%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW311+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:55 EDT 2023

% Result   : Theorem 47.10s 46.09s
% Output   : Proof 47.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWW311+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 22:49:59 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 47.10/46.09  
% 47.10/46.09  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 47.10/46.09  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.10/46.09  %-----------------------------------------------------
% 47.10/46.09  ncf(matrix, plain, [(52738 ^ _2085210) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, 52734 ^ [], v_ts)], (52736 ^ _2085210) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), 52734 ^ [])))], !, (2020 ^ _779854) ^ [_809183, _809185, _809187, _809189, _809191, _809193, _809195, _809197] : [-(c_Sum__Type_OPlus(_809197, _809193, _809189, _809185) = c_Sum__Type_OPlus(_809195, _809191, _809187, _809183)), _809197 = _809195, _809193 = _809191, _809189 = _809187, _809185 = _809183], (28693 ^ _779854) ^ [_1298424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1298424)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1298424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44805 ^ _779854) ^ [_1676668] : [class_Orderings_Olinorder(_1676668), -(c_Finite__Set_Ofun__left__comm(_1676668, tc_List_Olist(_1676668), c_List_Olinorder__class_Oinsort__key(_1676668, _1676668, c_COMBI(_1676668))))], (36975 ^ _779854) ^ [_1473238, _1473240, _1473242, _1473244, _1473246, _1473248] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473238, _1473238)), hAPP(hAPP(c_Product__Type_OPair(_1473238, _1473238), _1473240), _1473242)), hAPP(hAPP(c_Relation_Oinv__image(_1473244, _1473238), _1473246), _1473248))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473244, _1473244)), hAPP(hAPP(c_Product__Type_OPair(_1473244, _1473244), hAPP(_1473248, _1473240)), hAPP(_1473248, _1473242))), _1473246)))], (36245 ^ _779854) ^ [_1456205] : [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), _1456205))), -(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), _1456205)) = 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), _1456205))))], (24264 ^ _779854) ^ [_1219846, _1219848, _1219850] : [class_Rings_Olinordered__semidom(_1219846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219846), c_Groups_Oone__class_Oone(_1219846)), _1219848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219846), c_Groups_Oone__class_Oone(_1219846)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219846), _1219848), hAPP(c_Nat_OSuc, _1219850)))))], (45577 ^ _779854) ^ [_1693045, _1693047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1693045), _1693047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693045)), hAPP(c_Code__Numeral_Onat__of, _1693047))))], (34141 ^ _779854) ^ [_1411588, _1411590, _1411592, _1411594] : [class_Rings_Osemiring__1(_1411588), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1411590, _1411588), hAPP(c_COMBK(_1411588, _1411590), _1411592)), _1411594) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411588), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1411588), hAPP(c_Finite__Set_Ocard(_1411590), _1411594))), _1411592))], (17821 ^ _779854) ^ [_1102656, _1102658] : [17822 ^ _779854 : [(17825 ^ _779854) ^ [] : [_1102656 = _1102658], (17823 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102656), _1102658))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102656), hAPP(c_Nat_OSuc, _1102658))))], (4418 ^ _779854) ^ [_847100, _847102, _847104, _847106] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_847106, _847102) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_847104, _847100)), _847106 = _847104, _847102 = _847100], (38251 ^ _779854) ^ [_1504684, _1504686, _1504688, _1504690, _1504692, _1504694] : [-(_1504684 = c_Orderings_Obot__class_Obot(tc_fun(_1504686, tc_HOL_Obool))), 38257 ^ _779854 : [(38260 ^ _779854) ^ [] : [c_Fun_Oinj__on(_1504688, _1504690, _1504692, hAPP(_1504694, 38256 ^ [_1504684, _1504686, _1504688, _1504690, _1504692, _1504694]))], (38258 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504686), 38256 ^ [_1504684, _1504686, _1504688, _1504690, _1504692, _1504694]), _1504684)))]], -(c_Fun_Oinj__on(_1504688, _1504690, _1504692, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1504686, tc_fun(_1504688, tc_HOL_Obool)), _1504684), _1504694)))], (21857 ^ _779854) ^ [_1174712, _1174714] : [class_Rings_Odivision__ring__inverse__zero(_1174712), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174712), _1174714), c_Groups_Ozero__class_Ozero(_1174712)) = c_Groups_Ozero__class_Ozero(_1174712))], (36395 ^ _779854) ^ [_1459149, _1459151, _1459153, _1459155, _1459157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1459149, _1459151)), hAPP(_1459149, _1459153))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1459155, _1459155)), hAPP(hAPP(c_Product__Type_OPair(_1459155, _1459155), _1459151), _1459153)), c_Wellfounded_Omlex__prod(_1459155, _1459149, _1459157))))], (38340 ^ _779854) ^ [_1507273, _1507275, _1507277, _1507279, _1507281] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507273, _1507275), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507273, tc_HOL_Obool)), _1507277), _1507279)), hAPP(c_COMBK(tc_fun(_1507275, tc_HOL_Obool), _1507273), _1507281)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507273, _1507275), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507273, _1507275), _1507277), hAPP(c_COMBK(tc_fun(_1507275, tc_HOL_Obool), _1507273), _1507281))), hAPP(hAPP(c_Product__Type_OSigma(_1507273, _1507275), _1507279), hAPP(c_COMBK(tc_fun(_1507275, tc_HOL_Obool), _1507273), _1507281))))], (12338 ^ _779854) ^ [_995036, _995038, _995040, _995042] : [-(hBOOL(hAPP(hAPP(c_member(_995036), _995038), _995040))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995036, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995036), _995038), _995042)), _995040) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995036, tc_HOL_Obool)), _995042), _995040))], (33319 ^ _779854) ^ [_1385303, _1385305, _1385307, _1385309] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385303, tc_fun(_1385305, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385303, tc_HOL_Obool), _1385307)), _1385309) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1385303, tc_HOL_Obool), tc_fun(_1385305, tc_HOL_Obool)), _1385307), hAPP(hAPP(c_COMBC(tc_fun(_1385303, tc_HOL_Obool), tc_fun(_1385303, tc_fun(_1385305, tc_HOL_Obool)), tc_fun(_1385305, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385303, tc_fun(_1385305, tc_HOL_Obool))), _1385309)))], (26581 ^ _779854) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27081 ^ _779854) ^ [_1270929, _1270931, _1270933] : [class_Divides_Osemiring__div(_1270929), -(_1270931 = c_Groups_Ozero__class_Ozero(_1270929)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1270929), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1270929), _1270933), _1270931)), _1270931) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1270929), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1270929), _1270933), _1270931)), c_Groups_Oone__class_Oone(_1270929)))], (16455 ^ _779854) ^ [_1076032, _1076034, _1076036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076032), _1076034)), 16458 ^ _779854 : [(16465 ^ _779854) ^ [] : [_1076034 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076036), _1076032), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076034), _1076032) = _1076036)], (16459 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076034), _1076032) = _1076036, -(_1076034 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076036), _1076032))]]], (42679 ^ _779854) ^ [_1627233, _1627235, _1627237, _1627239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627233), _1627235)), -(hAPP(hAPP(c_List_Onth(_1627237), hAPP(hAPP(c_List_Otake(_1627237), _1627235), _1627239)), _1627233) = hAPP(hAPP(c_List_Onth(_1627237), _1627239), _1627233))], (37664 ^ _779854) ^ [_1490195, _1490197, _1490199, _1490201, _1490203, _1490205, _1490207, _1490209, _1490211] : [c_Equiv__Relations_Oequiv(_1490195, _1490197, _1490199), c_Equiv__Relations_Oequiv(_1490201, _1490203, _1490205), c_Equiv__Relations_Ocongruent2(_1490195, _1490201, tc_fun(_1490207, tc_HOL_Obool), _1490199, _1490205, _1490209), hBOOL(hAPP(hAPP(c_member(_1490201), _1490211), _1490203)), -(c_Equiv__Relations_Ocongruent(_1490195, tc_fun(_1490207, tc_HOL_Obool), _1490199, hAPP(hAPP(c_COMBB(tc_fun(_1490201, tc_fun(_1490207, tc_HOL_Obool)), tc_fun(_1490207, tc_HOL_Obool), _1490195), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490201, tc_fun(_1490207, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1490201, _1490201, _1490205), hAPP(hAPP(c_Set_Oinsert(_1490201), _1490211), c_Orderings_Obot__class_Obot(tc_fun(_1490201, tc_HOL_Obool)))))), _1490209)))], (8878 ^ _779854) ^ [_927713, _927715, _927717, _927719] : [class_Lattices_Osemilattice__sup(_927713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927713), _927715), _927717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927713), _927715), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927713), _927717), _927719))))], (28595 ^ _779854) ^ [_1296810] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1296810))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1296810)))))], (35260 ^ _779854) ^ [_1436812, _1436814, _1436816, _1436818, _1436820, _1436822] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1436812, _1436814, _1436816), _1436818), hAPP(hAPP(c_Product__Type_OPair(_1436812, _1436814), _1436820), _1436822)) = hAPP(hAPP(_1436818, _1436820), _1436822))], (24096 ^ _779854) ^ [_1216870, _1216872, _1216874] : [class_Power_Opower(_1216870), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1216870), _1216872), hAPP(c_Nat_OSuc, _1216874)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216870), _1216872), hAPP(hAPP(c_Power_Opower__class_Opower(_1216870), _1216872), _1216874)))], (41254 ^ _779854) ^ [_1588196, _1588198, _1588200, _1588202] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588196, _1588196)), hAPP(hAPP(c_Product__Type_OPair(_1588196, _1588196), _1588198), _1588200)), c_Transitive__Closure_Ortrancl(_1588196, _1588202))), -(_1588198 = _1588200), 41261 ^ _779854 : [(41264 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588196, _1588196)), hAPP(hAPP(c_Product__Type_OPair(_1588196, _1588196), _1588198), _1588200)), c_Transitive__Closure_Otrancl(_1588196, _1588202))))], (41262 ^ _779854) ^ [] : [_1588198 = _1588200]]], (52137 ^ _779854) ^ [_1833156, _1833158] : [class_Orderings_Oorder(_1833156), -(class_Orderings_Oorder(tc_fun(_1833158, _1833156)))], (51901 ^ _779854) ^ [_1829596, _1829598] : [_1829596 = _1829598, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829596), _1829598)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829598), _1829596)))], (29245 ^ _779854) ^ [_1307465, _1307467] : [class_Int_Onumber__ring(_1307465), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1307465), hAPP(c_Int_Onumber__class_Onumber__of(_1307465), _1307467)), c_Groups_Oone__class_Oone(_1307465)) = hAPP(c_Int_Onumber__class_Onumber__of(_1307465), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1307467), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (11626 ^ _779854) ^ [_981441, _981443] : [hBOOL(hAPP(hAPP(c_member(_981441), _981443), c_Orderings_Obot__class_Obot(tc_fun(_981441, tc_HOL_Obool))))], (50876 ^ _779854) ^ [_1808747, _1808749, _1808751, _1808753, _1808755] : [-(c_Fun_Obij__betw(_1808747, _1808749, _1808751, _1808753, _1808755)), c_Fun_Oinj__on(_1808747, _1808749, _1808751, _1808753), hAPP(c_Set_Oimage(_1808747, _1808749, _1808751), _1808753) = _1808755], (29733 ^ _779854) ^ [_1316066] : [class_Rings_Osemiring__1(_1316066), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1316066), c_Groups_Oone__class_Oone(_1316066)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1316066))], (30471 ^ _779854) ^ [_1329996, _1329998, _1330000] : [class_Divides_Osemiring__div(_1329996), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329996), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1329996), _1329998), _1330000)), _1330000)), c_Divides_Odiv__class_Omod(_1329996, _1329998, _1330000)) = _1329998)], (20063 ^ _779854) ^ [_1141567, _1141569] : [class_Groups_Ogroup__add(_1141567), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141567), c_Groups_Ozero__class_Ozero(_1141567)), _1141569) = hAPP(c_Groups_Ouminus__class_Ouminus(_1141567), _1141569))], (44538 ^ _779854) ^ [_1670785, _1670787, _1670789] : [-(hAPP(c_List_Oset(_1670785), hAPP(c_List_Orotate(_1670785, _1670787), _1670789)) = hAPP(c_List_Oset(_1670785), _1670789))], (19803 ^ _779854) ^ [_1137112, _1137114, _1137116, _1137118] : [class_Rings_Olinordered__ring__strict(_1137112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137112), _1137114), _1137116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137112), _1137118), c_Groups_Ozero__class_Ozero(_1137112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137112), _1137118), _1137116)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137112), _1137118), _1137114))))], (49465 ^ _779854) ^ [_1777786, _1777788, _1777790, _1777792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1777786), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1777788, _1777790, _1777786, _1777792) = 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(_1777788)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1777788)))], (16505 ^ _779854) ^ [_1077063, _1077065, _1077067, _1077069, _1077071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077063), _1077065)), -(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), _1077063), _1077067)), _1077069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077065), _1077067)), _1077071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1077069), 