1397039, tc_HOL_Obool), tc_fun(_1397039, tc_HOL_Obool)), _1397041), _1397043)), c_Wellfounded_Ofinite__psubset(_1397039)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1397039, tc_HOL_Obool)), _1397041), _1397043)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397039), _1397043))], (22566 ^ _778908) ^ [_1170077] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170077)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1170077)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170077)), 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)))))], (38376 ^ _778908) ^ [_1498410, _1498412, _1498414] : [c_Equiv__Relations_Oequivp(_1498410, _1498412), -(hBOOL(hAPP(hAPP(_1498412, _1498414), _1498414)))], (5238 ^ _778908) ^ [_859939, _859941] : [_859941 = _859939, -(c_SetInterval_Oord__class_OatMost(_859941) = c_SetInterval_Oord__class_OatMost(_859939))], (42358 ^ _778908) ^ [_1597316, _1597318, _1597320, _1597322] : [hBOOL(hAPP(hAPP(c_member(_1597316), _1597318), hAPP(c_Relation_ODomain(_1597316, _1597320), _1597322))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597316, _1597320)), hAPP(hAPP(c_Product__Type_OPair(_1597316, _1597320), _1597318), 42361 ^ [_1597316, _1597318, _1597320, _1597322])), _1597322)))], (49151 ^ _778908) ^ [_1764750, _1764752] : [-(_1764750 = c_List_Olist_ONil(_1764752)), -(hAPP(c_List_Ohd(_1764752), _1764750) = hAPP(hAPP(c_List_Onth(_1764752), _1764750), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36446 ^ _778908) ^ [_1454728, _1454730, _1454732] : [class_Lattices_Osemilattice__inf(_1454728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454728), _1454730), _1454732)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454728), _1454732), _1454730) = _1454730)], (36484 ^ _778908) ^ [_1455387, _1455389, _1455391, _1455393, _1455395] : [class_Lattices_Osemilattice__inf(_1455387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455387), _1455389), _1455391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455387), _1455393), _1455395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455387), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455387), _1455389), _1455393)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455387), _1455391), _1455395))))], (51447 ^ _778908) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (47405 ^ _778908) ^ [_1721983, _1721985, _1721987, _1721989] : [hAPP(hAPP(c_List_Omap(_1721983, _1721985), _1721987), _1721989) = c_List_Olist_ONil(_1721985), -(_1721989 = c_List_Olist_ONil(_1721983))], (46146 ^ _778908) ^ [_1688783, _1688785, _1688787, _1688789, _1688791, _1688793] : [-(hAPP(hAPP(c_List_Omap(_1688783, _1688785), _1688787), hAPP(hAPP(c_List_Omap(_1688789, _1688783), _1688791), _1688793)) = hAPP(hAPP(c_List_Omap(_1688789, _1688785), hAPP(c_Fun_Ocomp(_1688783, _1688785, _1688789, _1688787), _1688791)), _1688793))], (47962 ^ _778908) ^ [_1734957, _1734959, _1734961, _1734963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734957), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734959)), _1734961))), -(hBOOL(hAPP(hAPP(c_member(_1734959), _1734963), hAPP(c_List_Oset(_1734959), hAPP(hAPP(c_List_Olist__update(_1734959, _1734961), _1734957), _1734963)))))], (45259 ^ _778908) ^ [_1668156, _1668158, _1668160] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668156, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1668156, tc_HOL_Obool), _1668158)), _1668160) = c_Orderings_Obot__class_Obot(tc_fun(_1668156, tc_HOL_Obool)), 45262 ^ _778908 : [(45263 ^ _778908) ^ [_1668291] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1668156, tc_HOL_Obool)), _1668291), _1668158)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668156, tc_HOL_Obool)), _1668291), _1668160) = c_Orderings_Obot__class_Obot(tc_fun(_1668156, tc_HOL_Obool)))]]], (49087 ^ _778908) ^ [_1763449, _1763451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763449)), _1763451)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1763449), _1763451) = _1763451)], (5758 ^ _778908) ^ [_867827, _867829, _867831, _867833] : [-(hAPP(_867833, _867829) = hAPP(_867831, _867827)), _867833 = _867831, _867829 = _867827], (22440 ^ _778908) ^ [_1167495, _1167497, _1167499, _1167501, _1167503] : [class_Groups_Ominus(_1167495), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1167497, _1167495)), _1167499), _1167501), _1167503) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167495), hAPP(_1167499, _1167503)), hAPP(_1167501, _1167503)))], (41418 ^ _778908) ^ [_1568699] : [-(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)))), _1568699)) = 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), _1568699), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (23329 ^ _778908) ^ [_1185198, _1185200] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1185198, _1185200) = 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), _1185198), _1185200)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1185198, _1185200)))], (7512 ^ _778908) ^ [_904583, _904585, _904587, _904589] : [class_Rings_Ocomm__semiring__1(_904583), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904583), _904585), _904587)), _904589) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904583), _904585), _904589)), _904587))], (28395 ^ _778908) ^ [_1283334, _1283336, _1283338, _1283340] : [class_Lattices_Osemilattice__sup(_1283334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283334), _1283336), _1283338)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283334), _1283340), _1283338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283334), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283334), _1283336), _1283340)), _1283338)))], (17103 ^ _778908) ^ [_1073801, _1073803, _1073805] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1073801), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073803), _1073805)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1073801), _1073803)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1073801), _1073805)))], (47589 ^ _778908) ^ [_1725464] : [-(c_List_Olistset(_1725464, c_List_Olist_ONil(tc_fun(_1725464, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1725464)), c_List_Olist_ONil(_1725464)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1725464), tc_HOL_Obool))))], (14216 ^ _778908) ^ [_1019504, _1019506, _1019508, _1019510] : [_1019504 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1019506), _1019508)), _1019510), -(_1019506 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019504, _1019506) = _1019510), 14223 ^ _778908 : [(14226 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019510), _1019506))], (14224 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019506)))]], 14231 ^ _778908 : [(14234 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019506), _1019510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019510), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14232 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019506))]]], (16216 ^ _778908) ^ [_1056911, _1056913, _1056915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1056911), _1056913)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1056915), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1056913), _1056911))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1056915), _1056911)), hAPP(c_Nat_OSuc, _1056913)))], (39528 ^ _778908) ^ [_1522732, _1522734, _1522736, _1522738, _1522740] : [hBOOL(hAPP(hAPP(c_member(_1522732), _1522734), hAPP(c_Set_Ovimage(_1522732, _1522736, _1522738), hAPP(hAPP(c_Set_Oinsert(_1522736), _1522740), c_Orderings_Obot__class_Obot(tc_fun(_1522736, tc_HOL_Obool)))))), -(hAPP(_1522738, _1522734) = _1522740)], (17377 ^ _778908) ^ [_1079114] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079114) = _1079114)], (17061 ^ _778908) ^ [_1072894, _1072896, _1072898] : [class_Int_Onumber__ring(_1072894), -(hAPP(c_Int_Onumber__class_Onumber__of(_1072894), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072896), _1072898)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072894), hAPP(c_Int_Onumber__class_Onumber__of(_1072894), _1072896)), hAPP(c_Int_Onumber__class_Onumber__of(_1072894), _1072898)))], (42348 ^ _778908) ^ [_1597064, _1597066, _1597068, _1597070] : [-(hAPP(c_Relation_ODomain(_1597064, _1597066), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1597064, _1597066), tc_HOL_Obool)), _1597068), _1597070)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597064, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1597064, _1597066), _1597068)), hAPP(c_Relation_ODomain(_1597064, _1597066), _1597070)))], (46491 ^ _778908) ^ [_1697001, _1697003, _1697005] : [-(hBOOL(hAPP(hAPP(c_member(_1697001), _1697003), hAPP(c_List_Oset(_1697001), _1697005)))), -(c_List_Oremove1(_1697001, _1697003, _1697005) = _1697005)], (2826 ^ _778908) ^ [_821771, _821773] : [_821773 = _821771, -(c_Nitpick_Ofrac(_821773) = c_Nitpick_Ofrac(_821771))], (42062 ^ _778908) ^ [_1590261, _1590263, _1590265] : [c_Wellfounded_Owf(_1590261, _1590263), c_Wellfounded_Owf(_1590261, _1590265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590261, _1590261), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1590261, _1590261, _1590261), _1590263), _1590265)), _1590263)), -(c_Wellfounded_Owf(_1590261, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1590261, _1590261), tc_HOL_Obool)), _1590263), _1590265)))], (49275 ^ _778908) ^ [_1767099, _1767101, _1767103, _1767105] : [-(c_List_Olist_Olist__size(_1767099, _1767101, hAPP(hAPP(c_List_Olist_OCons(_1767099), _1767103), _1767105)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1767101, _1767103)), c_List_Olist_Olist__size(_1767099, _1767101, _1767105))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31870 ^ _778908) ^ [_1356528, _1356530, _1356532, _1356534, _1356536] : [class_Groups_Ocomm__monoid__add(_1356528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356530), _1356532)), 31877 ^ _778908 : [(31884 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356530), _1356534), _1356532))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356530, _1356528), hAPP(hAPP(c_COMBC(_1356530, _1356528, _1356528), hAPP(hAPP(c_COMBS(_1356530, _1356528, tc_fun(_1356528, _1356528)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1356528, tc_fun(_1356528, _1356528)), _1356530), c_If(_1356528)), hAPP(hAPP(c_COMBC(_1356530, _1356530, tc_HOL_Obool), c_fequal), _1356534))), _1356536)), c_Groups_Ozero__class_Ozero(_1356528))), _1356532) = c_Groups_Ozero__class_Ozero(_1356528))], (31878 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1356530), _1356534), _1356532)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356530, _1356528), hAPP(hAPP(c_COMBC(_1356530, _1356528, _1356528), hAPP(hAPP(c_COMBS(_1356530, _1356528, tc_fun(_1356528, _1356528)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1356528, tc_fun(_1356528, _1356528)), _1356530), c_If(_1356528)), hAPP(hAPP(c_COMBC(_1356530, _1356530, tc_HOL_Obool), c_fequal), _1356534))), _1356536)), c_Groups_Ozero__class_Ozero(_1356528))), _1356532) = hAPP(_1356536, _1356534))]]], (39202 ^ _778908) ^ [_1515088, _1515090, _1515092, _1515094, _1515096] : [c_Fun_Oinj__on(_1515088, _1515090, _1515092, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1515088, tc_HOL_Obool)), _1515094), _1515096)), 39205 ^ _778908 : [(39210 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1515090, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1515088, _1515090, _1515092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1515088, tc_HOL_Obool)), _1515094), _1515096))), hAPP(c_Set_Oimage(_1515088, _1515090, _1515092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1515088, tc_HOL_Obool)), _1515096), _1515094))) = c_Orderings_Obot__class_Obot(tc_fun(_1515090, tc_HOL_Obool)))], (39208 ^ _778908) ^ [] : [-(c_Fun_Oinj__on(_1515088, _1515090, _1515092, _1515096))], (39206 ^ _778908) ^ [] : [-(c_Fun_Oinj__on(_1515088, _1515090, _1515092, _1515094))]]], (28335 ^ _778908) ^ [_1282127, _1282129, _1282131, _1282133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282127, tc_HOL_Obool)), _1282129), _1282131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282127, tc_HOL_Obool)), _1282133), _1282131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282127, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282127, tc_HOL_Obool)), _1282129), _1282133)), _1282131)))], (47830 ^ _778908) ^ [_1732167, _1732169, _1732171, _1732173, _1732175] : [class_Orderings_Olinorder(_1732167), -(hBOOL(hAPP(hAPP(c_member(_1732167), hAPP(_1732169, _1732171)), hAPP(c_Set_Oimage(_1732173, _1732167, _1732169), hAPP(c_List_Oset(_1732173), _1732175))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1732173, _1732167, _1732169, _1732171, _1732175) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1732173, _1732167, _1732169), _1732171), _1732175))], (32094 ^ _778908) ^ [_1361428, _1361430, _1361432, _1361434, _1361436] : [class_Rings_Oring(_1361428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361430), _1361432)), hBOOL(hAPP(hAPP(c_member(_1361430), _1361434), _1361432)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361430, _1361428), _1361436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361430, tc_HOL_Obool)), _1361432), hAPP(hAPP(c_Set_Oinsert(_1361430), _1361434), c_Orderings_Obot__class_Obot(tc_fun(_1361430, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1361428), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361430, _1361428), _1361436), _1361432)), hAPP(_1361436, _1361434)))], (44601 ^ _778908) ^ [_1650887, _1650889, _1650891, _1650893, _1650895, _1650897, _1650899, _1650901] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650887, tc_fun(_1650889, tc_fun(_1650891, tc_HOL_Obool))), _1650893), _1650895), _1650897), _1650899)), hBOOL(hAPP(hAPP(c_member(_1650887), _1650901), _1650893)), -(hBOOL(hAPP(hAPP(hAPP(_1650895, _1650901), _1650897), _1650899)))], (26101 ^ _778908) ^ [_1237968, _1237970, _1237972, _1237974, _1237976] : [class_Rings_Osemiring__0(_1237968), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237968), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237970, _1237968), _1237972), _1237974)), _1237976) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237970, _1237968), hAPP(hAPP(c_COMBC(_1237970, _1237968, _1237968), hAPP(hAPP(c_COMBB(_1237968, tc_fun(_1237968, _1237968), _1237970), c_Groups_Otimes__class_Otimes(_1237968)), _1237972)), _1237976)), _1237974))], (51469 ^ _778908) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (9878 ^ _778908) ^ [_944614, _944616, _944618] : [class_Rings_Olinordered__semiring__strict(_944614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944614), c_Groups_Ozero__class_Ozero(_944614)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944614), _944616), _944618))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944614), c_Groups_Ozero__class_Ozero(_944614)), _944618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944614), c_Groups_Ozero__class_Ozero(_944614)), _944616)))], (49233 ^ _778908) ^ [_1766231, _1766233, _1766235] : [-(hAPP(c_List_Orotate(_1766231, hAPP(c_Nat_OSuc, _1766233)), _1766235) = hAPP(c_List_Orotate1(_1766231), hAPP(c_List_Orotate(_1766231, _1766233), _1766235)))], (48166 ^ _778908) ^ [_1739957, _1739959, _1739961] : [-(hAPP(c_List_Oset(_1739957), hAPP(hAPP(c_List_Oappend(_1739957), _1739959), _1739961)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1739957, tc_HOL_Obool)), hAPP(c_List_Oset(_1739957), _1739959)), hAPP(c_List_Oset(_1739957), _1739961)))], (6419 ^ _778908) ^ [_882541, _882543, _882545] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_882541, _882543, _882545))), 6422 ^ _778908 : [(6425 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _882545)))], (6423 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _882543)))]]], (29918 ^ _778908) ^ [_1314455, _1314457, _1314459, _1314461] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1314455, _1314459)), c_Sum__Type_OPlus(_1314455, _1314459, _1314457, _1314461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1314455), _1314457)), hAPP(c_Finite__Set_Ocard(_1314459), _1314461))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314455), _1314457)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314459), _1314461))], (47615 ^ _778908) ^ [_1726499, _1726501, _1726503, _1726505, _1726507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726499), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726501)), _1726503))), -(hAPP(hAPP(c_List_Onth(_1726505), hAPP(hAPP(c_List_Omap(_1726501, _1726505), _1726507), _1726503)), _1726499) = hAPP(_1726507, hAPP(hAPP(c_List_Onth(_1726501), _1726503), _1726499)))], (24587 ^ _778908) ^ [_1209071, _1209073, _1209075] : [class_Orderings_Olinorder(_1209071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209071), _1209073), _1209075)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209071), _1209073), _1209075) = _1209075)], (45493 ^ _778908) ^ [_1673740, _1673742, _1673744] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1673740, tc_HOL_Obool)), _1673742)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1673740), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673740, tc_HOL_Obool), _1673742))), 45503 ^ _778908 : [(45506 ^ _778908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1673740), 45502 ^ [_1673740, _1673742, _1673744]) = _1673744], (45504 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1673740, tc_HOL_Obool)), 45502 ^ [_1673740, _1673742, _1673744]), _1673742)))]], 45510 ^ _778908 : [(45514 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1673740, tc_HOL_Obool)), 45512 ^ [_1673740, _1673742, _1673744]), _1673742)))], (45516 ^ _778908) ^ [] : [45509 ^ [_1673740, _1673742, _1673744] = 45512 ^ [_1673740, _1673742, _1673744]], (45518 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1673740, tc_HOL_Obool)), 45509 ^ [_1673740, _1673742, _1673744]), 45512 ^ [_1673740, _1673742, _1673744]) = c_Orderings_Obot__class_Obot(tc_fun(_1673740, tc_HOL_Obool))], (45511 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1673740, tc_HOL_Obool)), 45509 ^ [_1673740, _1673742, _1673744]), _1673742)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1673744), hAPP(c_Finite__Set_Ocard(tc_fun(_1673740, tc_HOL_Obool)), _1673742)) = hAPP(c_Finite__Set_Ocard(_1673740), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673740, tc_HOL_Obool), _1673742)))], (14308 ^ _778908) ^ [_1021091, _1021093, _1021095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021091), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14311 ^ _778908 : [(14312 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1021093, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021095), _1021091)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1021095, _1021091))), 14315 ^ _778908 : [(14316 ^ _778908) ^ [_1021301, _1021303] : [-(hBOOL(hAPP(hAPP(_1021093, _1021303), _1021301))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021091), _1021301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021301), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1021095 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1021091), _1021303)), _1021301)]]], (14330 ^ _778908) ^ [] : [14333 ^ _778908 : [(14336 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14332 ^ [_1021091, _1021093, _1021095]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14338 ^ _778908) ^ [] : [-(_1021095 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1021091), 14331 ^ [_1021091, _1021093, _1021095])), 14332 ^ [_1021091, _1021093, _1021095]))], (14340 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1021093, 14331 ^ [_1021091, _1021093, _1021095]), 14332 ^ [_1021091, _1021093, _1021095]))], (14334 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021091), 14332 ^ [_1021091, _1021093, _1021095])))]], -(hBOOL(hAPP(hAPP(_1021093, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021095), _1021091)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1021095, _1021091))))]]], (2626 ^ _778908) ^ [_818719, _818721] : [_818721 = _818719, -(c_Lazy__Sequence_Ohb__not__seq(_818721) = c_Lazy__Sequence_Ohb__not__seq(_818719))], (43235 ^ _778908) ^ [_1619414, _1619416] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619414, _1619414), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1619414, _1619416)), c_Relation_OId(_1619414)) = c_Transitive__Closure_Ortrancl(_1619414, _1619416))], (41313 ^ _778908) ^ [_1565067, _1565069, _1565071, _1565073, _1565075] : [class_Groups_Ocomm__monoid__add(_1565067), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565069), _1565071)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565069, _1565067), _1565073), hAPP(c_Set_OCollect(_1565069), hAPP(hAPP(c_COMBS(_1565069, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565069), c_fconj), hAPP(hAPP(c_COMBC(_1565069, tc_fun(_1565069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565069)), _1565071))), hAPP(hAPP(c_COMBC(_1565069, tc_fun(_1565069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565069)), _1565075)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565069, _1565067), hAPP(hAPP(c_COMBC(_1565069, _1565067, _1565067), hAPP(hAPP(c_COMBS(_1565069, _1565067, tc_fun(_1565067, _1565067)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1565067, tc_fun(_1565067, _1565067)), _1565069), c_If(_1565067)), hAPP(hAPP(c_COMBC(_1565069, tc_fun(_1565069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565069)), _1565075))), _1565073)), c_Groups_Ozero__class_Ozero(_1565067))), _1565071))], (19239 ^ _778908) ^ [_1110069, _1110071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110069), 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)))), _1110071)), 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)))), _1110069)) = 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), _1110071), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1110069))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27807 ^ _778908) ^ [_1272048, _1272050] : [class_Groups_Oordered__ab__group__add(_1272048), -(hAPP(c_Set_Oimage(_1272048, _1272048, c_Groups_Ouminus__class_Ouminus(_1272048)), hAPP(c_SetInterval_Oord__class_OlessThan(_1272048), _1272050)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1272048), hAPP(c_Groups_Ouminus__class_Ouminus(_1272048), _1272050)))], (16725 ^ _778908) ^ [_1066492, _1066494] : [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), _1066492)), _1066494))), _1066492 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1066494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10579 ^ _778908) ^ [_956535, _956537, _956539, _956541] : [class_Orderings_Oorder(_956535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956535), _956537), _956539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956535), _956541), _956537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956535), _956541), _956539)))], (36542 ^ _778908) ^ [_1456587, _1456589, _1456591] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456587, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456587, tc_HOL_Obool)), _1456589), _1456591)), _1456591)))], (22452 ^ _778908) ^ [_1167731] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1167731) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167731)))], (41768 ^ _778908) ^ [_1582308, _1582310, _1582312, _1582314, _1582316, _1582318, _1582320] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582308, _1582310, _1582312), hAPP(hAPP(c_Relation_Orel__comp(_1582308, _1582314, _1582310), _1582316), _1582318)), _1582320) = hAPP(hAPP(c_Relation_Orel__comp(_1582308, _1582314, _1582312), _1582316), hAPP(hAPP(c_Relation_Orel__comp(_1582314, _1582310, _1582312), _1582318), _1582320)))], (48941 ^ _778908) ^ [_1759907, _1759909] : [hBOOL(hAPP(c_List_Odistinct(_1759907), _1759909)), -(hBOOL(hAPP(c_List_Odistinct(_1759907), hAPP(c_List_Orotate1(_1759907), _1759909))))], (29446 ^ _778908) ^ [_1305312, _1305314, _1305316] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305312), _1305314)), 29449 ^ _778908 : [(29469 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1305312, tc_Nat_Onat), _1305316), _1305314) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 29470 ^ _778908 : [(29471 ^ _778908) ^ [_1305793] : [hBOOL(hAPP(hAPP(c_member(_1305312), _1305793), _1305314)), hAPP(_1305316, _1305793) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 29479 ^ _778908 : [(29484 ^ _778908) ^ [] : [hAPP(_1305316, 29478 ^ [_1305312, _1305314, _1305316, _1305793]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29482 ^ _778908) ^ [] : [_1305793 = 29478 ^ [_1305312, _1305314, _1305316, _1305793]], (29480 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305312), 29478 ^ [_1305312, _1305314, _1305316, _1305793]), _1305314)))]]]]], (29450 ^ _778908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1305312, tc_Nat_Onat), _1305316), _1305314) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 29454 ^ _778908 : [(29459 ^ _778908) ^ [_1305632] : [hBOOL(hAPP(hAPP(c_member(_1305312), _1305632), _1305314)), -(29453 ^ [_1305312, _1305314, _1305316] = _1305632), -(hAPP(_1305316, _1305632) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29457 ^ _778908) ^ [] : [-(hAPP(_1305316, 29453 ^ [_1305312, _1305314, _1305316]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (29455 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305312), 29453 ^ [_1305312, _1305314, _1305316]), _1305314)))]]]]], (46521 ^ _778908) ^ [_1697523, _1697525, _1697527] : [hBOOL(hAPP(c_List_Odistinct(_1697523), _1697525)), -(hBOOL(hAPP(c_List_Odistinct(_1697523), c_List_Oremove1(_1697523, _1697527, _1697525))))], (25669 ^ _778908) ^ [_1229819, _1229821, _1229823] : [class_Orderings_Olinorder(_1229819), 25672 ^ _778908 : [(25679 ^ _778908) ^ [] : [_1229821 = _1229823, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1229819), _1229821) = hAPP(c_SetInterval_Oord__class_OlessThan(_1229819), _1229823))], (25673 ^ _778908) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1229819), _1229821) = hAPP(c_SetInterval_Oord__class_OlessThan(_1229819), _1229823), -(_1229821 = _1229823)]]], (8728 ^ _778908) ^ [_924604, _924606, _924608] : [class_Orderings_Oorder(_924604), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924604), _924606), _924608)), _924606 = _924608], (10431 ^ _778908) ^ [_954136, _954138] : [-(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), _954136))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _954138))))], (39277 ^ _778908) ^ [_1516963, _1516965, _1516967, _1516969, _1516971] : [class_Groups_Ocomm__monoid__mult(_1516963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516965), _1516967)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516965), _1516969)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1516963), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516963, _1516965, c_Groups_Otimes__class_Otimes(_1516963)), _1516971), c_Groups_Oone__class_Oone(_1516963)), _1516967)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516963, _1516965, c_Groups_Otimes__class_Otimes(_1516963)), _1516971), c_Groups_Oone__class_Oone(_1516963)), _1516969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1516963), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516963, _1516965, c_Groups_Otimes__class_Otimes(_1516963)), _1516971), c_Groups_Oone__class_Oone(_1516963)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1516965, tc_HOL_Obool)), _1516967), _1516969))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1516963, _1516965, c_Groups_Otimes__class_Otimes(_1516963)), _1516971), c_Groups_Oone__class_Oone(_1516963)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1516965, tc_HOL_Obool)), _1516967), _1516969))))], (12691 ^ _778908) ^ [_992279, _992281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992279), _992281)), -(_992281 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _992279), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12694 ^ [_992279, _992281])))], (29398 ^ _778908) ^ [_1304345, _1304347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1304345), hAPP(c_Nat_OSuc, _1304347))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1304345, hAPP(c_Nat_OSuc, _1304347)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304347)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1304345, _1304347)))], (39500 ^ _778908) ^ [_1521989, _1521991, _1521993, _1521995, _1521997] : [-(hAPP(c_Set_Ovimage(_1521989, _1521991, _1521993), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521991, tc_HOL_Obool)), _1521995), _1521997)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521989, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521989, _1521991, _1521993), _1521995)), hAPP(c_Set_Ovimage(_1521989, _1521991, _1521993), _1521997)))], (41414 ^ _778908) ^ [_1568298] : [-(c_Wellfounded_Ofinite__psubset(_1568298) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1568298, tc_HOL_Obool), tc_fun(_1568298, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1568298, tc_HOL_Obool), tc_fun(_1568298, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1568298, tc_HOL_Obool), tc_fun(tc_fun(_1568298, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1568298, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1568298, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1568298, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1568298, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1568298, tc_HOL_Obool)), c_COMBS(tc_fun(_1568298, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1568298, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1568298, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1568298, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1568298, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1568298, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1568298)))))], (7090 ^ _778908) ^ [_897449, _897451, _897453] : [hAPP(c_Option_Ooption_OSome(_897449), _897451) = hAPP(c_Option_Ooption_OSome(_897449), _897453), -(_897451 = _897453)], (40652 ^ _778908) ^ [_1551206, _1551208] : [class_Orderings_Olinorder(_1551206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551206), _1551208)), -(c_Big__Operators_Olattice_OSup__fin(_1551206, c_Orderings_Oord__class_Omax(_1551206), _1551208) = hAPP(c_Finite__Set_Ofold1(_1551206, c_Orderings_Oord__class_Omax(_1551206)), _1551208))], (48311 ^ _778908) ^ [_1743062, _1743064, _1743066] : [_1743066 = c_List_Olist_ONil(_1743064), -(_1743062 = hAPP(hAPP(c_List_Oappend(_1743064), _1743066), _1743062))], (47449 ^ _778908) ^ [_1722747, _1722749] : [_1722749 = c_List_Olist_ONil(_1722747), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722747)), _1722749) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19505 ^ _778908) ^ [_1114866, _1114868] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1114866)), c_Int_OBit1(_1114868)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1114866), _1114868)))], (29299 ^ _778908) ^ [_1302609, _1302611, _1302613, _1302615] : [29300 ^ _778908 : [(29303 ^ _778908) ^ [] : [hBOOL(hAPP(_1302613, _1302615))], (29301 ^ _778908) ^ [] : [_1302611 = _1302615]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1302609), _1302611), _1302613), _1302615)))], (49981 ^ _778908) ^ [_1782445, _1782447, _1782449] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1782445), tc_List_Olist(_1782445)), c_List_Opartition(_1782445, _1782447, _1782449)) = hAPP(c_List_Ofilter(_1782445, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1782445, c_fNot), _1782447)), _1782449))], (33745 ^ _778908) ^ [_1394217, _1394219] : [class_Orderings_Olinorder(_1394217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394217), _1394219)), -(_1394219 = c_Orderings_Obot__class_Obot(tc_fun(_1394217, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1394217), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1394217), 33758 ^ [_1394217, _1394219]), 33759 ^ [_1394217, _1394219])), hAPP(hAPP(c_Set_Oinsert(_1394217), 33758 ^ [_1394217, _1394219]), hAPP(hAPP(c_Set_Oinsert(_1394217), 33759 ^ [_1394217, _1394219]), c_Orderings_Obot__class_Obot(tc_fun(_1394217, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1394217), c_Big__Operators_Olinorder__class_OMax(_1394217, _1394219)), _1394219)))], (25131 ^ _778908) ^ [_1220673, _1220675] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1220673), _1220675))), -(c_Quickcheck_Obeyond(_1220673, _1220675) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (23573 ^ _778908) ^ [_1189670, _1189672] : [23574 ^ _778908 : [(23577 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189672), _1189670))], (23575 ^ _778908) ^ [] : [_1189670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1189672, _1189670) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189672))], (11096 ^ _778908) ^ [_964724, _964726, _964728] : [class_Orderings_Opreorder(_964724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964724), _964726), _964728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964724), _964726), _964728)))], (14509 ^ _778908) ^ [_1025007, _1025009, _1025011] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025007), _1025009)), _1025011) = 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), _1025007), _1025011)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025009), _1025011))), 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, _1025007, _1025011)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025009, _1025011))), _1025011)))], (48875 ^ _778908) ^ [_1758264, _1758266] : [-(hAPP(c_List_Orotate1(_1758264), _1758266) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1758264), _1758264, c_List_Olist_ONil(_1758264), hAPP(hAPP(c_COMBB(tc_List_Olist(_1758264), tc_fun(tc_List_Olist(_1758264), tc_List_Olist(_1758264)), _1758264), hAPP(c_COMBC(tc_List_Olist(_1758264), tc_List_Olist(_1758264), tc_List_Olist(_1758264)), c_List_Oappend(_1758264))), hAPP(hAPP(c_COMBC(_1758264, tc_List_Olist(_1758264), tc_List_Olist(_1758264)), c_List_Olist_OCons(_1758264)), c_List_Olist_ONil(_1758264)))), _1758266))], (22516 ^ _778908) ^ [_1169060, _1169062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169060), _1169062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1169060)), hAPP(c_Code__Numeral_Oof__nat, _1169062))))], (36394 ^ _778908) ^ [_1453829, _1453831, _1453833, _1453835] : [class_Lattices_Osemilattice__inf(_1453829), 36397 ^ _778908 : [(36406 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453829), _1453831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453829), _1453833), _1453835)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453829), _1453831), _1453833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453829), _1453831), _1453835))], (36398 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453829), _1453831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453829), _1453833), _1453835))), 36401 ^ _778908 : [(36404 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453829), _1453831), _1453835)))], (36402 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453829), _1453831), _1453833)))]]]]], (48478 ^ _778908) ^ [_1747389, _1747391, _1747393, _1747395] : [-(c_Map_Omap__upds(_1747389, _1747391, _1747393, c_List_Olist_ONil(_1747389), _1747395) = _1747393)], (7605 ^ _778908) ^ [_906209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906209), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17881 ^ _778908) ^ [_1088246, _1088248, _1088250] : [class_Rings_Olinordered__semidom(_1088246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088246), c_Groups_Ozero__class_Ozero(_1088246)), _1088248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088246), _1088248), c_Groups_Oone__class_Oone(_1088246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088246), _1088248), hAPP(hAPP(c_Power_Opower__class_Opower(_1088246), _1088248), _1088250))), hAPP(hAPP(c_Power_Opower__class_Opower(_1088246), _1088248), _1088250))))], (4428 ^ _778908) ^ [_847404, _847406] : [_847406 = _847404, -(c_Groups_Ouminus__class_Ouminus(_847406) = c_Groups_Ouminus__class_Ouminus(_847404))], (34050 ^ _778908) ^ [_1401034, _1401036, _1401038] : [class_Orderings_Olinorder(_1401034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401034), _1401036)), -(_1401038 = c_Orderings_Obot__class_Obot(tc_fun(_1401034, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401034, tc_HOL_Obool)), _1401038), _1401036)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1401034), c_Big__Operators_Olattice_OSup__fin(_1401034, c_Orderings_Oord__class_Omax(_1401034), _1401038)), c_Big__Operators_Olattice_OSup__fin(_1401034, c_Orderings_Oord__class_Omax(_1401034), _1401036)) = c_Big__Operators_Olattice_OSup__fin(_1401034, c_Orderings_Oord__class_Omax(_1401034), _1401036))], (5376 ^ _778908) ^ [_862022, _862024] : [_862024 = _862022, -(c_List_Otake(_862024) = c_List_Otake(_862022))], (25395 ^ _778908) ^ [_1225444, _1225446] : [_1225446 = _1225444, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225444), _1225446)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225446), _1225444)))], (24295 ^ _778908) ^ [_1203538, _1203540, _1203542] : [_1203540 = _1203542, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203538, tc_HOL_Obool)), _1203540) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203538, tc_HOL_Obool)), _1203542))], (35821 ^ _778908) ^ [_1440294] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1440294) = 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), _1440294), 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))))))], (13726 ^ _778908) ^ [_1010320, _1010322] : [-(hBOOL(hAPP(_1010320, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1010320, _1010322)), 13734 ^ _778908 : [(13737 ^ _778908) ^ [_1010558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1010558), 13733 ^ [_1010320, _1010322])), hBOOL(hAPP(_1010320, _1010558))], (13743 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1010320, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13733 ^ [_1010320, _1010322]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13735 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13733 ^ [_1010320, _1010322]), _1010322)))]]], (50505 ^ _778908) ^ [_1793065, _1793067, _1793069, _1793071, _1793073] : [class_Orderings_Olinorder(_1793065), c_List_Olinorder__class_Osorted(_1793065, hAPP(hAPP(c_List_Omap(_1793067, _1793065), _1793069), _1793071)), -(c_List_Olinorder__class_Osorted(_1793065, hAPP(hAPP(c_List_Omap(_1793067, _1793065), _1793069), c_List_Oremove1(_1793067, _1793073, _1793071))))], (24313 ^ _778908) ^ [_1203908, _1203910] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1203908), _1203910) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1203908, _1203910)))], (17307 ^ _778908) ^ [_1077800, _1077802, _1077804, _1077806] : [class_Rings_Olinordered__semidom(_1077800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077800), c_Groups_Oone__class_Oone(_1077800)), _1077802)), 17314 ^ _778908 : [(17321 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077804), _1077806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077800), hAPP(hAPP(c_Power_Opower__class_Opower(_1077800), _1077802), _1077804)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077800), _1077802), _1077806))))], (17315 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077800), hAPP(hAPP(c_Power_Opower__class_Opower(_1077800), _1077802), _1077804)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077800), _1077802), _1077806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077804), _1077806)))]]], (6520 ^ _778908) ^ [_884515, _884517, _884519] : [c_Com_Ocom_OCond(_884515, _884517, _884519) = c_Com_Ocom_OSKIP], (40642 ^ _778908) ^ [_1551043, _1551045] : [class_Orderings_Olinorder(_1551043), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551043), _1551045)), -(c_Big__Operators_Olattice_OInf__fin(_1551043, c_Orderings_Oord__class_Omin(_1551043), _1551045) = hAPP(c_Finite__Set_Ofold1(_1551043, c_Orderings_Oord__class_Omin(_1551043)), _1551045))], (45269 ^ _778908) ^ [_1668424, _1668426, _1668428] : [45271 ^ _778908 : [(45274 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668424, tc_HOL_Obool)), 45270 ^ [_1668424, _1668426, _1668428]), _1668428) = c_Orderings_Obot__class_Obot(tc_fun(_1668424, tc_HOL_Obool))], (45272 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1668424, tc_HOL_Obool)), 45270 ^ [_1668424, _1668426, _1668428]), _1668426)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668424, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1668424, tc_HOL_Obool), _1668426)), _1668428) = c_Orderings_Obot__class_Obot(tc_fun(_1668424, tc_HOL_Obool)))], (45583 ^ _778908) ^ [_1675997, _1675999, _1676001, _1676003, _1676005, _1676007] : [-(_1675997 = c_Orderings_Obot__class_Obot(tc_fun(_1675999, tc_HOL_Obool))), 45589 ^ _778908 : [(45592 ^ _778908) ^ [] : [c_Fun_Oinj__on(_1676001, _1676003, _1676005, hAPP(_1676007, 45588 ^ [_1675997, _1675999, _1676001, _1676003, _1676005, _1676007]))], (45590 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675999), 45588 ^ [_1675997, _1675999, _1676001, _1676003, _1676005, _1676007]), _1675997)))]], -(c_Fun_Oinj__on(_1676001, _1676003, _1676005, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1675999, tc_fun(_1676001, tc_HOL_Obool)), _1675997), _1676007)))], (45522 ^ _778908) ^ [_1674522, _1674524] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1674522, tc_HOL_Obool), _1674524) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1674522, tc_HOL_Obool), tc_fun(_1674522, tc_HOL_Obool)), _1674524), c_COMBI(tc_fun(_1674522, tc_HOL_Obool))))], (23351 ^ _778908) ^ [_1185683, _1185685] : [-(c_Divides_Odivmod__int__rel(_1185683, _1185685) = 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, _1185683))), 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), _1185685)))))), 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)), _1185685))), 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)), _1185685))))), 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)), _1185685)))), 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), _1185685))), 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))))))))], (43024 ^ _778908) ^ [_1613551, _1613553] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613551, _1613551)), hAPP(hAPP(c_Product__Type_OPair(_1613551, _1613551), 43025 ^ [_1613551, _1613553]), 43025 ^ [_1613551, _1613553])), c_Transitive__Closure_Otrancl(_1613551, _1613553)))), -(c_Wellfounded_Oacyclic(_1613551, _1613553))], (18355 ^ _778908) ^ [_1095922, _1095924] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095922), _1095924) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 18356 ^ _778908 : [(18363 ^ _778908) ^ [] : [_1095922 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1095924 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (18357 ^ _778908) ^ [] : [_1095922 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1095924 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (42743 ^ _778908) ^ [_1607315, _1607317, _1607319] : [hBOOL(hAPP(_1607315, _1607317)), -(hBOOL(hAPP(_1607315, c_Hilbert__Choice_OEps(_1607319, _1607315))))], (1282 ^ _778908) ^ [_797807, _797809] : [-(class_Orderings_Owellorder(_797807)), _797809 = _797807, class_Orderings_Owellorder(_797809)], (28177 ^ _778908) ^ [_1279058, _1279060, _1279062, _1279064] : [class_Lattices_Osemilattice__sup(_1279058), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279058), _1279060), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279058), _1279062), _1279064)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279058), _1279062), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279058), _1279060), _1279064)))], (24183 ^ _778908) ^ [_1201307, _1201309, _1201311] : [24184 ^ _778908 : [(24187 ^ _778908) ^ [] : [_1201309 = _1201311], (24185 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201307, tc_HOL_Obool)), _1201309), _1201311))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201307, tc_HOL_Obool)), _1201309), _1201311)))], (36047 ^ _778908) ^ [_1446160, _1446162, _1446164] : [_1446162 = c_Orderings_Obot__class_Obot(tc_fun(_1446160, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446160), _1446162), _1446164) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446160, tc_HOL_Obool), tc_HOL_Obool)))], (49225 ^ _778908) ^ [_1766051] : [-(hAPP(c_List_Otl(_1766051), c_List_Olist_ONil(_1766051)) = c_List_Olist_ONil(_1766051))], (47789 ^ _778908) ^ [_1730711, _1730713, _1730715, _1730717] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730711) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1730713), hAPP(hAPP(c_List_Olist_OCons(_1730713), _1730715), _1730717)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730711)) = hAPP(hAPP(c_List_Onth(_1730713), _1730717), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730711)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (28671 ^ _778908) ^ [_1288583, _1288585] : [class_Orderings_Olinorder(_1288583), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1288583, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1288583), _1288585)) = hAPP(c_SetInterval_Oord__class_OatMost(_1288583), _1288585))], (25827 ^ _778908) ^ [_1232558, _1232560, _1232562, _1232564, _1232566] : [class_Rings_Ocomm__semiring__1(_1232558), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232558), _1232560), _1232562)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232558), _1232564), _1232566)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232558), _1232560), _1232564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232558), _1232562), _1232566))))], (29165 ^ _778908) ^ [_1299770, _1299772, _1299774, _1299776] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299770, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29166 ^ [_1299770, _1299772, _1299774, _1299776])), _1299772) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299770, 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), 29166 ^ [_1299770, _1299772, _1299774, _1299776]), _1299774))), _1299776), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299770, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1299772) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299770, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1299776))], (29229 ^ _778908) ^ [_1301204, _1301206, _1301208, _1301210] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301204, tc_HOL_Obool)), _1301206), hAPP(hAPP(c_Set_Oinsert(_1301204), _1301208), _1301210)) = hAPP(hAPP(c_Set_Oinsert(_1301204), _1301208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301204, tc_HOL_Obool)), _1301206), _1301210)))], (40174 ^ _778908) ^ [_1539127, _1539129, _1539131, _1539133, _1539135, _1539137] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539127, _1539129)), hAPP(hAPP(c_Product__Type_OPair(_1539127, _1539129), _1539131), _1539133)), hAPP(hAPP(c_Product__Type_OSigma(_1539127, _1539129), _1539135), _1539137)))), hBOOL(hAPP(hAPP(c_member(_1539127), _1539131), _1539135)), hBOOL(hAPP(hAPP(c_member(_1539129), _1539133), hAPP(_1539137, _1539131)))], (6512 ^ _778908) ^ [_884286, _884288, _884290, _884292, _884294] : [c_Com_Ocom_OCond(_884286, _884288, _884290) = c_Com_Ocom_OAss(_884292, _884294)], (48995 ^ _778908) ^ [_1761102, _1761104, _1761106] : [-(hAPP(hAPP(c_List_Oappend(_1761102), hAPP(hAPP(c_List_Otake(_1761102), _1761104), _1761106)), hAPP(hAPP(c_List_Odrop(_1761102), _1761104), _1761106)) = _1761106)], (20863 ^ _778908) ^ [_1138793, _1138795, _1138797] : [class_Fields_Olinordered__field(_1138793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138793), _1138795), c_Groups_Ozero__class_Ozero(_1138793))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138793), c_Groups_Ozero__class_Ozero(_1138793)), _1138797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138793), _1138795), _1138797)), c_Groups_Ozero__class_Ozero(_1138793))))], (46142 ^ _778908) ^ [_1688641, _1688643, _1688645, _1688647, _1688649] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1688641), tc_List_Olist(_1688643), tc_List_Olist(_1688645), hAPP(c_List_Omap(_1688641, _1688643), _1688647)), hAPP(c_List_Omap(_1688645, _1688641), _1688649)) = hAPP(c_List_Omap(_1688645, _1688643), hAPP(c_Fun_Ocomp(_1688641, _1688643, _1688645, _1688647), _1688649)))], (34831 ^ _778908) ^ [_1417122, _1417124, _1417126, _1417128, _1417130] : [hAPP(_1417122, _1417124) = c_Option_Ooption_ONone(_1417126), -(c_Map_Oran(_1417128, _1417126, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1417128, tc_Option_Ooption(_1417126)), _1417122), _1417124), hAPP(c_Option_Ooption_OSome(_1417126), _1417130))) = hAPP(hAPP(c_Set_Oinsert(_1417126), _1417130), c_Map_Oran(_1417128, _1417126, _1417122)))], (27045 ^ _778908) ^ [_1256244, _1256246, _1256248, _1256250] : [class_Groups_Ocomm__monoid__add(_1256244), 27048 ^ _778908 : [(27055 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1256246)), _1256248))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256244), _1256250), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1256248, hAPP(c_Nat_OSuc, _1256246))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256244), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256244), _1256250), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1256248, _1256246))), hAPP(_1256250, hAPP(c_Nat_OSuc, _1256246))))], (27049 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1256246)), _1256248)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256244), _1256250), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1256248, hAPP(c_Nat_OSuc, _1256246))) = c_Groups_Ozero__class_Ozero(_1256244))]]], (22650 ^ _778908) ^ [_1171937, _1171939] : [22651 ^ _778908 : [(22654 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171939), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22652 ^ _778908) ^ [] : [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), _1171937), _1171939)))]], -(c_Divides_OnegDivAlg(_1171937, _1171939) = 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), _1171937), _1171939)))], (5781 ^ _778908) ^ [_871043, _871045] : [hAPP(c_Com_Ocom_OBODY, _871043) = hAPP(c_Com_Ocom_OBODY, _871045), -(_871043 = _871045)], (30752 ^ _778908) ^ [_1330361, _1330363, _1330365] : [class_Orderings_Olinorder(_1330361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330361), _1330363), _1330365)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330361, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330361, _1330363, _1330365)), hAPP(hAPP(c_Set_Oinsert(_1330361), _1330365), c_Orderings_Obot__class_Obot(tc_fun(_1330361, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1330361, _1330363, _1330365))], (46454 ^ _778908) ^ [_1696264, _1696266, _1696268, _1696270, _1696272] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1696264, _1696266)), hAPP(hAPP(c_Product__Type_OPair(_1696264, _1696266), _1696268), _1696270)), hAPP(c_List_Oset(tc_prod(_1696264, _1696266)), _1696272))), -(hAPP(c_Map_Omap__of(_1696264, _1696266, _1696272), _1696268) = hAPP(c_Option_Ooption_OSome(_1696266), 46457 ^ [_1696264, _1696266, _1696268, _1696270, _1696272]))], (44941 ^ _778908) ^ [_1661301, _1661303, _1661305, _1661307, _1661309] : [-(_1661301 = c_Orderings_Obot__class_Obot(tc_fun(_1661303, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661303, tc_fun(_1661305, tc_HOL_Obool)), _1661301), hAPP(hAPP(c_COMBC(_1661303, tc_fun(_1661305, tc_HOL_Obool), tc_fun(_1661305, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1661305, tc_HOL_Obool), tc_fun(tc_fun(_1661305, tc_HOL_Obool), tc_fun(_1661305, tc_HOL_Obool)), _1661303), c_Groups_Ominus__class_Ominus(tc_fun(_1661305, tc_HOL_Obool))), _1661307)), _1661309)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661305, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661303, tc_fun(_1661305, tc_HOL_Obool)), _1661301), _1661307)), _1661309))], (18301 ^ _778908) ^ [_1095144, _1095146] : [class_Int_Onumber__ring(_1095144), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095144), _1095146), hAPP(c_Int_Onumber__class_Onumber__of(_1095144), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1095144), _1095146))], (30580 ^ _778908) ^ [_1326806] : [class_Lattices_Oboolean__algebra(_1326806), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1326806), c_Orderings_Obot__class_Obot(_1326806)) = c_Orderings_Otop__class_Otop(_1326806))], (14543 ^ _778908) ^ [_1025779, _1025781, _1025783] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025779, _1025781)), _1025783) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025779), _1025783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025781), _1025783)))], (19581 ^ _778908) ^ [_1116153, _1116155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1116153)), c_Int_OBit0(_1116155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116153), _1116155)))], (20019 ^ _778908) ^ [_1124036, _1124038] : [class_Rings_Oring__1(_1124036), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1124036), hAPP(c_Groups_Ouminus__class_Ouminus(_1124036), c_Groups_Oone__class_Oone(_1124036))), 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)))), _1124038)) = c_Groups_Oone__class_Oone(_1124036))], (43487 ^ _778908) ^ [_1625367, _1625369, _1625371, _1625373, _1625375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625367, _1625367)), hAPP(hAPP(c_Product__Type_OPair(_1625367, _1625367), hAPP(_1625369, hAPP(c_Nat_OSuc, 43488 ^ [_1625367, _1625369, _1625371, _1625373, _1625375]))), hAPP(_1625369, 43488 ^ [_1625367, _1625369, _1625371, _1625373, _1625375]))), c_Transitive__Closure_Ortrancl(_1625367, _1625371))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625367, _1625367)), hAPP(hAPP(c_Product__Type_OPair(_1625367, _1625367), hAPP(_1625369, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1625373), _1625375))), hAPP(_1625369, _1625373))), c_Transitive__Closure_Ortrancl(_1625367, _1625371))))], (30326 ^ _778908) ^ [_1322193, _1322195, _1322197] : [class_Orderings_Oorder(_1322193), 30329 ^ _778908 : [(30336 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322193), _1322195), _1322197))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1322193, _1322195), _1322197) = c_Orderings_Obot__class_Obot(tc_fun(_1322193, tc_HOL_Obool)))], (30330 ^ _778908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1322193, _1322195), _1322197) = c_Orderings_Obot__class_Obot(tc_fun(_1322193, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322193), _1322195), _1322197))]]], (32080 ^ _778908) ^ [_1361103, _1361105, _1361107, _1361109, _1361111] : [class_Groups_Ocomm__monoid__add(_1361103), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361105), _1361107)), hBOOL(hAPP(hAPP(c_member(_1361105), _1361109), _1361107)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361105, _1361103), _1361111), _1361107) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361103), hAPP(_1361111, _1361109)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361105, _1361103), _1361111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361105, tc_HOL_Obool)), _1361107), hAPP(hAPP(c_Set_Oinsert(_1361105), _1361109), c_Orderings_Obot__class_Obot(tc_fun(_1361105, tc_HOL_Obool)))))))], (23637 ^ _778908) ^ [_1190737, _1190739, _1190741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1190737, tc_HOL_Obool)), _1190739), _1190741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1190737, tc_HOL_Obool)), _1190741), _1190739)), -(_1190739 = _1190741)], (20195 ^ _778908) ^ [_1127359, _1127361] : [class_Rings_Odivision__ring__inverse__zero(_1127359), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127359), _1127361), c_Groups_Ozero__class_Ozero(_1127359)) = c_Groups_Ozero__class_Ozero(_1127359))], (29815 ^ _778908) ^ [_1312426, _1312428, _1312430] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312426), _1312428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1312426, tc_HOL_Obool)), _1312430), _1312428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312426), _1312430)), hAPP(c_Finite__Set_Ocard(_1312426), _1312428))))], (51443 ^ _778908) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (4524 ^ _778908) ^ [_848916, _848918, _848920, _848922] : [-(c_Random_Oselect(_848922, _848918) = c_Random_Oselect(_848920, _848916)), _848922 = _848920, _848918 = _848916], (2890 ^ _778908) ^ [_822895, _822897, _822899, _822901, _822903, _822905] : [-(c_Nitpick_Oplus__frac(_822905, _822901, _822897) = c_Nitpick_Oplus__frac(_822903, _822899, _822895)), _822905 = _822903, _822901 = _822899, _822897 = _822895], (4218 ^ _778908) ^ [_843945, _843947, _843949, _843951, _843953, _843955] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_843955, _843951, _843947) = c_Smallcheck_Ofull__small__class_Ofull__small(_843953, _843949, _843945)), _843955 = _843953, _843951 = _843949, _843947 = _843945], (8548 ^ _778908) ^ [_922236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922236)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8388 ^ _778908) ^ [_919454, _919456, _919458] : [class_Rings_Olinordered__semidom(_919454), 8391 ^ _778908 : [(8398 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919456), _919458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919454), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919454), _919456)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919454), _919458))))], (8392 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919454), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919454), _919456)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919454), _919458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919456), _919458)))]]], (41490 ^ _778908) ^ [_1571575, _1571577, _1571579, _1571581] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1571575), hAPP(c_Set_OCollect(_1571575), _1571577))), 41493 ^ _778908 : [(41494 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1571579), hAPP(c_Set_OCollect(_1571579), hAPP(hAPP(c_COMBB(tc_fun(_1571575, tc_HOL_Obool), tc_HOL_Obool, _1571579), c_HOL_OEx(_1571575)), hAPP(hAPP(c_COMBB(tc_fun(_1571575, tc_HOL_Obool), tc_fun(_1571575, tc_HOL_Obool), _1571579), hAPP(c_COMBS(_1571575, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571575), c_fconj), _1571577))), _1571581))))), 41497 ^ _778908 : [(41498 ^ _778908) ^ [_1571858] : [hBOOL(hAPP(_1571577, _1571858)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1571579), hAPP(c_Set_OCollect(_1571579), hAPP(hAPP(c_COMBC(_1571579, _1571575, tc_HOL_Obool), _1571581), _1571858)))))]]], (41504 ^ _778908) ^ [] : [41506 ^ _778908 : [(41509 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1571579), hAPP(c_Set_OCollect(_1571579), hAPP(hAPP(c_COMBC(_1571579, _1571575, tc_HOL_Obool), _1571581), 41505 ^ [_1571575, _1571577, _1571579, _1571581]))))], (41507 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1571577, 41505 ^ [_1571575, _1571577, _1571579, _1571581])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1571579), hAPP(c_Set_OCollect(_1571579), hAPP(hAPP(c_COMBB(tc_fun(_1571575, tc_HOL_Obool), tc_HOL_Obool, _1571579), c_HOL_OEx(_1571575)), hAPP(hAPP(c_COMBB(tc_fun(_1571575, tc_HOL_Obool), tc_fun(_1571575, tc_HOL_Obool), _1571579), hAPP(c_COMBS(_1571575, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571575), c_fconj), _1571577))), _1571581))))))]]], (38200 ^ _778908) ^ [_1494639, _1494641] : [class_Lattices_Olattice(_1494639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494639), _1494641)), -(_1494641 = c_Orderings_Obot__class_Obot(tc_fun(_1494639, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494639), c_Big__Operators_Olattice__class_OInf__fin(_1494639, _1494641)), c_Big__Operators_Olattice__class_OSup__fin(_1494639, _1494641))))], (23987 ^ _778908) ^ [_1197227, _1197229, _1197231] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1197227), _1197229)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1197231), _1197229)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1197227), _1197231)), _1197229))], (22456 ^ _778908) ^ [_1167800, _1167802] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1167800)), hAPP(c_Code__Numeral_Oof__nat, _1167802)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167800), _1167802)))], (40797 ^ _778908) ^ [_1553819, _1553821, _1553823] : [class_Lattices_Oab__semigroup__idem__mult(_1553819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553819), _1553821)), -(_1553821 = c_Orderings_Obot__class_Obot(tc_fun(_1553819, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553819), _1553823)), -(_1553823 = c_Orderings_Obot__class_Obot(tc_fun(_1553819, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1553819, c_Groups_Otimes__class_Otimes(_1553819)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1553819, tc_HOL_Obool)), _1553821), _1553823)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1553819), hAPP(c_Finite__Set_Ofold1(_1553819, c_Groups_Otimes__class_Otimes(_1553819)), _1553821)), hAPP(c_Finite__Set_Ofold1(_1553819, c_Groups_Otimes__class_Otimes(_1553819)), _1553823)))], (13352 ^ _778908) ^ [_1003961, _1003963] : [_1003961 = hAPP(c_Int_Onat, _1003963), 13355 ^ _778908 : [(13362 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003963))), -(_1003961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13356 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003963)), -(_1003963 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1003961))]]], (7108 ^ _778908) ^ [_897767] : [hAPP(c_Nat_OSuc, _897767) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25861 ^ _778908) ^ [_1233187, _1233189, _1233191] : [class_Rings_Ocomm__semiring__1(_1233187), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233187), _1233189), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233187), _1233191), _1233189))))], (33415 ^ _778908) ^ [_1388751, _1388753] : [class_Groups_Olinordered__ab__group__add(_1388751), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388751), _1388753)), -(_1388753 = c_Orderings_Obot__class_Obot(tc_fun(_1388751, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1388751), c_Big__Operators_Olinorder__class_OMin(_1388751, _1388753)) = c_Big__Operators_Olinorder__class_OMax(_1388751, hAPP(c_Set_Oimage(_1388751, _1388751, c_Groups_Ouminus__class_Ouminus(_1388751)), _1388753)))], (44989 ^ _778908) ^ [_1662393, _1662395, _1662397, _1662399, _1662401] : [-(_1662393 = c_Orderings_Obot__class_Obot(tc_fun(_1662395, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662395, tc_fun(_1662397, tc_HOL_Obool)), _1662393), hAPP(hAPP(c_COMBB(tc_fun(_1662397, tc_HOL_Obool), tc_fun(_1662397, tc_HOL_Obool), _1662395), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1662397, tc_HOL_Obool)), _1662399)), _1662401)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1662397, tc_HOL_Obool)), _1662399), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1662395, tc_fun(_1662397, tc_HOL_Obool)), _1662393), _1662401)))], (38342 ^ _778908) ^ [_1497745] : [-(c_Equiv__Relations_Oequivp(_1497745, c_fequal))], (51411 ^ _778908) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (30108 ^ _778908) ^ [_1318184, _1318186, _1318188, _1318190] : [30110 ^ _778908 : [(30113 ^ _778908) ^ [] : [hAPP(_1318190, 30109 ^ [_1318184, _1318186, _1318188, _1318190]) = c_Orderings_Obot__class_Obot(tc_fun(_1318184, tc_HOL_Obool))], (30111 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318186), 30109 ^ [_1318184, _1318186, _1318188, _1318190]), _1318188)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1318184, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318186, tc_fun(_1318184, tc_HOL_Obool)), _1318188), _1318190))], (46577 ^ _778908) ^ [_1699032, _1699034, _1699036, _1699038, _1699040, _1699042] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1699032, _1699034)), hAPP(hAPP(c_Product__Type_OPair(_1699032, _1699034), _1699036), _1699038)), hAPP(c_List_Oset(tc_prod(_1699032, _1699034)), hAPP(hAPP(c_List_Ozip(_1699032, _1699034), _1699040), _1699042)))), -(hBOOL(hAPP(hAPP(c_member(_1699034), _1699038), hAPP(c_List_Oset(_1699034), _1699042))))], (17475 ^ _778908) ^ [_1080755, _1080757] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080755)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080757)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1080755), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1080757))))], (50477 ^ _778908) ^ [_1792547, _1792549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792547)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792549))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792547), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792549)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792547)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792547)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792549))))], (29560 ^ _778908) ^ [_1307595, _1307597, _1307599] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307595), _1307597)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307595), hAPP(hAPP(c_Set_Oinsert(_1307595), _1307599), _1307597))))], (27035 ^ _778908) ^ [_1256019, _1256021, _1256023, _1256025] : [class_Groups_Ocomm__monoid__add(_1256019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1256021), _1256023)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256019), _1256025), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1256021, _1256023)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256019), hAPP(_1256025, _1256021)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256019), _1256025), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1256021), _1256023))))], (16523 ^ _778908) ^ [_1062918, _1062920, _1062922] : [class_Rings_Oring__1(_1062918), -(hAPP(c_Int_Oring__1__class_Oof__int(_1062918), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1062920), _1062922)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1062918), hAPP(c_Int_Oring__1__class_Oof__int(_1062918), _1062920)), _1062922))], (44524 ^ _778908) ^ [_1649225, _1649227, _1649229, _1649231, _1649233, _1649235, _1649237] : [c_Finite__Set_Ofun__left__comm(_1649225, _1649227, _1649229), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1649225, _1649227, _1649229, _1649231, _1649233), _1649235)), hBOOL(hAPP(hAPP(c_member(_1649225), _1649237), _1649233)), 44536 ^ _778908 : [(44539 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1649225, _1649227, _1649229, _1649231, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1649225, tc_HOL_Obool)), _1649233), hAPP(hAPP(c_Set_Oinsert(_1649225), _1649237), c_Orderings_Obot__class_Obot(tc_fun(_1649225, tc_HOL_Obool))))), 44535 ^ [_1649225, _1649227, _1649229, _1649231, _1649233, _1649235, _1649237])))], (44537 ^ _778908) ^ [] : [-(_1649235 = hAPP(hAPP(_1649229, _1649237), 44535 ^ [_1649225, _1649227, _1649229, _1649231, _1649233, _1649235, _1649237]))]]], (14136 ^ _778908) ^ [_1018188, _1018190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018188), _1018190)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018188, _1018190) = _1018188)], (10535 ^ _778908) ^ [_955904, _955906, _955908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _955904), _955906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _955906), _955908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _955904), _955908)))], (33669 ^ _778908) ^ [_1392803, _1392805, _1392807] : [class_Orderings_Olinorder(_1392803), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392803), _1392805)), -(hBOOL(hAPP(hAPP(c_member(_1392803), _1392807), _1392805))), -(_1392805 = c_Orderings_Obot__class_Obot(tc_fun(_1392803, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1392803, hAPP(hAPP(c_Set_Oinsert(_1392803), _1392807), _1392805)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1392803), _1392807), c_Big__Operators_Olinorder__class_OMin(_1392803, _1392805)))], (46218 ^ _778908) ^ [_1690755, _1690757, _1690759, _1690761, _1690763, _1690765, _1690767] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1690755), tc_Option_Ooption(_1690757), tc_sum(_1690759, _1690761), hAPP(c_Option_Omap(_1690755, _1690757), _1690763)), c_Sum__Type_Osum_Osum__case(_1690759, tc_Option_Ooption(_1690755), _1690761, _1690765, _1690767)) = c_Sum__Type_Osum_Osum__case(_1690759, tc_Option_Ooption(_1690757), _1690761, hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1690755), tc_Option_Ooption(_1690757), _1690759, hAPP(c_Option_Omap(_1690755, _1690757), _1690763)), _1690765), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1690755), tc_Option_Ooption(_1690757), _1690761, hAPP(c_Option_Omap(_1690755, _1690757), _1690763)), _1690767)))], (16420 ^ _778908) ^ [_1061074, _1061076] : [_1061074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061074), _1061076) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37987 ^ _778908) ^ [_1490346, _1490348, _1490350, _1490352, _1490354] : [class_Groups_Ocomm__monoid__mult(_1490346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490348), _1490350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490348), _1490352)), 38001 ^ _778908 : [(38004 ^ _778908) ^ [] : [hAPP(_1490354, 38000 ^ [_1490346, _1490348, _1490350, _1490352, _1490354]) = c_Groups_Oone__class_Oone(_1490346)], (38002 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490348), 38000 ^ [_1490346, _1490348, _1490350, _1490352, _1490354]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490348, tc_HOL_Obool)), _1490350), _1490352))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490348, _1490346), _1490354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490348, tc_HOL_Obool)), _1490350), _1490352)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1490346), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490348, _1490346), _1490354), _1490350)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490348, _1490346), _1490354), _1490352)))], (22420 ^ _778908) ^ [_1167184, _1167186] : [hAPP(c_Code__Numeral_Oof__nat, _1167184) = hAPP(c_Code__Numeral_Oof__nat, _1167186), -(_1167184 = _1167186)], (17079 ^ _778908) ^ [_1073261, _1073263, _1073265] : [class_Int_Onumber__ring(_1073261), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073261), hAPP(c_Int_Onumber__class_Onumber__of(_1073261), _1073263)), hAPP(c_Int_Onumber__class_Onumber__of(_1073261), _1073265)) = hAPP(c_Int_Onumber__class_Onumber__of(_1073261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1073263), _1073265)))], (31774 ^ _778908) ^ [_1353194, _1353196, _1353198, _1353200, _1353202, _1353204] : [hBOOL(hAPP(hAPP(c_member(_1353194), _1353196), _1353198)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353194, tc_fun(_1353200, tc_HOL_Obool)), _1353198), hAPP(hAPP(c_COMBB(tc_fun(_1353200, tc_HOL_Obool), tc_fun(_1353200, tc_HOL_Obool), _1353194), hAPP(c_Set_Oinsert(_1353200), _1353202)), _1353204)) = hAPP(hAPP(c_Set_Oinsert(_1353200), _1353202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353194, tc_fun(_1353200, tc_HOL_Obool)), _1353198), _1353204)))], (25239 ^ _778908) ^ [_1222713] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222713), _1222713)))], (49954 ^ _778908) ^ [_1781876, _1781878, _1781880] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1781876), tc_List_Olist(_1781876)), c_List_Opartition(_1781876, _1781878, _1781880)) = hAPP(c_List_Ofilter(_1781876, _1781878), _1781880))], (9424 ^ _778908) ^ [_936560, _936562, _936564] : [class_Groups_Ogroup__add(_936560), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936560), hAPP(c_Groups_Ouminus__class_Ouminus(_936560), _936562)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936560), _936562), _936564)) = _936564)], (22684 ^ _778908) ^ [_1172566, _1172568, _1172570] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1172566, _1172568, _1172570, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1172568)], (18083 ^ _778908) ^ [_1091557, _1091559, _1091561] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091557)))), 18086 ^ _778908 : [(18093 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091559)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091557)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091559)), _1091561)) = 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), _1091557), _1091559))), _1091561))], (18087 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091559))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091557)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091559)), _1091561)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091557)), _1091561))]]], (32207 ^ _778908) ^ [_1364079, _1364081, _1364083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1364079)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1364081), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1364083)), 32214 ^ _778908 : [(32215 ^ _778908) ^ [_1364287] : [32217 ^ _778908 : [(32223 ^ _778908) ^ [] : [-(_1364287 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32219 ^ [_1364079, _1364081, _1364083, _1364287]), 32216 ^ [_1364079, _1364081, _1364083, _1364287]))], (32221 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32219 ^ [_1364079, _1364081, _1364083, _1364287]), _1364083)))], (32218 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32216 ^ [_1364079, _1364081, _1364083, _1364287]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1364079))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1364287), _1364081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1364287), _1364079)), _1364081)))]]], (16052 ^ _778908) ^ [_1053231, _1053233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1053231), _1053233)), -(c_Nat__Transfer_Otsub(_1053233, _1053231) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1053233), _1053231))], (10078 ^ _778908) ^ [_948282, _948284] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948282)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948284)), _948282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _948284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41694 ^ _778908) ^ [_1580391, _1580393] : [-(hAPP(c_Fun_Oid(_1580391), _1580393) = _1580393)], (50815 ^ _778908) ^ [_1800130, _1800132] : [50817 ^ _778908 : [(50820 ^ _778908) ^ [] : [50816 ^ [_1800130, _1800132] = c_List_Olist_ONil(_1800130)], (50818 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1800130)), 50816 ^ [_1800130, _1800132]), hAPP(c_List_Oset(tc_List_Olist(_1800130)), _1800132))))]], -(c_List_Olist_ONil(_1800130) = c_List_Oconcat(_1800130, _1800132))], (49341 ^ _778908) ^ [_1768573, _1768575] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1768573), _1768575) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1768573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 49347 ^ _778908 : [(49350 ^ _778908) ^ [] : [49346 ^ [_1768573, _1768575] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49348 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49346 ^ [_1768573, _1768575]), hAPP(c_List_Oset(tc_Nat_Onat), _1768575))))]]], (46061 ^ _778908) ^ [_1686932, _1686934, _1686936, _1686938, _1686940, _1686942, _1686944] : [hAPP(_1686932, _1686934) = hAPP(c_Option_Ooption_OSome(_1686936), _1686938), -(c_Map_Omap__comp(_1686936, _1686940, _1686942, _1686944, _1686932, _1686934) = hAPP(_1686944, _1686938))], (49191 ^ _778908) ^ [_1765408, _1765410, _1765412] : [-(hAPP(c_List_Oset(_1765408), hAPP(c_List_Orotate(_1765408, _1765410), _1765412)) = hAPP(c_List_Oset(_1765408), _1765412))], (51241 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (16276 ^ _778908) ^ [_1058374, _1058376, _1058378, _1058380, _1058382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058374), _1058376)), -(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), _1058376), _1058378)), _1058380)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058374), _1058378)), _1058382)) = 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), _1058376), _1058374)), _1058378)), _1058380)), _1058382))], (4738 ^ _778908) ^ [_852251, _852253, _852255, _852257] : [-(c_Complete__Lattice_OInf__class_OInf(_852257, _852253) = c_Complete__Lattice_OInf__class_OInf(_852255, _852251)), _852257 = _852255, _852253 = _852251], (44434 ^ _778908) ^ [_1647532, _1647534, _1647536, _1647538, _1647540, _1647542] : [c_Finite__Set_Ofun__left__comm(_1647532, _1647534, _1647536), -(hAPP(hAPP(_1647536, _1647538), hAPP(hAPP(_1647536, _1647540), _1647542)) = hAPP(hAPP(_1647536, _1647540), hAPP(hAPP(_1647536, _1647538), _1647542)))], (18795 ^ _778908) ^ [_1102728, _1102730] : [class_Int_Onumber__ring(_1102728), 18798 ^ _778908 : [(18805 ^ _778908) ^ [] : [c_Int_Oiszero(_1102728, hAPP(c_Int_Onumber__class_Onumber__of(_1102728), 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), _1102730)))), -(c_Groups_Oone__class_Oone(_1102728) = hAPP(c_Int_Onumber__class_Onumber__of(_1102728), _1102730))], (18799 ^ _778908) ^ [] : [c_Groups_Oone__class_Oone(_1102728) = hAPP(c_Int_Onumber__class_Onumber__of(_1102728), _1102730), -(c_Int_Oiszero(_1102728, hAPP(c_Int_Onumber__class_Onumber__of(_1102728), 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), _1102730)))))]]], (24789 ^ _778908) ^ [_1213206, _1213208, _1213210] : [class_Groups_Olinordered__ab__group__add(_1213206), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1213206), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213206), _1213208), _1213210)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213206), hAPP(c_Groups_Ouminus__class_Ouminus(_1213206), _1213208)), hAPP(c_Groups_Ouminus__class_Ouminus(_1213206), _1213210)))], (46053 ^ _778908) ^ [_1686746, _1686748, _1686750, _1686752, _1686754, _1686756] : [-(c_Map_Omap__comp(_1686746, _1686748, _1686750, _1686752, _1686754, _1686756) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1686748), _1686746, c_Option_Ooption_ONone(_1686748), _1686752), hAPP(_1686754, _1686756)))], (25873 ^ _778908) ^ [_1233401, _1233403, _1233405] : [class_Rings_Olinordered__idom(_1233401), 25876 ^ _778908 : [(25883 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233401), _1233403), _1233405)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233401), _1233403), hAPP(c_Groups_Oabs__class_Oabs(_1233401), _1233405))))], (25877 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233401), _1233403), hAPP(c_Groups_Oabs__class_Oabs(_1233401), _1233405))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233401), _1233403), _1233405)))]]], (46228 ^ _778908) ^ [_1691078, _1691080, _1691082, _1691084, _1691086] : [hAPP(hAPP(c_Option_Omap(_1691078, _1691080), _1691082), _1691084) = hAPP(c_Option_Ooption_OSome(_1691080), _1691086), 46232 ^ _778908 : [(46235 ^ _778908) ^ [] : [-(hAPP(_1691082, 46231 ^ [_1691078, _1691080, _1691082, _1691084, _1691086]) = _1691086)], (46233 ^ _778908) ^ [] : [-(_1691084 = hAPP(c_Option_Ooption_OSome(_1691078), 46231 ^ [_1691078, _1691080, _1691082, _1691084, _1691086]))]]], (42489 ^ _778908) ^ [_1600799, _1600801] : [c_Nitpick_Owf_H(_1600799, _1600801), 42492 ^ _778908 : [(42495 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1600799, _1600799)), _1600801))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (42493 ^ _778908) ^ [] : [-(c_Wellfounded_Oacyclic(_1600799, _1600801))]]], (4950 ^ _778908) ^ [_855495, _855497] : [_855497 = _855495, -(c_Set_Oinsert(_855497) = c_Set_Oinsert(_855495))], (35909 ^ _778908) ^ [_1442705, _1442707, _1442709, _1442711, _1442713, _1442715] : [c_Finite__Set_Ofolding(_1442705, _1442707, _1442709, _1442711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442705), _1442713)), -(hAPP(_1442711, hAPP(hAPP(c_Set_Oinsert(_1442705), _1442715), _1442713)) = hAPP(c_Fun_Ocomp(_1442707, _1442707, _1442707, hAPP(_1442711, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1442705, tc_HOL_Obool)), _1442713), hAPP(hAPP(c_Set_Oinsert(_1442705), _1442715), c_Orderings_Obot__class_Obot(tc_fun(_1442705, tc_HOL_Obool)))))), hAPP(_1442709, _1442715)))], (46697 ^ _778908) ^ [_1702290, _1702292, _1702294, _1702296] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702290)), hAPP(hAPP(c_List_Omap(_1702292, _1702290), _1702294), _1702296)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702292)), _1702296))], (24805 ^ _778908) ^ [_1213629] : [class_Orderings_Olinorder(_1213629), -(c_Orderings_Oord_Omin(_1213629, hAPP(c_COMBC(_1213629, _1213629, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1213629))) = c_Orderings_Oord__class_Omax(_1213629))], (18471 ^ _778908) ^ [_1097710, _1097712, _1097714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097710), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097710)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097712)), _1097714)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45322 ^ _778908) ^ [_1670132] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670132, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1670132, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1670132, tc_HOL_Obool)))], (38406 ^ _778908) ^ [_1498885, _1498887, _1498889, _1498891, _1498893] : [c_Finite__Set_Ofolding__idem(_1498885, _1498887, _1498889, _1498891), -(hAPP(c_Fun_Ocomp(_1498887, _1498887, _1498887, hAPP(_1498889, _1498893)), hAPP(_1498889, _1498893)) = hAPP(_1498889, _1498893))], (22668 ^ _778908) ^ [_1172168, _1172170, _1172172] : [class_Int_Onumber__ring(_1172168), 22671 ^ _778908 : [(22678 ^ _778908) ^ [] : [-(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), _1172170)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172168), hAPP(c_Int_Onumber__class_Onumber__of(_1172168), _1172172)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1172170))) = c_Groups_Oone__class_Oone(_1172168))], (22672 ^ _778908) ^ [] : [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), _1172170))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172168), hAPP(c_Int_Onumber__class_Onumber__of(_1172168), _1172172)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1172170))) = hAPP(hAPP(c_HOL_OLet(_1172168, _1172168), hAPP(hAPP(c_Power_Opower__class_Opower(_1172168), hAPP(c_Int_Onumber__class_Onumber__of(_1172168), _1172172)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172170))), hAPP(hAPP(c_COMBS(_1172168, _1172168, _1172168), hAPP(hAPP(c_COMBB(_1172168, tc_fun(_1172168, _1172168), _1172168), c_Groups_Otimes__class_Otimes(_1172168)), hAPP(c_Groups_Otimes__class_Otimes(_1172168), hAPP(c_Int_Onumber__class_Onumber__of(_1172168), _1172172)))), c_COMBI(_1172168))))]]], (3174 ^ _778908) ^ [_827525, _827527] : [_827527 = _827525, -(c_Int_OBit1(_827527) = c_Int_OBit1(_827525))], (16919 ^ _778908) ^ [_1069986, _1069988, _1069990] : [class_Int_Onumber(_1069986), class_Orderings_Olinorder(_1069986), 16926 ^ _778908 : [(16933 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069986), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069990)), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069988)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069986), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069988)), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069990))))], (16927 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069986), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069988)), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069990))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069986), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069990)), hAPP(c_Int_Onumber__class_Onumber__of(_1069986), _1069988)))]]], (31562 ^ _778908) ^ [_1348541, _1348543, _1348545, _1348547] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348541, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1348541), _1348543), _1348545)), _1348547))), hBOOL(hAPP(hAPP(c_member(_1348541), _1348543), _1348547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348541, tc_HOL_Obool)), _1348545), _1348547))], (15044 ^ _778908) ^ [_1034106, _1034108, _1034110, _1034112] : [class_Divides_Osemiring__div(_1034106), -(_1034108 = c_Groups_Ozero__class_Ozero(_1034106)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034106), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034106), _1034110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034106), _1034108), _1034112))), _1034108) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034106), _1034112), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034106), _1034110), _1034108)))], (7907 ^ _778908) ^ [_910982, _910984] : [7908 ^ _778908 : [(7911 ^ _778908) ^ [] : [_910982 = _910984], (7909 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910982), _910984))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910982), hAPP(c_Nat_OSuc, _910984))))], (25241 ^ _778908) ^ [_1222741, _1222743] : [class_Rings_Ocomm__semiring__1(_1222741), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222741), _1222743), c_Groups_Ozero__class_Ozero(_1222741))))], (31816 ^ _778908) ^ [_1354439, _1354441, _1354443, _1354445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1354439, tc_fun(_1354441, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1354439, tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_fun(_1354441, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354441, tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_fun(_1354441, tc_HOL_Obool)), _1354439), c_COMBC(_1354441, tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354441, tc_prod(_1354439, _1354441)), tc_fun(_1354441, tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool)), _1354439), hAPP(c_COMBB(tc_prod(_1354439, _1354441), tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool), _1354441), c_member(tc_prod(_1354439, _1354441)))), c_Product__Type_OPair(_1354439, _1354441)))), _1354443)), hAPP(hAPP(c_COMBC(_1354439, tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_fun(_1354441, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354441, tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_fun(_1354441, tc_HOL_Obool)), _1354439), c_COMBC(_1354441, tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1354441, tc_prod(_1354439, _1354441)), tc_fun(_1354441, tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool)), _1354439), hAPP(c_COMBB(tc_prod(_1354439, _1354441), tc_fun(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool), tc_HOL_Obool), _1354441), c_member(tc_prod(_1354439, _1354441)))), c_Product__Type_OPair(_1354439, _1354441)))), _1354445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1354439, _1354441), tc_HOL_Obool)), _1354443), _1354445)))], (40158 ^ _778908) ^ [_1538558, _1538560, _1538562, _1538564, _1538566] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1538558, _1538560), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1538558, tc_HOL_Obool)), _1538562), _1538564)), hAPP(c_COMBK(tc_fun(_1538560, tc_HOL_Obool), _1538558), _1538566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538558, _1538560), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1538558, _1538560), _1538562), hAPP(c_COMBK(tc_fun(_1538560, tc_HOL_Obool), _1538558), _1538566))), hAPP(hAPP(c_Product__Type_OSigma(_1538558, _1538560), _1538564), hAPP(c_COMBK(tc_fun(_1538560, tc_HOL_Obool), _1538558), _1538566))))], (30762 ^ _778908) ^ [_1330570, _1330572, _1330574] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330570), _1330572)), -(hAPP(c_Finite__Set_Ocard(_1330570), hAPP(hAPP(c_Set_Oinsert(_1330570), _1330574), _1330572)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1330570), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330570, tc_HOL_Obool)), _1330572), hAPP(hAPP(c_Set_Oinsert(_1330570), _1330574), c_Orderings_Obot__class_Obot(tc_fun(_1330570, tc_HOL_Obool)))))))], (50779 ^ _778908) ^ [_1799310, _1799312, _1799314] : [-(c_List_Oconcat(_1799310, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1799310)), _1799312), _1799314)) = hAPP(hAPP(c_List_Oappend(_1799310), _1799312), c_List_Oconcat(_1799310, _1799314)))], (30224 ^ _778908) ^ [_1320435, _1320437] : [-(c_Sum__Type_OPlus(_1320435, _1320437, c_Orderings_Otop__class_Otop(tc_fun(_1320435, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1320437, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1320435, _1320437), tc_HOL_Obool)))], (42785 ^ _778908) ^ [_1608182, _1608184, _1608186, _1608188, _1608190, _1608192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608182, tc_HOL_Obool)), _1608184), _1608186)), 42791 ^ _778908 : [(42794 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608188, tc_HOL_Obool)), hAPP(_1608190, 42790 ^ [_1608182, _1608184, _1608186, _1608188, _1608190, _1608192])), hAPP(_1608192, 42790 ^ [_1608182, _1608184, _1608186, _1608188, _1608190, _1608192])))], (42792 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608182), 42790 ^ [_1608182, _1608184, _1608186, _1608188, _1608190, _1608192]), _1608184)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1608182, _1608188), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1608182, _1608188), _1608184), _1608190)), hAPP(hAPP(c_Product__Type_OSigma(_1608182, _1608188), _1608186), _1608192))))], (10455 ^ _778908) ^ [_954563] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954563), _954563))))], (28969 ^ _778908) ^ [_1295039, _1295041, _1295043, _1295045, _1295047, _1295049] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295039, tc_fun(_1295041, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295043, tc_fun(_1295039, tc_HOL_Obool)), _1295045), _1295047)), _1295049) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295043, tc_fun(_1295041, tc_HOL_Obool)), _1295045), hAPP(hAPP(c_COMBC(_1295043, tc_fun(_1295039, tc_fun(_1295041, tc_HOL_Obool)), tc_fun(_1295041, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1295039, tc_HOL_Obool), tc_fun(tc_fun(_1295039, tc_fun(_1295041, tc_HOL_Obool)), tc_fun(_1295041, tc_HOL_Obool)), _1295043), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295039, tc_fun(_1295041, tc_HOL_Obool))), _1295047)), _1295049)))], (19383 ^ _778908) ^ [_1112719] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1112719)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1112719)))], (28505 ^ _778908) ^ [_1285220, _1285222, _1285224] : [class_Lattices_Olattice(_1285220), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285220), _1285222), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285220), _1285222), _1285224))))], (23228 ^ _778908) ^ [_1183124, _1183126, _1183128, _1183130, _1183132, _1183134] : [-(hAPP(c_Product__Type_Oapsnd(_1183124, _1183126, _1183128, _1183130), hAPP(hAPP(c_Product__Type_OPair(_1183128, _1183124), _1183132), _1183134)) = hAPP(hAPP(c_Product__Type_OPair(_1183128, _1183126), _1183132), hAPP(_1183130, _1183134)))], (27071 ^ _778908) ^ [_1256886, _1256888] : [27079 ^ _778908 : [(27082 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1256888, 27078 ^ [_1256886, _1256888])))], (27080 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27078 ^ [_1256886, _1256888]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1256886))))]], 27072 ^ _778908 : [(27073 ^ _778908) ^ [_1256955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1256955), _1256886)), hBOOL(hAPP(_1256888, _1256955))]]], (8835 ^ _778908) ^ [_926256, _926258] : [class_Rings_Olinordered__idom(_926256), 8838 ^ _778908 : [(8845 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _926258), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926256), hAPP(c_Int_Oring__1__class_Oof__int(_926256), _926258)), c_Groups_Ozero__class_Ozero(_926256))))], (8839 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926256), hAPP(c_Int_Oring__1__class_Oof__int(_926256), _926258)), c_Groups_Ozero__class_Ozero(_926256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _926258), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (43251 ^ _778908) ^ [_1619845, _1619847, _1619849, _1619851, _1619853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619845, _1619845)), hAPP(hAPP(c_Product__Type_OPair(_1619845, _1619845), _1619847), _1619849)), c_Transitive__Closure_Ortrancl(_1619845, _1619851))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1619845, _1619845)), hAPP(hAPP(c_Product__Type_OPair(_1619845, _1619845), _1619849), _1619853)), _1619851)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619845, _1619845)), hAPP(hAPP(c_Product__Type_OPair(_1619845, _1619845), _1619847), _1619853)), c_Transitive__Closure_Ortrancl(_1619845, _1619851))))], (4822 ^ _778908) ^ [_853523, _853525, _853527, _853529] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_853529, _853525) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_853527, _853523)), _853529 = _853527, _853525 = _853523], (10090 ^ _778908) ^ [_948482, _948484, _948486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _948482), _948484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _948486), _948482)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _948486), _948484))))], (48891 ^ _778908) ^ [_1758751, _1758753, _1758755, _1758757] : [-(hAPP(hAPP(c_List_Oappend(_1758751), _1758753), _1758755) = _1758757), _1758753 = hAPP(hAPP(c_List_Otake(_1758751), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758751)), _1758753)), _1758757), _1758755 = hAPP(hAPP(c_List_Odrop(_1758751), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758751)), _1758753)), _1758757)], (45929 ^ _778908) ^ [_1683506, _1683508, _1683510, _1683512] : [c_Fun_Oinj__on(_1683506, tc_Option_Ooption(_1683508), c_Map_Omap__add(_1683506, _1683508, _1683510, _1683512), c_Map_Odom(_1683506, _1683508, _1683512)), -(c_Fun_Oinj__on(_1683506, tc_Option_Ooption(_1683508), _1683512, c_Map_Odom(_1683506, _1683508, _1683512)))], (33135 ^ _778908) ^ [_1383359, _1383361] : [class_Int_Onumber__ring(_1383359), -(hBOOL(hAPP(hAPP(c_member(_1383359), hAPP(c_Int_Onumber__class_Onumber__of(_1383359), _1383361)), c_Int_Oring__1__class_OInts(_1383359))))], (23291 ^ _778908) ^ [_1184489, _1184491, _1184493, _1184495, _1184497, _1184499, _1184501, _1184503] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184489, _1184491, _1184493), _1184495), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184497, _1184499, tc_prod(_1184489, _1184491)), _1184501), _1184503)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184497, _1184499, _1184493), hAPP(hAPP(c_COMBB(tc_fun(_1184499, tc_prod(_1184489, _1184491)), tc_fun(_1184499, _1184493), _1184497), hAPP(c_COMBB(tc_prod(_1184489, _1184491), _1184493, _1184499), hAPP(c_Product__Type_Oprod_Oprod__case(_1184489, _1184491, _1184493), _1184495))), _1184501)), _1184503))], (15986 ^ _778908) ^ [_1051873, _1051875, _1051877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051873), _1051875)), 15989 ^ _778908 : [(15996 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051877), _1051873)), _1051875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051875), _1051873))))], (15990 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051875), _1051873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051877), _1051873)), _1051875)))]]], (43303 ^ _778908) ^ [_1621103, _1621105, _1621107, _1621109, _1621111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621103, _1621103)), hAPP(hAPP(c_Product__Type_OPair(_1621103, _1621103), _1621105), _1621107)), c_Transitive__Closure_Otrancl(_1621103, _1621109))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1621103, _1621103)), hAPP(hAPP(c_Product__Type_OPair(_1621103, _1621103), _1621107), _1621111)), c_Transitive__Closure_Ortrancl(_1621103, _1621109))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621103, _1621103)), hAPP(hAPP(c_Product__Type_OPair(_1621103, _1621103), _1621105), _1621111)), c_Transitive__Closure_Otrancl(_1621103, _1621109))))], (35440 ^ _778908) ^ [_1431200, _1431202, _1431204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431200, tc_HOL_Obool)), _1431202), _1431204)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1431200, tc_HOL_Obool)), _1431202), hAPP(c_Set_OPow(_1431200), _1431204))))], (7791 ^ _778908) ^ [_909279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _909279)), _909279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48010 ^ _778908) ^ [_1735916, _1735918, _1735920, _1735922] : [-(c_List_Osublist(_1735916, hAPP(hAPP(c_List_Olist_OCons(_1735916), _1735918), _1735920), _1735922) = hAPP(hAPP(c_List_Oappend(_1735916), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1735916)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1735922)), hAPP(hAPP(c_List_Olist_OCons(_1735916), _1735918), c_List_Olist_ONil(_1735916))), c_List_Olist_ONil(_1735916))), c_List_Osublist(_1735916, _1735920, 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)), _1735922)))))], (314 ^ _778908) ^ [_783495, _783497, _783499, _783501, _783503, _783505, _783507, _783509, _783511, _783513, _783515, _783517] : [-(c_Equiv__Relations_Ocongruent2(_783515, _783511, _783507, _783503, _783499, _783495)), c_Equiv__Relations_Ocongruent2(_783517, _783513, _783509, _783505, _783501, _783497), _783517 = _783515, _783513 = _783511, _783509 = _783507, _783505 = _783503, _783501 = _783499, _783497 = _783495], (14573 ^ _778908) ^ [_1026334, _1026336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026336)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1026334)), hAPP(c_Int_Onat, _1026336)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1026334), _1026336)))], (42399 ^ _778908) ^ [_1598734, _1598736, _1598738, _1598740] : [hBOOL(hAPP(c_Predicate_ODomainP(_1598734, _1598736, hAPP(hAPP(c_COMBC(_1598734, tc_fun(tc_prod(_1598734, _1598736), tc_HOL_Obool), tc_fun(_1598736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598736, tc_fun(tc_fun(tc_prod(_1598734, _1598736), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598734, _1598736), tc_HOL_Obool), tc_fun(_1598736, tc_HOL_Obool)), _1598734), c_COMBC(_1598736, tc_fun(tc_prod(_1598734, _1598736), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598736, tc_prod(_1598734, _1598736)), tc_fun(_1598736, tc_fun(tc_fun(tc_prod(_1598734, _1598736), tc_HOL_Obool), tc_HOL_Obool)), _1598734), hAPP(c_COMBB(tc_prod(_1598734, _1598736), tc_fun(tc_fun(tc_prod(_1598734, _1598736), tc_HOL_Obool), tc_HOL_Obool), _1598736), c_member(tc_prod(_1598734, _1598736)))), c_Product__Type_OPair(_1598734, _1598736)))), _1598738)), _1598740)), -(hBOOL(hAPP(hAPP(c_member(_1598734), _1598740), hAPP(c_Relation_ODomain(_1598734, _1598736), _1598738))))], (5833 ^ _778908) ^ [_871696, _871698] : [-(c_String_Ochar_Ochar__size(hAPP(hAPP(c_String_Ochar_OChar, _871696), _871698)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46299 ^ _778908) ^ [_1692600, _1692602, _1692604, _1692606] : [c_Fun_Oinj__on(_1692600, _1692602, _1692604, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1692600, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1692600), tc_fun(_1692600, tc_HOL_Obool), c_List_Oset(_1692600)), _1692606))), -(c_Fun_Oinj__on(tc_List_Olist(_1692600), tc_List_Olist(_1692602), hAPP(c_List_Omap(_1692600, _1692602), _1692604), _1692606))], (10910 ^ _778908) ^ [_962062, _962064, _962066] : [class_Orderings_Olinorder(_962062), 10913 ^ _778908 : [(10920 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962062), _962066), _962064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962062), _962064), _962066))], (10914 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962062), _962064), _962066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962062), _962066), _962064)))]]], (31127 ^ _778908) ^ [_1337935, _1337937, _1337939, _1337941] : [hBOOL(hAPP(hAPP(c_member(_1337935), _1337937), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337935, tc_HOL_Obool)), _1337939), _1337941))), -(hBOOL(hAPP(hAPP(c_member(_1337935), _1337937), _1337939))), -(hBOOL(hAPP(hAPP(c_member(_1337935), _1337937), _1337941)))], (9240 ^ _778908) ^ [_933607] : [class_Rings_Osemiring__1(_933607), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_933607), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_933607))], (7729 ^ _778908) ^ [_908153, _908155, _908157, _908159] : [class_Groups_Oordered__cancel__ab__semigroup__add(_908153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908153), _908155), _908157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908153), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908153), _908155), _908159)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908153), _908157), _908159))))], (5949 ^ _778908) ^ [_873899] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _873899)], (35661 ^ _778908) ^ [_1436183, _1436185, _1436187, _1436189, _1436191] : [class_Groups_Ocomm__monoid__add(_1436183), class_Groups_Ocomm__monoid__mult(_1436183), _1436185 = _1436187, c_Nat__Transfer_Onat__set(_1436187), 35679 ^ _778908 : [(35682 ^ _778908) ^ [] : [hAPP(_1436189, 35678 ^ [_1436183, _1436185, _1436187, _1436189, _1436191]) = hAPP(_1436191, 35678 ^ [_1436183, _1436185, _1436187, _1436189, _1436191])], (35680 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35678 ^ [_1436183, _1436185, _1436187, _1436189, _1436191])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1436183), _1436189), _1436185) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1436183), _1436191), _1436187))], (22362 ^ _778908) ^ [_1166209, _1166211, _1166213, _1166215] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1166209, _1166211, _1166213, c_Code__Numeral_OSuc__code__numeral(_1166215)) = hAPP(_1166213, _1166215))], (51417 ^ _778908) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (33455 ^ _778908) ^ [_1389392, _1389394, _1389396] : [class_Orderings_Olinorder(_1389392), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389392), _1389394)), hBOOL(hAPP(hAPP(c_member(_1389392), _1389396), _1389394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389392), _1389396), c_Big__Operators_Olinorder__class_OMax(_1389392, _1389394))))], (40260 ^ _778908) ^ [_1541154, _1541156, _1541158, _1541160] : [_1541154 = c_Orderings_Obot__class_Obot(tc_fun(_1541156, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1541156, _1541158), _1541158, c_Product__Type_Osnd(_1541156, _1541158)), hAPP(hAPP(c_Product__Type_OSigma(_1541156, _1541158), _1541154), hAPP(c_COMBK(tc_fun(_1541158, tc_HOL_Obool), _1541156), _1541160))) = c_Orderings_Obot__class_Obot(tc_fun(_1541158, tc_HOL_Obool)))], (20767 ^ _778908) ^ [_1137292, _1137294] : [class_Rings_Odivision__ring(_1137292), -(_1137294 = c_Groups_Ozero__class_Ozero(_1137292)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137292), _1137294), _1137294) = c_Groups_Oone__class_Oone(_1137292))], (9598 ^ _778908) ^ [_939738, _939740, _939742] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939738), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _939740), _939742)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939738), _939740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939738), _939742)))], (42180 ^ _778908) ^ [_1593044, _1593046] : [-(hAPP(c_Relation_ORange(_1593044, _1593044), c_Relation_OId__on(_1593044, _1593046)) = _1593046)], (22412 ^ _778908) ^ [_1167058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1167058)), _1167058 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11436 ^ _778908) ^ [_970295, _970297, _970299] : [class_Groups_Oordered__ab__group__add(_970295), 11439 ^ _778908 : [(11446 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970295), _970299), hAPP(c_Groups_Ouminus__class_Ouminus(_970295), _970297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970295), _970297), hAPP(c_Groups_Ouminus__class_Ouminus(_970295), _970299))))], (11440 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970295), _970297), hAPP(c_Groups_Ouminus__class_Ouminus(_970295), _970299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970295), _970299), hAPP(c_Groups_Ouminus__class_Ouminus(_970295), _970297))))]]], (44621 ^ _778908) ^ [_1651338, _1651340, _1651342, _1651344] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1651338, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1651340, tc_fun(_1651338, tc_HOL_Obool)), _1651342), _1651344)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651340, tc_fun(_1651338, tc_HOL_Obool)), _1651342), hAPP(hAPP(c_COMBB(tc_fun(_1651338, tc_HOL_Obool), tc_fun(_1651338, tc_HOL_Obool), _1651340), c_Groups_Ouminus__class_Ouminus(tc_fun(_1651338, tc_HOL_Obool))), _1651344)))], (7885 ^ _778908) ^ [_910639, _910641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _910639)), hAPP(c_Nat_OSuc, _910641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910639), _910641)))], (6141 ^ _778908) ^ [_877400, _877402] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _877400), _877402)), -(_877402 = _877400)], (45799 ^ _778908) ^ [_1680793, _1680795, _1680797, _1680799, _1680801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1680793, tc_HOL_Obool)), _1680795), _1680797)), 45805 ^ _778908 : [(45810 ^ _778908) ^ [] : [hBOOL(hAPP(_1680801, 45804 ^ [_1680793, _1680795, _1680797, _1680799, _1680801]))], (45808 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1680799, 45804 ^ [_1680793, _1680795, _1680797, _1680799, _1680801])))], (45806 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1680793), 45804 ^ [_1680793, _1680795, _1680797, _1680799, _1680801]), _1680795)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1680793, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680793, tc_HOL_Obool)), _1680795), hAPP(c_Set_OCollect(_1680793), _1680799))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680793, tc_HOL_Obool)), _1680797), hAPP(c_Set_OCollect(_1680793), _1680801)))))], (8574 ^ _778908) ^ [_922649, _922651] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922649), _922651) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922651), _922649))], (35190 ^ _778908) ^ [_1425851, _1425853, _1425855] : [class_Orderings_Olinorder(_1425851), hAPP(_1425853, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1425851), 35195 ^ [_1425851, _1425853, _1425855]), 35196 ^ [_1425851, _1425853, _1425855])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1425851), hAPP(_1425853, 35195 ^ [_1425851, _1425853, _1425855])), hAPP(_1425853, 35196 ^ [_1425851, _1425853, _1425855])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425851), _1425855)), -(_1425855 = c_Orderings_Obot__class_Obot(tc_fun(_1425851, tc_HOL_Obool))), -(hAPP(_1425853, c_Big__Operators_Olinorder__class_OMin(_1425851, _1425855)) = c_Big__Operators_Olinorder__class_OMin(_1425851, hAPP(c_Set_Oimage(_1425851, _1425851, _1425853), _1425855)))], (2422 ^ _778908) ^ [_815455, _815457] : [_815457 = _815455, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_815457) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_815455))], (46094 ^ _778908) ^ [_1687677] : [-(hAPP(c_List_Omap(_1687677, _1687677), c_Fun_Oid(_1687677)) = c_Fun_Oid(tc_List_Olist(_1687677)))], (27622 ^ _778908) ^ [_1268230, _1268232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1268230), _1268232)), -(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)), _1268230)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268232))))], (43498 ^ _778908) ^ [_1625751, _1625753] : [c_Wellfounded_Oacyclic(_1625751, hAPP(c_Relation_Oconverse(_1625751, _1625751), _1625753)), -(c_Wellfounded_Oacyclic(_1625751, _1625753))], (46247 ^ _778908) ^ [_1691470, _1691472, _1691474, _1691476] : [-(hAPP(hAPP(c_Option_Omap(_1691470, _1691472), _1691474), hAPP(c_Option_Ooption_OSome(_1691470), _1691476)) = hAPP(c_Option_Ooption_OSome(_1691472), hAPP(_1691474, _1691476)))], (50553 ^ _778908) ^ [_1793994, _1793996, _1793998, _1794000] : [class_Groups_Ocomm__monoid__add(_1793994), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1793994), _1793996), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1793998, _1794000))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1793994), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1793994), _1793996), c_List_Oupt(_1793998, _1794000))))], (33902 ^ _778908) ^ [_1398296, _1398298, _1398300] : [class_Orderings_Olinorder(_1398296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398296), _1398298)), hBOOL(hAPP(hAPP(c_member(_1398296), _1398300), _1398298)), 33913 ^ _778908 : [(33920 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398296, tc_HOL_Obool)), _1398298), hAPP(hAPP(c_Set_Oinsert(_1398296), _1398300), c_Orderings_Obot__class_Obot(tc_fun(_1398296, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1398296, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1398296, c_Orderings_Oord__class_Omax(_1398296), _1398298) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1398296), _1398300), c_Big__Operators_Olattice_OSup__fin(_1398296, c_Orderings_Oord__class_Omax(_1398296), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398296, tc_HOL_Obool)), _1398298), hAPP(hAPP(c_Set_Oinsert(_1398296), _1398300), c_Orderings_Obot__class_Obot(tc_fun(_1398296, tc_HOL_Obool)))))))], (33914 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398296, tc_HOL_Obool)), _1398298), hAPP(hAPP(c_Set_Oinsert(_1398296), _1398300), c_Orderings_Obot__class_Obot(tc_fun(_1398296, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1398296, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1398296, c_Orderings_Oord__class_Omax(_1398296), _1398298) = _1398300)]]], (11731 ^ _778908) ^ [_975328, _975330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975328)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _975328), _975330)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _975328)), hAPP(c_Int_Onat, _975330)))], (18939 ^ _778908) ^ [_1105202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105202), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105202)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33375 ^ _778908) ^ [_1388008, _1388010, _1388012] : [class_Orderings_Olinorder(_1388008), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388008), _1388010)), hBOOL(hAPP(hAPP(c_member(_1388008), _1388012), _1388010)), 33386 ^ _778908 : [(33393 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388008, tc_HOL_Obool)), _1388010), hAPP(hAPP(c_Set_Oinsert(_1388008), _1388012), c_Orderings_Obot__class_Obot(tc_fun(_1388008, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1388008, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1388008, _1388010) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388008), _1388012), c_Big__Operators_Olinorder__class_OMin(_1388008, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388008, tc_HOL_Obool)), _1388010), hAPP(hAPP(c_Set_Oinsert(_1388008), _1388012), c_Orderings_Obot__class_Obot(tc_fun(_1388008, tc_HOL_Obool)))))))], (33387 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388008, tc_HOL_Obool)), _1388010), hAPP(hAPP(c_Set_Oinsert(_1388008), _1388012), c_Orderings_Obot__class_Obot(tc_fun(_1388008, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1388008, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1388008, _1388010) = _1388012)]]], (34936 ^ _778908) ^ [_1419565, _1419567, _1419569, _1419571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1419565), _1419567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1419569), _1419571)), -(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), _1419565), _1419569)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1419567), _1419571))), c_FunDef_Opair__less)))], (7051 ^ _778908) ^ [_896887, _896889] : [-(c_Option_Ooption_Ooption__size(_896887, _896889, c_Option_Ooption_ONone(_896887)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45557 ^ _778908) ^ [_1675475, _1675477, _1675479, _1675481] : [-(_1675475 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1675477, tc_HOL_Obool), tc_HOL_Obool))), 45563 ^ _778908 : [(45566 ^ _778908) ^ [] : [c_Fun_Oinj__on(_1675477, _1675479, _1675481, 45562 ^ [_1675475, _1675477, _1675479, _1675481])], (45564 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1675477, tc_HOL_Obool)), 45562 ^ [_1675475, _1675477, _1675479, _1675481]), _1675475)))]], -(c_Fun_Oinj__on(_1675477, _1675479, _1675481, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1675477, tc_HOL_Obool), _1675475)))], (7069 ^ _778908) ^ [_897119, _897121] : [7070 ^ _778908 : [(7071 ^ _778908) ^ [_897167] : [_897119 = hAPP(c_Option_Ooption_OSome(_897121), _897167)]], _897119 = c_Option_Ooption_ONone(_897121)], (10160 ^ _778908) ^ [_949543, _949545, _949547] : [class_Rings_Olinordered__idom(_949543), 10163 ^ _778908 : [(10170 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _949545), _949547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949543), hAPP(c_Int_Oring__1__class_Oof__int(_949543), _949545)), hAPP(c_Int_Oring__1__class_Oof__int(_949543), _949547))))], (10164 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949543), hAPP(c_Int_Oring__1__class_Oof__int(_949543), _949545)), hAPP(c_Int_Oring__1__class_Oof__int(_949543), _949547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _949545), _949547)))]]], (1102 ^ _778908) ^ [_795557, _795559] : [-(class_Groups_Oordered__ab__group__add(_795557)), _795559 = _795557, class_Groups_Oordered__ab__group__add(_795559)], (23763 ^ _778908) ^ [_1193106, _1193108, _1193110] : [class_Orderings_Olinorder(_1193106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193106), _1193108), _1193110)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193106), _1193110), _1193108) = _1193108)], (51309 ^ _778908) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (30010 ^ _778908) ^ [_1316275, _1316277] : [_1316277 = c_Orderings_Obot__class_Obot(tc_fun(_1316275, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316275, tc_HOL_Obool)), _1316277), c_Orderings_Obot__class_Obot(tc_fun(_1316275, tc_HOL_Obool)))))], (45416 ^ _778908) ^ [_1672255, _1672257, _1672259] : [class_Complete__Lattice_Ocomplete__lattice(_1672255), -(c_Complete__Lattice_OSup__class_OSup(_1672255, hAPP(hAPP(c_Set_Oinsert(_1672255), _1672257), hAPP(hAPP(c_Set_Oinsert(_1672255), _1672259), c_Orderings_Obot__class_Obot(tc_fun(_1672255, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1672255), _1672257), _1672259))], (34911 ^ _778908) ^ [_1419067, _1419069, _1419071, _1419073, _1419075] : [class_Groups_Oordered__ab__group__add(_1419067), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419069), _1419071)), 34921 ^ _778908 : [(34924 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419067), c_Groups_Ozero__class_Ozero(_1419067)), hAPP(_1419073, 34920 ^ [_1419067, _1419069, _1419071, _1419073, _1419075])))], (34922 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419069), 34920 ^ [_1419067, _1419069, _1419071, _1419073, _1419075]), _1419071)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419069, _1419067), _1419073), _1419071) = c_Groups_Ozero__class_Ozero(_1419067), hBOOL(hAPP(hAPP(c_member(_1419069), _1419075), _1419071)), -(hAPP(_1419073, _1419075) = c_Groups_Ozero__class_Ozero(_1419067))], (14065 ^ _778908) ^ [_1017012, _1017014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017014)), -(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, _1017012, _1017014))))], (2914 ^ _778908) ^ [_823265, _823267, _823269, _823271, _823273, _823275, _823277, _823279, _823281, _823283, _823285, _823287, _823289, _823291] : [-(c_New__Random__Sequence_Opos__decr__bind(_823291, _823287, _823283, _823279, _823275, _823271, _823267) = c_New__Random__Sequence_Opos__decr__bind(_823289, _823285, _823281, _823277, _823273, _823269, _823265)), _823291 = _823289, _823287 = _823285, _823283 = _823281, _823279 = _823277, _823275 = _823273, _823271 = _823269, _823267 = _823265], (6645 ^ _778908) ^ [_887858, _887860, _887862, _887864, _887866] : [hBOOL(hAPP(_887858, _887860)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887862), _887860), _887864)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887858, _887862)), _887864), _887866)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887858, _887862)), _887860), _887866)))], (49404 ^ _778908) ^ [_1769856, _1769858, _1769860] : [class_Orderings_Olinorder(_1769856), -(c_Big__Operators_Olattice_OSup__fin(_1769856, c_Orderings_Oord__class_Omax(_1769856), hAPP(c_List_Oset(_1769856), hAPP(hAPP(c_List_Olist_OCons(_1769856), _1769858), _1769860))) = hAPP(c_List_Ofoldl(_1769856, _1769856, c_Orderings_Oord__class_Omax(_1769856), _1769858), _1769860))], (24689 ^ _778908) ^ [_1210854, _1210856, _1210858] : [class_Orderings_Olinorder(_1210854), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210854), _1210856), _1210858) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210854), _1210858), _1210856))], (15304 ^ _778908) ^ [_1039001, _1039003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1039001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039001), _1039003)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1039003), _1039001) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039003), _1039001)), _1039001)))], (45476 ^ _778908) ^ [_1673251, _1673253, _1673255, _1673257, _1673259, _1673261, _1673263, _1673265] : [c_Fun_Oinj__on(_1673251, _1673253, _1673255, _1673257), 45482 ^ _778908 : [(45485 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673251, tc_HOL_Obool)), hAPP(_1673263, 45481 ^ [_1673251, _1673253, _1673255, _1673257, _1673259, _1673261, _1673263, _1673265])), _1673257))], (45483 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673259), 45481 ^ [_1673251, _1673253, _1673255, _1673257, _1673259, _1673261, _1673263, _1673265]), _1673261)))]], hBOOL(hAPP(hAPP(c_member(_1673259), _1673265), _1673261)), -(hAPP(c_Set_Oimage(_1673251, _1673253, _1673255), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1673259, tc_fun(_1673251, tc_HOL_Obool)), _1673261), _1673263)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1673259, tc_fun(_1673253, tc_HOL_Obool)), _1673261), hAPP(hAPP(c_COMBB(tc_fun(_1673251, tc_HOL_Obool), tc_fun(_1673253, tc_HOL_Obool), _1673259), c_Set_Oimage(_1673251, _1673253, _1673255)), _1673263)))], (47738 ^ _778908) ^ [_1729551, _1729553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1729553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1729553), _1729551)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1729553))))], (29156 ^ _778908) ^ [_1299344, _1299346] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299344, 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(_1299344, tc_HOL_Obool)), tc_fun(_1299344, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1299344, tc_HOL_Obool)), tc_fun(_1299344, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299344, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1299346)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1299344, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1299346))], (19379 ^ _778908) ^ [_1112635, _1112637] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1112635)), _1112637) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112635), _1112637)))], (43037 ^ _778908) ^ [_1613788, _1613790] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613788, _1613788), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1613788, _1613790)), hAPP(hAPP(c_Product__Type_OSigma(_1613788, _1613788), hAPP(c_Relation_OField(_1613788), _1613790)), hAPP(c_COMBK(tc_fun(_1613788, tc_HOL_Obool), _1613788), hAPP(c_Relation_OField(_1613788), _1613790))))))], (48050 ^ _778908) ^ [_1737165, _1737167, _1737169, _1737171, _1737173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737165), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737167)), _1737169))), -(hAPP(hAPP(c_List_Olist__update(_1737167, hAPP(hAPP(c_List_Oappend(_1737167), _1737169), _1737171)), _1737165), _1737173) = hAPP(hAPP(c_List_Oappend(_1737167), hAPP(hAPP(c_List_Olist__update(_1737167, _1737169), _1737165), _1737173)), _1737171))], (44712 ^ _778908) ^ [_1653711, _1653713, _1653715, _1653717, _1653719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1653711, tc_HOL_Obool)), _1653713), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653715, tc_fun(_1653711, tc_HOL_Obool)), _1653717), _1653719))), 44715 ^ _778908 : [(44716 ^ _778908) ^ [_1653844] : [hBOOL(hAPP(hAPP(c_member(_1653715), _1653844), _1653717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1653711, tc_HOL_Obool)), _1653713), hAPP(_1653719, _1653844))))]]], (47397 ^ _778908) ^ [_1721813, _1721815, _1721817, _1721819] : [_1721819 = c_List_Olist_ONil(_1721815), -(c_List_Olist_ONil(_1721813) = hAPP(hAPP(c_List_Omap(_1721815, _1721813), _1721817), _1721819))], (28309 ^ _778908) ^ [_1281579, _1281581, _1281583] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281579, tc_HOL_Obool)), _1281581), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281579, tc_HOL_Obool)), _1281583), _1281581))))], (9152 ^ _778908) ^ [_932199, _932201] : [class_Groups_Oone(_932199), 9155 ^ _778908 : [(9162 ^ _778908) ^ [] : [_932201 = c_Groups_Oone__class_Oone(_932199), -(c_Groups_Oone__class_Oone(_932199) = _932201)], (9156 ^ _778908) ^ [] : [c_Groups_Oone__class_Oone(_932199) = _932201, -(_932201 = c_Groups_Oone__class_Oone(_932199))]]], (28471 ^ _778908) ^ [_1284643, _1284645, _1284647] : [class_Lattices_Osemilattice__sup(_1284643), 28474 ^ _778908 : [(28481 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284643), _1284645), _1284647) = _1284647, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284643), _1284645), _1284647)))], (28475 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284643), _1284645), _1284647)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284643), _1284645), _1284647) = _1284647)]]], (5690 ^ _778908) ^ [_866781, _866783, _866785, _866787] : [-(tc_prod(_866787, _866783) = tc_prod(_866785, _866781)), _866787 = _866785, _866783 = _866781], (23395 ^ _778908) ^ [_1186809, _1186811, _1186813, _1186815, _1186817, _1186819] : [hAPP(_1186815, hAPP(c_Product__Type_Osnd(_1186813, _1186809), _1186817)) = hAPP(_1186819, hAPP(c_Product__Type_Osnd(_1186813, _1186809), _1186817)), -(hAPP(c_Product__Type_Oapsnd(_1186809, _1186811, _1186813, _1186815), _1186817) = hAPP(c_Product__Type_Oapsnd(_1186809, _1186811, _1186813, _1186819), _1186817))], (28189 ^ _778908) ^ [_1279344, _1279346, _1279348, _1279350] : [class_Lattices_Osemilattice__sup(_1279344), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279344), _1279346), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279344), _1279348), _1279350)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279344), _1279348), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279344), _1279346), _1279350)))], (29128 ^ _778908) ^ [] : [-(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)))], (51629 ^ _778908) ^ [_1813132, _1813134, _1813136, _1813138] : [-(hAPP(hAPP(c_COMBK(_1813132, _1813134), _1813136), _1813138) = _1813136)], (17987 ^ _778908) ^ [_1089985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089985)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1089985))], (14041 ^ _778908) ^ [_1016568, _1016570, _1016572, _1016574] : [class_Divides_Osemiring__div(_1016568), -(c_Divides_Odiv__class_Omod(_1016568, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016568), _1016570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016568), _1016572), _1016574)), _1016574) = c_Divides_Odiv__class_Omod(_1016568, _1016570, _1016574))], (3226 ^ _778908) ^ [_828361, _828363, _828365, _828367] : [-(c_Option_Oset(_828367, _828363) = c_Option_Oset(_828365, _828361)), _828367 = _828365, _828363 = _828361], (33847 ^ _778908) ^ [_1396844, _1396846, _1396848] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1396844, tc_HOL_Obool), tc_fun(_1396844, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1396844, tc_HOL_Obool), tc_fun(_1396844, tc_HOL_Obool)), _1396846), _1396848)), c_Wellfounded_Ofinite__psubset(_1396844))), 33850 ^ _778908 : [(33853 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1396844), _1396848)))], (33851 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1396844, tc_HOL_Obool)), _1396846), _1396848)))]]], (2522 ^ _778908) ^ [_817047, _817049, _817051, _817053] : [-(c_Divides_Opdivmod(_817053, _817049) = c_Divides_Opdivmod(_817051, _817047)), _817053 = _817051, _817049 = _817047], (49291 ^ _778908) ^ [_1767448, _1767450, _1767452, _1767454] : [class_Groups_Osemigroup__add(_1767448), -(hAPP(c_List_Ofoldl(_1767448, _1767448, c_Groups_Oplus__class_Oplus(_1767448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1767448), _1767450), _1767452)), _1767454) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1767448), _1767450), hAPP(c_List_Ofoldl(_1767448, _1767448, c_Groups_Oplus__class_Oplus(_1767448), _1767452), _1767454)))], (29743 ^ _778908) ^ [_1310997, _1310999, _1311001, _1311003, _1311005] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310997), _1310999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1311001, tc_HOL_Obool)), _1311003), hAPP(c_Set_Oimage(_1310997, _1311001, _1311005), _1310999))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311001), _1311003)))], (18017 ^ _778908) ^ [_1090382, _1090384, _1090386, _1090388] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1090382, _1090384, _1090386), _1090388), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1090384)], (41716 ^ _778908) ^ [_1580776, _1580778, _1580780, _1580782] : [-(c_Product__Type_Oapfst(_1580776, _1580778, _1580780, _1580782) = c_Product__Type_Omap__pair(_1580776, _1580778, _1580780, _1580780, _1580782, c_Fun_Oid(_1580780)))], (34236 ^ _778908) ^ [_1404494, _1404496] : [class_Orderings_Olinorder(_1404494), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404494), _1404496)), -(_1404496 = c_Orderings_Obot__class_Obot(tc_fun(_1404494, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1404494), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1404494), 34249 ^ [_1404494, _1404496]), 34250 ^ [_1404494, _1404496])), hAPP(hAPP(c_Set_Oinsert(_1404494), 34249 ^ [_1404494, _1404496]), hAPP(hAPP(c_Set_Oinsert(_1404494), 34250 ^ [_1404494, _1404496]), c_Orderings_Obot__class_Obot(tc_fun(_1404494, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1404494), c_Big__Operators_Olattice_OInf__fin(_1404494, c_Orderings_Oord__class_Omin(_1404494), _1404496)), _1404496)))], (45332 ^ _778908) ^ [_1670419, _1670421, _1670423] : [class_Complete__Lattice_Ocomplete__lattice(_1670419), hBOOL(hAPP(hAPP(c_member(_1670419), _1670421), _1670423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670419), _1670421), c_Complete__Lattice_OSup__class_OSup(_1670419, _1670423))))], (48225 ^ _778908) ^ [_1741328, _1741330, _1741332, _1741334] : [hAPP(hAPP(c_List_Oappend(_1741328), _1741330), _1741332) = hAPP(hAPP(c_List_Oappend(_1741328), _1741334), _1741332), -(_1741330 = _1741334)], (46777 ^ _778908) ^ [_1703946, _1703948, _1703950, _1703952, _1703954] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703946)), _1703948) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703950)), _1703952), 46780 ^ _778908 : [(46789 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1703946, _1703950), _1703948), _1703952) = _1703954), hAPP(hAPP(c_List_Omap(tc_prod(_1703946, _1703950), _1703946), c_Product__Type_Ofst(_1703946, _1703950)), _1703954) = _1703948, hAPP(hAPP(c_List_Omap(tc_prod(_1703946, _1703950), _1703950), c_Product__Type_Osnd(_1703946, _1703950)), _1703954) = _1703952], (46781 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Ozip(_1703946, _1703950), _1703948), _1703952) = _1703954, 46784 ^ _778908 : [(46787 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1703946, _1703950), _1703950), c_Product__Type_Osnd(_1703946, _1703950)), _1703954) = _1703952)], (46785 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1703946, _1703950), _1703946), c_Product__Type_Ofst(_1703946, _1703950)), _1703954) = _1703948)]]]]], (2084 ^ _778908) ^ [_809876, _809878] : [_809878 = _809876, -(c_Com_Ocom_Ocom__size(_809878) = c_Com_Ocom_Ocom__size(_809876))], (23166 ^ _778908) ^ [_1181973, _1181975, _1181977] : [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), _1181973), _1181975))), -(hBOOL(hAPP(hAPP(_1181977, _1181973), _1181975))), 23173 ^ _778908 : [(23176 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1181977, 23171 ^ [_1181973, _1181975, _1181977]), 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)))), 23172 ^ [_1181973, _1181975, _1181977])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23171 ^ [_1181973, _1181975, _1181977]), 23172 ^ [_1181973, _1181975, _1181977]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23172 ^ [_1181973, _1181975, _1181977]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23186 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1181977, 23171 ^ [_1181973, _1181975, _1181977]), 23172 ^ [_1181973, _1181975, _1181977]))], (23174 ^ _778908) ^ [] : [-(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), 23171 ^ [_1181973, _1181975, _1181977]), 23172 ^ [_1181973, _1181975, _1181977]))))]]], (33575 ^ _778908) ^ [_1391269, _1391271, _1391273] : [class_Orderings_Olinorder(_1391269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391269), _1391271)), -(_1391271 = c_Orderings_Obot__class_Obot(tc_fun(_1391269, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1391269, hAPP(hAPP(c_Set_Oinsert(_1391269), _1391273), _1391271)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1391269), _1391273), c_Big__Operators_Olinorder__class_OMax(_1391269, _1391271)))], (5815 ^ _778908) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31538 ^ _778908) ^ [_1348039, _1348041, _1348043, _1348045] : [-(hBOOL(hAPP(hAPP(c_member(_1348039), _1348041), _1348043))), 31541 ^ _778908 : [(31548 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348039, tc_HOL_Obool)), _1348043), _1348045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348039, tc_HOL_Obool)), _1348043), hAPP(hAPP(c_Set_Oinsert(_1348039), _1348041), _1348045))))], (31542 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348039, tc_HOL_Obool)), _1348043), hAPP(hAPP(c_Set_Oinsert(_1348039), _1348041), _1348045))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348039, tc_HOL_Obool)), _1348043), _1348045)))]]], (19629 ^ _778908) ^ [_1117030, _1117032] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1117030)), _1117032) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117030), _1117032))), _1117032))], (50602 ^ _778908) ^ [_1794978, _1794980] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1794978, _1794980) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1794978), _1794980)))], (7014 ^ _778908) ^ [_896024, _896026, _896028, _896030, _896032] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_896024, _896026, _896028)), _896030), _896032)), 7018 ^ _778908 : [(7021 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _896026)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896030), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_896028, _896030))), 7017 ^ [_896024, _896026, _896028, _896030, _896032])))], (7019 ^ _778908) ^ [] : [-(_896032 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7017 ^ [_896024, _896026, _896028, _896030, _896032]), hAPP(c_Natural_Ogetlocs, _896030))), _896024), hAPP(hAPP(c_Natural_Ogetlocs, 7017 ^ [_896024, _896026, _896028, _896030, _896032]), c_Com_ORes)))]]], (41702 ^ _778908) ^ [_1580513, _1580515] : [-(c_Product__Type_Omap__pair(_1580513, _1580513, _1580515, _1580515, c_COMBI(_1580513), c_COMBI(_1580515)) = c_Fun_Oid(tc_prod(_1580513, _1580515)))], (14094 ^ _778908) ^ [_1017485, _1017487] : [14095 ^ _778908 : [(14096 ^ _778908) ^ [_1017534] : [_1017485 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017487), _1017534)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017485, _1017487) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6518 ^ _778908) ^ [_884469, _884471, _884473] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_884469, _884471, _884473)], (25043 ^ _778908) ^ [_1218323, _1218325, _1218327, _1218329, _1218331, _1218333, _1218335] : [-(c_New__Random__Sequence_Opos__decr__bind(_1218323, _1218325, _1218327, _1218329, _1218331, _1218333, _1218335) = c_New__DSequence_Opos__decr__bind(_1218323, _1218325, hAPP(hAPP(hAPP(_1218327, _1218331), _1218333), _1218335), hAPP(hAPP(c_COMBC(_1218323, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1218325))), hAPP(hAPP(c_COMBC(_1218323, 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(_1218325)))), hAPP(hAPP(c_COMBC(_1218323, 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(_1218325))))), _1218329), _1218331)), _1218333)), _1218335)))], (34549 ^ _778908) ^ [_1410854, _1410856, _1410858] : [class_Groups_Ocomm__monoid__add(_1410854), class_Groups_Ocomm__monoid__mult(_1410854), c_Nat__Transfer_Onat__set(_1410856), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1410854), _1410858), _1410856) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1410854), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1410854, tc_Nat_Onat), _1410858), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1410856)))], (20313 ^ _778908) ^ [_1129572, _1129574] : [c_Nat__Transfer_Ois__nat(_1129572), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1129572), _1129574)))], (44889 ^ _778908) ^ [_1659587, _1659589, _1659591, _1659593, _1659595] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659587, tc_HOL_Obool)), _1659589), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659591, tc_fun(_1659587, tc_HOL_Obool)), _1659593), _1659595)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659591, tc_fun(_1659587, tc_HOL_Obool)), _1659593), hAPP(hAPP(c_COMBB(tc_fun(_1659587, tc_HOL_Obool), tc_fun(_1659587, tc_HOL_Obool), _1659591), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659587, tc_HOL_Obool)), _1659589)), _1659595)))], (48588 ^ _778908) ^ [_1749872, _1749874, _1749876, _1749878, _1749880, _1749882, _1749884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749872)), _1749874)), _1749876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749876), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749878)), _1749880))), -(c_Map_Omap__upds(_1749872, _1749878, _1749882, _1749874, hAPP(hAPP(c_List_Olist__update(_1749878, _1749880), _1749876), _1749884)) = c_Map_Omap__upds(_1749872, _1749878, _1749882, _1749874, _1749880))], (31016 ^ _778908) ^ [_1335767, _1335769] : [-(hBOOL(hAPP(hAPP(c_member(_1335767), 31017 ^ [_1335767, _1335769]), _1335769))), -(_1335769 = c_Orderings_Obot__class_Obot(tc_fun(_1335767, tc_HOL_Obool)))], (3842 ^ _778908) ^ [_838133, _838135, _838137, _838139, _838141, _838143, _838145, _838147] : [-(c_New__Random__Sequence_Opos__map(_838147, _838143, _838139, _838135) = c_New__Random__Sequence_Opos__map(_838145, _838141, _838137, _838133)), _838147 = _838145, _838143 = _838141, _838139 = _838137, _838135 = _838133], (32551 ^ _778908) ^ [_1370974, _1370976] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370974), _1370976)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1370974), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370976))))], (40238 ^ _778908) ^ [_1540725, _1540727, _1540729, _1540731] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1540725, _1540727)), hAPP(hAPP(c_Product__Type_OSigma(_1540725, _1540727), _1540729), hAPP(c_COMBK(tc_fun(_1540727, tc_HOL_Obool), _1540725), _1540731)))), -(_1540731 = c_Orderings_Obot__class_Obot(tc_fun(_1540727, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540725), _1540729)))], (39240 ^ _778908) ^ [_1515969, _1515971, _1515973, _1515975] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515969), _1515971)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515973), _1515975)), 39247 ^ _778908 : [(39248 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1515969), _1515971)), hAPP(c_Finite__Set_Ocard(_1515973), _1515975)))), 39249 ^ _778908 : [(39250 ^ _778908) ^ [_1516180] : [c_Fun_Oinj__on(_1515969, _1515973, _1516180, _1515971), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515973, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1515969, _1515973, _1516180), _1515971)), _1515975))]]], (39258 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1515969), _1515971)), hAPP(c_Finite__Set_Ocard(_1515973), _1515975))), 39262 ^ _778908 : [(39265 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515973, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1515969, _1515973, 39261 ^ [_1515969, _1515971, _1515973, _1515975]), _1515971)), _1515975)))], (39263 ^ _778908) ^ [] : [-(c_Fun_Oinj__on(_1515969, _1515973, 39261 ^ [_1515969, _1515971, _1515973, _1515975], _1515971))]]]]], (7004 ^ _778908) ^ [_895566, _895568, _895570, _895572, _895574] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_895566, _895568, _895570)), _895572), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895574), hAPP(c_Natural_Ogetlocs, _895572))), _895566), hAPP(hAPP(c_Natural_Ogetlocs, _895574), c_Com_ORes))))), 7005 ^ _778908 : [(7006 ^ _778908) ^ [_895723] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895574), hAPP(c_Natural_Ogetlocs, _895572))), _895566), hAPP(hAPP(c_Natural_Ogetlocs, _895574), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895723), hAPP(c_Natural_Ogetlocs, _895572))), _895566), hAPP(hAPP(c_Natural_Ogetlocs, _895723), c_Com_ORes)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _895568)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895572), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_895570, _895572))), _895723))]]], (742 ^ _778908) ^ [_790309, _790311, _790313, _790315, _790317, _790319, _790321, _790323] : [-(c_Finite__Set_Ofolding(_790321, _790317, _790313, _790309)), c_Finite__Set_Ofolding(_790323, _790319, _790315, _790311), _790323 = _790321, _790319 = _790317, _790315 = _790313, _790311 = _790309], (18931 ^ _778908) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (37050 ^ _778908) ^ [_1468534, _1468536, _1468538] : [-(hAPP(c_Relation_OImage(_1468534, _1468534, c_Relation_OId__on(_1468534, _1468536)), _1468538) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468534, tc_HOL_Obool)), _1468536), _1468538))], (45308 ^ _778908) ^ [_1669590, _1669592, _1669594, _1669596] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1669590, _1669592), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669590, tc_HOL_Obool), _1669594)), _1669596) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1669590, tc_HOL_Obool), tc_fun(tc_prod(_1669590, _1669592), tc_HOL_Obool)), _1669594), hAPP(hAPP(c_COMBC(tc_fun(_1669590, tc_HOL_Obool), tc_fun(_1669590, tc_fun(_1669592, tc_HOL_Obool)), tc_fun(tc_prod(_1669590, _1669592), tc_HOL_Obool)), c_Product__Type_OSigma(_1669590, _1669592)), _1669596)))], (2388 ^ _778908) ^ [_814936, _814938, _814940, _814942] : [-(c_Random_Olog(_814942, _814938) = c_Random_Olog(_814940, _814936)), _814942 = _814940, _814938 = _814936], (49075 ^ _778908) ^ [_1763159, _1763161, _1763163, _1763165] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1763159) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1763161), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1763159)), hAPP(hAPP(c_List_Olist_OCons(_1763161), _1763163), _1763165)) = hAPP(hAPP(c_List_Odrop(_1763161), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1763159)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1763165))], (41690 ^ _778908) ^ [_1580327, _1580329] : [-(hAPP(c_Set_Ovimage(_1580327, _1580327, c_Fun_Oid(_1580327)), _1580329) = _1580329)], (19657 ^ _778908) ^ [_1117502] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1117502)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1117502)))], (7953 ^ _778908) ^ [_911768, _911770, _911772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911768), _911770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911768), _911772)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911770), _911772))))], (27665 ^ _778908) ^ [_1269110, _1269112, _1269114, _1269116, _1269118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269110, tc_HOL_Obool)), _1269112), _1269114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269116, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1269110, _1269116, _1269118), _1269112)), hAPP(c_Set_Oimage(_1269110, _1269116, _1269118), _1269114))))], (23527 ^ _778908) ^ [_1188669, _1188671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188671)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1188669, _1188671) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1188669, _1188671)))], (29150 ^ _778908) ^ [_1299239, _1299241] : [class_Lattices_Oboolean__algebra(_1299239), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299239), hAPP(c_Groups_Ouminus__class_Ouminus(_1299239), _1299241)), _1299241) = c_Orderings_Otop__class_Otop(_1299239))], (50080 ^ _778908) ^ [_1785549, _1785551] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1785549))), c_List_Otranspose(_1785549, _1785551)) = c_List_Ofoldr(tc_List_Olist(_1785549), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1785549)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1785549))), _1785551, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36872 ^ _778908) ^ [_1463667, _1463669, _1463671, _1463673] : [class_Lattices_Osemilattice__inf(_1463667), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1463667), _1463669), _1463671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1463667), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463667), _1463673), _1463669)), _1463671)))], (35825 ^ _778908) ^ [_1440439, _1440441] : [-(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), _1440439), _1440441)), 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), _1440439), _1440441))], (49163 ^ _778908) ^ [_1764864, _1764866, _1764868] : [-(_1764864 = c_List_Olist_ONil(_1764866)), -(hAPP(c_List_Ohd(_1764866), hAPP(c_List_Orotate(_1764866, _1764868), _1764864)) = hAPP(hAPP(c_List_Onth(_1764866), _1764864), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1764868, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764866)), _1764864))))], (29386 ^ _778908) ^ [_1304050, _1304052, _1304054, _1304056, _1304058] : [class_Groups_Ocomm__monoid__add(_1304050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304052), _1304054)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1304052, _1304050), hAPP(hAPP(c_COMBS(_1304052, _1304050, _1304050), hAPP(hAPP(c_COMBB(_1304050, tc_fun(_1304050, _1304050), _1304052), c_Groups_Oplus__class_Oplus(_1304050)), _1304056)), _1304058)), _1304054) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304050), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1304052, _1304050), _1304056), _1304054)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1304052, _1304050), _1304058), _1304054)))], (35090 ^ _778908) ^ [_1422586, _1422588, _1422590, _1422592] : [c_Wellfounded_Omax__extp(_1422586, hAPP(hAPP(c_COMBC(_1422586, tc_fun(tc_prod(_1422586, _1422586), tc_HOL_Obool), tc_fun(_1422586, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422586, tc_fun(tc_fun(tc_prod(_1422586, _1422586), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1422586, _1422586), tc_HOL_Obool), tc_fun(_1422586, tc_HOL_Obool)), _1422586), c_COMBC(_1422586, tc_fun(tc_prod(_1422586, _1422586), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422586, tc_prod(_1422586, _1422586)), tc_fun(_1422586, tc_fun(tc_fun(tc_prod(_1422586, _1422586), tc_HOL_Obool), tc_HOL_Obool)), _1422586), hAPP(c_COMBB(tc_prod(_1422586, _1422586), tc_fun(tc_fun(tc_prod(_1422586, _1422586), tc_HOL_Obool), tc_HOL_Obool), _1422586), c_member(tc_prod(_1422586, _1422586)))), c_Product__Type_OPair(_1422586, _1422586)))), _1422588), _1422590, _1422592), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1422586, tc_HOL_Obool), tc_fun(_1422586, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1422586, tc_HOL_Obool), tc_fun(_1422586, tc_HOL_Obool)), _1422590), _1422592)), c_Wellfounded_Omax__ext(_1422586, _1422588))))], (49171 ^ _778908) ^ [_1764985, _1764987, _1764989] : [-(hAPP(c_List_Otl(_1764985), hAPP(hAPP(c_List_Odrop(_1764985), _1764987), _1764989)) = hAPP(hAPP(c_List_Odrop(_1764985), _1764987), hAPP(c_List_Otl(_1764985), _1764989)))], (42257 ^ _778908) ^ [_1595311, _1595313, _1595315, _1595317] : [42258 ^ _778908 : [(42259 ^ _778908) ^ [_1595365] : [hBOOL(hAPP(hAPP(_1595315, _1595365), _1595317))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1595311, _1595313, _1595315), _1595317)))], (16647 ^ _778908) ^ [_1065057, _1065059] : [class_Groups_Oordered__ab__group__add__abs(_1065057), -(hAPP(c_Groups_Oabs__class_Oabs(_1065057), hAPP(c_Groups_Ouminus__class_Ouminus(_1065057), _1065059)) = hAPP(c_Groups_Oabs__class_Oabs(_1065057), _1065059))], (18761 ^ _778908) ^ [_1102114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1102114)), -(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), _1102114))))], (24059 ^ _778908) ^ [_1198701, _1198703, _1198705, _1198707, _1198709, _1198711] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1198701, _1198703), _1198703, _1198705), hAPP(hAPP(c_COMBB(_1198707, tc_fun(_1198703, _1198705), tc_prod(_1198701, _1198703)), _1198709), hAPP(hAPP(c_COMBB(_1198701, _1198707, tc_prod(_1198701, _1198703)), _1198711), c_Product__Type_Ofst(_1198701, _1198703)))), c_Product__Type_Osnd(_1198701, _1198703)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1198701, _1198703, _1198705), hAPP(hAPP(c_COMBB(_1198707, tc_fun(_1198703, _1198705), _1198701), _1198709), _1198711)))], (28918 ^ _778908) ^ [_1293437, _1293439, _1293441, _1293443, _1293445] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293437, tc_fun(_1293439, tc_HOL_Obool)), _1293441), hAPP(hAPP(c_COMBC(_1293437, tc_fun(_1293439, tc_HOL_Obool), tc_fun(_1293439, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293439, tc_HOL_Obool), tc_fun(tc_fun(_1293439, tc_HOL_Obool), tc_fun(_1293439, tc_HOL_Obool)), _1293437), c_Groups_Ominus__class_Ominus(tc_fun(_1293439, tc_HOL_Obool))), _1293443)), _1293445)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1293439, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293437, tc_fun(_1293439, tc_HOL_Obool)), _1293441), _1293443)), _1293445))], (50927 ^ _778908) ^ [_1802374, _1802376, _1802378] : [_1802376 = _1802378, -(hAPP(c_List_Orev(_1802374), _1802376) = hAPP(c_List_Orev(_1802374), _1802378))], (37672 ^ _778908) ^ [_1481958, _1481960, _1481962] : [class_Orderings_Olinorder(_1481958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481958), _1481960)), -(_1481960 = c_Orderings_Obot__class_Obot(tc_fun(_1481958, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481958), _1481962)), -(_1481962 = c_Orderings_Obot__class_Obot(tc_fun(_1481958, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481958, tc_HOL_Obool)), _1481960), _1481962) = c_Orderings_Obot__class_Obot(tc_fun(_1481958, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1481958, c_Orderings_Oord__class_Omin(_1481958), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481958, tc_HOL_Obool)), _1481960), _1481962)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1481958), c_Big__Operators_Olattice_OInf__fin(_1481958, c_Orderings_Oord__class_Omin(_1481958), _1481960)), c_Big__Operators_Olattice_OInf__fin(_1481958, c_Orderings_Oord__class_Omin(_1481958), _1481962)))], (10443 ^ _778908) ^ [_954295, _954297, _954299] : [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, _954295)), _954297)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954295)), _954299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954297), _954299)))], (12864 ^ _778908) ^ [_995437, _995439, _995441, _995443] : [class_Rings_Olinordered__semiring(_995437), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995437), _995439), _995441)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995437), _995443), _995441))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995437), c_Groups_Ozero__class_Ozero(_995437)), _995441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995437), _995439), _995443)))], (8076 ^ _778908) ^ [_914045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914045), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_914045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28677 ^ _778908) ^ [_1288694, _1288696] : [class_Orderings_Olinorder(_1288694), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1288694, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1288694), _1288696)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1288694), _1288696))], (31479 ^ _778908) ^ [_1346791, _1346793, _1346795] : [-(hBOOL(hAPP(hAPP(c_member(_1346791), _1346793), hAPP(hAPP(c_Set_Oinsert(_1346791), _1346793), _1346795))))], (28795 ^ _778908) ^ [_1291004, _1291006, _1291008] : [class_Orderings_Olinorder(_1291004), 28798 ^ _778908 : [(28805 ^ _778908) ^ [] : [_1291006 = _1291008, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1291004), _1291006) = hAPP(c_SetInterval_Oord__class_OatLeast(_1291004), _1291008))], (28799 ^ _778908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1291004), _1291006) = hAPP(c_SetInterval_Oord__class_OatLeast(_1291004), _1291008), -(_1291006 = _1291008)]]], (38776 ^ _778908) ^ [_1506268, _1506270, _1506272, _1506274, _1506276] : [c_Fun_Oinj__on(_1506268, _1506270, _1506272, _1506274), c_Fun_Oinj__on(_1506268, _1506270, _1506272, _1506276), -(c_Fun_Oinj__on(_1506268, _1506270, _1506272, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506268, tc_HOL_Obool)), _1506274), _1506276)))], (31461 ^ _778908) ^ [_1346492, _1346494, _1346496, _1346498] : [hBOOL(hAPP(hAPP(c_member(_1346492), _1346494), hAPP(hAPP(c_Set_Oinsert(_1346492), _1346496), _1346498))), -(_1346494 = _1346496), -(hBOOL(hAPP(hAPP(c_member(_1346492), _1346494), _1346498)))], (40707 ^ _778908) ^ [_1552184, _1552186, _1552188] : [class_Orderings_Olinorder(_1552184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552184), _1552186)), hBOOL(hAPP(hAPP(c_member(_1552184), _1552188), _1552186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552184), hAPP(c_Finite__Set_Ofold1(_1552184, c_Orderings_Oord__class_Omin(_1552184)), _1552186)), _1552188)))], (42807 ^ _778908) ^ [_1608799, _1608801, _1608803] : [42809 ^ _778908 : [(42812 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1608799), 42808 ^ [_1608799, _1608801, _1608803]), c_Wellfounded_Oacc(_1608799, _1608803)))], (42810 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608799, _1608799)), hAPP(hAPP(c_Product__Type_OPair(_1608799, _1608799), 42808 ^ [_1608799, _1608801, _1608803]), _1608801)), _1608803)))]], -(hBOOL(hAPP(hAPP(c_member(_1608799), _1608801), c_Wellfounded_Oacc(_1608799, _1608803))))], (18495 ^ _778908) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (26219 ^ _778908) ^ [_1240471, _1240473, _1240475, _1240477] : [class_Rings_Oidom(_1240471), 26222 ^ _778908 : [(26223 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240471), _1240473), _1240475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240471), _1240477), _1240475))), -(_1240475 = c_Groups_Ozero__class_Ozero(_1240471)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240471), _1240473), _1240477)))], (26233 ^ _778908) ^ [] : [26234 ^ _778908 : [(26237 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240471), _1240473), _1240477))], (26235 ^ _778908) ^ [] : [_1240475 = c_Groups_Ozero__class_Ozero(_1240471)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240471), _1240473), _1240475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240471), _1240477), _1240475))))]]], (30624 ^ _778908) ^ [_1327657, _1327659, _1327661] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1327657, _1327659) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1327661), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1327657 = _1327659, _1327659 = _1327661], (41307 ^ _778908) ^ [_1564952, _1564954, _1564956, _1564958] : [_1564952 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1564954, _1564956), 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)), _1564958))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1564954), _1564952)))], (15654 ^ _778908) ^ [_1045416, _1045418, _1045420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045416), _1045418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045416), _1045420)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045418), _1045416)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045420), _1045416)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045418), _1045420))], (46907 ^ _778908) ^ [_1707740, _1707742, _1707744, _1707746] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707740), tc_List_Olist(_1707740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707740), tc_List_Olist(_1707740)), _1707742), _1707744)), c_List_Olistrel(_1707740, _1707746))), 46910 ^ _778908 : [(46913 ^ _778908) ^ [_1708076] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1707740, _1707740)), _1708076), hAPP(c_List_Oset(tc_prod(_1707740, _1707740)), hAPP(hAPP(c_List_Ozip(_1707740, _1707740), _1707742), _1707744)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1707740, _1707740, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1707740, tc_fun(tc_prod(_1707740, _1707740), tc_HOL_Obool), tc_fun(_1707740, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1707740, tc_fun(tc_fun(tc_prod(_1707740, _1707740), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1707740, _1707740), tc_HOL_Obool), tc_fun(_1707740, tc_HOL_Obool)), _1707740), c_COMBC(_1707740, tc_fun(tc_prod(_1707740, _1707740), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1707740, tc_prod(_1707740, _1707740)), tc_fun(_1707740, tc_fun(tc_fun(tc_prod(_1707740, _1707740), tc_HOL_Obool), tc_HOL_Obool)), _1707740), hAPP(c_COMBB(tc_prod(_1707740, _1707740), tc_fun(tc_fun(tc_prod(_1707740, _1707740), tc_HOL_Obool), tc_HOL_Obool), _1707740), c_member(tc_prod(_1707740, _1707740)))), c_Product__Type_OPair(_1707740, _1707740)))), _1707746)), _1708076)))], (46911 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707740)), _1707742) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707740)), _1707744))]]], (45079 ^ _778908) ^ [_1664209, _1664211, _1664213, _1664215] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1664209, tc_HOL_Obool), tc_fun(_1664211, tc_HOL_Obool)), _1664213), hAPP(hAPP(c_COMBC(tc_fun(_1664209, tc_HOL_Obool), tc_fun(_1664209, tc_fun(_1664211, tc_HOL_Obool)), tc_fun(_1664211, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664209, tc_fun(_1664211, tc_HOL_Obool))), _1664215)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664209, tc_fun(_1664211, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1664209, tc_HOL_Obool), _1664213)), _1664215))], (43913 ^ _778908) ^ [_1636252] : [-(c_Relation_Osingle__valued(_1636252, _1636252, c_Relation_OId(_1636252)))], (28581 ^ _778908) ^ [_1286829, _1286831, _1286833] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1286829, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286829, tc_HOL_Obool)), _1286831), _1286833)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286829, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1286829, tc_HOL_Obool)), _1286831)), _1286833))], (1562 ^ _778908) ^ [_801307, _801309] : [-(class_Groups_Ocomm__monoid__mult(_801307)), _801309 = _801307, class_Groups_Ocomm__monoid__mult(_801309)], (5863 ^ _778908) ^ [_872257, _872259] : [c_Com_Ocom_OAss(_872257, _872259) = c_Com_Ocom_OSKIP], (552 ^ _778908) ^ [_787406, _787408, _787410, _787412, _787414, _787416, _787418, _787420, _787422, _787424, _787426, _787428, _787430, _787432] : [-(c_Predicate_Opred__comp(_787430, _787426, _787422, _787418, _787414, _787410, _787406)), c_Predicate_Opred__comp(_787432, _787428, _787424, _787420, _787416, _787412, _787408), _787432 = _787430, _787428 = _787426, _787424 = _787422, _787420 = _787418, _787416 = _787414, _787412 = _787410, _787408 = _787406], (30016 ^ _778908) ^ [_1316394, _1316396, _1316398] : [class_Orderings_Obot(_1316394), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1316396, _1316394)), _1316398) = c_Orderings_Obot__class_Obot(_1316394))], (49237 ^ _778908) ^ [_1766364] : [-(c_List_Orotate(_1766364, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1766364)))], (30800 ^ _778908) ^ [_1331249, _1331251] : [c_Option_Oset(_1331249, _1331251) = c_Orderings_Obot__class_Obot(tc_fun(_1331249, tc_HOL_Obool)), -(_1331251 = c_Option_Ooption_ONone(_1331249))], (42223 ^ _778908) ^ [_1594094, _1594096, _1594098, _1594100] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1594094, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594094, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1594096, _1594094), _1594098)), hAPP(c_Relation_ORange(_1594096, _1594094), _1594100))), hAPP(c_Relation_ORange(_1594096, _1594094), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1594096, _1594094), tc_HOL_Obool)), _1594098), _1594100)))))], (42303 ^ _778908) ^ [_1596219, _1596221] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1596219, _1596221), 42304 ^ [_1596219, _1596221])), -(c_Wellfounded_OwfP(_1596219, _1596221))], (46611 ^ _778908) ^ [_1700095, _1700097, _1700099, _1700101, _1700103, _1700105, _1700107, _1700109] : [-(hAPP(hAPP(c_List_Ozip(_1700095, _1700097), hAPP(hAPP(c_List_Omap(_1700099, _1700095), _1700101), _1700103)), hAPP(hAPP(c_List_Omap(_1700105, _1700097), _1700107), _1700109)) = hAPP(hAPP(c_List_Omap(tc_prod(_1700099, _1700105), tc_prod(_1700095, _1700097)), hAPP(c_Product__Type_Oprod_Oprod__case(_1700099, _1700105, tc_prod(_1700095, _1700097)), hAPP(hAPP(c_COMBC(_1700099, tc_fun(_1700105, _1700097), tc_fun(_1700105, tc_prod(_1700095, _1700097))), hAPP(hAPP(c_COMBB(tc_fun(_1700097, tc_prod(_1700095, _1700097)), tc_fun(tc_fun(_1700105, _1700097), tc_fun(_1700105, tc_prod(_1700095, _1700097))), _1700099), c_COMBB(_1700097, tc_prod(_1700095, _1700097), _1700105)), hAPP(hAPP(c_COMBB(_1700095, tc_fun(_1700097, tc_prod(_1700095, _1700097)), _1700099), c_Product__Type_OPair(_1700095, _1700097)), _1700101))), _1700107))), hAPP(hAPP(c_List_Ozip(_1700099, _1700105), _1700103), _1700109)))], (968 ^ _778908) ^ [_793742, _793744, _793746, _793748, _793750, _793752] : [-(c_Equiv__Relations_Oequiv(_793750, _793746, _793742)), c_Equiv__Relations_Oequiv(_793752, _793748, _793744), _793752 = _793750, _793748 = _793746, _793744 = _793742], (30388 ^ _778908) ^ [_1323216, _1323218] : [_1323218 = c_Orderings_Obot__class_Obot(tc_fun(_1323216, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323216, tc_HOL_Obool)), _1323218), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323216, tc_HOL_Obool)), _1323218))))], (34393 ^ _778908) ^ [_1408226, _1408228, _1408230, _1408232, _1408234] : [hAPP(_1408230, _1408232) = _1408234, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408226, _1408228), _1408230), _1408232), _1408234) = _1408230)], (49486 ^ _778908) ^ [_1772040, _1772042, _1772044, _1772046] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772040)), hAPP(hAPP(c_List_Oappend(_1772040), _1772042), _1772044)), c_List_Olists(_1772040, _1772046)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772040)), _1772042), c_List_Olists(_1772040, _1772046))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772040)), _1772044), c_List_Olists(_1772040, _1772046)))], (12529 ^ _778908) ^ [_989597, _989599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989599)), -(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), _989597), _989599))))], (31389 ^ _778908) ^ [_1345192, _1345194, _1345196, _1345198, _1345200, _1345202, _1345204] : [c_Typedef_Otype__definition(_1345192, _1345194, _1345196, _1345198, _1345200), hBOOL(hAPP(hAPP(c_member(_1345194), _1345202), _1345200)), hBOOL(hAPP(hAPP(c_member(_1345194), _1345204), _1345200)), 31400 ^ _778908 : [(31407 ^ _778908) ^ [] : [_1345202 = _1345204, -(hAPP(_1345198, _1345202) = hAPP(_1345198, _1345204))], (31401 ^ _778908) ^ [] : [hAPP(_1345198, _1345202) = hAPP(_1345198, _1345204), -(_1345202 = _1345204)]]], (37951 ^ _778908) ^ [] : [-(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))], (39315 ^ _778908) ^ [_1517943, _1517945, _1517947, _1517949, _1517951, _1517953, _1517955] : [c_Big__Operators_Ocomm__monoid__big(_1517943, _1517945, _1517947, _1517949, _1517951), 39318 ^ _778908 : [(39325 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1517945), _1517953))), -(hAPP(hAPP(_1517951, _1517955), _1517953) = _1517949)], (39319 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517945), _1517953)), -(hAPP(hAPP(_1517951, _1517955), _1517953) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1517943, _1517945, _1517947), _1517955), _1517949), _1517953))]]], (51199 ^ _778908) ^ [_1808987, _1808989] : [class_Orderings_Otop(_1808987), -(class_Orderings_Otop(tc_fun(_1808989, _1808987)))], (1762 ^ _778908) ^ [_803807, _803809] : [-(class_Orderings_Oord(_803807)), _803809 = _803807, class_Orderings_Oord(_803809)], (17129 ^ _778908) ^ [_1074294, _1074296, _1074298] : [class_Rings_Olinordered__idom(_1074294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074294), c_Groups_Ozero__class_Ozero(_1074294)), _1074296)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074294), hAPP(c_Groups_Oabs__class_Oabs(_1074294), _1074298)), _1074296) = hAPP(c_Groups_Oabs__class_Oabs(_1074294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074294), _1074298), _1074296)))], (18509 ^ _778908) ^ [_1098244] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1098244), c_Int_OPls) = _1098244)], (44250 ^ _778908) ^ [_1644063, _1644065, _1644067] : [class_Orderings_Olinorder(_1644063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644063), _1644065)), -(c_Big__Operators_Olinorder__class_OMin(_1644063, hAPP(hAPP(c_Set_Oinsert(_1644063), _1644067), _1644065)) = hAPP(hAPP(c_Finite__Set_Ofold(_1644063, _1644063, c_Orderings_Oord__class_Omin(_1644063)), _1644067), _1644065))], (35724 ^ _778908) ^ [_1437725, _1437727, _1437729, _1437731, _1437733, _1437735, _1437737] : [hAPP(c_Fun_Ocomp(_1437725, _1437727, _1437729, _1437731), _1437733) = _1437735, -(hAPP(_1437731, hAPP(_1437733, _1437737)) = hAPP(_1437735, _1437737))], (48582 ^ _778908) ^ [_1749792, _1749794, _1749796, _1749798] : [-(_1749792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1749794), _1749792), hAPP(hAPP(c_List_Olist_OCons(_1749794), _1749796), _1749798)) = hAPP(hAPP(c_List_Olist_OCons(_1749794), _1749796), hAPP(hAPP(c_List_Otake(_1749794), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1749792), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1749798)))], (45917 ^ _778908) ^ [_1683169, _1683171, _1683173, _1683175, _1683177, _1683179] : [hAPP(_1683169, _1683171) = hAPP(c_Option_Ooption_OSome(_1683173), _1683175), -(hAPP(c_Map_Omap__add(_1683177, _1683173, _1683179, _1683169), _1683171) = hAPP(c_Option_Ooption_OSome(_1683173), _1683175))], (27773 ^ _778908) ^ [_1271376] : [-(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)), _1271376)) = _1271376)], (22338 ^ _778908) ^ [_1165831] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1165831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1165831)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24725 ^ _778908) ^ [_1211642, _1211644, _1211646, _1211648] : [class_Orderings_Olinorder(_1211642), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211642), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211642), _1211644), _1211646)), _1211648) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211642), _1211644), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211642), _1211646), _1211648)))], (5258 ^ _778908) ^ [_860245, _860247, _860249, _860251, _860253, _860255] : [-(c_List_Oremove1(_860255, _860251, _860247) = c_List_Oremove1(_860253, _860249, _860245)), _860255 = _860253, _860251 = _860249, _860247 = _860245], (23379 ^ _778908) ^ [_1186422, _1186424, _1186426, _1186428, _1186430] : [hAPP(c_Product__Type_Osnd(_1186422, _1186424), hAPP(hAPP(c_Product__Type_OPair(_1186422, _1186424), _1186426), _1186428)) = _1186430, -(_1186428 = _1186430)], (47441 ^ _778908) ^ [_1722598, _1722600, _1722602] : [-(hAPP(hAPP(c_List_Ozip(_1722598, _1722600), c_List_Olist_ONil(_1722598)), _1722602) = c_List_Olist_ONil(tc_prod(_1722598, _1722600)))], (6571 ^ _778908) ^ [_885745, _885747, _885749, _885751, _885753] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885745), hAPP(hAPP(hAPP(c_Natural_Oupdate, _885747), c_Com_Ovname_OLoc(_885749)), hAPP(_885751, _885747))), _885753)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_885749, _885751, _885745)), _885747), hAPP(hAPP(hAPP(c_Natural_Oupdate, _885753), c_Com_Ovname_OLoc(_885749)), hAPP(hAPP(c_Natural_Ogetlocs, _885747), _885749)))))], (14870 ^ _778908) ^ [_1031090, _1031092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031090)), 14873 ^ _778908 : [(14880 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031090), _1031092)), -(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), _1031092), _1031090))))], (14874 ^ _778908) ^ [] : [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), _1031092), _1031090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031090), _1031092)))]]], (47840 ^ _778908) ^ [_1732339, _1732341, _1732343, _1732345] : [hBOOL(hAPP(c_List_Odistinct(_1732339), _1732341)), -(hBOOL(hAPP(hAPP(c_member(_1732339), _1732343), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1732339, tc_HOL_Obool)), hAPP(c_List_Oset(_1732339), _1732341)), hAPP(hAPP(c_Set_Oinsert(_1732339), hAPP(hAPP(c_List_Onth(_1732339), _1732341), _1732345)), c_Orderings_Obot__class_Obot(tc_fun(_1732339, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1732339), hAPP(hAPP(c_List_Olist__update(_1732339, _1732341), _1732345), _1732343))))], (17073 ^ _778908) ^ [_1073126, _1073128, _1073130] : [class_Int_Onumber__ring(_1073126), -(hAPP(c_Int_Onumber__class_Onumber__of(_1073126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1073128), _1073130)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073126), hAPP(c_Int_Onumber__class_Onumber__of(_1073126), _1073128)), hAPP(c_Int_Onumber__class_Onumber__of(_1073126), _1073130)))], (42283 ^ _778908) ^ [_1595818, _1595820] : [c_Wellfounded_Owf(_1595818, hAPP(c_Set_OCollect(tc_prod(_1595818, _1595818)), hAPP(c_Product__Type_Oprod_Oprod__case(_1595818, _1595818, tc_HOL_Obool), _1595820))), -(c_Wellfounded_OwfP(_1595818, _1595820))], (29488 ^ _778908) ^ [_1306146, _1306148, _1306150, _1306152, _1306154, _1306156, _1306158] : [c_Typedef_Otype__definition(_1306146, _1306148, _1306150, _1306152, _1306154), 29491 ^ _778908 : [(29498 ^ _778908) ^ [] : [_1306156 = _1306158, -(hAPP(_1306150, _1306156) = hAPP(_1306150, _1306158))], (29492 ^ _778908) ^ [] : [hAPP(_1306150, _1306156) = hAPP(_1306150, _1306158), -(_1306156 = _1306158)]]], (40850 ^ _778908) ^ [_1554748, _1554750, _1554752] : [class_Orderings_Olinorder(_1554748), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554748), _1554750)), -(_1554750 = c_Orderings_Obot__class_Obot(tc_fun(_1554748, tc_HOL_Obool))), 40861 ^ _778908 : [(40862 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554748), _1554752), hAPP(c_Finite__Set_Ofold1(_1554748, c_Orderings_Oord__class_Omin(_1554748)), _1554750))), 40865 ^ _778908 : [(40866 ^ _778908) ^ [_1555041] : [hBOOL(hAPP(hAPP(c_member(_1554748), _1555041), _1554750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554748), _1554752), _1555041)))]]], (40872 ^ _778908) ^ [] : [40874 ^ _778908 : [(40877 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554748), _1554752), 40873 ^ [_1554748, _1554750, _1554752]))], (40875 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554748), 40873 ^ [_1554748, _1554750, _1554752]), _1554750)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554748), _1554752), hAPP(c_Finite__Set_Ofold1(_1554748, c_Orderings_Oord__class_Omin(_1554748)), _1554750))))]]], (18287 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40438 ^ _778908) ^ [_1546578, _1546580, _1546582, _1546584, _1546586, _1546588, _1546590] : [-(hAPP(c_Product__Type_Ofst(_1546578, _1546580), hAPP(c_Product__Type_Omap__pair(_1546582, _1546578, _1546584, _1546580, _1546586, _1546588), _1546590)) = hAPP(_1546586, hAPP(c_Product__Type_Ofst(_1546582, _1546584), _1546590)))], (47968 ^ _778908) ^ [_1735104, _1735106, _1735108] : [class_Orderings_Olinorder(_1735104), hBOOL(hAPP(hAPP(c_member(_1735104), _1735106), hAPP(c_List_Oset(_1735104), _1735108))), -(c_List_Olinorder__class_Oinsort__insert__key(_1735104, _1735104, c_COMBI(_1735104), _1735106, _1735108) = _1735108)], (38842 ^ _778908) ^ [_1507581, _1507583, _1507585, _1507587] : [-(_1507581 = c_Orderings_Obot__class_Obot(tc_fun(_1507583, tc_HOL_Obool))), 38845 ^ _778908 : [(38846 ^ _778908) ^ [] : [-(hAPP(c_Set_Oimage(_1507585, _1507583, 38853 ^ [_1507581, _1507583, _1507585, _1507587]), _1507587) = _1507581), 38847 ^ _778908 : [(38848 ^ _778908) ^ [_1507722] : [c_Fun_Oinj__on(_1507583, _1507585, _1507722, _1507581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507585, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1507583, _1507585, _1507722), _1507581)), _1507587))]]], (38857 ^ _778908) ^ [] : [38858 ^ _778908 : [(38859 ^ _778908) ^ [_1507914] : [hAPP(c_Set_Oimage(_1507585, _1507583, _1507914), _1507587) = _1507581]], 38861 ^ _778908 : [(38864 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507585, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1507583, _1507585, 38860 ^ [_1507581, _1507583, _1507585, _1507587]), _1507581)), _1507587)))], (38862 ^ _778908) ^ [] : [-(c_Fun_Oinj__on(_1507583, _1507585, 38860 ^ [_1507581, _1507583, _1507585, _1507587], _1507581))]]]]], (26989 ^ _778908) ^ [_1255248, _1255250, _1255252, _1255254, _1255256] : [class_Orderings_Oorder(_1255248), 26992 ^ _778908 : [(27013 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1255248, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1255248, _1255250, _1255252)), c_SetInterval_Oord__class_OatLeastAtMost(_1255248, _1255254, _1255256)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255254), _1255256)), 27016 ^ _778908 : [(27019 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255254), _1255250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255252), _1255256)), 27026 ^ _778908 : [(27029 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255248), _1255252), _1255256))], (27027 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255248), _1255254), _1255250))]]], (27017 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255250), _1255252)))]]], (26993 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1255248, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1255248, _1255250, _1255252)), c_SetInterval_Oord__class_OatLeastAtMost(_1255248, _1255254, _1255256))), 26996 ^ _778908 : [(26997 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255250), _1255252)), 27000 ^ _778908 : [(27005 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255248), _1255254), _1255250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255248), _1255252), _1255256)))], (27003 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255252), _1255256)))], (27001 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255254), _1255250)))]]], (27011 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255248), _1255254), _1255256)))]]]]], (15604 ^ _778908) ^ [_1044473, _1044475] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044473), _1044475)), _1044475) = _1044473)], (47152 ^ _778908) ^ [_1715819, _1715821, _1715823, _1715825, _1715827] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715819), tc_List_Olist(_1715819))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715819), tc_List_Olist(_1715819)), hAPP(hAPP(c_List_Olist_OCons(_1715819), _1715821), _1715823)), _1715825)), c_List_Olistrel(_1715819, _1715827))), 47157 ^ _778908 : [(47162 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715819), tc_List_Olist(_1715819))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715819), tc_List_Olist(_1715819)), _1715823), 47156 ^ [_1715819, _1715821, _1715823, _1715825, _1715827])), c_List_Olistrel(_1715819, _1715827))))], (47160 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1715819, _1715819)), hAPP(hAPP(c_Product__Type_OPair(_1715819, _1715819), _1715821), 47155 ^ [_1715819, _1715821, _1715823, _1715825, _1715827])), _1715827)))], (47158 ^ _778908) ^ [] : [-(_1715825 = hAPP(hAPP(c_List_Olist_OCons(_1715819), 47155 ^ [_1715819, _1715821, _1715823, _1715825, _1715827]), 47156 ^ [_1715819, _1715821, _1715823, _1715825, _1715827]))]]], (17567 ^ _778908) ^ [_1082494, _1082496] : [class_Groups_Omonoid__mult(_1082494), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1082494), _1082496), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1082496)], (51229 ^ _778908) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (47178 ^ _778908) ^ [_1716678, _1716680, _1716682, _1716684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1716678), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1716680), _1716682))), -(hAPP(c_Random_Opick(_1716680, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1716680)), _1716682), _1716684)), _1716678) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1716680), _1716682))], (46503 ^ _778908) ^ [_1697177, _1697179, _1697181, _1697183] : [-(_1697177 = _1697179), 46506 ^ _778908 : [(46513 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1697181), _1697177), hAPP(c_List_Oset(_1697181), _1697183))), -(hBOOL(hAPP(hAPP(c_member(_1697181), _1697177), hAPP(c_List_Oset(_1697181), c_List_Oremove1(_1697181, _1697179, _1697183)))))], (46507 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1697181), _1697177), hAPP(c_List_Oset(_1697181), c_List_Oremove1(_1697181, _1697179, _1697183)))), -(hBOOL(hAPP(hAPP(c_member(_1697181), _1697177), hAPP(c_List_Oset(_1697181), _1697183))))]]], (42949 ^ _778908) ^ [_1612011, _1612013, _1612015] : [class_Orderings_Olinorder(_1612011), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612011), _1612013)), 42959 ^ _778908 : [(42962 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612011), 42958 ^ [_1612011, _1612013, _1612015]), _1612015))], (42960 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612011), 42958 ^ [_1612011, _1612013, _1612015]), _1612013)))]], hBOOL(hAPP(hAPP(c_member(_1612011), _1612015), _1612013)), -(c_Big__Operators_Olinorder__class_OMax(_1612011, _1612013) = _1612015)], (8142 ^ _778908) ^ [_915102, _915104] : [8143 ^ _778908 : [(8144 ^ _778908) ^ [_915155] : [_915104 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915102), _915155))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915102), _915104)))], (7653 ^ _778908) ^ [_906927, _906929] : [-(_906927 = _906929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906927), _906929))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906929), _906927)))], (6927 ^ _778908) ^ [_893364, _893366, _893368, _893370] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _893364), _893366, hAPP(c_Nat_OSuc, _893368), _893370), -(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _893364)), _893366, _893368, _893370))], (48269 ^ _778908) ^ [_1742324, _1742326, _1742328] : [_1742326 = c_List_Olist_ONil(_1742324), -(hAPP(hAPP(c_List_Oappend(_1742324), _1742326), _1742328) = _1742328)], (17841 ^ _778908) ^ [_1087430, _1087432, _1087434, _1087436] : [class_Rings_Olinordered__semidom(_1087430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1087432), _1087434)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087430), c_Groups_Oone__class_Oone(_1087430)), _1087436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087430), hAPP(hAPP(c_Power_Opower__class_Opower(_1087430), _1087436), _1087432)), hAPP(hAPP(c_Power_Opower__class_Opower(_1087430), _1087436), _1087434))))], (38336 ^ _778908) ^ [_1497418, _1497420] : [c_Equiv__Relations_Oequivp(_1497418, hAPP(hAPP(c_COMBC(_1497418, tc_fun(tc_prod(_1497418, _1497418), tc_HOL_Obool), tc_fun(_1497418, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497418, tc_fun(tc_fun(tc_prod(_1497418, _1497418), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497418, _1497418), tc_HOL_Obool), tc_fun(_1497418, tc_HOL_Obool)), _1497418), c_COMBC(_1497418, tc_fun(tc_prod(_1497418, _1497418), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497418, tc_prod(_1497418, _1497418)), tc_fun(_1497418, tc_fun(tc_fun(tc_prod(_1497418, _1497418), tc_HOL_Obool), tc_HOL_Obool)), _1497418), hAPP(c_COMBB(tc_prod(_1497418, _1497418), tc_fun(tc_fun(tc_prod(_1497418, _1497418), tc_HOL_Obool), tc_HOL_Obool), _1497418), c_member(tc_prod(_1497418, _1497418)))), c_Product__Type_OPair(_1497418, _1497418)))), _1497420)), -(c_Equiv__Relations_Oequiv(_1497418, c_Orderings_Otop__class_Otop(tc_fun(_1497418, tc_HOL_Obool)), _1497420))], (47012 ^ _778908) ^ [_1711925, _1711927, _1711929, _1711931, _1711933, _1711935] : [-(c_List_Olistrelp(_1711925, _1711927, hAPP(hAPP(c_List_Olist_OCons(_1711925), _1711929), _1711931), hAPP(hAPP(c_List_Olist_OCons(_1711925), _1711933), _1711935))), hBOOL(hAPP(hAPP(_1711927, _1711929), _1711933)), c_List_Olistrelp(_1711925, _1711927, _1711931, _1711935)], (4998 ^ _778908) ^ [_856205, _856207] : [_856207 = _856205, -(c_Option_Othe(_856207) = c_Option_Othe(_856205))], (19889 ^ _778908) ^ [] : [-(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))))], (19013 ^ _778908) ^ [_1106424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1106424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1106424))))], (46699 ^ _778908) ^ [_1702342, _1702344, _1702346] : [class_Orderings_Olinorder(_1702342), -(c_List_Oremove1(_1702342, _1702344, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1702342, _1702342, c_COMBI(_1702342)), _1702344), _1702346)) = _1702346)], (47184 ^ _778908) ^ [_1716821, _1716823, _1716825, _1716827] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1716821), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1716823), _1716825)))), -(hAPP(c_Random_Opick(_1716823, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1716823)), _1716825), _1716827)), _1716821) = hAPP(c_Random_Opick(_1716823, _1716827), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1716821), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1716823), _1716825))))], (37756 ^ _778908) ^ [_1483657, _1483659, _1483661, _1483663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1483657), _1483659)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1483657), _1483661)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483657, tc_Nat_Onat), _1483663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483657, tc_HOL_Obool)), _1483659), _1483661)) = 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(_1483657, tc_Nat_Onat), _1483663), _1483659)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483657, tc_Nat_Onat), _1483663), _1483661))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483657, tc_Nat_Onat), _1483663), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483657, tc_HOL_Obool)), _1483659), _1483661))))], (16529 ^ _778908) ^ [_1063043, _1063045] : [class_Int_Onumber__ring(_1063043), -(hAPP(c_Int_Oring__1__class_Oof__int(_1063043), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1063045)) = hAPP(c_Int_Onumber__class_Onumber__of(_1063043), _1063045))], (44362 ^ _778908) ^ [_1646171, _1646173, _1646175] : [class_Orderings_Olinorder(_1646171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646171), _1646173)), -(hBOOL(hAPP(hAPP(c_member(_1646171), _1646175), _1646173))), -(c_Big__Operators_Olinorder__class_OMin(_1646171, hAPP(hAPP(c_Set_Oinsert(_1646171), _1646175), _1646173)) = hAPP(hAPP(c_Finite__Set_Ofold(_1646171, _1646171, c_Orderings_Oord__class_Omin(_1646171)), _1646175), _1646173))], (43113 ^ _778908) ^ [_1615622, _1615624] : [-(c_Transitive__Closure_Otrancl(_1615622, _1615624) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1615622, _1615622), tc_HOL_Obool)), _1615624), hAPP(hAPP(c_Relation_Orel__comp(_1615622, _1615622, _1615622), c_Transitive__Closure_Otrancl(_1615622, _1615624)), _1615624)))], (28499 ^ _778908) ^ [_1285113, _1285115, _1285117] : [class_Lattices_Osemilattice__sup(_1285113), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285113), _1285115), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285113), _1285115), _1285117))))], (43151 ^ _778908) ^ [_1617398, _1617400, _1617402] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617398, _1617398)), hAPP(hAPP(c_Product__Type_OPair(_1617398, _1617398), _1617400), _1617400)), c_Transitive__Closure_Ortrancl(_1617398, _1617402))))], (34375 ^ _778908) ^ [_1407777, _1407779, _1407781] : [class_Groups_Ocomm__monoid__mult(_1407777), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407779, _1407777), hAPP(c_COMBK(_1407777, _1407779), c_Groups_Oone__class_Oone(_1407777))), _1407781) = c_Groups_Oone__class_Oone(_1407777))], (45257 ^ _778908) ^ [_1668096] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1668096, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1668096, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1668096, tc_HOL_Obool)))], (25141 ^ _778908) ^ [_1220851, _1220853, _1220855] : [-(c_HOL_OThe(tc_prod(_1220851, _1220853), _1220855) = c_HOL_OThe(tc_prod(_1220851, _1220853), hAPP(c_Product__Type_Oprod_Oprod__case(_1220851, _1220853, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1220853, tc_prod(_1220851, _1220853)), tc_fun(_1220853, tc_HOL_Obool), _1220851), hAPP(c_COMBB(tc_prod(_1220851, _1220853), tc_HOL_Obool, _1220853), _1220855)), c_Product__Type_OPair(_1220851, _1220853)))))], (7464 ^ _778908) ^ [_903635, _903637, _903639, _903641, _903643] : [-(hAPP(c_Option_Ooption_Ooption__case(_903635, _903637, _903639, _903641), hAPP(c_Option_Ooption_OSome(_903637), _903643)) = hAPP(_903641, _903643))], (9064 ^ _778908) ^ [_930330, _930332, _930334] : [class_Rings_Ocomm__semiring__1(_930330), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930330), _930332), _930334) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930330), _930334), _930332))], (33483 ^ _778908) ^ [_1389799, _1389801] : [class_Orderings_Olinorder(_1389799), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389799), _1389801)), -(_1389801 = c_Orderings_Obot__class_Obot(tc_fun(_1389799, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1389799), c_Big__Operators_Olinorder__class_OMax(_1389799, _1389801)), _1389801)))], (16152 ^ _778908) ^ [_1055643, _1055645, _1055647] : [-(hBOOL(hAPP(_1055643, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055645), _1055647)))), 16155 ^ _778908 : [(16158 ^ _778908) ^ [] : [hBOOL(hAPP(_1055643, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16156 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1055645), _1055647)))]], 16160 ^ _778908 : [(16163 ^ _778908) ^ [] : [hBOOL(hAPP(_1055643, 16159 ^ [_1055643, _1055645, _1055647]))], (16161 ^ _778908) ^ [] : [-(_1055645 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1055647), 16159 ^ [_1055643, _1055645, _1055647]))]]], (41708 ^ _778908) ^ [_1580629] : [-(hAPP(c_Set_Oimage(_1580629, _1580629, c_Fun_Oid(_1580629)), c_Orderings_Otop__class_Otop(tc_fun(_1580629, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1580629, tc_HOL_Obool)))], (51487 ^ _778908) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (43455 ^ _778908) ^ [_1624691, _1624693] : [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), _1624691), _1624693)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1624691), _1624693)))], (51231 ^ _778908) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (30732 ^ _778908) ^ [_1329939, _1329941, _1329943] : [class_Orderings_Olinorder(_1329939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329939), _1329941), _1329943)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329939, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1329939), _1329941), c_Orderings_Obot__class_Obot(tc_fun(_1329939, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1329939, _1329941, _1329943)) = c_SetInterval_Oord__class_OatLeastAtMost(_1329939, _1329941, _1329943))], (51395 ^ _778908) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (13204 ^ _778908) ^ [_1001462] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001462))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1001462)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47288 ^ _778908) ^ [_1719435, _1719437, _1719439, _1719441] : [class_Groups_Ocomm__monoid__add(_1719435), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1719435), _1719437), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1719439, _1719441))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1719435), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1719435), _1719437), c_List_Oupto(_1719439, _1719441))))], (51063 ^ _778908) ^ [_1805968, _1805970, _1805972, _1805974] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1805968)), c_List_Otranspose__rel(_1805968)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1805968)), hAPP(hAPP(c_List_Olist_OCons(_1805968), _1805970), _1805972)), _1805974))), -(c_List_Otranspose(_1805968, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1805968)), hAPP(hAPP(c_List_Olist_OCons(_1805968), _1805970), _1805972)), _1805974)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1805968)), hAPP(hAPP(c_List_Olist_OCons(_1805968), _1805970), c_List_Oconcat(_1805968, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1805968), tc_List_Olist(_1805968)), c_List_Olist_Olist__case(tc_List_Olist(_1805968), _1805968, c_List_Olist_ONil(_1805968), hAPP(hAPP(c_COMBB(tc_List_Olist(_1805968), tc_fun(tc_List_Olist(_1805968), tc_List_Olist(_1805968)), _1805968), c_COMBK(tc_List_Olist(_1805968), tc_List_Olist(_1805968))), hAPP(hAPP(c_COMBC(_1805968, tc_List_Olist(_1805968), tc_List_Olist(_1805968)), c_List_Olist_OCons(_1805968)), c_List_Olist_ONil(_1805968))))), _1805974)))), c_List_Otranspose(_1805968, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1805968)), _1805972), c_List_Oconcat(tc_List_Olist(_1805968), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1805968), tc_List_Olist(tc_List_Olist(_1805968))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1805968)), _1805968, c_List_Olist_ONil(tc_List_Olist(_1805968)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1805968), tc_List_Olist(tc_List_Olist(_1805968))), _1805968), hAPP(hAPP(c_COMBC(tc_List_Olist(_1805968), tc_List_Olist(tc_List_Olist(_1805968)), tc_List_Olist(tc_List_Olist(_1805968))), c_List_Olist_OCons(tc_List_Olist(_1805968))), c_List_Olist_ONil(tc_List_Olist(_1805968)))))), _1805974))))))], (44104 ^ _778908) ^ [_1641114, _1641116, _1641118, _1641120] : [class_Orderings_Olinorder(_1641114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641114), _1641116)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1641114, _1641114, c_Orderings_Oord__class_Omin(_1641114)), _1641118), hAPP(hAPP(c_Set_Oinsert(_1641114), _1641120), _1641116)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1641114), _1641120), hAPP(hAPP(c_Finite__Set_Ofold(_1641114, _1641114, c_Orderings_Oord__class_Omin(_1641114)), _1641118), _1641116)))], (10022 ^ _778908) ^ [_947296, _947298, _947300] : [class_Rings_Olinordered__ring__strict(_947296), 10025 ^ _778908 : [(10034 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947296), _947298), _947298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947296), _947300), _947300)) = c_Groups_Ozero__class_Ozero(_947296)), _947298 = c_Groups_Ozero__class_Ozero(_947296), _947300 = c_Groups_Ozero__class_Ozero(_947296)], (10026 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947296), _947298), _947298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947296), _947300), _947300)) = c_Groups_Ozero__class_Ozero(_947296), 10029 ^ _778908 : [(10032 ^ _778908) ^ [] : [-(_947300 = c_Groups_Ozero__class_Ozero(_947296))], (10030 ^ _778908) ^ [] : [-(_947298 = c_Groups_Ozero__class_Ozero(_947296))]]]]], (36970 ^ _778908) ^ [_1466396, _1466398, _1466400, _1466402] : [-(hBOOL(hAPP(hAPP(c_member(_1466396), _1466398), _1466400))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466396, tc_HOL_Obool)), _1466400), hAPP(hAPP(c_Set_Oinsert(_1466396), _1466398), _1466402)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466396, tc_HOL_Obool)), _1466400), _1466402))], (24639 ^ _778908) ^ [_1209970, _1209972, _1209974] : [class_Orderings_Olinorder(_1209970), 24642 ^ _778908 : [(24649 ^ _778908) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209970), _1209972), _1209974) = _1209974, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209970), _1209972), _1209974)))], (24643 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209970), _1209972), _1209974)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209970), _1209972), _1209974) = _1209974)]]], (30048 ^ _778908) ^ [_1316989, _1316991] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316989, tc_HOL_Obool)), _1316991), c_Orderings_Obot__class_Obot(tc_fun(_1316989, tc_HOL_Obool))) = _1316991)], (4676 ^ _778908) ^ [_851328, _851330, _851332, _851334] : [-(c_Nat_Ocompow(_851334, _851330) = c_Nat_Ocompow(_851332, _851328)), _851334 = _851332, _851330 = _851328], (7500 ^ _778908) ^ [_904297, _904299, _904301, _904303] : [class_Rings_Ocomm__semiring__1(_904297), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904297), _904299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904297), _904301), _904303)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904297), _904299), _904301)), _904303))], (35764 ^ _778908) ^ [_1438748, _1438750, _1438752, _1438754, _1438756] : [hBOOL(hAPP(hAPP(c_member(_1438748), _1438750), hAPP(c_Relation_OImage(_1438752, _1438748, _1438754), _1438756))), 35768 ^ _778908 : [(35771 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1438752, _1438748)), hAPP(hAPP(c_Product__Type_OPair(_1438752, _1438748), 35767 ^ [_1438748, _1438750, _1438752, _1438754, _1438756]), _1438750)), _1438754)))], (35769 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438752), 35767 ^ [_1438748, _1438750, _1438752, _1438754, _1438756]), _1438756)))]]], (5684 ^ _778908) ^ [_866696, _866698] : [_866698 = _866696, -(tc_Option_Ooption(_866698) = tc_Option_Ooption(_866696))], (22528 ^ _778908) ^ [_1169309, _1169311] : [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(_1169309))), 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)), _1169311))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169309) = hAPP(c_Nat_OSuc, _1169311))], (20193 ^ _778908) ^ [] : [-(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))], (49410 ^ _778908) ^ [_1769991, _1769993, _1769995, _1769997] : [class_Complete__Lattice_Ocomplete__lattice(_1769991), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1769993, _1769991), hAPP(c_List_Oset(_1769993), _1769995)), _1769997) = hAPP(c_List_Ofoldl(_1769991, _1769993, hAPP(c_COMBC(_1769993, _1769991, _1769991), hAPP(hAPP(c_COMBB(_1769991, tc_fun(_1769991, _1769991), _1769993), c_Lattices_Osemilattice__sup__class_Osup(_1769991)), _1769997)), c_Orderings_Obot__class_Obot(_1769991)), _1769995))], (44959 ^ _778908) ^ [_1661756, _1661758, _1661760, _1661762, _1661764] : [_1661756 = c_Orderings_Obot__class_Obot(tc_fun(_1661758, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661760, tc_HOL_Obool)), _1661762), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1661758, tc_fun(_1661760, tc_HOL_Obool)), _1661756), _1661764)) = _1661762)], (30460 ^ _778908) ^ [_1324370, _1324372, _1324374, _1324376] : [-(_1324370 = c_Orderings_Obot__class_Obot(tc_fun(_1324372, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1324372, _1324374, hAPP(c_COMBK(_1324374, _1324372), _1324376)), _1324370) = hAPP(hAPP(c_Set_Oinsert(_1324374), _1324376), c_Orderings_Obot__class_Obot(tc_fun(_1324374, tc_HOL_Obool))))], (24677 ^ _778908) ^ [_1210654, _1210656] : [class_Orderings_Olinorder(_1210654), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210654), _1210656), _1210656) = _1210656)], (42601 ^ _778908) ^ [_1603908, _1603910, _1603912, _1603914] : [42603 ^ _778908 : [(42606 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1603908, _1603908, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1603908, tc_fun(_1603908, _1603910), tc_fun(_1603908, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603910, tc_HOL_Obool), tc_fun(tc_fun(_1603908, _1603910), tc_fun(_1603908, tc_HOL_Obool)), _1603908), c_COMBB(_1603910, tc_HOL_Obool, _1603908)), hAPP(hAPP(c_COMBB(_1603910, tc_fun(_1603910, tc_HOL_Obool), _1603908), c_fequal), _1603914))), _1603914)), 42602 ^ [_1603908, _1603910, _1603912, _1603914]))], (42604 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603908, _1603908)), 42602 ^ [_1603908, _1603910, _1603912, _1603914]), _1603912)))]], -(c_Equiv__Relations_Ocongruent(_1603908, _1603910, _1603912, _1603914))], (44629 ^ _778908) ^ [_1651740, _1651742, _1651744, _1651746, _1651748] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1651740, tc_HOL_Obool)), _1651742), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651744, tc_fun(_1651740, tc_HOL_Obool)), _1651746), _1651748)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1651744, tc_fun(_1651740, tc_HOL_Obool)), _1651746), hAPP(hAPP(c_COMBB(tc_fun(_1651740, tc_HOL_Obool), tc_fun(_1651740, tc_HOL_Obool), _1651744), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1651740, tc_HOL_Obool)), _1651742)), _1651748)))], (31091 ^ _778908) ^ [_1337138, _1337140] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1337138)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1337140))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1337138), _1337140)))], (26089 ^ _778908) ^ [_1237428, _1237430, _1237432, _1237434, _1237436] : [class_Groups_Ocomm__monoid__add(_1237428), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237430, _1237428), hAPP(hAPP(c_COMBS(_1237430, _1237428, _1237428), hAPP(hAPP(c_COMBB(_1237428, tc_fun(_1237428, _1237428), _1237430), c_Groups_Oplus__class_Oplus(_1237428)), _1237432)), _1237434)), _1237436) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1237428), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237430, _1237428), _1237432), _1237436)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237430, _1237428), _1237434), _1237436)))], (47230 ^ _778908) ^ [_1717927, _1717929, _1717931, _1717933, _1717935] : [class_Rings_Osemiring__0(_1717927), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717927), hAPP(hAPP(c_List_Omap(_1717929, _1717927), hAPP(hAPP(c_COMBB(_1717927, _1717927, _1717929), hAPP(c_Groups_Otimes__class_Otimes(_1717927), _1717931)), _1717933)), _1717935)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1717927), _1717931), hAPP(c_List_Omonoid__add__class_Olistsum(_1717927), hAPP(hAPP(c_List_Omap(_1717929, _1717927), _1717933), _1717935))))], (25807 ^ _778908) ^ [_1232214, _1232216, _1232218, _1232220] : [class_Rings_Ocomm__semiring__1(_1232214), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232214), _1232216), _1232218)), _1232220)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232214), _1232216), _1232220)))], (30052 ^ _778908) ^ [_1317092, _1317094, _1317096, _1317098] : [hAPP(c_Set_Oimage(_1317092, _1317094, _1317096), _1317098) = c_Orderings_Obot__class_Obot(tc_fun(_1317094, tc_HOL_Obool)), -(_1317098 = c_Orderings_Obot__class_Obot(tc_fun(_1317092, tc_HOL_Obool)))], (27936 ^ _778908) ^ [_1274135] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1274135) = 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)), _1274135)))], (48691 ^ _778908) ^ [_1752583, _1752585] : [-(c_List_Olistrel1(_1752583, hAPP(c_Relation_Oconverse(_1752583, _1752583), _1752585)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1752583), tc_List_Olist(_1752583)), c_List_Olistrel1(_1752583, _1752585)))], (43761 ^ _778908) ^ [_1632435, _1632437, _1632439, _1632441] : [-(hAPP(hAPP(c_Nat_Ocompow(_1632435, _1632435), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1632437), _1632439)), _1632441) = hAPP(c_Fun_Ocomp(_1632435, _1632435, _1632435, hAPP(hAPP(c_Nat_Ocompow(_1632435, _1632435), _1632437), _1632441)), hAPP(hAPP(c_Nat_Ocompow(_1632435, _1632435), _1632439), _1632441)))], (28255 ^ _778908) ^ [_1280712, _1280714] : [class_Lattices_Olattice(_1280712), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280712), _1280714), _1280714) = _1280714)], (22686 ^ _778908) ^ [_1172598, _1172600] : [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), _1172598))), 22689 ^ _778908 : [(22696 ^ _778908) ^ [] : [-(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), _1172600)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172598))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172600), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172598)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172598)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172600), 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), _1172598)))))], (22690 ^ _778908) ^ [] : [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), _1172600)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172598)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172600), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172598)) = 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), _1172600)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1172598))))]]], (48953 ^ _778908) ^ [_1760195, _1760197] : [hAPP(c_List_Orotate1(_1760195), _1760197) = c_List_Olist_ONil(_1760195), -(_1760197 = c_List_Olist_ONil(_1760195))], (38688 ^ _778908) ^ [_1504584, _1504586, _1504588, _1504590, _1504592, _1504594] : [c_Fun_Oinj__on(_1504584, _1504586, hAPP(c_Fun_Ocomp(_1504588, _1504586, _1504584, _1504590), _1504592), _1504594), -(c_Fun_Oinj__on(_1504584, _1504588, _1504592, _1504594))], (17363 ^ _778908) ^ [_1078853, _1078855, _1078857] : [class_Rings_Olinordered__semidom(_1078853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078853), c_Groups_Ozero__class_Ozero(_1078853)), _1078855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078853), _1078855), c_Groups_Oone__class_Oone(_1078853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078853), hAPP(hAPP(c_Power_Opower__class_Opower(_1078853), _1078855), hAPP(c_Nat_OSuc, _1078857))), c_Groups_Oone__class_Oone(_1078853))))], (18295 ^ _778908) ^ [_1095033, _1095035] : [class_Int_Onumber__ring(_1095033), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095033), hAPP(c_Int_Onumber__class_Onumber__of(_1095033), c_Int_OMin)), _1095035) = hAPP(c_Groups_Ouminus__class_Ouminus(_1095033), _1095035))], (47603 ^ _778908) ^ [_1726172, _1726174, _1726176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726172), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726174)), _1726176))), -(hAPP(c_Random_Opick(_1726174, hAPP(hAPP(c_List_Omap(_1726174, tc_prod(tc_Code__Numeral_Ocode__numeral, _1726174)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1726174), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1726176)), hAPP(c_Code__Numeral_Oof__nat, _1726172)) = hAPP(hAPP(c_List_Onth(_1726174), _1726176), _1726172))], (18755 ^ _778908) ^ [_1102029] : [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), _1102029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1102029)))], (46216 ^ _778908) ^ [_1690684, _1690686, _1690688, _1690690, _1690692] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1690684), tc_Option_Ooption(_1690686), tc_Option_Ooption(_1690688), hAPP(c_Option_Omap(_1690684, _1690686), _1690690)), hAPP(c_Option_Omap(_1690688, _1690684), _1690692)) = hAPP(c_Option_Omap(_1690688, _1690686), hAPP(c_Fun_Ocomp(_1690684, _1690686, _1690688, _1690690), _1690692)))], (40292 ^ _778908) ^ [_1542403, _1542405, _1542407] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542403), _1542405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542403, _1542403), tc_HOL_Obool)), _1542407), hAPP(hAPP(c_Product__Type_OSigma(_1542403, _1542403), _1542405), hAPP(c_COMBK(tc_fun(_1542403, tc_HOL_Obool), _1542403), _1542405)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1542403, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1542403), _1542405), _1542407))))], (46041 ^ _778908) ^ [] : [-(c_Com_Obody = c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom, c_Com_Obodies))], (22772 ^ _778908) ^ [_1174151, _1174153] : [-(c_Divides_OposDivAlg(_1174151, _1174153) = hAPP(c_Divides_Oadjust(_1174153), c_Divides_OposDivAlg(_1174151, 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)))), _1174153)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174151), _1174153))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1174153), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34068 ^ _778908) ^ [_1401366, _1401368, _1401370] : [class_Orderings_Olinorder(_1401366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401366), _1401368)), hBOOL(hAPP(hAPP(c_member(_1401366), _1401370), _1401368)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1401366), _1401370), c_Big__Operators_Olattice_OSup__fin(_1401366, c_Orderings_Oord__class_Omax(_1401366), _1401368)) = _1401370)], (48038 ^ _778908) ^ [_1736790, _1736792, _1736794, _1736796] : [-(hAPP(hAPP(c_List_Onth(_1736790), hAPP(hAPP(c_List_Oappend(_1736790), _1736792), _1736794)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736790)), _1736792)), _1736796)) = hAPP(hAPP(c_List_Onth(_1736790), _1736794), _1736796))], (12437 ^ _778908) ^ [_987951, _987953, _987955] : [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, _987951)), _987953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _987951)), _987955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987953), _987955)))], (24735 ^ _778908) ^ [_1211893, _1211895, _1211897, _1211899, _1211901] : [-(hAPP(c_Product__Type_Ofst(_1211893, _1211895), hAPP(c_Product__Type_Oapfst(_1211897, _1211893, _1211895, _1211899), _1211901)) = hAPP(_1211899, hAPP(c_Product__Type_Ofst(_1211897, _1211895), _1211901)))], (43844 ^ _778908) ^ [_1634637, _1634639, _1634641, _1634643, _1634645] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634637, _1634637)), hAPP(hAPP(c_Product__Type_OPair(_1634637, _1634637), _1634639), _1634641)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1634637, _1634637), tc_HOL_Obool), _1634643), _1634645))), 43849 ^ _778908 : [(43852 ^ _778908) ^ [] : [-(_1634639 = _1634641)], (43850 ^ _778908) ^ [] : [-(_1634643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 43855 ^ _778908 : [(43860 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634637, _1634637)), hAPP(hAPP(c_Product__Type_OPair(_1634637, _1634637), 43853 ^ [_1634637, _1634639, _1634641, _1634643, _1634645]), _1634641)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1634637, _1634637), tc_HOL_Obool), 43854 ^ [_1634637, _1634639, _1634641, _1634643, _1634645]), _1634645))))], (43858 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634637, _1634637)), hAPP(hAPP(c_Product__Type_OPair(_1634637, _1634637), _1634639), 43853 ^ [_1634637, _1634639, _1634641, _1634643, _1634645])), _1634645)))], (43856 ^ _778908) ^ [] : [-(_1634643 = hAPP(c_Nat_OSuc, 43854 ^ [_1634637, _1634639, _1634641, _1634643, _1634645]))]]], (38442 ^ _778908) ^ [_1499635, _1499637, _1499639, _1499641, _1499643, _1499645] : [c_Finite__Set_Ofolding__idem(_1499635, _1499637, _1499639, _1499641), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499635), _1499643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1499635, tc_HOL_Obool)), _1499645), _1499643)), -(hAPP(c_Fun_Ocomp(_1499637, _1499637, _1499637, hAPP(_1499641, _1499643)), hAPP(_1499641, _1499645)) = hAPP(_1499641, _1499643))], (19297 ^ _778908) ^ [_1111248, _1111250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1111248)), c_Int_OBit0(_1111250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111248), _1111250)))], (9390 ^ _778908) ^ [_935880, _935882, _935884] : [class_Groups_Oordered__ab__group__add(_935880), 9393 ^ _778908 : [(9400 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935880), _935884), _935882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935880), hAPP(c_Groups_Ouminus__class_Ouminus(_935880), _935882)), hAPP(c_Groups_Ouminus__class_Ouminus(_935880), _935884))))], (9394 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935880), hAPP(c_Groups_Ouminus__class_Ouminus(_935880), _935882)), hAPP(c_Groups_Ouminus__class_Ouminus(_935880), _935884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935880), _935884), _935882)))]]], (48703 ^ _778908) ^ [_1752960, _1752962, _1752964, _1752966, _1752968] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752960), tc_List_Olist(_1752960))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752960), tc_List_Olist(_1752960)), _1752962), _1752964)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1752960), c_List_Olistrel1(_1752960, _1752966)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752960), tc_List_Olist(_1752960))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752960), tc_List_Olist(_1752960)), hAPP(hAPP(c_List_Olist_OCons(_1752960), _1752968), _1752962)), hAPP(hAPP(c_List_Olist_OCons(_1752960), _1752968), _1752964))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1752960), c_List_Olistrel1(_1752960, _1752966)))))], (17085 ^ _778908) ^ [_1073396, _1073398, _1073400, _1073402] : [class_Int_Onumber__ring(_1073396), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073396), hAPP(c_Int_Onumber__class_Onumber__of(_1073396), _1073398)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073396), hAPP(c_Int_Onumber__class_Onumber__of(_1073396), _1073400)), _1073402)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073396), hAPP(c_Int_Onumber__class_Onumber__of(_1073396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1073398), _1073400))), _1073402))], (27771 ^ _778908) ^ [_1271331, _1271333] : [-(hAPP(c_Finite__Set_Ocard(_1271331), _1271333) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1271331, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1271331), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1271333))], (29285 ^ _778908) ^ [_1302362, _1302364, _1302366] : [-(hAPP(hAPP(c_Set_Oinsert(_1302362), _1302364), hAPP(hAPP(c_Set_Oinsert(_1302362), _1302364), _1302366)) = hAPP(hAPP(c_Set_Oinsert(_1302362), _1302364), _1302366))], (43155 ^ _778908) ^ [_1617493, _1617495, _1617497, _1617499] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617493, _1617493)), hAPP(hAPP(c_Product__Type_OPair(_1617493, _1617493), _1617495), _1617497)), c_Transitive__Closure_Otrancl(_1617493, _1617499))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617493, _1617493)), hAPP(hAPP(c_Product__Type_OPair(_1617493, _1617493), _1617495), _1617497)), c_Transitive__Closure_Ortrancl(_1617493, _1617499))))], (22510 ^ _778908) ^ [_1168955, _1168957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1168955)), hAPP(c_Code__Numeral_Oof__nat, _1168957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1168955), _1168957)))], (47753 ^ _778908) ^ [_1729878, _1729880, _1729882] : [-(hBOOL(hAPP(hAPP(c_member(_1729878), _1729880), hAPP(c_List_Oset(_1729878), _1729882)))), 47754 ^ _778908 : [(47755 ^ _778908) ^ [_1729952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729952), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729878)), _1729882))), hAPP(hAPP(c_List_Onth(_1729878), _1729882), _1729952) = _1729880]]], (30532 ^ _778908) ^ [_1325718, _1325720, _1325722, _1325724, _1325726] : [-(_1325718 = c_Orderings_Obot__class_Obot(tc_fun(_1325720, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1325720, tc_fun(_1325722, tc_HOL_Obool)), _1325718), hAPP(hAPP(c_COMBB(tc_fun(_1325722, tc_HOL_Obool), tc_fun(_1325722, tc_HOL_Obool), _1325720), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325722, tc_HOL_Obool)), _1325724)), _1325726)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325722, tc_HOL_Obool)), _1325724), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1325720, tc_fun(_1325722, tc_HOL_Obool)), _1325718), _1325726)))], (46677 ^ _778908) ^ [_1701845] : [class_Orderings_Olinorder(_1701845), -(c_Finite__Set_Ofun__left__comm(_1701845, tc_List_Olist(_1701845), c_List_Olinorder__class_Oinsort__key(_1701845, _1701845, c_COMBI(_1701845))))], (10753 ^ _778908) ^ [_959260, _959262, _959264] : [class_Orderings_Olinorder(_959260), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959260), _959262), _959264))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959260), _959264), _959262)))], (6417 ^ _778908) ^ [_882487, _882489, _882491, _882493] : [c_Com_Ocom_OLocal(_882487, _882489, _882491) = hAPP(c_Com_Ocom_OBODY, _882493)], (51357 ^ _778908) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (39534 ^ _778908) ^ [_1522871, _1522873, _1522875, _1522877, _1522879] : [hAPP(_1522877, _1522873) = _1522879, -(hBOOL(hAPP(hAPP(c_member(_1522871), _1522873), hAPP(c_Set_Ovimage(_1522871, _1522875, _1522877), hAPP(hAPP(c_Set_Oinsert(_1522875), _1522879), c_Orderings_Obot__class_Obot(tc_fun(_1522875, tc_HOL_Obool)))))))], (16629 ^ _778908) ^ [_1064710, _1064712] : [class_Rings_Olinordered__idom(_1064710), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064710), hAPP(c_Groups_Oabs__class_Oabs(_1064710), _1064712)), hAPP(c_Groups_Oabs__class_Oabs(_1064710), _1064712)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064710), _1064712), _1064712))], (6149 ^ _778908) ^ [_877536, _877538, _877540, _877542] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_877536, _877538)), _877540), _877542)), 6153 ^ _778908 : [(6156 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877538), 6152 ^ [_877536, _877538, _877540, _877542]), _877542)))], (6154 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_877536), _877540), 6152 ^ [_877536, _877538, _877540, _877542])))]]], (4098 ^ _778908) ^ [_842085, _842087] : [_842087 = _842085, -(c_Set_OBall(_842087) = c_Set_OBall(_842085))], (51397 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (49956 ^ _778908) ^ [_1781941, _1781943, _1781945] : [hAPP(c_List_Ofilter(_1781941, _1781943), _1781945) = c_List_Olist_ONil(_1781941), 49959 ^ _778908 : [(49960 ^ _778908) ^ [_1782038] : [hBOOL(hAPP(hAPP(c_member(_1781941), _1782038), hAPP(c_List_Oset(_1781941), _1781945))), hBOOL(hAPP(_1781943, _1782038))]]], (5288 ^ _778908) ^ [_860700, _860702] : [_860702 = _860700, -(c_Groups_Oplus__class_Oplus(_860702) = c_Groups_Oplus__class_Oplus(_860700))], (51287 ^ _778908) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (2638 ^ _778908) ^ [_818889, _818891, _818893, _818895] : [-(c_Orderings_Oord_Omin(_818895, _818891) = c_Orderings_Oord_Omin(_818893, _818889)), _818895 = _818893, _818891 = _818889], (9892 ^ _778908) ^ [_944869, _944871, _944873, _944875] : [class_Rings_Olinordered__ring__strict(_944869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944869), _944871), c_Groups_Ozero__class_Ozero(_944869))), 9899 ^ _778908 : [(9906 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944869), _944875), _944873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944869), _944871), _944873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944869), _944871), _944875))))], (9900 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944869), _944871), _944873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944869), _944871), _944875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944869), _944875), _944873)))]]], (41229 ^ _778908) ^ [_1562230] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1562230, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1562230), hAPP(c_COMBK(tc_HOL_Obool, _1562230), c_fTrue)))], (8908 ^ _778908) ^ [_927519] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _927519)) = 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), _927519)))], (18503 ^ _778908) ^ [_1098163] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098163), c_Int_OPls) = _1098163)], (40454 ^ _778908) ^ [_1547133, _1547135, _1547137, _1547139, _1547141, _1547143, _1547145, _1547147] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547133, _1547135)), _1547137), hAPP(c_Set_Oimage(tc_prod(_1547139, _1547141), tc_prod(_1547133, _1547135), c_Product__Type_Omap__pair(_1547139, _1547133, _1547141, _1547135, _1547143, _1547145)), _1547147))), 40459 ^ _778908 : [(40462 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547139, _1547141)), hAPP(hAPP(c_Product__Type_OPair(_1547139, _1547141), 40457 ^ [_1547133, _1547135, _1547137, _1547139, _1547141, _1547143, _1547145, _1547147]), 40458 ^ [_1547133, _1547135, _1547137, _1547139, _1547141, _1547143, _1547145, _1547147])), _1547147)))], (40460 ^ _778908) ^ [] : [-(_1547137 = hAPP(hAPP(c_Product__Type_OPair(_1547133, _1547135), hAPP(_1547143, 40457 ^ [_1547133, _1547135, _1547137, _1547139, _1547141, _1547143, _1547145, _1547147])), hAPP(_1547145, 40458 ^ [_1547133, _1547135, _1547137, _1547139, _1547141, _1547143, _1547145, _1547147])))]]], (23449 ^ _778908) ^ [_1187612, _1187614, _1187616] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187612), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187614)), _1187616)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187612, _1187614), hAPP(c_Divides_OnegateSnd, _1187616))))], (7420 ^ _778908) ^ [_902963, _902965] : [class_Rings_Ocomm__semiring__1(_902963), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902963), c_Groups_Ozero__class_Ozero(_902963)), _902965) = _902965)], (19133 ^ _778908) ^ [_1108264, _1108266] : [class_Int_Onumber__ring(_1108264), class_Rings_Olinordered__idom(_1108264), 19140 ^ _778908 : [(19147 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1108266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108264), c_Groups_Oone__class_Oone(_1108264)), hAPP(c_Int_Onumber__class_Onumber__of(_1108264), _1108266))))], (19141 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108264), c_Groups_Oone__class_Oone(_1108264)), hAPP(c_Int_Onumber__class_Onumber__of(_1108264), _1108266))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1108266)))]]], (29227 ^ _778908) ^ [_1301137, _1301139, _1301141, _1301143] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301137, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1301137), _1301139), _1301141)), _1301143) = hAPP(hAPP(c_Set_Oinsert(_1301137), _1301139), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301137, tc_HOL_Obool)), _1301141), _1301143)))], (29090 ^ _778908) ^ [_1298096, _1298098] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1298096, tc_HOL_Obool)), _1298098)))], (37032 ^ _778908) ^ [_1468014, _1468016] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468014, tc_HOL_Obool)), _1468016), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468014, tc_HOL_Obool)), _1468016)) = c_Orderings_Obot__class_Obot(tc_fun(_1468014, tc_HOL_Obool)))], (6833 ^ _778908) ^ [_891193, _891195] : [hBOOL(hAPP(c_Com_OWT, _891193)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_891195, _891193))))], (3236 ^ _778908) ^ [_828510, _828512, _828514, _828516, _828518, _828520] : [-(c_SetInterval_Oord_OlessThan(_828520, _828516, _828512) = c_SetInterval_Oord_OlessThan(_828518, _828514, _828510)), _828520 = _828518, _828516 = _828514, _828512 = _828510], (8242 ^ _778908) ^ [_916960, _916962, _916964] : [-(c_Sum__Type_OProjl(_916960, _916962, hAPP(c_Sum__Type_OInl(_916960, _916962), _916964)) = _916964)], (19437 ^ _778908) ^ [_1113658, _1113660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113658)), c_Int_OBit1(_1113660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113658), _1113660)))], (46589 ^ _778908) ^ [_1699415, _1699417, _1699419, _1699421] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1699415, _1699415)), hAPP(hAPP(c_Product__Type_OPair(_1699415, _1699415), _1699417), _1699419)), hAPP(c_List_Oset(tc_prod(_1699415, _1699415)), hAPP(hAPP(c_List_Ozip(_1699415, _1699415), _1699421), _1699421)))), 46592 ^ _778908 : [(46595 ^ _778908) ^ [] : [-(_1699417 = _1699419)], (46593 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699415), _1699417), hAPP(c_List_Oset(_1699415), _1699421))))]]], (27803 ^ _778908) ^ [_1271959, _1271961] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1271959), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1271961) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1271959, _1271961))], (27769 ^ _778908) ^ [_1271274, _1271276, _1271278] : [-(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)), _1271274)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1271276, _1271278)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1271276), _1271274), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1271278), _1271274)))], (35108 ^ _778908) ^ [_1423482, _1423484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1423482), _1423484)), -(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), _1423482), _1423484)), c_Wellfounded_Oless__than)))], (47521 ^ _778908) ^ [_1724099, _1724101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1724099), _1724101)), -(c_List_Oupto(_1724099, _1724101) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1724099), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1724099), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1724101)))], (29189 ^ _778908) ^ [_1300425, _1300427, _1300429, _1300431, _1300433] : [c_Typedef_Otype__definition(_1300425, _1300427, _1300429, _1300431, _1300433), -(hAPP(c_Set_Oimage(_1300425, _1300427, _1300429), c_Orderings_Otop__class_Otop(tc_fun(_1300425, tc_HOL_Obool))) = _1300433)], (14184 ^ _778908) ^ [_1018971, _1018973, _1018975, _1018977] : [class_Groups_Ouminus(_1018971), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018973, _1018971)), _1018975), _1018977) = hAPP(c_Groups_Ouminus__class_Ouminus(_1018971), hAPP(_1018975, _1018977)))], (50941 ^ _778908) ^ [_1802685, _1802687, _1802689, _1802691] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802685)), _1802687) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802689)), _1802691), -(hAPP(hAPP(c_List_Ozip(_1802685, _1802689), hAPP(c_List_Orev(_1802685), _1802687)), hAPP(c_List_Orev(_1802689), _1802691)) = hAPP(c_List_Orev(tc_prod(_1802685, _1802689)), hAPP(hAPP(c_List_Ozip(_1802685, _1802689), _1802687), _1802691)))], (18811 ^ _778908) ^ [_1102987, _1102989] : [class_Int_Onumber__ring(_1102987), 18814 ^ _778908 : [(18821 ^ _778908) ^ [] : [c_Int_Oiszero(_1102987, hAPP(c_Int_Onumber__class_Onumber__of(_1102987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1102989), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1102987), _1102989) = c_Groups_Oone__class_Oone(_1102987))], (18815 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1102987), _1102989) = c_Groups_Oone__class_Oone(_1102987), -(c_Int_Oiszero(_1102987, hAPP(c_Int_Onumber__class_Onumber__of(_1102987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1102989), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (48927 ^ _778908) ^ [_1759627, _1759629, _1759631] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1759627, tc_HOL_Obool)), hAPP(c_List_Oset(_1759627), hAPP(hAPP(c_List_Odrop(_1759627), _1759629), _1759631))), hAPP(c_List_Oset(_1759627), _1759631))))], (7985 ^ _778908) ^ [_912435, _912437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912435), _912437)), _912435))], (32712 ^ _778908) ^ [_1374382, _1374384, _1374386, _1374388, _1374390] : [class_Groups_Oordered__ab__semigroup__add(_1374382), class_Rings_Osemiring__1(_1374382), 32722 ^ _778908 : [(32725 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374382), hAPP(_1374388, 32721 ^ [_1374382, _1374384, _1374386, _1374388, _1374390])), _1374390))], (32723 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374384), 32721 ^ [_1374382, _1374384, _1374386, _1374388, _1374390]), _1374386)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374382), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1374384, _1374382), _1374388), _1374386)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374382), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1374382), hAPP(c_Finite__Set_Ocard(_1374384), _1374386))), _1374390))))], (45083 ^ _778908) ^ [_1664413, _1664415, _1664417, _1664419, _1664421] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664413, tc_fun(_1664415, tc_HOL_Obool)), _1664417), _1664419), _1664421)), 45086 ^ _778908 : [(45087 ^ _778908) ^ [_1664522] : [hBOOL(hAPP(hAPP(c_member(_1664413), _1664522), _1664417)), -(hBOOL(hAPP(hAPP(_1664419, _1664522), _1664421)))]]], (17559 ^ _778908) ^ [_1082327] : [-(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), _1082327)) = 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), _1082327))))], (5476 ^ _778908) ^ [_863506, _863508, _863510, _863512, _863514, _863516, _863518, _863520, _863522, _863524] : [-(c_List_Ofoldr(_863524, _863520, _863516, _863512, _863508) = c_List_Ofoldr(_863522, _863518, _863514, _863510, _863506)), _863524 = _863522, _863520 = _863518, _863516 = _863514, _863512 = _863510, _863508 = _863506], (48275 ^ _778908) ^ [_1742443, _1742445, _1742447] : [hAPP(hAPP(c_List_Oappend(_1742443), _1742445), _1742447) = _1742445, -(_1742447 = c_List_Olist_ONil(_1742443))], (45863 ^ _778908) ^ [_1682220, _1682222, _1682224, _1682226, _1682228, _1682230] : [hAPP(c_Map_Omap__add(_1682220, _1682222, _1682224, _1682226), _1682228) = hAPP(c_Option_Ooption_OSome(_1682222), _1682230), -(hAPP(_1682226, _1682228) = hAPP(c_Option_Ooption_OSome(_1682222), _1682230)), 45870 ^ _778908 : [(45873 ^ _778908) ^ [] : [-(hAPP(_1682224, _1682228) = hAPP(c_Option_Ooption_OSome(_1682222), _1682230))], (45871 ^ _778908) ^ [] : [-(hAPP(_1682226, _1682228) = c_Option_Ooption_ONone(_1682222))]]], (36582 ^ _778908) ^ [_1457241, _1457243] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457241, tc_HOL_Obool)), _1457243), c_Orderings_Otop__class_Otop(tc_fun(_1457241, tc_HOL_Obool))) = _1457243)], (31736 ^ _778908) ^ [_1351704] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1351704)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45310 ^ _778908) ^ [_1669680, _1669682, _1669684, _1669686] : [-(hAPP(c_Set_Ovimage(_1669680, _1669682, _1669684), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669682, tc_HOL_Obool), _1669686)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1669682, tc_HOL_Obool), tc_fun(_1669680, tc_HOL_Obool)), _1669686), c_Set_Ovimage(_1669680, _1669682, _1669684)))], (2358 ^ _778908) ^ [_814481, _814483, _814485, _814487, _814489, _814491] : [-(c_Power_Opower_Opower(_814491, _814487, _814483) = c_Power_Opower_Opower(_814489, _814485, _814481)), _814491 = _814489, _814487 = _814485, _814483 = _814481], (21275 ^ _778908) ^ [_1146458, _1146460, _1146462, _1146464] : [class_Fields_Ofield__inverse__zero(_1146458), -(_1146460 = c_Groups_Ozero__class_Ozero(_1146458)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146458), _1146462), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146458), _1146464), _1146460)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146458), _1146464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146458), _1146462), _1146460))), _1146460))], (51129 ^ _778908) ^ [_1808068, _1808070] : [class_Complete__Lattice_Ocomplete__lattice(_1808068), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1808070, _1808068)))], (32473 ^ _778908) ^ [_1369392, _1369394, _1369396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369392)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1369394), _1369396)), 32480 ^ _778908 : [(32481 ^ _778908) ^ [_1369582] : [32483 ^ _778908 : [(32489 ^ _778908) ^ [] : [-(_1369582 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32485 ^ [_1369392, _1369394, _1369396, _1369582]), 32482 ^ [_1369392, _1369394, _1369396, _1369582]))], (32487 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32485 ^ [_1369392, _1369394, _1369396, _1369582]), _1369396)))], (32484 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32482 ^ [_1369392, _1369394, _1369396, _1369582]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1369392))))]], -(_1369582 = _1369394), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1369582), _1369392) = _1369394]]], (10479 ^ _778908) ^ [_954932] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954932), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _954932)], (9140 ^ _778908) ^ [_932009, _932011] : [class_Groups_Omonoid__mult(_932009), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932009), c_Groups_Oone__class_Oone(_932009)), _932011) = _932011)], (6079 ^ _778908) ^ [_876261, _876263, _876265, _876267, _876269, _876271] : [-(hBOOL(hAPP(_876261, _876263))), c_Natural_Oevaln(_876265, _876263, _876267, _876269), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_876261, _876271, _876265), _876263, _876267, _876269))], (29023 ^ _778908) ^ [_1296313, _1296315, _1296317, _1296319, _1296321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296313, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296315, tc_fun(_1296313, tc_HOL_Obool)), _1296317), _1296319)), _1296321)), 29026 ^ _778908 : [(29027 ^ _778908) ^ [_1296446] : [hBOOL(hAPP(hAPP(c_member(_1296315), _1296446), _1296317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296313, tc_HOL_Obool)), hAPP(_1296319, _1296446)), _1296321)))]]], (9996 ^ _778908) ^ [_946836, _946838, _946840, _946842] : [class_Rings_Olinordered__ring__strict(_946836), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946836), _946838), _946840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946836), _946842), c_Groups_Ozero__class_Ozero(_946836))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946836), _946842), _946840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946836), _946842), _946838))))], (51579 ^ _778908) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (6015 ^ _778908) ^ [_875089, _875091, _875093, _875095, _875097, _875099, _875101, _875103, _875105, _875107, _875109] : [-(c_Com_Ocom_Ocom__rec(_875089, _875091, _875093, _875095, _875097, _875099, _875101, _875103, _875105, c_Com_Ocom_OAss(_875107, _875109)) = hAPP(hAPP(_875093, _875107), _875109))], (47517 ^ _778908) ^ [_1723957, _1723959, _1723961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1723957), tc_List_Olist(_1723957))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1723957), tc_List_Olist(_1723957)), c_List_Olist_ONil(_1723957)), _1723959)), c_List_Olex(_1723957, _1723961)))], (16813 ^ _778908) ^ [_1067915, _1067917, _1067919, _1067921, _1067923] : [class_Rings_Olinordered__idom(_1067915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067915), hAPP(c_Groups_Oabs__class_Oabs(_1067915), _1067917)), _1067919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067915), hAPP(c_Groups_Oabs__class_Oabs(_1067915), _1067921)), _1067923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067915), hAPP(c_Groups_Oabs__class_Oabs(_1067915), _1067917)), hAPP(c_Groups_Oabs__class_Oabs(_1067915), _1067921))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067915), _1067919), _1067923))))], (40590 ^ _778908) ^ [_1550210, _1550212, _1550214, _1550216] : [c_Finite__Set_Ofolding__one(_1550210, _1550212, _1550214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550210), _1550216)), -(hAPP(_1550214, _1550216) = hAPP(c_Finite__Set_Ofold1(_1550210, _1550212), _1550216))], (47573 ^ _778908) ^ [_1724953, _1724955, _1724957] : [-(hAPP(c_Map_Omap__of(_1724953, _1724955, c_List_Olist_ONil(tc_prod(_1724953, _1724955))), _1724957) = c_Option_Ooption_ONone(_1724955))], (1152 ^ _778908) ^ [_796182, _796184] : [-(class_Rings_Oordered__ring(_796182)), _796184 = _796182, class_Rings_Oordered__ring(_796184)], (31349 ^ _778908) ^ [_1344420, _1344422, _1344424] : [_1344422 = _1344424, -(hAPP(hAPP(c_COMBC(_1344420, tc_fun(_1344420, tc_HOL_Obool), tc_HOL_Obool), c_member(_1344420)), _1344422) = hAPP(hAPP(c_COMBC(_1344420, tc_fun(_1344420, tc_HOL_Obool), tc_HOL_Obool), c_member(_1344420)), _1344424))], (3616 ^ _778908) ^ [_834534, _834536] : [_834536 = _834534, -(c_SetInterval_Oord__class_OatLeast(_834536) = c_SetInterval_Oord__class_OatLeast(_834534))], (36910 ^ _778908) ^ [_1465102, _1465104, _1465106, _1465108] : [class_Lattices_Olattice(_1465102), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1465102), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1465102), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465102), _1465104), _1465106)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465102), _1465104), _1465108))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465102), _1465104), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1465102), _1465106), _1465108)))))], (43901 ^ _778908) ^ [_1636056, _1636058, _1636060, _1636062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1636056, _1636058), tc_HOL_Obool)), _1636060), _1636062)), c_Relation_Osingle__valued(_1636056, _1636058, _1636062), -(c_Relation_Osingle__valued(_1636056, _1636058, _1636060))], (41225 ^ _778908) ^ [_1562132, _1562134] : [-(hAPP(c_Set_OCollect(_1562132), hAPP(hAPP(c_COMBC(_1562132, tc_fun(_1562132, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562132)), _1562134)) = _1562134)], (41091 ^ _778908) ^ [_1559341, _1559343] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1559341))), -(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)), _1559341))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1559343)))) = 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)), _1559341))), 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, _1559343))))))], (24801 ^ _778908) ^ [_1213503, _1213505] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213503)), _1213505) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1213503), 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), _1213503)), _1213505))], (49997 ^ _778908) ^ [_1782830, _1782832, _1782834, _1782836, _1782838] : [c_List_Opartition(_1782830, _1782832, _1782834) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782830), tc_List_Olist(_1782830)), _1782836), _1782838), 50000 ^ _778908 : [(50007 ^ _778908) ^ [_1783092] : [hBOOL(hAPP(hAPP(c_member(_1782830), _1783092), hAPP(c_List_Oset(_1782830), _1782838))), hBOOL(hAPP(_1782832, _1783092))], (50001 ^ _778908) ^ [_1782983] : [hBOOL(hAPP(hAPP(c_member(_1782830), _1782983), hAPP(c_List_Oset(_1782830), _1782836))), -(hBOOL(hAPP(_1782832, _1782983)))]]], (10872 ^ _778908) ^ [_961408, _961410, _961412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961408), _961410)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961412), _961410))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961408), _961412)))], (30960 ^ _778908) ^ [_1334369, _1334371, _1334373, _1334375, _1334377, _1334379] : [hBOOL(hAPP(hAPP(c_member(_1334369), _1334371), _1334373)), hBOOL(hAPP(hAPP(_1334375, _1334371), _1334377)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334369, tc_fun(_1334379, tc_HOL_Obool)), _1334373), _1334375), _1334377)))], (36626 ^ _778908) ^ [_1458360, _1458362, _1458364, _1458366] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458360, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458360, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458360, tc_HOL_Obool)), _1458362), _1458364)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458360, tc_HOL_Obool)), _1458364), _1458366))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458360, tc_HOL_Obool)), _1458366), _1458362)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458360, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458360, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458360, tc_HOL_Obool)), _1458362), _1458364)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458360, tc_HOL_Obool)), _1458364), _1458366))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458360, tc_HOL_Obool)), _1458366), _1458362)))], (7416 ^ _778908) ^ [_902868, _902870] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_902868, _902870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _902868)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _902870))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43373 ^ _778908) ^ [_1622789] : [-(c_Relation_Orefl__on(_1622789, c_Orderings_Otop__class_Otop(tc_fun(_1622789, tc_HOL_Obool)), c_Relation_OId(_1622789)))], (49628 ^ _778908) ^ [_1775223, _1775225, _1775227] : [_1775223 = c_List_Olist_ONil(_1775225), -(c_List_Olast(_1775225, hAPP(hAPP(c_List_Olist_OCons(_1775225), _1775227), _1775223)) = _1775227)], (8230 ^ _778908) ^ [_916744, _916746, _916748, _916750] : [hAPP(c_Sum__Type_OInl(_916744, _916746), _916748) = hAPP(c_Sum__Type_OInl(_916744, _916746), _916750), -(_916748 = _916750)], (36029 ^ _778908) ^ [_1445785, _1445787, _1445789] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1445785, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445785), _1445787), _1445789), -(_1445787 = c_Orderings_Obot__class_Obot(tc_fun(_1445785, tc_HOL_Obool)))], (40190 ^ _778908) ^ [_1539519, _1539521, _1539523, _1539525, _1539527, _1539529] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539519, _1539521)), hAPP(hAPP(c_Product__Type_OPair(_1539519, _1539521), _1539523), _1539525)), hAPP(hAPP(c_Product__Type_OSigma(_1539519, _1539521), _1539527), _1539529))), -(hBOOL(hAPP(hAPP(c_member(_1539521), _1539525), hAPP(_1539529, _1539523))))], (11404 ^ _778908) ^ [_969729, _969731, _969733] : [class_Groups_Oordered__ab__group__add(_969729), 11407 ^ _778908 : [(11414 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969729), _969733), _969731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969729), hAPP(c_Groups_Ouminus__class_Ouminus(_969729), _969731)), hAPP(c_Groups_Ouminus__class_Ouminus(_969729), _969733))))], (11408 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969729), hAPP(c_Groups_Ouminus__class_Ouminus(_969729), _969731)), hAPP(c_Groups_Ouminus__class_Ouminus(_969729), _969733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969729), _969733), _969731)))]]], (18583 ^ _778908) ^ [_1099292, _1099294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1099292)), _1099294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099292), _1099294)))], (782 ^ _778908) ^ [_790931, _790933, _790935, _790937, _790939, _790941] : [-(c_Finite__Set_Ofolding__one(_790939, _790935, _790931)), c_Finite__Set_Ofolding__one(_790941, _790937, _790933), _790941 = _790939, _790937 = _790935, _790933 = _790931], (5941 ^ _778908) ^ [_873701, _873703, _873705] : [hAPP(c_Com_Ocom_OBODY, _873701) = c_Com_Ocom_OAss(_873703, _873705)], (50977 ^ _778908) ^ [_1803663, _1803665, _1803667] : [50979 ^ _778908 : [(50982 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1803663), tc_List_Olist(_1803663), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1803663), tc_fun(tc_List_Olist(_1803663), tc_Nat_Onat), tc_fun(tc_List_Olist(_1803663), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1803663), tc_Nat_Onat), tc_fun(tc_List_Olist(_1803663), tc_HOL_Obool)), tc_List_Olist(_1803663)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1803663))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1803663)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1803663))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1803663)))), 50978 ^ [_1803663, _1803665, _1803667]))], (50980 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1803663), tc_List_Olist(_1803663))), 50978 ^ [_1803663, _1803665, _1803667]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1803663), tc_List_Olist(_1803663))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1803663), tc_List_Olist(_1803663)), _1803665), _1803667)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1803663))), _1803665) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1803663))), _1803667), 50987 ^ _778908 : [(50994 ^ _778908) ^ [] : [_1803665 = _1803667, -(c_List_Oconcat(_1803663, _1803665) = c_List_Oconcat(_1803663, _1803667))], (50988 ^ _778908) ^ [] : [c_List_Oconcat(_1803663, _1803665) = c_List_Oconcat(_1803663, _1803667), -(_1803665 = _1803667)]]], (7032 ^ _778908) ^ [_896578, _896580] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _896578) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _896580), -(hBOOL(hAPP(c_Com_OWT, _896580)))], (1532 ^ _778908) ^ [_800932, _800934] : [-(class_Rings_Olinordered__semiring(_800932)), _800934 = _800932, class_Rings_Olinordered__semiring(_800934)], (6055 ^ _778908) ^ [_875855, _875857, _875859, _875861, _875863, _875865] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_875855, _875857, _875859), _875861, _875863, _875865), 6060 ^ _778908 : [(6063 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_875857, _875861, _875863, _875865))], (6061 ^ _778908) ^ [] : [-(hBOOL(hAPP(_875855, _875861)))]], 6064 ^ _778908 : [(6067 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_875859, _875861, _875863, _875865))], (6065 ^ _778908) ^ [] : [hBOOL(hAPP(_875855, _875861))]]], (42291 ^ _778908) ^ [_1595965, _1595967, _1595969, _1595971, _1595973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595965, _1595967)), hAPP(hAPP(c_Product__Type_OPair(_1595965, _1595967), _1595969), _1595971)), _1595973)), -(hBOOL(hAPP(hAPP(c_member(_1595965), _1595969), hAPP(c_Relation_ODomain(_1595965, _1595967), _1595973))))], (45953 ^ _778908) ^ [_1684078, _1684080, _1684082, _1684084, _1684086, _1684088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1684078, _1684080)), _1684082), hAPP(hAPP(c_Relation_Orel__comp(_1684078, _1684084, _1684080), _1684086), _1684088))), 45959 ^ _778908 : [(45964 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1684084, _1684080)), hAPP(hAPP(c_Product__Type_OPair(_1684084, _1684080), 45957 ^ [_1684078, _1684080, _1684082, _1684084, _1684086, _1684088]), 45958 ^ [_1684078, _1684080, _1684082, _1684084, _1684086, _1684088])), _1684088)))], (45962 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1684078, _1684084)), hAPP(hAPP(c_Product__Type_OPair(_1684078, _1684084), 45956 ^ [_1684078, _1684080, _1684082, _1684084, _1684086, _1684088]), 45957 ^ [_1684078, _1684080, _1684082, _1684084, _1684086, _1684088])), _1684086)))], (45960 ^ _778908) ^ [] : [-(_1684082 = hAPP(hAPP(c_Product__Type_OPair(_1684078, _1684080), 45956 ^ [_1684078, _1684080, _1684082, _1684084, _1684086, _1684088]), 45958 ^ [_1684078, _1684080, _1684082, _1684084, _1684086, _1684088]))]]], (44853 ^ _778908) ^ [_1658389, _1658391, _1658393, _1658395] : [44855 ^ _778908 : [(44858 ^ _778908) ^ [] : [hAPP(_1658395, 44854 ^ [_1658389, _1658391, _1658393, _1658395]) = c_Orderings_Otop__class_Otop(tc_fun(_1658391, tc_HOL_Obool))], (44856 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1658389), 44854 ^ [_1658389, _1658391, _1658393, _1658395]), _1658393)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658389, tc_fun(_1658391, tc_HOL_Obool)), _1658393), _1658395) = c_Orderings_Otop__class_Otop(tc_fun(_1658391, tc_HOL_Obool)))], (4906 ^ _778908) ^ [_854827, _854829, _854831, _854833] : [-(c_List_Olistrel1(_854833, _854829) = c_List_Olistrel1(_854831, _854827)), _854833 = _854831, _854829 = _854827], (51283 ^ _778908) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (47427 ^ _778908) ^ [_1722363] : [-(hBOOL(hAPP(c_List_Odistinct(_1722363), c_List_Olist_ONil(_1722363))))], (51489 ^ _778908) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (41384 ^ _778908) ^ [_1567725, _1567727, _1567729, _1567731, _1567733, _1567735] : [hBOOL(hAPP(hAPP(c_member(_1567725), _1567727), _1567729)), -(hAPP(c_Fun_Ooverride__on(_1567725, _1567731, _1567733, _1567735, _1567729), _1567727) = hAPP(_1567735, _1567727))], (48683 ^ _778908) ^ [_1752379, _1752381] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1752379), tc_List_Olist(_1752379)), tc_HOL_Obool)), c_List_Olistrel(_1752379, _1752381)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1752379), c_List_Olistrel1(_1752379, _1752381)))))], (16366 ^ _778908) ^ [_1060121, _1060123, _1060125, _1060127, _1060129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060121), _1060123)), 16369 ^ _778908 : [(16376 ^ _778908) ^ [] : [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), _1060123), _1060121)), _1060125)), _1060127)), _1060129)), -(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), _1060123), _1060125)), _1060127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060121), _1060125)), _1060129))))], (16370 ^ _778908) ^ [] : [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), _1060123), _1060125)), _1060127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060121), _1060125)), _1060129))), -(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), _1060123), _1060121)), _1060125)), _1060127)), _1060129)))]]], (13574 ^ _778908) ^ [_1007817, _1007819, _1007821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1007817)), 13577 ^ _778908 : [(13584 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1007819), _1007821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007817), _1007819)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007817), _1007821))))], (13578 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007817), _1007819)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007817), _1007821))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1007819), _1007821)))]]], (932 ^ _778908) ^ [_793204, _793206, _793208, _793210, _793212, _793214] : [-(c_Finite__Set_Ofun__left__comm__idem(_793212, _793208, _793204)), c_Finite__Set_Ofun__left__comm__idem(_793214, _793210, _793206), _793214 = _793212, _793210 = _793208, _793206 = _793204], (31970 ^ _778908) ^ [_1358784, _1358786, _1358788] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358784), _1358786)), -(hBOOL(hAPP(hAPP(c_member(_1358784), _1358788), _1358786))), -(hAPP(c_Finite__Set_Ocard(_1358784), hAPP(hAPP(c_Set_Oinsert(_1358784), _1358788), _1358786)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1358784), _1358786)))], (16551 ^ _778908) ^ [_1063385, _1063387, _1063389] : [class_Int_Onumber__ring(_1063385), class_Int_Oring__char__0(_1063385), 16558 ^ _778908 : [(16565 ^ _778908) ^ [] : [_1063387 = _1063389, -(hAPP(c_Int_Onumber__class_Onumber__of(_1063385), _1063387) = hAPP(c_Int_Onumber__class_Onumber__of(_1063385), _1063389))], (16559 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1063385), _1063387) = hAPP(c_Int_Onumber__class_Onumber__of(_1063385), _1063389), -(_1063387 = _1063389)]]], (16238 ^ _778908) ^ [_1057421, _1057423, _1057425, _1057427, _1057429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1057421), _1057423)), -(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), _1057421), _1057425)), _1057427)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057423), _1057425)), _1057429)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057427), 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), _1057423), _1057421)), _1057425)), _1057429)))], (31145 ^ _778908) ^ [_1338274, _1338276, _1338278, _1338280] : [hBOOL(hAPP(hAPP(c_member(_1338274), _1338276), _1338278)), -(hBOOL(hAPP(hAPP(c_member(_1338274), _1338276), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338274, tc_HOL_Obool)), _1338278), _1338280))))], (37162 ^ _778908) ^ [_1470929, _1470931, _1470933, _1470935, _1470937] : [class_Orderings_Olinorder(_1470929), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470929, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1470929, _1470931, _1470933)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1470929, _1470935, _1470937)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1470929, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1470929), _1470931), _1470935), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1470929), _1470933), _1470937)))], (32066 ^ _778908) ^ [_1360778, _1360780, _1360782, _1360784, _1360786] : [class_Groups_Ocomm__monoid__add(_1360778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360780), _1360782)), hBOOL(hAPP(hAPP(c_member(_1360780), _1360784), _1360782)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360780, _1360778), _1360786), _1360782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360778), hAPP(_1360786, _1360784)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360780, _1360778), _1360786), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360780, tc_HOL_Obool)), _1360782), hAPP(hAPP(c_Set_Oinsert(_1360780), _1360784), c_Orderings_Obot__class_Obot(tc_fun(_1360780, tc_HOL_Obool)))))))], (4292 ^ _778908) ^ [_845178, _845180, _845182, _845184, _845186, _845188, _845190, _845192, _845194, _845196] : [-(c_Sum__Type_Osum_Osum__case(_845196, _845192, _845188, _845184, _845180) = c_Sum__Type_Osum_Osum__case(_845194, _845190, _845186, _845182, _845178)), _845196 = _845194, _845192 = _845190, _845188 = _845186, _845184 = _845182, _845180 = _845178], (17029 ^ _778908) ^ [_1072259, _1072261, _1072263] : [class_Int_Onumber__ring(_1072259), class_Rings_Olinordered__idom(_1072259), 17036 ^ _778908 : [(17043 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072261), _1072263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072259), hAPP(c_Int_Onumber__class_Onumber__of(_1072259), _1072261)), hAPP(c_Int_Onumber__class_Onumber__of(_1072259), _1072263))))], (17037 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072259), hAPP(c_Int_Onumber__class_Onumber__of(_1072259), _1072261)), hAPP(c_Int_Onumber__class_Onumber__of(_1072259), _1072263))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072261), _1072263)))]]], (15158 ^ _778908) ^ [_1036418, _1036420, _1036422] : [hBOOL(hAPP(_1036418, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1036420, _1036422))), 15161 ^ _778908 : [(15168 ^ _778908) ^ [] : [-(_1036422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15171 ^ _778908 : [(15172 ^ _778908) ^ [_1036666, _1036668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036666), _1036422)), _1036420 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036422), _1036668)), _1036666), -(hBOOL(hAPP(_1036418, _1036666)))]]], (15162 ^ _778908) ^ [] : [_1036422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1036418, _1036420)))]]], (18569 ^ _778908) ^ [_1099079] : [class_Int_Onumber__ring(_1099079), -(c_Int_Oiszero(_1099079, hAPP(c_Int_Onumber__class_Onumber__of(_1099079), c_Int_OPls)))], (4768 ^ _778908) ^ [_852698, _852700, _852702, _852704] : [-(c_Big__Operators_Olinorder__class_OMin(_852704, _852700) = c_Big__Operators_Olinorder__class_OMin(_852702, _852698)), _852704 = _852702, _852700 = _852698], (29650 ^ _778908) ^ [_1309202, _1309204] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1309202, _1309204)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1309202, _1309204), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309202), c_Orderings_Otop__class_Otop(tc_fun(_1309202, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309204), c_Orderings_Otop__class_Otop(tc_fun(_1309204, tc_HOL_Obool))))], (34526 ^ _778908) ^ [_1410434, _1410436, _1410438] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1410434), _1410436)), 34529 ^ _778908 : [(34530 ^ _778908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410434, tc_Nat_Onat), _1410438), _1410436) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 34533 ^ _778908 : [(34534 ^ _778908) ^ [_1410596] : [hBOOL(hAPP(hAPP(c_member(_1410434), _1410596), _1410436)), -(hAPP(_1410438, _1410596) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (34540 ^ _778908) ^ [] : [34542 ^ _778908 : [(34545 ^ _778908) ^ [] : [hAPP(_1410438, 34541 ^ [_1410434, _1410436, _1410438]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (34543 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410434), 34541 ^ [_1410434, _1410436, _1410438]), _1410436)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410434, tc_Nat_Onat), _1410438), _1410436) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11530 ^ _778908) ^ [_971850, _971852] : [11531 ^ _778908 : [(11534 ^ _778908) ^ [] : [_971850 = _971852], (11532 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971850), _971852))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971850), _971852)))], (36750 ^ _778908) ^ [_1461252, _1461254, _1461256, _1461258, _1461260] : [class_Lattices_Olattice(_1461252), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461254, _1461252)), _1461256), _1461258), _1461260) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461252), hAPP(_1461256, _1461260)), hAPP(_1461258, _1461260)))], (18905 ^ _778908) ^ [_1104716] : [c_Int_OPls = c_Int_OBit1(_1104716)], (8576 ^ _778908) ^ [_922686, _922688, _922690] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922688), _922690)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922686), _922690)))], (5576 ^ _778908) ^ [_865068, _865070] : [_865070 = _865068, -(c_List_Onth(_865070) = c_List_Onth(_865068))], (19575 ^ _778908) ^ [_1115993, _1115995] : [class_Int_Onumber__ring(_1115993), -(hAPP(c_Int_Onumber__class_Onumber__of(_1115993), c_Int_OBit0(_1115995)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115993), c_Groups_Ozero__class_Ozero(_1115993)), hAPP(c_Int_Onumber__class_Onumber__of(_1115993), _1115995))), hAPP(c_Int_Onumber__class_Onumber__of(_1115993), _1115995)))], (44078 ^ _778908) ^ [_1640529, _1640531, _1640533] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1640529), _1640531)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640529, tc_HOL_Obool)), _1640531), _1640533) = hAPP(hAPP(c_Finite__Set_Ofold(_1640529, tc_fun(_1640529, tc_HOL_Obool), c_Set_Oinsert(_1640529)), _1640533), _1640531))], (31023 ^ _778908) ^ [_1335818, _1335820] : [_1335820 = c_Orderings_Obot__class_Obot(tc_fun(_1335818, tc_HOL_Obool)), 31026 ^ _778908 : [(31027 ^ _778908) ^ [_1335898] : [hBOOL(hAPP(hAPP(c_member(_1335818), _1335898), _1335820))]]], (25085 ^ _778908) ^ [_1219292, _1219294, _1219296, _1219298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219292, tc_HOL_Obool)), _1219294), _1219296)), hBOOL(hAPP(_1219294, _1219298)), -(hBOOL(hAPP(_1219296, _1219298)))], (39580 ^ _778908) ^ [_1523929, _1523931, _1523933, _1523935] : [hBOOL(hAPP(hAPP(c_member(_1523929), _1523931), _1523933)), -(hAPP(c_Set_Ovimage(_1523935, _1523929, hAPP(c_COMBK(_1523929, _1523935), _1523931)), _1523933) = c_Orderings_Otop__class_Otop(tc_fun(_1523935, tc_HOL_Obool)))], (51141 ^ _778908) ^ [_1808226, _1808228] : [class_Lattices_Obounded__lattice(_1808226), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1808228, _1808226)))], (28329 ^ _778908) ^ [_1282006, _1282008, _1282010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282006, tc_HOL_Obool)), _1282008), _1282010)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282006, tc_HOL_Obool)), _1282010), _1282008) = _1282010)], (43636 ^ _778908) ^ [_1629277, _1629279, _1629281] : [hAPP(hAPP(c_Relation_Orel__comp(_1629277, _1629277, _1629277), hAPP(c_Relation_Oconverse(_1629277, _1629277), _1629279)), _1629279) = _1629279, hAPP(c_Relation_ODomain(_1629277, _1629277), _1629279) = _1629281, -(c_Equiv__Relations_Oequiv(_1629277, _1629281, _1629279))], (33625 ^ _778908) ^ [_1392105, _1392107, _1392109] : [class_Orderings_Olinorder(_1392105), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392105), _1392107)), -(_1392107 = c_Orderings_Obot__class_Obot(tc_fun(_1392105, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392105), _1392109)), -(_1392109 = c_Orderings_Obot__class_Obot(tc_fun(_1392105, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1392105, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392105, tc_HOL_Obool)), _1392107), _1392109)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1392105), c_Big__Operators_Olinorder__class_OMin(_1392105, _1392107)), c_Big__Operators_Olinorder__class_OMin(_1392105, _1392109)))], (38278 ^ _778908) ^ [_1496009, _1496011, _1496013] : [class_Lattices_Olattice(_1496009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496009), _1496011)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496009), _1496013)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496009, tc_HOL_Obool)), _1496011), _1496013) = c_Orderings_Obot__class_Obot(tc_fun(_1496009, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1496009), c_Big__Operators_Olattice__class_OInf__fin(_1496009, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496009, tc_HOL_Obool)), _1496011), _1496013))), c_Big__Operators_Olattice__class_OInf__fin(_1496009, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496009, tc_HOL_Obool)), _1496011), _1496013))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1496009), c_Big__Operators_Olattice__class_OInf__fin(_1496009, _1496011)), c_Big__Operators_Olattice__class_OInf__fin(_1496009, _1496013)))], (28153 ^ _778908) ^ [_1278492, _1278494, _1278496, _1278498, _1278500] : [class_Lattices_Olattice(_1278492), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278494, _1278492)), _1278496), _1278498), _1278500) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278492), hAPP(_1278496, _1278500)), hAPP(_1278498, _1278500)))], (47118 ^ _778908) ^ [_1714307, _1714309, _1714311, _1714313, _1714315, _1714317] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714307), tc_List_Olist(_1714307))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714307), tc_List_Olist(_1714307)), hAPP(hAPP(c_List_Olist_OCons(_1714307), _1714309), _1714311)), hAPP(hAPP(c_List_Olist_OCons(_1714307), _1714313), _1714315))), c_List_Olex(_1714307, _1714317))), 47123 ^ _778908 : [(47126 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714307)), _1714311) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714307)), _1714315))], (47124 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714307, _1714307)), hAPP(hAPP(c_Product__Type_OPair(_1714307, _1714307), _1714309), _1714313)), _1714317)))]], 47127 ^ _778908 : [(47130 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714307), tc_List_Olist(_1714307))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714307), tc_List_Olist(_1714307)), _1714311), _1714315)), c_List_Olex(_1714307, _1714317))))], (47128 ^ _778908) ^ [] : [-(_1714309 = _1714313)]]], (25037 ^ _778908) ^ [_1218206, _1218208, _1218210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1218206), c_Nitpick_Oplus__frac(_1218206, _1218208, c_Nitpick_Ouminus__frac(_1218206, _1218210)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1218206, _1218208, _1218210))], (34972 ^ _778908) ^ [_1420320, _1420322, _1420324, _1420326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1420320), _1420322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1420324), _1420326)), -(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), _1420320), _1420324)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1420322), _1420326))), c_FunDef_Opair__leq)))], (42161 ^ _778908) ^ [_1592594, _1592596] : [-(hAPP(c_List_Olexn(_1592594, _1592596), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1592594), tc_List_Olist(_1592594)), tc_HOL_Obool)))], (41720 ^ _778908) ^ [_1580862, _1580864] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1580862, _1580864, tc_prod(_1580862, _1580864)), c_Product__Type_OPair(_1580862, _1580864)) = c_Fun_Oid(tc_prod(_1580862, _1580864)))], (49450 ^ _778908) ^ [_1771147, _1771149, _1771151] : [-(c_List_Olist_Olist__size(_1771147, _1771149, _1771151) = 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(_1771147, tc_Nat_Onat), _1771149), _1771151))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771147)), _1771151)))], (9078 ^ _778908) ^ [_930619, _930621, _930623, _930625] : [class_Rings_Ocomm__semiring__1(_930619), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930619), _930621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930619), _930623), _930625)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930619), _930621), _930623)), _930625))], (23627 ^ _778908) ^ [_1190515, _1190517, _1190519, _1190521, _1190523] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190515, _1190517), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1190519), _1190521))), -(_1190517 = 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), _1190523), _1190515), _1190517), 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), _1190523), _1190519)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190523), _1190521)), _1190517))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190523), _1190521), _1190517)))))], (24391 ^ _778908) ^ [_1205319, _1205321] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205319)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1205321)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1205321))), 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, _1205319))), 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), _1205319)), c_Int_Onat)))))], (4728 ^ _778908) ^ [_852102, _852104, _852106, _852108] : [-(c_Complete__Lattice_OSup__class_OSup(_852108, _852104) = c_Complete__Lattice_OSup__class_OSup(_852106, _852102)), _852108 = _852106, _852104 = _852102], (4588 ^ _778908) ^ [_849906, _849908, _849910, _849912, _849914, _849916, _849918, _849920] : [-(c_Map_Omap__add(_849920, _849916, _849912, _849908) = c_Map_Omap__add(_849918, _849914, _849910, _849906)), _849920 = _849918, _849916 = _849914, _849912 = _849910, _849908 = _849906], (4748 ^ _778908) ^ [_852400, _852402, _852404, _852406] : [-(c_Big__Operators_Olattice__class_OSup__fin(_852406, _852402) = c_Big__Operators_Olattice__class_OSup__fin(_852404, _852400)), _852406 = _852404, _852402 = _852400], (18593 ^ _778908) ^ [_1099454] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1099454), c_Int_OMin) = c_Int_Opred(_1099454))], (17999 ^ _778908) ^ [_1090168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090168), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1090168)))], (7053 ^ _778908) ^ [_896918] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _896918))), -(hAPP(c_Com_Obody, _896918) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 7056 ^ [_896918]))], (1008 ^ _778908) ^ [_794364, _794366, _794368, _794370] : [-(c_List_Olinorder__class_Osorted(_794368, _794364)), c_List_Olinorder__class_Osorted(_794370, _794366), _794370 = _794368, _794366 = _794364], (7506 ^ _778908) ^ [_904440, _904442, _904444, _904446] : [class_Rings_Ocomm__semiring__1(_904440), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904440), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904440), _904442), _904444)), _904446) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904440), _904442), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904440), _904444), _904446)))], (19519 ^ _778908) ^ [_1115129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1115129))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1115129)))], (36792 ^ _778908) ^ [_1462247, _1462249, _1462251] : [class_Lattices_Osemilattice__inf(_1462247), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462247), _1462249), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462247), _1462249), _1462251)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462247), _1462249), _1462251))], (36894 ^ _778908) ^ [_1464328, _1464330, _1464332, _1464334, _1464336] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464328, tc_fun(_1464330, tc_HOL_Obool)), _1464332), hAPP(hAPP(c_COMBC(_1464328, tc_fun(_1464330, tc_HOL_Obool), tc_fun(_1464330, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464330, tc_HOL_Obool), tc_fun(tc_fun(_1464330, tc_HOL_Obool), tc_fun(_1464330, tc_HOL_Obool)), _1464328), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464330, tc_HOL_Obool))), _1464334)), _1464336)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464330, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464328, tc_fun(_1464330, tc_HOL_Obool)), _1464332), _1464334)), _1464336))], (36886 ^ _778908) ^ [_1464003, _1464005, _1464007, _1464009] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464003, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464003, tc_HOL_Obool)), _1464005), _1464007)), _1464009) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464003, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464003, tc_HOL_Obool)), _1464005), _1464009)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464003, tc_HOL_Obool)), _1464007), _1464009)))], (34288 ^ _778908) ^ [_1405739, _1405741, _1405743, _1405745, _1405747, _1405749] : [class_Groups_Ocomm__monoid__mult(_1405739), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405741), _1405743)), 34295 ^ _778908 : [(34302 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405741), _1405745), _1405743))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405741, _1405739), hAPP(hAPP(c_COMBC(_1405741, _1405739, _1405739), hAPP(hAPP(c_COMBS(_1405741, _1405739, tc_fun(_1405739, _1405739)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1405739, tc_fun(_1405739, _1405739)), _1405741), c_If(_1405739)), hAPP(hAPP(c_COMBC(_1405741, _1405741, tc_HOL_Obool), c_fequal), _1405745))), _1405747)), _1405749)), _1405743) = hAPP(hAPP(c_Power_Opower__class_Opower(_1405739), _1405749), hAPP(c_Finite__Set_Ocard(_1405741), _1405743)))], (34296 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1405741), _1405745), _1405743)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405741, _1405739), hAPP(hAPP(c_COMBC(_1405741, _1405739, _1405739), hAPP(hAPP(c_COMBS(_1405741, _1405739, tc_fun(_1405739, _1405739)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1405739, tc_fun(_1405739, _1405739)), _1405741), c_If(_1405739)), hAPP(hAPP(c_COMBC(_1405741, _1405741, tc_HOL_Obool), c_fequal), _1405745))), _1405747)), _1405749)), _1405743) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405739), hAPP(_1405747, _1405745)), hAPP(hAPP(c_Power_Opower__class_Opower(_1405739), _1405749), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1405741), _1405743)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (41007 ^ _778908) ^ [_1557794, _1557796] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1557794), c_Int_OInteg)), hBOOL(hAPP(_1557796, hAPP(c_Int_ORep__Integ, 41012 ^ [_1557794, _1557796]))), -(hBOOL(hAPP(_1557796, _1557794)))], (28449 ^ _778908) ^ [_1284263, _1284265, _1284267, _1284269] : [class_Lattices_Osemilattice__sup(_1284263), 28452 ^ _778908 : [(28461 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284263), _1284265), _1284267)), _1284269))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284263), _1284265), _1284269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284263), _1284267), _1284269))], (28453 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284263), _1284265), _1284267)), _1284269)), 28456 ^ _778908 : [(28459 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284263), _1284267), _1284269)))], (28457 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284263), _1284265), _1284269)))]]]]], (27338 ^ _778908) ^ [_1262163, _1262165, _1262167, _1262169] : [class_Groups_Ocomm__monoid__add(_1262163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1262165), _1262167)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1262163), _1262169), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1262165), _1262167)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1262163), hAPP(_1262169, _1262165)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1262163), _1262169), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1262165)), _1262167))))], (44134 ^ _778908) ^ [_1641783, _1641785, _1641787, _1641789, _1641791, _1641793] : [c_Finite__Set_Ofun__left__comm__idem(_1641783, _1641785, _1641787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641783), _1641789)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1641783, _1641785, _1641787), _1641791), hAPP(hAPP(c_Set_Oinsert(_1641783), _1641793), _1641789)) = hAPP(hAPP(c_Finite__Set_Ofold(_1641783, _1641785, _1641787), hAPP(hAPP(_1641787, _1641793), _1641791)), _1641789))], (8015 ^ _778908) ^ [_912981, _912983] : [class_Groups_Olinordered__ab__group__add(_912981), 8018 ^ _778908 : [(8025 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912981), _912983), c_Groups_Ozero__class_Ozero(_912981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_912981), _912983), _912983)), c_Groups_Ozero__class_Ozero(_912981))))], (8019 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_912981), _912983), _912983)), c_Groups_Ozero__class_Ozero(_912981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912981), _912983), c_Groups_Ozero__class_Ozero(_912981))))]]], (25017 ^ _778908) ^ [_1217714, _1217716, _1217718, _1217720, _1217722, _1217724, _1217726] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1217714, _1217716, _1217718, _1217720, _1217722, _1217724, _1217726) = c_New__DSequence_Oneg__decr__bind(_1217714, _1217716, hAPP(hAPP(hAPP(_1217718, _1217722), _1217724), _1217726), hAPP(hAPP(c_COMBC(_1217714, 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(_1217716)))), hAPP(hAPP(c_COMBC(_1217714, 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(_1217716))))), hAPP(hAPP(c_COMBC(_1217714, 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(_1217716)))))), _1217720), _1217722)), _1217724)), _1217726)))], (26803 ^ _778908) ^ [_1251556, _1251558] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251556)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251558))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251558), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251556)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32861 ^ _778908) ^ [_1377381] : [class_Rings_Osemiring__1(_1377381), -(hBOOL(hAPP(hAPP(c_member(_1377381), c_Groups_Ozero__class_Ozero(_1377381)), c_Nat_Osemiring__1__class_ONats(_1377381))))], (34463 ^ _778908) ^ [_1409435, _1409437, _1409439, _1409441] : [class_Rings_Ocomm__semiring__1(_1409435), class_Rings_Ono__zero__divisors(_1409435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409437), _1409439)), 34474 ^ _778908 : [(34484 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409437, _1409435), _1409441), _1409439) = c_Groups_Ozero__class_Ozero(_1409435)), 34485 ^ _778908 : [(34486 ^ _778908) ^ [_1409813] : [hBOOL(hAPP(hAPP(c_member(_1409437), _1409813), _1409439)), hAPP(_1409441, _1409813) = c_Groups_Ozero__class_Ozero(_1409435)]]], (34475 ^ _778908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409437, _1409435), _1409441), _1409439) = c_Groups_Ozero__class_Ozero(_1409435), 34479 ^ _778908 : [(34482 ^ _778908) ^ [] : [-(hAPP(_1409441, 34478 ^ [_1409435, _1409437, _1409439, _1409441]) = c_Groups_Ozero__class_Ozero(_1409435))], (34480 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409437), 34478 ^ [_1409435, _1409437, _1409439, _1409441]), _1409439)))]]]]], (35869 ^ _778908) ^ [_1441935] : [-(c_Nitpick_Odenom(_1441935) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1441935, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1441935)))], (31305 ^ _778908) ^ [_1343627, _1343629, _1343631, _1343633] : [_1343627 = _1343629, 31308 ^ _778908 : [(31315 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1343631), _1343629), _1343633)), -(hBOOL(hAPP(hAPP(c_member(_1343631), _1343627), _1343633)))], (31309 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1343631), _1343627), _1343633)), -(hBOOL(hAPP(hAPP(c_member(_1343631), _1343629), _1343633)))]]], (37038 ^ _778908) ^ [_1468220, _1468222, _1468224] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468220, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468220, tc_HOL_Obool)), _1468222), _1468224)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468220, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468220, tc_HOL_Obool)), _1468222)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468220, tc_HOL_Obool)), _1468224)))], (47004 ^ _778908) ^ [_1711768, _1711770, _1711772, _1711774, _1711776, _1711778] : [c_List_Olistrelp(_1711768, _1711770, hAPP(hAPP(c_List_Olist_OCons(_1711768), _1711772), _1711774), hAPP(hAPP(c_List_Olist_OCons(_1711768), _1711776), _1711778)), 47007 ^ _778908 : [(47010 ^ _778908) ^ [] : [-(c_List_Olistrelp(_1711768, _1711770, _1711774, _1711778))], (47008 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1711770, _1711772), _1711776)))]]], (1112 ^ _778908) ^ [_795682, _795684] : [-(class_Rings_Oordered__ring__abs(_795682)), _795684 = _795682, class_Rings_Oordered__ring__abs(_795684)], (33589 ^ _778908) ^ [_1391477, _1391479, _1391481] : [class_Orderings_Olinorder(_1391477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391477), _1391479)), -(_1391481 = c_Orderings_Obot__class_Obot(tc_fun(_1391477, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1391477, tc_HOL_Obool)), _1391481), _1391479)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1391477), c_Big__Operators_Olinorder__class_OMin(_1391477, _1391481)), c_Big__Operators_Olinorder__class_OMin(_1391477, _1391479)) = c_Big__Operators_Olinorder__class_OMin(_1391477, _1391479))], (24393 ^ _778908) ^ [_1205391, _1205393, _1205395, _1205397, _1205399, _1205401, _1205403] : [-(hAPP(c_Product__Type_Oapfst(_1205391, _1205393, _1205395, _1205397), hAPP(c_Product__Type_Oapsnd(_1205399, _1205395, _1205391, _1205401), _1205403)) = hAPP(hAPP(c_Product__Type_OPair(_1205393, _1205395), hAPP(_1205397, hAPP(c_Product__Type_Ofst(_1205391, _1205399), _1205403))), hAPP(_1205401, hAPP(c_Product__Type_Osnd(_1205391, _1205399), _1205403))))], (17017 ^ _778908) ^ [_1072009, _1072011] : [class_Rings_Ocomm__semiring__1(_1072009), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1072009), _1072011), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1072009))], (18175 ^ _778908) ^ [_1092978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092978)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1092978) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1092978), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (51573 ^ _778908) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (9726 ^ _778908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11747 ^ _778908) ^ [_975630, _975632] : [class_Rings_Olinordered__idom(_975630), 11750 ^ _778908 : [(11757 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975630), c_Groups_Ozero__class_Ozero(_975630)), hAPP(c_Int_Oring__1__class_Oof__int(_975630), _975632))))], (11751 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975630), c_Groups_Ozero__class_Ozero(_975630)), hAPP(c_Int_Oring__1__class_Oof__int(_975630), _975632))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975632)))]]], (26055 ^ _778908) ^ [_1236711] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1236711), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1236711 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4068 ^ _778908) ^ [_841630, _841632] : [_841632 = _841630, -(c_Relation_OId(_841632) = c_Relation_OId(_841630))], (43215 ^ _778908) ^ [_1618948, _1618950, _1618952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618948, _1618948), tc_HOL_Obool)), _1618950), _1618952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618948, _1618948), tc_HOL_Obool)), _1618952), c_Transitive__Closure_Ortrancl(_1618948, _1618950))), -(c_Transitive__Closure_Ortrancl(_1618948, _1618952) = c_Transitive__Closure_Ortrancl(_1618948, _1618950))], (48759 ^ _778908) ^ [_1754855, _1754857, _1754859, _1754861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754855), tc_List_Olist(_1754855))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754855), tc_List_Olist(_1754855)), _1754857), _1754859)), c_List_Olistrel1(_1754855, _1754861))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754855), tc_List_Olist(_1754855))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754855), tc_List_Olist(_1754855)), _1754857), _1754859)), c_List_Olistrel(_1754855, c_Transitive__Closure_Ortrancl(_1754855, _1754861)))))], (41038 ^ _778908) ^ [_1558344] : [class_Lattices_Osemilattice__sup(_1558344), -(c_Finite__Set_Ofun__left__comm__idem(_1558344, _1558344, c_Lattices_Osemilattice__sup__class_Osup(_1558344)))], (6859 ^ _778908) ^ [_891711, _891713, _891715, _891717] : [c_Com_Ocom_OWhile(_891711, _891713) = c_Com_Ocom_OAss(_891715, _891717)], (22572 ^ _778908) ^ [_1170147, _1170149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170147)), hAPP(c_Nat_OSuc, _1170149))), -(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(_1170147))), 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)), _1170149)))))], (24147 ^ _778908) ^ [_1200667, _1200669, _1200671] : [_1200667 = _1200669, 24150 ^ _778908 : [(24153 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200671, tc_HOL_Obool)), _1200669), _1200667)))], (24151 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200671, tc_HOL_Obool)), _1200667), _1200669)))]]], (22446 ^ _778908) ^ [_1167632, _1167634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1167632), _1167634)), -(c_Divides_Odivmod__nat(_1167632, _1167634) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1167632))], (30636 ^ _778908) ^ [_1327848, _1327850] : [_1327848 = _1327850, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1327848, _1327850) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1327848), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (17651 ^ _778908) ^ [_1083895, _1083897] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1083895), c_Groups_Ozero__class_Ozero(_1083895)), hAPP(c_Nat_OSuc, _1083897)) = c_Groups_Ozero__class_Ozero(_1083895)), class_Power_Opower(_1083895), class_Rings_Osemiring__0(_1083895)], (7164 ^ _778908) ^ [_898741, _898743, _898745, _898747] : [class_Groups_Ocancel__semigroup__add(_898741), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898741), _898743), _898745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898741), _898743), _898747), -(_898745 = _898747)], (3922 ^ _778908) ^ [_839419, _839421, _839423, _839425, _839427, _839429, _839431, _839433] : [-(c_New__Random__Sequence_Oneg__bind(_839433, _839429, _839425, _839421) = c_New__Random__Sequence_Oneg__bind(_839431, _839427, _839423, _839419)), _839433 = _839431, _839429 = _839427, _839425 = _839423, _839421 = _839419], (13855 ^ _778908) ^ [_1012829, _1012831, _1012833, _1012835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012831), _1012833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012833), 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), _1012831), _1012829)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012831), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012835, _1012829))), _1012833))))], (43279 ^ _778908) ^ [_1620533, _1620535, _1620537] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1620533, _1620533, _1620535), c_Relation_OId(_1620533)), _1620537) = _1620537)], (43467 ^ _778908) ^ [_1624907, _1624909, _1624911, _1624913, _1624915] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624907, _1624907)), hAPP(hAPP(c_Product__Type_OPair(_1624907, _1624907), _1624909), _1624911)), c_Transitive__Closure_Ortrancl(_1624907, _1624913))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1624907, _1624907), tc_HOL_Obool)), _1624913), hAPP(hAPP(c_Product__Type_OSigma(_1624907, _1624907), _1624915), hAPP(c_COMBK(tc_fun(_1624907, tc_HOL_Obool), _1624907), _1624915)))), -(_1624909 = _1624911), -(hBOOL(hAPP(hAPP(c_member(_1624907), _1624909), _1624915)))], (48040 ^ _778908) ^ [_1736856, _1736858, _1736860, _1736862, _1736864, _1736866] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736856)), _1736858) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736860)), _1736862), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736856)), _1736864) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736860)), _1736866), -(hAPP(hAPP(c_List_Ozip(_1736856, _1736860), hAPP(hAPP(c_List_Oappend(_1736856), _1736858), _1736864)), hAPP(hAPP(c_List_Oappend(_1736860), _1736862), _1736866)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1736856, _1736860)), hAPP(hAPP(c_List_Ozip(_1736856, _1736860), _1736858), _1736862)), hAPP(hAPP(c_List_Ozip(_1736856, _1736860), _1736864), _1736866)))], (32060 ^ _778908) ^ [_1360687, _1360689, _1360691, _1360693] : [-(hBOOL(hAPP(hAPP(c_member(_1360687), _1360689), _1360691))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360687, tc_Nat_Onat), _1360693), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360687, tc_HOL_Obool)), _1360691), hAPP(hAPP(c_Set_Oinsert(_1360687), _1360689), c_Orderings_Obot__class_Obot(tc_fun(_1360687, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360687, tc_Nat_Onat), _1360693), _1360691))], (28287 ^ _778908) ^ [_1281173, _1281175, _1281177, _1281179] : [class_Lattices_Osemilattice__sup(_1281173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281173), _1281175), _1281177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281173), _1281175), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281173), _1281177), _1281179))))], (25285 ^ _778908) ^ [_1223608, _1223610] : [class_Rings_Ocomm__semiring__1(_1223608), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223608), c_Groups_Ozero__class_Ozero(_1223608)), _1223610)), -(_1223610 = c_Groups_Ozero__class_Ozero(_1223608))], (35817 ^ _778908) ^ [_1440212, _1440214] : [-(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), _1440212), _1440214)), 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), _1440214), _1440212)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (45400 ^ _778908) ^ [_1671697, _1671699, _1671701] : [class_Complete__Lattice_Ocomplete__lattice(_1671697), -(c_Complete__Lattice_OInf__class_OInf(_1671697, hAPP(hAPP(c_Set_Oinsert(_1671697), _1671699), _1671701)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1671697), _1671699), c_Complete__Lattice_OInf__class_OInf(_1671697, _1671701)))], (32943 ^ _778908) ^ [_1378832, _1378834, _1378836, _1378838, _1378840, _1378842, _1378844, _1378846] : [c_Hoare__Mirabelle_Ohoare__derivs(_1378832, _1378834, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1378832)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1378832), _1378836), hAPP(c_Com_Ocom_OBODY, _1378838)), hAPP(hAPP(c_COMBC(_1378832, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1378832), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1378840)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), hAPP(c_Natural_Ogetlocs, _1378842)))), _1378844)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Oloc, tc_Nat_Onat), c_Natural_Ogetlocs), c_Com_ORes))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1378832), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1378832, _1378834, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1378832)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1378832), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1378832), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _1378842)))), hAPP(hAPP(c_COMBC(_1378832, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1378832), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1378836)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), c_Natural_Onewlocs))), c_Com_Ovname_OLoc(c_Com_OArg))), _1378846)))), c_Com_Ocom_OCall(_1378844, _1378838, _1378846)), _1378840)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1378832), tc_HOL_Obool)))))], (14517 ^ _778908) ^ [_1025255, _1025257, _1025259] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025255, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025257), _1025259)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025257), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025255), _1025257), _1025259))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025255, _1025257)))], (24803 ^ _778908) ^ [_1213551, _1213553, _1213555, _1213557, _1213559, _1213561, _1213563] : [-(hAPP(c_Product__Type_Oapsnd(_1213551, _1213553, _1213555, _1213557), hAPP(c_Product__Type_Oapfst(_1213559, _1213555, _1213551, _1213561), _1213563)) = hAPP(hAPP(c_Product__Type_OPair(_1213555, _1213553), hAPP(_1213561, hAPP(c_Product__Type_Ofst(_1213559, _1213551), _1213563))), hAPP(_1213557, hAPP(c_Product__Type_Osnd(_1213559, _1213551), _1213563))))], (6881 ^ _778908) ^ [_892316, _892318, _892320] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _892316)), _892318), _892320)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _892316))), _892318), _892320)))], (37216 ^ _778908) ^ [_1472172, _1472174, _1472176] : [class_Orderings_Oorder(_1472172), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472172, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1472172), _1472174)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1472172, _1472174, _1472176)) = c_Orderings_Obot__class_Obot(tc_fun(_1472172, tc_HOL_Obool)))], (7965 ^ _778908) ^ [_912002, _912004, _912006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912002), _912004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912004), _912006))))], (5332 ^ _778908) ^ [_861338, _861340, _861342, _861344, _861346, _861348, _861350, _861352] : [-(c_List_Ofoldl(_861352, _861348, _861344, _861340) = c_List_Ofoldl(_861350, _861346, _861342, _861338)), _861352 = _861350, _861348 = _861346, _861344 = _861342, _861340 = _861338], (24315 ^ _778908) ^ [_1203963, _1203965, _1203967] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1203963, _1203965), _1203967)), 24318 ^ _778908 : [(24327 ^ _778908) ^ [] : [-(_1203965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24330 ^ _778908 : [(24339 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203965))), 24342 ^ _778908 : [(24345 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1203967)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24343 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203965), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1203967))))]]], (24331 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203965)), 24334 ^ _778908 : [(24337 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1203967)), _1203965)))], (24335 ^ _778908) ^ [] : [-(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), _1203967))))]]]]], (24321 ^ _778908) ^ [] : [_1203965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1203967) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24319 ^ _778908) ^ [] : [-(_1203963 = 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), _1203967)), _1203965)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1203967)))]]], (43313 ^ _778908) ^ [_1621376, _1621378, _1621380, _1621382, _1621384] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621376, _1621376)), hAPP(hAPP(c_Product__Type_OPair(_1621376, _1621376), _1621378), _1621380)), c_Transitive__Closure_Ortrancl(_1621376, _1621382))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1621376, _1621376)), hAPP(hAPP(c_Product__Type_OPair(_1621376, _1621376), _1621380), _1621384)), _1621382)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621376, _1621376)), hAPP(hAPP(c_Product__Type_OPair(_1621376, _1621376), _1621378), _1621384)), c_Transitive__Closure_Otrancl(_1621376, _1621382))))], (49037 ^ _778908) ^ [_1762153, _1762155, _1762157, _1762159, _1762161] : [-(hAPP(hAPP(c_List_Oappend(_1762153), _1762155), _1762157) = hAPP(hAPP(c_List_Oappend(_1762153), _1762159), _1762161)), 49040 ^ _778908 : [(49043 ^ _778908) ^ [] : [_1762155 = hAPP(hAPP(c_List_Otake(_1762153), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762155)), _1762159), _1762157 = hAPP(hAPP(c_List_Oappend(_1762153), hAPP(hAPP(c_List_Odrop(_1762153), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762155)), _1762159)), _1762161)], (49041 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762155)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762159))))]], 49048 ^ _778908 : [(49051 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Otake(_1762153), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762159)), _1762155) = _1762159, hAPP(hAPP(c_List_Oappend(_1762153), hAPP(hAPP(c_List_Odrop(_1762153), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762159)), _1762155)), _1762157) = _1762161], (49049 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762155)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762153)), _1762159)))]]], (40612 ^ _778908) ^ [_1550572, _1550574] : [class_Lattices_Olattice(_1550572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550572), _1550574)), -(c_Big__Operators_Olattice__class_OInf__fin(_1550572, _1550574) = hAPP(c_Finite__Set_Ofold1(_1550572, c_Lattices_Osemilattice__inf__class_Oinf(_1550572)), _1550574))], (31379 ^ _778908) ^ [_1345007, _1345009, _1345011, _1345013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1345007, tc_HOL_Obool)), _1345009), _1345011)), hBOOL(hAPP(hAPP(c_member(_1345007), _1345013), _1345009)), -(hBOOL(hAPP(hAPP(c_member(_1345007), _1345013), _1345011)))], (14665 ^ _778908) ^ [_1027787, _1027789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1027787), 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)), _1027789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027787), _1027789)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18957 ^ _778908) ^ [_1105499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105499)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105499), c_Int_OPls)))], (22784 ^ _778908) ^ [_1174281, _1174283, _1174285] : [-(c_Nat_Onat_Onat__case(_1174281, _1174283, _1174285, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1174283)], (50483 ^ _778908) ^ [_1792700, _1792702] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792700)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792702)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792700), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1792702)) = c_List_Olist_ONil(tc_Nat_Onat))], (3768 ^ _778908) ^ [_836986, _836988] : [_836988 = _836986, -(c_Int_Oint__ge__less__than(_836988) = c_Int_Oint__ge__less__than(_836986))], (17241 ^ _778908) ^ [_1076449, _1076451, _1076453] : [class_Int_Onumber__ring(_1076449), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076449), hAPP(c_Groups_Ouminus__class_Ouminus(_1076449), hAPP(c_Int_Onumber__class_Onumber__of(_1076449), _1076451))), _1076453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076449), hAPP(c_Int_Onumber__class_Onumber__of(_1076449), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076451))), _1076453))], (12794 ^ _778908) ^ [_994092, _994094, _994096, _994098] : [class_Rings_Olinordered__semiring__strict(_994092), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994092), _994094), _994096)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994092), _994094), _994098))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994092), c_Groups_Ozero__class_Ozero(_994092)), _994094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994092), _994096), _994098)))], (26073 ^ _778908) ^ [_1237152, _1237154] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1237152), _1237154)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1237154), _1237152)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1237152) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1237154))], (18963 ^ _778908) ^ [_1105594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105594), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105594)), c_Int_OPls)))], (45988 ^ _778908) ^ [_1685069, _1685071, _1685073] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1685069), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1685071), _1685073)))), 45991 ^ _778908 : [(45998 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1685071), _1685073))), -(c_Smallcheck_Osmall_H(_1685069, _1685071, _1685073) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1685069, _1685071, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1685073), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1685069, _1685073)))], (45992 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1685071), _1685073)), -(c_Smallcheck_Osmall_H(_1685069, _1685071, _1685073) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (33017 ^ _778908) ^ [_1380744, _1380746] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1380744, _1380746, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380744), tc_HOL_Obool))))], (29666 ^ _778908) ^ [_1309524, _1309526] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309524), c_Orderings_Otop__class_Otop(tc_fun(_1309524, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309526), c_Orderings_Otop__class_Otop(tc_fun(_1309526, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1309524, _1309526)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1309524, _1309526), tc_HOL_Obool)))))], (14053 ^ _778908) ^ [_1016822, _1016824] : [class_Divides_Osemiring__div(_1016822), -(c_Divides_Odiv__class_Omod(_1016822, _1016824, c_Groups_Oone__class_Oone(_1016822)) = c_Groups_Ozero__class_Ozero(_1016822))], (1742 ^ _778908) ^ [_803557, _803559] : [-(class_Orderings_Oorder(_803557)), _803559 = _803557, class_Orderings_Oorder(_803559)], (13156 ^ _778908) ^ [_1000736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1000736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1000736) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50045 ^ _778908) ^ [_1784538, _1784540, _1784542] : [-(c_List_Omap__filter(_1784538, _1784540, _1784542, c_List_Olist_ONil(_1784538)) = c_List_Olist_ONil(_1784540))], (34620 ^ _778908) ^ [_1412326, _1412328, _1412330, _1412332, _1412334] : [class_Groups_Ocomm__monoid__mult(_1412326), class_Rings_Odvd(_1412326), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412328), _1412330)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412328, tc_HOL_Obool)), _1412332), _1412330)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1412326), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1412328, _1412326), _1412334), _1412332)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1412328, _1412326), _1412334), _1412330))))], (50262 ^ _778908) ^ [_1788962, _1788964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1788962), _1788964)), -(c_List_Oupt(_1788962, hAPP(c_Nat_OSuc, _1788964)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1788962, _1788964)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1788964), c_List_Olist_ONil(tc_Nat_Onat))))], (45883 ^ _778908) ^ [_1682609, _1682611, _1682613, _1682615, _1682617] : [-(hBOOL(hAPP(hAPP(c_member(_1682609), _1682611), c_Map_Odom(_1682609, _1682613, _1682615)))), -(hAPP(c_Map_Omap__add(_1682609, _1682613, _1682617, _1682615), _1682611) = hAPP(_1682617, _1682611))], (26893 ^ _778908) ^ [_1253155, _1253157, _1253159, _1253161] : [class_Orderings_Oorder(_1253155), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1253155, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1253157), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1253159), _1253161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253155), hAPP(_1253157, _1253159)), hAPP(_1253157, _1253161))))], (46799 ^ _778908) ^ [_1704394, _1704396] : [-(c_List_Olenlex(_1704394, _1704396) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1704394), tc_List_Olist(_1704394), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1704394), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1704394), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), tc_List_Olist(_1704394)), c_COMBS(tc_List_Olist(_1704394), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1704394)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1704394)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704394), tc_fun(tc_List_Olist(_1704394), tc_Nat_Onat), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1704394), tc_Nat_Onat), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), tc_List_Olist(_1704394)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1704394))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1704394)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1704394))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1704394)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1704394), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1704394), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), tc_List_Olist(_1704394)), c_COMBS(tc_List_Olist(_1704394), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1704394)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1704394)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704394), tc_fun(tc_List_Olist(_1704394), tc_Nat_Onat), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1704394), tc_Nat_Onat), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), tc_List_Olist(_1704394)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1704394))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1704394)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1704394))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1704394)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704394), tc_fun(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1704394), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1704394), tc_HOL_Obool)), tc_List_Olist(_1704394)), c_COMBC(tc_List_Olist(_1704394), tc_fun(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1704394), tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394))), tc_fun(tc_List_Olist(_1704394), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1704394)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1704394)), c_member(tc_prod(tc_List_Olist(_1704394), tc_List_Olist(_1704394))))), c_Product__Type_OPair(tc_List_Olist(_1704394), tc_List_Olist(_1704394))))), c_List_Olex(_1704394, _1704396)))))))], (22748 ^ _778908) ^ [_1173741] : [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), _1173741))), 22751 ^ _778908 : [(22758 ^ _778908) ^ [] : [-(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), _1173741)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1173741)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1173741)), 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), _1173741)))))], (22752 ^ _778908) ^ [] : [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), _1173741))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1173741)) = 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)))]]], (4788 ^ _778908) ^ [_852996, _852998, _853000, _853002, _853004, _853006] : [-(c_Big__Operators_Olattice_OInf__fin(_853006, _853002, _852998) = c_Big__Operators_Olattice_OInf__fin(_853004, _853000, _852996)), _853006 = _853004, _853002 = _853000, _852998 = _852996], (27960 ^ _778908) ^ [_1274563, _1274565, _1274567, _1274569, _1274571] : [class_Groups_Ocomm__monoid__add(_1274563), class_Groups_Ocomm__monoid__mult(_1274563), _1274565 = _1274567, c_Nat__Transfer_Onat__set(_1274567), 27978 ^ _778908 : [(27981 ^ _778908) ^ [] : [hAPP(_1274569, 27977 ^ [_1274563, _1274565, _1274567, _1274569, _1274571]) = hAPP(_1274571, 27977 ^ [_1274563, _1274565, _1274567, _1274569, _1274571])], (27979 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27977 ^ [_1274563, _1274565, _1274567, _1274569, _1274571])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1274563), _1274569), _1274565) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1274563), _1274571), _1274567))], (46976 ^ _778908) ^ [_1711134, _1711136, _1711138, _1711140] : [hBOOL(hAPP(hAPP(c_member(_1711134), _1711136), hAPP(c_List_Oset(_1711134), hAPP(hAPP(c_List_Olist_OCons(_1711134), _1711138), _1711140)))), -(_1711136 = _1711138), -(hBOOL(hAPP(hAPP(c_member(_1711134), _1711136), hAPP(c_List_Oset(_1711134), _1711140))))], (51451 ^ _778908) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (7386 ^ _778908) ^ [_902292, _902294] : [_902292 = _902294, -(hAPP(c_Nat_OSuc, _902292) = hAPP(c_Nat_OSuc, _902294))], (44755 ^ _778908) ^ [_1655109, _1655111, _1655113, _1655115, _1655117, _1655119] : [class_Complete__Lattice_Ocomplete__lattice(_1655109), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655111, _1655109), _1655113), hAPP(hAPP(c_COMBB(tc_fun(_1655115, _1655109), _1655109, _1655111), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655115, _1655109), _1655117)), _1655119)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655115, _1655109), _1655117), hAPP(hAPP(c_COMBB(tc_fun(_1655111, _1655109), _1655109, _1655115), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655111, _1655109), _1655113)), hAPP(c_COMBC(_1655111, _1655115, _1655109), _1655119))))], (20105 ^ _778908) ^ [_1125752] : [_1125752 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1125752) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (41333 ^ _778908) ^ [_1565887, _1565889, _1565891, _1565893] : [-(hAPP(c_Relation_OImage(_1565887, _1565889, _1565891), hAPP(hAPP(c_Set_Oinsert(_1565887), _1565893), c_Orderings_Obot__class_Obot(tc_fun(_1565887, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1565889), hAPP(hAPP(c_COMBC(_1565889, tc_fun(tc_prod(_1565887, _1565889), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1565887, _1565889), tc_fun(tc_fun(tc_prod(_1565887, _1565889), tc_HOL_Obool), tc_HOL_Obool), _1565889), c_member(tc_prod(_1565887, _1565889))), hAPP(c_Product__Type_OPair(_1565887, _1565889), _1565893))), _1565891)))], (1512 ^ _778908) ^ [_800682, _800684] : [-(class_Rings_Oordered__comm__semiring(_800682)), _800684 = _800682, class_Rings_Oordered__comm__semiring(_800684)], (37040 ^ _778908) ^ [_1468293, _1468295, _1468297] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468293, tc_HOL_Obool)), _1468295), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468293, tc_HOL_Obool)), _1468297)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468293, tc_HOL_Obool)), _1468295), _1468297))], (10491 ^ _778908) ^ [_955124, _955126] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955124), _955126) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _955124 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _955126 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (38610 ^ _778908) ^ [_1502945, _1502947, _1502949, _1502951, _1502953, _1502955] : [c_Fun_Oinj__on(_1502945, _1502947, _1502949, _1502951), c_Fun_Oinj__on(_1502947, _1502953, _1502955, hAPP(c_Set_Oimage(_1502945, _1502947, _1502949), _1502951)), -(c_Fun_Oinj__on(_1502945, _1502953, hAPP(c_Fun_Ocomp(_1502947, _1502953, _1502945, _1502955), _1502949), _1502951))], (47421 ^ _778908) ^ [_1722257, _1722259, _1722261, _1722263, _1722265] : [class_Orderings_Olinorder(_1722257), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1722259, _1722257, _1722261), _1722263), _1722265) = c_List_Olist_ONil(_1722259)], (51473 ^ _778908) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (45755 ^ _778908) ^ [_1679911, _1679913, _1679915, _1679917, _1679919, _1679921, _1679923] : [c_Finite__Set_Ofolding__image__simple__idem(_1679911, _1679913, _1679915, _1679917, _1679919, _1679921), -(hAPP(hAPP(_1679915, _1679923), _1679923) = _1679923)], (48403 ^ _778908) ^ [_1744990, _1744992, _1744994, _1744996] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744990), tc_List_Olist(_1744990))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744990), tc_List_Olist(_1744990)), _1744992), _1744994)), c_List_Olex(_1744990, _1744996))), 48406 ^ _778908 : [(48409 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744990)), _1744992) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744990)), _1744994))], (48407 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744990), tc_List_Olist(_1744990))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744990), tc_List_Olist(_1744990)), _1744992), _1744994)), c_List_Olexord(_1744990, _1744996))))]]], (45970 ^ _778908) ^ [_1684546, _1684548, _1684550, _1684552] : [-(c_Map_Omap__add(_1684546, _1684548, _1684550, c_Map_Omap__of(_1684546, _1684548, _1684552)) = c_List_Ofoldr(tc_prod(_1684546, _1684548), tc_fun(_1684546, tc_Option_Ooption(_1684548)), hAPP(c_Product__Type_Oprod_Oprod__case(_1684546, _1684548, tc_fun(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_fun(_1684546, tc_Option_Ooption(_1684548)))), hAPP(hAPP(c_COMBC(_1684546, tc_fun(_1684548, tc_Option_Ooption(_1684548)), tc_fun(_1684548, tc_fun(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_fun(_1684546, tc_Option_Ooption(_1684548))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1684548), tc_fun(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_fun(_1684546, tc_Option_Ooption(_1684548)))), tc_fun(tc_fun(_1684548, tc_Option_Ooption(_1684548)), tc_fun(_1684548, tc_fun(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_fun(_1684546, tc_Option_Ooption(_1684548))))), _1684546), c_COMBB(tc_Option_Ooption(_1684548), tc_fun(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_fun(_1684546, tc_Option_Ooption(_1684548))), _1684548)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_fun(tc_Option_Ooption(_1684548), tc_fun(_1684546, tc_Option_Ooption(_1684548)))), tc_fun(tc_Option_Ooption(_1684548), tc_fun(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_fun(_1684546, tc_Option_Ooption(_1684548)))), _1684546), c_COMBC(tc_fun(_1684546, tc_Option_Ooption(_1684548)), tc_Option_Ooption(_1684548), tc_fun(_1684546, tc_Option_Ooption(_1684548)))), hAPP(c_COMBC(tc_fun(_1684546, tc_Option_Ooption(_1684548)), _1684546, tc_fun(tc_Option_Ooption(_1684548), tc_fun(_1684546, tc_Option_Ooption(_1684548)))), c_Fun_Ofun__upd(_1684546, tc_Option_Ooption(_1684548)))))), c_Option_Ooption_OSome(_1684548))), _1684552, _1684550))], (19771 ^ _778908) ^ [_1119482, _1119484] : [class_Rings_Olinordered__idom(_1119482), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1119482), hAPP(c_Groups_Oabs__class_Oabs(_1119482), _1119484)), 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(_1119482), _1119484), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (11807 ^ _778908) ^ [_976585, _976587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _976585), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _976585), _976587)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _976585))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _976587))))], (13382 ^ _778908) ^ [_1004377, _1004379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004379)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1004377)), hAPP(c_Int_Onat, _1004379)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1004377), _1004379)))], (7574 ^ _778908) ^ [_905819, _905821, _905823, _905825, _905827] : [-(c_Sum__Type_Osum_Osum__size(_905819, _905821, _905823, _905825, hAPP(c_Sum__Type_OInl(_905819, _905821), _905827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_905823, _905827)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49825 ^ _778908) ^ [_1779144, _1779146, _1779148] : [-(c_List_Obutlast(_1779144, hAPP(hAPP(c_List_Oappend(_1779144), _1779146), hAPP(hAPP(c_List_Olist_OCons(_1779144), _1779148), c_List_Olist_ONil(_1779144)))) = _1779146)], (10802 ^ _778908) ^ [_960121, _960123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960121), _960123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960121)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960123))))], (21299 ^ _778908) ^ [_1146883, _1146885, _1146887, _1146889] : [class_Fields_Ofield(_1146883), -(_1146885 = c_Groups_Ozero__class_Ozero(_1146883)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1146883), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146883), _1146887), _1146885)), _1146889) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1146883), _1146887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146883), _1146885), _1146889))), _1146885))], (586 ^ _778908) ^ [_788059, _788061, _788063, _788065] : [-(c_FunDef_Oreduction__pair(_788063, _788059)), c_FunDef_Oreduction__pair(_788065, _788061), _788065 = _788063, _788061 = _788059], (15616 ^ _778908) ^ [_1044736, _1044738, _1044740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044736), _1044738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044740), _1044738)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044740), _1044736))))], (24899 ^ _778908) ^ [_1215148] : [class_Orderings_Olinorder(_1215148), -(c_Orderings_Oord_Omax(_1215148, hAPP(c_COMBC(_1215148, _1215148, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1215148))) = c_Orderings_Oord__class_Omin(_1215148))], (41279 ^ _778908) ^ [_1563621, _1563623] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1563621, tc_HOL_Obool)), _1563623) = hAPP(c_Set_OCollect(_1563621), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1563621), c_fNot), hAPP(hAPP(c_COMBC(_1563621, tc_fun(_1563621, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563621)), _1563623))))], (41305 ^ _778908) ^ [_1564797, _1564799, _1564801, _1564803, _1564805] : [-(c_Map_Odom(_1564797, _1564799, hAPP(hAPP(c_COMBS(_1564797, tc_Option_Ooption(_1564799), tc_Option_Ooption(_1564799)), hAPP(hAPP(c_COMBS(_1564797, tc_Option_Ooption(_1564799), tc_fun(tc_Option_Ooption(_1564799), tc_Option_Ooption(_1564799))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1564799), tc_fun(tc_Option_Ooption(_1564799), tc_Option_Ooption(_1564799))), _1564797), c_If(tc_Option_Ooption(_1564799))), _1564801)), _1564803)), _1564805)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564797, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1564797, tc_HOL_Obool)), c_Map_Odom(_1564797, _1564799, _1564803)), hAPP(c_Set_OCollect(_1564797), _1564801))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1564797, tc_HOL_Obool)), c_Map_Odom(_1564797, _1564799, _1564805)), hAPP(c_Set_OCollect(_1564797), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564797), c_fNot), _1564801)))))], (3098 ^ _778908) ^ [_826365, _826367, _826369, _826371] : [-(c_Divides_Odivmod__nat(_826371, _826367) = c_Divides_Odivmod__nat(_826369, _826365)), _826371 = _826369, _826367 = _826365], (4204 ^ _778908) ^ [_843724, _843726, _843728, _843730, _843732, _843734] : [-(c_Smallcheck_Oorelse(_843734, _843730, _843726) = c_Smallcheck_Oorelse(_843732, _843728, _843724)), _843734 = _843732, _843730 = _843728, _843726 = _843724], (50389 ^ _778908) ^ [_1791259, _1791261, _1791263] : [class_Orderings_Olinorder(_1791259), c_List_Olinorder__class_Osorted(_1791259, _1791261), hBOOL(hAPP(c_List_Odistinct(_1791259), _1791261)), c_List_Olinorder__class_Osorted(_1791259, _1791263), hBOOL(hAPP(c_List_Odistinct(_1791259), _1791263)), hAPP(c_List_Oset(_1791259), _1791261) = hAPP(c_List_Oset(_1791259), _1791263), -(_1791261 = _1791263)], (50921 ^ _778908) ^ [_1802279, _1802281, _1802283] : [hAPP(c_List_Orev(_1802279), _1802281) = hAPP(c_List_Orev(_1802279), _1802283), -(_1802281 = _1802283)], (7088 ^ _778908) ^ [_897399, _897401] : [hAPP(c_Option_Ooption_OSome(_897399), _897401) = c_Option_Ooption_ONone(_897399)], (8578 ^ _778908) ^ [_922737, _922739, _922741] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922737), _922739)), _922741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922737), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922739), _922741)))], (50909 ^ _778908) ^ [_1802065, _1802067, _1802069] : [hAPP(c_List_Orev(_1802065), _1802067) = _1802069, -(_1802067 = hAPP(c_List_Orev(_1802065), _1802069))], (42153 ^ _778908) ^ [_1592449, _1592451] : [-(c_List_Olex(_1592449, _1592451) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1592449), tc_List_Olist(_1592449)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1592449, _1592451)))], (6534 ^ _778908) ^ [_884878, _884880] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_884878, _884880)], (44041 ^ _778908) ^ [_1639831, _1639833] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1639831, _1639831)), _1639833), c_Relation_OId(_1639831))), -(_1639833 = hAPP(hAPP(c_Product__Type_OPair(_1639831, _1639831), 44044 ^ [_1639831, _1639833]), 44044 ^ [_1639831, _1639833]))], (49017 ^ _778908) ^ [_1761640, _1761642, _1761644, _1761646, _1761648] : [hAPP(hAPP(c_List_Oappend(_1761640), _1761642), _1761644) = hAPP(hAPP(c_List_Oappend(_1761640), _1761646), _1761648), 49020 ^ _778908 : [(49029 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761642)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761646)))), 49032 ^ _778908 : [(49035 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1761640), hAPP(hAPP(c_List_Odrop(_1761640), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761646)), _1761642)), _1761644) = _1761648)], (49033 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1761640), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761646)), _1761642) = _1761646)]]], (49021 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761642)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761646))), 49024 ^ _778908 : [(49027 ^ _778908) ^ [] : [-(_1761644 = hAPP(hAPP(c_List_Oappend(_1761640), hAPP(hAPP(c_List_Odrop(_1761640), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761642)), _1761646)), _1761648))], (49025 ^ _778908) ^ [] : [-(_1761642 = hAPP(hAPP(c_List_Otake(_1761640), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761640)), _1761642)), _1761646))]]]]], (42038 ^ _778908) ^ [_1589780, _1589782] : [c_Wellfounded_Owf(_1589780, _1589782), 42042 ^ _778908 : [(42043 ^ _778908) ^ [_1589916] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589780, _1589780)), hAPP(hAPP(c_Product__Type_OPair(_1589780, _1589780), hAPP(_1589916, hAPP(c_Nat_OSuc, 42041 ^ [_1589780, _1589782, _1589916]))), hAPP(_1589916, 42041 ^ [_1589780, _1589782, _1589916]))), _1589782))]]], (6925 ^ _778908) ^ [_893304, _893306, _893308, _893310] : [-(c_Com_Ovname_Ovname__rec(_893304, _893306, _893308, c_Com_Ovname_OLoc(_893310)) = hAPP(_893308, _893310))], (22548 ^ _778908) ^ [_1169766, _1169768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1169766)), hAPP(c_Code__Numeral_Oof__nat, _1169768))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169766), _1169768)))], (14982 ^ _778908) ^ [_1032893, _1032895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032893), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032895), _1032893)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1032893), _1032895) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26473 ^ _778908) ^ [_1245105, _1245107, _1245109, _1245111, _1245113] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245105), _1245107)), 26476 ^ _778908 : [(26483 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245113), _1245107))), _1245111))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245109), _1245111))))], (26477 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245109), _1245111))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245113), _1245107))), _1245111))))]]], (1682 ^ _778908) ^ [_802807, _802809] : [-(class_Orderings_Olinorder(_802807)), _802809 = _802807, class_Orderings_Olinorder(_802809)], (45935 ^ _778908) ^ [_1683625, _1683627, _1683629, _1683631] : [c_Fun_Oinj__on(_1683625, tc_Option_Ooption(_1683627), _1683631, c_Map_Odom(_1683625, _1683627, _1683631)), -(c_Fun_Oinj__on(_1683625, tc_Option_Ooption(_1683627), c_Map_Omap__add(_1683625, _1683627, _1683629, _1683631), c_Map_Odom(_1683625, _1683627, _1683631)))], (10285 ^ _778908) ^ [_951786, _951788] : [class_Groups_Osgn__if(_951786), 10288 ^ _778908 : [(10295 ^ _778908) ^ [] : [-(_951788 = c_Groups_Ozero__class_Ozero(_951786)), 10298 ^ _778908 : [(10305 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951786), c_Groups_Ozero__class_Ozero(_951786)), _951788))), -(c_Groups_Osgn__class_Osgn(_951786, _951788) = hAPP(c_Groups_Ouminus__class_Ouminus(_951786), c_Groups_Oone__class_Oone(_951786)))], (10299 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951786), c_Groups_Ozero__class_Ozero(_951786)), _951788)), -(c_Groups_Osgn__class_Osgn(_951786, _951788) = c_Groups_Oone__class_Oone(_951786))]]], (10289 ^ _778908) ^ [] : [_951788 = c_Groups_Ozero__class_Ozero(_951786), -(c_Groups_Osgn__class_Osgn(_951786, _951788) = c_Groups_Ozero__class_Ozero(_951786))]]], (49504 ^ _778908) ^ [_1772461, _1772463, _1772465, _1772467] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772461)), hAPP(hAPP(c_List_Olist_OCons(_1772461), _1772463), _1772465)), c_List_Olists(_1772461, _1772467))), 49507 ^ _778908 : [(49510 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772461)), _1772465), c_List_Olists(_1772461, _1772467))))], (49508 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772461), _1772463), _1772467)))]]], (26891 ^ _778908) ^ [_1253074, _1253076, _1253078] : [-(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), _1253074)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1253076))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1253078))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1253078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1253078), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1253076)))))], (39848 ^ _778908) ^ [_1530464, _1530466, _1530468, _1530470] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530464, _1530466, _1530468, _1530470, c_Orderings_Obot__class_Obot(tc_fun(_1530464, tc_HOL_Obool))), _1530470)))], (6592 ^ _778908) ^ [_886415, _886417, _886419, _886421, _886423] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_886415, _886417, _886419)), _886421), hAPP(hAPP(hAPP(c_Natural_Oupdate, _886423), c_Com_Ovname_OLoc(_886415)), hAPP(hAPP(c_Natural_Ogetlocs, _886421), _886415))))), 6593 ^ _778908 : [(6594 ^ _778908) ^ [_886544] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _886423), c_Com_Ovname_OLoc(_886415)), hAPP(hAPP(c_Natural_Ogetlocs, _886421), _886415)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _886544), c_Com_Ovname_OLoc(_886415)), hAPP(hAPP(c_Natural_Ogetlocs, _886421), _886415)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886419), hAPP(hAPP(hAPP(c_Natural_Oupdate, _886421), c_Com_Ovname_OLoc(_886415)), hAPP(_886417, _886421))), _886544))]]], (21075 ^ _778908) ^ [_1142845, _1142847, _1142849, _1142851] : [class_Fields_Olinordered__field(_1142845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142845), c_Groups_Ozero__class_Ozero(_1142845)), _1142847)), 21082 ^ _778908 : [(21089 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142845), _1142849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142845), _1142851), _1142847))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142845), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142845), _1142849), _1142847)), _1142851)))], (21083 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142845), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142845), _1142849), _1142847)), _1142851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142845), _1142849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142845), _1142851), _1142847))))]]], (5086 ^ _778908) ^ [_857581, _857583] : [_857583 = _857581, -(c_Option_Ooption_ONone(_857583) = c_Option_Ooption_ONone(_857581))], (9056 ^ _778908) ^ [_930206, _930208] : [class_Rings_Ocomm__semiring__1(_930206), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930206), _930208), c_Groups_Oone__class_Oone(_930206)) = _930208)], (38554 ^ _778908) ^ [_1501932, _1501934, _1501936, _1501938, _1501940, _1501942] : [c_Fun_Oinj__on(_1501932, _1501934, _1501936, _1501938), hAPP(_1501936, _1501940) = hAPP(_1501936, _1501942), hBOOL(hAPP(hAPP(c_member(_1501932), _1501940), _1501938)), hBOOL(hAPP(hAPP(c_member(_1501932), _1501942), _1501938)), -(_1501940 = _1501942)], (14344 ^ _778908) ^ [_1021824, _1021826, _1021828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021824)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1021826, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1021828), _1021824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1021828), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021826), _1021828), _1021824))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1021826, _1021828)))], (51335 ^ _778908) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (7106 ^ _778908) ^ [_897726] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_897726)), c_Option_Ooption_ONone(_897726)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15480 ^ _778908) ^ [_1042244, _1042246, _1042248, _1042250, _1042252] : [class_Groups_Oordered__ab__group__add(_1042244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042244), _1042246), _1042248) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042244), _1042250), _1042252), 15487 ^ _778908 : [(15494 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042244), _1042250), _1042252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042244), _1042246), _1042248)))], (15488 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042244), _1042246), _1042248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042244), _1042250), _1042252)))]]], (12605 ^ _778908) ^ [_990812] : [12606 ^ _778908 : [(12607 ^ _778908) ^ [_990869] : [hBOOL(hAPP(_990812, _990869))]], 12609 ^ _778908 : [(12612 ^ _778908) ^ [] : [-(hBOOL(hAPP(_990812, hAPP(c_Int_Onat, 12608 ^ [_990812]))))], (12610 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12608 ^ [_990812])))]]], (41103 ^ _778908) ^ [_1559531, _1559533, _1559535] : [41104 ^ _778908 : [(41107 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559531), hAPP(c_Set_OCollect(_1559531), _1559535)))], (41105 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559531), hAPP(c_Set_OCollect(_1559531), _1559533)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559531), hAPP(c_Set_OCollect(_1559531), hAPP(hAPP(c_COMBS(_1559531, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559531), c_fconj), _1559533)), _1559535)))))], (41704 ^ _778908) ^ [_1580554, _1580556] : [-(c_Product__Type_Omap__pair(_1580554, _1580554, _1580556, _1580556, c_Fun_Oid(_1580554), c_Fun_Oid(_1580556)) = c_Fun_Oid(tc_prod(_1580554, _1580556)))], (9246 ^ _778908) ^ [_933694, _933696] : [class_Rings_Oring__1(_933694), 9249 ^ _778908 : [(9256 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _933696), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_933694), _933696) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_933694), hAPP(c_Int_Onat, _933696)))], (9250 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _933696), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_933694), _933696) = hAPP(c_Groups_Ouminus__class_Ouminus(_933694), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_933694), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _933696)))))]]], (33019 ^ _778908) ^ [_1380777, _1380779] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1380777, _1380779, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380777), tc_HOL_Obool))))], (49813 ^ _778908) ^ [_1778821, _1778823, _1778825] : [-(hAPP(hAPP(c_List_Odrop(_1778821), _1778823), c_List_Obutlast(_1778821, _1778825)) = c_List_Obutlast(_1778821, hAPP(hAPP(c_List_Odrop(_1778821), _1778823), _1778825)))], (29676 ^ _778908) ^ [_1309719, _1309721, _1309723] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309719), _1309721)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309719), _1309723)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309719), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309719, tc_HOL_Obool)), _1309721), _1309723))))], (15858 ^ _778908) ^ [_1049528, _1049530] : [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), _1049528), _1049530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049530), _1049528)))], (32263 ^ _778908) ^ [_1365230, _1365232, _1365234, _1365236, _1365238, _1365240] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365230, tc_fun(_1365232, tc_HOL_Obool))), _1365234), _1365236), _1365238), _1365240)), -(hBOOL(hAPP(hAPP(_1365234, _1365238), _1365240))), -(hBOOL(hAPP(hAPP(_1365236, _1365238), _1365240)))], (44290 ^ _778908) ^ [_1644815, _1644817, _1644819] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1644815), _1644817)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1644815, tc_HOL_Obool)), _1644819), _1644817) = hAPP(hAPP(c_Finite__Set_Ofold(_1644815, tc_fun(_1644815, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1644815, tc_HOL_Obool), tc_fun(tc_fun(_1644815, tc_HOL_Obool), tc_fun(_1644815, tc_HOL_Obool)), _1644815), hAPP(c_COMBC(tc_fun(_1644815, tc_HOL_Obool), tc_fun(_1644815, tc_HOL_Obool), tc_fun(_1644815, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1644815, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1644815, tc_fun(_1644815, tc_HOL_Obool), tc_fun(_1644815, tc_HOL_Obool)), c_Set_Oinsert(_1644815)), c_Orderings_Obot__class_Obot(tc_fun(_1644815, tc_HOL_Obool))))), _1644819), _1644817))], (18459 ^ _778908) ^ [_1097510] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1097510)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097510) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3306 ^ _778908) ^ [_829615, _829617, _829619, _829621, _829623, _829625, _829627, _829629, _829631, _829633] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_829633, _829629, _829625, _829621, _829617) = c_SetInterval_Oord_OgreaterThanAtMost(_829631, _829627, _829623, _829619, _829615)), _829633 = _829631, _829629 = _829627, _829625 = _829623, _829621 = _829619, _829617 = _829615], (15474 ^ _778908) ^ [_1042149, _1042151] : [class_Groups_Ogroup__add(_1042149), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042149), _1042151), c_Groups_Ozero__class_Ozero(_1042149)) = _1042151)], (25851 ^ _778908) ^ [_1233008, _1233010, _1233012, _1233014] : [class_Rings_Ocomm__semiring__1(_1233008), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233008), _1233010), _1233012)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233008), _1233010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233008), _1233012), _1233014))))], (5664 ^ _778908) ^ [_866398, _866400, _866402, _866404] : [-(tc_fun(_866404, _866400) = tc_fun(_866402, _866398)), _866404 = _866402, _866400 = _866398], (40184 ^ _778908) ^ [_1539364, _1539366, _1539368, _1539370, _1539372, _1539374] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539364, _1539366)), hAPP(hAPP(c_Product__Type_OPair(_1539364, _1539366), _1539368), _1539370)), hAPP(hAPP(c_Product__Type_OSigma(_1539364, _1539366), _1539372), _1539374))), -(hBOOL(hAPP(hAPP(c_member(_1539364), _1539368), _1539372)))], (39384 ^ _778908) ^ [_1519298, _1519300, _1519302] : [-(c_Fun_Oinj__on(tc_prod(_1519298, _1519300), tc_prod(_1519300, _1519298), hAPP(c_Product__Type_Oprod_Oprod__case(_1519298, _1519300, tc_prod(_1519300, _1519298)), hAPP(c_COMBC(_1519300, _1519298, tc_prod(_1519300, _1519298)), c_Product__Type_OPair(_1519300, _1519298))), _1519302))], (22876 ^ _778908) ^ [_1176551, _1176553, _1176555, _1176557, _1176559] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176551, _1176553), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1176555), _1176557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176559)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176551, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176553), _1176559)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1176555), _1176559)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176553), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1176555, _1176559))), _1176557)))))], (44899 ^ _778908) ^ [_1660055, _1660057, _1660059, _1660061, _1660063] : [class_Complete__Lattice_Ocomplete__lattice(_1660055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660057, tc_HOL_Obool)), _1660059), _1660061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660055), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660057, _1660055), _1660061), _1660063)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660057, _1660055), _1660059), _1660063))))], (18021 ^ _778908) ^ [_1090481] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090481))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090481) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41044 ^ _778908) ^ [_1558423, _1558425, _1558427, _1558429, _1558431] : [c_Finite__Set_Ofun__left__comm__idem(_1558423, _1558425, _1558427), -(c_Finite__Set_Ofun__left__comm__idem(_1558429, _1558425, hAPP(hAPP(c_COMBB(_1558423, tc_fun(_1558425, _1558425), _1558429), _1558427), _1558431)))], (142 ^ _778908) ^ [_780869, _780871, _780873, _780875, _780877, _780879] : [-(c_Nitpick_Oless__frac(_780877, _780873, _780869)), c_Nitpick_Oless__frac(_780879, _780875, _780871), _780879 = _780877, _780875 = _780873, _780871 = _780869], (8309 ^ _778908) ^ [_918082, _918084, _918086, _918088, _918090] : [c_Sum__Type_OSumr(_918082, _918084, _918086, _918088) = c_Sum__Type_OSumr(_918082, _918084, _918086, _918090), -(_918088 = _918090)], (7859 ^ _778908) ^ [_910243, _910245] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910243), _910245))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910243), hAPP(c_Nat_OSuc, _910245))), -(_910245 = _910243)], (13610 ^ _778908) ^ [_1008412, _1008414] : [_1008412 = _1008414, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008412), _1008414)))], (49783 ^ _778908) ^ [_1778328, _1778330, _1778332] : [hBOOL(hAPP(hAPP(c_member(_1778328), _1778330), hAPP(c_List_Oset(_1778328), c_List_Obutlast(_1778328, _1778332)))), -(hBOOL(hAPP(hAPP(c_member(_1778328), _1778330), hAPP(c_List_Oset(_1778328), _1778332))))], (14992 ^ _778908) ^ [_1033054, _1033056, _1033058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033054), _1033056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033054), _1033058)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033056), _1033058))))], (1312 ^ _778908) ^ [_798182, _798184] : [-(class_Lattices_Obounded__lattice__bot(_798182)), _798184 = _798182, class_Lattices_Obounded__lattice__bot(_798184)], (41416 ^ _778908) ^ [_1568458, _1568460, _1568462, _1568464] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1568458, _1568460), _1568462), _1568464) = hAPP(c_Set_OCollect(tc_prod(_1568460, _1568460)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568460, _1568460, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1568460, tc_fun(tc_prod(_1568458, _1568458), tc_HOL_Obool), tc_fun(_1568460, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568460, tc_fun(tc_fun(tc_prod(_1568458, _1568458), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568458, _1568458), tc_HOL_Obool), tc_fun(_1568460, tc_HOL_Obool)), _1568460), c_COMBC(_1568460, tc_fun(tc_prod(_1568458, _1568458), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568460, tc_prod(_1568458, _1568458)), tc_fun(_1568460, tc_fun(tc_fun(tc_prod(_1568458, _1568458), tc_HOL_Obool), tc_HOL_Obool)), _1568460), hAPP(c_COMBB(tc_prod(_1568458, _1568458), tc_fun(tc_fun(tc_prod(_1568458, _1568458), tc_HOL_Obool), tc_HOL_Obool), _1568460), c_member(tc_prod(_1568458, _1568458)))), hAPP(hAPP(c_COMBC(_1568460, tc_fun(_1568460, _1568458), tc_fun(_1568460, tc_prod(_1568458, _1568458))), hAPP(hAPP(c_COMBB(tc_fun(_1568458, tc_prod(_1568458, _1568458)), tc_fun(tc_fun(_1568460, _1568458), tc_fun(_1568460, tc_prod(_1568458, _1568458))), _1568460), c_COMBB(_1568458, tc_prod(_1568458, _1568458), _1568460)), hAPP(hAPP(c_COMBB(_1568458, tc_fun(_1568458, tc_prod(_1568458, _1568458)), _1568460), c_Product__Type_OPair(_1568458, _1568458)), _1568464))), _1568464)))), _1568462))))], (14489 ^ _778908) ^ [_1024609, _1024611, _1024613] : [-(hBOOL(hAPP(_1024609, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1024611), _1024613)))), 14490 ^ _778908 : [(14497 ^ _778908) ^ [_1024777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024613), _1024777)), _1024611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1024611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024613), hAPP(c_Nat_OSuc, _1024777)))), hBOOL(hAPP(_1024609, _1024777))], (14491 ^ _778908) ^ [] : [_1024613 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1024609, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (40074 ^ _778908) ^ [_1536121, _1536123, _1536125, _1536127, _1536129, _1536131] : [hBOOL(hAPP(hAPP(c_member(_1536121), _1536123), _1536125)), 40077 ^ _778908 : [(40084 ^ _778908) ^ [] : [_1536129 = _1536131, -(hAPP(hAPP(c_Product__Type_OSigma(_1536127, _1536121), _1536129), hAPP(c_COMBK(tc_fun(_1536121, tc_HOL_Obool), _1536127), _1536125)) = hAPP(hAPP(c_Product__Type_OSigma(_1536127, _1536121), _1536131), hAPP(c_COMBK(tc_fun(_1536121, tc_HOL_Obool), _1536127), _1536125)))], (40078 ^ _778908) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1536127, _1536121), _1536129), hAPP(c_COMBK(tc_fun(_1536121, tc_HOL_Obool), _1536127), _1536125)) = hAPP(hAPP(c_Product__Type_OSigma(_1536127, _1536121), _1536131), hAPP(c_COMBK(tc_fun(_1536121, tc_HOL_Obool), _1536127), _1536125)), -(_1536129 = _1536131)]]], (17067 ^ _778908) ^ [_1073029, _1073031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1073029)), -(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), _1073029), _1073031))))], (7677 ^ _778908) ^ [_907193, _907195, _907197] : [7678 ^ _778908 : [(7681 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_907197, _907195), _907193))], (7679 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907193), _907195)))]], 7684 ^ _778908 : [(7687 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_907197, _907195), _907193))], (7685 ^ _778908) ^ [] : [-(_907193 = _907195)]], 7690 ^ _778908 : [(7693 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_907197, _907195), _907193))], (7691 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907195), _907193)))]], -(hBOOL(hAPP(hAPP(_907197, _907195), _907193)))], (32925 ^ _778908) ^ [_1378523, _1378525] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1378523, _1378525) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378523), _1378525)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378525), _1378523)))], (8370 ^ _778908) ^ [_919172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919172)), -(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), _919172))))], (24501 ^ _778908) ^ [_1207569, _1207571, _1207573, _1207575] : [class_Orderings_Olinorder(_1207569), 24504 ^ _778908 : [(24505 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207569), _1207571), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207569), _1207573), _1207575))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207569), _1207571), _1207573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207569), _1207571), _1207575)))], (24515 ^ _778908) ^ [] : [24516 ^ _778908 : [(24519 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207569), _1207571), _1207575))], (24517 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207569), _1207571), _1207573))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207569), _1207571), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207569), _1207573), _1207575))))]]], (1042 ^ _778908) ^ [_794807, _794809] : [-(class_Groups_Oordered__ab__group__add__abs(_794807)), _794809 = _794807, class_Groups_Oordered__ab__group__add__abs(_794809)], (21903 ^ _778908) ^ [_1157785, _1157787, _1157789, _1157791] : [class_Fields_Olinordered__field__inverse__zero(_1157785), class_Int_Onumber(_1157785), 21910 ^ _778908 : [(21911 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157785), _1157787), _1157789)), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791))), 21914 ^ _778908 : [(21921 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), c_Groups_Ozero__class_Ozero(_1157785)), _1157789))), 21924 ^ _778908 : [(21931 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), _1157789), c_Groups_Ozero__class_Ozero(_1157785)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), c_Groups_Ozero__class_Ozero(_1157785)), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791))))], (21925 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), _1157789), c_Groups_Ozero__class_Ozero(_1157785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157785), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791)), _1157789)), _1157787)))]]], (21915 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), c_Groups_Ozero__class_Ozero(_1157785)), _1157789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), _1157787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157785), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791)), _1157789))))]]], (21937 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157785), _1157787), _1157789)), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791)))), 21940 ^ _778908 : [(21943 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), _1157787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157785), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791)), _1157789)))], (21941 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), c_Groups_Ozero__class_Ozero(_1157785)), _1157789)))]], 21944 ^ _778908 : [(21947 ^ _778908) ^ [] : [21948 ^ _778908 : [(21951 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157785), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791)), _1157789)), _1157787))], (21949 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), _1157789), c_Groups_Ozero__class_Ozero(_1157785))))]], 21952 ^ _778908 : [(21955 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), c_Groups_Ozero__class_Ozero(_1157785)), hAPP(c_Int_Onumber__class_Onumber__of(_1157785), _1157791)))], (21953 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), _1157789), c_Groups_Ozero__class_Ozero(_1157785)))]]], (21945 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157785), c_Groups_Ozero__class_Ozero(_1157785)), _1157789))]]]]], (12357 ^ _778908) ^ [_986475, _986477] : [class_Rings_Olinordered__semidom(_986475), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986475), c_Groups_Ozero__class_Ozero(_986475)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_986475), _986477))))], (21755 ^ _778908) ^ [_1154884, _1154886, _1154888, _1154890] : [class_Fields_Olinordered__field(_1154884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154884), _1154886), _1154888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154884), c_Groups_Ozero__class_Ozero(_1154884)), _1154890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154884), c_Groups_Ozero__class_Ozero(_1154884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154884), _1154888), _1154886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154884), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154884), _1154890), _1154888)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154884), _1154890), _1154886))))], (30876 ^ _778908) ^ [_1332872, _1332874] : [hBOOL(hAPP(hAPP(c_member(_1332872), _1332874), c_Orderings_Obot__class_Obot(tc_fun(_1332872, tc_HOL_Obool))))], (48556 ^ _778908) ^ [_1749106, _1749108, _1749110, _1749112, _1749114] : [-(c_Map_Odom(_1749106, _1749108, c_Map_Omap__upds(_1749106, _1749108, _1749110, _1749112, _1749114)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1749106, tc_HOL_Obool)), hAPP(c_List_Oset(_1749106), hAPP(hAPP(c_List_Otake(_1749106), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749108)), _1749114)), _1749112))), c_Map_Odom(_1749106, _1749108, _1749110)))], (35128 ^ _778908) ^ [_1423932, _1423934, _1423936] : [-(c_Wellfounded_Omlex__prod(_1423932, _1423934, _1423936) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1423932), _1423932), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1423932, c_Wellfounded_Oless__than, _1423936)), hAPP(hAPP(c_COMBS(_1423932, _1423932, tc_prod(tc_Nat_Onat, _1423932)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1423932, tc_prod(tc_Nat_Onat, _1423932)), _1423932), c_Product__Type_OPair(tc_Nat_Onat, _1423932)), _1423934)), c_COMBI(_1423932))))], (49422 ^ _778908) ^ [_1770333, _1770335, _1770337, _1770339, _1770341] : [hBOOL(hAPP(hAPP(c_member(_1770333), _1770335), hAPP(c_List_Oset(_1770333), _1770337))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770339), hAPP(_1770341, _1770335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770339), c_List_Olist_Olist__size(_1770333, _1770341, _1770337))))], (22434 ^ _778908) ^ [_1167378, _1167380, _1167382, _1167384] : [class_Groups_Ouminus(_1167378), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1167380, _1167378)), _1167382), _1167384) = hAPP(c_Groups_Ouminus__class_Ouminus(_1167378), hAPP(_1167382, _1167384)))], (1372 ^ _778908) ^ [_798932, _798934] : [-(class_Orderings_Otop(_798932)), _798934 = _798932, class_Orderings_Otop(_798934)], (28683 ^ _778908) ^ [_1288805, _1288807, _1288809, _1288811] : [class_Orderings_Olinorder(_1288805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288805), _1288807), _1288809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288805), _1288809), _1288811)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288805, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1288805, _1288807, _1288809)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288805, _1288809), _1288811)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1288805, _1288807, _1288811))], (41609 ^ _778908) ^ [_1576614, _1576616, _1576618] : [class_Lattices_Odistrib__lattice(_1576614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576614), _1576616)), -(_1576616 = c_Orderings_Obot__class_Obot(tc_fun(_1576614, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1576614), _1576618), c_Big__Operators_Olattice__class_OSup__fin(_1576614, _1576616)) = c_Big__Operators_Olattice__class_OSup__fin(_1576614, hAPP(c_Set_OCollect(_1576614), hAPP(hAPP(c_COMBB(tc_fun(_1576614, tc_HOL_Obool), tc_HOL_Obool, _1576614), c_HOL_OEx(_1576614)), hAPP(hAPP(c_COMBC(_1576614, tc_fun(_1576614, tc_HOL_Obool), tc_fun(_1576614, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576614, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1576614, tc_HOL_Obool), tc_fun(_1576614, tc_HOL_Obool)), _1576614), c_COMBS(_1576614, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576614, tc_HOL_Obool), tc_fun(_1576614, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1576614), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576614), c_fconj)), hAPP(hAPP(c_COMBC(_1576614, tc_fun(_1576614, _1576614), tc_fun(_1576614, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576614, tc_HOL_Obool), tc_fun(tc_fun(_1576614, _1576614), tc_fun(_1576614, tc_HOL_Obool)), _1576614), c_COMBB(_1576614, tc_HOL_Obool, _1576614)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1576614), _1576618))))), hAPP(hAPP(c_COMBC(_1576614, tc_fun(_1576614, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576614)), _1576616))))))], (51259 ^ _778908) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (6726 ^ _778908) ^ [_889170, _889172, _889174, _889176, _889178] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_889170, _889172), _889174, _889176, _889178)), 6727 ^ _778908 : [(6734 ^ _778908) ^ [] : [hBOOL(hAPP(_889170, _889174)), 6737 ^ _778908 : [(6738 ^ _778908) ^ [_889380] : [c_Natural_Oevaln(_889172, _889174, _889176, _889380), c_Natural_Oevaln(c_Com_Ocom_OWhile(_889170, _889172), _889380, _889176, _889178)]]], (6728 ^ _778908) ^ [] : [_889178 = _889174, -(hBOOL(hAPP(_889170, _889174)))]]], (4358 ^ _778908) ^ [_846235, _846237, _846239, _846241] : [-(c_Nitpick_Ocard_H(_846241, _846237) = c_Nitpick_Ocard_H(_846239, _846235)), _846241 = _846239, _846237 = _846235], (22614 ^ _778908) ^ [_1171153, _1171155] : [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(_1171155))), 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), _1171153)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1171153)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1171155))))], (6522 ^ _778908) ^ [_884561, _884563, _884565] : [hAPP(c_Com_Ocom_OBODY, _884561) = c_Com_Ocom_OSemi(_884563, _884565)], (21219 ^ _778908) ^ [_1145525] : [c_Nat__Transfer_Ois__nat(_1145525), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145525)))], (11106 ^ _778908) ^ [_964883, _964885, _964887] : [class_Orderings_Olinorder(_964883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964883), _964885), _964887)), 11113 ^ _778908 : [(11120 ^ _778908) ^ [] : [_964885 = _964887, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964883), _964885), _964887))], (11114 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964883), _964885), _964887))), -(_964885 = _964887)]]], (10276 ^ _778908) ^ [_951636, _951638] : [-(c_Int_Onat__aux(_951636, _951638) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _951636)), _951638))], (41287 ^ _778908) ^ [_1563914, _1563916] : [-(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), _1563914)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1563916))))))], (7592 ^ _778908) ^ [_905983, _905985] : [hBOOL(hAPP(_905983, _905985)), 7598 ^ _778908 : [(7601 ^ _778908) ^ [] : [hBOOL(hAPP(_905983, 7597 ^ [_905983, _905985]))], (7599 ^ _778908) ^ [] : [-(hBOOL(hAPP(_905983, hAPP(c_Nat_OSuc, 7597 ^ [_905983, _905985]))))]], -(hBOOL(hAPP(_905983, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51323 ^ _778908) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (35957 ^ _778908) ^ [_1443915, _1443917, _1443919, _1443921, _1443923, _1443925] : [c_Finite__Set_Ofolding(_1443915, _1443917, _1443919, _1443921), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443915), _1443923)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443915), _1443925)), -(hAPP(c_Fun_Ocomp(_1443917, _1443917, _1443917, hAPP(_1443921, _1443925)), hAPP(_1443921, _1443923)) = hAPP(c_Fun_Ocomp(_1443917, _1443917, _1443917, hAPP(_1443921, _1443923)), hAPP(_1443921, _1443925)))], (39890 ^ _778908) ^ [_1531329, _1531331, _1531333] : [hBOOL(hAPP(hAPP(c_member(_1531329), _1531331), c_Wellfounded_Oacc(_1531329, _1531333))), 39893 ^ _778908 : [(39894 ^ _778908) ^ [_1531443] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531329, _1531329)), hAPP(hAPP(c_Product__Type_OPair(_1531329, _1531329), _1531443), _1531331)), _1531333)), -(hBOOL(hAPP(hAPP(c_member(_1531329), _1531443), c_Wellfounded_Oacc(_1531329, _1531333))))]]], (32539 ^ _778908) ^ [_1370751, _1370753] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370753), _1370751)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1370751), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370753))))], (48512 ^ _778908) ^ [_1748040, _1748042, _1748044] : [hBOOL(hAPP(c_List_Odistinct(_1748040), _1748042)), -(hBOOL(hAPP(c_List_Odistinct(_1748040), hAPP(hAPP(c_List_Otake(_1748040), _1748044), _1748042))))], (32521 ^ _778908) ^ [_1370335, _1370337, _1370339, _1370341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1370335, _1370335)), hAPP(hAPP(c_Product__Type_OPair(_1370335, _1370335), _1370337), _1370339)), hAPP(c_Wellfounded_Omeasure(_1370335), _1370341))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1370341, _1370337)), hAPP(_1370341, _1370339))))], (51239 ^ _778908) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (18099 ^ _778908) ^ [_1091888] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091888))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091888)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29845 ^ _778908) ^ [_1312995, _1312997, _1312999] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312995), _1312997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1312995, tc_HOL_Obool)), _1312999), _1312997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312995), _1312999)), hAPP(c_Finite__Set_Ocard(_1312995), _1312997))))], (28237 ^ _778908) ^ [_1280280, _1280282] : [class_Lattices_Osemilattice__sup(_1280280), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280280), _1280282), _1280282) = _1280282)], (20971 ^ _778908) ^ [_1140827, _1140829, _1140831, _1140833] : [class_Fields_Olinordered__field(_1140827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140829), _1140831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), _1140833), c_Groups_Ozero__class_Ozero(_1140827))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), c_Groups_Ozero__class_Ozero(_1140827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140827), _1140829), _1140831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140827), _1140833), _1140829)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140827), _1140833), _1140831))))], (15936 ^ _778908) ^ [_1050905, _1050907, _1050909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050905), _1050907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050909), _1050905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050905), _1050909)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050907), _1050909))))], (5646 ^ _778908) ^ [_866097, _866099, _866101, _866103, _866105, _866107, _866109, _866111] : [-(c_Fun_Ocomp(_866111, _866107, _866103, _866099) = c_Fun_Ocomp(_866109, _866105, _866101, _866097)), _866111 = _866109, _866107 = _866105, _866103 = _866101, _866099 = _866097], (7220 ^ _778908) ^ [_899737, _899739, _899741] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899737), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899739), _899741)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899739), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899737), _899741)))], (3946 ^ _778908) ^ [_839805, _839807] : [_839807 = _839805, -(c_New__Random__Sequence_Oneg__single(_839807) = c_New__Random__Sequence_Oneg__single(_839805))], (40398 ^ _778908) ^ [_1545325, _1545327, _1545329, _1545331, _1545333, _1545335] : [hAPP(c_Set_Oimage(_1545325, _1545327, _1545329), c_Orderings_Otop__class_Otop(tc_fun(_1545325, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545327, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1545331, _1545333, _1545335), c_Orderings_Otop__class_Otop(tc_fun(_1545331, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545333, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1545325, _1545331), tc_prod(_1545327, _1545333), c_Product__Type_Omap__pair(_1545325, _1545327, _1545331, _1545333, _1545329, _1545335)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1545325, _1545331), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1545327, _1545333), tc_HOL_Obool)))], (25329 ^ _778908) ^ [_1224329, _1224331, _1224333] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224329), _1224331)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224331), _1224329))), 25344 ^ _778908 : [(25347 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224333), _1224329))], (25345 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224329), _1224333)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224331), _1224333)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224333), _1224331)))], (31151 ^ _778908) ^ [_1338405, _1338407, _1338409, _1338411] : [hBOOL(hAPP(hAPP(c_member(_1338405), _1338407), _1338409)), -(hBOOL(hAPP(hAPP(c_member(_1338405), _1338407), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338405, tc_HOL_Obool)), _1338411), _1338409))))], (15946 ^ _778908) ^ [_1051092, _1051094, _1051096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051092), _1051094)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051094), _1051096)), _1051092) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051094), _1051092)), _1051096))], (19057 ^ _778908) ^ [_1107160, _1107162] : [class_Int_Onumber__ring(_1107160), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107160), _1107162), hAPP(c_Int_Onumber__class_Onumber__of(_1107160), c_Int_OBit1(c_Int_OPls))) = _1107162)], (42418 ^ _778908) ^ [_1599607, _1599609, _1599611, _1599613, _1599615] : [hBOOL(hAPP(hAPP(_1599607, _1599609), _1599611)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1599613, _1599615, _1599607), _1599609)))], (20255 ^ _778908) ^ [_1128677, _1128679, _1128681, _1128683] : [class_Fields_Ofield__inverse__zero(_1128677), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1128677), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128677), _1128679), _1128681)), _1128683) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128677), hAPP(hAPP(c_Power_Opower__class_Opower(_1128677), _1128679), _1128683)), hAPP(hAPP(c_Power_Opower__class_Opower(_1128677), _1128681), _1128683)))], (47074 ^ _778908) ^ [_1713206, _1713208, _1713210] : [hBOOL(hAPP(c_List_Odistinct(_1713206), hAPP(hAPP(c_List_Olist_OCons(_1713206), _1713208), _1713210))), 47077 ^ _778908 : [(47080 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1713206), _1713210)))], (47078 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1713206), _1713208), hAPP(c_List_Oset(_1713206), _1713210)))]]], (9822 ^ _778908) ^ [_943594, _943596, _943598] : [class_Rings_Olinordered__semiring__strict(_943594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943594), c_Groups_Ozero__class_Ozero(_943594)), _943596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943594), c_Groups_Ozero__class_Ozero(_943594)), _943598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943594), c_Groups_Ozero__class_Ozero(_943594)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943594), _943596), _943598))))], (50074 ^ _778908) ^ [_1785306, _1785308, _1785310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785306), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1785308))), c_List_Otranspose(_1785308, _1785310)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1785308)), c_List_Otranspose(_1785308, _1785310)), _1785306) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1785308), _1785308), hAPP(hAPP(c_COMBC(tc_List_Olist(_1785308), tc_Nat_Onat, _1785308), c_List_Onth(_1785308)), _1785306)), hAPP(c_List_Ofilter(tc_List_Olist(_1785308), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1785308)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785306)), c_Nat_Osize__class_Osize(tc_List_Olist(_1785308)))), _1785310)))], (14836 ^ _778908) ^ [_1030554, _1030556] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030554), _1030556) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14837 ^ _778908 : [(14846 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1030554), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030556), _1030554))], (14840 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030554), _1030556))], (14838 ^ _778908) ^ [] : [_1030556 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (44240 ^ _778908) ^ [_1643878, _1643880, _1643882] : [class_Lattices_Olattice(_1643878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643878), _1643880)), -(c_Big__Operators_Olattice__class_OInf__fin(_1643878, hAPP(hAPP(c_Set_Oinsert(_1643878), _1643882), _1643880)) = hAPP(hAPP(c_Finite__Set_Ofold(_1643878, _1643878, c_Lattices_Osemilattice__inf__class_Oinf(_1643878)), _1643882), _1643880))], (51291 ^ _778908) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (50967 ^ _778908) ^ [_1803187, _1803189, _1803191] : [-(hAPP(c_List_Orotate(_1803187, _1803189), hAPP(c_List_Orev(_1803187), _1803191)) = hAPP(c_List_Orev(_1803187), hAPP(c_List_Orotate(_1803187, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803187)), _1803191)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1803189, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803187)), _1803191)))), _1803191)))], (15580 ^ _778908) ^ [_1044156, _1044158, _1044160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1044156), _1044158)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044156), _1044160)), _1044158)))], (7799 ^ _778908) ^ [_909398, _909400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909398), _909400)), _909400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7264 ^ _778908) ^ [_900421, _900423] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _900421)), _900423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900421), hAPP(c_Nat_OSuc, _900423)))], (28323 ^ _778908) ^ [_1281885, _1281887, _1281889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281885, tc_HOL_Obool)), _1281887), _1281889)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281885, tc_HOL_Obool)), _1281887), _1281889) = _1281889)], (51285 ^ _778908) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (47852 ^ _778908) ^ [_1732597, _1732599, _1732601, _1732603, _1732605] : [-(_1732597 = _1732599), -(hAPP(hAPP(c_List_Onth(_1732601), hAPP(hAPP(c_List_Olist__update(_1732601, _1732603), _1732597), _1732605)), _1732599) = hAPP(hAPP(c_List_Onth(_1732601), _1732603), _1732599))], (5947 ^ _778908) ^ [_873854, _873856, _873858, _873860] : [c_Com_Ocom_OCall(_873854, _873856, _873858) = hAPP(c_Com_Ocom_OBODY, _873860)], (8600 ^ _778908) ^ [_923015, _923017] : [class_Orderings_Opreorder(_923015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923015), _923017), _923017))], (25479 ^ _778908) ^ [_1226799, _1226801, _1226803] : [_1226799 = _1226801, 25490 ^ _778908 : [(25493 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226803), _1226799))], (25491 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226799), _1226803)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226801), _1226803)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226803), _1226801)))], (41742 ^ _778908) ^ [_1581306, _1581308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1581306), _1581308)), -(_1581308 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1581306, 41746 ^ [_1581306, _1581308]), 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)), 41745 ^ [_1581306, _1581308]))))], (7222 ^ _778908) ^ [_899788, _899790] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899788), _899790) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899790), _899788))], (18027 ^ _778908) ^ [_1090572] : [-(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, _1090572))))))], (9134 ^ _778908) ^ [_931914, _931916] : [class_Groups_Ogroup__add(_931914), -(hAPP(c_Groups_Ouminus__class_Ouminus(_931914), hAPP(c_Groups_Ouminus__class_Ouminus(_931914), _931916)) = _931916)], (27130 ^ _778908) ^ [_1258114, _1258116, _1258118] : [class_Fields_Ofield(_1258114), -(_1258116 = c_Groups_Oone__class_Oone(_1258114)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1258114), hAPP(c_Power_Opower__class_Opower(_1258114), _1258116)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258118)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1258114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1258114), hAPP(hAPP(c_Power_Opower__class_Opower(_1258114), _1258116), _1258118)), c_Groups_Oone__class_Oone(_1258114))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1258114), _1258116), c_Groups_Oone__class_Oone(_1258114))))], (33041 ^ _778908) ^ [_1381264, _1381266, _1381268, _1381270] : [c_Hoare__Mirabelle_Ohoare__derivs(_1381264, _1381266, _1381268), c_Hoare__Mirabelle_Ohoare__derivs(_1381264, _1381270, _1381266), -(c_Hoare__Mirabelle_Ohoare__derivs(_1381264, _1381270, _1381268))], (45354 ^ _778908) ^ [_1670791, _1670793, _1670795] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1670791, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1670791, tc_HOL_Obool), tc_HOL_Obool)), _1670793), _1670795)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670791, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1670791, tc_HOL_Obool), _1670793)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1670791, tc_HOL_Obool), _1670795)))], (5116 ^ _778908) ^ [_858036, _858038, _858040, _858042] : [-(c_List_Oupto(_858042, _858038) = c_List_Oupto(_858040, _858036)), _858042 = _858040, _858038 = _858036], (24061 ^ _778908) ^ [_1198802, _1198804, _1198806, _1198808, _1198810] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198802, _1198804, _1198806), _1198808), _1198810) = hAPP(hAPP(_1198808, hAPP(c_Product__Type_Ofst(_1198802, _1198804), _1198810)), hAPP(c_Product__Type_Osnd(_1198802, _1198804), _1198810)))], (42774 ^ _778908) ^ [_1607879, _1607881, _1607883, _1607885] : [-(c_Hilbert__Choice_OEps(tc_prod(_1607879, _1607881), hAPP(c_Product__Type_Oprod_Oprod__case(_1607879, _1607881, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1607879, tc_fun(_1607881, tc_HOL_Obool), tc_fun(_1607881, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1607881, tc_HOL_Obool), tc_fun(_1607881, tc_HOL_Obool)), _1607879), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1607881)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1607879), c_fconj), hAPP(c_fequal, _1607883)))), hAPP(c_fequal, _1607885)))) = hAPP(hAPP(c_Product__Type_OPair(_1607879, _1607881), _1607883), _1607885))], (16667 ^ _778908) ^ [_1065458, _1065460, _1065462, _1065464] : [class_Rings_Ocomm__semiring__1(_1065458), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1065458), hAPP(hAPP(c_Power_Opower__class_Opower(_1065458), _1065460), _1065462)), _1065464) = hAPP(hAPP(c_Power_Opower__class_Opower(_1065458), _1065460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065462), _1065464)))], (7697 ^ _778908) ^ [_907539, _907541, _907543, _907545] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_907539), 7700 ^ _778908 : [(7707 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907539), _907541), _907545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907539), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907539), _907541), _907543)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907539), _907545), _907543))))], (7701 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907539), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907539), _907541), _907543)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907539), _907545), _907543))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907539), _907541), _907545)))]]], (44270 ^ _778908) ^ [_1644433, _1644435, _1644437] : [class_Orderings_Olinorder(_1644433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644433), _1644435)), -(c_Big__Operators_Olattice_OInf__fin(_1644433, c_Orderings_Oord__class_Omin(_1644433), hAPP(hAPP(c_Set_Oinsert(_1644433), _1644437), _1644435)) = hAPP(hAPP(c_Finite__Set_Ofold(_1644433, _1644433, c_Orderings_Oord__class_Omin(_1644433)), _1644437), _1644435))], (14547 ^ _778908) ^ [_1025875, _1025877] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1025875), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1025877)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1025875)), _1025877))], (51269 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (12015 ^ _778908) ^ [_980377, _980379, _980381, _980383] : [class_Rings_Oordered__ring(_980377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980377), _980379), _980381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980377), _980383), c_Groups_Ozero__class_Ozero(_980377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980377), _980383), _980381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980377), _980383), _980379))))], (5326 ^ _778908) ^ [_861253, _861255] : [_861255 = _861253, -(c_List_Omonoid__add__class_Olistsum(_861255) = c_List_Omonoid__add__class_Olistsum(_861253))], (28053 ^ _778908) ^ [_1276249, _1276251, _1276253, _1276255] : [hBOOL(hAPP(_1276249, _1276251)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276253, tc_HOL_Obool)), _1276255), _1276249), _1276251)))], (25055 ^ _778908) ^ [_1218745, _1218747, _1218749, _1218751, _1218753, _1218755] : [hBOOL(hAPP(hAPP(_1218745, _1218747), _1218749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218751, tc_fun(_1218753, tc_HOL_Obool))), _1218745), _1218755)), -(hBOOL(hAPP(hAPP(_1218755, _1218747), _1218749)))], (22352 ^ _778908) ^ [_1166054, _1166056] : [_1166054 = _1166056, -(c_Code__Numeral_OSuc__code__numeral(_1166054) = c_Code__Numeral_OSuc__code__numeral(_1166056))], (6001 ^ _778908) ^ [_874820, _874822, _874824, _874826, _874828, _874830, _874832, _874834, _874836, _874838, _874840, _874842] : [-(c_Com_Ocom_Ocom__rec(_874820, _874822, _874824, _874826, _874828, _874830, _874832, _874834, _874836, c_Com_Ocom_OCall(_874838, _874840, _874842)) = hAPP(hAPP(hAPP(_874836, _874838), _874840), _874842))], (13590 ^ _778908) ^ [_1008100, _1008102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008100), _1008102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008102), _1008100)), -(_1008100 = _1008102)], (12489 ^ _778908) ^ [_988894, _988896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988894)), _988896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988894), _988896)))], (43167 ^ _778908) ^ [_1617777, _1617779] : [-(c_Transitive__Closure_Otrancl(_1617777, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1617777, _1617777), tc_HOL_Obool)), _1617779), c_Relation_OId(_1617777))) = c_Transitive__Closure_Ortrancl(_1617777, _1617779))], (45462 ^ _778908) ^ [_1673079, _1673081] : [class_Complete__Lattice_Ocomplete__lattice(_1673079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1673079), _1673081)), -(_1673081 = c_Orderings_Obot__class_Obot(tc_fun(_1673079, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1673079, _1673081) = c_Complete__Lattice_OInf__class_OInf(_1673079, _1673081))], (18867 ^ _778908) ^ [_1104019, _1104021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1104019)), c_Int_OBit1(_1104021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104019), _1104021)))], (11480 ^ _778908) ^ [_971025, _971027] : [11481 ^ _778908 : [(11484 ^ _778908) ^ [] : [_971025 = hAPP(c_Nat_OSuc, _971027)], (11482 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971025), _971027))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971025), hAPP(c_Nat_OSuc, _971027))))], (15836 ^ _778908) ^ [_1049138, _1049140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049138), _1049140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049138), _1049140)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6095 ^ _778908) ^ [_876517, _876519, _876521, _876523, _876525, _876527, _876529, _876531, _876533, _876535, _876537, _876539] : [-(c_Com_Ocom_Ocom__case(_876517, _876519, _876521, _876523, _876525, _876527, _876529, _876531, _876533, c_Com_Ocom_OCond(_876535, _876537, _876539)) = hAPP(hAPP(hAPP(_876527, _876535), _876537), _876539))], (42451 ^ _778908) ^ [_1600213, _1600215, _1600217] : [c_Wellfounded_Oacyclic(_1600213, _1600215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600213, _1600213), tc_HOL_Obool)), _1600217), _1600215)), -(c_Wellfounded_Oacyclic(_1600213, _1600217))], (37961 ^ _778908) ^ [_1489828, _1489830, _1489832, _1489834, _1489836, _1489838] : [hBOOL(hAPP(hAPP(_1489828, _1489830), _1489832)), hBOOL(hAPP(hAPP(_1489834, _1489830), _1489832)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489836, tc_fun(_1489838, tc_HOL_Obool))), _1489828), _1489834), _1489830), _1489832)))], (4002 ^ _778908) ^ [_840643, _840645, _840647, _840649, _840651, _840653] : [-(c_Predicate_ORangeP(_840653, _840649, _840645) = c_Predicate_ORangeP(_840651, _840647, _840643)), _840653 = _840651, _840649 = _840647, _840645 = _840643], (13943 ^ _778908) ^ [_1014541, _1014543, _1014545] : [class_Divides_Osemiring__div(_1014541), -(c_Divides_Odiv__class_Omod(_1014541, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014541), _1014543), _1014545), _1014545) = c_Divides_Odiv__class_Omod(_1014541, _1014543, _1014545))], (11154 ^ _778908) ^ [_965485, _965487, _965489] : [class_Orderings_Oorder(_965485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965485), _965487), _965489)), -(_965489 = _965487), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965485), _965487), _965489)))], (42657 ^ _778908) ^ [_1605322, _1605324, _1605326, _1605328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1605322), _1605324)), 42663 ^ _778908 : [(42666 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1605326), hAPP(_1605328, 42662 ^ [_1605322, _1605324, _1605326, _1605328])))], (42664 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605322), 42662 ^ [_1605322, _1605324, _1605326, _1605328]), _1605324)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1605326), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1605322, tc_fun(_1605326, tc_HOL_Obool)), _1605324), _1605328))))], (26131 ^ _778908) ^ [_1238847, _1238849, _1238851, _1238853] : [class_Groups_Oordered__ab__group__add__abs(_1238847), -(hAPP(c_Groups_Oabs__class_Oabs(_1238847), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238849, _1238847), hAPP(hAPP(c_COMBB(_1238847, _1238847, _1238849), c_Groups_Oabs__class_Oabs(_1238847)), _1238851)), _1238853)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238849, _1238847), hAPP(hAPP(c_COMBB(_1238847, _1238847, _1238849), c_Groups_Oabs__class_Oabs(_1238847)), _1238851)), _1238853))], (36648 ^ _778908) ^ [_1459153, _1459155, _1459157, _1459159] : [class_Lattices_Odistrib__lattice(_1459153), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1459153), _1459155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459153), _1459157), _1459159)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459153), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1459153), _1459155), _1459157)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1459153), _1459155), _1459159)))], (47715 ^ _778908) ^ [_1728957, _1728959, _1728961] : [-(_1728957 = _1728959), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728961)), _1728957) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728961)), _1728959), 47721 ^ _778908 : [(47724 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Onth(_1728961), _1728957), 47720 ^ [_1728957, _1728959, _1728961]) = hAPP(hAPP(c_List_Onth(_1728961), _1728959), 47720 ^ [_1728957, _1728959, _1728961])], (47722 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47720 ^ [_1728957, _1728959, _1728961]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728961)), _1728957))))]]], (34158 ^ _778908) ^ [_1402819, _1402821, _1402823] : [class_Orderings_Olinorder(_1402819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402819), _1402821)), -(hBOOL(hAPP(hAPP(c_member(_1402819), _1402823), _1402821))), -(_1402821 = c_Orderings_Obot__class_Obot(tc_fun(_1402819, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1402819, c_Orderings_Oord__class_Omax(_1402819), hAPP(hAPP(c_Set_Oinsert(_1402819), _1402823), _1402821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1402819), _1402823), c_Big__Operators_Olattice_OSup__fin(_1402819, c_Orderings_Oord__class_Omax(_1402819), _1402821)))], (15114 ^ _778908) ^ [_1035541, _1035543, _1035545] : [hBOOL(hAPP(_1035541, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1035543), _1035545))), 15117 ^ _778908 : [(15124 ^ _778908) ^ [] : [-(_1035545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15127 ^ _778908 : [(15128 ^ _778908) ^ [_1035793, _1035795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035793), _1035545)), _1035543 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035545), _1035795)), _1035793), -(hBOOL(hAPP(_1035541, _1035795)))]]], (15118 ^ _778908) ^ [] : [_1035545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1035541, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (3512 ^ _778908) ^ [_832916, _832918, _832920, _832922, _832924, _832926] : [-(c_Com_Ocom_OCond(_832926, _832922, _832918) = c_Com_Ocom_OCond(_832924, _832920, _832916)), _832926 = _832924, _832922 = _832920, _832918 = _832916], (51375 ^ _778908) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (13052 ^ _778908) ^ [_999022, _999024, _999026] : [class_Rings_Olinordered__idom(_999022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999022), c_Groups_Ozero__class_Ozero(_999022)), _999024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999022), c_Groups_Ozero__class_Ozero(_999022)), _999026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999022), _999026), c_Groups_Oone__class_Oone(_999022))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999022), _999024), _999026)), _999024)))], (28059 ^ _778908) ^ [_1276360, _1276362, _1276364, _1276366] : [hBOOL(hAPP(_1276360, _1276362)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276364, tc_HOL_Obool)), _1276360), _1276366), _1276362)))], (8954 ^ _778908) ^ [_928466, _928468, _928470] : [class_Rings_Oring(_928466), -(hAPP(c_Groups_Ouminus__class_Ouminus(_928466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928466), _928468), _928470)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928466), _928468), hAPP(c_Groups_Ouminus__class_Ouminus(_928466), _928470)))], (6027 ^ _778908) ^ [_875375, _875377] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_875375, _875377))), 6030 ^ _778908 : [(6033 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _875377)))], (6031 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _875375)))]]], (14617 ^ _778908) ^ [_1027020, _1027022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027022)), -(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), _1027020), _1027022))))], (16807 ^ _778908) ^ [_1067762, _1067764, _1067766] : [class_Groups_Oordered__ab__group__add__abs(_1067762), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067762), hAPP(c_Groups_Oabs__class_Oabs(_1067762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067762), _1067764), _1067766))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067762), hAPP(c_Groups_Oabs__class_Oabs(_1067762), _1067764)), hAPP(c_Groups_Oabs__class_Oabs(_1067762), _1067766)))))], (22796 ^ _778908) ^ [_1174497, _1174499] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174497), _1174499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1174497)), _1174499)))], (40150 ^ _778908) ^ [_1538332, _1538334, _1538336] : [c_Equiv__Relations_Oequiv(_1538332, _1538334, _1538336), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538332, _1538332), tc_HOL_Obool)), _1538336), hAPP(hAPP(c_Product__Type_OSigma(_1538332, _1538332), _1538334), hAPP(c_COMBK(tc_fun(_1538332, tc_HOL_Obool), _1538332), _1538334)))))], (14146 ^ _778908) ^ [_1018339, _1018341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018339)), 14149 ^ _778908 : [(14152 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018341, _1018339)), _1018339)))], (14150 ^ _778908) ^ [] : [-(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, _1018341, _1018339))))]]], (45428 ^ _778908) ^ [_1672537, _1672539, _1672541] : [class_Complete__Lattice_Ocomplete__lattice(_1672537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1672537), _1672539)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1672537), _1672541), c_Complete__Lattice_OSup__class_OSup(_1672537, _1672539)) = hAPP(hAPP(c_Finite__Set_Ofold(_1672537, _1672537, c_Lattices_Osemilattice__sup__class_Osup(_1672537)), _1672541), _1672539))], (276 ^ _778908) ^ [_782976, _782978] : [-(class_Fields_Ofield__inverse__zero(_782976)), _782978 = _782976, class_Fields_Ofield__inverse__zero(_782978)], (30684 ^ _778908) ^ [_1328761, _1328763] : [class_Orderings_Olinorder(_1328761), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328761, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1328761), _1328763), c_Orderings_Obot__class_Obot(tc_fun(_1328761, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1328761), _1328763)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1328761), _1328763))], (36898 ^ _778908) ^ [_1464527, _1464529, _1464531, _1464533, _1464535] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464527, tc_HOL_Obool)), _1464529), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464531, tc_fun(_1464527, tc_HOL_Obool)), _1464533), _1464535)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464531, tc_fun(_1464527, tc_HOL_Obool)), _1464533), hAPP(hAPP(c_COMBB(tc_fun(_1464527, tc_HOL_Obool), tc_fun(_1464527, tc_HOL_Obool), _1464531), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464527, tc_HOL_Obool)), _1464529)), _1464535)))], (27765 ^ _778908) ^ [_1271171, _1271173] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1271171, _1271173)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1271171), hAPP(c_Nat_OSuc, _1271173)))], (24825 ^ _778908) ^ [_1213892, _1213894, _1213896, _1213898] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1213892, _1213894, _1213896, _1213898) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1213892, _1213894), _1213896), _1213898)))], (22426 ^ _778908) ^ [_1167269, _1167271] : [_1167269 = _1167271, -(hAPP(c_Code__Numeral_Oof__nat, _1167269) = hAPP(c_Code__Numeral_Oof__nat, _1167271))], (1662 ^ _778908) ^ [_802557, _802559] : [-(class_Rings_Ozero__neq__one(_802557)), _802559 = _802557, class_Rings_Ozero__neq__one(_802559)], (236 ^ _778908) ^ [_782306, _782308, _782310, _782312, _782314, _782316, _782318, _782320, _782322, _782324, _782326, _782328] : [-(c_Nitpick_Ofold__graph_H(_782326, _782322, _782318, _782314, _782310, _782306)), c_Nitpick_Ofold__graph_H(_782328, _782324, _782320, _782316, _782312, _782308), _782328 = _782326, _782324 = _782322, _782320 = _782318, _782316 = _782314, _782312 = _782310, _782308 = _782306], (23989 ^ _778908) ^ [_1197284, _1197286, _1197288, _1197290] : [-(hAPP(c_Product__Type_Ofst(_1197284, _1197286), hAPP(hAPP(c_Product__Type_OPair(_1197284, _1197286), _1197288), _1197290)) = _1197288)], (27901 ^ _778908) ^ [_1273552] : [c_Nat__Transfer_Onat__set(_1273552), 27904 ^ _778908 : [(27905 ^ _778908) ^ [_1273618] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1273618), _1273552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1273618)))]]], (19087 ^ _778908) ^ [_1107631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107631)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107631), c_Int_OPls)))], (41257 ^ _778908) ^ [_1563055, _1563057, _1563059] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1563055, tc_HOL_Obool)), _1563057), _1563059) = hAPP(c_Set_OCollect(_1563055), hAPP(hAPP(c_COMBS(_1563055, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563055), c_fdisj), hAPP(hAPP(c_COMBC(_1563055, tc_fun(_1563055, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563055)), _1563057))), hAPP(hAPP(c_COMBC(_1563055, tc_fun(_1563055, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563055)), _1563059))))], (25963 ^ _778908) ^ [_1234952, _1234954] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234952), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234954))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234952), _1234954)))], (48709 ^ _778908) ^ [_1753215, _1753217, _1753219, _1753221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753215), tc_List_Olist(_1753215))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753215), tc_List_Olist(_1753215)), _1753217), _1753219)), c_List_Olistrel1(_1753215, _1753221))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753215)), _1753217) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753215)), _1753219))], (18913 ^ _778908) ^ [_1104828] : [_1104828 = c_Int_OMin, -(c_Int_OBit1(_1104828) = c_Int_OMin)], (37290 ^ _778908) ^ [_1473843, _1473845, _1473847, _1473849, _1473851] : [class_Groups_Ocomm__monoid__mult(_1473843), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473845), _1473847)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473845), _1473849)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1473843), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473845, _1473843), _1473851), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473845, tc_HOL_Obool)), _1473847), _1473849))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473845, _1473843), _1473851), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473845, tc_HOL_Obool)), _1473847), _1473849))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1473843), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473845, _1473843), _1473851), _1473847)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473845, _1473843), _1473851), _1473849)))], (18519 ^ _778908) ^ [_1098366] : [class_Int_Onumber__ring(_1098366), -(c_Groups_Ozero__class_Ozero(_1098366) = hAPP(c_Int_Onumber__class_Onumber__of(_1098366), c_Int_OPls))], (16008 ^ _778908) ^ [_1052299, _1052301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052299), _1052301)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052301), _1052299)) = _1052301)], (27260 ^ _778908) ^ [_1260449] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260449) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1260449))], (36642 ^ _778908) ^ [_1458994, _1458996, _1458998, _1459000] : [class_Lattices_Odistrib__lattice(_1458994), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1458994), _1458996), _1458998)), _1459000) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1458994), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458994), _1458996), _1459000)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458994), _1458998), _1459000)))], (46809 ^ _778908) ^ [_1705379, _1705381, _1705383] : [_1705379 = _1705381, 46812 ^ _778908 : [(46815 ^ _778908) ^ [_1705535] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1705383, _1705383)), _1705535), hAPP(c_List_Oset(tc_prod(_1705383, _1705383)), hAPP(hAPP(c_List_Ozip(_1705383, _1705383), _1705379), _1705381)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1705383, _1705383, tc_HOL_Obool), c_fequal), _1705535)))], (46813 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705383)), _1705379) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705383)), _1705381))]]], (49189 ^ _778908) ^ [_1765347, _1765349, _1765351, _1765353, _1765355] : [-(hAPP(c_List_Orotate(_1765347, _1765349), hAPP(hAPP(c_List_Omap(_1765351, _1765347), _1765353), _1765355)) = hAPP(hAPP(c_List_Omap(_1765351, _1765347), _1765353), hAPP(c_List_Orotate(_1765351, _1765349), _1765355)))], (31514 ^ _778908) ^ [_1347558, _1347560, _1347562, _1347564, _1347566, _1347568] : [c_Finite__Set_Ofolding__image__simple(_1347558, _1347560, _1347562, _1347564, _1347566, _1347568), -(hAPP(_1347568, c_Orderings_Obot__class_Obot(tc_fun(_1347560, tc_HOL_Obool))) = _1347564)], (5106 ^ _778908) ^ [_857887, _857889, _857891, _857893] : [-(c_List_Obutlast(_857893, _857889) = c_List_Obutlast(_857891, _857887)), _857893 = _857891, _857889 = _857887], (12766 ^ _778908) ^ [_993582, _993584, _993586] : [class_Groups_Oordered__comm__monoid__add(_993582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993582), c_Groups_Ozero__class_Ozero(_993582)), _993584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993582), c_Groups_Ozero__class_Ozero(_993582)), _993586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993582), c_Groups_Ozero__class_Ozero(_993582)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_993582), _993584), _993586))))], (17497 ^ _778908) ^ [_1081106, _1081108] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1081106) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081108)), _1081106 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081108)), 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), _1081108)))], (14360 ^ _778908) ^ [_1022126, _1022128, _1022130, _1022132] : [_1022126 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022128), _1022130)), _1022132), -(_1022128 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022126), _1022128) = _1022130), 14367 ^ _778908 : [(14370 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022132), _1022128))], (14368 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022128)))]], 14375 ^ _778908 : [(14378 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022128), _1022132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022132), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14376 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022128))]]], (30586 ^ _778908) ^ [_1326912, _1326914] : [hAPP(c_Finite__Set_Ocard(_1326912), _1326914) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1326914 = c_Orderings_Obot__class_Obot(tc_fun(_1326912, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326912), _1326914))], (18055 ^ _778908) ^ [_1091006, _1091008] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091006) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091008)), 18058 ^ _778908 : [(18061 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091008)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18059 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091006))))]], 18062 ^ _778908 : [(18065 ^ _778908) ^ [] : [18066 ^ _778908 : [(18069 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091006) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (18067 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091008))))]], 18070 ^ _778908 : [(18073 ^ _778908) ^ [] : [_1091006 = _1091008], (18071 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091008)))]]], (18063 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091006)))]]], (6839 ^ _778908) ^ [_891299, _891301] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_891299, _891301))), -(hBOOL(hAPP(c_Com_OWT, _891301)))], (7869 ^ _778908) ^ [_910390, _910392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910390), _910392))), 7872 ^ _778908 : [(7879 ^ _778908) ^ [] : [_910390 = _910392, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910390), hAPP(c_Nat_OSuc, _910392))))], (7873 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910390), hAPP(c_Nat_OSuc, _910392))), -(_910390 = _910392)]]], (49185 ^ _778908) ^ [_1765250, _1765252, _1765254] : [-(hAPP(c_List_Otl(_1765250), hAPP(hAPP(c_List_Olist_OCons(_1765250), _1765252), _1765254)) = _1765254)], (46469 ^ _778908) ^ [_1696586, _1696588] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1696586, _1696588) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1696586), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1696588)))], (31658 ^ _778908) ^ [_1350412, _1350414, _1350416] : [class_Orderings_Oord(_1350412), 31661 ^ _778908 : [(31668 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350412), _1350414), _1350416)), -(hBOOL(hAPP(hAPP(c_member(_1350412), _1350414), hAPP(c_SetInterval_Oord__class_OatMost(_1350412), _1350416))))], (31662 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1350412), _1350414), hAPP(c_SetInterval_Oord__class_OatMost(_1350412), _1350416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350412), _1350414), _1350416)))]]], (5018 ^ _778908) ^ [_856511, _856513, _856515, _856517, _856519, _856521, _856523, _856525] : [-(c_Option_Ooption_Ooption__case(_856525, _856521, _856517, _856513) = c_Option_Ooption_Ooption__case(_856523, _856519, _856515, _856511)), _856525 = _856523, _856521 = _856519, _856517 = _856515, _856513 = _856511], (49205 ^ _778908) ^ [_1765675, _1765677, _1765679] : [hBOOL(hAPP(c_List_Odistinct(_1765675), _1765679)), -(hBOOL(hAPP(c_List_Odistinct(_1765675), hAPP(c_List_Orotate(_1765675, _1765677), _1765679))))], (7394 ^ _778908) ^ [_902427] : [_902427 = hAPP(c_Nat_OSuc, _902427)], (19765 ^ _778908) ^ [_1119365, _1119367] : [class_Rings_Olinordered__idom(_1119365), -(hAPP(c_Groups_Oabs__class_Oabs(_1119365), hAPP(hAPP(c_Power_Opower__class_Opower(_1119365), _1119367), 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(_1119365), _1119367), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (41792 ^ _778908) ^ [_1583178, _1583180, _1583182, _1583184] : [hAPP(hAPP(c_Relation_Orel__comp(_1583178, _1583178, _1583178), _1583180), _1583182) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583178, _1583178), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1583178, _1583178, _1583178), _1583180), _1583184) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583178, _1583178), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1583178, _1583178, _1583178), _1583180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583178, _1583178), tc_HOL_Obool)), _1583182), _1583184)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583178, _1583178), tc_HOL_Obool)))], (23301 ^ _778908) ^ [_1184749, _1184751] : [-(_1184749 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1184751, _1184749) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184751), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184749)))], (48835 ^ _778908) ^ [_1757078, _1757080, _1757082, _1757084] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757078), tc_List_Olist(_1757078))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757078), tc_List_Olist(_1757078)), _1757080), _1757082)), c_List_Olistrel1(_1757078, _1757084))), 48840 ^ _778908 : [(48845 ^ _778908) ^ [] : [-(_1757082 = hAPP(hAPP(c_List_Olist__update(_1757078, _1757080), 48839 ^ [_1757078, _1757080, _1757082, _1757084]), 48838 ^ [_1757078, _1757080, _1757082, _1757084]))], (48843 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48839 ^ [_1757078, _1757080, _1757082, _1757084]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757078)), _1757080))))], (48841 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757078, _1757078)), hAPP(hAPP(c_Product__Type_OPair(_1757078, _1757078), hAPP(hAPP(c_List_Onth(_1757078), _1757080), 48839 ^ [_1757078, _1757080, _1757082, _1757084])), 48838 ^ [_1757078, _1757080, _1757082, _1757084])), _1757084)))]]], (17403 ^ _778908) ^ [_1079602, _1079604] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079602)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079604)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1079602), _1079604)))], (39783 ^ _778908) ^ [_1528703, _1528705, _1528707, _1528709, _1528711] : [_1528703 = c_Option_Ooption_ONone(_1528705), -(c_Map_Odom(_1528707, _1528705, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1528707, tc_Option_Ooption(_1528705)), _1528709), _1528711), _1528703)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1528707, tc_HOL_Obool)), c_Map_Odom(_1528707, _1528705, _1528709)), hAPP(hAPP(c_Set_Oinsert(_1528707), _1528711), c_Orderings_Obot__class_Obot(tc_fun(_1528707, tc_HOL_Obool)))))], (7380 ^ _778908) ^ [_902207, _902209] : [hAPP(c_Nat_OSuc, _902207) = hAPP(c_Nat_OSuc, _902209), -(_902207 = _902209)], (14178 ^ _778908) ^ [_1018876, _1018878] : [class_Lattices_Oboolean__algebra(_1018876), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1018876), hAPP(c_Groups_Ouminus__class_Ouminus(_1018876), _1018878)) = _1018878)], (45976 ^ _778908) ^ [_1684908, _1684910, _1684912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1684908), _1684910)), -(c_Smallcheck_Osmall_H(_1684912, _1684908, _1684910) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (37034 ^ _778908) ^ [_1468063, _1468065, _1468067, _1468069, _1468071] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468063, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1468065, _1468063, _1468067), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468065, tc_HOL_Obool)), _1468069), _1468071))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468063, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1468065, _1468063, _1468067), _1468069)), hAPP(c_Relation_OImage(_1468065, _1468063, _1468067), _1468071)))))], (31361 ^ _778908) ^ [_1344697, _1344699, _1344701] : [-(hBOOL(hAPP(hAPP(c_member(_1344697), _1344699), _1344701))), -(hBOOL(hAPP(hAPP(c_member(_1344697), _1344699), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1344697, tc_HOL_Obool)), _1344701))))], (33327 ^ _778908) ^ [_1386942, _1386944, _1386946, _1386948, _1386950, _1386952] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_1386942, _1386944, _1386946, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1386942), _1386948), _1386950), _1386952)) = hAPP(hAPP(hAPP(_1386946, _1386948), _1386950), _1386952))], (42318 ^ _778908) ^ [_1596460, _1596462, _1596464] : [c_Wellfounded_OwfP(_1596460, _1596462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1596460, tc_fun(_1596460, tc_HOL_Obool))), _1596464), _1596462)), -(c_Wellfounded_OwfP(_1596460, _1596464))], (47294 ^ _778908) ^ [_1719578, _1719580, _1719582, _1719584] : [class_Groups_Ocomm__monoid__add(_1719578), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1719578), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1719578), _1719580), c_List_Oupto(_1719582, _1719584))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1719578), _1719580), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1719582, _1719584))))], (51631 ^ _778908) ^ [_1813170, _1813172, _1813174, _1813176, _1813178, _1813180] : [-(hAPP(hAPP(hAPP(c_COMBB(_1813170, _1813172, _1813174), _1813176), _1813178), _1813180) = hAPP(_1813176, hAPP(_1813178, _1813180)))], (40543 ^ _778908) ^ [_1549191, _1549193, _1549195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549191, _1549191), tc_HOL_Obool)), _1549193), hAPP(hAPP(c_Product__Type_OSigma(_1549191, _1549191), _1549195), hAPP(c_COMBK(tc_fun(_1549191, tc_HOL_Obool), _1549191), _1549195)))), 40549 ^ _778908 : [(40552 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549191, _1549191)), hAPP(hAPP(c_Product__Type_OPair(_1549191, _1549191), 40548 ^ [_1549191, _1549193, _1549195]), 40548 ^ [_1549191, _1549193, _1549195])), _1549193))], (40550 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549191), 40548 ^ [_1549191, _1549193, _1549195]), _1549195)))]], -(c_Relation_Orefl__on(_1549191, _1549195, _1549193))], (26669 ^ _778908) ^ [_1248807, _1248809, _1248811, _1248813] : [class_Rings_Ocomm__ring(_1248807), class_Rings_Odvd(_1248807), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248807), _1248809), _1248811)), 26680 ^ _778908 : [(26687 ^ _778908) ^ [_1249233, _1249235] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248807), _1248809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248807), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1248807), _1249235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248807), _1249233), _1248811))), _1248813))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248807), _1248809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248807), _1249235), _1248813))))], (26681 ^ _778908) ^ [_1249060, _1249062] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248807), _1248809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248807), _1249062), _1248813))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248807), _1248809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248807), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1248807), _1249062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248807), _1249060), _1248811))), _1248813))))]]], (18211 ^ _778908) ^ [_1093694, _1093696, _1093698] : [18213 ^ _778908 : [(18216 ^ _778908) ^ [] : [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(_1093696, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18212 ^ [_1093694, _1093696, _1093698]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1093696, 18212 ^ [_1093694, _1093696, _1093698])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18214 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18212 ^ [_1093694, _1093696, _1093698]), _1093694)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1093696, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1093698), hAPP(_1093696, _1093694))), 18226 ^ _778908 : [(18229 ^ _778908) ^ [] : [-(hAPP(_1093696, 18225 ^ [_1093694, _1093696, _1093698]) = _1093698)], (18227 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18225 ^ [_1093694, _1093696, _1093698]), _1093694)))]]], (6107 ^ _778908) ^ [_876762, _876764, _876766, _876768, _876770] : [hBOOL(hAPP(_876762, _876764)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_876766), _876764), _876768)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_876762, _876766, _876770)), _876764), _876768)))], (36798 ^ _778908) ^ [_1462372, _1462374, _1462376] : [class_Lattices_Olattice(_1462372), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462372), _1462374), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462372), _1462374), _1462376)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462372), _1462374), _1462376))], (24051 ^ _778908) ^ [_1198522, _1198524, _1198526] : [-(_1198522 = hAPP(hAPP(c_Product__Type_OPair(_1198524, _1198526), hAPP(c_Product__Type_Ofst(_1198524, _1198526), _1198522)), hAPP(c_Product__Type_Osnd(_1198524, _1198526), _1198522)))], (19233 ^ _778908) ^ [_1109924, _1109926] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1109924))), _1109926) = 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)))), _1109924), _1109926))], (30656 ^ _778908) ^ [_1328268, _1328270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1328268), _1328270)))), -(_1328270 = c_Orderings_Obot__class_Obot(tc_fun(_1328268, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328268), _1328270))], (17827 ^ _778908) ^ [_1087165, _1087167, _1087169, _1087171] : [class_Rings_Olinordered__semidom(_1087165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087165), c_Groups_Oone__class_Oone(_1087165)), _1087167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087165), hAPP(hAPP(c_Power_Opower__class_Opower(_1087165), _1087167), _1087169)), hAPP(hAPP(c_Power_Opower__class_Opower(_1087165), _1087167), _1087171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1087169), _1087171)))], (44154 ^ _778908) ^ [_1642237, _1642239, _1642241, _1642243, _1642245] : [c_Finite__Set_Ofolding__one__idem(_1642237, _1642239, _1642241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642237), _1642243)), -(hAPP(_1642241, hAPP(hAPP(c_Set_Oinsert(_1642237), _1642245), _1642243)) = hAPP(hAPP(c_Finite__Set_Ofold(_1642237, _1642237, _1642239), _1642245), _1642243))], (34678 ^ _778908) ^ [_1413707, _1413709, _1413711, _1413713] : [class_Groups_Ocomm__monoid__mult(_1413707), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413709), _1413711)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413709, _1413707), hAPP(c_COMBK(_1413707, _1413709), _1413713)), _1413711) = hAPP(hAPP(c_Power_Opower__class_Opower(_1413707), _1413713), hAPP(c_Finite__Set_Ocard(_1413709), _1413711)))], (4698 ^ _778908) ^ [_851647, _851649, _851651, _851653] : [-(c_Finite__Set_Ofold1(_851653, _851649) = c_Finite__Set_Ofold1(_851651, _851647)), _851653 = _851651, _851649 = _851647], (24303 ^ _778908) ^ [_1203711, _1203713, _1203715, _1203717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1203711, tc_HOL_Obool)), _1203713), _1203715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1203711, tc_HOL_Obool)), _1203715), _1203717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1203711, tc_HOL_Obool)), _1203713), _1203717)))], (47515 ^ _778908) ^ [_1723883, _1723885] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1723883), tc_List_Olist(_1723883))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1723883), tc_List_Olist(_1723883)), c_List_Olist_ONil(_1723883)), c_List_Olist_ONil(_1723883))), c_List_Olistrel(_1723883, _1723885))))], (24485 ^ _778908) ^ [_1207231, _1207233, _1207235, _1207237] : [class_Orderings_Olinorder(_1207231), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207231), _1207233), _1207235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207231), _1207233), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207231), _1207237), _1207235))))], (39046 ^ _778908) ^ [_1511764] : [-(c_Fun_Oinj__on(_1511764, tc_fun(_1511764, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1511764, tc_fun(_1511764, tc_HOL_Obool), tc_fun(_1511764, tc_HOL_Obool)), c_Set_Oinsert(_1511764)), c_Orderings_Obot__class_Obot(tc_fun(_1511764, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1511764, tc_HOL_Obool))))], (46691 ^ _778908) ^ [_1702139, _1702141, _1702143, _1702145, _1702147, _1702149, _1702151] : [hAPP(hAPP(c_List_Omap(_1702139, _1702141), _1702143), _1702145) = hAPP(hAPP(c_List_Omap(_1702147, _1702141), _1702149), _1702151), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702139)), _1702145) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702147)), _1702151))], (51651 ^ _778908) ^ [] : [-(hBOOL(c_fTrue))], (49746 ^ _778908) ^ [_1777525, _1777527, _1777529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1777525), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777527)), _1777529))), -(c_List_Obutlast(_1777527, hAPP(hAPP(c_List_Otake(_1777527), _1777525), _1777529)) = hAPP(hAPP(c_List_Otake(_1777527), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1777525), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1777529))], (48550 ^ _778908) ^ [_1748981, _1748983, _1748985, _1748987, _1748989, _1748991, _1748993] : [-(hBOOL(hAPP(hAPP(c_member(_1748981), _1748983), hAPP(c_List_Oset(_1748981), hAPP(hAPP(c_List_Otake(_1748981), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748985)), _1748987)), _1748989))))), -(c_Map_Omap__upds(_1748981, _1748985, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1748981, tc_Option_Ooption(_1748985)), _1748991), _1748983), hAPP(c_Option_Ooption_OSome(_1748985), _1748993)), _1748989, _1748987) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1748981, tc_Option_Ooption(_1748985)), c_Map_Omap__upds(_1748981, _1748985, _1748991, _1748989, _1748987)), _1748983), hAPP(c_Option_Ooption_OSome(_1748985), _1748993)))], (32569 ^ _778908) ^ [_1371347, _1371349, _1371351, _1371353] : [hBOOL(hAPP(hAPP(c_member(_1371347), _1371349), c_SetInterval_Oord_OatMost(_1371347, _1371351, _1371353))), -(hBOOL(hAPP(hAPP(_1371351, _1371349), _1371353)))], (37020 ^ _778908) ^ [_1467700, _1467702, _1467704, _1467706] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467700, tc_HOL_Obool)), _1467702), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467700, tc_HOL_Obool)), _1467704), _1467706)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467700, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467700, tc_HOL_Obool)), _1467702), _1467704)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467700, tc_HOL_Obool)), _1467702), _1467706)))], (17489 ^ _778908) ^ [_1080973, _1080975] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1080973) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080975), 17492 ^ _778908 : [(17495 ^ _778908) ^ [] : [-(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), _1080975))))], (17493 ^ _778908) ^ [] : [-(_1080973 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080975)))]]], (6887 ^ _778908) ^ [_892437, _892439, _892441] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _892437))), _892439), _892441)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _892437)), _892439), _892441)))], (46420 ^ _778908) ^ [_1695457, _1695459, _1695461, _1695463, _1695465] : [hBOOL(hAPP(c_List_Odistinct(_1695457), hAPP(hAPP(c_List_Omap(tc_prod(_1695457, _1695459), _1695457), c_Product__Type_Ofst(_1695457, _1695459)), _1695461))), 46423 ^ _778908 : [(46430 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1695457, _1695459)), hAPP(hAPP(c_Product__Type_OPair(_1695457, _1695459), _1695463), _1695465)), hAPP(c_List_Oset(tc_prod(_1695457, _1695459)), _1695461))), -(hAPP(c_Map_Omap__of(_1695457, _1695459, _1695461), _1695463) = hAPP(c_Option_Ooption_OSome(_1695459), _1695465))], (46424 ^ _778908) ^ [] : [hAPP(c_Map_Omap__of(_1695457, _1695459, _1695461), _1695463) = hAPP(c_Option_Ooption_OSome(_1695459), _1695465), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1695457, _1695459)), hAPP(hAPP(c_Product__Type_OPair(_1695457, _1695459), _1695463), _1695465)), hAPP(c_List_Oset(tc_prod(_1695457, _1695459)), _1695461))))]]], (43179 ^ _778908) ^ [_1618020, _1618022, _1618024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618020, _1618020), tc_HOL_Obool)), c_Relation_OId(_1618020)), _1618022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618020, _1618020), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1618020, _1618020, _1618020), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1618020, _1618020), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1618020, _1618024)), _1618022)), _1618024)), _1618022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618020, _1618020), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1618020, _1618024)), _1618022)))], (1432 ^ _778908) ^ [_799682, _799684] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_799682)), _799684 = _799682, class_Groups_Oordered__ab__semigroup__add__imp__le(_799684)], (49005 ^ _778908) ^ [_1761367, _1761369, _1761371, _1761373] : [-(_1761367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1761369), _1761367), hAPP(hAPP(c_List_Olist_OCons(_1761369), _1761371), _1761373)) = hAPP(hAPP(c_List_Odrop(_1761369), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1761367), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1761373))], (11596 ^ _778908) ^ [_972859, _972861, _972863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972859), _972861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972859), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972863), _972861))))], (19643 ^ _778908) ^ [_1117297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1117297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1117297)))], (48753 ^ _778908) ^ [_1754644, _1754646, _1754648, _1754650] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754644), tc_List_Olist(_1754644))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754644), tc_List_Olist(_1754644)), _1754646), _1754648)), c_List_Olistrel(_1754644, _1754650))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754644), tc_List_Olist(_1754644))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754644), tc_List_Olist(_1754644)), _1754646), _1754648)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1754644), c_List_Olistrel1(_1754644, _1754650)))))], (49329 ^ _778908) ^ [_1768362, _1768364] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1768362), _1768364) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 49332 ^ _778908 : [(49335 ^ _778908) ^ [_1768476] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1768476), hAPP(c_List_Oset(tc_Nat_Onat), _1768364))), -(_1768476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49333 ^ _778908) ^ [] : [-(_1768362 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46565 ^ _778908) ^ [_1698473, _1698475, _1698477, _1698479, _1698481, _1698483, _1698485, _1698487] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1698473, _1698475), _1698477), _1698479), hAPP(hAPP(c_List_Ozip(_1698473, _1698475), _1698481), hAPP(hAPP(c_List_Omap(_1698483, _1698475), _1698485), _1698487))) = hAPP(hAPP(c_List_Omap(tc_prod(_1698473, _1698483), _1698477), hAPP(c_Product__Type_Oprod_Oprod__case(_1698473, _1698483, _1698477), hAPP(hAPP(c_COMBB(tc_fun(_1698483, tc_prod(_1698473, _1698475)), tc_fun(_1698483, _1698477), _1698473), hAPP(c_COMBB(tc_prod(_1698473, _1698475), _1698477, _1698483), _1698479)), hAPP(hAPP(c_COMBC(_1698473, tc_fun(_1698483, _1698475), tc_fun(_1698483, tc_prod(_1698473, _1698475))), hAPP(hAPP(c_COMBB(tc_fun(_1698475, tc_prod(_1698473, _1698475)), tc_fun(tc_fun(_1698483, _1698475), tc_fun(_1698483, tc_prod(_1698473, _1698475))), _1698473), c_COMBB(_1698475, tc_prod(_1698473, _1698475), _1698483)), c_Product__Type_OPair(_1698473, _1698475))), _1698485)))), hAPP(hAPP(c_List_Ozip(_1698473, _1698483), _1698481), _1698487)))], (7713 ^ _778908) ^ [_907846, _907848, _907850, _907852] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_907846), 7716 ^ _778908 : [(7723 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907846), _907850), _907852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907846), _907848), _907850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907846), _907848), _907852))))], (7717 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907846), _907848), _907850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_907846), _907848), _907852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907846), _907850), _907852)))]]], (43010 ^ _778908) ^ [_1613307, _1613309] : [c_Wellfounded_Owf(_1613307, _1613309), -(c_Wellfounded_Owf(_1613307, c_Transitive__Closure_Otrancl(_1613307, _1613309)))], (986 ^ _778908) ^ [_794011, _794013, _794015, _794017, _794019, _794021, _794023, _794025] : [-(c_Fun_Oinj__on(_794023, _794019, _794015, _794011)), c_Fun_Oinj__on(_794025, _794021, _794017, _794013), _794025 = _794023, _794021 = _794019, _794017 = _794015, _794013 = _794011], (538 ^ _778908) ^ [_787213, _787215, _787217, _787219] : [-(c_Predicate_Oreflp(_787217, _787213)), c_Predicate_Oreflp(_787219, _787215), _787219 = _787217, _787215 = _787213], (27673 ^ _778908) ^ [_1269345, _1269347, _1269349] : [class_Groups_Oordered__ab__group__add(_1269345), -(hAPP(c_Set_Oimage(_1269345, _1269345, c_Groups_Ouminus__class_Ouminus(_1269345)), c_SetInterval_Oord__class_OatLeastAtMost(_1269345, _1269347, _1269349)) = c_SetInterval_Oord__class_OatLeastAtMost(_1269345, hAPP(c_Groups_Ouminus__class_Ouminus(_1269345), _1269349), hAPP(c_Groups_Ouminus__class_Ouminus(_1269345), _1269347)))], (20261 ^ _778908) ^ [_1128836, _1128838, _1128840] : [class_Fields_Olinordered__field__inverse__zero(_1128836), -(hAPP(c_Groups_Oabs__class_Oabs(_1128836), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128836), _1128838), _1128840)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128836), hAPP(c_Groups_Oabs__class_Oabs(_1128836), _1128838)), hAPP(c_Groups_Oabs__class_Oabs(_1128836), _1128840)))], (41245 ^ _778908) ^ [_1562759, _1562761, _1562763, _1562765] : [-(hBOOL(hAPP(hAPP(c_member(_1562759), _1562761), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562759, tc_HOL_Obool)), _1562763), hAPP(c_Set_OCollect(_1562759), _1562765))))), hBOOL(hAPP(hAPP(c_member(_1562759), _1562761), _1562763)), hBOOL(hAPP(_1562765, _1562761))], (46067 ^ _778908) ^ [_1687085, _1687087, _1687089, _1687091, _1687093, _1687095, _1687097] : [c_Map_Omap__comp(_1687085, _1687087, _1687089, _1687091, _1687093, _1687095) = hAPP(c_Option_Ooption_OSome(_1687087), _1687097), 46071 ^ _778908 : [(46074 ^ _778908) ^ [] : [-(hAPP(_1687091, 46070 ^ [_1687085, _1687087, _1687089, _1687091, _1687093, _1687095, _1687097]) = hAPP(c_Option_Ooption_OSome(_1687087), _1687097))], (46072 ^ _778908) ^ [] : [-(hAPP(_1687093, _1687095) = hAPP(c_Option_Ooption_OSome(_1687085), 46070 ^ [_1687085, _1687087, _1687089, _1687091, _1687093, _1687095, _1687097]))]]], (5304 ^ _778908) ^ [_860934, _860936, _860938, _860940] : [-(c_List_Oupt(_860940, _860936) = c_List_Oupt(_860938, _860934)), _860940 = _860938, _860936 = _860934], (5448 ^ _778908) ^ [_863102, _863104, _863106, _863108] : [-(c_List_Olist__update(_863108, _863104) = c_List_Olist__update(_863106, _863102)), _863108 = _863106, _863104 = _863102], (7518 ^ _778908) ^ [_904726, _904728, _904730, _904732, _904734] : [class_Rings_Ocomm__semiring__1(_904726), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904726), _904728), _904730)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904726), _904732), _904734)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904726), _904728), _904732)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904726), _904730), _904734)))], (6893 ^ _778908) ^ [_892564, _892566, _892568, _892570, _892572, _892574, _892576, _892578, _892580, _892582, _892584] : [-(c_Com_Ocom_Ocom__case(_892564, _892566, _892568, _892570, _892572, _892574, _892576, _892578, _892580, c_Com_Ocom_OWhile(_892582, _892584)) = hAPP(hAPP(_892576, _892582), _892584))], (1032 ^ _778908) ^ [_794682, _794684] : [-(class_Rings_Olinordered__semiring__1__strict(_794682)), _794684 = _794682, class_Rings_Olinordered__semiring__1__strict(_794684)], (16394 ^ _778908) ^ [_1060663, _1060665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060663)), 16397 ^ _778908 : [(16404 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060665), _1060663))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1060665), _1060663) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060665), _1060663)), _1060663)))], (16398 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060665), _1060663)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1060665), _1060663) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4104 ^ _778908) ^ [_842170, _842172] : [_842172 = _842170, -(c_SetInterval_Oord__class_OgreaterThan(_842172) = c_SetInterval_Oord__class_OgreaterThan(_842170))], (20055 ^ _778908) ^ [_1124669, _1124671, _1124673] : [class_Int_Onumber__ring(_1124669), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1124669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124669), _1124671), _1124673)), 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(_1124669), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124669), hAPP(hAPP(c_Power_Opower__class_Opower(_1124669), _1124671), 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(_1124669), _1124673), 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(_1124669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124669), hAPP(c_Int_Onumber__class_Onumber__of(_1124669), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1124671)), _1124673)))], (49752 ^ _778908) ^ [_1777678, _1777680, _1777682, _1777684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1777678), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777680)), _1777682))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1777678), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777680)), _1777684))), 49762 ^ _778908 : [(49765 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Onth(_1777680), _1777682), 49761 ^ [_1777678, _1777680, _1777682, _1777684]) = hAPP(hAPP(c_List_Onth(_1777680), _1777684), 49761 ^ [_1777678, _1777680, _1777682, _1777684])], (49763 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49761 ^ [_1777678, _1777680, _1777682, _1777684]), _1777678)))]], -(hAPP(hAPP(c_List_Otake(_1777680), _1777678), _1777682) = hAPP(hAPP(c_List_Otake(_1777680), _1777678), _1777684))], (36916 ^ _778908) ^ [_1465275, _1465277] : [class_Lattices_Oboolean__algebra(_1465275), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465275), hAPP(c_Groups_Ouminus__class_Ouminus(_1465275), _1465277)), _1465277) = c_Orderings_Obot__class_Obot(_1465275))], (49305 ^ _778908) ^ [_1767816, _1767818, _1767820, _1767822, _1767824] : [-(c_List_Olist_Olist__size(_1767816, _1767818, hAPP(hAPP(c_List_Omap(_1767820, _1767816), _1767822), _1767824)) = c_List_Olist_Olist__size(_1767820, hAPP(c_Fun_Ocomp(_1767816, tc_Nat_Onat, _1767820, _1767818), _1767822), _1767824))], (46934 ^ _778908) ^ [_1709267, _1709269, _1709271, _1709273] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709267), tc_List_Olist(_1709267))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709267), tc_List_Olist(_1709267)), _1709269), _1709271)), c_List_Olistrel(_1709267, _1709273))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709267)), _1709269) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709267)), _1709271))], (17223 ^ _778908) ^ [_1076139, _1076141, _1076143, _1076145] : [class_Int_Onumber__ring(_1076139), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1076139), hAPP(c_Int_Onumber__class_Onumber__of(_1076139), _1076141)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1076139), hAPP(c_Int_Onumber__class_Onumber__of(_1076139), _1076143)), _1076145)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1076139), hAPP(c_Int_Onumber__class_Onumber__of(_1076139), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1076141), _1076143))), _1076145))], (42225 ^ _778908) ^ [_1594197, _1594199, _1594201, _1594203] : [hBOOL(hAPP(c_Predicate_ORangeP(_1594197, _1594199, hAPP(hAPP(c_COMBC(_1594197, tc_fun(tc_prod(_1594197, _1594199), tc_HOL_Obool), tc_fun(_1594199, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1594199, tc_fun(tc_fun(tc_prod(_1594197, _1594199), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1594197, _1594199), tc_HOL_Obool), tc_fun(_1594199, tc_HOL_Obool)), _1594197), c_COMBC(_1594199, tc_fun(tc_prod(_1594197, _1594199), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1594199, tc_prod(_1594197, _1594199)), tc_fun(_1594199, tc_fun(tc_fun(tc_prod(_1594197, _1594199), tc_HOL_Obool), tc_HOL_Obool)), _1594197), hAPP(c_COMBB(tc_prod(_1594197, _1594199), tc_fun(tc_fun(tc_prod(_1594197, _1594199), tc_HOL_Obool), tc_HOL_Obool), _1594199), c_member(tc_prod(_1594197, _1594199)))), c_Product__Type_OPair(_1594197, _1594199)))), _1594201)), _1594203)), -(hBOOL(hAPP(hAPP(c_member(_1594199), _1594203), hAPP(c_Relation_ORange(_1594197, _1594199), _1594201))))], (16038 ^ _778908) ^ [_1052932, _1052934] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052932), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1052934)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052932), _1052934))], (28065 ^ _778908) ^ [_1276492, _1276494, _1276496, _1276498] : [28067 ^ _778908 : [(28070 ^ _778908) ^ [] : [hBOOL(hAPP(_1276498, 28066 ^ [_1276492, _1276494, _1276496, _1276498]))], (28068 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276492), 28066 ^ [_1276492, _1276494, _1276496, _1276498]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276492, tc_HOL_Obool)), _1276494), _1276496))))]], 28071 ^ _778908 : [(28078 ^ _778908) ^ [_1276809] : [hBOOL(hAPP(hAPP(c_member(_1276492), _1276809), _1276496)), -(hBOOL(hAPP(_1276498, _1276809)))], (28072 ^ _778908) ^ [_1276712] : [hBOOL(hAPP(hAPP(c_member(_1276492), _1276712), _1276494)), -(hBOOL(hAPP(_1276498, _1276712)))]]], (15874 ^ _778908) ^ [_1049808, _1049810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049808), _1049810)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049808), _1049810) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9510 ^ _778908) ^ [_937847] : [class_Rings_Ozero__neq__one(_937847), c_Groups_Ozero__class_Ozero(_937847) = c_Groups_Oone__class_Oone(_937847)], (13869 ^ _778908) ^ [_1013100, _1013102, _1013104] : [class_Divides_Osemiring__div(_1013100), -(c_Divides_Odiv__class_Omod(_1013100, c_Divides_Odiv__class_Omod(_1013100, _1013102, _1013104), _1013104) = c_Divides_Odiv__class_Omod(_1013100, _1013102, _1013104))], (27442 ^ _778908) ^ [_1264236, _1264238, _1264240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264236)), 27445 ^ _778908 : [(27446 ^ _778908) ^ [_1264370] : [27448 ^ _778908 : [(27454 ^ _778908) ^ [] : [-(_1264370 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27450 ^ [_1264236, _1264238, _1264240, _1264370]), 27447 ^ [_1264236, _1264238, _1264240, _1264370]))], (27452 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27450 ^ [_1264236, _1264238, _1264240, _1264370]), _1264238)))], (27449 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27447 ^ [_1264236, _1264238, _1264240, _1264370]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1264236))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264370), _1264240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1264370), _1264236)), _1264240)))]]], (22418 ^ _778908) ^ [_1167140] : [-(c_Divides_Odivmod__nat(_1167140, 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)), _1167140))], (33765 ^ _778908) ^ [_1394661, _1394663] : [class_Orderings_Olinorder(_1394661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394661), _1394663)), -(_1394663 = c_Orderings_Obot__class_Obot(tc_fun(_1394661, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1394661), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1394661), 33778 ^ [_1394661, _1394663]), 33779 ^ [_1394661, _1394663])), hAPP(hAPP(c_Set_Oinsert(_1394661), 33778 ^ [_1394661, _1394663]), hAPP(hAPP(c_Set_Oinsert(_1394661), 33779 ^ [_1394661, _1394663]), c_Orderings_Obot__class_Obot(tc_fun(_1394661, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1394661), c_Big__Operators_Olinorder__class_OMin(_1394661, _1394663)), _1394663)))], (9476 ^ _778908) ^ [_937373, _937375, _937377] : [class_Rings_Ono__zero__divisors(_937373), -(_937375 = c_Groups_Ozero__class_Ozero(_937373)), -(_937377 = c_Groups_Ozero__class_Ozero(_937373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937373), _937375), _937377) = c_Groups_Ozero__class_Ozero(_937373)], (14611 ^ _778908) ^ [_1026961, _1026963] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1026961, _1026963)) = _1026963), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1026961), _1026963) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1026961, _1026963)))], (34445 ^ _778908) ^ [_1409105, _1409107, _1409109, _1409111] : [class_Rings_Ocomm__semiring__1(_1409105), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409107), _1409109)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409107, _1409105), _1409111), _1409109) = c_Groups_Ozero__class_Ozero(_1409105)), 34454 ^ _778908 : [(34455 ^ _778908) ^ [_1409286] : [hBOOL(hAPP(hAPP(c_member(_1409107), _1409286), _1409109)), hAPP(_1409111, _1409286) = c_Groups_Ozero__class_Ozero(_1409105)]]], (47922 ^ _778908) ^ [_1734162, _1734164, _1734166, _1734168] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1734162, tc_HOL_Obool)), hAPP(c_List_Oset(_1734162), hAPP(hAPP(c_List_Olist__update(_1734162, _1734164), _1734166), _1734168))), hAPP(hAPP(c_Set_Oinsert(_1734162), _1734168), hAPP(c_List_Oset(_1734162), _1734164)))))], (34140 ^ _778908) ^ [_1402570, _1402572, _1402574] : [class_Orderings_Olinorder(_1402570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402570), _1402572)), -(hBOOL(hAPP(hAPP(c_member(_1402570), _1402574), _1402572))), -(_1402572 = c_Orderings_Obot__class_Obot(tc_fun(_1402570, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1402570, c_Orderings_Oord__class_Omin(_1402570), hAPP(hAPP(c_Set_Oinsert(_1402570), _1402574), _1402572)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402570), _1402574), c_Big__Operators_Olattice_OInf__fin(_1402570, c_Orderings_Oord__class_Omin(_1402570), _1402572)))], (40432 ^ _778908) ^ [_1546388, _1546390, _1546392, _1546394, _1546396, _1546398, _1546400, _1546402, _1546404, _1546406, _1546408] : [-(hAPP(c_Product__Type_Omap__pair(_1546388, _1546390, _1546392, _1546394, _1546396, _1546398), hAPP(c_Product__Type_Omap__pair(_1546400, _1546388, _1546402, _1546392, _1546404, _1546406), _1546408)) = hAPP(c_Product__Type_Omap__pair(_1546400, _1546390, _1546402, _1546394, hAPP(c_Fun_Ocomp(_1546388, _1546390, _1546400, _1546396), _1546404), hAPP(c_Fun_Ocomp(_1546392, _1546394, _1546402, _1546398), _1546406)), _1546408))], (29225 ^ _778908) ^ [_1301106, _1301108] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1301106, _1301108))))], (45278 ^ _778908) ^ [_1668687, _1668689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1668687), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1668687, tc_HOL_Obool), _1668689))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1668687, tc_HOL_Obool)), _1668689)))], (51659 ^ _778908) ^ [_1813625] : [-(hBOOL(_1813625)), -(hBOOL(hAPP(c_fNot, _1813625)))], (51373 ^ _778908) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (8863 ^ _778908) ^ [_926763, _926765] : [hBOOL(hAPP(_926763, hAPP(c_Int_Onat, _926765))), 8866 ^ _778908 : [(8873 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _926765), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_926763, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8867 ^ _778908) ^ [_926863] : [_926765 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926863), -(hBOOL(hAPP(_926763, _926863)))]]], (40160 ^ _778908) ^ [_1538668, _1538670, _1538672, _1538674, _1538676] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1538668, _1538670), _1538672), hAPP(hAPP(c_COMBS(_1538668, tc_fun(_1538670, tc_HOL_Obool), tc_fun(_1538670, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538670, tc_HOL_Obool), tc_fun(tc_fun(_1538670, tc_HOL_Obool), tc_fun(_1538670, tc_HOL_Obool)), _1538668), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1538670, tc_HOL_Obool))), _1538674)), _1538676)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538668, _1538670), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1538668, _1538670), _1538672), _1538674)), hAPP(hAPP(c_Product__Type_OSigma(_1538668, _1538670), _1538672), _1538676)))], (45829 ^ _778908) ^ [_1681484, _1681486, _1681488, _1681490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681484, _1681486)), _1681488), hAPP(c_Relation_Oconverse(_1681486, _1681484), _1681490))), 45834 ^ _778908 : [(45837 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681486, _1681484)), hAPP(hAPP(c_Product__Type_OPair(_1681486, _1681484), 45832 ^ [_1681484, _1681486, _1681488, _1681490]), 45833 ^ [_1681484, _1681486, _1681488, _1681490])), _1681490)))], (45835 ^ _778908) ^ [] : [-(_1681488 = hAPP(hAPP(c_Product__Type_OPair(_1681484, _1681486), 45833 ^ [_1681484, _1681486, _1681488, _1681490]), 45832 ^ [_1681484, _1681486, _1681488, _1681490]))]]], (24981 ^ _778908) ^ [_1217023, _1217025, _1217027, _1217029, _1217031] : [-(_1217023 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1217025, _1217027, _1217029, _1217031), _1217023) = c_Lazy__Sequence_Obind(_1217025, _1217027, hAPP(_1217029, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1217023), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1217025, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1217027)), _1217031), _1217023)))], (14035 ^ _778908) ^ [_1016463, _1016465, _1016467] : [class_Divides_Osemiring__div(_1016463), -(c_Divides_Odiv__class_Omod(_1016463, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016463), _1016465), _1016467), _1016465) = c_Groups_Ozero__class_Ozero(_1016463))], (9022 ^ _778908) ^ [_929608] : [class_Rings_Oring__1(_929608), -(hAPP(c_Int_Oring__1__class_Oof__int(_929608), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_929608))], (12351 ^ _778908) ^ [_986372, _986374] : [class_Rings_Olinordered__semidom(_986372), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986372), c_Groups_Ozero__class_Ozero(_986372)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_986372), _986374))))], (9696 ^ _778908) ^ [_941389, _941391] : [class_Groups_Ogroup__add(_941389), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941389), hAPP(c_Groups_Ouminus__class_Ouminus(_941389), _941391)), _941391) = c_Groups_Ozero__class_Ozero(_941389))], (14106 ^ _778908) ^ [_1017686, _1017688] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1017686), _1017688) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017686, _1017688) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (4500 ^ _778908) ^ [_848546, _848548, _848550, _848552, _848554, _848556] : [-(c_List_Oset__Cons(_848556, _848552, _848548) = c_List_Oset__Cons(_848554, _848550, _848546)), _848556 = _848554, _848552 = _848550, _848548 = _848546], (13969 ^ _778908) ^ [_1015068, _1015070, _1015072, _1015074] : [class_Divides_Osemiring__div(_1015068), -(c_Divides_Odiv__class_Omod(_1015068, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015068), _1015070), _1015072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015068), _1015074), _1015072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015068), c_Divides_Odiv__class_Omod(_1015068, _1015070, _1015074)), _1015072))], (26095 ^ _778908) ^ [_1237629, _1237631, _1237633, _1237635, _1237637, _1237639, _1237641] : [class_Rings_Osemiring__0(_1237629), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237629), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237631, _1237629), _1237633), _1237635)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237637, _1237629), _1237639), _1237641)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237631, _1237629), hAPP(hAPP(c_COMBC(_1237631, tc_fun(_1237637, tc_HOL_Obool), _1237629), hAPP(hAPP(c_COMBB(tc_fun(_1237637, _1237629), tc_fun(tc_fun(_1237637, tc_HOL_Obool), _1237629), _1237631), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237637, _1237629)), hAPP(hAPP(c_COMBC(_1237631, tc_fun(_1237637, _1237629), tc_fun(_1237637, _1237629)), hAPP(hAPP(c_COMBB(tc_fun(_1237629, _1237629), tc_fun(tc_fun(_1237637, _1237629), tc_fun(_1237637, _1237629)), _1237631), c_COMBB(_1237629, _1237629, _1237637)), hAPP(hAPP(c_COMBB(_1237629, tc_fun(_1237629, _1237629), _1237631), c_Groups_Otimes__class_Otimes(_1237629)), _1237633))), _1237639))), _1237641)), _1237635))], (35931 ^ _778908) ^ [_1443286, _1443288, _1443290, _1443292, _1443294, _1443296, _1443298, _1443300, _1443302, _1443304, _1443306] : [c_Finite__Set_Ofolding(_1443286, _1443288, _1443290, _1443292), -(hAPP(c_Fun_Ocomp(_1443294, _1443296, _1443298, _1443300), hAPP(c_Fun_Ocomp(_1443302, _1443294, _1443298, _1443304), _1443306)) = hAPP(c_Fun_Ocomp(_1443302, _1443296, _1443298, hAPP(c_Fun_Ocomp(_1443294, _1443296, _1443302, _1443300), _1443304)), _1443306))], (42163 ^ _778908) ^ [_1592637, _1592639, _1592641, _1592643] : [42165 ^ _778908 : [(42168 ^ _778908) ^ [] : [c_Wellfounded_Owf(_1592639, hAPP(_1592641, 42164 ^ [_1592637, _1592639, _1592641, _1592643]))], (42166 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1592637, 42164 ^ [_1592637, _1592639, _1592641, _1592643])))]], -(c_Wellfounded_Owf(tc_prod(_1592643, _1592639), c_Recdef_Osame__fst(_1592643, _1592639, _1592637, _1592641)))], (30080 ^ _778908) ^ [_1317674] : [c_Orderings_Otop__class_Otop(tc_fun(_1317674, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1317674, tc_HOL_Obool))], (47898 ^ _778908) ^ [_1733515, _1733517, _1733519, _1733521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733515)), _1733517)), _1733519)), -(hAPP(hAPP(c_List_Olist__update(_1733515, _1733517), _1733519), _1733521) = _1733517)], (30226 ^ _778908) ^ [_1320483, _1320485, _1320487] : [class_Groups_Ocomm__monoid__add(_1320483), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320485, _1320483), _1320487), c_Orderings_Obot__class_Obot(tc_fun(_1320485, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1320483))], (11554 ^ _778908) ^ [_972209, _972211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972209), _972211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972209), _972211))), -(_972209 = _972211)], (13306 ^ _778908) ^ [_1003256, _1003258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003256)), 13309 ^ _778908 : [(13316 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003256), _1003258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1003256)), hAPP(c_Int_Onat, _1003258))))], (13310 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1003256)), hAPP(c_Int_Onat, _1003258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1003256), _1003258)))]]], (18977 ^ _778908) ^ [_1105836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105836), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1105836)), c_Int_OMin)))], (614 ^ _778908) ^ [_788445, _788447] : [-(c_Nitpick_Ounknown(_788445)), _788447 = _788445, c_Nitpick_Ounknown(_788447)], (36964 ^ _778908) ^ [_1466321, _1466323, _1466325, _1466327] : [-(hBOOL(hAPP(hAPP(c_member(_1466321), _1466323), _1466325))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466321, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1466321), _1466323), _1466327)), _1466325) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466321, tc_HOL_Obool)), _1466327), _1466325))], (4468 ^ _778908) ^ [_848024, _848026, _848028, _848030, _848032, _848034] : [-(c_Relation_OImage(_848034, _848030, _848026) = c_Relation_OImage(_848032, _848028, _848024)), _848034 = _848032, _848030 = _848028, _848026 = _848024], (39618 ^ _778908) ^ [_1524638, _1524640, _1524642, _1524644] : [c_Fun_Oinj__on(_1524638, _1524640, _1524642, c_Orderings_Otop__class_Otop(tc_fun(_1524638, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1524638, _1524640, c_Orderings_Otop__class_Otop(tc_fun(_1524638, tc_HOL_Obool)), _1524642), hAPP(_1524642, _1524644)) = _1524644)], (45077 ^ _778908) ^ [_1664152, _1664154, _1664156, _1664158] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1664152, tc_HOL_Obool), hAPP(c_Set_Oimage(_1664154, tc_fun(_1664152, tc_HOL_Obool), _1664156), _1664158)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664154, tc_fun(_1664152, tc_HOL_Obool)), _1664158), _1664156))], (32690 ^ _778908) ^ [_1373875, _1373877, _1373879] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373875, tc_HOL_Obool)), _1373877), hAPP(hAPP(c_Set_Oinsert(_1373875), _1373879), c_Orderings_Obot__class_Obot(tc_fun(_1373875, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1373875, _1373879, _1373877) = c_HOL_OThe(_1373875, hAPP(hAPP(c_COMBC(_1373875, tc_fun(_1373875, tc_HOL_Obool), tc_HOL_Obool), c_member(_1373875)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373875, tc_HOL_Obool)), _1373877), hAPP(hAPP(c_Set_Oinsert(_1373875), _1373879), c_Orderings_Obot__class_Obot(tc_fun(_1373875, tc_HOL_Obool)))))))], (46497 ^ _778908) ^ [_1697054, _1697056, _1697058, _1697060] : [-(hBOOL(hAPP(hAPP(c_member(_1697054), _1697056), hAPP(c_List_Oset(_1697054), _1697058)))), hBOOL(hAPP(hAPP(c_member(_1697054), _1697056), hAPP(c_List_Oset(_1697054), c_List_Oremove1(_1697054, _1697060, _1697058))))], (32306 ^ _778908) ^ [_1366203, _1366205, _1366207, _1366209, _1366211, _1366213] : [hBOOL(hAPP(hAPP(_1366203, _1366205), _1366207)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1366209, tc_fun(_1366211, tc_HOL_Obool))), _1366203), _1366213), _1366205), _1366207)))], (27616 ^ _778908) ^ [_1268104, _1268106] : [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)), _1268104)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1268104), _1268106)))], (10070 ^ _778908) ^ [_948165, _948167] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948165)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948167), 10073 ^ _778908 : [(10076 ^ _778908) ^ [] : [-(_948167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10074 ^ _778908) ^ [] : [-(_948165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42391 ^ _778908) ^ [_1598330, _1598332] : [c_Wellfounded_Owf(_1598330, _1598332), -(c_Wellfounded_OwfP(_1598330, hAPP(hAPP(c_COMBC(_1598330, tc_fun(tc_prod(_1598330, _1598330), tc_HOL_Obool), tc_fun(_1598330, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598330, tc_fun(tc_fun(tc_prod(_1598330, _1598330), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598330, _1598330), tc_HOL_Obool), tc_fun(_1598330, tc_HOL_Obool)), _1598330), c_COMBC(_1598330, tc_fun(tc_prod(_1598330, _1598330), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598330, tc_prod(_1598330, _1598330)), tc_fun(_1598330, tc_fun(tc_fun(tc_prod(_1598330, _1598330), tc_HOL_Obool), tc_HOL_Obool)), _1598330), hAPP(c_COMBB(tc_prod(_1598330, _1598330), tc_fun(tc_fun(tc_prod(_1598330, _1598330), tc_HOL_Obool), tc_HOL_Obool), _1598330), c_member(tc_prod(_1598330, _1598330)))), c_Product__Type_OPair(_1598330, _1598330)))), _1598332)))], (33725 ^ _778908) ^ [_1393747, _1393749, _1393751] : [class_Orderings_Olinorder(_1393747), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393747), _1393749)), 33732 ^ _778908 : [(33739 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393747, tc_HOL_Obool)), _1393749), hAPP(hAPP(c_Set_Oinsert(_1393747), _1393751), c_Orderings_Obot__class_Obot(tc_fun(_1393747, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1393747, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1393747, hAPP(hAPP(c_Set_Oinsert(_1393747), _1393751), _1393749)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1393747), _1393751), c_Big__Operators_Olinorder__class_OMax(_1393747, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393747, tc_HOL_Obool)), _1393749), hAPP(hAPP(c_Set_Oinsert(_1393747), _1393751), c_Orderings_Obot__class_Obot(tc_fun(_1393747, tc_HOL_Obool)))))))], (33733 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393747, tc_HOL_Obool)), _1393749), hAPP(hAPP(c_Set_Oinsert(_1393747), _1393751), c_Orderings_Obot__class_Obot(tc_fun(_1393747, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1393747, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1393747, hAPP(hAPP(c_Set_Oinsert(_1393747), _1393751), _1393749)) = _1393751)]]], (35241 ^ _778908) ^ [_1427027, _1427029, _1427031] : [-(hAPP(c_Relation_OField(_1427027), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1427027, _1427027), tc_HOL_Obool)), _1427029), _1427031)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427027, tc_HOL_Obool)), hAPP(c_Relation_OField(_1427027), _1427029)), hAPP(c_Relation_OField(_1427027), _1427031)))], (8206 ^ _778908) ^ [_916303, _916305, _916307, _916309] : [_916307 = _916309, -(hAPP(c_Sum__Type_OInr(_916303, _916305), _916307) = hAPP(c_Sum__Type_OInr(_916303, _916305), _916309))], (32747 ^ _778908) ^ [_1375208, _1375210, _1375212] : [-(hAPP(c_Finite__Set_Ocard(_1375208), _1375210) = hAPP(c_Nat_OSuc, _1375212)), 32748 ^ _778908 : [(32749 ^ _778908) ^ [_1375308, _1375310] : [_1375210 = hAPP(hAPP(c_Set_Oinsert(_1375208), _1375310), _1375308), -(hBOOL(hAPP(hAPP(c_member(_1375208), _1375310), _1375308))), hAPP(c_Finite__Set_Ocard(_1375208), _1375308) = _1375212, 32760 ^ _778908 : [(32763 ^ _778908) ^ [] : [_1375308 = c_Orderings_Obot__class_Obot(tc_fun(_1375208, tc_HOL_Obool))], (32761 ^ _778908) ^ [] : [-(_1375212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (17973 ^ _778908) ^ [_1089814, _1089816] : [-(c_Nitpick_Oint__lcm(_1089814, _1089816) = 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), _1089814)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1089816)))))], (21225 ^ _778908) ^ [_1145598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145598)), -(c_Nat__Transfer_Ois__nat(_1145598))], (19485 ^ _778908) ^ [_1114496, _1114498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1114496)), c_Int_OBit0(_1114498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114496), _1114498)))], (10262 ^ _778908) ^ [_951382] : [class_Rings_Olinordered__semidom(_951382), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951382), c_Groups_Ozero__class_Ozero(_951382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951382), c_Groups_Oone__class_Oone(_951382)), c_Groups_Oone__class_Oone(_951382)))))], (19389 ^ _778908) ^ [_1112832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1112832)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112832), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33003 ^ _778908) ^ [_1380303, _1380305, _1380307] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1380303, _1380305, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1380303)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1380303), _1380307), c_Com_Ocom_OSKIP), _1380307)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380303), tc_HOL_Obool)))))], (34849 ^ _778908) ^ [_1417571, _1417573, _1417575, _1417577, _1417579] : [hBOOL(hAPP(hAPP(c_member(_1417571), _1417573), _1417575)), -(hAPP(c_Map_Orestrict__map(_1417571, _1417577, _1417579, _1417575), _1417573) = hAPP(_1417579, _1417573))], (35889 ^ _778908) ^ [_1442306] : [-(c_Nitpick_Onum(_1442306) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1442306, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1442306)))], (29289 ^ _778908) ^ [_1302495, _1302497, _1302499, _1302501] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1302495), _1302497), _1302499), _1302501)), -(_1302497 = _1302501), -(hBOOL(hAPP(_1302499, _1302501)))], (41784 ^ _778908) ^ [_1582832, _1582834, _1582836, _1582838] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582832, _1582834, _1582836), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582832, _1582834), tc_HOL_Obool))), _1582838) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582832, _1582836), tc_HOL_Obool)))], (1242 ^ _778908) ^ [_797307, _797309] : [-(class_Rings_Oring__1(_797307)), _797309 = _797307, class_Rings_Oring__1(_797309)], (28171 ^ _778908) ^ [_1278915, _1278917, _1278919, _1278921] : [class_Lattices_Osemilattice__sup(_1278915), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278915), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278915), _1278917), _1278919)), _1278921) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278915), _1278917), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278915), _1278919), _1278921)))], (41551 ^ _778908) ^ [_1573930, _1573932, _1573934] : [class_Lattices_Odistrib__lattice(_1573930), hBOOL(hAPP(c_Finite__Set_Ofinite(_1573930), _1573932)), -(_1573932 = c_Orderings_Obot__class_Obot(tc_fun(_1573930, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1573930), _1573934), c_Big__Operators_Olattice__class_OInf__fin(_1573930, _1573932)) = c_Big__Operators_Olattice__class_OInf__fin(_1573930, hAPP(c_Set_OCollect(_1573930), hAPP(hAPP(c_COMBB(tc_fun(_1573930, tc_HOL_Obool), tc_HOL_Obool, _1573930), c_HOL_OEx(_1573930)), hAPP(hAPP(c_COMBC(_1573930, tc_fun(_1573930, tc_HOL_Obool), tc_fun(_1573930, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573930, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1573930, tc_HOL_Obool), tc_fun(_1573930, tc_HOL_Obool)), _1573930), c_COMBS(_1573930, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573930, tc_HOL_Obool), tc_fun(_1573930, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1573930), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573930), c_fconj)), hAPP(hAPP(c_COMBC(_1573930, tc_fun(_1573930, _1573930), tc_fun(_1573930, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573930, tc_HOL_Obool), tc_fun(tc_fun(_1573930, _1573930), tc_fun(_1573930, tc_HOL_Obool)), _1573930), c_COMBB(_1573930, tc_HOL_Obool, _1573930)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1573930), _1573934))))), hAPP(hAPP(c_COMBC(_1573930, tc_fun(_1573930, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573930)), _1573932))))))], (41722 ^ _778908) ^ [_1580905, _1580907, _1580909, _1580911] : [class_Groups_Ocomm__monoid__add(_1580905), c_Fun_Oinj__on(_1580907, _1580905, _1580909, _1580911), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580907, _1580905), _1580909), _1580911) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580905, _1580905), c_Fun_Oid(_1580905)), hAPP(c_Set_Oimage(_1580907, _1580905, _1580909), _1580911)))], (19751 ^ _778908) ^ [_1119131] : [-(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)))), _1119131) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119131), _1119131))], (11506 ^ _778908) ^ [_971508, _971510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971508), hAPP(c_Nat_OSuc, _971510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971508), _971510))), -(_971508 = hAPP(c_Nat_OSuc, _971510))], (17439 ^ _778908) ^ [_1080193, _1080195] : [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), _1080193), _1080195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1080193))), -(_1080195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30568 ^ _778908) ^ [_1326588, _1326590, _1326592, _1326594, _1326596] : [-(_1326588 = c_Orderings_Obot__class_Obot(tc_fun(_1326590, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326592, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326590, tc_fun(_1326592, tc_HOL_Obool)), _1326588), _1326594)), _1326596) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326590, tc_fun(_1326592, tc_HOL_Obool)), _1326588), hAPP(hAPP(c_COMBC(_1326590, tc_fun(_1326592, tc_HOL_Obool), tc_fun(_1326592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326592, tc_HOL_Obool), tc_fun(tc_fun(_1326592, tc_HOL_Obool), tc_fun(_1326592, tc_HOL_Obool)), _1326590), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326592, tc_HOL_Obool))), _1326594)), _1326596)))], (41868 ^ _778908) ^ [_1586529] : [-(c_Wellfounded_Owf(_1586529, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1586529, _1586529), tc_HOL_Obool))))], (19075 ^ _778908) ^ [_1107447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1107447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107447)))], (18139 ^ _778908) ^ [_1092474, _1092476] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092474))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092474)), _1092476) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1092476))], (19841 ^ _778908) ^ [_1120688, _1120690] : [class_Rings_Olinordered__idom(_1120688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120688), hAPP(hAPP(c_Power_Opower__class_Opower(_1120688), _1120690), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1120688)))], (39416 ^ _778908) ^ [_1519946, _1519948, _1519950, _1519952, _1519954, _1519956, _1519958] : [c_Fun_Oinj__on(_1519946, _1519948, _1519950, hAPP(c_Set_Oimage(_1519952, _1519946, _1519954), _1519956)), c_Fun_Oinj__on(_1519952, _1519946, _1519954, _1519956), hBOOL(hAPP(hAPP(c_member(_1519948), _1519958), hAPP(c_Set_Oimage(_1519946, _1519948, _1519950), hAPP(c_Set_Oimage(_1519952, _1519946, _1519954), _1519956)))), -(hAPP(c_Fun_Othe__inv__into(_1519952, _1519948, _1519956, hAPP(c_Fun_Ocomp(_1519946, _1519948, _1519952, _1519950), _1519954)), _1519958) = hAPP(hAPP(c_Fun_Ocomp(_1519946, _1519952, _1519948, c_Fun_Othe__inv__into(_1519952, _1519946, _1519956, _1519954)), c_Fun_Othe__inv__into(_1519946, _1519948, hAPP(c_Set_Oimage(_1519952, _1519946, _1519954), _1519956), _1519950)), _1519958))], (13122 ^ _778908) ^ [_1000193, _1000195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1000193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1000195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000195), _1000193))))], (3046 ^ _778908) ^ [_825529, _825531, _825533, _825535, _825537, _825539, _825541, _825543] : [-(c_New__DSequence_Opos__bind(_825543, _825539, _825535, _825531) = c_New__DSequence_Opos__bind(_825541, _825537, _825533, _825529)), _825543 = _825541, _825539 = _825537, _825535 = _825533, _825531 = _825529], (26861 ^ _778908) ^ [_1252567, _1252569, _1252571] : [class_Rings_Ocomm__semiring__1(_1252567), 26866 ^ _778908 : [(26869 ^ _778908) ^ [] : [_1252571 = c_Groups_Oone__class_Oone(_1252567)], (26867 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1252569))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1252567), _1252571), hAPP(hAPP(c_Power_Opower__class_Opower(_1252567), _1252571), _1252569))))], (36994 ^ _778908) ^ [_1466888, _1466890, _1466892, _1466894, _1466896] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466888, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466890, _1466888, _1466892), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466890, tc_HOL_Obool)), _1466894), _1466896))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466888, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466890, _1466888, _1466892), _1466894)), hAPP(c_Set_Oimage(_1466890, _1466888, _1466892), _1466896)))))], (41957 ^ _778908) ^ [_1588308, _1588310, _1588312, _1588314] : [c_Wellfounded_Owf(_1588308, _1588310), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588308, _1588308)), hAPP(hAPP(c_Product__Type_OPair(_1588308, _1588308), _1588312), _1588314)), _1588310)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588308, _1588308)), hAPP(hAPP(c_Product__Type_OPair(_1588308, _1588308), _1588314), _1588312)), _1588310))], (16046 ^ _778908) ^ [_1053090, _1053092] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1053090, _1053092) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1053090), _1053092)), _1053092)))], (42694 ^ _778908) ^ [_1606224, _1606226, _1606228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1606224), c_Map_Odom(_1606224, _1606226, _1606228))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1606224), c_Orderings_Otop__class_Otop(tc_fun(_1606224, tc_HOL_Obool))))), -(hAPP(_1606228, 42701 ^ [_1606224, _1606226, _1606228]) = c_Option_Ooption_ONone(_1606226))], (17385 ^ _778908) ^ [_1079260, _1079262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079260), _1079262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079260)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079262))))], (8063 ^ _778908) ^ [_913842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _913842)), -(_913842 = hAPP(c_Nat_OSuc, 8066 ^ [_913842]))], (27899 ^ _778908) ^ [_1273502, _1273504] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1273502, _1273504)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1273504), _1273502))], (6544 ^ _778908) ^ [_885217, _885219, _885221, _885223, _885225, _885227, _885229, _885231, _885233, _885235, _885237, _885239] : [-(c_Com_Ocom_Ocom__case(_885217, _885219, _885221, _885223, _885225, _885227, _885229, _885231, _885233, c_Com_Ocom_OLocal(_885235, _885237, _885239)) = hAPP(hAPP(hAPP(_885223, _885235), _885237), _885239))], (1262 ^ _778908) ^ [_797557, _797559] : [-(class_Rings_Oidom(_797557)), _797559 = _797557, class_Rings_Oidom(_797559)], (12043 ^ _778908) ^ [_980915, _980917, _980919, _980921] : [class_Rings_Oordered__comm__semiring(_980915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980915), _980917), _980919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980915), c_Groups_Ozero__class_Ozero(_980915)), _980921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980915), _980921), _980917)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980915), _980921), _980919))))], (44685 ^ _778908) ^ [_1653022, _1653024, _1653026, _1653028, _1653030, _1653032] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1653022, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1653024, _1653022, _1653026), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653028, tc_fun(_1653024, tc_HOL_Obool)), _1653030), _1653032))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653028, tc_fun(_1653022, tc_HOL_Obool)), _1653030), hAPP(hAPP(c_COMBB(tc_fun(_1653024, tc_HOL_Obool), tc_fun(_1653022, tc_HOL_Obool), _1653028), c_Relation_OImage(_1653024, _1653022, _1653026)), _1653032)))))], (33950 ^ _778908) ^ [_1399344, _1399346] : [class_Orderings_Olinorder(_1399344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399344), _1399346)), -(_1399346 = c_Orderings_Obot__class_Obot(tc_fun(_1399344, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399344), c_Big__Operators_Olattice_OInf__fin(_1399344, c_Orderings_Oord__class_Omin(_1399344), _1399346)), c_Big__Operators_Olattice_OSup__fin(_1399344, c_Orderings_Oord__class_Omax(_1399344), _1399346))))], (17427 ^ _778908) ^ [_1079971] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1079971) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16855 ^ _778908) ^ [_1068874, _1068876, _1068878] : [class_Groups_Oordered__ab__group__add__abs(_1068874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068874), _1068876), _1068878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068874), hAPP(c_Groups_Ouminus__class_Ouminus(_1068874), _1068876)), _1068878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068874), hAPP(c_Groups_Oabs__class_Oabs(_1068874), _1068876)), _1068878)))], (17179 ^ _778908) ^ [_1075429, _1075431] : [class_Groups_Oordered__ab__group__add__abs(_1075429), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075429), hAPP(c_Groups_Ouminus__class_Ouminus(_1075429), hAPP(c_Groups_Oabs__class_Oabs(_1075429), _1075431))), c_Groups_Ozero__class_Ozero(_1075429))))], (28041 ^ _778908) ^ [_1276040, _1276042, _1276044, _1276046, _1276048] : [-(hAPP(c_Set_Oimage(_1276040, _1276042, _1276044), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276040, tc_HOL_Obool)), _1276046), _1276048)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276042, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1276040, _1276042, _1276044), _1276046)), hAPP(c_Set_Oimage(_1276040, _1276042, _1276044), _1276048)))], (51043 ^ _778908) ^ [_1805654, _1805656, _1805658] : [class_Orderings_Olinorder(_1805654), c_List_Olinorder__class_Osorted(_1805654, hAPP(c_List_Orev(_1805654), _1805656)), 51050 ^ _778908 : [(51057 ^ _778908) ^ [] : [-(_1805656 = c_List_Olist_ONil(_1805654)), -(c_List_Ofoldr(_1805654, _1805654, c_Orderings_Oord__class_Omax(_1805654), _1805656, _1805658) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1805654), hAPP(hAPP(c_List_Onth(_1805654), _1805656), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1805658))], (51051 ^ _778908) ^ [] : [_1805656 = c_List_Olist_ONil(_1805654), -(c_List_Ofoldr(_1805654, _1805654, c_Orderings_Oord__class_Omax(_1805654), _1805656, _1805658) = _1805658)]]], (45707 ^ _778908) ^ [_1678821, _1678823] : [-(c_Wellfounded_Owf(_1678821, _1678823)), 45710 ^ _778908 : [(45713 ^ _778908) ^ [_1679041] : [hBOOL(hAPP(hAPP(c_member(_1678821), _1679041), 45708 ^ [_1678821, _1678823])), 45717 ^ _778908 : [(45720 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678821), 45716 ^ [_1678821, _1678823, _1679041]), 45708 ^ [_1678821, _1678823])))], (45718 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678821, _1678821)), hAPP(hAPP(c_Product__Type_OPair(_1678821, _1678821), 45716 ^ [_1678821, _1678823, _1679041]), _1679041)), _1678823)))]]], (45711 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678821), 45709 ^ [_1678821, _1678823]), 45708 ^ [_1678821, _1678823])))]]], (47795 ^ _778908) ^ [_1730792, _1730794] : [class_Groups_Ocomm__monoid__add(_1730792), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1730792), _1730794) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1730792), hAPP(c_List_Onth(_1730792), _1730794)), 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(_1730792)), _1730794))))], (50881 ^ _778908) ^ [_1801480, _1801482, _1801484] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1801480), tc_List_Olist(_1801480), c_List_Oappend(_1801480), _1801482), _1801484) = hAPP(hAPP(c_List_Oappend(_1801480), _1801482), c_List_Oconcat(_1801480, _1801484)))], (5869 ^ _778908) ^ [_872411, _872413, _872415, _872417, _872419] : [c_Com_Ocom_OCall(_872411, _872413, _872415) = c_Com_Ocom_OAss(_872417, _872419)], (43277 ^ _778908) ^ [_1620494, _1620496, _1620498] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1620494, _1620496, _1620496), _1620498), c_Relation_OId(_1620496)) = _1620498)], (29347 ^ _778908) ^ [_1303350, _1303352, _1303354, _1303356] : [class_Groups_Ocomm__monoid__add(_1303350), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1303352), _1303354))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1303352, _1303350), _1303356), _1303354) = c_Groups_Ozero__class_Ozero(_1303350))], (25249 ^ _778908) ^ [_1222859, _1222861, _1222863, _1222865] : [class_Groups_Oordered__ab__group__add__abs(_1222859), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222859), hAPP(c_Groups_Oabs__class_Oabs(_1222859), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222861, _1222859), _1222863), _1222865))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222861, _1222859), hAPP(hAPP(c_COMBB(_1222859, _1222859, _1222861), c_Groups_Oabs__class_Oabs(_1222859)), _1222863)), _1222865))))], (45127 ^ _778908) ^ [_1665628, _1665630, _1665632] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665628, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1665628, tc_HOL_Obool)), _1665630), _1665632)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665628, tc_HOL_Obool)), _1665630), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665628, tc_HOL_Obool), _1665632)))], (25945 ^ _778908) ^ [_1234634, _1234636] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234634), _1234636)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234634)), _1234636)))], (22406 ^ _778908) ^ [_1167026] : [-(_1167026 = 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)), _1167026)))], (33511 ^ _778908) ^ [_1390214, _1390216, _1390218] : [class_Orderings_Olinorder(_1390214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390214), _1390216)), hBOOL(hAPP(hAPP(c_member(_1390214), _1390218), _1390216)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1390214), _1390218), c_Big__Operators_Olinorder__class_OMax(_1390214, _1390216)) = c_Big__Operators_Olinorder__class_OMax(_1390214, _1390216))], (5560 ^ _778908) ^ [_864834, _864836, _864838, _864840] : [-(c_List_Ofilter(_864840, _864836) = c_List_Ofilter(_864838, _864834)), _864840 = _864838, _864836 = _864834], (28595 ^ _778908) ^ [_1287091, _1287093] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1287091, _1287093)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1287093), hAPP(c_Nat_OSuc, _1287091)))], (18465 ^ _778908) ^ [_1097601] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097601) = 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(_1097601)))))], (26163 ^ _778908) ^ [_1239461, _1239463] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1239461))), _1239463)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239461), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239463))))], (4534 ^ _778908) ^ [_849065, _849067, _849069, _849071, _849073, _849075, _849077, _849079] : [-(c_Product__Type_Oscomp(_849079, _849075, _849071, _849067) = c_Product__Type_Oscomp(_849077, _849073, _849069, _849065)), _849079 = _849077, _849075 = _849073, _849071 = _849069, _849067 = _849065], (3972 ^ _778908) ^ [_840188, _840190, _840192, _840194] : [-(c_Predicate_OPowp(_840194, _840190) = c_Predicate_OPowp(_840192, _840188)), _840194 = _840192, _840190 = _840188], (40274 ^ _778908) ^ [_1541542, _1541544, _1541546, _1541548] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1541542), _1541544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541542, _1541542), tc_HOL_Obool)), _1541546), hAPP(hAPP(c_Product__Type_OSigma(_1541542, _1541542), _1541544), hAPP(c_COMBK(tc_fun(_1541542, tc_HOL_Obool), _1541542), _1541544)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1541542, tc_HOL_Obool)), _1541548), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1541542), _1541544), _1541546))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1541542), _1541548)))], (20877 ^ _778908) ^ [_1139048, _1139050, _1139052, _1139054, _1139056] : [class_Fields_Olinordered__field(_1139048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139048), c_Groups_Ozero__class_Ozero(_1139048)), _1139050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139048), _1139050), _1139052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139048), c_Groups_Ozero__class_Ozero(_1139048)), _1139054)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139048), _1139054), _1139056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139048), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139048), _1139050), _1139056)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139048), _1139052), _1139054))))], (42036 ^ _778908) ^ [_1589740] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1589740)))], (46380 ^ _778908) ^ [_1694590, _1694592, _1694594, _1694596] : [-(hBOOL(hAPP(c_List_Odistinct(_1694590), hAPP(hAPP(c_List_Omap(_1694592, _1694590), _1694594), _1694596)))), hBOOL(hAPP(c_List_Odistinct(_1694592), _1694596)), c_Fun_Oinj__on(_1694592, _1694590, _1694594, hAPP(c_List_Oset(_1694592), _1694596))], (490 ^ _778908) ^ [_786399, _786401, _786403, _786405, _786407, _786409] : [-(c_Big__Operators_Osemilattice__big(_786407, _786403, _786399)), c_Big__Operators_Osemilattice__big(_786409, _786405, _786401), _786409 = _786407, _786405 = _786403, _786401 = _786399], (37248 ^ _778908) ^ [_1472886, _1472888, _1472890] : [class_Lattices_Oboolean__algebra(_1472886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1472886), _1472888), _1472890) = c_Orderings_Obot__class_Obot(_1472886), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1472886), _1472888), _1472890) = c_Orderings_Otop__class_Otop(_1472886), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1472886), _1472888) = _1472890)], (43177 ^ _778908) ^ [_1617984] : [-(c_Transitive__Closure_Ortrancl(_1617984, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1617984, _1617984), tc_HOL_Obool))) = c_Relation_OId(_1617984))], (47703 ^ _778908) ^ [_1728670, _1728672, _1728674] : [_1728670 = _1728672, 47706 ^ _778908 : [(47709 ^ _778908) ^ [_1728818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728818), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728674)), _1728670))), -(hAPP(hAPP(c_List_Onth(_1728674), _1728670), _1728818) = hAPP(hAPP(c_List_Onth(_1728674), _1728672), _1728818))], (47707 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728674)), _1728670) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728674)), _1728672))]]], (28553 ^ _778908) ^ [_1286208, _1286210, _1286212, _1286214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286208, tc_HOL_Obool)), _1286210), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286208, tc_HOL_Obool)), _1286212), _1286214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286208, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286208, tc_HOL_Obool)), _1286210), _1286212)), _1286214)))], (22332 ^ _778908) ^ [_1165784, _1165786] : [-(_1165784 = _1165786), -(c_Random_Oinc__shift(_1165784, _1165786) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1165786), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (48506 ^ _778908) ^ [_1747850, _1747852, _1747854, _1747856, _1747858] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1747850, _1747852)), _1747854), hAPP(hAPP(c_List_Ozip(_1747850, _1747852), _1747856), _1747858)) = hAPP(hAPP(c_List_Ozip(_1747850, _1747852), hAPP(hAPP(c_List_Otake(_1747850), _1747854), _1747856)), hAPP(hAPP(c_List_Otake(_1747852), _1747854), _1747858)))], (42670 ^ _778908) ^ [_1605609, _1605611] : [42672 ^ _778908 : [(42675 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1605611), 42671 ^ [_1605609, _1605611]))], (42673 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42671 ^ [_1605609, _1605611]), _1605609)))]], -(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)), _1605611), _1605609))], (34982 ^ _778908) ^ [_1420523, _1420525, _1420527, _1420529] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1420523), _1420525)), 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)), _1420523), _1420527)), 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)), _1420525), _1420529)), c_FunDef_Omin__strict)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1420525), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1420527), _1420529))), c_FunDef_Omin__strict)))], (18163 ^ _778908) ^ [_1092835] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092835))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092835)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4440 ^ _778908) ^ [_847574, _847576, _847578, _847580] : [-(c_Hilbert__Choice_OEps(_847580, _847576) = c_Hilbert__Choice_OEps(_847578, _847574)), _847580 = _847578, _847576 = _847574], (11703 ^ _778908) ^ [_974868, _974870, _974872, _974874, _974876] : [c_Natural_Oevaln(_974868, _974870, _974872, _974874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974872), _974876)), -(c_Natural_Oevaln(_974868, _974870, _974876, _974874))], (41113 ^ _778908) ^ [_1559773] : [-(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)), _1559773)))))], (47886 ^ _778908) ^ [_1733290, _1733292, _1733294, _1733296, _1733298] : [-(hAPP(hAPP(c_List_Olist__update(_1733290, hAPP(hAPP(c_List_Olist__update(_1733290, _1733292), _1733294), _1733296)), _1733294), _1733298) = hAPP(hAPP(c_List_Olist__update(_1733290, _1733292), _1733294), _1733298))], (48078 ^ _778908) ^ [_1737921, _1737923, _1737925, _1737927, _1737929] : [hAPP(hAPP(c_List_Olist_OCons(_1737921), _1737923), _1737925) = hAPP(hAPP(c_List_Oappend(_1737921), _1737927), _1737929), 48083 ^ _778908 : [(48086 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1737921), _1737923), _1737925) = _1737929)], (48084 ^ _778908) ^ [] : [-(_1737927 = c_List_Olist_ONil(_1737921))]], 48088 ^ _778908 : [(48091 ^ _778908) ^ [] : [-(_1737925 = hAPP(hAPP(c_List_Oappend(_1737921), 48087 ^ [_1737921, _1737923, _1737925, _1737927, _1737929]), _1737929))], (48089 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1737921), _1737923), 48087 ^ [_1737921, _1737923, _1737925, _1737927, _1737929]) = _1737927)]]], (45875 ^ _778908) ^ [_1682429, _1682431, _1682433, _1682435] : [-(c_Map_Odom(_1682429, _1682431, c_Map_Omap__add(_1682429, _1682431, _1682433, _1682435)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1682429, tc_HOL_Obool)), c_Map_Odom(_1682429, _1682431, _1682435)), c_Map_Odom(_1682429, _1682431, _1682433)))], (31584 ^ _778908) ^ [_1349024, _1349026, _1349028, _1349030] : [-(hBOOL(hAPP(hAPP(c_member(_1349024), hAPP(_1349026, _1349028)), hAPP(c_Set_Oimage(_1349030, _1349024, _1349026), c_Orderings_Otop__class_Otop(tc_fun(_1349030, tc_HOL_Obool))))))], (31044 ^ _778908) ^ [_1336164, _1336166, _1336168] : [_1336164 = c_Orderings_Obot__class_Obot(tc_fun(_1336166, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1336166), _1336168), _1336164))], (31526 ^ _778908) ^ [_1347800, _1347802, _1347804] : [_1347802 = _1347804, -(hBOOL(hAPP(hAPP(c_member(_1347800), _1347802), hAPP(hAPP(c_Set_Oinsert(_1347800), _1347804), c_Orderings_Obot__class_Obot(tc_fun(_1347800, tc_HOL_Obool))))))], (29181 ^ _778908) ^ [] : [-(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))))], (40662 ^ _778908) ^ [_1551369, _1551371, _1551373] : [class_Lattices_Osemilattice__inf(_1551369), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551369), _1551371)), hBOOL(hAPP(hAPP(c_member(_1551369), _1551373), _1551371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551369), hAPP(c_Finite__Set_Ofold1(_1551369, c_Lattices_Osemilattice__inf__class_Oinf(_1551369)), _1551371)), _1551373)))], (17607 ^ _778908) ^ [_1083220, _1083222, _1083224] : [class_Power_Opower(_1083220), class_Rings_Omult__zero(_1083220), class_Rings_Ono__zero__divisors(_1083220), class_Rings_Ozero__neq__one(_1083220), 17622 ^ _778908 : [(17631 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1083220), _1083222), _1083224) = c_Groups_Ozero__class_Ozero(_1083220)), _1083222 = c_Groups_Ozero__class_Ozero(_1083220), -(_1083224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17623 ^ _778908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1083220), _1083222), _1083224) = c_Groups_Ozero__class_Ozero(_1083220), 17626 ^ _778908 : [(17629 ^ _778908) ^ [] : [_1083224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17627 ^ _778908) ^ [] : [-(_1083222 = c_Groups_Ozero__class_Ozero(_1083220))]]]]], (34885 ^ _778908) ^ [_1418217, _1418219, _1418221, _1418223, _1418225, _1418227] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418217, tc_Option_Ooption(_1418219)), c_Map_Orestrict__map(_1418217, _1418219, _1418221, _1418223)), _1418225), _1418227) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418217, tc_Option_Ooption(_1418219)), c_Map_Orestrict__map(_1418217, _1418219, _1418221, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1418217, tc_HOL_Obool)), _1418223), hAPP(hAPP(c_Set_Oinsert(_1418217), _1418225), c_Orderings_Obot__class_Obot(tc_fun(_1418217, tc_HOL_Obool)))))), _1418225), _1418227))], (42550 ^ _778908) ^ [_1602382, _1602384, _1602386] : [-(c_Relation_Orefl__on(_1602382, _1602384, _1602386)), 42554 ^ _778908 : [(42557 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1602382, _1602382, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1602382, tc_fun(_1602382, tc_HOL_Obool), tc_fun(_1602382, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1602382, tc_HOL_Obool), tc_fun(_1602382, tc_HOL_Obool)), _1602382), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1602382)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1602382), c_fconj), hAPP(hAPP(c_COMBC(_1602382, tc_fun(_1602382, tc_HOL_Obool), tc_HOL_Obool), c_member(_1602382)), _1602384)))), hAPP(hAPP(c_COMBC(_1602382, tc_fun(_1602382, tc_HOL_Obool), tc_HOL_Obool), c_member(_1602382)), _1602384))), 42553 ^ [_1602382, _1602384, _1602386]))], (42555 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602382, _1602382)), 42553 ^ [_1602382, _1602384, _1602386]), _1602386)))]], 42559 ^ _778908 : [(42562 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602382, _1602382)), hAPP(hAPP(c_Product__Type_OPair(_1602382, _1602382), 42558 ^ [_1602382, _1602384, _1602386]), 42558 ^ [_1602382, _1602384, _1602386])), _1602386))], (42560 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602382), 42558 ^ [_1602382, _1602384, _1602386]), _1602384)))]]], (37042 ^ _778908) ^ [_1468350, _1468352, _1468354] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468350, tc_HOL_Obool)), _1468352), _1468354) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468350, tc_HOL_Obool)), _1468352), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468350, tc_HOL_Obool)), _1468354)))], (6536 ^ _778908) ^ [_884918, _884920] : [c_Com_Ocom_OSemi(_884918, _884920) = c_Com_Ocom_OSKIP], (24191 ^ _778908) ^ [_1201466, _1201468, _1201470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201466, tc_HOL_Obool)), _1201468), _1201470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201466, tc_HOL_Obool)), _1201468), _1201470)))], (32325 ^ _778908) ^ [_1366653, _1366655] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1366653), 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)))), _1366655))), 32328 ^ _778908 : [(32331 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1366655), _1366653))], (32329 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1366653), _1366655)))]]], (1612 ^ _778908) ^ [_801932, _801934] : [-(class_Rings_Ocomm__semiring__1(_801932)), _801934 = _801932, class_Rings_Ocomm__semiring__1(_801934)], (39564 ^ _778908) ^ [_1523610, _1523612, _1523614, _1523616] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523610), _1523612)), c_Fun_Oinj__on(_1523614, _1523610, _1523616, c_Orderings_Otop__class_Otop(tc_fun(_1523614, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523614), hAPP(c_Set_Ovimage(_1523614, _1523610, _1523616), _1523612))))], (21433 ^ _778908) ^ [_1149039, _1149041, _1149043, _1149045] : [class_Fields_Ofield__inverse__zero(_1149039), class_Int_Onumber(_1149039), 21440 ^ _778908 : [(21441 ^ _778908) ^ [] : [_1149041 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149039), _1149043), hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045)), 21444 ^ _778908 : [(21451 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045) = c_Groups_Ozero__class_Ozero(_1149039), -(_1149041 = c_Groups_Ozero__class_Ozero(_1149039))], (21445 ^ _778908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045) = c_Groups_Ozero__class_Ozero(_1149039)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149039), _1149041), hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045)) = _1149043)]]], (21457 ^ _778908) ^ [] : [-(_1149041 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149039), _1149043), hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045))), 21460 ^ _778908 : [(21463 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149039), _1149041), hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045)) = _1149043], (21461 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045) = c_Groups_Ozero__class_Ozero(_1149039)]], 21464 ^ _778908 : [(21467 ^ _778908) ^ [] : [_1149041 = c_Groups_Ozero__class_Ozero(_1149039)], (21465 ^ _778908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1149039), _1149045) = c_Groups_Ozero__class_Ozero(_1149039))]]]]], (48903 ^ _778908) ^ [_1759048, _1759050, _1759052, _1759054, _1759056] : [hAPP(hAPP(c_List_Odrop(_1759048), _1759050), _1759052) = hAPP(hAPP(c_List_Olist_OCons(_1759048), _1759054), _1759056), -(hAPP(hAPP(c_List_Onth(_1759048), _1759052), _1759050) = _1759054)], (12383 ^ _778908) ^ [_986958, _986960, _986962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986958), _986960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986962), _986960))), 12386 ^ _778908 : [(12389 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986958), _986962)))], (12387 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _986960)))]]], (11168 ^ _778908) ^ [_965659, _965661, _965663, _965665] : [class_Orderings_Opreorder(_965659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965659), _965661), _965663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965659), _965663), _965665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965659), _965661), _965665)))], (35490 ^ _778908) ^ [_1432383, _1432385, _1432387] : [hAPP(c_Set_Oimage(_1432385, tc_fun(_1432385, tc_HOL_Obool), _1432383), _1432387) = hAPP(c_Set_OPow(_1432385), _1432387)], (18551 ^ _778908) ^ [_1098820, _1098822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1098820)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1098822)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098820)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1098822), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1098820))))], (51289 ^ _778908) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (30398 ^ _778908) ^ [_1323423] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1323423), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (39828 ^ _778908) ^ [_1529857, _1529859, _1529861] : [hBOOL(hAPP(hAPP(c_member(_1529857), _1529861), c_Wellfounded_Oacc(_1529857, _1529859))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1529857, hAPP(hAPP(c_COMBC(_1529857, tc_fun(tc_prod(_1529857, _1529857), tc_HOL_Obool), tc_fun(_1529857, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529857, tc_fun(tc_fun(tc_prod(_1529857, _1529857), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529857, _1529857), tc_HOL_Obool), tc_fun(_1529857, tc_HOL_Obool)), _1529857), c_COMBC(_1529857, tc_fun(tc_prod(_1529857, _1529857), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529857, tc_prod(_1529857, _1529857)), tc_fun(_1529857, tc_fun(tc_fun(tc_prod(_1529857, _1529857), tc_HOL_Obool), tc_HOL_Obool)), _1529857), hAPP(c_COMBB(tc_prod(_1529857, _1529857), tc_fun(tc_fun(tc_prod(_1529857, _1529857), tc_HOL_Obool), tc_HOL_Obool), _1529857), c_member(tc_prod(_1529857, _1529857)))), c_Product__Type_OPair(_1529857, _1529857)))), _1529859)), _1529861)))], (38766 ^ _778908) ^ [_1506055, _1506057, _1506059, _1506061, _1506063] : [c_Fun_Oinj__on(_1506055, _1506057, _1506059, _1506061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1506055, tc_HOL_Obool)), _1506063), _1506061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1506057, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1506055, _1506057, _1506059), _1506063)), hAPP(c_Set_Oimage(_1506055, _1506057, _1506059), _1506061))))], (6316 ^ _778908) ^ [_880712, _880714, _880716] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_880712), _880714), _880716)), -(c_Natural_Oevaln(_880712, _880714, 6319 ^ [_880712, _880714, _880716], _880716))], (36346 ^ _778908) ^ [_1452982, _1452984, _1452986] : [36347 ^ _778908 : [(36350 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1452982), _1452986))], (36348 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1452982), _1452984))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1452982), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452982, tc_HOL_Obool)), _1452984), _1452986))))], (19785 ^ _778908) ^ [_1119750] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119750), _1119750)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1119750)], (19303 ^ _778908) ^ [_1111349, _1111351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111349), _1111351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1111349)), c_Int_OBit0(_1111351))))], (18531 ^ _778908) ^ [_1098540, _1098542] : [class_Int_Onumber__ring(_1098540), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098540), _1098542), hAPP(c_Int_Onumber__class_Onumber__of(_1098540), c_Int_OPls)) = _1098542)], (2552 ^ _778908) ^ [_817494, _817496, _817498, _817500] : [-(c_Divides_Odivmod__int(_817500, _817496) = c_Divides_Odivmod__int(_817498, _817494)), _817500 = _817498, _817496 = _817494], (46358 ^ _778908) ^ [_1693851, _1693853, _1693855, _1693857] : [-(c_Map_Omap__of(_1693851, _1693853, hAPP(hAPP(c_List_Omap(_1693851, tc_prod(_1693851, _1693853)), hAPP(hAPP(c_COMBS(_1693851, _1693853, tc_prod(_1693851, _1693853)), c_Product__Type_OPair(_1693851, _1693853)), _1693855)), _1693857)) = c_Map_Orestrict__map(_1693851, _1693853, hAPP(c_Fun_Ocomp(_1693853, tc_Option_Ooption(_1693853), _1693851, c_Option_Ooption_OSome(_1693853)), _1693855), hAPP(c_List_Oset(_1693851), _1693857)))], (10525 ^ _778908) ^ [_955755, _955757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _955755), _955757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _955757), _955755)), -(_955755 = _955757)], (30400 ^ _778908) ^ [_1323452, _1323454, _1323456] : [class_Orderings_Oorder(_1323452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323452), _1323454), _1323456)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1323452, _1323456, _1323454) = c_Orderings_Obot__class_Obot(tc_fun(_1323452, tc_HOL_Obool)))], (24287 ^ _778908) ^ [_1203372, _1203374] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203372, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203372, tc_HOL_Obool)), _1203374)) = _1203374)], (11028 ^ _778908) ^ [_963709, _963711, _963713] : [class_Orderings_Olinorder(_963709), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963709), _963711), _963713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963709), _963713), _963711)))], (32935 ^ _778908) ^ [_1378684, _1378686] : [32936 ^ _778908 : [(32939 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378686), _1378684))], (32937 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378684), _1378686)))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1378684, _1378686) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (48993 ^ _778908) ^ [_1761035, _1761037, _1761039, _1761041] : [-(hAPP(hAPP(c_List_Odrop(_1761035), _1761037), hAPP(hAPP(c_List_Otake(_1761035), _1761039), _1761041)) = hAPP(hAPP(c_List_Otake(_1761035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1761039), _1761037)), hAPP(hAPP(c_List_Odrop(_1761035), _1761037), _1761041)))], (51499 ^ _778908) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (48825 ^ _778908) ^ [_1756696, _1756698, _1756700, _1756702, _1756704, _1756706] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756696, _1756696)), hAPP(hAPP(c_Product__Type_OPair(_1756696, _1756696), _1756698), _1756700)), c_Transitive__Closure_Ortrancl(_1756696, _1756702))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756696), tc_List_Olist(_1756696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756696), tc_List_Olist(_1756696)), _1756704), _1756706)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756696), c_List_Olistrel1(_1756696, _1756702)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756696), tc_List_Olist(_1756696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756696), tc_List_Olist(_1756696)), hAPP(hAPP(c_List_Olist_OCons(_1756696), _1756698), _1756704)), hAPP(hAPP(c_List_Olist_OCons(_1756696), _1756700), _1756706))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756696), c_List_Olistrel1(_1756696, _1756702)))))], (31532 ^ _778908) ^ [_1347921, _1347923, _1347925] : [hBOOL(hAPP(hAPP(c_member(_1347921), _1347923), hAPP(hAPP(c_Set_Oinsert(_1347921), _1347925), c_Orderings_Obot__class_Obot(tc_fun(_1347921, tc_HOL_Obool))))), -(_1347923 = _1347925)], (12269 ^ _778908) ^ [_985019, _985021] : [class_Groups_Oordered__ab__group__add(_985019), 12272 ^ _778908 : [(12279 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985019), _985021), c_Groups_Ozero__class_Ozero(_985019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985019), c_Groups_Ozero__class_Ozero(_985019)), hAPP(c_Groups_Ouminus__class_Ouminus(_985019), _985021))))], (12273 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985019), c_Groups_Ozero__class_Ozero(_985019)), hAPP(c_Groups_Ouminus__class_Ouminus(_985019), _985021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985019), _985021), c_Groups_Ozero__class_Ozero(_985019))))]]], (27284 ^ _778908) ^ [_1260930, _1260932, _1260934, _1260936, _1260938] : [class_Groups_Ocomm__monoid__add(_1260930), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1260930), _1260932), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1260934), _1260936)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1260938), _1260936))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1260930), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1260930, tc_Nat_Onat), _1260932), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1260936))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1260934), _1260938)))], (11643 ^ _778908) ^ [_973762, _973764, _973766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973762), _973764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973762), _973766)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973764), _973766))))], (22097 ^ _778908) ^ [_1161565, _1161567, _1161569, _1161571] : [class_Fields_Olinordered__field__inverse__zero(_1161565), class_Int_Onumber(_1161565), 22104 ^ _778908 : [(22105 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161565), _1161567), _1161569)), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571))), 22108 ^ _778908 : [(22115 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), c_Groups_Ozero__class_Ozero(_1161565)), _1161569))), 22118 ^ _778908 : [(22125 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), _1161569), c_Groups_Ozero__class_Ozero(_1161565)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), c_Groups_Ozero__class_Ozero(_1161565)), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571))))], (22119 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), _1161569), c_Groups_Ozero__class_Ozero(_1161565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161565), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571)), _1161569)), _1161567)))]]], (22109 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), c_Groups_Ozero__class_Ozero(_1161565)), _1161569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), _1161567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161565), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571)), _1161569))))]]], (22131 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161565), _1161567), _1161569)), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571)))), 22134 ^ _778908 : [(22137 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), _1161567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161565), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571)), _1161569)))], (22135 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), c_Groups_Ozero__class_Ozero(_1161565)), _1161569)))]], 22138 ^ _778908 : [(22141 ^ _778908) ^ [] : [22142 ^ _778908 : [(22145 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161565), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571)), _1161569)), _1161567))], (22143 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), _1161569), c_Groups_Ozero__class_Ozero(_1161565))))]], 22146 ^ _778908 : [(22149 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161565), c_Groups_Ozero__class_Ozero(_1161565)), hAPP(c_Int_Onumber__class_Onumber__of(_1161565), _1161571)))], (22147 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), _1161569), c_Groups_Ozero__class_Ozero(_1161565)))]]], (22139 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161565), c_Groups_Ozero__class_Ozero(_1161565)), _1161569))]]]]], (24885 ^ _778908) ^ [_1214929, _1214931] : [-(c_Code__Numeral_Onat__of__aux(_1214929, _1214931) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1214929)), _1214931))], (18307 ^ _778908) ^ [_1095255] : [class_Int_Onumber__ring(_1095255), -(hAPP(c_Int_Onumber__class_Onumber__of(_1095255), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1095255), c_Groups_Oone__class_Oone(_1095255)))], (42182 ^ _778908) ^ [_1593096, _1593098, _1593100] : [hAPP(c_Relation_ORange(_1593096, _1593098), _1593100) = c_Orderings_Obot__class_Obot(tc_fun(_1593098, tc_HOL_Obool)), -(_1593100 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1593096, _1593098), tc_HOL_Obool)))], (24863 ^ _778908) ^ [_1214526, _1214528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1214526)), hAPP(c_Code__Numeral_Onat__of, _1214528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1214526), _1214528)))], (30452 ^ _778908) ^ [] : [-(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)))], (9850 ^ _778908) ^ [_944104, _944106, _944108] : [class_Rings_Olinordered__semiring__strict(_944104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944104), c_Groups_Ozero__class_Ozero(_944104)), _944106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944104), _944108), c_Groups_Ozero__class_Ozero(_944104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944104), _944108), _944106)), c_Groups_Ozero__class_Ozero(_944104))))], (1422 ^ _778908) ^ [_799557, _799559] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_799557)), _799559 = _799557, class_Groups_Oordered__cancel__ab__semigroup__add(_799559)], (33233 ^ _778908) ^ [_1385260, _1385262, _1385264] : [class_Lattices_Olattice(_1385260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385260), _1385262)), -(_1385264 = c_Orderings_Obot__class_Obot(tc_fun(_1385260, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1385260, tc_HOL_Obool)), _1385264), _1385262)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1385260), c_Big__Operators_Olattice__class_OSup__fin(_1385260, _1385264)), c_Big__Operators_Olattice__class_OSup__fin(_1385260, _1385262)) = c_Big__Operators_Olattice__class_OSup__fin(_1385260, _1385262))], (19683 ^ _778908) ^ [_1118020, _1118022] : [class_Int_Onumber__ring(_1118020), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118020), _1118022), hAPP(c_Int_Onumber__class_Onumber__of(_1118020), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118020), _1118022), _1118022))], (17123 ^ _778908) ^ [_1074187, _1074189] : [class_Rings_Olinordered__idom(_1074187), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074187), c_Groups_Osgn__class_Osgn(_1074187, _1074189)), hAPP(c_Groups_Oabs__class_Oabs(_1074187), _1074189)) = _1074189)], (11346 ^ _778908) ^ [_968817, _968819] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968817), _968819) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_968817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_968819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6343 ^ _778908) ^ [_881167, _881169, _881171] : [hBOOL(hAPP(c_Com_OWT, _881171)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_881167, _881169, _881171))))], (51617 ^ _778908) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (23997 ^ _778908) ^ [_1197462, _1197464, _1197466, _1197468] : [_1197462 = _1197464, 24000 ^ _778908 : [(24003 ^ _778908) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1197466, _1197468), _1197462) = hAPP(c_Product__Type_Osnd(_1197466, _1197468), _1197464))], (24001 ^ _778908) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1197466, _1197468), _1197462) = hAPP(c_Product__Type_Ofst(_1197466, _1197468), _1197464))]]], (48124 ^ _778908) ^ [_1738878, _1738880, _1738882, _1738884, _1738886] : [-(hAPP(hAPP(c_List_Oappend(_1738878), _1738880), _1738882) = hAPP(hAPP(c_List_Olist_OCons(_1738878), _1738884), _1738886)), 48125 ^ _778908 : [(48132 ^ _778908) ^ [_1739061] : [_1738880 = hAPP(hAPP(c_List_Olist_OCons(_1738878), _1738884), _1739061), hAPP(hAPP(c_List_Oappend(_1738878), _1739061), _1738882) = _1738886], (48126 ^ _778908) ^ [] : [_1738880 = c_List_Olist_ONil(_1738878), _1738882 = hAPP(hAPP(c_List_Olist_OCons(_1738878), _1738884), _1738886)]]], (51247 ^ _778908) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (41139 ^ _778908) ^ [_1560317, _1560319] : [-(hAPP(c_Set_OCollect(_1560317), hAPP(hAPP(c_COMBC(_1560317, _1560317, tc_HOL_Obool), c_fequal), _1560319)) = hAPP(hAPP(c_Set_Oinsert(_1560317), _1560319), c_Orderings_Obot__class_Obot(tc_fun(_1560317, tc_HOL_Obool))))], (18601 ^ _778908) ^ [_1099588] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099588), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099588)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1099588)))], (28739 ^ _778908) ^ [_1289981, _1289983, _1289985, _1289987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289981, _1289983)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289985, _1289987))), 28742 ^ _778908 : [(28743 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289981), _1289983)), 28746 ^ _778908 : [(28751 ^ _778908) ^ [] : [28752 ^ _778908 : [(28755 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289981), _1289985))], (28753 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289985), _1289981)))]], 28756 ^ _778908 : [(28759 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289987), _1289983))], (28757 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289983), _1289987)))]]], (28749 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289983), _1289987)))], (28747 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289985), _1289981)))]]], (28761 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1289985), _1289987)))]]], (20401 ^ _778908) ^ [_1131106, _1131108, _1131110, _1131112] : [class_Fields_Olinordered__field__inverse__zero(_1131106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131106), _1131108), _1131110)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131106), _1131112), c_Groups_Ozero__class_Ozero(_1131106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131106), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131106), _1131110), _1131112)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131106), _1131108), _1131112))))], (40012 ^ _778908) ^ [_1534091, _1534093, _1534095, _1534097] : [_1534095 = _1534097, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1534091, _1534093, hAPP(hAPP(c_Set_Oinsert(_1534091), _1534095), c_Orderings_Obot__class_Obot(tc_fun(_1534091, tc_HOL_Obool)))), _1534097)))], (25177 ^ _778908) ^ [_1221670, _1221672, _1221674, _1221676] : [-(c_Product__Type_Ocurry(_1221670, _1221672, _1221674, hAPP(c_Product__Type_Oprod_Oprod__case(_1221670, _1221672, _1221674), _1221676)) = _1221676)], (45135 ^ _778908) ^ [_1665798, _1665800, _1665802] : [class_Complete__Lattice_Ocomplete__lattice(_1665798), class_Orderings_Olinorder(_1665798), 45142 ^ _778908 : [(45152 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665798), c_Complete__Lattice_OInf__class_OInf(_1665798, _1665800)), _1665802))), 45153 ^ _778908 : [(45154 ^ _778908) ^ [_1666104] : [hBOOL(hAPP(hAPP(c_member(_1665798), _1666104), _1665800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665798), _1666104), _1665802))]]], (45143 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665798), c_Complete__Lattice_OInf__class_OInf(_1665798, _1665800)), _1665802)), 45147 ^ _778908 : [(45150 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665798), 45146 ^ [_1665798, _1665800, _1665802]), _1665802)))], (45148 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1665798), 45146 ^ [_1665798, _1665800, _1665802]), _1665800)))]]]]], (51345 ^ _778908) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (36716 ^ _778908) ^ [_1460547, _1460549, _1460551, _1460553, _1460555] : [-(c_Map_Orestrict__map(_1460547, _1460549, c_Map_Orestrict__map(_1460547, _1460549, _1460551, _1460553), _1460555) = c_Map_Orestrict__map(_1460547, _1460549, _1460551, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460547, tc_HOL_Obool)), _1460553), _1460555)))], (35807 ^ _778908) ^ [_1439995, _1439997, _1439999, _1440001, _1440003, _1440005] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1439995, tc_fun(_1439997, tc_HOL_Obool)), _1439999), hAPP(c_Fun_Ocomp(_1440001, tc_fun(_1439997, tc_HOL_Obool), _1439995, _1440003), _1440005)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1440001, tc_fun(_1439997, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1439995, _1440001, _1440005), _1439999)), _1440003))], (24099 ^ _778908) ^ [_1199752, _1199754, _1199756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199752, tc_HOL_Obool)), _1199754), _1199756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199752, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199752, tc_HOL_Obool)), _1199756)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199752, tc_HOL_Obool)), _1199754))))], (23735 ^ _778908) ^ [_1192608, _1192610, _1192612, _1192614] : [class_Orderings_Olinorder(_1192608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192608), _1192610), _1192612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192608), _1192610), _1192614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192608), _1192610), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192608), _1192612), _1192614))))], (43948 ^ _778908) ^ [_1637147, _1637149, _1637151, _1637153, _1637155, _1637157] : [c_Relation_Osingle__valued(_1637147, _1637149, _1637151), hBOOL(hAPP(hAPP(c_member(tc_prod(_1637147, _1637149)), hAPP(hAPP(c_Product__Type_OPair(_1637147, _1637149), _1637153), _1637155)), _1637151)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1637147, _1637149)), hAPP(hAPP(c_Product__Type_OPair(_1637147, _1637149), _1637153), _1637157)), _1637151)), -(_1637155 = _1637157)], (13622 ^ _778908) ^ [_1008541] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008541), _1008541)))], (37018 ^ _778908) ^ [_1467616, _1467618, _1467620, _1467622] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467616, tc_HOL_Obool)), _1467618), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467616, tc_HOL_Obool)), _1467620), _1467622)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467616, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467616, tc_HOL_Obool)), _1467618), _1467620)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467616, tc_HOL_Obool)), _1467618), _1467622)))], (38866 ^ _778908) ^ [_1508039, _1508041, _1508043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508039), _1508041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508039, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1508039, _1508039, _1508043), _1508041)), _1508041)), c_Fun_Oinj__on(_1508039, _1508039, _1508043, _1508041), -(hAPP(c_Set_Oimage(_1508039, _1508039, _1508043), _1508041) = _1508041)], (30816 ^ _778908) ^ [_1331512, _1331514, _1331516] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331512), _1331514)), 30819 ^ _778908 : [(30826 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331512), _1331516), _1331514))), -(hAPP(c_Finite__Set_Ocard(_1331512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331512, tc_HOL_Obool)), _1331514), hAPP(hAPP(c_Set_Oinsert(_1331512), _1331516), c_Orderings_Obot__class_Obot(tc_fun(_1331512, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1331512), _1331514))], (30820 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1331512), _1331516), _1331514)), -(hAPP(c_Finite__Set_Ocard(_1331512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331512, tc_HOL_Obool)), _1331514), hAPP(hAPP(c_Set_Oinsert(_1331512), _1331516), c_Orderings_Obot__class_Obot(tc_fun(_1331512, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1331512), _1331514)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (38682 ^ _778908) ^ [_1504471, _1504473, _1504475, _1504477, _1504479] : [c_Fun_Oinj__on(_1504471, _1504473, _1504475, _1504477), -(c_Fun_Oinj__on(_1504471, _1504473, _1504475, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1504471, tc_HOL_Obool)), _1504477), _1504479)))], (40556 ^ _778908) ^ [_1549538, _1549540, _1549542] : [class_Groups_Oab__semigroup__mult(_1549538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549538), _1549540)), -(_1549540 = c_Orderings_Obot__class_Obot(tc_fun(_1549538, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549538), _1549542)), -(_1549542 = c_Orderings_Obot__class_Obot(tc_fun(_1549538, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549538, tc_HOL_Obool)), _1549540), _1549542) = c_Orderings_Obot__class_Obot(tc_fun(_1549538, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1549538, c_Groups_Otimes__class_Otimes(_1549538)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1549538, tc_HOL_Obool)), _1549540), _1549542)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1549538), hAPP(c_Finite__Set_Ofold1(_1549538, c_Groups_Otimes__class_Otimes(_1549538)), _1549540)), hAPP(c_Finite__Set_Ofold1(_1549538, c_Groups_Otimes__class_Otimes(_1549538)), _1549542)))], (51265 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (394 ^ _778908) ^ [_784803, _784805, _784807, _784809, _784811, _784813, _784815, _784817] : [-(c_Finite__Set_Ofolding__idem(_784815, _784811, _784807, _784803)), c_Finite__Set_Ofolding__idem(_784817, _784813, _784809, _784805), _784817 = _784815, _784813 = _784811, _784809 = _784807, _784805 = _784803], (35532 ^ _778908) ^ [_1433346, _1433348, _1433350, _1433352, _1433354] : [c_Finite__Set_Ofolding__one__idem(_1433346, _1433348, _1433350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433346), _1433352)), -(_1433352 = c_Orderings_Obot__class_Obot(tc_fun(_1433346, tc_HOL_Obool))), -(hAPP(_1433350, hAPP(hAPP(c_Set_Oinsert(_1433346), _1433354), _1433352)) = hAPP(hAPP(_1433348, _1433354), hAPP(_1433350, _1433352)))], (50515 ^ _778908) ^ [_1793248, _1793250] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1793248, _1793250)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1793248), hAPP(c_Nat_OSuc, _1793250)))], (27278 ^ _778908) ^ [_1260759, _1260761, _1260763, _1260765] : [class_Groups_Ocomm__monoid__add(_1260759), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1260759), _1260761), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1260763)), hAPP(c_Nat_OSuc, _1260765))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1260759), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1260759, tc_Nat_Onat), _1260761), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1260763), _1260765)))], (7184 ^ _778908) ^ [_899075, _899077, _899079, _899081] : [class_Groups_Ocancel__semigroup__add(_899075), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899075), _899077), _899079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899075), _899081), _899079), -(_899077 = _899081)], (43203 ^ _778908) ^ [_1618672, _1618674, _1618676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1618672, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1618672, _1618672, _1618674), _1618676)), _1618676)), -(hAPP(c_Relation_OImage(_1618672, _1618672, c_Transitive__Closure_Ortrancl(_1618672, _1618674)), _1618676) = _1618676)], (42705 ^ _778908) ^ [_1606376, _1606378, _1606380, _1606382, _1606384, _1606386] : [42708 ^ _778908 : [(42711 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1606382), _1606384), hAPP(hAPP(_1606386, 42706 ^ [_1606376, _1606378, _1606380, _1606382, _1606384, _1606386]), 42707 ^ [_1606376, _1606378, _1606380, _1606382, _1606384, _1606386])))], (42709 ^ _778908) ^ [] : [-(_1606376 = hAPP(hAPP(c_Product__Type_OPair(_1606378, _1606380), 42706 ^ [_1606376, _1606378, _1606380, _1606382, _1606384, _1606386]), 42707 ^ [_1606376, _1606378, _1606380, _1606382, _1606384, _1606386]))]], -(hBOOL(hAPP(hAPP(c_member(_1606382), _1606384), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1606378, _1606380, tc_fun(_1606382, tc_HOL_Obool)), _1606386), _1606376))))], (42907 ^ _778908) ^ [_1611143, _1611145, _1611147, _1611149, _1611151, _1611153] : [class_Rings_Ocomm__semiring__1(_1611143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611145), _1611147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611145, tc_HOL_Obool)), _1611149), _1611147)), 42921 ^ _778908 : [(42924 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1611143), hAPP(_1611151, 42920 ^ [_1611143, _1611145, _1611147, _1611149, _1611151, _1611153])), hAPP(_1611153, 42920 ^ [_1611143, _1611145, _1611147, _1611149, _1611151, _1611153])))], (42922 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611145), 42920 ^ [_1611143, _1611145, _1611147, _1611149, _1611151, _1611153]), _1611149)))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1611143), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1611145, _1611143), _1611151), _1611149)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1611145, _1611143), _1611153), _1611147))))], (11665 ^ _778908) ^ [_974187, _974189, _974191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974187), _974189)), _974191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974187), _974191)))], (36756 ^ _778908) ^ [_1461389, _1461391, _1461393, _1461395] : [class_Lattices_Osemilattice__inf(_1461389), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461389), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461389), _1461391), _1461393)), _1461395) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461389), _1461391), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461389), _1461393), _1461395)))], (49133 ^ _778908) ^ [_1764589, _1764591, _1764593] : [-(_1764589 = c_List_Olist_ONil(_1764591)), -(hAPP(c_List_Ohd(_1764591), hAPP(hAPP(c_List_Oappend(_1764591), _1764589), _1764593)) = hAPP(c_List_Ohd(_1764591), _1764589))], (40132 ^ _778908) ^ [_1537720, _1537722, _1537724, _1537726, _1537728] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1537720, _1537722), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1537720, tc_HOL_Obool)), _1537724), _1537726)), _1537728) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537720, _1537722), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1537720, _1537722), _1537724), _1537728)), hAPP(hAPP(c_Product__Type_OSigma(_1537720, _1537722), _1537726), _1537728)))], (43701 ^ _778908) ^ [_1630910, _1630912, _1630914, _1630916] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630910, _1630910), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1630912), _1630914)), _1630916) = hAPP(hAPP(c_Relation_Orel__comp(_1630910, _1630910, _1630910), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630910, _1630910), tc_HOL_Obool), _1630912), _1630916)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630910, _1630910), tc_HOL_Obool), _1630914), _1630916)))], (30282 ^ _778908) ^ [_1321372, _1321374, _1321376] : [class_Orderings_Oorder(_1321372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321372), _1321374), _1321376)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1321372, _1321376, _1321374) = c_Orderings_Obot__class_Obot(tc_fun(_1321372, tc_HOL_Obool)))], (24549 ^ _778908) ^ [_1208412, _1208414, _1208416, _1208418] : [class_Orderings_Olinorder(_1208412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208412), _1208414), _1208416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208412), _1208418), _1208416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208412), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208412), _1208414), _1208418)), _1208416)))], (15034 ^ _778908) ^ [_1033811, _1033813, _1033815] : [-(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), _1033811), _1033813)), _1033815)), _1033813) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1033815), _1033813))], (33687 ^ _778908) ^ [_1393040, _1393042, _1393044] : [class_Orderings_Olinorder(_1393040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393040), _1393042)), -(hBOOL(hAPP(hAPP(c_member(_1393040), _1393044), _1393042))), -(_1393042 = c_Orderings_Obot__class_Obot(tc_fun(_1393040, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1393040, hAPP(hAPP(c_Set_Oinsert(_1393040), _1393044), _1393042)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1393040), _1393044), c_Big__Operators_Olinorder__class_OMax(_1393040, _1393042)))], (28593 ^ _778908) ^ [_1287061] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1287061) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1287061))], (37022 ^ _778908) ^ [_1467784, _1467786, _1467788, _1467790] : [class_Orderings_Oorder(_1467784), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467784, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1467784, _1467786), _1467788)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1467784, _1467788), _1467790)) = c_Orderings_Obot__class_Obot(tc_fun(_1467784, tc_HOL_Obool)))], (23401 ^ _778908) ^ [_1186964, _1186966, _1186968] : [-(hAPP(c_Product__Type_Osnd(_1186964, _1186966), _1186968) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186964, _1186966, _1186966), hAPP(c_COMBK(tc_fun(_1186966, _1186966), _1186964), c_COMBI(_1186966))), _1186968))], (44671 ^ _778908) ^ [_1652768, _1652770, _1652772, _1652774] : [_1652768 = c_Orderings_Obot__class_Obot(tc_fun(_1652770, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652770, tc_fun(_1652772, tc_HOL_Obool)), _1652768), hAPP(c_COMBK(tc_fun(_1652772, tc_HOL_Obool), _1652770), _1652774)) = c_Orderings_Otop__class_Otop(tc_fun(_1652772, tc_HOL_Obool)))], (51023 ^ _778908) ^ [_1805230, _1805232, _1805234, _1805236] : [-(c_List_Oconcat(_1805230, hAPP(hAPP(c_List_Omap(_1805232, tc_List_Olist(_1805230)), hAPP(hAPP(c_COMBC(_1805232, tc_List_Olist(_1805230), tc_List_Olist(_1805230)), hAPP(hAPP(c_COMBB(_1805230, tc_fun(tc_List_Olist(_1805230), tc_List_Olist(_1805230)), _1805232), c_List_Olist_OCons(_1805230)), _1805234)), c_List_Olist_ONil(_1805230))), _1805236)) = hAPP(hAPP(c_List_Omap(_1805232, _1805230), _1805234), _1805236))], (7370 ^ _778908) ^ [_902033, _902035] : [c_Com_Ovname_OGlb(_902033) = c_Com_Ovname_OLoc(_902035)], (20803 ^ _778908) ^ [_1137776, _1137778, _1137780] : [class_Rings_Odivision__ring(_1137776), -(_1137778 = c_Groups_Ozero__class_Ozero(_1137776)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1137776), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137776), _1137780), _1137778)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137776), _1137780), hAPP(c_Groups_Ouminus__class_Ouminus(_1137776), _1137778)))], (80 ^ _778908) ^ [_780016, _780018] : [-(class_Rings_Odivision__ring__inverse__zero(_780016)), _780018 = _780016, class_Rings_Odivision__ring__inverse__zero(_780018)], (36130 ^ _778908) ^ [_1448162, _1448164, _1448166, _1448168, _1448170, _1448172, _1448174] : [c_Equiv__Relations_Oequiv(_1448162, _1448164, _1448166), hBOOL(hAPP(hAPP(c_member(tc_fun(_1448162, tc_HOL_Obool)), _1448168), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448162), _1448164), _1448166))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1448162, tc_HOL_Obool)), _1448170), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448162), _1448164), _1448166))), hBOOL(hAPP(hAPP(c_member(_1448162), _1448172), _1448168)), hBOOL(hAPP(hAPP(c_member(_1448162), _1448174), _1448170)), 36149 ^ _778908 : [(36156 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1448162, _1448162)), hAPP(hAPP(c_Product__Type_OPair(_1448162, _1448162), _1448172), _1448174)), _1448166)), -(_1448168 = _1448170)], (36150 ^ _778908) ^ [] : [_1448168 = _1448170, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448162, _1448162)), hAPP(hAPP(c_Product__Type_OPair(_1448162, _1448162), _1448172), _1448174)), _1448166)))]]], (45814 ^ _778908) ^ [_1681193, _1681195, _1681197] : [hBOOL(hAPP(hAPP(c_member(_1681193), _1681195), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1681193, tc_HOL_Obool), _1681197))), 45818 ^ _778908 : [(45821 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1681193, tc_HOL_Obool)), 45817 ^ [_1681193, _1681195, _1681197]), _1681197)))], (45819 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1681193), _1681195), 45817 ^ [_1681193, _1681195, _1681197])))]]], (49815 ^ _778908) ^ [_1778870, _1778872, _1778874] : [-(c_List_Obutlast(_1778870, hAPP(hAPP(c_List_Odrop(_1778870), _1778872), _1778874)) = hAPP(hAPP(c_List_Odrop(_1778870), _1778872), c_List_Obutlast(_1778870, _1778874)))], (1892 ^ _778908) ^ [_806288, _806290] : [_806290 = _806288, -(c_HOL_Obool_Obool__size(_806290) = c_HOL_Obool_Obool__size(_806288))], (19103 ^ _778908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (34004 ^ _778908) ^ [_1400262, _1400264, _1400266] : [class_Orderings_Olinorder(_1400262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400262), _1400264)), -(_1400264 = c_Orderings_Obot__class_Obot(tc_fun(_1400262, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1400262, c_Orderings_Oord__class_Omin(_1400262), hAPP(hAPP(c_Set_Oinsert(_1400262), _1400266), _1400264)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1400262), _1400266), c_Big__Operators_Olattice_OInf__fin(_1400262, c_Orderings_Oord__class_Omin(_1400262), _1400264)))], (6808 ^ _778908) ^ [_890701, _890703, _890705] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_890701, _890703)), _890705), _890705)), hBOOL(hAPP(_890701, _890705)), 6816 ^ _778908 : [(6819 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_890701, _890703)), 6815 ^ [_890701, _890703, _890705]), _890705)))], (6817 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890703), _890705), 6815 ^ [_890701, _890703, _890705])))]]], (24855 ^ _778908) ^ [_1214377] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1214377)) = _1214377)], (25013 ^ _778908) ^ [_1217618, _1217620] : [-(c_Nitpick_Oinverse__frac(_1217618, _1217620) = hAPP(hAPP(c_Nitpick_Ofrac(_1217618), hAPP(c_Nitpick_Odenom(_1217618), _1217620)), hAPP(c_Nitpick_Onum(_1217618), _1217620)))], (15288 ^ _778908) ^ [_1038727, _1038729] : [-(_1038727 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15291 ^ _778908 : [(15298 ^ _778908) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038729, _1038727) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038729), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1038727)) = 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), _1038729), _1038727))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15292 ^ _778908) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038729, _1038727) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038729), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1038727)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038729), _1038727)))]]], (37174 ^ _778908) ^ [_1471231, _1471233, _1471235, _1471237] : [class_Orderings_Olinorder(_1471231), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471231, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1471231, _1471233, _1471235)), hAPP(c_SetInterval_Oord__class_OatMost(_1471231), _1471237)) = c_SetInterval_Oord__class_OatLeastAtMost(_1471231, _1471233, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1471231), _1471235), _1471237)))], (6863 ^ _778908) ^ [_891820, _891822, _891824, _891826, _891828] : [c_Com_Ocom_OCall(_891820, _891822, _891824) = c_Com_Ocom_OWhile(_891826, _891828)], (46224 ^ _778908) ^ [_1690984] : [-(hAPP(c_Option_Omap(_1690984, _1690984), c_COMBI(_1690984)) = c_Fun_Oid(tc_Option_Ooption(_1690984)))], (43584 ^ _778908) ^ [_1627783, _1627785, _1627787] : [-(hAPP(c_Relation_ORange(_1627783, _1627785), _1627787) = hAPP(c_Relation_ODomain(_1627785, _1627783), hAPP(c_Relation_Oconverse(_1627783, _1627785), _1627787)))], (34399 ^ _778908) ^ [_1408341, _1408343, _1408345, _1408347, _1408349, _1408351] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408341, _1408343), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408341, _1408343), _1408345), _1408347), _1408349)), _1408347), _1408351) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408341, _1408343), _1408345), _1408347), _1408351))], (12572 ^ _778908) ^ [_990306] : [hBOOL(hAPP(_990306, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12573 ^ [_990306]))), 12576 ^ _778908 : [(12577 ^ _778908) ^ [_990406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990406)), -(hBOOL(hAPP(_990306, _990406)))]]], (26125 ^ _778908) ^ [_1238664, _1238666, _1238668, _1238670, _1238672] : [class_Fields_Ofield(_1238664), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238664), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238666, _1238664), _1238668), _1238670)), _1238672) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238666, _1238664), hAPP(hAPP(c_COMBC(_1238666, _1238664, _1238664), hAPP(hAPP(c_COMBB(_1238664, tc_fun(_1238664, _1238664), _1238666), c_Rings_Oinverse__class_Odivide(_1238664)), _1238668)), _1238672)), _1238670))], (43646 ^ _778908) ^ [_1629456, _1629458] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1629456, _1629456)), _1629458)), c_Wellfounded_Oacyclic(_1629456, _1629458), -(c_Wellfounded_Owf(_1629456, hAPP(c_Relation_Oconverse(_1629456, _1629456), _1629458)))], (42751 ^ _778908) ^ [_1607439, _1607441] : [-(c_Hilbert__Choice_OEps(_1607439, hAPP(hAPP(c_COMBC(_1607439, _1607439, tc_HOL_Obool), c_fequal), _1607441)) = _1607441)], (4578 ^ _778908) ^ [_849757, _849759, _849761, _849763] : [-(c_List_Olex(_849763, _849759) = c_List_Olex(_849761, _849757)), _849763 = _849761, _849759 = _849757], (37090 ^ _778908) ^ [_1469247, _1469249, _1469251] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469247, tc_HOL_Obool)), _1469249), _1469251) = c_Orderings_Obot__class_Obot(tc_fun(_1469247, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469247, tc_HOL_Obool)), _1469249), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1469247, tc_HOL_Obool)), _1469251))))], (29098 ^ _778908) ^ [_1298260, _1298262, _1298264] : [class_Orderings_Otop(_1298260), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1298262, _1298260)), _1298264) = c_Orderings_Otop__class_Otop(_1298260))], (37422 ^ _778908) ^ [_1476910, _1476912, _1476914, _1476916, _1476918] : [c_Finite__Set_Ofolding__one(_1476910, _1476912, _1476914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476910), _1476916)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476910), _1476918)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476910, tc_HOL_Obool)), _1476916), _1476918) = c_Orderings_Obot__class_Obot(tc_fun(_1476910, tc_HOL_Obool))), -(hAPP(hAPP(_1476912, hAPP(_1476914, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476910, tc_HOL_Obool)), _1476916), _1476918))), hAPP(_1476914, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476910, tc_HOL_Obool)), _1476916), _1476918))) = hAPP(hAPP(_1476912, hAPP(_1476914, _1476916)), hAPP(_1476914, _1476918)))], (19547 ^ _778908) ^ [_1115593] : [-(c_Int_Opred(c_Int_OBit1(_1115593)) = c_Int_OBit0(_1115593))], (23273 ^ _778908) ^ [_1184051, _1184053, _1184055, _1184057, _1184059, _1184061] : [_1184051 = _1184053, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184055, _1184057, _1184059), _1184061), _1184051) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184055, _1184057, _1184059), _1184061), _1184053))], (49634 ^ _778908) ^ [_1775324, _1775326, _1775328] : [-(_1775324 = c_List_Olist_ONil(_1775326)), -(c_List_Olast(_1775326, hAPP(hAPP(c_List_Olist_OCons(_1775326), _1775328), _1775324)) = c_List_Olast(_1775326, _1775324))], (49464 ^ _778908) ^ [_1771591, _1771593] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771591)), c_List_Olist_ONil(_1771591)), c_List_Olists(_1771591, _1771593))))], (29197 ^ _778908) ^ [_1300576, _1300578, _1300580, _1300582] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1300576), _1300578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300576, tc_HOL_Obool)), _1300578), _1300580)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1300576, tc_Nat_Onat), _1300582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300576, tc_HOL_Obool)), _1300580), _1300578)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1300576, tc_Nat_Onat), _1300582), _1300580)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1300576, tc_Nat_Onat), _1300582), _1300578)))], (50433 ^ _778908) ^ [_1791919, _1791921, _1791923] : [class_Orderings_Olinorder(_1791919), c_List_Olinorder__class_Osorted(_1791919, _1791921), -(c_List_Olinorder__class_Osorted(_1791919, c_List_Oremove1(_1791919, _1791923, _1791921)))], (33497 ^ _778908) ^ [_1389979, _1389981, _1389983] : [class_Orderings_Olinorder(_1389979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389979), _1389981)), hBOOL(hAPP(hAPP(c_member(_1389979), _1389983), _1389981)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1389979), _1389983), c_Big__Operators_Olinorder__class_OMin(_1389979, _1389981)) = c_Big__Operators_Olinorder__class_OMin(_1389979, _1389981))], (35170 ^ _778908) ^ [_1425448, _1425450, _1425452] : [class_Orderings_Olinorder(_1425448), hAPP(_1425450, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425448), 35175 ^ [_1425448, _1425450, _1425452]), 35176 ^ [_1425448, _1425450, _1425452])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425448), hAPP(_1425450, 35175 ^ [_1425448, _1425450, _1425452])), hAPP(_1425450, 35176 ^ [_1425448, _1425450, _1425452])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425448), _1425452)), -(_1425452 = c_Orderings_Obot__class_Obot(tc_fun(_1425448, tc_HOL_Obool))), -(hAPP(_1425450, c_Big__Operators_Olinorder__class_OMax(_1425448, _1425452)) = c_Big__Operators_Olinorder__class_OMax(_1425448, hAPP(c_Set_Oimage(_1425448, _1425448, _1425450), _1425452)))], (1832 ^ _778908) ^ [_804682, _804684] : [-(hBOOL(_804682)), _804684 = _804682, hBOOL(_804684)], (4896 ^ _778908) ^ [_854678, _854680, _854682, _854684] : [-(c_Wellfounded_Oacc(_854684, _854680) = c_Wellfounded_Oacc(_854682, _854678)), _854684 = _854682, _854680 = _854678], (5961 ^ _778908) ^ [_874070, _874072] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _874070, _874072, _874070))], (35604 ^ _778908) ^ [_1434871, _1434873, _1434875, _1434877, _1434879] : [class_Groups_Ocomm__monoid__add(_1434871), class_Groups_Oordered__cancel__ab__semigroup__add(_1434871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434873), _1434875)), -(_1434875 = c_Orderings_Obot__class_Obot(tc_fun(_1434873, tc_HOL_Obool))), 35622 ^ _778908 : [(35625 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434871), hAPP(_1434877, 35621 ^ [_1434871, _1434873, _1434875, _1434877, _1434879])), hAPP(_1434879, 35621 ^ [_1434871, _1434873, _1434875, _1434877, _1434879])))], (35623 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434873), 35621 ^ [_1434871, _1434873, _1434875, _1434877, _1434879]), _1434875)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434871), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434873, _1434871), _1434877), _1434875)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434873, _1434871), _1434879), _1434875))))], (8101 ^ _778908) ^ [_914408, _914410] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914408), hAPP(c_Nat_OSuc, _914410)))), 8102 ^ _778908 : [(8105 ^ _778908) ^ [_914496] : [_914408 = hAPP(c_Nat_OSuc, _914496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914496), _914410))], (8103 ^ _778908) ^ [] : [_914408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (29106 ^ _778908) ^ [_1298429, _1298431] : [class_Orderings_Otop(_1298429), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298429), _1298431), c_Orderings_Otop__class_Otop(_1298429))))], (31916 ^ _778908) ^ [_1357562, _1357564, _1357566, _1357568, _1357570] : [class_Groups_Ocomm__monoid__add(_1357562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357564), _1357566)), -(hBOOL(hAPP(hAPP(c_member(_1357564), _1357568), _1357566))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357564, _1357562), _1357570), hAPP(hAPP(c_Set_Oinsert(_1357564), _1357568), _1357566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357562), hAPP(_1357570, _1357568)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357564, _1357562), _1357570), _1357566)))], (43323 ^ _778908) ^ [_1621643, _1621645, _1621647, _1621649] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621643, _1621643)), hAPP(hAPP(c_Product__Type_OPair(_1621643, _1621643), _1621645), _1621647)), c_Transitive__Closure_Ortrancl(_1621643, _1621649))), -(_1621645 = _1621647), 43330 ^ _778908 : [(43333 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621643, _1621643)), hAPP(hAPP(c_Product__Type_OPair(_1621643, _1621643), _1621645), _1621647)), c_Transitive__Closure_Otrancl(_1621643, _1621649))))], (43331 ^ _778908) ^ [] : [_1621645 = _1621647]]], (22764 ^ _778908) ^ [_1174010, _1174012] : [22765 ^ _778908 : [(22768 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1174012), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22766 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174010), _1174012))]], -(c_Divides_OposDivAlg(_1174010, _1174012) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174010))], (29221 ^ _778908) ^ [_1301044, _1301046] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1301044, _1301046))))], (46114 ^ _778908) ^ [_1688070, _1688072, _1688074, _1688076, _1688078] : [c_Fun_Oinj__on(_1688070, _1688072, _1688074, c_Orderings_Otop__class_Otop(tc_fun(_1688070, tc_HOL_Obool))), 46117 ^ _778908 : [(46124 ^ _778908) ^ [] : [_1688076 = _1688078, -(hAPP(hAPP(c_List_Omap(_1688070, _1688072), _1688074), _1688076) = hAPP(hAPP(c_List_Omap(_1688070, _1688072), _1688074), _1688078))], (46118 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Omap(_1688070, _1688072), _1688074), _1688076) = hAPP(hAPP(c_List_Omap(_1688070, _1688072), _1688074), _1688078), -(_1688076 = _1688078)]]], (39378 ^ _778908) ^ [_1519210, _1519212, _1519214] : [-(c_Fun_Oinj__on(_1519210, tc_sum(_1519212, _1519210), c_Sum__Type_OInr(_1519210, _1519212), _1519214))], (23345 ^ _778908) ^ [_1185548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1185548)), 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), _1185548)) = 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), _1185548))))))], (38946 ^ _778908) ^ [_1509714, _1509716, _1509718, _1509720] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509714), _1509716)), 38949 ^ _778908 : [(38956 ^ _778908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1509718), hAPP(c_Set_Oimage(_1509714, _1509718, _1509720), _1509716)) = hAPP(c_Finite__Set_Ocard(_1509714), _1509716), -(c_Fun_Oinj__on(_1509714, _1509718, _1509720, _1509716))], (38950 ^ _778908) ^ [] : [c_Fun_Oinj__on(_1509714, _1509718, _1509720, _1509716), -(hAPP(c_Finite__Set_Ocard(_1509718), hAPP(c_Set_Oimage(_1509714, _1509718, _1509720), _1509716)) = hAPP(c_Finite__Set_Ocard(_1509714), _1509716))]]], (6659 ^ _778908) ^ [_888115, _888117, _888119, _888121, _888123, _888125] : [hBOOL(hAPP(_888115, _888117)), c_Natural_Oevaln(_888119, _888117, _888121, _888123), c_Natural_Oevaln(c_Com_Ocom_OWhile(_888115, _888119), _888123, _888121, _888125), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_888115, _888119), _888117, _888121, _888125))], (40166 ^ _778908) ^ [_1538930, _1538932, _1538934, _1538936, _1538938, _1538940] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538930, _1538932)), hAPP(hAPP(c_Product__Type_OPair(_1538930, _1538932), _1538934), _1538936)), hAPP(hAPP(c_Product__Type_OSigma(_1538930, _1538932), _1538938), _1538940))), 40169 ^ _778908 : [(40172 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538932), _1538936), hAPP(_1538940, _1538934))))], (40170 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538930), _1538934), _1538938)))]]], (30131 ^ _778908) ^ [_1318713, _1318715, _1318717, _1318719] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318713, tc_fun(_1318715, tc_HOL_Obool)), _1318717), _1318719) = c_Orderings_Obot__class_Obot(tc_fun(_1318715, tc_HOL_Obool)), 30134 ^ _778908 : [(30135 ^ _778908) ^ [_1318829] : [hBOOL(hAPP(hAPP(c_member(_1318713), _1318829), _1318717)), -(hAPP(_1318719, _1318829) = c_Orderings_Obot__class_Obot(tc_fun(_1318715, tc_HOL_Obool)))]]], (26641 ^ _778908) ^ [_1248305, _1248307, _1248309] : [class_Rings_Odvd(_1248305), class_Rings_Osemiring__0(_1248305), 26648 ^ _778908 : [(26658 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1248307, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248305), _1248309), 26665 ^ [_1248305, _1248307, _1248309])))), 26659 ^ _778908 : [(26660 ^ _778908) ^ [_1248634] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248305), _1248309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248305), _1248634), c_Groups_Ozero__class_Ozero(_1248305)))), hBOOL(hAPP(_1248307, _1248634))]]], (26649 ^ _778908) ^ [] : [26650 ^ _778908 : [(26651 ^ _778908) ^ [_1248497] : [hBOOL(hAPP(_1248307, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248305), _1248309), _1248497)))]], 26653 ^ _778908 : [(26656 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1248307, 26652 ^ [_1248305, _1248307, _1248309])))], (26654 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248305), _1248309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248305), 26652 ^ [_1248305, _1248307, _1248309]), c_Groups_Ozero__class_Ozero(_1248305)))))]]]]], (10836 ^ _778908) ^ [_960755, _960757] : [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), _960755), _960757))), 10839 ^ _778908 : [(10842 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _960757)))], (10840 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _960755)))]]], (11310 ^ _778908) ^ [_968274, _968276, _968278] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968274), _968276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968278), _968276), -(_968274 = _968278), -(_968276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27999 ^ _778908) ^ [_1275291, _1275293, _1275295, _1275297] : [class_Orderings_Olinorder(_1275291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275291), _1275293), _1275295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275291), _1275295), _1275297)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275291, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1275291, _1275293, _1275295)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1275291, _1275295, _1275297)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1275291, _1275293), _1275297))], (14702 ^ _778908) ^ [_1028355, _1028357, _1028359] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1028355), _1028357)), _1028359) = 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), _1028355), _1028359)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028357), _1028359))), 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, _1028355, _1028359)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1028357, _1028359))), _1028359)))], (25189 ^ _778908) ^ [_1221892, _1221894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1221892)), 25192 ^ _778908 : [(25199 ^ _778908) ^ [] : [_1221894 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221894), _1221892)), _1221892)))], (25193 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221894), _1221892)), _1221892)), -(_1221894 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (16426 ^ _778908) ^ [_1061157, _1061159] : [-(_1061157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061157), _1061159) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1061159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061157), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1061159)))], (51557 ^ _778908) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (29576 ^ _778908) ^ [_1307899, _1307901] : [class_Finite__Set_Ofinite(_1307899), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307899), _1307901)))], (27710 ^ _778908) ^ [_1270044, _1270046, _1270048, _1270050, _1270052, _1270054, _1270056, _1270058] : [class_Groups_Ocomm__monoid__add(_1270044), class_Orderings_Oord(_1270046), _1270048 = _1270050, _1270052 = _1270054, 27728 ^ _778908 : [(27733 ^ _778908) ^ [] : [hAPP(_1270056, 27727 ^ [_1270044, _1270046, _1270048, _1270050, _1270052, _1270054, _1270056, _1270058]) = hAPP(_1270058, 27727 ^ [_1270044, _1270046, _1270048, _1270050, _1270052, _1270054, _1270056, _1270058])], (27731 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270046), 27727 ^ [_1270044, _1270046, _1270048, _1270050, _1270052, _1270054, _1270056, _1270058]), _1270054)))], (27729 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270046), _1270050), 27727 ^ [_1270044, _1270046, _1270048, _1270050, _1270052, _1270054, _1270056, _1270058])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1270046, _1270044), _1270056), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1270046, _1270048), _1270052)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1270046, _1270044), _1270058), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1270046, _1270050), _1270054)))], (13012 ^ _778908) ^ [_998303, _998305, _998307] : [class_Rings_Olinordered__ring__strict(_998303), 13015 ^ _778908 : [(13024 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998303), _998305), _998305)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998303), _998307), _998307))), c_Groups_Ozero__class_Ozero(_998303)))), _998305 = c_Groups_Ozero__class_Ozero(_998303), _998307 = c_Groups_Ozero__class_Ozero(_998303)], (13016 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998303), _998305), _998305)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998303), _998307), _998307))), c_Groups_Ozero__class_Ozero(_998303))), 13019 ^ _778908 : [(13022 ^ _778908) ^ [] : [-(_998307 = c_Groups_Ozero__class_Ozero(_998303))], (13020 ^ _778908) ^ [] : [-(_998305 = c_Groups_Ozero__class_Ozero(_998303))]]]]], (41894 ^ _778908) ^ [_1586950, _1586952] : [c_Wellfounded_Owf(_1586950, hAPP(hAPP(c_Relation_Orel__comp(_1586950, _1586950, _1586950), _1586952), _1586952)), -(c_Wellfounded_Owf(_1586950, _1586952))], (16042 ^ _778908) ^ [_1053012, _1053014] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053012), hAPP(c_Nat_OSuc, _1053014)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053012), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1053014))], (15566 ^ _778908) ^ [_1043869, _1043871] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1043869)), hAPP(c_Nat_OSuc, _1043871)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043869), _1043871))], (18559 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (36584 ^ _778908) ^ [_1457303, _1457305, _1457307, _1457309] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457303, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1457303, tc_fun(_1457303, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457303)), _1457305)), hAPP(hAPP(c_COMBC(_1457303, tc_fun(_1457303, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457303)), _1457307)), _1457309)), -(hBOOL(hAPP(hAPP(c_member(_1457303), _1457309), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457303, tc_HOL_Obool)), _1457305), _1457307))))], (2134 ^ _778908) ^ [_810739, _810741, _810743, _810745, _810747, _810749, _810751, _810753, _810755, _810757] : [-(c_Sum__Type_Osum_Osum__size(_810757, _810753, _810749, _810745, _810741) = c_Sum__Type_Osum_Osum__size(_810755, _810751, _810747, _810743, _810739)), _810757 = _810755, _810753 = _810751, _810749 = _810747, _810745 = _810743, _810741 = _810739], (15758 ^ _778908) ^ [_1047465, _1047467, _1047469] : [class_Groups_Oordered__ab__group__add(_1047465), 15761 ^ _778908 : [(15768 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047465), _1047467), _1047469)), c_Groups_Ozero__class_Ozero(_1047465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047465), _1047467), _1047469)))], (15762 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047465), _1047467), _1047469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047465), _1047467), _1047469)), c_Groups_Ozero__class_Ozero(_1047465))))]]], (20943 ^ _778908) ^ [_1140317, _1140319, _1140321] : [class_Fields_Olinordered__field(_1140317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140317), c_Groups_Ozero__class_Ozero(_1140317)), _1140319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140317), _1140321), c_Groups_Ozero__class_Ozero(_1140317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140317), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140317), _1140319), _1140321)), c_Groups_Ozero__class_Ozero(_1140317))))], (45839 ^ _778908) ^ [_1681764, _1681766, _1681768, _1681770, _1681772, _1681774] : [hAPP(c_Map_Omap__add(_1681764, _1681766, _1681768, _1681770), _1681772) = hAPP(c_Option_Ooption_OSome(_1681766), _1681774), -(hAPP(_1681770, _1681772) = hAPP(c_Option_Ooption_OSome(_1681766), _1681774)), 45846 ^ _778908 : [(45849 ^ _778908) ^ [] : [-(hAPP(_1681768, _1681772) = hAPP(c_Option_Ooption_OSome(_1681766), _1681774))], (45847 ^ _778908) ^ [] : [-(hAPP(_1681770, _1681772) = c_Option_Ooption_ONone(_1681766))]]], (42172 ^ _778908) ^ [_1592822, _1592824, _1592826] : [-(hAPP(c_Relation_ORange(_1592822, _1592824), hAPP(c_Set_OCollect(tc_prod(_1592822, _1592824)), hAPP(c_Product__Type_Oprod_Oprod__case(_1592822, _1592824, tc_HOL_Obool), _1592826))) = hAPP(c_Set_OCollect(_1592824), hAPP(hAPP(c_COMBB(tc_fun(_1592822, tc_HOL_Obool), tc_HOL_Obool, _1592824), c_HOL_OEx(_1592822)), hAPP(c_COMBC(_1592822, _1592824, tc_HOL_Obool), _1592826))))], (8286 ^ _778908) ^ [_917746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917746)), -(_917746 = hAPP(c_Nat_OSuc, 8289 ^ [_917746]))], (44819 ^ _778908) ^ [_1656696, _1656698, _1656700, _1656702] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656696, tc_fun(_1656698, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1656696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1656698, tc_HOL_Obool), tc_fun(_1656698, tc_HOL_Obool), _1656696), hAPP(c_COMBC(_1656698, tc_fun(_1656698, tc_HOL_Obool), tc_HOL_Obool), c_member(_1656698))), _1656700)), _1656702)), -(hBOOL(hAPP(hAPP(c_member(_1656698), _1656702), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656696, tc_fun(_1656698, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1656696, tc_HOL_Obool))), _1656700))))], (32696 ^ _778908) ^ [_1373984, _1373986, _1373988, _1373990, _1373992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1373984, _1373986)), hAPP(_1373984, _1373988))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1373990, _1373990)), hAPP(hAPP(c_Product__Type_OPair(_1373990, _1373990), _1373986), _1373988)), _1373992)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1373990, _1373990)), hAPP(hAPP(c_Product__Type_OPair(_1373990, _1373990), _1373986), _1373988)), c_Wellfounded_Omlex__prod(_1373990, _1373984, _1373992))))], (51267 ^ _778908) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (44220 ^ _778908) ^ [_1643498, _1643500, _1643502] : [class_Lattices_Oab__semigroup__idem__mult(_1643498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643498), _1643500)), -(hAPP(c_Finite__Set_Ofold1(_1643498, c_Groups_Otimes__class_Otimes(_1643498)), hAPP(hAPP(c_Set_Oinsert(_1643498), _1643502), _1643500)) = hAPP(hAPP(c_Finite__Set_Ofold(_1643498, _1643498, c_Groups_Otimes__class_Otimes(_1643498)), _1643502), _1643500))], (39008 ^ _778908) ^ [_1511042, _1511044, _1511046, _1511048, _1511050, _1511052] : [c_Fun_Oinj__on(_1511042, _1511044, _1511046, _1511048), -(hBOOL(hAPP(hAPP(c_member(_1511044), _1511050), hAPP(c_Set_Oimage(_1511042, _1511044, _1511046), _1511048)))), -(c_Fun_Oinj__on(_1511042, _1511044, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1511042, _1511044), _1511046), _1511052), _1511050), _1511048))], (18695 ^ _778908) ^ [_1101084, _1101086] : [class_Int_Onumber__ring(_1101084), class_Rings_Olinordered__idom(_1101084), 18702 ^ _778908 : [(18709 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1101086), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101084), hAPP(c_Int_Onumber__class_Onumber__of(_1101084), _1101086)), c_Groups_Ozero__class_Ozero(_1101084))))], (18703 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101084), hAPP(c_Int_Onumber__class_Onumber__of(_1101084), _1101086)), c_Groups_Ozero__class_Ozero(_1101084))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1101086), c_Int_OPls)))]]], (43271 ^ _778908) ^ [_1620379, _1620381] : [-(c_Transitive__Closure_Ortrancl(_1620379, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1620379, _1620379), tc_HOL_Obool)), _1620381), c_Relation_OId(_1620379))) = c_Transitive__Closure_Ortrancl(_1620379, _1620381))], (18313 ^ _778908) ^ [_1095352] : [class_Int_Onumber__ring(_1095352), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1095352), c_Groups_Oone__class_Oone(_1095352)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095352), c_Int_OMin))], (416 ^ _778908) ^ [_785156, _785158, _785160, _785162, _785164, _785166, _785168, _785170, _785172, _785174] : [-(c_Finite__Set_Ofolding__image(_785172, _785168, _785164, _785160, _785156)), c_Finite__Set_Ofolding__image(_785174, _785170, _785166, _785162, _785158), _785174 = _785172, _785170 = _785168, _785166 = _785164, _785162 = _785160, _785158 = _785156], (49698 ^ _778908) ^ [_1776433, _1776435, _1776437] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776433, _1776433)), hAPP(hAPP(c_Product__Type_OPair(_1776433, _1776433), 49699 ^ [_1776433, _1776435, _1776437]), 49699 ^ [_1776433, _1776435, _1776437])), _1776435))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1776433), tc_List_Olist(_1776433))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1776433), tc_List_Olist(_1776433)), _1776437), _1776437)), c_List_Olexord(_1776433, _1776435)))], (47202 ^ _778908) ^ [_1717148, _1717150, _1717152, _1717154] : [-(hBOOL(hAPP(hAPP(c_member(_1717148), _1717150), hAPP(c_List_Oset(_1717148), _1717152)))), hBOOL(hAPP(hAPP(c_member(_1717148), _1717150), hAPP(c_List_Oset(_1717148), c_List_Osublist(_1717148, _1717152, _1717154))))], (51425 ^ _778908) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (33607 ^ _778908) ^ [_1391791, _1391793, _1391795] : [class_Orderings_Olinorder(_1391791), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391791), _1391793)), -(_1391795 = c_Orderings_Obot__class_Obot(tc_fun(_1391791, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1391791, tc_HOL_Obool)), _1391795), _1391793)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1391791), c_Big__Operators_Olinorder__class_OMax(_1391791, _1391795)), c_Big__Operators_Olinorder__class_OMax(_1391791, _1391793)) = c_Big__Operators_Olinorder__class_OMax(_1391791, _1391793))], (10343 ^ _778908) ^ [_952692] : [-(_952692 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10346 ^ _778908 : [(10353 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952692))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _952692) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10347 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952692)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _952692) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (15586 ^ _778908) ^ [_1044263, _1044265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1044263), _1044265))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044263, _1044265) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044263), _1044265), _1044265))], (15002 ^ _778908) ^ [_1033235, _1033237, _1033239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033235), _1033237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033239), 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), _1033237), _1033239)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033235), _1033239))))], (36546 ^ _778908) ^ [_1456683, _1456685] : [class_Lattices_Obounded__lattice__top(_1456683), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456683), c_Orderings_Otop__class_Otop(_1456683)), _1456685) = _1456685)], (28848 ^ _778908) ^ [_1292005, _1292007] : [class_Orderings_Olinorder(_1292005), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1292005, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1292005), _1292007)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1292005), _1292007))], (11126 ^ _778908) ^ [_965139, _965141, _965143] : [class_Orderings_Oorder(_965139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965139), _965141), _965143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965139), _965141), _965143))), -(_965141 = _965143)], (51303 ^ _778908) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (46337 ^ _778908) ^ [_1693558, _1693560, _1693562] : [-(hAPP(c_Option_Omap(_1693558, _1693560), _1693562) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1693560), _1693558, c_Option_Ooption_ONone(_1693560), hAPP(hAPP(c_COMBB(_1693560, tc_Option_Ooption(_1693560), _1693558), c_Option_Ooption_OSome(_1693560)), _1693562)))], (32273 ^ _778908) ^ [_1365406, _1365408, _1365410, _1365412] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1365406, tc_fun(_1365408, tc_HOL_Obool))), _1365410), _1365412))], (17471 ^ _778908) ^ [_1080669, _1080671] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1080669)), _1080671) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1080669), _1080671)))], (39769 ^ _778908) ^ [_1528347, _1528349, _1528351] : [_1528351 = hAPP(c_COMBK(tc_Option_Ooption(_1528349), _1528347), c_Option_Ooption_ONone(_1528349)), -(c_Map_Odom(_1528347, _1528349, _1528351) = c_Orderings_Obot__class_Obot(tc_fun(_1528347, tc_HOL_Obool)))], (40309 ^ _778908) ^ [_1542888, _1542890, _1542892, _1542894, _1542896, _1542898] : [class_Groups_Ocomm__monoid__mult(_1542888), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542890), _1542892)), 40319 ^ _778908 : [(40322 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542894), hAPP(_1542896, 40318 ^ [_1542888, _1542890, _1542892, _1542894, _1542896, _1542898])))], (40320 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542890), 40318 ^ [_1542888, _1542890, _1542892, _1542894, _1542896, _1542898]), _1542892)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1542888, _1542890, c_Groups_Otimes__class_Otimes(_1542888)), hAPP(hAPP(c_COMBS(_1542890, tc_fun(_1542894, tc_HOL_Obool), _1542888), hAPP(hAPP(c_COMBC(_1542890, _1542888, tc_fun(tc_fun(_1542894, tc_HOL_Obool), _1542888)), hAPP(hAPP(c_COMBB(tc_fun(_1542894, _1542888), tc_fun(_1542888, tc_fun(tc_fun(_1542894, tc_HOL_Obool), _1542888)), _1542890), c_Finite__Set_Ofold__image(_1542888, _1542894, c_Groups_Otimes__class_Otimes(_1542888))), _1542898)), c_Groups_Oone__class_Oone(_1542888))), _1542896)), c_Groups_Oone__class_Oone(_1542888)), _1542892) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1542888, tc_prod(_1542890, _1542894), c_Groups_Otimes__class_Otimes(_1542888)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542890, _1542894, _1542888), _1542898)), c_Groups_Oone__class_Oone(_1542888)), hAPP(hAPP(c_Product__Type_OSigma(_1542890, _1542894), _1542892), _1542896)))], (7238 ^ _778908) ^ [_900034] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900034), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _900034)], (31010 ^ _778908) ^ [_1335595, _1335597, _1335599, _1335601] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1335595, _1335597)), hAPP(hAPP(c_Product__Type_OPair(_1335595, _1335597), _1335599), _1335601)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1335595, _1335597), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1335595, tc_fun(_1335597, tc_HOL_Obool))), _1335599), _1335601)))], (12822 ^ _778908) ^ [_994630, _994632, _994634, _994636] : [class_Rings_Olinordered__semiring__strict(_994630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994630), _994632), _994634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994630), _994632), _994636))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994630), c_Groups_Ozero__class_Ozero(_994630)), _994632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994630), _994634), _994636)))], (8224 ^ _778908) ^ [_916637, _916639, _916641, _916643] : [_916641 = _916643, -(hAPP(c_Sum__Type_OInl(_916637, _916639), _916641) = hAPP(c_Sum__Type_OInl(_916637, _916639), _916643))], (13210 ^ _778908) ^ [_1001521, _1001523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1001523), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1001521), _1001523)))], (9548 ^ _778908) ^ [_938547, _938549, _938551, _938553] : [class_Rings_Ocomm__semiring__1(_938547), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938547), _938549), _938551)), _938553) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938547), _938549), _938553)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938547), _938551), _938553)))], (47583 ^ _778908) ^ [_1725172, _1725174, _1725176, _1725178, _1725180] : [-(_1725172 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Lazy__Sequence_Oanamorph(_1725174, _1725176, _1725178, _1725172), _1725180) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1725176), _1725174), tc_prod(_1725176, _1725174), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725176), _1725174), c_List_Olist_ONil(_1725176)), _1725180), hAPP(c_Product__Type_Oprod_Oprod__case(_1725176, _1725174, tc_prod(tc_List_Olist(_1725176), _1725174)), hAPP(hAPP(c_COMBC(_1725176, tc_fun(_1725174, tc_prod(tc_List_Olist(_1725176), _1725174)), tc_fun(_1725174, tc_prod(tc_List_Olist(_1725176), _1725174))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1725176), _1725174), tc_prod(tc_List_Olist(_1725176), _1725174)), tc_fun(tc_fun(_1725174, tc_prod(tc_List_Olist(_1725176), _1725174)), tc_fun(_1725174, tc_prod(tc_List_Olist(_1725176), _1725174))), _1725176), c_COMBB(tc_prod(tc_List_Olist(_1725176), _1725174), tc_prod(tc_List_Olist(_1725176), _1725174), _1725174)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1725176), tc_fun(_1725174, tc_prod(tc_List_Olist(_1725176), _1725174))), tc_fun(tc_prod(tc_List_Olist(_1725176), _1725174), tc_prod(tc_List_Olist(_1725176), _1725174)), _1725176), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1725176), _1725174, tc_prod(tc_List_Olist(_1725176), _1725174))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1725176), tc_List_Olist(_1725176)), tc_fun(tc_List_Olist(_1725176), tc_fun(_1725174, tc_prod(tc_List_Olist(_1725176), _1725174))), _1725176), hAPP(c_COMBB(tc_List_Olist(_1725176), tc_fun(_1725174, tc_prod(tc_List_Olist(_1725176), _1725174)), tc_List_Olist(_1725176)), c_Product__Type_OPair(tc_List_Olist(_1725176), _1725174))), c_List_Olist_OCons(_1725176))))), c_Lazy__Sequence_Oanamorph(_1725174, _1725176, _1725178, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1725172), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1725178, _1725180)))], (4144 ^ _778908) ^ [_842744, _842746, _842748, _842750] : [-(c_Relation_ORange(_842750, _842746) = c_Relation_ORange(_842748, _842744)), _842750 = _842748, _842746 = _842744], (7324 ^ _778908) ^ [_901370, _901372] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901370), _901372)), 7325 ^ _778908 : [(7332 ^ _778908) ^ [] : [_901370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _901372 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7326 ^ _778908) ^ [] : [_901370 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19339 ^ _778908) ^ [_1112018, _1112020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112018), _1112020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1112018)), c_Int_OBit0(_1112020))))], (5498 ^ _778908) ^ [_863895, _863897] : [_863897 = _863895, -(c_Orderings_Oord__class_Omax(_863897) = c_Orderings_Oord__class_Omax(_863895))], (33823 ^ _778908) ^ [_1396126, _1396128, _1396130, _1396132, _1396134, _1396136, _1396138, _1396140] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1396126, _1396128), tc_prod(_1396126, _1396128))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1396126, _1396128), tc_prod(_1396126, _1396128)), hAPP(hAPP(c_Product__Type_OPair(_1396126, _1396128), _1396130), _1396132)), hAPP(hAPP(c_Product__Type_OPair(_1396126, _1396128), _1396134), _1396136))), c_Wellfounded_Olex__prod(_1396126, _1396128, _1396138, _1396140))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1396126, _1396126)), hAPP(hAPP(c_Product__Type_OPair(_1396126, _1396126), _1396130), _1396134)), _1396138))), 33830 ^ _778908 : [(33833 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1396128, _1396128)), hAPP(hAPP(c_Product__Type_OPair(_1396128, _1396128), _1396132), _1396136)), _1396140)))], (33831 ^ _778908) ^ [] : [-(_1396130 = _1396134)]]], (42377 ^ _778908) ^ [_1597868, _1597870] : [-(hAPP(c_Relation_OField(_1597868), _1597870) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597868, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1597868, _1597868), _1597870)), hAPP(c_Relation_ORange(_1597868, _1597868), _1597870)))], (12708 ^ _778908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25759 ^ _778908) ^ [_1231332, _1231334, _1231336, _1231338] : [class_Divides_Osemiring__div(_1231332), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231332), _1231334), c_Divides_Odiv__class_Omod(_1231332, _1231336, _1231338))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231332), _1231334), _1231338)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231332), _1231334), _1231336)))], (27926 ^ _778908) ^ [_1273988] : [-(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)), _1273988)))], (23281 ^ _778908) ^ [_1184234, _1184236, _1184238, _1184240, _1184242, _1184244] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184234, _1184236, _1184238), _1184240), hAPP(hAPP(c_Product__Type_OPair(_1184234, _1184236), _1184242), _1184244)) = hAPP(hAPP(_1184240, _1184242), _1184244))], (42375 ^ _778908) ^ [_1597786, _1597788, _1597790, _1597792] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597786, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1597786, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1597786, _1597788), _1597790)), hAPP(c_Relation_ODomain(_1597786, _1597788), _1597792))), hAPP(c_Relation_ODomain(_1597786, _1597788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1597786, _1597788), tc_HOL_Obool)), _1597790), _1597792)))))], (37150 ^ _778908) ^ [_1470639, _1470641, _1470643, _1470645, _1470647] : [class_Orderings_Olinorder(_1470639), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470639, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1470639, _1470641, _1470643)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1470639, _1470645, _1470647)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1470639, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1470639), _1470641), _1470645), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1470639), _1470643), _1470647)))], (5588 ^ _778908) ^ [_865238, _865240] : [_865240 = _865238, -(c_Nat_Osize__class_Osize(_865240) = c_Nat_Osize__class_Osize(_865238))], (45075 ^ _778908) ^ [_1664095, _1664097, _1664099, _1664101] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664095, tc_fun(_1664097, tc_HOL_Obool)), _1664099), _1664101) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1664097, tc_HOL_Obool), hAPP(c_Set_Oimage(_1664095, tc_fun(_1664097, tc_HOL_Obool), _1664101), _1664099)))], (35396 ^ _778908) ^ [_1430310, _1430312, _1430314] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1430310), _1430312)), hBOOL(hAPP(_1430314, _1430312)), 35407 ^ _778908 : [(35410 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1430310), 35405 ^ [_1430310, _1430312, _1430314]), 35406 ^ [_1430310, _1430312, _1430314])))], (35412 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1430314, 35406 ^ [_1430310, _1430312, _1430314])))], (35414 ^ _778908) ^ [] : [hBOOL(hAPP(_1430314, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430310, tc_HOL_Obool)), 35406 ^ [_1430310, _1430312, _1430314]), hAPP(hAPP(c_Set_Oinsert(_1430310), 35405 ^ [_1430310, _1430312, _1430314]), c_Orderings_Obot__class_Obot(tc_fun(_1430310, tc_HOL_Obool))))))], (35408 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1430310), 35406 ^ [_1430310, _1430312, _1430314])))]], -(hBOOL(hAPP(_1430314, c_Orderings_Obot__class_Obot(tc_fun(_1430310, tc_HOL_Obool)))))], (18169 ^ _778908) ^ [_1092926] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092926)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092926)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1092926)))], (6917 ^ _778908) ^ [_893152, _893154, _893156, _893158] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _893152)), _893154, _893156, _893158), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _893152), _893154, hAPP(c_Nat_OSuc, _893156), _893158))], (4880 ^ _778908) ^ [_854444, _854446, _854448, _854450] : [-(c_List_Olistrel(_854450, _854446) = c_List_Olistrel(_854448, _854444)), _854450 = _854448, _854446 = _854444], (47218 ^ _778908) ^ [_1717567, _1717569, _1717571] : [class_Groups_Omonoid__add(_1717567), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717567), hAPP(hAPP(c_List_Olist_OCons(_1717567), _1717569), _1717571)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1717567), _1717569), hAPP(c_List_Omonoid__add__class_Olistsum(_1717567), _1717571)))], (36718 ^ _778908) ^ [_1460604, _1460606] : [c_Nat__Transfer_Onat__set(_1460604), c_Nat__Transfer_Onat__set(_1460606), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1460604), _1460606)))], (40927 ^ _778908) ^ [_1556116, _1556118] : [class_Groups_Oab__semigroup__mult(_1556116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556116), _1556118)), -(_1556118 = c_Orderings_Obot__class_Obot(tc_fun(_1556116, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1556116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1556116), 40940 ^ [_1556116, _1556118]), 40941 ^ [_1556116, _1556118])), hAPP(hAPP(c_Set_Oinsert(_1556116), 40940 ^ [_1556116, _1556118]), hAPP(hAPP(c_Set_Oinsert(_1556116), 40941 ^ [_1556116, _1556118]), c_Orderings_Obot__class_Obot(tc_fun(_1556116, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1556116), hAPP(c_Finite__Set_Ofold1(_1556116, c_Groups_Otimes__class_Otimes(_1556116)), _1556118)), _1556118)))], (44965 ^ _778908) ^ [_1661889, _1661891, _1661893, _1661895, _1661897] : [-(_1661889 = c_Orderings_Obot__class_Obot(tc_fun(_1661891, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661893, tc_HOL_Obool)), _1661895), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1661891, tc_fun(_1661893, tc_HOL_Obool)), _1661889), _1661897)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661891, tc_fun(_1661893, tc_HOL_Obool)), _1661889), hAPP(hAPP(c_COMBB(tc_fun(_1661893, tc_HOL_Obool), tc_fun(_1661893, tc_HOL_Obool), _1661891), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661893, tc_HOL_Obool)), _1661895)), _1661897)))], (43209 ^ _778908) ^ [_1618805, _1618807, _1618809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618805, _1618805), tc_HOL_Obool)), _1618807), _1618809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618805, _1618805), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1618805, _1618807)), c_Transitive__Closure_Ortrancl(_1618805, _1618809))))], (32895 ^ _778908) ^ [_1377986] : [class_Rings_Osemiring__1(_1377986), -(hBOOL(hAPP(hAPP(c_member(_1377986), c_Groups_Oone__class_Oone(_1377986)), c_Nat_Osemiring__1__class_ONats(_1377986))))], (11524 ^ _778908) ^ [_971753, _971755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971753), _971755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971753), _971755)))], (16204 ^ _778908) ^ [_1056651, _1056653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056651), _1056653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056651), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1056653), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (36768 ^ _778908) ^ [_1461675, _1461677, _1461679, _1461681] : [class_Lattices_Osemilattice__inf(_1461675), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461675), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461675), _1461677), _1461679)), _1461681) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461675), _1461677), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461675), _1461679), _1461681)))], (47354 ^ _778908) ^ [_1720968, _1720970, _1720972] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1720968), tc_List_Olist(_1720968))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1720968), tc_List_Olist(_1720968)), _1720970), c_List_Olist_ONil(_1720968))), c_List_Olistrel(_1720968, _1720972))), -(_1720970 = c_List_Olist_ONil(_1720968))], (41941 ^ _778908) ^ [_1587976, _1587978, _1587980] : [c_Wellfounded_Owf(_1587976, _1587978), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587976, _1587976)), hAPP(hAPP(c_Product__Type_OPair(_1587976, _1587976), _1587980), _1587980)), _1587978))], (13999 ^ _778908) ^ [_1015767, _1015769, _1015771, _1015773] : [class_Divides_Oring__div(_1015767), c_Divides_Odiv__class_Omod(_1015767, _1015769, _1015771) = c_Divides_Odiv__class_Omod(_1015767, _1015773, _1015771), -(c_Divides_Odiv__class_Omod(_1015767, hAPP(c_Groups_Ouminus__class_Ouminus(_1015767), _1015769), _1015771) = c_Divides_Odiv__class_Omod(_1015767, hAPP(c_Groups_Ouminus__class_Ouminus(_1015767), _1015773), _1015771))], (16659 ^ _778908) ^ [_1065321, _1065323] : [class_Rings_Olinordered__idom(_1065321), -(hAPP(c_Groups_Oabs__class_Oabs(_1065321), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1065321), _1065323)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1065321), _1065323))], (45376 ^ _778908) ^ [_1671311] : [class_Complete__Lattice_Ocomplete__lattice(_1671311), -(c_Complete__Lattice_OSup__class_OSup(_1671311, c_Orderings_Otop__class_Otop(tc_fun(_1671311, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1671311))], (18525 ^ _778908) ^ [_1098453] : [class_Int_Onumber__ring(_1098453), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098453), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1098453))], (5809 ^ _778908) ^ [_871436] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _871436)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (468 ^ _778908) ^ [_786046, _786048, _786050, _786052, _786054, _786056, _786058, _786060] : [-(c_Wellfounded_Omax__extp(_786058, _786054, _786050, _786046)), c_Wellfounded_Omax__extp(_786060, _786056, _786052, _786048), _786060 = _786058, _786056 = _786054, _786052 = _786050, _786048 = _786046], (44192 ^ _778908) ^ [_1642964, _1642966, _1642968, _1642970] : [class_Orderings_Olinorder(_1642964), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642964), _1642966)), hBOOL(hAPP(hAPP(c_member(_1642964), _1642968), _1642966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1642964), hAPP(hAPP(c_Finite__Set_Ofold(_1642964, _1642964, c_Orderings_Oord__class_Omin(_1642964)), _1642970), _1642966)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1642964), _1642968), _1642970))))], (31277 ^ _778908) ^ [_1343174, _1343176, _1343178] : [hBOOL(hAPP(hAPP(c_member(_1343174), _1343176), _1343178)), -(hBOOL(hAPP(_1343178, _1343176)))], (5470 ^ _778908) ^ [_863421, _863423] : [_863423 = _863421, -(c_Orderings_Oord__class_Oless__eq(_863423) = c_Orderings_Oord__class_Oless__eq(_863421))], (42373 ^ _778908) ^ [_1597704, _1597706, _1597708, _1597710] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597704, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1597704, _1597706), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1597704, _1597706), tc_HOL_Obool)), _1597708), _1597710))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1597704, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1597704, _1597706), _1597708)), hAPP(c_Relation_ODomain(_1597704, _1597706), _1597710)))))], (30212 ^ _778908) ^ [_1320209, _1320211, _1320213, _1320215] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1320209, _1320211)), c_Sum__Type_OPlus(_1320209, _1320211, _1320213, _1320215))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1320209), _1320213)))], (10952 ^ _778908) ^ [_962598, _962600, _962602] : [class_Orderings_Oorder(_962598), 10955 ^ _778908 : [(10964 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962598), _962600), _962602))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962598), _962600), _962602)), -(_962600 = _962602)], (10956 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962598), _962600), _962602)), 10959 ^ _778908 : [(10962 ^ _778908) ^ [] : [_962600 = _962602], (10960 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962598), _962600), _962602)))]]]]], (16753 ^ _778908) ^ [_1066932, _1066934] : [class_Groups_Oordered__ab__group__add__abs(_1066932), 16756 ^ _778908 : [(16763 ^ _778908) ^ [] : [_1066934 = c_Groups_Ozero__class_Ozero(_1066932), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066932), hAPP(c_Groups_Oabs__class_Oabs(_1066932), _1066934)), c_Groups_Ozero__class_Ozero(_1066932))))], (16757 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066932), hAPP(c_Groups_Oabs__class_Oabs(_1066932), _1066934)), c_Groups_Ozero__class_Ozero(_1066932))), -(_1066934 = c_Groups_Ozero__class_Ozero(_1066932))]]], (44496 ^ _778908) ^ [_1648721, _1648723, _1648725, _1648727, _1648729, _1648731] : [c_Finite__Set_Ofun__left__comm(_1648721, _1648723, _1648725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648721), _1648727)), -(hBOOL(hAPP(hAPP(c_member(_1648721), _1648729), _1648727))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1648721, _1648723, _1648725), _1648731), hAPP(hAPP(c_Set_Oinsert(_1648721), _1648729), _1648727)) = hAPP(hAPP(_1648725, _1648729), hAPP(hAPP(c_Finite__Set_Ofold(_1648721, _1648723, _1648725), _1648731), _1648727)))], (39002 ^ _778908) ^ [_1510912, _1510914, _1510916, _1510918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1510912), hAPP(c_Set_Oimage(_1510914, _1510912, _1510916), _1510918))), hAPP(c_Finite__Set_Ocard(_1510914), _1510918))), c_Fun_Oinj__on(_1510914, _1510912, _1510916, _1510918)], (10607 ^ _778908) ^ [_956981, _956983, _956985, _956987] : [class_Orderings_Opreorder(_956981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956981), _956983), _956985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956981), _956985), _956987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956981), _956983), _956987)))], (18127 ^ _778908) ^ [_1092278, _1092280] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092278))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092278)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092280)) = 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), _1092280)))], (44655 ^ _778908) ^ [_1652511, _1652513, _1652515, _1652517, _1652519] : [-(_1652511 = c_Orderings_Obot__class_Obot(tc_fun(_1652513, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652515, tc_HOL_Obool)), _1652517), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652513, tc_fun(_1652515, tc_HOL_Obool)), _1652511), _1652519)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652513, tc_fun(_1652515, tc_HOL_Obool)), _1652511), hAPP(hAPP(c_COMBB(tc_fun(_1652515, tc_HOL_Obool), tc_fun(_1652515, tc_HOL_Obool), _1652513), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652515, tc_HOL_Obool)), _1652517)), _1652519)))], (49512 ^ _778908) ^ [_1772642, _1772644, _1772646, _1772648] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772642)), hAPP(hAPP(c_List_Olist_OCons(_1772642), _1772644), _1772646)), c_List_Olists(_1772642, _1772648)))), hBOOL(hAPP(hAPP(c_member(_1772642), _1772644), _1772648)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772642)), _1772646), c_List_Olists(_1772642, _1772648)))], (49666 ^ _778908) ^ [_1775698, _1775700, _1775702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1775698), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775700)), _1775702))), -(c_List_Olast(_1775700, hAPP(hAPP(c_List_Odrop(_1775700), _1775698), _1775702)) = c_List_Olast(_1775700, _1775702))], (49909 ^ _778908) ^ [_1781061, _1781063, _1781065] : [hAPP(c_List_Ofilter(_1781061, _1781063), _1781065) = _1781065, 49912 ^ _778908 : [(49913 ^ _778908) ^ [_1781152] : [hBOOL(hAPP(hAPP(c_member(_1781061), _1781152), hAPP(c_List_Oset(_1781061), _1781065))), -(hBOOL(hAPP(_1781063, _1781152)))]]], (7466 ^ _778908) ^ [_903682, _903684, _903686, _903688, _903690] : [-(c_Option_Ooption_Ooption__rec(_903682, _903684, _903686, _903688, hAPP(c_Option_Ooption_OSome(_903684), _903690)) = hAPP(_903688, _903690))], (12525 ^ _778908) ^ [_989536] : [-(hAPP(c_Nat_OSuc, _989536) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989536), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (19359 ^ _778908) ^ [_1112323] : [c_Int_OBit0(_1112323) = c_Int_OPls, -(_1112323 = c_Int_OPls)], (30202 ^ _778908) ^ [_1320032, _1320034, _1320036, _1320038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1320032), _1320034)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320036), _1320038)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1320032, _1320036)), c_Sum__Type_OPlus(_1320032, _1320036, _1320034, _1320038))))], (51301 ^ _778908) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (39494 ^ _778908) ^ [_1521838, _1521840, _1521842, _1521844, _1521846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521838, tc_HOL_Obool)), _1521840), _1521842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521844, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521844, _1521838, _1521846), _1521840)), hAPP(c_Set_Ovimage(_1521844, _1521838, _1521846), _1521842))))], (12645 ^ _778908) ^ [_991497, _991499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991499)), 12652 ^ _778908 : [(12659 ^ _778908) ^ [] : [_991497 = _991499, -(hAPP(c_Int_Onat, _991497) = hAPP(c_Int_Onat, _991499))], (12653 ^ _778908) ^ [] : [hAPP(c_Int_Onat, _991497) = hAPP(c_Int_Onat, _991499), -(_991497 = _991499)]]], (42100 ^ _778908) ^ [_1591254, _1591256, _1591258, _1591260] : [c_FunDef_Oreduction__pair(_1591254, _1591256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1591254, _1591254), tc_HOL_Obool)), _1591258), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1591254, _1591254), tc_HOL_Obool), tc_fun(tc_prod(_1591254, _1591254), tc_HOL_Obool)), _1591256))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1591254, _1591254), tc_HOL_Obool)), _1591260), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1591254, _1591254), tc_HOL_Obool), tc_fun(tc_prod(_1591254, _1591254), tc_HOL_Obool)), _1591256))), c_Wellfounded_Owf(_1591254, _1591260), -(c_Wellfounded_Owf(_1591254, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1591254, _1591254), tc_HOL_Obool)), _1591258), _1591260)))], (20031 ^ _778908) ^ [_1124297, _1124299] : [-(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), _1124297)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1124299))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124297))) = 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), _1124299)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1124297)))], (6302 ^ _778908) ^ [_880471, _880473, _880475, _880477, _880479, _880481] : [-(c_Com_Ocom_OLocal(_880471, _880473, _880475) = c_Com_Ocom_OLocal(_880477, _880479, _880481)), _880471 = _880477, _880473 = _880479, _880475 = _880481], (37198 ^ _778908) ^ [_1471775, _1471777, _1471779, _1471781] : [class_Orderings_Olinorder(_1471775), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471775, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1471775, _1471777, _1471779)), hAPP(c_SetInterval_Oord__class_OatLeast(_1471775), _1471781)) = c_SetInterval_Oord__class_OatLeastAtMost(_1471775, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1471775), _1471777), _1471781), _1471779))], (8445 ^ _778908) ^ [_920534, _920536, _920538, _920540] : [class_Orderings_Oorder(_920534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920534), hAPP(_920536, 8450 ^ [_920534, _920536, _920538, _920540])), hAPP(_920536, hAPP(c_Nat_OSuc, 8450 ^ [_920534, _920536, _920538, _920540])))), 8453 ^ _778908 : [(8460 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920538), _920540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920534), hAPP(_920536, _920538)), hAPP(_920536, _920540))))], (8454 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920534), hAPP(_920536, _920538)), hAPP(_920536, _920540))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920538), _920540)))]]], (5853 ^ _778908) ^ [_872064, _872066, _872068, _872070] : [c_Groups_Ocomm__monoid(_872064, _872066, _872068), -(hAPP(hAPP(_872066, _872070), _872068) = _872070)], (36762 ^ _778908) ^ [_1461532, _1461534, _1461536, _1461538] : [class_Lattices_Olattice(_1461532), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461532), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461532), _1461534), _1461536)), _1461538) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461532), _1461534), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461532), _1461536), _1461538)))], (24913 ^ _778908) ^ [_1215421, _1215423] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1215421), _1215423) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1215421)), hAPP(c_Code__Numeral_Onat__of, _1215423))))], (41651 ^ _778908) ^ [_1578096, _1578098, _1578100, _1578102, _1578104, _1578106, _1578108] : [class_Rings_Osemiring__0(_1578096), c_Fun_Oinj__on(tc_prod(_1578098, _1578100), _1578096, hAPP(c_Product__Type_Oprod_Oprod__case(_1578098, _1578100, _1578096), hAPP(hAPP(c_COMBC(_1578098, tc_fun(_1578100, _1578096), tc_fun(_1578100, _1578096)), hAPP(hAPP(c_COMBB(tc_fun(_1578096, _1578096), tc_fun(tc_fun(_1578100, _1578096), tc_fun(_1578100, _1578096)), _1578098), c_COMBB(_1578096, _1578096, _1578100)), hAPP(hAPP(c_COMBB(_1578096, tc_fun(_1578096, _1578096), _1578098), c_Groups_Otimes__class_Otimes(_1578096)), _1578102))), _1578104)), hAPP(hAPP(c_Product__Type_OSigma(_1578098, _1578100), _1578106), hAPP(c_COMBK(tc_fun(_1578100, tc_HOL_Obool), _1578098), _1578108))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1578096), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1578098, _1578096), _1578102), _1578106)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1578100, _1578096), _1578104), _1578108)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1578096, _1578096), c_Fun_Oid(_1578096)), hAPP(c_Set_OCollect(_1578096), hAPP(hAPP(c_COMBB(tc_fun(_1578098, tc_HOL_Obool), tc_HOL_Obool, _1578096), c_HOL_OEx(_1578098)), hAPP(hAPP(c_COMBB(tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool)), tc_fun(_1578098, tc_HOL_Obool), _1578096), hAPP(c_COMBB(tc_fun(_1578100, tc_HOL_Obool), tc_HOL_Obool, _1578098), c_HOL_OEx(_1578100))), hAPP(hAPP(c_COMBC(_1578096, tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool)), tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1578098, tc_fun(tc_fun(_1578100, tc_HOL_Obool), tc_fun(_1578100, tc_HOL_Obool))), tc_fun(tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool)), tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool))), _1578096), c_COMBS(_1578098, tc_fun(_1578100, tc_HOL_Obool), tc_fun(_1578100, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1578098, tc_fun(_1578100, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1578098, tc_fun(tc_fun(_1578100, tc_HOL_Obool), tc_fun(_1578100, tc_HOL_Obool))), _1578096), hAPP(c_COMBB(tc_fun(_1578100, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1578100, tc_HOL_Obool), tc_fun(_1578100, tc_HOL_Obool)), _1578098), c_COMBS(_1578100, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool)), tc_fun(_1578098, tc_fun(_1578100, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1578096), hAPP(c_COMBB(tc_fun(_1578100, tc_HOL_Obool), tc_fun(_1578100, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1578098), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578100), c_fconj))), hAPP(hAPP(c_COMBC(_1578096, tc_fun(_1578098, tc_fun(_1578100, _1578096)), tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1578100, _1578096), tc_fun(_1578100, tc_HOL_Obool)), tc_fun(tc_fun(_1578098, tc_fun(_1578100, _1578096)), tc_fun(_1578098, tc_fun(_1578100, tc_HOL_Obool))), _1578096), c_COMBB(tc_fun(_1578100, _1578096), tc_fun(_1578100, tc_HOL_Obool), _1578098)), hAPP(hAPP(c_COMBB(tc_fun(_1578096, tc_HOL_Obool), tc_fun(tc_fun(_1578100, _1578096), tc_fun(_1578100, tc_HOL_Obool)), _1578096), c_COMBB(_1578096, tc_HOL_Obool, _1578100)), c_fequal))), hAPP(hAPP(c_COMBC(_1578098, tc_fun(_1578100, _1578096), tc_fun(_1578100, _1578096)), hAPP(hAPP(c_COMBB(tc_fun(_1578096, _1578096), tc_fun(tc_fun(_1578100, _1578096), tc_fun(_1578100, _1578096)), _1578098), c_COMBB(_1578096, _1578096, _1578100)), hAPP(hAPP(c_COMBB(_1578096, tc_fun(_1578096, _1578096), _1578098), c_Groups_Otimes__class_Otimes(_1578096)), _1578102))), _1578104)))))), hAPP(hAPP(c_COMBC(_1578098, tc_fun(_1578100, tc_HOL_Obool), tc_fun(_1578100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1578100, tc_HOL_Obool), tc_fun(_1578100, tc_HOL_Obool)), _1578098), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1578100)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578098), c_fconj), hAPP(hAPP(c_COMBC(_1578098, tc_fun(_1578098, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578098)), _1578106)))), hAPP(hAPP(c_COMBC(_1578100, tc_fun(_1578100, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578100)), _1578108))))))))], (47904 ^ _778908) ^ [_1733638, _1733640, _1733642, _1733644, _1733646, _1733648] : [-(hAPP(hAPP(c_List_Omap(_1733638, _1733640), _1733642), hAPP(hAPP(c_List_Olist__update(_1733638, _1733644), _1733646), _1733648)) = hAPP(hAPP(c_List_Olist__update(_1733640, hAPP(hAPP(c_List_Omap(_1733638, _1733640), _1733642), _1733644)), _1733646), hAPP(_1733642, _1733648)))], (51237 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (16475 ^ _778908) ^ [_1062110, _1062112, _1062114] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062110, _1062112) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062114, _1062112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062114), _1062110)), -(_1062110 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1062114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062112), 16482 ^ [_1062110, _1062112, _1062114])))], (34401 ^ _778908) ^ [_1408410, _1408412, _1408414, _1408416, _1408418] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408410, _1408412), _1408414), _1408416), _1408418), _1408416) = _1408418)], (45526 ^ _778908) ^ [_1674624, _1674626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1674624, tc_HOL_Obool)), _1674626)), 45532 ^ _778908 : [(45535 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1674624), 45531 ^ [_1674624, _1674626]))], (45533 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1674624, tc_HOL_Obool)), 45531 ^ [_1674624, _1674626]), _1674626)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1674624), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1674624, tc_HOL_Obool), _1674626))))], (38008 ^ _778908) ^ [_1490841, _1490843, _1490845, _1490847, _1490849] : [class_Groups_Ocomm__monoid__mult(_1490841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490843), _1490845)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490843), _1490847)), 38022 ^ _778908 : [(38025 ^ _778908) ^ [] : [hAPP(_1490849, 38021 ^ [_1490841, _1490843, _1490845, _1490847, _1490849]) = c_Groups_Oone__class_Oone(_1490841)], (38023 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490843), 38021 ^ [_1490841, _1490843, _1490845, _1490847, _1490849]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490843, tc_HOL_Obool)), _1490845), _1490847))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490843, _1490841), _1490849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490843, tc_HOL_Obool)), _1490845), _1490847)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1490841), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490843, _1490841), _1490849), _1490845)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490843, _1490841), _1490849), _1490847)))], (44032 ^ _778908) ^ [_1639571, _1639573, _1639575, _1639577] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1639571, _1639571)), hAPP(hAPP(c_Product__Type_OPair(_1639571, _1639571), _1639573), _1639575)), c_Transitive__Closure_Otrancl(_1639571, _1639577))), 44036 ^ _778908 : [(44039 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639571, _1639571)), hAPP(hAPP(c_Product__Type_OPair(_1639571, _1639571), 44035 ^ [_1639571, _1639573, _1639575, _1639577]), _1639575)), c_Transitive__Closure_Ortrancl(_1639571, _1639577))))], (44037 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639571, _1639571)), hAPP(hAPP(c_Product__Type_OPair(_1639571, _1639571), _1639573), 44035 ^ [_1639571, _1639573, _1639575, _1639577])), _1639577)))]]], (24811 ^ _778908) ^ [_1213730] : [class_Orderings_Oord(_1213730), -(c_Orderings_Oord__class_Omax(_1213730) = c_Orderings_Oord_Omax(_1213730, c_Orderings_Oord__class_Oless__eq(_1213730)))], (24197 ^ _778908) ^ [_1201585, _1201587, _1201589, _1201591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201585, tc_HOL_Obool)), _1201587), _1201589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201585, tc_HOL_Obool)), _1201589), _1201591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201585, tc_HOL_Obool)), _1201587), _1201591)))], (14350 ^ _778908) ^ [_1021979, _1021981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1021979, _1021981))))], (51479 ^ _778908) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (31946 ^ _778908) ^ [_1358165, _1358167, _1358169, _1358171] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1358165, tc_HOL_Obool)), _1358167), hAPP(hAPP(c_Set_Oinsert(_1358165), _1358169), _1358171)))), 31949 ^ _778908 : [(31952 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1358165, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1358165, tc_HOL_Obool)), _1358167), hAPP(hAPP(c_Set_Oinsert(_1358165), _1358169), c_Orderings_Obot__class_Obot(tc_fun(_1358165, tc_HOL_Obool))))), _1358171))], (31950 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358165), _1358169), _1358167)))]], 31953 ^ _778908 : [(31956 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1358165, tc_HOL_Obool)), _1358167), _1358171))], (31954 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1358165), _1358169), _1358167))]]], (51563 ^ _778908) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (7112 ^ _778908) ^ [_897837] : [hAPP(c_Nat_OSuc, _897837) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43582 ^ _778908) ^ [_1627738, _1627740, _1627742] : [-(hAPP(c_Relation_ODomain(_1627738, _1627740), hAPP(c_Relation_Oconverse(_1627740, _1627738), _1627742)) = hAPP(c_Relation_ORange(_1627740, _1627738), _1627742))], (17541 ^ _778908) ^ [_1081964, _1081966] : [class_Groups_Omonoid__mult(_1081964), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1081964), c_Groups_Oone__class_Oone(_1081964)), _1081966) = c_Groups_Oone__class_Oone(_1081964))], (20823 ^ _778908) ^ [_1138102, _1138104, _1138106] : [class_Fields_Olinordered__field(_1138102), -(_1138104 = c_Groups_Ozero__class_Ozero(_1138102)), -(hAPP(c_Groups_Oabs__class_Oabs(_1138102), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138102), _1138106), _1138104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138102), hAPP(c_Groups_Oabs__class_Oabs(_1138102), _1138106)), hAPP(c_Groups_Oabs__class_Oabs(_1138102), _1138104)))], (50773 ^ _778908) ^ [_1799155, _1799157, _1799159, _1799161] : [_1799157 = hAPP(hAPP(c_List_Oappend(_1799155), hAPP(c_List_Orev(_1799155), _1799161)), hAPP(hAPP(c_List_Olist_OCons(_1799155), _1799159), c_List_Olist_ONil(_1799155))), -(hAPP(c_List_Orev(_1799155), _1799157) = hAPP(hAPP(c_List_Olist_OCons(_1799155), _1799159), _1799161))], (6703 ^ _778908) ^ [_888774, _888776] : [_888774 = _888776, -(c_Com_Ovname_OLoc(_888774) = c_Com_Ovname_OLoc(_888776))], (30644 ^ _778908) ^ [_1328021] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1328021)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1328021)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1328021), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (8277 ^ _778908) ^ [_917598, _917600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917598), _917600)), 8281 ^ _778908 : [(8284 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _917598), 8280 ^ [_917598, _917600]) = _917600)], (8282 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8280 ^ [_917598, _917600])))]]], (35716 ^ _778908) ^ [_1437512, _1437514, _1437516, _1437518, _1437520, _1437522, _1437524, _1437526, _1437528, _1437530, _1437532] : [hAPP(_1437512, hAPP(_1437514, _1437516)) = hAPP(_1437518, hAPP(_1437520, _1437522)), -(hAPP(hAPP(c_Fun_Ocomp(_1437524, _1437526, _1437528, _1437512), _1437514), _1437516) = hAPP(hAPP(c_Fun_Ocomp(_1437530, _1437526, _1437532, _1437518), _1437520), _1437522))], (8315 ^ _778908) ^ [_918185, _918187, _918189, _918191, _918193] : [c_Sum__Type_OSuml(_918185, _918187, _918189, _918191) = c_Sum__Type_OSuml(_918185, _918187, _918189, _918193), -(_918191 = _918193)], (27262 ^ _778908) ^ [_1260478, _1260480, _1260482, _1260484, _1260486] : [class_Orderings_Olinorder(_1260478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260478, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1260478, _1260480), _1260482)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1260478, _1260484), _1260486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260478), _1260482), _1260480))), 27273 ^ _778908 : [(27276 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260478), _1260482), _1260486)))], (27274 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260478), _1260484), _1260480)))]]], (45524 ^ _778908) ^ [_1674573, _1674575] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1674573, tc_HOL_Obool), _1674575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1674573, tc_HOL_Obool), tc_fun(_1674573, tc_HOL_Obool)), _1674575), c_COMBI(tc_fun(_1674573, tc_HOL_Obool))))], (29538 ^ _778908) ^ [_1307092, _1307094, _1307096] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307092), _1307094)), -(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(_1307092), _1307096)), hAPP(c_Finite__Set_Ocard(_1307092), _1307094))), hAPP(c_Finite__Set_Ocard(_1307092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307092, tc_HOL_Obool)), _1307096), _1307094)))))], (23160 ^ _778908) ^ [_1181844, _1181846, _1181848, _1181850, _1181852] : [hBOOL(hAPP(hAPP(_1181844, _1181846), _1181848)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1181850, _1181852, tc_HOL_Obool), _1181844), hAPP(hAPP(c_Product__Type_OPair(_1181850, _1181852), _1181846), _1181848))))], (9374 ^ _778908) ^ [_935597, _935599, _935601] : [class_Groups_Oordered__ab__group__add(_935597), 9377 ^ _778908 : [(9384 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935597), hAPP(c_Groups_Ouminus__class_Ouminus(_935597), _935601)), _935599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935597), hAPP(c_Groups_Ouminus__class_Ouminus(_935597), _935599)), _935601)))], (9378 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935597), hAPP(c_Groups_Ouminus__class_Ouminus(_935597), _935599)), _935601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935597), hAPP(c_Groups_Ouminus__class_Ouminus(_935597), _935601)), _935599)))]]], (34790 ^ _778908) ^ [_1416237, _1416239, _1416241, _1416243, _1416245, _1416247, _1416249] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1416237, tc_Option_Ooption(_1416239)), _1416241), _1416243), hAPP(c_Option_Ooption_OSome(_1416239), _1416245)), _1416247) = hAPP(c_Option_Ooption_OSome(_1416239), _1416249), 34795 ^ _778908 : [(34798 ^ _778908) ^ [] : [-(_1416245 = _1416249)], (34796 ^ _778908) ^ [] : [-(_1416247 = _1416243)]], 34799 ^ _778908 : [(34802 ^ _778908) ^ [] : [-(hAPP(_1416241, _1416247) = hAPP(c_Option_Ooption_OSome(_1416239), _1416249))], (34800 ^ _778908) ^ [] : [_1416247 = _1416243]]], (12687 ^ _778908) ^ [_992172, _992174] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992172)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992174)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992172), _992174)))], (38910 ^ _778908) ^ [_1508855, _1508857, _1508859, _1508861, _1508863] : [c_Fun_Oinj__on(_1508855, _1508857, _1508859, c_Orderings_Otop__class_Otop(tc_fun(_1508855, tc_HOL_Obool))), 38913 ^ _778908 : [(38920 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508855, tc_HOL_Obool)), _1508861), _1508863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508857, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1508855, _1508857, _1508859), _1508861)), hAPP(c_Set_Oimage(_1508855, _1508857, _1508859), _1508863))))], (38914 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508857, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1508855, _1508857, _1508859), _1508861)), hAPP(c_Set_Oimage(_1508855, _1508857, _1508859), _1508863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508855, tc_HOL_Obool)), _1508861), _1508863)))]]], (41991 ^ _778908) ^ [_1588946, _1588948, _1588950, _1588952, _1588954, _1588956, _1588958] : [c_Predicate_Opred__comp(_1588946, _1588948, _1588950, _1588952, _1588954, _1588956, _1588958), 41995 ^ _778908 : [(41998 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1588954, 41994 ^ [_1588946, _1588948, _1588950, _1588952, _1588954, _1588956, _1588958]), _1588958)))], (41996 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1588952, _1588956), 41994 ^ [_1588946, _1588948, _1588950, _1588952, _1588954, _1588956, _1588958])))]]], (50640 ^ _778908) ^ [_1795676, _1795678] : [class_Orderings_Olinorder(_1795676), 50643 ^ _778908 : [(50644 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1795676, _1795678), 50647 ^ _778908 : [(50648 ^ _778908) ^ [_1795847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1795847), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795676)), _1795678))), 50651 ^ _778908 : [(50652 ^ _778908) ^ [_1795964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1795964), _1795847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1795676), hAPP(hAPP(c_List_Onth(_1795676), _1795678), _1795964)), hAPP(hAPP(c_List_Onth(_1795676), _1795678), _1795847))))]]]]], (50658 ^ _778908) ^ [] : [50660 ^ _778908 : [(50666 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1795676), hAPP(hAPP(c_List_Onth(_1795676), _1795678), 50662 ^ [_1795676, _1795678])), hAPP(hAPP(c_List_Onth(_1795676), _1795678), 50659 ^ [_1795676, _1795678])))], (50664 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50662 ^ [_1795676, _1795678]), 50659 ^ [_1795676, _1795678])))], (50661 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50659 ^ [_1795676, _1795678]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795676)), _1795678))))]], -(c_List_Olinorder__class_Osorted(_1795676, _1795678))]]], (26395 ^ _778908) ^ [_1243780, _1243782, _1243784, _1243786, _1243788] : [class_Rings_Ocomm__semiring__1(_1243780), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243780), hAPP(hAPP(c_Power_Opower__class_Opower(_1243780), _1243782), _1243784)), _1243786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243788), _1243784)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243780), hAPP(hAPP(c_Power_Opower__class_Opower(_1243780), _1243782), _1243788)), _1243786)))], (26559 ^ _778908) ^ [_1246712, _1246714, _1246716] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246712), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1246714), _1246716))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246712), _1246716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246716), _1246714)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246712), _1246714)))], (30072 ^ _778908) ^ [_1317496, _1317498, _1317500, _1317502] : [_1317502 = c_Orderings_Obot__class_Obot(tc_fun(_1317498, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1317496, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1317498, _1317496, _1317500), _1317502))], (8031 ^ _778908) ^ [_913264, _913266] : [class_Groups_Olinordered__ab__group__add(_913264), 8034 ^ _778908 : [(8041 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913264), c_Groups_Ozero__class_Ozero(_913264)), _913266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913264), c_Groups_Ozero__class_Ozero(_913264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913264), _913266), _913266))))], (8035 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913264), c_Groups_Ozero__class_Ozero(_913264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913264), _913266), _913266))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913264), c_Groups_Ozero__class_Ozero(_913264)), _913266)))]]], (29928 ^ _778908) ^ [_1314660, _1314662, _1314664, _1314666] : [29929 ^ _778908 : [(29932 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1314664), _1314666)))], (29930 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1314660), _1314662)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1314660, _1314664)), c_Sum__Type_OPlus(_1314660, _1314664, _1314662, _1314666)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30672 ^ _778908) ^ [_1328586, _1328588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1328586), _1328588)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1328586), hAPP(c_Nat_OSuc, _1328588)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1328588), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1328586), _1328588)))], (51463 ^ _778908) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (48482 ^ _778908) ^ [_1747463, _1747465] : [-(hAPP(hAPP(c_List_Otake(_1747463), _1747465), c_List_Olist_ONil(_1747463)) = c_List_Olist_ONil(_1747463))], (34333 ^ _778908) ^ [_1406871, _1406873, _1406875, _1406877] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1406871, _1406873), _1406875), _1406877), hAPP(_1406875, _1406877)) = _1406875)], (43514 ^ _778908) ^ [_1626089, _1626091, _1626093] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1626089, _1626091)), hAPP(c_Relation_Oconverse(_1626091, _1626089), _1626093))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1626091, _1626089)), _1626093)))], (42749 ^ _778908) ^ [_1607408, _1607410] : [-(c_Hilbert__Choice_OEps(_1607408, hAPP(c_fequal, _1607410)) = _1607410)], (46950 ^ _778908) ^ [_1709775, _1709777, _1709779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1709775, _1709775), tc_HOL_Obool)), _1709777), _1709779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1709775), tc_List_Olist(_1709775)), tc_HOL_Obool)), c_List_Olistrel(_1709775, _1709777)), c_List_Olistrel(_1709775, _1709779))))], (15696 ^ _778908) ^ [_1046256, _1046258, _1046260] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046256), _1046258)), _1046260) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046256), _1046260)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046258), _1046260)))], (16743 ^ _778908) ^ [_1066777, _1066779] : [class_Groups_Oordered__ab__group__add__abs(_1066777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066777), c_Groups_Ozero__class_Ozero(_1066777)), _1066779)), -(hAPP(c_Groups_Oabs__class_Oabs(_1066777), _1066779) = _1066779)], (50895 ^ _778908) ^ [_1801751, _1801753, _1801755] : [-(c_List_Oconcat(_1801751, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1801751)), _1801753), _1801755)) = hAPP(hAPP(c_List_Oappend(_1801751), c_List_Oconcat(_1801751, _1801753)), c_List_Oconcat(_1801751, _1801755)))], (2502 ^ _778908) ^ [_816749, _816751, _816753, _816755] : [-(c_Nitpick_Onat__gcd(_816755, _816751) = c_Nitpick_Onat__gcd(_816753, _816749)), _816755 = _816753, _816751 = _816749], (29572 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (26157 ^ _778908) ^ [_1239350, _1239352] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239350), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239352))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1239350))), _1239352)))], (2412 ^ _778908) ^ [_815306, _815308, _815310, _815312] : [-(c_Random_Oinc__shift(_815312, _815308) = c_Random_Oinc__shift(_815310, _815306)), _815312 = _815310, _815308 = _815306], (27849 ^ _778908) ^ [_1272766, _1272768] : [c_Nat__Transfer_Onat__set(_1272766), c_Nat__Transfer_Onat__set(_1272768), 27856 ^ _778908 : [(27863 ^ _778908) ^ [] : [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), _1272766)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1272768))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1272766), _1272768)))], (27857 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1272766), _1272768)), -(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), _1272766)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1272768))))]]], (51521 ^ _778908) ^ [_1812070, _1812072] : [-(class_Finite__Set_Ofinite(tc_prod(_1812070, _1812072))), class_Finite__Set_Ofinite(_1812070), class_Finite__Set_Ofinite(_1812072)], (35046 ^ _778908) ^ [_1421654, _1421656, _1421658, _1421660] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1421654), _1421656)), 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)), _1421654), _1421658)), 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)), _1421656), _1421660)), 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)), _1421656), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1421658), _1421660))), c_FunDef_Omin__weak)))], (30308 ^ _778908) ^ [_1321935] : [-(hAPP(c_Finite__Set_Ocard(_1321935), c_Orderings_Obot__class_Obot(tc_fun(_1321935, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36900 ^ _778908) ^ [_1464617, _1464619, _1464621, _1464623, _1464625] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464617, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464619, tc_fun(_1464617, tc_HOL_Obool)), _1464621), _1464623)), _1464625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464619, tc_fun(_1464617, tc_HOL_Obool)), _1464621), hAPP(hAPP(c_COMBC(_1464619, tc_fun(_1464617, tc_HOL_Obool), tc_fun(_1464617, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464617, tc_HOL_Obool), tc_fun(tc_fun(_1464617, tc_HOL_Obool), tc_fun(_1464617, tc_HOL_Obool)), _1464619), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464617, tc_HOL_Obool))), _1464623)), _1464625)))], (38095 ^ _778908) ^ [_1492832, _1492834, _1492836, _1492838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492832), _1492834)), c_Equiv__Relations_Oequiv(_1492832, _1492834, _1492836), 38105 ^ _778908 : [(38108 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1492838), hAPP(c_Finite__Set_Ocard(_1492832), 38104 ^ [_1492832, _1492834, _1492836, _1492838])))], (38106 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1492832, tc_HOL_Obool)), 38104 ^ [_1492832, _1492834, _1492836, _1492838]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1492832), _1492834), _1492836))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1492838), hAPP(c_Finite__Set_Ocard(_1492832), _1492834))))], (42513 ^ _778908) ^ [_1601096, _1601098, _1601100] : [-(hAPP(c_New__DSequence_Opos__single(_1601096, _1601098), _1601100) = c_Lazy__Sequence_Osingle(_1601096, _1601098))], (23385 ^ _778908) ^ [_1186535, _1186537, _1186539, _1186541] : [-(hAPP(c_Product__Type_Osnd(_1186535, _1186537), hAPP(hAPP(c_Product__Type_OPair(_1186535, _1186537), _1186539), _1186541)) = _1186541)], (21481 ^ _778908) ^ [_1149864, _1149866, _1149868] : [class_Fields_Olinordered__field(_1149864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149864), _1149866), _1149868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149864), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149864), _1149866), _1149868)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149864), c_Groups_Oone__class_Oone(_1149864)), c_Groups_Oone__class_Oone(_1149864)))), _1149868)))], (39088 ^ _778908) ^ [_1512592, _1512594, _1512596, _1512598, _1512600] : [class_Groups_Ocomm__monoid__mult(_1512592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512594), _1512596)), c_Fun_Oinj__on(_1512594, _1512594, _1512598, _1512596), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1512594, _1512592), _1512600), hAPP(c_Set_Oimage(_1512594, _1512594, _1512598), _1512596)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1512594, _1512592), hAPP(c_Fun_Ocomp(_1512594, _1512592, _1512594, _1512600), _1512598)), _1512596))], (28145 ^ _778908) ^ [_1278274, _1278276, _1278278, _1278280] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278274, tc_HOL_Obool)), _1278276), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278274, tc_HOL_Obool)), _1278278), _1278280)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278274, tc_HOL_Obool)), _1278278), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278274, tc_HOL_Obool)), _1278276), _1278280)))], (28511 ^ _778908) ^ [_1285327] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1285327)) = hAPP(c_Nat_OSuc, _1285327))], (39158 ^ _778908) ^ [_1514102, _1514104, _1514106, _1514108] : [class_Groups_Ocomm__monoid__mult(_1514102), 39161 ^ _778908 : [(39168 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1514104), _1514106))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514104, _1514102), _1514108), _1514106) = c_Groups_Oone__class_Oone(_1514102))], (39162 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514104), _1514106)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514104, _1514102), _1514108), _1514106) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1514102, _1514104, c_Groups_Otimes__class_Otimes(_1514102)), _1514108), c_Groups_Oone__class_Oone(_1514102)), _1514106))]]], (28896 ^ _778908) ^ [_1292982, _1292984] : [class_Groups_Oordered__ab__group__add(_1292982), -(hAPP(c_Set_Oimage(_1292982, _1292982, c_Groups_Ouminus__class_Ouminus(_1292982)), hAPP(c_SetInterval_Oord__class_OatMost(_1292982), _1292984)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1292982), hAPP(c_Groups_Ouminus__class_Ouminus(_1292982), _1292984)))], (40162 ^ _778908) ^ [_1538783, _1538785] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538783, _1538783), tc_HOL_Obool)), c_Relation_OId__on(_1538783, _1538785)), hAPP(hAPP(c_Product__Type_OSigma(_1538783, _1538783), _1538785), hAPP(c_COMBK(tc_fun(_1538783, tc_HOL_Obool), _1538783), _1538785)))))], (3082 ^ _778908) ^ [_826131, _826133] : [_826133 = _826131, -(c_DSequence_Ounion(_826133) = c_DSequence_Ounion(_826131))], (46076 ^ _778908) ^ [_1687289, _1687291, _1687293, _1687295, _1687297, _1687299, _1687301] : [-(c_Map_Omap__comp(_1687289, _1687291, _1687293, _1687295, _1687297, _1687299) = hAPP(c_Option_Ooption_OSome(_1687291), _1687301)), 46077 ^ _778908 : [(46078 ^ _778908) ^ [_1687367] : [hAPP(_1687297, _1687299) = hAPP(c_Option_Ooption_OSome(_1687289), _1687367), hAPP(_1687295, _1687367) = hAPP(c_Option_Ooption_OSome(_1687291), _1687301)]]], (18591 ^ _778908) ^ [_1099426] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1099426) = c_Int_Opred(_1099426))], (49817 ^ _778908) ^ [_1778919, _1778921, _1778923, _1778925] : [49818 ^ _778908 : [(49821 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1778919), _1778921), hAPP(c_List_Oset(_1778919), c_List_Obutlast(_1778919, _1778925))))], (49819 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1778919), _1778921), hAPP(c_List_Oset(_1778919), c_List_Obutlast(_1778919, _1778923))))]], -(hBOOL(hAPP(hAPP(c_member(_1778919), _1778921), hAPP(c_List_Oset(_1778919), c_List_Obutlast(_1778919, hAPP(hAPP(c_List_Oappend(_1778919), _1778923), _1778925))))))], (19269 ^ _778908) ^ [_1110722, _1110724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110722)), -(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)))), _1110724)), 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)))), _1110722)) = 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, _1110724, _1110722))))], (42411 ^ _778908) ^ [_1599442, _1599444, _1599446, _1599448] : [hBOOL(hAPP(hAPP(c_member(_1599442), _1599444), hAPP(c_Relation_ODomain(_1599442, _1599446), _1599448))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599442, _1599446)), hAPP(hAPP(c_Product__Type_OPair(_1599442, _1599446), _1599444), 42414 ^ [_1599442, _1599444, _1599446, _1599448])), _1599448)))], (3680 ^ _778908) ^ [_835524, _835526, _835528, _835530, _835532, _835534, _835536, _835538, _835540, _835542] : [-(c_Fun_Ooverride__on(_835542, _835538, _835534, _835530, _835526) = c_Fun_Ooverride__on(_835540, _835536, _835532, _835528, _835524)), _835542 = _835540, _835538 = _835536, _835534 = _835532, _835530 = _835528, _835526 = _835524], (48401 ^ _778908) ^ [_1744890, _1744892, _1744894, _1744896] : [-(c_List_Osublist(_1744890, hAPP(hAPP(c_List_Oappend(_1744890), _1744892), _1744894), _1744896) = hAPP(hAPP(c_List_Oappend(_1744890), c_List_Osublist(_1744890, _1744892, _1744896)), c_List_Osublist(_1744890, _1744894, 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(_1744890)), _1744892)))), _1744896)))))], (39720 ^ _778908) ^ [_1527289, _1527291, _1527293, _1527295] : [c_Map_Odom(_1527289, _1527291, _1527293) = hAPP(hAPP(c_Set_Oinsert(_1527289), _1527295), c_Orderings_Obot__class_Obot(tc_fun(_1527289, tc_HOL_Obool))), -(_1527293 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1527289, tc_Option_Ooption(_1527291)), hAPP(c_COMBK(tc_Option_Ooption(_1527291), _1527289), c_Option_Ooption_ONone(_1527291))), _1527295), hAPP(c_Option_Ooption_OSome(_1527291), 39723 ^ [_1527289, _1527291, _1527293, _1527295])))], (42437 ^ _778908) ^ [_1599966, _1599968] : [c_Wellfounded_OwfP(_1599966, _1599968), -(c_Wellfounded_Oacyclic(_1599966, hAPP(c_Set_OCollect(tc_prod(_1599966, _1599966)), hAPP(c_Product__Type_Oprod_Oprod__case(_1599966, _1599966, tc_HOL_Obool), _1599968))))], (7270 ^ _778908) ^ [_900550, _900552] : [class_Groups_Omonoid__add(_900550), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900550), c_Groups_Ozero__class_Ozero(_900550)), _900552) = _900552)], (39048 ^ _778908) ^ [_1511820, _1511822, _1511824, _1511826, _1511828] : [class_Groups_Ocomm__monoid__add(_1511820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511822), _1511824)), c_Fun_Oinj__on(_1511822, _1511822, _1511826, _1511824), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511822, _1511820), _1511828), hAPP(c_Set_Oimage(_1511822, _1511822, _1511826), _1511824)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511822, _1511820), hAPP(c_Fun_Ocomp(_1511822, _1511820, _1511822, _1511828), _1511826)), _1511824))], (36536 ^ _778908) ^ [_1456466, _1456468, _1456470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456466, tc_HOL_Obool)), _1456468), _1456470)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456466, tc_HOL_Obool)), _1456468), _1456470) = _1456468)], (49646 ^ _778908) ^ [_1775489, _1775491, _1775493] : [-(_1775489 = c_List_Olist_ONil(_1775491)), -(c_List_Olast(_1775491, hAPP(hAPP(c_List_Olist_OCons(_1775491), _1775493), _1775489)) = c_List_Olast(_1775491, _1775489))], (6482 ^ _778908) ^ [_883793, _883795] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_883793, _883795))), 6485 ^ _778908 : [(6488 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _883795)))], (6486 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _883793)))]]], (17979 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35088 ^ _778908) ^ [] : [-(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)))], (48494 ^ _778908) ^ [_1747630, _1747632, _1747634] : [48495 ^ _778908 : [(48498 ^ _778908) ^ [] : [_1747634 = c_List_Olist_ONil(_1747630)], (48496 ^ _778908) ^ [] : [_1747632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1747630), _1747632), _1747634) = c_List_Olist_ONil(_1747630))], (38648 ^ _778908) ^ [_1503644, _1503646] : [-(c_Fun_Oinj__on(_1503644, _1503644, c_COMBI(_1503644), _1503646))], (42928 ^ _778908) ^ [_1611639, _1611641, _1611643] : [class_Orderings_Olinorder(_1611639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611639), _1611641)), 42938 ^ _778908 : [(42941 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1611639), _1611643), 42937 ^ [_1611639, _1611641, _1611643]))], (42939 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611639), 42937 ^ [_1611639, _1611641, _1611643]), _1611641)))]], hBOOL(hAPP(hAPP(c_member(_1611639), _1611643), _1611641)), -(c_Big__Operators_Olinorder__class_OMin(_1611639, _1611641) = _1611643)], (51355 ^ _778908) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (32664 ^ _778908) ^ [_1373254, _1373256, _1373258, _1373260, _1373262] : [c_Finite__Set_Ofolding__one(_1373254, _1373256, _1373258), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373254), _1373260)), 32671 ^ _778908 : [(32678 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373254, tc_HOL_Obool)), _1373260), hAPP(hAPP(c_Set_Oinsert(_1373254), _1373262), c_Orderings_Obot__class_Obot(tc_fun(_1373254, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373254, tc_HOL_Obool))), -(hAPP(_1373258, hAPP(hAPP(c_Set_Oinsert(_1373254), _1373262), _1373260)) = hAPP(hAPP(_1373256, _1373262), hAPP(_1373258, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373254, tc_HOL_Obool)), _1373260), hAPP(hAPP(c_Set_Oinsert(_1373254), _1373262), c_Orderings_Obot__class_Obot(tc_fun(_1373254, tc_HOL_Obool)))))))], (32672 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373254, tc_HOL_Obool)), _1373260), hAPP(hAPP(c_Set_Oinsert(_1373254), _1373262), c_Orderings_Obot__class_Obot(tc_fun(_1373254, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373254, tc_HOL_Obool)), -(hAPP(_1373258, hAPP(hAPP(c_Set_Oinsert(_1373254), _1373262), _1373260)) = _1373262)]]], (44611 ^ _778908) ^ [_1651110, _1651112, _1651114, _1651116] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1651114), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651110, tc_fun(_1651114, tc_HOL_Obool)), _1651112), _1651116)))), 44612 ^ _778908 : [(44613 ^ _778908) ^ [_1651184] : [hBOOL(hAPP(hAPP(c_member(_1651110), _1651184), _1651112)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1651114), hAPP(_1651116, _1651184)))]]], (30050 ^ _778908) ^ [_1317030, _1317032] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317030, tc_HOL_Obool)), _1317032), _1317032) = c_Orderings_Obot__class_Obot(tc_fun(_1317030, tc_HOL_Obool)))], (21715 ^ _778908) ^ [_1154122, _1154124, _1154126, _1154128] : [class_Fields_Olinordered__field(_1154122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154122), _1154124), c_Groups_Ozero__class_Ozero(_1154122))), 21722 ^ _778908 : [(21729 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154122), _1154128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154122), _1154126), _1154124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154122), _1154126), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154122), _1154128), _1154124))))], (21723 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154122), _1154126), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154122), _1154128), _1154124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154122), _1154128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154122), _1154126), _1154124))))]]], (43560 ^ _778908) ^ [_1627300, _1627302, _1627304] : [c_Relation_Orefl__on(_1627300, _1627302, hAPP(c_Relation_Oconverse(_1627300, _1627300), _1627304)), -(c_Relation_Orefl__on(_1627300, _1627302, _1627304))], (22782 ^ _778908) ^ [_1174220] : [-(c_Divides_Oadjust(_1174220) = 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)), _1174220))))), 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)), _1174220))))), 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))))))))], (49356 ^ _778908) ^ [_1768830, _1768832, _1768834, _1768836, _1768838] : [c_Finite__Set_Ofun__left__comm__idem(_1768830, _1768832, _1768834), -(hAPP(hAPP(c_Finite__Set_Ofold(_1768830, _1768832, _1768834), _1768836), hAPP(c_List_Oset(_1768830), _1768838)) = hAPP(c_List_Ofoldl(_1768832, _1768830, hAPP(c_COMBC(_1768830, _1768832, _1768832), _1768834), _1768836), _1768838))], (2582 ^ _778908) ^ [_817941, _817943, _817945, _817947, _817949, _817951, _817953, _817955, _817957, _817959] : [-(c_Product__Type_Oprod_Oprod__size(_817959, _817955, _817951, _817947, _817943) = c_Product__Type_Oprod_Oprod__size(_817957, _817953, _817949, _817945, _817941)), _817959 = _817957, _817955 = _817953, _817951 = _817949, _817947 = _817945, _817943 = _817941], (44767 ^ _778908) ^ [_1655493, _1655495, _1655497, _1655499, _1655501] : [hBOOL(hAPP(hAPP(c_member(_1655493), _1655495), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655497, tc_fun(_1655493, tc_HOL_Obool)), _1655499), _1655501))), 44770 ^ _778908 : [(44771 ^ _778908) ^ [_1655617] : [hBOOL(hAPP(hAPP(c_member(_1655497), _1655617), _1655499)), -(hBOOL(hAPP(hAPP(c_member(_1655493), _1655495), hAPP(_1655501, _1655617))))]]], (36686 ^ _778908) ^ [_1460021, _1460023, _1460025] : [36688 ^ _778908 : [(36694 ^ _778908) ^ [] : [-(36687 ^ [_1460021, _1460023, _1460025] = 36690 ^ [_1460021, _1460023, _1460025])], (36692 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460021), 36690 ^ [_1460021, _1460023, _1460025]), _1460025)))], (36689 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460021), 36687 ^ [_1460021, _1460023, _1460025]), _1460023)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460021, tc_HOL_Obool)), _1460023), _1460025) = c_Orderings_Obot__class_Obot(tc_fun(_1460021, tc_HOL_Obool)))], (3264 ^ _778908) ^ [_828952, _828954, _828956, _828958, _828960, _828962] : [-(c_SetInterval_Oord_OatLeast(_828962, _828958, _828954) = c_SetInterval_Oord_OatLeast(_828960, _828956, _828952)), _828962 = _828960, _828958 = _828956, _828954 = _828952], (41402 ^ _778908) ^ [_1568116, _1568118, _1568120, _1568122, _1568124, _1568126] : [hBOOL(hAPP(hAPP(c_member(_1568116), _1568118), _1568120)), -(hAPP(c_Fun_Ooverride__on(_1568116, _1568122, _1568124, _1568126, _1568120), _1568118) = hAPP(_1568126, _1568118))], (38756 ^ _778908) ^ [_1505856, _1505858, _1505860, _1505862, _1505864] : [c_Fun_Oinj__on(_1505856, _1505858, _1505860, c_Orderings_Otop__class_Otop(tc_fun(_1505856, tc_HOL_Obool))), c_Fun_Oinj__on(_1505862, _1505856, _1505864, c_Orderings_Otop__class_Otop(tc_fun(_1505862, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1505862, _1505858, hAPP(c_Fun_Ocomp(_1505856, _1505858, _1505862, _1505860), _1505864), c_Orderings_Otop__class_Otop(tc_fun(_1505862, tc_HOL_Obool))))], (14958 ^ _778908) ^ [_1032483, _1032485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032483), 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)), _1032485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1032483), _1032485)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20213 ^ _778908) ^ [_1127716, _1127718, _1127720, _1127722, _1127724] : [class_Fields_Ofield__inverse__zero(_1127716), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127716), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127716), _1127718), _1127720)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127716), _1127722), _1127724)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127716), _1127718), _1127722)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127716), _1127720), _1127724)))], (41422 ^ _778908) ^ [_1568781, _1568783, _1568785, _1568787] : [-(c_Nitpick_Oprod(_1568781, _1568783, _1568785, _1568787) = hAPP(c_Set_OCollect(tc_prod(_1568781, _1568783)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568781, _1568783, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1568781, tc_fun(_1568783, tc_HOL_Obool), tc_fun(_1568783, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1568783, tc_HOL_Obool), tc_fun(_1568783, tc_HOL_Obool)), _1568781), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1568783)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1568781), c_fconj), hAPP(hAPP(c_COMBC(_1568781, tc_fun(_1568781, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568781)), _1568785)))), hAPP(hAPP(c_COMBC(_1568783, tc_fun(_1568783, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568783)), _1568787)))))], (20087 ^ _778908) ^ [_1125405, _1125407] : [class_Int_Onumber__ring(_1125405), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1125405), hAPP(c_Int_Onumber__class_Onumber__of(_1125405), 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)))), _1125407)) = c_Groups_Oone__class_Oone(_1125405))], (33219 ^ _778908) ^ [_1385052, _1385054, _1385056] : [class_Lattices_Olattice(_1385052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385052), _1385054)), -(_1385054 = c_Orderings_Obot__class_Obot(tc_fun(_1385052, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1385052, hAPP(hAPP(c_Set_Oinsert(_1385052), _1385056), _1385054)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1385052), _1385056), c_Big__Operators_Olattice__class_OSup__fin(_1385052, _1385054)))], (37983 ^ _778908) ^ [_1490297] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1490297)), c_Int_OInteg)))], (45320 ^ _778908) ^ [_1670071, _1670073, _1670075, _1670077] : [-(hAPP(c_Set_Oimage(_1670071, _1670073, _1670075), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670071, tc_HOL_Obool), _1670077)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1670071, tc_HOL_Obool), tc_fun(_1670073, tc_HOL_Obool)), _1670077), c_Set_Oimage(_1670071, _1670073, _1670075)))], (35879 ^ _778908) ^ [_1442131, _1442133, _1442135, _1442137, _1442139] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1442131, _1442133, _1442135), _1442137), _1442139))), hBOOL(hAPP(hAPP(_1442133, _1442137), _1442139)), hBOOL(hAPP(_1442135, _1442139))], (41967 ^ _778908) ^ [_1588522, _1588524, _1588526] : [c_Wellfounded_Owf(_1588522, _1588524), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588522, _1588522)), hAPP(hAPP(c_Product__Type_OPair(_1588522, _1588522), _1588526), _1588526)), _1588524))], (12519 ^ _778908) ^ [_989431, _989433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _989431)), _989433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989431), _989433)))], (18381 ^ _778908) ^ [_1096304, _1096306] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1096304), hAPP(hAPP(c_Power_Opower__class_Opower(_1096304), hAPP(c_Int_Onumber__class_Onumber__of(_1096304), c_Int_OMin)), _1096306)) = c_Groups_Oone__class_Oone(_1096304)), class_Int_Onumber__ring(_1096304), class_Rings_Olinordered__idom(_1096304)], (45102 ^ _778908) ^ [_1664884, _1664886, _1664888, _1664890, _1664892, _1664894, _1664896] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664884, tc_fun(_1664886, tc_fun(_1664888, tc_HOL_Obool))), _1664890), _1664892), _1664894), _1664896)), 45105 ^ _778908 : [(45106 ^ _778908) ^ [_1665012] : [hBOOL(hAPP(hAPP(c_member(_1664884), _1665012), _1664890)), -(hBOOL(hAPP(hAPP(hAPP(_1664892, _1665012), _1664894), _1664896)))]]], (7110 ^ _778908) ^ [_897802] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _897802)], (42445 ^ _778908) ^ [_1600136, _1600138] : [c_Wellfounded_Owf(_1600136, _1600138), -(c_Wellfounded_Oacyclic(_1600136, _1600138))], (40464 ^ _778908) ^ [_1547484, _1547486, _1547488] : [c_Relation_Orefl__on(_1547484, _1547486, _1547488), 40467 ^ _778908 : [(40470 ^ _778908) ^ [_1547666] : [hBOOL(hAPP(hAPP(c_member(_1547484), _1547666), _1547486)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547484, _1547484)), hAPP(hAPP(c_Product__Type_OPair(_1547484, _1547484), _1547666), _1547666)), _1547488)))], (40468 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547484, _1547484), tc_HOL_Obool)), _1547488), hAPP(hAPP(c_Product__Type_OSigma(_1547484, _1547484), _1547486), hAPP(c_COMBK(tc_fun(_1547484, tc_HOL_Obool), _1547484), _1547486)))))]]], (7406 ^ _778908) ^ [_902645, _902647] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_902645, _902647)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_902647)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18907 ^ _778908) ^ [_1104753] : [c_Int_OBit1(_1104753) = c_Int_OMin, -(_1104753 = c_Int_OMin)], (7635 ^ _778908) ^ [_906744, _906746] : [-(_906744 = _906746), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906744), _906746))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906746), _906744)))], (19779 ^ _778908) ^ [_1119617] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1119617)), 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, _1119617, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (47545 ^ _778908) ^ [_1724466, _1724468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724466)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724468))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724468)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724466)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724466)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1724468))))], (15351 ^ _778908) ^ [_1039904, _1039906, _1039908] : [class_Fields_Olinordered__field__inverse__zero(_1039904), 15357 ^ _778908 : [(15362 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039904), 15356 ^ [_1039904, _1039906, _1039908]), _1039906)), _1039908))], (15360 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039904), 15356 ^ [_1039904, _1039906, _1039908]), c_Groups_Oone__class_Oone(_1039904))))], (15358 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039904), c_Groups_Ozero__class_Ozero(_1039904)), 15356 ^ [_1039904, _1039906, _1039908])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039904), _1039906), _1039908)))], (28043 ^ _778908) ^ [_1276114, _1276116] : [c_Nat__Transfer_Onat__set(_1276114), c_Nat__Transfer_Onat__set(_1276116), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1276114), _1276116)))], (27097 ^ _778908) ^ [_1257371, _1257373] : [27099 ^ _778908 : [(27102 ^ _778908) ^ [] : [hBOOL(hAPP(_1257373, 27098 ^ [_1257371, _1257373]))], (27100 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27098 ^ [_1257371, _1257373]), _1257371)))]], 27103 ^ _778908 : [(27104 ^ _778908) ^ [_1257522] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1257522), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1257371))), -(hBOOL(hAPP(_1257373, _1257522)))]]], (11210 ^ _778908) ^ [_966358, _966360, _966362, _966364] : [class_Orderings_Oorder(_966358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966358), _966360), _966362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966358), _966364), _966360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966358), _966364), _966362)))], (42760 ^ _778908) ^ [_1607591, _1607593] : [42761 ^ _778908 : [(42762 ^ _778908) ^ [_1607637] : [hBOOL(hAPP(_1607591, _1607637))]], -(hBOOL(hAPP(_1607591, c_Hilbert__Choice_OEps(_1607593, _1607591))))], (44348 ^ _778908) ^ [_1645957, _1645959, _1645961] : [class_Lattices_Olattice(_1645957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645957), _1645959)), -(hBOOL(hAPP(hAPP(c_member(_1645957), _1645961), _1645959))), -(c_Big__Operators_Olattice__class_OInf__fin(_1645957, hAPP(hAPP(c_Set_Oinsert(_1645957), _1645961), _1645959)) = hAPP(hAPP(c_Finite__Set_Ofold(_1645957, _1645957, c_Lattices_Osemilattice__inf__class_Oinf(_1645957)), _1645961), _1645959))], (14633 ^ _778908) ^ [_1027272, _1027274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027272)), 14636 ^ _778908 : [(14643 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1027274), 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), _1027274), _1027272)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14637 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027274), _1027272)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1027274), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (7472 ^ _778908) ^ [_903815, _903817] : [c_Option_Ois__none(_903815, hAPP(c_Option_Ooption_OSome(_903815), _903817))], (49354 ^ _778908) ^ [_1768799, _1768801] : [-(c_List_Olist_Olist__size(_1768799, _1768801, c_List_Olist_ONil(_1768799)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32527 ^ _778908) ^ [_1370482, _1370484, _1370486, _1370488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1370488, _1370484)), hAPP(_1370488, _1370486))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1370482, _1370482)), hAPP(hAPP(c_Product__Type_OPair(_1370482, _1370482), _1370484), _1370486)), hAPP(c_Wellfounded_Omeasure(_1370482), _1370488))))], (44872 ^ _778908) ^ [_1658869, _1658871, _1658873, _1658875] : [44874 ^ _778908 : [(44877 ^ _778908) ^ [] : [hAPP(_1658875, 44873 ^ [_1658869, _1658871, _1658873, _1658875]) = c_Orderings_Otop__class_Otop(tc_fun(_1658869, tc_HOL_Obool))], (44875 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1658871), 44873 ^ [_1658869, _1658871, _1658873, _1658875]), _1658873)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1658869, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658871, tc_fun(_1658869, tc_HOL_Obool)), _1658873), _1658875))], (2328 ^ _778908) ^ [_814034, _814036, _814038, _814040] : [-(c_SMT_Oz3mod(_814040, _814036) = c_SMT_Oz3mod(_814038, _814034)), _814040 = _814038, _814036 = _814034], (35259 ^ _778908) ^ [_1427419, _1427421, _1427423, _1427425] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1427419, _1427419)), hAPP(hAPP(c_Product__Type_OPair(_1427419, _1427419), _1427421), _1427423)), c_Relation_OId__on(_1427419, _1427425))), 35262 ^ _778908 : [(35265 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1427419), _1427421), _1427425)))], (35263 ^ _778908) ^ [] : [-(_1427421 = _1427423)]]], (30472 ^ _778908) ^ [_1324624, _1324626, _1324628, _1324630, _1324632] : [-(_1324624 = c_Orderings_Obot__class_Obot(tc_fun(_1324626, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324626, tc_fun(_1324628, tc_HOL_Obool)), _1324624), hAPP(hAPP(c_COMBB(tc_fun(_1324628, tc_HOL_Obool), tc_fun(_1324628, tc_HOL_Obool), _1324626), hAPP(c_Set_Oinsert(_1324628), _1324630)), _1324632)) = hAPP(hAPP(c_Set_Oinsert(_1324628), _1324630), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324626, tc_fun(_1324628, tc_HOL_Obool)), _1324624), _1324632)))], (43699 ^ _778908) ^ [_1630846, _1630848, _1630850] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630846, _1630846), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1630848)), _1630850) = hAPP(hAPP(c_Relation_Orel__comp(_1630846, _1630846, _1630846), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630846, _1630846), tc_HOL_Obool), _1630848), _1630850)), _1630850))], (28251 ^ _778908) ^ [_1280592, _1280594, _1280596] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280592, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280592, tc_HOL_Obool)), _1280594), _1280596)), _1280596) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280592, tc_HOL_Obool)), _1280594), _1280596))], (35907 ^ _778908) ^ [_1442654] : [-(_1442654 = 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), 35904 ^ [_1442654]), 35905 ^ [_1442654])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (34032 ^ _778908) ^ [_1400702, _1400704, _1400706] : [class_Orderings_Olinorder(_1400702), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400702), _1400704)), -(_1400706 = c_Orderings_Obot__class_Obot(tc_fun(_1400702, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1400702, tc_HOL_Obool)), _1400706), _1400704)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1400702), c_Big__Operators_Olattice_OInf__fin(_1400702, c_Orderings_Oord__class_Omin(_1400702), _1400706)), c_Big__Operators_Olattice_OInf__fin(_1400702, c_Orderings_Oord__class_Omin(_1400702), _1400704)) = c_Big__Operators_Olattice_OInf__fin(_1400702, c_Orderings_Oord__class_Omin(_1400702), _1400704))], (22364 ^ _778908) ^ [_1166248] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1166248)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1166248)], (40721 ^ _778908) ^ [_1552421, _1552423, _1552425] : [class_Lattices_Oab__semigroup__idem__mult(_1552421), -(_1552423 = c_Orderings_Obot__class_Obot(tc_fun(_1552421, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552421), _1552423)), -(hAPP(c_Finite__Set_Ofold1(_1552421, c_Groups_Otimes__class_Otimes(_1552421)), hAPP(hAPP(c_Set_Oinsert(_1552421), _1552425), _1552423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1552421), _1552425), hAPP(c_Finite__Set_Ofold1(_1552421, c_Groups_Otimes__class_Otimes(_1552421)), _1552423)))], (34415 ^ _778908) ^ [_1408646, _1408648, _1408650, _1408652, _1408654, _1408656, _1408658] : [-(_1408646 = _1408648), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408650, _1408652), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408650, _1408652), _1408654), _1408646), _1408656)), _1408648), _1408658) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408650, _1408652), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408650, _1408652), _1408654), _1408648), _1408658)), _1408646), _1408656))], (29126 ^ _778908) ^ [] : [-(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)))], (1362 ^ _778908) ^ [_798807, _798809] : [-(class_Lattices_Olattice(_798807)), _798809 = _798807, class_Lattices_Olattice(_798809)], (26717 ^ _778908) ^ [_1250033, _1250035, _1250037] : [class_Divides_Osemiring__div(_1250033), class_Int_Onumber(_1250033), 26724 ^ _778908 : [(26731 ^ _778908) ^ [] : [c_Divides_Odiv__class_Omod(_1250033, hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250037), hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250035)) = c_Groups_Ozero__class_Ozero(_1250033), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250033), hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250035)), hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250037))))], (26725 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250033), hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250035)), hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250037))), -(c_Divides_Odiv__class_Omod(_1250033, hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250037), hAPP(c_Int_Onumber__class_Onumber__of(_1250033), _1250035)) = c_Groups_Ozero__class_Ozero(_1250033))]]], (32907 ^ _778908) ^ [_1378199, _1378201] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1378199, _1378201), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378199), _1378201)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378201), _1378199)))], (10509 ^ _778908) ^ [_955441, _955443, _955445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955441), _955443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955445), _955441)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955445), _955443))))], (37234 ^ _778908) ^ [_1472553, _1472555, _1472557, _1472559, _1472561, _1472563, _1472565, _1472567] : [c_Finite__Set_Ofolding__image__simple(_1472553, _1472555, _1472557, _1472559, _1472561, _1472563), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472555), _1472565)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472555), _1472567)), -(hAPP(hAPP(_1472557, hAPP(_1472563, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472555, tc_HOL_Obool)), _1472565), _1472567))), hAPP(_1472563, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472555, tc_HOL_Obool)), _1472565), _1472567))) = hAPP(hAPP(_1472557, hAPP(_1472563, _1472565)), hAPP(_1472563, _1472567)))], (21687 ^ _778908) ^ [_1153584, _1153586, _1153588, _1153590] : [class_Fields_Olinordered__field(_1153584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153584), c_Groups_Ozero__class_Ozero(_1153584)), _1153586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153584), _1153588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153584), _1153590), _1153586))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153584), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153584), _1153588), _1153586)), _1153590)))], (50763 ^ _778908) ^ [_1798869, _1798871] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798869)), c_List_Oconcat(_1798869, _1798871)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798869), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1798869))), _1798871)))], (51541 ^ _778908) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (20081 ^ _778908) ^ [_1125274, _1125276] : [class_Rings_Oring__1(_1125274), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1125274), hAPP(c_Groups_Ouminus__class_Ouminus(_1125274), c_Groups_Oone__class_Oone(_1125274))), 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)))), _1125276))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1125274), c_Groups_Oone__class_Oone(_1125274)))], (8928 ^ _778908) ^ [_927921, _927923, _927925] : [class_Rings_Ocomm__semiring__1(_927921), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927921), _927923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927921), _927925), _927923)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927921), _927925), c_Groups_Oone__class_Oone(_927921))), _927923))], (42591 ^ _778908) ^ [_1603532, _1603534, _1603536, _1603538] : [c_Equiv__Relations_Ocongruent(_1603532, _1603534, _1603536, _1603538), 42594 ^ _778908 : [(42595 ^ _778908) ^ [_1603677] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603532, _1603532)), _1603677), _1603536)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1603532, _1603532, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1603532, tc_fun(_1603532, _1603534), tc_fun(_1603532, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603534, tc_HOL_Obool), tc_fun(tc_fun(_1603532, _1603534), tc_fun(_1603532, tc_HOL_Obool)), _1603532), c_COMBB(_1603534, tc_HOL_Obool, _1603532)), hAPP(hAPP(c_COMBB(_1603534, tc_fun(_1603534, tc_HOL_Obool), _1603532), c_fequal), _1603538))), _1603538)), _1603677)))]]], (1332 ^ _778908) ^ [_798432, _798434] : [-(class_Lattices_Osemilattice__inf(_798432)), _798434 = _798432, class_Lattices_Osemilattice__inf(_798434)], (36952 ^ _778908) ^ [_1466062, _1466064, _1466066, _1466068] : [-(hBOOL(hAPP(hAPP(c_member(_1466062), _1466064), _1466066))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466062, tc_HOL_Obool)), _1466066), hAPP(hAPP(c_Set_Oinsert(_1466062), _1466064), _1466068)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466062, tc_HOL_Obool)), _1466066), _1466068))], (35504 ^ _778908) ^ [_1432696, _1432698] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1432696), _1432698)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1432696, tc_HOL_Obool)), hAPP(c_Set_OPow(_1432696), _1432698))))], (49979 ^ _778908) ^ [_1782381, _1782383, _1782385] : [-(c_List_Opartition(_1782381, _1782383, _1782385) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782381), tc_List_Olist(_1782381)), hAPP(c_List_Ofilter(_1782381, _1782383), _1782385)), hAPP(c_List_Ofilter(_1782381, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1782381, c_fNot), _1782383)), _1782385)))], (45306 ^ _778908) ^ [_1669527, _1669529, _1669531] : [-(hAPP(c_Relation_ORange(_1669527, _1669529), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1669527, _1669529), tc_HOL_Obool), _1669531)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1669527, _1669529), tc_HOL_Obool), tc_fun(_1669529, tc_HOL_Obool)), _1669531), c_Relation_ORange(_1669527, _1669529)))], (17977 ^ _778908) ^ [_1089893] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1089893)))], (27084 ^ _778908) ^ [_1257116, _1257118] : [27092 ^ _778908 : [(27095 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1257118, 27091 ^ [_1257116, _1257118])))], (27093 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27091 ^ [_1257116, _1257118]), _1257116)))]], 27085 ^ _778908 : [(27086 ^ _778908) ^ [_1257185] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1257185), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1257116))), hBOOL(hAPP(_1257118, _1257185))]]], (728 ^ _778908) ^ [_790116, _790118, _790120, _790122] : [-(c_Wellfounded_Oacyclic(_790120, _790116)), c_Wellfounded_Oacyclic(_790122, _790118), _790122 = _790120, _790118 = _790116], (38962 ^ _778908) ^ [_1509998, _1510000, _1510002, _1510004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509998), _1510000)), hAPP(c_Finite__Set_Ocard(_1510002), hAPP(c_Set_Oimage(_1509998, _1510002, _1510004), _1510000)) = hAPP(c_Finite__Set_Ocard(_1509998), _1510000), -(c_Fun_Oinj__on(_1509998, _1510002, _1510004, _1510000))], (50915 ^ _778908) ^ [_1802160, _1802162, _1802164] : [_1802162 = hAPP(c_List_Orev(_1802160), _1802164), -(hAPP(c_List_Orev(_1802160), _1802162) = _1802164)], (12243 ^ _778908) ^ [_984557, _984559, _984561, _984563, _984565] : [class_Groups_Oordered__cancel__ab__semigroup__add(_984557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984557), _984559), _984561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984557), _984563), _984565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984557), _984559), _984563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984557), _984561), _984565))))], (26835 ^ _778908) ^ [_1252126, _1252128, _1252130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1252126)), 26838 ^ _778908 : [(26845 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252128), _1252130)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252126), _1252128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252126), _1252130))))], (26839 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252126), _1252128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252126), _1252130))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252128), _1252130)))]]], (28151 ^ _778908) ^ [_1278456, _1278458] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278456, tc_HOL_Obool)), _1278458), _1278458) = _1278458)], (39482 ^ _778908) ^ [_1521576, _1521578, _1521580, _1521582, _1521584] : [hBOOL(hAPP(hAPP(c_member(_1521576), _1521578), hAPP(c_Set_Ovimage(_1521576, _1521580, _1521582), _1521584))), -(hBOOL(hAPP(hAPP(c_member(_1521580), hAPP(_1521582, _1521578)), _1521584)))], (13791 ^ _778908) ^ [_1011605, _1011607, _1011609] : [-(hBOOL(hAPP(_1011605, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011607, _1011609)))), 13794 ^ _778908 : [(13797 ^ _778908) ^ [] : [hBOOL(hAPP(_1011605, _1011607))], (13795 ^ _778908) ^ [] : [-(_1011609 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 13800 ^ _778908 : [(13801 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011609)))], (13807 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13803 ^ [_1011605, _1011607, _1011609]), _1011609)))], (13811 ^ _778908) ^ [] : [hBOOL(hAPP(_1011605, 13803 ^ [_1011605, _1011607, _1011609]))], (13809 ^ _778908) ^ [] : [-(_1011607 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011609), 13802 ^ [_1011605, _1011607, _1011609])), 13803 ^ [_1011605, _1011607, _1011609]))], (13805 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13803 ^ [_1011605, _1011607, _1011609])))]], 13812 ^ _778908 : [(13813 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011609), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13819 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13815 ^ [_1011605, _1011607, _1011609]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13823 ^ _778908) ^ [] : [hBOOL(hAPP(_1011605, 13815 ^ [_1011605, _1011607, _1011609]))], (13821 ^ _778908) ^ [] : [-(_1011607 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011609), 13814 ^ [_1011605, _1011607, _1011609])), 13815 ^ [_1011605, _1011607, _1011609]))], (13817 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011609), 13815 ^ [_1011605, _1011607, _1011609])))]]], (51111 ^ _778908) ^ [_1807695, _1807697] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1807695), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1807695))), _1807697))), -(c_List_Otranspose(_1807695, c_List_Otranspose(_1807695, _1807697)) = c_List_OtakeWhile(tc_List_Olist(_1807695), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1807695)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1807695), tc_List_Olist(_1807695), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1807695))), _1807697))], (25591 ^ _778908) ^ [_1228538, _1228540] : [-(_1228538 = _1228540), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228538), _1228540)), 25598 ^ _778908 : [(25601 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228540), _1228538))], (25599 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228538), _1228540)))]]], (22522 ^ _778908) ^ [_1169186, _1169188] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169186) = hAPP(c_Nat_OSuc, _1169188), -(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(_1169186))), 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)), _1169188))))))], (24597 ^ _778908) ^ [_1209232, _1209234, _1209236, _1209238] : [class_Orderings_Olinorder(_1209232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209232), _1209234), _1209236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209232), _1209234), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209232), _1209238), _1209236))))], (16044 ^ _778908) ^ [_1053058] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1053058)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1053058)], (21357 ^ _778908) ^ [_1147849, _1147851, _1147853, _1147855] : [class_Fields_Ofield__inverse__zero(_1147849), class_Int_Onumber(_1147849), 21364 ^ _778908 : [(21365 ^ _778908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147849), _1147851), _1147853) = hAPP(c_Int_Onumber__class_Onumber__of(_1147849), _1147855), 21368 ^ _778908 : [(21375 ^ _778908) ^ [] : [_1147853 = c_Groups_Ozero__class_Ozero(_1147849), -(hAPP(c_Int_Onumber__class_Onumber__of(_1147849), _1147855) = c_Groups_Ozero__class_Ozero(_1147849))], (21369 ^ _778908) ^ [] : [-(_1147853 = c_Groups_Ozero__class_Ozero(_1147849)), -(_1147851 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147849), hAPP(c_Int_Onumber__class_Onumber__of(_1147849), _1147855)), _1147853))]]], (21381 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147849), _1147851), _1147853) = hAPP(c_Int_Onumber__class_Onumber__of(_1147849), _1147855)), 21384 ^ _778908 : [(21387 ^ _778908) ^ [] : [_1147851 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147849), hAPP(c_Int_Onumber__class_Onumber__of(_1147849), _1147855)), _1147853)], (21385 ^ _778908) ^ [] : [_1147853 = c_Groups_Ozero__class_Ozero(_1147849)]], 21388 ^ _778908 : [(21391 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1147849), _1147855) = c_Groups_Ozero__class_Ozero(_1147849)], (21389 ^ _778908) ^ [] : [-(_1147853 = c_Groups_Ozero__class_Ozero(_1147849))]]]]], (23373 ^ _778908) ^ [_1186271, _1186273, _1186275, _1186277, _1186279, _1186281, _1186283] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186271, _1186273, tc_fun(_1186275, tc_HOL_Obool)), _1186277), hAPP(hAPP(c_Product__Type_OPair(_1186271, _1186273), _1186279), _1186281)), _1186283)), -(hBOOL(hAPP(hAPP(hAPP(_1186277, _1186279), _1186281), _1186283)))], (44440 ^ _778908) ^ [_1647667] : [class_Groups_Oab__semigroup__mult(_1647667), -(c_Finite__Set_Ofun__left__comm(_1647667, _1647667, c_Groups_Otimes__class_Otimes(_1647667)))], (18255 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (26693 ^ _778908) ^ [_1249420, _1249422, _1249424, _1249426] : [class_Rings_Ocomm__ring(_1249420), class_Rings_Odvd(_1249420), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249420), _1249422), _1249424)), 26704 ^ _778908 : [(26711 ^ _778908) ^ [_1249846, _1249848] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249420), _1249422), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249420), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249420), _1249848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249420), _1249846), _1249424))), _1249426))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249420), _1249422), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249420), _1249848), _1249426))))], (26705 ^ _778908) ^ [_1249673, _1249675] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249420), _1249422), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249420), _1249675), _1249426))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249420), _1249422), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249420), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249420), _1249675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249420), _1249673), _1249424))), _1249426))))]]], (45356 ^ _778908) ^ [_1670861] : [class_Complete__Lattice_Ocomplete__lattice(_1670861), -(c_Complete__Lattice_OSup__class_OSup(_1670861, c_Orderings_Obot__class_Obot(tc_fun(_1670861, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1670861))], (9264 ^ _778908) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43393 ^ _778908) ^ [_1623133, _1623135, _1623137, _1623139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623133, _1623133)), hAPP(hAPP(c_Product__Type_OPair(_1623133, _1623133), _1623135), _1623137)), c_Transitive__Closure_Ortrancl(_1623133, _1623139))), hBOOL(hAPP(hAPP(c_member(_1623133), _1623137), c_Wellfounded_Oacc(_1623133, _1623139))), -(hBOOL(hAPP(hAPP(c_member(_1623133), _1623135), c_Wellfounded_Oacc(_1623133, _1623139))))], (19787 ^ _778908) ^ [_1119785, _1119787] : [class_Rings_Olinordered__idom(_1119785), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119785), c_Groups_Ozero__class_Ozero(_1119785)), hAPP(hAPP(c_Power_Opower__class_Opower(_1119785), _1119787), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (14675 ^ _778908) ^ [_1027948] : [-(_1027948 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027948), _1027948) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21521 ^ _778908) ^ [_1150586, _1150588] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150586), _1150588), hAPP(c_Int_Onumber__class_Onumber__of(_1150586), c_Int_OBit1(c_Int_OPls))) = _1150588), class_Fields_Ofield(_1150586), class_Int_Onumber__ring(_1150586)], (15742 ^ _778908) ^ [_1047182, _1047184, _1047186] : [class_Groups_Oordered__ab__group__add(_1047182), 15745 ^ _778908 : [(15752 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047182), _1047184), _1047186)), c_Groups_Ozero__class_Ozero(_1047182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047182), _1047184), _1047186)))], (15746 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047182), _1047184), _1047186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047182), _1047184), _1047186)), c_Groups_Ozero__class_Ozero(_1047182))))]]], (14706 ^ _778908) ^ [_1028480, _1028482] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028480), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028482)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028480, _1028482)))], (35742 ^ _778908) ^ [_1438183, _1438185, _1438187, _1438189, _1438191, _1438193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1438183, _1438185), tc_HOL_Obool)), _1438187), _1438189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438183, tc_HOL_Obool)), _1438191), _1438193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438185, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1438183, _1438185, _1438187), _1438191)), hAPP(c_Relation_OImage(_1438183, _1438185, _1438189), _1438193))))], (41519 ^ _778908) ^ [_1572584, _1572586, _1572588] : [-(c_Map_Oran(_1572584, _1572586, _1572588) = hAPP(c_Set_OCollect(_1572586), hAPP(hAPP(c_COMBB(tc_fun(_1572584, tc_HOL_Obool), tc_HOL_Obool, _1572586), c_HOL_OEx(_1572584)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1572586), tc_fun(_1572584, tc_HOL_Obool), _1572586), hAPP(c_COMBC(_1572584, tc_Option_Ooption(_1572586), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1572586), tc_fun(tc_Option_Ooption(_1572586), tc_HOL_Obool), _1572584), c_fequal), _1572588))), c_Option_Ooption_OSome(_1572586)))))], (36608 ^ _778908) ^ [_1457990, _1457992, _1457994, _1457996] : [hBOOL(hAPP(hAPP(c_member(_1457990), _1457992), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457990, tc_HOL_Obool)), _1457994), _1457996))), 36611 ^ _778908 : [(36614 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457990), _1457992), _1457996)))], (36612 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457990), _1457992), _1457994)))]]], (47457 ^ _778908) ^ [_1722876] : [class_Orderings_Olinorder(_1722876), -(c_List_Olinorder__class_Osorted__list__of__set(_1722876, c_Orderings_Obot__class_Obot(tc_fun(_1722876, tc_HOL_Obool))) = c_List_Olist_ONil(_1722876))], (21847 ^ _778908) ^ [_1156716, _1156718, _1156720, _1156722] : [class_Fields_Olinordered__field__inverse__zero(_1156716), class_Int_Onumber(_1156716), 21854 ^ _778908 : [(21855 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156716), _1156720), _1156722))), 21858 ^ _778908 : [(21865 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), c_Groups_Ozero__class_Ozero(_1156716)), _1156722))), 21868 ^ _778908 : [(21875 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), _1156722), c_Groups_Ozero__class_Ozero(_1156716)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), c_Groups_Ozero__class_Ozero(_1156716))))], (21869 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), _1156722), c_Groups_Ozero__class_Ozero(_1156716))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), _1156720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), _1156722))))]]], (21859 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), c_Groups_Ozero__class_Ozero(_1156716)), _1156722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), _1156722)), _1156720)))]]], (21881 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156716), _1156720), _1156722)))), 21884 ^ _778908 : [(21887 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), _1156722)), _1156720))], (21885 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), c_Groups_Ozero__class_Ozero(_1156716)), _1156722)))]], 21888 ^ _778908 : [(21891 ^ _778908) ^ [] : [21892 ^ _778908 : [(21895 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), _1156720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), _1156722)))], (21893 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), _1156722), c_Groups_Ozero__class_Ozero(_1156716))))]], 21896 ^ _778908 : [(21899 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), hAPP(c_Int_Onumber__class_Onumber__of(_1156716), _1156718)), c_Groups_Ozero__class_Ozero(_1156716)))], (21897 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), _1156722), c_Groups_Ozero__class_Ozero(_1156716)))]]], (21889 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156716), c_Groups_Ozero__class_Ozero(_1156716)), _1156722))]]]]], (5594 ^ _778908) ^ [_865323, _865325, _865327, _865329] : [-(c_List_Otranspose(_865329, _865325) = c_List_Otranspose(_865327, _865323)), _865329 = _865327, _865325 = _865323], (17535 ^ _778908) ^ [_1081823, _1081825, _1081827] : [class_Groups_Omonoid__mult(_1081823), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081823), hAPP(hAPP(c_Power_Opower__class_Opower(_1081823), _1081825), _1081827)), _1081825) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081823), _1081825), hAPP(hAPP(c_Power_Opower__class_Opower(_1081823), _1081825), _1081827)))], (24025 ^ _778908) ^ [_1197985, _1197987, _1197989, _1197991, _1197993] : [-(hAPP(c_Product__Type_Ofst(_1197985, _1197987), hAPP(c_Product__Type_Oapsnd(_1197989, _1197987, _1197985, _1197991), _1197993)) = hAPP(c_Product__Type_Ofst(_1197985, _1197989), _1197993))], (20989 ^ _778908) ^ [_1141186, _1141188, _1141190, _1141192] : [class_Fields_Olinordered__field(_1141186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141186), _1141188), _1141190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141186), c_Groups_Ozero__class_Ozero(_1141186)), _1141192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141186), c_Groups_Ozero__class_Ozero(_1141186)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141186), _1141190), _1141188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141186), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141186), _1141192), _1141190)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141186), _1141192), _1141188))))], (23256 ^ _778908) ^ [_1183708, _1183710, _1183712] : [hBOOL(hAPP(_1183708, 23257 ^ [_1183708, _1183710, _1183712])), 23260 ^ _778908 : [(23261 ^ _778908) ^ [_1183819, _1183821] : [-(hBOOL(hAPP(_1183708, hAPP(hAPP(c_Product__Type_OPair(_1183710, _1183712), _1183821), _1183819))))]]], (24795 ^ _778908) ^ [_1213345, _1213347] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1213345), _1213347)), _1213347) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1213345), _1213347))], (18903 ^ _778908) ^ [_1104682] : [c_Int_OBit1(_1104682) = c_Int_OPls], (29048 ^ _778908) ^ [_1297072, _1297074, _1297076, _1297078, _1297080] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297072, tc_fun(_1297074, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297072, tc_HOL_Obool)), _1297076), _1297078)), _1297080) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297074, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297072, tc_fun(_1297074, tc_HOL_Obool)), _1297076), _1297080)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297072, tc_fun(_1297074, tc_HOL_Obool)), _1297078), _1297080)))], (30610 ^ _778908) ^ [_1327370, _1327372, _1327374, _1327376] : [-(hAPP(c_Set_Oimage(_1327370, _1327372, _1327374), _1327376) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1327370, tc_fun(_1327372, tc_HOL_Obool)), _1327376), hAPP(hAPP(c_COMBC(_1327370, tc_fun(_1327372, tc_HOL_Obool), tc_fun(_1327372, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1327372, tc_fun(tc_fun(_1327372, tc_HOL_Obool), tc_fun(_1327372, tc_HOL_Obool)), _1327370), c_Set_Oinsert(_1327372)), _1327374)), c_Orderings_Obot__class_Obot(tc_fun(_1327372, tc_HOL_Obool)))))], (19031 ^ _778908) ^ [_1106721] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1106721)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1106721))))], (22474 ^ _778908) ^ [_1168312, _1168314] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1168312)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1168314)), hAPP(c_Int_Onat, _1168312)) = hAPP(c_Int_Onat, _1168314))], (22382 ^ _778908) ^ [_1166578, _1166580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166578), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166580)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166578)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166580))], (30466 ^ _778908) ^ [_1324461, _1324463, _1324465, _1324467, _1324469] : [_1324461 = c_Orderings_Obot__class_Obot(tc_fun(_1324463, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324463, tc_fun(_1324465, tc_HOL_Obool)), _1324461), hAPP(hAPP(c_COMBB(tc_fun(_1324465, tc_HOL_Obool), tc_fun(_1324465, tc_HOL_Obool), _1324463), hAPP(c_Set_Oinsert(_1324465), _1324467)), _1324469)) = c_Orderings_Obot__class_Obot(tc_fun(_1324465, tc_HOL_Obool)))], (23855 ^ _778908) ^ [_1194665] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1194665) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28996 ^ _778908) ^ [_1295771, _1295773, _1295775, _1295777, _1295779] : [class_Complete__Lattice_Ocomplete__lattice(_1295771), class_Orderings_Olinorder(_1295771), 29003 ^ _778908 : [(29013 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295771), _1295773), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295775, _1295771), _1295777), _1295779)))), 29014 ^ _778908 : [(29015 ^ _778908) ^ [_1296119] : [hBOOL(hAPP(hAPP(c_member(_1295775), _1296119), _1295777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295771), _1295773), hAPP(_1295779, _1296119)))]]], (29004 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295771), _1295773), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1295775, _1295771), _1295777), _1295779))), 29008 ^ _778908 : [(29011 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295771), _1295773), hAPP(_1295779, 29007 ^ [_1295771, _1295773, _1295775, _1295777, _1295779]))))], (29009 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295775), 29007 ^ [_1295771, _1295773, _1295775, _1295777, _1295779]), _1295777)))]]]]], (33169 ^ _778908) ^ [_1384220, _1384222, _1384224] : [class_Rings_Oring__1(_1384220), hBOOL(hAPP(hAPP(c_member(_1384220), _1384222), c_Int_Oring__1__class_OInts(_1384220))), -(hBOOL(hAPP(hAPP(c_member(_1384220), hAPP(hAPP(c_Power_Opower__class_Opower(_1384220), _1384222), _1384224)), c_Int_Oring__1__class_OInts(_1384220))))], (46004 ^ _778908) ^ [_1685355, _1685357] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1685355), _1685357) = c_Smallcheck_Osmall_H(_1685355, hAPP(c_Code__Numeral_Oint__of, _1685357), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1685357))))], (50573 ^ _778908) ^ [_1794452, _1794454, _1794456] : [class_Orderings_Olinorder(_1794452), 50576 ^ _778908 : [(50589 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1794452, hAPP(hAPP(c_List_Olist_OCons(_1794452), _1794454), _1794456))), 50593 ^ _778908 : [(50596 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1794452), _1794454), 50592 ^ [_1794452, _1794454, _1794456]))], (50594 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794452), 50592 ^ [_1794452, _1794454, _1794456]), hAPP(c_List_Oset(_1794452), _1794456))))]], c_List_Olinorder__class_Osorted(_1794452, _1794456)], (50577 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1794452, hAPP(hAPP(c_List_Olist_OCons(_1794452), _1794454), _1794456)), 50580 ^ _778908 : [(50581 ^ _778908) ^ [_1794620] : [hBOOL(hAPP(hAPP(c_member(_1794452), _1794620), hAPP(c_List_Oset(_1794452), _1794456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1794452), _1794454), _1794620)))], (50587 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1794452, _1794456))]]]]], (23927 ^ _778908) ^ [_1196160, _1196162, _1196164, _1196166] : [class_Orderings_Olinorder(_1196160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196160), _1196162), _1196164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196160), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196160), _1196162), _1196166)), _1196164)))], (2512 ^ _778908) ^ [_816898, _816900, _816902, _816904] : [-(c_Groups_Osgn__class_Osgn(_816904, _816900) = c_Groups_Osgn__class_Osgn(_816902, _816898)), _816904 = _816902, _816900 = _816898], (49125 ^ _778908) ^ [_1764424, _1764426, _1764428] : [-(hAPP(c_List_Ohd(_1764424), hAPP(hAPP(c_List_Olist_OCons(_1764424), _1764426), _1764428)) = _1764426)], (48847 ^ _778908) ^ [_1757426, _1757428, _1757430, _1757432] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757426), tc_List_Olist(_1757426))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757426), tc_List_Olist(_1757426)), _1757428), _1757430)), c_List_Olistrel1(_1757426, _1757432)))), 48848 ^ _778908 : [(48849 ^ _778908) ^ [_1757559, _1757561] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757426, _1757426)), hAPP(hAPP(c_Product__Type_OPair(_1757426, _1757426), hAPP(hAPP(c_List_Onth(_1757426), _1757428), _1757559)), _1757561)), _1757432)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757559), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757426)), _1757428))), _1757430 = hAPP(hAPP(c_List_Olist__update(_1757426, _1757428), _1757559), _1757561)]]], (32108 ^ _778908) ^ [_1361753, _1361755, _1361757, _1361759, _1361761] : [class_Groups_Oab__group__add(_1361753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361755), _1361757)), 32115 ^ _778908 : [(32122 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361755), _1361759), _1361757))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361755, _1361753), _1361761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361755, tc_HOL_Obool)), _1361757), hAPP(hAPP(c_Set_Oinsert(_1361755), _1361759), c_Orderings_Obot__class_Obot(tc_fun(_1361755, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361755, _1361753), _1361761), _1361757))], (32116 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1361755), _1361759), _1361757)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361755, _1361753), _1361761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361755, tc_HOL_Obool)), _1361757), hAPP(hAPP(c_Set_Oinsert(_1361755), _1361759), c_Orderings_Obot__class_Obot(tc_fun(_1361755, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1361753), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361755, _1361753), _1361761), _1361757)), hAPP(_1361761, _1361759)))]]], (32867 ^ _778908) ^ [_1377476, _1377478, _1377480] : [class_Rings_Osemiring__1(_1377476), hBOOL(hAPP(hAPP(c_member(_1377476), _1377478), c_Nat_Osemiring__1__class_ONats(_1377476))), hBOOL(hAPP(hAPP(c_member(_1377476), _1377480), c_Nat_Osemiring__1__class_ONats(_1377476))), -(hBOOL(hAPP(hAPP(c_member(_1377476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1377476), _1377478), _1377480)), c_Nat_Osemiring__1__class_ONats(_1377476))))], (40266 ^ _778908) ^ [_1541311, _1541313, _1541315, _1541317] : [-(_1541311 = c_Orderings_Obot__class_Obot(tc_fun(_1541313, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1541313, _1541315), _1541315, c_Product__Type_Osnd(_1541313, _1541315)), hAPP(hAPP(c_Product__Type_OSigma(_1541313, _1541315), _1541311), hAPP(c_COMBK(tc_fun(_1541315, tc_HOL_Obool), _1541313), _1541317))) = _1541317)], (18773 ^ _778908) ^ [_1102326, _1102328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102326), c_Int_OPls))), 18776 ^ _778908 : [(18783 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102328), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102326)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102328)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1102326), _1102328)))], (18777 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102328), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102326)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102328)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102326))]]], (16971 ^ _778908) ^ [_1071061, _1071063, _1071065] : [class_Rings_Ocomm__semiring__1(_1071061), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1071061), _1071063), hAPP(c_Nat_OSuc, _1071065)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071061), _1071063), hAPP(hAPP(c_Power_Opower__class_Opower(_1071061), _1071063), _1071065)))], (43261 ^ _778908) ^ [_1620112, _1620114, _1620116, _1620118, _1620120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620112, _1620112)), hAPP(hAPP(c_Product__Type_OPair(_1620112, _1620112), _1620114), _1620116)), _1620118)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1620112, _1620112)), hAPP(hAPP(c_Product__Type_OPair(_1620112, _1620112), _1620116), _1620120)), c_Transitive__Closure_Ortrancl(_1620112, _1620118))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620112, _1620112)), hAPP(hAPP(c_Product__Type_OPair(_1620112, _1620112), _1620114), _1620120)), c_Transitive__Closure_Ortrancl(_1620112, _1620118))))], (8768 ^ _778908) ^ [_925216, _925218, _925220, _925222] : [class_Orderings_Oord(_925216), _925218 = _925220, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925216), _925220), _925222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925216), _925218), _925222)))], (46707 ^ _778908) ^ [_1702498, _1702500] : [hBOOL(hAPP(c_List_Odistinct(_1702498), _1702500)), -(hAPP(c_Finite__Set_Ocard(_1702498), hAPP(c_List_Oset(_1702498), _1702500)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702498)), _1702500))], (29309 ^ _778908) ^ [_1302830] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1302830)), -(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)), _1302830))))], (20007 ^ _778908) ^ [_1123714, _1123716, _1123718] : [class_Rings_Ocomm__semiring__1(_1123714), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123714), _1123716), 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)))), _1123718))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123714), _1123716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123714), hAPP(hAPP(c_Power_Opower__class_Opower(_1123714), _1123716), _1123718)), hAPP(hAPP(c_Power_Opower__class_Opower(_1123714), _1123716), _1123718))))], (30614 ^ _778908) ^ [] : [-(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))))], (2482 ^ _778908) ^ [_816443, _816445, _816447, _816449, _816451, _816453] : [-(c_Nat_Onat_Onat__rec(_816453, _816449, _816445) = c_Nat_Onat_Onat__rec(_816451, _816447, _816443)), _816453 = _816451, _816449 = _816447, _816445 = _816443], (48801 ^ _778908) ^ [_1756100, _1756102, _1756104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1756100, _1756100), tc_HOL_Obool)), _1756102), _1756104)), c_Relation_Orefl__on(_1756100, c_Orderings_Otop__class_Otop(tc_fun(_1756100, tc_HOL_Obool)), _1756104), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1756100), tc_List_Olist(_1756100)), tc_HOL_Obool)), c_List_Olistrel1(_1756100, _1756102)), c_List_Olistrel(_1756100, _1756104))))], (34863 ^ _778908) ^ [_1417794, _1417796, _1417798, _1417800, _1417802] : [-(c_Map_Orestrict__map(_1417794, _1417796, _1417798, hAPP(hAPP(c_Set_Oinsert(_1417794), _1417800), _1417802)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1417794, tc_Option_Ooption(_1417796)), c_Map_Orestrict__map(_1417794, _1417796, _1417798, _1417802)), _1417800), hAPP(_1417798, _1417800)))], (38668 ^ _778908) ^ [_1504079, _1504081, _1504083, _1504085] : [38670 ^ _778908 : [(38674 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504079), 38672 ^ [_1504079, _1504081, _1504083, _1504085]), _1504085)))], (38676 ^ _778908) ^ [] : [-(hAPP(_1504083, 38669 ^ [_1504079, _1504081, _1504083, _1504085]) = hAPP(_1504083, 38672 ^ [_1504079, _1504081, _1504083, _1504085]))], (38678 ^ _778908) ^ [] : [38669 ^ [_1504079, _1504081, _1504083, _1504085] = 38672 ^ [_1504079, _1504081, _1504083, _1504085]], (38671 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504079), 38669 ^ [_1504079, _1504081, _1504083, _1504085]), _1504085)))]], -(c_Fun_Oinj__on(_1504079, _1504081, _1504083, _1504085))], (266 ^ _778908) ^ [_782851, _782853] : [-(class_Fields_Olinordered__field(_782851)), _782853 = _782851, class_Fields_Olinordered__field(_782853)], (12922 ^ _778908) ^ [_996552, _996554, _996556, _996558, _996560] : [class_Rings_Olinordered__semiring__strict(_996552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996552), _996554), _996556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996552), _996558), _996560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996552), c_Groups_Ozero__class_Ozero(_996552)), _996554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996552), c_Groups_Ozero__class_Ozero(_996552)), _996558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996552), _996554), _996558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996552), _996556), _996560))))], (1412 ^ _778908) ^ [_799432, _799434] : [-(class_Smallcheck_Osmall(_799432)), _799434 = _799432, class_Smallcheck_Osmall(_799434)], (8362 ^ _778908) ^ [_919015, _919017, _919019] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _919015)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _919017)), _919019)) = 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), _919015), _919017))), _919019))], (7400 ^ _778908) ^ [_902527, _902529, _902531, _902533] : [-(c_Com_Ovname_Ovname__rec(_902527, _902529, _902531, c_Com_Ovname_OGlb(_902533)) = hAPP(_902529, _902533))], (33093 ^ _778908) ^ [_1382594, _1382596, _1382598] : [class_Rings_Oring__1(_1382594), hBOOL(hAPP(hAPP(c_member(_1382594), _1382596), c_Int_Oring__1__class_OInts(_1382594))), hBOOL(hAPP(hAPP(c_member(_1382594), _1382598), c_Int_Oring__1__class_OInts(_1382594))), -(hBOOL(hAPP(hAPP(c_member(_1382594), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382594), _1382596), _1382598)), c_Int_Oring__1__class_OInts(_1382594))))], (51095 ^ _778908) ^ [_1807120, _1807122] : [-(c_List_Oconcat(tc_List_Olist(_1807120), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1807120), tc_List_Olist(tc_List_Olist(_1807120))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1807120)), _1807120, c_List_Olist_ONil(tc_List_Olist(_1807120)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1807120), tc_List_Olist(tc_List_Olist(_1807120))), _1807120), hAPP(hAPP(c_COMBC(tc_List_Olist(_1807120), tc_List_Olist(tc_List_Olist(_1807120)), tc_List_Olist(tc_List_Olist(_1807120))), c_List_Olist_OCons(tc_List_Olist(_1807120))), c_List_Olist_ONil(tc_List_Olist(_1807120)))))), _1807122)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1807120), tc_List_Olist(_1807120)), c_List_Otl(_1807120)), hAPP(c_List_Ofilter(tc_List_Olist(_1807120), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1807120)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1807120), tc_List_Olist(_1807120), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1807120)))), _1807122)))], (50767 ^ _778908) ^ [_1799006, _1799008, _1799010, _1799012] : [hAPP(c_List_Orev(_1799006), _1799008) = hAPP(hAPP(c_List_Olist_OCons(_1799006), _1799010), _1799012), -(_1799008 = hAPP(hAPP(c_List_Oappend(_1799006), hAPP(c_List_Orev(_1799006), _1799012)), hAPP(hAPP(c_List_Olist_OCons(_1799006), _1799010), c_List_Olist_ONil(_1799006))))], (7060 ^ _778908) ^ [_897029, _897031] : [-(hAPP(c_Option_Othe(_897029), hAPP(c_Option_Ooption_OSome(_897029), _897031)) = _897031)], (39132 ^ _778908) ^ [_1513635, _1513637, _1513639, _1513641] : [class_Groups_Ocomm__monoid__add(_1513635), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513637), _1513639)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513637, _1513635), _1513641), _1513639) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1513635, _1513637, c_Groups_Oplus__class_Oplus(_1513635)), _1513641), c_Groups_Ozero__class_Ozero(_1513635)), _1513639))], (31896 ^ _778908) ^ [_1357215] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1357215), 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, _1357215)) = _1357215)], (11380 ^ _778908) ^ [_969357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969357), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_969357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46436 ^ _778908) ^ [_1695837, _1695839, _1695841, _1695843, _1695845] : [hBOOL(hAPP(c_List_Odistinct(_1695837), hAPP(hAPP(c_List_Omap(tc_prod(_1695837, _1695839), _1695837), c_Product__Type_Ofst(_1695837, _1695839)), _1695841))), 46439 ^ _778908 : [(46446 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1695837, _1695839)), hAPP(hAPP(c_Product__Type_OPair(_1695837, _1695839), _1695845), _1695843)), hAPP(c_List_Oset(tc_prod(_1695837, _1695839)), _1695841))), -(hAPP(c_Option_Ooption_OSome(_1695839), _1695843) = hAPP(c_Map_Omap__of(_1695837, _1695839, _1695841), _1695845))], (46440 ^ _778908) ^ [] : [hAPP(c_Option_Ooption_OSome(_1695839), _1695843) = hAPP(c_Map_Omap__of(_1695837, _1695839, _1695841), _1695845), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1695837, _1695839)), hAPP(hAPP(c_Product__Type_OPair(_1695837, _1695839), _1695845), _1695843)), hAPP(c_List_Oset(tc_prod(_1695837, _1695839)), _1695841))))]]], (39372 ^ _778908) ^ [_1519124, _1519126] : [-(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)), _1519124), _1519126))], (28104 ^ _778908) ^ [_1277399, _1277401, _1277403, _1277405] : [28105 ^ _778908 : [(28106 ^ _778908) ^ [_1277509] : [hBOOL(hAPP(hAPP(c_member(_1277399), _1277509), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277399, tc_HOL_Obool)), _1277401), _1277403))), hBOOL(hAPP(_1277405, _1277509))]], 28114 ^ _778908 : [(28117 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1277405, 28113 ^ [_1277399, _1277401, _1277403, _1277405])))], (28115 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277399), 28113 ^ [_1277399, _1277401, _1277403, _1277405]), _1277401)))]], 28119 ^ _778908 : [(28122 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1277405, 28118 ^ [_1277399, _1277401, _1277403, _1277405])))], (28120 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277399), 28118 ^ [_1277399, _1277401, _1277403, _1277405]), _1277403)))]]], (26507 ^ _778908) ^ [_1245797] : [_1245797 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1245797), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (6873 ^ _778908) ^ [_892106, _892108, _892110, _892112] : [c_Com_Ocom_OSemi(_892106, _892108) = c_Com_Ocom_OWhile(_892110, _892112)], (19385 ^ _778908) ^ [_1112761] : [c_Int_OMin = c_Int_OBit0(_1112761)], (39646 ^ _778908) ^ [_1525224, _1525226, _1525228, _1525230, _1525232] : [-(hAPP(c_Fun_Othe__inv__into(_1525224, _1525226, _1525228, _1525230), _1525232) = c_HOL_OThe(_1525224, hAPP(hAPP(c_COMBS(_1525224, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525224), c_fconj), hAPP(hAPP(c_COMBC(_1525224, tc_fun(_1525224, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525224)), _1525228))), hAPP(hAPP(c_COMBC(_1525224, _1525226, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1525226, tc_fun(_1525226, tc_HOL_Obool), _1525224), c_fequal), _1525230)), _1525232))))], (49897 ^ _778908) ^ [_1780844, _1780846, _1780848, _1780850] : [hBOOL(hAPP(_1780844, _1780846)), -(hAPP(c_List_Ofilter(_1780848, _1780844), hAPP(hAPP(c_List_Olist_OCons(_1780848), _1780846), _1780850)) = hAPP(hAPP(c_List_Olist_OCons(_1780848), _1780846), hAPP(c_List_Ofilter(_1780848, _1780844), _1780850)))], (7218 ^ _778908) ^ [_899686, _899688, _899690] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899686), _899688)), _899690) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899688), _899690)))], (10423 ^ _778908) ^ [_954022, _954024] : [class_Orderings_Opreorder(_954022), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954022), _954024), _954024)))], (32290 ^ _778908) ^ [_1365817, _1365819, _1365821, _1365823, _1365825, _1365827, _1365829] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1365817, tc_fun(_1365819, tc_fun(_1365821, tc_HOL_Obool))), _1365823), _1365825), _1365827), _1365829))), 32291 ^ _778908 : [(32292 ^ _778908) ^ [_1365902] : [hBOOL(hAPP(hAPP(c_member(_1365817), _1365902), _1365823)), hBOOL(hAPP(hAPP(hAPP(_1365825, _1365902), _1365827), _1365829))]]], (5036 ^ _778908) ^ [_856812, _856814, _856816, _856818] : [-(c_Random_Oselect__weight(_856818, _856814) = c_Random_Oselect__weight(_856816, _856812)), _856818 = _856816, _856814 = _856812], (6244 ^ _778908) ^ [_879445, _879447, _879449, _879451, _879453] : [c_Com_Ocom_OLocal(_879445, _879447, _879449) = c_Com_Ocom_OSemi(_879451, _879453)], (9864 ^ _778908) ^ [_944359, _944361, _944363] : [class_Rings_Olinordered__semiring__strict(_944359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944359), c_Groups_Ozero__class_Ozero(_944359)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944359), _944361), _944363))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944359), c_Groups_Ozero__class_Ozero(_944359)), _944361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944359), c_Groups_Ozero__class_Ozero(_944359)), _944363)))], (20303 ^ _778908) ^ [_1129437, _1129439] : [c_Nat__Transfer_Ois__nat(_1129437), c_Nat__Transfer_Ois__nat(_1129439), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129437), _1129439)))], (42566 ^ _778908) ^ [_1603041, _1603043, _1603045] : [hBOOL(hAPP(c_Predicate_OPowp(_1603041, _1603043), _1603045)), 42569 ^ _778908 : [(42570 ^ _778908) ^ [_1603125] : [hBOOL(hAPP(hAPP(c_member(_1603041), _1603125), _1603045)), -(hBOOL(hAPP(_1603043, _1603125)))]]], (50549 ^ _778908) ^ [_1793924, _1793926] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1793924, _1793926) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1793924, hAPP(c_Nat_OSuc, _1793926))))], (49705 ^ _778908) ^ [_1776626, _1776628, _1776630] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776626)), _1776628), c_List_Olists(_1776626, _1776630))), -(_1776628 = c_List_Olist_ONil(_1776626)), 49714 ^ _778908 : [(49719 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776626)), 49713 ^ [_1776626, _1776628, _1776630]), c_List_Olists(_1776626, _1776630))))], (49717 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776626), 49712 ^ [_1776626, _1776628, _1776630]), _1776630)))], (49715 ^ _778908) ^ [] : [-(_1776628 = hAPP(hAPP(c_List_Olist_OCons(_1776626), 49712 ^ [_1776626, _1776628, _1776630]), 49713 ^ [_1776626, _1776628, _1776630]))]]], (44689 ^ _778908) ^ [_1653193, _1653195, _1653197, _1653199, _1653201] : [class_Complete__Lattice_Ocomplete__lattice(_1653193), 44692 ^ _778908 : [(44693 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653193), _1653195), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653197, _1653193), _1653199), _1653201))), 44696 ^ _778908 : [(44697 ^ _778908) ^ [_1653374] : [hBOOL(hAPP(hAPP(c_member(_1653197), _1653374), _1653199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653193), _1653195), hAPP(_1653201, _1653374))))]]], (44703 ^ _778908) ^ [] : [44705 ^ _778908 : [(44708 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653193), _1653195), hAPP(_1653201, 44704 ^ [_1653193, _1653195, _1653197, _1653199, _1653201])))], (44706 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653197), 44704 ^ [_1653193, _1653195, _1653197, _1653199, _1653201]), _1653199)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1653193), _1653195), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653197, _1653193), _1653199), _1653201))))]]], (46970 ^ _778908) ^ [_1710998, _1711000, _1711002, _1711004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710998)), _1711000)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710998)), _1711002))), _1711000 = hAPP(hAPP(c_List_Olist_OCons(_1710998), _1711004), _1711002)], (17449 ^ _778908) ^ [_1080299, _1080301] : [17450 ^ _778908 : [(17453 ^ _778908) ^ [] : [_1080301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17451 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1080299))]], -(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), _1080299), _1080301))))], (51599 ^ _778908) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (32557 ^ _778908) ^ [_1371102, _1371104, _1371106, _1371108] : [hBOOL(hAPP(hAPP(c_member(_1371102), _1371104), c_SetInterval_Oord_OatLeast(_1371102, _1371106, _1371108))), -(hBOOL(hAPP(hAPP(_1371106, _1371108), _1371104)))], (51513 ^ _778908) ^ [_1811977] : [class_Finite__Set_Ofinite(_1811977), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1811977)))], (51615 ^ _778908) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (8333 ^ _778908) ^ [] : [-(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))], (3064 ^ _778908) ^ [_825830, _825832, _825834, _825836, _825838, _825840, _825842, _825844] : [-(c_Random__Sequence_ORandom(_825844, _825840, _825836, _825832) = c_Random__Sequence_ORandom(_825842, _825838, _825834, _825830)), _825844 = _825842, _825840 = _825838, _825836 = _825834, _825832 = _825830], (18181 ^ _778908) ^ [_1093077, _1093079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093077), _1093079)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1093077), _1093079) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (8906 ^ _778908) ^ [_927477, _927479] : [-(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, _927477)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _927479))))], (38146 ^ _778908) ^ [_1493768, _1493770, _1493772] : [class_Lattices_Olattice(_1493768), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493768), _1493770)), -(_1493770 = c_Orderings_Obot__class_Obot(tc_fun(_1493768, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1493768, hAPP(hAPP(c_Set_Oinsert(_1493768), _1493772), _1493770)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493768), _1493772), c_Big__Operators_Olattice__class_OInf__fin(_1493768, _1493770)))], (45290 ^ _778908) ^ [_1669039, _1669041] : [class_Complete__Lattice_Ocomplete__lattice(_1669039), -(c_Complete__Lattice_OInf__class_OInf(_1669039, _1669041) = c_Complete__Lattice_OSup__class_OSup(_1669039, hAPP(c_Set_OCollect(_1669039), hAPP(hAPP(c_COMBB(tc_fun(_1669039, tc_HOL_Obool), tc_HOL_Obool, _1669039), c_HOL_OAll(_1669039)), hAPP(hAPP(c_COMBB(tc_fun(_1669039, tc_HOL_Obool), tc_fun(_1669039, tc_HOL_Obool), _1669039), hAPP(c_COMBS(_1669039, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1669039), c_fimplies), hAPP(hAPP(c_COMBC(_1669039, tc_fun(_1669039, tc_HOL_Obool), tc_HOL_Obool), c_member(_1669039)), _1669041)))), c_Orderings_Oord__class_Oless__eq(_1669039))))))], (16092 ^ _778908) ^ [_1054257, _1054259, _1054261, _1054263, _1054265, _1054267] : [class_Rings_Oordered__ring(_1054257), 16095 ^ _778908 : [(16102 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054257), _1054263), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054257), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054257), _1054265), _1054259)), _1054261)), _1054267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054257), _1054259), _1054261)), _1054263)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054257), _1054265), _1054261)), _1054267))))], (16096 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054257), _1054259), _1054261)), _1054263)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054257), _1054265), _1054261)), _1054267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054257), _1054263), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054257), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054257), _1054265), _1054259)), _1054261)), _1054267))))]]], (24973 ^ _778908) ^ [] : [-(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)))], (4972 ^ _778908) ^ [_855814, _855816, _855818, _855820, _855822, _855824] : [-(c_List_Opartition(_855824, _855820, _855816) = c_List_Opartition(_855822, _855818, _855814)), _855824 = _855822, _855820 = _855818, _855816 = _855814], (32605 ^ _778908) ^ [_1372093, _1372095, _1372097, _1372099, _1372101, _1372103, _1372105] : [hBOOL(hAPP(hAPP(c_member(_1372093), _1372095), _1372097)), c_Nitpick_Ofold__graph_H(_1372093, _1372099, _1372101, _1372103, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372093, tc_HOL_Obool)), _1372097), hAPP(hAPP(c_Set_Oinsert(_1372093), _1372095), c_Orderings_Obot__class_Obot(tc_fun(_1372093, tc_HOL_Obool)))), _1372105), -(c_Nitpick_Ofold__graph_H(_1372093, _1372099, _1372101, _1372103, _1372097, hAPP(hAPP(_1372101, _1372095), _1372105)))], (14015 ^ _778908) ^ [_1016075] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1016075) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (3328 ^ _778908) ^ [_830004, _830006] : [_830006 = _830004, -(c_Nat_Osemiring__1__class_ONats(_830006) = c_Nat_Osemiring__1__class_ONats(_830004))], (40204 ^ _778908) ^ [_1539885, _1539887, _1539889, _1539891] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1539885, _1539887)), hAPP(hAPP(c_Product__Type_OSigma(_1539885, _1539887), hAPP(hAPP(c_Set_Oinsert(_1539885), _1539889), c_Orderings_Obot__class_Obot(tc_fun(_1539885, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1539887, tc_HOL_Obool), _1539885), _1539891))) = hAPP(c_Finite__Set_Ocard(_1539887), _1539891))], (30886 ^ _778908) ^ [_1333074, _1333076, _1333078, _1333080] : [hBOOL(hAPP(hAPP(c_member(_1333074), _1333076), hAPP(hAPP(c_Set_Oinsert(_1333074), _1333078), _1333080))), -(_1333076 = _1333078), -(hBOOL(hAPP(hAPP(c_member(_1333074), _1333076), _1333080)))], (51135 ^ _778908) ^ [_1808147, _1808149] : [class_Lattices_Obounded__lattice(_1808147), -(class_Lattices_Obounded__lattice__top(tc_fun(_1808149, _1808147)))], (13624 ^ _778908) ^ [_1008569, _1008571, _1008573, _1008575] : [class_Orderings_Oord(_1008569), 13627 ^ _778908 : [(13636 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008571, _1008569)), _1008573), _1008575))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008571, _1008569)), _1008573), _1008575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008571, _1008569)), _1008575), _1008573)))], (13628 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008571, _1008569)), _1008573), _1008575)), 13631 ^ _778908 : [(13634 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008571, _1008569)), _1008575), _1008573))], (13632 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008571, _1008569)), _1008573), _1008575)))]]]]], (27166 ^ _778908) ^ [_1258811, _1258813] : [27168 ^ _778908 : [(27171 ^ _778908) ^ [] : [hBOOL(hAPP(_1258813, 27167 ^ [_1258811, _1258813]))], (27169 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27167 ^ [_1258811, _1258813]), _1258811)))]], 27172 ^ _778908 : [(27173 ^ _778908) ^ [_1258961] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1258961), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258811))), -(hBOOL(hAPP(_1258813, _1258961)))]]], (35227 ^ _778908) ^ [_1426584, _1426586] : [-(c_Relation_OId__on(_1426584, _1426586) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426584, tc_fun(tc_prod(_1426584, _1426584), tc_HOL_Obool)), _1426586), hAPP(hAPP(c_COMBC(_1426584, tc_fun(tc_prod(_1426584, _1426584), tc_HOL_Obool), tc_fun(tc_prod(_1426584, _1426584), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1426584, _1426584), tc_fun(tc_fun(tc_prod(_1426584, _1426584), tc_HOL_Obool), tc_fun(tc_prod(_1426584, _1426584), tc_HOL_Obool)), _1426584), c_Set_Oinsert(tc_prod(_1426584, _1426584))), hAPP(hAPP(c_COMBS(_1426584, _1426584, tc_prod(_1426584, _1426584)), c_Product__Type_OPair(_1426584, _1426584)), c_COMBI(_1426584)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1426584, _1426584), tc_HOL_Obool)))))], (25889 ^ _778908) ^ [_1233669, _1233671, _1233673] : [class_Rings_Olinordered__idom(_1233669), 25892 ^ _778908 : [(25899 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233669), _1233671), _1233673)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233669), hAPP(c_Groups_Oabs__class_Oabs(_1233669), _1233671)), _1233673)))], (25893 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233669), hAPP(c_Groups_Oabs__class_Oabs(_1233669), _1233671)), _1233673)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233669), _1233671), _1233673)))]]], (18391 ^ _778908) ^ [_1096469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096469)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1096469) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (5889 ^ _778908) ^ [_872757, _872759, _872761, _872763] : [hAPP(hAPP(c_String_Ochar_OChar, _872757), _872759) = hAPP(hAPP(c_String_Ochar_OChar, _872761), _872763), 5892 ^ _778908 : [(5895 ^ _778908) ^ [] : [-(_872759 = _872763)], (5893 ^ _778908) ^ [] : [-(_872757 = _872761)]]], (37028 ^ _778908) ^ [_1467919, _1467921] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1467919), _1467921) = 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)), _1467919)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1467921))))], (42045 ^ _778908) ^ [_1589983, _1589985] : [42047 ^ _778908 : [(42048 ^ _778908) ^ [_1590008] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589983, _1589983)), hAPP(hAPP(c_Product__Type_OPair(_1589983, _1589983), hAPP(42046 ^ [_1589983, _1589985], hAPP(c_Nat_OSuc, _1590008))), hAPP(42046 ^ [_1589983, _1589985], _1590008))), _1589985)))]], -(c_Wellfounded_Owf(_1589983, _1589985))], (45316 ^ _778908) ^ [_1669891, _1669893, _1669895, _1669897] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1669891, tc_fun(_1669893, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669891, tc_HOL_Obool), _1669895)), _1669897) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1669891, tc_HOL_Obool), tc_fun(_1669893, tc_HOL_Obool)), _1669895), hAPP(hAPP(c_COMBC(tc_fun(_1669891, tc_HOL_Obool), tc_fun(_1669891, tc_fun(_1669893, tc_HOL_Obool)), tc_fun(_1669893, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1669891, tc_fun(_1669893, tc_HOL_Obool))), _1669897)))], (38382 ^ _778908) ^ [_1498499, _1498501, _1498503, _1498505] : [c_Equiv__Relations_Oequivp(_1498499, _1498501), hBOOL(hAPP(hAPP(_1498501, _1498503), _1498505)), -(hBOOL(hAPP(hAPP(_1498501, _1498505), _1498503)))], (32385 ^ _778908) ^ [_1367792, _1367794, _1367796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367792)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1367794), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1367796)), 32395 ^ _778908 : [(32401 ^ _778908) ^ [] : [-(_1367794 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32397 ^ [_1367792, _1367794, _1367796]), 32394 ^ [_1367792, _1367794, _1367796]))], (32399 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32397 ^ [_1367792, _1367794, _1367796]), _1367796)))], (32396 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32394 ^ [_1367792, _1367794, _1367796]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1367792))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1367794), _1367792) = _1367794)], (12223 ^ _778908) ^ [_984177, _984179] : [class_Rings_Olinordered__ring(_984177), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984177), c_Groups_Ozero__class_Ozero(_984177)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984177), _984179), _984179))))], (9048 ^ _778908) ^ [_930085, _930087] : [class_Rings_Ocomm__semiring__1(_930085), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930085), c_Groups_Oone__class_Oone(_930085)), _930087) = _930087)], (51569 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (15830 ^ _778908) ^ [_1049004, _1049006, _1049008] : [class_Rings_Ocomm__ring__1(_1049004), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049004), _1049006), _1049008) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049004), _1049006), hAPP(c_Groups_Ouminus__class_Ouminus(_1049004), _1049008)))], (29524 ^ _778908) ^ [_1306827, _1306829, _1306831] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1306827), _1306829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306827, tc_HOL_Obool)), _1306831), _1306829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1306827), _1306831)), hAPP(c_Finite__Set_Ocard(_1306827), _1306829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1306827, tc_HOL_Obool)), _1306831), _1306829)))], (38132 ^ _778908) ^ [_1493533, _1493535, _1493537] : [class_Lattices_Olattice(_1493533), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493533), _1493535)), hBOOL(hAPP(hAPP(c_member(_1493533), _1493537), _1493535)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493533), _1493537), c_Big__Operators_Olattice__class_OInf__fin(_1493533, _1493535)) = c_Big__Operators_Olattice__class_OInf__fin(_1493533, _1493535))], (25685 ^ _778908) ^ [_1230060, _1230062, _1230064, _1230066] : [class_Rings_Ocomm__semiring__1(_1230060), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230060), _1230062), _1230064)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230060), _1230064), _1230066)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230060), _1230062), _1230066)))], (29096 ^ _778908) ^ [_1298220, _1298222] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298220, tc_HOL_Obool)), _1298222), c_Orderings_Otop__class_Otop(tc_fun(_1298220, tc_HOL_Obool)))))], (23581 ^ _778908) ^ [_1189801, _1189803] : [-(c_Divides_Odivmod__nat(_1189803, _1189801) = 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), _1189803), _1189801), _1189801))), -(_1189801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189803), _1189801)))], (1552 ^ _778908) ^ [_801182, _801184] : [-(class_Groups_Oab__semigroup__mult(_801182)), _801184 = _801182, class_Groups_Oab__semigroup__mult(_801184)], (47864 ^ _778908) ^ [_1732788, _1732790, _1732792, _1732794] : [_1732790 = c_List_Olist_ONil(_1732788), -(hAPP(hAPP(c_List_Olist__update(_1732788, _1732790), _1732792), _1732794) = c_List_Olist_ONil(_1732788))], (19677 ^ _778908) ^ [_1117903, _1117905] : [class_Int_Onumber__ring(_1117903), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117903), hAPP(c_Int_Onumber__class_Onumber__of(_1117903), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1117905) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117903), _1117905), _1117905))], (16222 ^ _778908) ^ [_1057060, _1057062, _1057064, _1057066, _1057068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1057060), _1057062)), 16225 ^ _778908 : [(16232 ^ _778908) ^ [] : [_1057066 = 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), _1057062), _1057060)), _1057064)), _1057068), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057060), _1057064)), _1057066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057062), _1057064)), _1057068))], (16226 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057060), _1057064)), _1057066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057062), _1057064)), _1057068), -(_1057066 = 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), _1057062), _1057060)), _1057064)), _1057068))]]], (35641 ^ _778908) ^ [_1435685, _1435687] : [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)), _1435685), _1435687)), 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)), _1435685), 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)), _1435687), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (20283 ^ _778908) ^ [_1129171, _1129173] : [c_Nat__Transfer_Ois__nat(_1129171), c_Nat__Transfer_Ois__nat(_1129173), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1129171), _1129173)))], (6238 ^ _778908) ^ [_879268, _879270, _879272, _879274, _879276] : [c_Com_Ocom_OSemi(_879268, _879270) = c_Com_Ocom_OCond(_879272, _879274, _879276)], (24049 ^ _778908) ^ [_1198474, _1198476, _1198478] : [-(hAPP(hAPP(c_Product__Type_OPair(_1198474, _1198476), hAPP(c_Product__Type_Ofst(_1198474, _1198476), _1198478)), hAPP(c_Product__Type_Osnd(_1198474, _1198476), _1198478)) = _1198478)], (49879 ^ _778908) ^ [_1780173, _1780175, _1780177, _1780179] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780173)), _1780175))), c_List_Ofoldr(tc_List_Olist(_1780177), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1780177)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1780177))), _1780179, 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(_1780173)), _1780175)), c_List_Ofoldr(tc_List_Olist(_1780177), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1780177)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1780177), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1780177)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1780177)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1780177), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1780177)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1780177), tc_List_Olist(_1780177), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1780177)))), _1780179), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (48305 ^ _778908) ^ [_1742967, _1742969, _1742971] : [_1742967 = hAPP(hAPP(c_List_Oappend(_1742969), _1742971), _1742967), -(_1742971 = c_List_Olist_ONil(_1742969))], (5314 ^ _778908) ^ [_861083, _861085] : [_861085 = _861083, -(c_List_Odistinct(_861085) = c_List_Odistinct(_861083))], (13286 ^ _778908) ^ [_1002941, _1002943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002943)), 13293 ^ _778908 : [(13300 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002941), _1002943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1002941)), hAPP(c_Int_Onat, _1002943))))], (13294 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1002941)), hAPP(c_Int_Onat, _1002943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002941), _1002943)))]]], (24655 ^ _778908) ^ [_1210226, _1210228, _1210230] : [class_Orderings_Olinorder(_1210226), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210226), _1210228), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210226), _1210230), _1210228))))], (90 ^ _778908) ^ [_780141, _780143] : [-(class_Rings_Odivision__ring(_780141)), _780143 = _780141, class_Rings_Odivision__ring(_780143)], (10461 ^ _778908) ^ [_954678, _954680] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954678), _954680), 10464 ^ _778908 : [(10467 ^ _778908) ^ [] : [-(_954680 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10465 ^ _778908) ^ [] : [-(_954678 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (48329 ^ _778908) ^ [_1743377, _1743379] : [-(hAPP(hAPP(c_List_Oappend(_1743377), _1743379), c_List_Olist_ONil(_1743377)) = _1743379)], (3278 ^ _778908) ^ [_829173, _829175, _829177, _829179, _829181, _829183] : [-(c_SetInterval_Oord_OatMost(_829183, _829179, _829175) = c_SetInterval_Oord_OatMost(_829181, _829177, _829173)), _829183 = _829181, _829179 = _829177, _829175 = _829173], (49229 ^ _778908) ^ [_1766139, _1766141] : [-(c_List_Orotate(_1766139, _1766141) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1766139), tc_List_Olist(_1766139)), _1766141), c_List_Orotate1(_1766139)))], (3774 ^ _778908) ^ [_837071, _837073, _837075, _837077] : [-(c_Wellfounded_Omin__ext(_837077, _837073) = c_Wellfounded_Omin__ext(_837075, _837071)), _837077 = _837075, _837073 = _837071], (37846 ^ _778908) ^ [_1485919, _1485921, _1485923, _1485925, _1485927, _1485929, _1485931, _1485933, _1485935, _1485937, _1485939] : [c_Equiv__Relations_Oequiv(_1485919, _1485921, _1485923), c_Equiv__Relations_Oequiv(_1485925, _1485927, _1485929), c_Equiv__Relations_Ocongruent2(_1485919, _1485925, tc_fun(_1485931, tc_HOL_Obool), _1485923, _1485929, _1485933), hBOOL(hAPP(hAPP(c_member(tc_fun(_1485919, tc_HOL_Obool)), _1485935), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1485919), _1485921), _1485923))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1485925, tc_HOL_Obool)), _1485937), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1485925), _1485927), _1485929))), 37868 ^ _778908 : [(37874 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1485931, tc_HOL_Obool)), hAPP(hAPP(_1485933, 37867 ^ [_1485919, _1485921, _1485923, _1485925, _1485927, _1485929, _1485931, _1485933, _1485935, _1485937, _1485939]), 37870 ^ [_1485919, _1485921, _1485923, _1485925, _1485927, _1485929, _1485931, _1485933, _1485935, _1485937, _1485939])), _1485939))], (37872 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485925), 37870 ^ [_1485919, _1485921, _1485923, _1485925, _1485927, _1485929, _1485931, _1485933, _1485935, _1485937, _1485939]), _1485927)))], (37869 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485919), 37867 ^ [_1485919, _1485921, _1485923, _1485925, _1485927, _1485929, _1485931, _1485933, _1485935, _1485937, _1485939]), _1485921)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1485931, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485919, tc_fun(_1485931, tc_HOL_Obool)), _1485935), hAPP(hAPP(c_COMBB(tc_fun(_1485925, tc_fun(_1485931, tc_HOL_Obool)), tc_fun(_1485931, tc_HOL_Obool), _1485919), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485925, tc_fun(_1485931, tc_HOL_Obool)), _1485937)), _1485933))), _1485939)))], (50013 ^ _778908) ^ [_1783212, _1783214] : [-(c_List_Opartition(_1783212, _1783214, c_List_Olist_ONil(_1783212)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1783212), tc_List_Olist(_1783212)), c_List_Olist_ONil(_1783212)), c_List_Olist_ONil(_1783212)))], (47236 ^ _778908) ^ [_1718110, _1718112, _1718114, _1718116, _1718118] : [class_Rings_Osemiring__0(_1718110), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1718110), hAPP(hAPP(c_List_Omap(_1718112, _1718110), hAPP(hAPP(c_COMBC(_1718112, _1718110, _1718110), hAPP(hAPP(c_COMBB(_1718110, tc_fun(_1718110, _1718110), _1718112), c_Groups_Otimes__class_Otimes(_1718110)), _1718114)), _1718116)), _1718118)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1718110), hAPP(c_List_Omonoid__add__class_Olistsum(_1718110), hAPP(hAPP(c_List_Omap(_1718112, _1718110), _1718114), _1718118))), _1718116))], (27328 ^ _778908) ^ [_1261974, _1261976, _1261978] : [class_Groups_Ocomm__monoid__add(_1261974), hAPP(_1261976, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1261974), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261974), _1261976), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1261978)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261974), _1261976), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261978)))], (39522 ^ _778908) ^ [_1522528, _1522530, _1522532, _1522534, _1522536, _1522538] : [-(hAPP(c_Set_Ovimage(_1522528, _1522530, hAPP(c_Fun_Ocomp(_1522532, _1522530, _1522528, _1522534), _1522536)), _1522538) = hAPP(c_Set_Ovimage(_1522528, _1522532, _1522536), hAPP(c_Set_Ovimage(_1522532, _1522530, _1522534), _1522538)))], (45851 ^ _778908) ^ [_1681969, _1681971, _1681973, _1681975, _1681977, _1681979] : [-(hAPP(c_Map_Omap__add(_1681969, _1681971, _1681973, _1681975), _1681977) = hAPP(c_Option_Ooption_OSome(_1681971), _1681979)), 45852 ^ _778908 : [(45855 ^ _778908) ^ [] : [hAPP(_1681975, _1681977) = c_Option_Ooption_ONone(_1681971), hAPP(_1681973, _1681977) = hAPP(c_Option_Ooption_OSome(_1681971), _1681979)], (45853 ^ _778908) ^ [] : [hAPP(_1681975, _1681977) = hAPP(c_Option_Ooption_OSome(_1681971), _1681979)]]], (19939 ^ _778908) ^ [_1122324, _1122326, _1122328] : [class_Rings_Olinordered__idom(_1122324), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122324), c_Groups_Ozero__class_Ozero(_1122324)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122324), hAPP(hAPP(c_Power_Opower__class_Opower(_1122324), _1122326), 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(_1122324), _1122328), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (10222 ^ _778908) ^ [_950647, _950649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _950647), hAPP(c_Int_Onat, _950649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950647)), _950649)))], (31255 ^ _778908) ^ [_1342780, _1342782, _1342784, _1342786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1342780, tc_HOL_Obool)), _1342782), _1342784)), hBOOL(hAPP(hAPP(c_member(_1342780), _1342786), _1342782)), -(hBOOL(hAPP(hAPP(c_member(_1342780), _1342786), _1342784)))], (33964 ^ _778908) ^ [_1399542, _1399544, _1399546] : [class_Orderings_Olinorder(_1399542), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399542), _1399544)), hBOOL(hAPP(hAPP(c_member(_1399542), _1399546), _1399544)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1399542), _1399546), c_Big__Operators_Olattice_OInf__fin(_1399542, c_Orderings_Oord__class_Omin(_1399542), _1399544)) = c_Big__Operators_Olattice_OInf__fin(_1399542, c_Orderings_Oord__class_Omin(_1399542), _1399544))], (4620 ^ _778908) ^ [_850428, _850430, _850432, _850434, _850436, _850438, _850440, _850442] : [-(c_Map_Orestrict__map(_850442, _850438, _850434, _850430) = c_Map_Orestrict__map(_850440, _850436, _850432, _850428)), _850442 = _850440, _850438 = _850436, _850434 = _850432, _850430 = _850428], (17895 ^ _778908) ^ [_1088529, _1088531, _1088533, _1088535] : [class_Rings_Olinordered__semidom(_1088529), hAPP(hAPP(c_Power_Opower__class_Opower(_1088529), _1088531), _1088533) = hAPP(hAPP(c_Power_Opower__class_Opower(_1088529), _1088535), _1088533), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088529), c_Groups_Ozero__class_Ozero(_1088529)), _1088531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088529), c_Groups_Ozero__class_Ozero(_1088529)), _1088535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1088533)), -(_1088531 = _1088535)], (29315 ^ _778908) ^ [_1302915] : [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)), _1302915))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1302915)))], (354 ^ _778908) ^ [_784165, _784167, _784169, _784171, _784173, _784175, _784177, _784179, _784181, _784183] : [-(c_Typedef_Otype__definition(_784181, _784177, _784173, _784169, _784165)), c_Typedef_Otype__definition(_784183, _784179, _784175, _784171, _784167), _784183 = _784181, _784179 = _784177, _784175 = _784173, _784171 = _784169, _784167 = _784165], (28711 ^ _778908) ^ [_1289339, _1289341, _1289343] : [class_Groups_Ocomm__monoid__add(_1289339), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1289339), _1289341), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1289343))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1289339), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1289339), _1289341), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1289343))), hAPP(_1289341, hAPP(c_Nat_OSuc, _1289343))))], (31004 ^ _778908) ^ [_1335438, _1335440, _1335442, _1335444] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1335438, tc_fun(_1335440, tc_HOL_Obool))), _1335442), _1335444)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1335438, _1335440)), hAPP(hAPP(c_Product__Type_OPair(_1335438, _1335440), _1335442), _1335444)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1335438, _1335440), tc_HOL_Obool)))))], (7927 ^ _778908) ^ [_911285, _911287, _911289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911285), _911287)), _911289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911285), _911289)))], (41097 ^ _778908) ^ [_1559424, _1559426, _1559428] : [hBOOL(hAPP(_1559424, _1559426)), -(hBOOL(hAPP(hAPP(c_member(_1559428), _1559426), hAPP(c_Set_OCollect(_1559428), _1559424))))], (47503 ^ _778908) ^ [_1723740, _1723742] : [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(_1723740)), _1723742))), _1723742 = c_List_Olist_ONil(_1723740)], (9604 ^ _778908) ^ [_939863] : [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, _939863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _939863)))], (7372 ^ _778908) ^ [_902074, _902076] : [c_Com_Ovname_OLoc(_902074) = c_Com_Ovname_OGlb(_902076)], (8782 ^ _778908) ^ [_925435, _925437, _925439, _925441] : [class_Orderings_Oorder(_925435), _925437 = _925439, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925435), _925441), _925439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925435), _925441), _925437)))], (42012 ^ _778908) ^ [_1589350, _1589352, _1589354] : [c_Wellfounded_Owf(_1589350, _1589352), -(c_Wellfounded_Owf(_1589350, c_Wellfounded_Omlex__prod(_1589350, _1589354, _1589352)))], (19623 ^ _778908) ^ [_1116923, _1116925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116923), _1116925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116923)), c_Int_OBit1(_1116925))))], (29604 ^ _778908) ^ [_1308345, _1308347, _1308349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308345, tc_HOL_Obool)), _1308347), _1308349)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308345), _1308349)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308345), _1308347)))], (24125 ^ _778908) ^ [_1200272, _1200274, _1200276] : [_1200272 = _1200274, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200276, tc_HOL_Obool)), _1200272), _1200274)))], (49478 ^ _778908) ^ [_1771849, _1771851, _1771853, _1771855] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771849)), hAPP(hAPP(c_List_Oappend(_1771849), _1771851), _1771853)), c_List_Olists(_1771849, _1771855))), 49481 ^ _778908 : [(49484 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771849)), _1771853), c_List_Olists(_1771849, _1771855))))], (49482 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771849)), _1771851), c_List_Olists(_1771849, _1771855))))]]], (46203 ^ _778908) ^ [_1690291, _1690293, _1690295, _1690297, _1690299] : [46205 ^ _778908 : [(46208 ^ _778908) ^ [] : [hAPP(_1690295, 46204 ^ [_1690291, _1690293, _1690295, _1690297, _1690299]) = hAPP(_1690299, 46204 ^ [_1690291, _1690293, _1690295, _1690297, _1690299])], (46206 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1690291), 46204 ^ [_1690291, _1690293, _1690295, _1690297, _1690299]), hAPP(c_List_Oset(_1690291), _1690297))))]], -(hAPP(hAPP(c_List_Omap(_1690291, _1690293), _1690295), _1690297) = hAPP(hAPP(c_List_Omap(_1690291, _1690293), _1690299), _1690297))], (28967 ^ _778908) ^ [_1294920, _1294922, _1294924, _1294926, _1294928, _1294930] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294920, tc_fun(_1294922, tc_HOL_Obool)), _1294924), hAPP(hAPP(c_COMBC(_1294920, tc_fun(_1294926, tc_fun(_1294922, tc_HOL_Obool)), tc_fun(_1294922, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1294926, tc_HOL_Obool), tc_fun(tc_fun(_1294926, tc_fun(_1294922, tc_HOL_Obool)), tc_fun(_1294922, tc_HOL_Obool)), _1294920), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294926, tc_fun(_1294922, tc_HOL_Obool))), _1294928)), _1294930)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294926, tc_fun(_1294922, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294920, tc_fun(_1294926, tc_HOL_Obool)), _1294924), _1294928)), _1294930))], (19869 ^ _778908) ^ [_1121173, _1121175] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1121173), hAPP(c_Int_Onumber__class_Onumber__of(_1121173), _1121175)), 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(_1121173), hAPP(c_Int_Onumber__class_Onumber__of(_1121173), _1121175)), hAPP(c_Int_Onumber__class_Onumber__of(_1121173), _1121175))), class_Groups_Omonoid__mult(_1121173), class_Int_Onumber(_1121173)], (31620 ^ _778908) ^ [_1349773, _1349775, _1349777, _1349779, _1349781] : [hBOOL(hAPP(hAPP(c_member(_1349773), _1349775), c_SetInterval_Oord_OgreaterThanLessThan(_1349773, _1349777, _1349779, _1349781))), 31623 ^ _778908 : [(31626 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1349777, _1349775), _1349781)))], (31624 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1349777, _1349779), _1349775)))]]], (47260 ^ _778908) ^ [_1718810, _1718812, _1718814, _1718816] : [class_Groups_Oab__group__add(_1718810), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1718810), hAPP(c_List_Omonoid__add__class_Olistsum(_1718810), hAPP(hAPP(c_List_Omap(_1718812, _1718810), _1718814), _1718816))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1718810), hAPP(hAPP(c_List_Omap(_1718812, _1718810), hAPP(c_Fun_Ocomp(_1718810, _1718810, _1718812, c_Groups_Ouminus__class_Ouminus(_1718810)), _1718814)), _1718816)))], (43083 ^ _778908) ^ [_1614879, _1614881, _1614883, _1614885, _1614887] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614879, _1614879)), hAPP(hAPP(c_Product__Type_OPair(_1614879, _1614879), _1614881), _1614883)), _1614885)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614879, _1614879)), hAPP(hAPP(c_Product__Type_OPair(_1614879, _1614879), _1614883), _1614887)), c_Transitive__Closure_Otrancl(_1614879, _1614885))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614879, _1614879)), hAPP(hAPP(c_Product__Type_OPair(_1614879, _1614879), _1614881), _1614887)), c_Transitive__Closure_Otrancl(_1614879, _1614885))))], (34361 ^ _778908) ^ [_1407458, _1407460, _1407462] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407458, tc_Nat_Onat), _1407460), _1407462) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407458, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1407458), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1407460)), _1407462)))], (38214 ^ _778908) ^ [_1494825, _1494827, _1494829] : [class_Lattices_Olattice(_1494825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494825), _1494827)), -(hBOOL(hAPP(hAPP(c_member(_1494825), _1494829), _1494827))), -(_1494827 = c_Orderings_Obot__class_Obot(tc_fun(_1494825, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1494825, hAPP(hAPP(c_Set_Oinsert(_1494825), _1494829), _1494827)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1494825), _1494829), c_Big__Operators_Olattice__class_OInf__fin(_1494825, _1494827)))], (2078 ^ _778908) ^ [_809791, _809793] : [_809793 = _809791, -(c_Com_Ovname_OGlb(_809793) = c_Com_Ovname_OGlb(_809791))], (45318 ^ _778908) ^ [_1669981, _1669983, _1669985, _1669987] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1669981, tc_HOL_Obool), tc_fun(_1669983, tc_HOL_Obool)), _1669985), hAPP(hAPP(c_COMBC(tc_fun(_1669981, tc_HOL_Obool), tc_fun(_1669981, tc_fun(_1669983, tc_HOL_Obool)), tc_fun(_1669983, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1669981, tc_fun(_1669983, tc_HOL_Obool))), _1669987)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1669981, tc_fun(_1669983, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669981, tc_HOL_Obool), _1669985)), _1669987))], (46249 ^ _778908) ^ [_1691542, _1691544, _1691546, _1691548] : [hAPP(hAPP(c_Option_Omap(_1691542, _1691544), _1691546), _1691548) = c_Option_Ooption_ONone(_1691544), -(_1691548 = c_Option_Ooption_ONone(_1691542))], (24701 ^ _778908) ^ [_1211088, _1211090, _1211092] : [class_Orderings_Olinorder(_1211088), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211088), _1211090), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211088), _1211090), _1211092)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211088), _1211090), _1211092))], (39630 ^ _778908) ^ [_1524888, _1524890, _1524892, _1524894] : [c_Fun_Oinj__on(_1524888, _1524890, _1524892, _1524894), -(c_Fun_Oinj__on(_1524890, _1524888, c_Fun_Othe__inv__into(_1524888, _1524890, _1524894, _1524892), hAPP(c_Set_Oimage(_1524888, _1524890, _1524892), _1524894)))], (50138 ^ _778908) ^ [_1786855, _1786857] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1786855, _1786857)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1786857), _1786855))], (9594 ^ _778908) ^ [_939635, _939637] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _939635), _939637)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _939635)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _939637)))], (32176 ^ _778908) ^ [_1363320, _1363322, _1363324] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363320), _1363322)), hBOOL(hAPP(hAPP(c_member(_1363320), _1363324), _1363322)), -(hAPP(c_Finite__Set_Ocard(_1363320), _1363322) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1363320), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363320, tc_HOL_Obool)), _1363322), hAPP(hAPP(c_Set_Oinsert(_1363320), _1363324), c_Orderings_Obot__class_Obot(tc_fun(_1363320, tc_HOL_Obool)))))))], (11458 ^ _778908) ^ [_970741, _970743] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970741), _970743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970743)), _970741)))], (51279 ^ _778908) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (34335 ^ _778908) ^ [_1406915, _1406917, _1406919] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1406915), _1406917), _1406919) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1406915), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1406915, tc_Int_Oint), _1406917), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1406919))), class_Groups_Ocomm__monoid__add(_1406915), class_Groups_Ocomm__monoid__mult(_1406915)], (10381 ^ _778908) ^ [_953246, _953248, _953250, _953252, _953254, _953256] : [class_Rings_Olinordered__semiring__1__strict(_953246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953246), _953248), _953250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953246), _953252), _953250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953246), c_Groups_Ozero__class_Ozero(_953246)), _953254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953246), c_Groups_Ozero__class_Ozero(_953246)), _953256)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953246), _953254), _953256) = c_Groups_Oone__class_Oone(_953246), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953246), _953254), _953248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953246), _953256), _953252))), _953250)))], (49193 ^ _778908) ^ [_1765451, _1765453] : [hBOOL(hAPP(c_List_Odistinct(_1765451), _1765453)), -(hBOOL(hAPP(c_List_Odistinct(_1765451), hAPP(c_List_Otl(_1765451), _1765453))))], (15506 ^ _778908) ^ [_1042708, _1042710, _1042712] : [class_Groups_Ogroup__add(_1042708), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042708), _1042710), _1042712)), _1042712) = _1042710)], (2156 ^ _778908) ^ [_811128, _811130, _811132, _811134] : [-(tc_Nitpick_Opair__box(_811134, _811130) = tc_Nitpick_Opair__box(_811132, _811128)), _811134 = _811132, _811130 = _811128], (50222 ^ _778908) ^ [_1788252, _1788254, _1788256, _1788258] : [class_Orderings_Olinorder(_1788252), 50225 ^ _778908 : [(50234 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1788252, hAPP(hAPP(c_List_Olist_OCons(_1788252), _1788254), hAPP(hAPP(c_List_Olist_OCons(_1788252), _1788256), _1788258)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1788252), _1788254), _1788256)), c_List_Olinorder__class_Osorted(_1788252, hAPP(hAPP(c_List_Olist_OCons(_1788252), _1788256), _1788258))], (50226 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1788252, hAPP(hAPP(c_List_Olist_OCons(_1788252), _1788254), hAPP(hAPP(c_List_Olist_OCons(_1788252), _1788256), _1788258))), 50229 ^ _778908 : [(50232 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1788252, hAPP(hAPP(c_List_Olist_OCons(_1788252), _1788256), _1788258)))], (50230 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1788252), _1788254), _1788256)))]]]]], (38330 ^ _778908) ^ [_1497097, _1497099] : [c_Equiv__Relations_Oequiv(_1497097, c_Orderings_Otop__class_Otop(tc_fun(_1497097, tc_HOL_Obool)), _1497099), -(c_Equiv__Relations_Oequivp(_1497097, hAPP(hAPP(c_COMBC(_1497097, tc_fun(tc_prod(_1497097, _1497097), tc_HOL_Obool), tc_fun(_1497097, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497097, tc_fun(tc_fun(tc_prod(_1497097, _1497097), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497097, _1497097), tc_HOL_Obool), tc_fun(_1497097, tc_HOL_Obool)), _1497097), c_COMBC(_1497097, tc_fun(tc_prod(_1497097, _1497097), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497097, tc_prod(_1497097, _1497097)), tc_fun(_1497097, tc_fun(tc_fun(tc_prod(_1497097, _1497097), tc_HOL_Obool), tc_HOL_Obool)), _1497097), hAPP(c_COMBB(tc_prod(_1497097, _1497097), tc_fun(tc_fun(tc_prod(_1497097, _1497097), tc_HOL_Obool), tc_HOL_Obool), _1497097), c_member(tc_prod(_1497097, _1497097)))), c_Product__Type_OPair(_1497097, _1497097)))), _1497099)))], (8922 ^ _778908) ^ [_927790, _927792] : [class_Rings_Ocomm__semiring__1(_927790), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927790), _927792), _927792) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927790), c_Groups_Oone__class_Oone(_927790)), c_Groups_Oone__class_Oone(_927790))), _927792))], (6437 ^ _778908) ^ [_882817, _882819, _882821] : [hBOOL(hAPP(c_Com_OWT, _882817)), hBOOL(hAPP(c_Com_OWT, _882819)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_882821, _882817, _882819))))], (32767 ^ _778908) ^ [_1375657, _1375659, _1375661, _1375663, _1375665, _1375667] : [hBOOL(hAPP(hAPP(c_member(_1375657), _1375659), c_SetInterval_Oord_OgreaterThanAtMost(_1375657, _1375661, _1375663, _1375665, _1375667))), 32770 ^ _778908 : [(32773 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1375661, _1375659), _1375667)))], (32771 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1375663, _1375665), _1375659)))]]], (5879 ^ _778908) ^ [_872585, _872587, _872589, _872591] : [-(c_Com_Ocom_OAss(_872585, _872587) = c_Com_Ocom_OAss(_872589, _872591)), _872585 = _872589, _872587 = _872591], (43719 ^ _778908) ^ [_1631364, _1631366, _1631368] : [c_Relation_Ototal__on(_1631364, _1631366, hAPP(c_Relation_Oconverse(_1631364, _1631364), _1631368)), -(c_Relation_Ototal__on(_1631364, _1631366, _1631368))], (6476 ^ _778908) ^ [_883645, _883647, _883649, _883651, _883653, _883655] : [c_Com_Ocom_OLocal(_883645, _883647, _883649) = c_Com_Ocom_OCall(_883651, _883653, _883655)], (25535 ^ _778908) ^ [_1227677, _1227679, _1227681] : [_1227677 = _1227679, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227679), _1227681)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227677), _1227681)))], (12689 ^ _778908) ^ [_992218, _992220] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992218)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992220)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992218), _992220)))], (47300 ^ _778908) ^ [_1719721, _1719723, _1719725, _1719727] : [class_Rings_Osemiring__1(_1719721), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1719721), hAPP(hAPP(c_List_Omap(_1719723, _1719721), hAPP(c_COMBK(_1719721, _1719723), _1719725)), _1719727)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1719721), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1719721), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719723)), _1719727))), _1719725))], (22506 ^ _778908) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41906 ^ _778908) ^ [_1587180, _1587182, _1587184] : [c_Wellfounded_Owf(_1587180, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587180, _1587180), tc_HOL_Obool)), _1587182), _1587184)), -(c_Wellfounded_Owf(_1587180, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587180, _1587180), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587180, _1587180), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1587180, _1587180, _1587180), _1587182), _1587182)), hAPP(hAPP(c_Relation_Orel__comp(_1587180, _1587180, _1587180), _1587184), _1587182))), _1587184)))], (33273 ^ _778908) ^ [_1385923, _1385925] : [class_Int_Oring__char__0(_1385923), hBOOL(hAPP(hAPP(c_member(_1385923), _1385925), c_Int_Oring__1__class_OInts(_1385923))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385923), c_Groups_Oone__class_Oone(_1385923)), _1385925)), _1385925) = c_Groups_Ozero__class_Ozero(_1385923)], (29251 ^ _778908) ^ [_1301649, _1301651, _1301653, _1301655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301649, tc_HOL_Obool)), _1301651), _1301653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301649, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1301649), _1301655), _1301651)), hAPP(hAPP(c_Set_Oinsert(_1301649), _1301655), _1301653))))], (32231 ^ _778908) ^ [_1364563, _1364565, _1364567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1364563)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1364565), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1364567)), 32238 ^ _778908 : [(32239 ^ _778908) ^ [_1364771] : [32241 ^ _778908 : [(32247 ^ _778908) ^ [] : [-(_1364771 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32243 ^ [_1364563, _1364565, _1364567, _1364771]), 32240 ^ [_1364563, _1364565, _1364567, _1364771]))], (32245 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32243 ^ [_1364563, _1364565, _1364567, _1364771]), _1364567)))], (32242 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32240 ^ [_1364563, _1364565, _1364567, _1364771]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1364563))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1364565), _1364771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1364565), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1364771), _1364563))))]]], (41928 ^ _778908) ^ [_1587741, _1587743] : [c_Wellfounded_Owf(_1587741, _1587743), 41931 ^ _778908 : [(41932 ^ _778908) ^ [_1587810] : [-(hBOOL(hAPP(hAPP(c_member(_1587741), _1587810), c_Wellfounded_Oacc(_1587741, _1587743))))]]], (41115 ^ _778908) ^ [_1559816, _1559818, _1559820] : [hBOOL(hAPP(_1559816, _1559818)), -(hAPP(c_Set_OCollect(_1559820), hAPP(hAPP(c_COMBS(_1559820, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559820), c_fconj), hAPP(hAPP(c_COMBC(_1559820, _1559820, tc_HOL_Obool), c_fequal), _1559818))), _1559816)) = hAPP(hAPP(c_Set_Oinsert(_1559820), _1559818), c_Orderings_Obot__class_Obot(tc_fun(_1559820, tc_HOL_Obool))))], (6906 ^ _778908) ^ [_892896, _892898, _892900, _892902, _892904, _892906] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_892896, _892898, _892900), _892902, _892904, _892906), 6910 ^ _778908 : [(6913 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_892900, hAPP(hAPP(hAPP(c_Natural_Oupdate, _892902), c_Com_Ovname_OLoc(_892896)), hAPP(_892898, _892902)), _892904, 6909 ^ [_892896, _892898, _892900, _892902, _892904, _892906]))], (6911 ^ _778908) ^ [] : [-(_892906 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6909 ^ [_892896, _892898, _892900, _892902, _892904, _892906]), c_Com_Ovname_OLoc(_892896)), hAPP(hAPP(c_Natural_Ogetlocs, _892902), _892896)))]]], (30294 ^ _778908) ^ [_1321618, _1321620, _1321622, _1321624] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321618, tc_HOL_Obool)), _1321620), hAPP(hAPP(c_Set_Oinsert(_1321618), _1321622), _1321624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321618, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321618, tc_HOL_Obool)), _1321620), hAPP(hAPP(c_Set_Oinsert(_1321618), _1321622), c_Orderings_Obot__class_Obot(tc_fun(_1321618, tc_HOL_Obool))))), _1321624))], (9168 ^ _778908) ^ [_932416, _932418] : [class_Groups_Omonoid__mult(_932416), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932416), _932418), c_Groups_Oone__class_Oone(_932416)) = _932418)], (14527 ^ _778908) ^ [_1025477] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025477) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7402 ^ _778908) ^ [_902566, _902568, _902570, _902572] : [-(c_Com_Ovname_Ovname__case(_902566, _902568, _902570, c_Com_Ovname_OGlb(_902572)) = hAPP(_902568, _902572))], (30478 ^ _778908) ^ [_1324726, _1324728] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324726, tc_fun(_1324726, tc_HOL_Obool)), _1324728), hAPP(hAPP(c_COMBC(_1324726, tc_fun(_1324726, tc_HOL_Obool), tc_fun(_1324726, tc_HOL_Obool)), c_Set_Oinsert(_1324726)), c_Orderings_Obot__class_Obot(tc_fun(_1324726, tc_HOL_Obool)))) = _1324728)], (34573 ^ _778908) ^ [_1411366, _1411368, _1411370, _1411372, _1411374] : [class_Fields_Ofield__inverse__zero(_1411366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411368), _1411370)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411368, _1411366), hAPP(hAPP(c_COMBS(_1411368, _1411366, _1411366), hAPP(hAPP(c_COMBB(_1411366, tc_fun(_1411366, _1411366), _1411368), c_Rings_Oinverse__class_Odivide(_1411366)), _1411372)), _1411374)), _1411370) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1411366), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411368, _1411366), _1411372), _1411370)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411368, _1411366), _1411374), _1411370)))], (23481 ^ _778908) ^ [_1188011, _1188013, _1188015, _1188017] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1188011, _1188013), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1188015), _1188017))), -(_1188013 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188011), _1188013) = _1188015)], (34363 ^ _778908) ^ [_1407516, _1407518, _1407520] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407516, tc_Nat_Onat), _1407518), _1407520)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407516, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1407516), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1407518)), _1407520))], (51601 ^ _778908) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (41026 ^ _778908) ^ [_1558186] : [class_Orderings_Olinorder(_1558186), -(c_Finite__Set_Ofun__left__comm__idem(_1558186, _1558186, c_Orderings_Oord__class_Omin(_1558186)))], (33705 ^ _778908) ^ [_1393277, _1393279, _1393281] : [class_Orderings_Olinorder(_1393277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393277), _1393279)), 33712 ^ _778908 : [(33719 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393277, tc_HOL_Obool)), _1393279), hAPP(hAPP(c_Set_Oinsert(_1393277), _1393281), c_Orderings_Obot__class_Obot(tc_fun(_1393277, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1393277, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1393277, hAPP(hAPP(c_Set_Oinsert(_1393277), _1393281), _1393279)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1393277), _1393281), c_Big__Operators_Olinorder__class_OMin(_1393277, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393277, tc_HOL_Obool)), _1393279), hAPP(hAPP(c_Set_Oinsert(_1393277), _1393281), c_Orderings_Obot__class_Obot(tc_fun(_1393277, tc_HOL_Obool)))))))], (33713 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393277, tc_HOL_Obool)), _1393279), hAPP(hAPP(c_Set_Oinsert(_1393277), _1393281), c_Orderings_Obot__class_Obot(tc_fun(_1393277, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1393277, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1393277, hAPP(hAPP(c_Set_Oinsert(_1393277), _1393281), _1393279)) = _1393281)]]], (13616 ^ _778908) ^ [_1008495, _1008497] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008495), _1008497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008497), _1008495)))], (10545 ^ _778908) ^ [_956063, _956065] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956063), _956065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956065), _956063)))], (13949 ^ _778908) ^ [_1014650, _1014652, _1014654, _1014656, _1014658, _1014660] : [class_Divides_Osemiring__div(_1014650), c_Divides_Odiv__class_Omod(_1014650, _1014652, _1014654) = c_Divides_Odiv__class_Omod(_1014650, _1014656, _1014654), c_Divides_Odiv__class_Omod(_1014650, _1014658, _1014654) = c_Divides_Odiv__class_Omod(_1014650, _1014660, _1014654), -(c_Divides_Odiv__class_Omod(_1014650, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014650), _1014652), _1014658), _1014654) = c_Divides_Odiv__class_Omod(_1014650, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014650), _1014656), _1014660), _1014654))], (36558 ^ _778908) ^ [_1456873, _1456875, _1456877] : [class_Lattices_Obounded__lattice__top(_1456873), 36561 ^ _778908 : [(36570 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456873), _1456875), _1456877) = c_Orderings_Otop__class_Otop(_1456873)), _1456875 = c_Orderings_Otop__class_Otop(_1456873), _1456877 = c_Orderings_Otop__class_Otop(_1456873)], (36562 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456873), _1456875), _1456877) = c_Orderings_Otop__class_Otop(_1456873), 36565 ^ _778908 : [(36568 ^ _778908) ^ [] : [-(_1456877 = c_Orderings_Otop__class_Otop(_1456873))], (36566 ^ _778908) ^ [] : [-(_1456875 = c_Orderings_Otop__class_Otop(_1456873))]]]]], (40104 ^ _778908) ^ [_1536936, _1536938, _1536940, _1536942] : [hAPP(hAPP(c_Product__Type_OSigma(_1536936, _1536938), _1536940), hAPP(c_COMBK(tc_fun(_1536938, tc_HOL_Obool), _1536936), _1536942)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1536936, _1536938), tc_HOL_Obool)), -(_1536940 = c_Orderings_Obot__class_Obot(tc_fun(_1536936, tc_HOL_Obool))), -(_1536942 = c_Orderings_Obot__class_Obot(tc_fun(_1536938, tc_HOL_Obool)))], (48024 ^ _778908) ^ [_1736357, _1736359, _1736361, _1736363, _1736365, _1736367] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736357), tc_List_Olist(_1736357))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736357), tc_List_Olist(_1736357)), hAPP(hAPP(c_List_Olist_OCons(_1736357), _1736359), _1736361)), hAPP(hAPP(c_List_Olist_OCons(_1736357), _1736363), _1736365))), c_List_Olexord(_1736357, _1736367)))), 48025 ^ _778908 : [(48028 ^ _778908) ^ [] : [_1736359 = _1736363, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736357), tc_List_Olist(_1736357))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736357), tc_List_Olist(_1736357)), _1736361), _1736365)), c_List_Olexord(_1736357, _1736367)))], (48026 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1736357, _1736357)), hAPP(hAPP(c_Product__Type_OPair(_1736357, _1736357), _1736359), _1736363)), _1736367))]]], (41283 ^ _778908) ^ [_1563756, _1563758, _1563760] : [-(hAPP(c_Set_OCollect(_1563756), hAPP(hAPP(c_COMBS(_1563756, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563756), c_fimplies), _1563758)), _1563760)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1563756, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1563756, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1563756), _1563758))), hAPP(c_Set_OCollect(_1563756), _1563760)))], (49311 ^ _778908) ^ [_1768000] : [class_Groups_Omonoid__add(_1768000), -(c_List_Omonoid__add__class_Olistsum(_1768000) = c_List_Ofoldl(_1768000, _1768000, c_Groups_Oplus__class_Oplus(_1768000), c_Groups_Ozero__class_Ozero(_1768000)))], (1182 ^ _778908) ^ [_796557, _796559] : [-(class_Divides_Oring__div(_796557)), _796559 = _796557, class_Divides_Oring__div(_796559)], (10559 ^ _778908) ^ [_956230, _956232, _956234] : [class_Orderings_Olinorder(_956230), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956230), _956232), _956234))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956230), _956234), _956232)))], (5831 ^ _778908) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51367 ^ _778908) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (33185 ^ _778908) ^ [_1384506, _1384508, _1384510] : [class_Lattices_Olattice(_1384506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384506), _1384508)), hBOOL(hAPP(hAPP(c_member(_1384506), _1384510), _1384508)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1384506), _1384510), c_Big__Operators_Olattice__class_OSup__fin(_1384506, _1384508)) = c_Big__Operators_Olattice__class_OSup__fin(_1384506, _1384508))], (17469 ^ _778908) ^ [_1080626, _1080628] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1080626)), _1080628) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1080626), _1080628)))], (39664 ^ _778908) ^ [_1525836, _1525838, _1525840, _1525842, _1525844, _1525846] : [-(hBOOL(hAPP(hAPP(c_member(_1525836), _1525838), _1525840))), 39667 ^ _778908 : [(39674 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525836), _1525842), _1525840))), -(hAPP(c_Set_Ovimage(_1525844, _1525836, hAPP(hAPP(c_COMBC(_1525844, _1525836, _1525836), hAPP(hAPP(c_COMBC(_1525844, _1525836, tc_fun(_1525836, _1525836)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525836, tc_fun(_1525836, _1525836)), _1525844), c_If(_1525836)), hAPP(hAPP(c_COMBC(_1525844, tc_fun(_1525844, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525844)), _1525846))), _1525838)), _1525842)), _1525840) = c_Orderings_Obot__class_Obot(tc_fun(_1525844, tc_HOL_Obool)))], (39668 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1525836), _1525842), _1525840)), -(hAPP(c_Set_Ovimage(_1525844, _1525836, hAPP(hAPP(c_COMBC(_1525844, _1525836, _1525836), hAPP(hAPP(c_COMBC(_1525844, _1525836, tc_fun(_1525836, _1525836)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525836, tc_fun(_1525836, _1525836)), _1525844), c_If(_1525836)), hAPP(hAPP(c_COMBC(_1525844, tc_fun(_1525844, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525844)), _1525846))), _1525838)), _1525842)), _1525840) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1525844, tc_HOL_Obool)), _1525846))]]], (15818 ^ _778908) ^ [_1048766, _1048768, _1048770] : [class_Groups_Oab__group__add(_1048766), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048766), _1048768), _1048770) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048766), _1048768), hAPP(c_Groups_Ouminus__class_Ouminus(_1048766), _1048770)))], (43293 ^ _778908) ^ [_1620830, _1620832, _1620834, _1620836, _1620838] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620830, _1620830)), hAPP(hAPP(c_Product__Type_OPair(_1620830, _1620830), _1620832), _1620834)), c_Transitive__Closure_Ortrancl(_1620830, _1620836))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1620830, _1620830)), hAPP(hAPP(c_Product__Type_OPair(_1620830, _1620830), _1620834), _1620838)), c_Transitive__Closure_Otrancl(_1620830, _1620836))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620830, _1620830)), hAPP(hAPP(c_Product__Type_OPair(_1620830, _1620830), _1620832), _1620838)), c_Transitive__Closure_Otrancl(_1620830, _1620836))))], (41398 ^ _778908) ^ [_1567947, _1567949] : [-(c_Fun_Oinj__on(tc_fun(_1567947, _1567949), tc_fun(tc_prod(_1567947, _1567949), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1567947, _1567949), tc_HOL_Obool), tc_fun(tc_prod(_1567947, _1567949), tc_HOL_Obool), tc_fun(_1567947, _1567949)), c_Set_OCollect(tc_prod(_1567947, _1567949))), hAPP(hAPP(c_COMBB(tc_fun(_1567947, tc_fun(_1567949, tc_HOL_Obool)), tc_fun(tc_prod(_1567947, _1567949), tc_HOL_Obool), tc_fun(_1567947, _1567949)), c_Product__Type_Oprod_Oprod__case(_1567947, _1567949, tc_HOL_Obool)), hAPP(c_COMBB(_1567949, tc_fun(_1567949, tc_HOL_Obool), _1567947), hAPP(c_COMBC(_1567949, _1567949, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1567947, _1567949), tc_HOL_Obool))))], (18563 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (41219 ^ _778908) ^ [_1562023, _1562025, _1562027] : [hBOOL(hAPP(_1562027, _1562025)), -(hBOOL(hAPP(hAPP(c_member(_1562023), _1562025), hAPP(c_Set_OCollect(_1562023), _1562027))))], (41018 ^ _778908) ^ [_1557976] : [-(c_Finite__Set_Ofun__left__comm__idem(_1557976, tc_fun(_1557976, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1557976, tc_HOL_Obool), tc_fun(tc_fun(_1557976, tc_HOL_Obool), tc_fun(_1557976, tc_HOL_Obool)), _1557976), hAPP(c_COMBC(tc_fun(_1557976, tc_HOL_Obool), tc_fun(_1557976, tc_HOL_Obool), tc_fun(_1557976, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1557976, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1557976, tc_fun(_1557976, tc_HOL_Obool), tc_fun(_1557976, tc_HOL_Obool)), c_Set_Oinsert(_1557976)), c_Orderings_Obot__class_Obot(tc_fun(_1557976, tc_HOL_Obool))))))], (6182 ^ _778908) ^ [_878214, _878216, _878218, _878220, _878222] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_878214, _878216, _878218)), _878220), _878222))), 6183 ^ _778908 : [(6190 ^ _778908) ^ [] : [-(hBOOL(hAPP(_878214, _878220))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878218), _878220), _878222))], (6184 ^ _778908) ^ [] : [hBOOL(hAPP(_878214, _878220)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878216), _878220), _878222))]]], (17767 ^ _778908) ^ [_1086128, _1086130, _1086132] : [class_Rings_Olinordered__semidom(_1086128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086128), c_Groups_Oone__class_Oone(_1086128)), _1086130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086128), c_Groups_Oone__class_Oone(_1086128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086128), _1086130), hAPP(hAPP(c_Power_Opower__class_Opower(_1086128), _1086130), _1086132)))))], (7783 ^ _778908) ^ [_909213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909213), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2398 ^ _778908) ^ [_815085, _815087, _815089, _815091, _815093, _815095] : [-(c_Random_Ominus__shift(_815095, _815091, _815087) = c_Random_Ominus__shift(_815093, _815089, _815085)), _815095 = _815093, _815091 = _815089, _815087 = _815085], (39735 ^ _778908) ^ [_1527701, _1527703, _1527705, _1527707] : [hBOOL(hAPP(hAPP(c_member(_1527701), _1527703), c_Map_Odom(_1527701, _1527705, _1527707))), hAPP(_1527707, _1527703) = c_Option_Ooption_ONone(_1527705)], (5861 ^ _778908) ^ [_872214, _872216, _872218] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_872214, _872216, _872218)], (42405 ^ _778908) ^ [_1599085, _1599087, _1599089, _1599091] : [hBOOL(hAPP(hAPP(c_member(_1599085), _1599091), hAPP(c_Relation_ODomain(_1599085, _1599087), _1599089))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1599085, _1599087, hAPP(hAPP(c_COMBC(_1599085, tc_fun(tc_prod(_1599085, _1599087), tc_HOL_Obool), tc_fun(_1599087, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599087, tc_fun(tc_fun(tc_prod(_1599085, _1599087), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1599085, _1599087), tc_HOL_Obool), tc_fun(_1599087, tc_HOL_Obool)), _1599085), c_COMBC(_1599087, tc_fun(tc_prod(_1599085, _1599087), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599087, tc_prod(_1599085, _1599087)), tc_fun(_1599087, tc_fun(tc_fun(tc_prod(_1599085, _1599087), tc_HOL_Obool), tc_HOL_Obool)), _1599085), hAPP(c_COMBB(tc_prod(_1599085, _1599087), tc_fun(tc_fun(tc_prod(_1599085, _1599087), tc_HOL_Obool), tc_HOL_Obool), _1599087), c_member(tc_prod(_1599085, _1599087)))), c_Product__Type_OPair(_1599085, _1599087)))), _1599089)), _1599091)))], (43018 ^ _778908) ^ [_1613423, _1613425] : [c_Wellfounded_Oacyclic(_1613423, _1613425), 43021 ^ _778908 : [(43022 ^ _778908) ^ [_1613508] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613423, _1613423)), hAPP(hAPP(c_Product__Type_OPair(_1613423, _1613423), _1613508), _1613508)), c_Transitive__Closure_Otrancl(_1613423, _1613425)))]]], (49213 ^ _778908) ^ [_1765855, _1765857, _1765859] : [hAPP(c_List_Orotate(_1765855, _1765857), _1765859) = c_List_Olist_ONil(_1765855), -(_1765859 = c_List_Olist_ONil(_1765855))], (11659 ^ _778908) ^ [_974076, _974078, _974080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974076), _974078)), _974080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974078), _974080)))], (29642 ^ _778908) ^ [_1309037, _1309039] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1309037, _1309039)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1309037, _1309039), tc_HOL_Obool)))), 29645 ^ _778908 : [(29648 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309039), c_Orderings_Otop__class_Otop(tc_fun(_1309039, tc_HOL_Obool)))))], (29646 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309037), c_Orderings_Otop__class_Otop(tc_fun(_1309037, tc_HOL_Obool)))))]]], (41351 ^ _778908) ^ [_1566550, _1566552] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1566550)), 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)), _1566550))), 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, _1566552))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3726 ^ _778908) ^ [_836299, _836301, _836303, _836305, _836307, _836309, _836311, _836313] : [-(c_Product__Type_Oapfst(_836313, _836309, _836305, _836301) = c_Product__Type_Oapfst(_836311, _836307, _836303, _836299)), _836313 = _836311, _836309 = _836307, _836305 = _836303, _836301 = _836299], (49239 ^ _778908) ^ [_1766394, _1766396, _1766398] : [-(c_List_Orotate(_1766394, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1766396), _1766398)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1766394), tc_List_Olist(_1766394), tc_List_Olist(_1766394), c_List_Orotate(_1766394, _1766396)), c_List_Orotate(_1766394, _1766398)))], (7607 ^ _778908) ^ [_906237, _906239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906237), _906239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _906237)), hAPP(c_Nat_OSuc, _906239))))], (18879 ^ _778908) ^ [_1104242, _1104244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1104242)), c_Int_OBit1(_1104244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104242), _1104244)))], (45613 ^ _778908) ^ [_1676615, _1676617, _1676619, _1676621] : [class_Orderings_Olinorder(_1676615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1676615), _1676617)), 45623 ^ _778908 : [(45626 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676615), 45622 ^ [_1676615, _1676617, _1676619, _1676621]), _1676619))], (45624 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676615), 45622 ^ [_1676615, _1676617, _1676619, _1676621]), _1676617)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676615), hAPP(hAPP(c_Finite__Set_Ofold(_1676615, _1676615, c_Orderings_Oord__class_Omax(_1676615)), _1676621), _1676617)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1676615), _1676619), _1676621))))], (24231 ^ _778908) ^ [_1202236, _1202238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202238)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202236), _1202238) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1202236, _1202238)))], (15040 ^ _778908) ^ [_1033984, _1033986, _1033988] : [-(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), _1033984), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033986), _1033984))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1033986, _1033984))), _1033988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1033986), _1033988))], (49835 ^ _778908) ^ [_1779381, _1779383] : [-(c_List_Obutlast(_1779381, _1779383) = hAPP(hAPP(c_List_Otake(_1779381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779381)), _1779383)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1779383))], (17483 ^ _778908) ^ [_1080896, _1080898] : [-(_1080896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1080898), _1080896) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1080898), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1080898), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1080896), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (12752 ^ _778908) ^ [_993329, _993331, _993333, _993335] : [class_Groups_Oordered__comm__monoid__add(_993329), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993329), c_Groups_Ozero__class_Ozero(_993329)), _993331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993329), _993333), _993335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993329), _993333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_993329), _993331), _993335))))], (9034 ^ _778908) ^ [_929810] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _929810)) = _929810)], (7633 ^ _778908) ^ [_906707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906707), _906707))], (32275 ^ _778908) ^ [_1365448, _1365450, _1365452] : [_1365448 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1365450, _1365450), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1365450, _1365450), tc_HOL_Obool)), _1365448), _1365452)))], (30442 ^ _778908) ^ [_1324053, _1324055, _1324057] : [class_Orderings_Oorder(_1324053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324053), _1324055), _1324057)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1324053, _1324057, _1324055) = c_Orderings_Obot__class_Obot(tc_fun(_1324053, tc_HOL_Obool)))], (14246 ^ _778908) ^ [_1019969, _1019971, _1019973, _1019975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019971), _1019973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019973), 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), _1019971), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019975, _1019969))), _1019973)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43670 ^ _778908) ^ [_1630033, _1630035, _1630037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630033, _1630033)), _1630035), c_Transitive__Closure_Ortrancl(_1630033, _1630037))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630033, _1630033)), _1630035), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1630033, _1630033), 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(_1630033, _1630033), tc_HOL_Obool), tc_fun(tc_prod(_1630033, _1630033), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1630033, _1630033), tc_HOL_Obool)), _1630037)))))], (38992 ^ _778908) ^ [_1510699, _1510701, _1510703, _1510705, _1510707, _1510709] : [class_Groups_Ocomm__monoid__add(_1510699), c_Fun_Oinj__on(_1510701, _1510703, _1510705, _1510707), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510703, _1510699), _1510709), hAPP(c_Set_Oimage(_1510701, _1510703, _1510705), _1510707)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510701, _1510699), hAPP(c_Fun_Ocomp(_1510703, _1510699, _1510701, _1510709), _1510705)), _1510707))], (43031 ^ _778908) ^ [_1613625, _1613627, _1613629, _1613631] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613625, _1613625)), hAPP(hAPP(c_Product__Type_OPair(_1613625, _1613625), _1613627), _1613629)), _1613631)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613625, _1613625)), hAPP(hAPP(c_Product__Type_OPair(_1613625, _1613625), _1613627), _1613629)), c_Transitive__Closure_Otrancl(_1613625, _1613631))))], (45889 ^ _778908) ^ [_1682669, _1682671, _1682673, _1682675, _1682677] : [-(hBOOL(hAPP(hAPP(c_member(_1682669), _1682671), c_Map_Odom(_1682669, _1682673, _1682675)))), -(hAPP(c_Map_Omap__add(_1682669, _1682673, _1682675, _1682677), _1682671) = hAPP(_1682677, _1682671))], (1322 ^ _778908) ^ [_798307, _798309] : [-(class_Lattices_Osemilattice__sup(_798307)), _798309 = _798307, class_Lattices_Osemilattice__sup(_798309)], (47431 ^ _778908) ^ [_1722425, _1722427, _1722429, _1722431] : [-(c_List_Ofoldr(_1722425, _1722427, _1722429, c_List_Olist_ONil(_1722425), _1722431) = _1722431)], (39741 ^ _778908) ^ [_1527809, _1527811, _1527813, _1527815] : [-(hAPP(_1527815, _1527811) = c_Option_Ooption_ONone(_1527813)), -(hBOOL(hAPP(hAPP(c_member(_1527809), _1527811), c_Map_Odom(_1527809, _1527813, _1527815))))], (42727 ^ _778908) ^ [_1607051, _1607053, _1607055] : [42728 ^ _778908 : [(42729 ^ _778908) ^ [_1607105] : [hBOOL(hAPP(_1607051, _1607105))]], _1607053 = c_Hilbert__Choice_OEps(_1607055, _1607051), -(hBOOL(hAPP(_1607051, _1607053)))], (50969 ^ _778908) ^ [_1803260, _1803262, _1803264, _1803266] : [-(c_List_Otranspose(_1803260, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803260)), hAPP(hAPP(c_List_Olist_OCons(_1803260), _1803262), _1803264)), _1803266)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803260)), hAPP(hAPP(c_List_Olist_OCons(_1803260), _1803262), c_List_Oconcat(_1803260, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803260), tc_List_Olist(_1803260)), c_List_Olist_Olist__case(tc_List_Olist(_1803260), _1803260, c_List_Olist_ONil(_1803260), hAPP(hAPP(c_COMBB(tc_List_Olist(_1803260), tc_fun(tc_List_Olist(_1803260), tc_List_Olist(_1803260)), _1803260), c_COMBK(tc_List_Olist(_1803260), tc_List_Olist(_1803260))), hAPP(hAPP(c_COMBC(_1803260, tc_List_Olist(_1803260), tc_List_Olist(_1803260)), c_List_Olist_OCons(_1803260)), c_List_Olist_ONil(_1803260))))), _1803266)))), c_List_Otranspose(_1803260, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1803260)), _1803264), c_List_Oconcat(tc_List_Olist(_1803260), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803260), tc_List_Olist(tc_List_Olist(_1803260))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1803260)), _1803260, c_List_Olist_ONil(tc_List_Olist(_1803260)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1803260), tc_List_Olist(tc_List_Olist(_1803260))), _1803260), hAPP(hAPP(c_COMBC(tc_List_Olist(_1803260), tc_List_Olist(tc_List_Olist(_1803260)), tc_List_Olist(tc_List_Olist(_1803260))), c_List_Olist_OCons(tc_List_Olist(_1803260))), c_List_Olist_ONil(tc_List_Olist(_1803260)))))), _1803266))))))], (1878 ^ _778908) ^ [_805349, _805351, _805353, _805355] : [-(v_Q(_805353, _805349)), v_Q(_805355, _805351), _805355 = _805353, _805351 = _805349], (51331 ^ _778908) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (49827 ^ _778908) ^ [_1779192, _1779194, _1779196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1779192), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779194)), _1779196))), -(hAPP(hAPP(c_List_Otake(_1779194), _1779192), c_List_Obutlast(_1779194, _1779196)) = hAPP(hAPP(c_List_Otake(_1779194), _1779192), _1779196))], (35925 ^ _778908) ^ [_1443141, _1443143, _1443145, _1443147, _1443149, _1443151] : [c_Finite__Set_Ofolding(_1443141, _1443143, _1443145, _1443147), -(hAPP(c_Fun_Ocomp(_1443143, _1443143, _1443143, hAPP(_1443145, _1443149)), hAPP(_1443145, _1443151)) = hAPP(c_Fun_Ocomp(_1443143, _1443143, _1443143, hAPP(_1443145, _1443151)), hAPP(_1443145, _1443149)))], (42641 ^ _778908) ^ [_1604921, _1604923, _1604925] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1604921, _1604923, _1604925)), 42643 ^ _778908 : [(42644 ^ _778908) ^ [_1605067] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1604921)), _1605067), _1604923)), -(c_Hoare__Mirabelle_Otriple__valid(_1604921, 42642 ^ [_1604921, _1604923, _1604925], _1605067))], (42653 ^ _778908) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1604921, 42642 ^ [_1604921, _1604923, _1604925], 42649 ^ [_1604921, _1604923, _1604925])], (42651 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1604921)), 42649 ^ [_1604921, _1604923, _1604925]), _1604925)))]]], (37228 ^ _778908) ^ [_1472426, _1472428, _1472430] : [class_Orderings_Oorder(_1472426), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472426, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1472426, _1472428, _1472430)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1472426), _1472430)) = c_Orderings_Obot__class_Obot(tc_fun(_1472426, tc_HOL_Obool)))], (46016 ^ _778908) ^ [_1685684, _1685686, _1685688, _1685690] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1685684), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1685686), _1685688)))), -(hBOOL(hAPP(hAPP(hAPP(_1685690, _1685684), _1685686), _1685688))), 46024 ^ _778908 : [(46027 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 46022 ^ [_1685684, _1685686, _1685688, _1685690]), 46023 ^ [_1685684, _1685686, _1685688, _1685690]))), hAPP(46021 ^ [_1685684, _1685686, _1685688, _1685690], 46023 ^ [_1685684, _1685686, _1685688, _1685690]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1685690, 46021 ^ [_1685684, _1685686, _1685688, _1685690]), 46022 ^ [_1685684, _1685686, _1685688, _1685690]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 46023 ^ [_1685684, _1685686, _1685688, _1685690]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (46037 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1685690, 46021 ^ [_1685684, _1685686, _1685688, _1685690]), 46022 ^ [_1685684, _1685686, _1685688, _1685690]), 46023 ^ [_1685684, _1685686, _1685688, _1685690]))], (46025 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 46021 ^ [_1685684, _1685686, _1685688, _1685690]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 46022 ^ [_1685684, _1685686, _1685688, _1685690]), 46023 ^ [_1685684, _1685686, _1685688, _1685690])))))]]], (27767 ^ _778908) ^ [_1271213, _1271215, _1271217] : [-(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)), _1271213)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1271215), _1271217)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1271215), _1271213)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1271217), _1271213)))], (43169 ^ _778908) ^ [_1617824, _1617826] : [-(c_Transitive__Closure_Otrancl(_1617824, _1617826) = hAPP(hAPP(c_Relation_Orel__comp(_1617824, _1617824, _1617824), _1617826), c_Transitive__Closure_Ortrancl(_1617824, _1617826)))], (17409 ^ _778908) ^ [_1079744, _1079746] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1079744), _1079746) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1079746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1079744 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50039 ^ _778908) ^ [_1784348, _1784350, _1784352, _1784354] : [-(c_List_Otranspose(_1784348, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1784350), tc_List_Olist(_1784348)), hAPP(c_List_Omap(_1784350, _1784348), _1784352)), _1784354)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1784350), tc_List_Olist(_1784348)), hAPP(c_List_Omap(_1784350, _1784348), _1784352)), c_List_Otranspose(_1784350, _1784354)))], (43377 ^ _778908) ^ [_1622837, _1622839, _1622841, _1622843] : [-(hBOOL(hAPP(hAPP(c_member(_1622837), _1622839), hAPP(c_Relation_ODomain(_1622837, _1622837), _1622841)))), 43380 ^ _778908 : [(43387 ^ _778908) ^ [] : [_1622839 = _1622843, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622837, _1622837)), hAPP(hAPP(c_Product__Type_OPair(_1622837, _1622837), _1622839), _1622843)), c_Transitive__Closure_Ortrancl(_1622837, _1622841))))], (43381 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622837, _1622837)), hAPP(hAPP(c_Product__Type_OPair(_1622837, _1622837), _1622839), _1622843)), c_Transitive__Closure_Ortrancl(_1622837, _1622841))), -(_1622839 = _1622843)]]], (50367 ^ _778908) ^ [_1790911, _1790913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790911), _1790913)), -(c_List_Oupt(_1790911, _1790913) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1790911), c_List_Oupt(hAPP(c_Nat_OSuc, _1790911), _1790913)))], (47978 ^ _778908) ^ [_1735275, _1735277, _1735279] : [class_Orderings_Olinorder(_1735275), -(hAPP(c_List_Oset(_1735275), c_List_Olinorder__class_Oinsort__insert__key(_1735275, _1735275, c_COMBI(_1735275), _1735277, _1735279)) = hAPP(hAPP(c_Set_Oinsert(_1735275), _1735277), hAPP(c_List_Oset(_1735275), _1735279)))], (51147 ^ _778908) ^ [_1808305, _1808307] : [class_Lattices_Olattice(_1808305), -(class_Lattices_Osemilattice__sup(tc_fun(_1808307, _1808305)))], (29590 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (36318 ^ _778908) ^ [_1452435, _1452437, _1452439, _1452441] : [hBOOL(hAPP(_1452435, _1452437)), hBOOL(hAPP(_1452439, _1452437)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452441, tc_HOL_Obool)), _1452435), _1452439), _1452437)))], (3648 ^ _778908) ^ [_835002, _835004, _835006, _835008, _835010, _835012, _835014, _835016] : [-(c_Fun_Othe__inv__into(_835016, _835012, _835008, _835004) = c_Fun_Othe__inv__into(_835014, _835010, _835006, _835002)), _835016 = _835014, _835012 = _835010, _835008 = _835006, _835004 = _835002], (14802 ^ _778908) ^ [_1030018, _1030020, _1030022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030018)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030018), _1030020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030018), _1030022)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1030020), _1030022))], (42385 ^ _778908) ^ [_1598021, _1598023] : [c_Wellfounded_OwfP(_1598021, hAPP(hAPP(c_COMBC(_1598021, tc_fun(tc_prod(_1598021, _1598021), tc_HOL_Obool), tc_fun(_1598021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598021, tc_fun(tc_fun(tc_prod(_1598021, _1598021), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598021, _1598021), tc_HOL_Obool), tc_fun(_1598021, tc_HOL_Obool)), _1598021), c_COMBC(_1598021, tc_fun(tc_prod(_1598021, _1598021), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598021, tc_prod(_1598021, _1598021)), tc_fun(_1598021, tc_fun(tc_fun(tc_prod(_1598021, _1598021), tc_HOL_Obool), tc_HOL_Obool)), _1598021), hAPP(c_COMBB(tc_prod(_1598021, _1598021), tc_fun(tc_fun(tc_prod(_1598021, _1598021), tc_HOL_Obool), tc_HOL_Obool), _1598021), c_member(tc_prod(_1598021, _1598021)))), c_Product__Type_OPair(_1598021, _1598021)))), _1598023)), -(c_Wellfounded_Owf(_1598021, _1598023))], (15518 ^ _778908) ^ [_1042936, _1042938, _1042940, _1042942, _1042944, _1042946] : [class_Divides_Oring__div(_1042936), c_Divides_Odiv__class_Omod(_1042936, _1042938, _1042940) = c_Divides_Odiv__class_Omod(_1042936, _1042942, _1042940), c_Divides_Odiv__class_Omod(_1042936, _1042944, _1042940) = c_Divides_Odiv__class_Omod(_1042936, _1042946, _1042940), -(c_Divides_Odiv__class_Omod(_1042936, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042936), _1042938), _1042944), _1042940) = c_Divides_Odiv__class_Omod(_1042936, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042936), _1042942), _1042946), _1042940))], (43045 ^ _778908) ^ [_1613982] : [-(c_Transitive__Closure_Otrancl(_1613982, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1613982, _1613982), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1613982, _1613982), tc_HOL_Obool)))], (14748 ^ _778908) ^ [_1029102, _1029104, _1029106, _1029108] : [class_Divides_Osemiring__div(_1029102), 14751 ^ _778908 : [(14758 ^ _778908) ^ [] : [-(_1029104 = c_Groups_Ozero__class_Ozero(_1029102)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029102), _1029104), _1029106)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029102), _1029104), _1029108)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029102), _1029106), _1029108))], (14752 ^ _778908) ^ [] : [_1029104 = c_Groups_Ozero__class_Ozero(_1029102), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029102), _1029104), _1029106)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029102), _1029104), _1029108)) = c_Groups_Ozero__class_Ozero(_1029102))]]], (3542 ^ _778908) ^ [_833371, _833373] : [_833373 = _833371, -(c_Nitpick_Odenom(_833373) = c_Nitpick_Odenom(_833371))], (30238 ^ _778908) ^ [_1320701, _1320703, _1320705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320701, tc_HOL_Obool)), _1320703), hAPP(hAPP(c_Set_Oinsert(_1320701), _1320705), c_Orderings_Obot__class_Obot(tc_fun(_1320701, tc_HOL_Obool))))), -(_1320703 = c_Orderings_Obot__class_Obot(tc_fun(_1320701, tc_HOL_Obool))), -(_1320703 = hAPP(hAPP(c_Set_Oinsert(_1320701), _1320705), c_Orderings_Obot__class_Obot(tc_fun(_1320701, tc_HOL_Obool))))], (49309 ^ _778908) ^ [_1767935, _1767937, _1767939, _1767941, _1767943, _1767945] : [-(hAPP(c_List_Ofoldl(_1767935, _1767937, _1767939, _1767941), hAPP(hAPP(c_List_Oappend(_1767937), _1767943), _1767945)) = hAPP(c_List_Ofoldl(_1767935, _1767937, _1767939, hAPP(c_List_Ofoldl(_1767935, _1767937, _1767939, _1767941), _1767943)), _1767945))], (16839 ^ _778908) ^ [_1068542, _1068544, _1068546] : [class_Groups_Oordered__ab__group__add__abs(_1068542), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068542), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068542), hAPP(c_Groups_Oabs__class_Oabs(_1068542), _1068544)), hAPP(c_Groups_Oabs__class_Oabs(_1068542), _1068546))), hAPP(c_Groups_Oabs__class_Oabs(_1068542), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068542), _1068546), _1068544)))))], (28647 ^ _778908) ^ [_1288123, _1288125, _1288127, _1288129] : [class_Orderings_Olinorder(_1288123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288123), _1288125), _1288127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288123), _1288127), _1288129)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288123, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1288123, _1288125, _1288127)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288123, _1288127, _1288129)) = c_SetInterval_Oord__class_OatLeastAtMost(_1288123, _1288125, _1288129))], (49069 ^ _778908) ^ [_1763024, _1763026, _1763028, _1763030] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1763024) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1763026), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1763024)), hAPP(hAPP(c_List_Olist_OCons(_1763026), _1763028), _1763030)) = hAPP(hAPP(c_List_Olist_OCons(_1763026), _1763028), _1763030))], (46043 ^ _778908) ^ [_1686441, _1686443, _1686445, _1686447, _1686449, _1686451, _1686453] : [c_Fun_Oinj__on(_1686441, _1686443, _1686445, c_Orderings_Otop__class_Otop(tc_fun(_1686441, tc_HOL_Obool))), hAPP(c_Map_Omap__of(_1686441, _1686447, _1686449), _1686451) = hAPP(c_Option_Ooption_OSome(_1686447), _1686453), -(hAPP(c_Map_Omap__of(_1686443, _1686447, hAPP(hAPP(c_List_Omap(tc_prod(_1686441, _1686447), tc_prod(_1686443, _1686447)), hAPP(c_Product__Type_Oprod_Oprod__case(_1686441, _1686447, tc_prod(_1686443, _1686447)), hAPP(hAPP(c_COMBB(_1686443, tc_fun(_1686447, tc_prod(_1686443, _1686447)), _1686441), c_Product__Type_OPair(_1686443, _1686447)), _1686445))), _1686449)), hAPP(_1686445, _1686451)) = hAPP(c_Option_Ooption_OSome(_1686447), _1686453))], (5845 ^ _778908) ^ [_871875, _871877, _871879, _871881, _871883, _871885, _871887, _871889, _871891, _871893] : [-(c_Com_Ocom_Ocom__case(_871875, _871877, _871879, _871881, _871883, _871885, _871887, _871889, _871891, hAPP(c_Com_Ocom_OBODY, _871893)) = hAPP(_871889, _871893))], (8082 ^ _778908) ^ [_914126] : [_914126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914126), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (45162 ^ _778908) ^ [_1666258, _1666260, _1666262] : [class_Complete__Lattice_Ocomplete__lattice(_1666258), class_Orderings_Olinorder(_1666258), 45169 ^ _778908 : [(45179 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666258), _1666260), c_Complete__Lattice_OSup__class_OSup(_1666258, _1666262)))), 45180 ^ _778908 : [(45181 ^ _778908) ^ [_1666564] : [hBOOL(hAPP(hAPP(c_member(_1666258), _1666564), _1666262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666258), _1666260), _1666564))]]], (45170 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666258), _1666260), c_Complete__Lattice_OSup__class_OSup(_1666258, _1666262))), 45174 ^ _778908 : [(45177 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666258), _1666260), 45173 ^ [_1666258, _1666260, _1666262])))], (45175 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666258), 45173 ^ [_1666258, _1666260, _1666262]), _1666262)))]]]]], (16048 ^ _778908) ^ [_1053137, _1053139] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053137), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1053139), _1053137)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053139), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1053139, _1053137)))], (15702 ^ _778908) ^ [_1046415, _1046417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1046415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1046415), _1046417)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046417), _1046415)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1046417)), hAPP(c_Int_Onat, _1046415)))], (16579 ^ _778908) ^ [_1063821, _1063823] : [class_Groups_Oordered__ab__group__add__abs(_1063821), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063821), _1063823), hAPP(c_Groups_Oabs__class_Oabs(_1063821), _1063823))))], (18933 ^ _778908) ^ [_1105107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105107)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105107), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40523 ^ _778908) ^ [_1548801, _1548803, _1548805, _1548807, _1548809] : [c_Relation_Orefl__on(_1548801, _1548803, _1548805), hBOOL(hAPP(hAPP(c_member(tc_prod(_1548801, _1548801)), hAPP(hAPP(c_Product__Type_OPair(_1548801, _1548801), _1548807), _1548809)), _1548805)), -(hBOOL(hAPP(hAPP(c_member(_1548801), _1548807), _1548803)))], (47621 ^ _778908) ^ [_1726680, _1726682, _1726684] : [47623 ^ _778908 : [(47626 ^ _778908) ^ [] : [hBOOL(hAPP(_1726684, 47622 ^ [_1726680, _1726682, _1726684]))], (47624 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726680), 47622 ^ [_1726680, _1726682, _1726684]), hAPP(c_List_Oset(_1726680), _1726682))))]], 47627 ^ _778908 : [(47628 ^ _778908) ^ [_1726864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726864), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726680)), _1726682))), -(hBOOL(hAPP(_1726684, hAPP(hAPP(c_List_Onth(_1726680), _1726682), _1726864))))]]], (5730 ^ _778908) ^ [_867385, _867387, _867389, _867391, _867393, _867395] : [-(c_COMBC(_867395, _867391, _867387) = c_COMBC(_867393, _867389, _867385)), _867395 = _867393, _867391 = _867389, _867387 = _867385], (51597 ^ _778908) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (22486 ^ _778908) ^ [_1168481, _1168483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1168481), 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)), _1168483)), -(c_Divides_OnegDivAlg(_1168481, _1168483) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1168481), _1168483)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1168481, _1168483)))], (33435 ^ _778908) ^ [_1389058, _1389060] : [class_Orderings_Olinorder(_1389058), -(c_Big__Operators_Olinorder__class_OMax(_1389058, hAPP(hAPP(c_Set_Oinsert(_1389058), _1389060), c_Orderings_Obot__class_Obot(tc_fun(_1389058, tc_HOL_Obool)))) = _1389060)], (16949 ^ _778908) ^ [_1070556, _1070558, _1070560, _1070562] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070556), _1070558), _1070560)), hAPP(c_Int_Onumber__class_Onumber__of(_1070556), _1070562)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070556), _1070558), hAPP(c_Int_Onumber__class_Onumber__of(_1070556), _1070562))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070556), _1070560), hAPP(c_Int_Onumber__class_Onumber__of(_1070556), _1070562)))), class_Int_Onumber(_1070556), class_Rings_Osemiring(_1070556)], (50268 ^ _778908) ^ [_1789091, _1789093, _1789095] : [class_Orderings_Olinorder(_1789091), 50271 ^ _778908 : [(50284 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1789091, hAPP(hAPP(c_List_Olist_OCons(_1789091), _1789093), _1789095))), c_List_Olinorder__class_Osorted(_1789091, _1789095), 50290 ^ _778908 : [(50293 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789091), _1789093), 50289 ^ [_1789091, _1789093, _1789095]))], (50291 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789091), 50289 ^ [_1789091, _1789093, _1789095]), hAPP(c_List_Oset(_1789091), _1789095))))]]], (50272 ^ _778908) ^ [] : [c_List_Olinorder__class_Osorted(_1789091, hAPP(hAPP(c_List_Olist_OCons(_1789091), _1789093), _1789095)), 50275 ^ _778908 : [(50278 ^ _778908) ^ [_1789277] : [hBOOL(hAPP(hAPP(c_member(_1789091), _1789277), hAPP(c_List_Oset(_1789091), _1789095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789091), _1789093), _1789277)))], (50276 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1789091, _1789095))]]]]], (14764 ^ _778908) ^ [_1029408, _1029410] : [class_Divides_Osemiring__div(_1029408), -(_1029410 = c_Groups_Ozero__class_Ozero(_1029408)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029408), _1029410), _1029410) = c_Groups_Oone__class_Oone(_1029408))], (3962 ^ _778908) ^ [_840039, _840041, _840043, _840045] : [-(c_Lazy__Sequence_Ohb__single(_840045, _840041) = c_Lazy__Sequence_Ohb__single(_840043, _840039)), _840045 = _840043, _840041 = _840039], (40373 ^ _778908) ^ [_1544686, _1544688, _1544690, _1544692] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544686), _1544688)), 40379 ^ _778908 : [(40382 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544690), hAPP(_1544692, 40378 ^ [_1544686, _1544688, _1544690, _1544692])))], (40380 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544686), 40378 ^ [_1544686, _1544688, _1544690, _1544692]), _1544688)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1544686, _1544690)), hAPP(hAPP(c_Product__Type_OSigma(_1544686, _1544690), _1544688), _1544692)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544686, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1544690, tc_HOL_Obool), tc_Nat_Onat, _1544686), c_Finite__Set_Ocard(_1544690)), _1544692)), _1544688))], (51317 ^ _778908) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (50451 ^ _778908) ^ [_1792177] : [class_Orderings_Olinorder(_1792177), -(c_List_Olinorder__class_Osorted(_1792177, c_List_Olist_ONil(_1792177)))], (15712 ^ _778908) ^ [_1046618, _1046620, _1046622] : [hBOOL(hAPP(_1046618, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046620), _1046622)))), 15715 ^ _778908 : [(15722 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046620), _1046622)), -(hBOOL(hAPP(_1046618, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15716 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046622), _1046620)), -(hBOOL(hAPP(_1046618, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1046620)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1046622)))))]]], (41858 ^ _778908) ^ [_1586346, _1586348, _1586350, _1586352, _1586354, _1586356, _1586358, _1586360] : [hBOOL(hAPP(hAPP(_1586346, _1586348), _1586350)), hBOOL(hAPP(hAPP(_1586352, _1586350), _1586354)), -(c_Predicate_Opred__comp(_1586356, _1586358, _1586360, _1586346, _1586352, _1586348, _1586354))], (18409 ^ _778908) ^ [_1096776] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096776), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096776)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1096776)))], (6532 ^ _778908) ^ [_884828, _884830, _884832, _884834, _884836] : [c_Com_Ocom_OCall(_884828, _884830, _884832) = c_Com_Ocom_OSemi(_884834, _884836)], (26011 ^ _778908) ^ [_1235861, _1235863, _1235865] : [class_Rings_Ocomm__ring__1(_1235861), 26014 ^ _778908 : [(26021 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235861), _1235863), _1235865)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235861), hAPP(c_Groups_Ouminus__class_Ouminus(_1235861), _1235863)), _1235865)))], (26015 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235861), hAPP(c_Groups_Ouminus__class_Ouminus(_1235861), _1235863)), _1235865)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235861), _1235863), _1235865)))]]], (18145 ^ _778908) ^ [_1092579, _1092581] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092579)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092579)), _1092581) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092579)), _1092581)))], (10407 ^ _778908) ^ [_953775, _953777] : [class_Rings_Olinordered__idom(_953775), 10410 ^ _778908 : [(10417 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953775), c_Groups_Ozero__class_Ozero(_953775)), _953777)), -(c_Groups_Osgn__class_Osgn(_953775, _953777) = c_Groups_Oone__class_Oone(_953775))], (10411 ^ _778908) ^ [] : [c_Groups_Osgn__class_Osgn(_953775, _953777) = c_Groups_Oone__class_Oone(_953775), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953775), c_Groups_Ozero__class_Ozero(_953775)), _953777)))]]], (29936 ^ _778908) ^ [_1314760] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1314760), c_Orderings_Obot__class_Obot(tc_fun(_1314760, tc_HOL_Obool)))))], (49664 ^ _778908) ^ [_1775650, _1775652, _1775654] : [-(c_List_Olast(_1775650, hAPP(hAPP(c_List_Oappend(_1775650), _1775652), hAPP(hAPP(c_List_Olist_OCons(_1775650), _1775654), c_List_Olist_ONil(_1775650)))) = _1775654)], (19669 ^ _778908) ^ [_1117764] : [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), _1117764))), 19672 ^ _778908 : [(19675 ^ _778908) ^ [] : [-(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(_1117764)))))], (19673 ^ _778908) ^ [] : [-(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(_1117764)))))]]], (4422 ^ _778908) ^ [_847319, _847321] : [_847321 = _847319, -(c_Groups_Oabs__class_Oabs(_847321) = c_Groups_Oabs__class_Oabs(_847319))], (8131 ^ _778908) ^ [_914896, _914898] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914896), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914896), _914898)))))], (47557 ^ _778908) ^ [_1724683, _1724685] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1724683), tc_List_Olist(_1724683), c_List_Olistrel(_1724683, _1724685)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1724683)), c_List_Olist_ONil(_1724683)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1724683), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1724683)), c_List_Olist_ONil(_1724683)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1724683), tc_HOL_Obool))))], (19479 ^ _778908) ^ [_1114374, _1114376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114374), _1114376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1114374)), c_Int_OBit0(_1114376))))], (51233 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11613 ^ _778908) ^ [_973164, _973166] : [11614 ^ _778908 : [(11615 ^ _778908) ^ [_973214] : [_973166 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973164), _973214)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973164), _973166)))], (37262 ^ _778908) ^ [_1473121, _1473123, _1473125, _1473127, _1473129] : [class_Groups_Ocomm__monoid__add(_1473121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473123), _1473125)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473123), _1473127)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1473121), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473123, _1473121), _1473129), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473123, tc_HOL_Obool)), _1473125), _1473127))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473123, _1473121), _1473129), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473123, tc_HOL_Obool)), _1473125), _1473127))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1473121), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473123, _1473121), _1473129), _1473125)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473123, _1473121), _1473129), _1473127)))], (24387 ^ _778908) ^ [_1205215, _1205217] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1205215), _1205217) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1205215, 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)))), _1205217))))], (39574 ^ _778908) ^ [_1523791, _1523793, _1523795, _1523797] : [c_Fun_Oinj__on(_1523791, _1523793, _1523795, c_Orderings_Otop__class_Otop(tc_fun(_1523791, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1523791, _1523793, _1523795), hAPP(c_Set_Oimage(_1523791, _1523793, _1523795), _1523797)) = _1523797)], (49127 ^ _778908) ^ [_1764476, _1764478, _1764480] : [_1764476 = c_List_Olist_ONil(_1764478), -(hAPP(c_List_Ohd(_1764478), hAPP(hAPP(c_List_Oappend(_1764478), _1764476), _1764480)) = hAPP(c_List_Ohd(_1764478), _1764480))], (6025 ^ _778908) ^ [_875326, _875328, _875330] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_875326, _875328)), _875330), hAPP(hAPP(hAPP(c_Natural_Oupdate, _875330), _875326), hAPP(_875328, _875330)))))], (46543 ^ _778908) ^ [_1698018, _1698020, _1698022, _1698024, _1698026] : [-(hBOOL(hAPP(hAPP(c_member(_1698018), _1698020), hAPP(c_List_Oset(_1698018), _1698022)))), -(hAPP(c_Map_Omap__of(_1698018, _1698024, hAPP(hAPP(c_List_Ozip(_1698018, _1698024), _1698022), hAPP(hAPP(c_List_Omap(_1698018, _1698024), _1698026), _1698022))), _1698020) = c_Option_Ooption_ONone(_1698024))], (18537 ^ _778908) ^ [_1098641, _1098643] : [class_Int_Onumber__ring(_1098641), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098641), hAPP(c_Int_Onumber__class_Onumber__of(_1098641), c_Int_OPls)), _1098643) = _1098643)], (23010 ^ _778908) ^ [_1179155, _1179157] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1179155, _1179157), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1179155), _1179157)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1179155, _1179157)))))], (15952 ^ _778908) ^ [_1051229, _1051231, _1051233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051229), _1051231)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051231), _1051229)), _1051233) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051231), _1051233)), _1051229))], (22724 ^ _778908) ^ [_1173325, _1173327] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173325), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 22727 ^ _778908 : [(22736 ^ _778908) ^ [] : [-(c_Nitpick_Onorm__frac(_1173327, _1173325) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1173327), _1173325)), 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), _1173327))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1173325)))), -(_1173327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1173325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22728 ^ _778908) ^ [] : [22729 ^ _778908 : [(22732 ^ _778908) ^ [] : [_1173325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22730 ^ _778908) ^ [] : [_1173327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1173327, _1173325) = 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)))]]], (18019 ^ _778908) ^ [_1090421, _1090423, _1090425, _1090427, _1090429] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1090421, _1090423, _1090425), _1090427), hAPP(c_Nat_OSuc, _1090429)) = hAPP(hAPP(_1090425, _1090427), hAPP(hAPP(c_Power_Opower_Opower(_1090421, _1090423, _1090425), _1090427), _1090429)))], (35235 ^ _778908) ^ [_1426882, _1426884, _1426886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1426882, _1426882), tc_HOL_Obool)), _1426884), _1426886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1426882, tc_HOL_Obool)), hAPP(c_Relation_OField(_1426882), _1426884)), hAPP(c_Relation_OField(_1426882), _1426886))))], (28945 ^ _778908) ^ [_1294266, _1294268, _1294270, _1294272, _1294274] : [28947 ^ _778908 : [(28953 ^ _778908) ^ [] : [hBOOL(hAPP(_1294274, 28949 ^ [_1294266, _1294268, _1294270, _1294272, _1294274]))], (28951 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294266), 28949 ^ [_1294266, _1294268, _1294270, _1294272, _1294274]), hAPP(_1294272, 28946 ^ [_1294266, _1294268, _1294270, _1294272, _1294274]))))], (28948 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294268), 28946 ^ [_1294266, _1294268, _1294270, _1294272, _1294274]), _1294270)))]], 28954 ^ _778908 : [(28955 ^ _778908) ^ [_1294576] : [hBOOL(hAPP(hAPP(c_member(_1294266), _1294576), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1294268, tc_fun(_1294266, tc_HOL_Obool)), _1294270), _1294272))), -(hBOOL(hAPP(_1294274, _1294576)))]]], (49807 ^ _778908) ^ [_1778757, _1778759, _1778761] : [-(_1778757 = c_List_Olist_ONil(_1778759)), -(c_List_Obutlast(_1778759, hAPP(hAPP(c_List_Oappend(_1778759), _1778761), _1778757)) = hAPP(hAPP(c_List_Oappend(_1778759), _1778761), c_List_Obutlast(_1778759, _1778757)))], (39880 ^ _778908) ^ [_1531096, _1531098, _1531100, _1531102] : [hBOOL(hAPP(hAPP(c_member(_1531096), _1531098), c_Wellfounded_Oacc(_1531096, _1531100))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531096, _1531096)), hAPP(hAPP(c_Product__Type_OPair(_1531096, _1531096), _1531102), _1531098)), _1531100)), -(hBOOL(hAPP(hAPP(c_member(_1531096), _1531102), c_Wellfounded_Oacc(_1531096, _1531100))))], (9632 ^ _778908) ^ [_940313, _940315] : [class_Groups_Oordered__ab__group__add(_940313), 9635 ^ _778908 : [(9642 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940313), c_Groups_Ozero__class_Ozero(_940313)), _940315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940313), hAPP(c_Groups_Ouminus__class_Ouminus(_940313), _940315)), c_Groups_Ozero__class_Ozero(_940313))))], (9636 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940313), hAPP(c_Groups_Ouminus__class_Ouminus(_940313), _940315)), c_Groups_Ozero__class_Ozero(_940313))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940313), c_Groups_Ozero__class_Ozero(_940313)), _940315)))]]], (48991 ^ _778908) ^ [_1760968, _1760970, _1760972, _1760974] : [-(hAPP(hAPP(c_List_Otake(_1760968), _1760970), hAPP(hAPP(c_List_Odrop(_1760968), _1760972), _1760974)) = hAPP(hAPP(c_List_Odrop(_1760968), _1760972), hAPP(hAPP(c_List_Otake(_1760968), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1760970), _1760972)), _1760974)))], (19033 ^ _778908) ^ [_1106756, _1106758] : [c_Int_Oiszero(_1106756, hAPP(c_Int_Onumber__class_Onumber__of(_1106756), c_Int_OBit1(_1106758))), class_Int_Onumber__ring(_1106756), class_Int_Oring__char__0(_1106756)], (39142 ^ _778908) ^ [_1513830, _1513832, _1513834, _1513836] : [class_Groups_Ocomm__monoid__add(_1513830), 39145 ^ _778908 : [(39152 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1513832), _1513834))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513832, _1513830), _1513836), _1513834) = c_Groups_Ozero__class_Ozero(_1513830))], (39146 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513832), _1513834)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513832, _1513830), _1513836), _1513834) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1513830, _1513832, c_Groups_Oplus__class_Oplus(_1513830)), _1513836), c_Groups_Ozero__class_Ozero(_1513830)), _1513834))]]], (14942 ^ _778908) ^ [_1032227, _1032229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032227), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14945 ^ _778908 : [(14952 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032229), 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), _1032229), _1032227))))], (14946 ^ _778908) ^ [] : [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), _1032229), _1032227))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032229), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (9596 ^ _778908) ^ [_939681, _939683, _939685] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _939681), _939683)), _939685) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939681), _939685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939683), _939685)))], (45296 ^ _778908) ^ [_1669266, _1669268] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1669266, tc_HOL_Obool), tc_HOL_Obool)), _1669268), hAPP(c_Set_OPow(_1669266), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669266, tc_HOL_Obool), _1669268)))))], (50102 ^ _778908) ^ [_1786115, _1786117, _1786119] : [-(c_List_Osublist(_1786115, _1786117, _1786119) = hAPP(hAPP(c_List_Omap(tc_prod(_1786115, tc_Nat_Onat), _1786115), c_Product__Type_Ofst(_1786115, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1786115, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1786115, 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(_1786115, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1786115, tc_Nat_Onat))), _1786119)), hAPP(hAPP(c_List_Ozip(_1786115, tc_Nat_Onat), _1786117), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786115)), _1786117))))))], (3370 ^ _778908) ^ [_830699, _830701, _830703, _830705] : [-(c_Com_Ocom_OSemi(_830705, _830701) = c_Com_Ocom_OSemi(_830703, _830699)), _830705 = _830703, _830701 = _830699], (23154 ^ _778908) ^ [_1181715, _1181717, _1181719, _1181721, _1181723] : [hBOOL(hAPP(hAPP(_1181715, _1181717), _1181719)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1181721, _1181723, tc_HOL_Obool), _1181715), hAPP(hAPP(c_Product__Type_OPair(_1181721, _1181723), _1181717), _1181719))))], (6323 ^ _778908) ^ [_880819, _880821, _880823] : [6324 ^ _778908 : [(6325 ^ _778908) ^ [_880869] : [c_Natural_Oevaln(_880819, _880821, _880869, _880823)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_880819), _880821), _880823)))], (10429 ^ _778908) ^ [_954111] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954111)))], (19101 ^ _778908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (51571 ^ _778908) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (30376 ^ _778908) ^ [_1322973, _1322975] : [class_Orderings_Oorder(_1322973), -(c_SetInterval_Oord__class_OatLeastAtMost(_1322973, _1322975, _1322975) = hAPP(hAPP(c_Set_Oinsert(_1322973), _1322975), c_Orderings_Obot__class_Obot(tc_fun(_1322973, tc_HOL_Obool))))], (41147 ^ _778908) ^ [_1560604, _1560606, _1560608] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1560604), hAPP(c_Set_OCollect(_1560604), hAPP(hAPP(c_COMBS(_1560604, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560604), c_fdisj), _1560606)), _1560608)))), 41150 ^ _778908 : [(41153 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560604), hAPP(c_Set_OCollect(_1560604), _1560608))))], (41151 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560604), hAPP(c_Set_OCollect(_1560604), _1560606))))]]], (45414 ^ _778908) ^ [_1672175, _1672177, _1672179] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1672175, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1672175, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1672175, tc_HOL_Obool), _1672177)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1672175, tc_HOL_Obool), _1672179))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1672175, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1672175, tc_HOL_Obool), tc_HOL_Obool)), _1672177), _1672179)))))], (31035 ^ _778908) ^ [_1336058, _1336060] : [-(_1336060 = c_Orderings_Obot__class_Obot(tc_fun(_1336058, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1336058), 31038 ^ [_1336058, _1336060]), _1336060)))], (27745 ^ _778908) ^ [_1270843, _1270845] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1270843, _1270845)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1270845), _1270843)))], (9954 ^ _778908) ^ [_946029, _946031, _946033, _946035] : [class_Rings_Olinordered__semiring__strict(_946029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946029), _946031), _946033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946029), c_Groups_Ozero__class_Ozero(_946029)), _946035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946029), _946035), _946031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946029), _946035), _946033))))], (29893 ^ _778908) ^ [_1313896, _1313898, _1313900, _1313902, _1313904] : [class_Groups_Ocomm__monoid__add(_1313896), class_Groups_Oordered__ab__semigroup__add(_1313896), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313898), _1313900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313898, tc_HOL_Obool)), _1313902), _1313900)), 29911 ^ _778908 : [(29914 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313896), c_Groups_Ozero__class_Ozero(_1313896)), hAPP(_1313904, 29910 ^ [_1313896, _1313898, _1313900, _1313902, _1313904])))], (29912 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313898), 29910 ^ [_1313896, _1313898, _1313900, _1313902, _1313904]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313898, tc_HOL_Obool)), _1313900), _1313902))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313896), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1313898, _1313896), _1313904), _1313902)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1313898, _1313896), _1313904), _1313900))))], (19807 ^ _778908) ^ [_1120157, _1120159, _1120161] : [class_Rings_Olinordered__semidom(_1120157), hAPP(hAPP(c_Power_Opower__class_Opower(_1120157), _1120159), 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(_1120157), _1120161), 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(_1120157), c_Groups_Ozero__class_Ozero(_1120157)), _1120159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120157), c_Groups_Ozero__class_Ozero(_1120157)), _1120161)), -(_1120159 = _1120161)], (35797 ^ _778908) ^ [_1439693, _1439695, _1439697] : [class_Rings_Oring__1(_1439693), -(hAPP(c_Int_Oring__1__class_Oof__int(_1439693), 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), _1439695), _1439697)), 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(_1439693), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1439693), _1439695)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1439693), _1439697)))], (16891 ^ _778908) ^ [_1069499, _1069501] : [class_Groups_Oordered__ab__group__add__abs(_1069499), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069499), hAPP(c_Groups_Ouminus__class_Ouminus(_1069499), _1069501)), hAPP(c_Groups_Oabs__class_Oabs(_1069499), _1069501))))], (3548 ^ _778908) ^ [_833456, _833458, _833460, _833462, _833464, _833466] : [-(c_Hoare__Mirabelle_Opeek__and(_833466, _833462, _833458) = c_Hoare__Mirabelle_Opeek__and(_833464, _833460, _833456)), _833466 = _833464, _833462 = _833460, _833458 = _833456], (30986 ^ _778908) ^ [_1334954, _1334956, _1334958, _1334960, _1334962, _1334964, _1334966] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1334954, _1334956)), hAPP(hAPP(c_Product__Type_OPair(_1334954, _1334956), _1334958), _1334960)), _1334962)), -(hBOOL(hAPP(hAPP(c_member(_1334964), hAPP(hAPP(_1334966, _1334958), _1334960)), hAPP(c_Set_Oimage(tc_prod(_1334954, _1334956), _1334964, hAPP(c_Product__Type_Oprod_Oprod__case(_1334954, _1334956, _1334964), _1334966)), _1334962))))], (11931 ^ _778908) ^ [_978779, _978781, _978783] : [class_Rings_Oordered__cancel__semiring(_978779), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978779), _978781), _978783)), c_Groups_Ozero__class_Ozero(_978779)))), 11936 ^ _778908 : [(11943 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978779), _978781), c_Groups_Ozero__class_Ozero(_978779))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978779), c_Groups_Ozero__class_Ozero(_978779)), _978783))], (11937 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978779), c_Groups_Ozero__class_Ozero(_978779)), _978781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978779), _978783), c_Groups_Ozero__class_Ozero(_978779)))]]], (35722 ^ _778908) ^ [_1437675, _1437677, _1437679, _1437681, _1437683, _1437685] : [-(hAPP(hAPP(c_Fun_Ocomp(_1437675, _1437677, _1437679, hAPP(c_COMBK(_1437677, _1437675), _1437681)), _1437683), _1437685) = _1437681)], (48911 ^ _778908) ^ [_1759234, _1759236] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759234)), hAPP(c_List_Orotate1(_1759234), _1759236)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759234)), _1759236))], (11356 ^ _778908) ^ [_968915, _968917] : [11357 ^ _778908 : [(11360 ^ _778908) ^ [] : [_968917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11358 ^ _778908) ^ [] : [_968915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968915), _968917) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9146 ^ _778908) ^ [_932104, _932106] : [class_Groups_Ocomm__monoid__mult(_932104), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932104), c_Groups_Oone__class_Oone(_932104)), _932106) = _932106)], (9412 ^ _778908) ^ [_936302, _936304, _936306] : [class_Groups_Ogroup__add(_936302), -(hAPP(c_Groups_Ouminus__class_Ouminus(_936302), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936302), _936304), _936306)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936302), hAPP(c_Groups_Ouminus__class_Ouminus(_936302), _936306)), hAPP(c_Groups_Ouminus__class_Ouminus(_936302), _936304)))], (33785 ^ _778908) ^ [_1395135, _1395137, _1395139, _1395141, _1395143, _1395145, _1395147] : [c_Nitpick_Ofold__graph_H(_1395135, _1395137, _1395139, _1395141, _1395143, hAPP(hAPP(_1395139, _1395145), _1395147)), 33790 ^ _778908 : [(33793 ^ _778908) ^ [] : [-(hAPP(hAPP(_1395139, _1395145), _1395147) = _1395141)], (33791 ^ _778908) ^ [] : [-(_1395143 = c_Orderings_Obot__class_Obot(tc_fun(_1395135, tc_HOL_Obool)))]], 33796 ^ _778908 : [(33801 ^ _778908) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1395135, _1395137, _1395139, _1395141, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395135, tc_HOL_Obool)), _1395143), hAPP(hAPP(c_Set_Oinsert(_1395135), 33794 ^ [_1395135, _1395137, _1395139, _1395141, _1395143, _1395145, _1395147]), c_Orderings_Obot__class_Obot(tc_fun(_1395135, tc_HOL_Obool)))), 33795 ^ [_1395135, _1395137, _1395139, _1395141, _1395143, _1395145, _1395147]))], (33799 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395135), 33794 ^ [_1395135, _1395137, _1395139, _1395141, _1395143, _1395145, _1395147]), _1395143)))], (33797 ^ _778908) ^ [] : [-(hAPP(hAPP(_1395139, _1395145), _1395147) = hAPP(hAPP(_1395139, 33794 ^ [_1395135, _1395137, _1395139, _1395141, _1395143, _1395145, _1395147]), 33795 ^ [_1395135, _1395137, _1395139, _1395141, _1395143, _1395145, _1395147]))]]], (14154 ^ _778908) ^ [_1018476, _1018478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018476)), -(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, _1018478, _1018476))))], (35692 ^ _778908) ^ [_1436848, _1436850, _1436852, _1436854, _1436856, _1436858] : [-(hAPP(c_Set_Oimage(_1436848, _1436850, hAPP(c_Fun_Ocomp(_1436852, _1436850, _1436848, _1436854), _1436856)), _1436858) = hAPP(c_Set_Oimage(_1436852, _1436850, _1436854), hAPP(c_Set_Oimage(_1436848, _1436852, _1436856), _1436858)))], (36748 ^ _778908) ^ [_1461216, _1461218] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461216, tc_HOL_Obool)), _1461218), _1461218) = _1461218)], (8248 ^ _778908) ^ [_917083, _917085, _917087, _917089, _917091, _917093] : [-(c_Sum__Type_Osum_Osum__rec(_917083, _917085, _917087, _917089, _917091, hAPP(c_Sum__Type_OInr(_917087, _917083), _917093)) = hAPP(_917091, _917093))], (51475 ^ _778908) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (44561 ^ _778908) ^ [_1650025, _1650027, _1650029, _1650031, _1650033, _1650035] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650025, tc_fun(_1650027, tc_HOL_Obool)), _1650029), _1650031), _1650033)), hBOOL(hAPP(hAPP(c_member(_1650025), _1650035), _1650029)), -(hBOOL(hAPP(hAPP(_1650031, _1650035), _1650033)))], (43189 ^ _778908) ^ [_1618295, _1618297] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1618295, _1618295, _1618295), c_Transitive__Closure_Ortrancl(_1618295, _1618297)), c_Transitive__Closure_Ortrancl(_1618295, _1618297)) = c_Transitive__Closure_Ortrancl(_1618295, _1618297))], (50899 ^ _778908) ^ [_1801863, _1801865] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801863)), hAPP(c_List_Orev(_1801863), _1801865)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801863)), _1801865))], (3380 ^ _778908) ^ [_830848, _830850, _830852, _830854] : [-(c_Com_Ocom_OAss(_830854, _830850) = c_Com_Ocom_OAss(_830852, _830848)), _830854 = _830852, _830850 = _830848], (24077 ^ _778908) ^ [_1199213, _1199215, _1199217, _1199219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199213, tc_HOL_Obool)), _1199215), _1199217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199213, tc_HOL_Obool)), _1199217), _1199219)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1199213, tc_HOL_Obool)), _1199217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1199213, tc_HOL_Obool)), _1199219), _1199215)) = _1199215)], (22314 ^ _778908) ^ [_1165528, _1165530, _1165532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1165528), _1165530)), -(c_Random_Ominus__shift(_1165532, _1165528, _1165530) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1165532), _1165528)), _1165530))], (24905 ^ _778908) ^ [_1215249] : [-(c_Code__Numeral_OSuc__code__numeral(_1215249) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1215249))))], (27671 ^ _778908) ^ [_1269261, _1269263, _1269265, _1269267, _1269269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269261, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1269261, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1269263, _1269261, _1269265), _1269267)), hAPP(c_Set_Oimage(_1269263, _1269261, _1269265), _1269269))), hAPP(c_Set_Oimage(_1269263, _1269261, _1269265), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1269263, tc_HOL_Obool)), _1269267), _1269269)))))], (43131 ^ _778908) ^ [_1616157, _1616159, _1616161, _1616163] : [-(c_Transitive__Closure_Otrancl(_1616157, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1616157, _1616157)), hAPP(hAPP(c_Product__Type_OPair(_1616157, _1616157), _1616159), _1616161)), _1616163)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616157, _1616157), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1616157, _1616163)), hAPP(c_Set_OCollect(tc_prod(_1616157, _1616157)), hAPP(c_Product__Type_Oprod_Oprod__case(_1616157, _1616157, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1616157, tc_fun(_1616157, tc_HOL_Obool), tc_fun(_1616157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1616157, tc_HOL_Obool), tc_fun(_1616157, tc_HOL_Obool)), _1616157), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1616157)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1616157), c_fconj), hAPP(hAPP(c_COMBC(_1616157, tc_fun(tc_prod(_1616157, _1616157), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1616157, _1616157), tc_fun(tc_fun(tc_prod(_1616157, _1616157), tc_HOL_Obool), tc_HOL_Obool), _1616157), c_member(tc_prod(_1616157, _1616157))), hAPP(hAPP(c_COMBC(_1616157, _1616157, tc_prod(_1616157, _1616157)), c_Product__Type_OPair(_1616157, _1616157)), _1616159))), c_Transitive__Closure_Ortrancl(_1616157, _1616163))))), hAPP(hAPP(c_COMBC(_1616157, tc_fun(tc_prod(_1616157, _1616157), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1616157, _1616157), tc_fun(tc_fun(tc_prod(_1616157, _1616157), tc_HOL_Obool), tc_HOL_Obool), _1616157), c_member(tc_prod(_1616157, _1616157))), hAPP(c_Product__Type_OPair(_1616157, _1616157), _1616161))), c_Transitive__Closure_Ortrancl(_1616157, _1616163)))))))], (46613 ^ _778908) ^ [_1700266, _1700268, _1700270] : [class_Orderings_Olinorder(_1700266), hBOOL(hAPP(c_Finite__Set_Ofinite(_1700266), _1700268)), -(c_List_Olinorder__class_Osorted__list__of__set(_1700266, hAPP(hAPP(c_Set_Oinsert(_1700266), _1700270), _1700268)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1700266, _1700266, c_COMBI(_1700266)), _1700270), c_List_Olinorder__class_Osorted__list__of__set(_1700266, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1700266, tc_HOL_Obool)), _1700268), hAPP(hAPP(c_Set_Oinsert(_1700266), _1700270), c_Orderings_Obot__class_Obot(tc_fun(_1700266, tc_HOL_Obool)))))))], (24869 ^ _778908) ^ [_1214637] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1214637)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1214637))], (21309 ^ _778908) ^ [_1147061, _1147063, _1147065, _1147067] : [class_Fields_Ofield(_1147061), -(_1147063 = c_Groups_Ozero__class_Ozero(_1147061)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1147061), _1147065), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147061), _1147067), _1147063)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147061), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1147061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147061), _1147063), _1147065)), _1147067)), _1147063))], (7075 ^ _778908) ^ [_897235, _897237] : [-(_897235 = hAPP(c_Option_Ooption_OSome(_897237), 7076 ^ [_897235, _897237])), -(_897235 = c_Option_Ooption_ONone(_897237))], (44761 ^ _778908) ^ [_1655318, _1655320, _1655322, _1655324, _1655326, _1655328] : [class_Complete__Lattice_Ocomplete__lattice(_1655318), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655320, tc_fun(_1655322, _1655318)), _1655324), _1655326), _1655328) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655320, _1655318), _1655324), hAPP(hAPP(c_COMBC(_1655320, _1655322, _1655318), _1655326), _1655328)))], (2748 ^ _778908) ^ [_820576, _820578, _820580, _820582] : [-(c_HOL_OLet(_820582, _820578) = c_HOL_OLet(_820580, _820576)), _820582 = _820580, _820578 = _820576], (32425 ^ _778908) ^ [_1368470, _1368472, _1368474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368470)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1368472), _1368474)), 32432 ^ _778908 : [(32433 ^ _778908) ^ [_1368666] : [32435 ^ _778908 : [(32441 ^ _778908) ^ [] : [-(_1368666 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 32437 ^ [_1368470, _1368472, _1368474, _1368666]), 32434 ^ [_1368470, _1368472, _1368474, _1368666]))], (32439 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32437 ^ [_1368470, _1368472, _1368474, _1368666]), _1368474)))], (32436 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32434 ^ [_1368470, _1368472, _1368474, _1368666]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1368470))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368666), _1368472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1368666), _1368470)), _1368472)))]]], (50877 ^ _778908) ^ [_1801381, _1801383] : [-(c_List_Oconcat(_1801381, _1801383) = hAPP(c_List_Ofoldl(tc_List_Olist(_1801381), tc_List_Olist(_1801381), c_List_Oappend(_1801381), c_List_Olist_ONil(_1801381)), _1801383))], (37204 ^ _778908) ^ [_1471918, _1471920, _1471922] : [class_Orderings_Oorder(_1471918), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471918, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1471918), _1471920)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1471918, _1471920, _1471922)) = c_Orderings_Obot__class_Obot(tc_fun(_1471918, tc_HOL_Obool)))], (12966 ^ _778908) ^ [_997398, _997400, _997402, _997404] : [class_Rings_Olinordered__ring__strict(_997398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997398), _997400), c_Groups_Ozero__class_Ozero(_997398))), 12973 ^ _778908 : [(12980 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997398), _997404), _997402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997398), _997400), _997402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997398), _997400), _997404))))], (12974 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997398), _997400), _997402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997398), _997400), _997404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997398), _997404), _997402)))]]], (51483 ^ _778908) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (45342 ^ _778908) ^ [_1670584] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1670584, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1670584, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1670584, tc_HOL_Obool)))], (19847 ^ _778908) ^ [_1120798, _1120800, _1120802] : [class_Rings_Olinordered__idom(_1120798), 19850 ^ _778908 : [(19859 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120798), hAPP(hAPP(c_Power_Opower__class_Opower(_1120798), _1120800), 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(_1120798), _1120802), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1120798)), _1120800 = c_Groups_Ozero__class_Ozero(_1120798), _1120802 = c_Groups_Ozero__class_Ozero(_1120798)], (19851 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120798), hAPP(hAPP(c_Power_Opower__class_Opower(_1120798), _1120800), 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(_1120798), _1120802), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1120798), 19854 ^ _778908 : [(19857 ^ _778908) ^ [] : [-(_1120802 = c_Groups_Ozero__class_Ozero(_1120798))], (19855 ^ _778908) ^ [] : [-(_1120800 = c_Groups_Ozero__class_Ozero(_1120798))]]]]], (42134 ^ _778908) ^ [_1591933, _1591935, _1591937, _1591939] : [42136 ^ _778908 : [(42139 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1591935, hAPP(_1591937, 42135 ^ [_1591933, _1591935, _1591937, _1591939]))), hAPP(_1591935, 42135 ^ [_1591933, _1591935, _1591937, _1591939])))], (42137 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1591933, 42135 ^ [_1591933, _1591935, _1591937, _1591939])))]], -(c_Wellfounded_Owf(_1591939, hAPP(c_Set_OCollect(tc_prod(_1591939, _1591939)), hAPP(c_Product__Type_Oprod_Oprod__case(_1591939, _1591939, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1591939, tc_HOL_Obool), tc_fun(_1591939, tc_HOL_Obool), _1591939), hAPP(c_COMBS(_1591939, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1591939), c_fconj), _1591933))), hAPP(hAPP(c_COMBC(_1591939, tc_fun(_1591939, _1591939), tc_fun(_1591939, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1591939, tc_HOL_Obool), tc_fun(tc_fun(_1591939, _1591939), tc_fun(_1591939, tc_HOL_Obool)), _1591939), c_COMBB(_1591939, tc_HOL_Obool, _1591939)), c_fequal)), _1591937))))))], (41706 ^ _778908) ^ [_1580595, _1580597] : [-(hAPP(c_Set_Oimage(_1580595, _1580595, c_Fun_Oid(_1580595)), _1580597) = _1580597)], (7448 ^ _778908) ^ [_903394, _903396] : [class_Groups_Olinordered__ab__group__add(_903394), 7451 ^ _778908 : [(7458 ^ _778908) ^ [] : [_903396 = c_Groups_Ozero__class_Ozero(_903394), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903394), _903396), _903396) = c_Groups_Ozero__class_Ozero(_903394))], (7452 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903394), _903396), _903396) = c_Groups_Ozero__class_Ozero(_903394), -(_903396 = c_Groups_Ozero__class_Ozero(_903394))]]], (29130 ^ _778908) ^ [_1298774, _1298776, _1298778, _1298780] : [hAPP(c_Set_Oimage(_1298774, _1298776, _1298778), c_Orderings_Otop__class_Otop(tc_fun(_1298774, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1298776, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298776, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298776, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1298774, _1298776, _1298778), _1298780))), hAPP(c_Set_Oimage(_1298774, _1298776, _1298778), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1298774, tc_HOL_Obool)), _1298780)))))], (37156 ^ _778908) ^ [_1470798, _1470800, _1470802, _1470804] : [class_Orderings_Oorder(_1470798), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470798, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1470798, _1470800, _1470802)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1470798, _1470802), _1470804)) = c_Orderings_Obot__class_Obot(tc_fun(_1470798, tc_HOL_Obool)))], (7282 ^ _778908) ^ [_900740, _900742] : [class_Groups_Olinordered__ab__group__add(_900740), 7285 ^ _778908 : [(7292 ^ _778908) ^ [] : [_900742 = c_Groups_Ozero__class_Ozero(_900740), -(c_Groups_Ozero__class_Ozero(_900740) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900740), _900742), _900742))], (7286 ^ _778908) ^ [] : [c_Groups_Ozero__class_Ozero(_900740) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900740), _900742), _900742), -(_900742 = c_Groups_Ozero__class_Ozero(_900740))]]], (43431 ^ _778908) ^ [_1624038, _1624040, _1624042, _1624044] : [c_Wellfounded_Oacyclic(_1624038, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1624038, _1624038)), hAPP(hAPP(c_Product__Type_OPair(_1624038, _1624038), _1624040), _1624042)), _1624044)), 43434 ^ _778908 : [(43437 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624038, _1624038)), hAPP(hAPP(c_Product__Type_OPair(_1624038, _1624038), _1624042), _1624040)), c_Transitive__Closure_Ortrancl(_1624038, _1624044)))], (43435 ^ _778908) ^ [] : [-(c_Wellfounded_Oacyclic(_1624038, _1624044))]]], (9542 ^ _778908) ^ [_938388, _938390, _938392, _938394] : [class_Rings_Ocomm__semiring__1(_938388), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938388), _938390), _938392)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938388), _938394), _938392)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938388), _938390), _938394)), _938392))], (4714 ^ _778908) ^ [_851881, _851883, _851885, _851887, _851889, _851891] : [-(c_Finite__Set_Ofold(_851891, _851887, _851883) = c_Finite__Set_Ofold(_851889, _851885, _851881)), _851891 = _851889, _851887 = _851885, _851883 = _851881], (21047 ^ _778908) ^ [_1142307, _1142309, _1142311, _1142313] : [class_Fields_Olinordered__field(_1142307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142307), c_Groups_Ozero__class_Ozero(_1142307)), _1142309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142307), _1142311), _1142309)), _1142313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142307), _1142311), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142307), _1142313), _1142309))))], (13168 ^ _778908) ^ [_1000918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1000918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1000918)))], (32706 ^ _778908) ^ [_1374231, _1374233, _1374235, _1374237, _1374239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1374231, _1374233)), hAPP(_1374231, _1374235))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1374237, _1374237)), hAPP(hAPP(c_Product__Type_OPair(_1374237, _1374237), _1374233), _1374235)), c_Wellfounded_Omlex__prod(_1374237, _1374231, _1374239))))], (37878 ^ _778908) ^ [_1486921, _1486923, _1486925, _1486927, _1486929, _1486931, _1486933] : [c_Equiv__Relations_Oequiv(_1486921, _1486923, _1486925), c_Equiv__Relations_Ocongruent(_1486921, tc_fun(_1486927, tc_HOL_Obool), _1486925, _1486929), hBOOL(hAPP(hAPP(c_member(tc_fun(_1486921, tc_HOL_Obool)), _1486931), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486921), _1486923), _1486925))), 37892 ^ _778908 : [(37895 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1486927, tc_HOL_Obool)), hAPP(_1486929, 37891 ^ [_1486921, _1486923, _1486925, _1486927, _1486929, _1486931, _1486933])), _1486933))], (37893 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486921), 37891 ^ [_1486921, _1486923, _1486925, _1486927, _1486929, _1486931, _1486933]), _1486923)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486927, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486921, tc_fun(_1486927, tc_HOL_Obool)), _1486931), _1486929)), _1486933)))], (32615 ^ _778908) ^ [_1372332, _1372334, _1372336, _1372338, _1372340] : [class_Groups_Oordered__comm__monoid__add(_1372332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372334), _1372336)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372334, tc_HOL_Obool)), _1372338), _1372336)), 32629 ^ _778908 : [(32632 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372332), c_Groups_Ozero__class_Ozero(_1372332)), hAPP(_1372340, 32628 ^ [_1372332, _1372334, _1372336, _1372338, _1372340])))], (32630 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372334), 32628 ^ [_1372332, _1372334, _1372336, _1372338, _1372340]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372334, tc_HOL_Obool)), _1372336), _1372338))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372332), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372334, _1372332), _1372340), _1372338)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372334, _1372332), _1372340), _1372336))))], (28599 ^ _778908) ^ [_1287164, _1287166] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1287164)), _1287166) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1287164, _1287166))], (28409 ^ _778908) ^ [_1283583, _1283585, _1283587] : [class_Lattices_Osemilattice__sup(_1283583), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283583), _1283585), _1283587)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283583), _1283587), _1283585) = _1283587)], (51235 ^ _778908) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (15916 ^ _778908) ^ [_1050552, _1050554, _1050556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050552), _1050554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050552), _1050556)), 15923 ^ _778908 : [(15930 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050554), _1050556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050554), _1050552)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050556), _1050552))))], (15924 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050554), _1050552)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050556), _1050552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050554), _1050556)))]]], (25773 ^ _778908) ^ [_1231588, _1231590] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231588), _1231590)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231588)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231590))))], (50250 ^ _778908) ^ [_1788790, _1788792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1788790), _1788792)), -(c_List_Oupt(_1788790, hAPP(c_Nat_OSuc, _1788792)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1788790, _1788792)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1788792), c_List_Olist_ONil(tc_Nat_Onat))))], (19727 ^ _778908) ^ [_1118725, _1118727] : [class_Groups_Omonoid__mult(_1118725), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1118725), _1118727), 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(_1118725), _1118727), _1118727))], (5933 ^ _778908) ^ [_873494, _873496, _873498, _873500, _873502, _873504, _873506, _873508, _873510, _873512, _873514] : [-(c_Com_Ocom_Ocom__case(_873494, _873496, _873498, _873500, _873502, _873504, _873506, _873508, _873510, c_Com_Ocom_OAss(_873512, _873514)) = hAPP(hAPP(_873498, _873512), _873514))], (51503 ^ _778908) ^ [_1811848, _1811850] : [-(class_Finite__Set_Ofinite(tc_sum(_1811848, _1811850))), class_Finite__Set_Ofinite(_1811848), class_Finite__Set_Ofinite(_1811850)], (6355 ^ _778908) ^ [_881386, _881388, _881390, _881392, _881394, _881396] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_881386, _881388, _881390), _881392, _881394, _881396), 6360 ^ _778908 : [(6363 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_881388, _881392, _881394, _881396))], (6361 ^ _778908) ^ [] : [-(hBOOL(hAPP(_881386, _881392)))]], 6364 ^ _778908 : [(6367 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_881390, _881392, _881394, _881396))], (6365 ^ _778908) ^ [] : [hBOOL(hAPP(_881386, _881392))]]], (51337 ^ _778908) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (10 ^ _778908) ^ [_779031, _779033, _779035] : [-(_779035 = _779031), _779035 = _779033, _779033 = _779031], (1752 ^ _778908) ^ [_803682, _803684] : [-(class_Rings_Osemiring(_803682)), _803684 = _803682, class_Rings_Osemiring(_803684)], (42213 ^ _778908) ^ [_1593781, _1593783, _1593785, _1593787] : [42214 ^ _778908 : [(42215 ^ _778908) ^ [_1593856] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593785, _1593781)), hAPP(hAPP(c_Product__Type_OPair(_1593785, _1593781), _1593856), _1593783)), _1593787))]], -(hBOOL(hAPP(hAPP(c_member(_1593781), _1593783), hAPP(c_Relation_ORange(_1593785, _1593781), _1593787))))], (1822 ^ _778908) ^ [_804557, _804559] : [-(class_Rings_Odvd(_804557)), _804559 = _804557, class_Rings_Odvd(_804559)], (48951 ^ _778908) ^ [_1760104, _1760106, _1760108, _1760110, _1760112] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1760104, _1760106)), _1760108), hAPP(hAPP(c_List_Ozip(_1760104, _1760106), _1760110), _1760112)) = hAPP(hAPP(c_List_Ozip(_1760104, _1760106), hAPP(hAPP(c_List_Odrop(_1760104), _1760108), _1760110)), hAPP(hAPP(c_List_Odrop(_1760106), _1760108), _1760112)))], (25639 ^ _778908) ^ [_1229339, _1229341] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229339), _1229341))), 25640 ^ _778908 : [(25641 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229339), _1229341)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229341), _1229339)))], (25647 ^ _778908) ^ [] : [_1229339 = _1229341]]], (7576 ^ _778908) ^ [_905867, _905869] : [-(_905867 = c_Option_Ooption_ONone(_905869)), -(_905867 = hAPP(c_Option_Ooption_OSome(_905869), 7579 ^ [_905867, _905869]))], (24915 ^ _778908) ^ [_1215467, _1215469] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1215467, _1215469) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1215467), hAPP(c_Code__Numeral_Onat__of, _1215469))))], (18827 ^ _778908) ^ [_1103246, _1103248] : [class_Int_Onumber__ring(_1103246), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103246), c_Groups_Oone__class_Oone(_1103246)), hAPP(c_Int_Onumber__class_Onumber__of(_1103246), _1103248)) = hAPP(c_Int_Onumber__class_Onumber__of(_1103246), 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), _1103248))))], (27602 ^ _778908) ^ [_1267785, _1267787, _1267789] : [class_Groups_Oordered__ab__group__add(_1267785), -(hAPP(c_Set_Oimage(_1267785, _1267785, c_Groups_Ouminus__class_Ouminus(_1267785)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1267785, _1267787), _1267789)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1267785, hAPP(c_Groups_Ouminus__class_Ouminus(_1267785), _1267789), hAPP(c_Groups_Ouminus__class_Ouminus(_1267785), _1267787)))], (23030 ^ _778908) ^ [_1179737, _1179739] : [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), _1179737), _1179739))), 23033 ^ _778908 : [(23042 ^ _778908) ^ [] : [-(c_Divides_OposDivAlg(_1179737, _1179739) = hAPP(c_Divides_Oadjust(_1179739), c_Divides_OposDivAlg(_1179737, 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)))), _1179739)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179737), _1179739))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179739), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23034 ^ _778908) ^ [] : [23035 ^ _778908 : [(23038 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179739), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23036 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179737), _1179739))]], -(c_Divides_OposDivAlg(_1179737, _1179739) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179737))]]], (11548 ^ _778908) ^ [_972097, _972099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972097), _972099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972097), _972099)))], (8480 ^ _778908) ^ [] : [-(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)))], (11631 ^ _778908) ^ [_973540, _973542, _973544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973540), _973542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973540), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973542), _973544))))], (17529 ^ _778908) ^ [_1081664, _1081666, _1081668, _1081670] : [class_Groups_Ocomm__monoid__mult(_1081664), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1081664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081664), _1081666), _1081668)), _1081670) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081664), hAPP(hAPP(c_Power_Opower__class_Opower(_1081664), _1081666), _1081670)), hAPP(hAPP(c_Power_Opower__class_Opower(_1081664), _1081668), _1081670)))], (20813 ^ _778908) ^ [_1137924, _1137926, _1137928, _1137930] : [class_Fields_Ofield(_1137924), -(_1137926 = c_Groups_Ozero__class_Ozero(_1137924)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1137924), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137924), _1137928), _1137926)), _1137930) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137924), hAPP(hAPP(c_Power_Opower__class_Opower(_1137924), _1137928), _1137930)), hAPP(hAPP(c_Power_Opower__class_Opower(_1137924), _1137926), _1137930)))], (46671 ^ _778908) ^ [_1701753, _1701755, _1701757] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701753)), _1701755) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701753)), _1701757)), _1701755 = _1701757], (17975 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (47208 ^ _778908) ^ [_1717272, _1717274, _1717276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1717272, tc_HOL_Obool)), hAPP(c_List_Oset(_1717272), c_List_Osublist(_1717272, _1717274, _1717276))), hAPP(c_List_Oset(_1717272), _1717274))))], (29050 ^ _778908) ^ [_1297161, _1297163, _1297165, _1297167, _1297169] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297161, tc_fun(_1297163, tc_HOL_Obool)), _1297165), hAPP(hAPP(c_COMBS(_1297161, tc_fun(_1297163, tc_HOL_Obool), tc_fun(_1297163, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297163, tc_HOL_Obool), tc_fun(tc_fun(_1297163, tc_HOL_Obool), tc_fun(_1297163, tc_HOL_Obool)), _1297161), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297163, tc_HOL_Obool))), _1297167)), _1297169)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297163, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297161, tc_fun(_1297163, tc_HOL_Obool)), _1297165), _1297167)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297161, tc_fun(_1297163, tc_HOL_Obool)), _1297165), _1297169)))], (44296 ^ _778908) ^ [_1645082, _1645084, _1645086, _1645088, _1645090] : [c_Finite__Set_Ofolding__one(_1645082, _1645084, _1645086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645082), _1645088)), -(hBOOL(hAPP(hAPP(c_member(_1645082), _1645090), _1645088))), -(hAPP(_1645086, hAPP(hAPP(c_Set_Oinsert(_1645082), _1645090), _1645088)) = hAPP(hAPP(c_Finite__Set_Ofold(_1645082, _1645082, _1645084), _1645090), _1645088))], (7739 ^ _778908) ^ [_908348, _908350, _908352, _908354] : [class_Groups_Oordered__cancel__ab__semigroup__add(_908348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908348), _908350), _908352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908348), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908348), _908354), _908350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908348), _908354), _908352))))], (40339 ^ _778908) ^ [_1543732, _1543734, _1543736, _1543738, _1543740, _1543742] : [class_Groups_Ocomm__monoid__mult(_1543732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543734), _1543736)), 40349 ^ _778908 : [(40352 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543738), hAPP(_1543740, 40348 ^ [_1543732, _1543734, _1543736, _1543738, _1543740, _1543742])))], (40350 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543734), 40348 ^ [_1543732, _1543734, _1543736, _1543738, _1543740, _1543742]), _1543736)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1543734, _1543732), hAPP(hAPP(c_COMBS(_1543734, tc_fun(_1543738, tc_HOL_Obool), _1543732), hAPP(hAPP(c_COMBB(tc_fun(_1543738, _1543732), tc_fun(tc_fun(_1543738, tc_HOL_Obool), _1543732), _1543734), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1543738, _1543732)), _1543742)), _1543740)), _1543736) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1543734, _1543738), _1543732), hAPP(c_Product__Type_Oprod_Oprod__case(_1543734, _1543738, _1543732), _1543742)), hAPP(hAPP(c_Product__Type_OSigma(_1543734, _1543738), _1543736), _1543740)))], (50025 ^ _778908) ^ [_1783914, _1783916, _1783918, _1783920] : [-(c_List_Omap__filter(_1783914, _1783916, _1783918, _1783920) = hAPP(hAPP(c_List_Omap(_1783914, _1783916), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1783916), _1783916, _1783914, c_Option_Othe(_1783916)), _1783918)), hAPP(c_List_Ofilter(_1783914, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1783914), c_fNot), hAPP(hAPP(c_COMBC(_1783914, tc_Option_Ooption(_1783916), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1783916), tc_fun(tc_Option_Ooption(_1783916), tc_HOL_Obool), _1783914), c_fequal), _1783918)), c_Option_Ooption_ONone(_1783916)))), _1783920)))], (46895 ^ _778908) ^ [_1707437, _1707439] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1707437), _1707439)), -(c_Nitpick_Ocard_H(_1707437, _1707439) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707437)), c_Hilbert__Choice_OEps(tc_List_Olist(_1707437), hAPP(hAPP(c_COMBS(tc_List_Olist(_1707437), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1707437)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707437), tc_fun(_1707437, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1707437, tc_HOL_Obool), tc_fun(tc_fun(_1707437, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1707437)), c_fequal), c_List_Oset(_1707437))), _1707439))), c_List_Odistinct(_1707437)))))], (5360 ^ _778908) ^ [_861788, _861790, _861792, _861794] : [-(c_List_Olast(_861794, _861790) = c_List_Olast(_861792, _861788)), _861794 = _861792, _861790 = _861788], (40134 ^ _778908) ^ [_1537803, _1537805, _1537807, _1537809, _1537811] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1537803, _1537805), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1537803, tc_HOL_Obool)), _1537807), _1537809)), hAPP(c_COMBK(tc_fun(_1537805, tc_HOL_Obool), _1537803), _1537811)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537803, _1537805), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1537803, _1537805), _1537807), hAPP(c_COMBK(tc_fun(_1537805, tc_HOL_Obool), _1537803), _1537811))), hAPP(hAPP(c_Product__Type_OSigma(_1537803, _1537805), _1537809), hAPP(c_COMBK(tc_fun(_1537805, tc_HOL_Obool), _1537803), _1537811))))], (27464 ^ _778908) ^ [_1264685, _1264687, _1264689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264685)), 27467 ^ _778908 : [(27468 ^ _778908) ^ [_1264819] : [27470 ^ _778908 : [(27476 ^ _778908) ^ [] : [-(_1264819 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27472 ^ [_1264685, _1264687, _1264689, _1264819]), 27469 ^ [_1264685, _1264687, _1264689, _1264819]))], (27474 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27472 ^ [_1264685, _1264687, _1264689, _1264819]), _1264687)))], (27471 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27469 ^ [_1264685, _1264687, _1264689, _1264819]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1264685))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264689), _1264819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264689), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1264819), _1264685))))]]], (13198 ^ _778908) ^ [_1001377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001377)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1001377)) = _1001377)], (44947 ^ _778908) ^ [_1661446, _1661448, _1661450, _1661452, _1661454] : [_1661446 = c_Orderings_Obot__class_Obot(tc_fun(_1661448, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661450, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661448, tc_fun(_1661450, tc_HOL_Obool)), _1661446), _1661452)), _1661454) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661450, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1661450, tc_HOL_Obool))), _1661454))], (32343 ^ _778908) ^ [_1366985, _1366987] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1366985), 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)))), _1366987))), 32346 ^ _778908 : [(32349 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1366985), _1366987))], (32347 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1366987), _1366985)))]]], (25111 ^ _778908) ^ [_1220180, _1220182, _1220184, _1220186, _1220188, _1220190, _1220192] : [hBOOL(hAPP(hAPP(_1220180, hAPP(c_Product__Type_Osnd(_1220182, _1220184), _1220186)), hAPP(c_Product__Type_Ofst(_1220182, _1220184), _1220186))), 25118 ^ _778908 : [(25121 ^ _778908) ^ [] : [hBOOL(hAPP(_1220188, hAPP(hAPP(_1220190, 25116 ^ [_1220180, _1220182, _1220184, _1220186, _1220188, _1220190, _1220192]), 25117 ^ [_1220180, _1220182, _1220184, _1220186, _1220188, _1220190, _1220192])))], (25119 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1220180, 25117 ^ [_1220180, _1220182, _1220184, _1220186, _1220188, _1220190, _1220192]), 25116 ^ [_1220180, _1220182, _1220184, _1220186, _1220188, _1220190, _1220192])))]], -(hBOOL(hAPP(_1220188, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1220182, _1220184, _1220192), _1220190), _1220186))))], (30141 ^ _778908) ^ [_1318942, _1318944, _1318946, _1318948] : [30143 ^ _778908 : [(30146 ^ _778908) ^ [] : [hAPP(_1318948, 30142 ^ [_1318942, _1318944, _1318946, _1318948]) = c_Orderings_Obot__class_Obot(tc_fun(_1318944, tc_HOL_Obool))], (30144 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318942), 30142 ^ [_1318942, _1318944, _1318946, _1318948]), _1318946)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318942, tc_fun(_1318944, tc_HOL_Obool)), _1318946), _1318948) = c_Orderings_Obot__class_Obot(tc_fun(_1318944, tc_HOL_Obool)))], (26501 ^ _778908) ^ [_1245716] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1245716), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1245716 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16388 ^ _778908) ^ [_1060604, _1060606] : [-(_1060604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1060604), _1060606) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060604), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1060606)))], (1542 ^ _778908) ^ [_801057, _801059] : [-(class_Rings_Olinordered__semidom(_801057)), _801059 = _801057, class_Rings_Olinordered__semidom(_801059)], (49067 ^ _778908) ^ [_1762947, _1762949, _1762951, _1762953] : [-(hAPP(c_List_Orotate1(_1762949), hAPP(hAPP(c_List_Olist_OCons(_1762949), _1762951), _1762953)) = hAPP(hAPP(c_List_Oappend(_1762949), _1762953), hAPP(hAPP(c_List_Olist_OCons(_1762949), _1762951), c_List_Olist_ONil(_1762949))))], (43439 ^ _778908) ^ [_1624233, _1624235, _1624237, _1624239] : [-(c_Wellfounded_Oacyclic(_1624233, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1624233, _1624233)), hAPP(hAPP(c_Product__Type_OPair(_1624233, _1624233), _1624235), _1624237)), _1624239))), c_Wellfounded_Oacyclic(_1624233, _1624239), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624233, _1624233)), hAPP(hAPP(c_Product__Type_OPair(_1624233, _1624233), _1624237), _1624235)), c_Transitive__Closure_Ortrancl(_1624233, _1624239))))], (27504 ^ _778908) ^ [_1265557, _1265559, _1265561, _1265563] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1265557), _1265559)), 27507 ^ _778908 : [(27508 ^ _778908) ^ [_1265711] : [27510 ^ _778908 : [(27516 ^ _778908) ^ [] : [-(_1265711 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27512 ^ [_1265557, _1265559, _1265561, _1265563, _1265711]), 27509 ^ [_1265557, _1265559, _1265561, _1265563, _1265711]))], (27514 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27512 ^ [_1265557, _1265559, _1265561, _1265563, _1265711]), _1265561)))], (27511 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27509 ^ [_1265557, _1265559, _1265561, _1265563, _1265711]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1265559))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1265557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1265711), _1265563))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1265557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1265711), _1265559)), _1265563))))]]], (5744 ^ _778908) ^ [_867606, _867608, _867610, _867612, _867614, _867616] : [-(c_COMBS(_867616, _867612, _867608) = c_COMBS(_867614, _867610, _867606)), _867616 = _867614, _867612 = _867610, _867608 = _867606], (35448 ^ _778908) ^ [_1431411] : [-(hAPP(c_Set_OPow(_1431411), c_Orderings_Obot__class_Obot(tc_fun(_1431411, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1431411, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1431411, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1431411, tc_HOL_Obool), tc_HOL_Obool))))], (6242 ^ _778908) ^ [_879386, _879388, _879390, _879392, _879394] : [c_Com_Ocom_OCond(_879386, _879388, _879390) = c_Com_Ocom_OSemi(_879392, _879394)], (38972 ^ _778908) ^ [_1510181, _1510183, _1510185, _1510187, _1510189, _1510191] : [c_Fun_Oinj__on(_1510181, _1510183, _1510185, _1510187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510181, tc_HOL_Obool)), _1510189), _1510187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510181, tc_HOL_Obool)), _1510191), _1510187)), -(hAPP(c_Set_Oimage(_1510181, _1510183, _1510185), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510181, tc_HOL_Obool)), _1510189), _1510191)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510183, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510181, _1510183, _1510185), _1510189)), hAPP(c_Set_Oimage(_1510181, _1510183, _1510185), _1510191)))], (50351 ^ _778908) ^ [_1790656, _1790658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790656), _1790658)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1790656, _1790658)) = _1790656)], (13664 ^ _778908) ^ [_1009234, _1009236, _1009238, _1009240] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009234), _1009236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009238), _1009236)), _1009240)) = 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), _1009234), _1009238)), _1009236)), _1009240))], (24941 ^ _778908) ^ [_1216064, _1216066, _1216068, _1216070, _1216072, _1216074, _1216076] : [_1216064 = _1216066, -(hAPP(c_Sum__Type_Osum_Osum__case(_1216068, _1216070, _1216072, _1216074, _1216076), _1216064) = hAPP(c_Sum__Type_Osum_Osum__case(_1216068, _1216070, _1216072, _1216074, _1216076), _1216066))], (29990 ^ _778908) ^ [_1315878, _1315880, _1315882] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315878, tc_HOL_Obool)), _1315880), _1315882) = c_Orderings_Obot__class_Obot(tc_fun(_1315878, tc_HOL_Obool))), _1315880 = c_Orderings_Obot__class_Obot(tc_fun(_1315878, tc_HOL_Obool)), _1315882 = c_Orderings_Obot__class_Obot(tc_fun(_1315878, tc_HOL_Obool))], (16442 ^ _778908) ^ [_1061404, _1061406, _1061408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1061404)), 16448 ^ _778908 : [(16451 ^ _778908) ^ [] : [hBOOL(hAPP(_1061406, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16447 ^ [_1061404, _1061406, _1061408]), _1061404)))], (16449 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1061406, 16447 ^ [_1061404, _1061406, _1061408])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1061408)), 16456 ^ _778908 : [(16457 ^ _778908) ^ [_1061693] : [hBOOL(hAPP(_1061406, _1061693)), -(hBOOL(hAPP(_1061406, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1061693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1061408), _1061404)))))]]], (28533 ^ _778908) ^ [_1285749, _1285751, _1285753, _1285755] : [class_Orderings_Olinorder(_1285749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285749), _1285751), _1285753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285749), _1285753), _1285755)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285749, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1285749, _1285751), _1285753)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1285749, _1285753), _1285755)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1285749, _1285751), _1285755))], (46986 ^ _778908) ^ [_1711292, _1711294, _1711296, _1711298, _1711300, _1711302] : [-(hAPP(hAPP(c_List_Ozip(_1711292, _1711294), hAPP(hAPP(c_List_Olist_OCons(_1711292), _1711296), _1711298)), hAPP(hAPP(c_List_Olist_OCons(_1711294), _1711300), _1711302)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1711292, _1711294)), hAPP(hAPP(c_Product__Type_OPair(_1711292, _1711294), _1711296), _1711300)), hAPP(hAPP(c_List_Ozip(_1711292, _1711294), _1711298), _1711302)))], (46226 ^ _778908) ^ [_1691019] : [-(hAPP(c_Option_Omap(_1691019, _1691019), c_Fun_Oid(_1691019)) = c_Fun_Oid(tc_Option_Ooption(_1691019)))], (16026 ^ _778908) ^ [_1052670, _1052672, _1052674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052674), _1052672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052670), _1052672)), _1052674)))], (13228 ^ _778908) ^ [_1001857, _1001859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001857), _1001859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1001857), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1001859)))], (37584 ^ _778908) ^ [_1480284, _1480286, _1480288] : [class_Orderings_Olinorder(_1480284), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480284), _1480286)), -(_1480286 = c_Orderings_Obot__class_Obot(tc_fun(_1480284, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480284), _1480288)), -(_1480288 = c_Orderings_Obot__class_Obot(tc_fun(_1480284, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480284, tc_HOL_Obool)), _1480286), _1480288) = c_Orderings_Obot__class_Obot(tc_fun(_1480284, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1480284, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480284, tc_HOL_Obool)), _1480286), _1480288)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1480284), c_Big__Operators_Olinorder__class_OMin(_1480284, _1480286)), c_Big__Operators_Olinorder__class_OMin(_1480284, _1480288)))], (5398 ^ _778908) ^ [_862341, _862343, _862345, _862347, _862349, _862351] : [-(c_Divides_Odiv__class_Omod(_862351, _862347, _862343) = c_Divides_Odiv__class_Omod(_862349, _862345, _862341)), _862351 = _862349, _862347 = _862345, _862343 = _862341], (18633 ^ _778908) ^ [_1100060, _1100062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100060)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100062))), 18636 ^ _778908 : [(18637 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100060), _1100062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1100062)))], (18643 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100060), _1100062)))]]], (14780 ^ _778908) ^ [_1029627, _1029629, _1029631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029627), _1029629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029631), _1029629)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029631), _1029627))))], (10114 ^ _778908) ^ [_948855, _948857] : [10115 ^ _778908 : [(10118 ^ _778908) ^ [] : [_948855 = _948857], (10116 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _948855), _948857))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _948855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _948857), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (32638 ^ _778908) ^ [_1372856, _1372858, _1372860, _1372862] : [-(c_Nitpick_Ofold__graph_H(_1372856, _1372858, _1372860, _1372862, c_Orderings_Obot__class_Obot(tc_fun(_1372856, tc_HOL_Obool)), _1372862))], (43496 ^ _778908) ^ [_1625703] : [-(hAPP(c_Relation_Oconverse(_1625703, _1625703), c_Relation_OId(_1625703)) = c_Relation_OId(_1625703))], (646 ^ _778908) ^ [_788923, _788925, _788927, _788929, _788931, _788933] : [-(c_Hoare__Mirabelle_Ohoare__valids(_788931, _788927, _788923)), c_Hoare__Mirabelle_Ohoare__valids(_788933, _788929, _788925), _788933 = _788931, _788929 = _788927, _788925 = _788923], (8879 ^ _778908) ^ [_927026, _927028] : [-(hBOOL(hAPP(_927026, hAPP(c_Int_Onat, _927028)))), 8883 ^ _778908 : [(8886 ^ _778908) ^ [] : [hBOOL(hAPP(_927026, 8882 ^ [_927026, _927028]))], (8884 ^ _778908) ^ [] : [-(_927028 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8882 ^ [_927026, _927028]))]], 8887 ^ _778908 : [(8890 ^ _778908) ^ [] : [hBOOL(hAPP(_927026, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8888 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _927028), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (26793 ^ _778908) ^ [_1251388, _1251390] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1251388), _1251390)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251388), _1251390)))], (26241 ^ _778908) ^ [_1240829, _1240831, _1240833] : [class_Divides_Osemiring__div(_1240829), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240829), _1240831), _1240833)), -(c_Divides_Odiv__class_Omod(_1240829, _1240833, _1240831) = c_Groups_Ozero__class_Ozero(_1240829))], (17699 ^ _778908) ^ [_1084746, _1084748, _1084750, _1084752] : [class_Groups_Omonoid__mult(_1084746), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084746), _1084748), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084750), _1084752)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084746), hAPP(hAPP(c_Power_Opower__class_Opower(_1084746), _1084748), _1084750)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084746), _1084748), _1084752)))], (8360 ^ _778908) ^ [_918969, _918971] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918969)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918971)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _918969), _918971)))], (46191 ^ _778908) ^ [_1689968, _1689970, _1689972, _1689974] : [-(hAPP(c_List_Oset(_1689968), hAPP(hAPP(c_List_Omap(_1689970, _1689968), _1689972), _1689974)) = hAPP(c_Set_Oimage(_1689970, _1689968, _1689972), hAPP(c_List_Oset(_1689970), _1689974)))], (30716 ^ _778908) ^ [_1329561, _1329563, _1329565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329561), _1329563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1329561), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329561, tc_HOL_Obool)), _1329563), hAPP(hAPP(c_Set_Oinsert(_1329561), _1329565), c_Orderings_Obot__class_Obot(tc_fun(_1329561, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1329561), _1329563))))], (44895 ^ _778908) ^ [_1659876, _1659878, _1659880, _1659882, _1659884] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659876, tc_fun(_1659878, tc_HOL_Obool)), _1659880), hAPP(hAPP(c_COMBB(tc_fun(_1659878, tc_HOL_Obool), tc_fun(_1659878, tc_HOL_Obool), _1659876), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659878, tc_HOL_Obool)), _1659882)), _1659884)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659878, tc_HOL_Obool)), _1659882), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659876, tc_fun(_1659878, tc_HOL_Obool)), _1659880), _1659884)))], (27934 ^ _778908) ^ [_1274094, _1274096] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1274094, _1274096)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1274096)), _1274094))], (38296 ^ _778908) ^ [_1496357, _1496359] : [class_Lattices_Olattice(_1496357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496357), _1496359)), -(_1496359 = c_Orderings_Obot__class_Obot(tc_fun(_1496357, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1496357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1496357), 38309 ^ [_1496357, _1496359]), 38310 ^ [_1496357, _1496359])), hAPP(hAPP(c_Set_Oinsert(_1496357), 38309 ^ [_1496357, _1496359]), hAPP(hAPP(c_Set_Oinsert(_1496357), 38310 ^ [_1496357, _1496359]), c_Orderings_Obot__class_Obot(tc_fun(_1496357, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1496357), c_Big__Operators_Olattice__class_OInf__fin(_1496357, _1496359)), _1496359)))], (34506 ^ _778908) ^ [_1410186, _1410188, _1410190, _1410192] : [class_Groups_Ocomm__monoid__mult(_1410186), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1410188), _1410190))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410188, _1410186), _1410192), _1410190) = c_Groups_Oone__class_Oone(_1410186))], (16977 ^ _778908) ^ [_1071192, _1071194, _1071196, _1071198] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071192), hAPP(c_Int_Onumber__class_Onumber__of(_1071192), _1071194)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071192), _1071196), _1071198)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071192), hAPP(c_Int_Onumber__class_Onumber__of(_1071192), _1071194)), _1071196)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071192), hAPP(c_Int_Onumber__class_Onumber__of(_1071192), _1071194)), _1071198))), class_Int_Onumber(_1071192), class_Rings_Oring(_1071192)], (46737 ^ _778908) ^ [_1703109, _1703111, _1703113, _1703115] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703109)), _1703111) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703113)), _1703115), -(hAPP(hAPP(c_List_Omap(tc_prod(_1703109, _1703113), _1703109), c_Product__Type_Ofst(_1703109, _1703113)), hAPP(hAPP(c_List_Ozip(_1703109, _1703113), _1703111), _1703115)) = _1703111)], (40156 ^ _778908) ^ [_1538475, _1538477, _1538479, _1538481, _1538483] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1538475, _1538477), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1538475, tc_HOL_Obool)), _1538479), _1538481)), _1538483) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538475, _1538477), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1538475, _1538477), _1538479), _1538483)), hAPP(hAPP(c_Product__Type_OSigma(_1538475, _1538477), _1538481), _1538483)))], (49227 ^ _778908) ^ [_1766083, _1766085, _1766087] : [-(hAPP(hAPP(c_List_Otake(_1766083), _1766085), hAPP(c_List_Otl(_1766083), _1766087)) = hAPP(c_List_Otl(_1766083), hAPP(hAPP(c_List_Otake(_1766083), hAPP(c_Nat_OSuc, _1766085)), _1766087)))], (47046 ^ _778908) ^ [_1712641, _1712643, _1712645, _1712647] : [_1712641 = _1712643, -(c_List_Oremove1(_1712645, _1712641, hAPP(hAPP(c_List_Olist_OCons(_1712645), _1712643), _1712647)) = _1712647)], (7418 ^ _778908) ^ [_902917, _902919] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_902917, _902919)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_902917)), c_Com_Ocom_Ocom__size(_902919))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10820 ^ _778908) ^ [_960463, _960465, _960467] : [class_Rings_Olinordered__idom(_960463), 10823 ^ _778908 : [(10830 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960465), _960467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960463), hAPP(c_Int_Oring__1__class_Oof__int(_960463), _960465)), hAPP(c_Int_Oring__1__class_Oof__int(_960463), _960467))))], (10824 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960463), hAPP(c_Int_Oring__1__class_Oof__int(_960463), _960465)), hAPP(c_Int_Oring__1__class_Oof__int(_960463), _960467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _960465), _960467)))]]], (3810 ^ _778908) ^ [_837611, _837613, _837615, _837617, _837619, _837621, _837623, _837625] : [-(c_Recdef_Osame__fst(_837625, _837621, _837617, _837613) = c_Recdef_Osame__fst(_837623, _837619, _837615, _837611)), _837625 = _837623, _837621 = _837619, _837617 = _837615, _837613 = _837611], (10780 ^ _778908) ^ [_959724, _959726, _959728] : [class_Rings_Olinordered__semidom(_959724), 10783 ^ _778908 : [(10790 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959726), _959728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959724), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_959724), _959726)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_959724), _959728))))], (10784 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959724), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_959724), _959726)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_959724), _959728))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959726), _959728)))]]], (46193 ^ _778908) ^ [_1690047, _1690049, _1690051, _1690053, _1690055] : [hAPP(hAPP(c_List_Omap(_1690047, _1690049), _1690051), _1690053) = hAPP(hAPP(c_List_Omap(_1690047, _1690049), _1690055), _1690053), 46196 ^ _778908 : [(46197 ^ _778908) ^ [_1690170] : [hBOOL(hAPP(hAPP(c_member(_1690047), _1690170), hAPP(c_List_Oset(_1690047), _1690053))), -(hAPP(_1690051, _1690170) = hAPP(_1690055, _1690170))]]], (39366 ^ _778908) ^ [_1519043] : [class_Nat_Osemiring__char__0(_1519043), -(c_Fun_Oinj__on(tc_Nat_Onat, _1519043, c_Nat_Osemiring__1__class_Oof__nat(_1519043), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (11845 ^ _778908) ^ [_977292, _977294, _977296] : [class_Groups_Oordered__comm__monoid__add(_977292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977292), c_Groups_Ozero__class_Ozero(_977292)), _977294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977292), c_Groups_Ozero__class_Ozero(_977292)), _977296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977292), c_Groups_Ozero__class_Ozero(_977292)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977292), _977294), _977296))))], (2228 ^ _778908) ^ [_812356, _812358, _812360, _812362, _812364, _812366] : [-(c_Sum__Type_OProjl(_812366, _812362, _812358) = c_Sum__Type_OProjl(_812364, _812360, _812356)), _812366 = _812364, _812362 = _812360, _812358 = _812356], (23471 ^ _778908) ^ [_1187885, _1187887, _1187889, _1187891] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187885, _1187887), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187889), _1187891))), -(_1187887 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187885, _1187887) = _1187891)], (18231 ^ _778908) ^ [_1094144, _1094146, _1094148] : [class_Int_Onumber__ring(_1094144), 18234 ^ _778908 : [(18241 ^ _778908) ^ [] : [c_Int_Oiszero(_1094144, hAPP(c_Int_Onumber__class_Onumber__of(_1094144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094146), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094148)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1094144), _1094146) = hAPP(c_Int_Onumber__class_Onumber__of(_1094144), _1094148))], (18235 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1094144), _1094146) = hAPP(c_Int_Onumber__class_Onumber__of(_1094144), _1094148), -(c_Int_Oiszero(_1094144, hAPP(c_Int_Onumber__class_Onumber__of(_1094144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094146), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094148)))))]]], (12057 ^ _778908) ^ [_981184, _981186, _981188, _981190] : [class_Rings_Oordered__semiring(_981184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981184), _981186), _981188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981184), c_Groups_Ozero__class_Ozero(_981184)), _981190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981184), _981190), _981186)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981184), _981190), _981188))))], (24661 ^ _778908) ^ [_1210333, _1210335, _1210337] : [class_Orderings_Olinorder(_1210333), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210333), _1210335), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210333), _1210335), _1210337))))], (43784 ^ _778908) ^ [_1633025, _1633027, _1633029] : [c_Relation_Ototal__on(_1633025, _1633027, _1633029), 43787 ^ _778908 : [(43788 ^ _778908) ^ [_1633169] : [hBOOL(hAPP(hAPP(c_member(_1633025), _1633169), _1633027)), 43791 ^ _778908 : [(43792 ^ _778908) ^ [_1633309] : [hBOOL(hAPP(hAPP(c_member(_1633025), _1633309), _1633027)), -(_1633169 = _1633309), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633025, _1633025)), hAPP(hAPP(c_Product__Type_OPair(_1633025, _1633025), _1633169), _1633309)), _1633029))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633025, _1633025)), hAPP(hAPP(c_Product__Type_OPair(_1633025, _1633025), _1633309), _1633169)), _1633029)))]]]]], (8148 ^ _778908) ^ [_915222, _915224, _915226, _915228] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_915222, _915224)), c_Nitpick_Opair__box_OPairBox(_915222, _915224, _915226, _915228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29211 ^ _778908) ^ [_1300893, _1300895] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300893, _1300895))))], (4860 ^ _778908) ^ [_854146, _854148, _854150, _854152] : [-(c_Fun_Ofun__upd(_854152, _854148) = c_Fun_Ofun__upd(_854150, _854146)), _854152 = _854150, _854148 = _854146], (51493 ^ _778908) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (26547 ^ _778908) ^ [_1246480, _1246482, _1246484] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246480, _1246482) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246484, _1246482), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1246482), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246480), _1246484))))], (17429 ^ _778908) ^ [_1079997, _1079999, _1080001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1079997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1079997), _1079999)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1079997), _1080001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1079999), _1080001)))], (23084 ^ _778908) ^ [] : [-(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)))))], (18789 ^ _778908) ^ [_1102599, _1102601] : [class_Int_Onumber__ring(_1102599), -(hAPP(c_Int_Onumber__class_Onumber__of(_1102599), c_Int_Opred(_1102601)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102599), hAPP(c_Groups_Ouminus__class_Ouminus(_1102599), c_Groups_Oone__class_Oone(_1102599))), hAPP(c_Int_Onumber__class_Onumber__of(_1102599), _1102601)))], (47501 ^ _778908) ^ [_1723692, _1723694] : [-(c_List_Osublist(_1723692, c_List_Olist_ONil(_1723692), _1723694) = c_List_Olist_ONil(_1723692))], (3442 ^ _778908) ^ [_831779, _831781, _831783, _831785, _831787, _831789, _831791, _831793] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_831793, _831789, _831785, _831781) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_831791, _831787, _831783, _831779)), _831793 = _831791, _831789 = _831787, _831785 = _831783, _831781 = _831779], (40584 ^ _778908) ^ [_1550091, _1550093, _1550095, _1550097] : [_1550091 = c_Finite__Set_Ofold1(_1550093, _1550095), -(hAPP(_1550091, hAPP(hAPP(c_Set_Oinsert(_1550093), _1550097), c_Orderings_Obot__class_Obot(tc_fun(_1550093, tc_HOL_Obool)))) = _1550097)], (27763 ^ _778908) ^ [_1271125, _1271127] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1271125), _1271127)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1271125)), hAPP(c_Nat_OSuc, _1271127)))], (51471 ^ _778908) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (17917 ^ _778908) ^ [_1088904, _1088906] : [-(c_Nitpick_Onat__lcm(_1088904, _1088906) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088904), _1088906)), c_Nitpick_Onat__gcd(_1088904, _1088906)))], (34276 ^ _778908) ^ [_1405451, _1405453, _1405455, _1405457, _1405459, _1405461] : [hBOOL(hAPP(hAPP(c_member(_1405451), _1405453), _1405455)), -(hAPP(c_Set_Oimage(_1405451, _1405457, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1405451, _1405457), _1405459), _1405453), _1405461)), _1405455) = hAPP(hAPP(c_Set_Oinsert(_1405457), _1405461), hAPP(c_Set_Oimage(_1405451, _1405457, _1405459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1405451, tc_HOL_Obool)), _1405455), hAPP(hAPP(c_Set_Oinsert(_1405451), _1405453), c_Orderings_Obot__class_Obot(tc_fun(_1405451, tc_HOL_Obool)))))))], (21061 ^ _778908) ^ [_1142576, _1142578, _1142580, _1142582] : [class_Fields_Olinordered__field(_1142576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142576), c_Groups_Ozero__class_Ozero(_1142576)), _1142578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142576), _1142580), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142576), _1142582), _1142578))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142576), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142576), _1142580), _1142578)), _1142582)))], (16410 ^ _778908) ^ [_1060917, _1060919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060919), _1060917))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1060919), _1060917) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060919), _1060917)), _1060917)))], (43658 ^ _778908) ^ [_1629805, _1629807, _1629809] : [c_Relation_Ototal__on(_1629805, _1629807, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1629805, _1629805), tc_HOL_Obool)), _1629809), c_Relation_OId(_1629805))), -(c_Relation_Ototal__on(_1629805, _1629807, _1629809))], (25167 ^ _778908) ^ [_1221448, _1221450, _1221452, _1221454, _1221456] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1221448, _1221450, tc_HOL_Obool, _1221452), _1221454), _1221456)), -(hBOOL(hAPP(_1221452, hAPP(hAPP(c_Product__Type_OPair(_1221448, _1221450), _1221454), _1221456))))], (50961 ^ _778908) ^ [_1803009, _1803011] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803009), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1803009))), c_List_Otranspose(_1803009, _1803011)))))], (5434 ^ _778908) ^ [_862881, _862883, _862885, _862887, _862889, _862891] : [-(c_Product__Type_Oprod_Oprod__case(_862891, _862887, _862883) = c_Product__Type_Oprod_Oprod__case(_862889, _862885, _862881)), _862891 = _862889, _862887 = _862885, _862883 = _862881], (49604 ^ _778908) ^ [_1774889, _1774891, _1774893] : [_1774889 = c_List_Olist_ONil(_1774891), -(c_List_Olast(_1774891, hAPP(hAPP(c_List_Oappend(_1774891), _1774893), _1774889)) = c_List_Olast(_1774891, _1774893))], (15500 ^ _778908) ^ [_1042599, _1042601, _1042603] : [class_Groups_Ogroup__add(_1042599), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042599), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042599), _1042601), _1042603)), _1042603) = _1042601)], (49919 ^ _778908) ^ [_1781261, _1781263, _1781265] : [49921 ^ _778908 : [(49924 ^ _778908) ^ [] : [hBOOL(hAPP(_1781263, 49920 ^ [_1781261, _1781263, _1781265]))], (49922 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781261), 49920 ^ [_1781261, _1781263, _1781265]), hAPP(c_List_Oset(_1781261), _1781265))))]], -(hAPP(c_List_Ofilter(_1781261, _1781263), _1781265) = _1781265)], (24381 ^ _778908) ^ [_1205108, _1205110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1205108)), -(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(_1205108), _1205110))), _1205108)))], (15886 ^ _778908) ^ [_1050017, _1050019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050017), _1050019)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050017), _1050019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49307 ^ _778908) ^ [_1767872, _1767874, _1767876, _1767878, _1767880, _1767882] : [-(hAPP(c_List_Ofoldl(_1767872, _1767874, _1767876, _1767878), hAPP(hAPP(c_List_Olist_OCons(_1767874), _1767880), _1767882)) = hAPP(c_List_Ofoldl(_1767872, _1767874, _1767876, hAPP(hAPP(_1767876, _1767878), _1767880)), _1767882))], (40126 ^ _778908) ^ [_1537475, _1537477, _1537479, _1537481, _1537483, _1537485] : [class_Groups_Ocomm__monoid__mult(_1537475), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537477, _1537475), hAPP(hAPP(c_COMBC(_1537477, tc_fun(_1537479, tc_HOL_Obool), _1537475), hAPP(hAPP(c_COMBB(tc_fun(_1537479, _1537475), tc_fun(tc_fun(_1537479, tc_HOL_Obool), _1537475), _1537477), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537479, _1537475)), _1537481)), _1537483)), _1537485) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1537477, _1537479), _1537475), hAPP(c_Product__Type_Oprod_Oprod__case(_1537477, _1537479, _1537475), _1537481)), hAPP(hAPP(c_Product__Type_OSigma(_1537477, _1537479), _1537485), hAPP(c_COMBK(tc_fun(_1537479, tc_HOL_Obool), _1537477), _1537483))))], (51315 ^ _778908) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (51245 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (41732 ^ _778908) ^ [_1581098, _1581100, _1581102, _1581104] : [class_Groups_Ocomm__monoid__mult(_1581098), c_Fun_Oinj__on(_1581100, _1581098, _1581102, _1581104), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1581100, _1581098), _1581102), _1581104) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1581098, _1581098), c_Fun_Oid(_1581098)), hAPP(c_Set_Oimage(_1581100, _1581098, _1581102), _1581104)))], (41127 ^ _778908) ^ [_1560083, _1560085, _1560087] : [hBOOL(hAPP(_1560083, _1560085)), -(hAPP(c_Set_OCollect(_1560087), hAPP(hAPP(c_COMBS(_1560087, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560087), c_fconj), hAPP(c_fequal, _1560085))), _1560083)) = hAPP(hAPP(c_Set_Oinsert(_1560087), _1560085), c_Orderings_Obot__class_Obot(tc_fun(_1560087, tc_HOL_Obool))))], (22874 ^ _778908) ^ [_1176399, _1176401, _1176403, _1176405, _1176407] : [-(hAPP(c_Nat_Onat_Onat__rec(_1176399, _1176401, _1176403), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1176405)), _1176407)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1176399), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1176405))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1176399, _1176399), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1176399, tc_fun(_1176399, _1176399)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1176399, tc_fun(_1176399, _1176399)), tc_Int_Oint), c_If(_1176399)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1176399, _1176401, _1176403), _1176407))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1176399, _1176399), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1176399, _1176399), tc_Int_Oint), _1176403), 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)), _1176407))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1176399, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1176399, _1176401, _1176403)), 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)), _1176407))))))], (48564 ^ _778908) ^ [_1749301, _1749303, _1749305] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749301)), hAPP(hAPP(c_List_Otake(_1749301), _1749303), _1749305)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749301)), _1749305)), _1749303))], (38392 ^ _778908) ^ [_1498656, _1498658, _1498660, _1498662, _1498664] : [c_Equiv__Relations_Oequivp(_1498656, _1498658), hBOOL(hAPP(hAPP(_1498658, _1498660), _1498662)), hBOOL(hAPP(hAPP(_1498658, _1498662), _1498664)), -(hBOOL(hAPP(hAPP(_1498658, _1498660), _1498664)))], (47465 ^ _778908) ^ [_1723019, _1723021] : [c_Orderings_Obot__class_Obot(tc_fun(_1723019, tc_HOL_Obool)) = hAPP(c_List_Oset(_1723019), _1723021), -(_1723021 = c_List_Olist_ONil(_1723019))], (37522 ^ _778908) ^ [_1479111, _1479113, _1479115] : [class_Lattices_Olattice(_1479111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479111), _1479113)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479111), _1479115)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479111, tc_HOL_Obool)), _1479113), _1479115) = c_Orderings_Obot__class_Obot(tc_fun(_1479111, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1479111), c_Big__Operators_Olattice__class_OSup__fin(_1479111, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479111, tc_HOL_Obool)), _1479113), _1479115))), c_Big__Operators_Olattice__class_OSup__fin(_1479111, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479111, tc_HOL_Obool)), _1479113), _1479115))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1479111), c_Big__Operators_Olattice__class_OSup__fin(_1479111, _1479113)), c_Big__Operators_Olattice__class_OSup__fin(_1479111, _1479115)))], (43287 ^ _778908) ^ [_1620707, _1620709, _1620711] : [_1620709 = _1620711, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620707, _1620707)), hAPP(hAPP(c_Product__Type_OPair(_1620707, _1620707), _1620709), _1620711)), c_Relation_OId(_1620707))))], (42340 ^ _778908) ^ [_1596869, _1596871] : [-(hAPP(c_Relation_ODomain(_1596869, _1596871), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1596869, _1596871), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1596869, tc_HOL_Obool)))], (10274 ^ _778908) ^ [] : [-(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))], (15182 ^ _778908) ^ [_1036851, _1036853, _1036855] : [-(hBOOL(hAPP(_1036851, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1036853, _1036855)))), 15185 ^ _778908 : [(15188 ^ _778908) ^ [] : [hBOOL(hAPP(_1036851, _1036853))], (15186 ^ _778908) ^ [] : [-(_1036855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 15189 ^ _778908 : [(15194 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15192 ^ [_1036851, _1036853, _1036855]), _1036855)))], (15196 ^ _778908) ^ [] : [-(_1036853 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1036855), 15191 ^ [_1036851, _1036853, _1036855])), 15192 ^ [_1036851, _1036853, _1036855]))], (15198 ^ _778908) ^ [] : [hBOOL(hAPP(_1036851, 15192 ^ [_1036851, _1036853, _1036855]))], (15190 ^ _778908) ^ [] : [_1036855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (4514 ^ _778908) ^ [_848767, _848769, _848771, _848773] : [-(c_List_Olistset(_848773, _848769) = c_List_Olistset(_848771, _848767)), _848773 = _848771, _848769 = _848767], (28355 ^ _778908) ^ [_1282591, _1282593, _1282595, _1282597] : [class_Lattices_Osemilattice__sup(_1282591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282591), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282591), _1282593), _1282595)), _1282597)), 28362 ^ _778908 : [(28365 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282591), _1282595), _1282597)))], (28363 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282591), _1282593), _1282597)))]]], (45093 ^ _778908) ^ [_1664631, _1664633, _1664635, _1664637, _1664639] : [45095 ^ _778908 : [(45098 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1664637, 45094 ^ [_1664631, _1664633, _1664635, _1664637, _1664639]), _1664639))], (45096 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664631), 45094 ^ [_1664631, _1664633, _1664635, _1664637, _1664639]), _1664635)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664631, tc_fun(_1664633, tc_HOL_Obool)), _1664635), _1664637), _1664639)))], (28429 ^ _778908) ^ [_1283905, _1283907, _1283909, _1283911] : [class_Lattices_Osemilattice__sup(_1283905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283905), _1283907), _1283909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283905), _1283907), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283905), _1283911), _1283909))))], (36602 ^ _778908) ^ [_1457838, _1457840, _1457842, _1457844] : [hBOOL(hAPP(hAPP(c_member(_1457838), _1457840), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457838, tc_HOL_Obool)), _1457842), _1457844))), -(hBOOL(hAPP(hAPP(c_member(_1457838), _1457840), _1457842)))], (45055 ^ _778908) ^ [_1663701, _1663703, _1663705, _1663707] : [hBOOL(hAPP(hAPP(c_member(_1663701), _1663703), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663701, tc_HOL_Obool), _1663705))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1663701, tc_HOL_Obool)), _1663707), _1663705)), -(hBOOL(hAPP(hAPP(c_member(_1663701), _1663703), _1663707)))], (46323 ^ _778908) ^ [_1693252, _1693254, _1693256] : [-(c_Map_Odom(_1693252, _1693254, c_Map_Omap__of(_1693252, _1693254, _1693256)) = hAPP(c_Set_Oimage(tc_prod(_1693252, _1693254), _1693252, c_Product__Type_Ofst(_1693252, _1693254)), hAPP(c_List_Oset(tc_prod(_1693252, _1693254)), _1693256)))], (2496 ^ _778908) ^ [_816664, _816666] : [_816666 = _816664, -(c_Divides_Oadjust(_816666) = c_Divides_Oadjust(_816664))], (6349 ^ _778908) ^ [_881264, _881266, _881268] : [hBOOL(hAPP(c_Com_OWT, _881264)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_881266, _881268, _881264))))], (28183 ^ _778908) ^ [_1279201, _1279203, _1279205, _1279207] : [class_Lattices_Olattice(_1279201), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279201), _1279203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279201), _1279205), _1279207)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279201), _1279205), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279201), _1279203), _1279207)))], (42206 ^ _778908) ^ [_1593624, _1593626, _1593628, _1593630] : [hBOOL(hAPP(hAPP(c_member(_1593624), _1593626), hAPP(c_Relation_ORange(_1593628, _1593624), _1593630))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593628, _1593624)), hAPP(hAPP(c_Product__Type_OPair(_1593628, _1593624), 42209 ^ [_1593624, _1593626, _1593628, _1593630]), _1593626)), _1593630)))], (6976 ^ _778908) ^ [_894375, _894377, _894379, _894381, _894383, _894385] : [c_Natural_Oevaln(c_Com_Ocom_OCall(_894375, _894377, _894379), _894381, _894383, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894385), hAPP(c_Natural_Ogetlocs, _894381))), _894375), hAPP(hAPP(c_Natural_Ogetlocs, _894385), c_Com_ORes))), 6980 ^ _778908 : [(6983 ^ _778908) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _894377), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894381), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_894379, _894381)), _894383, 6979 ^ [_894375, _894377, _894379, _894381, _894383, _894385]))], (6981 ^ _778908) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894385), hAPP(c_Natural_Ogetlocs, _894381))), _894375), hAPP(hAPP(c_Natural_Ogetlocs, _894385), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 6979 ^ [_894375, _894377, _894379, _894381, _894383, _894385]), hAPP(c_Natural_Ogetlocs, _894381))), _894375), hAPP(hAPP(c_Natural_Ogetlocs, 6979 ^ [_894375, _894377, _894379, _894381, _894383, _894385]), c_Com_ORes)))]]], (40632 ^ _778908) ^ [_1550886, _1550888] : [class_Orderings_Olinorder(_1550886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550886), _1550888)), -(c_Big__Operators_Olinorder__class_OMax(_1550886, _1550888) = hAPP(c_Finite__Set_Ofold1(_1550886, c_Orderings_Oord__class_Omax(_1550886)), _1550888))], (47411 ^ _778908) ^ [_1722086, _1722088, _1722090, _1722092] : [_1722092 = c_List_Olist_ONil(_1722086), -(hAPP(hAPP(c_List_Omap(_1722086, _1722088), _1722090), _1722092) = c_List_Olist_ONil(_1722088))], (35462 ^ _778908) ^ [_1431786, _1431788, _1431790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431786, tc_HOL_Obool)), _1431788), _1431790)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1431786, tc_HOL_Obool)), _1431788), hAPP(c_Set_OPow(_1431786), _1431790))))], (30992 ^ _778908) ^ [_1335139, _1335141, _1335143, _1335145, _1335147] : [hBOOL(hAPP(hAPP(c_member(_1335139), _1335141), _1335143)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1335145, _1335139)), hAPP(c_Sum__Type_OInr(_1335139, _1335145), _1335141)), c_Sum__Type_OPlus(_1335145, _1335139, _1335147, _1335143))))], (51281 ^ _778908) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (25151 ^ _778908) ^ [_1221104, _1221106] : [-(c_HOL_OThe(_1221104, hAPP(hAPP(c_COMBC(_1221104, _1221104, tc_HOL_Obool), c_fequal), _1221106)) = _1221106)], (10711 ^ _778908) ^ [_958603, _958605, _958607, _958609, _958611] : [class_Orderings_Oord(_958603), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958605, _958603)), _958607), _958609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958603), hAPP(_958607, _958611)), hAPP(_958609, _958611))))], (7943 ^ _778908) ^ [_911577, _911579, _911581, _911583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911577), _911579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911581), _911583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911577), _911581)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911579), _911583))))], (36654 ^ _778908) ^ [_1459312, _1459314, _1459316, _1459318] : [class_Lattices_Odistrib__lattice(_1459312), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459312), _1459314), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1459312), _1459316), _1459318)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1459312), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459312), _1459314), _1459316)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459312), _1459314), _1459318)))], (43504 ^ _778908) ^ [_1625836, _1625838] : [c_Wellfounded_Oacyclic(_1625836, _1625838), -(c_Wellfounded_Oacyclic(_1625836, hAPP(c_Relation_Oconverse(_1625836, _1625836), _1625838)))], (47338 ^ _778908) ^ [_1720714, _1720716] : [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), _1720714), _1720716))), 47341 ^ _778908 : [(47348 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1720714), _1720716))), -(c_List_Oupto(_1720714, _1720716) = c_List_Olist_ONil(tc_Int_Oint))], (47342 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1720714), _1720716)), -(c_List_Oupto(_1720714, _1720716) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1720714), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1720714), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1720716)))]]], (46325 ^ _778908) ^ [_1693329, _1693331, _1693333, _1693335] : [hAPP(c_Map_Omap__of(_1693329, _1693331, _1693333), _1693335) = c_Option_Ooption_ONone(_1693331), hBOOL(hAPP(hAPP(c_member(_1693329), _1693335), hAPP(c_Set_Oimage(tc_prod(_1693329, _1693331), _1693329, c_Product__Type_Ofst(_1693329, _1693331)), hAPP(c_List_Oset(tc_prod(_1693329, _1693331)), _1693333))))], (11590 ^ _778908) ^ [_972748, _972750, _972752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972748), _972750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972748), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972750), _972752))))], (44074 ^ _778908) ^ [_1640426, _1640428, _1640430, _1640432] : [-(hAPP(c_Finite__Set_Ofold__image(_1640426, _1640428, _1640430), _1640432) = c_Finite__Set_Ofold(_1640428, _1640426, hAPP(hAPP(c_COMBB(_1640426, tc_fun(_1640426, _1640426), _1640428), _1640430), _1640432)))], (42151 ^ _778908) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (45189 ^ _778908) ^ [_1666718, _1666720] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1666718, tc_HOL_Obool), hAPP(c_Set_OPow(_1666718), _1666720)) = _1666720)], (35476 ^ _778908) ^ [_1432086] : [-(hAPP(c_Set_OPow(_1432086), c_Orderings_Otop__class_Otop(tc_fun(_1432086, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1432086, tc_HOL_Obool), tc_HOL_Obool)))], (12944 ^ _778908) ^ [_996975, _996977, _996979, _996981, _996983] : [class_Rings_Olinordered__semiring__strict(_996975), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996975), _996977), _996979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996975), _996981), _996983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996975), c_Groups_Ozero__class_Ozero(_996975)), _996979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996975), c_Groups_Ozero__class_Ozero(_996975)), _996981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996975), _996977), _996981)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996975), _996979), _996983))))], (17117 ^ _778908) ^ [_1074080, _1074082] : [class_Rings_Olinordered__idom(_1074080), -(hAPP(c_Groups_Oabs__class_Oabs(_1074080), _1074082) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074080), _1074082), c_Groups_Osgn__class_Osgn(_1074080, _1074082)))], (46743 ^ _778908) ^ [_1703266, _1703268, _1703270, _1703272] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703266)), _1703268) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703270)), _1703272), -(hAPP(hAPP(c_List_Omap(tc_prod(_1703266, _1703270), _1703270), c_Product__Type_Osnd(_1703266, _1703270)), hAPP(hAPP(c_List_Ozip(_1703266, _1703270), _1703268), _1703272)) = _1703272)], (15694 ^ _778908) ^ [_1046199, _1046201, _1046203] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046201), _1046203)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046199), _1046201)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046199), _1046203)))], (12071 ^ _778908) ^ [_981453, _981455, _981457, _981459] : [class_Rings_Oordered__semiring(_981453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981453), _981455), _981457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981453), c_Groups_Ozero__class_Ozero(_981453)), _981459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981453), _981455), _981459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981453), _981457), _981459))))], (36470 ^ _778908) ^ [_1455138, _1455140, _1455142, _1455144] : [class_Lattices_Osemilattice__inf(_1455138), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455138), _1455140), _1455142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455138), _1455140), _1455144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455138), _1455140), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1455138), _1455142), _1455144))))], (49452 ^ _778908) ^ [_1771203, _1771205, _1771207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1771203, _1771203), tc_HOL_Obool)), _1771205), hAPP(hAPP(c_Product__Type_OSigma(_1771203, _1771203), _1771207), hAPP(c_COMBK(tc_fun(_1771203, tc_HOL_Obool), _1771203), _1771207)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1771203), tc_List_Olist(_1771203)), tc_HOL_Obool)), c_List_Olistrel(_1771203, _1771205)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1771203), tc_List_Olist(_1771203)), c_List_Olists(_1771203, _1771207)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1771203), tc_HOL_Obool), tc_List_Olist(_1771203)), c_List_Olists(_1771203, _1771207))))))], (23537 ^ _778908) ^ [_1188826] : [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), _1188826))), -(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), _1188826)) = 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), _1188826))))], (51253 ^ _778908) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (9070 ^ _778908) ^ [_930439, _930441] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930439), _930441) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930441), _930439))], (35815 ^ _778908) ^ [] : [-(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))], (36734 ^ _778908) ^ [_1460850, _1460852, _1460854, _1460856] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460850, tc_HOL_Obool)), _1460852), _1460854), _1460856)), -(hBOOL(hAPP(_1460852, _1460856)))], (2572 ^ _778908) ^ [_817792, _817794, _817796, _817798] : [-(c_Divides_OnegDivAlg(_817798, _817794) = c_Divides_OnegDivAlg(_817796, _817792)), _817798 = _817796, _817794 = _817792], (48765 ^ _778908) ^ [_1755089, _1755091, _1755093, _1755095, _1755097, _1755099] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755089), tc_List_Olist(_1755089))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755089), tc_List_Olist(_1755089)), hAPP(hAPP(c_List_Olist_OCons(_1755089), _1755091), _1755093)), hAPP(hAPP(c_List_Olist_OCons(_1755089), _1755095), _1755097))), c_List_Olistrel1(_1755089, _1755099))), 48770 ^ _778908 : [(48773 ^ _778908) ^ [] : [-(_1755093 = _1755097)], (48771 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1755089, _1755089)), hAPP(hAPP(c_Product__Type_OPair(_1755089, _1755089), _1755091), _1755095)), _1755099)))]], 48774 ^ _778908 : [(48777 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755089), tc_List_Olist(_1755089))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755089), tc_List_Olist(_1755089)), _1755093), _1755097)), c_List_Olistrel1(_1755089, _1755099))))], (48775 ^ _778908) ^ [] : [-(_1755091 = _1755095)]]], (43826 ^ _778908) ^ [_1634195, _1634197, _1634199, _1634201, _1634203] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634195, _1634195)), hAPP(hAPP(c_Product__Type_OPair(_1634195, _1634195), _1634197), _1634199)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1634195, _1634195), tc_HOL_Obool), _1634201), _1634203))), 43831 ^ _778908 : [(43834 ^ _778908) ^ [] : [-(_1634197 = _1634199)], (43832 ^ _778908) ^ [] : [-(_1634201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 43837 ^ _778908 : [(43842 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634195, _1634195)), hAPP(hAPP(c_Product__Type_OPair(_1634195, _1634195), 43835 ^ [_1634195, _1634197, _1634199, _1634201, _1634203]), _1634199)), _1634203)))], (43840 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634195, _1634195)), hAPP(hAPP(c_Product__Type_OPair(_1634195, _1634195), _1634197), 43835 ^ [_1634195, _1634197, _1634199, _1634201, _1634203])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1634195, _1634195), tc_HOL_Obool), 43836 ^ [_1634195, _1634197, _1634199, _1634201, _1634203]), _1634203))))], (43838 ^ _778908) ^ [] : [-(_1634201 = hAPP(c_Nat_OSuc, 43836 ^ [_1634195, _1634197, _1634199, _1634201, _1634203]))]]], (13560 ^ _778908) ^ [_1007584, _1007586, _1007588] : [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), _1007584), _1007586)), _1007588))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007588), _1007584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007586)))], (23279 ^ _778908) ^ [_1184176, _1184178, _1184180, _1184182, _1184184, _1184186] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184176, _1184178, _1184180), _1184182), hAPP(hAPP(c_Product__Type_OPair(_1184176, _1184178), _1184184), _1184186)) = hAPP(hAPP(_1184182, _1184184), _1184186))], (14728 ^ _778908) ^ [_1028846, _1028848, _1028850] : [class_Divides_Osemiring__div(_1028846), -(_1028848 = c_Groups_Ozero__class_Ozero(_1028846)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028846), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028846), _1028848), _1028850)), _1028848) = _1028850)], (7921 ^ _778908) ^ [_911179, _911181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911181), hAPP(c_Nat_OSuc, _911179))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911179), _911181))], (41856 ^ _778908) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (5548 ^ _778908) ^ [_864664, _864666] : [_864666 = _864664, -(c_List_Olist_OCons(_864666) = c_List_Olist_OCons(_864664))], (9588 ^ _778908) ^ [_939476, _939478, _939480, _939482] : [class_Rings_Ocomm__semiring(_939476), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939476), _939478), _939480)), _939482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939476), _939478), _939482)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939476), _939480), _939482)))], (4338 ^ _778908) ^ [_845937, _845939, _845941, _845943] : [-(c_List_Olenlex(_845943, _845939) = c_List_Olenlex(_845941, _845937)), _845943 = _845941, _845939 = _845937], (46992 ^ _778908) ^ [_1711487, _1711489, _1711491, _1711493, _1711495, _1711497] : [-(c_List_Ofoldr(_1711487, _1711489, _1711491, hAPP(hAPP(c_List_Olist_OCons(_1711487), _1711493), _1711495), _1711497) = hAPP(hAPP(_1711491, _1711493), c_List_Ofoldr(_1711487, _1711489, _1711491, _1711495, _1711497)))], (15272 ^ _778908) ^ [_1038454, _1038456] : [-(_1038454 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15275 ^ _778908 : [(15282 ^ _778908) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038456, _1038454) = 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), _1038456)), _1038454) = 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), _1038456), _1038454))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15276 ^ _778908) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1038456, _1038454) = 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), _1038456)), _1038454) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1038456), _1038454)))]]], (26283 ^ _778908) ^ [_1241528, _1241530, _1241532, _1241534] : [class_Divides_Osemiring__div(_1241528), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241528), _1241530), _1241532)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1241528), _1241530), _1241534)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241528), _1241532), _1241534)), _1241530) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241528), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241528), _1241532), _1241530)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1241528), _1241534), _1241530)))], (25105 ^ _778908) ^ [_1219801, _1219803, _1219805, _1219807] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1219801), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1219803, _1219805, _1219801, _1219807) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1219803, 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(_1219803)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1219805, _1219807)), 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(_1219803)))), 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(_1219803)))), 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(_1219803)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1219803, 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(_1219803)))), 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(_1219803)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1219803, _1219805, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1219801), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1219807))), 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(_1219803)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1219803))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1219803)))), 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(_1219803)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1219803, 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(_1219803)))), 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(_1219803)))), 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(_1219803))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1219803)))), 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(_1219803)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1219803)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1219803))))), tc_prod(_1219803, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1219803)), hAPP(hAPP(c_COMBB(_1219803, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1219803)))), tc_prod(_1219803, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1219803)), c_Product__Type_Ofst(_1219803, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (48323 ^ _778908) ^ [_1743276, _1743278, _1743280] : [_1743280 = c_List_Olist_ONil(_1743278), -(_1743276 = hAPP(hAPP(c_List_Oappend(_1743278), _1743276), _1743280))], (38900 ^ _778908) ^ [_1508660, _1508662] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508660), c_Orderings_Otop__class_Otop(tc_fun(_1508660, tc_HOL_Obool)))), c_Fun_Oinj__on(_1508660, _1508660, _1508662, c_Orderings_Otop__class_Otop(tc_fun(_1508660, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1508660, _1508660, _1508662), c_Orderings_Otop__class_Otop(tc_fun(_1508660, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1508660, tc_HOL_Obool)))], (31760 ^ _778908) ^ [_1352869, _1352871, _1352873, _1352875, _1352877, _1352879, _1352881, _1352883] : [c_Finite__Set_Ofolding__image__simple(_1352869, _1352871, _1352873, _1352875, _1352877, _1352879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352871), _1352881)), hBOOL(hAPP(hAPP(c_member(_1352871), _1352883), _1352881)), -(hAPP(_1352879, _1352881) = hAPP(hAPP(_1352873, hAPP(_1352877, _1352883)), hAPP(_1352879, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352871, tc_HOL_Obool)), _1352881), hAPP(hAPP(c_Set_Oinsert(_1352871), _1352883), c_Orderings_Obot__class_Obot(tc_fun(_1352871, tc_HOL_Obool)))))))], (24163 ^ _778908) ^ [_1200983, _1200985, _1200987] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1200983, tc_HOL_Obool)), _1200985), _1200987))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200983, tc_HOL_Obool)), _1200985), _1200987)), -(_1200985 = _1200987)], (47870 ^ _778908) ^ [_1732897, _1732899, _1732901] : [-(hAPP(hAPP(c_List_Olist__update(_1732897, c_List_Olist_ONil(_1732897)), _1732899), _1732901) = c_List_Olist_ONil(_1732897))], (43594 ^ _778908) ^ [_1627978, _1627980, _1627982, _1627984] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627978, _1627978)), hAPP(hAPP(c_Product__Type_OPair(_1627978, _1627978), _1627980), _1627982)), c_Transitive__Closure_Ortrancl(_1627978, _1627984))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627978, _1627978)), hAPP(hAPP(c_Product__Type_OPair(_1627978, _1627978), _1627982), _1627980)), c_Transitive__Closure_Ortrancl(_1627978, hAPP(c_Relation_Oconverse(_1627978, _1627978), _1627984)))))], (16965 ^ _778908) ^ [_1070930, _1070932, _1070934] : [class_Rings_Ocomm__semiring__1(_1070930), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070930), _1070932), hAPP(hAPP(c_Power_Opower__class_Opower(_1070930), _1070932), _1070934)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1070930), _1070932), hAPP(c_Nat_OSuc, _1070934)))], (14555 ^ _778908) ^ [_1026017, _1026019] : [class_Divides_Osemiring__div(_1026017), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1026017), _1026019), c_Groups_Ozero__class_Ozero(_1026017)) = c_Groups_Ozero__class_Ozero(_1026017))], (33081 ^ _778908) ^ [_1381978, _1381980, _1381982, _1381984, _1381986] : [c_Hoare__Mirabelle_Ohoare__derivs(_1381978, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1381978), tc_HOL_Obool)), _1381980), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1381978), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978))), hAPP(hAPP(c_COMBB(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1381978)), _1381982)), c_Com_Ocom_OBODY)), _1381984)), _1381986)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1381978), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978))), hAPP(hAPP(c_COMBB(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1381978)), _1381982)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1381984)), _1381986)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1381978, _1381980, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1381978), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978))), hAPP(hAPP(c_COMBB(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1381978, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1381978))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1381978)), _1381982)), c_Com_Ocom_OBODY)), _1381984)), _1381986)))], (27544 ^ _778908) ^ [_1266493, _1266495, _1266497, _1266499] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1266493), _1266495)), 27547 ^ _778908 : [(27548 ^ _778908) ^ [_1266651] : [27550 ^ _778908 : [(27556 ^ _778908) ^ [] : [-(_1266651 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27552 ^ [_1266493, _1266495, _1266497, _1266499, _1266651]), 27549 ^ [_1266493, _1266495, _1266497, _1266499, _1266651]))], (27554 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27552 ^ [_1266493, _1266495, _1266497, _1266499, _1266651]), _1266497)))], (27551 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27549 ^ [_1266493, _1266495, _1266497, _1266499, _1266651]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1266495))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1266493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266651), _1266499)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1266493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266651), _1266495)), _1266499)))]]], (9734 ^ _778908) ^ [_942001, _942003, _942005, _942007] : [class_Rings_Olinordered__ring__strict(_942001), 9737 ^ _778908 : [(9752 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942001), _942003), _942005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942001), _942007), _942005)))), 9753 ^ _778908 : [(9760 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), _942005), c_Groups_Ozero__class_Ozero(_942001))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), _942007), _942003))], (9754 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), c_Groups_Ozero__class_Ozero(_942001)), _942005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), _942003), _942007))]]], (9738 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942001), _942003), _942005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942001), _942007), _942005))), 9743 ^ _778908 : [(9746 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), _942003), _942007)))], (9744 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), c_Groups_Ozero__class_Ozero(_942001)), _942005)))]], 9747 ^ _778908 : [(9750 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), _942007), _942003)))], (9748 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942001), _942005), c_Groups_Ozero__class_Ozero(_942001))))]]]]], (49277 ^ _778908) ^ [_1767159, _1767161, _1767163, _1767165] : [-(hAPP(c_List_Ofoldl(_1767159, _1767161, _1767163, _1767165), c_List_Olist_ONil(_1767161)) = _1767165)], (18561 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (16350 ^ _778908) ^ [_1059730, _1059732, _1059734, _1059736, _1059738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059730), _1059732)), 16353 ^ _778908 : [(16360 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1059736), 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), _1059732), _1059730)), _1059734)), _1059738))), -(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), _1059730), _1059734)), _1059736)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059732), _1059734)), _1059738))))], (16354 ^ _778908) ^ [] : [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), _1059730), _1059734)), _1059736)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059732), _1059734)), _1059738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1059736), 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), _1059732), _1059730)), _1059734)), _1059738))))]]], (20457 ^ _778908) ^ [_1132168, _1132170, _1132172] : [class_Fields_Olinordered__field(_1132168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132168), _1132170), c_Groups_Ozero__class_Ozero(_1132168))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132168), c_Groups_Ozero__class_Ozero(_1132168)), _1132172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132168), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132168), _1132170), _1132172)), c_Groups_Ozero__class_Ozero(_1132168))))], (41121 ^ _778908) ^ [_1559989, _1559991, _1559993] : [-(hBOOL(hAPP(_1559989, _1559991))), -(hAPP(c_Set_OCollect(_1559993), hAPP(hAPP(c_COMBS(_1559993, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559993), c_fconj), hAPP(hAPP(c_COMBC(_1559993, _1559993, tc_HOL_Obool), c_fequal), _1559991))), _1559989)) = c_Orderings_Obot__class_Obot(tc_fun(_1559993, tc_HOL_Obool)))], (49257 ^ _778908) ^ [_1766783, _1766785, _1766787] : [-(_1766783 = c_List_Olist_ONil(_1766785)), -(hAPP(hAPP(c_List_Otake(_1766785), hAPP(c_Nat_OSuc, _1766787)), _1766783) = hAPP(hAPP(c_List_Olist_OCons(_1766785), hAPP(c_List_Ohd(_1766785), _1766783)), hAPP(hAPP(c_List_Otake(_1766785), _1766787), hAPP(c_List_Otl(_1766785), _1766783))))], (8293 ^ _778908) ^ [_917841, _917843, _917845] : [class_Nat_Osemiring__char__0(_917841), 8296 ^ _778908 : [(8303 ^ _778908) ^ [] : [_917843 = _917845, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917841), _917843) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917841), _917845))], (8297 ^ _778908) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917841), _917843) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917841), _917845), -(_917843 = _917845)]]], (51653 ^ _778908) ^ [_1813549] : [hBOOL(hAPP(c_fNot, _1813549)), hBOOL(_1813549)], (30125 ^ _778908) ^ [_1318624, _1318626, _1318628, _1318630] : [-(_1318624 = c_Orderings_Obot__class_Obot(tc_fun(_1318626, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318626, tc_fun(_1318628, tc_HOL_Obool)), _1318624), hAPP(c_COMBK(tc_fun(_1318628, tc_HOL_Obool), _1318626), _1318630)) = _1318630)], (47493 ^ _778908) ^ [_1723538, _1723540, _1723542, _1723544] : [class_Orderings_Olinorder(_1723538), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723540, _1723538, _1723542), _1723544), c_List_Olist_ONil(_1723540)) = hAPP(hAPP(c_List_Olist_OCons(_1723540), _1723544), c_List_Olist_ONil(_1723540)))], (12636 ^ _778908) ^ [_991331] : [12638 ^ _778908 : [(12641 ^ _778908) ^ [] : [hBOOL(hAPP(_991331, hAPP(c_Int_Onat, 12637 ^ [_991331])))], (12639 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12637 ^ [_991331])))]], 12642 ^ _778908 : [(12643 ^ _778908) ^ [_991464] : [-(hBOOL(hAPP(_991331, _991464)))]]], (23246 ^ _778908) ^ [_1183507, _1183509, _1183511, _1183513, _1183515, _1183517] : [-(hAPP(hAPP(c_Product__Type_OPair(_1183507, _1183509), _1183511), _1183513) = hAPP(hAPP(c_Product__Type_OPair(_1183507, _1183509), _1183515), _1183517)), _1183511 = _1183515, _1183513 = _1183517], (32949 ^ _778908) ^ [_1379217, _1379219] : [class_Rings_Olinordered__idom(_1379217), hBOOL(hAPP(hAPP(c_member(_1379217), _1379219), c_Int_Oring__1__class_OInts(_1379217))), 32956 ^ _778908 : [(32963 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379217), _1379219), c_Groups_Ozero__class_Ozero(_1379217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379217), c_Groups_Oone__class_Oone(_1379217)), _1379219)), _1379219)), c_Groups_Ozero__class_Ozero(_1379217))))], (32957 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379217), c_Groups_Oone__class_Oone(_1379217)), _1379219)), _1379219)), c_Groups_Ozero__class_Ozero(_1379217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379217), _1379219), c_Groups_Ozero__class_Ozero(_1379217))))]]], (14704 ^ _778908) ^ [_1028438, _1028440] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028438, _1028440)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028438), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028440)))], (39586 ^ _778908) ^ [_1524054, _1524056, _1524058, _1524060] : [-(hBOOL(hAPP(hAPP(c_member(_1524054), _1524056), _1524058))), -(hAPP(c_Set_Ovimage(_1524060, _1524054, hAPP(c_COMBK(_1524054, _1524060), _1524056)), _1524058) = c_Orderings_Obot__class_Obot(tc_fun(_1524060, tc_HOL_Obool)))], (14531 ^ _778908) ^ [_1025546, _1025548, _1025550] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025548), _1025550)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025546), _1025548)), _1025550))], (30004 ^ _778908) ^ [_1316162, _1316164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316162, tc_HOL_Obool)), _1316164), c_Orderings_Obot__class_Obot(tc_fun(_1316162, tc_HOL_Obool)))), -(_1316164 = c_Orderings_Obot__class_Obot(tc_fun(_1316162, tc_HOL_Obool)))], (27524 ^ _778908) ^ [_1266021, _1266023, _1266025, _1266027] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1266021), _1266023)), 27527 ^ _778908 : [(27528 ^ _778908) ^ [_1266179] : [27530 ^ _778908 : [(27536 ^ _778908) ^ [] : [-(_1266179 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27532 ^ [_1266021, _1266023, _1266025, _1266027, _1266179]), 27529 ^ [_1266021, _1266023, _1266025, _1266027, _1266179]))], (27534 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27532 ^ [_1266021, _1266023, _1266025, _1266027, _1266179]), _1266025)))], (27531 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27529 ^ [_1266021, _1266023, _1266025, _1266027, _1266179]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1266023))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1266021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266179), _1266027)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1266021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1266179), _1266023)), _1266027)))]]], (29052 ^ _778908) ^ [] : [-(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))))], (50604 ^ _778908) ^ [_1795016, _1795018, _1795020, _1795022, _1795024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1795016), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1795018), _1795020))), -(hAPP(hAPP(c_List_Onth(_1795022), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1795022), _1795024), c_List_Oupt(_1795020, _1795018))), _1795016) = hAPP(_1795024, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1795020), _1795016)))], (48508 ^ _778908) ^ [_1747926, _1747928, _1747930, _1747932] : [-(hAPP(hAPP(c_List_Otake(_1747926), _1747928), hAPP(hAPP(c_List_Otake(_1747926), _1747930), _1747932)) = hAPP(hAPP(c_List_Otake(_1747926), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1747928), _1747930)), _1747932))], (11564 ^ _778908) ^ [_972315, _972317] : [11565 ^ _778908 : [(11568 ^ _778908) ^ [] : [_972315 = _972317], (11566 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972315), _972317))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972315), _972317)))], (23403 ^ _778908) ^ [_1187018, _1187020] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187018, _1187020) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1187018, _1187020)))], (49983 ^ _778908) ^ [_1782500, _1782502, _1782504, _1782506, _1782508] : [-(hAPP(c_List_Ofilter(_1782500, _1782502), hAPP(hAPP(c_List_Omap(_1782504, _1782500), _1782506), _1782508)) = hAPP(hAPP(c_List_Omap(_1782504, _1782500), _1782506), hAPP(c_List_Ofilter(_1782504, hAPP(c_Fun_Ocomp(_1782500, tc_HOL_Obool, _1782504, _1782502), _1782506)), _1782508)))], (43233 ^ _778908) ^ [_1619347, _1619349, _1619351] : [-(c_Transitive__Closure_Ortrancl(_1619347, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619347, _1619347), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1619347, _1619349)), c_Transitive__Closure_Ortrancl(_1619347, _1619351))) = c_Transitive__Closure_Ortrancl(_1619347, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619347, _1619347), tc_HOL_Obool)), _1619349), _1619351)))], (44751 ^ _778908) ^ [_1654906, _1654908, _1654910, _1654912, _1654914] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654906, tc_fun(_1654908, tc_HOL_Obool)), _1654910), hAPP(hAPP(c_COMBS(_1654906, tc_fun(_1654908, tc_HOL_Obool), tc_fun(_1654908, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654908, tc_HOL_Obool), tc_fun(tc_fun(_1654908, tc_HOL_Obool), tc_fun(_1654908, tc_HOL_Obool)), _1654906), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654908, tc_HOL_Obool))), _1654912)), _1654914)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654908, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654906, tc_fun(_1654908, tc_HOL_Obool)), _1654910), _1654912)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654906, tc_fun(_1654908, tc_HOL_Obool)), _1654910), _1654914)))], (23263 ^ _778908) ^ [_1183855, _1183857, _1183859] : [hBOOL(hAPP(_1183855, hAPP(hAPP(c_Product__Type_OPair(_1183857, _1183859), 23264 ^ [_1183855, _1183857, _1183859]), 23265 ^ [_1183855, _1183857, _1183859]))), 23268 ^ _778908 : [(23269 ^ _778908) ^ [_1184002] : [-(hBOOL(hAPP(_1183855, _1184002)))]]], (3410 ^ _778908) ^ [_831303, _831305] : [_831305 = _831303, -(c_Int_Oring__1__class_OInts(_831305) = c_Int_Oring__1__class_OInts(_831303))], (46152 ^ _778908) ^ [_1688986, _1688988, _1688990, _1688992, _1688994] : [-(c_Map_Omap__comp(_1688986, _1688988, _1688990, hAPP(c_COMBK(tc_Option_Ooption(_1688988), _1688986), c_Option_Ooption_ONone(_1688988)), _1688992, _1688994) = c_Option_Ooption_ONone(_1688988))], (45438 ^ _778908) ^ [_1672722, _1672724] : [class_Complete__Lattice_Ocomplete__lattice(_1672722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1672722), _1672724)), -(_1672724 = c_Orderings_Obot__class_Obot(tc_fun(_1672722, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1672722, _1672724) = c_Complete__Lattice_OSup__class_OSup(_1672722, _1672724))], (39834 ^ _778908) ^ [_1530204, _1530206, _1530208, _1530210, _1530212, _1530214] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530204, _1530206, _1530208, _1530210, _1530212), _1530214)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1530204), _1530212)))], (48287 ^ _778908) ^ [_1742657, _1742659, _1742661] : [hAPP(hAPP(c_List_Oappend(_1742657), _1742659), _1742661) = c_List_Olist_ONil(_1742657), 48290 ^ _778908 : [(48293 ^ _778908) ^ [] : [-(_1742661 = c_List_Olist_ONil(_1742657))], (48291 ^ _778908) ^ [] : [-(_1742659 = c_List_Olist_ONil(_1742657))]]], (6017 ^ _778908) ^ [_875152, _875154, _875156] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_875152, _875154)), _875156), hAPP(hAPP(hAPP(c_Natural_Oupdate, _875156), _875152), hAPP(_875154, _875156)))))], (39998 ^ _778908) ^ [_1533798, _1533800, _1533802, _1533804] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1533798, _1533800, _1533802), _1533804)), _1533802 = c_Orderings_Obot__class_Obot(tc_fun(_1533798, tc_HOL_Obool))], (50021 ^ _778908) ^ [_1783415, _1783417, _1783419, _1783421] : [-(c_List_Opartition(_1783415, _1783417, hAPP(hAPP(c_List_Olist_OCons(_1783415), _1783419), _1783421)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1783415), tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1783415), tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1783415), tc_fun(tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), tc_fun(tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), tc_List_Olist(_1783415)), c_COMBS(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), tc_fun(tc_List_Olist(_1783415), tc_fun(tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), tc_List_Olist(_1783415)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_fun(tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), tc_List_Olist(_1783415)), hAPP(c_If(tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), hAPP(_1783417, _1783419)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1783415), tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), tc_List_Olist(_1783415)), c_Product__Type_OPair(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), hAPP(c_List_Olist_OCons(_1783415), _1783419))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1783415), tc_fun(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415))), tc_fun(tc_fun(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_fun(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), tc_List_Olist(_1783415)), c_COMBB(tc_List_Olist(_1783415), tc_prod(tc_List_Olist(_1783415), tc_List_Olist(_1783415)), tc_List_Olist(_1783415))), c_Product__Type_OPair(tc_List_Olist(_1783415), tc_List_Olist(_1783415)))), hAPP(c_List_Olist_OCons(_1783415), _1783419)))), c_List_Opartition(_1783415, _1783417, _1783421)))], (48861 ^ _778908) ^ [_1757859, _1757861, _1757863, _1757865] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757859), tc_List_Olist(_1757859))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757859), tc_List_Olist(_1757859)), _1757861), _1757863)), c_List_Olistrel1(_1757859, _1757865))), 48866 ^ _778908 : [(48873 ^ _778908) ^ [] : [-(_1757863 = hAPP(hAPP(c_List_Oappend(_1757859), 48868 ^ [_1757859, _1757861, _1757863, _1757865]), hAPP(hAPP(c_List_Olist_OCons(_1757859), 48865 ^ [_1757859, _1757861, _1757863, _1757865]), 48869 ^ [_1757859, _1757861, _1757863, _1757865])))], (48871 ^ _778908) ^ [] : [-(_1757861 = hAPP(hAPP(c_List_Oappend(_1757859), 48868 ^ [_1757859, _1757861, _1757863, _1757865]), hAPP(hAPP(c_List_Olist_OCons(_1757859), 48864 ^ [_1757859, _1757861, _1757863, _1757865]), 48869 ^ [_1757859, _1757861, _1757863, _1757865])))], (48867 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757859, _1757859)), hAPP(hAPP(c_Product__Type_OPair(_1757859, _1757859), 48864 ^ [_1757859, _1757861, _1757863, _1757865]), 48865 ^ [_1757859, _1757861, _1757863, _1757865])), _1757865)))]]], (46567 ^ _778908) ^ [_1698654, _1698656, _1698658, _1698660, _1698662, _1698664, _1698666, _1698668] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1698654, _1698656), _1698658), _1698660), hAPP(hAPP(c_List_Ozip(_1698654, _1698656), hAPP(hAPP(c_List_Omap(_1698662, _1698654), _1698664), _1698666)), _1698668)) = hAPP(hAPP(c_List_Omap(tc_prod(_1698662, _1698656), _1698658), hAPP(c_Product__Type_Oprod_Oprod__case(_1698662, _1698656, _1698658), hAPP(hAPP(c_COMBB(tc_fun(_1698656, tc_prod(_1698654, _1698656)), tc_fun(_1698656, _1698658), _1698662), hAPP(c_COMBB(tc_prod(_1698654, _1698656), _1698658, _1698656), _1698660)), hAPP(hAPP(c_COMBB(_1698654, tc_fun(_1698656, tc_prod(_1698654, _1698656)), _1698662), c_Product__Type_OPair(_1698654, _1698656)), _1698664)))), hAPP(hAPP(c_List_Ozip(_1698662, _1698656), _1698666), _1698668)))], (6853 ^ _778908) ^ [_891542, _891544, _891546] : [hAPP(c_Com_Ocom_OBODY, _891542) = c_Com_Ocom_OWhile(_891544, _891546)], (5843 ^ _778908) ^ [_871844, _871846] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_871844, _871846)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6089 ^ _778908) ^ [_876422, _876424, _876426] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_876422, _876424, _876426))), -(hBOOL(hAPP(c_Com_OWT, _876426)))], (41281 ^ _778908) ^ [_1563684, _1563686, _1563688, _1563690] : [-(hAPP(c_Set_Ovimage(_1563684, _1563686, _1563688), _1563690) = hAPP(c_Set_OCollect(_1563684), hAPP(hAPP(c_COMBC(_1563684, tc_fun(_1563686, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1563686, tc_fun(tc_fun(_1563686, tc_HOL_Obool), tc_HOL_Obool), _1563684), c_member(_1563686)), _1563688)), _1563690)))], (31834 ^ _778908) ^ [_1355720, _1355722, _1355724] : [hBOOL(hAPP(hAPP(c_member(_1355720), _1355722), _1355724)), -(hAPP(hAPP(c_Set_Oinsert(_1355720), _1355722), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355720, tc_HOL_Obool)), _1355724), hAPP(hAPP(c_Set_Oinsert(_1355720), _1355722), c_Orderings_Obot__class_Obot(tc_fun(_1355720, tc_HOL_Obool))))) = _1355724)], (40489 ^ _778908) ^ [_1548150, _1548152] : [-(c_Relation_Orefl__on(_1548150, _1548152, c_Relation_OId__on(_1548150, _1548152)))], (9108 ^ _778908) ^ [_931189, _931191, _931193] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931189), _931191)), _931193) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931189), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931191), _931193)))], (5825 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10449 ^ _778908) ^ [_954426, _954428, _954430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954428), _954430)), -(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, _954426)), _954428)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954426)), _954430))))], (44466 ^ _778908) ^ [_1648132, _1648134, _1648136, _1648138, _1648140, _1648142] : [c_Finite__Set_Ofun__left__comm(_1648132, _1648134, _1648136), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648132), _1648138)), -(hAPP(hAPP(_1648136, _1648140), hAPP(hAPP(c_Finite__Set_Ofold(_1648132, _1648134, _1648136), _1648142), _1648138)) = hAPP(hAPP(c_Finite__Set_Ofold(_1648132, _1648134, _1648136), hAPP(hAPP(_1648136, _1648140), _1648142)), _1648138))], (9690 ^ _778908) ^ [_941284, _941286] : [class_Groups_Oab__group__add(_941284), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941284), hAPP(c_Groups_Ouminus__class_Ouminus(_941284), _941286)), _941286) = c_Groups_Ozero__class_Ozero(_941284))], (34583 ^ _778908) ^ [_1411633, _1411635, _1411637, _1411639, _1411641] : [class_Rings_Ocomm__semiring__1(_1411633), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411635), _1411637)), hBOOL(hAPP(hAPP(c_member(_1411635), _1411639), _1411637)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1411633), hAPP(_1411641, _1411639)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411635, _1411633), _1411641), _1411637))))], (16020 ^ _778908) ^ [_1052551, _1052553, _1052555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052551), _1052553)), _1052555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052555), _1052553))))], (39733 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (16469 ^ _778908) ^ [_1061963, _1061965, _1061967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1061963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1061965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1061967), 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), _1061967), _1061965))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1061963)))))], (48795 ^ _778908) ^ [_1755887, _1755889, _1755891, _1755893, _1755895] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1755887, _1755887)), hAPP(hAPP(c_Product__Type_OPair(_1755887, _1755887), _1755889), _1755891)), _1755893)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755887), tc_List_Olist(_1755887))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755887), tc_List_Olist(_1755887)), hAPP(hAPP(c_List_Olist_OCons(_1755887), _1755889), _1755895)), hAPP(hAPP(c_List_Olist_OCons(_1755887), _1755891), _1755895))), c_List_Olistrel1(_1755887, _1755893))))], (32917 ^ _778908) ^ [_1378360, _1378362] : [32918 ^ _778908 : [(32921 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378362), _1378360))], (32919 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1378360), _1378362)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1378360, _1378362))], (48182 ^ _778908) ^ [_1740343, _1740345, _1740347, _1740349, _1740351] : [hAPP(hAPP(c_List_Oappend(_1740343), _1740345), _1740347) = hAPP(hAPP(c_List_Oappend(_1740343), _1740349), _1740351), 48188 ^ _778908 : [(48191 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1740343), 48185 ^ [_1740343, _1740345, _1740347, _1740349, _1740351]), _1740347) = _1740351)], (48189 ^ _778908) ^ [] : [-(_1740345 = hAPP(hAPP(c_List_Oappend(_1740343), _1740349), 48185 ^ [_1740343, _1740345, _1740347, _1740349, _1740351]))]], 48192 ^ _778908 : [(48195 ^ _778908) ^ [] : [-(_1740347 = hAPP(hAPP(c_List_Oappend(_1740343), 48185 ^ [_1740343, _1740345, _1740347, _1740349, _1740351]), _1740351))], (48193 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1740343), _1740345), 48185 ^ [_1740343, _1740345, _1740347, _1740349, _1740351]) = _1740349)]]], (6857 ^ _778908) ^ [_891655, _891657, _891659, _891661, _891663] : [c_Com_Ocom_OWhile(_891655, _891657) = c_Com_Ocom_OCond(_891659, _891661, _891663)], (25137 ^ _778908) ^ [_1220719] : [-(c_Quickcheck_Obeyond(_1220719, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (6621 ^ _778908) ^ [_887471, _887473, _887475] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _887471))), _887473), _887475)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _887471)), _887473), _887475)))], (45899 ^ _778908) ^ [_1682841, _1682843, _1682845, _1682847, _1682849] : [hAPP(c_Map_Omap__add(_1682841, _1682843, _1682845, _1682847), _1682849) = c_Option_Ooption_ONone(_1682843), 45902 ^ _778908 : [(45905 ^ _778908) ^ [] : [-(hAPP(_1682845, _1682849) = c_Option_Ooption_ONone(_1682843))], (45903 ^ _778908) ^ [] : [-(hAPP(_1682847, _1682849) = c_Option_Ooption_ONone(_1682843))]]], (48168 ^ _778908) ^ [_1740033, _1740035, _1740037, _1740039] : [hBOOL(hAPP(hAPP(c_member(_1740033), _1740035), hAPP(c_List_Oset(_1740033), _1740037))), -(c_List_Oremove1(_1740033, _1740035, hAPP(hAPP(c_List_Oappend(_1740033), _1740037), _1740039)) = hAPP(hAPP(c_List_Oappend(_1740033), c_List_Oremove1(_1740033, _1740035, _1740037)), _1740039))], (37132 ^ _778908) ^ [_1470258, _1470260, _1470262, _1470264] : [class_Orderings_Oorder(_1470258), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470258, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1470258, _1470260, _1470262)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1470258, _1470262, _1470264)) = c_Orderings_Obot__class_Obot(tc_fun(_1470258, tc_HOL_Obool)))], (31367 ^ _778908) ^ [_1344759, _1344761, _1344763] : [hBOOL(hAPP(hAPP(c_member(_1344759), _1344761), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1344759, tc_HOL_Obool)), _1344763))), hBOOL(hAPP(hAPP(c_member(_1344759), _1344761), _1344763))], (29940 ^ _778908) ^ [_1314832] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1314832), c_Orderings_Obot__class_Obot(tc_fun(_1314832, tc_HOL_Obool)))))], (35714 ^ _778908) ^ [_1437445, _1437447, _1437449, _1437451, _1437453, _1437455, _1437457] : [-(hAPP(c_Product__Type_Oapsnd(_1437445, _1437447, _1437449, _1437451), hAPP(c_Product__Type_Oapsnd(_1437453, _1437445, _1437449, _1437455), _1437457)) = hAPP(c_Product__Type_Oapsnd(_1437453, _1437447, _1437449, hAPP(c_Fun_Ocomp(_1437445, _1437447, _1437453, _1437451), _1437455)), _1437457))], (41111 ^ _778908) ^ [_1559742] : [-(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)), _1559742)))))], (32186 ^ _778908) ^ [_1363573, _1363575, _1363577, _1363579, _1363581] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1363573, _1363575, _1363577), _1363579), _1363581)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1363573, _1363575)), hAPP(hAPP(c_Product__Type_OPair(_1363573, _1363575), _1363579), _1363581)), _1363577)))], (27920 ^ _778908) ^ [_1273857, _1273859, _1273861] : [class_Groups_Oordered__ab__group__add(_1273857), -(hAPP(c_Set_Oimage(_1273857, _1273857, c_Groups_Ouminus__class_Ouminus(_1273857)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1273857, _1273859, _1273861)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1273857, hAPP(c_Groups_Ouminus__class_Ouminus(_1273857), _1273861), hAPP(c_Groups_Ouminus__class_Ouminus(_1273857), _1273859)))], (35450 ^ _778908) ^ [_1431468, _1431470] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1431468, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1431468, tc_HOL_Obool))), hAPP(c_Set_OPow(_1431468), _1431470))))], (19777 ^ _778908) ^ [] : [-(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))))], (47519 ^ _778908) ^ [_1724031, _1724033, _1724035] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724031), tc_List_Olist(_1724031))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724031), tc_List_Olist(_1724031)), _1724033), c_List_Olist_ONil(_1724031))), c_List_Olex(_1724031, _1724035)))], (2986 ^ _778908) ^ [_824541, _824543, _824545, _824547, _824549, _824551, _824553, _824555] : [-(c_New__Random__Sequence_Opos__empty(_824555, _824551, _824547, _824543) = c_New__Random__Sequence_Opos__empty(_824553, _824549, _824545, _824541)), _824555 = _824553, _824551 = _824549, _824547 = _824545, _824543 = _824541], (15436 ^ _778908) ^ [_1041572, _1041574, _1041576] : [class_Groups_Ogroup__add(_1041572), 15439 ^ _778908 : [(15446 ^ _778908) ^ [] : [_1041574 = _1041576, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041572), _1041574), _1041576) = c_Groups_Ozero__class_Ozero(_1041572))], (15440 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041572), _1041574), _1041576) = c_Groups_Ozero__class_Ozero(_1041572), -(_1041574 = _1041576)]]], (39291 ^ _778908) ^ [_1517388, _1517390, _1517392, _1517394] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517388), _1517390)), -(hAPP(c_Set_Oimage(_1517388, _1517392, _1517394), _1517390) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1517392, tc_HOL_Obool), _1517388, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517392, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1517388, tc_fun(_1517392, tc_HOL_Obool), tc_fun(_1517392, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1517392, tc_fun(tc_fun(_1517392, tc_HOL_Obool), tc_fun(_1517392, tc_HOL_Obool)), _1517388), c_Set_Oinsert(_1517392)), _1517394)), c_Orderings_Obot__class_Obot(tc_fun(_1517392, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1517392, tc_HOL_Obool))), _1517390))], (23052 ^ _778908) ^ [_1180060, _1180062] : [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), _1180060), _1180062))), 23055 ^ _778908 : [(23062 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180062), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23065 ^ _778908 : [(23074 ^ _778908) ^ [] : [-(c_Nitpick_Onorm__frac(_1180060, _1180062) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1180060), _1180062)), 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), _1180060))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180062)))), -(_1180060 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1180062 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23066 ^ _778908) ^ [] : [23067 ^ _778908 : [(23070 ^ _778908) ^ [] : [_1180062 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23068 ^ _778908) ^ [] : [_1180060 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1180060, _1180062) = 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)))]]], (23056 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180062), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1180060, _1180062) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180060), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180062)))]]], (1632 ^ _778908) ^ [_802182, _802184] : [-(class_Divides_Osemiring__div(_802182)), _802184 = _802182, class_Divides_Osemiring__div(_802184)], (8468 ^ _778908) ^ [_921013, _921015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921013)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _921013), _921015)))], (28021 ^ _778908) ^ [_1275715, _1275717, _1275719, _1275721] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275715, tc_HOL_Obool)), _1275717), _1275719), _1275721)), -(hBOOL(hAPP(_1275717, _1275721))), -(hBOOL(hAPP(_1275719, _1275721)))], (40030 ^ _778908) ^ [_1534627, _1534629, _1534631, _1534633, _1534635] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1534627, _1534629, hAPP(hAPP(c_Set_Oinsert(_1534627), _1534631), _1534633)), _1534635))), 40031 ^ _778908 : [(40032 ^ _778908) ^ [_1534731, _1534733] : [hAPP(hAPP(c_Set_Oinsert(_1534627), _1534631), _1534633) = hAPP(hAPP(c_Set_Oinsert(_1534627), _1534733), _1534731), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1534627, _1534627, _1534629, _1534733, _1534731), _1534635)), -(hBOOL(hAPP(hAPP(c_member(_1534627), _1534733), _1534731)))]]], (47878 ^ _778908) ^ [_1733162, _1733164, _1733166, _1733168] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733162)), hAPP(hAPP(c_List_Olist__update(_1733162, _1733164), _1733166), _1733168)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733162)), _1733164))], (45690 ^ _778908) ^ [_1678302, _1678304] : [c_Wellfounded_Owf(_1678302, _1678304), 45693 ^ _778908 : [(45694 ^ _778908) ^ [_1678434] : [45695 ^ _778908 : [(45696 ^ _778908) ^ [_1678539] : [hBOOL(hAPP(hAPP(c_member(_1678302), _1678539), _1678434))]], 45698 ^ _778908 : [(45701 ^ _778908) ^ [_1678661] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1678302, _1678302)), hAPP(hAPP(c_Product__Type_OPair(_1678302, _1678302), _1678661), 45697 ^ [_1678302, _1678304, _1678434])), _1678304)), hBOOL(hAPP(hAPP(c_member(_1678302), _1678661), _1678434))], (45699 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678302), 45697 ^ [_1678302, _1678304, _1678434]), _1678434)))]]]]], (21491 ^ _778908) ^ [_1150079, _1150081] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150079), _1150081), hAPP(c_Int_Onumber__class_Onumber__of(_1150079), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1150079)), class_Fields_Ofield__inverse__zero(_1150079), class_Int_Onumber__ring(_1150079)], (45125 ^ _778908) ^ [_1665500, _1665502] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1665500, tc_HOL_Obool), _1665502) = hAPP(c_Set_OCollect(_1665500), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1665500, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1665500), c_HOL_OAll(tc_fun(_1665500, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1665500, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1665500, tc_HOL_Obool), tc_HOL_Obool), _1665500), hAPP(c_COMBS(tc_fun(_1665500, 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(_1665500, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1665500, tc_HOL_Obool), tc_fun(tc_fun(_1665500, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1665500, tc_HOL_Obool))), _1665502)))), c_member(_1665500)))))], (10337 ^ _778908) ^ [_952616] : [_952616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _952616) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20219 ^ _778908) ^ [_1127893, _1127895, _1127897, _1127899] : [class_Rings_Odivision__ring(_1127893), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127893), _1127895), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127893), _1127897), _1127899)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127893), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127893), _1127895), _1127897)), _1127899))], (20747 ^ _778908) ^ [_1136990, _1136992, _1136994] : [class_Rings_Odivision__ring(_1136990), -(_1136992 = c_Groups_Ozero__class_Ozero(_1136990)), 20754 ^ _778908 : [(20761 ^ _778908) ^ [] : [_1136994 = _1136992, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136990), _1136994), _1136992) = c_Groups_Oone__class_Oone(_1136990))], (20755 ^ _778908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136990), _1136994), _1136992) = c_Groups_Oone__class_Oone(_1136990), -(_1136994 = _1136992)]]], (6869 ^ _778908) ^ [_891997, _891999, _892001, _892003, _892005] : [c_Com_Ocom_OWhile(_891997, _891999) = c_Com_Ocom_OLocal(_892001, _892003, _892005)], (44627 ^ _778908) ^ [_1651621, _1651623, _1651625, _1651627, _1651629, _1651631] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651621, tc_fun(_1651623, tc_HOL_Obool)), _1651625), hAPP(hAPP(c_COMBC(_1651621, tc_fun(_1651627, tc_fun(_1651623, tc_HOL_Obool)), tc_fun(_1651623, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1651627, tc_HOL_Obool), tc_fun(tc_fun(_1651627, tc_fun(_1651623, tc_HOL_Obool)), tc_fun(_1651623, tc_HOL_Obool)), _1651621), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651627, tc_fun(_1651623, tc_HOL_Obool))), _1651629)), _1651631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651627, tc_fun(_1651623, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1651621, tc_fun(_1651627, tc_HOL_Obool)), _1651625), _1651629)), _1651631))], (24749 ^ _778908) ^ [_1212278, _1212280, _1212282, _1212284, _1212286] : [-(hAPP(c_Product__Type_Osnd(_1212278, _1212280), hAPP(c_Product__Type_Oapfst(_1212282, _1212278, _1212280, _1212284), _1212286)) = hAPP(c_Product__Type_Osnd(_1212282, _1212280), _1212286))], (45785 ^ _778908) ^ [_1680510, _1680512, _1680514, _1680516, _1680518, _1680520, _1680522, _1680524] : [c_Finite__Set_Ofolding__image__simple__idem(_1680510, _1680512, _1680514, _1680516, _1680518, _1680520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1680512), _1680522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1680512, tc_HOL_Obool)), _1680524), _1680522)), -(hAPP(hAPP(_1680514, hAPP(_1680520, _1680524)), hAPP(_1680520, _1680522)) = hAPP(_1680520, _1680522))], (10763 ^ _778908) ^ [_959378, _959380, _959382, _959384] : [class_Orderings_Oord(_959378), 10766 ^ _778908 : [(10773 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959378), hAPP(_959382, 10774 ^ [_959378, _959380, _959382, _959384])), hAPP(_959384, 10774 ^ [_959378, _959380, _959382, _959384]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959380, _959378)), _959382), _959384)))], (10767 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959380, _959378)), _959382), _959384)), 10770 ^ _778908 : [(10771 ^ _778908) ^ [_959535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959378), hAPP(_959382, _959535)), hAPP(_959384, _959535))))]]]]], (43705 ^ _778908) ^ [_1631028, _1631030, _1631032] : [c_Wellfounded_Owf(_1631028, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631028, _1631028), tc_HOL_Obool), _1631030), _1631032)), -(c_Wellfounded_Owf(_1631028, _1631032))], (35136 ^ _778908) ^ [_1424113, _1424115, _1424117] : [class_Orderings_Olinorder(_1424113), hAPP(_1424115, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424113), 35141 ^ [_1424113, _1424115, _1424117]), 35142 ^ [_1424113, _1424115, _1424117])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424113), hAPP(_1424115, 35141 ^ [_1424113, _1424115, _1424117])), hAPP(_1424115, 35142 ^ [_1424113, _1424115, _1424117])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424113), _1424117)), -(_1424117 = c_Orderings_Obot__class_Obot(tc_fun(_1424113, tc_HOL_Obool))), -(hAPP(_1424115, c_Big__Operators_Olattice_OInf__fin(_1424113, c_Orderings_Oord__class_Omin(_1424113), _1424117)) = c_Big__Operators_Olattice_OInf__fin(_1424113, c_Orderings_Oord__class_Omin(_1424113), hAPP(c_Set_Oimage(_1424113, _1424113, _1424115), _1424117)))], (41400 ^ _778908) ^ [_1568067] : [-(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)))), _1568067))))], (44813 ^ _778908) ^ [_1656502, _1656504, _1656506, _1656508, _1656510] : [hBOOL(hAPP(hAPP(c_member(_1656502), _1656504), _1656506)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1656508, tc_HOL_Obool)), hAPP(_1656510, _1656504)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656502, tc_fun(_1656508, tc_HOL_Obool)), _1656506), _1656510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656502, tc_fun(_1656508, tc_HOL_Obool)), _1656506), _1656510))], (40408 ^ _778908) ^ [_1545610, _1545612, _1545614, _1545616, _1545618, _1545620, _1545622, _1545624] : [c_Fun_Oinj__on(_1545610, _1545612, _1545614, _1545616), c_Fun_Oinj__on(_1545618, _1545620, _1545622, _1545624), -(c_Fun_Oinj__on(tc_prod(_1545610, _1545618), tc_prod(_1545612, _1545620), c_Product__Type_Omap__pair(_1545610, _1545612, _1545618, _1545620, _1545614, _1545622), hAPP(hAPP(c_Product__Type_OSigma(_1545610, _1545618), _1545616), hAPP(c_COMBK(tc_fun(_1545618, tc_HOL_Obool), _1545610), _1545624))))], (27985 ^ _778908) ^ [_1275026, _1275028, _1275030, _1275032] : [class_Orderings_Olinorder(_1275026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275026), _1275028), _1275030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275026), _1275030), _1275032)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275026, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1275026, _1275028, _1275030)), c_SetInterval_Oord__class_OatLeastAtMost(_1275026, _1275030, _1275032)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1275026, _1275028, _1275032))], (47224 ^ _778908) ^ [_1717696, _1717698, _1717700, _1717702, _1717704] : [class_Groups_Oab__group__add(_1717696), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717696), hAPP(hAPP(c_List_Omap(_1717698, _1717696), hAPP(hAPP(c_COMBS(_1717698, _1717696, _1717696), hAPP(hAPP(c_COMBB(_1717696, tc_fun(_1717696, _1717696), _1717698), c_Groups_Ominus__class_Ominus(_1717696)), _1717700)), _1717702)), _1717704)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1717696), hAPP(c_List_Omonoid__add__class_Olistsum(_1717696), hAPP(hAPP(c_List_Omap(_1717698, _1717696), _1717700), _1717704))), hAPP(c_List_Omonoid__add__class_Olistsum(_1717696), hAPP(hAPP(c_List_Omap(_1717698, _1717696), _1717702), _1717704))))], (27815 ^ _778908) ^ [_1272218, _1272220, _1272222] : [class_Groups_Ocomm__monoid__add(_1272218), class_Groups_Ocomm__monoid__mult(_1272218), c_Nat__Transfer_Onat__set(_1272220), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1272218), _1272222), _1272220) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1272218), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1272218, tc_Nat_Onat), _1272222), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1272220)))], (41390 ^ _778908) ^ [_1567844, _1567846, _1567848, _1567850, _1567852, _1567854] : [-(hBOOL(hAPP(hAPP(c_member(_1567844), _1567846), _1567848))), -(hAPP(c_Fun_Ooverride__on(_1567844, _1567850, _1567852, _1567854, _1567848), _1567846) = hAPP(_1567852, _1567846))], (18151 ^ _778908) ^ [_1092652, _1092654] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092652))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092652)), _1092654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1092654))], (2758 ^ _778908) ^ [_820725, _820727, _820729, _820731] : [-(c_Nitpick_Oint__lcm(_820731, _820727) = c_Nitpick_Oint__lcm(_820729, _820725)), _820731 = _820729, _820727 = _820725], (6871 ^ _778908) ^ [_892053, _892055, _892057, _892059] : [c_Com_Ocom_OWhile(_892053, _892055) = c_Com_Ocom_OSemi(_892057, _892059)], (13931 ^ _778908) ^ [_1014297, _1014299, _1014301, _1014303] : [class_Divides_Osemiring__div(_1014297), -(c_Divides_Odiv__class_Omod(_1014297, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014297), _1014299), _1014301), _1014303) = c_Divides_Odiv__class_Omod(_1014297, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014297), _1014299), c_Divides_Odiv__class_Omod(_1014297, _1014301, _1014303)), _1014303))], (47360 ^ _778908) ^ [_1721115, _1721117, _1721119] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721115), tc_List_Olist(_1721115))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721115), tc_List_Olist(_1721115)), c_List_Olist_ONil(_1721115)), _1721117)), c_List_Olistrel(_1721115, _1721119))), -(_1721117 = c_List_Olist_ONil(_1721115))], (11086 ^ _778908) ^ [_964564, _964566, _964568] : [class_Orderings_Olinorder(_964564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964564), _964566), _964568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964564), _964568), _964566))], (44476 ^ _778908) ^ [_1648351, _1648353, _1648355, _1648357, _1648359, _1648361] : [c_Finite__Set_Ofun__left__comm(_1648351, _1648353, _1648355), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1648351, _1648353, _1648355, _1648357, _1648359), _1648361)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1648351, _1648353, _1648355), _1648357), _1648359) = _1648361)], (22015 ^ _778908) ^ [_1159968, _1159970, _1159972, _1159974] : [class_Fields_Ofield(_1159968), -(_1159970 = c_Groups_Ozero__class_Ozero(_1159968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159972), _1159974)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1159968), _1159970), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1159974), _1159972)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159968), hAPP(hAPP(c_Power_Opower__class_Opower(_1159968), _1159970), _1159974)), hAPP(hAPP(c_Power_Opower__class_Opower(_1159968), _1159970), _1159972)))], (22279 ^ _778908) ^ [] : [-(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))], (2788 ^ _778908) ^ [_821180, _821182, _821184, _821186, _821188, _821190] : [-(c_Nitpick_Otimes__frac(_821190, _821186, _821182) = c_Nitpick_Otimes__frac(_821188, _821184, _821180)), _821190 = _821188, _821186 = _821184, _821182 = _821180], (862 ^ _778908) ^ [_792207, _792209] : [-(c_List_Onat__list(_792207)), _792209 = _792207, c_List_Onat__list(_792209)], (30117 ^ _778908) ^ [_1318414, _1318416, _1318418] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318414, tc_fun(_1318416, tc_HOL_Obool)), _1318418), hAPP(c_COMBK(tc_fun(_1318416, tc_HOL_Obool), _1318414), c_Orderings_Obot__class_Obot(tc_fun(_1318416, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1318416, tc_HOL_Obool)))], (33121 ^ _778908) ^ [_1383104, _1383106, _1383108] : [class_Rings_Oring__1(_1383104), hBOOL(hAPP(hAPP(c_member(_1383104), _1383106), c_Int_Oring__1__class_OInts(_1383104))), hBOOL(hAPP(hAPP(c_member(_1383104), _1383108), c_Int_Oring__1__class_OInts(_1383104))), -(hBOOL(hAPP(hAPP(c_member(_1383104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383104), _1383106), _1383108)), c_Int_Oring__1__class_OInts(_1383104))))], (42231 ^ _778908) ^ [_1594548, _1594550, _1594552, _1594554] : [hBOOL(hAPP(hAPP(c_member(_1594550), _1594554), hAPP(c_Relation_ORange(_1594548, _1594550), _1594552))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1594548, _1594550, hAPP(hAPP(c_COMBC(_1594548, tc_fun(tc_prod(_1594548, _1594550), tc_HOL_Obool), tc_fun(_1594550, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1594550, tc_fun(tc_fun(tc_prod(_1594548, _1594550), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1594548, _1594550), tc_HOL_Obool), tc_fun(_1594550, tc_HOL_Obool)), _1594548), c_COMBC(_1594550, tc_fun(tc_prod(_1594548, _1594550), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1594550, tc_prod(_1594548, _1594550)), tc_fun(_1594550, tc_fun(tc_fun(tc_prod(_1594548, _1594550), tc_HOL_Obool), tc_HOL_Obool)), _1594548), hAPP(c_COMBB(tc_prod(_1594548, _1594550), tc_fun(tc_fun(tc_prod(_1594548, _1594550), tc_HOL_Obool), tc_HOL_Obool), _1594550), c_member(tc_prod(_1594548, _1594550)))), c_Product__Type_OPair(_1594548, _1594550)))), _1594552)), _1594554)))], (42000 ^ _778908) ^ [_1589124, _1589126, _1589128, _1589130, _1589132, _1589134, _1589136] : [-(c_Predicate_Opred__comp(_1589124, _1589126, _1589128, _1589130, _1589132, _1589134, _1589136)), 42001 ^ _778908 : [(42002 ^ _778908) ^ [_1589189] : [hBOOL(hAPP(hAPP(_1589130, _1589134), _1589189)), hBOOL(hAPP(hAPP(_1589132, _1589189), _1589136))]]], (28565 ^ _778908) ^ [_1286518, _1286520] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1286518), _1286520) = 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)), _1286518)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1286520))))], (51551 ^ _778908) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (33007 ^ _778908) ^ [_1380415, _1380417, _1380419, _1380421, _1380423, _1380425, _1380427] : [c_Hoare__Mirabelle_Ohoare__derivs(_1380415, _1380417, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1380415)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1380415), _1380419), _1380421), _1380423)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380415), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1380415, _1380417, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1380415)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1380415), _1380423), _1380425), _1380427)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380415), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1380415, _1380417, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1380415)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1380415), _1380419), c_Com_Ocom_OSemi(_1380421, _1380425)), _1380427)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380415), tc_HOL_Obool)))))], (39018 ^ _778908) ^ [_1511202, _1511204, _1511206, _1511208, _1511210, _1511212, _1511214, _1511216] : [class_Groups_Ocomm__monoid__mult(_1511202), c_Fun_Oinj__on(_1511204, _1511206, _1511208, _1511210), _1511212 = hAPP(c_Set_Oimage(_1511204, _1511206, _1511208), _1511210), _1511214 = hAPP(c_Fun_Ocomp(_1511206, _1511202, _1511204, _1511216), _1511208), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1511206, _1511202), _1511216), _1511212) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1511204, _1511202), _1511214), _1511210))], (21027 ^ _778908) ^ [_1141926, _1141928, _1141930, _1141932] : [class_Fields_Olinordered__field(_1141926), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141926), _1141928), c_Groups_Ozero__class_Ozero(_1141926))), 21034 ^ _778908 : [(21041 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141926), _1141932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141926), _1141930), _1141928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141926), _1141930), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141926), _1141932), _1141928))))], (21035 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141926), _1141930), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141926), _1141932), _1141928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141926), _1141932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141926), _1141930), _1141928))))]]], (922 ^ _778908) ^ [_793079, _793081] : [-(class_Lattices_Oab__semigroup__idem__mult(_793079)), _793081 = _793079, class_Lattices_Oab__semigroup__idem__mult(_793081)], (31481 ^ _778908) ^ [_1346833, _1346835, _1346837, _1346839, _1346841, _1346843, _1346845, _1346847] : [c_Finite__Set_Ofolding__image__simple(_1346833, _1346835, _1346837, _1346839, _1346841, _1346843), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346835), _1346845)), -(hBOOL(hAPP(hAPP(c_member(_1346835), _1346847), _1346845))), -(hAPP(_1346843, hAPP(hAPP(c_Set_Oinsert(_1346835), _1346847), _1346845)) = hAPP(hAPP(_1346837, hAPP(_1346841, _1346847)), hAPP(_1346843, _1346845)))], (39192 ^ _778908) ^ [_1514812, _1514814, _1514816, _1514818, _1514820] : [-(c_Fun_Oinj__on(_1514812, _1514814, _1514816, hAPP(hAPP(c_Set_Oinsert(_1514812), _1514818), _1514820))), c_Fun_Oinj__on(_1514812, _1514814, _1514816, _1514820), -(hBOOL(hAPP(hAPP(c_member(_1514814), hAPP(_1514816, _1514818)), hAPP(c_Set_Oimage(_1514812, _1514814, _1514816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514812, tc_HOL_Obool)), _1514820), hAPP(hAPP(c_Set_Oinsert(_1514812), _1514818), c_Orderings_Obot__class_Obot(tc_fun(_1514812, tc_HOL_Obool))))))))], (10551 ^ _778908) ^ [_956109] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956109), _956109)))], (27179 ^ _778908) ^ [_1259062, _1259064] : [27181 ^ _778908 : [(27184 ^ _778908) ^ [] : [hBOOL(hAPP(_1259064, 27180 ^ [_1259062, _1259064]))], (27182 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27180 ^ [_1259062, _1259064]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1259062))))]], 27185 ^ _778908 : [(27186 ^ _778908) ^ [_1259215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1259215), _1259062)), -(hBOOL(hAPP(_1259064, _1259215)))]]], (50875 ^ _778908) ^ [_1801323, _1801325] : [-(hAPP(c_List_Orev(_1801323), c_List_Oconcat(_1801323, _1801325)) = c_List_Oconcat(_1801323, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1801323), tc_List_Olist(_1801323)), c_List_Orev(_1801323)), hAPP(c_List_Orev(tc_List_Olist(_1801323)), _1801325))))], (6923 ^ _778908) ^ [_893265, _893267, _893269, _893271] : [-(c_Com_Ovname_Ovname__case(_893265, _893267, _893269, c_Com_Ovname_OLoc(_893271)) = hAPP(_893269, _893271))], (12900 ^ _778908) ^ [_996129, _996131, _996133, _996135, _996137] : [class_Rings_Olinordered__semiring__strict(_996129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996129), _996131), _996133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996129), _996135), _996137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996129), c_Groups_Ozero__class_Ozero(_996129)), _996131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996129), c_Groups_Ozero__class_Ozero(_996129)), _996135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996129), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996129), _996131), _996135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996129), _996133), _996137))))], (23905 ^ _778908) ^ [_1195695, _1195697, _1195699, _1195701] : [class_Orderings_Olinorder(_1195695), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195695), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195695), _1195697), _1195699)), _1195701) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195695), _1195697), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195695), _1195699), _1195701)))], (50901 ^ _778908) ^ [_1801907, _1801909] : [class_Groups_Ocomm__monoid__add(_1801907), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1801907), hAPP(c_List_Orev(_1801907), _1801909)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1801907), _1801909))], (16623 ^ _778908) ^ [_1064571, _1064573, _1064575] : [class_Rings_Olinordered__idom(_1064571), -(hAPP(c_Groups_Oabs__class_Oabs(_1064571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064571), _1064573), _1064575)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064571), hAPP(c_Groups_Oabs__class_Oabs(_1064571), _1064573)), hAPP(c_Groups_Oabs__class_Oabs(_1064571), _1064575)))], (43403 ^ _778908) ^ [_1623354, _1623356, _1623358, _1623360] : [hBOOL(hAPP(hAPP(c_member(_1623354), _1623356), c_Wellfounded_Oacc(_1623354, _1623358))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1623354, _1623354)), hAPP(hAPP(c_Product__Type_OPair(_1623354, _1623354), _1623360), _1623356)), c_Transitive__Closure_Ortrancl(_1623354, _1623358))), -(hBOOL(hAPP(hAPP(c_member(_1623354), _1623360), c_Wellfounded_Oacc(_1623354, _1623358))))], (2210 ^ _778908) ^ [_812055, _812057, _812059, _812061, _812063, _812065, _812067, _812069] : [-(c_Nitpick_Opair__box_OPairBox(_812069, _812065, _812061, _812057) = c_Nitpick_Opair__box_OPairBox(_812067, _812063, _812059, _812055)), _812069 = _812067, _812065 = _812063, _812061 = _812059, _812057 = _812055], (14627 ^ _778908) ^ [_1027173, _1027175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027175, _1027173)), _1027173)))], (3208 ^ _778908) ^ [_828060, _828062, _828064, _828066, _828068, _828070, _828072, _828074] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_828074, _828070, _828066, _828062) = c_SetInterval_Oord_OgreaterThanLessThan(_828072, _828068, _828064, _828060)), _828074 = _828072, _828070 = _828068, _828066 = _828064, _828062 = _828060], (24005 ^ _778908) ^ [_1197613, _1197615, _1197617, _1197619] : [-(_1197613 = _1197615), hAPP(c_Product__Type_Ofst(_1197617, _1197619), _1197613) = hAPP(c_Product__Type_Ofst(_1197617, _1197619), _1197615), hAPP(c_Product__Type_Osnd(_1197617, _1197619), _1197613) = hAPP(c_Product__Type_Osnd(_1197617, _1197619), _1197615)], (35032 ^ _778908) ^ [_1421373, _1421375, _1421377, _1421379] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1421373), _1421375)), 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)), _1421377), _1421373)), 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)), _1421379), _1421375)), 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)), _1421377), _1421379)), _1421375)), c_FunDef_Omax__weak)))], (51325 ^ _778908) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (36890 ^ _778908) ^ [_1464171, _1464173, _1464175] : [-(hAPP(c_Set_OPow(_1464171), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464171, tc_HOL_Obool)), _1464173), _1464175)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1464171, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1464171), _1464173)), hAPP(c_Set_OPow(_1464171), _1464175)))], (50178 ^ _778908) ^ [_1787519, _1787521, _1787523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1787519), _1787521)), _1787523)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1787521), c_List_Oupt(_1787519, _1787523)) = c_List_Oupt(_1787519, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1787519), _1787521)))], (7398 ^ _778908) ^ [_902491] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _902491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_902491)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7663 ^ _778908) ^ [_906989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906989), _906989))], (26533 ^ _778908) ^ [_1246188, _1246190, _1246192] : [26534 ^ _778908 : [(26537 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246190), _1246192))], (26535 ^ _778908) ^ [] : [_1246188 = 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), _1246188), _1246190)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246188), _1246192))))], (30612 ^ _778908) ^ [_1327460] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1327460), hAPP(c_Nat_OSuc, _1327460)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1327460), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27640 ^ _778908) ^ [_1268546, _1268548] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268546) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268548), -(_1268546 = _1268548)], (16382 ^ _778908) ^ [_1060521, _1060523] : [_1060521 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1060521), _1060523) = _1060523)], (15568 ^ _778908) ^ [_1043912, _1043914, _1043916] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1043912)), _1043914)), hAPP(c_Nat_OSuc, _1043916)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043912), _1043914)), _1043916))], (24219 ^ _778908) ^ [_1202024, _1202026] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1202024)), _1202026) = 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), _1202024)), _1202026))], (31199 ^ _778908) ^ [_1340291, _1340293, _1340295, _1340297, _1340299, _1340301] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340291, tc_fun(_1340293, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1340291, tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_fun(_1340293, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340293, tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_fun(_1340293, tc_HOL_Obool)), _1340291), c_COMBC(_1340293, tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340293, tc_prod(_1340291, _1340293)), tc_fun(_1340293, tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool)), _1340291), hAPP(c_COMBB(tc_prod(_1340291, _1340293), tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool), _1340293), c_member(tc_prod(_1340291, _1340293)))), c_Product__Type_OPair(_1340291, _1340293)))), _1340295)), hAPP(hAPP(c_COMBC(_1340291, tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_fun(_1340293, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340293, tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_fun(_1340293, tc_HOL_Obool)), _1340291), c_COMBC(_1340293, tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340293, tc_prod(_1340291, _1340293)), tc_fun(_1340293, tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool)), _1340291), hAPP(c_COMBB(tc_prod(_1340291, _1340293), tc_fun(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool), tc_HOL_Obool), _1340293), c_member(tc_prod(_1340291, _1340293)))), c_Product__Type_OPair(_1340291, _1340293)))), _1340297)), _1340299), _1340301)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1340291, _1340293)), hAPP(hAPP(c_Product__Type_OPair(_1340291, _1340293), _1340299), _1340301)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1340291, _1340293), tc_HOL_Obool)), _1340295), _1340297))))], (36708 ^ _778908) ^ [_1460373, _1460375] : [class_Lattices_Obounded__lattice__bot(_1460373), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1460373), c_Orderings_Obot__class_Obot(_1460373)), _1460375) = c_Orderings_Obot__class_Obot(_1460373))], (45408 ^ _778908) ^ [_1671892, _1671894, _1671896, _1671898, _1671900] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1671892, tc_fun(_1671894, tc_HOL_Obool)), _1671896), hAPP(hAPP(c_COMBS(_1671892, tc_fun(_1671894, tc_HOL_Obool), tc_fun(_1671894, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1671894, tc_HOL_Obool), tc_fun(tc_fun(_1671894, tc_HOL_Obool), tc_fun(_1671894, tc_HOL_Obool)), _1671892), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1671894, tc_HOL_Obool))), _1671898)), _1671900)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1671894, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671894, tc_HOL_Obool), hAPP(c_Set_Oimage(_1671892, tc_fun(_1671894, tc_HOL_Obool), _1671898), _1671896))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671894, tc_HOL_Obool), hAPP(c_Set_Oimage(_1671892, tc_fun(_1671894, tc_HOL_Obool), _1671900), _1671896))))], (24917 ^ _778908) ^ [_1215509] : [-(c_Nitpick_Oone__frac(_1215509) = c_Nitpick_OAbs__Frac(_1215509, 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))))], (24115 ^ _778908) ^ [_1200097, _1200099, _1200101] : [-(_1200097 = _1200099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200101, tc_HOL_Obool)), _1200097), _1200099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200101, tc_HOL_Obool)), _1200099), _1200097))], (33441 ^ _778908) ^ [_1389165, _1389167, _1389169] : [class_Orderings_Olinorder(_1389165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389165), _1389167)), hBOOL(hAPP(hAPP(c_member(_1389165), _1389169), _1389167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389165), c_Big__Operators_Olinorder__class_OMin(_1389165, _1389167)), _1389169)))], (37044 ^ _778908) ^ [_1468407, _1468409, _1468411, _1468413] : [class_Orderings_Oorder(_1468407), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468407, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1468407, _1468409, _1468411)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1468407, _1468411, _1468413)) = c_Orderings_Obot__class_Obot(tc_fun(_1468407, tc_HOL_Obool)))], (18517 ^ _778908) ^ [_1098339] : [-(c_Int_Osucc(c_Int_Opred(_1098339)) = _1098339)], (47775 ^ _778908) ^ [_1730379, _1730381, _1730383, _1730385] : [-(_1730379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1730381), hAPP(hAPP(c_List_Olist_OCons(_1730381), _1730383), _1730385)), _1730379) = hAPP(hAPP(c_List_Onth(_1730381), _1730385), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1730379), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (39345 ^ _778908) ^ [_1518500, _1518502, _1518504, _1518506, _1518508] : [class_Groups_Ocomm__monoid__mult(_1518500), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518502), _1518504)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518502), _1518506)), 39359 ^ _778908 : [(39362 ^ _778908) ^ [] : [hAPP(_1518508, 39358 ^ [_1518500, _1518502, _1518504, _1518506, _1518508]) = c_Groups_Oone__class_Oone(_1518500)], (39360 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518502), 39358 ^ [_1518500, _1518502, _1518504, _1518506, _1518508]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518502, tc_HOL_Obool)), _1518504), _1518506))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518500, _1518502, c_Groups_Otimes__class_Otimes(_1518500)), _1518508), c_Groups_Oone__class_Oone(_1518500)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1518502, tc_HOL_Obool)), _1518504), _1518506)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1518500), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518500, _1518502, c_Groups_Otimes__class_Otimes(_1518500)), _1518508), c_Groups_Oone__class_Oone(_1518500)), _1518504)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518500, _1518502, c_Groups_Otimes__class_Otimes(_1518500)), _1518508), c_Groups_Oone__class_Oone(_1518500)), _1518506)))], (23190 ^ _778908) ^ [_1182459, _1182461] : [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), _1182459), _1182461))), 23193 ^ _778908 : [(23200 ^ _778908) ^ [] : [-(_1182461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1182459, _1182461) = c_Nitpick_Onat__gcd(_1182461, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1182459, _1182461)))], (23194 ^ _778908) ^ [] : [_1182461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1182459, _1182461) = _1182459)]]], (8972 ^ _778908) ^ [_928853, _928855, _928857] : [class_Rings_Oring(_928853), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928853), hAPP(c_Groups_Ouminus__class_Ouminus(_928853), _928855)), hAPP(c_Groups_Ouminus__class_Ouminus(_928853), _928857)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928853), _928855), _928857))], (32785 ^ _778908) ^ [_1376003, _1376005] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376003), _1376005)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1376005, _1376003) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (3622 ^ _778908) ^ [_834619, _834621] : [_834621 = _834619, -(c_Rings_Oinverse__class_Odivide(_834621) = c_Rings_Oinverse__class_Odivide(_834619))], (39540 ^ _778908) ^ [_1523016, _1523018, _1523020, _1523022, _1523024] : [-(hAPP(c_Set_Ovimage(_1523016, _1523018, _1523020), hAPP(hAPP(c_Set_Oinsert(_1523018), _1523022), _1523024)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523016, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1523016, _1523018, _1523020), hAPP(hAPP(c_Set_Oinsert(_1523018), _1523022), c_Orderings_Obot__class_Obot(tc_fun(_1523018, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1523016, _1523018, _1523020), _1523024)))], (3562 ^ _778908) ^ [_833677, _833679] : [_833679 = _833677, -(c_Nitpick_Onum(_833679) = c_Nitpick_Onum(_833677))], (51561 ^ _778908) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (43765 ^ _778908) ^ [_1632559, _1632561, _1632563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632559, _1632559)), _1632561), c_Transitive__Closure_Otrancl(_1632559, _1632563))), 43769 ^ _778908 : [(43772 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632559, _1632559)), _1632561), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1632559, _1632559), tc_HOL_Obool), 43768 ^ [_1632559, _1632561, _1632563]), _1632563))))], (43770 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 43768 ^ [_1632559, _1632561, _1632563])))]]], (33879 ^ _778908) ^ [_1397610, _1397612, _1397614, _1397616, _1397618] : [33882 ^ _778908 : [(33888 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1397618, 33880 ^ [_1397610, _1397612, _1397614, _1397616, _1397618]), 33884 ^ [_1397610, _1397612, _1397614, _1397616, _1397618]))], (33886 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_1397616, 33881 ^ [_1397610, _1397612, _1397614, _1397616, _1397618], _1397612, 33884 ^ [_1397610, _1397612, _1397614, _1397616, _1397618]))], (33883 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1397614, 33880 ^ [_1397610, _1397612, _1397614, _1397616, _1397618]), 33881 ^ [_1397610, _1397612, _1397614, _1397616, _1397618])))]], -(c_Hoare__Mirabelle_Otriple__valid(_1397610, _1397612, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1397610), _1397614), _1397616), _1397618)))], (43004 ^ _778908) ^ [_1613196, _1613198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613196), _1613198)), -(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), _1613196), _1613198)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (30780 ^ _778908) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (12808 ^ _778908) ^ [_994361, _994363, _994365, _994367] : [class_Rings_Olinordered__semiring__strict(_994361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994361), _994363), _994365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994361), _994367), _994365))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994361), c_Groups_Ozero__class_Ozero(_994361)), _994365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994361), _994363), _994367)))], (51363 ^ _778908) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (40917 ^ _778908) ^ [_1555951, _1555953, _1555955, _1555957] : [c_Big__Operators_Osemilattice__big(_1555951, _1555953, _1555955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555951), _1555957)), -(hAPP(_1555955, _1555957) = hAPP(c_Finite__Set_Ofold1(_1555951, _1555953), _1555957))], (38344 ^ _778908) ^ [_1497783, _1497785] : [c_Equiv__Relations_Oequivp(_1497783, _1497785), 38347 ^ _778908 : [(38354 ^ _778908) ^ [_1497976, _1497978] : [hAPP(_1497785, _1497978) = hAPP(_1497785, _1497976), -(hBOOL(hAPP(hAPP(_1497785, _1497978), _1497976)))], (38348 ^ _778908) ^ [_1497877, _1497879] : [hBOOL(hAPP(hAPP(_1497785, _1497879), _1497877)), -(hAPP(_1497785, _1497879) = hAPP(_1497785, _1497877))]]], (36744 ^ _778908) ^ [_1461107, _1461109, _1461111] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461107, tc_HOL_Obool)), _1461109), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461107, tc_HOL_Obool)), _1461109), _1461111)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461107, tc_HOL_Obool)), _1461109), _1461111))], (23647 ^ _778908) ^ [_1190910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1190910)), 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), _1190910)) = 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), _1190910))))))], (11454 ^ _778908) ^ [_970635, _970637, _970639] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970635), _970637)), _970639) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970635), _970639)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970637), _970639)))], (9600 ^ _778908) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (16076 ^ _778908) ^ [_1053818, _1053820, _1053822, _1053824, _1053826, _1053828] : [class_Rings_Oordered__ring(_1053818), 16079 ^ _778908 : [(16086 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053818), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053818), _1053820), _1053826)), _1053822)), _1053824)), _1053828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053818), _1053820), _1053822)), _1053824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053818), _1053826), _1053822)), _1053828))))], (16080 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053818), _1053820), _1053822)), _1053824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053818), _1053826), _1053822)), _1053828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053818), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053818), _1053820), _1053826)), _1053822)), _1053824)), _1053828)))]]], (8133 ^ _778908) ^ [_914935, _914937] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914935), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914937), _914935)))))], (25603 ^ _778908) ^ [_1228744, _1228746] : [25610 ^ _778908 : [(25613 ^ _778908) ^ [] : [_1228744 = _1228746], (25611 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228744), _1228746)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228744), _1228746)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228746), _1228744)))], (9430 ^ _778908) ^ [_936679, _936681] : [class_Rings_Ocomm__semiring__1(_936679), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936679), c_Groups_Ozero__class_Ozero(_936679)), _936681) = c_Groups_Ozero__class_Ozero(_936679))], (31471 ^ _778908) ^ [_1346626, _1346628, _1346630, _1346632] : [31472 ^ _778908 : [(31475 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1346626), _1346628), _1346632))], (31473 ^ _778908) ^ [] : [_1346628 = _1346630]], -(hBOOL(hAPP(hAPP(c_member(_1346626), _1346628), hAPP(hAPP(c_Set_Oinsert(_1346626), _1346630), _1346632))))], (46655 ^ _778908) ^ [_1701429, _1701431, _1701433, _1701435, _1701437, _1701439] : [class_Orderings_Olinorder(_1701429), -(hAPP(_1701431, _1701433) = hAPP(_1701431, _1701435)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701437, _1701429, _1701431), _1701435), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701437, _1701429, _1701431), _1701433), _1701439)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701437, _1701429, _1701431), _1701433), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701437, _1701429, _1701431), _1701435), _1701439)))], (24241 ^ _778908) ^ [_1202397] : [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), _1202397))), -(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), _1202397)) = 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), _1202397))))], (15812 ^ _778908) ^ [_1048647, _1048649, _1048651] : [class_Groups_Ogroup__add(_1048647), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048647), _1048649), _1048651) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048647), _1048649), hAPP(c_Groups_Ouminus__class_Ouminus(_1048647), _1048651)))], (21595 ^ _778908) ^ [_1151869, _1151871, _1151873, _1151875] : [class_Fields_Olinordered__field__inverse__zero(_1151869), 21598 ^ _778908 : [(21599 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151869), _1151871), _1151873)), _1151875)), 21602 ^ _778908 : [(21609 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151873))), 21612 ^ _778908 : [(21619 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), _1151873), c_Groups_Ozero__class_Ozero(_1151869)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151875)))], (21613 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), _1151873), c_Groups_Ozero__class_Ozero(_1151869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), _1151873)), _1151871)))]]], (21603 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), _1151871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), _1151873))))]]], (21625 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151869), _1151871), _1151873)), _1151875))), 21628 ^ _778908 : [(21631 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), _1151871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), _1151873)))], (21629 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151873)))]], 21632 ^ _778908 : [(21635 ^ _778908) ^ [] : [21636 ^ _778908 : [(21639 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151869), _1151875), _1151873)), _1151871))], (21637 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), _1151873), c_Groups_Ozero__class_Ozero(_1151869))))]], 21640 ^ _778908 : [(21643 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151875))], (21641 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), _1151873), c_Groups_Ozero__class_Ozero(_1151869)))]]], (21633 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151869), c_Groups_Ozero__class_Ozero(_1151869)), _1151873))]]]]], (11697 ^ _778908) ^ [_974745, _974747, _974749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _974745), _974747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _974749), _974745)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _974749), _974747))))], (48662 ^ _778908) ^ [_1751819, _1751821, _1751823, _1751825, _1751827] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751819), tc_List_Olist(_1751819))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751819), tc_List_Olist(_1751819)), hAPP(hAPP(c_List_Oappend(_1751819), _1751821), _1751823)), hAPP(hAPP(c_List_Oappend(_1751819), _1751821), _1751825))), c_List_Olexord(_1751819, _1751827))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751819, _1751819)), hAPP(hAPP(c_Product__Type_OPair(_1751819, _1751819), 48667 ^ [_1751819, _1751821, _1751823, _1751825, _1751827]), 48667 ^ [_1751819, _1751821, _1751823, _1751825, _1751827])), _1751827))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751819), tc_List_Olist(_1751819))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751819), tc_List_Olist(_1751819)), _1751823), _1751825)), c_List_Olexord(_1751819, _1751827))))], (29809 ^ _778908) ^ [_1312293, _1312295, _1312297] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312293), _1312295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312293), _1312295)), hAPP(c_Finite__Set_Ocard(_1312293), hAPP(hAPP(c_Set_Oinsert(_1312293), _1312297), _1312295)))))], (9028 ^ _778908) ^ [_929695, _929697] : [class_Rings_Ocomm__ring__1(_929695), -(hAPP(c_Groups_Ouminus__class_Ouminus(_929695), _929697) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929695), hAPP(c_Groups_Ouminus__class_Ouminus(_929695), c_Groups_Oone__class_Oone(_929695))), _929697))], (9418 ^ _778908) ^ [_936441, _936443, _936445] : [class_Groups_Ogroup__add(_936441), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936441), _936443), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936441), hAPP(c_Groups_Ouminus__class_Ouminus(_936441), _936443)), _936445)) = _936445)], (34176 ^ _778908) ^ [_1403068, _1403070, _1403072] : [class_Orderings_Olinorder(_1403068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403068), _1403070)), 34183 ^ _778908 : [(34190 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1403068, tc_HOL_Obool)), _1403070), hAPP(hAPP(c_Set_Oinsert(_1403068), _1403072), c_Orderings_Obot__class_Obot(tc_fun(_1403068, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1403068, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1403068, c_Orderings_Oord__class_Omin(_1403068), hAPP(hAPP(c_Set_Oinsert(_1403068), _1403072), _1403070)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1403068), _1403072), c_Big__Operators_Olattice_OInf__fin(_1403068, c_Orderings_Oord__class_Omin(_1403068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1403068, tc_HOL_Obool)), _1403070), hAPP(hAPP(c_Set_Oinsert(_1403068), _1403072), c_Orderings_Obot__class_Obot(tc_fun(_1403068, tc_HOL_Obool)))))))], (34184 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1403068, tc_HOL_Obool)), _1403070), hAPP(hAPP(c_Set_Oinsert(_1403068), _1403072), c_Orderings_Obot__class_Obot(tc_fun(_1403068, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1403068, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1403068, c_Orderings_Oord__class_Omin(_1403068), hAPP(hAPP(c_Set_Oinsert(_1403068), _1403072), _1403070)) = _1403072)]]], (34196 ^ _778908) ^ [_1403556, _1403558, _1403560] : [class_Orderings_Olinorder(_1403556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403556), _1403558)), 34203 ^ _778908 : [(34210 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1403556, tc_HOL_Obool)), _1403558), hAPP(hAPP(c_Set_Oinsert(_1403556), _1403560), c_Orderings_Obot__class_Obot(tc_fun(_1403556, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1403556, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1403556, c_Orderings_Oord__class_Omax(_1403556), hAPP(hAPP(c_Set_Oinsert(_1403556), _1403560), _1403558)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1403556), _1403560), c_Big__Operators_Olattice_OSup__fin(_1403556, c_Orderings_Oord__class_Omax(_1403556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1403556, tc_HOL_Obool)), _1403558), hAPP(hAPP(c_Set_Oinsert(_1403556), _1403560), c_Orderings_Obot__class_Obot(tc_fun(_1403556, tc_HOL_Obool)))))))], (34204 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1403556, tc_HOL_Obool)), _1403558), hAPP(hAPP(c_Set_Oinsert(_1403556), _1403560), c_Orderings_Obot__class_Obot(tc_fun(_1403556, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1403556, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1403556, c_Orderings_Oord__class_Omax(_1403556), hAPP(hAPP(c_Set_Oinsert(_1403556), _1403560), _1403558)) = _1403560)]]], (5136 ^ _778908) ^ [_858334, _858336] : [_858336 = _858334, -(c_Int_Onumber__class_Onumber__of(_858336) = c_Int_Onumber__class_Onumber__of(_858334))], (5610 ^ _778908) ^ [_865557, _865559] : [_865559 = _865557, -(c_List_Oreturn__list(_865559) = c_List_Oreturn__list(_865557))], (19719 ^ _778908) ^ [] : [-(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))))], (32901 ^ _778908) ^ [_1378081, _1378083] : [class_Rings_Osemiring__1(_1378081), -(hBOOL(hAPP(hAPP(c_member(_1378081), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1378081), _1378083)), c_Nat_Osemiring__1__class_ONats(_1378081))))], (14694 ^ _778908) ^ [_1028218] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028218), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35999 ^ _778908) ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767] : [class_Groups_Ocomm__monoid__add(_1444757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444759), _1444761)), 36009 ^ _778908 : [(36010 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444759), 36008 ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767]), _1444761)))], (36015 ^ _778908) ^ [] : [36008 ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767] = 36011 ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767]], (36019 ^ _778908) ^ [] : [hAPP(_1444765, hAPP(_1444763, 36008 ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767])) = c_Groups_Ozero__class_Ozero(_1444757)], (36017 ^ _778908) ^ [] : [-(hAPP(_1444763, 36008 ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767]) = hAPP(_1444763, 36011 ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767]))], (36013 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444759), 36011 ^ [_1444757, _1444759, _1444761, _1444763, _1444765, _1444767]), _1444761)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444767, _1444757), _1444765), hAPP(c_Set_Oimage(_1444759, _1444767, _1444763), _1444761)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444759, _1444757), hAPP(c_Fun_Ocomp(_1444767, _1444757, _1444759, _1444765), _1444763)), _1444761))], (51293 ^ _778908) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (13600 ^ _778908) ^ [_1008249, _1008251, _1008253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008249), _1008251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008251), _1008253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1008249), _1008253)))], (11182 ^ _778908) ^ [_965892, _965894, _965896, _965898] : [class_Orderings_Oorder(_965892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965892), _965894), _965896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965892), _965898), _965894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965892), _965898), _965896)))], (20777 ^ _778908) ^ [_1137406, _1137408] : [class_Rings_Odivision__ring__inverse__zero(_1137406), 20780 ^ _778908 : [(20787 ^ _778908) ^ [] : [-(_1137408 = c_Groups_Ozero__class_Ozero(_1137406)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137406), _1137408), _1137408) = c_Groups_Oone__class_Oone(_1137406))], (20781 ^ _778908) ^ [] : [_1137408 = c_Groups_Ozero__class_Ozero(_1137406), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137406), _1137408), _1137408) = c_Groups_Ozero__class_Ozero(_1137406))]]], (15074 ^ _778908) ^ [_1034626, _1034628, _1034630] : [class_Divides_Osemiring__div(_1034626), -(_1034628 = c_Groups_Ozero__class_Ozero(_1034626)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034626), _1034628), _1034630)), _1034628) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034626), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034626), _1034630), _1034628)), c_Groups_Oone__class_Oone(_1034626)))], (15824 ^ _778908) ^ [_1048885, _1048887, _1048889] : [class_Groups_Ogroup__add(_1048885), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048885), _1048887), hAPP(c_Groups_Ouminus__class_Ouminus(_1048885), _1048889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048885), _1048887), _1048889))], (18477 ^ _778908) ^ [_1097829, _1097831, _1097833] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097829), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097829)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097831)), _1097833)) = 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), _1097829), _1097831))), _1097833))], (10469 ^ _778908) ^ [_954789, _954791] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954789), _954791)), _954789 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _954791 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (41521 ^ _778908) ^ [_1572678, _1572680] : [-(hAPP(c_Set_OPow(_1572678), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1572678, tc_HOL_Obool)), _1572680)) = hAPP(c_Set_OCollect(tc_fun(_1572678, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1572678, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1572678, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1572678, tc_HOL_Obool), tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1572678, tc_HOL_Obool)), c_COMBS(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1572678, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1572678, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1572678, tc_HOL_Obool), tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_fun(_1572678, tc_HOL_Obool)), tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_fun(_1572678, tc_HOL_Obool)), tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1572678, tc_HOL_Obool)), c_COMBB(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1572678, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1572678, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1572678, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1572678, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1572678, tc_HOL_Obool)), _1572680)), c_Set_OPow(_1572678))))))], (9406 ^ _778908) ^ [_936163, _936165, _936167] : [class_Groups_Oab__group__add(_936163), -(hAPP(c_Groups_Ouminus__class_Ouminus(_936163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936163), _936165), _936167)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936163), hAPP(c_Groups_Ouminus__class_Ouminus(_936163), _936165)), hAPP(c_Groups_Ouminus__class_Ouminus(_936163), _936167)))], (8404 ^ _778908) ^ [_919731, _919733, _919735] : [class_Rings_Olinordered__semidom(_919731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919733), _919735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919731), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919731), _919733)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919731), _919735))))], (46932 ^ _778908) ^ [_1709207, _1709209, _1709211] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709207), tc_List_Olist(_1709207))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709207), tc_List_Olist(_1709207)), _1709209), _1709209)), c_List_Olistrel(_1709207, c_Transitive__Closure_Ortrancl(_1709207, _1709211)))))], (30646 ^ _778908) ^ [_1328065] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1328065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1328065)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1328065)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (38512 ^ _778908) ^ [_1501218, _1501220, _1501222, _1501224, _1501226, _1501228] : [c_Fun_Oinj__on(_1501218, _1501220, _1501222, _1501224), -(_1501226 = _1501228), hBOOL(hAPP(hAPP(c_member(_1501218), _1501226), _1501224)), hBOOL(hAPP(hAPP(c_member(_1501218), _1501228), _1501224)), hAPP(_1501222, _1501226) = hAPP(_1501222, _1501228)], (22508 ^ _778908) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13546 ^ _778908) ^ [_1007345, _1007347, _1007349] : [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), _1007345), _1007347)), _1007349)), 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)), _1007349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1007347), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9042 ^ _778908) ^ [_929950, _929952, _929954] : [class_Rings_Oring__1(_929950), -(hAPP(c_Int_Oring__1__class_Oof__int(_929950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _929952), _929954)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929950), hAPP(c_Int_Oring__1__class_Oof__int(_929950), _929952)), hAPP(c_Int_Oring__1__class_Oof__int(_929950), _929954)))], (14790 ^ _778908) ^ [_1029808, _1029810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029808)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029810), _1029808)), _1029808) = _1029810)], (39520 ^ _778908) ^ [_1522444, _1522446, _1522448, _1522450, _1522452, _1522454] : [-(hAPP(c_Set_Ovimage(_1522444, _1522446, _1522448), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522450, tc_fun(_1522446, tc_HOL_Obool)), _1522452), _1522454)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522450, tc_fun(_1522444, tc_HOL_Obool)), _1522452), hAPP(hAPP(c_COMBB(tc_fun(_1522446, tc_HOL_Obool), tc_fun(_1522444, tc_HOL_Obool), _1522450), c_Set_Ovimage(_1522444, _1522446, _1522448)), _1522454)))], (1252 ^ _778908) ^ [_797432, _797434] : [-(class_Rings_Oring(_797432)), _797434 = _797432, class_Rings_Oring(_797434)], (15202 ^ _778908) ^ [_1037260, _1037262, _1037264, _1037266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1037260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037262), _1037264)), -(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), _1037264), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1037266, _1037260))), _1037262)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037264), _1037260))))], (43193 ^ _778908) ^ [_1618390, _1618392] : [-(c_Transitive__Closure_Ortrancl(_1618390, _1618392) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1618390, _1618390), tc_HOL_Obool)), c_Relation_OId(_1618390)), hAPP(hAPP(c_Relation_Orel__comp(_1618390, _1618390, _1618390), c_Transitive__Closure_Ortrancl(_1618390, _1618392)), _1618392)))], (17397 ^ _778908) ^ [_1079491, _1079493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079491), _1079493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079491)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079493))))], (26907 ^ _778908) ^ [_1253386, _1253388, _1253390, _1253392] : [class_Groups_Oab__group__add(_1253386), 26910 ^ _778908 : [(26917 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253388), _1253390))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253386), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1253386, _1253386), hAPP(hAPP(c_COMBB(_1253386, tc_fun(_1253386, _1253386), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1253386)), _1253392)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1253386, tc_Nat_Onat), _1253392), 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, _1253388, _1253390)) = c_Groups_Ozero__class_Ozero(_1253386))], (26911 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253388), _1253390)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253386), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1253386, _1253386), hAPP(hAPP(c_COMBB(_1253386, tc_fun(_1253386, _1253386), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1253386)), _1253392)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1253386, tc_Nat_Onat), _1253392), 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, _1253388, _1253390)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1253386), hAPP(_1253392, _1253388)), hAPP(_1253392, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253390), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (20921 ^ _778908) ^ [_1139894, _1139896, _1139898, _1139900, _1139902] : [class_Fields_Olinordered__field(_1139894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139894), c_Groups_Ozero__class_Ozero(_1139894)), _1139896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139894), _1139896), _1139898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139894), c_Groups_Ozero__class_Ozero(_1139894)), _1139900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139894), _1139900), _1139902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139894), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139894), _1139896), _1139902)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139894), _1139898), _1139900))))], (15560 ^ _778908) ^ [_1043785] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043785), _1043785) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35267 ^ _778908) ^ [_1427580, _1427582, _1427584, _1427586] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1427580, _1427580)), hAPP(hAPP(c_Product__Type_OPair(_1427580, _1427580), _1427582), _1427584)), c_Relation_OId__on(_1427580, _1427586)))), _1427582 = _1427584, hBOOL(hAPP(hAPP(c_member(_1427580), _1427582), _1427586))], (51519 ^ _778908) ^ [] : [-(class_Finite__Set_Ofinite(tc_String_Onibble))], (18619 ^ _778908) ^ [_1099847] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099847), c_Int_OPls)))], (6474 ^ _778908) ^ [_883580, _883582, _883584, _883586, _883588, _883590] : [c_Com_Ocom_OCall(_883580, _883582, _883584) = c_Com_Ocom_OLocal(_883586, _883588, _883590)], (47092 ^ _778908) ^ [_1713588, _1713590, _1713592, _1713594, _1713596, _1713598] : [_1713588 = _1713590, -(hAPP(c_Map_Omap__of(_1713592, _1713594, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1713592, _1713594)), hAPP(hAPP(c_Product__Type_OPair(_1713592, _1713594), _1713588), _1713596)), _1713598)), _1713590) = hAPP(c_Option_Ooption_OSome(_1713594), _1713596))], (44623 ^ _778908) ^ [_1651420, _1651422, _1651424, _1651426] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1651420, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651422, tc_fun(_1651420, tc_HOL_Obool)), _1651424), _1651426)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1651422, tc_fun(_1651420, tc_HOL_Obool)), _1651424), hAPP(hAPP(c_COMBB(tc_fun(_1651420, tc_HOL_Obool), tc_fun(_1651420, tc_HOL_Obool), _1651422), c_Groups_Ouminus__class_Ouminus(tc_fun(_1651420, tc_HOL_Obool))), _1651426)))], (8150 ^ _778908) ^ [_915264, _915266, _915268, _915270, _915272, _915274] : [-(c_Nitpick_Opair__box_Opair__box__case(_915264, _915266, _915268, _915270, c_Nitpick_Opair__box_OPairBox(_915264, _915266, _915272, _915274)) = hAPP(hAPP(_915270, _915272), _915274))], (9718 ^ _778908) ^ [_941750, _941752] : [class_Groups_Ogroup__add(_941750), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941750), _941752), hAPP(c_Groups_Ouminus__class_Ouminus(_941750), _941752)) = c_Groups_Ozero__class_Ozero(_941750))], (19019 ^ _778908) ^ [_1106525] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1106525)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106525))))], (9326 ^ _778908) ^ [_934856, _934858] : [class_Groups_Ogroup__add(_934856), 9329 ^ _778908 : [(9336 ^ _778908) ^ [] : [_934858 = c_Groups_Ozero__class_Ozero(_934856), -(hAPP(c_Groups_Ouminus__class_Ouminus(_934856), _934858) = c_Groups_Ozero__class_Ozero(_934856))], (9330 ^ _778908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_934856), _934858) = c_Groups_Ozero__class_Ozero(_934856), -(_934858 = c_Groups_Ozero__class_Ozero(_934856))]]], (30520 ^ _778908) ^ [_1325483, _1325485] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325483), _1325485))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325483, _1325485))], (46483 ^ _778908) ^ [_1696791, _1696793, _1696795] : [hBOOL(hAPP(c_List_Odistinct(_1696791), _1696793)), -(hAPP(c_List_Oset(_1696791), c_List_Oremove1(_1696791, _1696795, _1696793)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1696791, tc_HOL_Obool)), hAPP(c_List_Oset(_1696791), _1696793)), hAPP(hAPP(c_Set_Oinsert(_1696791), _1696795), c_Orderings_Obot__class_Obot(tc_fun(_1696791, tc_HOL_Obool)))))], (2282 ^ _778908) ^ [_813283, _813285, _813287, _813289, _813291, _813293, _813295, _813297] : [-(c_Sum__Type_OSumr(_813297, _813293, _813289, _813285) = c_Sum__Type_OSumr(_813295, _813291, _813287, _813283)), _813297 = _813295, _813293 = _813291, _813289 = _813287, _813285 = _813283], (8520 ^ _778908) ^ [_921775, _921777, _921779, _921781] : [class_Orderings_Opreorder(_921775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921775), _921777), _921779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921775), _921779), _921781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921775), _921777), _921781)))], (50867 ^ _778908) ^ [_1801139] : [-(c_List_Oconcat(_1801139, c_List_Olist_ONil(tc_List_Olist(_1801139))) = c_List_Olist_ONil(_1801139))], (30192 ^ _778908) ^ [_1319853, _1319855, _1319857, _1319859] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1319853, _1319855)), c_Sum__Type_OPlus(_1319853, _1319855, _1319857, _1319859)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319853), _1319857)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319855), _1319859))], (48949 ^ _778908) ^ [_1760071, _1760073] : [-(hAPP(hAPP(c_List_Odrop(_1760071), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1760073) = _1760073)], (37304 ^ _778908) ^ [_1474204, _1474206, _1474208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474204), _1474206)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474204), _1474208)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474204), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474204, tc_HOL_Obool)), _1474206), _1474208))), hAPP(c_Finite__Set_Ocard(_1474204), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474204, tc_HOL_Obool)), _1474206), _1474208))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474204), _1474206)), hAPP(c_Finite__Set_Ocard(_1474204), _1474208)))], (7583 ^ _778908) ^ [_905917] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _905917))))], (29855 ^ _778908) ^ [_1313186] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1313186), c_Orderings_Otop__class_Otop(tc_fun(_1313186, 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(_1313186), c_Orderings_Otop__class_Otop(tc_fun(_1313186, tc_HOL_Obool))))))], (7340 ^ _778908) ^ [_901611, _901613] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901611), _901613) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7345 ^ _778908 : [(7348 ^ _778908) ^ [] : [-(_901613 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7346 ^ _778908) ^ [] : [-(_901611 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7349 ^ _778908 : [(7352 ^ _778908) ^ [] : [-(_901613 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7350 ^ _778908) ^ [] : [-(_901611 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10593 ^ _778908) ^ [_956768, _956770, _956772] : [class_Orderings_Oorder(_956768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956768), _956770), _956772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956768), _956772), _956770)), -(_956772 = _956770)], (25735 ^ _778908) ^ [_1230918, _1230920, _1230922, _1230924] : [class_Divides_Osemiring__div(_1230918), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230918), _1230920), _1230922)), -(c_Divides_Odiv__class_Omod(_1230918, c_Divides_Odiv__class_Omod(_1230918, _1230924, _1230922), _1230920) = c_Divides_Odiv__class_Omod(_1230918, _1230924, _1230920))], (14081 ^ _778908) ^ [_1017266, _1017268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017268, _1017266)), _1017266)))], (50933 ^ _778908) ^ [_1802475, _1802477, _1802479, _1802481, _1802483] : [-(hAPP(c_List_Ofoldl(_1802475, _1802477, _1802479, _1802481), _1802483) = c_List_Ofoldr(_1802477, _1802475, hAPP(c_COMBC(_1802475, _1802477, _1802475), _1802479), hAPP(c_List_Orev(_1802477), _1802483), _1802481))], (27123 ^ _778908) ^ [_1257881, _1257883, _1257885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1257881, 27124 ^ [_1257881, _1257883, _1257885])), hAPP(_1257883, 27124 ^ [_1257881, _1257883, _1257885]))), -(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), _1257883), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1257885))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1257881), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1257885))) = 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)), _1257883)), _1257881)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1257885)))], (47888 ^ _778908) ^ [_1733348, _1733350, _1733352, _1733354, _1733356] : [class_Orderings_Olinorder(_1733348), hBOOL(hAPP(c_List_Odistinct(_1733350), _1733352)), -(hBOOL(hAPP(c_List_Odistinct(_1733350), c_List_Olinorder__class_Oinsort__insert__key(_1733350, _1733348, _1733354, _1733356, _1733352))))], (49737 ^ _778908) ^ [_1777275, _1777277, _1777279, _1777281] : [49739 ^ _778908 : [(49742 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1777279, 49738 ^ [_1777275, _1777277, _1777279, _1777281])), hAPP(_1777281, 49738 ^ [_1777275, _1777277, _1777279, _1777281])))], (49740 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777275), 49738 ^ [_1777275, _1777277, _1777279, _1777281]), hAPP(c_List_Oset(_1777275), _1777277))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1777275, _1777279, _1777277)), c_List_Olist_Olist__size(_1777275, _1777281, _1777277))))], (33061 ^ _778908) ^ [_1381614, _1381616, _1381618, _1381620, _1381622, _1381624, _1381626] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1381614), _1381616), _1381618), _1381620) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1381614), _1381622), _1381624), _1381626)), _1381616 = _1381622, _1381618 = _1381624, _1381620 = _1381626], (26573 ^ _778908) ^ [_1246951, _1246953, _1246955] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246951), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1246953), _1246955))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246951), _1246953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246955), _1246953)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246951), _1246955)))], (25935 ^ _778908) ^ [_1234448, _1234450, _1234452] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234448), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234450, _1234452))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234448), _1234452)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234448), _1234450)))], (29598 ^ _778908) ^ [_1308232, _1308234, _1308236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308232), _1308236)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308232), hAPP(hAPP(c_Set_Oinsert(_1308232), _1308234), _1308236))))], (46771 ^ _778908) ^ [_1703825, _1703827, _1703829] : [hBOOL(hAPP(hAPP(c_member(_1703825), _1703827), hAPP(c_List_Oset(_1703825), _1703829))), -(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(_1703825)), _1703829))))], (37698 ^ _778908) ^ [_1482453, _1482455, _1482457] : [class_Orderings_Olinorder(_1482453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482453), _1482455)), -(_1482455 = c_Orderings_Obot__class_Obot(tc_fun(_1482453, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482453), _1482457)), -(_1482457 = c_Orderings_Obot__class_Obot(tc_fun(_1482453, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482453, tc_HOL_Obool)), _1482455), _1482457) = c_Orderings_Obot__class_Obot(tc_fun(_1482453, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1482453, c_Orderings_Oord__class_Omax(_1482453), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482453, tc_HOL_Obool)), _1482455), _1482457)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1482453), c_Big__Operators_Olattice_OSup__fin(_1482453, c_Orderings_Oord__class_Omax(_1482453), _1482455)), c_Big__Operators_Olattice_OSup__fin(_1482453, c_Orderings_Oord__class_Omax(_1482453), _1482457)))], (5616 ^ _778908) ^ [_865642, _865644] : [_865644 = _865642, -(c_List_Olist_ONil(_865644) = c_List_Olist_ONil(_865642))], (34516 ^ _778908) ^ [_1410310, _1410312, _1410314, _1410316] : [class_Groups_Ocomm__monoid__mult(_1410310), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1410312), _1410314))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410312, _1410310), _1410316), _1410314) = c_Groups_Oone__class_Oone(_1410310))], (48317 ^ _778908) ^ [_1743181, _1743183, _1743185] : [_1743181 = hAPP(hAPP(c_List_Oappend(_1743183), _1743181), _1743185), -(_1743185 = c_List_Olist_ONil(_1743183))], (25045 ^ _778908) ^ [_1218434, _1218436, _1218438, _1218440, _1218442] : [-(hAPP(c_New__DSequence_Oneg__bind(_1218434, _1218436, _1218438, _1218440), _1218442) = c_Lazy__Sequence_Ohb__bind(_1218434, _1218436, hAPP(_1218438, _1218442), hAPP(hAPP(c_COMBC(_1218434, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1218436))), _1218440), _1218442)))], (46130 ^ _778908) ^ [_1688381, _1688383, _1688385] : [c_Fun_Oinj__on(tc_List_Olist(_1688381), tc_List_Olist(_1688383), hAPP(c_List_Omap(_1688381, _1688383), _1688385), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1688381), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1688381, _1688383, _1688385, c_Orderings_Otop__class_Otop(tc_fun(_1688381, tc_HOL_Obool))))], (31930 ^ _778908) ^ [_1357833, _1357835, _1357837, _1357839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357833, tc_HOL_Obool)), _1357835), hAPP(hAPP(c_Set_Oinsert(_1357833), _1357837), _1357839))), 31933 ^ _778908 : [(31940 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357833), _1357837), _1357835))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357833, tc_HOL_Obool)), _1357835), _1357839)))], (31934 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1357833), _1357837), _1357835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357833, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357833, tc_HOL_Obool)), _1357835), hAPP(hAPP(c_Set_Oinsert(_1357833), _1357837), c_Orderings_Obot__class_Obot(tc_fun(_1357833, tc_HOL_Obool))))), _1357839)))]]], (30690 ^ _778908) ^ [_1328904, _1328906, _1328908, _1328910] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1328904), _1328906)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328908), _1328910)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1328904, _1328908)), c_Sum__Type_OPlus(_1328904, _1328908, _1328906, _1328910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1328904), _1328906)), hAPP(c_Finite__Set_Ocard(_1328908), _1328910)))], (46713 ^ _778908) ^ [_1702617, _1702619] : [hAPP(c_Finite__Set_Ocard(_1702617), hAPP(c_List_Oset(_1702617), _1702619)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702617)), _1702619), -(hBOOL(hAPP(c_List_Odistinct(_1702617), _1702619)))], (40196 ^ _778908) ^ [_1539680, _1539682, _1539684, _1539686, _1539688, _1539690] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539680, _1539682)), hAPP(hAPP(c_Product__Type_OPair(_1539680, _1539682), _1539684), _1539686)), hAPP(hAPP(c_Product__Type_OSigma(_1539680, _1539682), _1539688), _1539690))), 40199 ^ _778908 : [(40202 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539682), _1539686), hAPP(_1539690, _1539684))))], (40200 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539680), _1539684), _1539688)))]]], (12665 ^ _778908) ^ [_991782, _991784, _991786, _991788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _991782), _991784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _991786), _991788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _991782), _991786)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _991784), _991788))))], (51305 ^ _778908) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (19063 ^ _778908) ^ [_1107261] : [class_Int_Onumber__ring(_1107261), -(c_Groups_Oone__class_Oone(_1107261) = hAPP(c_Int_Onumber__class_Onumber__of(_1107261), c_Int_OBit1(c_Int_OPls)))], (49977 ^ _778908) ^ [_1782298, _1782300, _1782302] : [-(hAPP(c_List_Oset(_1782298), hAPP(c_List_Ofilter(_1782298, _1782300), _1782302)) = hAPP(c_Set_OCollect(_1782298), hAPP(hAPP(c_COMBS(_1782298, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1782298), c_fconj), hAPP(hAPP(c_COMBC(_1782298, tc_fun(_1782298, tc_HOL_Obool), tc_HOL_Obool), c_member(_1782298)), hAPP(c_List_Oset(_1782298), _1782302)))), _1782300)))], (4986 ^ _778908) ^ [_856035, _856037] : [_856037 = _856035, -(c_Finite__Set_Ocard(_856037) = c_Finite__Set_Ocard(_856035))], (44637 ^ _778908) ^ [_1652100, _1652102, _1652104, _1652106, _1652108] : [_1652100 = c_Orderings_Obot__class_Obot(tc_fun(_1652102, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652104, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652102, tc_fun(_1652104, tc_HOL_Obool)), _1652100), _1652106)), _1652108) = _1652108)], (39909 ^ _778908) ^ [_1531822, _1531824, _1531826, _1531828, _1531830, _1531832, _1531834] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1531822, _1531824, _1531826, _1531828, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1531822, tc_HOL_Obool)), _1531830), hAPP(hAPP(c_Set_Oinsert(_1531822), _1531832), c_Orderings_Obot__class_Obot(tc_fun(_1531822, tc_HOL_Obool))))), _1531834)), hBOOL(hAPP(hAPP(c_member(_1531822), _1531832), _1531830)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1531822, _1531824, _1531826, _1531828, _1531830), hAPP(hAPP(_1531826, _1531832), _1531834))))], (44541 ^ _778908) ^ [_1649609, _1649611, _1649613, _1649615] : [class_Complete__Lattice_Ocomplete__lattice(_1649609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1649611), _1649613)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649611, _1649609), _1649613), _1649615) = hAPP(hAPP(c_Finite__Set_Ofold(_1649611, _1649609, hAPP(hAPP(c_COMBB(_1649609, tc_fun(_1649609, _1649609), _1649611), c_Lattices_Osemilattice__inf__class_Oinf(_1649609)), _1649615)), c_Orderings_Otop__class_Otop(_1649609)), _1649613))], (16198 ^ _778908) ^ [_1056546, _1056548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056546), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1056548), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056546), _1056548)))], (51333 ^ _778908) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (25925 ^ _778908) ^ [_1234277, _1234279, _1234281] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234277), _1234279)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234277), _1234281)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234277), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234279, _1234281))))], (6117 ^ _778908) ^ [_876943, _876945, _876947, _876949, _876951] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_876943, _876945, _876947)), _876949), _876951)), 6122 ^ _778908 : [(6125 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_876945), _876949), _876951)))], (6123 ^ _778908) ^ [] : [-(hBOOL(hAPP(_876943, _876949)))]], 6126 ^ _778908 : [(6129 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_876947), _876949), _876951)))], (6127 ^ _778908) ^ [] : [hBOOL(hAPP(_876943, _876949))]]], (45326 ^ _778908) ^ [_1670244, _1670246, _1670248] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1670244, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1670244, tc_HOL_Obool)), _1670246), _1670248)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670244, tc_HOL_Obool)), _1670246), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1670244, tc_HOL_Obool), _1670248)))], (12698 ^ _778908) ^ [_992392, _992394] : [12699 ^ _778908 : [(12700 ^ _778908) ^ [_992445] : [_992394 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _992392), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992445))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992392), _992394)))], (20165 ^ _778908) ^ [_1126715, _1126717, _1126719, _1126721] : [20167 ^ _778908 : [(20172 ^ _778908) ^ [] : [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(_1126719, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 20166 ^ [_1126715, _1126717, _1126719, _1126721]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1126719, 20166 ^ [_1126715, _1126717, _1126719, _1126721])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20170 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20166 ^ [_1126715, _1126717, _1126719, _1126721]), _1126717)))], (20168 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126715), 20166 ^ [_1126715, _1126717, _1126719, _1126721])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126715), _1126717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1126719, _1126715)), _1126721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1126721), hAPP(_1126719, _1126717))), 20186 ^ _778908 : [(20191 ^ _778908) ^ [] : [-(hAPP(_1126719, 20185 ^ [_1126715, _1126717, _1126719, _1126721]) = _1126721)], (20189 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20185 ^ [_1126715, _1126717, _1126719, _1126721]), _1126717)))], (20187 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126715), 20185 ^ [_1126715, _1126717, _1126719, _1126721])))]]], (47471 ^ _778908) ^ [_1723116, _1723118] : [_1723118 = c_List_Olist_ONil(_1723116), -(c_Orderings_Obot__class_Obot(tc_fun(_1723116, tc_HOL_Obool)) = hAPP(c_List_Oset(_1723116), _1723118))], (44320 ^ _778908) ^ [_1645519, _1645521, _1645523] : [class_Groups_Oab__semigroup__mult(_1645519), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645519), _1645521)), -(hBOOL(hAPP(hAPP(c_member(_1645519), _1645523), _1645521))), -(hAPP(c_Finite__Set_Ofold1(_1645519, c_Groups_Otimes__class_Otimes(_1645519)), hAPP(hAPP(c_Set_Oinsert(_1645519), _1645523), _1645521)) = hAPP(hAPP(c_Finite__Set_Ofold(_1645519, _1645519, c_Groups_Otimes__class_Otimes(_1645519)), _1645523), _1645521))], (14605 ^ _778908) ^ [_1026862, _1026864] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1026862, _1026864)) = _1026864, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1026862), _1026864) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3478 ^ _778908) ^ [_832381, _832383, _832385, _832387] : [-(c_FunDef_Orp__inv__image(_832387, _832383) = c_FunDef_Orp__inv__image(_832385, _832381)), _832387 = _832385, _832383 = _832381], (2372 ^ _778908) ^ [_814702, _814704] : [_814704 = _814702, -(c_Int_Osucc(_814704) = c_Int_Osucc(_814702))], (5829 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23803 ^ _778908) ^ [_1193786, _1193788, _1193790, _1193792] : [class_Orderings_Olinorder(_1193786), 23806 ^ _778908 : [(23815 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193786), _1193788), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193786), _1193790), _1193792)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193786), _1193788), _1193790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193786), _1193788), _1193792))], (23807 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193786), _1193788), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193786), _1193790), _1193792))), 23810 ^ _778908 : [(23813 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193786), _1193788), _1193792)))], (23811 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193786), _1193788), _1193790)))]]]]], (43173 ^ _778908) ^ [_1617906, _1617908] : [-(hAPP(c_Relation_ODomain(_1617906, _1617906), c_Transitive__Closure_Ortrancl(_1617906, _1617908)) = c_Orderings_Otop__class_Otop(tc_fun(_1617906, tc_HOL_Obool)))], (51555 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (43822 ^ _778908) ^ [_1634096, _1634098] : [-(c_Transitive__Closure_Ortrancl(_1634096, _1634098) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1634096, _1634096), 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(_1634096, _1634096), tc_HOL_Obool), tc_fun(tc_prod(_1634096, _1634096), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1634096, _1634096), tc_HOL_Obool)), _1634098)))], (18565 ^ _778908) ^ [] : [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)], (29976 ^ _778908) ^ [_1315576, _1315578, _1315580] : [hAPP(hAPP(c_Set_Oinsert(_1315576), _1315578), c_Orderings_Obot__class_Obot(tc_fun(_1315576, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1315576), _1315580), c_Orderings_Obot__class_Obot(tc_fun(_1315576, tc_HOL_Obool))), -(_1315578 = _1315580)], (27691 ^ _778908) ^ [_1269703, _1269705] : [c_Nat__Transfer_Ois__nat(_1269703), c_Nat__Transfer_Ois__nat(_1269705), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1269703, _1269705) = 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, _1269703), hAPP(c_Int_Onat, _1269705))))], (11649 ^ _778908) ^ [_973885, _973887, _973889, _973891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973885), _973887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973889), _973891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973885), _973889)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973887), _973891))))], (36035 ^ _778908) ^ [_1445902, _1445904, _1445906] : [_1445904 = c_Orderings_Obot__class_Obot(tc_fun(_1445902, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1445902, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445902), _1445904), _1445906))], (39973 ^ _778908) ^ [_1533167, _1533169, _1533171, _1533173] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1533167), _1533169)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533167), _1533171)), -(_1533171 = c_Orderings_Obot__class_Obot(tc_fun(_1533167, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1533167, tc_HOL_Obool), tc_fun(_1533167, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1533167, tc_HOL_Obool), tc_fun(_1533167, tc_HOL_Obool)), _1533169), _1533171)), c_Wellfounded_Omax__ext(_1533167, _1533173)))), 39987 ^ _778908 : [(39990 ^ _778908) ^ [_1533572] : [hBOOL(hAPP(hAPP(c_member(_1533167), _1533572), _1533171)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1533167, _1533167)), hAPP(hAPP(c_Product__Type_OPair(_1533167, _1533167), 39986 ^ [_1533167, _1533169, _1533171, _1533173]), _1533572)), _1533173))], (39988 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1533167), 39986 ^ [_1533167, _1533169, _1533171, _1533173]), _1533169)))]]], (6577 ^ _778908) ^ [_885926, _885928, _885930, _885932, _885934, _885936] : [c_Natural_Oevaln(_885926, hAPP(hAPP(hAPP(c_Natural_Oupdate, _885928), c_Com_Ovname_OLoc(_885930)), hAPP(_885932, _885928)), _885934, _885936), -(c_Natural_Oevaln(c_Com_Ocom_OLocal(_885930, _885932, _885926), _885928, _885934, hAPP(hAPP(hAPP(c_Natural_Oupdate, _885936), c_Com_Ovname_OLoc(_885930)), hAPP(hAPP(c_Natural_Ogetlocs, _885928), _885930))))], (46519 ^ _778908) ^ [_1697478, _1697480, _1697482, _1697484] : [-(c_List_Oremove1(_1697478, _1697480, c_List_Oremove1(_1697478, _1697482, _1697484)) = c_List_Oremove1(_1697478, _1697482, c_List_Oremove1(_1697478, _1697480, _1697484)))], (8254 ^ _778908) ^ [_917228, _917230] : [class_Rings_Olinordered__semidom(_917228), 8257 ^ _778908 : [(8264 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917228), c_Groups_Ozero__class_Ozero(_917228)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917228), _917230))))], (8258 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917228), c_Groups_Ozero__class_Ozero(_917228)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917228), _917230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917230)))]]], (51477 ^ _778908) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (44206 ^ _778908) ^ [_1643231, _1643233, _1643235, _1643237] : [class_Orderings_Olinorder(_1643231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643231), _1643233)), hBOOL(hAPP(hAPP(c_member(_1643231), _1643235), _1643233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1643231), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1643231), _1643235), _1643237)), hAPP(hAPP(c_Finite__Set_Ofold(_1643231, _1643231, c_Orderings_Oord__class_Omax(_1643231)), _1643237), _1643233))))], (31495 ^ _778908) ^ [_1347101, _1347103, _1347105, _1347107, _1347109] : [hBOOL(hAPP(hAPP(c_member(_1347101), _1347103), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1347105, tc_fun(_1347101, tc_HOL_Obool)), _1347107), _1347109))), 31499 ^ _778908 : [(31502 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347101), _1347103), hAPP(_1347109, 31498 ^ [_1347101, _1347103, _1347105, _1347107, _1347109]))))], (31500 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347105), 31498 ^ [_1347101, _1347103, _1347105, _1347107, _1347109]), _1347107)))]]], (7749 ^ _778908) ^ [_908543, _908545, _908547, _908549, _908551] : [class_Groups_Oordered__cancel__ab__semigroup__add(_908543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908543), _908545), _908547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908543), _908549), _908551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908543), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908543), _908545), _908549)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908543), _908547), _908551))))], (48811 ^ _778908) ^ [_1756317, _1756319, _1756321, _1756323, _1756325, _1756327, _1756329, _1756331] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756317, _1756317)), hAPP(hAPP(c_Product__Type_OPair(_1756317, _1756317), _1756319), _1756321)), _1756323)), _1756325 = hAPP(hAPP(c_List_Oappend(_1756317), _1756327), hAPP(hAPP(c_List_Olist_OCons(_1756317), _1756319), _1756329)), _1756331 = hAPP(hAPP(c_List_Oappend(_1756317), _1756327), hAPP(hAPP(c_List_Olist_OCons(_1756317), _1756321), _1756329)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756317), tc_List_Olist(_1756317))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756317), tc_List_Olist(_1756317)), _1756325), _1756331)), c_List_Olistrel1(_1756317, _1756323))))], (47499 ^ _778908) ^ [_1723661, _1723663] : [-(c_List_Osublist(_1723661, _1723663, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1723661))], (32281 ^ _778908) ^ [_1365599, _1365601, _1365603, _1365605, _1365607, _1365609, _1365611] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1365599, tc_fun(_1365601, tc_fun(_1365603, tc_HOL_Obool))), _1365605), _1365607), _1365609), _1365611)), 32285 ^ _778908 : [(32288 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1365607, 32284 ^ [_1365599, _1365601, _1365603, _1365605, _1365607, _1365609, _1365611]), _1365609), _1365611)))], (32286 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365599), 32284 ^ [_1365599, _1365601, _1365603, _1365605, _1365607, _1365609, _1365611]), _1365605)))]]], (41680 ^ _778908) ^ [_1580112, _1580114, _1580116] : [-(hAPP(c_Fun_Ocomp(_1580112, _1580114, _1580112, _1580116), c_Fun_Oid(_1580112)) = _1580116)], (40248 ^ _778908) ^ [_1540904, _1540906, _1540908, _1540910] : [_1540904 = c_Orderings_Obot__class_Obot(tc_fun(_1540906, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1540908, _1540906), _1540908, c_Product__Type_Ofst(_1540908, _1540906)), hAPP(hAPP(c_Product__Type_OSigma(_1540908, _1540906), _1540910), hAPP(c_COMBK(tc_fun(_1540906, tc_HOL_Obool), _1540908), _1540904))) = c_Orderings_Obot__class_Obot(tc_fun(_1540908, tc_HOL_Obool)))], (46150 ^ _778908) ^ [_1688919, _1688921, _1688923, _1688925, _1688927, _1688929, _1688931] : [-(c_List_Ofoldr(_1688919, _1688921, _1688923, hAPP(hAPP(c_List_Omap(_1688925, _1688919), _1688927), _1688929), _1688931) = c_List_Ofoldr(_1688925, _1688921, hAPP(c_Fun_Ocomp(_1688919, tc_fun(_1688921, _1688921), _1688925, _1688923), _1688927), _1688929, _1688931))], (48427 ^ _778908) ^ [_1745800, _1745802, _1745804, _1745806] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1745800), tc_List_Olist(_1745800))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1745800), tc_List_Olist(_1745800)), _1745802), _1745804)), c_List_Olexord(_1745800, _1745806))), 48432 ^ _778908 : [(48435 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1745800), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745800)), _1745802)), _1745804) = _1745802)], (48433 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745800)), _1745802)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745800)), _1745804))))]], 48437 ^ _778908 : [(48442 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1745800, _1745800)), hAPP(hAPP(c_Product__Type_OPair(_1745800, _1745800), hAPP(hAPP(c_List_Onth(_1745800), _1745802), 48436 ^ [_1745800, _1745802, _1745804, _1745806])), hAPP(hAPP(c_List_Onth(_1745800), _1745804), 48436 ^ [_1745800, _1745802, _1745804, _1745806]))), _1745806)))], (48440 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1745800), 48436 ^ [_1745800, _1745802, _1745804, _1745806]), _1745802) = hAPP(hAPP(c_List_Otake(_1745800), 48436 ^ [_1745800, _1745802, _1745804, _1745806]), _1745804))], (48438 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48436 ^ [_1745800, _1745802, _1745804, _1745806]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745800)), _1745802)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745800)), _1745804)))))]]], (2904 ^ _778908) ^ [_823116, _823118, _823120, _823122] : [-(c_Nitpick_Ouminus__frac(_823122, _823118) = c_Nitpick_Ouminus__frac(_823120, _823116)), _823122 = _823120, _823118 = _823116], (13258 ^ _778908) ^ [_1002378] : [-(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), _1002378))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45035 ^ _778908) ^ [_1663296, _1663298] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1663296), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663296, tc_HOL_Obool), _1663298)))), 45036 ^ _778908 : [(45037 ^ _778908) ^ [_1663360] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1663296, tc_HOL_Obool)), _1663360), _1663298)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1663296), _1663360))]]], (23012 ^ _778908) ^ [_1179201, _1179203] : [-(c_Divides_Odivmod__int(_1179201, _1179203) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179201), _1179203)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179201, _1179203)))], (2944 ^ _778908) ^ [_823854, _823856, _823858, _823860, _823862, _823864, _823866, _823868] : [-(c_New__DSequence_Opos__decr__bind(_823868, _823864, _823860, _823856) = c_New__DSequence_Opos__decr__bind(_823866, _823862, _823858, _823854)), _823868 = _823866, _823864 = _823862, _823860 = _823858, _823856 = _823854], (16505 ^ _778908) ^ [_1062669] : [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), _1062669))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062669) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062669)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (4074 ^ _778908) ^ [_841715, _841717, _841719, _841721, _841723, _841725] : [-(c_Finite__Set_Ofold__image(_841725, _841721, _841717) = c_Finite__Set_Ofold__image(_841723, _841719, _841715)), _841725 = _841723, _841721 = _841719, _841717 = _841715], (36698 ^ _778908) ^ [_1460182, _1460184] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460182, tc_HOL_Obool)), _1460184), c_Orderings_Obot__class_Obot(tc_fun(_1460182, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1460182, tc_HOL_Obool)))], (7763 ^ _778908) ^ [_908814, _908816, _908818, _908820] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_908814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908814), _908816), _908818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_908814), _908820), _908818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908814), _908816), _908820)))], (28243 ^ _778908) ^ [_1280371, _1280373, _1280375, _1280377, _1280379] : [class_Lattices_Olattice(_1280371), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280373, _1280371)), _1280375), _1280377), _1280379) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280371), hAPP(_1280375, _1280379)), hAPP(_1280377, _1280379)))], (16463 ^ _778908) ^ [_1061816, _1061818, _1061820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1061816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1061818), 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), _1061818), _1061820))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1061816))), _1061820)))], (45974 ^ _778908) ^ [_1684854, _1684856] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1684854, _1684856) = c_Smallcheck_Ofull__small_H(_1684854, hAPP(c_Code__Numeral_Oint__of, _1684856), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1684856))))], (39464 ^ _778908) ^ [_1521149, _1521151, _1521153, _1521155] : [hAPP(c_Set_Oimage(_1521149, _1521151, _1521153), c_Orderings_Otop__class_Otop(tc_fun(_1521149, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1521151, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1521149, _1521151, _1521153), hAPP(c_Set_Ovimage(_1521149, _1521151, _1521153), _1521155)) = _1521155)], (20849 ^ _778908) ^ [_1138538, _1138540, _1138542] : [class_Fields_Olinordered__field(_1138538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138538), _1138540), c_Groups_Ozero__class_Ozero(_1138538))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138538), _1138542), c_Groups_Ozero__class_Ozero(_1138538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138538), c_Groups_Ozero__class_Ozero(_1138538)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138538), _1138540), _1138542))))], (7120 ^ _778908) ^ [_897968] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(_897968)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6047 ^ _778908) ^ [_875726, _875728, _875730] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_875726, _875728, _875730))), 6050 ^ _778908 : [(6053 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _875730)))], (6051 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _875728)))]]], (110 ^ _778908) ^ [_780391, _780393, _780395, _780397, _780399, _780401, _780403, _780405] : [-(c_Nat__Transfer_Otransfer__morphism(_780403, _780399, _780395, _780391)), c_Nat__Transfer_Otransfer__morphism(_780405, _780401, _780397, _780393), _780405 = _780403, _780401 = _780399, _780397 = _780395, _780393 = _780391], (51343 ^ _778908) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (2842 ^ _778908) ^ [_822005, _822007, _822009, _822011, _822013, _822015, _822017, _822019, _822021, _822023, _822025, _822027, _822029, _822031] : [-(c_New__Random__Sequence_Oneg__decr__bind(_822031, _822027, _822023, _822019, _822015, _822011, _822007) = c_New__Random__Sequence_Oneg__decr__bind(_822029, _822025, _822021, _822017, _822013, _822009, _822005)), _822031 = _822029, _822027 = _822025, _822023 = _822021, _822019 = _822017, _822015 = _822013, _822011 = _822009, _822007 = _822005], (25745 ^ _778908) ^ [_1231091, _1231093, _1231095, _1231097] : [class_Divides_Osemiring__div(_1231091), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231091), _1231093), _1231095)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231091), _1231093), _1231097)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231091), _1231093), c_Divides_Odiv__class_Omod(_1231091, _1231095, _1231097))))], (22340 ^ _778908) ^ [_1165868] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1165868)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1165868)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5716 ^ _778908) ^ [_867164, _867166, _867168, _867170, _867172, _867174] : [-(c_COMBB(_867174, _867170, _867166) = c_COMBB(_867172, _867168, _867164)), _867174 = _867172, _867170 = _867168, _867166 = _867164], (49995 ^ _778908) ^ [_1782743, _1782745, _1782747] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1782743, tc_HOL_Obool)), hAPP(c_List_Oset(_1782743), _1782745)), hAPP(hAPP(c_Set_Oinsert(_1782743), _1782747), c_Orderings_Obot__class_Obot(tc_fun(_1782743, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1782743), hAPP(c_List_Ofilter(_1782743, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1782743), c_fNot), hAPP(hAPP(c_COMBC(_1782743, _1782743, tc_HOL_Obool), c_fequal), _1782747))), _1782745)))], (10104 ^ _778908) ^ [_948737, _948739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _948737), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _948739), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _948737), _948739))), -(_948737 = _948739)], (14166 ^ _778908) ^ [_1018660, _1018662] : [class_Lattices_Oab__semigroup__idem__mult(_1018660), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018660), _1018662), _1018662) = _1018662)], (6147 ^ _778908) ^ [_877487] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _877487), _877487)))], (26049 ^ _778908) ^ [_1236550, _1236552, _1236554, _1236556] : [class_Rings_Oring__1(_1236550), -(hAPP(c_Int_Oring__1__class_Oof__int(_1236550), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236552, tc_Int_Oint), _1236554), _1236556)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236552, _1236550), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1236550, _1236552), c_Int_Oring__1__class_Oof__int(_1236550)), _1236554)), _1236556))], (29231 ^ _778908) ^ [_1301283] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1301283)), 29235 ^ _778908 : [(29236 ^ _778908) ^ [_1301363] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1301363), _1301283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1301363), 29234 ^ [_1301283])))]]], (15806 ^ _778908) ^ [_1048542, _1048544] : [class_Groups_Ogroup__add(_1048542), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048542), c_Groups_Ozero__class_Ozero(_1048542)), _1048544) = hAPP(c_Groups_Ouminus__class_Ouminus(_1048542), _1048544))], (44094 ^ _778908) ^ [_1640891, _1640893, _1640895, _1640897] : [class_Lattices_Osemilattice__inf(_1640891), hBOOL(hAPP(c_Finite__Set_Ofinite(_1640891), _1640893)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1640891, _1640891, c_Lattices_Osemilattice__inf__class_Oinf(_1640891)), _1640895), hAPP(hAPP(c_Set_Oinsert(_1640891), _1640897), _1640893)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1640891), _1640897), hAPP(hAPP(c_Finite__Set_Ofold(_1640891, _1640891, c_Lattices_Osemilattice__inf__class_Oinf(_1640891)), _1640895), _1640893)))], (18613 ^ _778908) ^ [_1099742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099742), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099742))], (19755 ^ _778908) ^ [_1119198, _1119200, _1119202] : [class_Groups_Omonoid__mult(_1119198), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1119198), _1119200), 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)))), _1119202)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1119198), hAPP(hAPP(c_Power_Opower__class_Opower(_1119198), _1119200), _1119202)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (3180 ^ _778908) ^ [_827610, _827612, _827614, _827616] : [-(c_Set_Othe__elem(_827616, _827612) = c_Set_Othe__elem(_827614, _827610)), _827616 = _827614, _827612 = _827610], (36946 ^ _778908) ^ [_1465897, _1465899, _1465901, _1465903] : [hBOOL(hAPP(hAPP(c_member(_1465897), _1465899), _1465901)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465897, tc_HOL_Obool)), _1465901), hAPP(hAPP(c_Set_Oinsert(_1465897), _1465899), _1465903)) = hAPP(hAPP(c_Set_Oinsert(_1465897), _1465899), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465897, tc_HOL_Obool)), _1465901), _1465903)))], (37052 ^ _778908) ^ [_1468582, _1468584] : [c_Nat__Transfer_Onat__set(_1468582), c_Nat__Transfer_Onat__set(_1468584), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1468582), _1468584) = 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), _1468582)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1468584))))], (42076 ^ _778908) ^ [_1590522] : [class_Orderings_Owellorder(_1590522), -(c_Wellfounded_Owf(_1590522, hAPP(c_Set_OCollect(tc_prod(_1590522, _1590522)), hAPP(c_Product__Type_Oprod_Oprod__case(_1590522, _1590522, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1590522)))))], (4606 ^ _778908) ^ [_850207, _850209, _850211, _850213, _850215, _850217] : [-(c_Map_Odom(_850217, _850213, _850209) = c_Map_Odom(_850215, _850211, _850207)), _850217 = _850215, _850213 = _850211, _850209 = _850207], (42585 ^ _778908) ^ [_1603404, _1603406, _1603408] : [hBOOL(hAPP(hAPP(c_member(_1603406), _1603404), c_Orderings_Obot__class_Obot(tc_fun(_1603406, tc_HOL_Obool)))), -(hBOOL(hAPP(_1603408, _1603404)))], (36660 ^ _778908) ^ [_1459471, _1459473, _1459475] : [class_Lattices_Olattice(_1459471), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1459471), _1459473), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1459471), _1459473), _1459475)) = _1459473)], (6035 ^ _778908) ^ [_875500, _875502, _875504, _875506, _875508, _875510] : [c_Natural_Oevaln(_875500, _875502, _875504, _875506), c_Natural_Oevaln(_875508, _875506, _875504, _875510), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_875500, _875508), _875502, _875504, _875510))], (9228 ^ _778908) ^ [_933329, _933331, _933333, _933335] : [class_Groups_Oab__semigroup__mult(_933329), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933329), _933331), _933333)), _933335) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933329), _933331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933329), _933333), _933335)))], (50688 ^ _778908) ^ [_1796727, _1796729, _1796731, _1796733, _1796735] : [class_Orderings_Olinorder(_1796727), c_Fun_Oinj__on(_1796729, _1796727, _1796731, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1796729, tc_HOL_Obool)), hAPP(c_List_Oset(_1796729), _1796733)), hAPP(c_List_Oset(_1796729), _1796735))), c_List_Olinorder__class_Osorted(_1796727, hAPP(hAPP(c_List_Omap(_1796729, _1796727), _1796731), _1796733)), hBOOL(hAPP(c_List_Odistinct(_1796727), hAPP(hAPP(c_List_Omap(_1796729, _1796727), _1796731), _1796733))), c_List_Olinorder__class_Osorted(_1796727, hAPP(hAPP(c_List_Omap(_1796729, _1796727), _1796731), _1796735)), hBOOL(hAPP(c_List_Odistinct(_1796727), hAPP(hAPP(c_List_Omap(_1796729, _1796727), _1796731), _1796735))), hAPP(c_List_Oset(_1796729), _1796733) = hAPP(c_List_Oset(_1796729), _1796735), -(_1796733 = _1796735)], (36025 ^ _778908) ^ [_1445565, _1445567, _1445569] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1445565), _1445567), _1445569) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1445565, tc_fun(tc_fun(_1445565, tc_HOL_Obool), tc_HOL_Obool)), _1445567), hAPP(hAPP(c_COMBC(_1445565, tc_fun(tc_fun(_1445565, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1445565, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445565, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1445565, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1445565, tc_HOL_Obool), tc_HOL_Obool)), _1445565), c_Set_Oinsert(tc_fun(_1445565, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1445565, tc_HOL_Obool), tc_fun(_1445565, tc_HOL_Obool), _1445565), c_Relation_OImage(_1445565, _1445565, _1445569)), hAPP(hAPP(c_COMBC(_1445565, tc_fun(_1445565, tc_HOL_Obool), tc_fun(_1445565, tc_HOL_Obool)), c_Set_Oinsert(_1445565)), c_Orderings_Obot__class_Obot(tc_fun(_1445565, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1445565, tc_HOL_Obool), tc_HOL_Obool)))))], (16673 ^ _778908) ^ [_1065597, _1065599, _1065601] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1065597), _1065599)), _1065601) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1065597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065599), _1065601)))], (51383 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (1382 ^ _778908) ^ [_799057, _799059] : [-(class_Orderings_Obot(_799057)), _799059 = _799057, class_Orderings_Obot(_799059)], (13410 ^ _778908) ^ [_1004867, _1004869] : [class_Rings_Oring__1(_1004867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004869)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1004867), hAPP(c_Int_Onat, _1004869)) = hAPP(c_Int_Oring__1__class_Oof__int(_1004867), _1004869))], (46749 ^ _778908) ^ [_1703423, _1703425, _1703427, _1703429, _1703431] : [class_Orderings_Olinorder(_1703423), 46752 ^ _778908 : [(46761 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1703425), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1703425, _1703423, _1703427), _1703429), _1703431)))), -(hBOOL(hAPP(hAPP(c_member(_1703425), _1703429), hAPP(c_List_Oset(_1703425), _1703431)))), hBOOL(hAPP(c_List_Odistinct(_1703425), _1703431))], (46753 ^ _778908) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1703425), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1703425, _1703423, _1703427), _1703429), _1703431))), 46756 ^ _778908 : [(46759 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1703425), _1703431)))], (46757 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1703425), _1703429), hAPP(c_List_Oset(_1703425), _1703431)))]]]]], (27928 ^ _778908) ^ [_1274013, _1274015] : [c_Nat__Transfer_Ois__nat(_1274013), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1274013, _1274015)))], (45199 ^ _778908) ^ [_1666948, _1666950, _1666952] : [class_Complete__Lattice_Ocomplete__lattice(_1666948), 45202 ^ _778908 : [(45203 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666948), c_Complete__Lattice_OSup__class_OSup(_1666948, _1666950)), _1666952)), 45206 ^ _778908 : [(45207 ^ _778908) ^ [_1667106] : [hBOOL(hAPP(hAPP(c_member(_1666948), _1667106), _1666950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666948), _1667106), _1666952)))]]], (45213 ^ _778908) ^ [] : [45215 ^ _778908 : [(45218 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666948), 45214 ^ [_1666948, _1666950, _1666952]), _1666952))], (45216 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666948), 45214 ^ [_1666948, _1666950, _1666952]), _1666950)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666948), c_Complete__Lattice_OSup__class_OSup(_1666948, _1666950)), _1666952)))]]], (8321 ^ _778908) ^ [_918300] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918300) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_918300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5917 ^ _778908) ^ [_873221, _873223, _873225, _873227, _873229, _873231] : [-(c_Com_Ocom_OCall(_873221, _873223, _873225) = c_Com_Ocom_OCall(_873227, _873229, _873231)), _873221 = _873227, _873223 = _873229, _873225 = _873231], (9454 ^ _778908) ^ [_937075, _937077, _937079] : [class_Rings_Oring__no__zero__divisors(_937075), 9457 ^ _778908 : [(9458 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937075), _937077), _937079) = c_Groups_Ozero__class_Ozero(_937075), -(_937077 = c_Groups_Ozero__class_Ozero(_937075)), -(_937079 = c_Groups_Ozero__class_Ozero(_937075))], (9468 ^ _778908) ^ [] : [9469 ^ _778908 : [(9472 ^ _778908) ^ [] : [_937079 = c_Groups_Ozero__class_Ozero(_937075)], (9470 ^ _778908) ^ [] : [_937077 = c_Groups_Ozero__class_Ozero(_937075)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937075), _937077), _937079) = c_Groups_Ozero__class_Ozero(_937075))]]], (25957 ^ _778908) ^ [_1234853, _1234855] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234853), _1234855)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234853), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234855))))], (50849 ^ _778908) ^ [_1800839, _1800841] : [_1800841 = c_List_Olist_ONil(_1800839), -(hAPP(c_List_Orev(_1800839), _1800841) = c_List_Olist_ONil(_1800839))], (43163 ^ _778908) ^ [_1617696, _1617698] : [-(c_Transitive__Closure_Ortrancl(_1617696, c_Transitive__Closure_Otrancl(_1617696, _1617698)) = c_Transitive__Closure_Ortrancl(_1617696, _1617698))], (4564 ^ _778908) ^ [_849536, _849538, _849540, _849542, _849544, _849546] : [-(c_Set_Oimage(_849546, _849542, _849538) = c_Set_Oimage(_849544, _849540, _849536)), _849546 = _849544, _849542 = _849540, _849538 = _849536], (51387 ^ _778908) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (30292 ^ _778908) ^ [_1321535, _1321537, _1321539, _1321541] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321535, tc_HOL_Obool)), _1321537), hAPP(hAPP(c_Set_Oinsert(_1321535), _1321539), _1321541)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321535, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321535, tc_HOL_Obool)), _1321537), _1321541)), hAPP(hAPP(c_Set_Oinsert(_1321535), _1321539), c_Orderings_Obot__class_Obot(tc_fun(_1321535, tc_HOL_Obool)))))], (5935 ^ _778908) ^ [_873557, _873559, _873561, _873563, _873565, _873567, _873569, _873571, _873573, _873575, _873577, _873579] : [-(c_Com_Ocom_Ocom__case(_873557, _873559, _873561, _873563, _873565, _873567, _873569, _873571, _873573, c_Com_Ocom_OCall(_873575, _873577, _873579)) = hAPP(hAPP(hAPP(_873573, _873575), _873577), _873579))], (23543 ^ _778908) ^ [_1188943, _1188945, _1188947, _1188949, _1188951, _1188953, _1188955] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1188943, _1188945), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1188947), _1188949))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1188951, _1188945), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1188953), _1188955))), -(_1188945 = 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), _1188943), _1188951), _1188945), 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), _1188947), _1188953)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1188949), _1188955)), _1188945))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1188949), _1188955), _1188945)))))], (48965 ^ _778908) ^ [_1760383, _1760385] : [-(hAPP(hAPP(c_List_Odrop(_1760383), _1760385), c_List_Olist_ONil(_1760383)) = c_List_Olist_ONil(_1760383))], (34702 ^ _778908) ^ [_1414156, _1414158, _1414160, _1414162, _1414164] : [class_Groups_Ocomm__monoid__mult(_1414156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414158), _1414160)), -(hBOOL(hAPP(hAPP(c_member(_1414158), _1414162), _1414160))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1414158, _1414156), _1414164), hAPP(hAPP(c_Set_Oinsert(_1414158), _1414162), _1414160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414156), hAPP(_1414164, _1414162)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1414158, _1414156), _1414164), _1414160)))], (6995 ^ _778908) ^ [_895195, _895197, _895199, _895201, _895203] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_895195, _895197, _895199)), _895201), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895203), hAPP(c_Natural_Ogetlocs, _895201))), _895195), hAPP(hAPP(c_Natural_Ogetlocs, _895203), c_Com_ORes)))), 6999 ^ _778908 : [(7002 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _895197)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895201), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_895199, _895201))), 6998 ^ [_895195, _895197, _895199, _895201, _895203])))], (7000 ^ _778908) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895203), hAPP(c_Natural_Ogetlocs, _895201))), _895195), hAPP(hAPP(c_Natural_Ogetlocs, _895203), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 6998 ^ [_895195, _895197, _895199, _895201, _895203]), hAPP(c_Natural_Ogetlocs, _895201))), _895195), hAPP(hAPP(c_Natural_Ogetlocs, 6998 ^ [_895195, _895197, _895199, _895201, _895203]), c_Com_ORes)))]]], (34409 ^ _778908) ^ [_1408586, _1408588, _1408590, _1408592, _1408594, _1408596] : [-(_1408586 = _1408588), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408590, _1408592), _1408594), _1408588), _1408596), _1408586) = hAPP(_1408594, _1408586))], (46136 ^ _778908) ^ [_1688508, _1688510, _1688512] : [c_Fun_Oinj__on(_1688508, _1688510, _1688512, c_Orderings_Otop__class_Otop(tc_fun(_1688508, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1688508), tc_List_Olist(_1688510), hAPP(c_List_Omap(_1688508, _1688510), _1688512), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1688508), tc_HOL_Obool))))], (47665 ^ _778908) ^ [_1727785, _1727787] : [47667 ^ _778908 : [(47671 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47669 ^ [_1727785, _1727787]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727785)), _1727787))))], (47673 ^ _778908) ^ [] : [47666 ^ [_1727785, _1727787] = 47669 ^ [_1727785, _1727787]], (47675 ^ _778908) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1727785), _1727787), 47666 ^ [_1727785, _1727787]) = hAPP(hAPP(c_List_Onth(_1727785), _1727787), 47669 ^ [_1727785, _1727787]))], (47668 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47666 ^ [_1727785, _1727787]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727785)), _1727787))))]], -(hBOOL(hAPP(c_List_Odistinct(_1727785), _1727787)))], (47634 ^ _778908) ^ [_1726991, _1726993, _1726995] : [47636 ^ _778908 : [(47639 ^ _778908) ^ [] : [hBOOL(hAPP(_1726995, hAPP(hAPP(c_List_Onth(_1726991), _1726993), 47635 ^ [_1726991, _1726993, _1726995])))], (47637 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47635 ^ [_1726991, _1726993, _1726995]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726991)), _1726993))))]], 47640 ^ _778908 : [(47641 ^ _778908) ^ [_1727193] : [hBOOL(hAPP(hAPP(c_member(_1726991), _1727193), hAPP(c_List_Oset(_1726991), _1726993))), -(hBOOL(hAPP(_1726995, _1727193)))]]], (28697 ^ _778908) ^ [_1289074, _1289076, _1289078, _1289080] : [class_Orderings_Olinorder(_1289074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289074), _1289076), _1289078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289074), _1289078), _1289080)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289074, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1289074, _1289076, _1289078)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1289074, _1289078, _1289080)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1289074, _1289076, _1289080))], (50110 ^ _778908) ^ [_1786295, _1786297] : [class_Orderings_Olinorder(_1786295), -(c_List_Olinorder__class_Osorted(_1786295, hAPP(hAPP(c_List_Olist_OCons(_1786295), _1786297), c_List_Olist_ONil(_1786295))))], (45314 ^ _778908) ^ [_1669824, _1669826, _1669828] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1669824, tc_HOL_Obool)), _1669826), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669824, tc_HOL_Obool), _1669828)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1669824, tc_HOL_Obool), tc_fun(_1669824, tc_HOL_Obool)), _1669828), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1669824, tc_HOL_Obool)), _1669826)))], (44404 ^ _778908) ^ [_1646819, _1646821, _1646823, _1646825, _1646827, _1646829] : [c_Finite__Set_Ofun__left__comm(_1646819, _1646821, _1646823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646819), _1646825)), hBOOL(hAPP(hAPP(c_member(_1646819), _1646827), _1646825)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1646819, _1646821, _1646823), _1646829), _1646825) = hAPP(hAPP(_1646823, _1646827), hAPP(hAPP(c_Finite__Set_Ofold(_1646819, _1646821, _1646823), _1646829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1646819, tc_HOL_Obool)), _1646825), hAPP(hAPP(c_Set_Oinsert(_1646819), _1646827), c_Orderings_Obot__class_Obot(tc_fun(_1646819, tc_HOL_Obool)))))))], (42613 ^ _778908) ^ [_1604309] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42609 ^ [_1604309]), c_Int_OInteg)))], (9086 ^ _778908) ^ [_930805, _930807, _930809] : [class_Int_Oring__char__0(_930805), 9089 ^ _778908 : [(9096 ^ _778908) ^ [] : [_930807 = _930809, -(hAPP(c_Int_Oring__1__class_Oof__int(_930805), _930807) = hAPP(c_Int_Oring__1__class_Oof__int(_930805), _930809))], (9090 ^ _778908) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_930805), _930807) = hAPP(c_Int_Oring__1__class_Oof__int(_930805), _930809), -(_930807 = _930809)]]], (6865 ^ _778908) ^ [_891879, _891881, _891883, _891885, _891887] : [c_Com_Ocom_OWhile(_891879, _891881) = c_Com_Ocom_OCall(_891883, _891885, _891887)], (19115 ^ _778908) ^ [] : [-(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)))))], (19745 ^ _778908) ^ [_1119014, _1119016] : [class_Rings_Oring__1(_1119014), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1119014), hAPP(c_Groups_Ouminus__class_Ouminus(_1119014), _1119016)), 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(_1119014), _1119016), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19425 ^ _778908) ^ [_1113435, _1113437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113435)), c_Int_OBit1(_1113437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113435), _1113437)))], (45877 ^ _778908) ^ [_1682486, _1682488, _1682490, _1682492, _1682494] : [hBOOL(hAPP(hAPP(c_member(_1682486), _1682488), c_Map_Odom(_1682486, _1682490, _1682492))), -(hAPP(c_Map_Omap__add(_1682486, _1682490, _1682494, _1682492), _1682488) = hAPP(_1682492, _1682488))], (4832 ^ _778908) ^ [_853672, _853674] : [_853674 = _853672, -(c_Lattices_Osemilattice__inf__class_Oinf(_853674) = c_Lattices_Osemilattice__inf__class_Oinf(_853672))], (20043 ^ _778908) ^ [_1124477] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1124477, 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, _1124477, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35156 ^ _778908) ^ [_1424528, _1424530] : [-(c_FunDef_Orp__inv__image(_1424528, _1424530) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool), tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool), tc_fun(tc_fun(_1424530, _1424528), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool), tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool), tc_fun(tc_fun(_1424530, _1424528), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)), tc_fun(tc_fun(_1424530, _1424528), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool), tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool), tc_fun(tc_fun(_1424530, _1424528), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool))))), tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)), tc_fun(tc_fun(_1424530, _1424528), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool))), tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)), tc_fun(tc_fun(_1424530, _1424528), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)))), tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool)), c_COMBS(tc_fun(_1424530, _1424528), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)), tc_fun(tc_fun(_1424530, _1424528), tc_fun(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)))), tc_fun(tc_prod(_1424528, _1424528), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool))), tc_fun(_1424530, _1424528)), c_Product__Type_OPair(tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool), tc_fun(tc_prod(_1424530, _1424530), tc_HOL_Obool)))), c_Relation_Oinv__image(_1424528, _1424530))))), c_Relation_Oinv__image(_1424528, _1424530))))], (45941 ^ _778908) ^ [_1683750, _1683752, _1683754, _1683756] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1683750, tc_HOL_Obool)), c_Map_Odom(_1683750, _1683752, _1683754)), c_Map_Odom(_1683750, _1683752, _1683756)) = c_Orderings_Obot__class_Obot(tc_fun(_1683750, tc_HOL_Obool)), -(c_Map_Omap__add(_1683750, _1683752, _1683754, _1683756) = c_Map_Omap__add(_1683750, _1683752, _1683756, _1683754))], (35478 ^ _778908) ^ [_1432127, _1432129, _1432131, _1432133] : [c_Finite__Set_Ofolding__one__idem(_1432127, _1432129, _1432131), -(hAPP(hAPP(_1432129, _1432133), _1432133) = _1432133)], (46156 ^ _778908) ^ [_1689113, _1689115, _1689117, _1689119, _1689121, _1689123] : [c_Map_Omap__comp(_1689113, _1689115, _1689117, _1689119, _1689121, _1689123) = c_Option_Ooption_ONone(_1689115), -(hAPP(_1689121, _1689123) = c_Option_Ooption_ONone(_1689113)), 46164 ^ _778908 : [(46167 ^ _778908) ^ [] : [-(hAPP(_1689119, 46163 ^ [_1689113, _1689115, _1689117, _1689119, _1689121, _1689123]) = c_Option_Ooption_ONone(_1689115))], (46165 ^ _778908) ^ [] : [-(hAPP(_1689121, _1689123) = hAPP(c_Option_Ooption_OSome(_1689113), 46163 ^ [_1689113, _1689115, _1689117, _1689119, _1689121, _1689123]))]]], (29337 ^ _778908) ^ [_1303226, _1303228, _1303230, _1303232] : [class_Groups_Ocomm__monoid__add(_1303226), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1303228), _1303230))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1303228, _1303226), _1303232), _1303230) = c_Groups_Ozero__class_Ozero(_1303226))], (30066 ^ _778908) ^ [_1317385, _1317387, _1317389, _1317391] : [c_Orderings_Obot__class_Obot(tc_fun(_1317385, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1317387, _1317385, _1317389), _1317391), -(_1317391 = c_Orderings_Obot__class_Obot(tc_fun(_1317387, tc_HOL_Obool)))], (2678 ^ _778908) ^ [_819509, _819511, _819513, _819515] : [-(c_Code__Numeral_Onat__of__aux(_819515, _819511) = c_Code__Numeral_Onat__of__aux(_819513, _819509)), _819515 = _819513, _819511 = _819509], (34308 ^ _778908) ^ [_1406351, _1406353, _1406355, _1406357, _1406359, _1406361] : [class_Groups_Oordered__ab__group__add(_1406351), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406353), _1406355)), 34318 ^ _778908 : [(34321 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406351), c_Groups_Ozero__class_Ozero(_1406351)), hAPP(_1406357, 34317 ^ [_1406351, _1406353, _1406355, _1406357, _1406359, _1406361])))], (34319 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406353), 34317 ^ [_1406351, _1406353, _1406355, _1406357, _1406359, _1406361]), _1406355)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406353, _1406351), _1406357), _1406355) = _1406359, hBOOL(hAPP(hAPP(c_member(_1406353), _1406361), _1406355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406351), hAPP(_1406357, _1406361)), _1406359)))], (41468 ^ _778908) ^ [_1570458, _1570460, _1570462] : [class_Orderings_Olinorder(_1570458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570458), _1570460)), -(_1570460 = c_Orderings_Obot__class_Obot(tc_fun(_1570458, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570458), _1570462)), -(_1570462 = c_Orderings_Obot__class_Obot(tc_fun(_1570458, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1570458), c_Big__Operators_Olattice_OInf__fin(_1570458, c_Orderings_Oord__class_Omin(_1570458), _1570460)), c_Big__Operators_Olattice_OInf__fin(_1570458, c_Orderings_Oord__class_Omin(_1570458), _1570462)) = c_Big__Operators_Olattice_OInf__fin(_1570458, c_Orderings_Oord__class_Omin(_1570458), hAPP(c_Set_OCollect(_1570458), hAPP(hAPP(c_COMBB(tc_fun(_1570458, tc_HOL_Obool), tc_HOL_Obool, _1570458), c_HOL_OEx(_1570458)), hAPP(hAPP(c_COMBB(tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool)), tc_fun(_1570458, tc_HOL_Obool), _1570458), hAPP(c_COMBB(tc_fun(_1570458, tc_HOL_Obool), tc_HOL_Obool, _1570458), c_HOL_OEx(_1570458))), hAPP(hAPP(c_COMBC(_1570458, tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool)), tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570458, tc_fun(tc_fun(_1570458, tc_HOL_Obool), tc_fun(_1570458, tc_HOL_Obool))), tc_fun(tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool)), tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool))), _1570458), c_COMBS(_1570458, tc_fun(_1570458, tc_HOL_Obool), tc_fun(_1570458, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570458, tc_fun(_1570458, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1570458, tc_fun(tc_fun(_1570458, tc_HOL_Obool), tc_fun(_1570458, tc_HOL_Obool))), _1570458), hAPP(c_COMBB(tc_fun(_1570458, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1570458, tc_HOL_Obool), tc_fun(_1570458, tc_HOL_Obool)), _1570458), c_COMBS(_1570458, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool)), tc_fun(_1570458, tc_fun(_1570458, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1570458), hAPP(c_COMBB(tc_fun(_1570458, tc_HOL_Obool), tc_fun(_1570458, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1570458), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570458), c_fconj))), hAPP(hAPP(c_COMBC(_1570458, tc_fun(_1570458, tc_fun(_1570458, _1570458)), tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1570458, _1570458), tc_fun(_1570458, tc_HOL_Obool)), tc_fun(tc_fun(_1570458, tc_fun(_1570458, _1570458)), tc_fun(_1570458, tc_fun(_1570458, tc_HOL_Obool))), _1570458), c_COMBB(tc_fun(_1570458, _1570458), tc_fun(_1570458, tc_HOL_Obool), _1570458)), hAPP(hAPP(c_COMBB(tc_fun(_1570458, tc_HOL_Obool), tc_fun(tc_fun(_1570458, _1570458), tc_fun(_1570458, tc_HOL_Obool)), _1570458), c_COMBB(_1570458, tc_HOL_Obool, _1570458)), c_fequal))), c_Orderings_Oord__class_Omax(_1570458)))))), hAPP(hAPP(c_COMBC(_1570458, tc_fun(_1570458, tc_HOL_Obool), tc_fun(_1570458, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1570458, tc_HOL_Obool), tc_fun(_1570458, tc_HOL_Obool)), _1570458), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570458)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570458), c_fconj), hAPP(hAPP(c_COMBC(_1570458, tc_fun(_1570458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570458)), _1570460)))), hAPP(hAPP(c_COMBC(_1570458, tc_fun(_1570458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570458)), _1570462))))))))], (43161 ^ _778908) ^ [_1617662, _1617664] : [-(c_Transitive__Closure_Otrancl(_1617662, c_Transitive__Closure_Ortrancl(_1617662, _1617664)) = c_Transitive__Closure_Ortrancl(_1617662, _1617664))], (44084 ^ _778908) ^ [_1640668, _1640670, _1640672, _1640674] : [class_Lattices_Osemilattice__sup(_1640668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1640668), _1640670)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1640668, _1640668, c_Lattices_Osemilattice__sup__class_Osup(_1640668)), _1640672), hAPP(hAPP(c_Set_Oinsert(_1640668), _1640674), _1640670)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1640668), _1640674), hAPP(hAPP(c_Finite__Set_Ofold(_1640668, _1640668, c_Lattices_Osemilattice__sup__class_Osup(_1640668)), _1640672), _1640670)))], (16050 ^ _778908) ^ [_1053184, _1053186] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1053184), _1053186)), _1053186) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053184), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1053184, _1053186)))], (29544 ^ _778908) ^ [_1307253, _1307255, _1307257] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307253), _1307255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307253, tc_HOL_Obool)), _1307255), _1307257)), -(hAPP(c_Finite__Set_Ocard(_1307253), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307253, tc_HOL_Obool)), _1307257), _1307255)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1307253), _1307257)), hAPP(c_Finite__Set_Ocard(_1307253), _1307255)))], (48626 ^ _778908) ^ [_1750721, _1750723, _1750725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750721), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750723)), _1750725))), -(hAPP(hAPP(c_List_Otake(_1750723), hAPP(c_Nat_OSuc, _1750721)), _1750725) = hAPP(hAPP(c_List_Oappend(_1750723), hAPP(hAPP(c_List_Otake(_1750723), _1750721), _1750725)), hAPP(hAPP(c_List_Olist_OCons(_1750723), hAPP(hAPP(c_List_Onth(_1750723), _1750725), _1750721)), c_List_Olist_ONil(_1750723))))], (38594 ^ _778908) ^ [_1502653, _1502655, _1502657, _1502659, _1502661, _1502663] : [c_Fun_Oinj__on(_1502653, _1502655, _1502657, _1502659), 38597 ^ _778908 : [(38604 ^ _778908) ^ [] : [c_Fun_Oinj__on(_1502653, _1502661, hAPP(c_Fun_Ocomp(_1502655, _1502661, _1502653, _1502663), _1502657), _1502659), -(c_Fun_Oinj__on(_1502655, _1502661, _1502663, hAPP(c_Set_Oimage(_1502653, _1502655, _1502657), _1502659)))], (38598 ^ _778908) ^ [] : [c_Fun_Oinj__on(_1502655, _1502661, _1502663, hAPP(c_Set_Oimage(_1502653, _1502655, _1502657), _1502659)), -(c_Fun_Oinj__on(_1502653, _1502661, hAPP(c_Fun_Ocomp(_1502655, _1502661, _1502653, _1502663), _1502657), _1502659))]]], (12455 ^ _778908) ^ [_988329, _988331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988329)), _988331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988329), _988331)))], (18969 ^ _778908) ^ [_1105695] : [-(c_Int_OBit1(_1105695) = 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)), _1105695)), _1105695))], (22596 ^ _778908) ^ [_1170733, _1170735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170733)), hAPP(c_Nat_OSuc, _1170735))), -(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(_1170733))), 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)), _1170735)))))], (7212 ^ _778908) ^ [_899581, _899583, _899585] : [_899583 = _899585, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899581), _899583) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899581), _899585))], (38432 ^ _778908) ^ [_1499428, _1499430, _1499432, _1499434, _1499436, _1499438] : [c_Finite__Set_Ofolding__idem(_1499428, _1499430, _1499432, _1499434), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499428), _1499436)), -(hAPP(_1499434, hAPP(hAPP(c_Set_Oinsert(_1499428), _1499438), _1499436)) = hAPP(c_Fun_Ocomp(_1499430, _1499430, _1499430, hAPP(_1499434, _1499436)), hAPP(_1499432, _1499438)))], (23028 ^ _778908) ^ [_1179606, _1179608, _1179610, _1179612] : [-(hAPP(c_Nat_Onat_Onat__rec(_1179606, _1179608, _1179610), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179612)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1179606), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1179612))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1179606, _1179606), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1179606, tc_fun(_1179606, _1179606)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1179606, tc_fun(_1179606, _1179606)), tc_Int_Oint), c_If(_1179606)), c_Nat__Numeral_Oneg)), _1179608)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1179606, _1179606), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1179606, _1179606), tc_Int_Oint), _1179610), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1179606, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1179606, _1179608, _1179610)), c_Int_Onat)))))], (27646 ^ _778908) ^ [_1268661, _1268663, _1268665, _1268667, _1268669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268661, tc_HOL_Obool)), _1268663), hAPP(c_Set_Oimage(_1268665, _1268661, _1268667), _1268669))), 27650 ^ _778908 : [(27653 ^ _778908) ^ [] : [-(_1268663 = hAPP(c_Set_Oimage(_1268665, _1268661, _1268667), 27649 ^ [_1268661, _1268663, _1268665, _1268667, _1268669]))], (27651 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1268665, tc_HOL_Obool)), 27649 ^ [_1268661, _1268663, _1268665, _1268667, _1268669]), _1268669)))]]], (44677 ^ _778908) ^ [_1652905, _1652907, _1652909, _1652911] : [-(_1652905 = c_Orderings_Obot__class_Obot(tc_fun(_1652907, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652907, tc_fun(_1652909, tc_HOL_Obool)), _1652905), hAPP(c_COMBK(tc_fun(_1652909, tc_HOL_Obool), _1652907), _1652911)) = _1652911)], (23857 ^ _778908) ^ [_1194691, _1194693, _1194695, _1194697] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1194691), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194691), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194691), _1194693), _1194695)), _1194697) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194691), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194691), _1194693), _1194697)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194691), _1194695), _1194697)))], (4032 ^ _778908) ^ [_841098, _841100, _841102, _841104] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_841104, _841100) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_841102, _841098)), _841104 = _841102, _841100 = _841098], (48349 ^ _778908) ^ [_1743722, _1743724] : [-(hAPP(hAPP(c_List_Oappend(_1743722), c_List_Olist_ONil(_1743722)), _1743724) = _1743724)], (15512 ^ _778908) ^ [_1042817, _1042819, _1042821] : [class_Groups_Oab__group__add(_1042817), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1042817), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042817), _1042819), _1042821)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042817), _1042821), _1042819))], (50937 ^ _778908) ^ [_1802589, _1802591] : [-(hAPP(c_List_Oset(_1802589), c_List_Oconcat(_1802589, _1802591)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1802589), tc_fun(_1802589, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1802589)), _1802591)), c_List_Oset(_1802589)))], (442 ^ _778908) ^ [_785601, _785603, _785605, _785607, _785609, _785611, _785613, _785615, _785617, _785619] : [-(c_Big__Operators_Ocomm__monoid__big(_785617, _785613, _785609, _785605, _785601)), c_Big__Operators_Ocomm__monoid__big(_785619, _785615, _785611, _785607, _785603), _785619 = _785617, _785615 = _785613, _785611 = _785609, _785607 = _785605, _785603 = _785601], (35072 ^ _778908) ^ [] : [-(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)))], (6514 ^ _778908) ^ [_884348, _884350, _884352, _884354, _884356, _884358] : [c_Com_Ocom_OCall(_884348, _884350, _884352) = c_Com_Ocom_OCond(_884354, _884356, _884358)], (39850 ^ _778908) ^ [_1530505, _1530507, _1530509, _1530511, _1530513, _1530515, _1530517] : [-(hBOOL(hAPP(hAPP(c_member(_1530505), _1530507), _1530509))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530505, _1530511, _1530513, _1530515, _1530509), _1530517)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530505, _1530511, _1530513, _1530515, hAPP(hAPP(c_Set_Oinsert(_1530505), _1530507), _1530509)), hAPP(hAPP(_1530513, _1530507), _1530517))))], (26587 ^ _778908) ^ [_1247202] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1247202), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1247202) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (2980 ^ _778908) ^ [_824456, _824458] : [_824458 = _824456, -(c_Lazy__Sequence_Oempty(_824458) = c_Lazy__Sequence_Oempty(_824456))], (18715 ^ _778908) ^ [_1101398, _1101400] : [class_Int_Onumber__ring(_1101398), class_Rings_Olinordered__idom(_1101398), 18722 ^ _778908 : [(18729 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101400), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101398), hAPP(c_Int_Onumber__class_Onumber__of(_1101398), _1101400)), c_Groups_Ozero__class_Ozero(_1101398))))], (18723 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101398), hAPP(c_Int_Onumber__class_Onumber__of(_1101398), _1101400)), c_Groups_Ozero__class_Ozero(_1101398))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1101400), c_Int_OPls)))]]], (900 ^ _778908) ^ [_792726, _792728, _792730, _792732, _792734, _792736, _792738, _792740] : [-(c_List_Olistrelp(_792738, _792734, _792730, _792726)), c_List_Olistrelp(_792740, _792736, _792732, _792728), _792740 = _792738, _792736 = _792734, _792732 = _792730, _792728 = _792726], (6555 ^ _778908) ^ [_885472, _885474, _885476, _885478, _885480] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_885472, _885474), _885476, _885478, _885480), 6559 ^ _778908 : [(6562 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_885474, 6558 ^ [_885472, _885474, _885476, _885478, _885480], _885478, _885480))], (6560 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_885472, _885476, _885478, 6558 ^ [_885472, _885474, _885476, _885478, _885480]))]]], (33325 ^ _778908) ^ [_1386895, _1386897, _1386899, _1386901] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1386895)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1386895), _1386897), _1386899), _1386901)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29765 ^ _778908) ^ [_1311517, _1311519] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311517), _1311519))), -(hAPP(c_Finite__Set_Ocard(_1311517), _1311519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1092 ^ _778908) ^ [_795432, _795434] : [-(class_Rings_Olinordered__semiring__1(_795432)), _795434 = _795432, class_Rings_Olinordered__semiring__1(_795434)], (24087 ^ _778908) ^ [_1199452, _1199454, _1199456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199452, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199452, tc_HOL_Obool)), _1199454)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199452, tc_HOL_Obool)), _1199456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199452, tc_HOL_Obool)), _1199456), _1199454)))], (41661 ^ _778908) ^ [_1579373, _1579375, _1579377, _1579379, _1579381, _1579383] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1579373), _1579375)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579377), _1579379)), 41671 ^ _778908 : [(41674 ^ _778908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1579373), hAPP(c_Set_OCollect(_1579373), hAPP(hAPP(c_COMBS(_1579373, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579373), c_fconj), hAPP(hAPP(c_COMBC(_1579373, tc_fun(_1579373, tc_HOL_Obool), tc_HOL_Obool), c_member(_1579373)), _1579375))), hAPP(hAPP(c_COMBC(_1579373, _1579377, tc_HOL_Obool), _1579381), 41670 ^ [_1579373, _1579375, _1579377, _1579379, _1579381, _1579383])))) = hAPP(_1579383, 41670 ^ [_1579373, _1579375, _1579377, _1579379, _1579381, _1579383])], (41672 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579377), 41670 ^ [_1579373, _1579375, _1579377, _1579379, _1579381, _1579383]), _1579379)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579373, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1579377, tc_HOL_Obool), tc_Nat_Onat, _1579373), c_Finite__Set_Ocard(_1579377)), hAPP(hAPP(c_COMBB(tc_fun(_1579377, tc_HOL_Obool), tc_fun(_1579377, tc_HOL_Obool), _1579373), c_Set_OCollect(_1579377)), hAPP(hAPP(c_COMBB(tc_fun(_1579377, tc_HOL_Obool), tc_fun(_1579377, tc_HOL_Obool), _1579373), hAPP(c_COMBS(_1579377, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579377), c_fconj), hAPP(hAPP(c_COMBC(_1579377, tc_fun(_1579377, tc_HOL_Obool), tc_HOL_Obool), c_member(_1579377)), _1579379)))), _1579381)))), _1579375) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579377, tc_Nat_Onat), _1579383), _1579379))], (15064 ^ _778908) ^ [_1034462, _1034464, _1034466] : [class_Divides_Osemiring__div(_1034462), -(_1034464 = c_Groups_Ozero__class_Ozero(_1034462)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034462), _1034466), _1034464)), _1034464) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034462), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034462), _1034466), _1034464)), c_Groups_Oone__class_Oone(_1034462)))], (30232 ^ _778908) ^ [_1320592, _1320594, _1320596] : [class_Groups_Ocomm__monoid__add(_1320592), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320594, _1320592), _1320596), c_Orderings_Obot__class_Obot(tc_fun(_1320594, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1320592))], (15864 ^ _778908) ^ [_1049627, _1049629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049629), _1049627)), -(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), _1049627), _1049629))))], (20833 ^ _778908) ^ [_1138260, _1138262, _1138264] : [class_Fields_Ofield__inverse__zero(_1138260), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138260), c_Groups_Oone__class_Oone(_1138260)), hAPP(hAPP(c_Power_Opower__class_Opower(_1138260), _1138262), _1138264)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1138260), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138260), c_Groups_Oone__class_Oone(_1138260)), _1138262)), _1138264))], (31804 ^ _778908) ^ [_1354202, _1354204, _1354206] : [hBOOL(hAPP(hAPP(c_member(_1354202), _1354204), c_Option_Oset(_1354202, _1354206))), -(_1354206 = hAPP(c_Option_Ooption_OSome(_1354202), _1354204))], (27801 ^ _778908) ^ [_1271917, _1271919] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1271917, _1271919) = 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), _1271917), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1271919))))], (16108 ^ _778908) ^ [_1054696, _1054698, _1054700, _1054702, _1054704, _1054706] : [class_Rings_Oordered__ring(_1054696), 16111 ^ _778908 : [(16118 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054696), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054696), _1054698), _1054704)), _1054700)), _1054702)), _1054706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054696), _1054698), _1054700)), _1054702)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054696), _1054704), _1054700)), _1054706))))], (16112 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054696), _1054698), _1054700)), _1054702)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054696), _1054704), _1054700)), _1054706))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054696), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054696), _1054698), _1054704)), _1054700)), _1054702)), _1054706)))]]], (30310 ^ _778908) ^ [_1321968, _1321970, _1321972] : [class_Orderings_Oorder(_1321968), 30313 ^ _778908 : [(30320 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321968), _1321970), _1321972))), -(c_Orderings_Obot__class_Obot(tc_fun(_1321968, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321968, _1321970), _1321972))], (30314 ^ _778908) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1321968, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321968, _1321970), _1321972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321968), _1321970), _1321972))]]], (25099 ^ _778908) ^ [_1219670, _1219672, _1219674, _1219676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1219670), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1219672, _1219674, _1219670, _1219676) = 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(_1219672)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1219672)))], (10569 ^ _778908) ^ [_956350, _956352, _956354, _956356, _956358] : [class_Orderings_Oord(_956350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_956352, _956350)), _956354), _956356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956350), hAPP(_956354, _956358)), hAPP(_956356, _956358))))], (39331 ^ _778908) ^ [_1518211, _1518213, _1518215, _1518217, _1518219, _1518221, _1518223, _1518225] : [c_Finite__Set_Ofolding__image(_1518211, _1518213, _1518215, _1518217, _1518219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518213), _1518221)), c_Fun_Oinj__on(_1518213, _1518213, _1518223, _1518221), -(hAPP(hAPP(_1518219, _1518225), hAPP(c_Set_Oimage(_1518213, _1518213, _1518223), _1518221)) = hAPP(hAPP(_1518219, hAPP(c_Fun_Ocomp(_1518213, _1518211, _1518213, _1518225), _1518223)), _1518221))], (43375 ^ _778908) ^ [] : [-(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))))], (25439 ^ _778908) ^ [_1226142, _1226144] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226142), _1226144)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226144), _1226142))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226144), _1226142)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226142), _1226144)))], (49887 ^ _778908) ^ [_1780511, _1780513, _1780515, _1780517, _1780519] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780511)), hAPP(c_List_Ofilter(_1780511, _1780513), hAPP(hAPP(c_List_Omap(_1780515, _1780511), _1780517), _1780519))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780515)), hAPP(c_List_Ofilter(_1780515, hAPP(c_Fun_Ocomp(_1780511, tc_HOL_Obool, _1780515, _1780513), _1780517)), _1780519)))], (31103 ^ _778908) ^ [_1337381, _1337383, _1337385, _1337387] : [hBOOL(hAPP(hAPP(c_member(_1337381), _1337383), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337381, tc_HOL_Obool)), _1337385), _1337387))), -(hBOOL(hAPP(hAPP(c_member(_1337381), _1337383), _1337385)))], (19593 ^ _778908) ^ [_1116376, _1116378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1116376)), c_Int_OBit0(_1116378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116376), _1116378)))], (33835 ^ _778908) ^ [_1396451, _1396453, _1396455, _1396457, _1396459, _1396461, _1396463, _1396465] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1396451, _1396453), tc_prod(_1396451, _1396453))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1396451, _1396453), tc_prod(_1396451, _1396453)), hAPP(hAPP(c_Product__Type_OPair(_1396451, _1396453), _1396455), _1396457)), hAPP(hAPP(c_Product__Type_OPair(_1396451, _1396453), _1396459), _1396461))), c_Wellfounded_Olex__prod(_1396451, _1396453, _1396463, _1396465)))), 33836 ^ _778908 : [(33839 ^ _778908) ^ [] : [_1396455 = _1396459, hBOOL(hAPP(hAPP(c_member(tc_prod(_1396453, _1396453)), hAPP(hAPP(c_Product__Type_OPair(_1396453, _1396453), _1396457), _1396461)), _1396465))], (33837 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1396451, _1396451)), hAPP(hAPP(c_Product__Type_OPair(_1396451, _1396451), _1396455), _1396459)), _1396463))]]], (49173 ^ _778908) ^ [_1765038, _1765040, _1765042] : [-(hAPP(hAPP(c_List_Odrop(_1765038), _1765040), hAPP(c_List_Otl(_1765038), _1765042)) = hAPP(c_List_Otl(_1765038), hAPP(hAPP(c_List_Odrop(_1765038), _1765040), _1765042)))], (49181 ^ _778908) ^ [_1765153, _1765155, _1765157] : [-(hAPP(c_List_Orotate(_1765153, _1765155), _1765157) = hAPP(c_List_Orotate(_1765153, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1765155, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765153)), _1765157))), _1765157))], (39102 ^ _778908) ^ [_1512867, _1512869, _1512871, _1512873, _1512875] : [class_Groups_Ocomm__monoid__mult(_1512867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512869), _1512871)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1512867, _1512869, c_Groups_Otimes__class_Otimes(_1512867)), hAPP(hAPP(c_COMBS(_1512869, _1512867, _1512867), hAPP(hAPP(c_COMBB(_1512867, tc_fun(_1512867, _1512867), _1512869), c_Groups_Otimes__class_Otimes(_1512867)), _1512873)), _1512875)), c_Groups_Oone__class_Oone(_1512867)), _1512871) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1512867), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1512867, _1512869, c_Groups_Otimes__class_Otimes(_1512867)), _1512873), c_Groups_Oone__class_Oone(_1512867)), _1512871)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1512867, _1512869, c_Groups_Otimes__class_Otimes(_1512867)), _1512875), c_Groups_Oone__class_Oone(_1512867)), _1512871)))], (24967 ^ _778908) ^ [_1216651, _1216653, _1216655, _1216657, _1216659, _1216661, _1216663] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1216651, _1216653, _1216655, _1216657), _1216659), _1216661), _1216663) = hAPP(hAPP(_1216661, hAPP(c_Product__Type_Ofst(_1216653, _1216655), hAPP(_1216659, _1216663))), hAPP(c_Product__Type_Osnd(_1216653, _1216655), hAPP(_1216659, _1216663))))], (4926 ^ _778908) ^ [_855125, _855127, _855129, _855131] : [-(c_List_Olists(_855131, _855127) = c_List_Olists(_855129, _855125)), _855131 = _855129, _855127 = _855125], (12495 ^ _778908) ^ [_988993, _988995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988993), _988995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988993)), _988995)))], (23721 ^ _778908) ^ [_1192337, _1192339, _1192341, _1192343, _1192345] : [class_Orderings_Olinorder(_1192337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192337), _1192339), _1192341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192337), _1192343), _1192345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192337), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192337), _1192339), _1192343)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192337), _1192341), _1192345))))], (34909 ^ _778908) ^ [_1418965, _1418967, _1418969, _1418971, _1418973] : [-(c_Map_Orestrict__map(_1418965, _1418967, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418965, tc_Option_Ooption(_1418967)), _1418969), _1418971), hAPP(c_Option_Ooption_OSome(_1418967), _1418973)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1418965, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1418965), _1418971), c_Orderings_Obot__class_Obot(tc_fun(_1418965, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1418965, _1418967, _1418969, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1418965, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1418965), _1418971), c_Orderings_Obot__class_Obot(tc_fun(_1418965, tc_HOL_Obool))))))], (19309 ^ _778908) ^ [_1111471, _1111473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1111471)), c_Int_OBit0(_1111473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111471), _1111473)))], (1572 ^ _778908) ^ [_801432, _801434] : [-(class_Groups_Oab__semigroup__add(_801432)), _801434 = _801432, class_Groups_Oab__semigroup__add(_801434)], (28860 ^ _778908) ^ [_1292227, _1292229, _1292231, _1292233] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1292227, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1292229)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1292227, tc_HOL_Obool), tc_Nat_Onat), _1292231), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1292233))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1292227, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1292233, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1292229), _1292233))), _1292231))], (34 ^ _778908) ^ [_779361, _779363, _779365, _779367, _779369, _779371] : [-(c_Groups_Ocomm__monoid(_779369, _779365, _779361)), c_Groups_Ocomm__monoid(_779371, _779367, _779363), _779371 = _779369, _779367 = _779365, _779363 = _779361], (14681 ^ _778908) ^ [_1028003, _1028005] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028003, _1028005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1028003 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028005), 14684 ^ [_1028003, _1028005]))], (1582 ^ _778908) ^ [_801557, _801559] : [-(class_Rings_Oordered__semiring(_801557)), _801559 = _801557, class_Rings_Oordered__semiring(_801559)], (43153 ^ _778908) ^ [_1617447, _1617449] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617447, _1617447)), hAPP(hAPP(c_Product__Type_OPair(_1617447, _1617447), _1617449), _1617449)), c_Relation_OId(_1617447))))], (19219 ^ _778908) ^ [_1109629, _1109631] : [class_Int_Onumber__ring(_1109629), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109629), c_Groups_Oone__class_Oone(_1109629)), hAPP(c_Int_Onumber__class_Onumber__of(_1109629), _1109631)) = hAPP(c_Int_Onumber__class_Onumber__of(_1109629), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1109631)))], (12583 ^ _778908) ^ [] : [-(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))))], (24453 ^ _778908) ^ [_1206703, _1206705, _1206707, _1206709] : [class_Orderings_Olinorder(_1206703), 24456 ^ _778908 : [(24457 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206703), _1206705), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206703), _1206707), _1206709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206703), _1206705), _1206707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206703), _1206705), _1206709)))], (24467 ^ _778908) ^ [] : [24468 ^ _778908 : [(24471 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206703), _1206705), _1206709))], (24469 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206703), _1206705), _1206707))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206703), _1206705), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206703), _1206707), _1206709))))]]], (9940 ^ _778908) ^ [_945760, _945762, _945764, _945766] : [class_Rings_Olinordered__semiring__strict(_945760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945760), _945762), _945764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945760), c_Groups_Ozero__class_Ozero(_945760)), _945766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945760), _945762), _945766)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945760), _945764), _945766))))], (34879 ^ _778908) ^ [_1418096, _1418098, _1418100, _1418102, _1418104] : [hAPP(_1418096, _1418098) = hAPP(c_Option_Ooption_OSome(_1418100), _1418102), -(hBOOL(hAPP(hAPP(c_member(_1418100), _1418102), c_Map_Oran(_1418104, _1418100, _1418096))))], (21501 ^ _778908) ^ [_1150234, _1150236, _1150238] : [class_Fields_Olinordered__field__inverse__zero(_1150234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150234), c_Groups_Ozero__class_Ozero(_1150234)), _1150236)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150234), hAPP(c_Groups_Oabs__class_Oabs(_1150234), _1150238)), _1150236) = hAPP(c_Groups_Oabs__class_Oabs(_1150234), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150234), _1150238), _1150236)))], (51117 ^ _778908) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (6292 ^ _778908) ^ [_880324, _880326, _880328, _880330, _880332, _880334] : [c_Com_Ocom_OLocal(_880324, _880326, _880328) = c_Com_Ocom_OLocal(_880330, _880332, _880334), 6295 ^ _778908 : [(6300 ^ _778908) ^ [] : [-(_880328 = _880334)], (6298 ^ _778908) ^ [] : [-(_880326 = _880332)], (6296 ^ _778908) ^ [] : [-(_880324 = _880330)]]], (18515 ^ _778908) ^ [] : [c_Int_OPls = c_Int_OMin], (5554 ^ _778908) ^ [_864749, _864751] : [_864751 = _864749, -(c_List_Otl(_864751) = c_List_Otl(_864749))], (15138 ^ _778908) ^ [_1035978, _1035980, _1035982] : [-(hBOOL(hAPP(_1035978, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1035980), _1035982)))), 15141 ^ _778908 : [(15144 ^ _778908) ^ [] : [hBOOL(hAPP(_1035978, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15142 ^ _778908) ^ [] : [-(_1035982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 15145 ^ _778908 : [(15150 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15148 ^ [_1035978, _1035980, _1035982]), _1035982)))], (15152 ^ _778908) ^ [] : [-(_1035980 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1035982), 15147 ^ [_1035978, _1035980, _1035982])), 15148 ^ [_1035978, _1035980, _1035982]))], (15154 ^ _778908) ^ [] : [hBOOL(hAPP(_1035978, 15147 ^ [_1035978, _1035980, _1035982]))], (15146 ^ _778908) ^ [] : [_1035982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (36862 ^ _778908) ^ [_1463488, _1463490, _1463492, _1463494] : [class_Lattices_Osemilattice__inf(_1463488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1463488), _1463490), _1463492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1463488), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463488), _1463490), _1463494)), _1463492)))], (3638 ^ _778908) ^ [_834853, _834855, _834857, _834859] : [-(c_Sum__Type_OInl(_834859, _834855) = c_Sum__Type_OInl(_834857, _834853)), _834859 = _834857, _834855 = _834853], (46366 ^ _778908) ^ [_1694109, _1694111, _1694113] : [hBOOL(hAPP(c_List_Odistinct(_1694109), hAPP(hAPP(c_List_Omap(tc_prod(_1694109, _1694111), _1694109), c_Product__Type_Ofst(_1694109, _1694111)), _1694113))), -(hAPP(c_List_Oset(tc_prod(_1694109, _1694111)), _1694113) = hAPP(c_Set_OCollect(tc_prod(_1694109, _1694111)), hAPP(c_Product__Type_Oprod_Oprod__case(_1694109, _1694111, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1694109, tc_fun(_1694111, tc_Option_Ooption(_1694111)), tc_fun(_1694111, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1694111), tc_HOL_Obool), tc_fun(tc_fun(_1694111, tc_Option_Ooption(_1694111)), tc_fun(_1694111, tc_HOL_Obool)), _1694109), c_COMBB(tc_Option_Ooption(_1694111), tc_HOL_Obool, _1694111)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1694111), tc_fun(tc_Option_Ooption(_1694111), tc_HOL_Obool), _1694109), c_fequal), c_Map_Omap__of(_1694109, _1694111, _1694113)))), c_Option_Ooption_OSome(_1694111)))))], (47042 ^ _778908) ^ [_1712523, _1712525, _1712527] : [_1712523 = hAPP(hAPP(c_List_Olist_OCons(_1712525), _1712527), _1712523)], (3828 ^ _778908) ^ [_837912, _837914, _837916, _837918, _837920, _837922] : [-(c_FunDef_Oin__rel(_837922, _837918, _837914) = c_FunDef_Oin__rel(_837920, _837916, _837912)), _837922 = _837920, _837918 = _837916, _837914 = _837912], (5700 ^ _778908) ^ [_866930, _866932] : [_866932 = _866930, -(c_COMBI(_866932) = c_COMBI(_866930))], (44909 ^ _778908) ^ [_1660264, _1660266, _1660268, _1660270] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660264, tc_fun(_1660266, tc_HOL_Obool)), _1660268), _1660270) = hAPP(c_Set_OCollect(_1660266), hAPP(hAPP(c_COMBB(tc_fun(_1660264, tc_HOL_Obool), tc_HOL_Obool, _1660266), c_HOL_OAll(_1660264)), hAPP(hAPP(c_COMBB(tc_fun(_1660264, tc_HOL_Obool), tc_fun(_1660264, tc_HOL_Obool), _1660266), hAPP(c_COMBS(_1660264, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1660264), c_fimplies), hAPP(hAPP(c_COMBC(_1660264, tc_fun(_1660264, tc_HOL_Obool), tc_HOL_Obool), c_member(_1660264)), _1660268)))), hAPP(hAPP(c_COMBC(_1660266, tc_fun(_1660264, tc_fun(_1660266, tc_HOL_Obool)), tc_fun(_1660264, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1660266, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1660264, tc_fun(_1660266, tc_HOL_Obool)), tc_fun(_1660264, tc_HOL_Obool)), _1660266), c_COMBB(tc_fun(_1660266, tc_HOL_Obool), tc_HOL_Obool, _1660264)), c_member(_1660266))), _1660270)))))], (20231 ^ _778908) ^ [_1128195, _1128197] : [class_Rings_Odivision__ring(_1128195), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128195), _1128197), c_Groups_Oone__class_Oone(_1128195)) = _1128197)], (47376 ^ _778908) ^ [_1721442] : [47378 ^ _778908 : [(47381 ^ _778908) ^ [] : [47377 ^ [_1721442] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47379 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 47377 ^ [_1721442]), hAPP(c_List_Oset(tc_Nat_Onat), _1721442))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1721442) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35863 ^ _778908) ^ [_1441708, _1441710, _1441712, _1441714, _1441716] : [c_Hoare__Mirabelle_Ohoare__derivs(_1441708, _1441710, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1441708)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1441708), c_Hoare__Mirabelle_Opeek__and(_1441708, _1441712, _1441714)), _1441716), _1441712)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1441708), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1441708, _1441710, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1441708)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1441708), _1441712), c_Com_Ocom_OWhile(_1441714, _1441716)), c_Hoare__Mirabelle_Opeek__and(_1441708, _1441712, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1441714)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1441708), tc_HOL_Obool)))))], (34082 ^ _778908) ^ [_1401601, _1401603, _1401605] : [class_Orderings_Olinorder(_1401601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401601), _1401603)), hBOOL(hAPP(hAPP(c_member(_1401601), _1401605), _1401603)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1401601), _1401605), c_Big__Operators_Olattice_OInf__fin(_1401601, c_Orderings_Oord__class_Omin(_1401601), _1401603)) = _1401605)], (46154 ^ _778908) ^ [_1689036, _1689038, _1689040, _1689042, _1689044] : [-(c_Map_Omap__comp(_1689036, _1689038, _1689040, _1689042, hAPP(c_COMBK(tc_Option_Ooption(_1689036), _1689040), c_Option_Ooption_ONone(_1689036)), _1689044) = c_Option_Ooption_ONone(_1689038))], (26489 ^ _778908) ^ [_1245460, _1245462, _1245464] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245460), _1245464)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245460), _1245462)))], (36061 ^ _778908) ^ [_1446541, _1446543, _1446545, _1446547, _1446549] : [c_Equiv__Relations_Oequiv(_1446541, _1446543, _1446545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446541, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446541, _1446541, _1446545), hAPP(hAPP(c_Set_Oinsert(_1446541), _1446547), c_Orderings_Obot__class_Obot(tc_fun(_1446541, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1446541, _1446541, _1446545), hAPP(hAPP(c_Set_Oinsert(_1446541), _1446549), c_Orderings_Obot__class_Obot(tc_fun(_1446541, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1446541), _1446547), _1446543)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446541, _1446541)), hAPP(hAPP(c_Product__Type_OPair(_1446541, _1446541), _1446549), _1446547)), _1446545)))], (19375 ^ _778908) ^ [_1112561, _1112563] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1112561)), c_Int_OBit0(_1112563)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112561), _1112563)))], (44722 ^ _778908) ^ [_1653969, _1653971, _1653973, _1653975, _1653977] : [44724 ^ _778908 : [(44727 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1653969, tc_HOL_Obool)), _1653971), hAPP(_1653977, 44723 ^ [_1653969, _1653971, _1653973, _1653975, _1653977])))], (44725 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653973), 44723 ^ [_1653969, _1653971, _1653973, _1653975, _1653977]), _1653975)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1653969, tc_HOL_Obool)), _1653971), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653973, tc_fun(_1653969, tc_HOL_Obool)), _1653975), _1653977))))], (19315 ^ _778908) ^ [_1111572, _1111574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111572), _1111574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1111572)), c_Int_OBit0(_1111574))))], (40072 ^ _778908) ^ [_1536038, _1536040, _1536042, _1536044, _1536046] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1536038, _1536040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1536038, tc_HOL_Obool)), _1536042), _1536044)), _1536046) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1536038, _1536040), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1536038, _1536040), _1536042), _1536046)), hAPP(hAPP(c_Product__Type_OSigma(_1536038, _1536040), _1536044), _1536046)))], (22432 ^ _778908) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (27829 ^ _778908) ^ [_1272463, _1272465] : [c_Nat__Transfer_Onat__set(_1272463), c_Nat__Transfer_Onat__set(_1272465), 27836 ^ _778908 : [(27843 ^ _778908) ^ [] : [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), _1272463)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1272465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1272463), _1272465)))], (27837 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1272463), _1272465)), -(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), _1272463)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1272465))))]]], (1072 ^ _778908) ^ [_795182, _795184] : [-(class_Rings_Olinordered__ring__strict(_795182)), _795184 = _795182, class_Rings_Olinordered__ring__strict(_795184)], (42833 ^ _778908) ^ [_1609378, _1609380] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1609378), _1609380)), 42839 ^ _778908 : [(42842 ^ _778908) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42840 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609378), 42838 ^ [_1609378, _1609380]), _1609380)))]], -(hAPP(c_Finite__Set_Ocard(_1609378), _1609380) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46463 ^ _778908) ^ [_1696478, _1696480] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1696478, _1696480) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1696478, _1696480)))], (46527 ^ _778908) ^ [_1697626, _1697628, _1697630] : [class_Orderings_Olinorder(_1697626), hBOOL(hAPP(c_Finite__Set_Ofinite(_1697626), _1697628)), -(c_List_Olinorder__class_Osorted__list__of__set(_1697626, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1697626, tc_HOL_Obool)), _1697628), hAPP(hAPP(c_Set_Oinsert(_1697626), _1697630), c_Orderings_Obot__class_Obot(tc_fun(_1697626, tc_HOL_Obool))))) = c_List_Oremove1(_1697626, _1697630, c_List_Olinorder__class_Osorted__list__of__set(_1697626, _1697628)))], (2022 ^ _778908) ^ [_808883, _808885, _808887, _808889, _808891, _808893] : [-(c_Option_Ooption_Ooption__size(_808893, _808889, _808885) = c_Option_Ooption_Ooption__size(_808891, _808887, _808883)), _808893 = _808891, _808889 = _808887, _808885 = _808883], (6019 ^ _778908) ^ [_875201, _875203, _875205, _875207] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_875201, _875203)), _875205), _875207)), -(_875207 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _875205), _875201), hAPP(_875203, _875205)))], (43703 ^ _778908) ^ [_1630991, _1630993] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630991, _1630991), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1630993) = _1630993)], (26769 ^ _778908) ^ [_1250990, _1250992, _1250994, _1250996] : [class_Divides_Osemiring__div(_1250990), -(_1250992 = c_Groups_Ozero__class_Ozero(_1250990)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250990), _1250992), _1250994)), 26780 ^ _778908 : [(26787 ^ _778908) ^ [] : [_1250994 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250990), _1250996), _1250992), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250990), _1250994), _1250992) = _1250996)], (26781 ^ _778908) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250990), _1250994), _1250992) = _1250996, -(_1250994 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250990), _1250996), _1250992))]]], (51321 ^ _778908) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (5244 ^ _778908) ^ [_860024, _860026, _860028, _860030, _860032, _860034] : [-(c_List_Olinorder__class_Oinsort__key(_860034, _860030, _860026) = c_List_Olinorder__class_Oinsort__key(_860032, _860028, _860024)), _860034 = _860032, _860030 = _860028, _860026 = _860024], (25651 ^ _778908) ^ [_1229549, _1229551] : [_1229549 = _1229551, 25654 ^ _778908 : [(25657 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229551), _1229549)))], (25655 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229549), _1229551)))]]], (2256 ^ _778908) ^ [_812798, _812800, _812802, _812804, _812806, _812808, _812810, _812812, _812814, _812816, _812818, _812820] : [-(c_Sum__Type_Osum_Osum__rec(_812820, _812816, _812812, _812808, _812804, _812800) = c_Sum__Type_Osum_Osum__rec(_812818, _812814, _812810, _812806, _812802, _812798)), _812820 = _812818, _812816 = _812814, _812812 = _812810, _812808 = _812806, _812804 = _812802, _812800 = _812798], (48544 ^ _778908) ^ [_1748784, _1748786, _1748788, _1748790, _1748792, _1748794, _1748796] : [hBOOL(hAPP(hAPP(c_member(_1748784), _1748786), hAPP(c_List_Oset(_1748784), hAPP(hAPP(c_List_Otake(_1748784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748788)), _1748790)), _1748792)))), -(c_Map_Omap__upds(_1748784, _1748788, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1748784, tc_Option_Ooption(_1748788)), _1748794), _1748786), hAPP(c_Option_Ooption_OSome(_1748788), _1748796)), _1748792, _1748790) = c_Map_Omap__upds(_1748784, _1748788, _1748794, _1748792, _1748790))], (29287 ^ _778908) ^ [_1302413, _1302415, _1302417, _1302419] : [-(hAPP(hAPP(c_Set_Oinsert(_1302413), _1302415), hAPP(hAPP(c_Set_Oinsert(_1302413), _1302417), _1302419)) = hAPP(hAPP(c_Set_Oinsert(_1302413), _1302417), hAPP(hAPP(c_Set_Oinsert(_1302413), _1302415), _1302419)))], (6528 ^ _778908) ^ [_884713, _884715, _884717, _884719] : [c_Com_Ocom_OSemi(_884713, _884715) = c_Com_Ocom_OAss(_884717, _884719)], (27314 ^ _778908) ^ [_1261651, _1261653, _1261655, _1261657, _1261659] : [class_Groups_Oab__group__add(_1261651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1261653), _1261655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1261655), _1261657)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1261651), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261651), _1261659), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261653), _1261657))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261651), _1261659), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261653), _1261655))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261651), _1261659), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261655), _1261657)))], (15880 ^ _778908) ^ [_1049922, _1049924] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049922), _1049924) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049922), _1049924)))], (296 ^ _778908) ^ [_783226, _783228, _783230, _783232, _783234, _783236] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_783234, _783230, _783226)), c_Hoare__Mirabelle_Ohoare__derivs(_783236, _783232, _783228), _783236 = _783234, _783232 = _783230, _783228 = _783226], (7042 ^ _778908) ^ [_896717, _896719, _896721, _896723] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _896717), _896719, _896721, _896723), 7046 ^ _778908 : [(7049 ^ _778908) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _896717)), _896719, 7045 ^ [_896717, _896719, _896721, _896723], _896723))], (7047 ^ _778908) ^ [] : [-(_896721 = hAPP(c_Nat_OSuc, 7045 ^ [_896717, _896719, _896721, _896723]))]]], (20269 ^ _778908) ^ [_1128993, _1128995] : [c_Nat__Transfer_Ois__nat(_1128993), c_Nat__Transfer_Ois__nat(_1128995), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1128993), _1128995)))], (17921 ^ _778908) ^ [_1089002] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089002))), -(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), _1089002)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33647 ^ _778908) ^ [_1392454, _1392456, _1392458] : [class_Orderings_Olinorder(_1392454), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392454), _1392456)), -(_1392456 = c_Orderings_Obot__class_Obot(tc_fun(_1392454, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392454), _1392458)), -(_1392458 = c_Orderings_Obot__class_Obot(tc_fun(_1392454, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1392454, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392454, tc_HOL_Obool)), _1392456), _1392458)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1392454), c_Big__Operators_Olinorder__class_OMax(_1392454, _1392456)), c_Big__Operators_Olinorder__class_OMax(_1392454, _1392458)))], (11538 ^ _778908) ^ [_971985, _971987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971985), _971987)), -(_971985 = _971987), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971985), _971987)))], (31217 ^ _778908) ^ [_1341804, _1341806, _1341808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341804, tc_HOL_Obool)), _1341806), _1341808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341804, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1341804, tc_fun(_1341804, tc_HOL_Obool), tc_HOL_Obool), c_member(_1341804)), _1341806)), hAPP(hAPP(c_COMBC(_1341804, tc_fun(_1341804, tc_HOL_Obool), tc_HOL_Obool), c_member(_1341804)), _1341808))))], (19499 ^ _778908) ^ [_1114747, _1114749] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1114747)), c_Int_OBit0(_1114749)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1114747), _1114749)))], (39747 ^ _778908) ^ [_1527867, _1527869, _1527871, _1527873, _1527875] : [hAPP(_1527867, _1527869) = hAPP(c_Option_Ooption_OSome(_1527871), _1527873), -(hBOOL(hAPP(hAPP(c_member(_1527875), _1527869), c_Map_Odom(_1527875, _1527871, _1527867))))], (47419 ^ _778908) ^ [_1722226, _1722228] : [-(c_List_Olistrelp(_1722226, _1722228, c_List_Olist_ONil(_1722226), c_List_Olist_ONil(_1722226)))], (25019 ^ _778908) ^ [_1217849, _1217851, _1217853] : [c_Nitpick_Oless__frac(_1217849, _1217851, _1217853), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1217849), c_Nitpick_Oplus__frac(_1217849, _1217851, c_Nitpick_Ouminus__frac(_1217849, _1217853)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35823 ^ _778908) ^ [_1440338, _1440340, _1440342, _1440344] : [-(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), _1440338), _1440340)), 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), _1440342), _1440344)), 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), _1440338), _1440342)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440340), _1440344))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (44428 ^ _778908) ^ [_1647419, _1647421, _1647423, _1647425, _1647427] : [c_Finite__Set_Ofun__left__comm(_1647419, _1647421, _1647423), -(c_Finite__Set_Ofun__left__comm(_1647425, _1647421, hAPP(hAPP(c_COMBB(_1647419, tc_fun(_1647421, _1647421), _1647425), _1647423), _1647427)))], (15314 ^ _778908) ^ [_1039186, _1039188, _1039190] : [class_Divides_Osemiring__div(_1039186), -(_1039188 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039186), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1039186), _1039188), _1039190)), _1039190)), c_Divides_Odiv__class_Omod(_1039186, _1039188, _1039190)))], (10864 ^ _778908) ^ [_961228, _961230, _961232] : [10865 ^ _778908 : [(10868 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961230), _961232))], (10866 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961228)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961228), _961230)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961228), _961232))))], (46821 ^ _778908) ^ [_1705690, _1705692, _1705694] : [-(_1705690 = _1705692), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705694)), _1705690) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705694)), _1705692), 46827 ^ _778908 : [(46830 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1705694, _1705694, tc_HOL_Obool), c_fequal), 46826 ^ [_1705690, _1705692, _1705694]))], (46828 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1705694, _1705694)), 46826 ^ [_1705690, _1705692, _1705694]), hAPP(c_List_Oset(tc_prod(_1705694, _1705694)), hAPP(hAPP(c_List_Ozip(_1705694, _1705694), _1705690), _1705692)))))]]], (48466 ^ _778908) ^ [_1747083, _1747085, _1747087, _1747089, _1747091, _1747093] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747083)), _1747085) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747087)), _1747089), -(c_Map_Omap__upds(_1747083, _1747087, _1747091, _1747085, hAPP(hAPP(c_List_Oappend(_1747087), _1747089), _1747093)) = c_Map_Omap__upds(_1747083, _1747087, _1747091, _1747085, _1747089))], (19825 ^ _778908) ^ [_1120464, _1120466] : [class_Rings_Olinordered__idom(_1120464), 19828 ^ _778908 : [(19835 ^ _778908) ^ [] : [-(_1120466 = c_Groups_Ozero__class_Ozero(_1120464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120464), c_Groups_Ozero__class_Ozero(_1120464)), hAPP(hAPP(c_Power_Opower__class_Opower(_1120464), _1120466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19829 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120464), c_Groups_Ozero__class_Ozero(_1120464)), hAPP(hAPP(c_Power_Opower__class_Opower(_1120464), _1120466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1120466 = c_Groups_Ozero__class_Ozero(_1120464)]]], (8236 ^ _778908) ^ [_916849, _916851, _916853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916849), _916851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _916851), _916853))))], (7570 ^ _778908) ^ [_905705, _905707, _905709, _905711, _905713, _905715] : [-(c_Nitpick_Opair__box_Opair__box__size(_905705, _905707, _905709, _905711, c_Nitpick_Opair__box_OPairBox(_905705, _905707, _905713, _905715)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_905709, _905713)), hAPP(_905711, _905715))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31890 ^ _778908) ^ [_1357066, _1357068, _1357070, _1357072, _1357074] : [hBOOL(hAPP(hAPP(c_member(_1357066), _1357068), _1357070)), -(hAPP(c_Set_Oimage(_1357066, _1357072, hAPP(c_COMBK(_1357072, _1357066), _1357074)), _1357070) = hAPP(hAPP(c_Set_Oinsert(_1357072), _1357074), c_Orderings_Obot__class_Obot(tc_fun(_1357072, tc_HOL_Obool))))], (50949 ^ _778908) ^ [_1802911, _1802913] : [-(_1802911 = c_List_Olist_ONil(_1802913)), -(hAPP(c_List_Ohd(_1802913), hAPP(c_List_Orev(_1802913), _1802911)) = c_List_Olast(_1802913, _1802911))], (8664 ^ _778908) ^ [_923744, _923746, _923748] : [class_Orderings_Olinorder(_923744), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923744), _923746), _923748))), 8671 ^ _778908 : [(8678 ^ _778908) ^ [] : [_923748 = _923746, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923744), _923748), _923746))], (8672 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923744), _923748), _923746))), -(_923748 = _923746)]]], (36922 ^ _778908) ^ [_1465380, _1465382] : [class_Lattices_Oboolean__algebra(_1465380), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465380), _1465382), hAPP(c_Groups_Ouminus__class_Ouminus(_1465380), _1465382)) = c_Orderings_Obot__class_Obot(_1465380))], (32497 ^ _778908) ^ [_1369842, _1369844, _1369846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369842)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1369844), _1369846)), 32504 ^ _778908 : [(32505 ^ _778908) ^ [_1370038] : [32507 ^ _778908 : [(32513 ^ _778908) ^ [] : [-(_1370038 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 32509 ^ [_1369842, _1369844, _1369846, _1370038]), 32506 ^ [_1369842, _1369844, _1369846, _1370038]))], (32511 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32509 ^ [_1369842, _1369844, _1369846, _1370038]), _1369846)))], (32508 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 32506 ^ [_1369842, _1369844, _1369846, _1370038]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1369842))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369844), _1370038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1370038), _1369842))))]]], (41155 ^ _778908) ^ [_1560799, _1560801, _1560803] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560799), hAPP(c_Set_OCollect(_1560799), hAPP(hAPP(c_COMBS(_1560799, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560799), c_fdisj), _1560801)), _1560803))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560799), hAPP(c_Set_OCollect(_1560799), _1560801))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560799), hAPP(c_Set_OCollect(_1560799), _1560803)))], (16797 ^ _778908) ^ [_1067607, _1067609] : [class_Groups_Oordered__ab__group__add__abs(_1067607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067607), c_Groups_Ozero__class_Ozero(_1067607)), _1067609)), -(hAPP(c_Groups_Oabs__class_Oabs(_1067607), _1067609) = _1067609)], (37953 ^ _778908) ^ [_1489655, _1489657, _1489659, _1489661, _1489663, _1489665] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489655, tc_fun(_1489657, tc_HOL_Obool))), _1489659), _1489661), _1489663), _1489665)), 37956 ^ _778908 : [(37959 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1489661, _1489663), _1489665)))], (37957 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1489659, _1489663), _1489665)))]]], (37222 ^ _778908) ^ [_1472299, _1472301, _1472303] : [class_Orderings_Oorder(_1472299), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472299, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1472299, _1472301, _1472303)), hAPP(c_SetInterval_Oord__class_OatLeast(_1472299), _1472303)) = c_Orderings_Obot__class_Obot(tc_fun(_1472299, tc_HOL_Obool)))], (31283 ^ _778908) ^ [_1343267, _1343269, _1343271] : [hBOOL(hAPP(_1343271, _1343269)), -(hBOOL(hAPP(hAPP(c_member(_1343267), _1343269), _1343271)))], (22620 ^ _778908) ^ [_1171304, _1171306] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1171304)), hAPP(c_Code__Numeral_Oof__nat, _1171306)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171304), _1171306)))], (41192 ^ _778908) ^ [_1561558, _1561560] : [-(hBOOL(hAPP(_1561560, 41193 ^ [_1561558, _1561560]))), -(hAPP(c_Set_OCollect(_1561558), _1561560) = c_Orderings_Obot__class_Obot(tc_fun(_1561558, tc_HOL_Obool)))], (33998 ^ _778908) ^ [_1400149, _1400151] : [class_Orderings_Olinorder(_1400149), -(c_Big__Operators_Olattice_OSup__fin(_1400149, c_Orderings_Oord__class_Omax(_1400149), hAPP(hAPP(c_Set_Oinsert(_1400149), _1400151), c_Orderings_Obot__class_Obot(tc_fun(_1400149, tc_HOL_Obool)))) = _1400151)], (51675 ^ _778908) ^ [_1813799, _1813801] : [hBOOL(hAPP(hAPP(c_fconj, _1813799), _1813801)), -(hBOOL(_1813799))], (25525 ^ _778908) ^ [_1227524, _1227526, _1227528] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227524), _1227526)), _1227526 = _1227528, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227524), _1227528)))], (49903 ^ _778908) ^ [_1780979, _1780981, _1780983, _1780985] : [-(hBOOL(hAPP(_1780979, _1780981))), -(hAPP(c_List_Ofilter(_1780983, _1780979), hAPP(hAPP(c_List_Olist_OCons(_1780983), _1780981), _1780985)) = hAPP(c_List_Ofilter(_1780983, _1780979), _1780985))], (43063 ^ _778908) ^ [_1614339, _1614341, _1614343, _1614345, _1614347] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614339, _1614339)), hAPP(hAPP(c_Product__Type_OPair(_1614339, _1614339), _1614341), _1614343)), c_Transitive__Closure_Otrancl(_1614339, _1614345))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614339, _1614339)), hAPP(hAPP(c_Product__Type_OPair(_1614339, _1614339), _1614343), _1614347)), c_Transitive__Closure_Otrancl(_1614339, _1614345))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614339, _1614339)), hAPP(hAPP(c_Product__Type_OPair(_1614339, _1614339), _1614341), _1614347)), c_Transitive__Closure_Otrancl(_1614339, _1614345))))], (44625 ^ _778908) ^ [_1651502, _1651504, _1651506, _1651508, _1651510, _1651512] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651502, tc_fun(_1651504, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1651506, tc_fun(_1651502, tc_HOL_Obool)), _1651508), _1651510)), _1651512) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651506, tc_fun(_1651504, tc_HOL_Obool)), _1651508), hAPP(hAPP(c_COMBC(_1651506, tc_fun(_1651502, tc_fun(_1651504, tc_HOL_Obool)), tc_fun(_1651504, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1651502, tc_HOL_Obool), tc_fun(tc_fun(_1651502, tc_fun(_1651504, tc_HOL_Obool)), tc_fun(_1651504, tc_HOL_Obool)), _1651506), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651502, tc_fun(_1651504, tc_HOL_Obool))), _1651510)), _1651512)))], (36520 ^ _778908) ^ [_1456126, _1456128, _1456130, _1456132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456126, tc_HOL_Obool)), _1456128), _1456130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456126, tc_HOL_Obool)), _1456128), _1456132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456126, tc_HOL_Obool)), _1456128), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456126, tc_HOL_Obool)), _1456130), _1456132))))], (26251 ^ _778908) ^ [_1240986, _1240988, _1240990] : [class_Divides_Osemiring__div(_1240986), 26254 ^ _778908 : [(26261 ^ _778908) ^ [] : [c_Divides_Odiv__class_Omod(_1240986, _1240990, _1240988) = c_Groups_Ozero__class_Ozero(_1240986), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240986), _1240988), _1240990)))], (26255 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240986), _1240988), _1240990)), -(c_Divides_Odiv__class_Omod(_1240986, _1240990, _1240988) = c_Groups_Ozero__class_Ozero(_1240986))]]], (25047 ^ _778908) ^ [_1218495, _1218497] : [-(hAPP(c_New__DSequence_Opos__empty(_1218495), _1218497) = c_Lazy__Sequence_Oempty(_1218495))], (3940 ^ _778908) ^ [_839720, _839722] : [_839722 = _839720, -(tc_Lazy__Sequence_Olazy__sequence(_839722) = tc_Lazy__Sequence_Olazy__sequence(_839720))], (23841 ^ _778908) ^ [_1194422, _1194424, _1194426] : [class_Orderings_Olinorder(_1194422), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194422), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194422), _1194424), _1194426)), _1194426)))], (25379 ^ _778908) ^ [_1225178, _1225180, _1225182] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225178), _1225180)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225180), _1225178))), _1225180 = _1225182, 25390 ^ _778908 : [(25393 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225182), _1225178))], (25391 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225178), _1225182)))]]], (6470 ^ _778908) ^ [_883459, _883461, _883463, _883465, _883467] : [c_Com_Ocom_OAss(_883459, _883461) = c_Com_Ocom_OLocal(_883463, _883465, _883467)], (8178 ^ _778908) ^ [_915894, _915896, _915898] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_915894, _915896)), hAPP(c_Sum__Type_OInr(_915896, _915894), _915898)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18951 ^ _778908) ^ [_1105398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1105398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1105398))))], (17169 ^ _778908) ^ [_1075264, _1075266] : [class_Groups_Oordered__ab__group__add__abs(_1075264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075264), _1075266), c_Groups_Ozero__class_Ozero(_1075264))), -(hAPP(c_Groups_Oabs__class_Oabs(_1075264), _1075266) = hAPP(c_Groups_Ouminus__class_Ouminus(_1075264), _1075266))], (8568 ^ _778908) ^ [_922558, _922560] : [_922558 = _922560, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922558) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922560))], (40094 ^ _778908) ^ [_1536541, _1536543, _1536545, _1536547] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1536541, _1536543)), hAPP(hAPP(c_Product__Type_OSigma(_1536541, _1536543), _1536545), hAPP(c_COMBK(tc_fun(_1536543, tc_HOL_Obool), _1536541), _1536547))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1536541), _1536545)), hAPP(c_Finite__Set_Ocard(_1536543), _1536547)))], (42715 ^ _778908) ^ [_1606701, _1606703, _1606705, _1606707, _1606709, _1606711] : [hBOOL(hAPP(hAPP(c_member(_1606701), _1606703), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1606705, _1606707, tc_fun(_1606701, tc_HOL_Obool)), _1606709), _1606711))), 42720 ^ _778908 : [(42723 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606701), _1606703), hAPP(hAPP(_1606709, 42718 ^ [_1606701, _1606703, _1606705, _1606707, _1606709, _1606711]), 42719 ^ [_1606701, _1606703, _1606705, _1606707, _1606709, _1606711]))))], (42721 ^ _778908) ^ [] : [-(_1606711 = hAPP(hAPP(c_Product__Type_OPair(_1606705, _1606707), 42718 ^ [_1606701, _1606703, _1606705, _1606707, _1606709, _1606711]), 42719 ^ [_1606701, _1606703, _1606705, _1606707, _1606709, _1606711]))]]], (18319 ^ _778908) ^ [_1095449] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1095449), hAPP(c_Int_Onumber__class_Onumber__of(_1095449), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1095449)), class_Int_Onumber__ring(_1095449), class_Rings_Olinordered__idom(_1095449)], (41623 ^ _778908) ^ [_1577100, _1577102, _1577104] : [class_Orderings_Olinorder(_1577100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577100), _1577102)), -(_1577102 = c_Orderings_Obot__class_Obot(tc_fun(_1577100, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1577100), _1577104), c_Big__Operators_Olattice_OInf__fin(_1577100, c_Orderings_Oord__class_Omin(_1577100), _1577102)) = c_Big__Operators_Olattice_OInf__fin(_1577100, c_Orderings_Oord__class_Omin(_1577100), hAPP(c_Set_OCollect(_1577100), hAPP(hAPP(c_COMBB(tc_fun(_1577100, tc_HOL_Obool), tc_HOL_Obool, _1577100), c_HOL_OEx(_1577100)), hAPP(hAPP(c_COMBC(_1577100, tc_fun(_1577100, tc_HOL_Obool), tc_fun(_1577100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577100, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1577100, tc_HOL_Obool), tc_fun(_1577100, tc_HOL_Obool)), _1577100), c_COMBS(_1577100, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577100, tc_HOL_Obool), tc_fun(_1577100, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1577100), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577100), c_fconj)), hAPP(hAPP(c_COMBC(_1577100, tc_fun(_1577100, _1577100), tc_fun(_1577100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577100, tc_HOL_Obool), tc_fun(tc_fun(_1577100, _1577100), tc_fun(_1577100, tc_HOL_Obool)), _1577100), c_COMBB(_1577100, tc_HOL_Obool, _1577100)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1577100), _1577104))))), hAPP(hAPP(c_COMBC(_1577100, tc_fun(_1577100, tc_HOL_Obool), tc_HOL_Obool), c_member(_1577100)), _1577102))))))], (30896 ^ _778908) ^ [_1333214, _1333216, _1333218, _1333220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333214, tc_HOL_Obool)), _1333216), _1333218)), hBOOL(hAPP(hAPP(c_member(_1333214), _1333220), _1333216)), -(hBOOL(hAPP(hAPP(c_member(_1333214), _1333220), _1333218)))], (37812 ^ _778908) ^ [_1484949, _1484951, _1484953, _1484955, _1484957, _1484959, _1484961] : [c_Equiv__Relations_Oequiv(_1484949, _1484951, _1484953), c_Equiv__Relations_Ocongruent(_1484949, tc_fun(_1484955, tc_HOL_Obool), _1484953, _1484957), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484949, tc_fun(_1484955, tc_HOL_Obool)), _1484959), _1484957) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484949, tc_fun(_1484955, tc_HOL_Obool)), _1484961), _1484957), hBOOL(hAPP(hAPP(c_member(tc_fun(_1484949, tc_HOL_Obool)), _1484959), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1484949), _1484951), _1484953))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1484949, tc_HOL_Obool)), _1484961), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1484949), _1484951), _1484953))), 37834 ^ _778908 : [(37838 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484949), 37836 ^ [_1484949, _1484951, _1484953, _1484955, _1484957, _1484959, _1484961]), _1484951)))], (37840 ^ _778908) ^ [] : [-(hAPP(_1484957, 37833 ^ [_1484949, _1484951, _1484953, _1484955, _1484957, _1484959, _1484961]) = hAPP(_1484957, 37836 ^ [_1484949, _1484951, _1484953, _1484955, _1484957, _1484959, _1484961]))], (37842 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484949, _1484949)), hAPP(hAPP(c_Product__Type_OPair(_1484949, _1484949), 37833 ^ [_1484949, _1484951, _1484953, _1484955, _1484957, _1484959, _1484961]), 37836 ^ [_1484949, _1484951, _1484953, _1484955, _1484957, _1484959, _1484961])), _1484953))], (37835 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484949), 37833 ^ [_1484949, _1484951, _1484953, _1484955, _1484957, _1484959, _1484961]), _1484951)))]], -(_1484959 = _1484961)], (41000 ^ _778908) ^ [_1557689] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1557689), c_Int_OInteg)), -(_1557689 = hAPP(c_Int_ORep__Integ, 41003 ^ [_1557689]))], (4658 ^ _778908) ^ [_851027, _851029, _851031, _851033, _851035, _851037, _851039, _851041] : [-(c_Nat_Onat_Onat__case(_851041, _851037, _851033, _851029) = c_Nat_Onat_Onat__case(_851039, _851035, _851031, _851027)), _851041 = _851039, _851037 = _851035, _851033 = _851031, _851029 = _851027], (38029 ^ _778908) ^ [_1491336, _1491338, _1491340, _1491342, _1491344] : [class_Groups_Ocomm__monoid__add(_1491336), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491338), _1491340)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491338), _1491342)), 38043 ^ _778908 : [(38046 ^ _778908) ^ [] : [hAPP(_1491344, 38042 ^ [_1491336, _1491338, _1491340, _1491342, _1491344]) = c_Groups_Ozero__class_Ozero(_1491336)], (38044 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491338), 38042 ^ [_1491336, _1491338, _1491340, _1491342, _1491344]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491338, tc_HOL_Obool)), _1491340), _1491342))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491338, _1491336), _1491344), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491338, tc_HOL_Obool)), _1491340), _1491342)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1491336), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491338, _1491336), _1491344), _1491340)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491338, _1491336), _1491344), _1491342)))], (5955 ^ _778908) ^ [_873987, _873989, _873991] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _873987, _873989, _873991), -(_873991 = _873987)], (48616 ^ _778908) ^ [_1750442, _1750444, _1750446, _1750448, _1750450, _1750452] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750442)), _1750444) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750446)), _1750448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1750442, tc_HOL_Obool)), hAPP(c_List_Oset(_1750442), _1750444)), _1750450)), -(c_Map_Orestrict__map(_1750442, _1750446, c_Map_Omap__upds(_1750442, _1750446, _1750452, _1750444, _1750448), _1750450) = c_Map_Omap__upds(_1750442, _1750446, c_Map_Orestrict__map(_1750442, _1750446, _1750452, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1750442, tc_HOL_Obool)), _1750450), hAPP(c_List_Oset(_1750442), _1750444))), _1750444, _1750448))], (10268 ^ _778908) ^ [_951497, _951499] : [class_Rings_Osemiring__1(_951497), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_951497), hAPP(c_Nat_OSuc, _951499)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951497), c_Groups_Oone__class_Oone(_951497)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_951497), _951499)))], (6855 ^ _778908) ^ [_891596, _891598, _891600, _891602, _891604] : [c_Com_Ocom_OCond(_891596, _891598, _891600) = c_Com_Ocom_OWhile(_891602, _891604)], (51263 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (30814 ^ _778908) ^ [_1331474] : [-(hAPP(c_Int_Onat, _1331474) = 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, _1331474)), 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)))))))], (8376 ^ _778908) ^ [_919263, _919265] : [class_Rings_Olinordered__semidom(_919263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919263), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919263), _919265)), c_Groups_Ozero__class_Ozero(_919263)))], (48411 ^ _778908) ^ [_1745241, _1745243, _1745245, _1745247] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1745241), tc_List_Olist(_1745241))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1745241), tc_List_Olist(_1745241)), _1745243), _1745245)), c_List_Olex(_1745241, _1745247)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1745241), tc_List_Olist(_1745241))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1745241), tc_List_Olist(_1745241)), _1745243), _1745245)), c_List_Olexord(_1745241, _1745247))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745241)), _1745243) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745241)), _1745245)], (6530 ^ _778908) ^ [_884769, _884771, _884773, _884775, _884777] : [c_Com_Ocom_OSemi(_884769, _884771) = c_Com_Ocom_OCall(_884773, _884775, _884777)], (51699 ^ _778908) ^ [_1814147, _1814149] : [hBOOL(hAPP(hAPP(c_fdisj, _1814147), _1814149)), -(hBOOL(_1814147)), -(hBOOL(_1814149))], (48504 ^ _778908) ^ [_1747808, _1747810, _1747812] : [-(c_List_Osublist(_1747808, _1747810, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1747812)) = hAPP(hAPP(c_List_Otake(_1747808), _1747812), _1747810))], (19235 ^ _778908) ^ [_1109969, _1109971] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1109969, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1109971)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1109969, 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)))), _1109971)))], (49175 ^ _778908) ^ [_1765087, _1765089, _1765091] : [-(_1765087 = c_List_Olist_ONil(_1765089)), -(hAPP(c_List_Otl(_1765089), hAPP(hAPP(c_List_Oappend(_1765089), _1765087), _1765091)) = hAPP(hAPP(c_List_Oappend(_1765089), hAPP(c_List_Otl(_1765089), _1765087)), _1765091))], (10062 ^ _778908) ^ [_948009, _948011] : [class_Rings_Olinordered__semidom(_948009), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948009), _948011), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948009), _948011), c_Groups_Oone__class_Oone(_948009)))))], (13402 ^ _778908) ^ [_1004735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004735)), -(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)), _1004735))))], (44777 ^ _778908) ^ [_1655736, _1655738, _1655740, _1655742, _1655744] : [44779 ^ _778908 : [(44782 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1655736), _1655738), hAPP(_1655744, 44778 ^ [_1655736, _1655738, _1655740, _1655742, _1655744])))], (44780 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655740), 44778 ^ [_1655736, _1655738, _1655740, _1655742, _1655744]), _1655742)))]], -(hBOOL(hAPP(hAPP(c_member(_1655736), _1655738), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655740, tc_fun(_1655736, tc_HOL_Obool)), _1655742), _1655744))))], (9982 ^ _778908) ^ [_946567, _946569, _946571, _946573] : [class_Rings_Olinordered__ring__strict(_946567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946567), _946569), _946571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946567), _946573), c_Groups_Ozero__class_Ozero(_946567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946567), _946571), _946573)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946567), _946569), _946573))))], (34778 ^ _778908) ^ [_1415907, _1415909, _1415911, _1415913, _1415915, _1415917, _1415919] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1415907, tc_Option_Ooption(_1415909)), _1415911), _1415913), hAPP(c_Option_Ooption_OSome(_1415909), _1415915)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1415907, tc_Option_Ooption(_1415909)), _1415917), _1415913), hAPP(c_Option_Ooption_OSome(_1415909), _1415919)), -(_1415915 = _1415919)], (18379 ^ _778908) ^ [_1096273] : [-(c_Int_Osucc(_1096273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1096273), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24777 ^ _778908) ^ [_1212894, _1212896, _1212898, _1212900] : [class_Orderings_Olinorder(_1212894), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212894), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212894), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212894), _1212896), _1212898)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212894), _1212896), _1212900))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212894), _1212896), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212894), _1212898), _1212900)))))], (49253 ^ _778908) ^ [_1766678, _1766680] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766678)), hAPP(c_List_Otl(_1766678), _1766680)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766678)), _1766680)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (33399 ^ _778908) ^ [_1388514, _1388516] : [-(hBOOL(hAPP(hAPP(c_member(_1388514), _1388516), c_Orderings_Otop__class_Otop(tc_fun(_1388514, tc_HOL_Obool)))))], (15544 ^ _778908) ^ [_1043497, _1043499, _1043501, _1043503] : [class_Divides_Oring__div(_1043497), -(c_Divides_Odiv__class_Omod(_1043497, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043497), _1043499), _1043501), _1043503) = c_Divides_Odiv__class_Omod(_1043497, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043497), _1043499), c_Divides_Odiv__class_Omod(_1043497, _1043501, _1043503)), _1043503))], (6246 ^ _778908) ^ [_879507, _879509, _879511, _879513, _879515, _879517] : [c_Com_Ocom_OCond(_879507, _879509, _879511) = c_Com_Ocom_OLocal(_879513, _879515, _879517)], (48695 ^ _778908) ^ [_1752669, _1752671] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1752669), tc_List_Olist(_1752669)), tc_HOL_Obool)), c_List_Olistrel1(_1752669, c_Transitive__Closure_Ortrancl(_1752669, _1752671))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1752669), c_List_Olistrel1(_1752669, _1752671)))))], (5991 ^ _778908) ^ [_874607, _874609, _874611, _874613] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_874607, _874609), _874611, _874613, hAPP(hAPP(hAPP(c_Natural_Oupdate, _874611), _874607), hAPP(_874609, _874611))))], (30970 ^ _778908) ^ [_1334566, _1334568, _1334570, _1334572, _1334574, _1334576] : [hBOOL(hAPP(hAPP(c_member(_1334566), _1334568), _1334570)), hBOOL(hAPP(hAPP(c_member(_1334572), _1334574), hAPP(_1334576, _1334568))), -(hBOOL(hAPP(hAPP(c_member(_1334572), _1334574), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1334566, tc_fun(_1334572, tc_HOL_Obool)), _1334570), _1334576))))], (14585 ^ _778908) ^ [_1026542, _1026544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026542), _1026544)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026542), _1026544) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51255 ^ _778908) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (1792 ^ _778908) ^ [_804182, _804184] : [-(class_Groups_Ozero(_804182)), _804184 = _804182, class_Groups_Ozero(_804184)], (20 ^ _778908) ^ [_779168, _779170, _779172, _779174] : [-(c_Groups_Osemigroup(_779172, _779168)), c_Groups_Osemigroup(_779174, _779170), _779174 = _779172, _779170 = _779168], (51405 ^ _778908) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (38456 ^ _778908) ^ [_1499906, _1499908, _1499910] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1499906), _1499908)), c_Fun_Oinj__on(_1499906, tc_fun(tc_fun(_1499906, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1499906, tc_fun(tc_prod(_1499906, _1499906), tc_HOL_Obool), tc_fun(tc_fun(_1499906, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499906, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1499906, _1499906), tc_HOL_Obool), tc_fun(tc_fun(_1499906, tc_HOL_Obool), tc_HOL_Obool)), _1499906), c_Equiv__Relations_Oquotient(_1499906)), hAPP(hAPP(c_COMBC(_1499906, tc_fun(_1499906, tc_HOL_Obool), tc_fun(_1499906, tc_HOL_Obool)), c_Set_Oinsert(_1499906)), c_Orderings_Obot__class_Obot(tc_fun(_1499906, tc_HOL_Obool))))), _1499910), _1499908), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1499906, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1499906), _1499908), _1499910)) = hAPP(c_Finite__Set_Ocard(_1499906), _1499908))], (4154 ^ _778908) ^ [_842893, _842895, _842897, _842899, _842901, _842903] : [-(c_Set_Ovimage(_842903, _842899, _842895) = c_Set_Ovimage(_842901, _842897, _842893)), _842903 = _842901, _842899 = _842897, _842895 = _842893], (45406 ^ _778908) ^ [_1671818, _1671820, _1671822] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1671818, tc_HOL_Obool)), _1671820), _1671822) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671818, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1671818, tc_HOL_Obool)), _1671820), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1671818, tc_HOL_Obool)), _1671822), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1671818, tc_HOL_Obool), tc_HOL_Obool))))))], (29946 ^ _778908) ^ [_1314998, _1315000, _1315002, _1315004, _1315006] : [hAPP(hAPP(c_Set_Oinsert(_1314998), _1315000), hAPP(hAPP(c_Set_Oinsert(_1314998), _1315002), c_Orderings_Obot__class_Obot(tc_fun(_1314998, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1314998), _1315004), hAPP(hAPP(c_Set_Oinsert(_1314998), _1315006), c_Orderings_Obot__class_Obot(tc_fun(_1314998, tc_HOL_Obool)))), 29951 ^ _778908 : [(29954 ^ _778908) ^ [] : [-(_1315002 = _1315006)], (29952 ^ _778908) ^ [] : [-(_1315000 = _1315004)]], 29955 ^ _778908 : [(29958 ^ _778908) ^ [] : [-(_1315002 = _1315004)], (29956 ^ _778908) ^ [] : [-(_1315000 = _1315006)]]], (49950 ^ _778908) ^ [_1781760, _1781762, _1781764, _1781766] : [-(hAPP(c_List_Ofilter(_1781760, _1781762), c_List_Oremove1(_1781760, _1781764, _1781766)) = c_List_Oremove1(_1781760, _1781764, hAPP(c_List_Ofilter(_1781760, _1781762), _1781766)))], (24279 ^ _778908) ^ [_1203231] : [class_Orderings_Oord(_1203231), -(c_Orderings_Oord__class_Omin(_1203231) = c_Orderings_Oord_Omin(_1203231, c_Orderings_Oord__class_Oless__eq(_1203231)))], (40070 ^ _778908) ^ [_1535928, _1535930, _1535932, _1535934, _1535936] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535928, _1535930), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1535928, tc_HOL_Obool)), _1535932), _1535934)), hAPP(c_COMBK(tc_fun(_1535930, tc_HOL_Obool), _1535928), _1535936)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535928, _1535930), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535928, _1535930), _1535932), hAPP(c_COMBK(tc_fun(_1535930, tc_HOL_Obool), _1535928), _1535936))), hAPP(hAPP(c_Product__Type_OSigma(_1535928, _1535930), _1535934), hAPP(c_COMBK(tc_fun(_1535930, tc_HOL_Obool), _1535928), _1535936))))], (20201 ^ _778908) ^ [_1127458, _1127460] : [class_Rings_Odivision__ring(_1127458), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127458), c_Groups_Ozero__class_Ozero(_1127458)), _1127460) = c_Groups_Ozero__class_Ozero(_1127458))], (50720 ^ _778908) ^ [_1797515, _1797517, _1797519] : [50721 ^ _778908 : [(50724 ^ _778908) ^ [] : [_1797519 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50722 ^ _778908) ^ [] : [-(_1797515 = c_List_Olist_ONil(tc_List_Olist(_1797517)))]], 50728 ^ _778908 : [(50731 ^ _778908) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797517)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1797517)), _1797515), 50727 ^ [_1797515, _1797517, _1797519])) = _1797519], (50729 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50727 ^ [_1797515, _1797517, _1797519]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1797517))), _1797515))))]], -(c_List_Otranspose(_1797517, _1797515) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1797517)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1797517)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1797517), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1797517)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1797517)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1797517), hAPP(hAPP(c_COMBB(tc_List_Olist(_1797517), tc_fun(tc_Nat_Onat, _1797517), tc_Nat_Onat), c_List_Onth(_1797517)), hAPP(c_List_Onth(tc_List_Olist(_1797517)), _1797515))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1797517))), _1797515)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1797519)))], (44418 ^ _778908) ^ [_1647148, _1647150, _1647152, _1647154, _1647156, _1647158] : [c_Finite__Set_Ofun__left__comm(_1647148, _1647150, _1647152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1647148), _1647154)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1647148, _1647150, _1647152), _1647156), hAPP(hAPP(c_Set_Oinsert(_1647148), _1647158), _1647154)) = hAPP(hAPP(_1647152, _1647158), hAPP(hAPP(c_Finite__Set_Ofold(_1647148, _1647150, _1647152), _1647156), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1647148, tc_HOL_Obool)), _1647154), hAPP(hAPP(c_Set_Oinsert(_1647148), _1647158), c_Orderings_Obot__class_Obot(tc_fun(_1647148, tc_HOL_Obool)))))))], (47106 ^ _778908) ^ [_1713866, _1713868, _1713870, _1713872, _1713874, _1713876] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713866, _1713866)), hAPP(hAPP(c_Product__Type_OPair(_1713866, _1713866), _1713868), _1713870)), _1713872)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713866), tc_List_Olist(_1713866))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713866), tc_List_Olist(_1713866)), _1713874), _1713876)), c_List_Olistrel(_1713866, _1713872))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713866), tc_List_Olist(_1713866))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713866), tc_List_Olist(_1713866)), hAPP(hAPP(c_List_Olist_OCons(_1713866), _1713868), _1713874)), hAPP(hAPP(c_List_Olist_OCons(_1713866), _1713870), _1713876))), c_List_Olistrel(_1713866, _1713872))))], (19753 ^ _778908) ^ [_1119163] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119163), _1119163))], (29307 ^ _778908) ^ [_1302754, _1302756, _1302758, _1302760, _1302762] : [-(hAPP(c_Set_Oimage(_1302754, _1302756, _1302758), hAPP(hAPP(c_Set_Oinsert(_1302754), _1302760), _1302762)) = hAPP(hAPP(c_Set_Oinsert(_1302756), hAPP(_1302758, _1302760)), hAPP(c_Set_Oimage(_1302754, _1302756, _1302758), _1302762)))], (15036 ^ _778908) ^ [_1033864, _1033866] : [-(_1033864 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033866), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033864), _1033866))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1033864, _1033866)))], (39648 ^ _778908) ^ [_1525345, _1525347, _1525349, _1525351, _1525353, _1525355] : [hBOOL(hAPP(hAPP(c_member(_1525345), _1525347), _1525349)), 39651 ^ _778908 : [(39658 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525345), _1525351), _1525349))), -(hAPP(c_Set_Ovimage(_1525353, _1525345, hAPP(hAPP(c_COMBC(_1525353, _1525345, _1525345), hAPP(hAPP(c_COMBC(_1525353, _1525345, tc_fun(_1525345, _1525345)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525345, tc_fun(_1525345, _1525345)), _1525353), c_If(_1525345)), hAPP(hAPP(c_COMBC(_1525353, tc_fun(_1525353, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525353)), _1525355))), _1525347)), _1525351)), _1525349) = _1525355)], (39652 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1525345), _1525351), _1525349)), -(hAPP(c_Set_Ovimage(_1525353, _1525345, hAPP(hAPP(c_COMBC(_1525353, _1525345, _1525345), hAPP(hAPP(c_COMBC(_1525353, _1525345, tc_fun(_1525345, _1525345)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525345, tc_fun(_1525345, _1525345)), _1525353), c_If(_1525345)), hAPP(hAPP(c_COMBC(_1525353, tc_fun(_1525353, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525353)), _1525355))), _1525347)), _1525351)), _1525349) = c_Orderings_Otop__class_Otop(tc_fun(_1525353, tc_HOL_Obool)))]]], (6524 ^ _778908) ^ [_884609, _884611, _884613] : [c_Com_Ocom_OSemi(_884609, _884611) = hAPP(c_Com_Ocom_OBODY, _884613)], (44929 ^ _778908) ^ [_1660968, _1660970, _1660972, _1660974, _1660976] : [-(_1660968 = c_Orderings_Obot__class_Obot(tc_fun(_1660970, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660970, tc_fun(_1660972, tc_HOL_Obool)), _1660968), hAPP(hAPP(c_COMBB(tc_fun(_1660972, tc_HOL_Obool), tc_fun(_1660972, tc_HOL_Obool), _1660970), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660972, tc_HOL_Obool)), _1660974)), _1660976)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660972, tc_HOL_Obool)), _1660974), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660970, tc_fun(_1660972, tc_HOL_Obool)), _1660968), _1660976)))], (6385 ^ _778908) ^ [_881914, _881916, _881918, _881920, _881922, _881924] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_881914, _881916, _881918), _881920, _881922, _881924), 6390 ^ _778908 : [(6393 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_881916, _881920, _881922, _881924))], (6391 ^ _778908) ^ [] : [-(hBOOL(hAPP(_881914, _881920)))]], 6394 ^ _778908 : [(6397 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_881918, _881920, _881922, _881924))], (6395 ^ _778908) ^ [] : [hBOOL(hAPP(_881914, _881920))]]], (30866 ^ _778908) ^ [_1332637, _1332639, _1332641, _1332643, _1332645, _1332647, _1332649, _1332651] : [hBOOL(hAPP(hAPP(c_member(_1332637), _1332639), _1332641)), hBOOL(hAPP(hAPP(hAPP(_1332643, _1332639), _1332645), _1332647)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1332637, tc_fun(_1332649, tc_fun(_1332651, tc_HOL_Obool))), _1332641), _1332643), _1332645), _1332647)))], (872 ^ _778908) ^ [_792332, _792334] : [-(c_Nat__Transfer_Onat__set(_792332)), _792334 = _792332, c_Nat__Transfer_Onat__set(_792334)], (22041 ^ _778908) ^ [_1160451, _1160453, _1160455, _1160457] : [class_Fields_Olinordered__field__inverse__zero(_1160451), class_Int_Onumber(_1160451), 22048 ^ _778908 : [(22049 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160451), _1160453), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455))), _1160457)), 22052 ^ _778908 : [(22059 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), c_Groups_Ozero__class_Ozero(_1160451)), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455)))), 22062 ^ _778908 : [(22069 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455)), c_Groups_Ozero__class_Ozero(_1160451)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), c_Groups_Ozero__class_Ozero(_1160451)), _1160457)))], (22063 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455)), c_Groups_Ozero__class_Ozero(_1160451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160451), _1160457), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455))), _1160453)))]]], (22053 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), c_Groups_Ozero__class_Ozero(_1160451)), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), _1160453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160451), _1160457), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455)))))]]], (22075 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160451), _1160453), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455))), _1160457))), 22078 ^ _778908 : [(22081 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), _1160453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160451), _1160457), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455))))], (22079 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), c_Groups_Ozero__class_Ozero(_1160451)), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455))))]], 22082 ^ _778908 : [(22085 ^ _778908) ^ [] : [22086 ^ _778908 : [(22089 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160451), _1160457), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455))), _1160453))], (22087 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455)), c_Groups_Ozero__class_Ozero(_1160451))))]], 22090 ^ _778908 : [(22093 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160451), c_Groups_Ozero__class_Ozero(_1160451)), _1160457))], (22091 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455)), c_Groups_Ozero__class_Ozero(_1160451)))]]], (22083 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160451), c_Groups_Ozero__class_Ozero(_1160451)), hAPP(c_Int_Onumber__class_Onumber__of(_1160451), _1160455)))]]]]], (25031 ^ _778908) ^ [_1218095, _1218097, _1218099] : [c_Nitpick_Oless__eq__frac(_1218095, _1218097, _1218099), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1218095), c_Nitpick_Oplus__frac(_1218095, _1218097, c_Nitpick_Ouminus__frac(_1218095, _1218099)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45947 ^ _778908) ^ [_1683899, _1683901, _1683903, _1683905] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1683899)), hAPP(c_Set_Oimage(_1683901, tc_Option_Ooption(_1683899), _1683903), c_Orderings_Otop__class_Otop(tc_fun(_1683901, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1683899)), hAPP(c_Set_Oimage(_1683901, tc_Option_Ooption(_1683899), c_Map_Omap__add(_1683901, _1683899, _1683903, c_Map_Omap__of(_1683901, _1683899, _1683905))), c_Orderings_Otop__class_Otop(tc_fun(_1683901, tc_HOL_Obool))))))], (43047 ^ _778908) ^ [_1614024, _1614026] : [-(hAPP(c_Relation_ODomain(_1614024, _1614024), c_Transitive__Closure_Otrancl(_1614024, _1614026)) = hAPP(c_Relation_ODomain(_1614024, _1614024), _1614026))], (16577 ^ _778908) ^ [_1063785, _1063787] : [-(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), _1063785)), _1063787))))], (16282 ^ _778908) ^ [_1058575, _1058577, _1058579, _1058581, _1058583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058575), _1058577)), 16285 ^ _778908 : [(16292 ^ _778908) ^ [] : [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), _1058577), _1058575)), _1058579)), _1058581)), _1058583)), -(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), _1058577), _1058579)), _1058581)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058575), _1058579)), _1058583))))], (16286 ^ _778908) ^ [] : [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), _1058577), _1058579)), _1058581)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058575), _1058579)), _1058583))), -(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), _1058577), _1058575)), _1058579)), _1058581)), _1058583)))]]], (10808 ^ _778908) ^ [_960247, _960249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960247)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960247), _960249)))], (30296 ^ _778908) ^ [_1321701, _1321703, _1321705] : [-(hAPP(hAPP(c_Set_Oinsert(_1321701), _1321703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321701, tc_HOL_Obool)), _1321705), hAPP(hAPP(c_Set_Oinsert(_1321701), _1321703), c_Orderings_Obot__class_Obot(tc_fun(_1321701, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1321701), _1321703), _1321705))], (23331 ^ _778908) ^ [_1185242, _1185244, _1185246, _1185248, _1185250] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1185242, _1185244), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1185246), _1185248))), -(_1185244 = 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)), _1185250)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1185242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1185244), _1185250)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1185246), _1185250)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1185244), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1185246, _1185250))), _1185248)))))], (6821 ^ _778908) ^ [_890937, _890939, _890941] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_890937, _890939)), _890941), _890941))), 6822 ^ _778908 : [(6825 ^ _778908) ^ [_891037] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890939), _890941), _891037)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_890937, _890939)), _891037), _890941))], (6823 ^ _778908) ^ [] : [-(hBOOL(hAPP(_890937, _890941)))]]], (44753 ^ _778908) ^ [_1655027, _1655029, _1655031, _1655033] : [-(hAPP(c_Set_OPow(_1655027), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655029, tc_fun(_1655027, tc_HOL_Obool)), _1655031), _1655033)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655029, tc_fun(tc_fun(_1655027, tc_HOL_Obool), tc_HOL_Obool)), _1655031), hAPP(hAPP(c_COMBB(tc_fun(_1655027, tc_HOL_Obool), tc_fun(tc_fun(_1655027, tc_HOL_Obool), tc_HOL_Obool), _1655029), c_Set_OPow(_1655027)), _1655033)))], (42737 ^ _778908) ^ [_1607211, _1607213] : [42738 ^ _778908 : [(42739 ^ _778908) ^ [_1607257] : [hBOOL(hAPP(_1607211, _1607257))]], -(hBOOL(hAPP(_1607211, c_Hilbert__Choice_OEps(_1607213, _1607211))))], (50787 ^ _778908) ^ [_1799504, _1799506, _1799508] : [_1799508 = hAPP(hAPP(c_List_Olist_OCons(_1799504), _1799506), c_List_Olist_ONil(_1799504)), -(hAPP(hAPP(c_List_Olist_OCons(_1799504), _1799506), c_List_Olist_ONil(_1799504)) = hAPP(c_List_Orev(_1799504), _1799508))], (36075 ^ _778908) ^ [_1446894, _1446896, _1446898, _1446900] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1446894, tc_HOL_Obool)), _1446896), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446894), _1446898), _1446900))), 36079 ^ _778908 : [(36082 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446894), 36078 ^ [_1446894, _1446896, _1446898, _1446900]), _1446898)))], (36080 ^ _778908) ^ [] : [-(_1446896 = hAPP(c_Relation_OImage(_1446894, _1446894, _1446900), hAPP(hAPP(c_Set_Oinsert(_1446894), 36078 ^ [_1446894, _1446896, _1446898, _1446900]), c_Orderings_Obot__class_Obot(tc_fun(_1446894, tc_HOL_Obool)))))]]], (37636 ^ _778908) ^ [_1481238, _1481240, _1481242] : [class_Orderings_Olinorder(_1481238), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481238), _1481240)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481238), _1481242)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481238, tc_HOL_Obool)), _1481240), _1481242) = c_Orderings_Obot__class_Obot(tc_fun(_1481238, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1481238), c_Big__Operators_Olinorder__class_OMax(_1481238, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481238, tc_HOL_Obool)), _1481240), _1481242))), c_Big__Operators_Olinorder__class_OMax(_1481238, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481238, tc_HOL_Obool)), _1481240), _1481242))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1481238), c_Big__Operators_Olinorder__class_OMax(_1481238, _1481240)), c_Big__Operators_Olinorder__class_OMax(_1481238, _1481242)))], (45121 ^ _778908) ^ [_1665391, _1665393, _1665395] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665391, tc_HOL_Obool)), _1665393), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1665391, tc_HOL_Obool), _1665395)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1665391, tc_HOL_Obool), tc_fun(_1665391, tc_HOL_Obool)), _1665395), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665391, tc_HOL_Obool)), _1665393)))], (49587 ^ _778908) ^ [_1774465, _1774467, _1774469, _1774471, _1774473] : [class_Groups_Omonoid__add(_1774465), class_Groups_Oordered__ab__semigroup__add(_1774465), 49597 ^ _778908 : [(49600 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1774465), hAPP(_1774471, 49596 ^ [_1774465, _1774467, _1774469, _1774471, _1774473])), hAPP(_1774473, 49596 ^ [_1774465, _1774467, _1774469, _1774471, _1774473])))], (49598 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774467), 49596 ^ [_1774465, _1774467, _1774469, _1774471, _1774473]), hAPP(c_List_Oset(_1774467), _1774469))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1774465), hAPP(c_List_Omonoid__add__class_Olistsum(_1774465), hAPP(hAPP(c_List_Omap(_1774467, _1774465), _1774471), _1774469))), hAPP(c_List_Omonoid__add__class_Olistsum(_1774465), hAPP(hAPP(c_List_Omap(_1774467, _1774465), _1774473), _1774469)))))], (23353 ^ _778908) ^ [_1185798, _1185800, _1185802] : [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), _1185798), _1185800))), -(hBOOL(hAPP(hAPP(_1185802, _1185798), _1185800))), 23360 ^ _778908 : [(23363 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23359 ^ [_1185798, _1185800, _1185802]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1185802, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23358 ^ [_1185798, _1185800, _1185802])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23359 ^ [_1185798, _1185800, _1185802]))))], (23369 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1185802, 23358 ^ [_1185798, _1185800, _1185802]), 23359 ^ [_1185798, _1185800, _1185802]))], (23361 ^ _778908) ^ [] : [-(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), 23358 ^ [_1185798, _1185800, _1185802]), 23359 ^ [_1185798, _1185800, _1185802]))))]]], (5514 ^ _778908) ^ [_864129, _864131] : [_864131 = _864129, -(c_List_Otranspose__rel(_864131) = c_List_Otranspose__rel(_864129))], (28661 ^ _778908) ^ [_1288388, _1288390, _1288392] : [class_Orderings_Olinorder(_1288388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288388), _1288390), _1288392)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288388, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288388, _1288390, _1288392)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1288388), _1288392)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1288388), _1288390))], (28617 ^ _778908) ^ [_1287494, _1287496, _1287498, _1287500] : [class_Orderings_Olinorder(_1287494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287494), _1287496), _1287498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287494), _1287498), _1287500)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287494, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1287494, _1287496), _1287498)), c_SetInterval_Oord__class_OatLeastAtMost(_1287494, _1287498, _1287500)) = c_SetInterval_Oord__class_OatLeastAtMost(_1287494, _1287496, _1287500))], (14932 ^ _778908) ^ [_1032072, _1032074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032072)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032072), _1032074)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1032072), _1032074) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (49551 ^ _778908) ^ [_1773595, _1773597, _1773599, _1773601] : [49552 ^ _778908 : [(49553 ^ _778908) ^ [_1773692, _1773694] : [_1773595 = hAPP(hAPP(c_List_Olist_OCons(_1773597), _1773694), _1773692)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773597), tc_List_Olist(_1773597))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773597), tc_List_Olist(_1773597)), _1773599), hAPP(hAPP(c_List_Oappend(_1773597), _1773599), _1773595))), c_List_Olexord(_1773597, _1773601))))], (50761 ^ _778908) ^ [_1798814, _1798816, _1798818] : [-(hAPP(c_List_Ofilter(_1798814, _1798816), c_List_Oconcat(_1798814, _1798818)) = c_List_Oconcat(_1798814, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798814), tc_List_Olist(_1798814)), c_List_Ofilter(_1798814, _1798816)), _1798818)))], (51567 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (10691 ^ _778908) ^ [_958303, _958305, _958307] : [class_Orderings_Oorder(_958303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958303), _958305), _958307)), 10698 ^ _778908 : [(10705 ^ _778908) ^ [] : [_958307 = _958305, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958303), _958307), _958305)))], (10699 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958303), _958307), _958305)), -(_958307 = _958305)]]], (49789 ^ _778908) ^ [_1778473, _1778475, _1778477] : [_1778473 = c_List_Olist_ONil(_1778475), -(c_List_Obutlast(_1778475, hAPP(hAPP(c_List_Olist_OCons(_1778475), _1778477), _1778473)) = c_List_Olist_ONil(_1778475))], (51495 ^ _778908) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (49297 ^ _778908) ^ [_1767599, _1767601, _1767603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1767599), _1767601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1767599), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1767601), _1767603))))], (24957 ^ _778908) ^ [_1216374, _1216376, _1216378, _1216380, _1216382] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1216374, _1216376, _1216374, _1216378), hAPP(c_Product__Type_OPair(_1216376, _1216374), _1216380)), _1216382) = hAPP(_1216382, _1216380))], (27061 ^ _778908) ^ [_1256580, _1256582, _1256584, _1256586, _1256588] : [class_Groups_Ocomm__monoid__add(_1256580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1256582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1256584), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256580), _1256586), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1256582, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1256584), _1256588))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256580), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256580), _1256586), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1256582, _1256584))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256580), _1256586), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1256584), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1256584), _1256588)))))], (40272 ^ _778908) ^ [_1541389, _1541391, _1541393, _1541395, _1541397, _1541399] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1541389, _1541391), hAPP(hAPP(c_Set_Oinsert(_1541389), _1541393), _1541395)), hAPP(c_COMBK(tc_fun(_1541391, tc_HOL_Obool), _1541389), hAPP(hAPP(c_Set_Oinsert(_1541391), _1541397), _1541399))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1541389, _1541391)), hAPP(hAPP(c_Product__Type_OPair(_1541389, _1541391), _1541393), _1541397)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541389, _1541391), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1541389, _1541391), _1541395), hAPP(c_COMBK(tc_fun(_1541391, tc_HOL_Obool), _1541389), hAPP(hAPP(c_Set_Oinsert(_1541391), _1541397), _1541399)))), hAPP(hAPP(c_Product__Type_OSigma(_1541389, _1541391), hAPP(hAPP(c_Set_Oinsert(_1541389), _1541393), _1541395)), hAPP(c_COMBK(tc_fun(_1541391, tc_HOL_Obool), _1541389), _1541399)))))], (49211 ^ _778908) ^ [_1765784, _1765786, _1765788, _1765790] : [-(hAPP(c_List_Orotate(_1765784, _1765786), hAPP(c_List_Orotate(_1765784, _1765788), _1765790)) = hAPP(c_List_Orotate(_1765784, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1765786), _1765788)), _1765790))], (35752 ^ _778908) ^ [_1438422, _1438424, _1438426, _1438428, _1438430] : [-(hAPP(c_Relation_OImage(_1438422, _1438424, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1438422, _1438424), tc_HOL_Obool)), _1438426), _1438428)), _1438430) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1438424, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1438422, _1438424, _1438426), _1438430)), hAPP(c_Relation_OImage(_1438422, _1438424, _1438428), _1438430)))], (29938 ^ _778908) ^ [_1314792, _1314794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314792, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1314792, tc_HOL_Obool))), _1314794)))], (32801 ^ _778908) ^ [_1376278, _1376280] : [32802 ^ _778908 : [(32805 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376280), _1376278))], (32803 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376278), _1376280)))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1376278, _1376280) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (20839 ^ _778908) ^ [_1138409, _1138411] : [c_Nat__Transfer_Ois__nat(_1138409), c_Nat__Transfer_Ois__nat(_1138411), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1138409, _1138411)))], (24395 ^ _778908) ^ [_1205469, _1205471, _1205473] : [class_Orderings_Olinorder(_1205469), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205469), _1205471), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205469), _1205471), _1205473)) = _1205471)], (19371 ^ _778908) ^ [_1112491, _1112493] : [c_Int_OBit0(_1112491) = c_Int_OBit1(_1112493)], (34740 ^ _778908) ^ [_1415000, _1415002, _1415004, _1415006, _1415008] : [class_Fields_Ofield(_1415000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415002), _1415004)), -(hAPP(_1415006, _1415008) = c_Groups_Ozero__class_Ozero(_1415000)), 34751 ^ _778908 : [(34758 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415002), _1415008), _1415004))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415002, _1415000), _1415006), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1415002, tc_HOL_Obool)), _1415004), hAPP(hAPP(c_Set_Oinsert(_1415002), _1415008), c_Orderings_Obot__class_Obot(tc_fun(_1415002, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415002, _1415000), _1415006), _1415004))], (34752 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1415002), _1415008), _1415004)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415002, _1415000), _1415006), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1415002, tc_HOL_Obool)), _1415004), hAPP(hAPP(c_Set_Oinsert(_1415002), _1415008), c_Orderings_Obot__class_Obot(tc_fun(_1415002, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1415000), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415002, _1415000), _1415006), _1415004)), hAPP(_1415006, _1415008)))]]], (47242 ^ _778908) ^ [_1718313, _1718315, _1718317, _1718319, _1718321] : [class_Groups_Ocomm__monoid__add(_1718313), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1718313), hAPP(hAPP(c_List_Omap(_1718315, _1718313), hAPP(hAPP(c_COMBS(_1718315, _1718313, _1718313), hAPP(hAPP(c_COMBB(_1718313, tc_fun(_1718313, _1718313), _1718315), c_Groups_Oplus__class_Oplus(_1718313)), _1718317)), _1718319)), _1718321)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1718313), hAPP(c_List_Omonoid__add__class_Olistsum(_1718313), hAPP(hAPP(c_List_Omap(_1718315, _1718313), _1718317), _1718321))), hAPP(c_List_Omonoid__add__class_Olistsum(_1718313), hAPP(hAPP(c_List_Omap(_1718315, _1718313), _1718319), _1718321))))], (46261 ^ _778908) ^ [_1691754, _1691756, _1691758] : [-(hAPP(hAPP(c_Option_Omap(_1691754, _1691756), _1691758), c_Option_Ooption_ONone(_1691754)) = c_Option_Ooption_ONone(_1691756))], (7785 ^ _778908) ^ [_909247] : [-(_909247 = 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)), _909247)))], (33992 ^ _778908) ^ [_1400036, _1400038] : [class_Orderings_Olinorder(_1400036), -(c_Big__Operators_Olattice_OInf__fin(_1400036, c_Orderings_Oord__class_Omin(_1400036), hAPP(hAPP(c_Set_Oinsert(_1400036), _1400038), c_Orderings_Obot__class_Obot(tc_fun(_1400036, tc_HOL_Obool)))) = _1400038)], (36672 ^ _778908) ^ [_1459707, _1459709, _1459711] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459707, tc_HOL_Obool)), _1459709), _1459711) = c_Orderings_Obot__class_Obot(tc_fun(_1459707, tc_HOL_Obool)), 36675 ^ _778908 : [(36676 ^ _778908) ^ [_1459831] : [hBOOL(hAPP(hAPP(c_member(_1459707), _1459831), _1459709)), 36679 ^ _778908 : [(36680 ^ _778908) ^ [_1459921] : [hBOOL(hAPP(hAPP(c_member(_1459707), _1459921), _1459711)), _1459831 = _1459921]]]]], (41710 ^ _778908) ^ [_1580671, _1580673, _1580675, _1580677] : [c_Finite__Set_Ofolding(_1580671, _1580673, _1580675, _1580677), -(hAPP(_1580677, c_Orderings_Obot__class_Obot(tc_fun(_1580671, tc_HOL_Obool))) = c_Fun_Oid(_1580673))], (36053 ^ _778908) ^ [_1446283, _1446285, _1446287, _1446289] : [hBOOL(hAPP(hAPP(c_member(_1446283), _1446285), _1446287)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1446283, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446283, _1446283, _1446289), hAPP(hAPP(c_Set_Oinsert(_1446283), _1446285), c_Orderings_Obot__class_Obot(tc_fun(_1446283, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446283), _1446287), _1446289))))], (30782 ^ _778908) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49183 ^ _778908) ^ [_1765203, _1765205, _1765207] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765203)), hAPP(c_List_Orotate(_1765203, _1765205), _1765207)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765203)), _1765207))], (7553 ^ _778908) ^ [_905414, _905416, _905418, _905420, _905422] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_905414, _905416), _905418, _905420, _905422), 7558 ^ _778908 : [(7561 ^ _778908) ^ [] : [hBOOL(hAPP(_905414, _905418))], (7559 ^ _778908) ^ [] : [-(_905422 = _905418)]], 7562 ^ _778908 : [(7568 ^ _778908) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_905414, _905416), 7564 ^ [_905414, _905416, _905418, _905420, _905422], _905420, _905422))], (7566 ^ _778908) ^ [] : [-(c_Natural_Oevaln(_905416, _905418, _905420, 7564 ^ [_905414, _905416, _905418, _905420, _905422]))], (7563 ^ _778908) ^ [] : [-(hBOOL(hAPP(_905414, _905418)))]]], (6540 ^ _778908) ^ [_885029, _885031, _885033, _885035, _885037, _885039, _885041, _885043, _885045, _885047, _885049, _885051] : [-(c_Com_Ocom_Ocom__rec(_885029, _885031, _885033, _885035, _885037, _885039, _885041, _885043, _885045, c_Com_Ocom_OCond(_885047, _885049, _885051)) = hAPP(hAPP(hAPP(hAPP(hAPP(_885039, _885047), _885049), _885051), c_Com_Ocom_Ocom__rec(_885029, _885031, _885033, _885035, _885037, _885039, _885041, _885043, _885045, _885049)), c_Com_Ocom_Ocom__rec(_885029, _885031, _885033, _885035, _885037, _885039, _885041, _885043, _885045, _885051)))], (16316 ^ _778908) ^ [_1059229, _1059231] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059229, _1059231) = 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), _1059229), _1059231) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059231), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059229, _1059231)))], (5520 ^ _778908) ^ [_864214, _864216, _864218, _864220] : [-(c_List_Oconcat(_864220, _864216) = c_List_Oconcat(_864218, _864214)), _864220 = _864218, _864216 = _864214], (13138 ^ _778908) ^ [_1000451] : [_1000451 = 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), _1000451)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44731 ^ _778908) ^ [_1654232, _1654234, _1654236, _1654238, _1654240] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654232, tc_fun(_1654234, tc_HOL_Obool)), _1654236), hAPP(hAPP(c_COMBB(tc_fun(_1654234, tc_HOL_Obool), tc_fun(_1654234, tc_HOL_Obool), _1654232), hAPP(c_Set_Oinsert(_1654234), _1654238)), _1654240)) = hAPP(hAPP(c_Set_Oinsert(_1654234), _1654238), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654232, tc_fun(_1654234, tc_HOL_Obool)), _1654236), _1654240)))], (47030 ^ _778908) ^ [_1712283, _1712285, _1712287, _1712289, _1712291] : [-(hAPP(hAPP(c_List_Olist_OCons(_1712283), _1712285), _1712287) = hAPP(hAPP(c_List_Olist_OCons(_1712283), _1712289), _1712291)), _1712285 = _1712289, _1712287 = _1712291], (17467 ^ _778908) ^ [_1080594] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080594)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080594))], (37378 ^ _778908) ^ [_1476020, _1476022, _1476024, _1476026, _1476028, _1476030, _1476032, _1476034] : [c_Finite__Set_Ofolding__image__simple(_1476020, _1476022, _1476024, _1476026, _1476028, _1476030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476022), _1476032)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476022), _1476034)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476022, tc_HOL_Obool)), _1476032), _1476034) = c_Orderings_Obot__class_Obot(tc_fun(_1476022, tc_HOL_Obool)), -(hAPP(_1476030, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476022, tc_HOL_Obool)), _1476032), _1476034)) = hAPP(hAPP(_1476024, hAPP(_1476030, _1476032)), hAPP(_1476030, _1476034)))], (22802 ^ _778908) ^ [_1174606, _1174608] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174606), hAPP(c_Nat_OSuc, _1174608)) = 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), _1174606), _1174608)))], (23206 ^ _778908) ^ [_1182686, _1182688] : [_1182686 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1182686, _1182688) = 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)))], (42532 ^ _778908) ^ [_1601709, _1601711, _1601713] : [-(hAPP(c_New__DSequence_Oneg__single(_1601709, _1601711), _1601713) = c_Lazy__Sequence_Ohb__single(_1601709, _1601711))], (42371 ^ _778908) ^ [_1597633, _1597635, _1597637, _1597639, _1597641] : [-(hAPP(c_Relation_ODomain(_1597633, _1597635), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1597633, _1597635)), hAPP(hAPP(c_Product__Type_OPair(_1597633, _1597635), _1597637), _1597639)), _1597641)) = hAPP(hAPP(c_Set_Oinsert(_1597633), _1597637), hAPP(c_Relation_ODomain(_1597633, _1597635), _1597641)))], (12317 ^ _778908) ^ [_985835, _985837] : [class_Groups_Olinordered__ab__group__add(_985835), 12320 ^ _778908 : [(12327 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985835), c_Groups_Ozero__class_Ozero(_985835)), _985837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985835), hAPP(c_Groups_Ouminus__class_Ouminus(_985835), _985837)), _985837)))], (12321 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985835), hAPP(c_Groups_Ouminus__class_Ouminus(_985835), _985837)), _985837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985835), c_Groups_Ozero__class_Ozero(_985835)), _985837)))]]], (38708 ^ _778908) ^ [_1505004, _1505006, _1505008, _1505010, _1505012] : [c_Fun_Oinj__on(_1505004, _1505006, _1505008, c_Orderings_Otop__class_Otop(tc_fun(_1505004, tc_HOL_Obool))), 38711 ^ _778908 : [(38718 ^ _778908) ^ [] : [_1505010 = _1505012, -(hAPP(c_Set_Oimage(_1505004, _1505006, _1505008), _1505010) = hAPP(c_Set_Oimage(_1505004, _1505006, _1505008), _1505012))], (38712 ^ _778908) ^ [] : [hAPP(c_Set_Oimage(_1505004, _1505006, _1505008), _1505010) = hAPP(c_Set_Oimage(_1505004, _1505006, _1505008), _1505012), -(_1505010 = _1505012)]]], (11320 ^ _778908) ^ [_968386, _968388, _968390] : [11321 ^ _778908 : [(11324 ^ _778908) ^ [] : [_968388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11322 ^ _778908) ^ [] : [_968386 = _968390]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968386), _968388) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968390), _968388))], (49833 ^ _778908) ^ [_1779333, _1779335] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779333)), c_List_Obutlast(_1779333, _1779335)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779333)), _1779335)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18291 ^ _778908) ^ [_1094986] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1094986) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094986))], (25237 ^ _778908) ^ [_1222626, _1222628, _1222630] : [-(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), _1222626)), 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))), _1222628))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1222630))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222630)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1222626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1222626), 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), _1222630), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1222628)))))], (38926 ^ _778908) ^ [_1509196, _1509198, _1509200, _1509202, _1509204, _1509206] : [c_Fun_Oinj__on(_1509196, _1509198, _1509200, _1509202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509196, tc_HOL_Obool)), _1509204), _1509202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509196, tc_HOL_Obool)), _1509206), _1509202)), -(hAPP(c_Set_Oimage(_1509196, _1509198, _1509200), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509196, tc_HOL_Obool)), _1509204), _1509206)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509198, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509196, _1509198, _1509200), _1509204)), hAPP(c_Set_Oimage(_1509196, _1509198, _1509200), _1509206)))], (34907 ^ _778908) ^ [_1418894, _1418896, _1418898, _1418900] : [-(c_Map_Orestrict__map(_1418894, _1418896, _1418898, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1418894, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1418894), _1418900), c_Orderings_Obot__class_Obot(tc_fun(_1418894, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418894, tc_Option_Ooption(_1418896)), _1418898), _1418900), c_Option_Ooption_ONone(_1418896)))], (35096 ^ _778908) ^ [_1422971, _1422973, _1422975, _1422977] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1422971, tc_HOL_Obool), tc_fun(_1422971, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1422971, tc_HOL_Obool), tc_fun(_1422971, tc_HOL_Obool)), _1422975), _1422977)), c_Wellfounded_Omax__ext(_1422971, _1422973))), -(c_Wellfounded_Omax__extp(_1422971, hAPP(hAPP(c_COMBC(_1422971, tc_fun(tc_prod(_1422971, _1422971), tc_HOL_Obool), tc_fun(_1422971, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422971, tc_fun(tc_fun(tc_prod(_1422971, _1422971), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1422971, _1422971), tc_HOL_Obool), tc_fun(_1422971, tc_HOL_Obool)), _1422971), c_COMBC(_1422971, tc_fun(tc_prod(_1422971, _1422971), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422971, tc_prod(_1422971, _1422971)), tc_fun(_1422971, tc_fun(tc_fun(tc_prod(_1422971, _1422971), tc_HOL_Obool), tc_HOL_Obool)), _1422971), hAPP(c_COMBB(tc_prod(_1422971, _1422971), tc_fun(tc_fun(tc_prod(_1422971, _1422971), tc_HOL_Obool), tc_HOL_Obool), _1422971), c_member(tc_prod(_1422971, _1422971)))), c_Product__Type_OPair(_1422971, _1422971)))), _1422973), _1422975, _1422977))], (19967 ^ _778908) ^ [_1122863, _1122865, _1122867] : [class_Rings_Olinordered__idom(_1122863), 19970 ^ _778908 : [(19971 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122863), c_Groups_Ozero__class_Ozero(_1122863)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122863), hAPP(hAPP(c_Power_Opower__class_Opower(_1122863), _1122865), 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(_1122863), _1122867), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1122865 = c_Groups_Ozero__class_Ozero(_1122863), _1122867 = c_Groups_Ozero__class_Ozero(_1122863)], (19981 ^ _778908) ^ [] : [19982 ^ _778908 : [(19985 ^ _778908) ^ [] : [-(_1122867 = c_Groups_Ozero__class_Ozero(_1122863))], (19983 ^ _778908) ^ [] : [-(_1122865 = c_Groups_Ozero__class_Ozero(_1122863))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122863), c_Groups_Ozero__class_Ozero(_1122863)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122863), hAPP(hAPP(c_Power_Opower__class_Opower(_1122863), _1122865), 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(_1122863), _1122867), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (2188 ^ _778908) ^ [_811666, _811668, _811670, _811672, _811674, _811676, _811678, _811680, _811682, _811684] : [-(c_Nitpick_Opair__box_Opair__box__rec(_811684, _811680, _811676, _811672, _811668) = c_Nitpick_Opair__box_Opair__box__rec(_811682, _811678, _811674, _811670, _811666)), _811684 = _811682, _811680 = _811678, _811676 = _811674, _811672 = _811670, _811668 = _811666], (15228 ^ _778908) ^ [_1037743, _1037745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037745)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1037743), hAPP(c_Int_Onat, _1037745)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1037743, _1037745)))], (12986 ^ _778908) ^ [_997779, _997781, _997783, _997785] : [class_Rings_Olinordered__ring__strict(_997779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997779), c_Groups_Ozero__class_Ozero(_997779)), _997781)), 12993 ^ _778908 : [(13000 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997779), _997783), _997785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997779), _997781), _997783)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997779), _997781), _997785))))], (12994 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997779), _997781), _997783)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997779), _997781), _997785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997779), _997783), _997785)))]]], (50965 ^ _778908) ^ [_1803121, _1803123, _1803125] : [-(hAPP(c_List_Orev(_1803121), hAPP(hAPP(c_List_Otake(_1803121), _1803123), _1803125)) = hAPP(hAPP(c_List_Odrop(_1803121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803121)), _1803125)), _1803123)), hAPP(c_List_Orev(_1803121), _1803125)))], (21667 ^ _778908) ^ [_1153203, _1153205, _1153207, _1153209] : [class_Fields_Olinordered__field(_1153203), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153203), c_Groups_Ozero__class_Ozero(_1153203)), _1153205)), 21674 ^ _778908 : [(21681 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153203), _1153207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153203), _1153209), _1153205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153203), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153203), _1153207), _1153205)), _1153209)))], (21675 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153203), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153203), _1153207), _1153205)), _1153209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153203), _1153207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153203), _1153209), _1153205))))]]], (36740 ^ _778908) ^ [_1460961, _1460963, _1460965, _1460967] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460961, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460961, tc_HOL_Obool)), _1460963), _1460965)), _1460967) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460961, tc_HOL_Obool)), _1460963), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460961, tc_HOL_Obool)), _1460965), _1460967)))], (50208 ^ _778908) ^ [_1787999, _1788001, _1788003, _1788005] : [class_Orderings_Olinorder(_1787999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1787999), _1788001), _1788003)), c_List_Olinorder__class_Osorted(_1787999, hAPP(hAPP(c_List_Olist_OCons(_1787999), _1788003), _1788005)), -(c_List_Olinorder__class_Osorted(_1787999, hAPP(hAPP(c_List_Olist_OCons(_1787999), _1788001), hAPP(hAPP(c_List_Olist_OCons(_1787999), _1788003), _1788005))))], (29124 ^ _778908) ^ [] : [-(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)))], (31271 ^ _778908) ^ [_1343065, _1343067] : [_1343065 = _1343067, -(hAPP(c_Int_ORep__Integ, _1343065) = hAPP(c_Int_ORep__Integ, _1343067))], (30480 ^ _778908) ^ [_1324804, _1324806, _1324808, _1324810, _1324812] : [_1324804 = c_Orderings_Obot__class_Obot(tc_fun(_1324806, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1324808), _1324810), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324806, tc_fun(_1324808, tc_HOL_Obool)), _1324804), _1324812)) = hAPP(hAPP(c_Set_Oinsert(_1324808), _1324810), c_Orderings_Obot__class_Obot(tc_fun(_1324808, tc_HOL_Obool))))], (1712 ^ _778908) ^ [_803182, _803184] : [-(class_Rings_Osemiring__1(_803182)), _803184 = _803182, class_Rings_Osemiring__1(_803184)], (36846 ^ _778908) ^ [_1463268] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1463268) = c_Orderings_Oord__class_Omin(_1463268)), class_Lattices_Osemilattice__inf(_1463268), class_Orderings_Olinorder(_1463268)], (1812 ^ _778908) ^ [_804432, _804434] : [-(class_Groups_Oone(_804432)), _804434 = _804432, class_Groups_Oone(_804434)], (10621 ^ _778908) ^ [_957214, _957216, _957218] : [class_Orderings_Oorder(_957214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957214), _957216), _957218)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957214), _957218), _957216)), -(_957216 = _957218)], (18873 ^ _778908) ^ [_1104120, _1104122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104120), _1104122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1104120)), c_Int_OBit1(_1104122))))], (48480 ^ _778908) ^ [_1747426, _1747428, _1747430, _1747432] : [-(c_Map_Omap__upds(_1747426, _1747428, _1747430, _1747432, c_List_Olist_ONil(_1747428)) = _1747430)], (46086 ^ _778908) ^ [_1687529, _1687531, _1687533, _1687535, _1687537, _1687539] : [hAPP(_1687529, _1687531) = c_Option_Ooption_ONone(_1687533), -(c_Map_Omap__comp(_1687533, _1687535, _1687537, _1687539, _1687529, _1687531) = c_Option_Ooption_ONone(_1687535))], (38178 ^ _778908) ^ [_1494290, _1494292, _1494294] : [class_Lattices_Olattice(_1494290), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494290), _1494292)), -(_1494292 = c_Orderings_Obot__class_Obot(tc_fun(_1494290, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494290), _1494294)), -(_1494294 = c_Orderings_Obot__class_Obot(tc_fun(_1494290, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1494290, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494290, tc_HOL_Obool)), _1494292), _1494294)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1494290), c_Big__Operators_Olattice__class_OInf__fin(_1494290, _1494292)), c_Big__Operators_Olattice__class_OInf__fin(_1494290, _1494294)))], (49199 ^ _778908) ^ [_1765572, _1765574, _1765576] : [hBOOL(hAPP(c_List_Odistinct(_1765572), hAPP(c_List_Orotate(_1765572, _1765574), _1765576))), -(hBOOL(hAPP(c_List_Odistinct(_1765572), _1765576)))], (48421 ^ _778908) ^ [_1745528, _1745530, _1745532, _1745534, _1745536, _1745538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745528)), _1745530)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745532)), _1745534))), -(c_Map_Omap__upds(_1745528, _1745532, _1745536, hAPP(hAPP(c_List_Oappend(_1745528), _1745530), hAPP(hAPP(c_List_Olist_OCons(_1745528), _1745538), c_List_Olist_ONil(_1745528))), _1745534) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1745528, tc_Option_Ooption(_1745532)), c_Map_Omap__upds(_1745528, _1745532, _1745536, _1745530, _1745534)), _1745538), hAPP(c_Option_Ooption_OSome(_1745532), hAPP(hAPP(c_List_Onth(_1745532), _1745534), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745528)), _1745530)))))], (16833 ^ _778908) ^ [_1068389, _1068391, _1068393] : [class_Groups_Oordered__ab__group__add__abs(_1068389), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068389), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068389), hAPP(c_Groups_Oabs__class_Oabs(_1068389), _1068391)), hAPP(c_Groups_Oabs__class_Oabs(_1068389), _1068393))), hAPP(c_Groups_Oabs__class_Oabs(_1068389), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068389), _1068391), _1068393)))))], (4394 ^ _778908) ^ [_846869, _846871, _846873, _846875, _846877, _846879, _846881, _846883] : [-(c_Wellfounded_Olex__prod(_846883, _846879, _846875, _846871) = c_Wellfounded_Olex__prod(_846881, _846877, _846873, _846869)), _846883 = _846881, _846879 = _846877, _846875 = _846873, _846871 = _846869], (46801 ^ _778908) ^ [_1704950, _1704952] : [-(c_List_Olenlex(_1704950, _1704952) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1704950)), tc_List_Olist(_1704950)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1704950), c_Wellfounded_Oless__than, c_List_Olex(_1704950, _1704952))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1704950), tc_List_Olist(_1704950), tc_prod(tc_Nat_Onat, tc_List_Olist(_1704950))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1704950), tc_prod(tc_Nat_Onat, tc_List_Olist(_1704950))), tc_List_Olist(_1704950)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1704950))), c_Nat_Osize__class_Osize(tc_List_Olist(_1704950)))), c_COMBI(tc_List_Olist(_1704950)))))], (49059 ^ _778908) ^ [_1762741, _1762743, _1762745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762741), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762743)), _1762745))), -(hAPP(hAPP(c_List_Olist_OCons(_1762743), hAPP(hAPP(c_List_Onth(_1762743), _1762745), _1762741)), hAPP(hAPP(c_List_Odrop(_1762743), hAPP(c_Nat_OSuc, _1762741)), _1762745)) = hAPP(hAPP(c_List_Odrop(_1762743), _1762741), _1762745))], (45015 ^ _778908) ^ [_1662958, _1662960] : [class_Complete__Lattice_Ocomplete__lattice(_1662958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1662958), _1662960)), -(c_Complete__Lattice_OInf__class_OInf(_1662958, _1662960) = hAPP(hAPP(c_Finite__Set_Ofold(_1662958, _1662958, c_Lattices_Osemilattice__inf__class_Oinf(_1662958)), c_Orderings_Otop__class_Otop(_1662958)), _1662960))], (34784 ^ _778908) ^ [_1416070, _1416072, _1416074, _1416076, _1416078] : [hAPP(_1416070, _1416072) = hAPP(c_Option_Ooption_OSome(_1416074), _1416076), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1416078, tc_Option_Ooption(_1416074)), _1416070), _1416072), hAPP(c_Option_Ooption_OSome(_1416074), _1416076)) = _1416070)], (19105 ^ _778908) ^ [_1107881] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1107881)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1107881)))], (22790 ^ _778908) ^ [_1174394, _1174396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1174394)), _1174396)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174394), _1174396)))], (43453 ^ _778908) ^ [_1624635, _1624637] : [-(c_Relation_Oirrefl(_1624635, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1624635, _1624635), tc_HOL_Obool)), _1624637), c_Relation_OId(_1624635))))], (8186 ^ _778908) ^ [_916046, _916048, _916050] : [class_Rings_Olinordered__idom(_916046), -(_916048 = _916050), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916046), _916048), _916050))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916046), _916050), _916048)))], (7823 ^ _778908) ^ [_909730, _909732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909730), hAPP(c_Nat_OSuc, _909732))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909730), _909732))), -(_909730 = _909732)], (14122 ^ _778908) ^ [_1017934, _1017936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017934), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14125 ^ _778908 : [(14128 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017934), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017936, _1017934))))], (14126 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017936, _1017934)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (31520 ^ _778908) ^ [_1347685, _1347687, _1347689] : [hBOOL(hAPP(hAPP(c_member(_1347685), _1347687), hAPP(hAPP(c_Set_Oinsert(_1347685), _1347689), c_Orderings_Obot__class_Obot(tc_fun(_1347685, tc_HOL_Obool))))), -(_1347687 = _1347689)], (50799 ^ _778908) ^ [_1799778, _1799780, _1799782] : [_1799780 = hAPP(hAPP(c_List_Olist_OCons(_1799778), _1799782), c_List_Olist_ONil(_1799778)), -(hAPP(c_List_Orev(_1799778), _1799780) = hAPP(hAPP(c_List_Olist_OCons(_1799778), _1799782), c_List_Olist_ONil(_1799778)))], (21095 ^ _778908) ^ [_1143226, _1143228, _1143230, _1143232] : [class_Fields_Olinordered__field(_1143226), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143226), c_Groups_Ozero__class_Ozero(_1143226)), _1143228)), 21102 ^ _778908 : [(21109 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143226), _1143230), _1143228)), _1143232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143226), _1143230), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143226), _1143232), _1143228))))], (21103 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143226), _1143230), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143226), _1143232), _1143228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143226), _1143230), _1143228)), _1143232)))]]], (41692 ^ _778908) ^ [_1580361, _1580363] : [-(hAPP(c_Fun_Oid(_1580361), _1580363) = _1580363)], (17919 ^ _778908) ^ [_1088947, _1088949] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1088947), _1088949) = 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), _1088947)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1088949)))))], (44891 ^ _778908) ^ [_1659677, _1659679, _1659681, _1659683, _1659685] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659677, tc_HOL_Obool)), _1659679), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659681, tc_fun(_1659677, tc_HOL_Obool)), _1659683), _1659685)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659681, tc_fun(_1659677, tc_HOL_Obool)), _1659683), hAPP(hAPP(c_COMBB(tc_fun(_1659677, tc_HOL_Obool), tc_fun(_1659677, tc_HOL_Obool), _1659681), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659677, tc_HOL_Obool)), _1659679)), _1659685)))], (14190 ^ _778908) ^ [_1019088, _1019090, _1019092] : [class_Lattices_Oboolean__algebra(_1019088), 14193 ^ _778908 : [(14200 ^ _778908) ^ [] : [_1019090 = _1019092, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1019088), _1019090) = hAPP(c_Groups_Ouminus__class_Ouminus(_1019088), _1019092))], (14194 ^ _778908) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1019088), _1019090) = hAPP(c_Groups_Ouminus__class_Ouminus(_1019088), _1019092), -(_1019090 = _1019092)]]], (41870 ^ _778908) ^ [_1586560, _1586562, _1586564, _1586566] : [c_Wellfounded_Owf(_1586560, _1586562), -(c_Wellfounded_Owf(_1586564, hAPP(hAPP(c_Relation_Oinv__image(_1586560, _1586564), _1586562), _1586566)))], (17861 ^ _778908) ^ [_1087816, _1087818, _1087820, _1087822] : [class_Rings_Olinordered__semidom(_1087816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1087818), _1087820)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087816), c_Groups_Oone__class_Oone(_1087816)), _1087822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087816), hAPP(hAPP(c_Power_Opower__class_Opower(_1087816), _1087822), _1087818)), hAPP(hAPP(c_Power_Opower__class_Opower(_1087816), _1087822), _1087820))))], (5178 ^ _778908) ^ [_859029, _859031] : [_859031 = _859029, -(c_SetInterval_Oord__class_OlessThan(_859031) = c_SetInterval_Oord__class_OlessThan(_859029))], (13875 ^ _778908) ^ [_1013201, _1013203] : [class_Divides_Osemiring__div(_1013201), -(c_Divides_Odiv__class_Omod(_1013201, c_Groups_Ozero__class_Ozero(_1013201), _1013203) = c_Groups_Ozero__class_Ozero(_1013201))], (18105 ^ _778908) ^ [_1091979] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091979)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091979)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091979))], (43195 ^ _778908) ^ [_1618447, _1618449, _1618451, _1618453] : [43196 ^ _778908 : [(43199 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618447, _1618447)), _1618449), c_Transitive__Closure_Ortrancl(_1618447, _1618453)))], (43197 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618447, _1618447)), _1618449), c_Transitive__Closure_Ortrancl(_1618447, _1618451)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618447, _1618447)), _1618449), c_Transitive__Closure_Ortrancl(_1618447, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1618447, _1618447), tc_HOL_Obool)), _1618451), _1618453)))))], (34996 ^ _778908) ^ [_1420804, _1420806, _1420808, _1420810] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1420804), _1420806)), 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)), _1420808), _1420804)), 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)), _1420810), _1420806)), 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)), _1420808), _1420810)), _1420806)), c_FunDef_Omax__strict)))], (44591 ^ _778908) ^ [_1650660, _1650662, _1650664, _1650666, _1650668, _1650670, _1650672, _1650674] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650660, tc_fun(_1650662, tc_fun(_1650664, tc_HOL_Obool))), _1650666), _1650668), _1650670), _1650672)), -(hBOOL(hAPP(hAPP(hAPP(_1650668, _1650674), _1650670), _1650672))), hBOOL(hAPP(hAPP(c_member(_1650660), _1650674), _1650666))], (47815 ^ _778908) ^ [_1731498, _1731500, _1731502, _1731504] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731498), tc_List_Olist(_1731498))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731498), tc_List_Olist(_1731498)), _1731500), _1731502)), c_List_Olistrel(_1731498, _1731504)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731498)), _1731500) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731498)), _1731502), 47821 ^ _778908 : [(47824 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1731498, _1731498)), hAPP(hAPP(c_Product__Type_OPair(_1731498, _1731498), hAPP(hAPP(c_List_Onth(_1731498), _1731500), 47820 ^ [_1731498, _1731500, _1731502, _1731504])), hAPP(hAPP(c_List_Onth(_1731498), _1731502), 47820 ^ [_1731498, _1731500, _1731502, _1731504]))), _1731504))], (47822 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47820 ^ [_1731498, _1731500, _1731502, _1731504]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731498)), _1731500))))]]], (8910 ^ _778908) ^ [_927566] : [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)), _927566)), _927566)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _927566), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (2532 ^ _778908) ^ [_817196, _817198, _817200, _817202] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_817202, _817198) = c_Code__Numeral_Odiv__mod__code__numeral(_817200, _817196)), _817202 = _817200, _817198 = _817196], (16781 ^ _778908) ^ [_1067392, _1067394] : [class_Groups_Oordered__ab__group__add__abs(_1067392), 16784 ^ _778908 : [(16791 ^ _778908) ^ [] : [-(_1067394 = c_Groups_Ozero__class_Ozero(_1067392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067392), c_Groups_Ozero__class_Ozero(_1067392)), hAPP(c_Groups_Oabs__class_Oabs(_1067392), _1067394))))], (16785 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067392), c_Groups_Ozero__class_Ozero(_1067392)), hAPP(c_Groups_Oabs__class_Oabs(_1067392), _1067394))), _1067394 = c_Groups_Ozero__class_Ozero(_1067392)]]], (2802 ^ _778908) ^ [_821401, _821403, _821405, _821407, _821409, _821411] : [-(c_Nitpick_Oof__frac(_821411, _821407, _821403) = c_Nitpick_Oof__frac(_821409, _821405, _821401)), _821411 = _821409, _821407 = _821405, _821403 = _821401], (49187 ^ _778908) ^ [_1765290, _1765292, _1765294, _1765296] : [-(hAPP(hAPP(c_List_Omap(_1765290, _1765292), _1765294), hAPP(c_List_Otl(_1765290), _1765296)) = hAPP(c_List_Otl(_1765292), hAPP(hAPP(c_List_Omap(_1765290, _1765292), _1765294), _1765296)))], (13913 ^ _778908) ^ [_1013884, _1013886, _1013888, _1013890] : [class_Divides_Osemiring__div(_1013884), -(c_Divides_Odiv__class_Omod(_1013884, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013884), _1013886), c_Divides_Odiv__class_Omod(_1013884, _1013888, _1013890)), _1013890) = c_Divides_Odiv__class_Omod(_1013884, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013884), _1013886), _1013888), _1013890))], (45284 ^ _778908) ^ [_1668798, _1668800] : [class_Complete__Lattice_Ocomplete__lattice(_1668798), -(c_Complete__Lattice_OSup__class_OSup(_1668798, _1668800) = c_Complete__Lattice_OInf__class_OInf(_1668798, hAPP(c_Set_OCollect(_1668798), hAPP(hAPP(c_COMBB(tc_fun(_1668798, tc_HOL_Obool), tc_HOL_Obool, _1668798), c_HOL_OAll(_1668798)), hAPP(hAPP(c_COMBB(tc_fun(_1668798, tc_HOL_Obool), tc_fun(_1668798, tc_HOL_Obool), _1668798), hAPP(c_COMBS(_1668798, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1668798), c_fimplies), hAPP(hAPP(c_COMBC(_1668798, tc_fun(_1668798, tc_HOL_Obool), tc_HOL_Obool), c_member(_1668798)), _1668800)))), hAPP(c_COMBC(_1668798, _1668798, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1668798)))))))], (28717 ^ _778908) ^ [_1289498, _1289500, _1289502] : [class_Orderings_Olinorder(_1289498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289498), _1289500), _1289502)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289498, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1289498, _1289500, _1289502)), hAPP(c_SetInterval_Oord__class_OatLeast(_1289498), _1289502)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1289498), _1289500))], (43133 ^ _778908) ^ [_1616425, _1616427, _1616429, _1616431] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1616425, tc_fun(_1616425, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1616425, tc_fun(tc_prod(_1616425, _1616425), tc_HOL_Obool), tc_fun(_1616425, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616425, tc_fun(tc_fun(tc_prod(_1616425, _1616425), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1616425, _1616425), tc_HOL_Obool), tc_fun(_1616425, tc_HOL_Obool)), _1616425), c_COMBC(_1616425, tc_fun(tc_prod(_1616425, _1616425), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616425, tc_prod(_1616425, _1616425)), tc_fun(_1616425, tc_fun(tc_fun(tc_prod(_1616425, _1616425), tc_HOL_Obool), tc_HOL_Obool)), _1616425), hAPP(c_COMBB(tc_prod(_1616425, _1616425), tc_fun(tc_fun(tc_prod(_1616425, _1616425), tc_HOL_Obool), tc_HOL_Obool), _1616425), c_member(tc_prod(_1616425, _1616425)))), c_Product__Type_OPair(_1616425, _1616425)))), _1616427)), c_fequal), _1616429), _1616431)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616425, _1616425)), hAPP(hAPP(c_Product__Type_OPair(_1616425, _1616425), _1616429), _1616431)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1616425, _1616425), tc_HOL_Obool)), _1616427), c_Relation_OId(_1616425)))))], (14172 ^ _778908) ^ [_1018751, _1018753, _1018755] : [class_Lattices_Oab__semigroup__idem__mult(_1018751), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018751), _1018753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018751), _1018753), _1018755)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018751), _1018753), _1018755))], (17097 ^ _778908) ^ [_1073666, _1073668, _1073670] : [class_Int_Onumber__ring(_1073666), -(hAPP(c_Int_Onumber__class_Onumber__of(_1073666), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1073668), _1073670)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073666), hAPP(c_Int_Onumber__class_Onumber__of(_1073666), _1073668)), hAPP(c_Int_Onumber__class_Onumber__of(_1073666), _1073670)))], (20225 ^ _778908) ^ [_1128036, _1128038, _1128040, _1128042] : [class_Rings_Odivision__ring(_1128036), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128036), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1128036), _1128038), _1128040)), _1128042) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1128036), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128036), _1128038), _1128042)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128036), _1128040), _1128042)))], (10501 ^ _778908) ^ [_955267, _955269, _955271] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955267), _955269)), _955271) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955269), _955271)))], (36416 ^ _778908) ^ [_1454209, _1454211, _1454213, _1454215] : [class_Lattices_Osemilattice__inf(_1454209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454209), _1454211), _1454213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454209), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454209), _1454211), _1454215)), _1454213)))], (13887 ^ _778908) ^ [_1013379, _1013381] : [class_Divides_Osemiring__div(_1013379), -(c_Divides_Odiv__class_Omod(_1013379, _1013381, _1013381) = c_Groups_Ozero__class_Ozero(_1013379))], (23128 ^ _778908) ^ [_1181177, _1181179, _1181181] : [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), _1181177), _1181179))), -(hBOOL(hAPP(hAPP(_1181181, _1181177), _1181179))), 23135 ^ _778908 : [(23138 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1181181, 23133 ^ [_1181177, _1181179, _1181181]), 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)))), 23134 ^ [_1181177, _1181179, _1181181])))), -(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), 23133 ^ [_1181177, _1181179, _1181181]), 23134 ^ [_1181177, _1181179, _1181181])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23134 ^ [_1181177, _1181179, _1181181]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23148 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1181181, 23133 ^ [_1181177, _1181179, _1181181]), 23134 ^ [_1181177, _1181179, _1181181]))], (23136 ^ _778908) ^ [] : [-(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), 23133 ^ [_1181177, _1181179, _1181181]), 23134 ^ [_1181177, _1181179, _1181181]))))]]], (19213 ^ _778908) ^ [_1109502, _1109504] : [class_Int_Onumber__ring(_1109502), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109502), hAPP(c_Int_Onumber__class_Onumber__of(_1109502), _1109504)), c_Groups_Oone__class_Oone(_1109502)) = hAPP(c_Int_Onumber__class_Onumber__of(_1109502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1109504), c_Int_OBit1(c_Int_OPls))))], (45907 ^ _778908) ^ [_1682986, _1682988, _1682990, _1682992, _1682994] : [-(hAPP(c_Map_Omap__add(_1682986, _1682988, _1682990, _1682992), _1682994) = c_Option_Ooption_ONone(_1682988)), hAPP(_1682992, _1682994) = c_Option_Ooption_ONone(_1682988), hAPP(_1682990, _1682994) = c_Option_Ooption_ONone(_1682988)], (49543 ^ _778908) ^ [_1773402] : [-(c_List_Olists(_1773402, c_Orderings_Obot__class_Obot(tc_fun(_1773402, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1773402)), c_List_Olist_ONil(_1773402)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1773402), tc_HOL_Obool))))], (9912 ^ _778908) ^ [_945250, _945252, _945254] : [class_Rings_Olinordered__semiring__strict(_945250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945250), _945252), c_Groups_Ozero__class_Ozero(_945250))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945250), c_Groups_Ozero__class_Ozero(_945250)), _945254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945250), _945252), _945254)), c_Groups_Ozero__class_Ozero(_945250))))], (41780 ^ _778908) ^ [_1582650, _1582652, _1582654, _1582656, _1582658, _1582660] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582650, _1582652, _1582654), _1582656), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582652, _1582654), tc_HOL_Obool)), _1582658), _1582660)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582650, _1582654), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1582650, _1582652, _1582654), _1582656), _1582658)), hAPP(hAPP(c_Relation_Orel__comp(_1582650, _1582652, _1582654), _1582656), _1582660)))], (30088 ^ _778908) ^ [_1317800, _1317802, _1317804, _1317806] : [class_Complete__Lattice_Ocomplete__lattice(_1317800), -(_1317802 = c_Orderings_Obot__class_Obot(tc_fun(_1317804, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1317804, _1317800), _1317802), hAPP(c_COMBK(_1317800, _1317804), _1317806)) = _1317806)], (6875 ^ _778908) ^ [_892153, _892155] : [c_Com_Ocom_OWhile(_892153, _892155) = c_Com_Ocom_OSKIP], (37977 ^ _778908) ^ [_1490164, _1490166, _1490168, _1490170, _1490172, _1490174] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490164, tc_fun(_1490166, tc_HOL_Obool))), _1490168), _1490170), _1490172), _1490174)), -(hBOOL(hAPP(hAPP(_1490168, _1490172), _1490174)))], (44178 ^ _778908) ^ [_1642697, _1642699, _1642701, _1642703] : [class_Lattices_Osemilattice__inf(_1642697), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642697), _1642699)), hBOOL(hAPP(hAPP(c_member(_1642697), _1642701), _1642699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1642697), hAPP(hAPP(c_Finite__Set_Ofold(_1642697, _1642697, c_Lattices_Osemilattice__inf__class_Oinf(_1642697)), _1642703), _1642699)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1642697), _1642701), _1642703))))], (5993 ^ _778908) ^ [_874653, _874655, _874657, _874659, _874661] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_874653, _874655), _874657, _874659, _874661), -(_874661 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _874657), _874653), hAPP(_874655, _874657)))], (20281 ^ _778908) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19497 ^ _778908) ^ [_1114704, _1114706] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1114704)), c_Int_OBit1(_1114706)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1114704), _1114706)))], (25463 ^ _778908) ^ [_1226525, _1226527, _1226529] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226525), _1226527)), 25474 ^ _778908 : [(25477 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226529), _1226525))], (25475 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226525), _1226529)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226527), _1226529)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1226529), _1226527)))], (40206 ^ _778908) ^ [_1539958, _1539960, _1539962, _1539964, _1539966, _1539968] : [hBOOL(hAPP(hAPP(c_member(_1539958), _1539960), _1539962)), 40209 ^ _778908 : [(40216 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1539964, tc_HOL_Obool)), _1539966), _1539968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539964, _1539958), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1539964, _1539958), _1539966), hAPP(c_COMBK(tc_fun(_1539958, tc_HOL_Obool), _1539964), _1539962))), hAPP(hAPP(c_Product__Type_OSigma(_1539964, _1539958), _1539968), hAPP(c_COMBK(tc_fun(_1539958, tc_HOL_Obool), _1539964), _1539962)))))], (40210 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539964, _1539958), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1539964, _1539958), _1539966), hAPP(c_COMBK(tc_fun(_1539958, tc_HOL_Obool), _1539964), _1539962))), hAPP(hAPP(c_Product__Type_OSigma(_1539964, _1539958), _1539968), hAPP(c_COMBK(tc_fun(_1539958, tc_HOL_Obool), _1539964), _1539962)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1539964, tc_HOL_Obool)), _1539966), _1539968)))]]], (43039 ^ _778908) ^ [_1613857, _1613859, _1613861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613857, _1613857)), _1613859), _1613861)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613857, _1613857)), _1613859), c_Transitive__Closure_Otrancl(_1613857, _1613861))))], (1602 ^ _778908) ^ [_801807, _801809] : [-(class_Groups_Ocomm__monoid__add(_801807)), _801809 = _801807, class_Groups_Ocomm__monoid__add(_801809)], (44062 ^ _778908) ^ [_1640193, _1640195, _1640197, _1640199] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1640193, _1640195, _1640197), _1640199), c_Orderings_Obot__class_Obot(tc_fun(_1640193, tc_HOL_Obool))) = _1640199)], (4232 ^ _778908) ^ [_844166, _844168, _844170, _844172, _844174, _844176] : [-(c_Smallcheck_Ofull__small_H(_844176, _844172, _844168) = c_Smallcheck_Ofull__small_H(_844174, _844170, _844166)), _844176 = _844174, _844172 = _844170, _844168 = _844166], (29046 ^ _778908) ^ [_1296995, _1296997, _1296999, _1297001, _1297003, _1297005] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296995, tc_fun(_1296997, tc_HOL_Obool)), _1296999), hAPP(hAPP(c_COMBB(_1297001, tc_fun(_1296997, tc_HOL_Obool), _1296995), _1297003), _1297005)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297001, tc_fun(_1296997, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1296995, _1297001, _1297005), _1296999)), _1297003))], (28345 ^ _778908) ^ [_1282346, _1282348, _1282350, _1282352, _1282354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282346, tc_HOL_Obool)), _1282348), _1282350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282346, tc_HOL_Obool)), _1282352), _1282354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282346, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282346, tc_HOL_Obool)), _1282348), _1282352)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282346, tc_HOL_Obool)), _1282350), _1282354))))], (14796 ^ _778908) ^ [_1029913, _1029915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029913)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029913), _1029915)), _1029913) = _1029915)], (29636 ^ _778908) ^ [_1308901] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308901), c_Orderings_Otop__class_Otop(tc_fun(_1308901, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1308901)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1308901), tc_HOL_Obool)))))], (35454 ^ _778908) ^ [_1431563, _1431565, _1431567] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1431563, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1431563, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1431563), _1431565)), hAPP(c_Set_OPow(_1431563), _1431567))), hAPP(c_Set_OPow(_1431563), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431563, tc_HOL_Obool)), _1431565), _1431567)))))], (6335 ^ _778908) ^ [_881030] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _881030), _881030)))], (39761 ^ _778908) ^ [_1528172, _1528174] : [-(c_Map_Odom(_1528172, _1528174, hAPP(c_COMBK(tc_Option_Ooption(_1528174), _1528172), c_Option_Ooption_ONone(_1528174))) = c_Orderings_Obot__class_Obot(tc_fun(_1528172, tc_HOL_Obool)))], (43921 ^ _778908) ^ [_1636403, _1636405, _1636407] : [c_Relation_Osingle__valued(_1636403, _1636405, _1636407), 43924 ^ _778908 : [(43925 ^ _778908) ^ [_1636524, _1636526] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636403, _1636405)), hAPP(hAPP(c_Product__Type_OPair(_1636403, _1636405), _1636526), _1636524)), _1636407)), 43928 ^ _778908 : [(43929 ^ _778908) ^ [_1636650] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636403, _1636405)), hAPP(hAPP(c_Product__Type_OPair(_1636403, _1636405), _1636526), _1636650)), _1636407)), -(_1636524 = _1636650)]]]]], (42461 ^ _778908) ^ [_1600372, _1600374] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1600372, _1600372)), _1600374)), c_Wellfounded_Oacyclic(_1600372, _1600374), -(c_Wellfounded_Owf(_1600372, _1600374))], (10188 ^ _778908) ^ [_950056, _950058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950056)), 10191 ^ _778908 : [(10198 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _950058), _950056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _950058)), hAPP(c_Int_Onat, _950056))))], (10192 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _950058)), hAPP(c_Int_Onat, _950056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _950058), _950056)))]]], (10068 ^ _778908) ^ [_948118] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _948118)), _948118) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23313 ^ _778908) ^ [_1184886, _1184888] : [-(_1184886 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23316 ^ _778908 : [(23323 ^ _778908) ^ [] : [-(_1184888 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1184886, _1184888) = 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, _1184888))), 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, _1184886)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1184888))), c_Divides_Opdivmod(_1184886, _1184888)), 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), _1184888))))), c_Divides_Opdivmod(_1184886, _1184888)))))], (23317 ^ _778908) ^ [] : [_1184888 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1184886, _1184888) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184886))]]], (40967 ^ _778908) ^ [_1556993, _1556995, _1556997] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1556993), _1556995)), 40973 ^ _778908 : [(40976 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1556997, 40972 ^ [_1556993, _1556995, _1556997])))], (40974 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556993), 40972 ^ [_1556993, _1556995, _1556997]), _1556995)))]], -(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(_1556993, tc_Nat_Onat), _1556997), _1556995))))], (47876 ^ _778908) ^ [_1733069, _1733071, _1733073, _1733075, _1733077, _1733079] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1733069, _1733071), hAPP(hAPP(c_List_Ozip(_1733069, _1733071), _1733073), _1733075)), _1733077), _1733079) = hAPP(hAPP(c_List_Ozip(_1733069, _1733071), hAPP(hAPP(c_List_Olist__update(_1733069, _1733073), _1733077), hAPP(c_Product__Type_Ofst(_1733069, _1733071), _1733079))), hAPP(hAPP(c_List_Olist__update(_1733071, _1733075), _1733077), hAPP(c_Product__Type_Osnd(_1733069, _1733071), _1733079))))], (6268 ^ _778908) ^ [_879927, _879929, _879931, _879933, _879935, _879937] : [c_Com_Ocom_OCond(_879927, _879929, _879931) = c_Com_Ocom_OCond(_879933, _879935, _879937), 6271 ^ _778908 : [(6276 ^ _778908) ^ [] : [-(_879931 = _879937)], (6274 ^ _778908) ^ [] : [-(_879929 = _879935)], (6272 ^ _778908) ^ [] : [-(_879927 = _879933)]]], (36630 ^ _778908) ^ [_1458583, _1458585, _1458587, _1458589] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458583, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458583, tc_HOL_Obool)), _1458585), _1458587)), _1458589) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458583, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458583, tc_HOL_Obool)), _1458585), _1458589)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458583, tc_HOL_Obool)), _1458587), _1458589)))], (35076 ^ _778908) ^ [_1422136, _1422138, _1422140, _1422142, _1422144, _1422146] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1422136, tc_HOL_Obool), tc_fun(_1422136, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1422136, tc_HOL_Obool), tc_fun(_1422136, tc_HOL_Obool)), _1422138), _1422140)), c_Wellfounded_Omax__ext(_1422136, _1422142))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1422136, tc_HOL_Obool), tc_fun(_1422136, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1422136, tc_HOL_Obool), tc_fun(_1422136, tc_HOL_Obool)), _1422144), _1422146)), c_Wellfounded_Omax__ext(_1422136, _1422142))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1422136, tc_HOL_Obool), tc_fun(_1422136, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1422136, tc_HOL_Obool), tc_fun(_1422136, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422136, tc_HOL_Obool)), _1422138), _1422144)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422136, tc_HOL_Obool)), _1422140), _1422146))), c_Wellfounded_Omax__ext(_1422136, _1422142))))], (13222 ^ _778908) ^ [_1001752, _1001754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1001752), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1001754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001752), _1001754)))], (39542 ^ _778908) ^ [_1523100, _1523102, _1523104, _1523106] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523100), hAPP(c_Set_Ovimage(_1523100, _1523102, _1523104), _1523106))), hAPP(c_Set_Oimage(_1523100, _1523102, _1523104), c_Orderings_Otop__class_Otop(tc_fun(_1523100, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1523102, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523102), _1523106)))], (8342 ^ _778908) ^ [_918612, _918614] : [8343 ^ _778908 : [(8344 ^ _778908) ^ [_918668] : [_918614 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _918612), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _918668)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _918612), _918614)))], (49081 ^ _778908) ^ [_1763240, _1763242, _1763244, _1763246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1763240), _1763242)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763244)), _1763246))), -(hAPP(hAPP(c_List_Otake(_1763244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1763240), _1763242)), _1763246) = hAPP(hAPP(c_List_Oappend(_1763244), hAPP(hAPP(c_List_Otake(_1763244), _1763240), _1763246)), hAPP(hAPP(c_List_Otake(_1763244), _1763242), hAPP(hAPP(c_List_Odrop(_1763244), _1763240), _1763246))))], (22301 ^ _778908) ^ [_1165238, _1165240, _1165242] : [class_Fields_Olinordered__field(_1165238), 22307 ^ _778908 : [(22310 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165238), _1165240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165238), _1165242), 22306 ^ [_1165238, _1165240, _1165242])))], (22308 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165238), c_Groups_Ozero__class_Ozero(_1165238)), 22306 ^ [_1165238, _1165240, _1165242])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165238), _1165240), _1165242)))], (40140 ^ _778908) ^ [_1538129, _1538131, _1538133, _1538135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538129), _1538131)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538133), _1538135)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538129, _1538133)), hAPP(hAPP(c_Product__Type_OSigma(_1538129, _1538133), _1538131), hAPP(c_COMBK(tc_fun(_1538133, tc_HOL_Obool), _1538129), _1538135)))))], (47391 ^ _778908) ^ [_1721710, _1721712, _1721714, _1721716] : [c_List_Olist_ONil(_1721710) = hAPP(hAPP(c_List_Omap(_1721712, _1721710), _1721714), _1721716), -(_1721716 = c_List_Olist_ONil(_1721712))], (42052 ^ _778908) ^ [_1590084, _1590086, _1590088] : [c_Wellfounded_Owf(_1590084, _1590086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590084, tc_HOL_Obool)), _1590088), hAPP(c_Relation_OImage(_1590084, _1590084, _1590086), _1590088))), -(_1590088 = c_Orderings_Obot__class_Obot(tc_fun(_1590084, tc_HOL_Obool)))], (16244 ^ _778908) ^ [_1057622, _1057624, _1057626, _1057628, _1057630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1057622), _1057624)), 16247 ^ _778908 : [(16254 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1057628), 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), _1057624), _1057622)), _1057626)), _1057630))), -(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), _1057622), _1057626)), _1057628)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057624), _1057626)), _1057630))))], (16248 ^ _778908) ^ [] : [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), _1057622), _1057626)), _1057628)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057624), _1057626)), _1057630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1057628), 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), _1057624), _1057622)), _1057626)), _1057630))))]]], (37458 ^ _778908) ^ [_1477661, _1477663, _1477665, _1477667, _1477669] : [class_Groups_Oab__group__add(_1477661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477663), _1477665)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477663), _1477667)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477663, _1477661), _1477669), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477663, tc_HOL_Obool)), _1477665), _1477667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1477661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1477661), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477663, _1477661), _1477669), _1477665)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477663, _1477661), _1477669), _1477667))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477663, _1477661), _1477669), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1477663, tc_HOL_Obool)), _1477665), _1477667))))], (37002 ^ _778908) ^ [_1467105, _1467107, _1467109] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467105, tc_HOL_Obool)), _1467107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467105, tc_HOL_Obool)), _1467109), _1467107)) = c_Orderings_Obot__class_Obot(tc_fun(_1467105, tc_HOL_Obool)))], (2698 ^ _778908) ^ [_819807, _819809] : [_819809 = _819807, -(c_Code__Numeral_OSuc__code__numeral(_819809) = c_Code__Numeral_OSuc__code__numeral(_819807))], (43664 ^ _778908) ^ [_1629916, _1629918, _1629920] : [c_Relation_Ototal__on(_1629916, _1629918, _1629920), -(c_Relation_Ototal__on(_1629916, _1629918, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1629916, _1629916), tc_HOL_Obool)), _1629920), c_Relation_OId(_1629916))))], (27747 ^ _778908) ^ [_1270884, _1270886, _1270888] : [class_Orderings_Olinorder(_1270884), 27750 ^ _778908 : [(27757 ^ _778908) ^ [] : [_1270886 = _1270888, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1270884), _1270886) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1270884), _1270888))], (27751 ^ _778908) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1270884), _1270886) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1270884), _1270888), -(_1270886 = _1270888)]]], (26419 ^ _778908) ^ [_1244276, _1244278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244278)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244276), _1244278)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244278), _1244276)), -(_1244276 = _1244278)], (37108 ^ _778908) ^ [_1469670, _1469672, _1469674, _1469676, _1469678] : [class_Orderings_Olinorder(_1469670), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469670, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1469670, _1469672, _1469674)), c_SetInterval_Oord__class_OatLeastAtMost(_1469670, _1469676, _1469678)) = c_SetInterval_Oord__class_OatLeastAtMost(_1469670, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1469670), _1469672), _1469676), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1469670), _1469674), _1469678)))], (46873 ^ _778908) ^ [_1706838, _1706840, _1706842] : [-(hBOOL(hAPP(hAPP(c_member(_1706838), _1706840), hAPP(c_List_Oset(_1706838), _1706842)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706838)), c_List_Oremove1(_1706838, _1706840, _1706842)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706838)), _1706842))], (30526 ^ _778908) ^ [_1325549, _1325551, _1325553, _1325555, _1325557] : [_1325549 = c_Orderings_Obot__class_Obot(tc_fun(_1325551, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1325551, tc_fun(_1325553, tc_HOL_Obool)), _1325549), hAPP(hAPP(c_COMBB(tc_fun(_1325553, tc_HOL_Obool), tc_fun(_1325553, tc_HOL_Obool), _1325551), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325553, tc_HOL_Obool)), _1325555)), _1325557)) = c_Orderings_Obot__class_Obot(tc_fun(_1325553, tc_HOL_Obool)))], (9122 ^ _778908) ^ [_931560, _931562, _931564, _931566, _931568] : [class_Rings_Ocomm__semiring__1(_931560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931560), _931562), _931564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931560), _931566), _931568)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931560), _931566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931560), _931562), _931564)), _931568)))], (49771 ^ _778908) ^ [_1778147, _1778149] : [-(_1778147 = c_List_Olist_ONil(_1778149)), hBOOL(hAPP(c_List_Odistinct(_1778149), _1778147)), -(hBOOL(hAPP(c_List_Odistinct(_1778149), c_List_Obutlast(_1778149, _1778147))))], (17957 ^ _778908) ^ [_1089541, _1089543] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089541)))), 17960 ^ _778908 : [(17967 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089543)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089541), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089543)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089541), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089543))))], (17961 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089543))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089541), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089543)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089541))]]], (14549 ^ _778908) ^ [_1025918, _1025920] : [class_Divides_Osemiring__div(_1025918), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025918), c_Groups_Ozero__class_Ozero(_1025918)), _1025920) = c_Groups_Ozero__class_Ozero(_1025918))], (34895 ^ _778908) ^ [_1418594, _1418596, _1418598, _1418600, _1418602, _1418604] : [-(hBOOL(hAPP(hAPP(c_member(_1418594), _1418596), _1418598))), -(c_Map_Orestrict__map(_1418594, _1418600, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418594, tc_Option_Ooption(_1418600)), _1418602), _1418596), _1418604), _1418598) = c_Map_Orestrict__map(_1418594, _1418600, _1418602, _1418598))], (49255 ^ _778908) ^ [_1766728, _1766730, _1766732] : [-(hAPP(c_List_Otl(_1766728), hAPP(hAPP(c_List_Otake(_1766728), _1766730), _1766732)) = hAPP(hAPP(c_List_Otake(_1766728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1766730), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1766728), _1766732)))], (45123 ^ _778908) ^ [_1665458] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1665458, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1665458, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1665458, tc_HOL_Obool)))], (8628 ^ _778908) ^ [_923359, _923361, _923363] : [class_Orderings_Olinorder(_923359), 8631 ^ _778908 : [(8632 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923359), _923361), _923363))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923359), _923363), _923361))), -(_923361 = _923363)], (8642 ^ _778908) ^ [] : [8643 ^ _778908 : [(8646 ^ _778908) ^ [] : [_923361 = _923363], (8644 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923359), _923363), _923361))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923359), _923361), _923363))]]], (24347 ^ _778908) ^ [_1204499, _1204501, _1204503] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1204499, _1204501), _1204503))), _1204499 = 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), _1204503)), _1204501)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1204503)), 24354 ^ _778908 : [(24357 ^ _778908) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1204503) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24355 ^ _778908) ^ [] : [-(_1204501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 24358 ^ _778908 : [(24361 ^ _778908) ^ [] : [24362 ^ _778908 : [(24365 ^ _778908) ^ [] : [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), _1204503))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1204503)), _1204501))], (24363 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204501)))]], 24370 ^ _778908 : [(24373 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204501), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1204503))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1204503)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24371 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204501))]]], (24359 ^ _778908) ^ [] : [_1204501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (9358 ^ _778908) ^ [_935314, _935316, _935318] : [class_Groups_Oordered__ab__group__add(_935314), 9361 ^ _778908 : [(9368 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935314), _935318), hAPP(c_Groups_Ouminus__class_Ouminus(_935314), _935316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935314), _935316), hAPP(c_Groups_Ouminus__class_Ouminus(_935314), _935318))))], (9362 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935314), _935316), hAPP(c_Groups_Ouminus__class_Ouminus(_935314), _935318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935314), _935318), hAPP(c_Groups_Ouminus__class_Ouminus(_935314), _935316))))]]], (40881 ^ _778908) ^ [_1555326, _1555328, _1555330] : [class_Groups_Oab__semigroup__mult(_1555326), -(_1555328 = c_Orderings_Obot__class_Obot(tc_fun(_1555326, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555326), _1555328)), -(hBOOL(hAPP(hAPP(c_member(_1555326), _1555330), _1555328))), -(hAPP(c_Finite__Set_Ofold1(_1555326, c_Groups_Otimes__class_Otimes(_1555326)), hAPP(hAPP(c_Set_Oinsert(_1555326), _1555330), _1555328)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1555326), _1555330), hAPP(c_Finite__Set_Ofold1(_1555326, c_Groups_Otimes__class_Otimes(_1555326)), _1555328)))], (16635 ^ _778908) ^ [_1064837, _1064839, _1064841] : [class_Groups_Oordered__ab__group__add__abs(_1064837), -(hAPP(c_Groups_Oabs__class_Oabs(_1064837), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064837), _1064839), _1064841)) = hAPP(c_Groups_Oabs__class_Oabs(_1064837), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064837), _1064841), _1064839)))], (22271 ^ _778908) ^ [_1164903, _1164905] : [-(_1164903 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1164903, _1164905) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1164903), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1164905)))], (11951 ^ _778908) ^ [_979155, _979157, _979159] : [class_Rings_Oordered__ring(_979155), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979155), c_Groups_Ozero__class_Ozero(_979155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979155), _979157), _979159)))), 11956 ^ _778908 : [(11963 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979155), _979157), c_Groups_Ozero__class_Ozero(_979155))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979155), _979159), c_Groups_Ozero__class_Ozero(_979155)))], (11957 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979155), c_Groups_Ozero__class_Ozero(_979155)), _979157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979155), c_Groups_Ozero__class_Ozero(_979155)), _979159))]]], (26311 ^ _778908) ^ [_1242148, _1242150, _1242152, _1242154] : [class_Divides_Osemiring__div(_1242148), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242148), _1242150), _1242152)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242148), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242148), _1242152), _1242150)), _1242154) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242148), _1242152), _1242154)), _1242150))], (43875 ^ _778908) ^ [_1635330, _1635332, _1635334, _1635336, _1635338] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635330, _1635330)), hAPP(hAPP(c_Product__Type_OPair(_1635330, _1635330), _1635332), _1635334)), c_Transitive__Closure_Ortrancl(_1635330, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1635330, _1635330), tc_HOL_Obool)), _1635336), _1635338)))), 43881 ^ _778908 : [(43887 ^ _778908) ^ [] : [43883 ^ [_1635330, _1635332, _1635334, _1635336, _1635338] = 43880 ^ [_1635330, _1635332, _1635334, _1635336, _1635338]], (43885 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635330, _1635330)), hAPP(hAPP(c_Product__Type_OPair(_1635330, _1635330), 43883 ^ [_1635330, _1635332, _1635334, _1635336, _1635338]), 43880 ^ [_1635330, _1635332, _1635334, _1635336, _1635338])), _1635338)))], (43882 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635330, _1635330)), hAPP(hAPP(c_Product__Type_OPair(_1635330, _1635330), 43880 ^ [_1635330, _1635332, _1635334, _1635336, _1635338]), _1635334)), c_Transitive__Closure_Ortrancl(_1635330, _1635336))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635330, _1635330)), hAPP(hAPP(c_Product__Type_OPair(_1635330, _1635330), _1635332), _1635334)), c_Transitive__Closure_Ortrancl(_1635330, _1635336))))], (34500 ^ _778908) ^ [_1410077, _1410079, _1410081] : [class_Groups_Ocomm__monoid__mult(_1410077), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410079, _1410077), _1410081), c_Orderings_Obot__class_Obot(tc_fun(_1410079, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1410077))], (48999 ^ _778908) ^ [_1761244, _1761246, _1761248, _1761250] : [_1761244 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1761246), _1761244), hAPP(hAPP(c_List_Olist_OCons(_1761246), _1761248), _1761250)) = hAPP(hAPP(c_List_Olist_OCons(_1761246), _1761248), _1761250))], (44885 ^ _778908) ^ [_1659275, _1659277, _1659279, _1659281, _1659283, _1659285, _1659287] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659275, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659277, tc_fun(_1659275, tc_HOL_Obool)), _1659279), _1659281)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659283, tc_fun(_1659275, tc_HOL_Obool)), _1659285), _1659287)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659277, tc_fun(_1659275, tc_HOL_Obool)), _1659279), hAPP(hAPP(c_COMBB(tc_fun(_1659283, tc_fun(_1659275, tc_HOL_Obool)), tc_fun(_1659275, tc_HOL_Obool), _1659277), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659283, tc_fun(_1659275, tc_HOL_Obool)), _1659285)), hAPP(hAPP(c_COMBC(_1659277, tc_fun(_1659283, tc_fun(_1659275, tc_HOL_Obool)), tc_fun(_1659283, tc_fun(_1659275, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1659275, tc_HOL_Obool), tc_fun(_1659275, tc_HOL_Obool)), tc_fun(tc_fun(_1659283, tc_fun(_1659275, tc_HOL_Obool)), tc_fun(_1659283, tc_fun(_1659275, tc_HOL_Obool))), _1659277), c_COMBB(tc_fun(_1659275, tc_HOL_Obool), tc_fun(_1659275, tc_HOL_Obool), _1659283)), hAPP(hAPP(c_COMBB(tc_fun(_1659275, tc_HOL_Obool), tc_fun(tc_fun(_1659275, tc_HOL_Obool), tc_fun(_1659275, tc_HOL_Obool)), _1659277), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659275, tc_HOL_Obool))), _1659281))), _1659287))))], (41523 ^ _778908) ^ [_1572958, _1572960, _1572962] : [class_Groups_Olinordered__ab__semigroup__add(_1572958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572958), _1572960)), -(_1572960 = c_Orderings_Obot__class_Obot(tc_fun(_1572958, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1572958), _1572962), c_Big__Operators_Olinorder__class_OMin(_1572958, _1572960)) = c_Big__Operators_Olinorder__class_OMin(_1572958, hAPP(c_Set_OCollect(_1572958), hAPP(hAPP(c_COMBB(tc_fun(_1572958, tc_HOL_Obool), tc_HOL_Obool, _1572958), c_HOL_OEx(_1572958)), hAPP(hAPP(c_COMBC(_1572958, tc_fun(_1572958, tc_HOL_Obool), tc_fun(_1572958, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572958, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1572958, tc_HOL_Obool), tc_fun(_1572958, tc_HOL_Obool)), _1572958), c_COMBS(_1572958, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572958, tc_HOL_Obool), tc_fun(_1572958, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1572958), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572958), c_fconj)), hAPP(hAPP(c_COMBC(_1572958, tc_fun(_1572958, _1572958), tc_fun(_1572958, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572958, tc_HOL_Obool), tc_fun(tc_fun(_1572958, _1572958), tc_fun(_1572958, tc_HOL_Obool)), _1572958), c_COMBB(_1572958, tc_HOL_Obool, _1572958)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1572958), _1572962))))), hAPP(hAPP(c_COMBC(_1572958, tc_fun(_1572958, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572958)), _1572960))))))], (49362 ^ _778908) ^ [_1768975, _1768977] : [class_Complete__Lattice_Ocomplete__lattice(_1768975), -(c_Complete__Lattice_OSup__class_OSup(_1768975, hAPP(c_List_Oset(_1768975), _1768977)) = hAPP(c_List_Ofoldl(_1768975, _1768975, c_Lattices_Osemilattice__sup__class_Osup(_1768975), c_Orderings_Obot__class_Obot(_1768975)), _1768977))], (2016 ^ _778908) ^ [_808798, _808800] : [_808800 = _808798, -(c_Com_Ovname_Ovname__size(_808800) = c_Com_Ovname_Ovname__size(_808798))], (1062 ^ _778908) ^ [_795057, _795059] : [-(class_Rings_Oring__1__no__zero__divisors(_795057)), _795059 = _795057, class_Rings_Oring__1__no__zero__divisors(_795059)], (23881 ^ _778908) ^ [_1195159, _1195161, _1195163] : [class_Orderings_Olinorder(_1195159), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195159), _1195161), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195159), _1195161), _1195163)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195159), _1195161), _1195163))], (47176 ^ _778908) ^ [_1716597, _1716599, _1716601] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716597)), c_List_Osublist(_1716597, _1716599, _1716601)) = 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(_1716597)), _1716599)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1716601)))))], (20353 ^ _778908) ^ [_1130247, _1130249, _1130251] : [class_Fields_Olinordered__field__inverse__zero(_1130247), 20356 ^ _778908 : [(20371 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130247), _1130249), _1130251)), c_Groups_Ozero__class_Ozero(_1130247)))), 20372 ^ _778908 : [(20379 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), _1130249), c_Groups_Ozero__class_Ozero(_1130247))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), c_Groups_Ozero__class_Ozero(_1130247)), _1130251))], (20373 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), c_Groups_Ozero__class_Ozero(_1130247)), _1130249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), _1130251), c_Groups_Ozero__class_Ozero(_1130247)))]]], (20357 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130247), _1130249), _1130251)), c_Groups_Ozero__class_Ozero(_1130247))), 20362 ^ _778908 : [(20365 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), _1130251), c_Groups_Ozero__class_Ozero(_1130247))))], (20363 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), c_Groups_Ozero__class_Ozero(_1130247)), _1130249)))]], 20366 ^ _778908 : [(20369 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), c_Groups_Ozero__class_Ozero(_1130247)), _1130251)))], (20367 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130247), _1130249), c_Groups_Ozero__class_Ozero(_1130247))))]]]]], (16136 ^ _778908) ^ [_1055359, _1055361, _1055363] : [hBOOL(hAPP(_1055359, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055361), _1055363))), 16139 ^ _778908 : [(16146 ^ _778908) ^ [_1055544] : [_1055361 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1055363), _1055544), -(hBOOL(hAPP(_1055359, _1055544)))], (16140 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1055361), _1055363)), -(hBOOL(hAPP(_1055359, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (5632 ^ _778908) ^ [_865876, _865878, _865880, _865882, _865884, _865886] : [-(c_List_OtakeWhile(_865886, _865882, _865878) = c_List_OtakeWhile(_865884, _865880, _865876)), _865886 = _865884, _865882 = _865880, _865878 = _865876], (29686 ^ _778908) ^ [_1309916, _1309918, _1309920] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309916, tc_HOL_Obool)), _1309918), _1309920))), 29689 ^ _778908 : [(29692 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309916), _1309920)))], (29690 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309916), _1309918)))]]], (51243 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (19387 ^ _778908) ^ [_1112795] : [c_Int_OBit0(_1112795) = c_Int_OMin], (15388 ^ _778908) ^ [_1040617, _1040619, _1040621] : [class_Rings_Oring__1(_1040617), -(hAPP(c_Int_Oring__1__class_Oof__int(_1040617), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040619), _1040621)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040617), hAPP(c_Int_Oring__1__class_Oof__int(_1040617), _1040619)), hAPP(c_Int_Oring__1__class_Oof__int(_1040617), _1040621)))], (25779 ^ _778908) ^ [_1231693, _1231695] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231693)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231695))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231693), _1231695)))], (832 ^ _778908) ^ [_791662, _791664, _791666, _791668, _791670, _791672, _791674, _791676, _791678, _791680, _791682, _791684] : [-(c_Finite__Set_Ofolding__image__simple__idem(_791682, _791678, _791674, _791670, _791666, _791662)), c_Finite__Set_Ofolding__image__simple__idem(_791684, _791680, _791676, _791672, _791668, _791664), _791684 = _791682, _791680 = _791678, _791676 = _791674, _791672 = _791670, _791668 = _791666, _791664 = _791662], (17405 ^ _778908) ^ [_1079648, _1079650] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079648)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079650)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1079648), _1079650)))], (12541 ^ _778908) ^ [_989778] : [-(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), _989778))))], (25545 ^ _778908) ^ [_1227830, _1227832] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227830), _1227832)), -(_1227830 = _1227832), 25552 ^ _778908 : [(25555 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227832), _1227830))], (25553 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227830), _1227832)))]]], (35805 ^ _778908) ^ [_1439870, _1439872, _1439874, _1439876] : [-(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), _1439870), _1439872)), 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), _1439874), _1439876)), 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), _1439870), _1439874)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439872), _1439876))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439870), _1439876)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439872), _1439874)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (12850 ^ _778908) ^ [_995168, _995170, _995172, _995174] : [class_Rings_Olinordered__semiring__strict(_995168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995168), _995170), _995172)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995168), _995174), _995172))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995168), c_Groups_Ozero__class_Ozero(_995168)), _995172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995168), _995170), _995174)))], (6879 ^ _778908) ^ [_892221, _892223, _892225, _892227, _892229, _892231, _892233, _892235, _892237, _892239, _892241] : [-(c_Com_Ocom_Ocom__rec(_892221, _892223, _892225, _892227, _892229, _892231, _892233, _892235, _892237, c_Com_Ocom_OWhile(_892239, _892241)) = hAPP(hAPP(hAPP(_892233, _892239), _892241), c_Com_Ocom_Ocom__rec(_892221, _892223, _892225, _892227, _892229, _892231, _892233, _892235, _892237, _892241)))], (17111 ^ _778908) ^ [_1073969, _1073971] : [class_Int_Onumber__ring(_1073969), -(hAPP(c_Int_Onumber__class_Onumber__of(_1073969), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1073971)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1073969), hAPP(c_Int_Onumber__class_Onumber__of(_1073969), _1073971)))], (49097 ^ _778908) ^ [_1763774, _1763776, _1763778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763774), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763776)), _1763778))), -(_1763778 = hAPP(hAPP(c_List_Oappend(_1763776), hAPP(hAPP(c_List_Otake(_1763776), _1763774), _1763778)), hAPP(hAPP(c_List_Olist_OCons(_1763776), hAPP(hAPP(c_List_Onth(_1763776), _1763778), _1763774)), hAPP(hAPP(c_List_Odrop(_1763776), hAPP(c_Nat_OSuc, _1763774)), _1763778))))], (10926 ^ _778908) ^ [_962271, _962273, _962275] : [class_Orderings_Olinorder(_962271), 10929 ^ _778908 : [(10936 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962271), _962275), _962273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962271), _962273), _962275))], (10930 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962271), _962273), _962275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962271), _962275), _962273)))]]], (51399 ^ _778908) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (6240 ^ _778908) ^ [_879327, _879329, _879331, _879333, _879335] : [c_Com_Ocom_OSemi(_879327, _879329) = c_Com_Ocom_OLocal(_879331, _879333, _879335)], (14583 ^ _778908) ^ [_1026513] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026513), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1026513)], (33401 ^ _778908) ^ [_1388551, _1388553] : [class_Groups_Olinordered__ab__group__add(_1388551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388551), _1388553)), -(_1388553 = c_Orderings_Obot__class_Obot(tc_fun(_1388551, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1388551), c_Big__Operators_Olinorder__class_OMax(_1388551, _1388553)) = c_Big__Operators_Olinorder__class_OMin(_1388551, hAPP(c_Set_Oimage(_1388551, _1388551, c_Groups_Ouminus__class_Ouminus(_1388551)), _1388553)))], (36510 ^ _778908) ^ [_1455881, _1455883, _1455885, _1455887, _1455889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455881, tc_HOL_Obool)), _1455883), _1455885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455881, tc_HOL_Obool)), _1455887), _1455889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455881, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455881, tc_HOL_Obool)), _1455883), _1455887)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455881, tc_HOL_Obool)), _1455885), _1455889))))], (24055 ^ _778908) ^ [_1198629, _1198631] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1198629), _1198631) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1198629, _1198631)))], (33163 ^ _778908) ^ [_1384117, _1384119] : [class_Rings_Oring__1(_1384117), -(hBOOL(hAPP(hAPP(c_member(_1384117), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1384117), _1384119)), c_Int_Oring__1__class_OInts(_1384117))))], (18421 ^ _778908) ^ [_1096928] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096928), 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), _1096928)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1096928)))], (28311 ^ _778908) ^ [_1281645, _1281647, _1281649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281645, tc_HOL_Obool)), _1281647), _1281649)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281645, tc_HOL_Obool)), _1281647), _1281649) = _1281649)], (42772 ^ _778908) ^ [_1607801, _1607803, _1607805] : [-(c_Hilbert__Choice_OEps(tc_prod(_1607801, _1607803), _1607805) = c_Hilbert__Choice_OEps(tc_prod(_1607801, _1607803), hAPP(c_Product__Type_Oprod_Oprod__case(_1607801, _1607803, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1607803, tc_prod(_1607801, _1607803)), tc_fun(_1607803, tc_HOL_Obool), _1607801), hAPP(c_COMBB(tc_prod(_1607801, _1607803), tc_HOL_Obool, _1607803), _1607805)), c_Product__Type_OPair(_1607801, _1607803)))))], (51377 ^ _778908) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (51433 ^ _778908) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (10102 ^ _778908) ^ [_948690] : [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)), _948690)), _948690) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (48917 ^ _778908) ^ [_1759377, _1759379, _1759381, _1759383, _1759385] : [-(hAPP(hAPP(c_List_Odrop(_1759377), _1759379), hAPP(hAPP(c_List_Omap(_1759381, _1759377), _1759383), _1759385)) = hAPP(hAPP(c_List_Omap(_1759381, _1759377), _1759383), hAPP(hAPP(c_List_Odrop(_1759381), _1759379), _1759385)))], (2688 ^ _778908) ^ [_819658, _819660, _819662, _819664] : [-(c_Orderings_Oord_Omax(_819664, _819660) = c_Orderings_Oord_Omax(_819662, _819658)), _819664 = _819662, _819660 = _819658], (8466 ^ _778908) ^ [_920952, _920954] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920952)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920954)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920952), _920954)))], (37784 ^ _778908) ^ [_1484323, _1484325, _1484327, _1484329, _1484331, _1484333] : [c_Equiv__Relations_Ocongruent(_1484323, _1484325, _1484327, _1484329), hBOOL(hAPP(hAPP(c_member(tc_prod(_1484323, _1484323)), hAPP(hAPP(c_Product__Type_OPair(_1484323, _1484323), _1484331), _1484333)), _1484327)), -(hAPP(_1484329, _1484331) = hAPP(_1484329, _1484333))], (25139 ^ _778908) ^ [_1220745, _1220747, _1220749, _1220751] : [-(c_HOL_OThe(tc_prod(_1220745, _1220747), hAPP(c_Product__Type_Oprod_Oprod__case(_1220745, _1220747, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1220745, tc_fun(_1220747, tc_HOL_Obool), tc_fun(_1220747, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1220747, tc_HOL_Obool), tc_fun(_1220747, tc_HOL_Obool)), _1220745), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1220747)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1220745), c_fconj), hAPP(c_fequal, _1220749)))), hAPP(c_fequal, _1220751)))) = hAPP(hAPP(c_Product__Type_OPair(_1220745, _1220747), _1220749), _1220751))], (50200 ^ _778908) ^ [_1787866, _1787868] : [50201 ^ _778908 : [(50204 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1787868), _1787866))], (50202 ^ _778908) ^ [] : [_1787868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1787866, _1787868) = c_List_Olist_ONil(tc_Nat_Onat))], (12085 ^ _778908) ^ [_981722, _981724, _981726] : [class_Rings_Oordered__ring(_981722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981722), _981724), c_Groups_Ozero__class_Ozero(_981722))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981722), _981726), c_Groups_Ozero__class_Ozero(_981722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981722), c_Groups_Ozero__class_Ozero(_981722)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981722), _981724), _981726))))], (8152 ^ _778908) ^ [_915314, _915316, _915318, _915320, _915322, _915324] : [-(c_Nitpick_Opair__box_Opair__box__rec(_915314, _915316, _915318, _915320, c_Nitpick_Opair__box_OPairBox(_915314, _915316, _915322, _915324)) = hAPP(hAPP(_915320, _915322), _915324))], (22638 ^ _778908) ^ [_1171717, _1171719] : [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), _1171717))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171719), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1171717))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171719), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1171717))), 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), _1171719))), c_COMBI(tc_Int_Oint))))], (26119 ^ _778908) ^ [_1238515, _1238517, _1238519, _1238521] : [class_Groups_Oab__group__add(_1238515), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238517, _1238515), hAPP(hAPP(c_COMBB(_1238515, _1238515, _1238517), c_Groups_Ouminus__class_Ouminus(_1238515)), _1238519)), _1238521) = hAPP(c_Groups_Ouminus__class_Ouminus(_1238515), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238517, _1238515), _1238519), _1238521)))], (51211 ^ _778908) ^ [_1809145, _1809147] : [class_Orderings_Obot(_1809145), -(class_Orderings_Obot(tc_fun(_1809147, _1809145)))], (13987 ^ _778908) ^ [_1015497, _1015499, _1015501, _1015503] : [class_Divides_Osemiring__div(_1015497), -(c_Divides_Odiv__class_Omod(_1015497, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015497), _1015499), _1015501), _1015503) = c_Divides_Odiv__class_Omod(_1015497, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015497), c_Divides_Odiv__class_Omod(_1015497, _1015499, _1015503)), _1015501), _1015503))], (45570 ^ _778908) ^ [_1675736, _1675738, _1675740] : [45572 ^ _778908 : [(45575 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1675736, tc_HOL_Obool)), 45571 ^ [_1675736, _1675738, _1675740]), _1675740))], (45573 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1675736, tc_HOL_Obool)), 45571 ^ [_1675736, _1675738, _1675740]), _1675738)))]], -(_1675738 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1675736, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1675736, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1675736, tc_HOL_Obool), _1675738)), _1675740)))], (43534 ^ _778908) ^ [_1626517, _1626519, _1626521, _1626523] : [-(hAPP(c_Relation_Oconverse(_1626517, _1626517), hAPP(hAPP(c_Relation_Oinv__image(_1626519, _1626517), _1626521), _1626523)) = hAPP(hAPP(c_Relation_Oinv__image(_1626519, _1626517), hAPP(c_Relation_Oconverse(_1626519, _1626519), _1626521)), _1626523))], (3028 ^ _778908) ^ [_825228, _825230, _825232, _825234, _825236, _825238, _825240, _825242] : [-(c_Lazy__Sequence_Obind(_825242, _825238, _825234, _825230) = c_Lazy__Sequence_Obind(_825240, _825236, _825232, _825228)), _825242 = _825240, _825238 = _825236, _825234 = _825232, _825230 = _825228], (11420 ^ _778908) ^ [_970012, _970014, _970016] : [class_Groups_Oordered__ab__group__add(_970012), 11423 ^ _778908 : [(11430 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970012), hAPP(c_Groups_Ouminus__class_Ouminus(_970012), _970016)), _970014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970012), hAPP(c_Groups_Ouminus__class_Ouminus(_970012), _970014)), _970016)))], (11424 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970012), hAPP(c_Groups_Ouminus__class_Ouminus(_970012), _970014)), _970016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970012), hAPP(c_Groups_Ouminus__class_Ouminus(_970012), _970016)), _970014)))]]], (5622 ^ _778908) ^ [_865727, _865729, _865731, _865733] : [-(c_List_Omap(_865733, _865729) = c_List_Omap(_865731, _865727)), _865733 = _865731, _865729 = _865727], (3982 ^ _778908) ^ [_840337, _840339] : [_840339 = _840337, -(tc_Hoare__Mirabelle_Otriple(_840339) = tc_Hoare__Mirabelle_Otriple(_840337))], (48180 ^ _778908) ^ [_1740258, _1740260, _1740262, _1740264] : [-(hAPP(hAPP(c_List_Oappend(_1740258), hAPP(hAPP(c_List_Oappend(_1740258), _1740260), _1740262)), _1740264) = hAPP(hAPP(c_List_Oappend(_1740258), _1740260), hAPP(hAPP(c_List_Oappend(_1740258), _1740262), _1740264)))], (25495 ^ _778908) ^ [_1227063, _1227065, _1227067] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227063), _1227065)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227065), _1227067)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227063), _1227067)))], (29207 ^ _778908) ^ [_1300829, _1300831] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1300829), _1300831))))], (30878 ^ _778908) ^ [_1332909, _1332911, _1332913, _1332915] : [30879 ^ _778908 : [(30882 ^ _778908) ^ [] : [_1332911 = _1332915], (30880 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332909), _1332911), _1332913))]], -(hBOOL(hAPP(hAPP(c_member(_1332909), _1332911), hAPP(hAPP(c_Set_Oinsert(_1332909), _1332915), _1332913))))], (23917 ^ _778908) ^ [_1195981, _1195983, _1195985, _1195987] : [class_Orderings_Olinorder(_1195981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195981), _1195983), _1195985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195981), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195981), _1195987), _1195983)), _1195985)))], (50023 ^ _778908) ^ [_1783834, _1783836, _1783838] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783834)), hAPP(c_List_Ofilter(_1783834, _1783836), _1783838)) = 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(_1783834)), _1783838)))), hAPP(hAPP(c_COMBB(_1783834, tc_HOL_Obool, tc_Nat_Onat), _1783836), hAPP(c_List_Onth(_1783834), _1783838))))))], (47212 ^ _778908) ^ [_1717376, _1717378, _1717380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1717376), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1717378), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1717378)), _1717380)))), -(hBOOL(hAPP(hAPP(c_member(_1717378), hAPP(c_Random_Opick(_1717378, _1717380), _1717376)), hAPP(c_List_Oset(_1717378), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1717378), _1717378), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1717378)), _1717380)))))], (51467 ^ _778908) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (36804 ^ _778908) ^ [_1462497, _1462499, _1462501] : [class_Lattices_Osemilattice__inf(_1462497), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462497), _1462499), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462497), _1462499), _1462501)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462497), _1462499), _1462501))], (5774 ^ _778908) ^ [_870902, _870904] : [hAPP(_870902, 5775 ^ [_870902, _870904]) = hAPP(_870904, 5775 ^ [_870902, _870904]), -(_870902 = _870904)], (24955 ^ _778908) ^ [_1216328, _1216330, _1216332, _1216334] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1216328, _1216330, _1216332, tc_prod(_1216330, _1216332)), _1216334), c_Product__Type_OPair(_1216330, _1216332)) = _1216334)], (29720 ^ _778908) ^ [_1310522, _1310524, _1310526, _1310528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310522), _1310524)), 29723 ^ _778908 : [(29724 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310526), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310522, tc_fun(_1310526, tc_HOL_Obool)), _1310524), _1310528))), 29727 ^ _778908 : [(29728 ^ _778908) ^ [_1310706] : [hBOOL(hAPP(hAPP(c_member(_1310522), _1310706), _1310524)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310526), hAPP(_1310528, _1310706))))]]], (29734 ^ _778908) ^ [] : [29736 ^ _778908 : [(29739 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1310526), hAPP(_1310528, 29735 ^ [_1310522, _1310524, _1310526, _1310528])))], (29737 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1310522), 29735 ^ [_1310522, _1310524, _1310526, _1310528]), _1310524)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1310526), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310522, tc_fun(_1310526, tc_HOL_Obool)), _1310524), _1310528))))]]], (51577 ^ _778908) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (48140 ^ _778908) ^ [_1739225, _1739227, _1739229, _1739231, _1739233, _1739235, _1739237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1739225, _1739225)), hAPP(hAPP(c_Product__Type_OPair(_1739225, _1739225), _1739227), _1739229)), _1739231)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1739225), tc_List_Olist(_1739225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1739225), tc_List_Olist(_1739225)), hAPP(hAPP(c_List_Oappend(_1739225), _1739233), hAPP(hAPP(c_List_Olist_OCons(_1739225), _1739227), _1739235))), hAPP(hAPP(c_List_Oappend(_1739225), _1739233), hAPP(hAPP(c_List_Olist_OCons(_1739225), _1739229), _1739237)))), c_List_Olexord(_1739225, _1739231))))], (44124 ^ _778908) ^ [_1641560, _1641562, _1641564, _1641566, _1641568, _1641570] : [c_Finite__Set_Ofun__left__comm__idem(_1641560, _1641562, _1641564), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641560), _1641566)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1641560, _1641562, _1641564), _1641568), hAPP(hAPP(c_Set_Oinsert(_1641560), _1641570), _1641566)) = hAPP(hAPP(_1641564, _1641570), hAPP(hAPP(c_Finite__Set_Ofold(_1641560, _1641562, _1641564), _1641568), _1641566)))], (12391 ^ _778908) ^ [_987107, _987109, _987111] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987107), _987109)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987111), _987109)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987107), _987111))], (18293 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (51481 ^ _778908) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (50190 ^ _778908) ^ [_1787764, _1787766] : [c_List_Oupt(_1787764, _1787766) = c_List_Olist_ONil(tc_Nat_Onat), -(_1787766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1787766), _1787764)))], (6097 ^ _778908) ^ [_876585, _876587, _876589, _876591, _876593] : [-(hBOOL(hAPP(_876585, _876587))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_876589), _876587), _876591)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_876585, _876593, _876589)), _876587), _876591)))], (17875 ^ _778908) ^ [_1088081, _1088083, _1088085] : [class_Rings_Oring__1(_1088081), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1088081), hAPP(c_Groups_Ouminus__class_Ouminus(_1088081), _1088083)), _1088085) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088081), hAPP(hAPP(c_Power_Opower__class_Opower(_1088081), hAPP(c_Groups_Ouminus__class_Ouminus(_1088081), c_Groups_Oone__class_Oone(_1088081))), _1088085)), hAPP(hAPP(c_Power_Opower__class_Opower(_1088081), _1088083), _1088085)))], (15598 ^ _778908) ^ [_1044416, _1044418] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1044416), _1044418))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044416, _1044418) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044416), _1044418), _1044418))], (25255 ^ _778908) ^ [_1223022, _1223024, _1223026, _1223028] : [class_Groups_Oordered__ab__group__add__abs(_1223022), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223022), c_Groups_Ozero__class_Ozero(_1223022)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223024, _1223022), hAPP(hAPP(c_COMBB(_1223022, _1223022, _1223024), c_Groups_Oabs__class_Oabs(_1223022)), _1223026)), _1223028))))], (39846 ^ _778908) ^ [_1530422, _1530424, _1530426, _1530428] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530422, _1530424, _1530426, _1530428, c_Orderings_Obot__class_Obot(tc_fun(_1530422, tc_HOL_Obool))), _1530428)))], (12141 ^ _778908) ^ [_982742, _982744, _982746] : [class_Rings_Oordered__cancel__semiring(_982742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982742), c_Groups_Ozero__class_Ozero(_982742)), _982744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982742), c_Groups_Ozero__class_Ozero(_982742)), _982746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982742), c_Groups_Ozero__class_Ozero(_982742)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982742), _982744), _982746))))], (37610 ^ _778908) ^ [_1480761, _1480763, _1480765] : [class_Orderings_Olinorder(_1480761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480761), _1480763)), -(_1480763 = c_Orderings_Obot__class_Obot(tc_fun(_1480761, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480761), _1480765)), -(_1480765 = c_Orderings_Obot__class_Obot(tc_fun(_1480761, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480761, tc_HOL_Obool)), _1480763), _1480765) = c_Orderings_Obot__class_Obot(tc_fun(_1480761, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1480761, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480761, tc_HOL_Obool)), _1480763), _1480765)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1480761), c_Big__Operators_Olinorder__class_OMax(_1480761, _1480763)), c_Big__Operators_Olinorder__class_OMax(_1480761, _1480765)))], (38572 ^ _778908) ^ [_1502241, _1502243, _1502245, _1502247] : [c_Fun_Oinj__on(_1502241, _1502243, _1502245, _1502247), -(hAPP(c_Finite__Set_Ocard(_1502243), hAPP(c_Set_Oimage(_1502241, _1502243, _1502245), _1502247)) = hAPP(c_Finite__Set_Ocard(_1502241), _1502247))], (29140 ^ _778908) ^ [_1299067, _1299069] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1299067, tc_HOL_Obool)), _1299069) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1299067, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1299067, tc_HOL_Obool))), _1299069))], (28084 ^ _778908) ^ [_1276914, _1276916, _1276918, _1276920] : [28088 ^ _778908 : [(28091 ^ _778908) ^ [] : [hBOOL(hAPP(_1276920, 28087 ^ [_1276914, _1276916, _1276918, _1276920]))], (28089 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276914), 28087 ^ [_1276914, _1276916, _1276918, _1276920]), _1276916)))]], 28093 ^ _778908 : [(28096 ^ _778908) ^ [] : [hBOOL(hAPP(_1276920, 28092 ^ [_1276914, _1276916, _1276918, _1276920]))], (28094 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276914), 28092 ^ [_1276914, _1276916, _1276918, _1276920]), _1276918)))]], 28097 ^ _778908 : [(28098 ^ _778908) ^ [_1277247] : [hBOOL(hAPP(hAPP(c_member(_1276914), _1277247), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276914, tc_HOL_Obool)), _1276916), _1276918))), -(hBOOL(hAPP(_1276920, _1277247)))]]], (3666 ^ _778908) ^ [_835303, _835305, _835307, _835309, _835311, _835313] : [-(c_Finite__Set_Ofold1Set(_835313, _835309, _835305) = c_Finite__Set_Ofold1Set(_835311, _835307, _835303)), _835313 = _835311, _835309 = _835307, _835305 = _835303], (7432 ^ _778908) ^ [_903153, _903155, _903157] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_903153), 7435 ^ _778908 : [(7442 ^ _778908) ^ [] : [_903157 = c_Groups_Ozero__class_Ozero(_903153), -(_903155 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903153), _903155), _903157))], (7436 ^ _778908) ^ [] : [_903155 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903153), _903155), _903157), -(_903157 = c_Groups_Ozero__class_Ozero(_903153))]]], (7426 ^ _778908) ^ [_903058, _903060] : [class_Rings_Ocomm__semiring__1(_903058), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903058), _903060), c_Groups_Ozero__class_Ozero(_903058)) = _903060)], (24925 ^ _778908) ^ [_1215700, _1215702, _1215704, _1215706, _1215708] : [_1215700 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1215702, _1215704, _1215700, _1215706), _1215708) = hAPP(c_Product__Type_OPair(_1215702, _1215704), _1215708))], (28902 ^ _778908) ^ [_1293105, _1293107] : [class_Groups_Oordered__ab__group__add(_1293105), -(hAPP(c_Set_Oimage(_1293105, _1293105, c_Groups_Ouminus__class_Ouminus(_1293105)), hAPP(c_SetInterval_Oord__class_OatLeast(_1293105), _1293107)) = hAPP(c_SetInterval_Oord__class_OatMost(_1293105), hAPP(c_Groups_Ouminus__class_Ouminus(_1293105), _1293107)))], (27364 ^ _778908) ^ [_1262726, _1262728, _1262730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262726)), 27367 ^ _778908 : [(27368 ^ _778908) ^ [_1262860] : [27370 ^ _778908 : [(27376 ^ _778908) ^ [] : [-(_1262860 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27372 ^ [_1262726, _1262728, _1262730, _1262860]), 27369 ^ [_1262726, _1262728, _1262730, _1262860]))], (27374 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27372 ^ [_1262726, _1262728, _1262730, _1262860]), _1262728)))], (27371 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27369 ^ [_1262726, _1262728, _1262730, _1262860]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1262726))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262730), _1262860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262730), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262860), _1262726))))]]], (8916 ^ _778908) ^ [_927675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _927675), 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)), _927675)), _927675)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33031 ^ _778908) ^ [_1380975, _1380977, _1380979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380975), tc_HOL_Obool)), _1380977), _1380979)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1380975, _1380979, _1380977))], (20207 ^ _778908) ^ [_1127557, _1127559, _1127561, _1127563] : [class_Rings_Odivision__ring(_1127557), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127557), _1127559), _1127561)), _1127563) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127557), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127557), _1127559), _1127563)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127557), _1127561), _1127563)))], (15980 ^ _778908) ^ [_1051762, _1051764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051762), _1051764)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051764), _1051762)), _1051762) = _1051764)], (38118 ^ _778908) ^ [_1493304, _1493306, _1493308] : [class_Lattices_Olattice(_1493304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493304), _1493306)), hBOOL(hAPP(hAPP(c_member(_1493304), _1493308), _1493306)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1493304), _1493308), c_Big__Operators_Olattice__class_OInf__fin(_1493304, _1493306)) = _1493308)], (30250 ^ _778908) ^ [_1320934, _1320936, _1320938] : [class_Orderings_Oorder(_1320934), 30253 ^ _778908 : [(30260 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320934), _1320936), _1320938))), -(c_Orderings_Obot__class_Obot(tc_fun(_1320934, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1320934, _1320936, _1320938))], (30254 ^ _778908) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1320934, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1320934, _1320936, _1320938), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320934), _1320936), _1320938))]]], (44923 ^ _778908) ^ [_1660799, _1660801, _1660803, _1660805, _1660807] : [_1660799 = c_Orderings_Obot__class_Obot(tc_fun(_1660801, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660801, tc_fun(_1660803, tc_HOL_Obool)), _1660799), hAPP(hAPP(c_COMBB(tc_fun(_1660803, tc_HOL_Obool), tc_fun(_1660803, tc_HOL_Obool), _1660801), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660803, tc_HOL_Obool)), _1660805)), _1660807)) = c_Orderings_Otop__class_Otop(tc_fun(_1660803, tc_HOL_Obool)))], (43239 ^ _778908) ^ [_1619538, _1619540] : [-(c_Transitive__Closure_Ortrancl(_1619538, c_Transitive__Closure_Ortrancl(_1619538, _1619540)) = c_Transitive__Closure_Ortrancl(_1619538, _1619540))], (17477 ^ _778908) ^ [_1080813, _1080815] : [_1080813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1080815), _1080813) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24731 ^ _778908) ^ [_1211785, _1211787] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1211785)), hAPP(c_Nat_OSuc, _1211787)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1211785), _1211787)))], (50457 ^ _778908) ^ [_1792254, _1792256, _1792258] : [class_Orderings_Olinorder(_1792254), c_List_Olinorder__class_Osorted(_1792254, _1792256), -(c_List_Olinorder__class_Osorted(_1792254, hAPP(hAPP(c_List_Otake(_1792254), _1792258), _1792256)))], (15320 ^ _778908) ^ [_1039319, _1039321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1039319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1039321)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1039319)), hAPP(c_Int_Onat, _1039321)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1039319, _1039321)))], (35348 ^ _778908) ^ [_1429281, _1429283, _1429285, _1429287, _1429289] : [class_Groups_Ocomm__monoid__add(_1429281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429283), _1429285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429283, tc_HOL_Obool)), _1429287), _1429285)), 35362 ^ _778908 : [(35365 ^ _778908) ^ [] : [hAPP(_1429289, 35361 ^ [_1429281, _1429283, _1429285, _1429287, _1429289]) = c_Groups_Ozero__class_Ozero(_1429281)], (35363 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429283), 35361 ^ [_1429281, _1429283, _1429285, _1429287, _1429289]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429283, tc_HOL_Obool)), _1429285), _1429287))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1429283, _1429281), _1429289), _1429285) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1429283, _1429281), _1429289), _1429287))], (14472 ^ _778908) ^ [_1024305, _1024307, _1024309] : [hBOOL(hAPP(_1024305, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1024307), _1024309))), 14477 ^ _778908 : [(14480 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1024305, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14478 ^ _778908) ^ [] : [-(_1024309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14482 ^ _778908 : [(14487 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1024305, 14481 ^ [_1024305, _1024307, _1024309])))], (14485 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1024307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024309), hAPP(c_Nat_OSuc, 14481 ^ [_1024305, _1024307, _1024309])))))], (14483 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024309), 14481 ^ [_1024305, _1024307, _1024309])), _1024307)))]]], (31075 ^ _778908) ^ [_1336800, _1336802, _1336804, _1336806, _1336808] : [-(hBOOL(hAPP(hAPP(c_member(_1336800), _1336802), hAPP(c_Set_Oimage(_1336804, _1336800, _1336806), _1336808)))), 31076 ^ _778908 : [(31077 ^ _778908) ^ [_1336870] : [hBOOL(hAPP(hAPP(c_member(_1336804), _1336870), _1336808)), _1336802 = hAPP(_1336806, _1336870)]]], (11500 ^ _778908) ^ [_971405, _971407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971405), _971407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971405), hAPP(c_Nat_OSuc, _971407))))], (18577 ^ _778908) ^ [_1099195, _1099197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099195), _1099197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1099195)), _1099197)))], (46461 ^ _778908) ^ [_1696443, _1696445] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1696443, _1696445)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1696443, _1696445))], (36300 ^ _778908) ^ [_1451989, _1451991, _1451993, _1451995, _1451997, _1451999] : [c_Equiv__Relations_Oequiv(_1451989, _1451991, _1451993), hBOOL(hAPP(hAPP(c_member(_1451989), _1451995), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451989, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1451989, _1451989, _1451993), hAPP(hAPP(c_Set_Oinsert(_1451989), _1451997), c_Orderings_Obot__class_Obot(tc_fun(_1451989, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1451989, _1451989, _1451993), hAPP(hAPP(c_Set_Oinsert(_1451989), _1451999), c_Orderings_Obot__class_Obot(tc_fun(_1451989, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451989, _1451989)), hAPP(hAPP(c_Product__Type_OPair(_1451989, _1451989), _1451997), _1451999)), _1451993)))], (46283 ^ _778908) ^ [_1692295, _1692297, _1692299, _1692301, _1692303] : [hAPP(hAPP(c_List_Omap(_1692295, _1692297), _1692299), _1692301) = hAPP(hAPP(c_List_Omap(_1692295, _1692297), _1692299), _1692303), c_Fun_Oinj__on(_1692295, _1692297, _1692299, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1692295, tc_HOL_Obool)), hAPP(c_List_Oset(_1692295), _1692301)), hAPP(c_List_Oset(_1692295), _1692303))), -(_1692301 = _1692303)], (29592 ^ _778908) ^ [_1308125, _1308127, _1308129] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308125), hAPP(hAPP(c_Set_Oinsert(_1308125), _1308127), _1308129))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308125), _1308129)))], (34563 ^ _778908) ^ [_1411099, _1411101, _1411103, _1411105, _1411107] : [class_Groups_Ocomm__monoid__mult(_1411099), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411101), _1411103)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411101, _1411099), hAPP(hAPP(c_COMBS(_1411101, _1411099, _1411099), hAPP(hAPP(c_COMBB(_1411099, tc_fun(_1411099, _1411099), _1411101), c_Groups_Otimes__class_Otimes(_1411099)), _1411105)), _1411107)), _1411103) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411099), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411101, _1411099), _1411105), _1411103)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1411101, _1411099), _1411107), _1411103)))], (36426 ^ _778908) ^ [_1454388, _1454390, _1454392, _1454394] : [class_Lattices_Osemilattice__inf(_1454388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454388), _1454390), _1454392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454388), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454388), _1454394), _1454390)), _1454392)))], (36702 ^ _778908) ^ [_1460274, _1460276] : [class_Lattices_Obounded__lattice__bot(_1460274), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1460274), _1460276), c_Orderings_Obot__class_Obot(_1460274)) = c_Orderings_Obot__class_Obot(_1460274))], (46968 ^ _778908) ^ [_1710707, _1710709, _1710711] : [-(hAPP(c_List_Olexn(_1710707, _1710709), hAPP(c_Nat_OSuc, _1710711)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1710707), tc_List_Olist(_1710707)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1710707, tc_List_Olist(_1710707)), tc_prod(_1710707, tc_List_Olist(_1710707))), tc_prod(tc_List_Olist(_1710707), tc_List_Olist(_1710707)), c_Product__Type_Omap__pair(tc_prod(_1710707, tc_List_Olist(_1710707)), tc_List_Olist(_1710707), tc_prod(_1710707, tc_List_Olist(_1710707)), tc_List_Olist(_1710707), hAPP(c_Product__Type_Oprod_Oprod__case(_1710707, tc_List_Olist(_1710707), tc_List_Olist(_1710707)), c_List_Olist_OCons(_1710707)), hAPP(c_Product__Type_Oprod_Oprod__case(_1710707, tc_List_Olist(_1710707), tc_List_Olist(_1710707)), c_List_Olist_OCons(_1710707)))), c_Wellfounded_Olex__prod(_1710707, tc_List_Olist(_1710707), _1710709, hAPP(c_List_Olexn(_1710707, _1710709), _1710711)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1710707), tc_List_Olist(_1710707))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1710707), tc_List_Olist(_1710707), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710707), tc_fun(tc_List_Olist(_1710707), tc_HOL_Obool), tc_fun(tc_List_Olist(_1710707), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1710707), tc_HOL_Obool), tc_fun(tc_List_Olist(_1710707), tc_HOL_Obool)), tc_List_Olist(_1710707)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1710707))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1710707)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710707), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1710707)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1710707)))), hAPP(c_Nat_OSuc, _1710711))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710707), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1710707)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1710707)))), hAPP(c_Nat_OSuc, _1710711)))))))], (7971 ^ _778908) ^ [_912131, _912133, _912135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912131), _912133)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912131), _912135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912133), _912135)))], (42519 ^ _778908) ^ [_1601244, _1601246, _1601248, _1601250] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1601244), _1601246))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1601248), hAPP(c_Set_Oimage(_1601244, _1601248, _1601250), _1601246))), 42527 ^ _778908 : [(42530 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1601244), hAPP(c_Set_OCollect(_1601244), hAPP(hAPP(c_COMBS(_1601244, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1601244), c_fconj), hAPP(hAPP(c_COMBC(_1601244, tc_fun(_1601244, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601244)), _1601246))), hAPP(hAPP(c_COMBC(_1601244, _1601248, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1601248, tc_fun(_1601248, tc_HOL_Obool), _1601244), c_fequal), _1601250)), hAPP(_1601250, 42526 ^ [_1601244, _1601246, _1601248, _1601250]))))))], (42528 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601244), 42526 ^ [_1601244, _1601246, _1601248, _1601250]), _1601246)))]]], (50624 ^ _778908) ^ [_1795400] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1795400) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1795400))))], (34843 ^ _778908) ^ [_1417494, _1417496, _1417498, _1417500, _1417502] : [-(hBOOL(hAPP(hAPP(c_member(_1417494), _1417496), _1417498))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1417494, tc_Option_Ooption(_1417500)), c_Map_Orestrict__map(_1417494, _1417500, _1417502, _1417498)), _1417496), c_Option_Ooption_ONone(_1417500)) = c_Map_Orestrict__map(_1417494, _1417500, _1417502, _1417498))], (7915 ^ _778908) ^ [_911134, _911136] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911134), _911136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911136), hAPP(c_Nat_OSuc, _911134))))], (51497 ^ _778908) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (24407 ^ _778908) ^ [_1205687, _1205689, _1205691, _1205693] : [class_Orderings_Olinorder(_1205687), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205687), _1205689), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205687), _1205691), _1205693)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205687), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205687), _1205689), _1205691)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205687), _1205689), _1205693)))], (46683 ^ _778908) ^ [_1701936, _1701938, _1701940, _1701942, _1701944] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1701936), tc_List_Olist(_1701936))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701936), tc_List_Olist(_1701936)), _1701938), _1701940)), hAPP(c_List_Olexn(_1701936, _1701942), _1701944))), 46686 ^ _778908 : [(46689 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701936)), _1701940) = _1701944)], (46687 ^ _778908) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701936)), _1701938) = _1701944)]]], (50747 ^ _778908) ^ [_1798311, _1798313, _1798315] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798311), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1798311))), _1798313))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1798315), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1798311))), _1798313))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1798311), _1798311), hAPP(hAPP(c_COMBC(tc_List_Olist(_1798311), tc_Nat_Onat, _1798311), c_List_Onth(_1798311)), _1798315)), hAPP(c_List_Ofilter(tc_List_Olist(_1798311), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1798311)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1798315)), c_Nat_Osize__class_Osize(tc_List_Olist(_1798311)))), c_List_Otranspose(_1798311, _1798313))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1798311)), _1798313), _1798315))], (41357 ^ _778908) ^ [_1566680, _1566682, _1566684, _1566686, _1566688] : [-(c_Map_Odom(_1566680, _1566682, c_Fun_Ooverride__on(_1566680, tc_Option_Ooption(_1566682), _1566684, _1566686, _1566688)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1566680, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1566680, tc_HOL_Obool)), c_Map_Odom(_1566680, _1566682, _1566684)), hAPP(c_Set_OCollect(_1566680), hAPP(hAPP(c_COMBC(_1566680, tc_fun(_1566680, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566680)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1566680, tc_HOL_Obool)), _1566688), c_Map_Odom(_1566680, _1566682, _1566686)))))), hAPP(c_Set_OCollect(_1566680), hAPP(hAPP(c_COMBC(_1566680, tc_fun(_1566680, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566680)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566680, tc_HOL_Obool)), _1566688), c_Map_Odom(_1566680, _1566682, _1566686))))))], (23653 ^ _778908) ^ [_1191043, _1191045, _1191047] : [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), _1191043), _1191045))), -(hBOOL(hAPP(hAPP(_1191047, _1191043), _1191045))), 23660 ^ _778908 : [(23663 ^ _778908) ^ [] : [-(23659 ^ [_1191043, _1191045, _1191047] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1191047, 23659 ^ [_1191043, _1191045, _1191047]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 23658 ^ [_1191043, _1191045, _1191047], 23659 ^ [_1191043, _1191045, _1191047]))))], (23669 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1191047, 23658 ^ [_1191043, _1191045, _1191047]), 23659 ^ [_1191043, _1191045, _1191047]))], (23661 ^ _778908) ^ [] : [-(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), 23658 ^ [_1191043, _1191045, _1191047]), 23659 ^ [_1191043, _1191045, _1191047]))))]]], (39562 ^ _778908) ^ [_1523544, _1523546, _1523548, _1523550] : [-(hAPP(c_Set_Oimage(_1523544, _1523546, _1523548), hAPP(c_Set_Ovimage(_1523544, _1523546, _1523548), _1523550)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523546, tc_HOL_Obool)), _1523550), hAPP(c_Set_Oimage(_1523544, _1523546, _1523548), c_Orderings_Otop__class_Otop(tc_fun(_1523544, tc_HOL_Obool)))))], (17473 ^ _778908) ^ [_1080712, _1080714] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1080712), _1080714)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1080712)), _1080714))], (50379 ^ _778908) ^ [_1791068, _1791070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1791068), _1791070)), -(c_List_Oupt(_1791068, _1791070) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1791068), c_List_Oupt(hAPP(c_Nat_OSuc, _1791068), _1791070)))], (24771 ^ _778908) ^ [_1212721, _1212723, _1212725, _1212727] : [class_Orderings_Olinorder(_1212721), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212721), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212721), _1212723), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212721), _1212725), _1212727))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1212721), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212721), _1212723), _1212725)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212721), _1212723), _1212727)))))], (11763 ^ _778908) ^ [_975883, _975885] : [class_Rings_Olinordered__idom(_975883), 11766 ^ _778908 : [(11773 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _975885), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975883), hAPP(c_Int_Oring__1__class_Oof__int(_975883), _975885)), c_Groups_Ozero__class_Ozero(_975883))))], (11767 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975883), hAPP(c_Int_Oring__1__class_Oof__int(_975883), _975885)), c_Groups_Ozero__class_Ozero(_975883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _975885), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (7468 ^ _778908) ^ [_903727, _903729, _903731, _903733] : [-(hAPP(c_Option_Ooption_Ooption__case(_903727, _903729, _903731, _903733), c_Option_Ooption_ONone(_903729)) = _903731)], (13216 ^ _778908) ^ [_1001626, _1001628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1001626), _1001628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1001628), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (5370 ^ _778908) ^ [_861937, _861939] : [_861939 = _861937, -(c_List_Ohd(_861939) = c_List_Ohd(_861937))], (49889 ^ _778908) ^ [_1780585, _1780587, _1780589] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1780585, tc_HOL_Obool)), hAPP(c_List_Oset(_1780585), hAPP(c_List_Ofilter(_1780585, _1780587), _1780589))), hAPP(c_List_Oset(_1780585), _1780589))))], (1492 ^ _778908) ^ [_800432, _800434] : [-(class_Groups_Ocancel__ab__semigroup__add(_800432)), _800434 = _800432, class_Groups_Ocancel__ab__semigroup__add(_800434)], (8550 ^ _778908) ^ [_922282, _922284] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922282) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922284), -(_922282 = _922284)], (20099 ^ _778908) ^ [_1125639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1125639)), -(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), _1125639), 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)))))))], (43739 ^ _778908) ^ [_1631753, _1631755, _1631757, _1631759, _1631761, _1631763] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631753, _1631753)), hAPP(hAPP(c_Product__Type_OPair(_1631753, _1631753), _1631755), _1631757)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631753, _1631753), tc_HOL_Obool), _1631759), _1631761))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1631753, _1631753)), hAPP(hAPP(c_Product__Type_OPair(_1631753, _1631753), _1631757), _1631763)), _1631761)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631753, _1631753)), hAPP(hAPP(c_Product__Type_OPair(_1631753, _1631753), _1631755), _1631763)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631753, _1631753), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1631759)), _1631761))))], (40124 ^ _778908) ^ [_1537383, _1537385, _1537387] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1537383, _1537385), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1537383, _1537385), _1537387), hAPP(c_COMBK(tc_fun(_1537385, tc_HOL_Obool), _1537383), c_Orderings_Otop__class_Otop(tc_fun(_1537385, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1537383, _1537385), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1537383, tc_HOL_Obool)), _1537387)), hAPP(c_COMBK(tc_fun(_1537385, tc_HOL_Obool), _1537383), c_Orderings_Otop__class_Otop(tc_fun(_1537385, tc_HOL_Obool)))))], (42277 ^ _778908) ^ [_1595715, _1595717] : [c_Wellfounded_OwfP(_1595715, _1595717), -(c_Wellfounded_Owf(_1595715, hAPP(c_Set_OCollect(tc_prod(_1595715, _1595715)), hAPP(c_Product__Type_Oprod_Oprod__case(_1595715, _1595715, tc_HOL_Obool), _1595717))))], (43711 ^ _778908) ^ [_1631131, _1631133, _1631135, _1631137] : [-(hAPP(_1631131, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1631133, _1631133), _1631135), _1631131), _1631137)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1631133, _1631133), _1631135), _1631131), hAPP(_1631131, _1631137)))], (48685 ^ _778908) ^ [_1752432, _1752434, _1752436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752432, _1752432), tc_HOL_Obool)), _1752434), _1752436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1752432), tc_List_Olist(_1752432)), tc_HOL_Obool)), c_List_Olistrel1(_1752432, _1752434)), c_List_Olistrel1(_1752432, _1752436))))], (44310 ^ _778908) ^ [_1645304, _1645306, _1645308, _1645310] : [class_Complete__Lattice_Ocomplete__lattice(_1645304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645306), _1645308)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1645306, _1645304), _1645308), _1645310) = hAPP(hAPP(c_Finite__Set_Ofold(_1645306, _1645304, hAPP(hAPP(c_COMBB(_1645304, tc_fun(_1645304, _1645304), _1645306), c_Lattices_Osemilattice__sup__class_Osup(_1645304)), _1645310)), c_Orderings_Obot__class_Obot(_1645304)), _1645308))], (50855 ^ _778908) ^ [_1800951, _1800953] : [c_List_Olist_ONil(_1800951) = hAPP(c_List_Orev(_1800951), _1800953), -(_1800953 = c_List_Olist_ONil(_1800951))], (29217 ^ _778908) ^ [_1300980, _1300982] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1300980), _1300982))))], (48381 ^ _778908) ^ [_1744435, _1744437, _1744439, _1744441] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744437)), _1744439)))), -(hAPP(hAPP(c_List_Onth(_1744437), hAPP(hAPP(c_List_Oappend(_1744437), _1744439), _1744441)), _1744435) = hAPP(hAPP(c_List_Onth(_1744437), _1744441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1744435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744437)), _1744439))))], (17201 ^ _778908) ^ [_1075782, _1075784] : [class_Groups_Oordered__ab__group__add__abs(_1075782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075782), _1075784), c_Groups_Ozero__class_Ozero(_1075782))), -(hAPP(c_Groups_Oabs__class_Oabs(_1075782), _1075784) = hAPP(c_Groups_Ouminus__class_Ouminus(_1075782), _1075784))], (25175 ^ _778908) ^ [_1221629, _1221631, _1221633, _1221635] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1221629, _1221631, _1221633), c_Product__Type_Ocurry(_1221629, _1221631, _1221633, _1221635)) = _1221635)], (7805 ^ _778908) ^ [_909482] : [-(_909482 = 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)), _909482)))], (8088 ^ _778908) ^ [_914228, _914230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914228), hAPP(c_Nat_OSuc, _914230))), -(_914228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8096 ^ _778908 : [(8099 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 8095 ^ [_914228, _914230]), _914230)))], (8097 ^ _778908) ^ [] : [-(_914228 = hAPP(c_Nat_OSuc, 8095 ^ [_914228, _914230]))]]], (26371 ^ _778908) ^ [_1243322, _1243324, _1243326, _1243328] : [class_Rings_Ocomm__semiring__1(_1243322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1243324), _1243326)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243322), hAPP(hAPP(c_Power_Opower__class_Opower(_1243322), _1243328), _1243324)), hAPP(hAPP(c_Power_Opower__class_Opower(_1243322), _1243328), _1243326))))], (6687 ^ _778908) ^ [_888527, _888529, _888531, _888533] : [-(c_Com_Ocom_OWhile(_888527, _888529) = c_Com_Ocom_OWhile(_888531, _888533)), _888527 = _888531, _888529 = _888533], (18625 ^ _778908) ^ [_1099934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099934), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099934) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19321 ^ _778908) ^ [_1111694, _1111696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1111694)), c_Int_OBit0(_1111696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111694), _1111696)))], (28832 ^ _778908) ^ [_1291713, _1291715, _1291717] : [class_Orderings_Oorder(_1291713), 28835 ^ _778908 : [(28842 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291713), _1291717), _1291715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291713, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1291713), _1291715)), hAPP(c_SetInterval_Oord__class_OatLeast(_1291713), _1291717))))], (28836 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291713, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1291713), _1291715)), hAPP(c_SetInterval_Oord__class_OatLeast(_1291713), _1291717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291713), _1291717), _1291715)))]]], (24401 ^ _778908) ^ [_1205578, _1205580, _1205582] : [class_Orderings_Olinorder(_1205578), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205578), _1205580), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1205578), _1205580), _1205582)) = _1205580)], (35783 ^ _778908) ^ [_1439230, _1439232, _1439234, _1439236] : [-(hAPP(c_Relation_OImage(_1439230, _1439232, _1439234), _1439236) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1439230, tc_fun(_1439232, tc_HOL_Obool)), _1439236), hAPP(hAPP(c_COMBB(tc_fun(_1439230, tc_HOL_Obool), tc_fun(_1439232, tc_HOL_Obool), _1439230), c_Relation_OImage(_1439230, _1439232, _1439234)), hAPP(hAPP(c_COMBC(_1439230, tc_fun(_1439230, tc_HOL_Obool), tc_fun(_1439230, tc_HOL_Obool)), c_Set_Oinsert(_1439230)), c_Orderings_Obot__class_Obot(tc_fun(_1439230, tc_HOL_Obool))))))], (34837 ^ _778908) ^ [_1417303, _1417305, _1417307, _1417309, _1417311] : [hBOOL(hAPP(hAPP(c_member(_1417303), _1417305), _1417307)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1417303, tc_Option_Ooption(_1417309)), c_Map_Orestrict__map(_1417303, _1417309, _1417311, _1417307)), _1417305), c_Option_Ooption_ONone(_1417309)) = c_Map_Orestrict__map(_1417303, _1417309, _1417311, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417303, tc_HOL_Obool)), _1417307), hAPP(hAPP(c_Set_Oinsert(_1417303), _1417305), c_Orderings_Obot__class_Obot(tc_fun(_1417303, tc_HOL_Obool))))))], (5382 ^ _778908) ^ [_862107, _862109] : [_862109 = _862107, -(c_List_Odrop(_862109) = c_List_Odrop(_862107))], (19193 ^ _778908) ^ [_1109188, _1109190] : [class_Int_Onumber__ring(_1109188), class_Rings_Olinordered__idom(_1109188), 19200 ^ _778908 : [(19207 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109190), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109188), hAPP(c_Int_Onumber__class_Onumber__of(_1109188), _1109190)), c_Groups_Oone__class_Oone(_1109188))))], (19201 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109188), hAPP(c_Int_Onumber__class_Onumber__of(_1109188), _1109190)), c_Groups_Oone__class_Oone(_1109188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109190), c_Int_OBit1(c_Int_OPls))))]]], (35809 ^ _778908) ^ [_1440070] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1440070)) = _1440070)], (1592 ^ _778908) ^ [_801682, _801684] : [-(class_Rings_Ono__zero__divisors(_801682)), _801684 = _801682, class_Rings_Ono__zero__divisors(_801684)], (49557 ^ _778908) ^ [_1773809, _1773811, _1773813] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773809), tc_List_Olist(_1773809))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773809), tc_List_Olist(_1773809)), c_List_Olist_ONil(_1773809)), _1773811)), c_List_Olexord(_1773809, _1773813))), -(_1773811 = hAPP(hAPP(c_List_Olist_OCons(_1773809), 49560 ^ [_1773809, _1773811, _1773813]), 49561 ^ [_1773809, _1773811, _1773813]))], (8708 ^ _778908) ^ [_924284, _924286, _924288] : [class_Orderings_Opreorder(_924284), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924284), _924286), _924288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924284), _924288), _924286))], (36746 ^ _778908) ^ [_1461167, _1461169, _1461171] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461167, tc_HOL_Obool)), _1461169), _1461171) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461167, tc_HOL_Obool)), _1461171), _1461169))], (41233 ^ _778908) ^ [_1562325, _1562327, _1562329, _1562331] : [-(hAPP(c_Set_OCollect(tc_prod(_1562325, _1562327)), hAPP(c_Product__Type_Oprod_Oprod__case(_1562325, _1562327, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1562325, tc_fun(_1562327, tc_HOL_Obool), tc_fun(_1562327, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1562327, tc_HOL_Obool), tc_fun(_1562327, tc_HOL_Obool)), _1562325), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1562327)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562325), c_fconj), _1562329))), _1562331))) = hAPP(hAPP(c_Product__Type_OSigma(_1562325, _1562327), hAPP(c_Set_OCollect(_1562325), _1562329)), hAPP(c_COMBK(tc_fun(_1562327, tc_HOL_Obool), _1562325), hAPP(c_Set_OCollect(_1562327), _1562331))))], (8123 ^ _778908) ^ [_914755, _914757] : [8124 ^ _778908 : [(8127 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _914757))], (8125 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _914755))]], -(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), _914755), _914757))))], (29404 ^ _778908) ^ [_1304478, _1304480, _1304482] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304478), _1304480)), 29407 ^ _778908 : [(29427 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1304478, tc_Nat_Onat), _1304482), _1304480) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 29428 ^ _778908 : [(29429 ^ _778908) ^ [_1304959] : [hBOOL(hAPP(hAPP(c_member(_1304478), _1304959), _1304480)), hAPP(_1304482, _1304959) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29437 ^ _778908 : [(29442 ^ _778908) ^ [] : [hAPP(_1304482, 29436 ^ [_1304478, _1304480, _1304482, _1304959]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29440 ^ _778908) ^ [] : [_1304959 = 29436 ^ [_1304478, _1304480, _1304482, _1304959]], (29438 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304478), 29436 ^ [_1304478, _1304480, _1304482, _1304959]), _1304480)))]]]]], (29408 ^ _778908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1304478, tc_Nat_Onat), _1304482), _1304480) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29412 ^ _778908 : [(29417 ^ _778908) ^ [_1304798] : [hBOOL(hAPP(hAPP(c_member(_1304478), _1304798), _1304480)), -(29411 ^ [_1304478, _1304480, _1304482] = _1304798), -(hAPP(_1304482, _1304798) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29415 ^ _778908) ^ [] : [-(hAPP(_1304482, 29411 ^ [_1304478, _1304480, _1304482]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29413 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304478), 29411 ^ [_1304478, _1304480, _1304482]), _1304480)))]]]]], (37330 ^ _778908) ^ [_1474913, _1474915, _1474917, _1474919, _1474921] : [class_Groups_Ocomm__monoid__add(_1474913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474915), _1474917)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474915, _1474913), _1474919), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474915, tc_HOL_Obool)), _1474917), _1474921)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474915, _1474913), hAPP(hAPP(c_COMBC(_1474915, _1474913, _1474913), hAPP(hAPP(c_COMBS(_1474915, _1474913, tc_fun(_1474913, _1474913)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1474913, tc_fun(_1474913, _1474913)), _1474915), c_If(_1474913)), hAPP(hAPP(c_COMBC(_1474915, tc_fun(_1474915, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474915)), _1474921))), _1474919)), c_Groups_Ozero__class_Ozero(_1474913))), _1474917))], (19989 ^ _778908) ^ [_1123238, _1123240, _1123242] : [class_Rings_Olinordered__idom(_1123238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123238), hAPP(hAPP(c_Power_Opower__class_Opower(_1123238), _1123240), 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(_1123238), _1123242), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1123238)))], (24617 ^ _778908) ^ [_1209590, _1209592, _1209594, _1209596] : [class_Orderings_Olinorder(_1209590), 24620 ^ _778908 : [(24629 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209590), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209590), _1209592), _1209594)), _1209596))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209590), _1209592), _1209596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209590), _1209594), _1209596))], (24621 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209590), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209590), _1209592), _1209594)), _1209596)), 24624 ^ _778908 : [(24627 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209590), _1209594), _1209596)))], (24625 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209590), _1209592), _1209596)))]]]]], (18885 ^ _778908) ^ [_1104343, _1104345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104343), _1104345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1104343)), c_Int_OBit1(_1104345))))], (51623 ^ _778908) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (4450 ^ _778908) ^ [_847723, _847725, _847727, _847729, _847731, _847733, _847735, _847737] : [-(c_Nitpick_Osetsum_H(_847737, _847733, _847729, _847725) = c_Nitpick_Osetsum_H(_847735, _847731, _847727, _847723)), _847737 = _847735, _847733 = _847731, _847729 = _847727, _847725 = _847723], (23461 ^ _778908) ^ [_1187769, _1187771, _1187773] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187769, _1187769), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187771), _1187773))), -(_1187769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1187771 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (15238 ^ _778908) ^ [_1037914, _1037916, _1037918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1037914)), 15241 ^ _778908 : [(15242 ^ _778908) ^ [] : [-(_1037916 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1037918), _1037914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037914), _1037916)), _1037918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037914), hAPP(c_Nat_OSuc, _1037916))))], (15252 ^ _778908) ^ [] : [_1037916 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1037918), _1037914), 15255 ^ _778908 : [(15258 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037914), hAPP(c_Nat_OSuc, _1037916)))))], (15256 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037914), _1037916)), _1037918)))]]]]], (44683 ^ _778908) ^ [_1652973, _1652975, _1652977] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652973, tc_fun(_1652975, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1652973, tc_HOL_Obool))), _1652977) = c_Orderings_Otop__class_Otop(tc_fun(_1652975, tc_HOL_Obool)))], (48915 ^ _778908) ^ [_1759321, _1759323, _1759325, _1759327] : [-(hAPP(hAPP(c_List_Odrop(_1759321), hAPP(c_Nat_OSuc, _1759323)), hAPP(hAPP(c_List_Olist_OCons(_1759321), _1759325), _1759327)) = hAPP(hAPP(c_List_Odrop(_1759321), _1759323), _1759327))], (49444 ^ _778908) ^ [_1771038, _1771040] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1771038), hAPP(c_List_Oset(tc_Nat_Onat), _1771040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1771038), 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)), _1771040))))], (33157 ^ _778908) ^ [_1383730, _1383732, _1383734, _1383736, _1383738, _1383740, _1383742, _1383744] : [c_Hoare__Mirabelle_Ohoare__derivs(_1383730, _1383732, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1383730)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1383730), _1383734), _1383736), hAPP(hAPP(c_COMBC(_1383730, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1383730), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1383738)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_1383740))), hAPP(hAPP(c_Natural_Ogetlocs, _1383742), _1383740))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1383730), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1383730, _1383732, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1383730)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1383730), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1383730), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _1383742)))), hAPP(hAPP(c_COMBC(_1383730, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1383730), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1383734)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_1383740))), _1383744)))), c_Com_Ocom_OLocal(_1383740, _1383744, _1383736)), _1383738)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1383730), tc_HOL_Obool)))))], (4808 ^ _778908) ^ [_853302, _853304, _853306, _853308, _853310, _853312] : [-(c_Big__Operators_Olattice_OSup__fin(_853312, _853308, _853304) = c_Big__Operators_Olattice_OSup__fin(_853310, _853306, _853302)), _853312 = _853310, _853308 = _853306, _853304 = _853302], (36110 ^ _778908) ^ [_1447694, _1447696, _1447698, _1447700] : [c_Equiv__Relations_Oequiv(_1447694, _1447696, _1447698), hBOOL(hAPP(hAPP(c_member(_1447694), _1447700), _1447696)), -(hBOOL(hAPP(hAPP(c_member(_1447694), _1447700), hAPP(c_Relation_OImage(_1447694, _1447694, _1447698), hAPP(hAPP(c_Set_Oinsert(_1447694), _1447700), c_Orderings_Obot__class_Obot(tc_fun(_1447694, tc_HOL_Obool)))))))], (35829 ^ _778908) ^ [_1440550, _1440552, _1440554, _1440556] : [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), _1440550), _1440552)), 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), _1440554), _1440556)), 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), _1440550), _1440556)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440554), _1440552))))], (19131 ^ _778908) ^ [] : [-(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)))))], (16641 ^ _778908) ^ [_1064966] : [class_Rings_Olinordered__idom(_1064966), -(hAPP(c_Groups_Oabs__class_Oabs(_1064966), c_Groups_Oone__class_Oone(_1064966)) = c_Groups_Oone__class_Oone(_1064966))], (18483 ^ _778908) ^ [_1097916, _1097918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097916), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097916)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097918)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28253 ^ _778908) ^ [_1280652, _1280654, _1280656] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280652, tc_HOL_Obool)), _1280654), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280652, tc_HOL_Obool)), _1280656), _1280654)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280652, tc_HOL_Obool)), _1280654), _1280656))], (45895 ^ _778908) ^ [_1682733, _1682735, _1682737] : [-(c_Map_Omap__add(_1682733, _1682735, hAPP(c_COMBK(tc_Option_Ooption(_1682735), _1682733), c_Option_Ooption_ONone(_1682735)), _1682737) = _1682737)], (36084 ^ _778908) ^ [_1447122, _1447124, _1447126, _1447128, _1447130] : [c_Equiv__Relations_Oequiv(_1447122, _1447124, _1447126), hBOOL(hAPP(hAPP(c_member(_1447122), _1447128), _1447124)), hBOOL(hAPP(hAPP(c_member(_1447122), _1447130), _1447124)), 36095 ^ _778908 : [(36102 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447122, _1447122)), hAPP(hAPP(c_Product__Type_OPair(_1447122, _1447122), _1447128), _1447130)), _1447126)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447122), hAPP(hAPP(c_Set_Oinsert(_1447122), _1447128), c_Orderings_Obot__class_Obot(tc_fun(_1447122, tc_HOL_Obool)))), _1447126) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447122), hAPP(hAPP(c_Set_Oinsert(_1447122), _1447130), c_Orderings_Obot__class_Obot(tc_fun(_1447122, tc_HOL_Obool)))), _1447126))], (36096 ^ _778908) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447122), hAPP(hAPP(c_Set_Oinsert(_1447122), _1447128), c_Orderings_Obot__class_Obot(tc_fun(_1447122, tc_HOL_Obool)))), _1447126) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447122), hAPP(hAPP(c_Set_Oinsert(_1447122), _1447130), c_Orderings_Obot__class_Obot(tc_fun(_1447122, tc_HOL_Obool)))), _1447126), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447122, _1447122)), hAPP(hAPP(c_Product__Type_OPair(_1447122, _1447122), _1447128), _1447130)), _1447126)))]]], (29033 ^ _778908) ^ [_1296571, _1296573, _1296575, _1296577, _1296579] : [29035 ^ _778908 : [(29038 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296571, tc_HOL_Obool)), hAPP(_1296577, 29034 ^ [_1296571, _1296573, _1296575, _1296577, _1296579])), _1296579))], (29036 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1296573), 29034 ^ [_1296571, _1296573, _1296575, _1296577, _1296579]), _1296575)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296571, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296573, tc_fun(_1296571, tc_HOL_Obool)), _1296575), _1296577)), _1296579)))], (36828 ^ _778908) ^ [_1462949, _1462951] : [class_Lattices_Osemilattice__inf(_1462949), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462949), _1462951), _1462951) = _1462951)], (22560 ^ _778908) ^ [_1169988] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1169988))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1169988)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47098 ^ _778908) ^ [_1713731, _1713733, _1713735, _1713737, _1713739, _1713741] : [-(_1713731 = _1713733), -(hAPP(c_Map_Omap__of(_1713735, _1713737, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1713735, _1713737)), hAPP(hAPP(c_Product__Type_OPair(_1713735, _1713737), _1713731), _1713739)), _1713741)), _1713733) = hAPP(c_Map_Omap__of(_1713735, _1713737, _1713741), _1713733))], (24093 ^ _778908) ^ [_1199599, _1199601, _1199603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199599, tc_HOL_Obool)), _1199603), _1199601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199599, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199599, tc_HOL_Obool)), _1199601)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1199599, tc_HOL_Obool)), _1199603))))], (34118 ^ _778908) ^ [_1402203, _1402205, _1402207] : [class_Orderings_Olinorder(_1402203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402203), _1402205)), -(_1402205 = c_Orderings_Obot__class_Obot(tc_fun(_1402203, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402203), _1402207)), -(_1402207 = c_Orderings_Obot__class_Obot(tc_fun(_1402203, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1402203, c_Orderings_Oord__class_Omax(_1402203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402203, tc_HOL_Obool)), _1402205), _1402207)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1402203), c_Big__Operators_Olattice_OSup__fin(_1402203, c_Orderings_Oord__class_Omax(_1402203), _1402205)), c_Big__Operators_Olattice_OSup__fin(_1402203, c_Orderings_Oord__class_Omax(_1402203), _1402207)))], (41335 ^ _778908) ^ [_1565990, _1565992, _1565994, _1565996, _1565998, _1566000] : [class_Groups_Ocomm__monoid__add(_1565990), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565992), _1565994)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565992, _1565990), hAPP(hAPP(c_COMBS(_1565992, _1565990, _1565990), hAPP(hAPP(c_COMBS(_1565992, _1565990, tc_fun(_1565990, _1565990)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1565990, tc_fun(_1565990, _1565990)), _1565992), c_If(_1565990)), _1565996)), _1565998)), _1566000)), _1565994) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1565990), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565992, _1565990), _1565998), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1565992, tc_HOL_Obool)), _1565994), hAPP(c_Set_OCollect(_1565992), _1565996)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565992, _1565990), _1566000), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1565992, tc_HOL_Obool)), _1565994), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1565992, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1565992), _1565996))))))], (5837 ^ _778908) ^ [_871747, _871749, _871751] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_871747, _871749, _871751)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2562 ^ _778908) ^ [_817643, _817645, _817647, _817649] : [-(c_Divides_OposDivAlg(_817649, _817645) = c_Divides_OposDivAlg(_817647, _817643)), _817649 = _817647, _817645 = _817643], (29357 ^ _778908) ^ [_1303474] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1303474)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1303474), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1303474)))], (14027 ^ _778908) ^ [_1016315, _1016317] : [-(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, _1016315, _1016317)), _1016317) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016315), _1016317))], (7194 ^ _778908) ^ [_899260, _899262, _899264] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899260), _899262) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899264), _899262), -(_899260 = _899264)], (24893 ^ _778908) ^ [_1215057, _1215059] : [class_Orderings_Olinorder(_1215057), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215057), _1215059), _1215059) = _1215059)], (17757 ^ _778908) ^ [_1085917, _1085919, _1085921] : [class_Rings_Olinordered__semidom(_1085917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085917), c_Groups_Oone__class_Oone(_1085917)), _1085919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085917), hAPP(hAPP(c_Power_Opower__class_Opower(_1085917), _1085919), _1085921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085917), _1085919), hAPP(hAPP(c_Power_Opower__class_Opower(_1085917), _1085919), _1085921)))))], (15612 ^ _778908) ^ [_1044649, _1044651, _1044653] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044649), _1044651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044653), _1044651)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044649), _1044653))], (40980 ^ _778908) ^ [_1557254, _1557256, _1557258, _1557260, _1557262] : [c_Finite__Set_Ofolding__one__idem(_1557254, _1557256, _1557258), hAPP(_1557260, hAPP(hAPP(_1557256, 40985 ^ [_1557254, _1557256, _1557258, _1557260, _1557262]), 40986 ^ [_1557254, _1557256, _1557258, _1557260, _1557262])) = hAPP(hAPP(_1557256, hAPP(_1557260, 40985 ^ [_1557254, _1557256, _1557258, _1557260, _1557262])), hAPP(_1557260, 40986 ^ [_1557254, _1557256, _1557258, _1557260, _1557262])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557254), _1557262)), -(_1557262 = c_Orderings_Obot__class_Obot(tc_fun(_1557254, tc_HOL_Obool))), -(hAPP(_1557260, hAPP(_1557258, _1557262)) = hAPP(_1557258, hAPP(c_Set_Oimage(_1557254, _1557254, _1557260), _1557262)))], (41973 ^ _778908) ^ [_1588640, _1588642, _1588644] : [c_Wellfounded_Owf(_1588640, _1588642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588640, _1588640), tc_HOL_Obool)), _1588644), _1588642)), -(c_Wellfounded_Owf(_1588640, _1588644))], (29054 ^ _778908) ^ [_1297300, _1297302] : [class_Orderings_Oorder(_1297300), 29061 ^ _778908 : [(29064 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297300), hAPP(_1297302, 29059 ^ [_1297300, _1297302])), hAPP(_1297302, 29060 ^ [_1297300, _1297302])))], (29062 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 29059 ^ [_1297300, _1297302]), 29060 ^ [_1297300, _1297302])))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1297300, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297302))], (28637 ^ _778908) ^ [_1287924, _1287926, _1287928] : [class_Orderings_Olinorder(_1287924), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287924), _1287926), _1287928)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287924, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1287924), _1287926)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1287924, _1287926), _1287928)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1287924), _1287928))], (39502 ^ _778908) ^ [_1522063, _1522065, _1522067] : [-(hAPP(c_Set_Ovimage(_1522063, _1522065, _1522067), c_Orderings_Obot__class_Obot(tc_fun(_1522065, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1522063, tc_HOL_Obool)))], (7494 ^ _778908) ^ [_904154, _904156, _904158, _904160] : [class_Rings_Ocomm__semiring__1(_904154), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904154), _904156), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904154), _904158), _904160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904154), _904158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904154), _904156), _904160)))], (24965 ^ _778908) ^ [_1216589, _1216591, _1216593, _1216595, _1216597, _1216599, _1216601] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1216589, _1216591, _1216593, _1216595), _1216597), _1216599), _1216601) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1216591, _1216593, _1216595), _1216599), hAPP(_1216597, _1216601)))], (51401 ^ _778908) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (47828 ^ _778908) ^ [_1731942, _1731944, _1731946, _1731948] : [-(hAPP(c_List_Oset(tc_prod(_1731942, _1731944)), hAPP(hAPP(c_List_Ozip(_1731942, _1731944), _1731946), _1731948)) = hAPP(c_Set_OCollect(tc_prod(_1731942, _1731944)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1731942, _1731944)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1731942, _1731944), 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(_1731942, _1731944)), 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(_1731942, _1731944)), 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(_1731942, _1731944), tc_fun(tc_Nat_Onat, tc_prod(_1731942, _1731944)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1731942, _1731944), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1731942, _1731944)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1731942, _1731944)), c_COMBB(tc_prod(_1731942, _1731944), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1731944, tc_prod(_1731942, _1731944)), hAPP(hAPP(c_COMBB(_1731942, tc_fun(_1731944, tc_prod(_1731942, _1731944)), tc_Nat_Onat), c_Product__Type_OPair(_1731942, _1731944)), hAPP(c_List_Onth(_1731942), _1731946))), hAPP(c_List_Onth(_1731944), _1731948)))))), 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(_1731942)), _1731946)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731944)), _1731948)))))))], (6250 ^ _778908) ^ [_879634, _879636, _879638, _879640] : [c_Com_Ocom_OSemi(_879634, _879636) = c_Com_Ocom_OSemi(_879638, _879640), 6253 ^ _778908 : [(6256 ^ _778908) ^ [] : [-(_879636 = _879640)], (6254 ^ _778908) ^ [] : [-(_879634 = _879638)]]], (40122 ^ _778908) ^ [_1537291, _1537293, _1537295] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1537291, _1537293), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1537291, _1537293), c_Orderings_Otop__class_Otop(tc_fun(_1537291, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1537293, tc_HOL_Obool), _1537291), _1537295))) = hAPP(hAPP(c_Product__Type_OSigma(_1537291, _1537293), c_Orderings_Otop__class_Otop(tc_fun(_1537291, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1537293, tc_HOL_Obool), _1537291), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1537293, tc_HOL_Obool)), _1537295))))], (32318 ^ _778908) ^ [_1366471, _1366473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1366471, _1366471)), hAPP(hAPP(c_Product__Type_OPair(_1366471, _1366471), 32319 ^ [_1366471, _1366473]), 32319 ^ [_1366471, _1366473])), _1366473)), -(c_Nitpick_Orefl_H(_1366471, _1366473))], (8606 ^ _778908) ^ [_923105, _923107, _923109] : [class_Orderings_Olinorder(_923105), 8609 ^ _778908 : [(8610 ^ _778908) ^ [] : [-(_923107 = _923109), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923105), _923107), _923109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923105), _923109), _923107)))], (8620 ^ _778908) ^ [] : [8621 ^ _778908 : [(8624 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923105), _923109), _923107))], (8622 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923105), _923107), _923109))]], _923107 = _923109]]], (50533 ^ _778908) ^ [_1793586, _1793588, _1793590, _1793592, _1793594, _1793596] : [class_Orderings_Olinorder(_1793586), c_List_Olinorder__class_Osorted(_1793586, hAPP(hAPP(c_List_Omap(_1793588, _1793586), _1793590), _1793592)), hBOOL(hAPP(_1793594, _1793596)), -(hAPP(c_List_Ofilter(_1793588, _1793594), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1793588, _1793586, _1793590), _1793596), _1793592)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1793588, _1793586, _1793590), _1793596), hAPP(c_List_Ofilter(_1793588, _1793594), _1793592)))], (11829 ^ _778908) ^ [_977009, _977011] : [class_Groups_Olinordered__ab__group__add(_977009), 11832 ^ _778908 : [(11839 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977009), _977011), c_Groups_Ozero__class_Ozero(_977009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977009), _977011), _977011)), c_Groups_Ozero__class_Ozero(_977009))))], (11833 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977009), _977011), _977011)), c_Groups_Ozero__class_Ozero(_977009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977009), _977011), c_Groups_Ozero__class_Ozero(_977009))))]]], (1898 ^ _778908) ^ [_806373, _806375] : [_806375 = _806373, -(c_String_Ochar_Ochar__size(_806375) = c_String_Ochar_Ochar__size(_806373))], (49139 ^ _778908) ^ [_1764645, _1764647, _1764649] : [-(_1764645 = c_List_Olist_ONil(_1764647)), -(hAPP(c_List_Ohd(_1764647), hAPP(hAPP(c_List_Oappend(_1764647), _1764645), _1764649)) = hAPP(c_List_Ohd(_1764647), _1764645))], (28195 ^ _778908) ^ [_1279487, _1279489, _1279491] : [class_Lattices_Osemilattice__sup(_1279487), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279487), _1279489), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279487), _1279489), _1279491)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279487), _1279489), _1279491))], (21541 ^ _778908) ^ [] : [-(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))], (15608 ^ _778908) ^ [_1044547, _1044549, _1044551] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044547), _1044549)), _1044551) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044549), _1044551)))], (18329 ^ _778908) ^ [_1095594] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1095594, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47912 ^ _778908) ^ [_1733929, _1733931, _1733933, _1733935, _1733937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1733929, tc_HOL_Obool)), hAPP(c_List_Oset(_1733929), _1733931)), _1733933)), hBOOL(hAPP(hAPP(c_member(_1733929), _1733935), _1733933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1733929, tc_HOL_Obool)), hAPP(c_List_Oset(_1733929), hAPP(hAPP(c_List_Olist__update(_1733929, _1733931), _1733937), _1733935))), _1733933)))], (47044 ^ _778908) ^ [_1712558, _1712560, _1712562, _1712564, _1712566] : [-(hAPP(hAPP(c_List_Omap(_1712558, _1712560), _1712562), hAPP(hAPP(c_List_Olist_OCons(_1712558), _1712564), _1712566)) = hAPP(hAPP(c_List_Olist_OCons(_1712560), hAPP(_1712562, _1712564)), hAPP(hAPP(c_List_Omap(_1712558, _1712560), _1712562), _1712566)))], (51391 ^ _778908) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (16959 ^ _778908) ^ [_1070799, _1070801, _1070803] : [class_Rings_Ocomm__semiring__1(_1070799), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070799), hAPP(hAPP(c_Power_Opower__class_Opower(_1070799), _1070801), _1070803)), _1070801) = hAPP(hAPP(c_Power_Opower__class_Opower(_1070799), _1070801), hAPP(c_Nat_OSuc, _1070803)))], (46994 ^ _778908) ^ [_1711546, _1711548, _1711550, _1711552, _1711554, _1711556] : [hBOOL(hAPP(hAPP(_1711546, _1711548), _1711550)), c_List_Olistrelp(_1711552, _1711546, _1711554, _1711556), -(c_List_Olistrelp(_1711552, _1711546, hAPP(hAPP(c_List_Olist_OCons(_1711552), _1711548), _1711554), hAPP(hAPP(c_List_Olist_OCons(_1711552), _1711550), _1711556)))], (24015 ^ _778908) ^ [_1197800, _1197802, _1197804, _1197806] : [hAPP(c_Product__Type_Ofst(_1197800, _1197802), _1197804) = hAPP(c_Product__Type_Ofst(_1197800, _1197802), _1197806), hAPP(c_Product__Type_Osnd(_1197800, _1197802), _1197804) = hAPP(c_Product__Type_Osnd(_1197800, _1197802), _1197806), -(_1197804 = _1197806)], (49541 ^ _778908) ^ [_1773324, _1773326] : [-(c_List_Olists(_1773324, _1773326) = hAPP(c_Set_OCollect(tc_List_Olist(_1773324)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1773324), tc_fun(_1773324, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1773324, tc_HOL_Obool), tc_fun(tc_fun(_1773324, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1773324)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1773324, tc_HOL_Obool))), c_List_Oset(_1773324))), _1773326)))], (17023 ^ _778908) ^ [_1072104, _1072106, _1072108, _1072110] : [class_Rings_Ocomm__semiring__1(_1072104), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072104), hAPP(hAPP(c_Power_Opower__class_Opower(_1072104), _1072106), _1072108)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072104), _1072106), _1072110)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1072104), _1072106), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1072108), _1072110)))], (38646 ^ _778908) ^ [_1503595, _1503597, _1503599, _1503601, _1503603] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1503595, _1503597, _1503599), _1503601), _1503603), c_Orderings_Obot__class_Obot(tc_fun(_1503597, tc_HOL_Obool))) = _1503603)], (28219 ^ _778908) ^ [_1279971, _1279973, _1279975] : [class_Lattices_Olattice(_1279971), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279971), _1279973), _1279975) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279971), _1279975), _1279973))], (31850 ^ _778908) ^ [_1356018, _1356020, _1356022, _1356024, _1356026] : [class_Groups_Ocomm__monoid__add(_1356018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356020), _1356022)), 31857 ^ _778908 : [(31864 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356020), _1356024), _1356022))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356020, _1356018), hAPP(hAPP(c_COMBC(_1356020, _1356018, _1356018), hAPP(hAPP(c_COMBS(_1356020, _1356018, tc_fun(_1356018, _1356018)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1356018, tc_fun(_1356018, _1356018)), _1356020), c_If(_1356018)), hAPP(c_fequal, _1356024))), _1356026)), c_Groups_Ozero__class_Ozero(_1356018))), _1356022) = c_Groups_Ozero__class_Ozero(_1356018))], (31858 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1356020), _1356024), _1356022)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356020, _1356018), hAPP(hAPP(c_COMBC(_1356020, _1356018, _1356018), hAPP(hAPP(c_COMBS(_1356020, _1356018, tc_fun(_1356018, _1356018)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1356018, tc_fun(_1356018, _1356018)), _1356020), c_If(_1356018)), hAPP(c_fequal, _1356024))), _1356026)), c_Groups_Ozero__class_Ozero(_1356018))), _1356022) = hAPP(_1356026, _1356024))]]], (40056 ^ _778908) ^ [_1535381, _1535383, _1535385, _1535387, _1535389, _1535391] : [-(hAPP(c_Set_Oimage(_1535381, tc_prod(_1535383, _1535385), hAPP(hAPP(c_COMBS(_1535381, _1535385, tc_prod(_1535383, _1535385)), hAPP(hAPP(c_COMBB(_1535383, tc_fun(_1535385, tc_prod(_1535383, _1535385)), _1535381), c_Product__Type_OPair(_1535383, _1535385)), _1535387)), _1535389)), _1535391) = hAPP(hAPP(c_Product__Type_OSigma(_1535383, _1535385), hAPP(c_Set_Oimage(_1535381, _1535383, _1535387), _1535391)), hAPP(hAPP(c_COMBB(tc_fun(_1535381, tc_HOL_Obool), tc_fun(_1535385, tc_HOL_Obool), _1535383), c_Set_Oimage(_1535381, _1535385, _1535389)), hAPP(hAPP(c_COMBC(_1535383, tc_fun(_1535381, tc_HOL_Obool), tc_fun(_1535381, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535381, tc_HOL_Obool), tc_fun(tc_fun(_1535381, tc_HOL_Obool), tc_fun(_1535381, tc_HOL_Obool)), _1535383), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535381, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535383, tc_HOL_Obool), tc_fun(_1535381, tc_HOL_Obool), _1535383), c_Set_Ovimage(_1535381, _1535383, _1535387)), hAPP(hAPP(c_COMBC(_1535383, tc_fun(_1535383, tc_HOL_Obool), tc_fun(_1535383, tc_HOL_Obool)), c_Set_Oinsert(_1535383)), c_Orderings_Obot__class_Obot(tc_fun(_1535383, tc_HOL_Obool)))))), _1535391))))], (9516 ^ _778908) ^ [] : [-(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))], (12363 ^ _778908) ^ [_986578, _986580, _986582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986578), _986580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _986582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986582), _986578)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986582), _986580))))], (35158 ^ _778908) ^ [_1425068, _1425070, _1425072, _1425074, _1425076, _1425078] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1425068, _1425068)), hAPP(hAPP(c_Product__Type_OPair(_1425068, _1425068), _1425070), _1425072)), hAPP(hAPP(c_Relation_Oinv__image(_1425074, _1425068), _1425076), _1425078))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1425074, _1425074)), hAPP(hAPP(c_Product__Type_OPair(_1425074, _1425074), hAPP(_1425078, _1425070)), hAPP(_1425078, _1425072))), _1425076)))], (9442 ^ _778908) ^ [_936877, _936879] : [class_Rings_Omult__zero(_936877), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936877), c_Groups_Ozero__class_Ozero(_936877)), _936879) = c_Groups_Ozero__class_Ozero(_936877))], (20533 ^ _778908) ^ [_1133523, _1133525, _1133527] : [class_Fields_Olinordered__field__inverse__zero(_1133523), 20536 ^ _778908 : [(20551 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), c_Groups_Ozero__class_Ozero(_1133523)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133523), _1133525), _1133527)))), 20552 ^ _778908 : [(20559 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), _1133525), c_Groups_Ozero__class_Ozero(_1133523))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), _1133527), c_Groups_Ozero__class_Ozero(_1133523)))], (20553 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), c_Groups_Ozero__class_Ozero(_1133523)), _1133525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), c_Groups_Ozero__class_Ozero(_1133523)), _1133527))]]], (20537 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), c_Groups_Ozero__class_Ozero(_1133523)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133523), _1133525), _1133527))), 20542 ^ _778908 : [(20545 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), c_Groups_Ozero__class_Ozero(_1133523)), _1133527)))], (20543 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), c_Groups_Ozero__class_Ozero(_1133523)), _1133525)))]], 20546 ^ _778908 : [(20549 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), _1133527), c_Groups_Ozero__class_Ozero(_1133523))))], (20547 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133523), _1133525), c_Groups_Ozero__class_Ozero(_1133523))))]]]]], (5074 ^ _778908) ^ [_857411, _857413] : [_857413 = _857411, -(c_If(_857413) = c_If(_857411))], (27192 ^ _778908) ^ [_1259316, _1259318, _1259320, _1259322, _1259324] : [class_Orderings_Olinorder(_1259316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259316), _1259318), _1259320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259316), _1259322), _1259324)), 27203 ^ _778908 : [(27212 ^ _778908) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259316, _1259318), _1259320) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259316, _1259322), _1259324)), _1259318 = _1259322, _1259320 = _1259324], (27204 ^ _778908) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259316, _1259318), _1259320) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259316, _1259322), _1259324), 27207 ^ _778908 : [(27210 ^ _778908) ^ [] : [-(_1259320 = _1259324)], (27208 ^ _778908) ^ [] : [-(_1259318 = _1259322)]]]]], (34946 ^ _778908) ^ [_1419768, _1419770, _1419772] : [class_Orderings_Olinorder(_1419768), hAPP(_1419770, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1419768), 34951 ^ [_1419768, _1419770, _1419772]), 34952 ^ [_1419768, _1419770, _1419772])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1419768), hAPP(_1419770, 34951 ^ [_1419768, _1419770, _1419772])), hAPP(_1419770, 34952 ^ [_1419768, _1419770, _1419772])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419768), _1419772)), -(_1419772 = c_Orderings_Obot__class_Obot(tc_fun(_1419768, tc_HOL_Obool))), -(hAPP(_1419770, c_Big__Operators_Olattice_OSup__fin(_1419768, c_Orderings_Oord__class_Omax(_1419768), _1419772)) = c_Big__Operators_Olattice_OSup__fin(_1419768, c_Orderings_Oord__class_Omax(_1419768), hAPP(c_Set_Oimage(_1419768, _1419768, _1419770), _1419772)))], (5839 ^ _778908) ^ [_871780, _871782, _871784] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_871780, _871782, _871784)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28922 ^ _778908) ^ [_1293655, _1293657, _1293659, _1293661, _1293663, _1293665] : [class_Complete__Lattice_Ocomplete__lattice(_1293655), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293657, tc_fun(_1293659, _1293655)), _1293661), _1293663), _1293665) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293657, _1293655), _1293661), hAPP(hAPP(c_COMBC(_1293657, _1293659, _1293655), _1293663), _1293665)))], (5943 ^ _778908) ^ [_873749, _873751, _873753] : [c_Com_Ocom_OAss(_873749, _873751) = hAPP(c_Com_Ocom_OBODY, _873753)], (36834 ^ _778908) ^ [_1463040, _1463042] : [class_Lattices_Osemilattice__inf(_1463040), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463040), _1463042), _1463042) = _1463042)], (43548 ^ _778908) ^ [_1626942, _1626944, _1626946, _1626948, _1626950] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626942, _1626944)), hAPP(hAPP(c_Product__Type_OPair(_1626942, _1626944), _1626946), _1626948)), hAPP(c_Relation_Oconverse(_1626944, _1626942), _1626950))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626944, _1626942)), hAPP(hAPP(c_Product__Type_OPair(_1626944, _1626942), _1626948), _1626946)), _1626950)))], (18607 ^ _778908) ^ [_1099655] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099655), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099655), c_Int_OPls)))], (47591 ^ _778908) ^ [_1725514, _1725516, _1725518] : [-(c_List_Olistset(_1725514, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1725514, tc_HOL_Obool)), _1725516), _1725518)) = c_List_Oset__Cons(_1725514, _1725516, c_List_Olistset(_1725514, _1725518)))], (16683 ^ _778908) ^ [_1065790, _1065792] : [class_Int_Onumber__ring(_1065790), 16686 ^ _778908 : [(16693 ^ _778908) ^ [] : [-(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), _1065792)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1065790), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1065792)) = c_Groups_Ozero__class_Ozero(_1065790))], (16687 ^ _778908) ^ [] : [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), _1065792))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1065790), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1065792)) = hAPP(c_Int_Onumber__class_Onumber__of(_1065790), _1065792))]]], (18839 ^ _778908) ^ [_1103500, _1103502] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1103500), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1103502)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1103500), 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)))), _1103502)))], (43713 ^ _778908) ^ [_1631190, _1631192, _1631194, _1631196] : [-(hAPP(hAPP(c_Nat_Ocompow(_1631190, _1631190), _1631192), hAPP(hAPP(c_Nat_Ocompow(_1631190, _1631190), _1631194), _1631196)) = hAPP(hAPP(c_Nat_Ocompow(_1631190, _1631190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1631194), _1631192)), _1631196))], (11456 ^ _778908) ^ [_970701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970701)), _970701))], (38530 ^ _778908) ^ [_1501531, _1501533, _1501535, _1501537, _1501539, _1501541] : [c_Fun_Oinj__on(_1501531, _1501533, _1501535, _1501537), hBOOL(hAPP(hAPP(c_member(_1501531), _1501539), _1501537)), hBOOL(hAPP(hAPP(c_member(_1501531), _1501541), _1501537)), 38541 ^ _778908 : [(38548 ^ _778908) ^ [] : [_1501539 = _1501541, -(hAPP(_1501535, _1501539) = hAPP(_1501535, _1501541))], (38542 ^ _778908) ^ [] : [hAPP(_1501535, _1501539) = hAPP(_1501535, _1501541), -(_1501539 = _1501541)]]], (25025 ^ _778908) ^ [_1217960, _1217962, _1217964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1217960), c_Nitpick_Oplus__frac(_1217960, _1217962, c_Nitpick_Ouminus__frac(_1217960, _1217964)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1217960, _1217962, _1217964))], (44144 ^ _778908) ^ [_1642006, _1642008, _1642010, _1642012, _1642014] : [class_Complete__Lattice_Ocomplete__lattice(_1642006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642008), _1642010)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1642006), _1642012), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1642008, _1642006), _1642010), _1642014)) = hAPP(hAPP(c_Finite__Set_Ofold(_1642008, _1642006, hAPP(hAPP(c_COMBB(_1642006, tc_fun(_1642006, _1642006), _1642008), c_Lattices_Osemilattice__sup__class_Osup(_1642006)), _1642014)), _1642012), _1642010))], (16681 ^ _778908) ^ [_1065739, _1065741, _1065743] : [-(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, _1065739, _1065741)), _1065743), _1065741) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1065739), _1065743), _1065741))], (36636 ^ _778908) ^ [_1458835, _1458837, _1458839, _1458841] : [class_Lattices_Odistrib__lattice(_1458835), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1458835), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458835), _1458837), _1458839)), _1458841) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458835), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1458835), _1458837), _1458841)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1458835), _1458839), _1458841)))], (51649 ^ _778908) ^ [] : [hBOOL(c_fFalse)], (19539 ^ _778908) ^ [_1115461] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115461))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115461)))))], (8900 ^ _778908) ^ [_927386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _927386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _927386))))], (27875 ^ _778908) ^ [_1273160] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1273160)) = _1273160)], (3292 ^ _778908) ^ [_829394, _829396, _829398, _829400, _829402, _829404] : [-(c_Partial__Function_Oflat__lub(_829404, _829400, _829396) = c_Partial__Function_Oflat__lub(_829402, _829398, _829394)), _829404 = _829402, _829400 = _829398, _829396 = _829394], (30162 ^ _778908) ^ [_1319362, _1319364, _1319366] : [class_Lattices_Obounded__lattice__bot(_1319362), 30165 ^ _778908 : [(30174 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1319362), _1319364), _1319366) = c_Orderings_Obot__class_Obot(_1319362)), _1319364 = c_Orderings_Obot__class_Obot(_1319362), _1319366 = c_Orderings_Obot__class_Obot(_1319362)], (30166 ^ _778908) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1319362), _1319364), _1319366) = c_Orderings_Obot__class_Obot(_1319362), 30169 ^ _778908 : [(30172 ^ _778908) ^ [] : [-(_1319366 = c_Orderings_Obot__class_Obot(_1319362))], (30170 ^ _778908) ^ [] : [-(_1319364 = c_Orderings_Obot__class_Obot(_1319362))]]]]], (51187 ^ _778908) ^ [_1808829, _1808831] : [class_Lattices_Olattice(_1808829), -(class_Lattices_Olattice(tc_fun(_1808831, _1808829)))], (18989 ^ _778908) ^ [_1106032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1106032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1106032))))], (24823 ^ _778908) ^ [_1213864] : [-(c_Nitpick_Ozero__frac(_1213864) = c_Nitpick_OAbs__Frac(_1213864, 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))))], (51351 ^ _778908) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (31373 ^ _778908) ^ [_1344883, _1344885, _1344887] : [hBOOL(hAPP(hAPP(c_member(_1344883), _1344885), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1344883, tc_HOL_Obool)), _1344887))), hBOOL(hAPP(hAPP(c_member(_1344883), _1344885), _1344887))], (7354 ^ _778908) ^ [_901795, _901797] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901795), _901797) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7355 ^ _778908 : [(7362 ^ _778908) ^ [] : [_901795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _901797 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7356 ^ _778908) ^ [] : [_901795 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19945 ^ _778908) ^ [_1122467, _1122469, _1122471] : [class_Rings_Olinordered__idom(_1122467), 19948 ^ _778908 : [(19957 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122467), hAPP(hAPP(c_Power_Opower__class_Opower(_1122467), _1122469), 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(_1122467), _1122471), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1122467)))), _1122469 = c_Groups_Ozero__class_Ozero(_1122467), _1122471 = c_Groups_Ozero__class_Ozero(_1122467)], (19949 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122467), hAPP(hAPP(c_Power_Opower__class_Opower(_1122467), _1122469), 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(_1122467), _1122471), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1122467))), 19952 ^ _778908 : [(19955 ^ _778908) ^ [] : [-(_1122471 = c_Groups_Ozero__class_Ozero(_1122467))], (19953 ^ _778908) ^ [] : [-(_1122469 = c_Groups_Ozero__class_Ozero(_1122467))]]]]], (51415 ^ _778908) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (51359 ^ _778908) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (28908 ^ _778908) ^ [_1293228, _1293230, _1293232, _1293234, _1293236] : [class_Complete__Lattice_Ocomplete__lattice(_1293228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1293230, tc_HOL_Obool)), _1293232), _1293234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293228), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293230, _1293228), _1293232), _1293236)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1293230, _1293228), _1293234), _1293236))))], (52 ^ _778908) ^ [_779630, _779632, _779634, _779636] : [-(c_Option_Ois__none(_779634, _779630)), c_Option_Ois__none(_779636, _779632), _779636 = _779634, _779632 = _779630], (27950 ^ _778908) ^ [_1274401] : [c_Nat__Transfer_Onat__set(_1274401), -(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), _1274401)) = _1274401)], (43962 ^ _778908) ^ [_1637430, _1637432, _1637434, _1637436, _1637438] : [c_Relation_Osingle__valued(_1637430, _1637430, _1637432), hBOOL(hAPP(hAPP(c_member(tc_prod(_1637430, _1637430)), hAPP(hAPP(c_Product__Type_OPair(_1637430, _1637430), _1637434), _1637436)), c_Transitive__Closure_Ortrancl(_1637430, _1637432))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1637430, _1637430)), hAPP(hAPP(c_Product__Type_OPair(_1637430, _1637430), _1637434), _1637438)), c_Transitive__Closure_Ortrancl(_1637430, _1637432))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637430, _1637430)), hAPP(hAPP(c_Product__Type_OPair(_1637430, _1637430), _1637436), _1637438)), c_Transitive__Closure_Ortrancl(_1637430, _1637432)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637430, _1637430)), hAPP(hAPP(c_Product__Type_OPair(_1637430, _1637430), _1637438), _1637436)), c_Transitive__Closure_Ortrancl(_1637430, _1637432))))], (49011 ^ _778908) ^ [_1761439, _1761441, _1761443, _1761445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1761439), _1761441)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761443)), _1761445))), -(hAPP(hAPP(c_List_Onth(_1761443), hAPP(hAPP(c_List_Odrop(_1761443), _1761439), _1761445)), _1761441) = hAPP(hAPP(c_List_Onth(_1761443), _1761445), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1761439), _1761441)))], (42890 ^ _778908) ^ [_1610738, _1610740, _1610742, _1610744, _1610746, _1610748] : [class_Groups_Oab__semigroup__mult(_1610738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610740), _1610742)), 42900 ^ _778908 : [(42903 ^ _778908) ^ [] : [hAPP(_1610744, 42899 ^ [_1610738, _1610740, _1610742, _1610744, _1610746, _1610748]) = hAPP(_1610746, 42899 ^ [_1610738, _1610740, _1610742, _1610744, _1610746, _1610748])], (42901 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1610740), 42899 ^ [_1610738, _1610740, _1610742, _1610744, _1610746, _1610748]), _1610742)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1610738, _1610740, c_Groups_Otimes__class_Otimes(_1610738)), _1610744), _1610748), _1610742) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1610738, _1610740, c_Groups_Otimes__class_Otimes(_1610738)), _1610746), _1610748), _1610742))], (50527 ^ _778908) ^ [_1793475, _1793477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1793475), _1793477)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1793475, _1793477)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1793477), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49374 ^ _778908) ^ [_1769205, _1769207, _1769209] : [class_Lattices_Olattice(_1769205), -(c_Big__Operators_Olattice__class_OSup__fin(_1769205, hAPP(c_List_Oset(_1769205), hAPP(hAPP(c_List_Olist_OCons(_1769205), _1769207), _1769209))) = hAPP(c_List_Ofoldl(_1769205, _1769205, c_Lattices_Osemilattice__sup__class_Osup(_1769205), _1769207), _1769209))], (35518 ^ _778908) ^ [_1433099, _1433101, _1433103, _1433105, _1433107] : [c_Finite__Set_Ofolding__one__idem(_1433099, _1433101, _1433103), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433099), _1433105)), hBOOL(hAPP(hAPP(c_member(_1433099), _1433107), _1433105)), -(hAPP(hAPP(_1433101, _1433107), hAPP(_1433103, _1433105)) = hAPP(_1433103, _1433105))], (31604 ^ _778908) ^ [_1349481, _1349483, _1349485] : [class_Orderings_Oord(_1349481), 31607 ^ _778908 : [(31614 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1349481), _1349483), _1349485)), -(hBOOL(hAPP(hAPP(c_member(_1349481), _1349483), hAPP(c_SetInterval_Oord__class_OlessThan(_1349481), _1349485))))], (31608 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1349481), _1349483), hAPP(c_SetInterval_Oord__class_OlessThan(_1349481), _1349485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1349481), _1349483), _1349485)))]]], (20093 ^ _778908) ^ [_1125516, _1125518] : [class_Int_Onumber__ring(_1125516), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1125516), hAPP(c_Int_Onumber__class_Onumber__of(_1125516), 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)))), _1125518))) = hAPP(c_Int_Onumber__class_Onumber__of(_1125516), c_Int_OMin))], (43335 ^ _778908) ^ [_1621905, _1621907, _1621909, _1621911, _1621913] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621905, _1621905)), hAPP(hAPP(c_Product__Type_OPair(_1621905, _1621905), _1621907), _1621909)), _1621911)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1621905, _1621905)), hAPP(hAPP(c_Product__Type_OPair(_1621905, _1621905), _1621909), _1621913)), c_Transitive__Closure_Ortrancl(_1621905, _1621911))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621905, _1621905)), hAPP(hAPP(c_Product__Type_OPair(_1621905, _1621905), _1621907), _1621913)), c_Transitive__Closure_Otrancl(_1621905, _1621911))))], (40735 ^ _778908) ^ [_1552691, _1552693, _1552695] : [class_Orderings_Olinorder(_1552691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552691), _1552693)), -(_1552693 = c_Orderings_Obot__class_Obot(tc_fun(_1552691, tc_HOL_Obool))), 40746 ^ _778908 : [(40747 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552691), _1552695), hAPP(c_Finite__Set_Ofold1(_1552691, c_Orderings_Oord__class_Omin(_1552691)), _1552693))), 40750 ^ _778908 : [(40751 ^ _778908) ^ [_1552984] : [hBOOL(hAPP(hAPP(c_member(_1552691), _1552984), _1552693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552691), _1552695), _1552984)))]]], (40757 ^ _778908) ^ [] : [40759 ^ _778908 : [(40762 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552691), _1552695), 40758 ^ [_1552691, _1552693, _1552695]))], (40760 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552691), 40758 ^ [_1552691, _1552693, _1552695]), _1552693)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552691), _1552695), hAPP(c_Finite__Set_Ofold1(_1552691, c_Orderings_Oord__class_Omin(_1552691)), _1552693))))]]], (13907 ^ _778908) ^ [_1013749, _1013751, _1013753, _1013755] : [class_Divides_Osemiring__div(_1013749), -(c_Divides_Odiv__class_Omod(_1013749, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013749), c_Divides_Odiv__class_Omod(_1013749, _1013751, _1013753)), _1013755), _1013753) = c_Divides_Odiv__class_Omod(_1013749, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013749), _1013751), _1013755), _1013753))], (8496 ^ _778908) ^ [_921382, _921384, _921386] : [class_Orderings_Opreorder(_921382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921382), _921384), _921386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921382), _921386), _921384))], (25969 ^ _778908) ^ [_1235057, _1235059, _1235061] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235059), _1235061))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235057), _1235061)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235057), _1235059)))], (3132 ^ _778908) ^ [_826884, _826886] : [_826886 = _826884, -(c_DSequence_Oempty(_826886) = c_DSequence_Oempty(_826884))], (11619 ^ _778908) ^ [_973296, _973298, _973300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973296), _973298)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973296), _973300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973298), _973300)))], (15848 ^ _778908) ^ [_1049354, _1049356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1049354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1049356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049356), _1049354)), _1049356)))], (11338 ^ _778908) ^ [_968659, _968661, _968663] : [11339 ^ _778908 : [(11342 ^ _778908) ^ [] : [_968659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11340 ^ _778908) ^ [] : [_968661 = _968663]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968659), _968661) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968659), _968663))], (22496 ^ _778908) ^ [_1168662] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1168662) = 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), _1168662), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (43273 ^ _778908) ^ [_1620426, _1620428] : [-(c_Relation_Orefl__on(_1620426, c_Orderings_Otop__class_Otop(tc_fun(_1620426, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1620426, _1620428)))], (7230 ^ _778908) ^ [_899921, _899923] : [_899921 = _899923, -(c_Com_Ovname_OGlb(_899921) = c_Com_Ovname_OGlb(_899923))], (51429 ^ _778908) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (7408 ^ _778908) ^ [_902683, _902685, _902687] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_902683, _902685, _902687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _902685)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _902687))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31441 ^ _778908) ^ [_1346126, _1346128, _1346130, _1346132] : [-(hBOOL(hAPP(hAPP(c_member(_1346126), _1346128), _1346130))), -(hBOOL(hAPP(hAPP(c_member(_1346126), _1346128), _1346132))), 31448 ^ _778908 : [(31455 ^ _778908) ^ [] : [_1346130 = _1346132, -(hAPP(hAPP(c_Set_Oinsert(_1346126), _1346128), _1346130) = hAPP(hAPP(c_Set_Oinsert(_1346126), _1346128), _1346132))], (31449 ^ _778908) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1346126), _1346128), _1346130) = hAPP(hAPP(c_Set_Oinsert(_1346126), _1346128), _1346132), -(_1346130 = _1346132)]]], (38620 ^ _778908) ^ [_1503132, _1503134, _1503136, _1503138, _1503140, _1503142] : [c_Fun_Oinj__on(_1503132, _1503134, hAPP(c_Fun_Ocomp(_1503136, _1503134, _1503132, _1503138), _1503140), _1503142), -(c_Fun_Oinj__on(_1503136, _1503134, _1503138, hAPP(c_Set_Oimage(_1503132, _1503136, _1503140), _1503142)))], (19525 ^ _778908) ^ [_1115212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1115212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1115212))))], (47439 ^ _778908) ^ [_1722555, _1722557, _1722559] : [-(hAPP(hAPP(c_List_Ozip(_1722555, _1722557), _1722559), c_List_Olist_ONil(_1722557)) = c_List_Olist_ONil(tc_prod(_1722555, _1722557)))], (43345 ^ _778908) ^ [_1622193, _1622195, _1622197, _1622199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622193, _1622193)), hAPP(hAPP(c_Product__Type_OPair(_1622193, _1622193), _1622195), _1622197)), c_Transitive__Closure_Ortrancl(_1622193, _1622199))), -(_1622195 = _1622197), 43352 ^ _778908 : [(43355 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622193, _1622193)), hAPP(hAPP(c_Product__Type_OPair(_1622193, _1622193), _1622195), _1622197)), c_Transitive__Closure_Otrancl(_1622193, _1622199))))], (43353 ^ _778908) ^ [] : [_1622195 = _1622197]]], (19501 ^ _778908) ^ [_1114790] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1114790)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1114790)))], (5821 ^ _778908) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51543 ^ _778908) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (29242 ^ _778908) ^ [_1301470] : [29244 ^ _778908 : [(29247 ^ _778908) ^ [_1301580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29243 ^ [_1301470, _1301580]), _1301580))], (29245 ^ _778908) ^ [_1301546] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29243 ^ [_1301470, _1301546]), _1301470)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1301470)))], (44831 ^ _778908) ^ [_1657167, _1657169, _1657171, _1657173, _1657175, _1657177] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657167, tc_fun(_1657169, tc_fun(_1657171, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1657167, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool), tc_fun(_1657169, tc_fun(_1657171, tc_HOL_Obool)), _1657167), hAPP(c_COMBC(_1657169, tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool), tc_fun(_1657171, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1657171, tc_fun(tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool), tc_fun(_1657171, tc_HOL_Obool)), _1657169), c_COMBC(_1657171, tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1657171, tc_prod(_1657169, _1657171)), tc_fun(_1657171, tc_fun(tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool), tc_HOL_Obool)), _1657169), hAPP(c_COMBB(tc_prod(_1657169, _1657171), tc_fun(tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool), tc_HOL_Obool), _1657171), c_member(tc_prod(_1657169, _1657171)))), c_Product__Type_OPair(_1657169, _1657171))))), _1657173)), _1657175), _1657177)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1657169, _1657171)), hAPP(hAPP(c_Product__Type_OPair(_1657169, _1657171), _1657175), _1657177)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657167, tc_fun(tc_prod(_1657169, _1657171), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1657167, tc_HOL_Obool))), _1657173))))], (8819 ^ _778908) ^ [_926003, _926005] : [class_Rings_Olinordered__idom(_926003), 8822 ^ _778908 : [(8829 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _926005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926003), c_Groups_Ozero__class_Ozero(_926003)), hAPP(c_Int_Oring__1__class_Oof__int(_926003), _926005))))], (8823 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926003), c_Groups_Ozero__class_Ozero(_926003)), hAPP(c_Int_Oring__1__class_Oof__int(_926003), _926005))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _926005)))]]], (12539 ^ _778908) ^ [_989750] : [-(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), _989750))))], (23014 ^ _778908) ^ [_1179245, _1179247, _1179249, _1179251, _1179253, _1179255, _1179257] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1179245, _1179247), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1179249), _1179251))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1179253, _1179247), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1179255), _1179257))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1179247)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1179245), _1179253), _1179247), 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), _1179249), _1179255)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1179251), _1179257)), _1179247))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1179251), _1179257), _1179247)))))], (45374 ^ _778908) ^ [_1671182, _1671184, _1671186, _1671188, _1671190] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1671182, tc_fun(_1671184, tc_HOL_Obool)), _1671186), hAPP(hAPP(c_COMBS(_1671182, tc_fun(_1671184, tc_HOL_Obool), tc_fun(_1671184, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1671184, tc_HOL_Obool), tc_fun(tc_fun(_1671184, tc_HOL_Obool), tc_fun(_1671184, tc_HOL_Obool)), _1671182), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1671184, tc_HOL_Obool))), _1671188)), _1671190)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1671184, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1671184, tc_HOL_Obool), hAPP(c_Set_Oimage(_1671182, tc_fun(_1671184, tc_HOL_Obool), _1671188), _1671186))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1671184, tc_HOL_Obool), hAPP(c_Set_Oimage(_1671182, tc_fun(_1671184, tc_HOL_Obool), _1671190), _1671186))))], (4 ^ _778908) ^ [_778958, _778960] : [_778960 = _778958, -(_778958 = _778960)], (37030 ^ _778908) ^ [_1467965, _1467967] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467965, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1467965, tc_HOL_Obool)), _1467967)), _1467967) = c_Orderings_Obot__class_Obot(tc_fun(_1467965, tc_HOL_Obool)))], (35576 ^ _778908) ^ [_1434206, _1434208, _1434210, _1434212] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1434206), _1434208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434206, tc_HOL_Obool)), _1434208), _1434210)), hBOOL(hAPP(_1434212, c_Orderings_Obot__class_Obot(tc_fun(_1434206, tc_HOL_Obool)))), 35591 ^ _778908 : [(35592 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1434206), 35590 ^ [_1434206, _1434208, _1434210, _1434212])))], (35596 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1434206), 35589 ^ [_1434206, _1434208, _1434210, _1434212]), 35590 ^ [_1434206, _1434208, _1434210, _1434212]))], (35600 ^ _778908) ^ [] : [hBOOL(hAPP(_1434212, hAPP(hAPP(c_Set_Oinsert(_1434206), 35589 ^ [_1434206, _1434208, _1434210, _1434212]), 35590 ^ [_1434206, _1434208, _1434210, _1434212])))], (35598 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1434212, 35590 ^ [_1434206, _1434208, _1434210, _1434212])))], (35594 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434206), 35589 ^ [_1434206, _1434208, _1434210, _1434212]), _1434210)))]], -(hBOOL(hAPP(_1434212, _1434208)))], (30556 ^ _778908) ^ [_1326329, _1326331, _1326333, _1326335, _1326337] : [-(_1326329 = c_Orderings_Obot__class_Obot(tc_fun(_1326331, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326333, tc_HOL_Obool)), _1326335), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326331, tc_fun(_1326333, tc_HOL_Obool)), _1326329), _1326337)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326331, tc_fun(_1326333, tc_HOL_Obool)), _1326329), hAPP(hAPP(c_COMBB(tc_fun(_1326333, tc_HOL_Obool), tc_fun(_1326333, tc_HOL_Obool), _1326331), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326333, tc_HOL_Obool)), _1326335)), _1326337)))], (36328 ^ _778908) ^ [_1452606, _1452608, _1452610, _1452612] : [hBOOL(hAPP(hAPP(c_member(_1452606), _1452608), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452606, tc_HOL_Obool)), _1452610), _1452612))), 36331 ^ _778908 : [(36334 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452606), _1452608), _1452612)))], (36332 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452606), _1452608), _1452610)))]]], (49103 ^ _778908) ^ [_1763963, _1763965, _1763967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763963), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763965)), _1763967))), -(hAPP(hAPP(c_List_Oappend(_1763965), hAPP(hAPP(c_List_Otake(_1763965), _1763963), _1763967)), hAPP(hAPP(c_List_Olist_OCons(_1763965), hAPP(c_List_Ohd(_1763965), hAPP(hAPP(c_List_Odrop(_1763965), _1763963), _1763967))), c_List_Olist_ONil(_1763965))) = hAPP(hAPP(c_List_Otake(_1763965), hAPP(c_Nat_OSuc, _1763963)), _1763967))], (31786 ^ _778908) ^ [_1353567, _1353569, _1353571, _1353573] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353567, tc_fun(_1353569, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1353567, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1353569, tc_HOL_Obool), tc_fun(_1353569, tc_HOL_Obool), _1353567), hAPP(c_COMBC(_1353569, tc_fun(_1353569, tc_HOL_Obool), tc_HOL_Obool), c_member(_1353569))), _1353571)), _1353573)), -(hBOOL(hAPP(hAPP(c_member(_1353569), _1353573), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353567, tc_fun(_1353569, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1353567, tc_HOL_Obool))), _1353571))))], (14533 ^ _778908) ^ [_1025597, _1025599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025597), _1025599)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025597, _1025599) = _1025597)], (30634 ^ _778908) ^ [_1327814] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1327814, _1327814) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1327814), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27222 ^ _778908) ^ [_1259797, _1259799, _1259801, _1259803, _1259805] : [class_Orderings_Olinorder(_1259797), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259797, _1259799), _1259801) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259797, _1259803), _1259805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259797), _1259799), _1259801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259797), _1259803), _1259805)), -(_1259799 = _1259803)], (4168 ^ _778908) ^ [_843114, _843116, _843118, _843120, _843122, _843124, _843126, _843128, _843130, _843132] : [-(c_Finite__Set_Ofold__graph(_843132, _843128, _843124, _843120, _843116) = c_Finite__Set_Ofold__graph(_843130, _843126, _843122, _843118, _843114)), _843132 = _843130, _843128 = _843126, _843124 = _843122, _843120 = _843118, _843116 = _843114], (42118 ^ _778908) ^ [_1591655, _1591657, _1591659, _1591661] : [c_Wellfounded_Owf(_1591655, _1591657), c_Fun_Oinj__on(_1591655, _1591659, _1591661, c_Orderings_Otop__class_Otop(tc_fun(_1591655, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1591659, hAPP(c_Set_Oimage(tc_prod(_1591655, _1591655), tc_prod(_1591659, _1591659), c_Product__Type_Omap__pair(_1591655, _1591659, _1591655, _1591659, _1591661, _1591661)), _1591657)))], (38750 ^ _778908) ^ [_1505709, _1505711, _1505713, _1505715] : [c_Fun_Oinj__on(_1505709, _1505711, _1505713, c_Orderings_Otop__class_Otop(tc_fun(_1505709, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1505709, tc_fun(_1505715, _1505711), hAPP(hAPP(c_COMBB(_1505711, tc_fun(_1505715, _1505711), _1505709), c_COMBK(_1505711, _1505715)), _1505713), c_Orderings_Otop__class_Otop(tc_fun(_1505709, tc_HOL_Obool))))], (12614 ^ _778908) ^ [_990955] : [-(hBOOL(hAPP(_990955, 12621 ^ [_990955]))), 12615 ^ _778908 : [(12616 ^ _778908) ^ [_991007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991007)), hBOOL(hAPP(_990955, hAPP(c_Int_Onat, _991007)))]]], (2832 ^ _778908) ^ [_821856, _821858, _821860, _821862] : [-(c_Nitpick_OAbs__Frac(_821862, _821858) = c_Nitpick_OAbs__Frac(_821860, _821856)), _821862 = _821860, _821858 = _821856], (39759 ^ _778908) ^ [_1528119, _1528121, _1528123, _1528125] : [-(c_Map_Odom(_1528119, _1528121, c_Map_Orestrict__map(_1528119, _1528121, _1528123, _1528125)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528119, tc_HOL_Obool)), c_Map_Odom(_1528119, _1528121, _1528123)), _1528125))], (44633 ^ _778908) ^ [_1651920, _1651922, _1651924, _1651926] : [-(hAPP(c_Set_OCollect(_1651920), hAPP(hAPP(c_COMBB(tc_fun(_1651922, tc_HOL_Obool), tc_HOL_Obool, _1651920), c_HOL_OAll(_1651922)), hAPP(hAPP(c_COMBB(tc_fun(_1651922, tc_HOL_Obool), tc_fun(_1651922, tc_HOL_Obool), _1651920), hAPP(c_COMBS(_1651922, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1651922), c_fimplies), hAPP(hAPP(c_COMBC(_1651922, tc_fun(_1651922, tc_HOL_Obool), tc_HOL_Obool), c_member(_1651922)), _1651924)))), _1651926))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651922, tc_fun(_1651920, tc_HOL_Obool)), _1651924), hAPP(hAPP(c_COMBB(tc_fun(_1651920, tc_HOL_Obool), tc_fun(_1651920, tc_HOL_Obool), _1651922), c_Set_OCollect(_1651920)), hAPP(c_COMBC(_1651920, _1651922, tc_HOL_Obool), _1651926))))], (36360 ^ _778908) ^ [_1453252, _1453254, _1453256] : [class_Lattices_Osemilattice__inf(_1453252), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453252), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1453252), _1453254), _1453256)), _1453254)))], (2604 ^ _778908) ^ [_818330, _818332, _818334, _818336, _818338, _818340, _818342, _818344, _818346, _818348] : [-(c_Product__Type_Oprod_Oprod__rec(_818348, _818344, _818340, _818336, _818332) = c_Product__Type_Oprod_Oprod__rec(_818346, _818342, _818338, _818334, _818330)), _818348 = _818346, _818344 = _818342, _818340 = _818338, _818336 = _818334, _818332 = _818330], (5194 ^ _778908) ^ [_859263, _859265, _859267, _859269, _859271, _859273] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_859273, _859269, _859265) = c_SetInterval_Oord__class_OgreaterThanAtMost(_859271, _859267, _859263)), _859273 = _859271, _859269 = _859267, _859265 = _859263], (39948 ^ _778908) ^ [_1532654, _1532656, _1532658, _1532660] : [-(c_Wellfounded_Omax__extp(_1532654, _1532656, _1532658, _1532660)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532654), _1532658)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532654), _1532660)), -(_1532660 = c_Orderings_Obot__class_Obot(tc_fun(_1532654, tc_HOL_Obool))), 39962 ^ _778908 : [(39965 ^ _778908) ^ [_1532999] : [hBOOL(hAPP(hAPP(c_member(_1532654), _1532999), _1532660)), hBOOL(hAPP(hAPP(_1532656, 39961 ^ [_1532654, _1532656, _1532658, _1532660]), _1532999))], (39963 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532654), 39961 ^ [_1532654, _1532656, _1532658, _1532660]), _1532658)))]]], (32575 ^ _778908) ^ [_1371456, _1371458, _1371460, _1371462] : [hBOOL(hAPP(hAPP(_1371460, _1371458), _1371462)), -(hBOOL(hAPP(hAPP(c_member(_1371456), _1371458), c_SetInterval_Oord_OatMost(_1371456, _1371460, _1371462))))], (3494 ^ _778908) ^ [_832615, _832617, _832619, _832621, _832623, _832625, _832627, _832629] : [-(c_Sum__Type_OPlus(_832629, _832625, _832621, _832617) = c_Sum__Type_OPlus(_832627, _832623, _832619, _832615)), _832629 = _832627, _832625 = _832623, _832621 = _832619, _832617 = _832615], (19401 ^ _778908) ^ [_1113040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1113040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1113040)))], (47058 ^ _778908) ^ [_1712806, _1712808, _1712810, _1712812, _1712814, _1712816] : [class_Orderings_Olinorder(_1712806), 47061 ^ _778908 : [(47068 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712806), hAPP(_1712808, _1712810)), hAPP(_1712808, _1712812)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712814, _1712806, _1712808), _1712810), hAPP(hAPP(c_List_Olist_OCons(_1712814), _1712812), _1712816)) = hAPP(hAPP(c_List_Olist_OCons(_1712814), _1712812), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712814, _1712806, _1712808), _1712810), _1712816)))], (47062 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712806), hAPP(_1712808, _1712810)), hAPP(_1712808, _1712812))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712814, _1712806, _1712808), _1712810), hAPP(hAPP(c_List_Olist_OCons(_1712814), _1712812), _1712816)) = hAPP(hAPP(c_List_Olist_OCons(_1712814), _1712810), hAPP(hAPP(c_List_Olist_OCons(_1712814), _1712812), _1712816)))]]], (51193 ^ _778908) ^ [_1808908, _1808910] : [class_Orderings_Oorder(_1808908), -(class_Orderings_Oorder(tc_fun(_1808910, _1808908)))], (21265 ^ _778908) ^ [_1146280, _1146282, _1146284, _1146286] : [class_Fields_Ofield(_1146280), -(_1146282 = c_Groups_Ozero__class_Ozero(_1146280)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146280), _1146284), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146280), _1146286), _1146282)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146280), _1146282), _1146284)), _1146286)), _1146282))], (6449 ^ _778908) ^ [_883042, _883044, _883046, _883048] : [c_Com_Ocom_OCond(_883042, _883044, _883046) = hAPP(c_Com_Ocom_OBODY, _883048)], (21167 ^ _778908) ^ [_1144560, _1144562, _1144564, _1144566] : [class_Fields_Olinordered__field__inverse__zero(_1144560), 21170 ^ _778908 : [(21171 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144562), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144560), _1144564), _1144566))), 21174 ^ _778908 : [(21181 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), c_Groups_Ozero__class_Ozero(_1144560)), _1144566))), 21184 ^ _778908 : [(21191 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144566), c_Groups_Ozero__class_Ozero(_1144560)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144562), c_Groups_Ozero__class_Ozero(_1144560))))], (21185 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144566), c_Groups_Ozero__class_Ozero(_1144560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144560), _1144562), _1144566))))]]], (21175 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), c_Groups_Ozero__class_Ozero(_1144560)), _1144566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144560), _1144562), _1144566)), _1144564)))]]], (21197 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144562), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144560), _1144564), _1144566)))), 21200 ^ _778908 : [(21203 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144560), _1144562), _1144566)), _1144564))], (21201 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), c_Groups_Ozero__class_Ozero(_1144560)), _1144566)))]], 21204 ^ _778908 : [(21207 ^ _778908) ^ [] : [21208 ^ _778908 : [(21211 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144560), _1144562), _1144566)))], (21209 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144566), c_Groups_Ozero__class_Ozero(_1144560))))]], 21212 ^ _778908 : [(21215 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144562), c_Groups_Ozero__class_Ozero(_1144560)))], (21213 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), _1144566), c_Groups_Ozero__class_Ozero(_1144560)))]]], (21205 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144560), c_Groups_Ozero__class_Ozero(_1144560)), _1144566))]]]]], (36928 ^ _778908) ^ [_1465485, _1465487, _1465489] : [class_Lattices_Oboolean__algebra(_1465485), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1465485), _1465487), _1465489) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465485), _1465487), hAPP(c_Groups_Ouminus__class_Ouminus(_1465485), _1465489)))], (11602 ^ _778908) ^ [_972970, _972972] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972970), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972972), _972970))))], (26043 ^ _778908) ^ [_1236397, _1236399, _1236401] : [class_Groups_Ocomm__monoid__add(_1236397), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1236397), _1236399), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1236401))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236397), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1236397), _1236399), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1236401))), hAPP(_1236399, _1236401)))], (35847 ^ _778908) ^ [_1441156, _1441158, _1441160, _1441162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1441156), _1441162)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1441160), _1441158))), -(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), _1441156), _1441158)), 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), _1441160), _1441162)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (14922 ^ _778908) ^ [_1031907, _1031909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031909), 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), _1031907), _1031909)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16124 ^ _778908) ^ [_1055135, _1055137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1055135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055135), hAPP(c_Nat_OSuc, _1055137))), _1055135)))], (18289 ^ _778908) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21543 ^ _778908) ^ [_1150916, _1150918, _1150920, _1150922] : [class_Fields_Olinordered__field__inverse__zero(_1150916), 21546 ^ _778908 : [(21547 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), _1150918), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150916), _1150920), _1150922))), 21550 ^ _778908 : [(21557 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), c_Groups_Ozero__class_Ozero(_1150916)), _1150922))), 21560 ^ _778908 : [(21567 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), _1150922), c_Groups_Ozero__class_Ozero(_1150916)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), _1150918), c_Groups_Ozero__class_Ozero(_1150916))))], (21561 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), _1150922), c_Groups_Ozero__class_Ozero(_1150916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), _1150920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150916), _1150918), _1150922))))]]], (21551 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), c_Groups_Ozero__class_Ozero(_1150916)), _1150922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150916), _1150918), _1150922)), _1150920)))]]], (21573 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), _1150918), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150916), _1150920), _1150922)))), 21576 ^ _778908 : [(21579 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150916), _1150918), _1150922)), _1150920))], (21577 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), c_Groups_Ozero__class_Ozero(_1150916)), _1150922)))]], 21580 ^ _778908 : [(21583 ^ _778908) ^ [] : [21584 ^ _778908 : [(21587 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), _1150920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150916), _1150918), _1150922)))], (21585 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), _1150922), c_Groups_Ozero__class_Ozero(_1150916))))]], 21588 ^ _778908 : [(21591 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150916), _1150918), c_Groups_Ozero__class_Ozero(_1150916)))], (21589 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), _1150922), c_Groups_Ozero__class_Ozero(_1150916)))]]], (21581 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150916), c_Groups_Ozero__class_Ozero(_1150916)), _1150922))]]]]], (20037 ^ _778908) ^ [_1124386] : [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, _1124386, 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, _1124386, 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))], (34820 ^ _778908) ^ [_1416832, _1416834, _1416836, _1416838] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1416832, tc_Option_Ooption(_1416834)), hAPP(c_COMBK(tc_Option_Ooption(_1416834), _1416832), c_Option_Ooption_ONone(_1416834))), _1416836), c_Option_Ooption_ONone(_1416834)), _1416838) = c_Option_Ooption_ONone(_1416834))], (51591 ^ _778908) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (6399 ^ _778908) ^ [_882146, _882148, _882150, _882152, _882154, _882156] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_882146, _882148, _882150), _882152, _882154, _882156)), 6400 ^ _778908 : [(6407 ^ _778908) ^ [] : [-(hBOOL(hAPP(_882146, _882152))), c_Natural_Oevaln(_882150, _882152, _882154, _882156)], (6401 ^ _778908) ^ [] : [hBOOL(hAPP(_882146, _882152)), c_Natural_Oevaln(_882148, _882152, _882154, _882156)]]], (8738 ^ _778908) ^ [_924750, _924752, _924754] : [class_Orderings_Oorder(_924750), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924750), _924752), _924754)), _924754 = _924752], (29361 ^ _778908) ^ [_1303553, _1303555, _1303557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1303553), _1303555)), 29364 ^ _778908 : [(29365 ^ _778908) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1303553, tc_Nat_Onat), _1303557), _1303555) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 29368 ^ _778908 : [(29369 ^ _778908) ^ [_1303715] : [hBOOL(hAPP(hAPP(c_member(_1303553), _1303715), _1303555)), -(hAPP(_1303557, _1303715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (29375 ^ _778908) ^ [] : [29377 ^ _778908 : [(29380 ^ _778908) ^ [] : [hAPP(_1303557, 29376 ^ [_1303553, _1303555, _1303557]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29378 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1303553), 29376 ^ [_1303553, _1303555, _1303557]), _1303555)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1303553, tc_Nat_Onat), _1303557), _1303555) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24063 ^ _778908) ^ [_1198861, _1198863, _1198865, _1198867, _1198869] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198861, _1198863, _1198865), _1198867), _1198869) = hAPP(hAPP(_1198867, hAPP(c_Product__Type_Ofst(_1198861, _1198863), _1198869)), hAPP(c_Product__Type_Osnd(_1198861, _1198863), _1198869)))], (20957 ^ _778908) ^ [_1140572, _1140574, _1140576] : [class_Fields_Olinordered__field(_1140572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140572), c_Groups_Ozero__class_Ozero(_1140572)), _1140574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140572), c_Groups_Ozero__class_Ozero(_1140572)), _1140576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140572), c_Groups_Ozero__class_Ozero(_1140572)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140572), _1140574), _1140576))))], (39526 ^ _778908) ^ [_1522634, _1522636, _1522638, _1522640, _1522642] : [-(hAPP(c_Set_Ovimage(_1522634, _1522636, _1522638), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522636, tc_HOL_Obool)), _1522640), _1522642)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522634, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522634, _1522636, _1522638), _1522640)), hAPP(c_Set_Ovimage(_1522634, _1522636, _1522638), _1522642)))], (6011 ^ _778908) ^ [_874985, _874987, _874989, _874991] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_874985, _874987), _874989, _874991, hAPP(hAPP(hAPP(c_Natural_Oupdate, _874989), _874985), hAPP(_874987, _874989))))], (51419 ^ _778908) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (19611 ^ _778908) ^ [_1116700, _1116702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116700), _1116702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116700)), c_Int_OBit1(_1116702))))], (28547 ^ _778908) ^ [_1286047, _1286049, _1286051, _1286053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286047, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286047, tc_HOL_Obool)), _1286049), _1286051)), _1286053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286047, tc_HOL_Obool)), _1286049), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286047, tc_HOL_Obool)), _1286051), _1286053))))], (41359 ^ _778908) ^ [_1566819, _1566821, _1566823, _1566825, _1566827, _1566829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1566819), _1566821)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566823), _1566825)), 41369 ^ _778908 : [(41372 ^ _778908) ^ [] : [hAPP(c_Finite__Set_Ocard(_1566819), hAPP(c_Set_OCollect(_1566819), hAPP(hAPP(c_COMBS(_1566819, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566819), c_fconj), hAPP(hAPP(c_COMBC(_1566819, tc_fun(_1566819, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566819)), _1566821))), hAPP(hAPP(c_COMBC(_1566819, _1566823, tc_HOL_Obool), _1566827), 41368 ^ [_1566819, _1566821, _1566823, _1566825, _1566827, _1566829])))) = _1566829], (41370 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566823), 41368 ^ [_1566819, _1566821, _1566823, _1566825, _1566827, _1566829]), _1566825)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566819, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1566823, tc_HOL_Obool), tc_Nat_Onat, _1566819), c_Finite__Set_Ocard(_1566823)), hAPP(hAPP(c_COMBB(tc_fun(_1566823, tc_HOL_Obool), tc_fun(_1566823, tc_HOL_Obool), _1566819), c_Set_OCollect(_1566823)), hAPP(hAPP(c_COMBB(tc_fun(_1566823, tc_HOL_Obool), tc_fun(_1566823, tc_HOL_Obool), _1566819), hAPP(c_COMBS(_1566823, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566823), c_fconj), hAPP(hAPP(c_COMBC(_1566823, tc_fun(_1566823, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566823)), _1566825)))), _1566827)))), _1566821) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1566829), hAPP(c_Finite__Set_Ocard(_1566823), _1566825)))], (49285 ^ _778908) ^ [_1767311, _1767313, _1767315] : [class_Groups_Omonoid__add(_1767311), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1767311), _1767313), hAPP(c_List_Ofoldl(_1767311, _1767311, c_Groups_Oplus__class_Oplus(_1767311), c_Groups_Ozero__class_Ozero(_1767311)), _1767315)) = hAPP(c_List_Ofoldl(_1767311, _1767311, c_Groups_Oplus__class_Oplus(_1767311), _1767313), _1767315))], (11494 ^ _778908) ^ [_971294, _971296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971294), _971296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _971294)), hAPP(c_Nat_OSuc, _971296))))], (41289 ^ _778908) ^ [_1563956, _1563958, _1563960, _1563962, _1563964, _1563966, _1563968] : [class_Groups_Ocomm__monoid__add(_1563956), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563958), _1563960)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563962), _1563964)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1563958, _1563956), hAPP(hAPP(c_COMBS(_1563958, tc_fun(_1563962, tc_HOL_Obool), _1563956), hAPP(hAPP(c_COMBB(tc_fun(_1563962, _1563956), tc_fun(tc_fun(_1563962, tc_HOL_Obool), _1563956), _1563958), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1563962, _1563956)), _1563966)), hAPP(hAPP(c_COMBB(tc_fun(_1563962, tc_HOL_Obool), tc_fun(_1563962, tc_HOL_Obool), _1563958), c_Set_OCollect(_1563962)), hAPP(hAPP(c_COMBB(tc_fun(_1563962, tc_HOL_Obool), tc_fun(_1563962, tc_HOL_Obool), _1563958), hAPP(c_COMBS(_1563962, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563962), c_fconj), hAPP(hAPP(c_COMBC(_1563962, tc_fun(_1563962, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563962)), _1563964)))), _1563968)))), _1563960) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1563962, _1563956), hAPP(hAPP(c_COMBS(_1563962, tc_fun(_1563958, tc_HOL_Obool), _1563956), hAPP(hAPP(c_COMBB(tc_fun(_1563958, _1563956), tc_fun(tc_fun(_1563958, tc_HOL_Obool), _1563956), _1563962), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1563958, _1563956)), hAPP(c_COMBC(_1563958, _1563962, _1563956), _1563966))), hAPP(hAPP(c_COMBB(tc_fun(_1563958, tc_HOL_Obool), tc_fun(_1563958, tc_HOL_Obool), _1563962), c_Set_OCollect(_1563958)), hAPP(hAPP(c_COMBB(tc_fun(_1563958, tc_HOL_Obool), tc_fun(_1563958, tc_HOL_Obool), _1563962), hAPP(c_COMBS(_1563958, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563958), c_fconj), hAPP(hAPP(c_COMBC(_1563958, tc_fun(_1563958, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563958)), _1563960)))), hAPP(c_COMBC(_1563958, _1563962, tc_HOL_Obool), _1563968))))), _1563964))], (29172 ^ _778908) ^ [_1300050, _1300052, _1300054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300050, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1300050, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29173 ^ [_1300050, _1300052, _1300054])), _1300052)), _1300054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300050, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1300050, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1300052)), _1300054)))], (45761 ^ _778908) ^ [_1680018, _1680020, _1680022, _1680024, _1680026, _1680028, _1680030, _1680032] : [c_Finite__Set_Ofolding__image__simple__idem(_1680018, _1680020, _1680022, _1680024, _1680026, _1680028), hBOOL(hAPP(c_Finite__Set_Ofinite(_1680020), _1680030)), hBOOL(hAPP(hAPP(c_member(_1680020), _1680032), _1680030)), -(hAPP(hAPP(_1680022, hAPP(_1680026, _1680032)), hAPP(_1680028, _1680030)) = hAPP(_1680028, _1680030))], (43618 ^ _778908) ^ [_1628750, _1628752, _1628754, _1628756, _1628758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628750, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628752, _1628750, _1628754), _1628756)), _1628758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628752, tc_HOL_Obool)), _1628756), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628752, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628750, _1628752, hAPP(c_Relation_Oconverse(_1628752, _1628750), _1628754)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628750, tc_HOL_Obool)), _1628758))))))], (9180 ^ _778908) ^ [_932606, _932608, _932610] : [class_Groups_Ogroup__add(_932606), 9183 ^ _778908 : [(9190 ^ _778908) ^ [] : [_932610 = hAPP(c_Groups_Ouminus__class_Ouminus(_932606), _932608), -(_932608 = hAPP(c_Groups_Ouminus__class_Ouminus(_932606), _932610))], (9184 ^ _778908) ^ [] : [_932608 = hAPP(c_Groups_Ouminus__class_Ouminus(_932606), _932610), -(_932610 = hAPP(c_Groups_Ouminus__class_Ouminus(_932606), _932608))]]], (22786 ^ _778908) ^ [_1174313, _1174315, _1174317, _1174319] : [-(c_Nat_Onat_Onat__case(_1174313, _1174315, _1174317, hAPP(c_Nat_OSuc, _1174319)) = hAPP(_1174317, _1174319))], (26137 ^ _778908) ^ [_1239020, _1239022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239022)), 26144 ^ _778908 : [(26151 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239020), _1239022)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1239020)), hAPP(c_Int_Onat, _1239022))))], (26145 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1239020)), hAPP(c_Int_Onat, _1239022))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239020), _1239022)))]]], (32729 ^ _778908) ^ [_1374790, _1374792, _1374794] : [hAPP(c_Finite__Set_Ocard(_1374790), _1374792) = hAPP(c_Nat_OSuc, _1374794), 32734 ^ _778908 : [(32737 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1374790), 32732 ^ [_1374790, _1374792, _1374794]), 32733 ^ [_1374790, _1374792, _1374794]))], (32739 ^ _778908) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1374790), 32733 ^ [_1374790, _1374792, _1374794]) = _1374794)], (32741 ^ _778908) ^ [] : [_1374794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(32733 ^ [_1374790, _1374792, _1374794] = c_Orderings_Obot__class_Obot(tc_fun(_1374790, tc_HOL_Obool)))], (32735 ^ _778908) ^ [] : [-(_1374792 = hAPP(hAPP(c_Set_Oinsert(_1374790), 32732 ^ [_1374790, _1374792, _1374794]), 32733 ^ [_1374790, _1374792, _1374794]))]]], (35498 ^ _778908) ^ [_1432591, _1432593] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1432591, tc_HOL_Obool)), hAPP(c_Set_OPow(_1432591), _1432593))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1432591), _1432593)))], (48351 ^ _778908) ^ [_1743775, _1743777, _1743779] : [hBOOL(hAPP(c_List_Odistinct(_1743775), hAPP(hAPP(c_List_Oappend(_1743775), _1743777), _1743779))), 48354 ^ _778908 : [(48359 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1743775, tc_HOL_Obool)), hAPP(c_List_Oset(_1743775), _1743777)), hAPP(c_List_Oset(_1743775), _1743779)) = c_Orderings_Obot__class_Obot(tc_fun(_1743775, tc_HOL_Obool)))], (48357 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1743775), _1743779)))], (48355 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1743775), _1743777)))]]], (28147 ^ _778908) ^ [_1278347, _1278349, _1278351] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278347, tc_HOL_Obool)), _1278349), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278347, tc_HOL_Obool)), _1278349), _1278351)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278347, tc_HOL_Obool)), _1278349), _1278351))], (31810 ^ _778908) ^ [_1354307, _1354309, _1354311] : [_1354311 = hAPP(c_Option_Ooption_OSome(_1354307), _1354309), -(hBOOL(hAPP(hAPP(c_member(_1354307), _1354309), c_Option_Oset(_1354307, _1354311))))], (17247 ^ _778908) ^ [_1076594, _1076596] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1076594), _1076596))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1076594))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1076596))))], (12461 ^ _778908) ^ [_988432, _988434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988432), _988434)), 12464 ^ _778908 : [(12471 ^ _778908) ^ [] : [_988434 = _988432, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988434), hAPP(c_Nat_OSuc, _988432))))], (12465 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988434), hAPP(c_Nat_OSuc, _988432))), -(_988434 = _988432)]]], (18897 ^ _778908) ^ [_1104566, _1104568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104566), _1104568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1104566)), c_Int_OBit1(_1104568))))], (35985 ^ _778908) ^ [_1444521, _1444523, _1444525, _1444527, _1444529, _1444531] : [c_Finite__Set_Ofolding(_1444521, _1444523, _1444525, _1444527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444521), _1444529)), -(hBOOL(hAPP(hAPP(c_member(_1444521), _1444531), _1444529))), -(hAPP(_1444527, hAPP(hAPP(c_Set_Oinsert(_1444521), _1444531), _1444529)) = hAPP(c_Fun_Ocomp(_1444523, _1444523, _1444523, hAPP(_1444527, _1444529)), hAPP(_1444525, _1444531)))], (43624 ^ _778908) ^ [_1628941, _1628943, _1628945, _1628947, _1628949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628943, tc_HOL_Obool)), _1628947), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628943, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628941, _1628943, hAPP(c_Relation_Oconverse(_1628943, _1628941), _1628945)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1628941, tc_HOL_Obool)), _1628949))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1628941, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1628943, _1628941, _1628945), _1628947)), _1628949)))], (50385 ^ _778908) ^ [_1791185, _1791187] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1791185, _1791187)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1791185), _1791187))], (36934 ^ _778908) ^ [_1465604, _1465606, _1465608] : [class_Lattices_Oboolean__algebra(_1465604), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1465604), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1465604), _1465606), _1465608)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465604), hAPP(c_Groups_Ouminus__class_Ouminus(_1465604), _1465606)), hAPP(c_Groups_Ouminus__class_Ouminus(_1465604), _1465608)))], (8940 ^ _778908) ^ [_928211, _928213, _928215] : [class_Rings_Olinordered__semidom(_928211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928211), c_Groups_Oone__class_Oone(_928211)), _928213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928211), c_Groups_Oone__class_Oone(_928211)), _928215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928211), c_Groups_Oone__class_Oone(_928211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928211), _928213), _928215))))], (37766 ^ _778908) ^ [_1483950, _1483952, _1483954, _1483956, _1483958, _1483960] : [c_Finite__Set_Ofolding(_1483950, _1483952, _1483954, _1483956), hBOOL(hAPP(c_Finite__Set_Ofinite(_1483950), _1483958)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1483950), _1483960)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483950, tc_HOL_Obool)), _1483958), _1483960) = c_Orderings_Obot__class_Obot(tc_fun(_1483950, tc_HOL_Obool)), -(hAPP(_1483956, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483950, tc_HOL_Obool)), _1483958), _1483960)) = hAPP(c_Fun_Ocomp(_1483952, _1483952, _1483952, hAPP(_1483956, _1483958)), hAPP(_1483956, _1483960)))], (6009 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (1452 ^ _778908) ^ [_799932, _799934] : [-(class_Groups_Olinordered__ab__semigroup__add(_799932)), _799934 = _799932, class_Groups_Olinordered__ab__semigroup__add(_799934)], (45410 ^ _778908) ^ [_1672021, _1672023, _1672025] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1672021, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672021, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1672021, tc_HOL_Obool), tc_HOL_Obool)), _1672023), _1672025))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1672021, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672021, tc_HOL_Obool), _1672023)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672021, tc_HOL_Obool), _1672025)))))], (17547 ^ _778908) ^ [_1082063, _1082065, _1082067] : [class_Rings_Osemiring__1(_1082063), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082063), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1082065), _1082067)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1082063), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082063), _1082065)), _1082067))], (27775 ^ _778908) ^ [_1271405, _1271407, _1271409] : [class_Orderings_Olinorder(_1271405), 27778 ^ _778908 : [(27785 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271405), _1271409), _1271407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271405, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1271405), _1271407)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1271405), _1271409))))], (27779 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271405, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1271405), _1271407)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1271405), _1271409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271405), _1271409), _1271407)))]]], (38232 ^ _778908) ^ [_1495062, _1495064, _1495066] : [class_Lattices_Olattice(_1495062), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495062), _1495064)), 38239 ^ _778908 : [(38246 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495062, tc_HOL_Obool)), _1495064), hAPP(hAPP(c_Set_Oinsert(_1495062), _1495066), c_Orderings_Obot__class_Obot(tc_fun(_1495062, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1495062, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1495062, hAPP(hAPP(c_Set_Oinsert(_1495062), _1495066), _1495064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1495062), _1495066), c_Big__Operators_Olattice__class_OInf__fin(_1495062, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495062, tc_HOL_Obool)), _1495064), hAPP(hAPP(c_Set_Oinsert(_1495062), _1495066), c_Orderings_Obot__class_Obot(tc_fun(_1495062, tc_HOL_Obool)))))))], (38240 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495062, tc_HOL_Obool)), _1495064), hAPP(hAPP(c_Set_Oinsert(_1495062), _1495066), c_Orderings_Obot__class_Obot(tc_fun(_1495062, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1495062, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1495062, hAPP(hAPP(c_Set_Oinsert(_1495062), _1495066), _1495064)) = _1495066)]]], (12333 ^ _778908) ^ [_986118, _986120] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986118), _986120) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12336 ^ _778908 : [(12339 ^ _778908) ^ [] : [-(_986120 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12337 ^ _778908) ^ [] : [-(_986118 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (5985 ^ _778908) ^ [_874504, _874506, _874508] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _874506))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_874504, _874506, _874508))))], (46889 ^ _778908) ^ [_1707125, _1707127, _1707129] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1707125), _1707127)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1707125)), hAPP(c_Set_OCollect(tc_List_Olist(_1707125)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1707125), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1707125)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707125), tc_fun(_1707125, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1707125, tc_HOL_Obool), tc_fun(tc_fun(_1707125, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1707125)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1707125, tc_HOL_Obool))), c_List_Oset(_1707125))), _1707127))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707125), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1707125)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1707125)))), _1707129))))))], (41983 ^ _778908) ^ [_1588799, _1588801] : [c_Wellfounded_Owf(_1588799, _1588801), -(c_Wellfounded_Owf(tc_fun(_1588799, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1588799, _1588801)))], (50741 ^ _778908) ^ [_1798184] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1798184)), c_List_Otranspose__rel(_1798184)), c_List_Olist_ONil(tc_List_Olist(_1798184)))), -(c_List_Otranspose(_1798184, c_List_Olist_ONil(tc_List_Olist(_1798184))) = c_List_Olist_ONil(tc_List_Olist(_1798184)))], (19739 ^ _778908) ^ [_1118917] : [class_Rings_Osemiring__1(_1118917), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1118917), c_Groups_Oone__class_Oone(_1118917)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1118917))], (32373 ^ _778908) ^ [_1367568, _1367570, _1367572, _1367574] : [hBOOL(hAPP(hAPP(c_member(_1367568), _1367570), c_SetInterval_Oord_OgreaterThan(_1367568, _1367572, _1367574))), -(hBOOL(hAPP(hAPP(_1367572, _1367574), _1367570)))], (45972 ^ _778908) ^ [_1684811, _1684813, _1684815] : [-(c_Smallcheck_Oorelse(_1684811, _1684813, _1684815) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1684811), _1684811, _1684815, c_Option_Ooption_OSome(_1684811)), _1684813))], (30046 ^ _778908) ^ [_1316943, _1316945] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316943, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1316943, tc_HOL_Obool))), _1316945) = c_Orderings_Obot__class_Obot(tc_fun(_1316943, tc_HOL_Obool)))], (51681 ^ _778908) ^ [_1813886, _1813888] : [hBOOL(hAPP(hAPP(c_fconj, _1813886), _1813888)), -(hBOOL(_1813888))], (50068 ^ _778908) ^ [_1785037, _1785039, _1785041, _1785043] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1785037, tc_Nat_Onat), _1785037), c_Product__Type_Ofst(_1785037, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1785037, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1785037, tc_Nat_Onat)), _1785039), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1785037, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1785037, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1785037, tc_Nat_Onat), _1785041), _1785043))) = hAPP(hAPP(c_List_Omap(tc_prod(_1785037, tc_Nat_Onat), _1785037), c_Product__Type_Ofst(_1785037, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1785037, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1785037, tc_Nat_Onat)), _1785039), c_Product__Type_Osnd(_1785037, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1785037, tc_Nat_Onat), _1785041), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1785043)))))], (25315 ^ _778908) ^ [_1224099, _1224101] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224099), _1224101)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224101), _1224099))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224101), _1224099)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224099), _1224101)))], (42624 ^ _778908) ^ [_1604531, _1604533, _1604535] : [c_Hoare__Mirabelle_Ohoare__valids(_1604531, _1604533, _1604535), 42627 ^ _778908 : [(42628 ^ _778908) ^ [_1604640] : [42630 ^ _778908 : [(42633 ^ _778908) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1604531, _1604640, 42629 ^ [_1604531, _1604533, _1604535, _1604640])], (42631 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1604531)), 42629 ^ [_1604531, _1604533, _1604535, _1604640]), _1604533)))]], 42634 ^ _778908 : [(42635 ^ _778908) ^ [_1604812] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1604531)), _1604812), _1604535)), -(c_Hoare__Mirabelle_Otriple__valid(_1604531, _1604640, _1604812))]]]]], (37566 ^ _778908) ^ [_1479936, _1479938, _1479940] : [class_Orderings_Olinorder(_1479936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479936), _1479938)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479936), _1479940)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479936, tc_HOL_Obool)), _1479938), _1479940) = c_Orderings_Obot__class_Obot(tc_fun(_1479936, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1479936), c_Big__Operators_Olinorder__class_OMin(_1479936, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479936, tc_HOL_Obool)), _1479938), _1479940))), c_Big__Operators_Olinorder__class_OMin(_1479936, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479936, tc_HOL_Obool)), _1479938), _1479940))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1479936), c_Big__Operators_Olinorder__class_OMin(_1479936, _1479938)), c_Big__Operators_Olinorder__class_OMin(_1479936, _1479940)))], (40426 ^ _778908) ^ [_1546127, _1546129, _1546131, _1546133, _1546135, _1546137] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1546127, _1546129), _1546129, tc_prod(_1546131, _1546133), c_Product__Type_Osnd(_1546127, _1546129)), c_Product__Type_Omap__pair(_1546131, _1546127, _1546133, _1546129, _1546135, _1546137)) = hAPP(c_Fun_Ocomp(_1546133, _1546129, tc_prod(_1546131, _1546133), _1546137), c_Product__Type_Osnd(_1546131, _1546133)))], (38650 ^ _778908) ^ [_1503694, _1503696, _1503698, _1503700] : [c_Fun_Oinj__on(_1503694, _1503696, _1503698, _1503700), 38653 ^ _778908 : [(38654 ^ _778908) ^ [_1503802] : [hBOOL(hAPP(hAPP(c_member(_1503694), _1503802), _1503700)), 38657 ^ _778908 : [(38658 ^ _778908) ^ [_1503904] : [hBOOL(hAPP(hAPP(c_member(_1503694), _1503904), _1503700)), hAPP(_1503698, _1503802) = hAPP(_1503698, _1503904), -(_1503802 = _1503904)]]]]], (13484 ^ _778908) ^ [_1006142, _1006144, _1006146, _1006148, _1006150] : [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), _1006142), _1006144)), _1006146)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006142), _1006148)), _1006150))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006150), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006142), _1006150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006142), _1006146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006148), _1006144)))], (24857 ^ _778908) ^ [_1214421, _1214423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1214421), _1214423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1214421)), hAPP(c_Code__Numeral_Onat__of, _1214423))))], (33351 ^ _778908) ^ [_1387502, _1387504, _1387506] : [class_Orderings_Olinorder(_1387502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387502), _1387504)), hBOOL(hAPP(hAPP(c_member(_1387502), _1387506), _1387504)), 33362 ^ _778908 : [(33369 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387502, tc_HOL_Obool)), _1387504), hAPP(hAPP(c_Set_Oinsert(_1387502), _1387506), c_Orderings_Obot__class_Obot(tc_fun(_1387502, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1387502, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1387502, _1387504) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1387502), _1387506), c_Big__Operators_Olinorder__class_OMax(_1387502, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387502, tc_HOL_Obool)), _1387504), hAPP(hAPP(c_Set_Oinsert(_1387502), _1387506), c_Orderings_Obot__class_Obot(tc_fun(_1387502, tc_HOL_Obool)))))))], (33363 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387502, tc_HOL_Obool)), _1387504), hAPP(hAPP(c_Set_Oinsert(_1387502), _1387506), c_Orderings_Obot__class_Obot(tc_fun(_1387502, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1387502, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1387502, _1387504) = _1387506)]]], (49622 ^ _778908) ^ [_1775167, _1775169, _1775171] : [-(_1775167 = c_List_Olist_ONil(_1775169)), -(c_List_Olast(_1775169, hAPP(hAPP(c_List_Oappend(_1775169), _1775171), _1775167)) = c_List_Olast(_1775169, _1775167))], (66 ^ _778908) ^ [_779823, _779825, _779827, _779829] : [-(c_Int_Oiszero(_779827, _779823)), c_Int_Oiszero(_779829, _779825), _779829 = _779827, _779825 = _779823], (31205 ^ _778908) ^ [_1340948, _1340950, _1340952, _1340954, _1340956, _1340958] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1340948, _1340950)), hAPP(hAPP(c_Product__Type_OPair(_1340948, _1340950), _1340956), _1340958)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool)), _1340952), _1340954))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340948, tc_fun(_1340950, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1340948, tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_fun(_1340950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340950, tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_fun(_1340950, tc_HOL_Obool)), _1340948), c_COMBC(_1340950, tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340950, tc_prod(_1340948, _1340950)), tc_fun(_1340950, tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool)), _1340948), hAPP(c_COMBB(tc_prod(_1340948, _1340950), tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool), _1340950), c_member(tc_prod(_1340948, _1340950)))), c_Product__Type_OPair(_1340948, _1340950)))), _1340952)), hAPP(hAPP(c_COMBC(_1340948, tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_fun(_1340950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340950, tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_fun(_1340950, tc_HOL_Obool)), _1340948), c_COMBC(_1340950, tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340950, tc_prod(_1340948, _1340950)), tc_fun(_1340950, tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool)), _1340948), hAPP(c_COMBB(tc_prod(_1340948, _1340950), tc_fun(tc_fun(tc_prod(_1340948, _1340950), tc_HOL_Obool), tc_HOL_Obool), _1340950), c_member(tc_prod(_1340948, _1340950)))), c_Product__Type_OPair(_1340948, _1340950)))), _1340954)), _1340956), _1340958)))], (41788 ^ _778908) ^ [_1582942, _1582944, _1582946, _1582948, _1582950, _1582952, _1582954] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582942, _1582944, _1582946), _1582948), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1582950, tc_fun(tc_prod(_1582944, _1582946), tc_HOL_Obool)), _1582952), _1582954)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1582950, tc_fun(tc_prod(_1582942, _1582946), tc_HOL_Obool)), _1582952), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1582944, _1582946), tc_HOL_Obool), tc_fun(tc_prod(_1582942, _1582946), tc_HOL_Obool), _1582950), hAPP(c_Relation_Orel__comp(_1582942, _1582944, _1582946), _1582948)), _1582954)))], (7470 ^ _778908) ^ [_903766, _903768, _903770, _903772] : [-(c_Option_Ooption_Ooption__rec(_903766, _903768, _903770, _903772, c_Option_Ooption_ONone(_903768)) = _903770)], (47052 ^ _778908) ^ [_1712740, _1712742, _1712744, _1712746] : [-(_1712740 = _1712742), -(c_List_Oremove1(_1712744, _1712740, hAPP(hAPP(c_List_Olist_OCons(_1712744), _1712742), _1712746)) = hAPP(hAPP(c_List_Olist_OCons(_1712744), _1712742), c_List_Oremove1(_1712744, _1712740, _1712746)))], (6510 ^ _778908) ^ [_884227, _884229, _884231, _884233, _884235] : [c_Com_Ocom_OAss(_884227, _884229) = c_Com_Ocom_OCond(_884231, _884233, _884235)], (39118 ^ _778908) ^ [_1513357, _1513359, _1513361, _1513363, _1513365, _1513367] : [class_Groups_Oab__semigroup__mult(_1513357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513359), _1513361)), -(hBOOL(hAPP(hAPP(c_member(_1513359), _1513363), _1513361))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1513357, _1513359, c_Groups_Otimes__class_Otimes(_1513357)), _1513365), _1513367), hAPP(hAPP(c_Set_Oinsert(_1513359), _1513363), _1513361)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1513357), hAPP(_1513365, _1513363)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1513357, _1513359, c_Groups_Otimes__class_Otimes(_1513357)), _1513365), _1513367), _1513361)))], (37192 ^ _778908) ^ [_1471632, _1471634, _1471636, _1471638] : [class_Orderings_Olinorder(_1471632), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471632, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1471632), _1471634)), c_SetInterval_Oord__class_OatLeastAtMost(_1471632, _1471636, _1471638)) = c_SetInterval_Oord__class_OatLeastAtMost(_1471632, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1471632), _1471634), _1471636), _1471638))], (14774 ^ _778908) ^ [_1029522, _1029524, _1029526] : [class_Divides_Osemiring__div(_1029522), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029522), c_Divides_Odiv__class_Omod(_1029522, _1029524, _1029526)), _1029526) = c_Groups_Ozero__class_Ozero(_1029522))], (37062 ^ _778908) ^ [_1468749, _1468751, _1468753, _1468755, _1468757, _1468759, _1468761, _1468763] : [c_Equiv__Relations_Oequiv(_1468749, _1468751, _1468753), c_Equiv__Relations_Ocongruent2(_1468749, _1468755, _1468757, _1468753, _1468759, _1468761), hBOOL(hAPP(hAPP(c_member(_1468749), _1468763), _1468751)), -(c_Equiv__Relations_Ocongruent(_1468755, _1468757, _1468759, hAPP(_1468761, _1468763)))], (51457 ^ _778908) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (40006 ^ _778908) ^ [_1533976, _1533978, _1533980, _1533982] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1533976, _1533978, hAPP(hAPP(c_Set_Oinsert(_1533976), _1533980), c_Orderings_Obot__class_Obot(tc_fun(_1533976, tc_HOL_Obool)))), _1533982)), -(_1533980 = _1533982)], (14130 ^ _778908) ^ [_1018083, _1018085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018083), 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, _1018085, _1018083)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (48997 ^ _778908) ^ [_1761153, _1761155, _1761157, _1761159] : [-(hAPP(hAPP(c_List_Odrop(_1761153), _1761155), hAPP(hAPP(c_List_Olist_OCons(_1761153), _1761157), _1761159)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1761153), hAPP(hAPP(c_List_Olist_OCons(_1761153), _1761157), _1761159), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1761153), tc_List_Olist(_1761153)), c_List_Odrop(_1761153)), _1761159), _1761155))], (49545 ^ _778908) ^ [_1773452, _1773454, _1773456] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1773452)), _1773454), c_List_Olists(_1773452, c_Wellfounded_Oacc(_1773452, _1773456)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1773452)), _1773454), c_Wellfounded_Oacc(tc_List_Olist(_1773452), c_List_Olistrel1(_1773452, _1773456)))))], (4916 ^ _778908) ^ [_854976, _854978, _854980, _854982] : [-(c_List_Olexord(_854982, _854978) = c_List_Olexord(_854980, _854976)), _854982 = _854980, _854978 = _854976], (49303 ^ _778908) ^ [_1767714, _1767716, _1767718, _1767720, _1767722, _1767724, _1767726] : [-(hAPP(c_List_Ofoldl(_1767714, _1767716, _1767718, _1767720), hAPP(hAPP(c_List_Omap(_1767722, _1767716), _1767724), _1767726)) = hAPP(c_List_Ofoldl(_1767714, _1767722, hAPP(hAPP(c_COMBC(_1767714, tc_fun(_1767722, _1767716), tc_fun(_1767722, _1767714)), hAPP(hAPP(c_COMBB(tc_fun(_1767716, _1767714), tc_fun(tc_fun(_1767722, _1767716), tc_fun(_1767722, _1767714)), _1767714), c_COMBB(_1767716, _1767714, _1767722)), _1767718)), _1767724), _1767720), _1767726))], (18005 ^ _778908) ^ [_1090259] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1090259)), -(hAPP(c_Int_Onat, _1090259) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25841 ^ _778908) ^ [_1232829, _1232831, _1232833, _1232835] : [class_Rings_Ocomm__semiring__1(_1232829), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232829), _1232831), _1232833)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232829), _1232831), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232829), _1232835), _1232833))))], (51589 ^ _778908) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (8474 ^ _778908) ^ [_921118, _921120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _921118), _921120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921118)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _921120))))], (47306 ^ _778908) ^ [_1719880, _1719882, _1719884, _1719886, _1719888] : [class_Groups_Ocomm__monoid__add(_1719880), hBOOL(hAPP(hAPP(c_member(_1719882), _1719884), hAPP(c_List_Oset(_1719882), _1719886))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1719880), hAPP(hAPP(c_List_Omap(_1719882, _1719880), _1719888), _1719886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1719880), hAPP(_1719888, _1719884)), hAPP(c_List_Omonoid__add__class_Olistsum(_1719880), hAPP(hAPP(c_List_Omap(_1719882, _1719880), _1719888), c_List_Oremove1(_1719882, _1719884, _1719886)))))], (40602 ^ _778908) ^ [_1550415, _1550417] : [class_Lattices_Olattice(_1550415), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550415), _1550417)), -(c_Big__Operators_Olattice__class_OSup__fin(_1550415, _1550417) = hAPP(c_Finite__Set_Ofold1(_1550415, c_Lattices_Osemilattice__sup__class_Osup(_1550415)), _1550417))], (51603 ^ _778908) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (7392 ^ _778908) ^ [_902392] : [hAPP(c_Nat_OSuc, _902392) = _902392], (37913 ^ _778908) ^ [_1488797, _1488799, _1488801] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488797), _1488799)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488797), _1488801)), 37923 ^ _778908 : [(37926 ^ _778908) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37924 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488797), 37922 ^ [_1488797, _1488799, _1488801]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488797, tc_HOL_Obool)), _1488799), _1488801))))]], -(hAPP(c_Finite__Set_Ocard(_1488797), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488797, tc_HOL_Obool)), _1488799), _1488801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1488797), _1488799)), hAPP(c_Finite__Set_Ocard(_1488797), _1488801)))], (29104 ^ _778908) ^ [_1298357, _1298359, _1298361, _1298363, _1298365] : [-(hAPP(c_Set_Oimage(_1298357, _1298359, hAPP(hAPP(c_COMBB(_1298361, _1298359, _1298357), _1298363), _1298365)), c_Orderings_Otop__class_Otop(tc_fun(_1298357, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1298361, _1298359, _1298363), hAPP(c_Set_Oimage(_1298357, _1298361, _1298365), c_Orderings_Otop__class_Otop(tc_fun(_1298357, tc_HOL_Obool)))))], (31229 ^ _778908) ^ [_1342205, _1342207, _1342209, _1342211] : [hBOOL(hAPP(hAPP(c_member(_1342205), _1342211), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342205, tc_HOL_Obool)), _1342207), _1342209))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342205, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1342205, tc_fun(_1342205, tc_HOL_Obool), tc_HOL_Obool), c_member(_1342205)), _1342207)), hAPP(hAPP(c_COMBC(_1342205, tc_fun(_1342205, tc_HOL_Obool), tc_HOL_Obool), c_member(_1342205)), _1342209)), _1342211)))], (30562 ^ _778908) ^ [_1326455, _1326457, _1326459, _1326461, _1326463] : [_1326455 = c_Orderings_Obot__class_Obot(tc_fun(_1326457, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326459, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326457, tc_fun(_1326459, tc_HOL_Obool)), _1326455), _1326461)), _1326463) = _1326463)], (32351 ^ _778908) ^ [_1367130, _1367132] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1367130), 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)))), _1367132)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1367132), _1367130)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1367130), _1367132)))], (36264 ^ _778908) ^ [_1451105, _1451107, _1451109, _1451111, _1451113, _1451115] : [c_Equiv__Relations_Oequiv(_1451105, _1451107, _1451109), c_Equiv__Relations_Ocongruent(_1451105, tc_fun(_1451111, tc_HOL_Obool), _1451109, _1451113), hBOOL(hAPP(hAPP(c_member(_1451105), _1451115), _1451107)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451105, tc_fun(_1451111, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1451105, _1451105, _1451109), hAPP(hAPP(c_Set_Oinsert(_1451105), _1451115), c_Orderings_Obot__class_Obot(tc_fun(_1451105, tc_HOL_Obool))))), _1451113) = hAPP(_1451113, _1451115))], (51381 ^ _778908) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (15692 ^ _778908) ^ [_1046142, _1046144, _1046146] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046144), _1046146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046142), _1046144)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046142), _1046146)))], (32255 ^ _778908) ^ [_1365047, _1365049, _1365051, _1365053, _1365055, _1365057] : [32256 ^ _778908 : [(32259 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1365053, _1365049), _1365051))], (32257 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1365047, _1365049), _1365051))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365055, tc_fun(_1365057, tc_HOL_Obool))), _1365053), _1365047), _1365049), _1365051)))], (16827 ^ _778908) ^ [_1068226, _1068228, _1068230] : [class_Groups_Oordered__ab__group__add__abs(_1068226), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068226), hAPP(c_Groups_Oabs__class_Oabs(_1068226), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068226), hAPP(c_Groups_Oabs__class_Oabs(_1068226), _1068228)), hAPP(c_Groups_Oabs__class_Oabs(_1068226), _1068230)))), hAPP(c_Groups_Oabs__class_Oabs(_1068226), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1068226), _1068228), _1068230)))))], (5582 ^ _778908) ^ [_865153, _865155] : [_865155 = _865153, -(c_List_Orev(_865155) = c_List_Orev(_865153))], (14017 ^ _778908) ^ [_1016102] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016102, _1016102) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44749 ^ _778908) ^ [_1654829, _1654831, _1654833, _1654835, _1654837, _1654839] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654829, tc_fun(_1654831, tc_HOL_Obool)), _1654833), hAPP(hAPP(c_COMBB(_1654835, tc_fun(_1654831, tc_HOL_Obool), _1654829), _1654837), _1654839)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654835, tc_fun(_1654831, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1654829, _1654835, _1654839), _1654833)), _1654837))], (48068 ^ _778908) ^ [_1737682, _1737684, _1737686, _1737688, _1737690] : [-(hAPP(hAPP(c_List_Oappend(_1737682), _1737684), hAPP(hAPP(c_List_Olist_OCons(_1737682), _1737686), c_List_Olist_ONil(_1737682))) = hAPP(hAPP(c_List_Oappend(_1737682), _1737688), hAPP(hAPP(c_List_Olist_OCons(_1737682), _1737690), c_List_Olist_ONil(_1737682)))), _1737684 = _1737688, _1737686 = _1737690], (42018 ^ _778908) ^ [_1589437, _1589439] : [c_Wellfounded_Owf(_1589437, _1589439), -(c_Wellfounded_Owf(tc_fun(_1589437, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1589437, _1589439)))], (1052 ^ _778908) ^ [_794932, _794934] : [-(class_Groups_Olinordered__ab__group__add(_794932)), _794934 = _794932, class_Groups_Olinordered__ab__group__add(_794934)], (29257 ^ _778908) ^ [_1301802, _1301804, _1301806, _1301808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301802, tc_HOL_Obool)), _1301804), _1301806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301802, tc_HOL_Obool)), _1301804), hAPP(hAPP(c_Set_Oinsert(_1301802), _1301808), _1301806))))], (44076 ^ _778908) ^ [_1640479, _1640481, _1640483, _1640485, _1640487] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1640479, _1640481, _1640483), _1640485), _1640487) = c_HOL_OThe(_1640481, c_Finite__Set_Ofold__graph(_1640479, _1640481, _1640483, _1640485, _1640487)))], (41922 ^ _778908) ^ [_1587627, _1587629, _1587631] : [c_Wellfounded_Owf(_1587627, _1587629), -(hBOOL(hAPP(hAPP(c_member(_1587627), _1587631), c_Wellfounded_Oacc(_1587627, _1587629))))], (43580 ^ _778908) ^ [_1627693, _1627695, _1627697] : [-(hAPP(c_Relation_ORange(_1627693, _1627695), hAPP(c_Relation_Oconverse(_1627695, _1627693), _1627697)) = hAPP(c_Relation_ODomain(_1627695, _1627693), _1627697))], (18157 ^ _778908) ^ [_1092763, _1092765] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092763)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092763)), _1092765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1092763))), _1092765))], (14513 ^ _778908) ^ [_1025136, _1025138] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025136)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025138)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1025136), _1025138)))], (32545 ^ _778908) ^ [_1370873, _1370875] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1370873), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370875))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370873), _1370875)))], (30944 ^ _778908) ^ [_1334153, _1334155, _1334157, _1334159] : [hBOOL(hAPP(hAPP(c_member(_1334153), _1334155), _1334157)), -(hBOOL(hAPP(hAPP(c_member(_1334153), _1334155), _1334159))), -(hBOOL(hAPP(hAPP(c_member(_1334153), _1334155), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334153, tc_HOL_Obool)), _1334157), _1334159))))], (51297 ^ _778908) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (6952 ^ _778908) ^ [_893741] : [6953 ^ _778908 : [(6954 ^ _778908) ^ [_893789] : [hAPP(c_Com_Obody, _893741) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _893789)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _893741))))], (40503 ^ _778908) ^ [_1548413, _1548415, _1548417, _1548419, _1548421] : [c_Relation_Orefl__on(_1548413, _1548415, _1548417), c_Relation_Orefl__on(_1548413, _1548419, _1548421), -(c_Relation_Orefl__on(_1548413, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1548413, tc_HOL_Obool)), _1548415), _1548419), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1548413, _1548413), tc_HOL_Obool)), _1548417), _1548421)))], (41920 ^ _778908) ^ [_1587602] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1587602)))], (26267 ^ _778908) ^ [_1241236, _1241238, _1241240] : [class_Orderings_Olinorder(_1241236), 26270 ^ _778908 : [(26277 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241236), _1241238), _1241240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1241236, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1241236), _1241238)), hAPP(c_SetInterval_Oord__class_OlessThan(_1241236), _1241240))))], (26271 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1241236, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1241236), _1241238)), hAPP(c_SetInterval_Oord__class_OlessThan(_1241236), _1241240))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241236), _1241238), _1241240)))]]], (40018 ^ _778908) ^ [_1534236, _1534238, _1534240, _1534242, _1534244] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1534236, _1534238, hAPP(hAPP(c_Set_Oinsert(_1534236), _1534240), _1534242)), _1534244)), 40023 ^ _778908 : [(40028 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1534236), 40021 ^ [_1534236, _1534238, _1534240, _1534242, _1534244]), 40022 ^ [_1534236, _1534238, _1534240, _1534242, _1534244]))], (40026 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1534236, _1534236, _1534238, 40021 ^ [_1534236, _1534238, _1534240, _1534242, _1534244], 40022 ^ [_1534236, _1534238, _1534240, _1534242, _1534244]), _1534244)))], (40024 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1534236), _1534240), _1534242) = hAPP(hAPP(c_Set_Oinsert(_1534236), 40021 ^ [_1534236, _1534238, _1534240, _1534242, _1534244]), 40022 ^ [_1534236, _1534238, _1534240, _1534242, _1534244]))]]], (12341 ^ _778908) ^ [_986229, _986231] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986229), _986231) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _986229 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _986231 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43554 ^ _778908) ^ [_1627109, _1627111, _1627113, _1627115, _1627117] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627111, _1627109)), hAPP(hAPP(c_Product__Type_OPair(_1627111, _1627109), _1627115), _1627113)), _1627117)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627109, _1627111)), hAPP(hAPP(c_Product__Type_OPair(_1627109, _1627111), _1627113), _1627115)), hAPP(c_Relation_Oconverse(_1627111, _1627109), _1627117))))], (23825 ^ _778908) ^ [_1194166, _1194168, _1194170] : [class_Orderings_Olinorder(_1194166), 23828 ^ _778908 : [(23835 ^ _778908) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194166), _1194168), _1194170) = _1194168, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194166), _1194168), _1194170)))], (23829 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194166), _1194168), _1194170)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194166), _1194168), _1194170) = _1194168)]]], (45412 ^ _778908) ^ [_1672101, _1672103, _1672105] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1672101, tc_HOL_Obool)), _1672103), _1672105) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1672101, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1672101, tc_HOL_Obool)), _1672103), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1672101, tc_HOL_Obool)), _1672105), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1672101, tc_HOL_Obool), tc_HOL_Obool))))))], (39380 ^ _778908) ^ [_1519245, _1519247, _1519249] : [-(c_Fun_Oinj__on(_1519245, tc_sum(_1519245, _1519247), c_Sum__Type_OInl(_1519245, _1519247), _1519249))], (46549 ^ _778908) ^ [_1698101, _1698103, _1698105, _1698107] : [hBOOL(hAPP(c_List_Odistinct(_1698101), _1698103)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1698101, _1698105)), hAPP(hAPP(c_List_Ozip(_1698101, _1698105), _1698103), _1698107))))], (2710 ^ _778908) ^ [_819977, _819979, _819981, _819983] : [-(c_Nitpick_Onumber__of__frac(_819983, _819979) = c_Nitpick_Onumber__of__frac(_819981, _819977)), _819983 = _819981, _819979 = _819977], (25261 ^ _778908) ^ [_1223161, _1223163, _1223165, _1223167] : [class_Divides_Osemiring__div(_1223161), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223161), _1223163), _1223165)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223161), _1223163), _1223167)), 25272 ^ _778908 : [(25279 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223161), _1223165), _1223167)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223161), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223161), _1223165), _1223163)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223161), _1223167), _1223163))))], (25273 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223161), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223161), _1223165), _1223163)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223161), _1223167), _1223163))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223161), _1223165), _1223167)))]]], (51485 ^ _778908) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (49502 ^ _778908) ^ [_1772402] : [-(c_List_Olists(_1772402, c_Orderings_Otop__class_Otop(tc_fun(_1772402, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1772402), tc_HOL_Obool)))], (22534 ^ _778908) ^ [_1169453, _1169455] : [hAPP(c_Nat_OSuc, _1169453) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169455), -(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(_1169455))), 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)), _1169453))))))], (16326 ^ _778908) ^ [_1059391, _1059393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059391), _1059393)), -(c_Nat__Transfer_Otsub(_1059393, _1059391) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059393), _1059391))], (33892 ^ _778908) ^ [_1397991, _1397993, _1397995, _1397997, _1397999, _1398001, _1398003] : [hBOOL(hAPP(_1397991, _1397993)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1397995, _1397995)), hAPP(hAPP(c_Product__Type_OPair(_1397995, _1397995), _1397997), _1397999)), hAPP(_1398001, _1397993))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1398003, _1397995), tc_prod(_1398003, _1397995))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1398003, _1397995), tc_prod(_1398003, _1397995)), hAPP(hAPP(c_Product__Type_OPair(_1398003, _1397995), _1397993), _1397997)), hAPP(hAPP(c_Product__Type_OPair(_1398003, _1397995), _1397993), _1397999))), c_Recdef_Osame__fst(_1398003, _1397995, _1397991, _1398001))))], (43763 ^ _778908) ^ [_1632505, _1632507] : [-(hAPP(hAPP(c_Nat_Ocompow(_1632505, _1632505), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632507) = c_Fun_Oid(_1632505))], (46265 ^ _778908) ^ [_1691858, _1691860, _1691862, _1691864, _1691866, _1691868, _1691870] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1691858), tc_Option_Ooption(_1691860), _1691862, hAPP(c_Option_Omap(_1691858, _1691860), _1691864)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1691862, tc_Option_Ooption(_1691858)), _1691866), _1691868), hAPP(c_Option_Ooption_OSome(_1691858), _1691870))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1691862, tc_Option_Ooption(_1691860)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1691858), tc_Option_Ooption(_1691860), _1691862, hAPP(c_Option_Omap(_1691858, _1691860), _1691864)), _1691866)), _1691868), hAPP(c_Option_Ooption_OSome(_1691860), hAPP(_1691864, _1691870))))], (6933 ^ _778908) ^ [_893473, _893475, _893477, _893479] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _893473)), _893475, _893477, _893479), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _893473), _893475, hAPP(c_Nat_OSuc, _893477), _893479))], (49093 ^ _778908) ^ [_1763560, _1763562, _1763564, _1763566, _1763568] : [-(hAPP(hAPP(c_List_Ozip(_1763560, _1763562), _1763564), hAPP(hAPP(c_List_Oappend(_1763562), _1763566), _1763568)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1763560, _1763562)), hAPP(hAPP(c_List_Ozip(_1763560, _1763562), hAPP(hAPP(c_List_Otake(_1763560), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763562)), _1763566)), _1763564)), _1763566)), hAPP(hAPP(c_List_Ozip(_1763560, _1763562), hAPP(hAPP(c_List_Odrop(_1763560), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763562)), _1763566)), _1763564)), _1763568)))], (46649 ^ _778908) ^ [_1701254, _1701256, _1701258, _1701260] : [class_Orderings_Olinorder(_1701254), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701254, _1701254, c_COMBI(_1701254)), _1701256), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701254, _1701254, c_COMBI(_1701254)), _1701258), _1701260)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701254, _1701254, c_COMBI(_1701254)), _1701258), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701254, _1701254, c_COMBI(_1701254)), _1701256), _1701260)))], (48598 ^ _778908) ^ [_1750107, _1750109, _1750111, _1750113, _1750115, _1750117, _1750119] : [-(hBOOL(hAPP(hAPP(c_member(_1750107), _1750109), hAPP(c_List_Oset(_1750107), _1750111)))), -(c_Map_Omap__upds(_1750107, _1750113, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1750107, tc_Option_Ooption(_1750113)), _1750115), _1750109), hAPP(c_Option_Ooption_OSome(_1750113), _1750117)), _1750111, _1750119) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1750107, tc_Option_Ooption(_1750113)), c_Map_Omap__upds(_1750107, _1750113, _1750115, _1750111, _1750119)), _1750109), hAPP(c_Option_Ooption_OSome(_1750113), _1750117)))], (25951 ^ _778908) ^ [_1234733, _1234735] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234733)), _1234735)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234733), _1234735)))], (21959 ^ _778908) ^ [_1158854, _1158856, _1158858, _1158860] : [class_Fields_Olinordered__field__inverse__zero(_1158854), class_Int_Onumber(_1158854), 21966 ^ _778908 : [(21967 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158854), _1158856), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858))), _1158860)), 21970 ^ _778908 : [(21977 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), c_Groups_Ozero__class_Ozero(_1158854)), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858)))), 21980 ^ _778908 : [(21987 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858)), c_Groups_Ozero__class_Ozero(_1158854)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), c_Groups_Ozero__class_Ozero(_1158854)), _1158860)))], (21981 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858)), c_Groups_Ozero__class_Ozero(_1158854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158854), _1158860), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858))), _1158856)))]]], (21971 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), c_Groups_Ozero__class_Ozero(_1158854)), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), _1158856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158854), _1158860), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858)))))]]], (21993 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158854), _1158856), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858))), _1158860))), 21996 ^ _778908 : [(21999 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), _1158856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158854), _1158860), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858))))], (21997 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), c_Groups_Ozero__class_Ozero(_1158854)), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858))))]], 22000 ^ _778908 : [(22003 ^ _778908) ^ [] : [22004 ^ _778908 : [(22007 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158854), _1158860), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858))), _1158856))], (22005 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858)), c_Groups_Ozero__class_Ozero(_1158854))))]], 22008 ^ _778908 : [(22011 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), c_Groups_Ozero__class_Ozero(_1158854)), _1158860))], (22009 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858)), c_Groups_Ozero__class_Ozero(_1158854)))]]], (22001 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158854), c_Groups_Ozero__class_Ozero(_1158854)), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), _1158858)))]]]]], (19491 ^ _778908) ^ [_1114597, _1114599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114597), _1114599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1114597)), c_Int_OBit0(_1114599))))], (23683 ^ _778908) ^ [_1191656, _1191658] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1191656)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1191658)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1191658))), 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), _1191656)), c_Int_Onat)))))], (15664 ^ _778908) ^ [_1045617, _1045619, _1045621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045617), _1045619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045617), _1045621)), 15671 ^ _778908 : [(15678 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045619), _1045621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045619), _1045617)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045621), _1045617))))], (15672 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045619), _1045617)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045621), _1045617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045619), _1045621)))]]], (23875 ^ _778908) ^ [_1195050, _1195052, _1195054] : [class_Orderings_Olinorder(_1195050), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195050), _1195052), _1195054) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195050), _1195054), _1195052))], (17855 ^ _778908) ^ [_1087695, _1087697, _1087699] : [class_Rings_Olinordered__idom(_1087695), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087695), c_Groups_Ozero__class_Ozero(_1087695)), hAPP(hAPP(c_Power_Opower__class_Opower(_1087695), hAPP(c_Groups_Oabs__class_Oabs(_1087695), _1087697)), _1087699))))], (36544 ^ _778908) ^ [_1456635, _1456637, _1456639] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456635, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456635, tc_HOL_Obool)), _1456637), _1456639)), _1456637)))], (17105 ^ _778908) ^ [_1073858, _1073860] : [class_Int_Onumber__ring(_1073858), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1073858), hAPP(c_Int_Onumber__class_Onumber__of(_1073858), _1073860)) = hAPP(c_Int_Onumber__class_Onumber__of(_1073858), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1073860)))], (5504 ^ _778908) ^ [_863980, _863982, _863984, _863986] : [-(c_Wellfounded_Oaccp(_863986, _863982) = c_Wellfounded_Oaccp(_863984, _863980)), _863986 = _863984, _863982 = _863980], (29118 ^ _778908) ^ [_1298621, _1298623] : [class_Lattices_Obounded__lattice__top(_1298621), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1298621), _1298623), c_Orderings_Otop__class_Otop(_1298621)) = c_Orderings_Otop__class_Otop(_1298621))], (17687 ^ _778908) ^ [_1084520, _1084522, _1084524] : [class_Power_Opower(_1084520), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084520), _1084522), hAPP(c_Nat_OSuc, _1084524)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084520), _1084522), hAPP(hAPP(c_Power_Opower__class_Opower(_1084520), _1084522), _1084524)))], (25003 ^ _778908) ^ [_1217425, _1217427, _1217429] : [-(c_Nitpick_Oof__frac(_1217427, _1217425, _1217429) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217425), hAPP(c_Int_Oring__1__class_Oof__int(_1217425), hAPP(c_Nitpick_Onum(_1217427), _1217429))), hAPP(c_Int_Oring__1__class_Oof__int(_1217425), hAPP(c_Nitpick_Odenom(_1217427), _1217429)))), class_Rings_Oinverse(_1217425), class_Rings_Oring__1(_1217425)], (22816 ^ _778908) ^ [_1174928, _1174930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174928)), 22819 ^ _778908 : [(22826 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174930), _1174928))), -(c_Divides_OposDivAlg(_1174930, _1174928) = hAPP(c_Divides_Oadjust(_1174928), c_Divides_OposDivAlg(_1174930, 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)))), _1174928))))], (22820 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174930), _1174928)), -(c_Divides_OposDivAlg(_1174930, _1174928) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174930))]]], (12675 ^ _778908) ^ [_991973, _991975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991975)), -(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), _991973), _991975))))], (18133 ^ _778908) ^ [_1092395, _1092397] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092395)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092397)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092397))))], (46940 ^ _778908) ^ [_1709436, _1709438, _1709440, _1709442, _1709444] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709436), tc_List_Olist(_1709436))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709436), tc_List_Olist(_1709436)), _1709438), _1709440)), c_List_Olistrel(_1709436, c_Transitive__Closure_Ortrancl(_1709436, _1709442)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709436), tc_List_Olist(_1709436))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709436), tc_List_Olist(_1709436)), _1709440), _1709444)), c_List_Olistrel(_1709436, c_Transitive__Closure_Ortrancl(_1709436, _1709442)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709436), tc_List_Olist(_1709436))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709436), tc_List_Olist(_1709436)), _1709438), _1709444)), c_List_Olistrel(_1709436, c_Transitive__Closure_Ortrancl(_1709436, _1709442)))))], (19573 ^ _778908) ^ [_1115964] : [-(c_Int_Osucc(c_Int_OBit0(_1115964)) = c_Int_OBit1(_1115964))], (50793 ^ _778908) ^ [_1799653, _1799655, _1799657] : [hAPP(c_List_Orev(_1799653), _1799655) = hAPP(hAPP(c_List_Olist_OCons(_1799653), _1799657), c_List_Olist_ONil(_1799653)), -(_1799655 = hAPP(hAPP(c_List_Olist_OCons(_1799653), _1799657), c_List_Olist_ONil(_1799653)))], (15614 ^ _778908) ^ [_1044700, _1044702] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044700), _1044702)), _1044700)))], (24931 ^ _778908) ^ [_1215805, _1215807, _1215809, _1215811, _1215813] : [-(_1215805 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1215807, _1215809, _1215805, _1215811), _1215813) = hAPP(hAPP(c_Product__Type_Oscomp(_1215809, _1215807, _1215809, tc_prod(_1215807, _1215809)), hAPP(_1215811, _1215813)), c_Random_Oiterate(_1215807, _1215809, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1215805), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1215811)))], (48566 ^ _778908) ^ [_1749356, _1749358, _1749360, _1749362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749356), _1749358)), -(hAPP(hAPP(c_List_Onth(_1749360), hAPP(hAPP(c_List_Otake(_1749360), _1749358), _1749362)), _1749356) = hAPP(hAPP(c_List_Onth(_1749360), _1749362), _1749356))], (18029 ^ _778908) ^ [_1090621, _1090623] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090621) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090623), 18032 ^ _778908 : [(18039 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090621)))), 18042 ^ _778908 : [(18049 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090623)))), -(_1090621 = _1090623)], (18043 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090623))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090621) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (18033 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090623)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (41790 ^ _778908) ^ [_1583046, _1583048, _1583050, _1583052, _1583054, _1583056, _1583058] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1583046, _1583048, _1583050), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583052, tc_fun(tc_prod(_1583046, _1583048), tc_HOL_Obool)), _1583054), _1583056)), _1583058) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583052, tc_fun(tc_prod(_1583046, _1583050), tc_HOL_Obool)), _1583054), hAPP(hAPP(c_COMBC(_1583052, tc_fun(tc_prod(_1583048, _1583050), tc_HOL_Obool), tc_fun(tc_prod(_1583046, _1583050), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1583046, _1583048), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1583048, _1583050), tc_HOL_Obool), tc_fun(tc_prod(_1583046, _1583050), tc_HOL_Obool)), _1583052), c_Relation_Orel__comp(_1583046, _1583048, _1583050)), _1583056)), _1583058)))], (41207 ^ _778908) ^ [_1561795, _1561797, _1561799] : [hBOOL(hAPP(hAPP(c_member(_1561795), _1561797), hAPP(c_Set_OCollect(_1561795), _1561799))), -(hBOOL(hAPP(_1561799, _1561797)))], (42263 ^ _778908) ^ [_1595429, _1595431, _1595433] : [c_Wellfounded_Owf(_1595429, _1595431), c_Wellfounded_Owf(_1595429, _1595433), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595429, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1595429, _1595429), _1595431)), hAPP(c_Relation_ORange(_1595429, _1595429), _1595433)) = c_Orderings_Obot__class_Obot(tc_fun(_1595429, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1595429, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595429, _1595429), tc_HOL_Obool)), _1595431), _1595433)))], (42766 ^ _778908) ^ [_1607697, _1607699] : [42767 ^ _778908 : [(42768 ^ _778908) ^ [_1607743] : [hBOOL(hAPP(_1607697, _1607743))]], -(hBOOL(hAPP(_1607697, c_Hilbert__Choice_OEps(_1607699, _1607697))))], (8562 ^ _778908) ^ [_922473, _922475] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922473) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _922475), -(_922473 = _922475)], (32563 ^ _778908) ^ [_1371211, _1371213, _1371215, _1371217] : [hBOOL(hAPP(hAPP(_1371215, _1371217), _1371213)), -(hBOOL(hAPP(hAPP(c_member(_1371211), _1371213), c_SetInterval_Oord_OatLeast(_1371211, _1371215, _1371217))))], (34716 ^ _778908) ^ [_1414406, _1414408, _1414410, _1414412, _1414414] : [class_Groups_Ocomm__monoid__mult(_1414406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414408), _1414410)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1414408, _1414406), _1414412), hAPP(hAPP(c_Set_Oinsert(_1414408), _1414414), _1414410)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414406), hAPP(_1414412, _1414414)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1414408, _1414406), _1414412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414408, tc_HOL_Obool)), _1414410), hAPP(hAPP(c_Set_Oinsert(_1414408), _1414414), c_Orderings_Obot__class_Obot(tc_fun(_1414408, tc_HOL_Obool)))))))], (40114 ^ _778908) ^ [_1537098, _1537100, _1537102, _1537104] : [40115 ^ _778908 : [(40118 ^ _778908) ^ [] : [_1537104 = c_Orderings_Obot__class_Obot(tc_fun(_1537100, tc_HOL_Obool))], (40116 ^ _778908) ^ [] : [_1537102 = c_Orderings_Obot__class_Obot(tc_fun(_1537098, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1537098, _1537100), _1537102), hAPP(c_COMBK(tc_fun(_1537100, tc_HOL_Obool), _1537098), _1537104)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537098, _1537100), tc_HOL_Obool)))], (42534 ^ _778908) ^ [_1601763, _1601765, _1601767] : [c_Relation_Orefl__on(_1601763, _1601765, _1601767), 42537 ^ _778908 : [(42544 ^ _778908) ^ [_1602247] : [hBOOL(hAPP(hAPP(c_member(_1601763), _1602247), _1601765)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601763, _1601763)), hAPP(hAPP(c_Product__Type_OPair(_1601763, _1601763), _1602247), _1602247)), _1601767)))], (42538 ^ _778908) ^ [_1601974] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601763, _1601763)), _1601974), _1601767)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1601763, _1601763, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1601763, tc_fun(_1601763, tc_HOL_Obool), tc_fun(_1601763, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1601763, tc_HOL_Obool), tc_fun(_1601763, tc_HOL_Obool)), _1601763), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1601763)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1601763), c_fconj), hAPP(hAPP(c_COMBC(_1601763, tc_fun(_1601763, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601763)), _1601765)))), hAPP(hAPP(c_COMBC(_1601763, tc_fun(_1601763, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601763)), _1601765))), _1601974)))]]], (39604 ^ _778908) ^ [_1524393, _1524395, _1524397, _1524399, _1524401, _1524403] : [c_Fun_Oinj__on(_1524393, _1524395, _1524397, _1524399), hAPP(_1524397, _1524401) = _1524403, hBOOL(hAPP(hAPP(c_member(_1524393), _1524401), _1524399)), -(hAPP(c_Fun_Othe__inv__into(_1524393, _1524395, _1524399, _1524397), _1524403) = _1524401)], (17807 ^ _778908) ^ [_1086790, _1086792, _1086794, _1086796] : [class_Rings_Olinordered__semidom(_1086790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086790), c_Groups_Oone__class_Oone(_1086790)), _1086792)), 17814 ^ _778908 : [(17821 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1086794), _1086796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086790), hAPP(hAPP(c_Power_Opower__class_Opower(_1086790), _1086792), _1086794)), hAPP(hAPP(c_Power_Opower__class_Opower(_1086790), _1086792), _1086796))))], (17815 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086790), hAPP(hAPP(c_Power_Opower__class_Opower(_1086790), _1086792), _1086794)), hAPP(hAPP(c_Power_Opower__class_Opower(_1086790), _1086792), _1086796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1086794), _1086796)))]]], (16322 ^ _778908) ^ [_1059288, _1059290] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059288), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1059290), _1059288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059290), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059290, _1059288)))], (40092 ^ _778908) ^ [] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_String_Ochar, tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_prod(tc_String_Onibble, tc_String_Onibble), tc_String_Ochar, hAPP(c_Product__Type_Oprod_Oprod__case(tc_String_Onibble, tc_String_Onibble, tc_String_Ochar), c_String_Ochar_OChar)), hAPP(hAPP(c_Product__Type_OSigma(tc_String_Onibble, tc_String_Onibble), c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(tc_String_Onibble, tc_HOL_Obool), tc_String_Onibble), c_Orderings_Otop__class_Otop(tc_fun(tc_String_Onibble, tc_HOL_Obool))))))], (25615 ^ _778908) ^ [_1228936, _1228938] : [25622 ^ _778908 : [(25625 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228938), _1228936))], (25623 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228936), _1228938)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228936), _1228938)), -(_1228936 = _1228938)], (13420 ^ _778908) ^ [_1005024, _1005026] : [class_Rings_Olinordered__idom(_1005024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005024), c_Groups_Ozero__class_Ozero(_1005024)), _1005026)), -(c_Groups_Osgn__class_Osgn(_1005024, _1005026) = c_Groups_Oone__class_Oone(_1005024))], (16324 ^ _778908) ^ [_1059335, _1059337] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1059335, _1059337) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1059335), _1059337)), _1059337)))], (16260 ^ _778908) ^ [_1058013, _1058015, _1058017, _1058019, _1058021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058013), _1058015)), 16263 ^ _778908 : [(16270 ^ _778908) ^ [] : [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), _1058015), _1058013)), _1058017)), _1058019) = _1058021, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058015), _1058017)), _1058019) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058013), _1058017)), _1058021))], (16264 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058015), _1058017)), _1058019) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058013), _1058017)), _1058021), -(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), _1058015), _1058013)), _1058017)), _1058019) = _1058021)]]], (39919 ^ _778908) ^ [_1532077, _1532079, _1532081, _1532083, _1532085] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1532077, _1532077, _1532079, _1532081, _1532083), _1532085)), -(hBOOL(hAPP(hAPP(c_member(_1532077), _1532081), _1532083))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1532077, _1532079, hAPP(hAPP(c_Set_Oinsert(_1532077), _1532081), _1532083)), _1532085)))], (3702 ^ _778908) ^ [_835913, _835915, _835917, _835919, _835921, _835923, _835925, _835927] : [-(c_Nitpick_Oprod(_835927, _835923, _835919, _835915) = c_Nitpick_Oprod(_835925, _835921, _835917, _835913)), _835927 = _835925, _835923 = _835921, _835919 = _835917, _835915 = _835913], (24419 ^ _778908) ^ [_1206005, _1206007, _1206009, _1206011] : [class_Orderings_Olinorder(_1206005), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206005), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206005), _1206007), _1206009)), _1206011) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206005), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206005), _1206007), _1206011)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206005), _1206009), _1206011)))], (50128 ^ _778908) ^ [_1786668, _1786670, _1786672, _1786674, _1786676] : [class_Orderings_Olinorder(_1786668), c_List_Olinorder__class_Osorted(_1786668, hAPP(hAPP(c_List_Omap(_1786670, _1786668), _1786672), _1786674)), -(c_List_Olinorder__class_Osorted(_1786668, hAPP(hAPP(c_List_Omap(_1786670, _1786668), _1786672), hAPP(c_List_Ofilter(_1786670, _1786676), _1786674))))], (38940 ^ _778908) ^ [_1509531, _1509533, _1509535, _1509537, _1509539] : [c_Fun_Oinj__on(_1509531, _1509533, _1509535, c_Orderings_Otop__class_Otop(tc_fun(_1509531, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1509531, _1509533, _1509535), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509531, tc_HOL_Obool)), _1509537), _1509539)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509533, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509531, _1509533, _1509535), _1509537)), hAPP(c_Set_Oimage(_1509531, _1509533, _1509535), _1509539)))], (4266 ^ _778908) ^ [_844693, _844695, _844697, _844699, _844701, _844703, _844705, _844707, _844709, _844711, _844713, _844715] : [-(c_Map_Omap__comp(_844715, _844711, _844707, _844703, _844699, _844695) = c_Map_Omap__comp(_844713, _844709, _844705, _844701, _844697, _844693)), _844715 = _844713, _844711 = _844709, _844707 = _844705, _844703 = _844701, _844699 = _844697, _844695 = _844693], (35062 ^ _778908) ^ [_1421969] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1421969)), -(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))), _1421969)), c_FunDef_Omax__weak)))], (35947 ^ _778908) ^ [_1443662, _1443664, _1443666, _1443668, _1443670, _1443672, _1443674, _1443676] : [c_Finite__Set_Ofolding(_1443662, _1443664, _1443666, _1443668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443662), _1443670)), -(hAPP(c_Fun_Ocomp(_1443664, _1443664, _1443672, hAPP(_1443666, _1443674)), hAPP(c_Fun_Ocomp(_1443664, _1443664, _1443672, hAPP(_1443668, _1443670)), _1443676)) = hAPP(c_Fun_Ocomp(_1443664, _1443664, _1443672, hAPP(_1443668, _1443670)), hAPP(c_Fun_Ocomp(_1443664, _1443664, _1443672, hAPP(_1443666, _1443674)), _1443676)))], (17185 ^ _778908) ^ [_1075542, _1075544] : [class_Groups_Oabs__if(_1075542), 17188 ^ _778908 : [(17195 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075542), _1075544), c_Groups_Ozero__class_Ozero(_1075542)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1075542), _1075544) = _1075544)], (17189 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075542), _1075544), c_Groups_Ozero__class_Ozero(_1075542))), -(hAPP(c_Groups_Oabs__class_Oabs(_1075542), _1075544) = hAPP(c_Groups_Ouminus__class_Ouminus(_1075542), _1075544))]]], (16705 ^ _778908) ^ [_1066125, _1066127] : [class_Int_Onumber__ring(_1066125), class_Rings_Olinordered__idom(_1066125), 16712 ^ _778908 : [(16719 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066125), hAPP(c_Int_Onumber__class_Onumber__of(_1066125), _1066127)), c_Groups_Ozero__class_Ozero(_1066125)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1066125), hAPP(c_Int_Onumber__class_Onumber__of(_1066125), _1066127)) = hAPP(c_Int_Onumber__class_Onumber__of(_1066125), _1066127))], (16713 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066125), hAPP(c_Int_Onumber__class_Onumber__of(_1066125), _1066127)), c_Groups_Ozero__class_Ozero(_1066125))), -(hAPP(c_Groups_Oabs__class_Oabs(_1066125), hAPP(c_Int_Onumber__class_Onumber__of(_1066125), _1066127)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1066125), hAPP(c_Int_Onumber__class_Onumber__of(_1066125), _1066127)))]]], (25095 ^ _778908) ^ [_1219457, _1219459, _1219461, _1219463, _1219465, _1219467, _1219469] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1219457, _1219459, _1219461, _1219463), _1219465), _1219467), _1219469) = c_New__DSequence_Opos__bind(_1219457, _1219459, hAPP(hAPP(hAPP(_1219461, _1219465), _1219467), _1219469), hAPP(hAPP(c_COMBC(_1219457, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1219459))), hAPP(hAPP(c_COMBC(_1219457, 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(_1219459)))), hAPP(hAPP(c_COMBC(_1219457, 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(_1219459))))), _1219463), _1219465)), _1219467)), _1219469)))], (42431 ^ _778908) ^ [_1599848, _1599850, _1599852, _1599854] : [42432 ^ _778908 : [(42433 ^ _778908) ^ [_1599902] : [hBOOL(hAPP(hAPP(_1599852, _1599854), _1599902))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1599848, _1599850, _1599852), _1599854)))], (39508 ^ _778908) ^ [_1522224, _1522226, _1522228, _1522230, _1522232] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1522224, _1522226, _1522228), _1522230), _1522232)), -(hBOOL(hAPP(_1522230, hAPP(_1522228, _1522232))))], (3860 ^ _778908) ^ [_838434, _838436, _838438, _838440, _838442, _838444, _838446, _838448] : [-(c_New__Random__Sequence_Opos__bind(_838448, _838444, _838440, _838436) = c_New__Random__Sequence_Opos__bind(_838446, _838442, _838438, _838434)), _838448 = _838446, _838444 = _838442, _838440 = _838438, _838436 = _838434], (50082 ^ _778908) ^ [_1785610, _1785612, _1785614, _1785616, _1785618] : [-(hAPP(hAPP(c_List_Omap(_1785610, _1785612), _1785614), hAPP(c_List_Ofilter(_1785610, _1785616), _1785618)) = c_List_Omap__filter(_1785610, _1785612, hAPP(hAPP(c_COMBC(_1785610, tc_Option_Ooption(_1785612), tc_Option_Ooption(_1785612)), hAPP(hAPP(c_COMBS(_1785610, tc_Option_Ooption(_1785612), tc_fun(tc_Option_Ooption(_1785612), tc_Option_Ooption(_1785612))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1785612), tc_fun(tc_Option_Ooption(_1785612), tc_Option_Ooption(_1785612))), _1785610), c_If(tc_Option_Ooption(_1785612))), _1785616)), hAPP(hAPP(c_COMBB(_1785612, tc_Option_Ooption(_1785612), _1785610), c_Option_Ooption_OSome(_1785612)), _1785614))), c_Option_Ooption_ONone(_1785612)), _1785618))], (46390 ^ _778908) ^ [_1694777, _1694779, _1694781, _1694783] : [hBOOL(hAPP(c_List_Odistinct(_1694777), hAPP(hAPP(c_List_Omap(tc_prod(_1694777, _1694779), _1694777), c_Product__Type_Ofst(_1694777, _1694779)), _1694781))), hBOOL(hAPP(c_List_Odistinct(_1694777), hAPP(hAPP(c_List_Omap(tc_prod(_1694777, _1694779), _1694777), c_Product__Type_Ofst(_1694777, _1694779)), _1694783))), 46397 ^ _778908 : [(46404 ^ _778908) ^ [] : [hAPP(c_List_Oset(tc_prod(_1694777, _1694779)), _1694781) = hAPP(c_List_Oset(tc_prod(_1694777, _1694779)), _1694783), -(c_Map_Omap__of(_1694777, _1694779, _1694781) = c_Map_Omap__of(_1694777, _1694779, _1694783))], (46398 ^ _778908) ^ [] : [c_Map_Omap__of(_1694777, _1694779, _1694781) = c_Map_Omap__of(_1694777, _1694779, _1694783), -(hAPP(c_List_Oset(tc_prod(_1694777, _1694779)), _1694781) = hAPP(c_List_Oset(tc_prod(_1694777, _1694779)), _1694783))]]], (19443 ^ _778908) ^ [_1113759, _1113761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113759), _1113761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113759)), c_Int_OBit1(_1113761))))], (12483 ^ _778908) ^ [_988776, _988778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988776), _988778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988776), hAPP(c_Nat_OSuc, _988778))))], (28381 ^ _778908) ^ [_1283085, _1283087, _1283089, _1283091] : [class_Lattices_Osemilattice__sup(_1283085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283085), _1283087), _1283089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283085), _1283091), _1283089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283085), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283085), _1283087), _1283091)), _1283089)))], (6964 ^ _778908) ^ [_894062, _894064, _894066, _894068, _894070, _894072] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _894062), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894064), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_894066, _894064)), _894068, _894070), -(c_Natural_Oevaln(c_Com_Ocom_OCall(_894072, _894062, _894066), _894064, _894068, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894070), hAPP(c_Natural_Ogetlocs, _894064))), _894072), hAPP(hAPP(c_Natural_Ogetlocs, _894070), c_Com_ORes))))], (49837 ^ _778908) ^ [_1779445, _1779447, _1779449, _1779451] : [_1779445 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779447)), _1779449)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1779447, hAPP(hAPP(c_List_Olist__update(_1779447, _1779449), _1779445), _1779451)) = c_List_Obutlast(_1779447, _1779449))], (47477 ^ _778908) ^ [_1723234, _1723236] : [hAPP(c_List_Oset(_1723234), _1723236) = c_Orderings_Obot__class_Obot(tc_fun(_1723234, tc_HOL_Obool)), -(_1723236 = c_List_Olist_ONil(_1723234))], (24671 ^ _778908) ^ [_1210495, _1210497, _1210499, _1210501] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1210495), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1210495), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210495), _1210497), _1210499)), _1210501) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1210495), _1210497), _1210501)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1210495), _1210499), _1210501)))], (7933 ^ _778908) ^ [_911396, _911398, _911400, _911402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911396), _911398)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911400), _911398) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911396), _911402), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911400), _911402)))], (27797 ^ _778908) ^ [_1271842] : [-(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)), _1271842)) = hAPP(c_Int_Onat, _1271842))], (44661 ^ _778908) ^ [_1652619, _1652621, _1652623, _1652625] : [class_Complete__Lattice_Ocomplete__lattice(_1652619), -(_1652621 = c_Orderings_Obot__class_Obot(tc_fun(_1652623, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652623, _1652619), _1652621), hAPP(c_COMBK(_1652619, _1652623), _1652625)) = _1652625)], (21255 ^ _778908) ^ [_1146102, _1146104, _1146106, _1146108] : [class_Fields_Ofield__inverse__zero(_1146102), -(_1146104 = c_Groups_Ozero__class_Ozero(_1146102)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146102), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146102), _1146106), _1146104)), _1146108) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146102), _1146106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146102), _1146108), _1146104))), _1146104))], (38071 ^ _778908) ^ [_1492326, _1492328, _1492330] : [class_Lattices_Olattice(_1492326), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492326), _1492328)), hBOOL(hAPP(hAPP(c_member(_1492326), _1492330), _1492328)), 38082 ^ _778908 : [(38089 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492326, tc_HOL_Obool)), _1492328), hAPP(hAPP(c_Set_Oinsert(_1492326), _1492330), c_Orderings_Obot__class_Obot(tc_fun(_1492326, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1492326, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1492326, _1492328) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1492326), _1492330), c_Big__Operators_Olattice__class_OInf__fin(_1492326, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492326, tc_HOL_Obool)), _1492328), hAPP(hAPP(c_Set_Oinsert(_1492326), _1492330), c_Orderings_Obot__class_Obot(tc_fun(_1492326, tc_HOL_Obool)))))))], (38083 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492326, tc_HOL_Obool)), _1492328), hAPP(hAPP(c_Set_Oinsert(_1492326), _1492330), c_Orderings_Obot__class_Obot(tc_fun(_1492326, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1492326, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1492326, _1492328) = _1492330)]]], (47533 ^ _778908) ^ [_1724274, _1724276, _1724278] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1724274)), -(c_List_Osublist(_1724276, hAPP(hAPP(c_List_Olist_OCons(_1724276), _1724278), c_List_Olist_ONil(_1724276)), _1724274) = hAPP(hAPP(c_List_Olist_OCons(_1724276), _1724278), c_List_Olist_ONil(_1724276)))], (6697 ^ _778908) ^ [_888693, _888695] : [c_Com_Ovname_OLoc(_888693) = c_Com_Ovname_OLoc(_888695), -(_888693 = _888695)], (45298 ^ _778908) ^ [_1669315, _1669317, _1669319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1669315, tc_HOL_Obool), tc_HOL_Obool)), _1669317), _1669319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1669315, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1669315, tc_HOL_Obool), _1669319)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1669315, tc_HOL_Obool), _1669317))))], (26331 ^ _778908) ^ [_1242538, _1242540, _1242542, _1242544] : [class_Divides_Osemiring__div(_1242538), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242538), _1242540), _1242542)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242538), _1242544), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242538), _1242542), _1242540)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1242538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242538), _1242544), _1242542)), _1242540))], (2962 ^ _778908) ^ [_824155, _824157, _824159, _824161, _824163, _824165, _824167, _824169] : [-(c_Lazy__Sequence_Ohb__bind(_824169, _824165, _824161, _824157) = c_Lazy__Sequence_Ohb__bind(_824167, _824163, _824159, _824155)), _824169 = _824167, _824165 = _824163, _824161 = _824159, _824157 = _824155], (22584 ^ _778908) ^ [_1170422, _1170424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1170422)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170424))), -(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(_1170424))), 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), _1170422)), c_Int_Onat))))))], (6369 ^ _778908) ^ [_881618, _881620, _881622, _881624, _881626, _881628] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_881618, _881620, _881622), _881624, _881626, _881628)), 6370 ^ _778908 : [(6377 ^ _778908) ^ [] : [-(hBOOL(hAPP(_881618, _881624))), c_Natural_Oevaln(_881622, _881624, _881626, _881628)], (6371 ^ _778908) ^ [] : [hBOOL(hAPP(_881618, _881624)), c_Natural_Oevaln(_881620, _881624, _881626, _881628)]]], (4936 ^ _778908) ^ [_855274, _855276, _855278, _855280, _855282, _855284] : [-(c_List_Olist_Olist__size(_855284, _855280, _855276) = c_List_Olist_Olist__size(_855282, _855278, _855274)), _855284 = _855282, _855280 = _855278, _855276 = _855274], (44935 ^ _778908) ^ [_1661094, _1661096, _1661098, _1661100, _1661102] : [_1661094 = c_Orderings_Obot__class_Obot(tc_fun(_1661096, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661096, tc_fun(_1661098, tc_HOL_Obool)), _1661094), hAPP(hAPP(c_COMBC(_1661096, tc_fun(_1661098, tc_HOL_Obool), tc_fun(_1661098, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1661098, tc_HOL_Obool), tc_fun(tc_fun(_1661098, tc_HOL_Obool), tc_fun(_1661098, tc_HOL_Obool)), _1661096), c_Groups_Ominus__class_Ominus(tc_fun(_1661098, tc_HOL_Obool))), _1661100)), _1661102)) = c_Orderings_Otop__class_Otop(tc_fun(_1661098, tc_HOL_Obool)))], (28583 ^ _778908) ^ [_1286894, _1286896] : [c_Nat__Transfer_Onat__set(_1286894), c_Nat__Transfer_Onat__set(_1286896), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1286894), _1286896) = 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), _1286894)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1286896))))], (20243 ^ _778908) ^ [_1128419, _1128421, _1128423] : [class_Fields_Ofield__inverse__zero(_1128419), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128419), hAPP(c_Groups_Ouminus__class_Ouminus(_1128419), _1128421)), hAPP(c_Groups_Ouminus__class_Ouminus(_1128419), _1128423)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128419), _1128421), _1128423))], (20655 ^ _778908) ^ [_1135425, _1135427, _1135429, _1135431, _1135433] : [class_Fields_Ofield(_1135425), -(_1135427 = c_Groups_Ozero__class_Ozero(_1135425)), -(_1135429 = c_Groups_Ozero__class_Ozero(_1135425)), 20666 ^ _778908 : [(20673 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135425), _1135431), _1135429) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135425), _1135433), _1135427), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135425), _1135431), _1135427) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135425), _1135433), _1135429))], (20667 ^ _778908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135425), _1135431), _1135427) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135425), _1135433), _1135429), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135425), _1135431), _1135429) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135425), _1135433), _1135427))]]], (7102 ^ _778908) ^ [_897657, _897659] : [c_Option_Ooption_ONone(_897657) = hAPP(c_Option_Ooption_OSome(_897657), _897659)], (17661 ^ _778908) ^ [_1084050, _1084052, _1084054, _1084056] : [class_Rings_Olinordered__semidom(_1084050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084050), c_Groups_Oone__class_Oone(_1084050)), _1084052)), 17668 ^ _778908 : [(17675 ^ _778908) ^ [] : [_1084054 = _1084056, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084050), _1084052), _1084054) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084050), _1084052), _1084056))], (17669 ^ _778908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1084050), _1084052), _1084054) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084050), _1084052), _1084056), -(_1084054 = _1084056)]]], (11196 ^ _778908) ^ [_966125, _966127, _966129, _966131] : [class_Orderings_Opreorder(_966125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966125), _966127), _966129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966125), _966129), _966131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966125), _966127), _966131)))], (44260 ^ _778908) ^ [_1644248, _1644250, _1644252] : [class_Orderings_Olinorder(_1644248), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644248), _1644250)), -(c_Big__Operators_Olinorder__class_OMax(_1644248, hAPP(hAPP(c_Set_Oinsert(_1644248), _1644252), _1644250)) = hAPP(hAPP(c_Finite__Set_Ofold(_1644248, _1644248, c_Orderings_Oord__class_Omax(_1644248)), _1644252), _1644250))], (26635 ^ _778908) ^ [_1247982, _1247984, _1247986, _1247988] : [class_Rings_Ocomm__semiring__1(_1247982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247982), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247982), c_Groups_Oone__class_Oone(_1247982)), c_Groups_Oone__class_Oone(_1247982))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1247982), hAPP(hAPP(c_COMBB(_1247982, _1247982, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1247982), _1247984)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1247982, _1247982), hAPP(hAPP(c_COMBB(_1247982, tc_fun(_1247982, _1247982), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1247982)), c_Nat_Osemiring__1__class_Oof__nat(_1247982))), _1247986))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1247988))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247982), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1247982), _1247988)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247982), _1247984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247982), _1247984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247982), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1247982), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247988), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1247986)))))], (44014 ^ _778908) ^ [_1638999, _1639001, _1639003, _1639005, _1639007] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638999, _1638999)), hAPP(hAPP(c_Product__Type_OPair(_1638999, _1638999), _1639001), _1639003)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638999, _1638999), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1639005)), _1639007))), 44018 ^ _778908 : [(44021 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638999, _1638999)), hAPP(hAPP(c_Product__Type_OPair(_1638999, _1638999), 44017 ^ [_1638999, _1639001, _1639003, _1639005, _1639007]), _1639003)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1638999, _1638999), tc_HOL_Obool), _1639005), _1639007))))], (44019 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638999, _1638999)), hAPP(hAPP(c_Product__Type_OPair(_1638999, _1638999), _1639001), 44017 ^ [_1638999, _1639001, _1639003, _1639005, _1639007])), _1639007)))]]], (11625 ^ _778908) ^ [_973415, _973417, _973419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973417), _973419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973415), _973417)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973415), _973419))))], (15628 ^ _778908) ^ [_1044982, _1044984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044982), _1044984)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044984), _1044982)) = _1044982)], (27958 ^ _778908) ^ [_1274527] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1274527) = 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), _1274527))))], (11058 ^ _778908) ^ [_964132, _964134, _964136] : [class_Orderings_Oorder(_964132), -(_964134 = _964136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964132), _964134), _964136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964132), _964134), _964136)))], (49263 ^ _778908) ^ [_1766860, _1766862, _1766864] : [-(hAPP(c_List_Orotate(_1766860, _1766862), _1766864) = hAPP(hAPP(c_List_Oappend(_1766860), hAPP(hAPP(c_List_Odrop(_1766860), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1766862, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766860)), _1766864))), _1766864)), hAPP(hAPP(c_List_Otake(_1766860), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1766862, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766860)), _1766864))), _1766864)))], (50869 ^ _778908) ^ [_1801171] : [-(hAPP(c_List_Orev(_1801171), c_List_Olist_ONil(_1801171)) = c_List_Olist_ONil(_1801171))], (49893 ^ _778908) ^ [_1780690, _1780692, _1780694, _1780696] : [-(hAPP(c_List_Ofilter(_1780690, _1780692), hAPP(hAPP(c_List_Oappend(_1780690), _1780694), _1780696)) = hAPP(hAPP(c_List_Oappend(_1780690), hAPP(c_List_Ofilter(_1780690, _1780692), _1780694)), hAPP(c_List_Ofilter(_1780690, _1780692), _1780696)))], (2166 ^ _778908) ^ [_811277, _811279, _811281, _811283, _811285, _811287, _811289, _811291, _811293, _811295] : [-(c_Nitpick_Opair__box_Opair__box__case(_811295, _811291, _811287, _811283, _811279) = c_Nitpick_Opair__box_Opair__box__case(_811293, _811289, _811285, _811281, _811277)), _811295 = _811293, _811291 = _811289, _811287 = _811285, _811283 = _811281, _811279 = _811277], (48693 ^ _778908) ^ [_1752630, _1752632] : [-(c_List_Olistrel(_1752630, c_Transitive__Closure_Ortrancl(_1752630, _1752632)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1752630), c_List_Olistrel1(_1752630, _1752632)))], (36786 ^ _778908) ^ [_1462104, _1462106, _1462108, _1462110] : [class_Lattices_Osemilattice__inf(_1462104), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462104), _1462106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462104), _1462108), _1462110)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462104), _1462108), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462104), _1462106), _1462110)))], (11671 ^ _778908) ^ [_974298, _974300, _974302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974298), _974300)), _974302)), 11674 ^ _778908 : [(11677 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974300), _974302)))], (11675 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974298), _974302)))]]], (49442 ^ _778908) ^ [_1770731, _1770733, _1770735, _1770737, _1770739] : [-(c_Map_Omap__upds(_1770731, _1770733, _1770735, _1770737, _1770739) = hAPP(c_List_Ofoldl(tc_fun(_1770731, tc_Option_Ooption(_1770733)), tc_prod(_1770731, _1770733), hAPP(hAPP(c_COMBB(tc_fun(_1770731, tc_fun(_1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733)))), tc_fun(tc_prod(_1770731, _1770733), tc_fun(_1770731, tc_Option_Ooption(_1770733))), tc_fun(_1770731, tc_Option_Ooption(_1770733))), c_Product__Type_Oprod_Oprod__case(_1770731, _1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733)))), hAPP(hAPP(c_COMBC(tc_fun(_1770731, tc_Option_Ooption(_1770733)), tc_fun(_1770733, tc_Option_Ooption(_1770733)), tc_fun(_1770731, tc_fun(_1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733))))), hAPP(hAPP(c_COMBB(tc_fun(_1770731, tc_fun(tc_fun(_1770733, tc_Option_Ooption(_1770733)), tc_fun(_1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733))))), tc_fun(tc_fun(_1770733, tc_Option_Ooption(_1770733)), tc_fun(_1770731, tc_fun(_1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733))))), tc_fun(_1770731, tc_Option_Ooption(_1770733))), c_COMBC(_1770731, tc_fun(_1770733, tc_Option_Ooption(_1770733)), tc_fun(_1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733))))), hAPP(hAPP(c_COMBB(tc_fun(_1770731, tc_fun(tc_Option_Ooption(_1770733), tc_fun(_1770731, tc_Option_Ooption(_1770733)))), tc_fun(_1770731, tc_fun(tc_fun(_1770733, tc_Option_Ooption(_1770733)), tc_fun(_1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733))))), tc_fun(_1770731, tc_Option_Ooption(_1770733))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1770733), tc_fun(_1770731, tc_Option_Ooption(_1770733))), tc_fun(tc_fun(_1770733, tc_Option_Ooption(_1770733)), tc_fun(_1770733, tc_fun(_1770731, tc_Option_Ooption(_1770733)))), _1770731), c_COMBB(tc_Option_Ooption(_1770733), tc_fun(_1770731, tc_Option_Ooption(_1770733)), _1770733))), c_Fun_Ofun__upd(_1770731, tc_Option_Ooption(_1770733))))), c_Option_Ooption_OSome(_1770733))), _1770735), hAPP(hAPP(c_List_Ozip(_1770731, _1770733), _1770737), _1770739)))], (42316 ^ _778908) ^ [_1596426, _1596428] : [-(hAPP(c_Relation_ODomain(_1596426, _1596426), c_Relation_OId__on(_1596426, _1596428)) = _1596428)], (16897 ^ _778908) ^ [_1069608, _1069610, _1069612] : [class_Rings_Olinordered__idom(_1069608), 16900 ^ _778908 : [(16909 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069608), hAPP(c_Groups_Oabs__class_Oabs(_1069608), _1069610)), _1069612))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069608), _1069610), _1069612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069608), hAPP(c_Groups_Ouminus__class_Ouminus(_1069608), _1069610)), _1069612))], (16901 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069608), hAPP(c_Groups_Oabs__class_Oabs(_1069608), _1069610)), _1069612)), 16904 ^ _778908 : [(16907 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069608), hAPP(c_Groups_Ouminus__class_Ouminus(_1069608), _1069610)), _1069612)))], (16905 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069608), _1069610), _1069612)))]]]]], (27737 ^ _778908) ^ [_1270673, _1270675] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1270673, _1270675)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1270675), _1270673)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38252 ^ _778908) ^ [_1495532, _1495534, _1495536] : [class_Lattices_Olattice(_1495532), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495532), _1495534)), -(_1495534 = c_Orderings_Obot__class_Obot(tc_fun(_1495532, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495532), _1495536)), -(_1495536 = c_Orderings_Obot__class_Obot(tc_fun(_1495532, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1495532, tc_HOL_Obool)), _1495534), _1495536) = c_Orderings_Obot__class_Obot(tc_fun(_1495532, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1495532, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1495532, tc_HOL_Obool)), _1495534), _1495536)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1495532), c_Big__Operators_Olattice__class_OInf__fin(_1495532, _1495534)), c_Big__Operators_Olattice__class_OInf__fin(_1495532, _1495536)))], (31029 ^ _778908) ^ [_1335949, _1335951] : [31030 ^ _778908 : [(31031 ^ _778908) ^ [_1336002] : [hBOOL(hAPP(hAPP(c_member(_1335949), _1336002), _1335951))]], _1335951 = c_Orderings_Obot__class_Obot(tc_fun(_1335949, tc_HOL_Obool))], (10010 ^ _778908) ^ [_947105] : [class_Rings_Olinordered__semidom(_947105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947105), c_Groups_Oone__class_Oone(_947105)), c_Groups_Ozero__class_Ozero(_947105)))], (32993 ^ _778908) ^ [_1380106, _1380108, _1380110, _1380112] : [c_Hoare__Mirabelle_Ohoare__derivs(_1380106, _1380108, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1380106)), _1380110), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380106), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1380106, _1380108, _1380112), -(c_Hoare__Mirabelle_Ohoare__derivs(_1380106, _1380108, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1380106)), _1380110), _1380112)))], (45193 ^ _778908) ^ [_1666817, _1666819, _1666821] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1666817, tc_HOL_Obool)), _1666819), _1666821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1666817, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1666817, tc_HOL_Obool), _1666821)), _1666819)))], (20001 ^ _778908) ^ [_1123597, _1123599, _1123601] : [class_Rings_Olinordered__idom(_1123597), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123597), c_Groups_Ozero__class_Ozero(_1123597)), hAPP(hAPP(c_Power_Opower__class_Opower(_1123597), _1123599), 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)))), _1123601)))))], (19127 ^ _778908) ^ [_1108193] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1108193))) = 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)))), _1108193))], (22277 ^ _778908) ^ [] : [-(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))], (42196 ^ _778908) ^ [_1593372, _1593374, _1593376, _1593378] : [-(hAPP(c_Relation_ORange(_1593372, _1593374), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593372, _1593374), tc_HOL_Obool)), _1593376), _1593378)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1593374, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1593372, _1593374), _1593376)), hAPP(c_Relation_ORange(_1593372, _1593374), _1593378)))], (30550 ^ _778908) ^ [_1326196, _1326198, _1326200, _1326202, _1326204] : [_1326196 = c_Orderings_Obot__class_Obot(tc_fun(_1326198, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326200, tc_HOL_Obool)), _1326202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326198, tc_fun(_1326200, tc_HOL_Obool)), _1326196), _1326204)) = _1326202)], (36700 ^ _778908) ^ [_1460228, _1460230] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460228, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1460228, tc_HOL_Obool))), _1460230) = c_Orderings_Obot__class_Obot(tc_fun(_1460228, tc_HOL_Obool)))], (48538 ^ _778908) ^ [_1748578, _1748580, _1748582, _1748584, _1748586] : [-(hAPP(hAPP(c_List_Otake(_1748578), _1748580), hAPP(hAPP(c_List_Omap(_1748582, _1748578), _1748584), _1748586)) = hAPP(hAPP(c_List_Omap(_1748582, _1748578), _1748584), hAPP(hAPP(c_List_Otake(_1748582), _1748580), _1748586)))], (2318 ^ _778908) ^ [_813885, _813887, _813889, _813891] : [-(c_Int_Onat__aux(_813891, _813887) = c_Int_Onat__aux(_813889, _813885)), _813891 = _813889, _813887 = _813885], (30426 ^ _778908) ^ [_1323834, _1323836, _1323838] : [class_Orderings_Oorder(_1323834), 30429 ^ _778908 : [(30436 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323834), _1323836), _1323838))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1323834, _1323836, _1323838) = c_Orderings_Obot__class_Obot(tc_fun(_1323834, tc_HOL_Obool)))], (30430 ^ _778908) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1323834, _1323836, _1323838) = c_Orderings_Obot__class_Obot(tc_fun(_1323834, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323834), _1323836), _1323838))]]], (4368 ^ _778908) ^ [_846384, _846386, _846388, _846390, _846392, _846394, _846396, _846398, _846400, _846402, _846404, _846406] : [-(c_Product__Type_Omap__pair(_846406, _846402, _846398, _846394, _846390, _846386) = c_Product__Type_Omap__pair(_846404, _846400, _846396, _846392, _846388, _846384)), _846406 = _846404, _846402 = _846400, _846398 = _846396, _846394 = _846392, _846390 = _846388, _846386 = _846384], (48237 ^ _778908) ^ [_1741552, _1741554, _1741556, _1741558, _1741560, _1741562] : [hAPP(hAPP(c_List_Oappend(_1741552), _1741554), _1741556) = _1741558, _1741560 = hAPP(hAPP(c_List_Oappend(_1741552), _1741556), _1741562), -(hAPP(hAPP(c_List_Oappend(_1741552), _1741554), _1741560) = hAPP(hAPP(c_List_Oappend(_1741552), _1741558), _1741562))], (32640 ^ _778908) ^ [_1372894, _1372896, _1372898, _1372900] : [c_Finite__Set_Ofolding__one(_1372894, _1372896, _1372898), -(hAPP(_1372898, hAPP(hAPP(c_Set_Oinsert(_1372894), _1372900), c_Orderings_Obot__class_Obot(tc_fun(_1372894, tc_HOL_Obool)))) = _1372900)], (28597 ^ _778908) ^ [_1287132] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1287132)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1287132))], (43512 ^ _778908) ^ [_1625996, _1625998, _1626000, _1626002] : [-(hAPP(c_Relation_Oconverse(_1625996, _1625998), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1625996, _1625998), tc_HOL_Obool)), _1626000), _1626002)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1625998, _1625996), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1625996, _1625998), _1626000)), hAPP(c_Relation_Oconverse(_1625996, _1625998), _1626002)))], (22848 ^ _778908) ^ [_1175486, _1175488] : [class_Rings_Oring__1(_1175486), 22851 ^ _778908 : [(22858 ^ _778908) ^ [] : [-(_1175488 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22861 ^ _778908 : [(22868 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175488), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1175486), _1175488) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1175486), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1175486, _1175486)), tc_fun(tc_Int_Oint, _1175486)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1175486, _1175486), _1175486), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1175486, _1175486)), tc_fun(tc_Int_Oint, _1175486)), tc_Int_Oint), c_COMBB(tc_fun(_1175486, _1175486), _1175486, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1175486, tc_fun(tc_fun(_1175486, _1175486), _1175486), tc_Int_Oint), c_HOL_OLet(_1175486, _1175486)), c_Int_Oring__1__class_Oof__int(_1175486)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1175486, _1175486), tc_fun(_1175486, _1175486)), hAPP(hAPP(c_COMBB(tc_fun(_1175486, tc_fun(_1175486, _1175486)), tc_fun(tc_fun(_1175486, _1175486), tc_fun(_1175486, _1175486)), tc_Int_Oint), c_COMBS(_1175486, _1175486, _1175486)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1175486, _1175486), tc_fun(_1175486, tc_fun(_1175486, _1175486))), hAPP(hAPP(c_COMBB(tc_fun(_1175486, tc_fun(_1175486, _1175486)), tc_fun(tc_fun(_1175486, _1175486), tc_fun(_1175486, tc_fun(_1175486, _1175486))), tc_Int_Oint), c_COMBB(_1175486, tc_fun(_1175486, _1175486), _1175486)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1175486, tc_fun(_1175486, _1175486)), tc_Int_Oint), c_If(_1175486)), 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(_1175486, _1175486, _1175486), c_Groups_Oplus__class_Oplus(_1175486)), c_COMBI(_1175486))))), hAPP(hAPP(c_COMBC(_1175486, _1175486, _1175486), hAPP(hAPP(c_COMBB(_1175486, tc_fun(_1175486, _1175486), _1175486), c_Groups_Oplus__class_Oplus(_1175486)), hAPP(hAPP(c_COMBS(_1175486, _1175486, _1175486), c_Groups_Oplus__class_Oplus(_1175486)), c_COMBI(_1175486)))), c_Groups_Oone__class_Oone(_1175486))))), c_Divides_Odivmod__int(_1175488, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (22862 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175488), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1175486), _1175488) = hAPP(c_Groups_Ouminus__class_Ouminus(_1175486), hAPP(c_Int_Oring__1__class_Oof__int(_1175486), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1175488))))]]], (22852 ^ _778908) ^ [] : [_1175488 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1175486), _1175488) = c_Groups_Ozero__class_Ozero(_1175486))]]], (25557 ^ _778908) ^ [_1228026, _1228028] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228026), _1228028)), 25562 ^ _778908 : [(25565 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228028), _1228026))], (25563 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228026), _1228028)))]], -(_1228026 = _1228028)], (28419 ^ _778908) ^ [_1283744, _1283746, _1283748] : [class_Lattices_Osemilattice__sup(_1283744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283744), _1283746), _1283748)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283744), _1283746), _1283748) = _1283748)], (37899 ^ _778908) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (51311 ^ _778908) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (41876 ^ _778908) ^ [_1586659, _1586661, _1586663, _1586665] : [c_Wellfounded_Owf(_1586659, _1586661), c_Wellfounded_Owf(_1586663, _1586665), -(c_Wellfounded_Owf(tc_prod(_1586659, _1586663), c_Wellfounded_Olex__prod(_1586659, _1586663, _1586661, _1586665)))], (49219 ^ _778908) ^ [_1765950, _1765952, _1765954] : [_1765954 = c_List_Olist_ONil(_1765950), -(hAPP(c_List_Orotate(_1765950, _1765952), _1765954) = c_List_Olist_ONil(_1765950))], (1162 ^ _778908) ^ [_796307, _796309] : [-(class_Rings_Ocomm__ring__1(_796307)), _796309 = _796307, class_Rings_Ocomm__ring__1(_796309)], (24173 ^ _778908) ^ [_1201179, _1201181, _1201183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201179, tc_HOL_Obool)), _1201181), _1201183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201179, tc_HOL_Obool)), _1201181), _1201183))), -(_1201181 = _1201183)], (31996 ^ _778908) ^ [_1359236, _1359238, _1359240] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359236), _1359238)), -(hBOOL(hAPP(hAPP(c_member(_1359236), _1359240), _1359238))), -(hAPP(c_Finite__Set_Ocard(_1359236), hAPP(hAPP(c_Set_Oinsert(_1359236), _1359240), _1359238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1359236), _1359238)))], (22546 ^ _778908) ^ [_1169705, _1169707] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1169705)), hAPP(c_Code__Numeral_Oof__nat, _1169707)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1169705), _1169707)))], (41678 ^ _778908) ^ [_1580083, _1580085] : [-(c_Fun_Oinj__on(_1580083, _1580083, c_Fun_Oid(_1580083), _1580085))], (46467 ^ _778908) ^ [_1696543, _1696545] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1696543), _1696545) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1696543, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1696545), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (37654 ^ _778908) ^ [_1481586, _1481588, _1481590] : [class_Orderings_Olinorder(_1481586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481586), _1481588)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481586), _1481590)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481586, tc_HOL_Obool)), _1481588), _1481590) = c_Orderings_Obot__class_Obot(tc_fun(_1481586, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1481586), c_Big__Operators_Olattice_OInf__fin(_1481586, c_Orderings_Oord__class_Omin(_1481586), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481586, tc_HOL_Obool)), _1481588), _1481590))), c_Big__Operators_Olattice_OInf__fin(_1481586, c_Orderings_Oord__class_Omin(_1481586), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481586, tc_HOL_Obool)), _1481588), _1481590))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1481586), c_Big__Operators_Olattice_OInf__fin(_1481586, c_Orderings_Oord__class_Omin(_1481586), _1481588)), c_Big__Operators_Olattice_OInf__fin(_1481586, c_Orderings_Oord__class_Omin(_1481586), _1481590)))], (30666 ^ _778908) ^ [_1328434, _1328436] : [class_Orderings_Olinorder(_1328434), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328434, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328434), _1328436)), hAPP(hAPP(c_Set_Oinsert(_1328434), _1328436), c_Orderings_Obot__class_Obot(tc_fun(_1328434, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1328434), _1328436))], (40136 ^ _778908) ^ [_1537913, _1537915, _1537917, _1537919, _1537921] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1537913, _1537915), _1537917), hAPP(hAPP(c_COMBS(_1537913, tc_fun(_1537915, tc_HOL_Obool), tc_fun(_1537915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537915, tc_HOL_Obool), tc_fun(tc_fun(_1537915, tc_HOL_Obool), tc_fun(_1537915, tc_HOL_Obool)), _1537913), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1537915, tc_HOL_Obool))), _1537919)), _1537921)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537913, _1537915), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1537913, _1537915), _1537917), _1537919)), hAPP(hAPP(c_Product__Type_OSigma(_1537913, _1537915), _1537917), _1537921)))], (26027 ^ _778908) ^ [_1236129, _1236131, _1236133] : [class_Rings_Ocomm__ring__1(_1236129), 26030 ^ _778908 : [(26037 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236129), _1236131), _1236133)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236129), _1236131), hAPP(c_Groups_Ouminus__class_Ouminus(_1236129), _1236133))))], (26031 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236129), _1236131), hAPP(c_Groups_Ouminus__class_Ouminus(_1236129), _1236133))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236129), _1236131), _1236133)))]]], (6212 ^ _778908) ^ [_878789, _878791, _878793, _878795, _878797] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_878789, _878791, _878793)), _878795), _878797))), 6213 ^ _778908 : [(6220 ^ _778908) ^ [] : [-(hBOOL(hAPP(_878789, _878795))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878793), _878795), _878797))], (6214 ^ _778908) ^ [] : [hBOOL(hAPP(_878789, _878795)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878791), _878795), _878797))]]], (16535 ^ _778908) ^ [_1063144, _1063146, _1063148] : [class_Int_Onumber(_1063144), 16538 ^ _778908 : [(16545 ^ _778908) ^ [] : [_1063148 = hAPP(c_Int_Onumber__class_Onumber__of(_1063144), _1063146), -(hAPP(c_Int_Onumber__class_Onumber__of(_1063144), _1063146) = _1063148)], (16539 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1063144), _1063146) = _1063148, -(_1063148 = hAPP(c_Int_Onumber__class_Onumber__of(_1063144), _1063146))]]], (20387 ^ _778908) ^ [_1130837, _1130839, _1130841, _1130843] : [class_Fields_Olinordered__field__inverse__zero(_1130837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130837), _1130839), _1130841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130837), c_Groups_Ozero__class_Ozero(_1130837)), _1130843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130837), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130837), _1130839), _1130843)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130837), _1130841), _1130843))))], (48741 ^ _778908) ^ [_1754180, _1754182, _1754184, _1754186] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754180), tc_List_Olist(_1754180))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754180), tc_List_Olist(_1754180)), _1754182), _1754184)), c_List_Olistrel1(_1754180, hAPP(c_Relation_Oconverse(_1754180, _1754180), _1754186)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754180), tc_List_Olist(_1754180))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754180), tc_List_Olist(_1754180)), _1754182), _1754184)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1754180), tc_List_Olist(_1754180)), c_List_Olistrel1(_1754180, _1754186)))))], (13745 ^ _778908) ^ [_1010728, _1010730, _1010732] : [hBOOL(hAPP(_1010728, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010730, _1010732))), 13748 ^ _778908 : [(13773 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010732), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13776 ^ _778908 : [(13777 ^ _778908) ^ [_1011350, _1011352] : [-(hBOOL(hAPP(_1010728, _1011350))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010732), _1011350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1011350), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1010730 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010732), _1011352)), _1011350)]]], (13755 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010732)), 13758 ^ _778908 : [(13759 ^ _778908) ^ [_1011058, _1011060] : [-(hBOOL(hAPP(_1010728, _1011058))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011058), _1010732)), _1010730 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010732), _1011060)), _1011058)]]], (13749 ^ _778908) ^ [] : [_1010732 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1010728, _1010730)))]]], (50781 ^ _778908) ^ [_1799379, _1799381, _1799383] : [hAPP(hAPP(c_List_Olist_OCons(_1799379), _1799381), c_List_Olist_ONil(_1799379)) = hAPP(c_List_Orev(_1799379), _1799383), -(_1799383 = hAPP(hAPP(c_List_Olist_OCons(_1799379), _1799381), c_List_Olist_ONil(_1799379)))], (4434 ^ _778908) ^ [_847489, _847491] : [_847491 = _847489, -(c_Nat_Osemiring__1__class_Oof__nat(_847491) = c_Nat_Osemiring__1__class_Oof__nat(_847489))], (49279 ^ _778908) ^ [_1767198, _1767200, _1767202] : [class_Groups_Oab__semigroup__add(_1767198), -(c_List_Ofoldr(_1767198, _1767198, c_Groups_Oplus__class_Oplus(_1767198), _1767200, _1767202) = hAPP(c_List_Ofoldl(_1767198, _1767198, c_Groups_Oplus__class_Oplus(_1767198), _1767202), _1767200))], (46990 ^ _778908) ^ [_1711434, _1711436, _1711438] : [-(hAPP(c_List_Oset(_1711434), hAPP(hAPP(c_List_Olist_OCons(_1711434), _1711436), _1711438)) = hAPP(hAPP(c_Set_Oinsert(_1711434), _1711436), hAPP(c_List_Oset(_1711434), _1711438)))], (49859 ^ _778908) ^ [_1779865, _1779867, _1779869, _1779871] : [-(hAPP(hAPP(c_List_Oappend(_1779865), _1779867), hAPP(hAPP(c_List_Olist_OCons(_1779865), _1779869), c_List_Olist_ONil(_1779865))) = _1779871), -(_1779871 = c_List_Olist_ONil(_1779865)), c_List_Obutlast(_1779865, _1779871) = _1779867, c_List_Olast(_1779865, _1779871) = _1779869], (51709 ^ _778908) ^ [_1814241, _1814243] : [-(hBOOL(_1814241)), -(hBOOL(hAPP(hAPP(c_fimplies, _1814241), _1814243)))], (46583 ^ _778908) ^ [_1699213, _1699215, _1699217, _1699219, _1699221, _1699223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1699213, _1699215)), hAPP(hAPP(c_Product__Type_OPair(_1699213, _1699215), _1699217), _1699219)), hAPP(c_List_Oset(tc_prod(_1699213, _1699215)), hAPP(hAPP(c_List_Ozip(_1699213, _1699215), _1699221), _1699223)))), -(hBOOL(hAPP(hAPP(c_member(_1699213), _1699217), hAPP(c_List_Oset(_1699213), _1699221))))], (19291 ^ _778908) ^ [_1111146, _1111148] : [_1111146 = _1111148, -(c_Int_OBit0(_1111146) = c_Int_OBit0(_1111148))], (25309 ^ _778908) ^ [_1224006, _1224008] : [class_Rings_Ocomm__semiring__1(_1224006), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224006), c_Groups_Oone__class_Oone(_1224006)), _1224008)))], (40533 ^ _778908) ^ [_1548996, _1548998, _1549000, _1549002, _1549004] : [c_Relation_Orefl__on(_1548996, _1548998, _1549000), hBOOL(hAPP(hAPP(c_member(tc_prod(_1548996, _1548996)), hAPP(hAPP(c_Product__Type_OPair(_1548996, _1548996), _1549002), _1549004)), _1549000)), -(hBOOL(hAPP(hAPP(c_member(_1548996), _1549004), _1548998)))], (23293 ^ _778908) ^ [_1184595, _1184597] : [-(c_Divides_Opdivmod(_1184595, _1184597) = 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), _1184595)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184597))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184595), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184597))))], (43588 ^ _778908) ^ [_1627871, _1627873] : [c_Wellfounded_Owf(_1627871, hAPP(c_Relation_Oconverse(_1627871, _1627871), _1627873)), -(c_Wellfounded_Owf(_1627871, hAPP(c_Relation_Oconverse(_1627871, _1627871), c_Transitive__Closure_Otrancl(_1627871, _1627873))))], (22366 ^ _778908) ^ [_1166279] : [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), _1166279))), 22369 ^ _778908 : [(22376 ^ _778908) ^ [] : [-(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), _1166279))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1166279)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1166279)), 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), _1166279)))))], (22370 ^ _778908) ^ [] : [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), _1166279)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1166279)) = 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), _1166279))))]]], (15700 ^ _778908) ^ [_1046364, _1046366, _1046368] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046364), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1046366, _1046368)), _1046368) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046364), _1046366), _1046368))], (24845 ^ _778908) ^ [_1214228, _1214230] : [_1214228 = _1214230, -(hAPP(c_Code__Numeral_Onat__of, _1214228) = hAPP(c_Code__Numeral_Onat__of, _1214230))], (34726 ^ _778908) ^ [_1414675, _1414677, _1414679, _1414681, _1414683] : [class_Groups_Ocomm__monoid__mult(_1414675), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414677), _1414679)), hBOOL(hAPP(hAPP(c_member(_1414677), _1414681), _1414679)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1414677, _1414675), _1414683), _1414679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414675), hAPP(_1414683, _1414681)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1414677, _1414675), _1414683), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414677, tc_HOL_Obool)), _1414679), hAPP(hAPP(c_Set_Oinsert(_1414677), _1414681), c_Orderings_Obot__class_Obot(tc_fun(_1414677, tc_HOL_Obool)))))))], (8135 ^ _778908) ^ [_914989, _914991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914989), _914991)), -(_914991 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914989), 8138 ^ [_914989, _914991])))], (6478 ^ _778908) ^ [_883701, _883703, _883705] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_883701, _883703, _883705)], (36856 ^ _778908) ^ [_1463397, _1463399] : [class_Lattices_Olattice(_1463397), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463397), _1463399), _1463399) = _1463399)], (11903 ^ _778908) ^ [_978271, _978273, _978275, _978277] : [class_Groups_Oordered__comm__monoid__add(_978271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978271), c_Groups_Ozero__class_Ozero(_978271)), _978273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978271), _978275), _978277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978271), _978275), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978271), _978277), _978273))))], (9036 ^ _778908) ^ [_929839, _929841] : [class_Rings_Oring__1(_929839), -(hAPP(c_Int_Oring__1__class_Oof__int(_929839), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _929841)) = hAPP(c_Groups_Ouminus__class_Ouminus(_929839), hAPP(c_Int_Oring__1__class_Oof__int(_929839), _929841)))], (44064 ^ _778908) ^ [_1640237, _1640239, _1640241, _1640243, _1640245, _1640247] : [c_Finite__Set_Ofolding(_1640237, _1640239, _1640241, _1640243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1640237), _1640245)), -(hAPP(hAPP(_1640243, _1640245), _1640247) = hAPP(hAPP(c_Finite__Set_Ofold(_1640237, _1640239, _1640241), _1640247), _1640245))], (34855 ^ _778908) ^ [_1417690, _1417692, _1417694, _1417696] : [-(hAPP(c_Map_Orestrict__map(_1417690, _1417692, hAPP(c_COMBK(tc_Option_Ooption(_1417692), _1417690), c_Option_Ooption_ONone(_1417692)), _1417694), _1417696) = c_Option_Ooption_ONone(_1417692))], (48520 ^ _778908) ^ [_1748206, _1748208, _1748210, _1748212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1748206), _1748208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1748210, tc_HOL_Obool)), hAPP(c_List_Oset(_1748210), hAPP(hAPP(c_List_Otake(_1748210), _1748206), _1748212))), hAPP(c_List_Oset(_1748210), hAPP(hAPP(c_List_Otake(_1748210), _1748208), _1748212)))))], (42725 ^ _778908) ^ [_1606970, _1606972, _1606974] : [-(c_Hilbert__Choice_OEps(tc_prod(_1606970, _1606972), hAPP(c_Product__Type_Oprod_Oprod__case(_1606970, _1606972, tc_HOL_Obool), _1606974)) = c_Hilbert__Choice_OEps(tc_prod(_1606970, _1606972), hAPP(hAPP(c_COMBS(tc_prod(_1606970, _1606972), _1606972, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1606970, tc_fun(_1606972, tc_HOL_Obool), tc_prod(_1606970, _1606972)), _1606974), c_Product__Type_Ofst(_1606970, _1606972))), c_Product__Type_Osnd(_1606970, _1606972))))], (24959 ^ _778908) ^ [_1216425, _1216427, _1216429, _1216431, _1216433, _1216435, _1216437] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1216425, _1216427, _1216429, _1216431), _1216433), _1216435), _1216437) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1216427, _1216429, _1216431), _1216435), hAPP(_1216433, _1216437)))], (30604 ^ _778908) ^ [_1327211, _1327213] : [class_Orderings_Oorder(_1327211), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327211, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1327211), _1327213), c_Orderings_Obot__class_Obot(tc_fun(_1327211, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1327211), _1327213)) = hAPP(hAPP(c_Set_Oinsert(_1327211), _1327213), c_Orderings_Obot__class_Obot(tc_fun(_1327211, tc_HOL_Obool))))], (49801 ^ _778908) ^ [_1778652, _1778654, _1778656] : [_1778652 = c_List_Olist_ONil(_1778654), -(c_List_Obutlast(_1778654, hAPP(hAPP(c_List_Oappend(_1778654), _1778656), _1778652)) = c_List_Obutlast(_1778654, _1778656))], (32312 ^ _778908) ^ [_1366351, _1366353] : [c_Nitpick_Orefl_H(_1366351, _1366353), 32315 ^ _778908 : [(32316 ^ _778908) ^ [_1366429] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1366351, _1366351)), hAPP(hAPP(c_Product__Type_OPair(_1366351, _1366351), _1366429), _1366429)), _1366353)))]]], (6003 ^ _778908) ^ [_874889, _874891] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_874889, _874891))))], (7773 ^ _778908) ^ [_909009, _909011, _909013, _909015] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_909009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909009), _909011), _909013)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_909009), _909011), _909015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909009), _909013), _909015)))], (40819 ^ _778908) ^ [_1554198, _1554200, _1554202] : [class_Orderings_Olinorder(_1554198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554198), _1554200)), -(_1554200 = c_Orderings_Obot__class_Obot(tc_fun(_1554198, tc_HOL_Obool))), 40830 ^ _778908 : [(40840 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554198), hAPP(c_Finite__Set_Ofold1(_1554198, c_Orderings_Oord__class_Omin(_1554198)), _1554200)), _1554202))), 40841 ^ _778908 : [(40842 ^ _778908) ^ [_1554587] : [hBOOL(hAPP(hAPP(c_member(_1554198), _1554587), _1554200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554198), _1554587), _1554202))]]], (40831 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554198), hAPP(c_Finite__Set_Ofold1(_1554198, c_Orderings_Oord__class_Omin(_1554198)), _1554200)), _1554202)), 40835 ^ _778908 : [(40838 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554198), 40834 ^ [_1554198, _1554200, _1554202]), _1554202)))], (40836 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554198), 40834 ^ [_1554198, _1554200, _1554202]), _1554200)))]]]]], (4692 ^ _778908) ^ [_851562, _851564] : [_851564 = _851562, -(c_Fun_Oid(_851564) = c_Fun_Oid(_851562))], (44460 ^ _778908) ^ [_1647991, _1647993, _1647995, _1647997, _1647999] : [c_Finite__Set_Ofun__left__comm(_1647991, _1647993, _1647995), -(hAPP(c_Fun_Ocomp(_1647993, _1647993, _1647993, hAPP(_1647995, _1647997)), hAPP(_1647995, _1647999)) = hAPP(c_Fun_Ocomp(_1647993, _1647993, _1647993, hAPP(_1647995, _1647999)), hAPP(_1647995, _1647997)))], (29044 ^ _778908) ^ [_1296911, _1296913, _1296915, _1296917, _1296919, _1296921] : [-(hAPP(c_Set_Oimage(_1296911, _1296913, _1296915), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296917, tc_fun(_1296911, tc_HOL_Obool)), _1296919), _1296921)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1296917, tc_fun(_1296913, tc_HOL_Obool)), _1296919), hAPP(hAPP(c_COMBB(tc_fun(_1296911, tc_HOL_Obool), tc_fun(_1296913, tc_HOL_Obool), _1296917), c_Set_Oimage(_1296911, _1296913, _1296915)), _1296921)))], (31235 ^ _778908) ^ [_1342410, _1342412, _1342414, _1342416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1342410, tc_HOL_Obool)), _1342412), _1342414)), hBOOL(hAPP(hAPP(c_member(_1342410), _1342416), _1342412)), -(hBOOL(hAPP(hAPP(c_member(_1342410), _1342416), _1342414)))], (19125 ^ _778908) ^ [] : [-(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))))))], (3190 ^ _778908) ^ [_827759, _827761, _827763, _827765, _827767, _827769, _827771, _827773] : [-(c_SetInterval_Oord_OatLeastAtMost(_827773, _827769, _827765, _827761) = c_SetInterval_Oord_OatLeastAtMost(_827771, _827767, _827763, _827759)), _827773 = _827771, _827769 = _827767, _827765 = _827763, _827761 = _827759], (26929 ^ _778908) ^ [_1254025, _1254027] : [hAPP(_1254025, 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), _1254025), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254027)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1254025), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1254027)))], (42342 ^ _778908) ^ [_1596913, _1596915, _1596917, _1596919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1596913, _1596915), tc_HOL_Obool)), _1596917), _1596919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1596913, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1596913, _1596915), _1596917)), hAPP(c_Relation_ODomain(_1596913, _1596915), _1596919))))], (41376 ^ _778908) ^ [_1567509, _1567511] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1567509), _1567511)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1567509, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1567509, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1567509, tc_HOL_Obool), tc_fun(_1567509, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1567509, tc_HOL_Obool))), _1567511)))))], (42397 ^ _778908) ^ [_1598645, _1598647, _1598649] : [-(hAPP(c_Relation_ODomain(_1598645, _1598647), hAPP(c_Set_OCollect(tc_prod(_1598645, _1598647)), hAPP(c_Product__Type_Oprod_Oprod__case(_1598645, _1598647, tc_HOL_Obool), _1598649))) = hAPP(c_Set_OCollect(_1598645), hAPP(hAPP(c_COMBB(tc_fun(_1598647, tc_HOL_Obool), tc_HOL_Obool, _1598645), c_HOL_OEx(_1598647)), _1598649)))], (2242 ^ _778908) ^ [_812577, _812579, _812581, _812583, _812585, _812587] : [-(c_Sum__Type_OProjr(_812587, _812583, _812579) = c_Sum__Type_OProjr(_812585, _812581, _812577)), _812587 = _812585, _812583 = _812581, _812579 = _812577], (42998 ^ _778908) ^ [_1613091, _1613093] : [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), _1613091), _1613093)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613091), _1613093)))], (19507 ^ _778908) ^ [_1114921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1114921)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114921), c_Int_OMin)))], (1122 ^ _778908) ^ [_795807, _795809] : [-(class_Rings_Olinordered__ring(_795807)), _795809 = _795807, class_Rings_Olinordered__ring(_795809)], (39624 ^ _778908) ^ [_1524765, _1524767, _1524769, _1524771] : [c_Fun_Oinj__on(_1524765, _1524767, _1524769, _1524771), -(hAPP(c_Set_Oimage(_1524767, _1524765, c_Fun_Othe__inv__into(_1524765, _1524767, _1524771, _1524769)), hAPP(c_Set_Oimage(_1524765, _1524767, _1524769), _1524771)) = _1524771)], (36888 ^ _778908) ^ [_1464087, _1464089, _1464091, _1464093] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464087, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464087, tc_HOL_Obool)), _1464089), _1464091)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464087, tc_HOL_Obool)), _1464093), _1464091)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464087, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464087, tc_HOL_Obool)), _1464089), _1464091)), _1464093))], (7480 ^ _778908) ^ [_903937, _903939] : [_903939 = c_Option_Ooption_ONone(_903937), -(c_Option_Ois__none(_903937, _903939))], (9294 ^ _778908) ^ [_934398, _934400] : [class_Groups_Ogroup__add(_934398), 9297 ^ _778908 : [(9304 ^ _778908) ^ [] : [c_Groups_Ozero__class_Ozero(_934398) = _934400, -(c_Groups_Ozero__class_Ozero(_934398) = hAPP(c_Groups_Ouminus__class_Ouminus(_934398), _934400))], (9298 ^ _778908) ^ [] : [c_Groups_Ozero__class_Ozero(_934398) = hAPP(c_Groups_Ouminus__class_Ouminus(_934398), _934400), -(c_Groups_Ozero__class_Ozero(_934398) = _934400)]]], (12738 ^ _778908) ^ [_993076, _993078, _993080, _993082] : [class_Groups_Oordered__comm__monoid__add(_993076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993076), c_Groups_Ozero__class_Ozero(_993076)), _993078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993076), _993080), _993082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993076), _993080), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_993076), _993078), _993082))))], (2648 ^ _778908) ^ [_819038, _819040] : [_819040 = _819038, -(c_Nitpick_Ozero__frac(_819040) = c_Nitpick_Ozero__frac(_819038))], (47984 ^ _778908) ^ [_1735404, _1735406, _1735408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735404), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1735406))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1735406), _1735404), _1735408)) = 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), _1735406)), _1735408)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1735406), _1735404)))], (48375 ^ _778908) ^ [_1744288, _1744290, _1744292, _1744294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744288), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744290)), _1744292))), -(hAPP(hAPP(c_List_Onth(_1744290), hAPP(hAPP(c_List_Oappend(_1744290), _1744292), _1744294)), _1744288) = hAPP(hAPP(c_List_Onth(_1744290), _1744292), _1744288))], (12099 ^ _778908) ^ [_981977, _981979, _981981] : [class_Rings_Oordered__cancel__semiring(_981977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981977), _981979), c_Groups_Ozero__class_Ozero(_981977))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981977), c_Groups_Ozero__class_Ozero(_981977)), _981981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981977), _981979), _981981)), c_Groups_Ozero__class_Ozero(_981977))))], (31423 ^ _778908) ^ [_1345782, _1345784, _1345786, _1345788, _1345790, _1345792] : [c_Typedef_Otype__definition(_1345782, _1345784, _1345786, _1345788, _1345790), -(hBOOL(hAPP(hAPP(c_member(_1345784), hAPP(_1345786, _1345792)), _1345790)))], (2632 ^ _778908) ^ [_818804, _818806] : [_818806 = _818804, -(c_Int_Opred(_818806) = c_Int_Opred(_818804))], (5819 ^ _778908) ^ [_871555] : [-(c_String_Ochar_Ochar__size(_871555) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8218 ^ _778908) ^ [_916536, _916538, _916540, _916542] : [hAPP(c_Sum__Type_OInl(_916536, _916538), _916540) = hAPP(c_Sum__Type_OInl(_916536, _916538), _916542), -(_916540 = _916542)], (51531 ^ _778908) ^ [_1812199, _1812201] : [-(class_Smallcheck_Osmall(tc_prod(_1812199, _1812201))), class_Smallcheck_Osmall(_1812199), class_Smallcheck_Osmall(_1812201)], (51295 ^ _778908) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (47906 ^ _778908) ^ [_1733710, _1733712, _1733714, _1733716, _1733718] : [-(hAPP(hAPP(c_List_Olist__update(_1733710, hAPP(hAPP(c_List_Olist_OCons(_1733710), _1733712), _1733714)), hAPP(c_Nat_OSuc, _1733716)), _1733718) = hAPP(hAPP(c_List_Olist_OCons(_1733710), _1733712), hAPP(hAPP(c_List_Olist__update(_1733710, _1733714), _1733716), _1733718)))], (26181 ^ _778908) ^ [_1239821, _1239823, _1239825] : [class_Orderings_Olinorder(_1239821), 26184 ^ _778908 : [(26191 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239821), _1239823), _1239825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239821, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239821), _1239823)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239821), _1239825))))], (26185 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239821, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239821), _1239823)), hAPP(c_SetInterval_Oord__class_OlessThan(_1239821), _1239825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239821), _1239823), _1239825)))]]], (6639 ^ _778908) ^ [_887808, _887810, _887812] : [-(hBOOL(hAPP(_887808, _887810))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_887808, _887812)), _887810), _887810)))], (5813 ^ _778908) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13112 ^ _778908) ^ [_1000034, _1000036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1000034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1000036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000034), _1000036))))], (19119 ^ _778908) ^ [_1108052, _1108054] : [class_Groups_Omonoid__mult(_1108052), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1108052), _1108054), 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(_1108052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108052), _1108054), _1108054)), _1108054))], (18567 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (37907 ^ _778908) ^ [_1488134, _1488136, _1488138, _1488140, _1488142, _1488144] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1488134, _1488136)), hAPP(hAPP(c_Product__Type_OPair(_1488134, _1488136), _1488142), _1488144)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool)), _1488138), _1488140))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488134, tc_fun(_1488136, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1488134, tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_fun(_1488136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488136, tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_fun(_1488136, tc_HOL_Obool)), _1488134), c_COMBC(_1488136, tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488136, tc_prod(_1488134, _1488136)), tc_fun(_1488136, tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool)), _1488134), hAPP(c_COMBB(tc_prod(_1488134, _1488136), tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool), _1488136), c_member(tc_prod(_1488134, _1488136)))), c_Product__Type_OPair(_1488134, _1488136)))), _1488138)), hAPP(hAPP(c_COMBC(_1488134, tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_fun(_1488136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488136, tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_fun(_1488136, tc_HOL_Obool)), _1488134), c_COMBC(_1488136, tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488136, tc_prod(_1488134, _1488136)), tc_fun(_1488136, tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool)), _1488134), hAPP(c_COMBB(tc_prod(_1488134, _1488136), tc_fun(tc_fun(tc_prod(_1488134, _1488136), tc_HOL_Obool), tc_HOL_Obool), _1488136), c_member(tc_prod(_1488134, _1488136)))), c_Product__Type_OPair(_1488134, _1488136)))), _1488140)), _1488142), _1488144)))], (35130 ^ _778908) ^ [_1424014, _1424016, _1424018, _1424020] : [c_FunDef_Oreduction__pair(_1424014, _1424016), -(c_FunDef_Oreduction__pair(_1424018, hAPP(hAPP(c_FunDef_Orp__inv__image(_1424014, _1424018), _1424016), _1424020)))], (17519 ^ _778908) ^ [_1081505, _1081507, _1081509] : [class_Rings_Oring__1__no__zero__divisors(_1081505), -(_1081507 = c_Groups_Ozero__class_Ozero(_1081505)), hAPP(hAPP(c_Power_Opower__class_Opower(_1081505), _1081507), _1081509) = c_Groups_Ozero__class_Ozero(_1081505)], (22804 ^ _778908) ^ [_1174651, _1174653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174653)), -(c_Divides_OposDivAlg(_1174651, _1174653) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1174651), _1174653)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174651, _1174653)))], (9582 ^ _778908) ^ [_939283, _939285, _939287, _939289, _939291] : [class_Rings_Osemiring(_939283), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939283), _939285), _939287)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939283), _939289), _939287)), _939291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939283), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939283), _939285), _939289)), _939287)), _939291))], (11394 ^ _778908) ^ [_969550, _969552, _969554] : [class_Groups_Oordered__ab__group__add(_969550), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969550), _969552), _969554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969550), hAPP(c_Groups_Ouminus__class_Ouminus(_969550), _969554)), hAPP(c_Groups_Ouminus__class_Ouminus(_969550), _969552))))], (2720 ^ _778908) ^ [_820126, _820128, _820130, _820132] : [-(c_Nitpick_Onorm__frac(_820132, _820128) = c_Nitpick_Onorm__frac(_820130, _820126)), _820132 = _820130, _820128 = _820126], (30928 ^ _778908) ^ [_1333789, _1333791, _1333793, _1333795] : [30929 ^ _778908 : [(30932 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333789), _1333791), _1333795))], (30930 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333789), _1333791), _1333793))]], -(hBOOL(hAPP(hAPP(c_member(_1333789), _1333791), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333789, tc_HOL_Obool)), _1333795), _1333793))))], (764 ^ _778908) ^ [_790662, _790664, _790666, _790668, _790670, _790672] : [-(c_Finite__Set_Ofolding__one__idem(_790670, _790666, _790662)), c_Finite__Set_Ofolding__one__idem(_790672, _790668, _790664), _790672 = _790670, _790668 = _790666, _790664 = _790662], (17457 ^ _778908) ^ [_1080436] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080436) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1080436))], (31429 ^ _778908) ^ [_1345893, _1345895, _1345897] : [hBOOL(hAPP(hAPP(c_member(_1345893), _1345895), _1345897)), -(hAPP(hAPP(c_Set_Oinsert(_1345893), _1345895), _1345897) = _1345897)], (15394 ^ _778908) ^ [_1040752, _1040754, _1040756, _1040758, _1040760] : [class_Groups_Ominus(_1040752), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1040754, _1040752)), _1040756), _1040758), _1040760) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1040752), hAPP(_1040756, _1040760)), hAPP(_1040758, _1040760)))], (22346 ^ _778908) ^ [_1165973, _1165975] : [c_Code__Numeral_OSuc__code__numeral(_1165973) = c_Code__Numeral_OSuc__code__numeral(_1165975), -(_1165973 = _1165975)], (48393 ^ _778908) ^ [_1744713, _1744715, _1744717, _1744719, _1744721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744713), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744715)), _1744717)))), -(hAPP(hAPP(c_List_Olist__update(_1744715, hAPP(hAPP(c_List_Oappend(_1744715), _1744717), _1744719)), _1744713), _1744721) = hAPP(hAPP(c_List_Oappend(_1744715), _1744717), hAPP(hAPP(c_List_Olist__update(_1744715, _1744719), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1744713), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744715)), _1744717))), _1744721)))], (46220 ^ _778908) ^ [_1690863, _1690865, _1690867, _1690869, _1690871] : [-(c_Map_Odom(_1690863, _1690865, hAPP(hAPP(c_COMBS(_1690863, tc_Option_Ooption(_1690867), tc_Option_Ooption(_1690865)), hAPP(hAPP(c_COMBB(tc_fun(_1690867, _1690865), tc_fun(tc_Option_Ooption(_1690867), tc_Option_Ooption(_1690865)), _1690863), c_Option_Omap(_1690867, _1690865)), _1690869)), _1690871)) = c_Map_Odom(_1690863, _1690867, _1690871))], (28811 ^ _778908) ^ [_1291269, _1291271, _1291273, _1291275, _1291277] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291269, tc_fun(_1291271, tc_HOL_Obool)), _1291273), _1291275), _1291277)), 28815 ^ _778908 : [(28818 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1291275, 28814 ^ [_1291269, _1291271, _1291273, _1291275, _1291277]), _1291277)))], (28816 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1291269), 28814 ^ [_1291269, _1291271, _1291273, _1291275, _1291277]), _1291273)))]]], (16653 ^ _778908) ^ [_1065162, _1065164, _1065166, _1065168] : [class_Rings_Ocomm__semiring__1(_1065162), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1065162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065162), _1065164), _1065166)), _1065168) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065162), hAPP(hAPP(c_Power_Opower__class_Opower(_1065162), _1065164), _1065168)), hAPP(hAPP(c_Power_Opower__class_Opower(_1065162), _1065166), _1065168)))], (39303 ^ _778908) ^ [_1517763, _1517765] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1517763), _1517765))), -(hAPP(c_Finite__Set_Ocard(_1517763), _1517765) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24923 ^ _778908) ^ [_1215615, _1215617, _1215619, _1215621] : [-(c_Sum__Type_Osum_Osum__case(_1215615, _1215617, _1215619, hAPP(hAPP(c_COMBB(tc_sum(_1215615, _1215619), _1215617, _1215615), _1215621), c_Sum__Type_OInl(_1215615, _1215619)), hAPP(hAPP(c_COMBB(tc_sum(_1215615, _1215619), _1215617, _1215619), _1215621), c_Sum__Type_OInr(_1215619, _1215615))) = _1215621)], (42328 ^ _778908) ^ [_1596637, _1596639, _1596641] : [hAPP(c_Relation_ODomain(_1596637, _1596639), _1596641) = c_Orderings_Obot__class_Obot(tc_fun(_1596637, tc_HOL_Obool)), -(_1596641 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1596637, _1596639), tc_HOL_Obool)))], (23212 ^ _778908) ^ [_1182764, _1182766] : [-(_1182764 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23215 ^ _778908 : [(23222 ^ _778908) ^ [] : [-(_1182766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1182764, _1182766) = 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, _1182766))), 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)), _1182766)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182764))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182766), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182764), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1182764, _1182766)), 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), _1182766))))), c_Divides_Opdivmod(_1182764, _1182766)))))], (23216 ^ _778908) ^ [] : [_1182766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1182764, _1182766) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182764))]]], (31085 ^ _778908) ^ [_1337033, _1337035] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1337033), _1337035)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1337033)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1337035))))], (18849 ^ _778908) ^ [_1103694, _1103696] : [_1103694 = _1103696, -(c_Int_OBit1(_1103694) = c_Int_OBit1(_1103696))], (35484 ^ _778908) ^ [_1432222, _1432224, _1432226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432222, tc_HOL_Obool)), _1432224), _1432226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1432222, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1432222), _1432224)), hAPP(c_Set_OPow(_1432222), _1432226))))], (35629 ^ _778908) ^ [_1435402, _1435404, _1435406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1435402, tc_HOL_Obool)), _1435404), _1435406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1435402, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1435402, _1435404)), c_Predicate_OPowp(_1435402, _1435406))))], (5967 ^ _778908) ^ [_874187, _874189, _874191] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_874187, _874189, _874191))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _874189))))], (12585 ^ _778908) ^ [_990515, _990517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _990517)), 12592 ^ _778908 : [(12599 ^ _778908) ^ [] : [_990515 = _990517, -(hAPP(c_Int_Onat, _990515) = hAPP(c_Int_Onat, _990517))], (12593 ^ _778908) ^ [] : [hAPP(c_Int_Onat, _990515) = hAPP(c_Int_Onat, _990517), -(_990515 = _990517)]]], (20127 ^ _778908) ^ [] : [-(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)))], (8244 ^ _778908) ^ [_916997, _916999, _917001] : [-(c_Sum__Type_OProjr(_916997, _916999, hAPP(c_Sum__Type_OInr(_916999, _916997), _917001)) = _917001)], (24155 ^ _778908) ^ [_1200834, _1200836, _1200838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1200834, tc_HOL_Obool)), _1200836), _1200838)), 24158 ^ _778908 : [(24161 ^ _778908) ^ [] : [_1200836 = _1200838], (24159 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200834, tc_HOL_Obool)), _1200836), _1200838)))]]], (51435 ^ _778908) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (6867 ^ _778908) ^ [_891938, _891940, _891942, _891944, _891946] : [c_Com_Ocom_OLocal(_891938, _891940, _891942) = c_Com_Ocom_OWhile(_891944, _891946)], (33179 ^ _778908) ^ [_1384403, _1384405] : [class_Rings_Oring__1(_1384403), -(hBOOL(hAPP(hAPP(c_member(_1384403), hAPP(c_Int_Oring__1__class_Oof__int(_1384403), _1384405)), c_Int_Oring__1__class_OInts(_1384403))))], (44983 ^ _778908) ^ [_1662224, _1662226, _1662228, _1662230, _1662232] : [_1662224 = c_Orderings_Obot__class_Obot(tc_fun(_1662226, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662226, tc_fun(_1662228, tc_HOL_Obool)), _1662224), hAPP(hAPP(c_COMBB(tc_fun(_1662228, tc_HOL_Obool), tc_fun(_1662228, tc_HOL_Obool), _1662226), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1662228, tc_HOL_Obool)), _1662230)), _1662232)) = c_Orderings_Otop__class_Otop(tc_fun(_1662228, tc_HOL_Obool)))], (44893 ^ _778908) ^ [_1659767, _1659769, _1659771, _1659773, _1659775] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659767, tc_fun(_1659769, tc_HOL_Obool)), _1659771), hAPP(hAPP(c_COMBC(_1659767, tc_fun(_1659769, tc_HOL_Obool), tc_fun(_1659769, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659769, tc_HOL_Obool), tc_fun(tc_fun(_1659769, tc_HOL_Obool), tc_fun(_1659769, tc_HOL_Obool)), _1659767), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659769, tc_HOL_Obool))), _1659773)), _1659775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659769, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659767, tc_fun(_1659769, tc_HOL_Obool)), _1659771), _1659773)), _1659775))], (7148 ^ _778908) ^ [_898476, _898478, _898480, _898482] : [class_Groups_Ocancel__semigroup__add(_898476), 7151 ^ _778908 : [(7158 ^ _778908) ^ [] : [_898478 = _898482, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898476), _898478), _898480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898476), _898482), _898480))], (7152 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898476), _898478), _898480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898476), _898482), _898480), -(_898478 = _898482)]]], (11572 ^ _778908) ^ [_972467, _972469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972467), _972469)), 11575 ^ _778908 : [(11578 ^ _778908) ^ [] : [_972467 = _972469], (11576 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972467), _972469)))]]], (34351 ^ _778908) ^ [_1407255, _1407257, _1407259, _1407261] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1407255), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407257, tc_Int_Oint), _1407259), _1407261)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407257, _1407255), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1407255, _1407257), c_Int_Oring__1__class_Oof__int(_1407255)), _1407259)), _1407261)), class_Groups_Ocomm__monoid__mult(_1407255), class_Rings_Oring__1(_1407255)], (46901 ^ _778908) ^ [_1707674, _1707676] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1707674), _1707676))), -(c_Nitpick_Ocard_H(_1707674, _1707676) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33803 ^ _778908) ^ [_1395572, _1395574, _1395576, _1395578, _1395580, _1395582, _1395584] : [-(c_Nitpick_Ofold__graph_H(_1395572, _1395574, _1395576, _1395578, _1395580, hAPP(hAPP(_1395576, _1395582), _1395584))), 33804 ^ _778908 : [(33811 ^ _778908) ^ [_1395801, _1395803] : [hAPP(hAPP(_1395576, _1395582), _1395584) = hAPP(hAPP(_1395576, _1395803), _1395801), hBOOL(hAPP(hAPP(c_member(_1395572), _1395803), _1395580)), c_Nitpick_Ofold__graph_H(_1395572, _1395574, _1395576, _1395578, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395572, tc_HOL_Obool)), _1395580), hAPP(hAPP(c_Set_Oinsert(_1395572), _1395803), c_Orderings_Obot__class_Obot(tc_fun(_1395572, tc_HOL_Obool)))), _1395801)], (33805 ^ _778908) ^ [] : [_1395580 = c_Orderings_Obot__class_Obot(tc_fun(_1395572, tc_HOL_Obool)), hAPP(hAPP(_1395576, _1395582), _1395584) = _1395578]]], (48604 ^ _778908) ^ [_1750230, _1750232, _1750234, _1750236] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1750230) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1750232), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1750230)), hAPP(hAPP(c_List_Olist_OCons(_1750232), _1750234), _1750236)) = c_List_Olist_ONil(_1750232))], (23230 ^ _778908) ^ [_1183186, _1183188, _1183190, _1183192, _1183194, _1183196] : [hAPP(hAPP(c_Product__Type_OPair(_1183186, _1183188), _1183190), _1183192) = hAPP(hAPP(c_Product__Type_OPair(_1183186, _1183188), _1183194), _1183196), 23233 ^ _778908 : [(23236 ^ _778908) ^ [] : [-(_1183192 = _1183196)], (23234 ^ _778908) ^ [] : [-(_1183190 = _1183194)]]], (47728 ^ _778908) ^ [_1729272, _1729274, _1729276, _1729278, _1729280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729272), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729274)), _1729276))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729272), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729278)), _1729280))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1729274, _1729278)), hAPP(hAPP(c_List_Ozip(_1729274, _1729278), _1729276), _1729280)), _1729272) = hAPP(hAPP(c_Product__Type_OPair(_1729274, _1729278), hAPP(hAPP(c_List_Onth(_1729274), _1729276), _1729272)), hAPP(hAPP(c_List_Onth(_1729278), _1729280), _1729272)))], (5945 ^ _778908) ^ [_873800, _873802, _873804, _873806] : [hAPP(c_Com_Ocom_OBODY, _873800) = c_Com_Ocom_OCall(_873802, _873804, _873806)], (33107 ^ _778908) ^ [_1382849, _1382851, _1382853] : [class_Rings_Oring__1(_1382849), hBOOL(hAPP(hAPP(c_member(_1382849), _1382851), c_Int_Oring__1__class_OInts(_1382849))), hBOOL(hAPP(hAPP(c_member(_1382849), _1382853), c_Int_Oring__1__class_OInts(_1382849))), -(hBOOL(hAPP(hAPP(c_member(_1382849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382849), _1382851), _1382853)), c_Int_Oring__1__class_OInts(_1382849))))], (31822 ^ _778908) ^ [_1355040, _1355042, _1355044, _1355046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool)), _1355044), _1355046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355040, tc_fun(_1355042, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1355040, tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_fun(_1355042, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355042, tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_fun(_1355042, tc_HOL_Obool)), _1355040), c_COMBC(_1355042, tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355042, tc_prod(_1355040, _1355042)), tc_fun(_1355042, tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool)), _1355040), hAPP(c_COMBB(tc_prod(_1355040, _1355042), tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool), _1355042), c_member(tc_prod(_1355040, _1355042)))), c_Product__Type_OPair(_1355040, _1355042)))), _1355044)), hAPP(hAPP(c_COMBC(_1355040, tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_fun(_1355042, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355042, tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_fun(_1355042, tc_HOL_Obool)), _1355040), c_COMBC(_1355042, tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1355042, tc_prod(_1355040, _1355042)), tc_fun(_1355042, tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool)), _1355040), hAPP(c_COMBB(tc_prod(_1355040, _1355042), tc_fun(tc_fun(tc_prod(_1355040, _1355042), tc_HOL_Obool), tc_HOL_Obool), _1355042), c_member(tc_prod(_1355040, _1355042)))), c_Product__Type_OPair(_1355040, _1355042)))), _1355046))))], (27110 ^ _778908) ^ [_1257625, _1257627] : [27112 ^ _778908 : [(27115 ^ _778908) ^ [] : [hBOOL(hAPP(_1257627, 27111 ^ [_1257625, _1257627]))], (27113 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27111 ^ [_1257625, _1257627]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1257625))))]], 27116 ^ _778908 : [(27117 ^ _778908) ^ [_1257780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1257780), _1257625)), -(hBOOL(hAPP(_1257627, _1257780)))]]], (42090 ^ _778908) ^ [_1590933, _1590935] : [-(c_FunDef_Oreduction__pair(_1590933, _1590935)), c_Wellfounded_Owf(_1590933, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool), tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool)), _1590935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1590933, _1590933, _1590933), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool), tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool)), _1590935)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool), tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool)), _1590935))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool), tc_fun(tc_prod(_1590933, _1590933), tc_HOL_Obool)), _1590935)))], (8180 ^ _778908) ^ [_915935, _915937, _915939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915935), _915937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915935), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915939), _915937))))], (35696 ^ _778908) ^ [_1436960, _1436962, _1436964, _1436966, _1436968, _1436970, _1436972, _1436974] : [hAPP(c_Fun_Ocomp(_1436960, _1436962, _1436964, _1436966), _1436968) = hAPP(c_Fun_Ocomp(_1436970, _1436962, _1436964, _1436972), _1436974), 35699 ^ _778908 : [(35700 ^ _778908) ^ [_1437075] : [-(hAPP(_1436966, hAPP(_1436968, _1437075)) = hAPP(_1436972, hAPP(_1436974, _1437075)))]]], (24683 ^ _778908) ^ [_1210745, _1210747, _1210749] : [class_Orderings_Olinorder(_1210745), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210745), _1210747), _1210749) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210745), _1210749), _1210747))], (25001 ^ _778908) ^ [_1217354, _1217356, _1217358] : [-(c_Nitpick_Otimes__frac(_1217354, _1217356, _1217358) = hAPP(hAPP(c_Nitpick_Ofrac(_1217354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1217354), _1217356)), hAPP(c_Nitpick_Onum(_1217354), _1217358))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1217354), _1217356)), hAPP(c_Nitpick_Odenom(_1217354), _1217358))))], (14272 ^ _778908) ^ [_1020376, _1020378, _1020380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020376)), 14275 ^ _778908 : [(14276 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1020378, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1020380), _1020376)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1020380, _1020376))), 14279 ^ _778908 : [(14280 ^ _778908) ^ [_1020577, _1020579] : [-(hBOOL(hAPP(hAPP(_1020378, _1020579), _1020577))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020577)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020577), _1020376)), _1020380 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1020376), _1020579)), _1020577)]]], (14294 ^ _778908) ^ [] : [14297 ^ _778908 : [(14300 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14296 ^ [_1020376, _1020378, _1020380]), _1020376)))], (14302 ^ _778908) ^ [] : [-(_1020380 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1020376), 14295 ^ [_1020376, _1020378, _1020380])), 14296 ^ [_1020376, _1020378, _1020380]))], (14304 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1020378, 14295 ^ [_1020376, _1020378, _1020380]), 14296 ^ [_1020376, _1020378, _1020380]))], (14298 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14296 ^ [_1020376, _1020378, _1020380])))]], -(hBOOL(hAPP(hAPP(_1020378, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1020380), _1020376)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1020380, _1020376))))]]], (1402 ^ _778908) ^ [_799307, _799309] : [-(class_Finite__Set_Ofinite(_799307)), _799309 = _799307, class_Finite__Set_Ofinite(_799309)], (51017 ^ _778908) ^ [_1805031, _1805033, _1805035, _1805037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1805031), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805033)), _1805035))), -(hAPP(c_List_Orev(_1805033), hAPP(hAPP(c_List_Olist__update(_1805033, _1805035), _1805031), _1805037)) = hAPP(hAPP(c_List_Olist__update(_1805033, hAPP(c_List_Orev(_1805033), _1805035)), 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(_1805033)), _1805035)), _1805031)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1805037))], (39184 ^ _778908) ^ [_1514593, _1514595, _1514597, _1514599, _1514601] : [c_Fun_Oinj__on(_1514593, _1514595, _1514597, hAPP(hAPP(c_Set_Oinsert(_1514593), _1514599), _1514601)), 39187 ^ _778908 : [(39190 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1514595), hAPP(_1514597, _1514599)), hAPP(c_Set_Oimage(_1514593, _1514595, _1514597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514593, tc_HOL_Obool)), _1514601), hAPP(hAPP(c_Set_Oinsert(_1514593), _1514599), c_Orderings_Obot__class_Obot(tc_fun(_1514593, tc_HOL_Obool)))))))], (39188 ^ _778908) ^ [] : [-(c_Fun_Oinj__on(_1514593, _1514595, _1514597, _1514601))]]], (51341 ^ _778908) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (30794 ^ _778908) ^ [_1331171, _1331173] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331171), _1331173))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1331173, _1331171) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1331173), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1331173), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1331171)))], (43526 ^ _778908) ^ [_1626325, _1626327, _1626329, _1626331] : [-(hAPP(c_Relation_Oconverse(_1626325, _1626327), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1626325, _1626327), tc_HOL_Obool)), _1626329), _1626331)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1626327, _1626325), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1626325, _1626327), _1626329)), hAPP(c_Relation_Oconverse(_1626325, _1626327), _1626331)))], (41770 ^ _778908) ^ [_1582383, _1582385, _1582387, _1582389, _1582391, _1582393, _1582395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582383, _1582385), tc_HOL_Obool)), _1582387), _1582389)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582385, _1582391), tc_HOL_Obool)), _1582393), _1582395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582383, _1582391), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1582383, _1582385, _1582391), _1582387), _1582393)), hAPP(hAPP(c_Relation_Orel__comp(_1582383, _1582385, _1582391), _1582389), _1582395))))], (19781 ^ _778908) ^ [_1119654] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1119654))), 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), _1119654), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34877 ^ _778908) ^ [_1418052, _1418054, _1418056, _1418058] : [-(hAPP(c_Map_Orestrict__map(_1418052, _1418054, _1418056, c_Orderings_Obot__class_Obot(tc_fun(_1418052, tc_HOL_Obool))), _1418058) = c_Option_Ooption_ONone(_1418054))], (16130 ^ _778908) ^ [_1055244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1055244)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055244), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1055244)], (43630 ^ _778908) ^ [_1629138, _1629140, _1629142] : [c_Relation_Orefl__on(_1629138, _1629140, _1629142), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1629138, _1629138), tc_HOL_Obool)), _1629142), hAPP(hAPP(c_Relation_Orel__comp(_1629138, _1629138, _1629138), hAPP(c_Relation_Oconverse(_1629138, _1629138), _1629142)), _1629142))))], (5228 ^ _778908) ^ [_859790, _859792, _859794, _859796] : [-(c_List_Olinorder__class_Osorted__list__of__set(_859796, _859792) = c_List_Olinorder__class_Osorted__list__of__set(_859794, _859790)), _859796 = _859794, _859792 = _859790], (6627 ^ _778908) ^ [_887596, _887598, _887600] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _887596)), _887598), _887600)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _887596))), _887598), _887600)))], (12543 ^ _778908) ^ [_989818] : [-(hBOOL(hAPP(_989818, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12550 ^ [_989818])))), 12544 ^ _778908 : [(12545 ^ _778908) ^ [_989870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _989870)), hBOOL(hAPP(_989818, _989870))]]], (46705 ^ _778908) ^ [_1702451, _1702453] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1702451), hAPP(c_List_Oset(_1702451), _1702453))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702451)), _1702453))))], (13322 ^ _778908) ^ [_1003530, _1003532] : [hAPP(c_Int_Onat, _1003530) = _1003532, 13325 ^ _778908 : [(13332 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003530))), -(_1003532 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13326 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1003530)), -(_1003530 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1003532))]]], (18191 ^ _778908) ^ [_1093244, _1093246, _1093248] : [18193 ^ _778908 : [(18196 ^ _778908) ^ [] : [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(_1093246, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18192 ^ [_1093244, _1093246, _1093248]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1093246, 18192 ^ [_1093244, _1093246, _1093248])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18194 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18192 ^ [_1093244, _1093246, _1093248]), _1093244)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1093246, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1093248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1093248), hAPP(_1093246, _1093244))), 18206 ^ _778908 : [(18209 ^ _778908) ^ [] : [-(hAPP(_1093246, 18205 ^ [_1093244, _1093246, _1093248]) = _1093248)], (18207 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18205 ^ [_1093244, _1093246, _1093248]), _1093244)))]]], (45065 ^ _778908) ^ [_1663898, _1663900, _1663902, _1663904] : [hBOOL(hAPP(hAPP(c_member(_1663898), _1663900), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663898, tc_HOL_Obool), _1663902))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1663898, tc_HOL_Obool)), _1663904), _1663902)), -(hBOOL(hAPP(hAPP(c_member(_1663898), _1663900), _1663904)))], (42798 ^ _778908) ^ [_1608572, _1608574, _1608576] : [-(hBOOL(hAPP(hAPP(c_member(_1608572), _1608574), c_Wellfounded_Oacc(_1608572, _1608576)))), 42802 ^ _778908 : [(42805 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1608572), 42801 ^ [_1608572, _1608574, _1608576]), c_Wellfounded_Oacc(_1608572, _1608576)))], (42803 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608572, _1608572)), hAPP(hAPP(c_Product__Type_OPair(_1608572, _1608572), 42801 ^ [_1608572, _1608574, _1608576]), _1608574)), _1608576)))]]], (11072 ^ _778908) ^ [_964348, _964350, _964352] : [class_Orderings_Oorder(_964348), -(_964350 = _964352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964348), _964352), _964350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964348), _964352), _964350)))], (19891 ^ _778908) ^ [_1121476, _1121478] : [class_Rings_Oring__1__no__zero__divisors(_1121476), 19894 ^ _778908 : [(19895 ^ _778908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1121476), _1121478), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1121476), -(_1121478 = c_Groups_Oone__class_Oone(_1121476)), -(_1121478 = hAPP(c_Groups_Ouminus__class_Ouminus(_1121476), c_Groups_Oone__class_Oone(_1121476)))], (19905 ^ _778908) ^ [] : [19906 ^ _778908 : [(19909 ^ _778908) ^ [] : [_1121478 = hAPP(c_Groups_Ouminus__class_Ouminus(_1121476), c_Groups_Oone__class_Oone(_1121476))], (19907 ^ _778908) ^ [] : [_1121478 = c_Groups_Oone__class_Oone(_1121476)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121476), _1121478), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1121476))]]], (1352 ^ _778908) ^ [_798682, _798684] : [-(class_Lattices_Oboolean__algebra(_798682)), _798684 = _798682, class_Lattices_Oboolean__algebra(_798684)], (32646 ^ _778908) ^ [_1373009, _1373011, _1373013, _1373015, _1373017] : [c_Finite__Set_Ofolding__one(_1373009, _1373011, _1373013), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373009), _1373015)), -(hBOOL(hAPP(hAPP(c_member(_1373009), _1373017), _1373015))), -(_1373015 = c_Orderings_Obot__class_Obot(tc_fun(_1373009, tc_HOL_Obool))), -(hAPP(_1373013, hAPP(hAPP(c_Set_Oinsert(_1373009), _1373017), _1373015)) = hAPP(hAPP(_1373011, _1373017), hAPP(_1373013, _1373015)))], (27300 ^ _778908) ^ [_1261328, _1261330, _1261332, _1261334, _1261336] : [class_Groups_Ocomm__monoid__add(_1261328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1261330), _1261332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1261332), _1261334)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1261328), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261328), _1261336), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261330), _1261332))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261328), _1261336), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261332), _1261334))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261328), _1261336), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261330), _1261334)))], (51165 ^ _778908) ^ [_1808542, _1808544] : [class_Lattices_Oboolean__algebra(_1808542), -(class_Lattices_Oboolean__algebra(tc_fun(_1808544, _1808542)))], (46360 ^ _778908) ^ [_1693934, _1693936, _1693938] : [hBOOL(hAPP(c_List_Odistinct(_1693934), hAPP(hAPP(c_List_Omap(tc_prod(_1693934, _1693936), _1693934), c_Product__Type_Ofst(_1693934, _1693936)), _1693938))), -(c_Map_Oran(_1693934, _1693936, c_Map_Omap__of(_1693934, _1693936, _1693938)) = hAPP(c_Set_Oimage(tc_prod(_1693934, _1693936), _1693936, c_Product__Type_Osnd(_1693934, _1693936)), hAPP(c_List_Oset(tc_prod(_1693934, _1693936)), _1693938)))], (43656 ^ _778908) ^ [_1629611, _1629613, _1629615] : [-(hAPP(c_Relation_Oconverse(_1629611, _1629613), _1629615) = hAPP(c_Set_OCollect(tc_prod(_1629613, _1629611)), hAPP(c_Product__Type_Oprod_Oprod__case(_1629613, _1629611, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1629613, tc_fun(tc_prod(_1629611, _1629613), tc_HOL_Obool), tc_fun(_1629611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1629611, tc_fun(tc_fun(tc_prod(_1629611, _1629613), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1629611, _1629613), tc_HOL_Obool), tc_fun(_1629611, tc_HOL_Obool)), _1629613), c_COMBC(_1629611, tc_fun(tc_prod(_1629611, _1629613), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1629611, tc_prod(_1629611, _1629613)), tc_fun(_1629611, tc_fun(tc_fun(tc_prod(_1629611, _1629613), tc_HOL_Obool), tc_HOL_Obool)), _1629613), hAPP(c_COMBB(tc_prod(_1629611, _1629613), tc_fun(tc_fun(tc_prod(_1629611, _1629613), tc_HOL_Obool), tc_HOL_Obool), _1629611), c_member(tc_prod(_1629611, _1629613)))), hAPP(c_COMBC(_1629611, _1629613, tc_prod(_1629611, _1629613)), c_Product__Type_OPair(_1629611, _1629613))))), _1629615))))], (7486 ^ _778908) ^ [_904020] : [-(c_Option_Ois__none(_904020, c_Option_Ooption_ONone(_904020)))], (25569 ^ _778908) ^ [_1228220, _1228222] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228220), _1228222)), 25572 ^ _778908 : [(25579 ^ _778908) ^ [] : [_1228222 = _1228220, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228222), _1228220)))], (25573 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228222), _1228220)), -(_1228222 = _1228220)]]], (46098 ^ _778908) ^ [_1687748, _1687750, _1687752, _1687754, _1687756] : [hAPP(hAPP(c_List_Omap(_1687748, _1687750), _1687752), _1687754) = hAPP(hAPP(c_List_Omap(_1687748, _1687750), _1687752), _1687756), c_Fun_Oinj__on(_1687748, _1687750, _1687752, c_Orderings_Otop__class_Otop(tc_fun(_1687748, tc_HOL_Obool))), -(_1687754 = _1687756)], (1212 ^ _778908) ^ [_796932, _796934] : [-(class_Int_Onumber__ring(_796932)), _796934 = _796932, class_Int_Onumber__ring(_796934)], (48947 ^ _778908) ^ [_1760012, _1760014, _1760016, _1760018] : [-(hAPP(hAPP(c_List_Odrop(_1760012), _1760014), hAPP(hAPP(c_List_Odrop(_1760012), _1760016), _1760018)) = hAPP(hAPP(c_List_Odrop(_1760012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1760014), _1760016)), _1760018))], (22718 ^ _778908) ^ [_1173219, _1173221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173219), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1173221, _1173219) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1173221), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1173219)))], (13919 ^ _778908) ^ [_1014019, _1014021, _1014023, _1014025] : [class_Divides_Osemiring__div(_1014019), -(c_Divides_Odiv__class_Omod(_1014019, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014019), _1014021), _1014023), _1014025) = c_Divides_Odiv__class_Omod(_1014019, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014019), c_Divides_Odiv__class_Omod(_1014019, _1014021, _1014025)), c_Divides_Odiv__class_Omod(_1014019, _1014023, _1014025)), _1014025))], (40476 ^ _778908) ^ [_1547801, _1547803, _1547805] : [-(c_Relation_Orefl__on(_1547801, _1547803, _1547805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547801, _1547801), tc_HOL_Obool)), _1547805), hAPP(hAPP(c_Product__Type_OSigma(_1547801, _1547801), _1547803), hAPP(c_COMBK(tc_fun(_1547801, tc_HOL_Obool), _1547801), _1547803)))), 40482 ^ _778908 : [(40485 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547801, _1547801)), hAPP(hAPP(c_Product__Type_OPair(_1547801, _1547801), 40481 ^ [_1547801, _1547803, _1547805]), 40481 ^ [_1547801, _1547803, _1547805])), _1547805))], (40483 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547801), 40481 ^ [_1547801, _1547803, _1547805]), _1547803)))]]], (27580 ^ _778908) ^ [_1267287, _1267289] : [class_Orderings_Oorder(_1267287), 27587 ^ _778908 : [(27592 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267287), hAPP(_1267289, 27585 ^ [_1267287, _1267289])), hAPP(_1267289, 27586 ^ [_1267287, _1267289])))], (27590 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 27586 ^ [_1267287, _1267289]), 27585 ^ [_1267287, _1267289]))], (27588 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 27585 ^ [_1267287, _1267289]), 27586 ^ [_1267287, _1267289])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1267287, 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)))), _1267289))], (7410 ^ _778908) ^ [_902735, _902737, _902739] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_902735, _902737, _902739)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_902737)), c_Com_Ocom_Ocom__size(_902739))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42310 ^ _778908) ^ [_1596337, _1596339, _1596341] : [c_Wellfounded_OwfP(_1596337, _1596339), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1596337, _1596339), _1596341)))], (25179 ^ _778908) ^ [_1221711, _1221713, _1221715] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1221711), _1221713)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1221711), _1221715))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1221711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221713), _1221715)))], (28523 ^ _778908) ^ [_1285554, _1285556, _1285558] : [class_Orderings_Olinorder(_1285554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285554), _1285556), _1285558)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285554, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1285554), _1285556)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1285554, _1285556, _1285558)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1285554), _1285558))], (9728 ^ _778908) ^ [_941891, _941893] : [class_Rings_Olinordered__ring(_941891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941891), _941893), _941893)), c_Groups_Ozero__class_Ozero(_941891)))], (37901 ^ _778908) ^ [_1487477, _1487479, _1487481, _1487483, _1487485, _1487487] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487477, tc_fun(_1487479, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1487477, tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_fun(_1487479, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487479, tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_fun(_1487479, tc_HOL_Obool)), _1487477), c_COMBC(_1487479, tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487479, tc_prod(_1487477, _1487479)), tc_fun(_1487479, tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool)), _1487477), hAPP(c_COMBB(tc_prod(_1487477, _1487479), tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool), _1487479), c_member(tc_prod(_1487477, _1487479)))), c_Product__Type_OPair(_1487477, _1487479)))), _1487481)), hAPP(hAPP(c_COMBC(_1487477, tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_fun(_1487479, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487479, tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_fun(_1487479, tc_HOL_Obool)), _1487477), c_COMBC(_1487479, tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487479, tc_prod(_1487477, _1487479)), tc_fun(_1487479, tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool)), _1487477), hAPP(c_COMBB(tc_prod(_1487477, _1487479), tc_fun(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool), tc_HOL_Obool), _1487479), c_member(tc_prod(_1487477, _1487479)))), c_Product__Type_OPair(_1487477, _1487479)))), _1487483)), _1487485), _1487487)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487477, _1487479)), hAPP(hAPP(c_Product__Type_OPair(_1487477, _1487479), _1487485), _1487487)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1487477, _1487479), tc_HOL_Obool)), _1487481), _1487483))))], (13458 ^ _778908) ^ [_1005637, _1005639, _1005641, _1005643, _1005645, _1005647] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005637), _1005639)), _1005641) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005643), _1005645)), _1005647), 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), _1005643), _1005645)), _1005647)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005641), _1005637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1005643), _1005637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1005645), _1005639)))], (9128 ^ _778908) ^ [_931737, _931739, _931741, _931743, _931745] : [class_Rings_Ocomm__semiring__1(_931737), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931737), _931739), _931741)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931737), _931743), _931745)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931737), _931739), _931743)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931737), _931741), _931745)))], (10483 ^ _778908) ^ [_955013, _955015] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955013), _955015) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 10486 ^ _778908 : [(10489 ^ _778908) ^ [] : [-(_955015 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10487 ^ _778908) ^ [] : [-(_955013 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (41165 ^ _778908) ^ [_1561028, _1561030, _1561032] : [-(hAPP(c_Set_OCollect(_1561028), hAPP(hAPP(c_COMBS(_1561028, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1561028), c_fconj), _1561030)), _1561032)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1561028, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1561028), _1561030)), hAPP(c_Set_OCollect(_1561028), _1561032)))], (49466 ^ _778908) ^ [_1771630, _1771632, _1771634] : [c_Relation_Orefl__on(_1771630, _1771632, _1771634), -(c_Relation_Orefl__on(tc_List_Olist(_1771630), c_List_Olists(_1771630, _1771632), c_List_Olistrel(_1771630, _1771634)))], (23749 ^ _778908) ^ [_1192857, _1192859, _1192861, _1192863] : [class_Orderings_Olinorder(_1192857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192857), _1192859), _1192861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192857), _1192859), _1192863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192857), _1192859), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192857), _1192861), _1192863))))], (18443 ^ _778908) ^ [_1097239, _1097241] : [class_Int_Onumber__ring(_1097239), 18446 ^ _778908 : [(18453 ^ _778908) ^ [] : [c_Int_Oiszero(_1097239, hAPP(c_Int_Onumber__class_Onumber__of(_1097239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1097241), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1097239), _1097241) = c_Groups_Ozero__class_Ozero(_1097239))], (18447 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1097239), _1097241) = c_Groups_Ozero__class_Ozero(_1097239), -(c_Int_Oiszero(_1097239, hAPP(c_Int_Onumber__class_Onumber__of(_1097239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1097241), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (28820 ^ _778908) ^ [_1291457, _1291459, _1291461, _1291463, _1291465] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291457, tc_fun(_1291459, tc_HOL_Obool)), _1291461), _1291463), _1291465))), 28821 ^ _778908 : [(28822 ^ _778908) ^ [_1291529] : [hBOOL(hAPP(hAPP(c_member(_1291457), _1291529), _1291461)), hBOOL(hAPP(hAPP(_1291463, _1291529), _1291465))]]], (29660 ^ _778908) ^ [_1309399, _1309401] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1309399, _1309401)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1309399, _1309401), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1309401), c_Orderings_Otop__class_Otop(tc_fun(_1309401, tc_HOL_Obool)))))], (21231 ^ _778908) ^ [_1145677, _1145679, _1145681, _1145683, _1145685] : [class_Fields_Ofield(_1145677), -(_1145679 = c_Groups_Ozero__class_Ozero(_1145677)), -(_1145681 = c_Groups_Ozero__class_Ozero(_1145677)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145677), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145677), _1145683), _1145679)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145677), _1145685), _1145681)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145677), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145677), _1145683), _1145681)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145677), _1145685), _1145679))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145677), _1145679), _1145681)))], (7853 ^ _778908) ^ [_910141, _910143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910141), _910143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910141), hAPP(c_Nat_OSuc, _910143))))], (13827 ^ _778908) ^ [_1012317, _1012319, _1012321, _1012323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012319), _1012321)), -(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), _1012321), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012323, _1012317))), _1012319))))], (35369 ^ _778908) ^ [_1429732, _1429734, _1429736, _1429738, _1429740] : [class_Groups_Ocomm__monoid__add(_1429732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429734), _1429736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429734, tc_HOL_Obool)), _1429738), _1429736)), 35383 ^ _778908 : [(35386 ^ _778908) ^ [] : [hAPP(_1429740, 35382 ^ [_1429732, _1429734, _1429736, _1429738, _1429740]) = c_Groups_Ozero__class_Ozero(_1429732)], (35384 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429734), 35382 ^ [_1429732, _1429734, _1429736, _1429738, _1429740]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429734, tc_HOL_Obool)), _1429736), _1429738))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1429734, _1429732), _1429740), _1429738) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1429734, _1429732), _1429740), _1429736))], (31321 ^ _778908) ^ [_1343888, _1343890, _1343892, _1343894] : [_1343888 = _1343890, hBOOL(hAPP(hAPP(c_member(_1343892), _1343890), _1343894)), -(hBOOL(hAPP(hAPP(c_member(_1343892), _1343888), _1343894)))], (7665 ^ _778908) ^ [_907017, _907019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907017), _907019)), _907019 = _907017], (34381 ^ _778908) ^ [_1407892, _1407894, _1407896, _1407898, _1407900] : [class_Groups_Ocomm__monoid__mult(_1407892), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407894, _1407892), hAPP(hAPP(c_COMBS(_1407894, _1407892, _1407892), hAPP(hAPP(c_COMBB(_1407892, tc_fun(_1407892, _1407892), _1407894), c_Groups_Otimes__class_Otimes(_1407892)), _1407896)), _1407898)), _1407900) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407892), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407894, _1407892), _1407896), _1407900)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407894, _1407892), _1407898), _1407900)))], (43237 ^ _778908) ^ [_1619461, _1619463, _1619465] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1619461, _1619461), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619461, _1619461), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1619461, _1619463)), c_Transitive__Closure_Ortrancl(_1619461, _1619465))), c_Transitive__Closure_Ortrancl(_1619461, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619461, _1619461), tc_HOL_Obool)), _1619463), _1619465)))))], (24797 ^ _778908) ^ [_1213388, _1213390, _1213392, _1213394, _1213396, _1213398, _1213400] : [-(hAPP(c_Product__Type_Oapsnd(_1213388, _1213390, _1213392, _1213394), hAPP(c_Product__Type_Oapfst(_1213396, _1213392, _1213388, _1213398), _1213400)) = hAPP(c_Product__Type_Oapfst(_1213396, _1213392, _1213390, _1213398), hAPP(c_Product__Type_Oapsnd(_1213388, _1213390, _1213396, _1213394), _1213400)))], (47248 ^ _778908) ^ [_1718544, _1718546, _1718548] : [class_Groups_Omonoid__add(_1718544), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1718544), hAPP(hAPP(c_List_Omap(_1718546, _1718544), hAPP(c_COMBK(_1718544, _1718546), c_Groups_Ozero__class_Ozero(_1718544))), _1718548)) = c_Groups_Ozero__class_Ozero(_1718544))], (44981 ^ _778908) ^ [] : [-(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)))], (17561 ^ _778908) ^ [_1082365, _1082367, _1082369] : [class_Rings_Olinordered__idom(_1082365), -(hAPP(c_Groups_Oabs__class_Oabs(_1082365), hAPP(hAPP(c_Power_Opower__class_Opower(_1082365), _1082367), _1082369)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1082365), hAPP(c_Groups_Oabs__class_Oabs(_1082365), _1082367)), _1082369))], (42010 ^ _778908) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (10796 ^ _778908) ^ [_960016, _960018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960016)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960016), _960018)))], (40436 ^ _778908) ^ [_1546518, _1546520, _1546522, _1546524, _1546526, _1546528, _1546530] : [-(hAPP(c_Product__Type_Osnd(_1546518, _1546520), hAPP(c_Product__Type_Omap__pair(_1546522, _1546518, _1546524, _1546520, _1546526, _1546528), _1546530)) = hAPP(_1546528, hAPP(c_Product__Type_Osnd(_1546522, _1546524), _1546530)))], (30022 ^ _778908) ^ [_1316491, _1316493, _1316495] : [class_Orderings_Obot(_1316491), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1316493, _1316491)), _1316495) = c_Orderings_Obot__class_Obot(_1316491))], (43510 ^ _778908) ^ [_1625927, _1625929, _1625931, _1625933, _1625935] : [-(hAPP(c_Relation_Oconverse(_1625927, _1625929), hAPP(hAPP(c_Relation_Orel__comp(_1625927, _1625931, _1625929), _1625933), _1625935)) = hAPP(hAPP(c_Relation_Orel__comp(_1625929, _1625931, _1625927), hAPP(c_Relation_Oconverse(_1625931, _1625929), _1625935)), hAPP(c_Relation_Oconverse(_1625927, _1625931), _1625933)))], (24993 ^ _778908) ^ [_1217216, _1217218, _1217220, _1217222, _1217224] : [-(_1217216 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1217218, _1217220, _1217222, _1217224), _1217216) = c_Lazy__Sequence_Ohb__bind(_1217218, _1217220, hAPP(_1217222, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1217216), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1217218, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1217220))), _1217224), _1217216)))], (5963 ^ _778908) ^ [_874097, _874099, _874101, _874103] : [-(c_String_Ochar_Ochar__rec(_874097, _874099, hAPP(hAPP(c_String_Ochar_OChar, _874101), _874103)) = hAPP(hAPP(_874099, _874101), _874103))], (48174 ^ _778908) ^ [_1740180, _1740182, _1740184, _1740186] : [-(hBOOL(hAPP(hAPP(c_member(_1740180), _1740182), hAPP(c_List_Oset(_1740180), _1740184)))), -(c_List_Oremove1(_1740180, _1740182, hAPP(hAPP(c_List_Oappend(_1740180), _1740184), _1740186)) = hAPP(hAPP(c_List_Oappend(_1740180), _1740184), c_List_Oremove1(_1740180, _1740182, _1740186)))], (15532 ^ _778908) ^ [_1043219, _1043221, _1043223, _1043225] : [class_Divides_Oring__div(_1043219), -(c_Divides_Odiv__class_Omod(_1043219, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043219), _1043221), _1043223), _1043225) = c_Divides_Odiv__class_Omod(_1043219, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043219), c_Divides_Odiv__class_Omod(_1043219, _1043221, _1043225)), c_Divides_Odiv__class_Omod(_1043219, _1043223, _1043225)), _1043225))], (49095 ^ _778908) ^ [_1763667, _1763669, _1763671, _1763673, _1763675] : [-(hAPP(hAPP(c_List_Ozip(_1763667, _1763669), hAPP(hAPP(c_List_Oappend(_1763667), _1763671), _1763673)), _1763675) = hAPP(hAPP(c_List_Oappend(tc_prod(_1763667, _1763669)), hAPP(hAPP(c_List_Ozip(_1763667, _1763669), _1763671), hAPP(hAPP(c_List_Otake(_1763669), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763667)), _1763671)), _1763675))), hAPP(hAPP(c_List_Ozip(_1763667, _1763669), _1763673), hAPP(hAPP(c_List_Odrop(_1763669), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763667)), _1763671)), _1763675))))], (12507 ^ _778908) ^ [_989212, _989214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989212), _989214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989212), hAPP(c_Nat_OSuc, _989214))))], (4260 ^ _778908) ^ [_844608, _844610] : [_844610 = _844608, -(c_Smallcheck_Osmall__class_Osmall(_844610) = c_Smallcheck_Osmall__class_Osmall(_844608))], (9520 ^ _778908) ^ [_937976, _937978, _937980, _937982, _937984] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_937976), 9523 ^ _778908 : [(9524 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937978), _937980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937982), _937984)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937978), _937984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937982), _937980)), -(_937978 = _937982), -(_937980 = _937984)], (9534 ^ _778908) ^ [] : [9535 ^ _778908 : [(9538 ^ _778908) ^ [] : [_937980 = _937984], (9536 ^ _778908) ^ [] : [_937978 = _937982]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937978), _937980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937982), _937984)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937978), _937984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937976), _937982), _937980)))]]], (34901 ^ _778908) ^ [_1418671, _1418673, _1418675, _1418677, _1418679, _1418681] : [hBOOL(hAPP(hAPP(c_member(_1418671), _1418673), _1418675)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418671, tc_Option_Ooption(_1418677)), c_Map_Orestrict__map(_1418671, _1418677, _1418679, _1418675)), _1418673), _1418681) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418671, tc_Option_Ooption(_1418677)), c_Map_Orestrict__map(_1418671, _1418677, _1418679, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1418671, tc_HOL_Obool)), _1418675), hAPP(hAPP(c_Set_Oinsert(_1418671), _1418673), c_Orderings_Obot__class_Obot(tc_fun(_1418671, tc_HOL_Obool)))))), _1418673), _1418681))], (11386 ^ _778908) ^ [_969438] : [_969438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969438), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48000 ^ _778908) ^ [_1735760, _1735762, _1735764] : [class_Orderings_Olinorder(_1735760), -(hBOOL(hAPP(hAPP(c_member(_1735760), _1735762), hAPP(c_List_Oset(_1735760), _1735764)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1735760, _1735760, c_COMBI(_1735760), _1735762, _1735764) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1735760, _1735760, c_COMBI(_1735760)), _1735762), _1735764))], (18891 ^ _778908) ^ [_1104465, _1104467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1104465)), c_Int_OBit1(_1104467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104465), _1104467)))], (38694 ^ _778908) ^ [_1504693, _1504695, _1504697, _1504699, _1504701, _1504703, _1504705] : [class_Groups_Oab__semigroup__mult(_1504693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504695), _1504697)), c_Fun_Oinj__on(_1504695, _1504699, _1504701, _1504697), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1504693, _1504699, c_Groups_Otimes__class_Otimes(_1504693)), _1504703), _1504705), hAPP(c_Set_Oimage(_1504695, _1504699, _1504701), _1504697)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1504693, _1504695, c_Groups_Otimes__class_Otimes(_1504693)), hAPP(c_Fun_Ocomp(_1504699, _1504693, _1504695, _1504703), _1504701)), _1504705), _1504697))], (50517 ^ _778908) ^ [_1793288, _1793290, _1793292, _1793294, _1793296] : [class_Orderings_Olinorder(_1793288), c_List_Olinorder__class_Osorted(_1793288, hAPP(hAPP(c_List_Omap(_1793290, _1793288), _1793292), _1793294)), -(c_List_Olinorder__class_Osorted(_1793288, hAPP(hAPP(c_List_Omap(_1793290, _1793288), _1793292), c_List_Olinorder__class_Oinsort__insert__key(_1793290, _1793288, _1793292, _1793296, _1793294))))], (28513 ^ _778908) ^ [_1285359, _1285361, _1285363] : [class_Orderings_Olinorder(_1285359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285359), _1285361), _1285363)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285359, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1285359), _1285361)), c_SetInterval_Oord__class_OatLeastAtMost(_1285359, _1285361, _1285363)) = hAPP(c_SetInterval_Oord__class_OatMost(_1285359), _1285363))], (11258 ^ _778908) ^ [_967252, _967254, _967256, _967258] : [class_Groups_Oordered__ab__semigroup__add(_967252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967252), _967254), _967256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967252), _967258), _967254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967252), _967258), _967256))))], (42174 ^ _778908) ^ [_1592897, _1592899, _1592901, _1592903, _1592905] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592897, _1592899)), hAPP(hAPP(c_Product__Type_OPair(_1592897, _1592899), _1592901), _1592903)), _1592905)), -(hBOOL(hAPP(hAPP(c_member(_1592899), _1592903), hAPP(c_Relation_ORange(_1592897, _1592899), _1592905))))], (46317 ^ _778908) ^ [_1693091, _1693093, _1693095, _1693097, _1693099] : [hAPP(c_Map_Omap__of(_1693091, _1693093, _1693095), _1693097) = hAPP(c_Option_Ooption_OSome(_1693093), _1693099), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1693091, _1693093)), hAPP(hAPP(c_Product__Type_OPair(_1693091, _1693093), _1693097), _1693099)), hAPP(c_List_Oset(tc_prod(_1693091, _1693093)), _1693095))))], (13430 ^ _778908) ^ [_1005179, _1005181, _1005183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005179)), _1005179 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1005181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005179), _1005183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1005181), _1005179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1005183)))], (46293 ^ _778908) ^ [_1692514, _1692516, _1692518, _1692520, _1692522, _1692524] : [-(hBOOL(hAPP(hAPP(c_member(_1692514), _1692516), hAPP(c_List_Oset(_1692514), _1692518)))), -(hAPP(hAPP(c_List_Omap(_1692514, _1692520), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1692514, _1692520), _1692522), _1692516), _1692524)), _1692518) = hAPP(hAPP(c_List_Omap(_1692514, _1692520), _1692522), _1692518))], (27911 ^ _778908) ^ [_1273709] : [27913 ^ _778908 : [(27916 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27912 ^ [_1273709]))], (27914 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27912 ^ [_1273709]), _1273709)))]], -(c_Nat__Transfer_Onat__set(_1273709))], (13881 ^ _778908) ^ [_1013292, _1013294] : [class_Divides_Osemiring__div(_1013292), -(c_Divides_Odiv__class_Omod(_1013292, _1013294, c_Groups_Ozero__class_Ozero(_1013292)) = _1013294)], (26935 ^ _778908) ^ [_1254148, _1254150] : [class_Orderings_Oorder(_1254148), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1254148, 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)))), _1254150), -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1254148, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1254150))], (51613 ^ _778908) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (9836 ^ _778908) ^ [_943849, _943851, _943853] : [class_Rings_Olinordered__semiring__strict(_943849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943849), c_Groups_Ozero__class_Ozero(_943849)), _943851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943849), _943853), c_Groups_Ozero__class_Ozero(_943849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943849), _943851), _943853)), c_Groups_Ozero__class_Ozero(_943849))))], (12373 ^ _778908) ^ [_986759, _986761, _986763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986759), _986761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _986763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986759), _986763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986761), _986763))))], (22504 ^ _778908) ^ [_1168824, _1168826, _1168828] : [-(hAPP(c_Divides_Oadjust(_1168824), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1168826), _1168828)) = 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), _1168828), _1168824)), 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)))), _1168826)), 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)))), _1168826)), _1168828))))], (9504 ^ _778908) ^ [_937765] : [class_Rings_Ozero__neq__one(_937765), c_Groups_Oone__class_Oone(_937765) = c_Groups_Ozero__class_Ozero(_937765)], (45968 ^ _778908) ^ [_1684495, _1684497, _1684499] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1684495)), hAPP(c_Set_Oimage(_1684497, tc_Option_Ooption(_1684495), c_Map_Omap__of(_1684497, _1684495, _1684499)), c_Orderings_Otop__class_Otop(tc_fun(_1684497, tc_HOL_Obool))))))], (15012 ^ _778908) ^ [_1033422, _1033424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1033422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1033424, _1033422)), _1033422)))], (11801 ^ _778908) ^ [_976458, _976460, _976462] : [class_Rings_Olinordered__idom(_976458), -(c_Groups_Osgn__class_Osgn(_976458, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976458), _976460), _976462)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976458), c_Groups_Osgn__class_Osgn(_976458, _976460)), c_Groups_Osgn__class_Osgn(_976458, _976462)))], (29510 ^ _778908) ^ [_1306510, _1306512, _1306514, _1306516, _1306518] : [class_Groups_Oab__group__add(_1306510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306512), _1306514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306512, tc_HOL_Obool)), _1306516), _1306514)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1306512, _1306510), _1306518), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306512, tc_HOL_Obool)), _1306514), _1306516)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1306510), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1306512, _1306510), _1306518), _1306514)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1306512, _1306510), _1306518), _1306516)))], (34256 ^ _778908) ^ [_1404944, _1404946, _1404948, _1404950] : [c_Finite__Set_Ofolding__one(_1404944, _1404946, _1404948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404944), _1404950)), -(_1404950 = c_Orderings_Obot__class_Obot(tc_fun(_1404944, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1404944), hAPP(hAPP(_1404946, 34269 ^ [_1404944, _1404946, _1404948, _1404950]), 34270 ^ [_1404944, _1404946, _1404948, _1404950])), hAPP(hAPP(c_Set_Oinsert(_1404944), 34269 ^ [_1404944, _1404946, _1404948, _1404950]), hAPP(hAPP(c_Set_Oinsert(_1404944), 34270 ^ [_1404944, _1404946, _1404948, _1404950]), c_Orderings_Obot__class_Obot(tc_fun(_1404944, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1404944), hAPP(_1404948, _1404950)), _1404950)))], (51153 ^ _778908) ^ [_1808384, _1808386] : [class_Lattices_Olattice(_1808384), -(class_Lattices_Osemilattice__inf(tc_fun(_1808386, _1808384)))], (2338 ^ _778908) ^ [_814183, _814185, _814187, _814189] : [-(c_SMT_Oz3div(_814189, _814185) = c_SMT_Oz3div(_814187, _814183)), _814189 = _814187, _814185 = _814183], (344 ^ _778908) ^ [_784040, _784042] : [-(class_Fields_Ofield(_784040)), _784042 = _784040, class_Fields_Ofield(_784042)], (43451 ^ _778908) ^ [_1624506] : [-(c_Relation_OId(_1624506) = hAPP(c_Set_OCollect(tc_prod(_1624506, _1624506)), hAPP(hAPP(c_COMBB(tc_fun(_1624506, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1624506, _1624506)), c_HOL_OEx(_1624506)), hAPP(hAPP(c_COMBC(tc_prod(_1624506, _1624506), tc_fun(_1624506, tc_prod(_1624506, _1624506)), tc_fun(_1624506, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1624506, _1624506), tc_HOL_Obool), tc_fun(tc_fun(_1624506, tc_prod(_1624506, _1624506)), tc_fun(_1624506, tc_HOL_Obool)), tc_prod(_1624506, _1624506)), c_COMBB(tc_prod(_1624506, _1624506), tc_HOL_Obool, _1624506)), c_fequal)), hAPP(hAPP(c_COMBS(_1624506, _1624506, tc_prod(_1624506, _1624506)), c_Product__Type_OPair(_1624506, _1624506)), c_COMBI(_1624506))))))], (13034 ^ _778908) ^ [_998699, _998701, _998703] : [class_Rings_Olinordered__idom(_998699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998699), c_Groups_Ozero__class_Ozero(_998699)), _998701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998699), c_Groups_Ozero__class_Ozero(_998699)), _998703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998699), _998703), c_Groups_Oone__class_Oone(_998699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998699), _998703), _998701)), _998701)))], (14541 ^ _778908) ^ [_1025726, _1025728, _1025730] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025726), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025728, _1025730)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025726), _1025728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025726), _1025730)))], (14100 ^ _778908) ^ [_1017596, _1017598] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017596, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1017598)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017596, _1017598) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24975 ^ _778908) ^ [_1216926, _1216928, _1216930, _1216932, _1216934] : [_1216926 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1216928, _1216930, _1216932, _1216934), _1216926) = c_Lazy__Sequence_Oempty(_1216930))], (38412 ^ _778908) ^ [_1499006, _1499008, _1499010, _1499012, _1499014, _1499016, _1499018] : [c_Finite__Set_Ofolding__idem(_1499006, _1499008, _1499010, _1499012), -(hAPP(c_Fun_Ocomp(_1499008, _1499008, _1499014, hAPP(_1499010, _1499016)), hAPP(c_Fun_Ocomp(_1499008, _1499008, _1499014, hAPP(_1499010, _1499016)), _1499018)) = hAPP(c_Fun_Ocomp(_1499008, _1499008, _1499014, hAPP(_1499010, _1499016)), _1499018))], (6759 ^ _778908) ^ [_889754, _889756, _889758, _889760] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_889754, _889756), _889758, _889760, _889758)), 6760 ^ _778908 : [(6763 ^ _778908) ^ [_889841] : [c_Natural_Oevaln(_889756, _889758, _889760, _889841), c_Natural_Oevaln(c_Com_Ocom_OWhile(_889754, _889756), _889841, _889760, _889758)], (6761 ^ _778908) ^ [] : [-(hBOOL(hAPP(_889754, _889758)))]]], (50626 ^ _778908) ^ [_1795435, _1795437, _1795439] : [class_Orderings_Olinorder(_1795435), hBOOL(hAPP(hAPP(c_member(_1795435), _1795437), hAPP(c_List_Oset(_1795435), _1795439))), c_List_Olinorder__class_Osorted(_1795435, _1795439), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1795435, _1795435, c_COMBI(_1795435)), _1795437), c_List_Oremove1(_1795435, _1795437, _1795439)) = _1795439)], (19449 ^ _778908) ^ [_1113878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1113878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1113878)))], (43481 ^ _778908) ^ [_1625181, _1625183, _1625185] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1625181, _1625181), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1625181, _1625181), _1625183)), c_Transitive__Closure_Ortrancl(_1625181, _1625183)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1625181, _1625181), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1625181, _1625181)), hAPP(hAPP(c_Product__Type_OPair(_1625181, _1625181), _1625185), _1625185)), c_Transitive__Closure_Otrancl(_1625181, _1625183)))], (35492 ^ _778908) ^ [_1432425, _1432427, _1432429, _1432431, _1432433] : [hAPP(c_Set_Oimage(_1432425, _1432427, _1432429), _1432431) = _1432433, -(hAPP(c_Set_Oimage(tc_fun(_1432425, tc_HOL_Obool), tc_fun(_1432427, tc_HOL_Obool), c_Set_Oimage(_1432425, _1432427, _1432429)), hAPP(c_Set_OPow(_1432425), _1432431)) = hAPP(c_Set_OPow(_1432427), _1432433))], (5768 ^ _778908) ^ [_867972, _867974] : [_867974 = _867972, -(c_Groups_Ozero__class_Ozero(_867974) = c_Groups_Ozero__class_Ozero(_867972))], (25153 ^ _778908) ^ [_1221142, _1221144, _1221146, _1221148, _1221150, _1221152] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1221142, _1221144, _1221146, _1221148), _1221150), _1221152) = hAPP(_1221148, hAPP(hAPP(c_Product__Type_OPair(_1221142, _1221144), _1221150), _1221152)))], (31902 ^ _778908) ^ [_1357312, _1357314, _1357316, _1357318, _1357320] : [class_Groups_Ocomm__monoid__add(_1357312), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357314), _1357316)), -(hBOOL(hAPP(hAPP(c_member(_1357314), _1357318), _1357316))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357314, _1357312), _1357320), hAPP(hAPP(c_Set_Oinsert(_1357314), _1357318), _1357316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357312), hAPP(_1357320, _1357318)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357314, _1357312), _1357320), _1357316)))], (18995 ^ _778908) ^ [_1106133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1106133)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106133), c_Int_OMin)))], (9968 ^ _778908) ^ [_946298, _946300, _946302, _946304] : [class_Rings_Olinordered__comm__semiring__strict(_946298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946298), _946300), _946302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946298), c_Groups_Ozero__class_Ozero(_946298)), _946304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946298), _946304), _946300)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946298), _946304), _946302))))], (9084 ^ _778908) ^ [_930762, _930764] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _930762)), _930764) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930762), _930764)))], (43225 ^ _778908) ^ [_1619151, _1619153, _1619155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1619151, _1619151), tc_HOL_Obool)), _1619153), c_Transitive__Closure_Ortrancl(_1619151, _1619155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1619151, _1619151), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1619151, _1619153)), c_Transitive__Closure_Ortrancl(_1619151, _1619155))))], (45647 ^ _778908) ^ [_1677343, _1677345, _1677347] : [45649 ^ _778908 : [(45652 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1677343), _1677347), 45648 ^ [_1677343, _1677345, _1677347]))], (45650 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1677343, tc_HOL_Obool)), 45648 ^ [_1677343, _1677345, _1677347]), _1677345)))]], -(hBOOL(hAPP(hAPP(c_member(_1677343), _1677347), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1677343, tc_HOL_Obool), _1677345))))], (32367 ^ _778908) ^ [_1367432, _1367434, _1367436, _1367438] : [hBOOL(hAPP(hAPP(_1367436, _1367434), _1367438)), -(hBOOL(hAPP(hAPP(c_member(_1367432), _1367434), c_SetInterval_Oord_OlessThan(_1367432, _1367436, _1367438))))], (32533 ^ _778908) ^ [_1370650, _1370652] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1370650), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370652))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1370652), _1370650)))], (11713 ^ _778908) ^ [_975027, _975029] : [11714 ^ _778908 : [(11717 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975029))], (11715 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _975027))]], 11718 ^ _778908 : [(11725 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _975027), _975029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _975027)), hAPP(c_Int_Onat, _975029))))], (11719 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _975027)), hAPP(c_Int_Onat, _975029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _975027), _975029)))]]], (14436 ^ _778908) ^ [_1023573, _1023575, _1023577] : [-(hBOOL(hAPP(_1023573, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023575), _1023577)))), 14439 ^ _778908 : [(14442 ^ _778908) ^ [] : [hBOOL(hAPP(_1023573, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14440 ^ _778908) ^ [] : [-(_1023577 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 14445 ^ _778908 : [(14446 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023577)))], (14452 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14448 ^ [_1023573, _1023575, _1023577]), _1023577)))], (14456 ^ _778908) ^ [] : [hBOOL(hAPP(_1023573, 14447 ^ [_1023573, _1023575, _1023577]))], (14454 ^ _778908) ^ [] : [-(_1023575 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023577), 14447 ^ [_1023573, _1023575, _1023577])), 14448 ^ [_1023573, _1023575, _1023577]))], (14450 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14448 ^ [_1023573, _1023575, _1023577])))]], 14457 ^ _778908 : [(14458 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023577), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14464 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14460 ^ [_1023573, _1023575, _1023577]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14468 ^ _778908) ^ [] : [hBOOL(hAPP(_1023573, 14459 ^ [_1023573, _1023575, _1023577]))], (14466 ^ _778908) ^ [] : [-(_1023575 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023577), 14459 ^ [_1023573, _1023575, _1023577])), 14460 ^ [_1023573, _1023575, _1023577]))], (14462 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023577), 14460 ^ [_1023573, _1023575, _1023577])))]]], (25097 ^ _778908) ^ [_1219574, _1219576, _1219578] : [-(c_HOL_OThe(tc_prod(_1219574, _1219576), hAPP(c_Product__Type_Oprod_Oprod__case(_1219574, _1219576, tc_HOL_Obool), _1219578)) = c_HOL_OThe(tc_prod(_1219574, _1219576), hAPP(hAPP(c_COMBS(tc_prod(_1219574, _1219576), _1219576, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1219574, tc_fun(_1219576, tc_HOL_Obool), tc_prod(_1219574, _1219576)), _1219578), c_Product__Type_Ofst(_1219574, _1219576))), c_Product__Type_Osnd(_1219574, _1219576))))], (41565 ^ _778908) ^ [_1574416, _1574418, _1574420] : [class_Lattices_Odistrib__lattice(_1574416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574416), _1574418)), -(_1574418 = c_Orderings_Obot__class_Obot(tc_fun(_1574416, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574416), _1574420)), -(_1574420 = c_Orderings_Obot__class_Obot(tc_fun(_1574416, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1574416), c_Big__Operators_Olattice__class_OInf__fin(_1574416, _1574418)), c_Big__Operators_Olattice__class_OInf__fin(_1574416, _1574420)) = c_Big__Operators_Olattice__class_OInf__fin(_1574416, hAPP(c_Set_OCollect(_1574416), hAPP(hAPP(c_COMBB(tc_fun(_1574416, tc_HOL_Obool), tc_HOL_Obool, _1574416), c_HOL_OEx(_1574416)), hAPP(hAPP(c_COMBB(tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool)), tc_fun(_1574416, tc_HOL_Obool), _1574416), hAPP(c_COMBB(tc_fun(_1574416, tc_HOL_Obool), tc_HOL_Obool, _1574416), c_HOL_OEx(_1574416))), hAPP(hAPP(c_COMBC(_1574416, tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool)), tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1574416, tc_fun(tc_fun(_1574416, tc_HOL_Obool), tc_fun(_1574416, tc_HOL_Obool))), tc_fun(tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool)), tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool))), _1574416), c_COMBS(_1574416, tc_fun(_1574416, tc_HOL_Obool), tc_fun(_1574416, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1574416, tc_fun(_1574416, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1574416, tc_fun(tc_fun(_1574416, tc_HOL_Obool), tc_fun(_1574416, tc_HOL_Obool))), _1574416), hAPP(c_COMBB(tc_fun(_1574416, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1574416, tc_HOL_Obool), tc_fun(_1574416, tc_HOL_Obool)), _1574416), c_COMBS(_1574416, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool)), tc_fun(_1574416, tc_fun(_1574416, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1574416), hAPP(c_COMBB(tc_fun(_1574416, tc_HOL_Obool), tc_fun(_1574416, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1574416), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574416), c_fconj))), hAPP(hAPP(c_COMBC(_1574416, tc_fun(_1574416, tc_fun(_1574416, _1574416)), tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1574416, _1574416), tc_fun(_1574416, tc_HOL_Obool)), tc_fun(tc_fun(_1574416, tc_fun(_1574416, _1574416)), tc_fun(_1574416, tc_fun(_1574416, tc_HOL_Obool))), _1574416), c_COMBB(tc_fun(_1574416, _1574416), tc_fun(_1574416, tc_HOL_Obool), _1574416)), hAPP(hAPP(c_COMBB(tc_fun(_1574416, tc_HOL_Obool), tc_fun(tc_fun(_1574416, _1574416), tc_fun(_1574416, tc_HOL_Obool)), _1574416), c_COMBB(_1574416, tc_HOL_Obool, _1574416)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1574416)))))), hAPP(hAPP(c_COMBC(_1574416, tc_fun(_1574416, tc_HOL_Obool), tc_fun(_1574416, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1574416, tc_HOL_Obool), tc_fun(_1574416, tc_HOL_Obool)), _1574416), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1574416)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574416), c_fconj), hAPP(hAPP(c_COMBC(_1574416, tc_fun(_1574416, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574416)), _1574418)))), hAPP(hAPP(c_COMBC(_1574416, tc_fun(_1574416, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574416)), _1574420))))))))], (8758 ^ _778908) ^ [_925056, _925058, _925060] : [class_Orderings_Oorder(_925056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925056), _925058), _925060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925056), _925060), _925058))], (18925 ^ _778908) ^ [_1104996] : [c_Int_OMin = _1104996, -(c_Int_OMin = c_Int_OBit1(_1104996))], (7645 ^ _778908) ^ [_906793, _906795] : [7646 ^ _778908 : [(7649 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906795), _906793))], (7647 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906793), _906795))]], _906793 = _906795], (882 ^ _778908) ^ [_792457, _792459, _792461, _792463, _792465, _792467] : [-(c_Finite__Set_Ofun__left__comm(_792465, _792461, _792457)), c_Finite__Set_Ofun__left__comm(_792467, _792463, _792459), _792467 = _792465, _792463 = _792461, _792459 = _792457], (43530 ^ _778908) ^ [_1626439, _1626441] : [-(hAPP(c_Relation_Oconverse(_1626439, _1626439), c_Relation_OId__on(_1626439, _1626441)) = c_Relation_OId__on(_1626439, _1626441))], (41145 ^ _778908) ^ [_1560501, _1560503, _1560505] : [-(hAPP(hAPP(c_Set_Oinsert(_1560501), _1560503), _1560505) = hAPP(c_Set_OCollect(_1560501), hAPP(hAPP(c_COMBS(_1560501, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560501), c_fdisj), hAPP(hAPP(c_COMBC(_1560501, _1560501, tc_HOL_Obool), c_fequal), _1560503))), hAPP(hAPP(c_COMBC(_1560501, tc_fun(_1560501, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560501)), _1560505))))], (19733 ^ _778908) ^ [] : [-(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))))))], (51445 ^ _778908) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (22454 ^ _778908) ^ [_1167763] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1167763)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167763)), 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))))], (35811 ^ _778908) ^ [_1440099, _1440101, _1440103, _1440105, _1440107, _1440109, _1440111] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1440099, _1440101, _1440103), hAPP(c_Fun_Ocomp(_1440105, tc_fun(_1440101, _1440103), _1440099, _1440107), _1440109)), _1440111) = hAPP(hAPP(_1440107, hAPP(_1440109, hAPP(c_Product__Type_Ofst(_1440099, _1440101), _1440111))), hAPP(c_Product__Type_Osnd(_1440099, _1440101), _1440111)))], (10122 ^ _778908) ^ [_949004] : [class_Rings_Oring__1(_949004), -(hAPP(c_Int_Oring__1__class_Oof__int(_949004), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_949004))], (46055 ^ _778908) ^ [_1686801, _1686803, _1686805] : [c_Fun_Oinj__on(_1686801, _1686803, _1686805, c_Orderings_Otop__class_Otop(tc_fun(_1686801, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1686801), tc_List_Olist(_1686803), hAPP(c_List_Omap(_1686801, _1686803), _1686805), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1686801), tc_HOL_Obool))))], (5859 ^ _778908) ^ [_872171, _872173] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_872171, _872173)], (34871 ^ _778908) ^ [_1417991, _1417993, _1417995, _1417997, _1417999] : [-(hBOOL(hAPP(hAPP(c_member(_1417991), _1417993), _1417995))), -(hAPP(c_Map_Orestrict__map(_1417991, _1417997, _1417999, _1417995), _1417993) = c_Option_Ooption_ONone(_1417997))], (10814 ^ _778908) ^ [_960352, _960354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960352), _960354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960352)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _960354))))], (27634 ^ _778908) ^ [_1268461, _1268463] : [_1268461 = _1268463, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268461) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1268463))], (46607 ^ _778908) ^ [_1699849, _1699851, _1699853, _1699855, _1699857, _1699859] : [-(hAPP(hAPP(c_List_Ozip(_1699849, _1699851), _1699853), hAPP(hAPP(c_List_Omap(_1699855, _1699851), _1699857), _1699859)) = hAPP(hAPP(c_List_Omap(tc_prod(_1699849, _1699855), tc_prod(_1699849, _1699851)), hAPP(c_Product__Type_Oprod_Oprod__case(_1699849, _1699855, tc_prod(_1699849, _1699851)), hAPP(hAPP(c_COMBC(_1699849, tc_fun(_1699855, _1699851), tc_fun(_1699855, tc_prod(_1699849, _1699851))), hAPP(hAPP(c_COMBB(tc_fun(_1699851, tc_prod(_1699849, _1699851)), tc_fun(tc_fun(_1699855, _1699851), tc_fun(_1699855, tc_prod(_1699849, _1699851))), _1699849), c_COMBB(_1699851, tc_prod(_1699849, _1699851), _1699855)), c_Product__Type_OPair(_1699849, _1699851))), _1699857))), hAPP(hAPP(c_List_Ozip(_1699849, _1699855), _1699853), _1699859)))], (43915 ^ _778908) ^ [_1636278, _1636280, _1636282] : [c_Relation_Osingle__valued(_1636278, _1636278, _1636280), -(c_Relation_Osingle__valued(_1636278, _1636278, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1636278, _1636278), tc_HOL_Obool), _1636282), _1636280)))], (41345 ^ _778908) ^ [_1566373, _1566375] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1566373)), -(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)), _1566373))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1566375))))) = 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)), _1566373))), 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, _1566375))))))], (24707 ^ _778908) ^ [_1211213, _1211215, _1211217, _1211219] : [class_Orderings_Olinorder(_1211213), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211213), _1211215), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211213), _1211217), _1211219)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211213), _1211217), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211213), _1211215), _1211219)))], (13408 ^ _778908) ^ [_1004833] : [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, _1004833)))))], (35286 ^ _778908) ^ [_1427976, _1427978, _1427980] : [class_Lattices_Olattice(_1427976), hAPP(_1427978, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1427976), 35291 ^ [_1427976, _1427978, _1427980]), 35292 ^ [_1427976, _1427978, _1427980])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1427976), hAPP(_1427978, 35291 ^ [_1427976, _1427978, _1427980])), hAPP(_1427978, 35292 ^ [_1427976, _1427978, _1427980])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427976), _1427980)), -(_1427980 = c_Orderings_Obot__class_Obot(tc_fun(_1427976, tc_HOL_Obool))), -(hAPP(_1427978, c_Big__Operators_Olattice__class_OSup__fin(_1427976, _1427980)) = c_Big__Operators_Olattice__class_OSup__fin(_1427976, hAPP(c_Set_Oimage(_1427976, _1427976, _1427978), _1427980)))], (39112 ^ _778908) ^ [_1513182, _1513184, _1513186, _1513188] : [c_Fun_Oinj__on(_1513182, _1513184, _1513186, c_Orderings_Otop__class_Otop(tc_fun(_1513182, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513184, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1513182, _1513184, _1513186), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1513182, tc_HOL_Obool)), _1513188))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1513184, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1513182, _1513184, _1513186), _1513188)))))], (48251 ^ _778908) ^ [_1741877, _1741879, _1741881, _1741883, _1741885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741877), tc_List_Olist(_1741877))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741877), tc_List_Olist(_1741877)), _1741879), _1741881)), c_List_Olexord(_1741877, _1741883))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741877), tc_List_Olist(_1741877))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741877), tc_List_Olist(_1741877)), hAPP(hAPP(c_List_Oappend(_1741877), _1741885), _1741879)), hAPP(hAPP(c_List_Oappend(_1741877), _1741885), _1741881))), c_List_Olexord(_1741877, _1741883))))], (8718 ^ _778908) ^ [_924444, _924446, _924448] : [class_Orderings_Opreorder(_924444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924444), _924446), _924448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924444), _924448), _924446))], (11234 ^ _778908) ^ [_966786, _966788, _966790, _966792] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_966786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966786), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966786), _966788), _966790)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966786), _966792), _966790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966786), _966788), _966792)))], (25065 ^ _778908) ^ [_1218936, _1218938, _1218940, _1218942, _1218944, _1218946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218936, tc_fun(_1218938, tc_HOL_Obool))), _1218940), _1218942)), hBOOL(hAPP(hAPP(_1218940, _1218944), _1218946)), -(hBOOL(hAPP(hAPP(_1218942, _1218944), _1218946)))], (35456 ^ _778908) ^ [_1431661, _1431663, _1431665] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1431661, tc_HOL_Obool)), _1431663), hAPP(c_Set_OPow(_1431661), _1431665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431661, tc_HOL_Obool)), _1431663), _1431665)))], (44581 ^ _778908) ^ [_1650443, _1650445, _1650447, _1650449, _1650451, _1650453] : [hBOOL(hAPP(hAPP(c_member(_1650443), _1650445), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650447, tc_fun(_1650443, tc_HOL_Obool)), _1650449), _1650451))), hBOOL(hAPP(hAPP(c_member(_1650447), _1650453), _1650449)), -(hBOOL(hAPP(hAPP(c_member(_1650443), _1650445), hAPP(_1650451, _1650453))))], (30082 ^ _778908) ^ [_1317707, _1317709] : [class_Orderings_Obot(_1317707), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317707), c_Orderings_Obot__class_Obot(_1317707)), _1317709)))], (43413 ^ _778908) ^ [_1623596, _1623598, _1623600, _1623602] : [c_Wellfounded_Owf(_1623596, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1623596, _1623596)), hAPP(hAPP(c_Product__Type_OPair(_1623596, _1623596), _1623598), _1623600)), _1623602)), 43416 ^ _778908 : [(43419 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623596, _1623596)), hAPP(hAPP(c_Product__Type_OPair(_1623596, _1623596), _1623600), _1623598)), c_Transitive__Closure_Ortrancl(_1623596, _1623602)))], (43417 ^ _778908) ^ [] : [-(c_Wellfounded_Owf(_1623596, _1623602))]]], (24971 ^ _778908) ^ [_1216855, _1216857, _1216859] : [-(c_Product__Type_Ointernal__split(_1216855, _1216857, _1216859) = c_Product__Type_Oprod_Oprod__case(_1216855, _1216857, _1216859))], (19173 ^ _778908) ^ [_1108883, _1108885] : [class_Int_Onumber__ring(_1108883), class_Rings_Olinordered__idom(_1108883), 19180 ^ _778908 : [(19187 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1108885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108883), c_Groups_Oone__class_Oone(_1108883)), hAPP(c_Int_Onumber__class_Onumber__of(_1108883), _1108885))))], (19181 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108883), c_Groups_Oone__class_Oone(_1108883)), hAPP(c_Int_Onumber__class_Onumber__of(_1108883), _1108885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1108885)))]]], (18341 ^ _778908) ^ [_1095738, _1095740] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095738), _1095740) = c_Groups_Oone__class_Oone(tc_Int_Oint), 18346 ^ _778908 : [(18349 ^ _778908) ^ [] : [-(_1095740 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18347 ^ _778908) ^ [] : [-(_1095738 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 18350 ^ _778908 : [(18353 ^ _778908) ^ [] : [-(_1095740 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18351 ^ _778908) ^ [] : [-(_1095738 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (49565 ^ _778908) ^ [_1773992, _1773994, _1773996] : [49566 ^ _778908 : [(49567 ^ _778908) ^ [_1774081, _1774083] : [_1773994 = hAPP(hAPP(c_List_Olist_OCons(_1773992), _1774083), _1774081)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773992), tc_List_Olist(_1773992))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773992), tc_List_Olist(_1773992)), c_List_Olist_ONil(_1773992)), _1773994)), c_List_Olexord(_1773992, _1773996))))], (49458 ^ _778908) ^ [_1771448, _1771450, _1771452] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771448)), _1771450), c_Wellfounded_Oacc(tc_List_Olist(_1771448), c_List_Olistrel1(_1771448, _1771452)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771448)), _1771450), c_List_Olists(_1771448, c_Wellfounded_Oacc(_1771448, _1771452)))))], (20025 ^ _778908) ^ [_1124160, _1124162] : [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), _1124160))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1124162))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124160))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1124162)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1124160)))], (6337 ^ _778908) ^ [_881076, _881078, _881080] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_881076, _881078, _881080))), -(hBOOL(hAPP(c_Com_OWT, _881080)))], (22990 ^ _778908) ^ [_1178801, _1178803] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1178801, _1178803), c_Divides_Odivmod__nat(_1178801, _1178803))))], (8430 ^ _778908) ^ [_920216, _920218, _920220, _920222] : [class_Orderings_Oorder(_920216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920216), hAPP(_920218, 8435 ^ [_920216, _920218, _920220, _920222])), hAPP(_920218, hAPP(c_Nat_OSuc, 8435 ^ [_920216, _920218, _920220, _920222])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920220), _920222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920216), hAPP(_920218, _920220)), hAPP(_920218, _920222))))], (24217 ^ _778908) ^ [_1201979, _1201981] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1201979), hAPP(c_Nat_OSuc, _1201981)) = 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)), _1201981)), _1201979))], (39450 ^ _778908) ^ [_1520829, _1520831, _1520833, _1520835, _1520837, _1520839] : [hAPP(_1520829, _1520831) = _1520833, hBOOL(hAPP(hAPP(c_member(_1520835), _1520833), _1520837)), -(hBOOL(hAPP(hAPP(c_member(_1520839), _1520831), hAPP(c_Set_Ovimage(_1520839, _1520835, _1520829), _1520837))))], (49265 ^ _778908) ^ [_1766939, _1766941] : [class_Lattices_Oab__semigroup__idem__mult(_1766939), -(_1766941 = c_List_Olist_ONil(_1766939)), -(hAPP(c_Finite__Set_Ofold1(_1766939, c_Groups_Otimes__class_Otimes(_1766939)), hAPP(c_List_Oset(_1766939), _1766941)) = hAPP(c_List_Ofoldl(_1766939, _1766939, c_Groups_Otimes__class_Otimes(_1766939), hAPP(c_List_Ohd(_1766939), _1766941)), hAPP(c_List_Otl(_1766939), _1766941)))], (1652 ^ _778908) ^ [_802432, _802434] : [-(class_Nat_Osemiring__char__0(_802432)), _802434 = _802432, class_Nat_Osemiring__char__0(_802434)], (4088 ^ _778908) ^ [_841936, _841938, _841940, _841942] : [-(c_HOL_OThe(_841942, _841938) = c_HOL_OThe(_841940, _841936)), _841942 = _841940, _841938 = _841936], (48572 ^ _778908) ^ [_1749495, _1749497, _1749499, _1749501, _1749503, _1749505, _1749507] : [-(c_Map_Omap__upds(_1749495, _1749497, _1749499, hAPP(hAPP(c_List_Olist_OCons(_1749495), _1749501), _1749503), hAPP(hAPP(c_List_Olist_OCons(_1749497), _1749505), _1749507)) = c_Map_Omap__upds(_1749495, _1749497, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1749495, tc_Option_Ooption(_1749497)), _1749499), _1749501), hAPP(c_Option_Ooption_OSome(_1749497), _1749505)), _1749503, _1749507))], (19605 ^ _778908) ^ [_1116599, _1116601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116599)), c_Int_OBit1(_1116601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116599), _1116601)))], (4638 ^ _778908) ^ [_850729, _850731, _850733, _850735] : [-(c_Relation_Oconverse(_850735, _850731) = c_Relation_Oconverse(_850733, _850729)), _850735 = _850733, _850731 = _850729], (29944 ^ _778908) ^ [_1314934, _1314936, _1314938] : [hAPP(hAPP(c_Set_Oinsert(_1314934), _1314936), _1314938) = c_Orderings_Obot__class_Obot(tc_fun(_1314934, tc_HOL_Obool))], (2036 ^ _778908) ^ [_809104, _809106] : [_809106 = _809104, -(c_Nat_Onat_Onat__size(_809106) = c_Nat_Onat_Onat__size(_809104))], (25145 ^ _778908) ^ [_1220963, _1220965, _1220967] : [-(c_Random__Sequence_Oempty(_1220963, _1220965, _1220967) = 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(_1220963)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1220963)))], (5046 ^ _778908) ^ [_856961, _856963, _856965, _856967] : [-(c_Random_Opick(_856967, _856963) = c_Random_Opick(_856965, _856961)), _856967 = _856965, _856963 = _856961], (3790 ^ _778908) ^ [_837305, _837307, _837309, _837311, _837313, _837315] : [-(c_Wellfounded_Omlex__prod(_837315, _837311, _837307) = c_Wellfounded_Omlex__prod(_837313, _837309, _837305)), _837315 = _837313, _837311 = _837309, _837307 = _837305], (3744 ^ _778908) ^ [_836600, _836602, _836604, _836606, _836608, _836610, _836612, _836614] : [-(c_Product__Type_Oapsnd(_836614, _836610, _836606, _836602) = c_Product__Type_Oapsnd(_836612, _836608, _836604, _836600)), _836614 = _836612, _836610 = _836608, _836606 = _836604, _836602 = _836600], (22970 ^ _778908) ^ [_1178421, _1178423, _1178425, _1178427] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1178421, _1178423), _1178425)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1178421, _1178423), _1178427)), -(_1178425 = _1178427)], (36436 ^ _778908) ^ [_1454567, _1454569, _1454571] : [class_Lattices_Osemilattice__inf(_1454567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454567), _1454569), _1454571)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1454567), _1454569), _1454571) = _1454569)], (24425 ^ _778908) ^ [_1206164, _1206166, _1206168, _1206170] : [class_Orderings_Olinorder(_1206164), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206164), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206164), _1206166), _1206168)), _1206170) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1206164), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206164), _1206166), _1206170)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206164), _1206168), _1206170)))], (31780 ^ _778908) ^ [_1353399, _1353401, _1353403, _1353405, _1353407] : [hBOOL(hAPP(hAPP(c_member(_1353399), _1353401), _1353403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1353405, tc_HOL_Obool)), hAPP(_1353407, _1353401)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353399, tc_fun(_1353405, tc_HOL_Obool)), _1353403), _1353407))))], (39396 ^ _778908) ^ [_1519617, _1519619, _1519621, _1519623, _1519625, _1519627, _1519629] : [c_Finite__Set_Ofolding__image(_1519617, _1519619, _1519621, _1519623, _1519625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519619), _1519627)), -(hAPP(hAPP(_1519625, _1519629), _1519627) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1519617, _1519619, _1519621), _1519629), _1519623), _1519627))], (37114 ^ _778908) ^ [_1469829, _1469831, _1469833, _1469835, _1469837] : [class_Orderings_Olinorder(_1469829), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469829, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1469829, _1469831), _1469833)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1469829, _1469835), _1469837)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1469829, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1469829), _1469831), _1469835)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1469829), _1469833), _1469837)))], (12443 ^ _778908) ^ [_988082, _988084, _988086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988084), _988086)), -(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, _988082)), _988084)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988082)), _988086))))], (31706 ^ _778908) ^ [_1351216, _1351218] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1351216), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1351218), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 31713 ^ _778908 : [(31720 ^ _778908) ^ [] : [_1351216 = _1351218, -(hAPP(c_Code__Numeral_Oof__nat, _1351216) = hAPP(c_Code__Numeral_Oof__nat, _1351218))], (31714 ^ _778908) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1351216) = hAPP(c_Code__Numeral_Oof__nat, _1351218), -(_1351216 = _1351218)]]], (29219 ^ _778908) ^ [_1301013, _1301015] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1301013, _1301015))))], (9000 ^ _778908) ^ [_929289, _929291, _929293] : [class_Rings_Oidom(_929289), 9003 ^ _778908 : [(9004 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929289), _929291), _929291) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929289), _929293), _929293), -(_929291 = _929293), -(_929291 = hAPP(c_Groups_Ouminus__class_Ouminus(_929289), _929293))], (9014 ^ _778908) ^ [] : [9015 ^ _778908 : [(9018 ^ _778908) ^ [] : [_929291 = hAPP(c_Groups_Ouminus__class_Ouminus(_929289), _929293)], (9016 ^ _778908) ^ [] : [_929291 = _929293]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929289), _929291), _929291) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929289), _929293), _929293))]]], (15728 ^ _778908) ^ [_1046907, _1046909, _1046911] : [-(hBOOL(hAPP(_1046907, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046909), _1046911))))), 15731 ^ _778908 : [(15734 ^ _778908) ^ [] : [hBOOL(hAPP(_1046907, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1046909)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1046911))))], (15732 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046911), _1046909)))]], 15735 ^ _778908 : [(15738 ^ _778908) ^ [] : [hBOOL(hAPP(_1046907, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15736 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046909), _1046911)))]]], (30544 ^ _778908) ^ [_1326051, _1326053, _1326055, _1326057, _1326059] : [-(_1326051 = c_Orderings_Obot__class_Obot(tc_fun(_1326053, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326053, tc_fun(_1326055, tc_HOL_Obool)), _1326051), hAPP(hAPP(c_COMBC(_1326053, tc_fun(_1326055, tc_HOL_Obool), tc_fun(_1326055, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326055, tc_HOL_Obool), tc_fun(tc_fun(_1326055, tc_HOL_Obool), tc_fun(_1326055, tc_HOL_Obool)), _1326053), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326055, tc_HOL_Obool))), _1326057)), _1326059)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326055, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326053, tc_fun(_1326055, tc_HOL_Obool)), _1326051), _1326057)), _1326059))], (47082 ^ _778908) ^ [_1713373, _1713375, _1713377] : [-(hBOOL(hAPP(c_List_Odistinct(_1713373), hAPP(hAPP(c_List_Olist_OCons(_1713373), _1713375), _1713377)))), -(hBOOL(hAPP(hAPP(c_member(_1713373), _1713375), hAPP(c_List_Oset(_1713373), _1713377)))), hBOOL(hAPP(c_List_Odistinct(_1713373), _1713377))], (47858 ^ _778908) ^ [_1732685, _1732687, _1732689, _1732691] : [hAPP(hAPP(c_List_Olist__update(_1732685, _1732687), _1732689), _1732691) = c_List_Olist_ONil(_1732685), -(_1732687 = c_List_Olist_ONil(_1732685))], (51177 ^ _778908) ^ [_1808700, _1808702] : [-(class_Finite__Set_Ofinite(tc_fun(_1808700, _1808702))), class_Finite__Set_Ofinite(_1808700), class_Finite__Set_Ofinite(_1808702)], (1722 ^ _778908) ^ [_803307, _803309] : [-(class_Rings_Osemiring__0(_803307)), _803309 = _803307, class_Rings_Osemiring__0(_803309)], (47609 ^ _778908) ^ [_1726345, _1726347, _1726349, _1726351] : [-(hAPP(hAPP(c_List_Onth(_1726345), hAPP(hAPP(c_List_Olist_OCons(_1726345), _1726347), _1726349)), _1726351) = c_Nat_Onat_Onat__case(_1726345, _1726347, hAPP(c_List_Onth(_1726345), _1726349), _1726351))], (51721 ^ _778908) ^ [_1814364, _1814366] : [hBOOL(hAPP(hAPP(c_fimplies, _1814364), _1814366)), hBOOL(_1814364), -(hBOOL(_1814366))], (37004 ^ _778908) ^ [_1467180, _1467182, _1467184, _1467186] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467180, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467180, tc_HOL_Obool)), _1467182), _1467184)), _1467186) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467180, tc_HOL_Obool)), _1467182), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467180, tc_HOL_Obool)), _1467184), _1467186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467180, tc_HOL_Obool)), _1467186), _1467182)))], (3356 ^ _778908) ^ [_830478, _830480, _830482, _830484, _830486, _830488] : [-(c_Com_Ocom_OCall(_830488, _830484, _830480) = c_Com_Ocom_OCall(_830486, _830482, _830478)), _830488 = _830486, _830484 = _830482, _830480 = _830478], (27681 ^ _778908) ^ [_1269512, _1269514, _1269516] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1269512), _1269514), _1269516) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1269512), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1269512, tc_Int_Oint), _1269514), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1269516))), class_Groups_Ocomm__monoid__add(_1269512), class_Groups_Ocomm__monoid__mult(_1269512)], (48197 ^ _778908) ^ [_1740674, _1740676, _1740678, _1740680, _1740682] : [-(hAPP(hAPP(c_List_Oappend(_1740674), _1740676), _1740678) = hAPP(hAPP(c_List_Oappend(_1740674), _1740680), _1740682)), 48198 ^ _778908 : [(48205 ^ _778908) ^ [_1740898] : [hAPP(hAPP(c_List_Oappend(_1740674), _1740676), _1740898) = _1740680, _1740678 = hAPP(hAPP(c_List_Oappend(_1740674), _1740898), _1740682)], (48199 ^ _778908) ^ [_1740786] : [_1740676 = hAPP(hAPP(c_List_Oappend(_1740674), _1740680), _1740786), hAPP(hAPP(c_List_Oappend(_1740674), _1740786), _1740678) = _1740682]]], (3334 ^ _778908) ^ [_830089, _830091, _830093, _830095, _830097, _830099, _830101, _830103, _830105, _830107] : [-(c_SetInterval_Oord_OatLeastLessThan(_830107, _830103, _830099, _830095, _830091) = c_SetInterval_Oord_OatLeastLessThan(_830105, _830101, _830097, _830093, _830089)), _830107 = _830105, _830103 = _830101, _830099 = _830097, _830095 = _830093, _830091 = _830089], (40430 ^ _778908) ^ [_1546293, _1546295, _1546297, _1546299, _1546301, _1546303, _1546305, _1546307, _1546309, _1546311] : [-(c_Product__Type_Omap__pair(_1546293, _1546295, _1546297, _1546299, hAPP(c_Fun_Ocomp(_1546301, _1546295, _1546293, _1546303), _1546305), hAPP(c_Fun_Ocomp(_1546307, _1546299, _1546297, _1546309), _1546311)) = hAPP(c_Fun_Ocomp(tc_prod(_1546301, _1546307), tc_prod(_1546295, _1546299), tc_prod(_1546293, _1546297), c_Product__Type_Omap__pair(_1546301, _1546295, _1546307, _1546299, _1546303, _1546309)), c_Product__Type_Omap__pair(_1546293, _1546301, _1546297, _1546307, _1546305, _1546311)))], (46597 ^ _778908) ^ [_1699614, _1699616, _1699618, _1699620] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1699614, _1699614)), hAPP(hAPP(c_Product__Type_OPair(_1699614, _1699614), _1699616), _1699618)), hAPP(c_List_Oset(tc_prod(_1699614, _1699614)), hAPP(hAPP(c_List_Ozip(_1699614, _1699614), _1699620), _1699620))))), hBOOL(hAPP(hAPP(c_member(_1699614), _1699616), hAPP(c_List_Oset(_1699614), _1699620))), _1699616 = _1699618], (21319 ^ _778908) ^ [_1147239, _1147241, _1147243, _1147245] : [class_Fields_Ofield__inverse__zero(_1147239), class_Int_Onumber(_1147239), 21326 ^ _778908 : [(21327 ^ _778908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147239), _1147241), hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243)) = _1147245, 21330 ^ _778908 : [(21337 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243) = c_Groups_Ozero__class_Ozero(_1147239), -(_1147245 = c_Groups_Ozero__class_Ozero(_1147239))], (21331 ^ _778908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243) = c_Groups_Ozero__class_Ozero(_1147239)), -(_1147241 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147239), _1147245), hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243)))]]], (21343 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147239), _1147241), hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243)) = _1147245), 21346 ^ _778908 : [(21349 ^ _778908) ^ [] : [_1147241 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147239), _1147245), hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243))], (21347 ^ _778908) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243) = c_Groups_Ozero__class_Ozero(_1147239)]], 21350 ^ _778908 : [(21353 ^ _778908) ^ [] : [_1147245 = c_Groups_Ozero__class_Ozero(_1147239)], (21351 ^ _778908) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1147239), _1147243) = c_Groups_Ozero__class_Ozero(_1147239))]]]]], (11224 ^ _778908) ^ [_966591, _966593, _966595, _966597] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_966591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966591), _966593), _966595)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966591), _966593), _966597))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966591), _966595), _966597)))], (7833 ^ _778908) ^ [_909848, _909850, _909852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909848), _909850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909850), _909852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909848)), _909852)))], (8698 ^ _778908) ^ [_924138, _924140, _924142] : [class_Orderings_Oorder(_924138), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924138), _924140), _924142)), _924140 = _924142], (30832 ^ _778908) ^ [_1331876, _1331878, _1331880] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331876), _1331878)), hBOOL(hAPP(hAPP(c_member(_1331876), _1331880), _1331878)), -(hAPP(c_Finite__Set_Ocard(_1331876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331876, tc_HOL_Obool)), _1331878), hAPP(hAPP(c_Set_Oinsert(_1331876), _1331880), c_Orderings_Obot__class_Obot(tc_fun(_1331876, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1331876), _1331878)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49610 ^ _778908) ^ [_1774996, _1774998, _1775000] : [-(_1774996 = c_List_Olist_ONil(_1774998)), -(c_List_Olast(_1774998, hAPP(hAPP(c_List_Oappend(_1774998), _1775000), _1774996)) = c_List_Olast(_1774998, _1774996))], (47443 ^ _778908) ^ [_1722656, _1722658] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722656)), _1722658) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1722658 = c_List_Olist_ONil(_1722656))], (23004 ^ _778908) ^ [_1179040, _1179042, _1179044, _1179046] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1179040, _1179042), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1179044), _1179046))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1179040), _1179042) = _1179044)], (30002 ^ _778908) ^ [_1316106, _1316108] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316106, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1316106, tc_HOL_Obool))), _1316108) = _1316108)], (7116 ^ _778908) ^ [_897907] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _897907)], (40138 ^ _778908) ^ [_1538028, _1538030, _1538032, _1538034] : [-(hAPP(c_Set_Oimage(tc_prod(_1538028, _1538030), tc_prod(_1538030, _1538028), hAPP(c_Product__Type_Oprod_Oprod__case(_1538028, _1538030, tc_prod(_1538030, _1538028)), hAPP(c_COMBC(_1538030, _1538028, tc_prod(_1538030, _1538028)), c_Product__Type_OPair(_1538030, _1538028)))), hAPP(hAPP(c_Product__Type_OSigma(_1538028, _1538030), _1538032), hAPP(c_COMBK(tc_fun(_1538030, tc_HOL_Obool), _1538028), _1538034))) = hAPP(hAPP(c_Product__Type_OSigma(_1538030, _1538028), _1538034), hAPP(c_COMBK(tc_fun(_1538028, tc_HOL_Obool), _1538030), _1538032)))], (36634 ^ _778908) ^ [_1458751, _1458753, _1458755, _1458757] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458751, tc_HOL_Obool)), _1458753), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458751, tc_HOL_Obool)), _1458755), _1458757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458751, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458751, tc_HOL_Obool)), _1458753), _1458755)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458751, tc_HOL_Obool)), _1458753), _1458757)))], (20793 ^ _778908) ^ [_1137628, _1137630, _1137632] : [class_Rings_Odivision__ring(_1137628), -(_1137630 = c_Groups_Ozero__class_Ozero(_1137628)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137628), hAPP(c_Groups_Ouminus__class_Ouminus(_1137628), _1137632)), hAPP(c_Groups_Ouminus__class_Ouminus(_1137628), _1137630)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137628), _1137632), _1137630))], (48056 ^ _778908) ^ [_1737340, _1737342, _1737344] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737340)), hAPP(hAPP(c_List_Oappend(_1737340), _1737342), _1737344)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737340)), _1737342)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737340)), _1737344)))], (8810 ^ _778908) ^ [_925873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _925873)), 8814 ^ _778908 : [(8817 ^ _778908) ^ [] : [-(_925873 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8813 ^ [_925873]))], (8815 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8813 ^ [_925873])))]]], (22992 ^ _778908) ^ [_1178834, _1178836, _1178838] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1178834, _1178836), _1178838)), -(c_Divides_Odivmod__nat(_1178834, _1178836) = _1178838)], (51643 ^ _778908) ^ [_1813418, _1813420] : [_1813418 = _1813420, -(hBOOL(hAPP(hAPP(c_fequal, _1813418), _1813420)))], (9664 ^ _778908) ^ [_940855, _940857] : [class_Rings_Olinordered__idom(_940855), 9667 ^ _778908 : [(9674 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940855), _940857), c_Groups_Ozero__class_Ozero(_940855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940855), _940857), hAPP(c_Groups_Ouminus__class_Ouminus(_940855), _940857))))], (9668 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940855), _940857), hAPP(c_Groups_Ouminus__class_Ouminus(_940855), _940857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940855), _940857), c_Groups_Ozero__class_Ozero(_940855))))]]], (31592 ^ _778908) ^ [_1349239, _1349241, _1349243, _1349245] : [-(hBOOL(hAPP(hAPP(c_member(_1349239), _1349241), _1349243))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349239, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1349239), _1349241), _1349245)), _1349243) = hAPP(hAPP(c_Set_Oinsert(_1349239), _1349241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349239, tc_HOL_Obool)), _1349245), _1349243)))], (37102 ^ _778908) ^ [_1469539, _1469541, _1469543, _1469545] : [class_Orderings_Oorder(_1469539), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469539, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1469539, _1469541), _1469543)), c_SetInterval_Oord__class_OatLeastAtMost(_1469539, _1469543, _1469545)) = c_Orderings_Obot__class_Obot(tc_fun(_1469539, tc_HOL_Obool)))], (44825 ^ _778908) ^ [_1656915, _1656917, _1656919, _1656921] : [hBOOL(hAPP(hAPP(c_member(_1656917), _1656921), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656915, tc_fun(_1656917, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1656915, tc_HOL_Obool))), _1656919))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1656915, tc_fun(_1656917, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1656915, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1656917, tc_HOL_Obool), tc_fun(_1656917, tc_HOL_Obool), _1656915), hAPP(c_COMBC(_1656917, tc_fun(_1656917, tc_HOL_Obool), tc_HOL_Obool), c_member(_1656917))), _1656919)), _1656921)))], (19545 ^ _778908) ^ [_1115562] : [-(c_Int_Opred(c_Int_OBit0(_1115562)) = c_Int_OBit1(c_Int_Opred(_1115562)))], (35218 ^ _778908) ^ [_1426422, _1426424] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1426422, _1426422)), hAPP(hAPP(c_Product__Type_OPair(_1426422, _1426422), 35219 ^ [_1426422, _1426424]), 35219 ^ [_1426422, _1426424])), _1426424))), -(c_Relation_Oirrefl(_1426422, _1426424))], (10234 ^ _778908) ^ [_950863, _950865, _950867] : [class_Rings_Olinordered__ring__strict(_950863), 10237 ^ _778908 : [(10238 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950863), c_Groups_Ozero__class_Ozero(_950863)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950863), _950865), _950865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950863), _950867), _950867)))), _950865 = c_Groups_Ozero__class_Ozero(_950863), _950867 = c_Groups_Ozero__class_Ozero(_950863)], (10248 ^ _778908) ^ [] : [10249 ^ _778908 : [(10252 ^ _778908) ^ [] : [-(_950867 = c_Groups_Ozero__class_Ozero(_950863))], (10250 ^ _778908) ^ [] : [-(_950865 = c_Groups_Ozero__class_Ozero(_950863))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950863), c_Groups_Ozero__class_Ozero(_950863)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950863), _950865), _950865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950863), _950867), _950867)))))]]], (1692 ^ _778908) ^ [_802932, _802934] : [-(class_Groups_Omonoid__mult(_802932)), _802934 = _802932, class_Groups_Omonoid__mult(_802934)], (47940 ^ _778908) ^ [_1734524, _1734526, _1734528, _1734530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734524), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734526)), _1734528))), 47943 ^ _778908 : [(47950 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Onth(_1734526), _1734528), _1734524) = _1734530, -(hAPP(hAPP(c_List_Olist__update(_1734526, _1734528), _1734524), _1734530) = _1734528)], (47944 ^ _778908) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1734526, _1734528), _1734524), _1734530) = _1734528, -(hAPP(hAPP(c_List_Onth(_1734526), _1734528), _1734524) = _1734530)]]], (19735 ^ _778908) ^ [_1118850] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118850), 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, _1118850)))], (51609 ^ _778908) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (46477 ^ _778908) ^ [_1696712] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1696712)), -(c_List_Onat__list(_1696712))], (45966 ^ _778908) ^ [_1684456, _1684458, _1684460] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1684456), c_Map_Odom(_1684456, _1684458, c_Map_Omap__of(_1684456, _1684458, _1684460)))))], (22602 ^ _778908) ^ [_1170860, _1170862] : [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(_1170860))), 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)), _1170862)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170860)), hAPP(c_Nat_OSuc, _1170862))))], (44843 ^ _778908) ^ [_1658160, _1658162, _1658164, _1658166] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658160, tc_fun(_1658162, tc_HOL_Obool)), _1658164), _1658166) = c_Orderings_Otop__class_Otop(tc_fun(_1658162, tc_HOL_Obool)), 44846 ^ _778908 : [(44847 ^ _778908) ^ [_1658276] : [hBOOL(hAPP(hAPP(c_member(_1658160), _1658276), _1658164)), -(hAPP(_1658166, _1658276) = c_Orderings_Otop__class_Otop(tc_fun(_1658162, tc_HOL_Obool)))]]], (19763 ^ _778908) ^ [] : [-(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)))))], (5979 ^ _778908) ^ [_874407, _874409, _874411] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_874407, _874409, _874411))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _874409))))], (15468 ^ _778908) ^ [_1042054, _1042056] : [class_Groups_Ogroup__add(_1042054), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042054), _1042056), _1042056) = c_Groups_Ozero__class_Ozero(_1042054))], (27897 ^ _778908) ^ [_1273462, _1273464] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1273462), _1273464)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1273464), _1273462))], (31265 ^ _778908) ^ [_1342980, _1342982] : [hAPP(c_Int_ORep__Integ, _1342980) = hAPP(c_Int_ORep__Integ, _1342982), -(_1342980 = _1342982)], (49985 ^ _778908) ^ [_1782569, _1782571, _1782573, _1782575] : [hBOOL(hAPP(hAPP(c_member(_1782569), _1782571), hAPP(c_List_Oset(_1782569), _1782573))), -(hBOOL(hAPP(_1782575, _1782571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782569)), hAPP(c_List_Ofilter(_1782569, _1782575), _1782573))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782569)), _1782573))))], (47647 ^ _778908) ^ [_1727325, _1727327] : [hBOOL(hAPP(c_List_Odistinct(_1727325), _1727327)), 47650 ^ _778908 : [(47651 ^ _778908) ^ [_1727457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727457), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727325)), _1727327))), 47654 ^ _778908 : [(47655 ^ _778908) ^ [_1727584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727584), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727325)), _1727327))), -(_1727457 = _1727584), hAPP(hAPP(c_List_Onth(_1727325), _1727327), _1727457) = hAPP(hAPP(c_List_Onth(_1727325), _1727327), _1727584)]]]]], (7248 ^ _778908) ^ [_900189, _900191] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _900189), _900191) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _900189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _900191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26987 ^ _778908) ^ [_1255190, _1255192, _1255194] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1255190, tc_Nat_Onat), _1255192), _1255194) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1255190, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1255190), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1255192)), _1255194)))], (18371 ^ _778908) ^ [_1096148] : [class_Int_Onumber__ring(_1096148), -(hAPP(c_Int_Oring__1__class_Oof__int(_1096148), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1096148), c_Int_OMin))], (31177 ^ _778908) ^ [_1338952, _1338954, _1338956, _1338958, _1338960] : [-(hBOOL(hAPP(hAPP(c_member(_1338952), _1338954), c_SetInterval_Oord_OatLeastAtMost(_1338952, _1338956, _1338958, _1338960)))), hBOOL(hAPP(hAPP(_1338956, _1338958), _1338954)), hBOOL(hAPP(hAPP(_1338956, _1338954), _1338960))], (45630 ^ _778908) ^ [_1676979, _1676981, _1676983, _1676985] : [class_Orderings_Olinorder(_1676979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1676979), _1676981)), 45640 ^ _778908 : [(45643 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676979), _1676983), 45639 ^ [_1676979, _1676981, _1676983, _1676985]))], (45641 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676979), 45639 ^ [_1676979, _1676981, _1676983, _1676985]), _1676981)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676979), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1676979), _1676983), _1676985)), hAPP(hAPP(c_Finite__Set_Ofold(_1676979, _1676979, c_Orderings_Oord__class_Omin(_1676979)), _1676985), _1676981))))], (22466 ^ _778908) ^ [_1168061, _1168063] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1168061), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1168063))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1168061), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168063))), 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))))], (4992 ^ _778908) ^ [_856120, _856122] : [_856122 = _856120, -(c_Set_OCollect(_856122) = c_Set_OCollect(_856120))], (15366 ^ _778908) ^ [_1040253, _1040255, _1040257] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040253), _1040255)), _1040257) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040253), _1040257)), _1040255))], (14886 ^ _778908) ^ [_1031340, _1031342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031340)), 14889 ^ _778908 : [(14898 ^ _778908) ^ [] : [-(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), _1031340), _1031342)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031342), _1031340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031342))], (14890 ^ _778908) ^ [] : [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), _1031340), _1031342))), 14893 ^ _778908 : [(14896 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031342)))], (14894 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031342), _1031340)))]]]]], (48339 ^ _778908) ^ [_1743559, _1743561, _1743563] : [-(c_List_Olist_ONil(_1743559) = hAPP(hAPP(c_List_Oappend(_1743559), _1743561), _1743563)), _1743561 = c_List_Olist_ONil(_1743559), _1743563 = c_List_Olist_ONil(_1743559)], (37314 ^ _778908) ^ [_1474461, _1474463, _1474465] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474461), _1474463)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474461), _1474465)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474461), _1474463)), hAPP(c_Finite__Set_Ocard(_1474461), _1474465)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474461), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474461, tc_HOL_Obool)), _1474463), _1474465))), hAPP(c_Finite__Set_Ocard(_1474461), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474461, tc_HOL_Obool)), _1474463), _1474465))))], (27484 ^ _778908) ^ [_1265093, _1265095, _1265097, _1265099] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1265093), _1265095)), 27487 ^ _778908 : [(27488 ^ _778908) ^ [_1265247] : [27490 ^ _778908 : [(27496 ^ _778908) ^ [] : [-(_1265247 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27492 ^ [_1265093, _1265095, _1265097, _1265099, _1265247]), 27489 ^ [_1265093, _1265095, _1265097, _1265099, _1265247]))], (27494 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27492 ^ [_1265093, _1265095, _1265097, _1265099, _1265247]), _1265097)))], (27491 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27489 ^ [_1265093, _1265095, _1265097, _1265099, _1265247]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1265095))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1265093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1265247), _1265099))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1265093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1265247), _1265095)), _1265099))))]]], (47908 ^ _778908) ^ [_1733778, _1733780, _1733782, _1733784] : [-(hAPP(hAPP(c_List_Olist__update(_1733778, hAPP(hAPP(c_List_Olist_OCons(_1733778), _1733780), _1733782)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1733784) = hAPP(hAPP(c_List_Olist_OCons(_1733778), _1733784), _1733782))], (47850 ^ _778908) ^ [_1732557, _1732559, _1732561] : [-(hAPP(hAPP(c_List_Olist__update(_1732557, _1732559), _1732561), hAPP(hAPP(c_List_Onth(_1732557), _1732559), _1732561)) = _1732559)], (6564 ^ _778908) ^ [_885634, _885636, _885638] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885634), _885636), _885638)), -(c_Natural_Oevaln(_885634, _885636, 6567 ^ [_885634, _885636, _885638], _885638))], (47561 ^ _778908) ^ [_1724831, _1724833] : [-(_1724831 = c_List_Olist_ONil(_1724833)), -(c_Random_Oselect__weight(_1724833, hAPP(hAPP(c_List_Omap(_1724833, tc_prod(tc_Code__Numeral_Ocode__numeral, _1724833)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1724833), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1724831)) = c_Random_Oselect(_1724833, _1724831))], (3904 ^ _778908) ^ [_839118, _839120, _839122, _839124, _839126, _839128, _839130, _839132] : [-(c_New__Random__Sequence_Oneg__map(_839132, _839128, _839124, _839120) = c_New__Random__Sequence_Oneg__map(_839130, _839126, _839122, _839118)), _839132 = _839130, _839128 = _839126, _839124 = _839122, _839120 = _839118], (36162 ^ _778908) ^ [_1448806, _1448808, _1448810, _1448812, _1448814, _1448816, _1448818] : [c_Equiv__Relations_Oequiv(_1448806, _1448808, _1448810), hBOOL(hAPP(hAPP(c_member(tc_fun(_1448806, tc_HOL_Obool)), _1448812), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448806), _1448808), _1448810))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1448806, tc_HOL_Obool)), _1448814), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448806), _1448808), _1448810))), hBOOL(hAPP(hAPP(c_member(_1448806), _1448816), _1448812)), hBOOL(hAPP(hAPP(c_member(_1448806), _1448818), _1448814)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1448806, _1448806)), hAPP(hAPP(c_Product__Type_OPair(_1448806, _1448806), _1448816), _1448818)), _1448810)), -(_1448812 = _1448814)], (2730 ^ _778908) ^ [_820275, _820277, _820279, _820281, _820283, _820285, _820287, _820289] : [-(c_Random_Oiterate(_820289, _820285, _820281, _820277) = c_Random_Oiterate(_820287, _820283, _820279, _820275)), _820289 = _820287, _820285 = _820283, _820281 = _820279, _820277 = _820275], (36108 ^ _778908) ^ [] : [-(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))], (45025 ^ _778908) ^ [_1663127, _1663129] : [class_Complete__Lattice_Ocomplete__lattice(_1663127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1663127), _1663129)), -(c_Complete__Lattice_OSup__class_OSup(_1663127, _1663129) = hAPP(hAPP(c_Finite__Set_Ofold(_1663127, _1663127, c_Lattices_Osemilattice__sup__class_Osup(_1663127)), c_Orderings_Obot__class_Obot(_1663127)), _1663129))], (28307 ^ _778908) ^ [_1281531, _1281533, _1281535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281531, tc_HOL_Obool)), _1281533), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281531, tc_HOL_Obool)), _1281533), _1281535))))], (45775 ^ _778908) ^ [_1680295, _1680297, _1680299, _1680301, _1680303, _1680305, _1680307, _1680309] : [c_Finite__Set_Ofolding__image__simple__idem(_1680295, _1680297, _1680299, _1680301, _1680303, _1680305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1680297), _1680307)), -(hAPP(_1680305, hAPP(hAPP(c_Set_Oinsert(_1680297), _1680309), _1680307)) = hAPP(hAPP(_1680299, hAPP(_1680303, _1680309)), hAPP(_1680305, _1680307)))], (6538 ^ _778908) ^ [_884946, _884948, _884950, _884952, _884954, _884956, _884958, _884960, _884962, _884964, _884966, _884968] : [-(c_Com_Ocom_Ocom__rec(_884946, _884948, _884950, _884952, _884954, _884956, _884958, _884960, _884962, c_Com_Ocom_OLocal(_884964, _884966, _884968)) = hAPP(hAPP(hAPP(hAPP(_884952, _884964), _884966), _884968), c_Com_Ocom_Ocom__rec(_884946, _884948, _884950, _884952, _884954, _884956, _884958, _884960, _884962, _884968)))], (17391 ^ _778908) ^ [_1079386, _1079388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079386)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079386), _1079388)))], (48959 ^ _778908) ^ [_1760286, _1760288] : [_1760288 = c_List_Olist_ONil(_1760286), -(hAPP(c_List_Orotate1(_1760286), _1760288) = c_List_Olist_ONil(_1760286))], (35891 ^ _778908) ^ [_1442341, _1442343, _1442345, _1442347, _1442349, _1442351] : [c_Finite__Set_Ofolding(_1442341, _1442343, _1442345, _1442347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442341), _1442349)), hBOOL(hAPP(hAPP(c_member(_1442341), _1442351), _1442349)), -(hAPP(_1442347, _1442349) = hAPP(c_Fun_Ocomp(_1442343, _1442343, _1442343, hAPP(_1442347, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1442341, tc_HOL_Obool)), _1442349), hAPP(hAPP(c_Set_Oinsert(_1442341), _1442351), c_Orderings_Obot__class_Obot(tc_fun(_1442341, tc_HOL_Obool)))))), hAPP(_1442345, _1442351)))], (36023 ^ _778908) ^ [_1445494, _1445496, _1445498, _1445500] : [-(c_Random__Sequence_Omap(_1445494, _1445496, _1445498, _1445500) = c_Random__Sequence_Obind(_1445494, _1445496, _1445500, hAPP(c_Fun_Ocomp(_1445496, 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(_1445496)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1445494, c_Random__Sequence_Osingle(_1445496)), _1445498)))], (17217 ^ _778908) ^ [_1076046] : [_1076046 = 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), _1076046)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (41428 ^ _778908) ^ [_1569016, _1569018] : [c_Predicate_Oreflp(_1569016, _1569018), -(c_Relation_Orefl__on(_1569016, c_Orderings_Otop__class_Otop(tc_fun(_1569016, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1569016, _1569016)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569016, _1569016, tc_HOL_Obool), _1569018))))], (41886 ^ _778908) ^ [_1586812, _1586814] : [-(c_Wellfounded_Owf(_1586812, hAPP(c_Wellfounded_Omeasure(_1586812), _1586814)))], (43532 ^ _778908) ^ [_1626476, _1626478] : [-(hAPP(c_Relation_OField(_1626476), hAPP(c_Relation_Oconverse(_1626476, _1626476), _1626478)) = hAPP(c_Relation_OField(_1626476), _1626478))], (2042 ^ _778908) ^ [_809189, _809191, _809193, _809195, _809197, _809199, _809201, _809203] : [-(c_Com_Ovname_Ovname__rec(_809203, _809199, _809195, _809191) = c_Com_Ovname_Ovname__rec(_809201, _809197, _809193, _809189)), _809203 = _809201, _809199 = _809197, _809195 = _809193, _809191 = _809189], (39636 ^ _778908) ^ [_1525001, _1525003, _1525005, _1525007, _1525009] : [c_Fun_Oinj__on(_1525001, _1525003, _1525005, c_Orderings_Otop__class_Otop(tc_fun(_1525001, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525003, tc_HOL_Obool)), _1525007), hAPP(c_Set_Oimage(_1525001, _1525003, _1525005), _1525009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525001, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1525001, _1525003, _1525005), _1525007)), _1525009)))], (5999 ^ _778908) ^ [_874770, _874772, _874774, _874776, _874778, _874780, _874782, _874784, _874786] : [-(c_Com_Ocom_Ocom__rec(_874770, _874772, _874774, _874776, _874778, _874780, _874782, _874784, _874786, c_Com_Ocom_OSKIP) = _874772)], (23283 ^ _778908) ^ [_1184292, _1184294, _1184296, _1184298, _1184300] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184292, _1184294, tc_HOL_Obool), _1184296), hAPP(hAPP(c_Product__Type_OPair(_1184292, _1184294), _1184298), _1184300))), -(hBOOL(hAPP(hAPP(_1184296, _1184298), _1184300)))], (4956 ^ _778908) ^ [_855580, _855582] : [_855582 = _855580, -(c_Orderings_Obot__class_Obot(_855582) = c_Orderings_Obot__class_Obot(_855580))], (33331 ^ _778908) ^ [_1387058, _1387060] : [class_Lattices_Olattice(_1387058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387058), _1387060)), -(_1387060 = c_Orderings_Obot__class_Obot(tc_fun(_1387058, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1387058), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1387058), 33344 ^ [_1387058, _1387060]), 33345 ^ [_1387058, _1387060])), hAPP(hAPP(c_Set_Oinsert(_1387058), 33344 ^ [_1387058, _1387060]), hAPP(hAPP(c_Set_Oinsert(_1387058), 33345 ^ [_1387058, _1387060]), c_Orderings_Obot__class_Obot(tc_fun(_1387058, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1387058), c_Big__Operators_Olattice__class_OSup__fin(_1387058, _1387060)), _1387060)))], (18861 ^ _778908) ^ [_1103897, _1103899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103897), _1103899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1103897)), c_Int_OBit1(_1103899))))], (3610 ^ _778908) ^ [_834449, _834451] : [_834451 = _834449, -(c_Random__Sequence_Osingle(_834451) = c_Random__Sequence_Osingle(_834449))], (30700 ^ _778908) ^ [_1329115, _1329117, _1329119, _1329121, _1329123] : [class_Groups_Ocomm__monoid__add(_1329115), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329117), _1329119)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329117, _1329115), _1329121), hAPP(hAPP(c_Set_Oinsert(_1329117), _1329123), _1329119)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329115), hAPP(_1329121, _1329123)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329117, _1329115), _1329121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329117, tc_HOL_Obool)), _1329119), hAPP(hAPP(c_Set_Oinsert(_1329117), _1329123), c_Orderings_Obot__class_Obot(tc_fun(_1329117, tc_HOL_Obool)))))))], (37472 ^ _778908) ^ [_1478022, _1478024, _1478026, _1478028, _1478030] : [class_Groups_Ocomm__monoid__mult(_1478022), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478024), _1478026)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478024), _1478028)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478024, tc_HOL_Obool)), _1478026), _1478028) = c_Orderings_Obot__class_Obot(tc_fun(_1478024, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478024, _1478022), _1478030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478024, tc_HOL_Obool)), _1478026), _1478028)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1478022), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478024, _1478022), _1478030), _1478026)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478024, _1478022), _1478030), _1478028)))], (33561 ^ _778908) ^ [_1391061, _1391063, _1391065] : [class_Orderings_Olinorder(_1391061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391061), _1391063)), -(_1391063 = c_Orderings_Obot__class_Obot(tc_fun(_1391061, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1391061, hAPP(hAPP(c_Set_Oinsert(_1391061), _1391065), _1391063)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1391061), _1391065), c_Big__Operators_Olinorder__class_OMin(_1391061, _1391063)))], (30396 ^ _778908) ^ [_1323382] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1323382, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1323382, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1323382, tc_HOL_Obool)))], (16601 ^ _778908) ^ [_1064180, _1064182] : [class_Groups_Oordered__ab__group__add__abs(_1064180), 16604 ^ _778908 : [(16611 ^ _778908) ^ [] : [_1064182 = c_Groups_Ozero__class_Ozero(_1064180), -(hAPP(c_Groups_Oabs__class_Oabs(_1064180), _1064182) = c_Groups_Ozero__class_Ozero(_1064180))], (16605 ^ _778908) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1064180), _1064182) = c_Groups_Ozero__class_Ozero(_1064180), -(_1064182 = c_Groups_Ozero__class_Ozero(_1064180))]]], (24871 ^ _778908) ^ [_1214684, _1214686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1214684), _1214686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1214684)), hAPP(c_Code__Numeral_Onat__of, _1214686))))], (8748 ^ _778908) ^ [_924896, _924898, _924900] : [class_Orderings_Opreorder(_924896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924896), _924898), _924900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924896), _924900), _924898))], (17693 ^ _778908) ^ [_1084651, _1084653] : [class_Power_Opower(_1084651), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084651), _1084653), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1084651))], (10677 ^ _778908) ^ [_958084, _958086, _958088, _958090] : [class_Orderings_Oord(_958084), _958086 = _958088, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958084), _958088), _958090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958084), _958086), _958090)))], (19919 ^ _778908) ^ [_1121930, _1121932, _1121934] : [class_Rings_Oring__1(_1121930), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121930), hAPP(c_Groups_Ouminus__class_Ouminus(_1121930), _1121932)), 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)))), _1121934)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1121930), _1121932), 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)))), _1121934)))], (28763 ^ _778908) ^ [_1290443, _1290445, _1290447, _1290449] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290443, _1290445)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290447, _1290449)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290447), _1290449)), 28766 ^ _778908 : [(28769 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290447), _1290443)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290445), _1290449)), 28776 ^ _778908 : [(28783 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290445), _1290449)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290449), _1290445)))], (28777 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290447), _1290443)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290443), _1290447)))]]], (28767 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1290443), _1290445)))]]], (36902 ^ _778908) ^ [_1464726, _1464728, _1464730, _1464732, _1464734, _1464736, _1464738] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464726, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464728, tc_fun(_1464726, tc_HOL_Obool)), _1464730), _1464732)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464734, tc_fun(_1464726, tc_HOL_Obool)), _1464736), _1464738)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464728, tc_fun(_1464726, tc_HOL_Obool)), _1464730), hAPP(hAPP(c_COMBB(tc_fun(_1464734, tc_fun(_1464726, tc_HOL_Obool)), tc_fun(_1464726, tc_HOL_Obool), _1464728), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464734, tc_fun(_1464726, tc_HOL_Obool)), _1464736)), hAPP(hAPP(c_COMBC(_1464728, tc_fun(_1464734, tc_fun(_1464726, tc_HOL_Obool)), tc_fun(_1464734, tc_fun(_1464726, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1464726, tc_HOL_Obool), tc_fun(_1464726, tc_HOL_Obool)), tc_fun(tc_fun(_1464734, tc_fun(_1464726, tc_HOL_Obool)), tc_fun(_1464734, tc_fun(_1464726, tc_HOL_Obool))), _1464728), c_COMBB(tc_fun(_1464726, tc_HOL_Obool), tc_fun(_1464726, tc_HOL_Obool), _1464734)), hAPP(hAPP(c_COMBB(tc_fun(_1464726, tc_HOL_Obool), tc_fun(tc_fun(_1464726, tc_HOL_Obool), tc_fun(_1464726, tc_HOL_Obool)), _1464728), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464726, tc_HOL_Obool))), _1464732))), _1464738))))], (15870 ^ _778908) ^ [_1049732, _1049734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049732), _1049734)), hAPP(c_Nat_OSuc, _1049732))))], (13893 ^ _778908) ^ [_1013466, _1013468, _1013470, _1013472, _1013474, _1013476] : [class_Divides_Osemiring__div(_1013466), c_Divides_Odiv__class_Omod(_1013466, _1013468, _1013470) = c_Divides_Odiv__class_Omod(_1013466, _1013472, _1013470), c_Divides_Odiv__class_Omod(_1013466, _1013474, _1013470) = c_Divides_Odiv__class_Omod(_1013466, _1013476, _1013470), -(c_Divides_Odiv__class_Omod(_1013466, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013466), _1013468), _1013474), _1013470) = c_Divides_Odiv__class_Omod(_1013466, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013466), _1013472), _1013476), _1013470))], (47254 ^ _778908) ^ [_1718669, _1718671] : [class_Groups_Oordered__ab__group__add__abs(_1718669), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718669), hAPP(c_Groups_Oabs__class_Oabs(_1718669), hAPP(c_List_Omonoid__add__class_Olistsum(_1718669), _1718671))), hAPP(c_List_Omonoid__add__class_Olistsum(_1718669), hAPP(hAPP(c_List_Omap(_1718669, _1718669), c_Groups_Oabs__class_Oabs(_1718669)), _1718671)))))], (19231 ^ _778908) ^ [_1109873, _1109875] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1109873))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109875)) = 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)))), _1109873), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109875)))], (10321 ^ _778908) ^ [_952348, _952350] : [class_Rings_Olinordered__idom(_952348), 10324 ^ _778908 : [(10331 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952348), _952350), c_Groups_Ozero__class_Ozero(_952348))), -(c_Groups_Osgn__class_Osgn(_952348, _952350) = hAPP(c_Groups_Ouminus__class_Ouminus(_952348), c_Groups_Oone__class_Oone(_952348)))], (10325 ^ _778908) ^ [] : [c_Groups_Osgn__class_Osgn(_952348, _952350) = hAPP(c_Groups_Ouminus__class_Ouminus(_952348), c_Groups_Oone__class_Oone(_952348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952348), _952350), c_Groups_Ozero__class_Ozero(_952348))))]]], (5278 ^ _778908) ^ [_860551, _860553, _860555, _860557] : [-(c_Product__Type_Ofst(_860557, _860553) = c_Product__Type_Ofst(_860555, _860551)), _860557 = _860555, _860553 = _860551], (40288 ^ _778908) ^ [_1541849, _1541851, _1541853, _1541855, _1541857, _1541859, _1541861, _1541863] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1541849, _1541851), tc_fun(tc_prod(_1541853, _1541855), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1541849, _1541851), _1541857), hAPP(c_COMBK(tc_fun(_1541851, tc_HOL_Obool), _1541849), _1541859))), hAPP(c_Product__Type_Oprod_Oprod__case(_1541849, _1541851, tc_fun(tc_prod(_1541853, _1541855), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1541849, tc_fun(_1541851, tc_fun(_1541853, tc_fun(_1541855, tc_HOL_Obool))), tc_fun(_1541851, tc_fun(tc_prod(_1541853, _1541855), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1541853, tc_fun(_1541855, tc_HOL_Obool)), tc_fun(tc_prod(_1541853, _1541855), tc_HOL_Obool)), tc_fun(tc_fun(_1541851, tc_fun(_1541853, tc_fun(_1541855, tc_HOL_Obool))), tc_fun(_1541851, tc_fun(tc_prod(_1541853, _1541855), tc_HOL_Obool))), _1541849), c_COMBB(tc_fun(_1541853, tc_fun(_1541855, tc_HOL_Obool)), tc_fun(tc_prod(_1541853, _1541855), tc_HOL_Obool), _1541851)), hAPP(hAPP(c_COMBB(tc_fun(_1541853, tc_HOL_Obool), tc_fun(tc_fun(_1541853, tc_fun(_1541855, tc_HOL_Obool)), tc_fun(tc_prod(_1541853, _1541855), tc_HOL_Obool)), _1541849), c_Product__Type_OSigma(_1541853, _1541855)), _1541861))), hAPP(hAPP(c_COMBB(tc_fun(_1541855, tc_HOL_Obool), tc_fun(_1541853, tc_fun(_1541855, tc_HOL_Obool)), _1541851), c_COMBK(tc_fun(_1541855, tc_HOL_Obool), _1541853)), _1541863)))) = hAPP(hAPP(c_Product__Type_OSigma(_1541853, _1541855), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541849, tc_fun(_1541853, tc_HOL_Obool)), _1541857), _1541861)), hAPP(c_COMBK(tc_fun(_1541855, tc_HOL_Obool), _1541853), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541851, tc_fun(_1541855, tc_HOL_Obool)), _1541859), _1541863))))], (45927 ^ _778908) ^ [_1683404, _1683406, _1683408, _1683410, _1683412, _1683414] : [-(c_Map_Omap__add(_1683404, _1683406, _1683408, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1683404, tc_Option_Ooption(_1683406)), _1683410), _1683412), hAPP(c_Option_Ooption_OSome(_1683406), _1683414))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1683404, tc_Option_Ooption(_1683406)), c_Map_Omap__add(_1683404, _1683406, _1683408, _1683410)), _1683412), hAPP(c_Option_Ooption_OSome(_1683406), _1683414)))], (43057 ^ _778908) ^ [_1614226, _1614228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1614226, _1614226)), _1614228)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1614226, _1614226)), c_Transitive__Closure_Otrancl(_1614226, _1614228))))], (28249 ^ _778908) ^ [_1280508, _1280510, _1280512, _1280514] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280508, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280508, tc_HOL_Obool)), _1280510), _1280512)), _1280514) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280508, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280508, tc_HOL_Obool)), _1280510), _1280514)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280508, tc_HOL_Obool)), _1280512), _1280514)))], (50244 ^ _778908) ^ [_1788638, _1788640, _1788642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1788638), _1788640)), -(c_List_Oupt(_1788638, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1788640), _1788642)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1788638, _1788640)), c_List_Oupt(_1788640, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1788640), _1788642))))], (17379 ^ _778908) ^ [_1079155, _1079157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079155)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079157))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079155), _1079157)))], (10882 ^ _778908) ^ [_961585, _961587, _961589] : [10883 ^ _778908 : [(10886 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961585), _961589))], (10884 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961587)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961585), _961587)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961589), _961587))))], (49881 ^ _778908) ^ [_1780342, _1780344, _1780346, _1780348, _1780350] : [c_List_Opartition(_1780342, _1780344, _1780346) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780342), tc_List_Olist(_1780342)), _1780348), _1780350), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1780342, tc_HOL_Obool)), hAPP(c_List_Oset(_1780342), _1780348)), hAPP(c_List_Oset(_1780342), _1780350)) = hAPP(c_List_Oset(_1780342), _1780346))], (36530 ^ _778908) ^ [_1456345, _1456347, _1456349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456345, tc_HOL_Obool)), _1456347), _1456349)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456345, tc_HOL_Obool)), _1456349), _1456347) = _1456347)], (46643 ^ _778908) ^ [_1701117, _1701119, _1701121, _1701123, _1701125] : [class_Orderings_Olinorder(_1701117), -(hAPP(c_List_Oset(_1701119), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701119, _1701117, _1701121), _1701123), _1701125)) = hAPP(hAPP(c_Set_Oinsert(_1701119), _1701123), hAPP(c_List_Oset(_1701119), _1701125)))], (19467 ^ _778908) ^ [_1114157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114157), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1114157)), c_Int_OPls)))], (44883 ^ _778908) ^ [_1659183, _1659185, _1659187, _1659189, _1659191] : [-(hAPP(c_Relation_Oconverse(_1659183, _1659185), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659187, tc_fun(tc_prod(_1659183, _1659185), tc_HOL_Obool)), _1659189), _1659191)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659187, tc_fun(tc_prod(_1659185, _1659183), tc_HOL_Obool)), _1659189), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1659183, _1659185), tc_HOL_Obool), tc_fun(tc_prod(_1659185, _1659183), tc_HOL_Obool), _1659187), c_Relation_Oconverse(_1659183, _1659185)), _1659191)))], (51441 ^ _778908) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (25905 ^ _778908) ^ [_1233937, _1233939, _1233941] : [class_Rings_Olinordered__idom(_1233937), hAPP(c_Groups_Oabs__class_Oabs(_1233937), _1233939) = hAPP(c_Groups_Oabs__class_Oabs(_1233937), _1233941), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233937), _1233939), _1233941)))], (46879 ^ _778908) ^ [_1706908, _1706910, _1706912, _1706914] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706908)), _1706910) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706912)), _1706914), hBOOL(hAPP(c_List_Odistinct(_1706908), _1706910)), -(c_Map_Odom(_1706908, _1706912, c_Map_Omap__of(_1706908, _1706912, hAPP(hAPP(c_List_Ozip(_1706908, _1706912), _1706910), _1706914))) = hAPP(c_List_Oset(_1706908), _1706910))], (37742 ^ _778908) ^ [_1483320, _1483322, _1483324, _1483326, _1483328, _1483330, _1483332, _1483334, _1483336, _1483338] : [c_Equiv__Relations_Ocongruent2(_1483320, _1483322, _1483324, _1483326, _1483328, _1483330), hBOOL(hAPP(hAPP(c_member(tc_prod(_1483320, _1483320)), hAPP(hAPP(c_Product__Type_OPair(_1483320, _1483320), _1483332), _1483334)), _1483326)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1483322, _1483322)), hAPP(hAPP(c_Product__Type_OPair(_1483322, _1483322), _1483336), _1483338)), _1483328)), -(hAPP(hAPP(_1483330, _1483332), _1483336) = hAPP(hAPP(_1483330, _1483334), _1483338))], (19461 ^ _778908) ^ [_1114062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1114062)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114062), c_Int_OPls)))], (2704 ^ _778908) ^ [_819892, _819894] : [_819894 = _819892, -(c_Nitpick_Oone__frac(_819894) = c_Nitpick_Oone__frac(_819892))], (31187 ^ _778908) ^ [_1339160, _1339162, _1339164, _1339166] : [hAPP(hAPP(c_COMBC(_1339160, tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_fun(_1339162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339162, tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_fun(_1339162, tc_HOL_Obool)), _1339160), c_COMBC(_1339162, tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339162, tc_prod(_1339160, _1339162)), tc_fun(_1339162, tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool)), _1339160), hAPP(c_COMBB(tc_prod(_1339160, _1339162), tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool), _1339162), c_member(tc_prod(_1339160, _1339162)))), c_Product__Type_OPair(_1339160, _1339162)))), _1339164) = hAPP(hAPP(c_COMBC(_1339160, tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_fun(_1339162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339162, tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_fun(_1339162, tc_HOL_Obool)), _1339160), c_COMBC(_1339162, tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339162, tc_prod(_1339160, _1339162)), tc_fun(_1339162, tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool)), _1339160), hAPP(c_COMBB(tc_prod(_1339160, _1339162), tc_fun(tc_fun(tc_prod(_1339160, _1339162), tc_HOL_Obool), tc_HOL_Obool), _1339162), c_member(tc_prod(_1339160, _1339162)))), c_Product__Type_OPair(_1339160, _1339162)))), _1339166), -(_1339164 = _1339166)], (18843 ^ _778908) ^ [_1103613, _1103615] : [c_Int_OBit1(_1103613) = c_Int_OBit1(_1103615), -(_1103613 = _1103615)], (41141 ^ _778908) ^ [_1560370, _1560372] : [-(hAPP(c_Set_OCollect(_1560370), hAPP(c_fequal, _1560372)) = hAPP(hAPP(c_Set_Oinsert(_1560370), _1560372), c_Orderings_Obot__class_Obot(tc_fun(_1560370, tc_HOL_Obool))))], (50610 ^ _778908) ^ [_1795179, _1795181] : [class_Orderings_Olinorder(_1795179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795179), _1795181)), 50617 ^ _778908 : [(50622 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1795179), c_List_Olinorder__class_Osorted__list__of__set(_1795179, _1795181))))], (50620 ^ _778908) ^ [] : [-(c_List_Olinorder__class_Osorted(_1795179, c_List_Olinorder__class_Osorted__list__of__set(_1795179, _1795181)))], (50618 ^ _778908) ^ [] : [-(hAPP(c_List_Oset(_1795179), c_List_Olinorder__class_Osorted__list__of__set(_1795179, _1795181)) = _1795181)]]], (43600 ^ _778908) ^ [_1628159, _1628161, _1628163, _1628165] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628159, _1628159)), hAPP(hAPP(c_Product__Type_OPair(_1628159, _1628159), _1628161), _1628163)), c_Transitive__Closure_Ortrancl(_1628159, hAPP(c_Relation_Oconverse(_1628159, _1628159), _1628165)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628159, _1628159)), hAPP(hAPP(c_Product__Type_OPair(_1628159, _1628159), _1628163), _1628161)), c_Transitive__Closure_Ortrancl(_1628159, _1628165))))], (14029 ^ _778908) ^ [_1016358, _1016360, _1016362] : [class_Divides_Osemiring__div(_1016358), -(c_Divides_Odiv__class_Omod(_1016358, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016358), _1016360), _1016362), _1016362) = c_Groups_Ozero__class_Ozero(_1016358))], (48263 ^ _778908) ^ [_1742229, _1742231, _1742233] : [hAPP(hAPP(c_List_Oappend(_1742229), _1742231), _1742233) = _1742233, -(_1742231 = c_List_Olist_ONil(_1742229))], (29582 ^ _778908) ^ [_1307982, _1307984] : [class_Finite__Set_Ofinite(_1307982), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307982), _1307984)))], (50843 ^ _778908) ^ [_1800748, _1800750] : [hAPP(c_List_Orev(_1800748), _1800750) = c_List_Olist_ONil(_1800748), -(_1800750 = c_List_Olist_ONil(_1800748))], (27564 ^ _778908) ^ [_1266965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266965)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266965) = 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, _1266965))))], (35114 ^ _778908) ^ [_1423614, _1423616, _1423618, _1423620] : [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), _1423614), _1423616)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1423618), _1423620))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423614), _1423620) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1423618), _1423616))], (28317 ^ _778908) ^ [_1281762, _1281764, _1281766] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281762, tc_HOL_Obool)), _1281764), _1281766) = _1281766, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281762, tc_HOL_Obool)), _1281764), _1281766)))], (41058 ^ _778908) ^ [_1558686] : [class_Lattices_Osemilattice__inf(_1558686), -(c_Finite__Set_Ofun__left__comm__idem(_1558686, _1558686, c_Lattices_Osemilattice__inf__class_Oinf(_1558686)))], (7126 ^ _778908) ^ [_898068, _898070, _898072, _898074] : [class_Groups_Oab__semigroup__add(_898068), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898068), _898070), _898072)), _898074) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898068), _898070), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898068), _898072), _898074)))], (35647 ^ _778908) ^ [_1435822, _1435824, _1435826, _1435828, _1435830, _1435832] : [class_Groups_Ocomm__monoid__add(_1435822), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435824), _1435826)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435828), _1435830)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(_1435824, _1435828), _1435822), _1435832), c_Sum__Type_OPlus(_1435824, _1435828, _1435826, _1435830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1435822), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1435824, _1435822), hAPP(c_Fun_Ocomp(tc_sum(_1435824, _1435828), _1435822, _1435824, _1435832), c_Sum__Type_OInl(_1435824, _1435828))), _1435826)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1435828, _1435822), hAPP(c_Fun_Ocomp(tc_sum(_1435824, _1435828), _1435822, _1435828, _1435832), c_Sum__Type_OInr(_1435828, _1435824))), _1435830)))], (16167 ^ _778908) ^ [_1055946, _1055948, _1055950] : [hBOOL(hAPP(_1055946, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055948), _1055950))), 16170 ^ _778908 : [(16177 ^ _778908) ^ [_1056137] : [_1055948 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1055950), _1056137), -(hBOOL(hAPP(_1055946, _1056137)))], (16171 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1055948), _1055950)), -(hBOOL(hAPP(_1055946, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (38986 ^ _778908) ^ [_1510516, _1510518, _1510520, _1510522, _1510524] : [c_Fun_Oinj__on(_1510516, _1510518, _1510520, c_Orderings_Otop__class_Otop(tc_fun(_1510516, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1510516, _1510518, _1510520), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510516, tc_HOL_Obool)), _1510522), _1510524)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510518, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510516, _1510518, _1510520), _1510522)), hAPP(c_Set_Oimage(_1510516, _1510518, _1510520), _1510524)))], (47990 ^ _778908) ^ [_1735565, _1735567, _1735569, _1735571, _1735573] : [class_Orderings_Olinorder(_1735565), hBOOL(hAPP(hAPP(c_member(_1735565), hAPP(_1735567, _1735569)), hAPP(c_Set_Oimage(_1735571, _1735565, _1735567), hAPP(c_List_Oset(_1735571), _1735573)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1735571, _1735565, _1735567, _1735569, _1735573) = _1735573)], (7224 ^ _778908) ^ [_899840, _899842] : [c_Com_Ovname_OGlb(_899840) = c_Com_Ovname_OGlb(_899842), -(_899840 = _899842)], (25149 ^ _778908) ^ [_1221073, _1221075] : [-(c_HOL_OThe(_1221073, hAPP(c_fequal, _1221075)) = _1221075)], (25015 ^ _778908) ^ [_1217664, _1217666] : [-(c_Nitpick_Ouminus__frac(_1217664, _1217666) = c_Nitpick_OAbs__Frac(_1217664, 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(_1217664), _1217666))), hAPP(c_Nitpick_Odenom(_1217664), _1217666))))], (47874 ^ _778908) ^ [_1732977, _1732979, _1732981, _1732983, _1732985, _1732987, _1732989] : [-(hAPP(hAPP(c_List_Ozip(_1732977, _1732979), hAPP(hAPP(c_List_Olist__update(_1732977, _1732981), _1732983), _1732985)), hAPP(hAPP(c_List_Olist__update(_1732979, _1732987), _1732983), _1732989)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1732977, _1732979), hAPP(hAPP(c_List_Ozip(_1732977, _1732979), _1732981), _1732987)), _1732983), hAPP(hAPP(c_Product__Type_OPair(_1732977, _1732979), _1732985), _1732989)))], (41231 ^ _778908) ^ [_1562269, _1562271, _1562273, _1562275] : [-(hAPP(c_Set_Ovimage(_1562269, _1562271, _1562273), hAPP(c_Set_OCollect(_1562271), _1562275)) = hAPP(c_Set_OCollect(_1562269), hAPP(hAPP(c_COMBB(_1562271, tc_HOL_Obool, _1562269), _1562275), _1562273)))], (47429 ^ _778908) ^ [_1722392, _1722394] : [-(c_List_Oremove1(_1722392, _1722394, c_List_Olist_ONil(_1722392)) = c_List_Olist_ONil(_1722392))], (32855 ^ _778908) ^ [_1377282, _1377284] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1377282), _1377284)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1377284, _1377282) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (1502 ^ _778908) ^ [_800557, _800559] : [-(class_Rings_Oordered__cancel__semiring(_800557)), _800559 = _800557, class_Rings_Oordered__cancel__semiring(_800559)], (5350 ^ _778908) ^ [_861639, _861641, _861643, _861645] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861645, _861641) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861643, _861639)), _861645 = _861643, _861641 = _861639], (51217 ^ _778908) ^ [_1809224, _1809226] : [class_Groups_Ouminus(_1809224), -(class_Groups_Ouminus(tc_fun(_1809226, _1809224)))], (41235 ^ _778908) ^ [_1562446, _1562448, _1562450, _1562452] : [-(hAPP(c_Set_OCollect(tc_prod(_1562446, _1562448)), hAPP(c_Product__Type_Oprod_Oprod__case(_1562446, _1562448, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1562446, tc_fun(_1562448, tc_HOL_Obool), tc_fun(_1562448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1562448, tc_HOL_Obool), tc_fun(_1562448, tc_HOL_Obool)), _1562446), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1562448)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562446), c_fconj), _1562450))), _1562452))) = hAPP(hAPP(c_Product__Type_OSigma(_1562446, _1562448), hAPP(c_Set_OCollect(_1562446), _1562450)), hAPP(hAPP(c_COMBB(tc_fun(_1562448, tc_HOL_Obool), tc_fun(_1562448, tc_HOL_Obool), _1562446), c_Set_OCollect(_1562448)), _1562452)))], (39470 ^ _778908) ^ [_1521316, _1521318, _1521320, _1521322, _1521324] : [hBOOL(hAPP(hAPP(c_member(_1521316), _1521318), hAPP(c_Set_Ovimage(_1521316, _1521320, _1521322), _1521324))), -(hBOOL(hAPP(hAPP(c_member(_1521320), hAPP(_1521322, _1521318)), _1521324)))], (22498 ^ _778908) ^ [_1168697, _1168699] : [class_Rings_Osemiring__1(_1168697), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168697), _1168699) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1168697, hAPP(hAPP(c_COMBC(_1168697, _1168697, _1168697), c_Groups_Oplus__class_Oplus(_1168697)), c_Groups_Oone__class_Oone(_1168697)), _1168699, c_Groups_Ozero__class_Ozero(_1168697)))], (19793 ^ _778908) ^ [_1119894, _1119896, _1119898] : [class_Rings_Olinordered__semidom(_1119894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119894), hAPP(hAPP(c_Power_Opower__class_Opower(_1119894), _1119896), 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(_1119894), _1119898), 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(_1119894), c_Groups_Ozero__class_Ozero(_1119894)), _1119898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119894), _1119896), _1119898)))], (45330 ^ _778908) ^ [_1670362, _1670364, _1670366, _1670368] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670362, tc_fun(_1670364, tc_HOL_Obool)), _1670366), _1670368) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670364, tc_HOL_Obool), hAPP(c_Set_Oimage(_1670362, tc_fun(_1670364, tc_HOL_Obool), _1670368), _1670366)))], (3390 ^ _778908) ^ [_830997, _830999] : [_830999 = _830997, -(c_Com_Ovname_OLoc(_830999) = c_Com_Ovname_OLoc(_830997))], (30596 ^ _778908) ^ [_1327067, _1327069] : [30597 ^ _778908 : [(30600 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1327067), _1327069)))], (30598 ^ _778908) ^ [] : [_1327069 = c_Orderings_Obot__class_Obot(tc_fun(_1327067, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1327067), _1327069) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (222 ^ _778908) ^ [_782113, _782115, _782117, _782119] : [-(c_Nitpick_Orefl_H(_782117, _782113)), c_Nitpick_Orefl_H(_782119, _782115), _782119 = _782117, _782115 = _782113], (51637 ^ _778908) ^ [_1813329, _1813331] : [hBOOL(hAPP(hAPP(c_fequal, _1813329), _1813331)), -(_1813329 = _1813331)], (27348 ^ _778908) ^ [_1262396, _1262398, _1262400, _1262402] : [class_Groups_Ocomm__monoid__add(_1262396), 27351 ^ _778908 : [(27358 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1262398), _1262400))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1262396), _1262402), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1262400), hAPP(c_Nat_OSuc, _1262398))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1262396), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1262396), _1262402), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1262400), _1262398))), hAPP(_1262402, _1262398)))], (27352 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1262398), _1262400)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1262396), _1262402), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1262400), hAPP(c_Nat_OSuc, _1262398))) = c_Groups_Ozero__class_Ozero(_1262396))]]], (51251 ^ _778908) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (36188 ^ _778908) ^ [_1449343, _1449345, _1449347, _1449349, _1449351] : [hAPP(c_Relation_OImage(_1449343, _1449343, _1449345), hAPP(hAPP(c_Set_Oinsert(_1449343), _1449347), c_Orderings_Obot__class_Obot(tc_fun(_1449343, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1449343, _1449343, _1449345), hAPP(hAPP(c_Set_Oinsert(_1449343), _1449349), c_Orderings_Obot__class_Obot(tc_fun(_1449343, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1449343, _1449351, _1449345), hBOOL(hAPP(hAPP(c_member(_1449343), _1449349), _1449351)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1449343, _1449343)), hAPP(hAPP(c_Product__Type_OPair(_1449343, _1449343), _1449347), _1449349)), _1449345)))], (24751 ^ _778908) ^ [_1212329, _1212331, _1212333] : [class_Int_Onumber(_1212329), class_Orderings_Oord(_1212329), 24758 ^ _778908 : [(24765 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212329), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212331)), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212333)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212329), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212331)), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212333)) = hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212331))], (24759 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212329), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212331)), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212333))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212329), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212331)), hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212333)) = hAPP(c_Int_Onumber__class_Onumber__of(_1212329), _1212333))]]], (13392 ^ _778908) ^ [_1004556, _1004558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1004558)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1004556), _1004558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1004556)), hAPP(c_Int_Onat, _1004558)))], (46563 ^ _778908) ^ [_1698407, _1698409, _1698411] : [-(hAPP(hAPP(c_List_Ozip(_1698407, _1698409), hAPP(hAPP(c_List_Omap(tc_prod(_1698407, _1698409), _1698407), c_Product__Type_Ofst(_1698407, _1698409)), _1698411)), hAPP(hAPP(c_List_Omap(tc_prod(_1698407, _1698409), _1698409), c_Product__Type_Osnd(_1698407, _1698409)), _1698411)) = _1698411)], (22460 ^ _778908) ^ [_1167890, _1167892, _1167894] : [class_Int_Onumber__ring(_1167890), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1167890), _1167892), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1167894))) = hAPP(hAPP(c_HOL_OLet(_1167890, _1167890), hAPP(hAPP(c_Power_Opower__class_Opower(_1167890), _1167892), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1167894))), hAPP(hAPP(c_COMBS(_1167890, _1167890, _1167890), c_Groups_Otimes__class_Otimes(_1167890)), c_COMBI(_1167890))))], (8172 ^ _778908) ^ [_915753, _915755, _915757, _915759] : [hAPP(c_Sum__Type_OInl(_915753, _915755), _915757) = hAPP(c_Sum__Type_OInr(_915755, _915753), _915759)], (39592 ^ _778908) ^ [_1524121, _1524123, _1524125, _1524127] : [-(hAPP(c_Set_Ovimage(_1524121, _1524123, _1524125), _1524127) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524123, tc_fun(_1524121, tc_HOL_Obool)), _1524127), hAPP(hAPP(c_COMBB(tc_fun(_1524123, tc_HOL_Obool), tc_fun(_1524121, tc_HOL_Obool), _1524123), c_Set_Ovimage(_1524121, _1524123, _1524125)), hAPP(hAPP(c_COMBC(_1524123, tc_fun(_1524123, tc_HOL_Obool), tc_fun(_1524123, tc_HOL_Obool)), c_Set_Oinsert(_1524123)), c_Orderings_Obot__class_Obot(tc_fun(_1524123, tc_HOL_Obool))))))], (26107 ^ _778908) ^ [_1238151, _1238153, _1238155, _1238157, _1238159] : [class_Rings_Osemiring__0(_1238151), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238151), _1238153), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238155, _1238151), _1238157), _1238159)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1238155, _1238151), hAPP(hAPP(c_COMBB(_1238151, _1238151, _1238155), hAPP(c_Groups_Otimes__class_Otimes(_1238151), _1238153)), _1238157)), _1238159))], (51261 ^ _778908) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (4026 ^ _778908) ^ [_841013, _841015] : [_841015 = _841013, -(c_Rings_Odvd__class_Odvd(_841015) = c_Rings_Odvd__class_Odvd(_841013))], (24853 ^ _778908) ^ [_1214348] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1214348)) = _1214348)], (7959 ^ _778908) ^ [_911891, _911893, _911895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911891), _911893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911891), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911895), _911893))))], (29213 ^ _778908) ^ [_1300924] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1300924))))], (35102 ^ _778908) ^ [_1423377, _1423379] : [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), _1423377), _1423379)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1423377), _1423379)))], (51275 ^ _778908) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (42816 ^ _778908) ^ [_1609037, _1609039, _1609041, _1609043] : [class_Groups_Ocomm__monoid__mult(_1609037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609039), _1609041)), 42826 ^ _778908 : [(42829 ^ _778908) ^ [] : [hAPP(_1609043, 42825 ^ [_1609037, _1609039, _1609041, _1609043]) = c_Groups_Oone__class_Oone(_1609037)], (42827 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609039), 42825 ^ [_1609037, _1609039, _1609041, _1609043]), _1609041)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1609037, _1609039, c_Groups_Otimes__class_Otimes(_1609037)), _1609043), c_Groups_Oone__class_Oone(_1609037)), _1609041) = c_Groups_Oone__class_Oone(_1609037))], (49317 ^ _778908) ^ [_1768095, _1768097, _1768099] : [class_Groups_Omonoid__add(_1768095), -(hAPP(c_List_Ofoldl(_1768095, _1768095, c_Groups_Oplus__class_Oplus(_1768095), _1768097), _1768099) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1768095), _1768097), c_List_Ofoldr(_1768095, _1768095, c_Groups_Oplus__class_Oplus(_1768095), _1768099, c_Groups_Ozero__class_Ozero(_1768095))))], (31066 ^ _778908) ^ [_1336616, _1336618, _1336620, _1336622, _1336624] : [hBOOL(hAPP(hAPP(c_member(_1336616), _1336618), hAPP(c_Set_Oimage(_1336620, _1336616, _1336622), _1336624))), 31070 ^ _778908 : [(31073 ^ _778908) ^ [] : [-(_1336618 = hAPP(_1336622, 31069 ^ [_1336616, _1336618, _1336620, _1336622, _1336624]))], (31071 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1336620), 31069 ^ [_1336616, _1336618, _1336620, _1336622, _1336624]), _1336624)))]]], (20129 ^ _778908) ^ [_1126106, _1126108] : [class_Fields_Olinordered__field__inverse__zero(_1126106), class_Int_Onumber__ring(_1126106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126106), c_Groups_Ozero__class_Ozero(_1126106)), _1126108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126106), c_Groups_Ozero__class_Ozero(_1126106)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126106), _1126108), hAPP(c_Int_Onumber__class_Onumber__of(_1126106), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (22900 ^ _778908) ^ [_1177127, _1177129] : [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), _1177127), _1177129))), 22903 ^ _778908 : [(22912 ^ _778908) ^ [] : [-(c_Divides_OnegDivAlg(_1177127, _1177129) = hAPP(c_Divides_Oadjust(_1177129), c_Divides_OnegDivAlg(_1177127, 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)))), _1177129)))), -(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), _1177127), _1177129)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177129), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22904 ^ _778908) ^ [] : [22905 ^ _778908 : [(22908 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177129), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22906 ^ _778908) ^ [] : [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), _1177127), _1177129)))]], -(c_Divides_OnegDivAlg(_1177127, _1177129) = 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), _1177127), _1177129)))]]], (682 ^ _778908) ^ [_789461, _789463, _789465, _789467] : [-(c_Wellfounded_OwfP(_789465, _789461)), c_Wellfounded_OwfP(_789467, _789463), _789467 = _789465, _789463 = _789461], (45923 ^ _778908) ^ [_1683296, _1683298, _1683300, _1683302, _1683304] : [-(c_Map_Omap__add(_1683296, _1683298, _1683300, c_Map_Omap__add(_1683296, _1683298, _1683302, _1683304)) = c_Map_Omap__add(_1683296, _1683298, c_Map_Omap__add(_1683296, _1683298, _1683300, _1683302), _1683304))], (49616 ^ _778908) ^ [_1775062, _1775064, _1775066] : [_1775062 = c_List_Olist_ONil(_1775064), -(c_List_Olast(_1775064, hAPP(hAPP(c_List_Oappend(_1775064), _1775066), _1775062)) = c_List_Olast(_1775064, _1775066))], (46867 ^ _778908) ^ [_1706693, _1706695, _1706697] : [hBOOL(hAPP(hAPP(c_member(_1706693), _1706695), hAPP(c_List_Oset(_1706693), _1706697))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706693)), c_List_Oremove1(_1706693, _1706695, _1706697)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706693)), _1706697)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (25797 ^ _778908) ^ [_1232035, _1232037, _1232039, _1232041] : [class_Rings_Ocomm__semiring__1(_1232035), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232035), _1232037), _1232039)), _1232041)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1232035), _1232039), _1232041)))], (42250 ^ _778908) ^ [_1595196, _1595198, _1595200, _1595202] : [hBOOL(hAPP(c_Predicate_ORangeP(_1595196, _1595198, _1595200), _1595202)), -(hBOOL(hAPP(hAPP(_1595200, 42253 ^ [_1595196, _1595198, _1595200, _1595202]), _1595202)))], (39860 ^ _778908) ^ [_1530719, _1530721, _1530723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530719, _1530719), tc_HOL_Obool)), _1530721), _1530723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530719, tc_HOL_Obool)), c_Wellfounded_Oacc(_1530719, _1530723)), c_Wellfounded_Oacc(_1530719, _1530721))))], (51299 ^ _778908) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (43715 ^ _778908) ^ [_1631252, _1631254, _1631256, _1631258] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1631252, _1631254), tc_fun(_1631252, _1631254)), _1631256), c_Fun_Ocomp(_1631254, _1631254, _1631252, _1631258)) = c_Fun_Ocomp(_1631254, _1631254, _1631252, hAPP(hAPP(c_Nat_Ocompow(_1631254, _1631254), _1631256), _1631258)))], (49532 ^ _778908) ^ [_1773104, _1773106, _1773108] : [49534 ^ _778908 : [(49537 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1773104), 49533 ^ [_1773104, _1773106, _1773108]), _1773108))], (49535 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773104), 49533 ^ [_1773104, _1773106, _1773108]), hAPP(c_List_Oset(_1773104), _1773106))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1773104)), _1773106), c_List_Olists(_1773104, _1773108))))], (29839 ^ _778908) ^ [_1312862, _1312864, _1312866, _1312868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312862), _1312864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1312866), hAPP(c_Set_Oimage(_1312862, _1312866, _1312868), _1312864))), hAPP(c_Finite__Set_Ocard(_1312862), _1312864))))], (47539 ^ _778908) ^ [_1724399, _1724401, _1724403] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1724399))), -(c_List_Osublist(_1724401, hAPP(hAPP(c_List_Olist_OCons(_1724401), _1724403), c_List_Olist_ONil(_1724401)), _1724399) = c_List_Olist_ONil(_1724401))], (40676 ^ _778908) ^ [_1551606, _1551608, _1551610] : [class_Lattices_Osemilattice__inf(_1551606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551606), _1551608)), -(_1551608 = c_Orderings_Obot__class_Obot(tc_fun(_1551606, tc_HOL_Obool))), 40687 ^ _778908 : [(40688 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551606), _1551610), hAPP(c_Finite__Set_Ofold1(_1551606, c_Lattices_Osemilattice__inf__class_Oinf(_1551606)), _1551608))), 40691 ^ _778908 : [(40692 ^ _778908) ^ [_1551899] : [hBOOL(hAPP(hAPP(c_member(_1551606), _1551899), _1551608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551606), _1551610), _1551899)))]]], (40698 ^ _778908) ^ [] : [40700 ^ _778908 : [(40703 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551606), _1551610), 40699 ^ [_1551606, _1551608, _1551610]))], (40701 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551606), 40699 ^ [_1551606, _1551608, _1551610]), _1551608)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551606), _1551610), hAPP(c_Finite__Set_Ofold1(_1551606, c_Lattices_Osemilattice__inf__class_Oinf(_1551606)), _1551608))))]]], (23591 ^ _778908) ^ [_1189866, _1189868, _1189870, _1189872] : [_1189866 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189868), _1189870)), _1189872), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189866, _1189868), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189870), _1189872)))), 23598 ^ _778908 : [(23601 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189872), _1189868))], (23599 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189868)))]], 23606 ^ _778908 : [(23609 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189868), _1189872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1189872), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23607 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189868))]]], (17939 ^ _778908) ^ [_1089255, _1089257] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089255))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089255)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089257)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35225 ^ _778908) ^ [_1426493, _1426495, _1426497, _1426499] : [-(hAPP(c_Relation_OField(_1426493), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1426493, _1426493)), hAPP(hAPP(c_Product__Type_OPair(_1426493, _1426493), _1426495), _1426497)), _1426499)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426493, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1426493), _1426495), hAPP(hAPP(c_Set_Oinsert(_1426493), _1426497), c_Orderings_Obot__class_Obot(tc_fun(_1426493, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1426493), _1426499)))], (20279 ^ _778908) ^ [_1129128] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1129128)))], (19353 ^ _778908) ^ [_1112230] : [c_Int_OPls = _1112230, -(c_Int_OPls = c_Int_OBit0(_1112230))], (39690 ^ _778908) ^ [_1526536, _1526538, _1526540, _1526542, _1526544] : [hBOOL(hAPP(hAPP(c_member(_1526536), _1526538), hAPP(c_Relation_OImage(_1526540, _1526536, _1526542), _1526544))), 39694 ^ _778908 : [(39697 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526540), 39693 ^ [_1526536, _1526538, _1526540, _1526542, _1526544]), _1526544)))], (39695 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526540, _1526536)), hAPP(hAPP(c_Product__Type_OPair(_1526540, _1526536), 39693 ^ [_1526536, _1526538, _1526540, _1526542, _1526544]), _1526538)), _1526542)))]]], (15054 ^ _778908) ^ [_1034284, _1034286, _1034288, _1034290] : [class_Divides_Osemiring__div(_1034284), -(_1034286 = c_Groups_Ozero__class_Ozero(_1034284)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034284), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034284), _1034288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034284), _1034290), _1034286))), _1034286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034284), _1034290), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1034284), _1034288), _1034286)))], (46988 ^ _778908) ^ [_1711379, _1711381, _1711383] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1711379, tc_HOL_Obool)), hAPP(c_List_Oset(_1711379), _1711381)), hAPP(c_List_Oset(_1711379), hAPP(hAPP(c_List_Olist_OCons(_1711379), _1711383), _1711381)))))], (1974 ^ _778908) ^ [_807849, _807851, _807853, _807855, _807857, _807859, _807861, _807863, _807865, _807867, _807869, _807871, _807873, _807875, _807877, _807879, _807881, _807883, _807885, _807887] : [-(c_Com_Ocom_Ocom__case(_807887, _807883, _807879, _807875, _807871, _807867, _807863, _807859, _807855, _807851) = c_Com_Ocom_Ocom__case(_807885, _807881, _807877, _807873, _807869, _807865, _807861, _807857, _807853, _807849)), _807887 = _807885, _807883 = _807881, _807879 = _807877, _807875 = _807873, _807871 = _807869, _807867 = _807865, _807863 = _807861, _807859 = _807857, _807855 = _807853, _807851 = _807849], (24909 ^ _778908) ^ [_1215329, _1215331] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1215329), _1215331) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1215329)), hAPP(c_Code__Numeral_Onat__of, _1215331))))], (12836 ^ _778908) ^ [_994899, _994901, _994903, _994905] : [class_Rings_Olinordered__semiring(_994899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994899), _994901), _994903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994899), _994901), _994905))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994899), c_Groups_Ozero__class_Ozero(_994899)), _994901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994899), _994903), _994905)))], (24911 ^ _778908) ^ [_1215375, _1215377] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1215375), _1215377) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1215375)), hAPP(c_Code__Numeral_Onat__of, _1215377))))], (19347 ^ _778908) ^ [_1112155] : [c_Int_OPls = c_Int_OBit0(_1112155), -(c_Int_OPls = _1112155)], (29797 ^ _778908) ^ [_1312027, _1312029, _1312031, _1312033, _1312035] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312027), hAPP(c_Set_Oimage(_1312029, _1312027, _1312031), c_Orderings_Otop__class_Otop(tc_fun(_1312029, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1312033), hAPP(c_Set_Oimage(_1312029, _1312033, hAPP(hAPP(c_COMBB(_1312027, _1312033, _1312029), _1312035), _1312031)), c_Orderings_Otop__class_Otop(tc_fun(_1312029, tc_HOL_Obool))))))], (4558 ^ _778908) ^ [_849451, _849453] : [_849453 = _849451, -(c_HOL_OEx(_849453) = c_HOL_OEx(_849451))], (19107 ^ _778908) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (35126 ^ _778908) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (24937 ^ _778908) ^ [_1215885, _1215887, _1215889, _1215891, _1215893, _1215895, _1215897, _1215899, _1215901] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1215885, _1215887, _1215889, _1215891), hAPP(hAPP(c_Product__Type_Oscomp(_1215885, _1215893, _1215895, tc_prod(_1215887, _1215889)), _1215897), _1215899)), _1215901) = hAPP(hAPP(c_Product__Type_Oscomp(_1215885, _1215893, _1215895, _1215891), _1215897), hAPP(hAPP(c_COMBC(_1215893, tc_fun(_1215887, tc_fun(_1215889, _1215891)), tc_fun(_1215895, _1215891)), hAPP(hAPP(c_COMBB(tc_fun(_1215895, tc_prod(_1215887, _1215889)), tc_fun(tc_fun(_1215887, tc_fun(_1215889, _1215891)), tc_fun(_1215895, _1215891)), _1215893), c_Product__Type_Oscomp(_1215895, _1215887, _1215889, _1215891)), _1215899)), _1215901)))], (950 ^ _778908) ^ [_793473, _793475, _793477, _793479, _793481, _793483] : [-(c_Relation_Orefl__on(_793481, _793477, _793473)), c_Relation_Orefl__on(_793483, _793479, _793475), _793483 = _793481, _793479 = _793477, _793475 = _793473], (2654 ^ _778908) ^ [_819123, _819125, _819127, _819129, _819131, _819133, _819135, _819137] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_819137, _819133, _819129, _819125) = c_New__Random__Sequence_Opos__not__random__dseq(_819135, _819131, _819127, _819123)), _819137 = _819135, _819133 = _819131, _819129 = _819127, _819125 = _819123], (19001 ^ _778908) ^ [_1106228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106228), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1106228)), c_Int_OMin)))], (22388 ^ _778908) ^ [_1166689, _1166691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166689), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166691)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1166689)) = 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), _1166691), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166689)))), 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)))], (15684 ^ _778908) ^ [_1045970, _1045972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045970), _1045972)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1045972, _1045970) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045972), _1045970), _1045970))], (41056 ^ _778908) ^ [_1558657] : [-(c_Finite__Set_Ofun__left__comm__idem(_1558657, tc_fun(_1558657, tc_HOL_Obool), c_Set_Oinsert(_1558657)))], (6329 ^ _778908) ^ [_880931, _880933, _880935, _880937] : [c_Natural_Oevaln(_880931, _880933, _880935, _880937), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_880931), _880933), _880937)))], (46183 ^ _778908) ^ [_1689743, _1689745, _1689747, _1689749] : [hAPP(c_List_Oset(_1689743), _1689745) = c_Map_Odom(_1689743, _1689747, _1689749), -(c_Map_Omap__of(_1689743, _1689747, hAPP(hAPP(c_List_Omap(_1689743, tc_prod(_1689743, _1689747)), hAPP(hAPP(c_COMBS(_1689743, _1689747, tc_prod(_1689743, _1689747)), c_Product__Type_OPair(_1689743, _1689747)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1689747), _1689747, _1689743), c_Option_Othe(_1689747)), _1689749))), _1689745)) = _1689749)], (24105 ^ _778908) ^ [_1199903, _1199905] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199903, tc_HOL_Obool)), _1199905), _1199905)))], (6460 ^ _778908) ^ [_883256, _883258, _883260, _883262, _883264] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_883256, _883258), _883260, _883262, _883264)), 6461 ^ _778908 : [(6462 ^ _778908) ^ [_883311] : [c_Natural_Oevaln(_883256, _883260, _883262, _883311), c_Natural_Oevaln(_883258, _883311, _883262, _883264)]]], (42297 ^ _778908) ^ [_1596127, _1596129] : [c_Wellfounded_OwfP(_1596127, _1596129), 42300 ^ _778908 : [(42301 ^ _778908) ^ [_1596191] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1596127, _1596129), _1596191)))]]], (19419 ^ _778908) ^ [_1113319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113319), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113319)), c_Int_OPls)))], (50879 ^ _778908) ^ [_1801425, _1801427] : [-(hAPP(c_List_Orev(_1801425), _1801427) = hAPP(c_List_Ofoldl(tc_List_Olist(_1801425), _1801425, hAPP(c_COMBC(_1801425, tc_List_Olist(_1801425), tc_List_Olist(_1801425)), c_List_Olist_OCons(_1801425)), c_List_Olist_ONil(_1801425)), _1801427))], (13981 ^ _778908) ^ [_1015354, _1015356, _1015358, _1015360] : [class_Divides_Osemiring__div(_1015354), -(c_Divides_Odiv__class_Omod(_1015354, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015354), _1015356), _1015358), _1015360) = c_Divides_Odiv__class_Omod(_1015354, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015354), c_Divides_Odiv__class_Omod(_1015354, _1015356, _1015360)), c_Divides_Odiv__class_Omod(_1015354, _1015358, _1015360)), _1015360))], (51587 ^ _778908) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (24535 ^ _778908) ^ [_1208141, _1208143, _1208145, _1208147, _1208149] : [class_Orderings_Olinorder(_1208141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208141), _1208143), _1208145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208141), _1208147), _1208149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208141), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208141), _1208143), _1208147)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208141), _1208145), _1208149))))], (34345 ^ _778908) ^ [_1407106, _1407108, _1407110, _1407112] : [class_Fields_Olinordered__field(_1407106), -(hAPP(c_Groups_Oabs__class_Oabs(_1407106), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407108, _1407106), _1407110), _1407112)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407108, _1407106), hAPP(hAPP(c_COMBB(_1407106, _1407106, _1407108), c_Groups_Oabs__class_Oabs(_1407106)), _1407110)), _1407112))], (19377 ^ _778908) ^ [_1112604] : [-(c_Int_OBit0(_1112604) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112604), _1112604))], (35452 ^ _778908) ^ [_1431525, _1431527] : [hAPP(c_Set_OPow(_1431525), _1431527) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1431525, tc_HOL_Obool), tc_HOL_Obool))], (27956 ^ _778908) ^ [_1274486, _1274488] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1274486), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1274488) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1274486, _1274488))], (19257 ^ _778908) ^ [_1110458, _1110460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110458), 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)))), _1110460))), 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)))), _1110458)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1110460), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1110458))], (34494 ^ _778908) ^ [_1409968, _1409970, _1409972] : [class_Groups_Ocomm__monoid__mult(_1409968), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409970, _1409968), _1409972), c_Orderings_Obot__class_Obot(tc_fun(_1409970, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1409968))], (31628 ^ _778908) ^ [_1349922, _1349924, _1349926, _1349928, _1349930] : [-(hBOOL(hAPP(hAPP(c_member(_1349922), _1349924), c_SetInterval_Oord_OgreaterThanLessThan(_1349922, _1349926, _1349928, _1349930)))), hBOOL(hAPP(hAPP(_1349926, _1349928), _1349924)), hBOOL(hAPP(hAPP(_1349926, _1349924), _1349930))], (35708 ^ _778908) ^ [_1437261, _1437263, _1437265, _1437267, _1437269, _1437271] : [-(hAPP(hAPP(c_Fun_Ocomp(_1437261, _1437263, _1437265, _1437267), _1437269), _1437271) = hAPP(_1437267, hAPP(_1437269, _1437271)))], (36616 ^ _778908) ^ [_1458157, _1458159, _1458161, _1458163] : [-(hBOOL(hAPP(hAPP(c_member(_1458157), _1458159), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458157, tc_HOL_Obool)), _1458161), _1458163)))), hBOOL(hAPP(hAPP(c_member(_1458157), _1458159), _1458161)), hBOOL(hAPP(hAPP(c_member(_1458157), _1458159), _1458163))], (17981 ^ _778908) ^ [_1089951] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1089951))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089951)))], (32791 ^ _778908) ^ [_1376117, _1376119] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1376117, _1376119) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376117), _1376119)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376119), _1376117)))], (34387 ^ _778908) ^ [_1408117, _1408119, _1408121, _1408123, _1408125] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1408117, _1408119), _1408121), _1408123), _1408125) = _1408121, -(hAPP(_1408121, _1408123) = _1408125)], (20013 ^ _778908) ^ [_1123883, _1123885, _1123887] : [class_Groups_Omonoid__mult(_1123883), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1123883), _1123885), 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)))), _1123887))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123883), _1123885), hAPP(hAPP(c_Power_Opower__class_Opower(_1123883), hAPP(hAPP(c_Power_Opower__class_Opower(_1123883), _1123885), _1123887)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (29504 ^ _778908) ^ [_1306407, _1306409, _1306411, _1306413, _1306415, _1306417] : [c_Typedef_Otype__definition(_1306407, _1306409, _1306411, _1306413, _1306415), -(hAPP(_1306413, hAPP(_1306411, _1306417)) = _1306417)], (41173 ^ _778908) ^ [_1561270, _1561272] : [c_Orderings_Obot__class_Obot(tc_fun(_1561270, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1561270), _1561272), 41176 ^ _778908 : [(41177 ^ _778908) ^ [_1561355] : [hBOOL(hAPP(_1561272, _1561355))]]], (18281 ^ _778908) ^ [_1094872] : [class_Rings_Osemiring__1(_1094872), c_Int_Oiszero(_1094872, c_Groups_Oone__class_Oone(_1094872))], (8047 ^ _778908) ^ [_913547, _913549] : [class_Rings_Olinordered__idom(_913547), 8050 ^ _778908 : [(8057 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913547), _913549), c_Groups_Ozero__class_Ozero(_913547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913547), _913549), _913549)), c_Groups_Ozero__class_Ozero(_913547))))], (8051 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_913547), _913549), _913549)), c_Groups_Ozero__class_Ozero(_913547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913547), _913549), c_Groups_Ozero__class_Ozero(_913547))))]]], (19365 ^ _778908) ^ [_1112398] : [_1112398 = c_Int_OPls, -(c_Int_OBit0(_1112398) = c_Int_OPls)], (31193 ^ _778908) ^ [_1339709, _1339711, _1339713, _1339715] : [_1339713 = _1339715, -(hAPP(hAPP(c_COMBC(_1339709, tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_fun(_1339711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339711, tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_fun(_1339711, tc_HOL_Obool)), _1339709), c_COMBC(_1339711, tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339711, tc_prod(_1339709, _1339711)), tc_fun(_1339711, tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool)), _1339709), hAPP(c_COMBB(tc_prod(_1339709, _1339711), tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool), _1339711), c_member(tc_prod(_1339709, _1339711)))), c_Product__Type_OPair(_1339709, _1339711)))), _1339713) = hAPP(hAPP(c_COMBC(_1339709, tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_fun(_1339711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339711, tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_fun(_1339711, tc_HOL_Obool)), _1339709), c_COMBC(_1339711, tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1339711, tc_prod(_1339709, _1339711)), tc_fun(_1339711, tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool)), _1339709), hAPP(c_COMBB(tc_prod(_1339709, _1339711), tc_fun(tc_fun(tc_prod(_1339709, _1339711), tc_HOL_Obool), tc_HOL_Obool), _1339711), c_member(tc_prod(_1339709, _1339711)))), c_Product__Type_OPair(_1339709, _1339711)))), _1339715))], (7132 ^ _778908) ^ [_898211, _898213, _898215, _898217] : [class_Groups_Ocancel__semigroup__add(_898211), 7135 ^ _778908 : [(7142 ^ _778908) ^ [] : [_898215 = _898217, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898211), _898213), _898215) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898211), _898213), _898217))], (7136 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898211), _898213), _898215) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_898211), _898213), _898217), -(_898215 = _898217)]]], (17229 ^ _778908) ^ [_1076314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076314), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1076314) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076314))], (48158 ^ _778908) ^ [_1739744, _1739746, _1739748] : [class_Groups_Omonoid__add(_1739744), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1739744), hAPP(hAPP(c_List_Oappend(_1739744), _1739746), _1739748)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1739744), hAPP(c_List_Omonoid__add__class_Olistsum(_1739744), _1739746)), hAPP(c_List_Omonoid__add__class_Olistsum(_1739744), _1739748)))], (1132 ^ _778908) ^ [_795932, _795934] : [-(class_Rings_Olinordered__idom(_795932)), _795934 = _795932, class_Rings_Olinordered__idom(_795934)], (45312 ^ _778908) ^ [_1669741, _1669743, _1669745] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1669741, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669741, tc_HOL_Obool), _1669743)), _1669745) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1669741, tc_HOL_Obool), tc_fun(_1669741, tc_HOL_Obool)), _1669743), hAPP(hAPP(c_COMBC(tc_fun(_1669741, tc_HOL_Obool), tc_fun(_1669741, tc_HOL_Obool), tc_fun(_1669741, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1669741, tc_HOL_Obool))), _1669745)))], (51627 ^ _778908) ^ [_1813102, _1813104] : [-(hAPP(c_COMBI(_1813102), _1813104) = _1813104)], (36976 ^ _778908) ^ [_1466469, _1466471, _1466473, _1466475] : [-(hBOOL(hAPP(hAPP(c_member(_1466469), _1466471), _1466473))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466469, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1466469), _1466471), _1466475)), _1466473) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466469, tc_HOL_Obool)), _1466475), _1466473))], (43685 ^ _778908) ^ [_1630460, _1630462, _1630464] : [43686 ^ _778908 : [(43687 ^ _778908) ^ [_1630536] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630460, _1630460)), _1630462), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630460, _1630460), tc_HOL_Obool), _1630536), _1630464)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630460, _1630460)), _1630462), c_Transitive__Closure_Ortrancl(_1630460, _1630464))))], (51159 ^ _778908) ^ [_1808463, _1808465] : [class_Lattices_Odistrib__lattice(_1808463), -(class_Lattices_Odistrib__lattice(tc_fun(_1808465, _1808463)))], (40228 ^ _778908) ^ [_1540561, _1540563, _1540565, _1540567] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1540561, _1540563)), hAPP(hAPP(c_Product__Type_OSigma(_1540561, _1540563), _1540565), hAPP(c_COMBK(tc_fun(_1540563, tc_HOL_Obool), _1540561), _1540567)))), -(_1540565 = c_Orderings_Obot__class_Obot(tc_fun(_1540561, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540563), _1540567)))], (11813 ^ _778908) ^ [_976726, _976728] : [class_Groups_Olinordered__ab__group__add(_976726), 11816 ^ _778908 : [(11823 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976726), c_Groups_Ozero__class_Ozero(_976726)), _976728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976726), c_Groups_Ozero__class_Ozero(_976726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976726), _976728), _976728))))], (11817 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976726), c_Groups_Ozero__class_Ozero(_976726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976726), _976728), _976728))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976726), c_Groups_Ozero__class_Ozero(_976726)), _976728)))]]], (13102 ^ _778908) ^ [_999881, _999883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _999881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _999883)), -(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), _999883), _999881))))], (24921 ^ _778908) ^ [_1215574, _1215576, _1215578] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1215574), _1215576), _1215578) = c_Nitpick_OAbs__Frac(_1215574, c_Nitpick_Onorm__frac(_1215576, _1215578)))], (32333 ^ _778908) ^ [_1366798, _1366800] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1366798), 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)))), _1366800)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1366798), _1366800)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1366800), _1366798)))], (14738 ^ _778908) ^ [_1028974, _1028976, _1028978] : [class_Divides_Osemiring__div(_1028974), -(_1028976 = c_Groups_Ozero__class_Ozero(_1028974)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028974), _1028978), _1028976)), _1028976) = _1028978)], (36059 ^ _778908) ^ [_1446454, _1446456, _1446458] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446454), hAPP(hAPP(c_Set_Oinsert(_1446454), _1446456), c_Orderings_Obot__class_Obot(tc_fun(_1446454, tc_HOL_Obool)))), _1446458) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1446454, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1446454, _1446454, _1446458), hAPP(hAPP(c_Set_Oinsert(_1446454), _1446456), c_Orderings_Obot__class_Obot(tc_fun(_1446454, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446454, tc_HOL_Obool), tc_HOL_Obool))))], (10844 ^ _778908) ^ [_960878, _960880] : [-(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), _960878), _960880)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _960878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _960880))], (29960 ^ _778908) ^ [_1315260, _1315262, _1315264, _1315266, _1315268] : [-(hAPP(hAPP(c_Set_Oinsert(_1315260), _1315262), hAPP(hAPP(c_Set_Oinsert(_1315260), _1315264), c_Orderings_Obot__class_Obot(tc_fun(_1315260, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1315260), _1315266), hAPP(hAPP(c_Set_Oinsert(_1315260), _1315268), c_Orderings_Obot__class_Obot(tc_fun(_1315260, tc_HOL_Obool))))), 29961 ^ _778908 : [(29968 ^ _778908) ^ [] : [_1315262 = _1315268, _1315264 = _1315266], (29962 ^ _778908) ^ [] : [_1315262 = _1315266, _1315264 = _1315268]]], (48213 ^ _778908) ^ [_1741083, _1741085, _1741087, _1741089] : [hAPP(hAPP(c_List_Oappend(_1741083), _1741085), _1741087) = hAPP(hAPP(c_List_Oappend(_1741083), _1741085), _1741089), -(_1741087 = _1741089)], (36552 ^ _778908) ^ [_1456778, _1456780] : [class_Lattices_Obounded__lattice__top(_1456778), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1456778), _1456780), c_Orderings_Otop__class_Otop(_1456778)) = _1456780)], (49781 ^ _778908) ^ [_1778298] : [-(c_List_Obutlast(_1778298, c_List_Olist_ONil(_1778298)) = c_List_Olist_ONil(_1778298))], (51549 ^ _778908) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (17597 ^ _778908) ^ [_1083037, _1083039, _1083041] : [class_Rings_Olinordered__semidom(_1083037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083037), c_Groups_Ozero__class_Ozero(_1083037)), _1083039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083037), c_Groups_Ozero__class_Ozero(_1083037)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083037), _1083039), _1083041))))], (48909 ^ _778908) ^ [_1759179, _1759181, _1759183] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759179)), hAPP(hAPP(c_List_Odrop(_1759179), _1759181), _1759183)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759179)), _1759183)), _1759181))], (26437 ^ _778908) ^ [_1244537, _1244539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244537), _1244539)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244539), _1244537))], (12685 ^ _778908) ^ [_992126, _992128] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992126), _992128)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992126)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992128)))], (20635 ^ _778908) ^ [_1135101, _1135103, _1135105, _1135107] : [class_Fields_Ofield__inverse__zero(_1135101), -(_1135103 = c_Groups_Ozero__class_Ozero(_1135101)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135101), _1135105), _1135103)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135101), _1135107), _1135103)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135101), _1135105), _1135107))], (5320 ^ _778908) ^ [_861168, _861170] : [_861170 = _861168, -(c_List_Oappend(_861170) = c_List_Oappend(_861168))], (46305 ^ _778908) ^ [_1692749, _1692751, _1692753, _1692755] : [c_Map_Omap__of(_1692749, _1692751, _1692753) = c_Map_Omap__of(_1692749, _1692751, _1692755), -(hAPP(c_Set_Oimage(tc_prod(_1692749, _1692751), _1692749, c_Product__Type_Ofst(_1692749, _1692751)), hAPP(c_List_Oset(tc_prod(_1692749, _1692751)), _1692753)) = hAPP(c_Set_Oimage(tc_prod(_1692749, _1692751), _1692749, c_Product__Type_Ofst(_1692749, _1692751)), hAPP(c_List_Oset(tc_prod(_1692749, _1692751)), _1692755)))], (5871 ^ _778908) ^ [_872470, _872472, _872474, _872476] : [c_Com_Ocom_OAss(_872470, _872472) = c_Com_Ocom_OAss(_872474, _872476), 5874 ^ _778908 : [(5877 ^ _778908) ^ [] : [-(_872472 = _872476)], (5875 ^ _778908) ^ [] : [-(_872470 = _872474)]]], (19473 ^ _778908) ^ [_1114273, _1114275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1114273)), c_Int_OBit0(_1114275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114273), _1114275)))], (17641 ^ _778908) ^ [_1083712, _1083714, _1083716] : [class_Rings_Olinordered__semidom(_1083712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083712), c_Groups_Oone__class_Oone(_1083712)), _1083714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083712), c_Groups_Oone__class_Oone(_1083712)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083712), _1083714), _1083716))))], (25429 ^ _778908) ^ [_1225980, _1225982] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225980), _1225982))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225980), _1225982)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225982), _1225980)))], (50449 ^ _778908) ^ [_1792151] : [-(c_List_Oupt(_1792151, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (43461 ^ _778908) ^ [_1624796, _1624798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1624796), _1624798)), -(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), _1624796), _1624798)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (18945 ^ _778908) ^ [_1105315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1105315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1105315)))], (36958 ^ _778908) ^ [_1466156, _1466158, _1466160, _1466162] : [hBOOL(hAPP(hAPP(c_member(_1466156), _1466158), _1466160)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466156, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1466156), _1466158), _1466162)), _1466160) = hAPP(hAPP(c_Set_Oinsert(_1466156), _1466158), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466156, tc_HOL_Obool)), _1466162), _1466160)))], (22644 ^ _778908) ^ [_1171874, _1171876] : [-(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), _1171874)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171876), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1171874))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (24563 ^ _778908) ^ [_1208661, _1208663, _1208665, _1208667] : [class_Orderings_Olinorder(_1208661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208661), _1208663), _1208665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208661), _1208667), _1208665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208661), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208661), _1208663), _1208667)), _1208665)))], (47769 ^ _778908) ^ [_1730272, _1730274, _1730276, _1730278] : [_1730272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1730274), hAPP(hAPP(c_List_Olist_OCons(_1730274), _1730276), _1730278)), _1730272) = _1730276)], (26979 ^ _778908) ^ [_1254949, _1254951, _1254953, _1254955, _1254957] : [class_Groups_Ocomm__monoid__add(_1254949), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254949), _1254951), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1254953), _1254955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1254957), _1254955))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254949), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1254949, tc_Nat_Onat), _1254951), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1254955))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1254953, _1254957)))], (20471 ^ _778908) ^ [_1132423, _1132425, _1132427] : [class_Fields_Olinordered__field(_1132423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132423), c_Groups_Ozero__class_Ozero(_1132423)), _1132425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132423), _1132427), c_Groups_Ozero__class_Ozero(_1132423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132423), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132423), _1132425), _1132427)), c_Groups_Ozero__class_Ozero(_1132423))))], (39840 ^ _778908) ^ [_1530313, _1530315, _1530317, _1530319, _1530321] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530313, _1530315, _1530317, _1530319, c_Orderings_Obot__class_Obot(tc_fun(_1530313, tc_HOL_Obool))), _1530321)), -(_1530321 = _1530319)], (29195 ^ _778908) ^ [_1300538] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300538)) = 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), _1300538))))], (31157 ^ _778908) ^ [_1338551, _1338553] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1338551, tc_HOL_Obool)), _1338553)), -(hBOOL(hAPP(hAPP(c_member(_1338551), _1338553), c_Orderings_Obot__class_Obot(tc_fun(_1338551, tc_HOL_Obool)))))], (35468 ^ _778908) ^ [_1431917, _1431919, _1431921] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1431917, tc_HOL_Obool)), _1431919), hAPP(c_Set_OPow(_1431917), _1431921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431917, tc_HOL_Obool)), _1431919), _1431921)))], (18543 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (12189 ^ _778908) ^ [_983587, _983589, _983591] : [class_Rings_Olinordered__ring__strict(_983587), 12192 ^ _778908 : [(12207 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), c_Groups_Ozero__class_Ozero(_983587)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983587), _983589), _983591)))), 12208 ^ _778908 : [(12215 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), _983589), c_Groups_Ozero__class_Ozero(_983587))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), _983591), c_Groups_Ozero__class_Ozero(_983587)))], (12209 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), c_Groups_Ozero__class_Ozero(_983587)), _983589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), c_Groups_Ozero__class_Ozero(_983587)), _983591))]]], (12193 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), c_Groups_Ozero__class_Ozero(_983587)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983587), _983589), _983591))), 12198 ^ _778908 : [(12201 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), c_Groups_Ozero__class_Ozero(_983587)), _983591)))], (12199 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), c_Groups_Ozero__class_Ozero(_983587)), _983589)))]], 12202 ^ _778908 : [(12205 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), _983591), c_Groups_Ozero__class_Ozero(_983587))))], (12203 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983587), _983589), c_Groups_Ozero__class_Ozero(_983587))))]]]]], (26923 ^ _778908) ^ [_1253824, _1253826] : [class_Rings_Ocomm__semiring__1(_1253824), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253824), c_Groups_Oone__class_Oone(_1253824)), c_Groups_Oone__class_Oone(_1253824))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253824), c_Nat_Osemiring__1__class_Oof__nat(_1253824)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1253826))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253824), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1253824), _1253826)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253824), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1253824), _1253826)), c_Groups_Oone__class_Oone(_1253824))))], (9724 ^ _778908) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12263 ^ _778908) ^ [_984923] : [class_Rings_Olinordered__semidom(_984923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984923), c_Groups_Oone__class_Oone(_984923)), c_Groups_Ozero__class_Ozero(_984923)))], (21531 ^ _778908) ^ [_1150737, _1150739] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150737), _1150739), hAPP(c_Int_Onumber__class_Onumber__of(_1150737), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1150737), _1150739)), class_Fields_Ofield__inverse__zero(_1150737), class_Int_Onumber__ring(_1150737)], (49398 ^ _778908) ^ [_1769721, _1769723, _1769725] : [class_Orderings_Olinorder(_1769721), -(c_Big__Operators_Olattice_OInf__fin(_1769721, c_Orderings_Oord__class_Omin(_1769721), hAPP(c_List_Oset(_1769721), hAPP(hAPP(c_List_Olist_OCons(_1769721), _1769723), _1769725))) = hAPP(c_List_Ofoldl(_1769721, _1769721, c_Orderings_Oord__class_Omin(_1769721), _1769723), _1769725))], (43371 ^ _778908) ^ [_1622753] : [-(hAPP(c_Relation_ORange(_1622753, _1622753), c_Relation_OId(_1622753)) = c_Orderings_Otop__class_Otop(tc_fun(_1622753, tc_HOL_Obool)))], (22788 ^ _778908) ^ [_1174353] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1174353) = 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)))], (13925 ^ _778908) ^ [_1014162, _1014164, _1014166, _1014168] : [class_Divides_Osemiring__div(_1014162), -(c_Divides_Odiv__class_Omod(_1014162, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014162), _1014164), _1014166), _1014168) = c_Divides_Odiv__class_Omod(_1014162, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014162), c_Divides_Odiv__class_Omod(_1014162, _1014164, _1014168)), _1014166), _1014168))], (30786 ^ _778908) ^ [] : [-(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))))], (48532 ^ _778908) ^ [_1748510, _1748512, _1748514, _1748516, _1748518, _1748520] : [-(hBOOL(hAPP(hAPP(c_member(_1748510), _1748512), hAPP(c_List_Oset(_1748510), _1748514)))), -(hAPP(c_Map_Omap__upds(_1748510, _1748516, _1748518, _1748514, _1748520), _1748512) = hAPP(_1748518, _1748512))], (48472 ^ _778908) ^ [_1747236, _1747238, _1747240, _1747242, _1747244, _1747246] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747236)), _1747238) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747240)), _1747242), -(c_Map_Omap__upds(_1747236, _1747240, _1747244, hAPP(hAPP(c_List_Oappend(_1747236), _1747238), _1747246), _1747242) = c_Map_Omap__upds(_1747236, _1747240, _1747244, _1747238, _1747242))], (47763 ^ _778908) ^ [_1730114, _1730116, _1730118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730114), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730116)), _1730118))), -(hBOOL(hAPP(hAPP(c_member(_1730116), hAPP(hAPP(c_List_Onth(_1730116), _1730118), _1730114)), hAPP(c_List_Oset(_1730116), _1730118))))], (27462 ^ _778908) ^ [_1264644, _1264646] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1264644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1264646), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1264644, _1264646))], (6945 ^ _778908) ^ [_893638] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _893638))), -(hAPP(c_Com_Obody, _893638) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6948 ^ [_893638]))], (26409 ^ _778908) ^ [_1244047, _1244049, _1244051, _1244053] : [class_Divides_Osemiring__div(_1244047), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244047), _1244049), _1244051)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1244047), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244047), _1244051), _1244049)), _1244053) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244047), hAPP(hAPP(c_Power_Opower__class_Opower(_1244047), _1244051), _1244053)), hAPP(hAPP(c_Power_Opower__class_Opower(_1244047), _1244049), _1244053)))], (41684 ^ _778908) ^ [_1580186, _1580188, _1580190, _1580192, _1580194, _1580196, _1580198] : [hAPP(c_Fun_Ocomp(_1580186, _1580188, _1580190, _1580192), _1580194) = hAPP(c_Fun_Ocomp(_1580188, _1580188, _1580190, c_Fun_Oid(_1580188)), _1580196), -(hAPP(_1580192, hAPP(_1580194, _1580198)) = hAPP(_1580196, _1580198))], (19081 ^ _778908) ^ [_1107530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1107530))))], (22702 ^ _778908) ^ [_1172946, _1172948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172946)), 22705 ^ _778908 : [(22712 ^ _778908) ^ [] : [-(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), _1172948), _1172946)))), -(c_Divides_OnegDivAlg(_1172948, _1172946) = hAPP(c_Divides_Oadjust(_1172946), c_Divides_OnegDivAlg(_1172948, 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)))), _1172946))))], (22706 ^ _778908) ^ [] : [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), _1172948), _1172946))), -(c_Divides_OnegDivAlg(_1172948, _1172946) = 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), _1172948), _1172946)))]]], (35937 ^ _778908) ^ [_1443449, _1443451, _1443453, _1443455, _1443457, _1443459] : [c_Finite__Set_Ofolding(_1443449, _1443451, _1443453, _1443455), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443449), _1443457)), -(hAPP(c_Fun_Ocomp(_1443451, _1443451, _1443451, hAPP(_1443453, _1443459)), hAPP(_1443455, _1443457)) = hAPP(c_Fun_Ocomp(_1443451, _1443451, _1443451, hAPP(_1443455, _1443457)), hAPP(_1443453, _1443459)))], (31117 ^ _778908) ^ [_1337708, _1337710, _1337712, _1337714] : [-(hBOOL(hAPP(hAPP(c_member(_1337708), _1337710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337708, tc_HOL_Obool)), _1337712), _1337714)))), hBOOL(hAPP(hAPP(c_member(_1337708), _1337710), _1337712)), -(hBOOL(hAPP(hAPP(c_member(_1337708), _1337710), _1337714)))], (19025 ^ _778908) ^ [_1106620] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106620))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1106620)))))], (23869 ^ _778908) ^ [_1194941, _1194943, _1194945] : [class_Orderings_Olinorder(_1194941), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194941), _1194943), _1194945) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194941), _1194945), _1194943))], (50871 ^ _778908) ^ [_1801203, _1801205, _1801207, _1801209] : [-(hAPP(hAPP(c_List_Omap(_1801203, _1801205), _1801207), c_List_Oconcat(_1801203, _1801209)) = c_List_Oconcat(_1801205, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1801203), tc_List_Olist(_1801205)), hAPP(c_List_Omap(_1801203, _1801205), _1801207)), _1801209)))], (1292 ^ _778908) ^ [_797932, _797934] : [-(class_Complete__Lattice_Ocomplete__lattice(_797932)), _797934 = _797932, class_Complete__Lattice_Ocomplete__lattice(_797934)], (29359 ^ _778908) ^ [_1303512] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1303512)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1303512)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1303512)))], (51000 ^ _778908) ^ [_1804390, _1804392, _1804394] : [c_List_Oconcat(_1804390, _1804392) = c_List_Oconcat(_1804390, _1804394), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1804390))), _1804392) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1804390))), _1804394), 51010 ^ _778908 : [(51013 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1804390), tc_List_Olist(_1804390), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1804390), tc_fun(tc_List_Olist(_1804390), tc_Nat_Onat), tc_fun(tc_List_Olist(_1804390), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1804390), tc_Nat_Onat), tc_fun(tc_List_Olist(_1804390), tc_HOL_Obool)), tc_List_Olist(_1804390)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1804390))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1804390)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1804390))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1804390)))), 51009 ^ [_1804390, _1804392, _1804394]))], (51011 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1804390), tc_List_Olist(_1804390))), 51009 ^ [_1804390, _1804392, _1804394]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1804390), tc_List_Olist(_1804390))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1804390), tc_List_Olist(_1804390)), _1804392), _1804394)))))]], -(_1804392 = _1804394)], (13646 ^ _778908) ^ [_1008979, _1008981, _1008983] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1008979), _1008981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1008979), _1008983), -(_1008979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1008981 = _1008983)], (51427 ^ _778908) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (20163 ^ _778908) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35210 ^ _778908) ^ [_1426254] : [-(c_Wellfounded_Omeasure(_1426254) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1426254), c_Wellfounded_Oless__than))], (48331 ^ _778908) ^ [_1743430, _1743432, _1743434] : [c_List_Olist_ONil(_1743430) = hAPP(hAPP(c_List_Oappend(_1743430), _1743432), _1743434), 48334 ^ _778908 : [(48337 ^ _778908) ^ [] : [-(_1743434 = c_List_Olist_ONil(_1743430))], (48335 ^ _778908) ^ [] : [-(_1743432 = c_List_Olist_ONil(_1743430))]]], (46555 ^ _778908) ^ [_1698222, _1698224, _1698226, _1698228] : [hBOOL(hAPP(c_List_Odistinct(_1698222), _1698224)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1698226, _1698222)), hAPP(hAPP(c_List_Ozip(_1698226, _1698222), _1698228), _1698224))))], (46372 ^ _778908) ^ [_1694439, _1694441, _1694443, _1694445] : [hBOOL(hAPP(c_List_Odistinct(_1694439), hAPP(hAPP(c_List_Omap(_1694441, _1694439), _1694443), _1694445))), 46375 ^ _778908 : [(46378 ^ _778908) ^ [] : [-(c_Fun_Oinj__on(_1694441, _1694439, _1694443, hAPP(c_List_Oset(_1694441), _1694445)))], (46376 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1694441), _1694445)))]]], (28213 ^ _778908) ^ [_1279862, _1279864, _1279866] : [class_Lattices_Osemilattice__sup(_1279862), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279862), _1279864), _1279866) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279862), _1279866), _1279864))], (48012 ^ _778908) ^ [_1736030, _1736032, _1736034, _1736036, _1736038, _1736040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736030), tc_List_Olist(_1736030))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736030), tc_List_Olist(_1736030)), hAPP(hAPP(c_List_Olist_OCons(_1736030), _1736032), _1736034)), hAPP(hAPP(c_List_Olist_OCons(_1736030), _1736036), _1736038))), c_List_Olexord(_1736030, _1736040))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1736030, _1736030)), hAPP(hAPP(c_Product__Type_OPair(_1736030, _1736030), _1736032), _1736036)), _1736040))), 48019 ^ _778908 : [(48022 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1736030), tc_List_Olist(_1736030))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1736030), tc_List_Olist(_1736030)), _1736034), _1736038)), c_List_Olexord(_1736030, _1736040))))], (48020 ^ _778908) ^ [] : [-(_1736032 = _1736036)]]], (2090 ^ _778908) ^ [_809961, _809963, _809965, _809967, _809969, _809971, _809973, _809975, _809977, _809979] : [-(c_Option_Ooption_Ooption__rec(_809979, _809975, _809971, _809967, _809963) = c_Option_Ooption_Ooption__rec(_809977, _809973, _809969, _809965, _809961)), _809979 = _809977, _809975 = _809973, _809971 = _809969, _809967 = _809965, _809963 = _809961], (30616 ^ _778908) ^ [_1327534, _1327536, _1327538] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1327534, _1327536) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1327538), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 30619 ^ _778908 : [(30622 ^ _778908) ^ [] : [-(_1327536 = _1327538)], (30620 ^ _778908) ^ [] : [-(_1327534 = _1327536)]]], (38724 ^ _778908) ^ [_1505285, _1505287, _1505289, _1505291, _1505293] : [c_Fun_Oinj__on(_1505285, _1505287, _1505289, c_Orderings_Otop__class_Otop(tc_fun(_1505285, tc_HOL_Obool))), 38727 ^ _778908 : [(38734 ^ _778908) ^ [] : [_1505291 = _1505293, -(hAPP(_1505289, _1505291) = hAPP(_1505289, _1505293))], (38728 ^ _778908) ^ [] : [hAPP(_1505289, _1505291) = hAPP(_1505289, _1505293), -(_1505291 = _1505293)]]], (24963 ^ _778908) ^ [_1216538, _1216540, _1216542, _1216544, _1216546, _1216548] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1216538, _1216540, _1216542, _1216544, _1216546), hAPP(c_Sum__Type_OInl(_1216538, _1216542), _1216548)) = hAPP(_1216544, _1216548))], (14908 ^ _778908) ^ [_1031668, _1031670, _1031672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031670), _1031672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1031668), _1031672)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1031668), _1031670))))], (10663 ^ _778908) ^ [_957865, _957867, _957869, _957871] : [class_Orderings_Oorder(_957865), _957867 = _957869, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957865), _957871), _957869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957865), _957871), _957867)))], (19695 ^ _778908) ^ [_1118244] : [class_Rings_Osemiring__1(_1118244), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1118244), c_Groups_Ozero__class_Ozero(_1118244)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1118244))], (46339 ^ _778908) ^ [] : [c_Com_OWT__bodies, 46342 ^ _778908 : [(46343 ^ _778908) ^ [_1693660] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1693660), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1693660)))]]], (23793 ^ _778908) ^ [_1193607, _1193609, _1193611, _1193613] : [class_Orderings_Olinorder(_1193607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193607), _1193609), _1193611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193607), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1193607), _1193609), _1193613)), _1193611)))], (19373 ^ _778908) ^ [_1112532, _1112534] : [c_Int_OBit1(_1112532) = c_Int_OBit0(_1112534)], (10481 ^ _778908) ^ [_954961, _954963] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954961), _954963) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954963), _954961))], (51581 ^ _778908) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (9436 ^ _778908) ^ [_936778, _936780] : [class_Rings_Ocomm__semiring__1(_936778), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936778), _936780), c_Groups_Ozero__class_Ozero(_936778)) = c_Groups_Ozero__class_Ozero(_936778))], (37340 ^ _778908) ^ [_1475234, _1475236, _1475238, _1475240, _1475242, _1475244] : [c_Finite__Set_Ofolding(_1475234, _1475236, _1475238, _1475240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475234), _1475242)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475234), _1475244)), -(hAPP(c_Fun_Ocomp(_1475236, _1475236, _1475236, hAPP(_1475240, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1475234, tc_HOL_Obool)), _1475242), _1475244))), hAPP(_1475240, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475234, tc_HOL_Obool)), _1475242), _1475244))) = hAPP(c_Fun_Ocomp(_1475236, _1475236, _1475236, hAPP(_1475240, _1475242)), hAPP(_1475240, _1475244)))], (508 ^ _778908) ^ [_786668, _786670, _786672, _786674, _786676, _786678, _786680, _786682, _786684, _786686, _786688, _786690] : [-(c_Finite__Set_Ofolding__image__simple(_786688, _786684, _786680, _786676, _786672, _786668)), c_Finite__Set_Ofolding__image__simple(_786690, _786686, _786682, _786678, _786674, _786670), _786690 = _786688, _786686 = _786684, _786682 = _786680, _786678 = _786676, _786674 = _786672, _786670 = _786668], (48697 ^ _778908) ^ [_1752725, _1752727, _1752729, _1752731, _1752733] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752725), tc_List_Olist(_1752725))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752725), tc_List_Olist(_1752725)), _1752727), _1752729)), c_List_Olistrel1(_1752725, _1752731))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1752725), tc_List_Olist(_1752725))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1752725), tc_List_Olist(_1752725)), hAPP(hAPP(c_List_Olist_OCons(_1752725), _1752733), _1752727)), hAPP(hAPP(c_List_Olist_OCons(_1752725), _1752733), _1752729))), c_List_Olistrel1(_1752725, _1752731))))], (51365 ^ _778908) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (24247 ^ _778908) ^ [_1202512, _1202514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202514), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202512), _1202514) = 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), _1202512), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1202514)))))], (42487 ^ _778908) ^ [_1600736, _1600738, _1600740, _1600742, _1600744] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1600736), _1600738), _1600740), _1600742), _1600744) = c_New__DSequence_Opos__single(_1600736, _1600738))], (16183 ^ _778908) ^ [_1056238, _1056240, _1056242] : [-(hBOOL(hAPP(_1056238, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1056240), _1056242)))), 16186 ^ _778908 : [(16189 ^ _778908) ^ [] : [hBOOL(hAPP(_1056238, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16187 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056240), _1056242)))]], 16191 ^ _778908 : [(16194 ^ _778908) ^ [] : [hBOOL(hAPP(_1056238, 16190 ^ [_1056238, _1056240, _1056242]))], (16192 ^ _778908) ^ [] : [-(_1056240 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1056242), 16190 ^ [_1056238, _1056240, _1056242]))]]], (50140 ^ _778908) ^ [_1786892, _1786894] : [class_Orderings_Olinorder(_1786892), -(_1786894 = c_List_Olist_ONil(_1786892)), c_List_Olinorder__class_Osorted(_1786892, _1786894), -(c_List_Olinorder__class_Osorted(_1786892, c_List_Obutlast(_1786892, _1786894)))], (49109 ^ _778908) ^ [_1764165, _1764167, _1764169] : [-(_1764165 = c_List_Olist_ONil(_1764167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1764169), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764167)), _1764165))), -(hAPP(c_List_Ohd(_1764167), hAPP(hAPP(c_List_Odrop(_1764167), _1764169), _1764165)) = hAPP(hAPP(c_List_Onth(_1764167), _1764165), _1764169))], (31638 ^ _778908) ^ [_1350109, _1350111] : [c_Nat__Transfer_Ois__nat(_1350109), c_Nat__Transfer_Onat__set(_1350111), 31645 ^ _778908 : [(31652 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1350109)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1350111))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1350109), _1350111)))], (31646 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1350109), _1350111)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1350109)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1350111))))]]], (5142 ^ _778908) ^ [_858419, _858421, _858423, _858425, _858427, _858429, _858431, _858433, _858435, _858437] : [-(c_List_Olinorder__class_Oinsort__insert__key(_858437, _858433, _858429, _858425, _858421) = c_List_Olinorder__class_Oinsort__insert__key(_858435, _858431, _858427, _858423, _858419)), _858437 = _858435, _858433 = _858431, _858429 = _858427, _858425 = _858423, _858421 = _858419], (51421 ^ _778908) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (15416 ^ _778908) ^ [_1041217, _1041219, _1041221, _1041223, _1041225] : [class_Groups_Oordered__ab__group__add(_1041217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041217), _1041219), _1041221) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041217), _1041223), _1041225), 15423 ^ _778908 : [(15430 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041217), _1041223), _1041225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041217), _1041219), _1041221)))], (15424 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041217), _1041219), _1041221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041217), _1041223), _1041225)))]]], (25505 ^ _778908) ^ [_1227226, _1227228] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227226), _1227228)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1227228), _1227226)), -(_1227226 = _1227228)], (31289 ^ _778908) ^ [_1343366, _1343368, _1343370, _1343372] : [_1343366 = _1343368, 31292 ^ _778908 : [(31299 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1343370), _1343372), _1343368)), -(hBOOL(hAPP(hAPP(c_member(_1343370), _1343372), _1343366)))], (31293 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1343370), _1343372), _1343366)), -(hBOOL(hAPP(hAPP(c_member(_1343370), _1343372), _1343368)))]]], (26197 ^ _778908) ^ [_1240113, _1240115, _1240117, _1240119] : [class_Rings_Oidom(_1240113), 26200 ^ _778908 : [(26201 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240113), _1240115), _1240117)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240113), _1240115), _1240119))), -(_1240115 = c_Groups_Ozero__class_Ozero(_1240113)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240113), _1240117), _1240119)))], (26211 ^ _778908) ^ [] : [26212 ^ _778908 : [(26215 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240113), _1240117), _1240119))], (26213 ^ _778908) ^ [] : [_1240115 = c_Groups_Ozero__class_Ozero(_1240113)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240113), _1240115), _1240117)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240113), _1240115), _1240119))))]]], (37276 ^ _778908) ^ [_1473482, _1473484, _1473486, _1473488, _1473490] : [class_Groups_Ocomm__monoid__mult(_1473482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473484), _1473486)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473484), _1473488)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1473482), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473484, _1473482), _1473490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473484, tc_HOL_Obool)), _1473486), _1473488))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473484, _1473482), _1473490), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473484, tc_HOL_Obool)), _1473486), _1473488))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1473482), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473484, _1473482), _1473490), _1473486)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1473484, _1473482), _1473490), _1473488)))], (4314 ^ _778908) ^ [_845567, _845569, _845571, _845573] : [-(c_Option_Omap(_845573, _845569) = c_Option_Omap(_845571, _845567)), _845573 = _845571, _845569 = _845567], (49323 ^ _778908) ^ [_1768228, _1768230] : [class_Groups_Omonoid__add(_1768228), -(hAPP(c_List_Ofoldl(_1768228, _1768228, c_Groups_Oplus__class_Oplus(_1768228), c_Groups_Ozero__class_Ozero(_1768228)), _1768230) = c_List_Ofoldr(_1768228, _1768228, c_Groups_Oplus__class_Oplus(_1768228), _1768230, c_Groups_Ozero__class_Ozero(_1768228)))], (14545 ^ _778908) ^ [_1025832, _1025834] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1025832)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1025834)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1025832), _1025834))], (15910 ^ _778908) ^ [_1050429, _1050431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050429), _1050431)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1050431)), _1050429) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050431), _1050429)))], (46410 ^ _778908) ^ [_1695200, _1695202, _1695204, _1695206, _1695208] : [hBOOL(hAPP(c_List_Odistinct(_1695200), hAPP(hAPP(c_List_Omap(tc_prod(_1695200, _1695202), _1695200), c_Product__Type_Ofst(_1695200, _1695202)), _1695204))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1695200, _1695202)), hAPP(hAPP(c_Product__Type_OPair(_1695200, _1695202), _1695206), _1695208)), hAPP(c_List_Oset(tc_prod(_1695200, _1695202)), _1695204))), -(hAPP(c_Map_Omap__of(_1695200, _1695202, _1695204), _1695206) = hAPP(c_Option_Ooption_OSome(_1695202), _1695208))], (31137 ^ _778908) ^ [_1338089, _1338091, _1338093, _1338095] : [31138 ^ _778908 : [(31141 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1338089), _1338091), _1338095))], (31139 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1338089), _1338091), _1338093))]], -(hBOOL(hAPP(hAPP(c_member(_1338089), _1338091), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338089, tc_HOL_Obool)), _1338093), _1338095))))], (14206 ^ _778908) ^ [_1019329, _1019331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019329), _1019331)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019329, _1019331) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019329), _1019331))], (19701 ^ _778908) ^ [_1118341, _1118343] : [class_Rings_Oring__1__no__zero__divisors(_1118341), 19704 ^ _778908 : [(19711 ^ _778908) ^ [] : [_1118343 = c_Groups_Ozero__class_Ozero(_1118341), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1118341), _1118343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1118341))], (19705 ^ _778908) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1118341), _1118343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1118341), -(_1118343 = c_Groups_Ozero__class_Ozero(_1118341))]]], (31169 ^ _778908) ^ [_1338803, _1338805, _1338807, _1338809, _1338811] : [hBOOL(hAPP(hAPP(c_member(_1338803), _1338805), c_SetInterval_Oord_OatLeastAtMost(_1338803, _1338807, _1338809, _1338811))), 31172 ^ _778908 : [(31175 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1338807, _1338805), _1338811)))], (31173 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1338807, _1338809), _1338805)))]]], (3144 ^ _778908) ^ [_827054, _827056, _827058, _827060, _827062, _827064, _827066, _827068] : [-(c_Product__Type_Ocurry(_827068, _827064, _827060, _827056) = c_Product__Type_Ocurry(_827066, _827062, _827058, _827054)), _827068 = _827066, _827064 = _827062, _827060 = _827058, _827056 = _827054], (5841 ^ _778908) ^ [_871814, _871816] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_871814, _871816)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18331 ^ _778908) ^ [_1095621, _1095623] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095621), _1095623) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1095621 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1095621 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (17055 ^ _778908) ^ [_1072759, _1072761, _1072763] : [class_Int_Onumber__ring(_1072759), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072759), hAPP(c_Int_Onumber__class_Onumber__of(_1072759), _1072761)), hAPP(c_Int_Onumber__class_Onumber__of(_1072759), _1072763)) = hAPP(c_Int_Onumber__class_Onumber__of(_1072759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072761), _1072763)))], (4042 ^ _778908) ^ [_841247, _841249] : [_841249 = _841247, -(c_Nat_Ofunpow(_841249) = c_Nat_Ofunpow(_841247))], (44735 ^ _778908) ^ [_1654400, _1654402, _1654404, _1654406, _1654408] : [hBOOL(hAPP(hAPP(c_member(_1654400), _1654402), _1654404)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654406, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654400, tc_fun(_1654406, tc_HOL_Obool)), _1654404), _1654408)), hAPP(_1654408, _1654402))))], (29554 ^ _778908) ^ [_1307478, _1307480, _1307482] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307478), _1307480)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307478, tc_HOL_Obool)), _1307480), _1307482))))], (6013 ^ _778908) ^ [_875031, _875033, _875035, _875037, _875039, _875041, _875043, _875045, _875047, _875049] : [-(c_Com_Ocom_Ocom__rec(_875031, _875033, _875035, _875037, _875039, _875041, _875043, _875045, _875047, hAPP(c_Com_Ocom_OBODY, _875049)) = hAPP(_875045, _875049))], (41032 ^ _778908) ^ [_1558265] : [class_Lattices_Oab__semigroup__idem__mult(_1558265), -(c_Finite__Set_Ofun__left__comm__idem(_1558265, _1558265, c_Groups_Otimes__class_Otimes(_1558265)))], (24695 ^ _778908) ^ [_1210963, _1210965, _1210967] : [class_Orderings_Olinorder(_1210963), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210963), _1210965), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210963), _1210965), _1210967)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210963), _1210965), _1210967))], (30906 ^ _778908) ^ [_1333399, _1333401] : [-(hBOOL(hAPP(hAPP(c_member(_1333399), _1333401), c_Orderings_Otop__class_Otop(tc_fun(_1333399, tc_HOL_Obool)))))], (3784 ^ _778908) ^ [_837220, _837222] : [_837222 = _837220, -(c_Wellfounded_Ofinite__psubset(_837222) = c_Wellfounded_Ofinite__psubset(_837220))], (38360 ^ _778908) ^ [_1498081, _1498083] : [-(c_Equiv__Relations_Oequivp(_1498081, _1498083)), 38365 ^ _778908 : [(38368 ^ _778908) ^ [] : [hAPP(_1498083, 38361 ^ [_1498081, _1498083]) = hAPP(_1498083, 38362 ^ [_1498081, _1498083])], (38366 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1498083, 38361 ^ [_1498081, _1498083]), 38362 ^ [_1498081, _1498083])))]], 38369 ^ _778908 : [(38372 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(_1498083, 38361 ^ [_1498081, _1498083]), 38362 ^ [_1498081, _1498083]))], (38370 ^ _778908) ^ [] : [-(hAPP(_1498083, 38361 ^ [_1498081, _1498083]) = hAPP(_1498083, 38362 ^ [_1498081, _1498083]))]]], (43281 ^ _778908) ^ [_1620590, _1620592, _1620594] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620590, _1620590)), hAPP(hAPP(c_Product__Type_OPair(_1620590, _1620590), _1620592), _1620594)), c_Relation_OId(_1620590))), -(_1620592 = _1620594)], (26083 ^ _778908) ^ [_1237313, _1237315, _1237317] : [class_Groups_Ocomm__monoid__add(_1237313), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1237315, _1237313), hAPP(c_COMBK(_1237313, _1237315), c_Groups_Ozero__class_Ozero(_1237313))), _1237317) = c_Groups_Ozero__class_Ozero(_1237313))], (12513 ^ _778908) ^ [_989332, _989334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989332), _989334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _989332)), _989334)))], (5604 ^ _778908) ^ [_865472, _865474] : [_865474 = _865472, -(tc_List_Olist(_865474) = tc_List_Olist(_865472))], (14087 ^ _778908) ^ [_1017380, _1017382] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017380, _1017382) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1017380 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017382), 14090 ^ [_1017380, _1017382]))], (44230 ^ _778908) ^ [_1643693, _1643695, _1643697] : [class_Lattices_Olattice(_1643693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643693), _1643695)), -(c_Big__Operators_Olattice__class_OSup__fin(_1643693, hAPP(hAPP(c_Set_Oinsert(_1643693), _1643697), _1643695)) = hAPP(hAPP(c_Finite__Set_Ofold(_1643693, _1643693, c_Lattices_Osemilattice__sup__class_Osup(_1643693)), _1643697), _1643695))], (41587 ^ _778908) ^ [_1575515, _1575517, _1575519] : [class_Lattices_Odistrib__lattice(_1575515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575515), _1575517)), -(_1575517 = c_Orderings_Obot__class_Obot(tc_fun(_1575515, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575515), _1575519)), -(_1575519 = c_Orderings_Obot__class_Obot(tc_fun(_1575515, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1575515), c_Big__Operators_Olattice__class_OSup__fin(_1575515, _1575517)), c_Big__Operators_Olattice__class_OSup__fin(_1575515, _1575519)) = c_Big__Operators_Olattice__class_OSup__fin(_1575515, hAPP(c_Set_OCollect(_1575515), hAPP(hAPP(c_COMBB(tc_fun(_1575515, tc_HOL_Obool), tc_HOL_Obool, _1575515), c_HOL_OEx(_1575515)), hAPP(hAPP(c_COMBB(tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool)), tc_fun(_1575515, tc_HOL_Obool), _1575515), hAPP(c_COMBB(tc_fun(_1575515, tc_HOL_Obool), tc_HOL_Obool, _1575515), c_HOL_OEx(_1575515))), hAPP(hAPP(c_COMBC(_1575515, tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool)), tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1575515, tc_fun(tc_fun(_1575515, tc_HOL_Obool), tc_fun(_1575515, tc_HOL_Obool))), tc_fun(tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool)), tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool))), _1575515), c_COMBS(_1575515, tc_fun(_1575515, tc_HOL_Obool), tc_fun(_1575515, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1575515, tc_fun(_1575515, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1575515, tc_fun(tc_fun(_1575515, tc_HOL_Obool), tc_fun(_1575515, tc_HOL_Obool))), _1575515), hAPP(c_COMBB(tc_fun(_1575515, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1575515, tc_HOL_Obool), tc_fun(_1575515, tc_HOL_Obool)), _1575515), c_COMBS(_1575515, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool)), tc_fun(_1575515, tc_fun(_1575515, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1575515), hAPP(c_COMBB(tc_fun(_1575515, tc_HOL_Obool), tc_fun(_1575515, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1575515), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1575515), c_fconj))), hAPP(hAPP(c_COMBC(_1575515, tc_fun(_1575515, tc_fun(_1575515, _1575515)), tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575515, _1575515), tc_fun(_1575515, tc_HOL_Obool)), tc_fun(tc_fun(_1575515, tc_fun(_1575515, _1575515)), tc_fun(_1575515, tc_fun(_1575515, tc_HOL_Obool))), _1575515), c_COMBB(tc_fun(_1575515, _1575515), tc_fun(_1575515, tc_HOL_Obool), _1575515)), hAPP(hAPP(c_COMBB(tc_fun(_1575515, tc_HOL_Obool), tc_fun(tc_fun(_1575515, _1575515), tc_fun(_1575515, tc_HOL_Obool)), _1575515), c_COMBB(_1575515, tc_HOL_Obool, _1575515)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1575515)))))), hAPP(hAPP(c_COMBC(_1575515, tc_fun(_1575515, tc_HOL_Obool), tc_fun(_1575515, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1575515, tc_HOL_Obool), tc_fun(_1575515, tc_HOL_Obool)), _1575515), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1575515)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1575515), c_fconj), hAPP(hAPP(c_COMBC(_1575515, tc_fun(_1575515, tc_HOL_Obool), tc_HOL_Obool), c_member(_1575515)), _1575517)))), hAPP(hAPP(c_COMBC(_1575515, tc_fun(_1575515, tc_HOL_Obool), tc_HOL_Obool), c_member(_1575515)), _1575519))))))))], (14649 ^ _778908) ^ [_1027531, _1027533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1027531), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14652 ^ _778908 : [(14659 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027533), _1027531)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14653 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027533), _1027531)), 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)), _1027533)))]]], (20679 ^ _778908) ^ [_1135874, _1135876, _1135878, _1135880] : [class_Rings_Odivision__ring(_1135874), -(_1135876 = c_Groups_Ozero__class_Ozero(_1135874)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135874), _1135878), _1135876) = _1135880, -(_1135878 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135874), _1135880), _1135876))], (38832 ^ _778908) ^ [_1507385, _1507387, _1507389, _1507391, _1507393, _1507395, _1507397] : [c_Finite__Set_Ofolding__image__simple(_1507385, _1507387, _1507389, _1507391, _1507393, _1507395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507387), _1507397)), -(hAPP(_1507395, _1507397) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1507385, _1507387, _1507389), _1507393), _1507391), _1507397))], (27869 ^ _778908) ^ [_1273069] : [c_Nat__Transfer_Onat__set(_1273069), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1273069) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1273069)))], (40356 ^ _778908) ^ [_1544209, _1544211, _1544213, _1544215, _1544217, _1544219] : [class_Groups_Ocomm__monoid__add(_1544209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544211), _1544213)), 40366 ^ _778908 : [(40369 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544215), hAPP(_1544217, 40365 ^ [_1544209, _1544211, _1544213, _1544215, _1544217, _1544219])))], (40367 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544211), 40365 ^ [_1544209, _1544211, _1544213, _1544215, _1544217, _1544219]), _1544213)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544211, _1544209), hAPP(hAPP(c_COMBS(_1544211, tc_fun(_1544215, tc_HOL_Obool), _1544209), hAPP(hAPP(c_COMBB(tc_fun(_1544215, _1544209), tc_fun(tc_fun(_1544215, tc_HOL_Obool), _1544209), _1544211), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544215, _1544209)), _1544219)), _1544217)), _1544213) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1544211, _1544215), _1544209), hAPP(c_Product__Type_Oprod_Oprod__case(_1544211, _1544215, _1544209), _1544219)), hAPP(hAPP(c_Product__Type_OSigma(_1544211, _1544215), _1544213), _1544217)))], (16486 ^ _778908) ^ [_1062307, _1062309, _1062311] : [16488 ^ _778908 : [(16493 ^ _778908) ^ [] : [hBOOL(hAPP(_1062309, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 16487 ^ [_1062307, _1062309, _1062311]), _1062307)))], (16491 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1062309, 16487 ^ [_1062307, _1062309, _1062311])))], (16489 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16487 ^ [_1062307, _1062309, _1062311]), _1062307)))]], hBOOL(hAPP(_1062309, _1062311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062311), _1062307)), -(hBOOL(hAPP(_1062309, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30064 ^ _778908) ^ [_1317320, _1317322, _1317324] : [-(hAPP(c_Set_Oimage(_1317320, _1317322, _1317324), c_Orderings_Obot__class_Obot(tc_fun(_1317320, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1317322, tc_HOL_Obool)))], (42024 ^ _778908) ^ [_1589526, _1589528, _1589530] : [c_Wellfounded_Owf(_1589526, _1589528), -(c_Wellfounded_Owf(_1589526, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1589526, _1589526), tc_HOL_Obool)), _1589528), _1589530)))], (14698 ^ _778908) ^ [_1028273, _1028275] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1028273, _1028275)), _1028275) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35871 ^ _778908) ^ [_1441994, _1441996, _1441998, _1442000, _1442002] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1441994, _1441996, _1441998), _1442000), _1442002)), 35874 ^ _778908 : [(35877 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1441998, _1442002)))], (35875 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1441996, _1442000), _1442002)))]]], (22622 ^ _778908) ^ [_1171350, _1171352, _1171354] : [class_Int_Onumber__ring(_1171350), 22625 ^ _778908 : [(22632 ^ _778908) ^ [] : [-(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), _1171352)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1171350), _1171354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1171352))) = c_Groups_Oone__class_Oone(_1171350))], (22626 ^ _778908) ^ [] : [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), _1171352))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1171350), _1171354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1171352))) = hAPP(hAPP(c_HOL_OLet(_1171350, _1171350), hAPP(hAPP(c_Power_Opower__class_Opower(_1171350), _1171354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1171352))), hAPP(hAPP(c_COMBS(_1171350, _1171350, _1171350), hAPP(hAPP(c_COMBB(_1171350, tc_fun(_1171350, _1171350), _1171350), c_Groups_Otimes__class_Otimes(_1171350)), hAPP(c_Groups_Otimes__class_Otimes(_1171350), _1171354))), c_COMBI(_1171350))))]]], (44649 ^ _778908) ^ [_1652378, _1652380, _1652382, _1652384, _1652386] : [_1652378 = c_Orderings_Obot__class_Obot(tc_fun(_1652380, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652382, tc_HOL_Obool)), _1652384), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652380, tc_fun(_1652382, tc_HOL_Obool)), _1652378), _1652386)) = _1652384)], (50154 ^ _778908) ^ [_1787105, _1787107, _1787109, _1787111] : [c_List_Oupt(_1787105, _1787107) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1787109), _1787111), 50157 ^ _778908 : [(50162 ^ _778908) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1787105), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1787107) = _1787111)], (50160 ^ _778908) ^ [] : [-(_1787105 = _1787109)], (50158 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787105), _1787107)))]]], (19533 ^ _778908) ^ [_1115366] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115366)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115366))))], (41700 ^ _778908) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (15958 ^ _778908) ^ [_1051366, _1051368, _1051370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051366), _1051368)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051370), _1051368)), _1051366) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051368), _1051366)))], (2542 ^ _778908) ^ [_817345, _817347, _817349, _817351] : [-(c_Divides_Odivmod__int__rel(_817351, _817347) = c_Divides_Odivmod__int__rel(_817349, _817345)), _817351 = _817349, _817347 = _817345], (45422 ^ _778908) ^ [_1672396, _1672398, _1672400] : [class_Complete__Lattice_Ocomplete__lattice(_1672396), -(c_Complete__Lattice_OInf__class_OInf(_1672396, hAPP(hAPP(c_Set_Oinsert(_1672396), _1672398), hAPP(hAPP(c_Set_Oinsert(_1672396), _1672400), c_Orderings_Obot__class_Obot(tc_fun(_1672396, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1672396), _1672398), _1672400))], (6546 ^ _778908) ^ [_885286, _885288, _885290, _885292] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_885286, _885288)), _885290), _885292)), 6550 ^ _778908 : [(6553 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885288), 6549 ^ [_885286, _885288, _885290, _885292]), _885292)))], (6551 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885286), _885290), 6549 ^ [_885286, _885288, _885290, _885292])))]]], (36202 ^ _778908) ^ [_1449676, _1449678, _1449680, _1449682, _1449684] : [c_Equiv__Relations_Oequiv(_1449676, _1449678, _1449680), hBOOL(hAPP(hAPP(c_member(_1449676), _1449682), _1449678)), hBOOL(hAPP(hAPP(c_member(_1449676), _1449684), _1449678)), 36213 ^ _778908 : [(36220 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1449676, _1449676)), hAPP(hAPP(c_Product__Type_OPair(_1449676, _1449676), _1449682), _1449684)), _1449680)), -(hAPP(c_Relation_OImage(_1449676, _1449676, _1449680), hAPP(hAPP(c_Set_Oinsert(_1449676), _1449682), c_Orderings_Obot__class_Obot(tc_fun(_1449676, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1449676, _1449676, _1449680), hAPP(hAPP(c_Set_Oinsert(_1449676), _1449684), c_Orderings_Obot__class_Obot(tc_fun(_1449676, tc_HOL_Obool)))))], (36214 ^ _778908) ^ [] : [hAPP(c_Relation_OImage(_1449676, _1449676, _1449680), hAPP(hAPP(c_Set_Oinsert(_1449676), _1449682), c_Orderings_Obot__class_Obot(tc_fun(_1449676, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1449676, _1449676, _1449680), hAPP(hAPP(c_Set_Oinsert(_1449676), _1449684), c_Orderings_Obot__class_Obot(tc_fun(_1449676, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1449676, _1449676)), hAPP(hAPP(c_Product__Type_OPair(_1449676, _1449676), _1449682), _1449684)), _1449680)))]]], (29276 ^ _778908) ^ [_1302183] : [29278 ^ _778908 : [(29281 ^ _778908) ^ [_1302293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29277 ^ [_1302183, _1302293]), _1302293))], (29279 ^ _778908) ^ [_1302259] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29277 ^ [_1302183, _1302259]), _1302183)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1302183)))], (46834 ^ _778908) ^ [_1706004, _1706006, _1706008, _1706010, _1706012] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706004)), _1706006) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706008)), _1706010), 46837 ^ _778908 : [(46844 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1706004), _1706012), hAPP(c_List_Oset(_1706004), _1706006)))), -(hAPP(c_Map_Omap__of(_1706004, _1706008, hAPP(hAPP(c_List_Ozip(_1706004, _1706008), _1706006), _1706010)), _1706012) = c_Option_Ooption_ONone(_1706008))], (46838 ^ _778908) ^ [] : [hAPP(c_Map_Omap__of(_1706004, _1706008, hAPP(hAPP(c_List_Ozip(_1706004, _1706008), _1706006), _1706010)), _1706012) = c_Option_Ooption_ONone(_1706008), hBOOL(hAPP(hAPP(c_member(_1706004), _1706012), hAPP(c_List_Oset(_1706004), _1706006)))]]], (49769 ^ _778908) ^ [_1778095, _1778097, _1778099, _1778101] : [-(hAPP(hAPP(c_List_Omap(_1778095, _1778097), _1778099), c_List_Obutlast(_1778095, _1778101)) = c_List_Obutlast(_1778097, hAPP(hAPP(c_List_Omap(_1778095, _1778097), _1778099), _1778101)))], (9116 ^ _778908) ^ [_931383, _931385, _931387, _931389, _931391] : [class_Rings_Ocomm__semiring__1(_931383), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931383), _931385), _931387)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931383), _931389), _931391)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931383), _931385), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931383), _931387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_931383), _931389), _931391))))], (38466 ^ _778908) ^ [_1500255, _1500257, _1500259, _1500261, _1500263] : [class_Groups_Ocomm__monoid__mult(_1500255), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500257), _1500259)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500257), _1500261)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500257, tc_HOL_Obool)), _1500259), _1500261) = c_Orderings_Obot__class_Obot(tc_fun(_1500257, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1500255, _1500257, c_Groups_Otimes__class_Otimes(_1500255)), _1500263), c_Groups_Oone__class_Oone(_1500255)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500257, tc_HOL_Obool)), _1500259), _1500261)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1500255), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1500255, _1500257, c_Groups_Otimes__class_Otimes(_1500255)), _1500263), c_Groups_Oone__class_Oone(_1500255)), _1500259)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1500255, _1500257, c_Groups_Otimes__class_Otimes(_1500255)), _1500263), c_Groups_Oone__class_Oone(_1500255)), _1500261)))], (36596 ^ _778908) ^ [_1457707, _1457709, _1457711, _1457713] : [hBOOL(hAPP(hAPP(c_member(_1457707), _1457709), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457707, tc_HOL_Obool)), _1457711), _1457713))), -(hBOOL(hAPP(hAPP(c_member(_1457707), _1457709), _1457713)))], (31738 ^ _778908) ^ [_1351735, _1351737] : [c_Nat__Transfer_Onat__set(_1351735), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1351737), _1351735)), -(c_Nat__Transfer_Ois__nat(_1351737))], (22890 ^ _778908) ^ [_1176858, _1176860, _1176862, _1176864, _1176866] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176858, _1176860), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1176862), _1176864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176860)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176866), _1176858), _1176860), 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), _1176866), _1176862)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176866), _1176864)), _1176860))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176866), _1176864), _1176860)))))], (24817 ^ _778908) ^ [_1213813] : [-(_1213813 = 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, _1213813)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1213813))))], (51501 ^ _778908) ^ [] : [-(class_Finite__Set_Ofinite(tc_String_Ochar))], (35068 ^ _778908) ^ [] : [-(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)))))], (32835 ^ _778908) ^ [_1376930, _1376932, _1376934, _1376936, _1376938, _1376940] : [-(hBOOL(hAPP(hAPP(c_member(_1376930), _1376932), c_SetInterval_Oord_OatLeastLessThan(_1376930, _1376934, _1376936, _1376938, _1376940)))), hBOOL(hAPP(hAPP(_1376934, _1376938), _1376932)), hBOOL(hAPP(hAPP(_1376936, _1376932), _1376940))], (24137 ^ _778908) ^ [_1200470, _1200472, _1200474, _1200476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200470, tc_HOL_Obool)), _1200472), _1200474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200470, tc_HOL_Obool)), _1200474), _1200476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1200470, tc_HOL_Obool)), _1200472), _1200476)))], (14529 ^ _778908) ^ [_1025503, _1025505] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1025503), _1025505) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1025503, _1025505)), _1025505))], (37126 ^ _778908) ^ [_1470127, _1470129, _1470131] : [class_Orderings_Oorder(_1470127), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470127, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1470127), _1470129)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1470127, _1470129), _1470131)) = c_Orderings_Obot__class_Obot(tc_fun(_1470127, tc_HOL_Obool)))], (8212 ^ _778908) ^ [_916410, _916412, _916414, _916416] : [hAPP(c_Sum__Type_OInr(_916410, _916412), _916414) = hAPP(c_Sum__Type_OInr(_916410, _916412), _916416), -(_916414 = _916416)], (13180 ^ _778908) ^ [_1001109, _1001111] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1001109) = _1001111, 13183 ^ _778908 : [(13186 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001111)))], (13184 ^ _778908) ^ [] : [-(_1001109 = hAPP(c_Int_Onat, _1001111))]]], (4116 ^ _778908) ^ [_842340, _842342] : [_842342 = _842340, -(c_Relation_OField(_842342) = c_Relation_OField(_842340))], (48295 ^ _778908) ^ [_1742786, _1742788, _1742790] : [-(hAPP(hAPP(c_List_Oappend(_1742786), _1742788), _1742790) = c_List_Olist_ONil(_1742786)), _1742788 = c_List_Olist_ONil(_1742786), _1742790 = c_List_Olist_ONil(_1742786)], (36988 ^ _778908) ^ [_1466717, _1466719, _1466721, _1466723] : [hBOOL(hAPP(hAPP(c_member(_1466717), _1466719), _1466721)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466717, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1466717), _1466719), _1466723)), _1466721) = hAPP(hAPP(c_Set_Oinsert(_1466717), _1466719), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466717, tc_HOL_Obool)), _1466723), _1466721)))], (4838 ^ _778908) ^ [_853757, _853759, _853761, _853763, _853765, _853767, _853769, _853771, _853773, _853775] : [-(c_Map_Omap__upds(_853775, _853771, _853767, _853763, _853759) = c_Map_Omap__upds(_853773, _853769, _853765, _853761, _853757)), _853775 = _853773, _853771 = _853769, _853767 = _853765, _853763 = _853761, _853759 = _853757], (47593 ^ _778908) ^ [_1725562, _1725564, _1725566, _1725568, _1725570] : [-(hAPP(hAPP(c_List_Ozip(_1725562, _1725564), hAPP(hAPP(c_List_Olist_OCons(_1725562), _1725566), _1725568)), _1725570) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1725562, _1725564)), _1725564, c_List_Olist_ONil(tc_prod(_1725562, _1725564)), hAPP(hAPP(c_COMBC(_1725564, tc_fun(tc_List_Olist(_1725564), tc_List_Olist(tc_prod(_1725562, _1725564))), tc_fun(tc_List_Olist(_1725564), tc_List_Olist(tc_prod(_1725562, _1725564)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1725562, _1725564)), tc_List_Olist(tc_prod(_1725562, _1725564))), tc_fun(tc_fun(tc_List_Olist(_1725564), tc_List_Olist(tc_prod(_1725562, _1725564))), tc_fun(tc_List_Olist(_1725564), tc_List_Olist(tc_prod(_1725562, _1725564)))), _1725564), c_COMBB(tc_List_Olist(tc_prod(_1725562, _1725564)), tc_List_Olist(tc_prod(_1725562, _1725564)), tc_List_Olist(_1725564))), hAPP(hAPP(c_COMBB(tc_prod(_1725562, _1725564), tc_fun(tc_List_Olist(tc_prod(_1725562, _1725564)), tc_List_Olist(tc_prod(_1725562, _1725564))), _1725564), c_List_Olist_OCons(tc_prod(_1725562, _1725564))), hAPP(c_Product__Type_OPair(_1725562, _1725564), _1725566)))), hAPP(c_List_Ozip(_1725562, _1725564), _1725568))), _1725570))], (6427 ^ _778908) ^ [_882662, _882664, _882666] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_882662, _882664, _882666)))), hBOOL(hAPP(c_Com_OWT, _882664)), hBOOL(hAPP(c_Com_OWT, _882666))], (15790 ^ _778908) ^ [_1048145, _1048147, _1048149, _1048151, _1048153, _1048155] : [class_Rings_Oring(_1048145), 15793 ^ _778908 : [(15800 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048145), _1048147), _1048153)), _1048149)), _1048151) = _1048155, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048145), _1048147), _1048149)), _1048151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048145), _1048153), _1048149)), _1048155))], (15794 ^ _778908) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048145), _1048147), _1048149)), _1048151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048145), _1048153), _1048149)), _1048155), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048145), _1048147), _1048153)), _1048149)), _1048151) = _1048155)]]], (35803 ^ _778908) ^ [] : [-(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))))))], (8684 ^ _778908) ^ [_924003, _924005, _924007] : [class_Orderings_Olinorder(_924003), -(_924005 = _924007), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924003), _924005), _924007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924003), _924007), _924005)))], (50551 ^ _778908) ^ [_1793962] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1793962) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1793962)))], (22960 ^ _778908) ^ [_1178254, _1178256, _1178258, _1178260] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1178254, _1178256), _1178258)), hBOOL(hAPP(hAPP(_1178256, _1178260), _1178258)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1178254, _1178256), _1178260)))], (34889 ^ _778908) ^ [_1418377, _1418379, _1418381, _1418383, _1418385, _1418387] : [hBOOL(hAPP(hAPP(c_member(_1418377), _1418379), _1418381)), -(c_Map_Orestrict__map(_1418377, _1418383, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418377, tc_Option_Ooption(_1418383)), _1418385), _1418379), _1418387), _1418381) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1418377, tc_Option_Ooption(_1418383)), c_Map_Orestrict__map(_1418377, _1418383, _1418385, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1418377, tc_HOL_Obool)), _1418381), hAPP(hAPP(c_Set_Oinsert(_1418377), _1418379), c_Orderings_Obot__class_Obot(tc_fun(_1418377, tc_HOL_Obool)))))), _1418379), _1418387))], (12409 ^ _778908) ^ [_987457, _987459, _987461] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987457), _987459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987457), _987461)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987459), _987461))], (23307 ^ _778908) ^ [_1184808, _1184810] : [_1184808 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1184808, _1184810) = 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)))], (7200 ^ _778908) ^ [_899359, _899361, _899363] : [_899359 = _899363, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899359), _899361) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899363), _899361))], (1082 ^ _778908) ^ [_795307, _795309] : [-(class_Rings_Oring__no__zero__divisors(_795307)), _795309 = _795307, class_Rings_Oring__no__zero__divisors(_795309)], (23501 ^ _778908) ^ [_1188300, _1188302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188300), 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)), _1188302)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1188300, _1188302) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1188300, _1188302)))], (18111 ^ _778908) ^ [_1092029, _1092031] : [class_Int_Onumber__ring(_1092029), 18114 ^ _778908 : [(18121 ^ _778908) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092031)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092029), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092031)) = hAPP(c_Int_Onumber__class_Onumber__of(_1092029), _1092031))], (18115 ^ _778908) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092031))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1092029), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092031)) = c_Groups_Ozero__class_Ozero(_1092029))]]], (13656 ^ _778908) ^ [_1009091, _1009093, _1009095] : [13657 ^ _778908 : [(13660 ^ _778908) ^ [] : [_1009093 = _1009095], (13658 ^ _778908) ^ [] : [_1009091 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009091), _1009093) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1009091), _1009095))], (41186 ^ _778908) ^ [_1561450, _1561452] : [hAPP(c_Set_OCollect(_1561450), _1561452) = c_Orderings_Obot__class_Obot(tc_fun(_1561450, tc_HOL_Obool)), 41189 ^ _778908 : [(41190 ^ _778908) ^ [_1561535] : [hBOOL(hAPP(_1561452, _1561535))]]], (45673 ^ _778908) ^ [_1677923, _1677925, _1677927, _1677929] : [class_Lattices_Osemilattice__sup(_1677923), hBOOL(hAPP(c_Finite__Set_Ofinite(_1677923), _1677925)), 45683 ^ _778908 : [(45686 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1677923), 45682 ^ [_1677923, _1677925, _1677927, _1677929]), _1677927))], (45684 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677923), 45682 ^ [_1677923, _1677925, _1677927, _1677929]), _1677925)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1677923), hAPP(hAPP(c_Finite__Set_Ofold(_1677923, _1677923, c_Lattices_Osemilattice__sup__class_Osup(_1677923)), _1677929), _1677925)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1677923), _1677927), _1677929))))], (14597 ^ _778908) ^ [_1026762, _1026764, _1026766] : [-(_1026762 = 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), _1026762), _1026764)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026762), _1026766)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026764), _1026766))], (11637 ^ _778908) ^ [_973651, _973653, _973655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973651), _973653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973655), _973653))))], (13234 ^ _778908) ^ [_1001968, _1001970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001968), _1001970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1001968), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1001970)))], (41261 ^ _778908) ^ [_1563251, _1563253] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1563251), hAPP(c_Set_OCollect(_1563251), _1563253))), 41264 ^ _778908 : [(41271 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1563251), c_Orderings_Otop__class_Otop(tc_fun(_1563251, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1563251), hAPP(c_Set_OCollect(_1563251), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1563251), c_fNot), _1563253)))))], (41265 ^ _778908) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1563251), hAPP(c_Set_OCollect(_1563251), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1563251), c_fNot), _1563253)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1563251), c_Orderings_Otop__class_Otop(tc_fun(_1563251, tc_HOL_Obool)))))]]], (8424 ^ _778908) ^ [_920081, _920083, _920085] : [class_Rings_Osemiring__1(_920081), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920081), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920083), _920085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920081), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920081), _920083)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920081), _920085)))], (34018 ^ _778908) ^ [_1400482, _1400484, _1400486] : [class_Orderings_Olinorder(_1400482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400482), _1400484)), -(_1400484 = c_Orderings_Obot__class_Obot(tc_fun(_1400482, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1400482, c_Orderings_Oord__class_Omax(_1400482), hAPP(hAPP(c_Set_Oinsert(_1400482), _1400486), _1400484)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1400482), _1400486), c_Big__Operators_Olattice_OSup__fin(_1400482, c_Orderings_Oord__class_Omax(_1400482), _1400484)))], (11294 ^ _778908) ^ [_967949, _967951, _967953, _967955] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_967949), 11297 ^ _778908 : [(11304 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967949), _967951), _967955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967949), _967951), _967953)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967949), _967955), _967953))))], (11298 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967949), _967951), _967953)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967949), _967955), _967953))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967949), _967951), _967955)))]]], (10365 ^ _778908) ^ [_952987, _952989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952987)), 10368 ^ _778908 : [(10375 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _952987), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _952987)), _952989)))], (10369 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _952987)), _952989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _952987), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952989))))]]], (30486 ^ _778908) ^ [_1324957, _1324959, _1324961, _1324963, _1324965] : [-(_1324957 = c_Orderings_Obot__class_Obot(tc_fun(_1324959, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1324961), _1324963), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324959, tc_fun(_1324961, tc_HOL_Obool)), _1324957), _1324965)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324959, tc_fun(_1324961, tc_HOL_Obool)), _1324957), hAPP(hAPP(c_COMBB(tc_fun(_1324961, tc_HOL_Obool), tc_fun(_1324961, tc_HOL_Obool), _1324959), hAPP(c_Set_Oinsert(_1324961), _1324963)), _1324965)))], (14696 ^ _778908) ^ [_1028244] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1028244, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1028244)], (1302 ^ _778908) ^ [_798057, _798059] : [-(class_Lattices_Obounded__lattice__top(_798057)), _798059 = _798057, class_Lattices_Obounded__lattice__top(_798059)], (41812 ^ _778908) ^ [_1583724, _1583726, _1583728, _1583730, _1583732, _1583734, _1583736, _1583738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583724, _1583726), tc_HOL_Obool)), _1583728), hAPP(hAPP(c_Product__Type_OSigma(_1583724, _1583726), _1583730), hAPP(c_COMBK(tc_fun(_1583726, tc_HOL_Obool), _1583724), _1583732)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583726, _1583734), tc_HOL_Obool)), _1583736), hAPP(hAPP(c_Product__Type_OSigma(_1583726, _1583734), _1583732), hAPP(c_COMBK(tc_fun(_1583734, tc_HOL_Obool), _1583726), _1583738)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583724, _1583734), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1583724, _1583726, _1583734), _1583728), _1583736)), hAPP(hAPP(c_Product__Type_OSigma(_1583724, _1583734), _1583730), hAPP(c_COMBK(tc_fun(_1583734, tc_HOL_Obool), _1583724), _1583738)))))], (49231 ^ _778908) ^ [_1766182, _1766184, _1766186] : [-(hAPP(c_List_Orotate1(_1766182), hAPP(c_List_Orotate(_1766182, _1766184), _1766186)) = hAPP(c_List_Orotate(_1766182, _1766184), hAPP(c_List_Orotate1(_1766182), _1766186)))], (48542 ^ _778908) ^ [_1748707, _1748709, _1748711] : [-(hAPP(hAPP(c_List_Otake(_1748707), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1748707), _1748709), _1748711)) = hAPP(hAPP(c_List_Olist_OCons(_1748707), _1748709), c_List_Olist_ONil(_1748707)))], (8594 ^ _778908) ^ [_922892, _922894, _922896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922892), _922894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922892), _922896)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _922894), _922896))))], (49169 ^ _778908) ^ [_1764934, _1764936, _1764938] : [-(hAPP(hAPP(c_List_Odrop(_1764934), hAPP(c_Nat_OSuc, _1764936)), _1764938) = hAPP(hAPP(c_List_Odrop(_1764934), _1764936), hAPP(c_List_Otl(_1764934), _1764938)))], (21773 ^ _778908) ^ [_1155243, _1155245, _1155247, _1155249] : [class_Fields_Olinordered__field__inverse__zero(_1155243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155243), _1155245), _1155247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155243), _1155249), c_Groups_Ozero__class_Ozero(_1155243))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155243), c_Groups_Ozero__class_Ozero(_1155243)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155243), _1155245), _1155247))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155243), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155243), _1155249), _1155245)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155243), _1155249), _1155247))))], (12285 ^ _778908) ^ [_985293, _985295] : [class_Groups_Olinordered__ab__group__add(_985293), 12288 ^ _778908 : [(12295 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985293), _985295), c_Groups_Ozero__class_Ozero(_985293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985293), _985295), hAPP(c_Groups_Ouminus__class_Ouminus(_985293), _985295))))], (12289 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985293), _985295), hAPP(c_Groups_Ouminus__class_Ouminus(_985293), _985295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985293), _985295), c_Groups_Ozero__class_Ozero(_985293))))]]], (26513 ^ _778908) ^ [_1245884, _1245886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1245884), _1245886)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1245886), _1245884))], (3628 ^ _778908) ^ [_834704, _834706, _834708, _834710] : [-(c_Sum__Type_OInr(_834710, _834706) = c_Sum__Type_OInr(_834708, _834704)), _834710 = _834708, _834706 = _834704], (27813 ^ _778908) ^ [_1272171, _1272173] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1272171, _1272173)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1272173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1272171), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (33141 ^ _778908) ^ [_1383462] : [class_Rings_Oring__1(_1383462), -(hBOOL(hAPP(hAPP(c_member(_1383462), c_Groups_Oone__class_Oone(_1383462)), c_Int_Oring__1__class_OInts(_1383462))))], (14112 ^ _778908) ^ [_1017777, _1017779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017777), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017779), _1017777)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017777, _1017779) = _1017777)], (10433 ^ _778908) ^ [_954175, _954177] : [_954175 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954175), _954177), -(_954177 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_954175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5004 ^ _778908) ^ [_856290, _856292, _856294, _856296, _856298, _856300] : [-(c_Map_Omap__of(_856300, _856296, _856292) = c_Map_Omap__of(_856298, _856294, _856290)), _856300 = _856298, _856296 = _856294, _856292 = _856290], (16735 ^ _778908) ^ [_1066641, _1066643] : [16736 ^ _778908 : [(16739 ^ _778908) ^ [] : [_1066643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16737 ^ _778908) ^ [] : [-(_1066641 = 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), _1066641)), _1066643))))], (14075 ^ _778908) ^ [_1017161, _1017163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017161), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017161), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017163, _1017161))))], (40290 ^ _778908) ^ [_1542123, _1542125, _1542127, _1542129] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1542123, _1542125), _1542127), _1542129) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542123, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool)), _1542127), hAPP(hAPP(c_COMBS(_1542123, tc_fun(_1542125, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool)), tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542125, tc_HOL_Obool), tc_fun(tc_fun(_1542125, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool)), tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool)), _1542123), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542125, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool))), _1542129)), hAPP(hAPP(c_COMBC(_1542123, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool), tc_fun(_1542125, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1542125, tc_fun(tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool), tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool), tc_fun(_1542125, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool))), _1542123), c_COMBC(_1542125, tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool), tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1542125, tc_prod(_1542123, _1542125)), tc_fun(_1542125, tc_fun(tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool), tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool))), _1542123), hAPP(c_COMBB(tc_prod(_1542123, _1542125), tc_fun(tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool), tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool)), _1542125), c_Set_Oinsert(tc_prod(_1542123, _1542125)))), c_Product__Type_OPair(_1542123, _1542125)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542123, _1542125), tc_HOL_Obool))))))], (26605 ^ _778908) ^ [_1247526, _1247528] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1247526)), _1247528)), 26608 ^ _778908 : [(26615 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247526))), -(_1247528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26609 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247526)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1247526), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247528))))]]], (27404 ^ _778908) ^ [_1263542, _1263544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263542)), 27413 ^ _778908 : [(27416 ^ _778908) ^ [] : [hBOOL(hAPP(_1263544, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27409 ^ [_1263542, _1263544]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27410 ^ [_1263542, _1263544]), _1263542))))], (27414 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1263544, 27409 ^ [_1263542, _1263544])))]], 27417 ^ _778908 : [(27420 ^ _778908) ^ [] : [hBOOL(hAPP(_1263544, 27409 ^ [_1263542, _1263544]))], (27418 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1263544, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 27409 ^ [_1263542, _1263544]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 27410 ^ [_1263542, _1263544]), _1263542)))))]], 27421 ^ _778908 : [(27431 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1263544, 27438 ^ [_1263542, _1263544]))), 27432 ^ _778908 : [(27433 ^ _778908) ^ [_1264089] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1264089), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1263542))), hBOOL(hAPP(_1263544, _1264089))]]], (27422 ^ _778908) ^ [] : [27423 ^ _778908 : [(27424 ^ _778908) ^ [_1263974] : [hBOOL(hAPP(_1263544, _1263974))]], 27426 ^ _778908 : [(27429 ^ _778908) ^ [] : [-(hBOOL(hAPP(_1263544, 27425 ^ [_1263542, _1263544])))], (27427 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27425 ^ [_1263542, _1263544]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1263542))))]]]]], (178 ^ _778908) ^ [_781407, _781409, _781411, _781413, _781415, _781417, _781419, _781421] : [-(c_Orderings_Oorder_Ostrict__mono(_781419, _781415, _781411, _781407)), c_Orderings_Oorder_Ostrict__mono(_781421, _781417, _781413, _781409), _781421 = _781419, _781417 = _781415, _781413 = _781411, _781409 = _781407], (38740 ^ _778908) ^ [_1505542, _1505544, _1505546, _1505548, _1505550] : [c_Fun_Oinj__on(_1505542, _1505544, _1505546, c_Orderings_Otop__class_Otop(tc_fun(_1505542, tc_HOL_Obool))), hAPP(_1505546, _1505548) = hAPP(_1505546, _1505550), -(_1505548 = _1505550)], (11889 ^ _778908) ^ [_978018, _978020, _978022, _978024] : [class_Groups_Oordered__comm__monoid__add(_978018), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978018), c_Groups_Ozero__class_Ozero(_978018)), _978020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978018), _978022), _978024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978018), _978022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978018), _978020), _978024))))], (28884 ^ _778908) ^ [_1292750, _1292752, _1292754, _1292756] : [-(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), _1292750, _1292752)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292754, _1292756)))), 28885 ^ _778908 : [(28888 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292754), _1292750)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292752), _1292756))], (28886 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292750), _1292752)))]]], (17951 ^ _778908) ^ [_1089439, _1089441] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089439))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089439), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089441)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15042 ^ _778908) ^ [_1034045, _1034047, _1034049] : [-(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), _1034045), _1034047)), _1034047)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1034045, _1034047))), _1034049) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1034045), _1034049))], (4778 ^ _778908) ^ [_852847, _852849, _852851, _852853] : [-(c_Big__Operators_Olinorder__class_OMax(_852853, _852849) = c_Big__Operators_Olinorder__class_OMax(_852851, _852847)), _852853 = _852851, _852849 = _852847], (20443 ^ _778908) ^ [_1131913, _1131915, _1131917] : [class_Fields_Olinordered__field(_1131913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131913), _1131915), c_Groups_Ozero__class_Ozero(_1131913))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131913), _1131917), c_Groups_Ozero__class_Ozero(_1131913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131913), c_Groups_Ozero__class_Ozero(_1131913)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131913), _1131915), _1131917))))], (49928 ^ _778908) ^ [_1781453, _1781455, _1781457, _1781459, _1781461, _1781463] : [class_Orderings_Olinorder(_1781453), -(hBOOL(hAPP(_1781455, _1781457))), -(hAPP(c_List_Ofilter(_1781459, _1781455), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1781459, _1781453, _1781461), _1781457), _1781463)) = hAPP(c_List_Ofilter(_1781459, _1781455), _1781463))], (41171 ^ _778908) ^ [_1561216] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1561216, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1561216), hAPP(c_COMBK(tc_HOL_Obool, _1561216), c_fFalse)))], (10212 ^ _778908) ^ [_950465, _950467] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _950465)), hAPP(c_Int_Onat, _950467)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _950465), _950467))], (25125 ^ _778908) ^ [_1220586, _1220588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1220586), _1220588)), -(c_Quickcheck_Obeyond(_1220586, _1220588) = _1220588)], (30574 ^ _778908) ^ [_1326715] : [class_Lattices_Oboolean__algebra(_1326715), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1326715), c_Orderings_Otop__class_Otop(_1326715)) = c_Orderings_Obot__class_Obot(_1326715))], (7897 ^ _778908) ^ [_910870, _910872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910870), hAPP(c_Nat_OSuc, _910872))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910870), _910872))), -(_910870 = _910872)], (50447 ^ _778908) ^ [_1792114, _1792116] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1792114), _1792116)) = c_List_Oupt(_1792114, _1792116))], (46471 ^ _778908) ^ [_1696639] : [c_List_Onat__list(_1696639), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1696639)))], (46803 ^ _778908) ^ [_1705058, _1705060, _1705062] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1705058), _1705060)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1705058)), hAPP(c_Set_OCollect(tc_List_Olist(_1705058)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1705058), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1705058)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705058), tc_fun(_1705058, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1705058, tc_HOL_Obool), tc_fun(tc_fun(_1705058, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1705058)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1705058, tc_HOL_Obool))), c_List_Oset(_1705058))), _1705060))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705058), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1705058)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1705058)))), _1705062))))))], (286 ^ _778908) ^ [_783101, _783103] : [-(c_Nat__Transfer_Ois__nat(_783101)), _783103 = _783101, c_Nat__Transfer_Ois__nat(_783103)], (47190 ^ _778908) ^ [_1716909, _1716911, _1716913] : [hBOOL(hAPP(c_List_Odistinct(_1716909), _1716911)), -(hBOOL(hAPP(c_List_Odistinct(_1716909), c_List_Osublist(_1716909, _1716911, _1716913))))], (48973 ^ _778908) ^ [_1760557, _1760559, _1760561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760557)), _1760561)), _1760559)), -(hAPP(hAPP(c_List_Odrop(_1760557), _1760559), _1760561) = c_List_Olist_ONil(_1760557))], (16665 ^ _778908) ^ [_1065426] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1065426)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1065426))], (16432 ^ _778908) ^ [_1061219, _1061221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1061219)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1061221)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1061221), _1061219)), _1061221) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1061221), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061219), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (14808 ^ _778908) ^ [_1030149, _1030151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1030149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1030151), _1030149)), _1030151)))], (6915 ^ _778908) ^ [_893124] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OLoc(_893124)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32827 ^ _778908) ^ [_1376777, _1376779, _1376781, _1376783, _1376785, _1376787] : [hBOOL(hAPP(hAPP(c_member(_1376777), _1376779), c_SetInterval_Oord_OatLeastLessThan(_1376777, _1376781, _1376783, _1376785, _1376787))), 32830 ^ _778908 : [(32833 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1376783, _1376779), _1376787)))], (32831 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(_1376781, _1376785), _1376779)))]]], (7114 ^ _778908) ^ [_897872] : [hAPP(c_Nat_OSuc, _897872) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43103 ^ _778908) ^ [_1615407, _1615409, _1615411, _1615413] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615407, _1615407)), _1615409), c_Transitive__Closure_Otrancl(_1615407, _1615411))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615407, _1615407), tc_HOL_Obool)), _1615411), _1615413)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615407, _1615407)), _1615409), c_Transitive__Closure_Otrancl(_1615407, _1615413))))], (11488 ^ _778908) ^ [_971189, _971191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _971189)), hAPP(c_Nat_OSuc, _971191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971189), _971191)))], (13528 ^ _778908) ^ [_1006996, _1006998, _1007000, _1007002, _1007004] : [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), _1006996), _1006998)), _1007000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1006996), _1007002)), _1007004))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007000), _1006996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007004), _1006996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006998), _1007002)))], (16617 ^ _778908) ^ [_1064412, _1064414, _1064416] : [class_Groups_Oordered__ab__group__add__abs(_1064412), -(hAPP(c_Groups_Oabs__class_Oabs(_1064412), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064412), hAPP(c_Groups_Oabs__class_Oabs(_1064412), _1064414)), hAPP(c_Groups_Oabs__class_Oabs(_1064412), _1064416))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064412), hAPP(c_Groups_Oabs__class_Oabs(_1064412), _1064414)), hAPP(c_Groups_Oabs__class_Oabs(_1064412), _1064416)))], (5817 ^ _778908) ^ [_871529] : [-(hAPP(c_Nat_Osize__class_Osize(tc_String_Oliteral), _871529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43697 ^ _778908) ^ [_1630775, _1630777, _1630779] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1630775, _1630775, _1630775), _1630777), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630775, _1630775), tc_HOL_Obool), _1630779), _1630777)) = hAPP(hAPP(c_Relation_Orel__comp(_1630775, _1630775, _1630775), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1630775, _1630775), tc_HOL_Obool), _1630779), _1630777)), _1630777))], (2300 ^ _778908) ^ [_813584, _813586, _813588, _813590, _813592, _813594, _813596, _813598] : [-(c_Sum__Type_OSuml(_813598, _813594, _813590, _813586) = c_Sum__Type_OSuml(_813596, _813592, _813588, _813584)), _813598 = _813596, _813594 = _813592, _813590 = _813588, _813586 = _813584], (6771 ^ _778908) ^ [_889995, _889997, _889999, _890001] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_889995, _889997)), _889999), _890001)), 6776 ^ _778908 : [(6779 ^ _778908) ^ [] : [hBOOL(hAPP(_889995, _889999))], (6777 ^ _778908) ^ [] : [-(_890001 = _889999)]], 6780 ^ _778908 : [(6786 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_889995, _889997)), 6782 ^ [_889995, _889997, _889999, _890001]), _890001)))], (6784 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889997), _889999), 6782 ^ [_889995, _889997, _889999, _890001])))], (6781 ^ _778908) ^ [] : [-(hBOOL(hAPP(_889995, _889999)))]]], (24743 ^ _778908) ^ [_1212123, _1212125, _1212127, _1212129, _1212131, _1212133] : [hAPP(_1212129, hAPP(c_Product__Type_Ofst(_1212123, _1212127), _1212131)) = hAPP(_1212133, hAPP(c_Product__Type_Ofst(_1212123, _1212127), _1212131)), -(hAPP(c_Product__Type_Oapfst(_1212123, _1212125, _1212127, _1212129), _1212131) = hAPP(c_Product__Type_Oapfst(_1212123, _1212125, _1212127, _1212133), _1212131))], (51371 ^ _778908) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (41912 ^ _778908) ^ [_1587379, _1587381, _1587383] : [c_Wellfounded_Owf(_1587379, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587379, _1587379), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587379, _1587379), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1587379, _1587379, _1587379), _1587381), _1587381)), hAPP(hAPP(c_Relation_Orel__comp(_1587379, _1587379, _1587379), _1587383), _1587381))), _1587383)), -(c_Wellfounded_Owf(_1587379, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587379, _1587379), tc_HOL_Obool)), _1587381), _1587383)))], (29179 ^ _778908) ^ [] : [-(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))))], (41420 ^ _778908) ^ [_1568740] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1568740) = 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), _1568740), c_Int_Onat)))))], (21701 ^ _778908) ^ [_1153853, _1153855, _1153857, _1153859] : [class_Fields_Olinordered__field(_1153853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153853), c_Groups_Ozero__class_Ozero(_1153853)), _1153855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153853), _1153857), _1153855)), _1153859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153853), _1153857), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153853), _1153859), _1153855))))], (43586 ^ _778908) ^ [_1627828, _1627830] : [-(c_Transitive__Closure_Otrancl(_1627828, hAPP(c_Relation_Oconverse(_1627828, _1627828), _1627830)) = hAPP(c_Relation_Oconverse(_1627828, _1627828), c_Transitive__Closure_Otrancl(_1627828, _1627830)))], (35212 ^ _778908) ^ [_1426300, _1426302] : [c_Relation_Oirrefl(_1426300, _1426302), 35215 ^ _778908 : [(35216 ^ _778908) ^ [_1426382] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1426300, _1426300)), hAPP(hAPP(c_Product__Type_OPair(_1426300, _1426300), _1426382), _1426382)), _1426302))]]], (18971 ^ _778908) ^ [_1105741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1105741)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105741), c_Int_OMin)))], (2112 ^ _778908) ^ [_810350, _810352, _810354, _810356, _810358, _810360, _810362, _810364, _810366, _810368] : [-(c_Nitpick_Opair__box_Opair__box__size(_810368, _810364, _810360, _810356, _810352) = c_Nitpick_Opair__box_Opair__box__size(_810366, _810362, _810358, _810354, _810350)), _810368 = _810366, _810364 = _810362, _810360 = _810358, _810356 = _810354, _810352 = _810350], (8327 ^ _778908) ^ [_918377] : [_918377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918377) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24667 ^ _778908) ^ [_1210440] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1210440), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1210440)], (11452 ^ _778908) ^ [_970578, _970580, _970582] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970578), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970580), _970582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970578), _970580)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970578), _970582)))], (49652 ^ _778908) ^ [_1775541, _1775543, _1775545, _1775547] : [-(_1775541 = c_List_Olist_ONil(_1775543)), -(c_List_Olast(_1775545, hAPP(hAPP(c_List_Omap(_1775543, _1775545), _1775547), _1775541)) = hAPP(_1775547, c_List_Olast(_1775543, _1775541)))], (24027 ^ _778908) ^ [_1198036, _1198038, _1198040] : [-(hAPP(c_Product__Type_Ofst(_1198036, _1198038), _1198040) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198036, _1198038, _1198036), c_COMBK(_1198036, _1198038)), _1198040))], (5847 ^ _778908) ^ [_871933, _871935, _871937, _871939, _871941] : [c_Groups_Osemigroup(_871933, _871935), -(hAPP(hAPP(_871935, hAPP(hAPP(_871935, _871937), _871939)), _871941) = hAPP(hAPP(_871935, _871937), hAPP(hAPP(_871935, _871939), _871941)))], (8584 ^ _778908) ^ [_922839, _922841] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922839), _922841))), -(_922839 = _922841), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _922841), _922839)))], (41900 ^ _778908) ^ [_1587049, _1587051] : [hAPP(hAPP(c_Relation_Orel__comp(_1587049, _1587049, _1587049), _1587051), _1587051) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1587049, _1587049), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1587049, _1587051))], (4708 ^ _778908) ^ [_851796, _851798] : [_851798 = _851796, -(c_Groups_Otimes__class_Otimes(_851798) = c_Groups_Otimes__class_Otimes(_851796))], (47597 ^ _778908) ^ [_1725990, _1725992, _1725994, _1725996, _1725998, _1726000] : [-(hAPP(c_List_Olist_Olist__case(_1725990, _1725992, _1725994, _1725996), hAPP(hAPP(c_List_Olist_OCons(_1725992), _1725998), _1726000)) = hAPP(hAPP(_1725996, _1725998), _1726000))], (20601 ^ _778908) ^ [_1134607, _1134609, _1134611, _1134613] : [class_Fields_Ofield__inverse__zero(_1134607), 20604 ^ _778908 : [(20605 ^ _778908) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134607), _1134609), _1134611) = _1134613, 20608 ^ _778908 : [(20615 ^ _778908) ^ [] : [_1134611 = c_Groups_Ozero__class_Ozero(_1134607), -(_1134613 = c_Groups_Ozero__class_Ozero(_1134607))], (20609 ^ _778908) ^ [] : [-(_1134611 = c_Groups_Ozero__class_Ozero(_1134607)), -(_1134609 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134607), _1134613), _1134611))]]], (20621 ^ _778908) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134607), _1134609), _1134611) = _1134613), 20624 ^ _778908 : [(20627 ^ _778908) ^ [] : [_1134609 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134607), _1134613), _1134611)], (20625 ^ _778908) ^ [] : [_1134611 = c_Groups_Ozero__class_Ozero(_1134607)]], 20628 ^ _778908 : [(20631 ^ _778908) ^ [] : [_1134613 = c_Groups_Ozero__class_Ozero(_1134607)], (20629 ^ _778908) ^ [] : [-(_1134611 = c_Groups_Ozero__class_Ozero(_1134607))]]]]], (25295 ^ _778908) ^ [_1223757, _1223759, _1223761, _1223763] : [class_Rings_Ocomm__semiring__1(_1223757), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223757), _1223759), _1223761)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223757), _1223759), _1223763)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223757), _1223759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223757), _1223761), _1223763))))], (28872 ^ _778908) ^ [_1292529, _1292531, _1292533, _1292535] : [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), _1292529, _1292531)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292533, _1292535))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292529), _1292531)), 28879 ^ _778908 : [(28882 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292531), _1292535)))], (28880 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1292533), _1292529)))]]], (23687 ^ _778908) ^ [_1191765, _1191767, _1191769, _1191771] : [class_Orderings_Olinorder(_1191765), 23690 ^ _778908 : [(23691 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191765), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191765), _1191767), _1191769)), _1191771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191765), _1191767), _1191771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191765), _1191769), _1191771)))], (23701 ^ _778908) ^ [] : [23702 ^ _778908 : [(23705 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191765), _1191769), _1191771))], (23703 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191765), _1191767), _1191771))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191765), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191765), _1191767), _1191769)), _1191771)))]]], (17507 ^ _778908) ^ [_1081271, _1081273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1081271)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1081271), _1081273)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1081271)), _1081273))], (42970 ^ _778908) ^ [_1612383, _1612385, _1612387] : [c_Wellfounded_Owf(_1612383, _1612385), hBOOL(hAPP(hAPP(c_member(tc_prod(_1612383, _1612383)), hAPP(hAPP(c_Product__Type_OPair(_1612383, _1612383), hAPP(_1612387, hAPP(c_Nat_OSuc, 42973 ^ [_1612383, _1612385, _1612387]))), hAPP(_1612387, 42973 ^ [_1612383, _1612385, _1612387]))), _1612385))], (50805 ^ _778908) ^ [_1799924, _1799926] : [c_List_Olist_ONil(_1799924) = c_List_Oconcat(_1799924, _1799926), 50808 ^ _778908 : [(50809 ^ _778908) ^ [_1800015] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1799924)), _1800015), hAPP(c_List_Oset(tc_List_Olist(_1799924)), _1799926))), -(_1800015 = c_List_Olist_ONil(_1799924))]]], (40004 ^ _778908) ^ [_1533917, _1533919, _1533921] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1533917, _1533919, c_Orderings_Obot__class_Obot(tc_fun(_1533917, tc_HOL_Obool))), _1533921))], (50939 ^ _778908) ^ [_1802645, _1802647] : [-(hAPP(c_List_Oset(_1802645), hAPP(c_List_Orev(_1802645), _1802647)) = hAPP(c_List_Oset(_1802645), _1802647))], (51025 ^ _778908) ^ [_1805317, _1805319, _1805321, _1805323] : [class_Orderings_Olinorder(_1805317), c_List_Olinorder__class_Osorted(_1805317, hAPP(c_List_Orev(_1805317), _1805319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1805321), _1805323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1805323), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805317)), _1805319))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1805317), hAPP(hAPP(c_List_Onth(_1805317), _1805319), _1805323)), hAPP(hAPP(c_List_Onth(_1805317), _1805319), _1805321))))], (17293 ^ _778908) ^ [_1077535, _1077537, _1077539, _1077541] : [class_Rings_Olinordered__semidom(_1077535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077535), c_Groups_Oone__class_Oone(_1077535)), _1077537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077535), hAPP(hAPP(c_Power_Opower__class_Opower(_1077535), _1077537), _1077539)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077535), _1077537), _1077541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077539), _1077541)))], (48877 ^ _778908) ^ [_1758358, _1758360, _1758362, _1758364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758358), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758360)), _1758362))), -(hAPP(hAPP(c_List_Olist__update(_1758360, _1758362), _1758358), _1758364) = hAPP(hAPP(c_List_Oappend(_1758360), hAPP(hAPP(c_List_Otake(_1758360), _1758358), _1758362)), hAPP(hAPP(c_List_Olist_OCons(_1758360), _1758364), hAPP(hAPP(c_List_Odrop(_1758360), hAPP(c_Nat_OSuc, _1758358)), _1758362))))], (8582 ^ _778908) ^ [_922817] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _922817) = _922817)], (32819 ^ _778908) ^ [_1376602, _1376604] : [32820 ^ _778908 : [(32823 ^ _778908) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376604), _1376602))], (32821 ^ _778908) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1376602), _1376604)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1376602, _1376604))], (18077 ^ _778908) ^ [_1091419, _1091421, _1091423] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091419))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091419)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091421)), _1091423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091421)), _1091423))], (13444 ^ _778908) ^ [_1005408, _1005410, _1005412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005408)), _1005408 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1005410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005408), _1005412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1005412), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (3430 ^ _778908) ^ [_831609, _831611] : [_831611 = _831609, -(c_Hoare__Mirabelle_OMGT(_831611) = c_Hoare__Mirabelle_OMGT(_831609))], (36940 ^ _778908) ^ [_1465743, _1465745, _1465747] : [class_Lattices_Oboolean__algebra(_1465743), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1465743), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465743), _1465745), _1465747)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1465743), hAPP(c_Groups_Ouminus__class_Ouminus(_1465743), _1465745)), hAPP(c_Groups_Ouminus__class_Ouminus(_1465743), _1465747)))], (26599 ^ _778908) ^ [_1247382, _1247384] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1247382), _1247384)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1247384), _1247382)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1247384)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1247382)))], (32162 ^ _778908) ^ [_1363040, _1363042, _1363044, _1363046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363040), _1363042)), hBOOL(hAPP(hAPP(c_member(_1363040), _1363044), _1363042)), -(hBOOL(hAPP(hAPP(c_member(_1363040), _1363044), _1363046))), -(hAPP(c_Finite__Set_Ocard(_1363040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363040, tc_HOL_Obool)), _1363042), hAPP(hAPP(c_Set_Oinsert(_1363040), _1363044), _1363046))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1363040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363040, tc_HOL_Obool)), _1363042), _1363046))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (39386 ^ _778908) ^ [_1519356, _1519358, _1519360, _1519362, _1519364, _1519366, _1519368, _1519370] : [c_Finite__Set_Ofolding__image(_1519356, _1519358, _1519360, _1519362, _1519364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519358), _1519366)), -(hAPP(hAPP(_1519364, hAPP(hAPP(c_COMBS(_1519358, _1519356, _1519356), hAPP(hAPP(c_COMBB(_1519356, tc_fun(_1519356, _1519356), _1519358), _1519360), _1519368)), _1519370)), _1519366) = hAPP(hAPP(_1519360, hAPP(hAPP(_1519364, _1519368), _1519366)), hAPP(hAPP(_1519364, _1519370), _1519366)))], (40305 ^ _778908) ^ [_1542748, _1542750, _1542752, _1542754] : [-(c_Fun_Oinj__on(_1542748, tc_prod(_1542750, _1542748), 40303 ^ [_1542748, _1542750, _1542752, _1542754], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542750, tc_fun(_1542748, tc_HOL_Obool)), _1542752), _1542754)))], (8934 ^ _778908) ^ [_928066, _928068, _928070] : [class_Rings_Ocomm__semiring__1(_928066), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928066), _928068), _928070)), _928070) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928066), _928068), c_Groups_Oone__class_Oone(_928066))), _928070))], (37354 ^ _778908) ^ [_1475559, _1475561, _1475563, _1475565, _1475567] : [c_Equiv__Relations_Oequiv(_1475559, _1475561, _1475563), hBOOL(hAPP(hAPP(c_member(tc_fun(_1475559, tc_HOL_Obool)), _1475565), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475559), _1475561), _1475563))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1475559, tc_HOL_Obool)), _1475567), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475559), _1475561), _1475563))), -(_1475565 = _1475567), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475559, tc_HOL_Obool)), _1475565), _1475567) = c_Orderings_Obot__class_Obot(tc_fun(_1475559, tc_HOL_Obool)))], (43731 ^ _778908) ^ [_1631552, _1631554, _1631556, _1631558] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631552, _1631552)), hAPP(hAPP(c_Product__Type_OPair(_1631552, _1631552), _1631554), _1631556)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1631552, _1631552), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1631558))), -(_1631554 = _1631556)], (50571 ^ _778908) ^ [_1794411, _1794413] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1794411, _1794413) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1794411), hAPP(c_Nat_OSuc, _1794413))))], (51583 ^ _778908) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (29215 ^ _778908) ^ [_1300952] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1300952))))], (6447 ^ _778908) ^ [_882988, _882990, _882992, _882994] : [hAPP(c_Com_Ocom_OBODY, _882988) = c_Com_Ocom_OCond(_882990, _882992, _882994)], (12724 ^ _778908) ^ [_992821, _992823, _992825] : [class_Groups_Oordered__comm__monoid__add(_992821), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992821), _992823), c_Groups_Ozero__class_Ozero(_992821))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992821), _992825), c_Groups_Ozero__class_Ozero(_992821))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_992821), _992823), _992825)), c_Groups_Ozero__class_Ozero(_992821))))], (33005 ^ _778908) ^ [_1380359, _1380361, _1380363] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1380359, _1380361, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1380359)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1380359), _1380363), c_Com_Ocom_OSKIP), _1380363)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1380359), tc_HOL_Obool)))))], (39062 ^ _778908) ^ [_1512095, _1512097, _1512099, _1512101, _1512103, _1512105] : [c_Fun_Oinj__on(_1512095, _1512097, _1512099, _1512101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512097, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512095, _1512097, _1512099), _1512101)), _1512103)), c_Fun_Oinj__on(_1512097, _1512095, _1512105, _1512103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512095, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512097, _1512095, _1512105), _1512103)), _1512101)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512095), _1512101)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512097), _1512103)), -(hAPP(c_Finite__Set_Ocard(_1512095), _1512101) = hAPP(c_Finite__Set_Ocard(_1512097), _1512103))], (30508 ^ _778908) ^ [_1325328, _1325330] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325328), _1325330))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1325328, _1325330) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (27258 ^ _778908) ^ [_1260411, _1260413] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1260411), hAPP(c_Nat_OSuc, _1260413)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1260411, _1260413))], (12704 ^ _778908) ^ [] : [-(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))], (47613 ^ _778908) ^ [_1726443, _1726445, _1726447, _1726449] : [-(hAPP(hAPP(c_List_Onth(_1726443), hAPP(hAPP(c_List_Olist_OCons(_1726443), _1726445), _1726447)), hAPP(c_Nat_OSuc, _1726449)) = hAPP(hAPP(c_List_Onth(_1726443), _1726447), _1726449))], (47463 ^ _778908) ^ [_1722969] : [-(hAPP(c_List_Oset(_1722969), c_List_Olist_ONil(_1722969)) = c_Orderings_Obot__class_Obot(tc_fun(_1722969, tc_HOL_Obool)))], (19549 ^ _778908) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (47575 ^ _778908) ^ [_1724994, _1724996, _1724998] : [-(hAPP(c_Map_Omap__of(_1724994, _1724996, c_List_Olist_ONil(tc_prod(_1724994, _1724996))), _1724998) = c_Option_Ooption_ONone(_1724996))]], input).
% 52.25/51.26  ncf('1',plain,[-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, v_pn), 51731 ^ [], c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 51734 ^ []))],start(51736 ^ 0)).
% 52.25/51.26  ncf('1.1',plain,[c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, v_pn), 51731 ^ [], c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 51734 ^ []), 7047 : -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, 7045 ^ [v_pn, 51731 ^ [], c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 51734 ^ []]))],extension(7042 ^ 1,bind([[_896717, _896719, _896721, _896723], [v_pn, 51731 ^ [], c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 51734 ^ []]]))).
% 52.25/51.26  ncf('1.1.1',plain,[c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, 7045 ^ [v_pn, 51731 ^ [], c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 51734 ^ []])],extension(7118 ^ 4,bind([[_897942], [7045 ^ [v_pn, 51731 ^ [], c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 51734 ^ []]]]))).
% 52.25/51.26  %-----------------------------------------------------
% 52.25/51.26  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------