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), _1077065), _1077063)), _1077067)), _1077071)))], (32788 ^ _779854) ^ [_1370379, _1370381, _1370383, _1370385] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1370383), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370379, tc_fun(_1370383, tc_HOL_Obool)), _1370381), _1370385)))), 32789 ^ _779854 : [(32790 ^ _779854) ^ [_1370453] : [hBOOL(hAPP(hAPP(c_member(_1370379), _1370453), _1370381)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370383), hAPP(_1370385, _1370453)))]]], (34467 ^ _779854) ^ [_1419123, _1419125, _1419127, _1419129, _1419131, _1419133] : [class_Groups_Ocomm__monoid__mult(_1419123), c_Fun_Oinj__on(_1419125, _1419127, _1419129, _1419131), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1419127, _1419123), _1419133), hAPP(c_Set_Oimage(_1419125, _1419127, _1419129), _1419131)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1419125, _1419123), hAPP(c_Fun_Ocomp(_1419127, _1419123, _1419125, _1419133), _1419129)), _1419131))], (30817 ^ _779854) ^ [_1336237, _1336239] : [-(_1336237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30820 ^ _779854 : [(30827 ^ _779854) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336239, _1336237) = 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), _1336239)), _1336237) = 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), _1336239), _1336237))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30821 ^ _779854) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336239, _1336237) = 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), _1336239)), _1336237) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336239), _1336237)))]]], (25571 ^ _779854) ^ [_1244967, _1244969, _1244971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244967), _1244969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244971), _1244967)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244971), _1244969))))], (29949 ^ _779854) ^ [_1319723, _1319725, _1319727] : [class_Rings_Olinordered__idom(_1319723), 29952 ^ _779854 : [(29961 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319723), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319723), hAPP(hAPP(c_Power_Opower__class_Opower(_1319723), _1319725), 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(_1319723), _1319727), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1319723)))), _1319725 = c_Groups_Ozero__class_Ozero(_1319723), _1319727 = c_Groups_Ozero__class_Ozero(_1319723)], (29953 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319723), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319723), hAPP(hAPP(c_Power_Opower__class_Opower(_1319723), _1319725), 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(_1319723), _1319727), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1319723))), 29956 ^ _779854 : [(29959 ^ _779854) ^ [] : [-(_1319727 = c_Groups_Ozero__class_Ozero(_1319723))], (29957 ^ _779854) ^ [] : [-(_1319725 = c_Groups_Ozero__class_Ozero(_1319723))]]]]], (43131 ^ _779854) ^ [_1639195, _1639197] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639195)), c_List_Obutlast(_1639195, _1639197)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639195)), _1639197)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43512 ^ _779854) ^ [_1647079, _1647081, _1647083] : [-(hAPP(hAPP(c_List_Olist__update(_1647079, c_List_Olist_ONil(_1647079)), _1647081), _1647083) = c_List_Olist_ONil(_1647079))], (22673 ^ _779854) ^ [_1189455, _1189457, _1189459, _1189461, _1189463] : [class_Fields_Olinordered__field(_1189455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189455), c_Groups_Ozero__class_Ozero(_1189455)), _1189457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189455), _1189457), _1189459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189455), c_Groups_Ozero__class_Ozero(_1189455)), _1189461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189455), _1189461), _1189463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189455), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189455), _1189457), _1189463)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189455), _1189459), _1189461))))], (45575 ^ _779854) ^ [] : [-(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))))], (35550 ^ _779854) ^ [_1442028, _1442030, _1442032] : [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), _1442028), _1442030))), -(hBOOL(hAPP(hAPP(_1442032, _1442028), _1442030))), 35557 ^ _779854 : [(35560 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1442032, 35555 ^ [_1442028, _1442030, _1442032]), 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)))), 35556 ^ [_1442028, _1442030, _1442032])))), -(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), 35555 ^ [_1442028, _1442030, _1442032]), 35556 ^ [_1442028, _1442030, _1442032])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 35556 ^ [_1442028, _1442030, _1442032]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35570 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1442032, 35555 ^ [_1442028, _1442030, _1442032]), 35556 ^ [_1442028, _1442030, _1442032]))], (35558 ^ _779854) ^ [] : [-(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), 35555 ^ [_1442028, _1442030, _1442032]), 35556 ^ [_1442028, _1442030, _1442032]))))]]], (852 ^ _779854) ^ [_792624, _792626, _792628, _792630] : [-(c_Predicate_Osymp(_792628, _792624)), c_Predicate_Osymp(_792630, _792626), _792630 = _792628, _792626 = _792624], (35028 ^ _779854) ^ [_1431325, _1431327] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1431325), hAPP(c_Nat_OSuc, _1431327)) = 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)), _1431327)), _1431325))], (49998 ^ _779854) ^ [_1790522, _1790524] : [c_Wellfounded_Oacyclic(_1790522, _1790524), -(c_Relation_Oantisym(_1790522, c_Transitive__Closure_Ortrancl(_1790522, _1790524)))], (28719 ^ _779854) ^ [_1298811, _1298813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298811), _1298813)), -(_1298813 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298811), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 28722 ^ [_1298811, _1298813]))))], (36798 ^ _779854) ^ [_1468600, _1468602, _1468604, _1468606] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1468600), _1468602)), 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)), _1468600), _1468604)), 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)), _1468602), _1468606)), 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)), _1468602), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1468604), _1468606))), c_FunDef_Omin__strict)))], (12184 ^ _779854) ^ [_992148, _992150, _992152] : [-(hBOOL(hAPP(hAPP(c_member(_992148), _992150), _992152))), -(hBOOL(hAPP(hAPP(c_member(_992148), _992150), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_992148, tc_HOL_Obool)), _992152))))], (21915 ^ _779854) ^ [_1175873, _1175875, _1175877, _1175879] : [class_Rings_Odivision__ring(_1175873), -(_1175875 = c_Groups_Ozero__class_Ozero(_1175873)), 21922 ^ _779854 : [(21929 ^ _779854) ^ [] : [_1175877 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175873), _1175879), _1175875), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175873), _1175877), _1175875) = _1175879)], (21923 ^ _779854) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175873), _1175877), _1175875) = _1175879, -(_1175877 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175873), _1175879), _1175875))]]], (41080 ^ _779854) ^ [_1583875, _1583877] : [-(c_Transitive__Closure_Ortrancl(_1583875, c_Transitive__Closure_Otrancl(_1583875, _1583877)) = c_Transitive__Closure_Ortrancl(_1583875, _1583877))], (36625 ^ _779854) ^ [_1464716, _1464718, _1464720, _1464722, _1464724, _1464726] : [c_Finite__Set_Ofolding__idem(_1464716, _1464718, _1464720, _1464722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464716), _1464724)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464716), _1464726)), -(hAPP(_1464722, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464716, tc_HOL_Obool)), _1464724), _1464726)) = hAPP(c_Fun_Ocomp(_1464718, _1464718, _1464718, hAPP(_1464722, _1464724)), hAPP(_1464722, _1464726)))], (17136 ^ _779854) ^ [_1089332, _1089334, _1089336] : [class_Lattices_Olattice(_1089332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089332), _1089334)), -(hBOOL(hAPP(hAPP(c_member(_1089332), _1089336), _1089334))), -(c_Big__Operators_Olattice__class_OSup__fin(_1089332, hAPP(hAPP(c_Set_Oinsert(_1089332), _1089336), _1089334)) = hAPP(hAPP(c_Finite__Set_Ofold(_1089332, _1089332, c_Lattices_Osemilattice__sup__class_Osup(_1089332)), _1089336), _1089334))], (36573 ^ _779854) ^ [_1463269, _1463271, _1463273, _1463275, _1463277, _1463279, _1463281, _1463283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1463269, _1463271), tc_prod(_1463269, _1463271))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1463269, _1463271), tc_prod(_1463269, _1463271)), hAPP(hAPP(c_Product__Type_OPair(_1463269, _1463271), _1463273), _1463275)), hAPP(hAPP(c_Product__Type_OPair(_1463269, _1463271), _1463277), _1463279))), c_Wellfounded_Olex__prod(_1463269, _1463271, _1463281, _1463283))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1463269, _1463269)), hAPP(hAPP(c_Product__Type_OPair(_1463269, _1463269), _1463273), _1463277)), _1463281))), 36580 ^ _779854 : [(36583 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1463271, _1463271)), hAPP(hAPP(c_Product__Type_OPair(_1463271, _1463271), _1463275), _1463279)), _1463283)))], (36581 ^ _779854) ^ [] : [-(_1463273 = _1463277)]]], (6657 ^ _779854) ^ [_886556, _886558, _886560] : [class_Orderings_Olinorder(_886556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886556), _886558), _886560)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886556, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_886556, _886558, _886560)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_886556), _886560)) = hAPP(c_SetInterval_Oord__class_OatLeast(_886556), _886558))], (43626 ^ _779854) ^ [_1649329, _1649331] : [-(c_List_Oset__Cons(_1649329, _1649331, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1649329)), c_List_Olist_ONil(_1649329)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1649329), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1649329, tc_List_Olist(_1649329), hAPP(hAPP(c_COMBC(_1649329, tc_List_Olist(_1649329), tc_List_Olist(_1649329)), c_List_Olist_OCons(_1649329)), c_List_Olist_ONil(_1649329))), _1649331))], (23239 ^ _779854) ^ [_1200002, _1200004, _1200006, _1200008, _1200010] : [class_Fields_Ofield(_1200002), hBOOL(hAPP(c_Finite__Set_Ofinite(_1200004), _1200006)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1200004), _1200008)), 23253 ^ _779854 : [(23256 ^ _779854) ^ [] : [-(hAPP(_1200010, 23252 ^ [_1200002, _1200004, _1200006, _1200008, _1200010]) = c_Groups_Ozero__class_Ozero(_1200002))], (23254 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200004), 23252 ^ [_1200002, _1200004, _1200006, _1200008, _1200010]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1200004, tc_HOL_Obool)), _1200006), _1200008))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1200004, _1200002), _1200010), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1200004, tc_HOL_Obool)), _1200006), _1200008)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1200002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200002), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1200004, _1200002), _1200010), _1200006)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1200004, _1200002), _1200010), _1200008))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1200004, _1200002), _1200010), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1200004, tc_HOL_Obool)), _1200006), _1200008))))], (33280 ^ _779854) ^ [_1383962, _1383964, _1383966, _1383968, _1383970, _1383972] : [-(hAPP(hAPP(c_Fun_Ocomp(_1383962, _1383964, _1383966, hAPP(c_COMBK(_1383964, _1383962), _1383968)), _1383970), _1383972) = _1383968)], (17336 ^ _779854) ^ [_1093134, _1093136] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1093134), _1093136)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1093136), _1093134))], (45659 ^ _779854) ^ [_1694634, _1694636, _1694638, _1694640] : [-(c_List_Opartition(_1694634, _1694636, hAPP(hAPP(c_List_Olist_OCons(_1694634), _1694638), _1694640)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1694634), tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1694634), tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1694634), tc_fun(tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), tc_fun(tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), tc_List_Olist(_1694634)), c_COMBS(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), tc_fun(tc_List_Olist(_1694634), tc_fun(tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), tc_List_Olist(_1694634)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_fun(tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), tc_List_Olist(_1694634)), hAPP(c_If(tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), hAPP(_1694636, _1694638)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1694634), tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), tc_List_Olist(_1694634)), c_Product__Type_OPair(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), hAPP(c_List_Olist_OCons(_1694634), _1694638))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694634), tc_fun(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634))), tc_fun(tc_fun(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_fun(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), tc_List_Olist(_1694634)), c_COMBB(tc_List_Olist(_1694634), tc_prod(tc_List_Olist(_1694634), tc_List_Olist(_1694634)), tc_List_Olist(_1694634))), c_Product__Type_OPair(tc_List_Olist(_1694634), tc_List_Olist(_1694634)))), hAPP(c_List_Olist_OCons(_1694634), _1694638)))), c_List_Opartition(_1694634, _1694636, _1694640)))], (39276 ^ _779854) ^ [_1536659, _1536661] : [c_Relation_Orefl__on(_1536659, c_Orderings_Otop__class_Otop(tc_fun(_1536659, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1536659, _1536659)), hAPP(c_Product__Type_Oprod_Oprod__case(_1536659, _1536659, tc_HOL_Obool), _1536661))), -(c_Predicate_Oreflp(_1536659, _1536661))], (43063 ^ _779854) ^ [_1637674, _1637676, _1637678, _1637680, _1637682] : [-(hAPP(hAPP(c_List_Olist__update(_1637674, hAPP(hAPP(c_List_Olist_OCons(_1637674), _1637676), _1637678)), _1637680), _1637682) = c_Nat_Onat_Onat__case(tc_List_Olist(_1637674), hAPP(hAPP(c_List_Olist_OCons(_1637674), _1637682), _1637678), hAPP(hAPP(c_COMBB(tc_List_Olist(_1637674), tc_List_Olist(_1637674), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1637674), _1637676)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1637674, tc_List_Olist(_1637674)), c_List_Olist__update(_1637674, _1637678)), _1637682)), _1637680))], (24070 ^ _779854) ^ [_1216400, _1216402, _1216404, _1216406] : [class_Rings_Olinordered__semidom(_1216400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216400), c_Groups_Oone__class_Oone(_1216400)), _1216402)), 24077 ^ _779854 : [(24084 ^ _779854) ^ [] : [_1216404 = _1216406, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1216400), _1216402), _1216404) = hAPP(hAPP(c_Power_Opower__class_Opower(_1216400), _1216402), _1216406))], (24078 ^ _779854) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1216400), _1216402), _1216404) = hAPP(hAPP(c_Power_Opower__class_Opower(_1216400), _1216402), _1216406), -(_1216404 = _1216406)]]], (14902 ^ _779854) ^ [_1044281, _1044283, _1044285] : [class_Groups_Oab__semigroup__mult(_1044281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044281), _1044283)), -(_1044283 = c_Orderings_Obot__class_Obot(tc_fun(_1044281, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044281), _1044285)), -(_1044285 = c_Orderings_Obot__class_Obot(tc_fun(_1044281, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1044281, tc_HOL_Obool)), _1044283), _1044285) = c_Orderings_Obot__class_Obot(tc_fun(_1044281, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1044281, c_Groups_Otimes__class_Otimes(_1044281)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1044281, tc_HOL_Obool)), _1044283), _1044285)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044281), hAPP(c_Finite__Set_Ofold1(_1044281, c_Groups_Otimes__class_Otimes(_1044281)), _1044283)), hAPP(c_Finite__Set_Ofold1(_1044281, c_Groups_Otimes__class_Otimes(_1044281)), _1044285)))], (41390 ^ _779854) ^ [_1591184, _1591186, _1591188] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1591184, _1591184), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1591184, _1591184), _1591186)), c_Transitive__Closure_Ortrancl(_1591184, _1591186)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1591184, _1591184), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591184, _1591184)), hAPP(hAPP(c_Product__Type_OPair(_1591184, _1591184), _1591188), _1591188)), c_Transitive__Closure_Otrancl(_1591184, _1591186)))], (8822 ^ _779854) ^ [_926429, _926431, _926433, _926435, _926437] : [hAPP(hAPP(c_Set_Oinsert(_926429), _926431), hAPP(hAPP(c_Set_Oinsert(_926429), _926433), c_Orderings_Obot__class_Obot(tc_fun(_926429, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_926429), _926435), hAPP(hAPP(c_Set_Oinsert(_926429), _926437), c_Orderings_Obot__class_Obot(tc_fun(_926429, tc_HOL_Obool)))), 8827 ^ _779854 : [(8830 ^ _779854) ^ [] : [-(_926433 = _926437)], (8828 ^ _779854) ^ [] : [-(_926431 = _926435)]], 8831 ^ _779854 : [(8834 ^ _779854) ^ [] : [-(_926433 = _926435)], (8832 ^ _779854) ^ [] : [-(_926431 = _926437)]]], (43328 ^ _779854) ^ [_1643789, _1643791, _1643793] : [hBOOL(hAPP(c_List_Odistinct(_1643789), _1643791)), -(hAPP(c_List_Oset(_1643789), c_List_Oremove1(_1643789, _1643793, _1643791)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1643789, tc_HOL_Obool)), hAPP(c_List_Oset(_1643789), _1643791)), hAPP(hAPP(c_Set_Oinsert(_1643789), _1643793), c_Orderings_Obot__class_Obot(tc_fun(_1643789, tc_HOL_Obool)))))], (52565 ^ _779854) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (24531 ^ _779854) ^ [_1224962, _1224964] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224962), _1224964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224964), _1224962))], (13429 ^ _779854) ^ [_1016293, _1016295, _1016297] : [class_Lattices_Olattice(_1016293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016293), _1016295)), -(_1016295 = c_Orderings_Obot__class_Obot(tc_fun(_1016293, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1016293, hAPP(hAPP(c_Set_Oinsert(_1016293), _1016297), _1016295)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1016293), _1016297), c_Big__Operators_Olattice__class_OInf__fin(_1016293, _1016295)))], (51060 ^ _779854) ^ [_1812242, _1812244, _1812246, _1812248, _1812250] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1812242, _1812244, tc_HOL_Obool, _1812246), _1812248), _1812250)), -(hBOOL(hAPP(_1812246, hAPP(hAPP(c_Product__Type_OPair(_1812242, _1812244), _1812248), _1812250))))], (7597 ^ _779854) ^ [_905499, _905501, _905503] : [7599 ^ _779854 : [(7602 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905499, tc_HOL_Obool)), 7598 ^ [_905499, _905501, _905503]), _905503) = c_Orderings_Obot__class_Obot(tc_fun(_905499, tc_HOL_Obool))], (7600 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_905499, tc_HOL_Obool)), 7598 ^ [_905499, _905501, _905503]), _905501)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905499, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_905499, tc_HOL_Obool), _905501)), _905503) = c_Orderings_Obot__class_Obot(tc_fun(_905499, tc_HOL_Obool)))], (34335 ^ _779854) ^ [_1416260, _1416262, _1416264, _1416266] : [class_Complete__Lattice_Ocomplete__lattice(_1416260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416262), _1416264)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416262, _1416260), _1416264), _1416266) = hAPP(hAPP(c_Finite__Set_Ofold(_1416262, _1416260, hAPP(hAPP(c_COMBB(_1416260, tc_fun(_1416260, _1416260), _1416262), c_Lattices_Osemilattice__sup__class_Osup(_1416260)), _1416266)), c_Orderings_Obot__class_Obot(_1416260)), _1416264))], (38500 ^ _779854) ^ [_1511987, _1511989, _1511991] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511987), _1511989)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511987, _1511987), tc_HOL_Obool)), _1511991), hAPP(hAPP(c_Product__Type_OSigma(_1511987, _1511987), _1511989), hAPP(c_COMBK(tc_fun(_1511987, tc_HOL_Obool), _1511987), _1511989)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1511987, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511987), _1511989), _1511991))))], (11788 ^ _779854) ^ [_984458, _984460, _984462, _984464] : [_984458 = _984460, 11791 ^ _779854 : [(11798 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_984462), _984464), _984460)), -(hBOOL(hAPP(hAPP(c_member(_984462), _984464), _984458)))], (11792 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_984462), _984464), _984458)), -(hBOOL(hAPP(hAPP(c_member(_984462), _984464), _984460)))]]], (32499 ^ _779854) ^ [_1364697, _1364699] : [-(c_Nitpick_Oint__lcm(_1364697, _1364699) = 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), _1364697)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1364699)))))], (15770 ^ _779854) ^ [_1062358, _1062360, _1062362, _1062364, _1062366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062358), _1062360)), 15773 ^ _779854 : [(15780 ^ _779854) ^ [] : [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), _1062360), _1062358)), _1062362)), _1062364) = _1062366, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062360), _1062362)), _1062364) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062358), _1062362)), _1062366))], (15774 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062360), _1062362)), _1062364) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062358), _1062362)), _1062366), -(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), _1062360), _1062358)), _1062362)), _1062364) = _1062366)]]], (44590 ^ _779854) ^ [_1671851, _1671853, _1671855] : [-(_1671851 = c_List_Olist_ONil(_1671853)), -(hAPP(hAPP(c_List_Otake(_1671853), hAPP(c_Nat_OSuc, _1671855)), _1671851) = hAPP(hAPP(c_List_Olist_OCons(_1671853), hAPP(c_List_Ohd(_1671853), _1671851)), hAPP(hAPP(c_List_Otake(_1671853), _1671855), hAPP(c_List_Otl(_1671853), _1671851))))], (10275 ^ _779854) ^ [_953535, _953537, _953539, _953541] : [class_Orderings_Olinorder(_953535), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_953535), _953537), hAPP(hAPP(c_Orderings_Oord__class_Omax(_953535), _953539), _953541)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_953535), hAPP(hAPP(c_Orderings_Oord__class_Omin(_953535), _953537), _953539)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_953535), _953537), _953541)))], (46932 ^ _779854) ^ [_1723633, _1723635, _1723637, _1723639] : [class_Orderings_Olinorder(_1723633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723633), _1723635), _1723637)), c_List_Olinorder__class_Osorted(_1723633, hAPP(hAPP(c_List_Olist_OCons(_1723633), _1723637), _1723639)), -(c_List_Olinorder__class_Osorted(_1723633, hAPP(hAPP(c_List_Olist_OCons(_1723633), _1723635), hAPP(hAPP(c_List_Olist_OCons(_1723633), _1723637), _1723639))))], (7491 ^ _779854) ^ [_903348, _903350] : [class_Lattices_Obounded__lattice__top(_903348), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903348), _903350), c_Orderings_Otop__class_Otop(_903348)) = _903350)], (11782 ^ _779854) ^ [_984357, _984359, _984361] : [_984359 = _984361, -(hBOOL(hAPP(hAPP(c_member(_984357), _984359), hAPP(c_fequal, _984361))))], (9514 ^ _779854) ^ [_939111, _939113, _939115, _939117] : [class_Orderings_Olinorder(_939111), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_939111), hAPP(hAPP(c_Orderings_Oord__class_Omax(_939111), _939113), _939115)), _939117) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_939111), _939113), hAPP(hAPP(c_Orderings_Oord__class_Omax(_939111), _939115), _939117)))], (44029 ^ _779854) ^ [_1658291, _1658293, _1658295, _1658297] : [-(hAPP(hAPP(c_List_Onth(_1658291), hAPP(hAPP(c_List_Oappend(_1658291), _1658293), _1658295)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658291)), _1658293)), _1658297)) = hAPP(hAPP(c_List_Onth(_1658291), _1658295), _1658297))], (36148 ^ _779854) ^ [_1454032] : [-(hAPP(c_Int_Onat, _1454032) = 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, _1454032)), 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)))))))], (31110 ^ _779854) ^ [_1341038, _1341040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1341038), _1341040)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1341040, _1341038) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1341040), _1341038), _1341038))], (27695 ^ _779854) ^ [_1281085, _1281087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1281085)), hAPP(c_Int_Onat, _1281087))), 27698 ^ _779854 : [(27701 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281085), _1281087)))], (27699 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281087)))]]], (27363 ^ _779854) ^ [_1275849] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275849), 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), _1275849)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1275849)))], (16686 ^ _779854) ^ [_1080463, _1080465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080463), _1080465)), _1080463 = _1080465], (5556 ^ _779854) ^ [_864889, _864891, _864893, _864895] : [-(tc_Nitpick_Opair__box(_864895, _864891) = tc_Nitpick_Opair__box(_864893, _864889)), _864895 = _864893, _864891 = _864889], (10281 ^ _779854) ^ [_953694, _953696, _953698, _953700] : [class_Orderings_Olinorder(_953694), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_953694), _953696), hAPP(hAPP(c_Orderings_Oord__class_Omin(_953694), _953698), _953700)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_953694), hAPP(hAPP(c_Orderings_Oord__class_Omax(_953694), _953696), _953698)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_953694), _953696), _953700)))], (38640 ^ _779854) ^ [_1515829, _1515831, _1515833, _1515835, _1515837, _1515839, _1515841, _1515843, _1515845, _1515847] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1515829, _1515831), tc_prod(_1515833, _1515835), tc_prod(_1515837, _1515839), c_Product__Type_Omap__pair(_1515829, _1515833, _1515831, _1515835, _1515841, _1515843)), c_Product__Type_Omap__pair(_1515837, _1515829, _1515839, _1515831, _1515845, _1515847)) = c_Product__Type_Omap__pair(_1515837, _1515833, _1515839, _1515835, hAPP(c_Fun_Ocomp(_1515829, _1515833, _1515837, _1515841), _1515845), hAPP(c_Fun_Ocomp(_1515831, _1515835, _1515839, _1515843), _1515847)))], (11830 ^ _779854) ^ [_985169, _985171, _985173, _985175, _985177] : [11832 ^ _779854 : [(11835 ^ _779854) ^ [] : [hBOOL(hAPP(_985177, 11831 ^ [_985169, _985171, _985173, _985175, _985177]))], (11833 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985169), 11831 ^ [_985169, _985171, _985173, _985175, _985177]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985171, tc_fun(_985169, tc_HOL_Obool)), _985173), _985175))))]], 11836 ^ _779854 : [(11837 ^ _779854) ^ [_985391] : [hBOOL(hAPP(hAPP(c_member(_985171), _985391), _985173)), 11840 ^ _779854 : [(11841 ^ _779854) ^ [_985488] : [hBOOL(hAPP(hAPP(c_member(_985169), _985488), hAPP(_985175, _985391))), -(hBOOL(hAPP(_985177, _985488)))]]]]], (18177 ^ _779854) ^ [_1108763, _1108765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108763), hAPP(c_Nat_OSuc, _1108765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108763), _1108765)))], (17620 ^ _779854) ^ [_1099055, _1099057, _1099059] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099055), _1099057)), hBOOL(hAPP(hAPP(c_member(_1099055), _1099059), _1099057)), -(hAPP(c_Finite__Set_Ocard(_1099055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099055, tc_HOL_Obool)), _1099057), hAPP(hAPP(c_Set_Oinsert(_1099055), _1099059), c_Orderings_Obot__class_Obot(tc_fun(_1099055, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1099055), _1099057)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2734 ^ _779854) ^ [_820504, _820506, _820508, _820510, _820512, _820514] : [-(c_FunDef_Oin__rel(_820514, _820510, _820506) = c_FunDef_Oin__rel(_820512, _820508, _820504)), _820514 = _820512, _820510 = _820508, _820506 = _820504], (28244 ^ _779854) ^ [_1290583, _1290585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1290583)), c_Int_OBit1(_1290585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290583), _1290585)))], (26583 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (6337 ^ _779854) ^ [_880658, _880660] : [class_Orderings_Olinorder(_880658), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_880658, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_880658), _880660)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_880658), _880660))], (15842 ^ _779854) ^ [_1063835, _1063837, _1063839, _1063841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063835), _1063837)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063839), _1063837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063835), _1063841), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063839), _1063841)))], (50084 ^ _779854) ^ [_1792328, _1792330] : [c_Relation_Osym(_1792328, _1792330), -(c_Relation_Osym(_1792328, hAPP(c_Relation_Oconverse(_1792328, _1792328), _1792330)))], (43416 ^ _779854) ^ [_1645435, _1645437, _1645439] : [hAPP(hAPP(c_List_Otake(_1645435), _1645437), _1645439) = c_List_Olist_ONil(_1645435), -(_1645437 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1645439 = c_List_Olist_ONil(_1645435))], (50036 ^ _779854) ^ [_1791496, _1791498] : [50039 ^ _779854 : [(50042 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1791496, _1791496)), hAPP(hAPP(c_Product__Type_OPair(_1791496, _1791496), 50038 ^ [_1791496, _1791498]), 50037 ^ [_1791496, _1791498])), _1791498))], (50040 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1791496, _1791496)), hAPP(hAPP(c_Product__Type_OPair(_1791496, _1791496), 50037 ^ [_1791496, _1791498]), 50038 ^ [_1791496, _1791498])), _1791498)))]], -(c_Relation_Osym(_1791496, _1791498))], (15658 ^ _779854) ^ [_1059955, _1059957, _1059959, _1059961, _1059963] : [class_Groups_Oab__group__add(_1059955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059957), _1059959)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059957), _1059961)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059957, _1059955), _1059963), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1059957, tc_HOL_Obool)), _1059959), _1059961)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059955), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059957, _1059955), _1059963), _1059959)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059957, _1059955), _1059963), _1059961))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059957, _1059955), _1059963), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1059957, tc_HOL_Obool)), _1059959), _1059961))))], (29759 ^ _779854) ^ [_1316514] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1316514))), 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), _1316514), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (21963 ^ _779854) ^ [_1176661, _1176663, _1176665] : [class_Rings_Odivision__ring(_1176661), -(_1176663 = c_Groups_Ozero__class_Ozero(_1176661)), 21970 ^ _779854 : [(21977 ^ _779854) ^ [] : [_1176665 = _1176663, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176661), _1176665), _1176663) = c_Groups_Oone__class_Oone(_1176661))], (21971 ^ _779854) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176661), _1176665), _1176663) = c_Groups_Oone__class_Oone(_1176661), -(_1176665 = _1176663)]]], (12074 ^ _779854) ^ [_990101, _990103, _990105, _990107] : [hBOOL(hAPP(hAPP(c_member(_990101), _990103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990101, tc_HOL_Obool)), _990105), _990107))), 12077 ^ _779854 : [(12080 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_990101), _990103), _990107))], (12078 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_990101), _990103), _990105)))]]], (7930 ^ _779854) ^ [_912516, _912518, _912520] : [class_Groups_Ogroup__add(_912516), 7933 ^ _779854 : [(7940 ^ _779854) ^ [] : [_912518 = _912520, -(hAPP(c_Groups_Ouminus__class_Ouminus(_912516), _912518) = hAPP(c_Groups_Ouminus__class_Ouminus(_912516), _912520))], (7934 ^ _779854) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_912516), _912518) = hAPP(c_Groups_Ouminus__class_Ouminus(_912516), _912520), -(_912518 = _912520)]]], (20463 ^ _779854) ^ [_1148112, _1148114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148112), _1148114)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1148112), _1148114) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24168 ^ _779854) ^ [_1218104, _1218106, _1218108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218104), _1218106)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218104), _1218108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1218106), _1218108)))], (52245 ^ _779854) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (8418 ^ _779854) ^ [_920290, _920292, _920294] : [class_Orderings_Olinorder(_920290), 8421 ^ _779854 : [(8428 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920290), _920292), _920294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920290, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_920290), _920292)), hAPP(c_SetInterval_Oord__class_OlessThan(_920290), _920294))))], (8422 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920290, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_920290), _920292)), hAPP(c_SetInterval_Oord__class_OlessThan(_920290), _920294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920290), _920292), _920294)))]]], (46671 ^ _779854) ^ [_1718929, _1718931] : [c_List_Oupt(_1718929, _1718931) = c_List_Olist_ONil(tc_Nat_Onat), -(_1718931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718931), _1718929)))], (52491 ^ _779854) ^ [_1836666] : [class_Enum_Oenum(_1836666), -(class_Enum_Oenum(tc_Option_Ooption(_1836666)))], (41643 ^ _779854) ^ [_1597281, _1597283, _1597285] : [c_Relation_Osingle__valued(_1597281, _1597283, _1597285), 41646 ^ _779854 : [(41647 ^ _779854) ^ [_1597402, _1597404] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597281, _1597283)), hAPP(hAPP(c_Product__Type_OPair(_1597281, _1597283), _1597404), _1597402)), _1597285)), 41650 ^ _779854 : [(41651 ^ _779854) ^ [_1597528] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597281, _1597283)), hAPP(hAPP(c_Product__Type_OPair(_1597281, _1597283), _1597404), _1597528)), _1597285)), -(_1597402 = _1597528)]]]]], (42237 ^ _779854) ^ [_1614352, _1614354, _1614356, _1614358] : [hBOOL(hAPP(hAPP(c_member(_1614352), _1614354), c_Wellfounded_Oacc(_1614352, _1614356))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1614352)), _1614358), c_Wellfounded_Oacc(tc_List_Olist(_1614352), c_List_Olistrel1(_1614352, _1614356)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1614352)), hAPP(hAPP(c_List_Olist_OCons(_1614352), _1614354), _1614358)), c_Wellfounded_Oacc(tc_List_Olist(_1614352), c_List_Olistrel1(_1614352, _1614356)))))], (40117 ^ _779854) ^ [_1560202, _1560204, _1560206] : [-(c_Relation_Orefl__on(_1560202, _1560204, _1560206)), 40121 ^ _779854 : [(40124 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1560202, _1560202, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1560202, tc_fun(_1560202, tc_HOL_Obool), tc_fun(_1560202, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1560202, tc_HOL_Obool), tc_fun(_1560202, tc_HOL_Obool)), _1560202), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1560202)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560202), c_fconj), hAPP(hAPP(c_COMBC(_1560202, tc_fun(_1560202, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560202)), _1560204)))), hAPP(hAPP(c_COMBC(_1560202, tc_fun(_1560202, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560202)), _1560204))), 40120 ^ [_1560202, _1560204, _1560206]))], (40122 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560202, _1560202)), 40120 ^ [_1560202, _1560204, _1560206]), _1560206)))]], 40126 ^ _779854 : [(40129 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560202, _1560202)), hAPP(hAPP(c_Product__Type_OPair(_1560202, _1560202), 40125 ^ [_1560202, _1560204, _1560206]), 40125 ^ [_1560202, _1560204, _1560206])), _1560206))], (40127 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560202), 40125 ^ [_1560202, _1560204, _1560206]), _1560204)))]]], (7407 ^ _779854) ^ [_901937, _901939, _901941, _901943] : [class_Lattices_Osemilattice__sup(_901937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901937), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901937), _901939), _901941)), _901943)), 7414 ^ _779854 : [(7417 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901937), _901941), _901943)))], (7415 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901937), _901939), _901943)))]]], (17656 ^ _779854) ^ [_1099883, _1099885, _1099887] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099883), _1099885)), -(hAPP(c_Finite__Set_Ocard(_1099883), hAPP(hAPP(c_Set_Oinsert(_1099883), _1099887), _1099885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1099883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099883, tc_HOL_Obool)), _1099885), hAPP(hAPP(c_Set_Oinsert(_1099883), _1099887), c_Orderings_Obot__class_Obot(tc_fun(_1099883, tc_HOL_Obool)))))))], (32947 ^ _779854) ^ [_1375656, _1375658, _1375660, _1375662] : [c_Orderings_Otop__class_Otop(tc_fun(_1375656, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375658, tc_fun(_1375656, tc_HOL_Obool)), _1375660), _1375662), 32950 ^ _779854 : [(32951 ^ _779854) ^ [_1375772] : [hBOOL(hAPP(hAPP(c_member(_1375658), _1375772), _1375660)), -(hAPP(_1375662, _1375772) = c_Orderings_Otop__class_Otop(tc_fun(_1375656, tc_HOL_Obool)))]]], (25677 ^ _779854) ^ [_1246667] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246667), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1246667)], (21054 ^ _779854) ^ [_1158721, _1158723, _1158725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158721), _1158723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158725), _1158723))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158721), _1158725)))], (3704 ^ _779854) ^ [_835557, _835559, _835561, _835563] : [-(c_List_Oremdups(_835563, _835559) = c_List_Oremdups(_835561, _835557)), _835563 = _835561, _835559 = _835557], (27757 ^ _779854) ^ [_1282062] : [class_Rings_Osemiring__1(_1282062), -(hBOOL(hAPP(hAPP(c_member(_1282062), c_Groups_Ozero__class_Ozero(_1282062)), c_Nat_Osemiring__1__class_ONats(_1282062))))], (42076 ^ _779854) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50052 ^ _779854) ^ [_1791844] : [-(c_Relation_Osym(_1791844, c_Relation_OId(_1791844)))], (45236 ^ _779854) ^ [_1685829, _1685831, _1685833, _1685835, _1685837] : [-(c_List_Olist_Olist__size(_1685829, _1685831, hAPP(hAPP(c_List_Omap(_1685833, _1685829), _1685835), _1685837)) = c_List_Olist_Olist__size(_1685833, hAPP(c_Fun_Ocomp(_1685829, tc_Nat_Onat, _1685833, _1685831), _1685835), _1685837))], (4084 ^ _779854) ^ [_841841, _841843, _841845, _841847, _841849, _841851, _841853, _841855] : [-(c_New__DSequence_Opos__bind(_841855, _841851, _841847, _841843) = c_New__DSequence_Opos__bind(_841853, _841849, _841845, _841841)), _841855 = _841853, _841851 = _841849, _841847 = _841845, _841843 = _841841], (41136 ^ _779854) ^ [_1585277, _1585279, _1585281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585277, _1585277), tc_HOL_Obool)), _1585279), _1585281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585277, _1585277), tc_HOL_Obool)), _1585281), c_Transitive__Closure_Ortrancl(_1585277, _1585279))), -(c_Transitive__Closure_Ortrancl(_1585277, _1585281) = c_Transitive__Closure_Ortrancl(_1585277, _1585279))], (28188 ^ _779854) ^ [_1289639] : [c_Int_OBit1(_1289639) = c_Int_OPls], (12356 ^ _779854) ^ [_995455, _995457, _995459, _995461, _995463] : [_995455 = hAPP(_995457, _995459), -(hBOOL(hAPP(hAPP(c_member(_995461), _995455), hAPP(c_Set_Oimage(_995463, _995461, _995457), c_Orderings_Otop__class_Otop(tc_fun(_995463, tc_HOL_Obool))))))], (13609 ^ _779854) ^ [_1019220, _1019222, _1019224] : [class_Orderings_Olinorder(_1019220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019220), _1019222)), -(_1019222 = c_Orderings_Obot__class_Obot(tc_fun(_1019220, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019220), _1019224)), -(_1019224 = c_Orderings_Obot__class_Obot(tc_fun(_1019220, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1019220, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1019220, tc_HOL_Obool)), _1019222), _1019224)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1019220), c_Big__Operators_Olinorder__class_OMax(_1019220, _1019222)), c_Big__Operators_Olinorder__class_OMax(_1019220, _1019224)))], (39463 ^ _779854) ^ [_1542878, _1542880, _1542882] : [hAPP(c_Relation_ORange(_1542878, _1542880), _1542882) = c_Orderings_Obot__class_Obot(tc_fun(_1542880, tc_HOL_Obool)), -(_1542882 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542878, _1542880), tc_HOL_Obool)))], (50193 ^ _779854) ^ [_1794022, _1794024] : [-(c_Equiv__Relations_Opart__equivp(_1794022, _1794024)), 50196 ^ _779854 : [(50197 ^ _779854) ^ [_1794099] : [hBOOL(hAPP(hAPP(_1794024, _1794099), _1794099))]], c_Predicate_Osymp(_1794022, _1794024), c_Predicate_Otransp(_1794022, _1794024)], (10331 ^ _779854) ^ [_954617, _954619, _954621, _954623] : [class_Orderings_Olinorder(_954617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954617), hAPP(hAPP(c_Orderings_Oord__class_Omax(_954617), hAPP(hAPP(c_Orderings_Oord__class_Omin(_954617), _954619), _954621)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_954617), _954619), _954623))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_954617), _954619), hAPP(hAPP(c_Orderings_Oord__class_Omax(_954617), _954621), _954623)))))], (10571 ^ _779854) ^ [_959527, _959529, _959531, _959533] : [10573 ^ _779854 : [(10577 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_959527), 10575 ^ [_959527, _959529, _959531, _959533]), _959533)))], (10579 ^ _779854) ^ [] : [-(hAPP(_959531, 10572 ^ [_959527, _959529, _959531, _959533]) = hAPP(_959531, 10575 ^ [_959527, _959529, _959531, _959533]))], (10581 ^ _779854) ^ [] : [10572 ^ [_959527, _959529, _959531, _959533] = 10575 ^ [_959527, _959529, _959531, _959533]], (10574 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_959527), 10572 ^ [_959527, _959529, _959531, _959533]), _959533)))]], -(c_Fun_Oinj__on(_959527, _959529, _959531, _959533))], (12268 ^ _779854) ^ [_993591, _993593, _993595, _993597] : [-(hBOOL(hAPP(hAPP(c_member(_993591), _993593), _993595))), 12271 ^ _779854 : [(12278 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993591, tc_HOL_Obool)), _993595), _993597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993591, tc_HOL_Obool)), _993595), hAPP(hAPP(c_Set_Oinsert(_993591), _993593), _993597))))], (12272 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993591, tc_HOL_Obool)), _993595), hAPP(hAPP(c_Set_Oinsert(_993591), _993593), _993597))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993591, tc_HOL_Obool)), _993595), _993597)))]]], (45107 ^ _779854) ^ [_1682536, _1682538, _1682540, _1682542] : [hAPP(hAPP(c_List_Omap(_1682536, _1682538), _1682540), _1682542) = c_List_Olist_ONil(_1682538), -(_1682542 = c_List_Olist_ONil(_1682536))], (27375 ^ _779854) ^ [_1276004] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276004), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276004)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1276004)))], (17164 ^ _779854) ^ [_1089760, _1089762, _1089764] : [class_Orderings_Olinorder(_1089760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089760), _1089762)), -(hBOOL(hAPP(hAPP(c_member(_1089760), _1089764), _1089762))), -(c_Big__Operators_Olinorder__class_OMin(_1089760, hAPP(hAPP(c_Set_Oinsert(_1089760), _1089764), _1089762)) = hAPP(hAPP(c_Finite__Set_Ofold(_1089760, _1089760, c_Orderings_Oord__class_Omin(_1089760)), _1089764), _1089762))], (52609 ^ _779854) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (19183 ^ _779854) ^ [_1125707, _1125709, _1125711] : [class_Rings_Oordered__ring(_1125707), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125707), c_Groups_Ozero__class_Ozero(_1125707)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125707), _1125709), _1125711)))), 19188 ^ _779854 : [(19195 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125707), _1125709), c_Groups_Ozero__class_Ozero(_1125707))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125707), _1125711), c_Groups_Ozero__class_Ozero(_1125707)))], (19189 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125707), c_Groups_Ozero__class_Ozero(_1125707)), _1125709)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125707), c_Groups_Ozero__class_Ozero(_1125707)), _1125711))]]], (724 ^ _779854) ^ [_790768, _790770, _790772, _790774, _790776, _790778] : [-(c_List_Oall__interval__int(_790776, _790772, _790768)), c_List_Oall__interval__int(_790778, _790774, _790770), _790778 = _790776, _790774 = _790772, _790770 = _790768], (43927 ^ _779854) ^ [_1656522, _1656524, _1656526] : [hAPP(hAPP(c_List_Oappend(_1656522), _1656524), _1656526) = _1656526, -(_1656524 = c_List_Olist_ONil(_1656522))], (39715 ^ _779854) ^ [_1550240] : [-(c_Wellfounded_Owf(tc_fun(_1550240, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1550240)))], (20385 ^ _779854) ^ [_1146719, _1146721, _1146723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146719)), 20388 ^ _779854 : [(20395 ^ _779854) ^ [] : [_1146721 = _1146723, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146719), _1146721) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146719), _1146723))], (20389 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146719), _1146721) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146719), _1146723), -(_1146721 = _1146723)]]], (29041 ^ _779854) ^ [] : [-(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)))))], (52511 ^ _779854) ^ [_1836921, _1836923] : [-(class_Finite__Set_Ofinite(tc_prod(_1836921, _1836923))), class_Finite__Set_Ofinite(_1836921), class_Finite__Set_Ofinite(_1836923)], (48419 ^ _779854) ^ [_1755383, _1755385, _1755387] : [hBOOL(hAPP(hAPP(c_member(_1755383), _1755385), hAPP(c_List_Oset(_1755383), _1755387))), 48424 ^ _779854 : [(48427 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1755383), _1755385), hAPP(c_List_Oset(_1755383), 48422 ^ [_1755383, _1755385, _1755387])))], (48425 ^ _779854) ^ [] : [-(_1755387 = hAPP(hAPP(c_List_Oappend(_1755383), 48422 ^ [_1755383, _1755385, _1755387]), hAPP(hAPP(c_List_Olist_OCons(_1755383), _1755385), 48423 ^ [_1755383, _1755385, _1755387])))]]], (23481 ^ _779854) ^ [_1205183] : [class_Groups_Osgn__if(_1205183), -(c_Groups_Osgn__class_Osgn(_1205183, c_Groups_Ozero__class_Ozero(_1205183)) = c_Groups_Ozero__class_Ozero(_1205183))], (50430 ^ _779854) ^ [_1798767, _1798769, _1798771] : [hAPP(c_Set_Oimage(_1798767, _1798769, _1798771), c_Orderings_Otop__class_Otop(tc_fun(_1798767, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1798769, tc_HOL_Obool)), 50433 ^ _779854 : [(50434 ^ _779854) ^ [_1798878] : [-(hAPP(_1798771, hAPP(c_Hilbert__Choice_Oinv__into(_1798767, _1798769, c_Orderings_Otop__class_Otop(tc_fun(_1798767, tc_HOL_Obool)), _1798771), _1798878)) = _1798878)]]], (15880 ^ _779854) ^ [_1064570, _1064572, _1064574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064570), _1064572)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064570), _1064574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064572), _1064574)))], (2442 ^ _779854) ^ [_815840, _815842, _815844, _815846] : [-(c_Divides_OposDivAlg(_815846, _815842) = c_Divides_OposDivAlg(_815844, _815840)), _815846 = _815844, _815842 = _815840], (8888 ^ _779854) ^ [_927892, _927894, _927896, _927898] : [class_Lattices_Osemilattice__sup(_927892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927892), _927894), _927896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927892), _927894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927892), _927898), _927896))))], (43814 ^ _779854) ^ [_1653831, _1653833, _1653835, _1653837] : [-(hAPP(hAPP(c_List_Oappend(_1653831), hAPP(hAPP(c_List_Olist_OCons(_1653831), _1653833), _1653835)), _1653837) = hAPP(hAPP(c_List_Olist_OCons(_1653831), _1653833), hAPP(hAPP(c_List_Oappend(_1653831), _1653835), _1653837)))], (51058 ^ _779854) ^ [_1812186, _1812188, _1812190, _1812192, _1812194, _1812196] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1812186, _1812188, _1812190, _1812192), _1812194), _1812196) = hAPP(_1812192, hAPP(hAPP(c_Product__Type_OPair(_1812186, _1812188), _1812194), _1812196)))], (17022 ^ _779854) ^ [_1087005, _1087007, _1087009] : [class_Orderings_Olinorder(_1087005), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087005), _1087007)), -(c_Big__Operators_Olinorder__class_OMax(_1087005, hAPP(hAPP(c_Set_Oinsert(_1087005), _1087009), _1087007)) = hAPP(hAPP(c_Finite__Set_Ofold(_1087005, _1087005, c_Orderings_Oord__class_Omax(_1087005)), _1087009), _1087007))], (1780 ^ _779854) ^ [_805056, _805058] : [-(class_Orderings_Olinorder(_805056)), _805058 = _805056, class_Orderings_Olinorder(_805058)], (29021 ^ _779854) ^ [_1303729, _1303731] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1303729), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1303731)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1303729), 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)))), _1303731)))], (11456 ^ _779854) ^ [_977821, _977823, _977825, _977827, _977829] : [c_Finite__Set_Ofolding__one(_977821, _977823, _977825), hBOOL(hAPP(c_Finite__Set_Ofinite(_977821), _977827)), hBOOL(hAPP(c_Finite__Set_Ofinite(_977821), _977829)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977821, tc_HOL_Obool)), _977827), _977829) = c_Orderings_Obot__class_Obot(tc_fun(_977821, tc_HOL_Obool))), -(hAPP(hAPP(_977823, hAPP(_977825, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977821, tc_HOL_Obool)), _977827), _977829))), hAPP(_977825, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977821, tc_HOL_Obool)), _977827), _977829))) = hAPP(hAPP(_977823, hAPP(_977825, _977827)), hAPP(_977825, _977829)))], (9508 ^ _779854) ^ [_938968, _938970, _938972, _938974] : [class_Orderings_Olinorder(_938968), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938968), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938968), _938970), _938972)), _938974) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_938968), _938970), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938968), _938972), _938974)))], (38634 ^ _779854) ^ [_1515627, _1515629, _1515631, _1515633, _1515635, _1515637, _1515639] : [-(hAPP(c_Product__Type_Ofst(_1515627, _1515629), hAPP(c_Product__Type_Omap__pair(_1515631, _1515627, _1515633, _1515629, _1515635, _1515637), _1515639)) = hAPP(_1515635, hAPP(c_Product__Type_Ofst(_1515631, _1515633), _1515639)))], (17532 ^ _779854) ^ [_1097218, _1097220, _1097222] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097218), _1097220)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097218), _1097222)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1097218, tc_HOL_Obool)), _1097220), _1097222) = c_Orderings_Obot__class_Obot(tc_fun(_1097218, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1097218), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097218, tc_HOL_Obool)), _1097220), _1097222)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1097218), _1097220)), hAPP(c_Finite__Set_Ocard(_1097218), _1097222)))], (43380 ^ _779854) ^ [_1644836, _1644838, _1644840] : [_1644836 = c_List_Olist_ONil(_1644838), -(c_List_Obutlast(_1644838, hAPP(hAPP(c_List_Olist_OCons(_1644838), _1644840), _1644836)) = c_List_Olist_ONil(_1644838))], (23647 ^ _779854) ^ [_1208482] : [class_Lattices_Oab__semigroup__idem__mult(_1208482), -(c_Finite__Set_Ofun__left__comm__idem(_1208482, _1208482, c_Groups_Otimes__class_Otimes(_1208482)))], (19023 ^ _779854) ^ [_1122903, _1122905, _1122907] : [class_Rings_Olinordered__ring__strict(_1122903), 19026 ^ _779854 : [(19027 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122903), c_Groups_Ozero__class_Ozero(_1122903)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122903), _1122905), _1122905)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122903), _1122907), _1122907)))), _1122905 = c_Groups_Ozero__class_Ozero(_1122903), _1122907 = c_Groups_Ozero__class_Ozero(_1122903)], (19037 ^ _779854) ^ [] : [19038 ^ _779854 : [(19041 ^ _779854) ^ [] : [-(_1122907 = c_Groups_Ozero__class_Ozero(_1122903))], (19039 ^ _779854) ^ [] : [-(_1122905 = c_Groups_Ozero__class_Ozero(_1122903))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122903), c_Groups_Ozero__class_Ozero(_1122903)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122903), _1122905), _1122905)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122903), _1122907), _1122907)))))]]], (28665 ^ _779854) ^ [_1297920] : [class_Nat_Osemiring__char__0(_1297920), -(c_Fun_Oinj__on(tc_Nat_Onat, _1297920, c_Nat_Osemiring__1__class_Oof__nat(_1297920), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (45446 ^ _779854) ^ [_1690280, _1690282] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1690280)), hAPP(c_Code__Numeral_Oof__nat, _1690282)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690280), _1690282)))], (8268 ^ _779854) ^ [_918309, _918311, _918313] : [class_Orderings_Opreorder(_918309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918309), _918311), _918313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918309), _918313), _918311))], (15530 ^ _779854) ^ [_1057250, _1057252, _1057254] : [class_Groups_Oab__group__add(_1057250), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057250), _1057252), _1057254) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057250), _1057252), hAPP(c_Groups_Ouminus__class_Ouminus(_1057250), _1057254)))], (31619 ^ _779854) ^ [_1349498, _1349500] : [c_Nat__Transfer_Ois__nat(_1349498), c_Nat__Transfer_Ois__nat(_1349500), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1349498), _1349500)))], (47619 ^ _779854) ^ [_1737594, _1737596, _1737598, _1737600, _1737602] : [-(hBOOL(hAPP(_1737594, _1737596))), -(c_List_OtakeWhile(_1737598, _1737594, hAPP(hAPP(c_List_Oappend(_1737598), _1737600), hAPP(hAPP(c_List_Olist_OCons(_1737598), _1737596), _1737602))) = c_List_OtakeWhile(_1737598, _1737594, _1737600))], (9959 ^ _779854) ^ [_947916, _947918, _947920, _947922] : [class_Orderings_Olinorder(_947916), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_947916), _947918), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947916), _947920), _947922)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_947916), _947920), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947916), _947918), _947922)))], (29159 ^ _779854) ^ [_1305904, _1305906] : [class_Int_Onumber__ring(_1305904), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305904), hAPP(c_Int_Onumber__class_Onumber__of(_1305904), _1305906)), c_Groups_Oone__class_Oone(_1305904)) = hAPP(c_Int_Onumber__class_Onumber__of(_1305904), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1305906), c_Int_OBit1(c_Int_OPls))))], (31047 ^ _779854) ^ [] : [c_Int_OMin = c_Int_OPls], (14105 ^ _779854) ^ [_1028857, _1028859, _1028861, _1028863] : [-(c_Fun_Ofun__upd(_1028857, _1028859, _1028861, _1028863, hAPP(_1028861, _1028863)) = _1028861)], (26443 ^ _779854) ^ [_1260341] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1260341)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1260341) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19017 ^ _779854) ^ [_1122759, _1122761, _1122763] : [class_Rings_Olinordered__ring(_1122759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122759), _1122761), _1122761)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122759), _1122763), _1122763))), c_Groups_Ozero__class_Ozero(_1122759)))], (29835 ^ _779854) ^ [_1317863, _1317865] : [class_Rings_Olinordered__idom(_1317863), 29838 ^ _779854 : [(29845 ^ _779854) ^ [] : [-(_1317865 = c_Groups_Ozero__class_Ozero(_1317863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317863), c_Groups_Ozero__class_Ozero(_1317863)), hAPP(hAPP(c_Power_Opower__class_Opower(_1317863), _1317865), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29839 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317863), c_Groups_Ozero__class_Ozero(_1317863)), hAPP(hAPP(c_Power_Opower__class_Opower(_1317863), _1317865), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1317865 = c_Groups_Ozero__class_Ozero(_1317863)]]], (1130 ^ _779854) ^ [_796931, _796933] : [-(class_Rings_Olinordered__semiring__1__strict(_796931)), _796933 = _796931, class_Rings_Olinordered__semiring__1__strict(_796933)], (44256 ^ _779854) ^ [_1664424, _1664426, _1664428] : [-(c_List_Obutlast(_1664424, hAPP(hAPP(c_List_Odrop(_1664424), _1664426), _1664428)) = hAPP(hAPP(c_List_Odrop(_1664424), _1664426), c_List_Obutlast(_1664424, _1664428)))], (42066 ^ _779854) ^ [_1608629] : [-(c_Nitpick_Odenom(_1608629) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1608629, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1608629)))], (17763 ^ _779854) ^ [_1101799, _1101801] : [class_Groups_Omonoid__mult(_1101799), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101799), c_Groups_Oone__class_Oone(_1101799)), _1101801) = _1101801)], (18235 ^ _779854) ^ [_1109736, _1109738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109736), _1109738)), hAPP(c_Nat_OSuc, _1109736))))], (16068 ^ _779854) ^ [_1068378, _1068380] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068378), _1068380))))], (22195 ^ _779854) ^ [_1180909, _1180911, _1180913, _1180915] : [class_Fields_Olinordered__field(_1180909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180909), c_Groups_Ozero__class_Ozero(_1180909)), _1180911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180909), _1180913), _1180911)), _1180915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180909), _1180913), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180909), _1180915), _1180911))))], (39335 ^ _779854) ^ [_1539215, _1539217] : [-(c_Product__Type_Oapfst(_1539215, _1539215, _1539217, c_Fun_Oid(_1539215)) = c_Fun_Oid(tc_prod(_1539215, _1539217)))], (26091 ^ _779854) ^ [_1254081, _1254083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254081)), 26100 ^ _779854 : [(26103 ^ _779854) ^ [] : [hBOOL(hAPP(_1254083, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26096 ^ [_1254081, _1254083]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26097 ^ [_1254081, _1254083]), _1254081))))], (26101 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1254083, 26096 ^ [_1254081, _1254083])))]], 26104 ^ _779854 : [(26107 ^ _779854) ^ [] : [hBOOL(hAPP(_1254083, 26096 ^ [_1254081, _1254083]))], (26105 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1254083, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26096 ^ [_1254081, _1254083]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26097 ^ [_1254081, _1254083]), _1254081)))))]], 26108 ^ _779854 : [(26118 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1254083, 26125 ^ [_1254081, _1254083]))), 26119 ^ _779854 : [(26120 ^ _779854) ^ [_1254628] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1254628), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1254081))), hBOOL(hAPP(_1254083, _1254628))]]], (26109 ^ _779854) ^ [] : [26110 ^ _779854 : [(26111 ^ _779854) ^ [_1254513] : [hBOOL(hAPP(_1254083, _1254513))]], 26113 ^ _779854 : [(26116 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1254083, 26112 ^ [_1254081, _1254083])))], (26114 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26112 ^ [_1254081, _1254083]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1254081))))]]]]], (39619 ^ _779854) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (31438 ^ _779854) ^ [_1346530, _1346532] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346530), hAPP(c_Int_Onumber__class_Onumber__of(_1346530), c_Int_OMin)), _1346532) = hAPP(c_Groups_Ouminus__class_Ouminus(_1346530), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346530), c_Groups_Oone__class_Oone(_1346530)), _1346532))), class_Fields_Ofield__inverse__zero(_1346530), class_Int_Onumber__ring(_1346530)], (14153 ^ _779854) ^ [_1029605, _1029607, _1029609, _1029611, _1029613, _1029615] : [c_Fun_Oinj__on(_1029605, _1029607, _1029609, _1029611), hAPP(_1029609, _1029613) = _1029615, hBOOL(hAPP(hAPP(c_member(_1029605), _1029613), _1029611)), -(hAPP(c_Fun_Othe__inv__into(_1029605, _1029607, _1029611, _1029609), _1029615) = _1029613)], (7750 ^ _779854) ^ [_908857, _908859] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908857, tc_HOL_Obool)), _908859), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_908857, tc_HOL_Obool)), _908859)) = c_Orderings_Otop__class_Otop(tc_fun(_908857, tc_HOL_Obool)))], (19761 ^ _779854) ^ [_1136305, _1136307, _1136309, _1136311] : [class_Rings_Olinordered__semiring__strict(_1136305), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136305), _1136307), _1136309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136305), c_Groups_Ozero__class_Ozero(_1136305)), _1136311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136305), _1136311), _1136307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136305), _1136311), _1136309))))], (44476 ^ _779854) ^ [_1669831, _1669833, _1669835] : [-(_1669831 = c_List_Olist_ONil(_1669833)), -(hAPP(c_List_Ohd(_1669833), hAPP(hAPP(c_List_Oappend(_1669833), _1669831), _1669835)) = hAPP(c_List_Ohd(_1669833), _1669831))], (31711 ^ _779854) ^ [_1350718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350718), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1350718 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 31714 ^ [_1350718]))))], (40744 ^ _779854) ^ [_1574432, _1574434, _1574436] : [class_Complete__Lattice_Ocomplete__lattice(_1574432), c_Orderings_Oorder__class_Omono(_1574432, _1574432, _1574434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574432), hAPP(_1574434, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1574432), c_Inductive_Ocomplete__lattice__class_Olfp(_1574432, _1574434)), _1574436))), _1574436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574432), c_Inductive_Ocomplete__lattice__class_Olfp(_1574432, _1574434)), _1574436)))], (11083 ^ _779854) ^ [_970544, _970546, _970548, _970550, _970552] : [c_Fun_Oinj__on(_970544, _970546, _970548, c_Orderings_Otop__class_Otop(tc_fun(_970544, tc_HOL_Obool))), 11086 ^ _779854 : [(11093 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970544, tc_HOL_Obool)), _970550), _970552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970546, tc_HOL_Obool)), hAPP(c_Set_Oimage(_970544, _970546, _970548), _970550)), hAPP(c_Set_Oimage(_970544, _970546, _970548), _970552))))], (11087 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970546, tc_HOL_Obool)), hAPP(c_Set_Oimage(_970544, _970546, _970548), _970550)), hAPP(c_Set_Oimage(_970544, _970546, _970548), _970552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970544, tc_HOL_Obool)), _970550), _970552)))]]], (13125 ^ _779854) ^ [_1011417, _1011419, _1011421, _1011423] : [c_Finite__Set_Ofolding__one(_1011417, _1011419, _1011421), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011417), _1011423)), -(_1011423 = c_Orderings_Obot__class_Obot(tc_fun(_1011417, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1011417), hAPP(hAPP(_1011419, 13138 ^ [_1011417, _1011419, _1011421, _1011423]), 13139 ^ [_1011417, _1011419, _1011421, _1011423])), hAPP(hAPP(c_Set_Oinsert(_1011417), 13138 ^ [_1011417, _1011419, _1011421, _1011423]), hAPP(hAPP(c_Set_Oinsert(_1011417), 13139 ^ [_1011417, _1011419, _1011421, _1011423]), c_Orderings_Obot__class_Obot(tc_fun(_1011417, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1011417), hAPP(_1011421, _1011423)), _1011423)))], (45083 ^ _779854) ^ [_1681501, _1681503, _1681505, _1681507, _1681509, _1681511, _1681513, _1681515] : [-(hAPP(hAPP(c_List_Ozip(_1681501, _1681503), hAPP(hAPP(c_List_Omap(_1681505, _1681501), _1681507), _1681509)), hAPP(hAPP(c_List_Omap(_1681511, _1681503), _1681513), _1681515)) = hAPP(hAPP(c_List_Omap(tc_prod(_1681505, _1681511), tc_prod(_1681501, _1681503)), hAPP(c_Product__Type_Oprod_Oprod__case(_1681505, _1681511, tc_prod(_1681501, _1681503)), hAPP(hAPP(c_COMBC(_1681505, tc_fun(_1681511, _1681503), tc_fun(_1681511, tc_prod(_1681501, _1681503))), hAPP(hAPP(c_COMBB(tc_fun(_1681503, tc_prod(_1681501, _1681503)), tc_fun(tc_fun(_1681511, _1681503), tc_fun(_1681511, tc_prod(_1681501, _1681503))), _1681505), c_COMBB(_1681503, tc_prod(_1681501, _1681503), _1681511)), hAPP(hAPP(c_COMBB(_1681501, tc_fun(_1681503, tc_prod(_1681501, _1681503)), _1681505), c_Product__Type_OPair(_1681501, _1681503)), _1681507))), _1681513))), hAPP(hAPP(c_List_Ozip(_1681505, _1681511), _1681509), _1681515)))], (4876 ^ _779854) ^ [_854337, _854339, _854341, _854343] : [-(c_Relation_OId__on(_854343, _854339) = c_Relation_OId__on(_854341, _854337)), _854343 = _854341, _854339 = _854337], (40035 ^ _779854) ^ [_1557797, _1557799, _1557801] : [c_Wellfounded_OwfP(_1557797, _1557799), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1557797, _1557799), _1557801)))], (41541 ^ _779854) ^ [_1595233, _1595235, _1595237] : [c_Relation_Orefl__on(_1595233, _1595235, _1595237), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1595233, _1595233), tc_HOL_Obool)), _1595237), hAPP(hAPP(c_Relation_Orel__comp(_1595233, _1595233, _1595233), hAPP(c_Relation_Oconverse(_1595233, _1595233), _1595237)), _1595237))))], (2938 ^ _779854) ^ [_823612, _823614] : [_823614 = _823612, -(c_Nitpick_Ofrac(_823614) = c_Nitpick_Ofrac(_823612))], (38370 ^ _779854) ^ [_1508312, _1508314] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1508312, _1508314), c_Orderings_Otop__class_Otop(tc_fun(_1508312, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1508314, tc_HOL_Obool), _1508312), c_Orderings_Otop__class_Otop(tc_fun(_1508314, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1508312, _1508314), tc_HOL_Obool)))], (32271 ^ _779854) ^ [_1360504, _1360506] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1360504), _1360506)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1360504) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (44330 ^ _779854) ^ [_1666184, _1666186, _1666188, _1666190] : [-(hAPP(hAPP(c_List_Oappend(_1666184), _1666186), _1666188) = _1666190), _1666186 = hAPP(hAPP(c_List_Otake(_1666184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666184)), _1666186)), _1666190), _1666188 = hAPP(hAPP(c_List_Odrop(_1666184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666184)), _1666186)), _1666190)], (30307 ^ _779854) ^ [_1327109, _1327111, _1327113, _1327115] : [class_Divides_Osemiring__div(_1327109), -(c_Divides_Odiv__class_Omod(_1327109, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327109), _1327111), _1327113), _1327115) = c_Divides_Odiv__class_Omod(_1327109, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327109), c_Divides_Odiv__class_Omod(_1327109, _1327111, _1327115)), _1327113), _1327115))], (34169 ^ _779854) ^ [_1412320] : [class_Orderings_Olinorder(_1412320), -(c_Orderings_Oord_Omin(_1412320, hAPP(c_COMBC(_1412320, _1412320, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1412320))) = c_Orderings_Oord__class_Omax(_1412320))], (46769 ^ _779854) ^ [_1720661] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1720661) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1720661))))], (33629 ^ _779854) ^ [_1397568, _1397570, _1397572, _1397574, _1397576] : [_1397568 = c_Orderings_Obot__class_Obot(tc_fun(_1397570, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397572, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397570, tc_fun(_1397572, tc_HOL_Obool)), _1397568), _1397574)), _1397576) = _1397576)], (43392 ^ _779854) ^ [_1645018, _1645020, _1645022, _1645024] : [_1645018 = _1645020, -(c_List_Oremove1(_1645022, _1645018, hAPP(hAPP(c_List_Olist_OCons(_1645022), _1645020), _1645024)) = _1645024)], (42933 ^ _779854) ^ [_1634921, _1634923, _1634925, _1634927, _1634929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634921), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634923)), _1634925))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634921), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634927)), _1634929))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1634923, _1634927)), hAPP(hAPP(c_List_Ozip(_1634923, _1634927), _1634925), _1634929)), _1634921) = hAPP(hAPP(c_Product__Type_OPair(_1634923, _1634927), hAPP(hAPP(c_List_Onth(_1634923), _1634925), _1634921)), hAPP(hAPP(c_List_Onth(_1634927), _1634929), _1634921)))], (40076 ^ _779854) ^ [_1558679, _1558681] : [c_Wellfounded_Owf(_1558679, _1558681), -(c_Wellfounded_OwfP(_1558679, hAPP(hAPP(c_COMBC(_1558679, tc_fun(tc_prod(_1558679, _1558679), tc_HOL_Obool), tc_fun(_1558679, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558679, tc_fun(tc_fun(tc_prod(_1558679, _1558679), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1558679, _1558679), tc_HOL_Obool), tc_fun(_1558679, tc_HOL_Obool)), _1558679), c_COMBC(_1558679, tc_fun(tc_prod(_1558679, _1558679), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558679, tc_prod(_1558679, _1558679)), tc_fun(_1558679, tc_fun(tc_fun(tc_prod(_1558679, _1558679), tc_HOL_Obool), tc_HOL_Obool)), _1558679), hAPP(c_COMBB(tc_prod(_1558679, _1558679), tc_fun(tc_fun(tc_prod(_1558679, _1558679), tc_HOL_Obool), tc_HOL_Obool), _1558679), c_member(tc_prod(_1558679, _1558679)))), c_Product__Type_OPair(_1558679, _1558679)))), _1558681)))], (9793 ^ _779854) ^ [_944197, _944199, _944201, _944203, _944205] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944197, tc_HOL_Obool)), _944199), hAPP(c_Set_Oimage(_944201, _944197, _944203), _944205)))), 9794 ^ _779854 : [(9795 ^ _779854) ^ [_944277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944201, tc_HOL_Obool)), _944277), _944205)), _944199 = hAPP(c_Set_Oimage(_944201, _944197, _944203), _944277)]]], (39557 ^ _779854) ^ [_1547215, _1547217, _1547219, _1547221, _1547223, _1547225, _1547227, _1547229] : [hBOOL(hAPP(hAPP(_1547215, _1547217), _1547219)), hBOOL(hAPP(hAPP(_1547221, _1547219), _1547223)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1547225, _1547227, _1547229, _1547215, _1547221), _1547217), _1547223)))], (17787 ^ _779854) ^ [_1102179, _1102181] : [class_Rings_Ocomm__semiring__1(_1102179), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102179), c_Groups_Oone__class_Oone(_1102179)), _1102181) = _1102181)], (3848 ^ _779854) ^ [_837825, _837827, _837829, _837831, _837833, _837835] : [-(c_List_Olinorder__class_Oinsort__key(_837835, _837831, _837827) = c_List_Olinorder__class_Oinsort__key(_837833, _837829, _837825)), _837835 = _837833, _837831 = _837829, _837827 = _837825], (9222 ^ _779854) ^ [_933809, _933811] : [class_Orderings_Oorder(_933809), -(c_SetInterval_Oord__class_OatLeastAtMost(_933809, _933811, _933811) = hAPP(hAPP(c_Set_Oinsert(_933809), _933811), c_Orderings_Obot__class_Obot(tc_fun(_933809, tc_HOL_Obool))))], (29319 ^ _779854) ^ [_1308899, _1308901] : [_1308899 = _1308901, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308899) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308901))], (27215 ^ _779854) ^ [_1273095, _1273097, _1273099] : [hBOOL(hAPP(_1273095, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1273097), _1273099))), 27218 ^ _779854 : [(27243 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1273099), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 27246 ^ _779854 : [(27247 ^ _779854) ^ [_1273759] : [-(hBOOL(hAPP(_1273095, _1273759))), 27248 ^ _779854 : [(27249 ^ _779854) ^ [_1273833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1273099), _1273833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1273833), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1273097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1273099), _1273759)), _1273833)]]]]], (27225 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1273099)), 27228 ^ _779854 : [(27229 ^ _779854) ^ [_1273429] : [-(hBOOL(hAPP(_1273095, _1273429))), 27230 ^ _779854 : [(27231 ^ _779854) ^ [_1273500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1273500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1273500), _1273099)), _1273097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1273099), _1273429)), _1273500)]]]]], (27219 ^ _779854) ^ [] : [_1273099 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1273095, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (48822 ^ _779854) ^ [_1763776, _1763778, _1763780, _1763782, _1763784] : [-(c_List_Osplice(_1763776, hAPP(hAPP(c_List_Olist_OCons(_1763776), _1763778), _1763780), hAPP(hAPP(c_List_Olist_OCons(_1763776), _1763782), _1763784)) = hAPP(hAPP(c_List_Olist_OCons(_1763776), _1763778), hAPP(hAPP(c_List_Olist_OCons(_1763776), _1763782), c_List_Osplice(_1763776, _1763780, _1763784))))], (52161 ^ _779854) ^ [_1833472, _1833474] : [class_Groups_Ouminus(_1833472), -(class_Groups_Ouminus(tc_fun(_1833474, _1833472)))], (41767 ^ _779854) ^ [_1600486, _1600488, _1600490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600486, _1600486)), _1600488), c_Transitive__Closure_Ortrancl(_1600486, _1600490))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600486, _1600486)), _1600488), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600486, _1600486), tc_HOL_Obool), 41770 ^ [_1600486, _1600488, _1600490]), _1600490))))], (35752 ^ _779854) ^ [_1445487, _1445489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1445487), 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)), _1445489)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445487, _1445489), c_Divides_OnegDivAlg(_1445487, _1445489))))], (10767 ^ _779854) ^ [_963550, _963552] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963550, tc_HOL_Obool)), _963552), _963552) = c_Orderings_Obot__class_Obot(tc_fun(_963550, tc_HOL_Obool)))], (13159 ^ _779854) ^ [_1012089, _1012091] : [class_Groups_Olinordered__ab__group__add(_1012089), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012089), _1012091)), -(_1012091 = c_Orderings_Obot__class_Obot(tc_fun(_1012089, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1012089), c_Big__Operators_Olinorder__class_OMax(_1012089, _1012091)) = c_Big__Operators_Olinorder__class_OMin(_1012089, hAPP(c_Set_Oimage(_1012089, _1012089, c_Groups_Ouminus__class_Ouminus(_1012089)), _1012091)))], (33897 ^ _779854) ^ [_1404724, _1404726, _1404728, _1404730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404724, tc_fun(_1404726, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1404724, tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_fun(_1404726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404726, tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_fun(_1404726, tc_HOL_Obool)), _1404724), c_COMBC(_1404726, tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404726, tc_prod(_1404724, _1404726)), tc_fun(_1404726, tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool)), _1404724), hAPP(c_COMBB(tc_prod(_1404724, _1404726), tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool), _1404726), c_member(tc_prod(_1404724, _1404726)))), c_Product__Type_OPair(_1404724, _1404726)))), _1404728)), hAPP(hAPP(c_COMBC(_1404724, tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_fun(_1404726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404726, tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_fun(_1404726, tc_HOL_Obool)), _1404724), c_COMBC(_1404726, tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404726, tc_prod(_1404724, _1404726)), tc_fun(_1404726, tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool)), _1404724), hAPP(c_COMBB(tc_prod(_1404724, _1404726), tc_fun(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool), tc_HOL_Obool), _1404726), c_member(tc_prod(_1404724, _1404726)))), c_Product__Type_OPair(_1404724, _1404726)))), _1404730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1404724, _1404726), tc_HOL_Obool)), _1404728), _1404730)))], (28457 ^ _779854) ^ [_1294396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1294396)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294396), c_Int_OPls)))], (29923 ^ _779854) ^ [_1319182, _1319184, _1319186] : [class_Rings_Ocomm__semiring__1(_1319182), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1319182), _1319184), 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)))), _1319186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319182), hAPP(hAPP(c_Power_Opower__class_Opower(_1319182), _1319184), _1319186)), hAPP(hAPP(c_Power_Opower__class_Opower(_1319182), _1319184), _1319186)))], (40982 ^ _779854) ^ [_1580615, _1580617, _1580619, _1580621, _1580623] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580615, _1580615)), hAPP(hAPP(c_Product__Type_OPair(_1580615, _1580615), _1580617), _1580619)), c_Transitive__Closure_Otrancl(_1580615, _1580621))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580615, _1580615)), hAPP(hAPP(c_Product__Type_OPair(_1580615, _1580615), _1580619), _1580623)), _1580621)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580615, _1580615)), hAPP(hAPP(c_Product__Type_OPair(_1580615, _1580615), _1580617), _1580623)), c_Transitive__Closure_Otrancl(_1580615, _1580621))))], (33292 ^ _779854) ^ [_1384459, _1384461, _1384463, _1384465, _1384467, _1384469] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384459, tc_fun(_1384461, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384463, tc_fun(_1384459, tc_HOL_Obool)), _1384465), _1384467)), _1384469) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384463, tc_fun(_1384461, tc_HOL_Obool)), _1384465), hAPP(hAPP(c_COMBC(_1384463, tc_fun(_1384459, tc_fun(_1384461, tc_HOL_Obool)), tc_fun(_1384461, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384459, tc_HOL_Obool), tc_fun(tc_fun(_1384459, tc_fun(_1384461, tc_HOL_Obool)), tc_fun(_1384461, tc_HOL_Obool)), _1384463), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384459, tc_fun(_1384461, tc_HOL_Obool))), _1384467)), _1384469)))], (23035 ^ _779854) ^ [_1196211, _1196213, _1196215, _1196217] : [class_Fields_Ofield(_1196211), -(_1196213 = c_Groups_Ozero__class_Ozero(_1196211)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1196211), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196211), _1196215), _1196213)), _1196217) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1196211), _1196215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196211), _1196213), _1196217))), _1196213))], (18883 ^ _779854) ^ [_1120638, _1120640, _1120642] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120638), _1120640) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120638), _1120642), -(_1120640 = _1120642), -(_1120638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10951 ^ _779854) ^ [_967519, _967521, _967523] : [class_Orderings_Olinorder(_967519), hBOOL(hAPP(c_Finite__Set_Ofinite(_967519), _967521)), 10958 ^ _779854 : [(10965 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967519, tc_HOL_Obool)), _967521), hAPP(hAPP(c_Set_Oinsert(_967519), _967523), c_Orderings_Obot__class_Obot(tc_fun(_967519, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_967519, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_967519, c_Orderings_Oord__class_Omax(_967519), hAPP(hAPP(c_Set_Oinsert(_967519), _967523), _967521)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_967519), _967523), c_Big__Operators_Olattice_OSup__fin(_967519, c_Orderings_Oord__class_Omax(_967519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967519, tc_HOL_Obool)), _967521), hAPP(hAPP(c_Set_Oinsert(_967519), _967523), c_Orderings_Obot__class_Obot(tc_fun(_967519, tc_HOL_Obool)))))))], (10959 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967519, tc_HOL_Obool)), _967521), hAPP(hAPP(c_Set_Oinsert(_967519), _967523), c_Orderings_Obot__class_Obot(tc_fun(_967519, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_967519, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_967519, c_Orderings_Oord__class_Omax(_967519), hAPP(hAPP(c_Set_Oinsert(_967519), _967523), _967521)) = _967523)]]], (22175 ^ _779854) ^ [_1180528, _1180530, _1180532, _1180534] : [class_Fields_Olinordered__field(_1180528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180528), _1180530), c_Groups_Ozero__class_Ozero(_1180528))), 22182 ^ _779854 : [(22189 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180528), _1180534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180528), _1180532), _1180530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180528), _1180532), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180528), _1180534), _1180530))))], (22183 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180528), _1180532), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180528), _1180534), _1180530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180528), _1180534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180528), _1180532), _1180530))))]]], (41849 ^ _779854) ^ [_1602698, _1602700, _1602702, _1602704, _1602706] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602698, _1602698)), hAPP(hAPP(c_Product__Type_OPair(_1602698, _1602698), _1602700), _1602702)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1602698, _1602698), tc_HOL_Obool), _1602704), _1602706))), 41854 ^ _779854 : [(41857 ^ _779854) ^ [] : [-(_1602700 = _1602702)], (41855 ^ _779854) ^ [] : [-(_1602704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41860 ^ _779854 : [(41865 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602698, _1602698)), hAPP(hAPP(c_Product__Type_OPair(_1602698, _1602698), 41858 ^ [_1602698, _1602700, _1602702, _1602704, _1602706]), _1602702)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1602698, _1602698), tc_HOL_Obool), 41859 ^ [_1602698, _1602700, _1602702, _1602704, _1602706]), _1602706))))], (41863 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602698, _1602698)), hAPP(hAPP(c_Product__Type_OPair(_1602698, _1602698), _1602700), 41858 ^ [_1602698, _1602700, _1602702, _1602704, _1602706])), _1602706)))], (41861 ^ _779854) ^ [] : [-(_1602704 = hAPP(c_Nat_OSuc, 41859 ^ [_1602698, _1602700, _1602702, _1602704, _1602706]))]]], (21769 ^ _779854) ^ [_1172789, _1172791, _1172793, _1172795, _1172797] : [class_Fields_Ofield(_1172789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172791), _1172793)), -(hAPP(_1172795, _1172797) = c_Groups_Ozero__class_Ozero(_1172789)), 21780 ^ _779854 : [(21787 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1172791), _1172797), _1172793))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172791, _1172789), _1172795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172791, tc_HOL_Obool)), _1172793), hAPP(hAPP(c_Set_Oinsert(_1172791), _1172797), c_Orderings_Obot__class_Obot(tc_fun(_1172791, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172791, _1172789), _1172795), _1172793))], (21781 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1172791), _1172797), _1172793)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172791, _1172789), _1172795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172791, tc_HOL_Obool)), _1172793), hAPP(hAPP(c_Set_Oinsert(_1172791), _1172797), c_Orderings_Obot__class_Obot(tc_fun(_1172791, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1172789), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172791, _1172789), _1172795), _1172793)), hAPP(_1172795, _1172797)))]]], (37769 ^ _779854) ^ [] : [-(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))], (29307 ^ _779854) ^ [_1308688, _1308690] : [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)), _1308688)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1308690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1308688), _1308690)))], (44636 ^ _779854) ^ [_1672868, _1672870, _1672872, _1672874, _1672876, _1672878] : [-(hAPP(c_List_Ofoldl(_1672868, _1672870, _1672872, _1672874), hAPP(hAPP(c_List_Oappend(_1672870), _1672876), _1672878)) = hAPP(c_List_Ofoldl(_1672868, _1672870, _1672872, hAPP(c_List_Ofoldl(_1672868, _1672870, _1672872, _1672874), _1672876)), _1672878))], (45216 ^ _779854) ^ [_1685352, _1685354, _1685356, _1685358] : [-(_1685352 = c_List_Olist_ONil(_1685354)), -(hAPP(c_List_Ohd(_1685356), hAPP(hAPP(c_List_Omap(_1685354, _1685356), _1685358), _1685352)) = hAPP(_1685358, hAPP(c_List_Ohd(_1685354), _1685352)))], (46382 ^ _779854) ^ [_1711281, _1711283, _1711285, _1711287] : [-(c_List_Oconcat(_1711281, hAPP(hAPP(c_List_Omap(_1711283, tc_List_Olist(_1711281)), hAPP(hAPP(c_COMBC(_1711283, tc_List_Olist(_1711281), tc_List_Olist(_1711281)), hAPP(hAPP(c_COMBB(_1711281, tc_fun(tc_List_Olist(_1711281), tc_List_Olist(_1711281)), _1711283), c_List_Olist_OCons(_1711281)), _1711285)), c_List_Olist_ONil(_1711281))), _1711287)) = hAPP(hAPP(c_List_Omap(_1711283, _1711281), _1711285), _1711287))], (14277 ^ _779854) ^ [_1032068, _1032070, _1032072, _1032074, _1032076] : [c_Finite__Set_Ofolding__one__idem(_1032068, _1032070, _1032072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032068), _1032074)), -(_1032074 = c_Orderings_Obot__class_Obot(tc_fun(_1032068, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032068), _1032076)), -(_1032076 = c_Orderings_Obot__class_Obot(tc_fun(_1032068, tc_HOL_Obool))), -(hAPP(_1032072, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1032068, tc_HOL_Obool)), _1032074), _1032076)) = hAPP(hAPP(_1032070, hAPP(_1032072, _1032074)), hAPP(_1032072, _1032076)))], (21697 ^ _779854) ^ [_1171407, _1171409, _1171411, _1171413] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1171407, _1171409)), c_Sum__Type_OPlus(_1171407, _1171409, _1171411, _1171413)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171407), _1171411)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171409), _1171413))], (52249 ^ _779854) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (33425 ^ _779854) ^ [_1388322, _1388324, _1388326, _1388328] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1388322, _1388324)), hAPP(hAPP(c_Product__Type_OPair(_1388322, _1388324), _1388326), _1388328)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1388322, _1388324), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1388322, tc_fun(_1388324, tc_HOL_Obool))), _1388326), _1388328)))], (2888 ^ _779854) ^ [_822851, _822853, _822855, _822857, _822859, _822861] : [-(c_Nitpick_Otimes__frac(_822861, _822857, _822853) = c_Nitpick_Otimes__frac(_822859, _822855, _822851)), _822861 = _822859, _822857 = _822855, _822853 = _822851], (33917 ^ _779854) ^ [_1406163] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1406163) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1406163)))], (4024 ^ _779854) ^ [_840853, _840855, _840857, _840859, _840861, _840863, _840865, _840867] : [-(c_New__DSequence_Oneg__bind(_840867, _840863, _840859, _840855) = c_New__DSequence_Oneg__bind(_840865, _840861, _840857, _840853)), _840867 = _840865, _840863 = _840861, _840859 = _840857, _840855 = _840853], (17686 ^ _779854) ^ [_1100569] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100569), hAPP(c_Nat_OSuc, _1100569))))], (42313 ^ _779854) ^ [_1616780, _1616782, _1616784, _1616786, _1616788, _1616790] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616780), tc_List_Olist(_1616780))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616780), tc_List_Olist(_1616780)), hAPP(hAPP(c_List_Olist_OCons(_1616780), _1616782), _1616784)), hAPP(hAPP(c_List_Olist_OCons(_1616780), _1616786), _1616788))), c_List_Olistrel1(_1616780, _1616790)))), 42314 ^ _779854 : [(42321 ^ _779854) ^ [] : [_1616782 = _1616786, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616780), tc_List_Olist(_1616780))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616780), tc_List_Olist(_1616780)), _1616784), _1616788)), c_List_Olistrel1(_1616780, _1616790)))], (42315 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616780, _1616780)), hAPP(hAPP(c_Product__Type_OPair(_1616780, _1616780), _1616782), _1616786)), _1616790)), _1616784 = _1616788]]], (16109 ^ _779854) ^ [_1069081, _1069083, _1069085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069081), _1069083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069081), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1069083), _1069085))))], (38128 ^ _779854) ^ [_1501501, _1501503, _1501505, _1501507] : [-(hAPP(c_Set_Ovimage(_1501501, _1501503, _1501505), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1501503, tc_HOL_Obool), _1501507)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1501503, tc_HOL_Obool), tc_fun(_1501501, tc_HOL_Obool)), _1501507), c_Set_Ovimage(_1501501, _1501503, _1501505)))], (10095 ^ _779854) ^ [_950369, _950371, _950373] : [class_Orderings_Olinorder(_950369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950369), _950371), _950373)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_950369), _950371), _950373) = _950371)], (40027 ^ _779854) ^ [_1557650, _1557652] : [c_Wellfounded_Owf(_1557650, hAPP(c_Set_OCollect(tc_prod(_1557650, _1557650)), hAPP(c_Product__Type_Oprod_Oprod__case(_1557650, _1557650, tc_HOL_Obool), _1557652))), -(c_Wellfounded_OwfP(_1557650, _1557652))], (52079 ^ _779854) ^ [_1832395, _1832397] : [class_Lattices_Obounded__lattice(_1832395), -(class_Lattices_Obounded__lattice__top(tc_fun(_1832397, _1832395)))], (48508 ^ _779854) ^ [_1757105, _1757107, _1757109] : [hBOOL(hAPP(hAPP(c_member(_1757105), _1757107), hAPP(c_List_Oset(_1757105), _1757109))), -(_1757109 = hAPP(hAPP(c_List_Oappend(_1757105), 48511 ^ [_1757105, _1757107, _1757109]), hAPP(hAPP(c_List_Olist_OCons(_1757105), _1757107), 48512 ^ [_1757105, _1757107, _1757109])))], (9520 ^ _779854) ^ [_939254, _939256, _939258, _939260, _939262] : [hAPP(c_Set_Oimage(_939254, _939256, _939258), _939260) = _939262, -(hAPP(c_Set_Oimage(tc_fun(_939254, tc_HOL_Obool), tc_fun(_939256, tc_HOL_Obool), c_Set_Oimage(_939254, _939256, _939258)), hAPP(c_Set_OPow(_939254), _939260)) = hAPP(c_Set_OPow(_939256), _939262))], (33200 ^ _779854) ^ [_1381953, _1381955, _1381957, _1381959] : [class_Complete__Lattice_Ocomplete__lattice(_1381953), -(_1381955 = c_Orderings_Obot__class_Obot(tc_fun(_1381957, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1381957, _1381953), _1381955), hAPP(c_COMBK(_1381953, _1381957), _1381959)) = _1381959)], (34799 ^ _779854) ^ [_1426604, _1426606] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426604), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 34802 ^ _779854 : [(34811 ^ _779854) ^ [] : [-(c_Nitpick_Onorm__frac(_1426606, _1426604) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1426606), _1426604)), 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), _1426606))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1426604)))), -(_1426606 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1426604 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34803 ^ _779854) ^ [] : [34804 ^ _779854 : [(34807 ^ _779854) ^ [] : [_1426604 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (34805 ^ _779854) ^ [] : [_1426606 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1426606, _1426604) = 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)))]]], (6865 ^ _779854) ^ [_891253, _891255, _891257, _891259, _891261] : [class_Lattices_Olattice(_891253), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891255, _891253)), _891257), _891259), _891261) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891253), hAPP(_891257, _891261)), hAPP(_891259, _891261)))], (18321 ^ _779854) ^ [_1111345, _1111347] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1111345, _1111347)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111347)), _1111345))], (12732 ^ _779854) ^ [_1002965, _1002967, _1002969] : [class_Orderings_Olinorder(_1002965), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002965), _1002967)), -(hBOOL(hAPP(hAPP(c_member(_1002965), _1002969), _1002967))), -(_1002967 = c_Orderings_Obot__class_Obot(tc_fun(_1002965, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1002965, c_Orderings_Oord__class_Omax(_1002965), hAPP(hAPP(c_Set_Oinsert(_1002965), _1002969), _1002967)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1002965), _1002969), c_Big__Operators_Olattice_OSup__fin(_1002965, c_Orderings_Oord__class_Omax(_1002965), _1002967)))], (2178 ^ _779854) ^ [_811610, _811612, _811614, _811616, _811618, _811620, _811622, _811624, _811626, _811628] : [-(c_Nitpick_Opair__box_Opair__box__size(_811628, _811624, _811620, _811616, _811612) = c_Nitpick_Opair__box_Opair__box__size(_811626, _811622, _811618, _811614, _811610)), _811628 = _811626, _811624 = _811622, _811620 = _811618, _811616 = _811614, _811612 = _811610], (43472 ^ _779854) ^ [_1646341] : [-(hAPP(c_List_Oset(_1646341), c_List_Olist_ONil(_1646341)) = c_Orderings_Obot__class_Obot(tc_fun(_1646341, tc_HOL_Obool)))], (30849 ^ _779854) ^ [_1336784] : [c_Nat__Transfer_Onat__set(_1336784), -(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), _1336784)) = _1336784)], (34847 ^ _779854) ^ [_1427430, _1427432] : [-(c_Divides_OposDivAlg(_1427430, _1427432) = hAPP(c_Divides_Oadjust(_1427432), c_Divides_OposDivAlg(_1427430, 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)))), _1427432)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427430), _1427432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427432), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51132 ^ _779854) ^ [_1813663, _1813665, _1813667, _1813669] : [c_Equiv__Relations_Oequivp(_1813663, _1813665), 51138 ^ _779854 : [(51141 ^ _779854) ^ [] : [hBOOL(hAPP(_1813669, 51137 ^ [_1813663, _1813665, _1813667, _1813669]))], (51139 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1813667, 51137 ^ [_1813663, _1813665, _1813667, _1813669])))]], 51144 ^ _779854 : [(51145 ^ _779854) ^ [_1813922] : [hBOOL(hAPP(_1813667, _1813922))]], 51147 ^ _779854 : [(51150 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1813669, 51146 ^ [_1813663, _1813665, _1813667, _1813669])))], (51148 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1813663), 51146 ^ [_1813663, _1813665, _1813667, _1813669]), c_Quotient_ORespects(_1813663, _1813665))))]]], (5872 ^ _779854) ^ [_872833, _872835, _872837] : [class_Orderings_Oorder(_872833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872833), _872835), _872837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872833), _872837), _872835)), -(_872835 = _872837)], (14345 ^ _779854) ^ [_1033428, _1033430, _1033432, _1033434, _1033436] : [c_Finite__Set_Ofolding__one__idem(_1033428, _1033430, _1033432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033428), _1033434)), -(_1033434 = c_Orderings_Obot__class_Obot(tc_fun(_1033428, tc_HOL_Obool))), -(hAPP(_1033432, hAPP(hAPP(c_Set_Oinsert(_1033428), _1033436), _1033434)) = hAPP(hAPP(_1033430, _1033436), hAPP(_1033432, _1033434)))], (35955 ^ _779854) ^ [_1449722, _1449724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449722), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1449724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1449722, _1449724) = 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), _1449722), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1449724)))))], (50523 ^ _779854) ^ [_1801095, _1801097, _1801099] : [hAPP(c_Fun_Ocomp(_1801095, _1801097, _1801097, _1801099), c_Hilbert__Choice_Oinv__into(_1801095, _1801097, c_Orderings_Otop__class_Otop(tc_fun(_1801095, tc_HOL_Obool)), _1801099)) = c_Fun_Oid(_1801097), -(hAPP(c_Set_Oimage(_1801095, _1801097, _1801099), c_Orderings_Otop__class_Otop(tc_fun(_1801095, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1801097, tc_HOL_Obool)))], (29017 ^ _779854) ^ [_1303625, _1303627] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1303625)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1303627)) = 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)))), _1303625)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1303627)))], (21174 ^ _779854) ^ [_1161085, _1161087, _1161089, _1161091, _1161093, _1161095] : [class_Rings_Olinordered__semiring__1(_1161085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161085), _1161087), _1161089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161085), _1161091), _1161089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161085), c_Groups_Ozero__class_Ozero(_1161085)), _1161093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161085), c_Groups_Ozero__class_Ozero(_1161085)), _1161095)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161085), _1161093), _1161095) = c_Groups_Oone__class_Oone(_1161085), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161085), _1161093), _1161087)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161085), _1161095), _1161091))), _1161089)))], (37536 ^ _779854) ^ [_1487304, _1487306, _1487308, _1487310, _1487312, _1487314] : [c_Equiv__Relations_Oequiv(_1487304, _1487306, _1487308), c_Equiv__Relations_Ocongruent(_1487304, tc_fun(_1487310, tc_HOL_Obool), _1487308, _1487312), hBOOL(hAPP(hAPP(c_member(_1487304), _1487314), _1487306)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1487304, tc_fun(_1487310, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1487304, _1487304, _1487308), hAPP(hAPP(c_Set_Oinsert(_1487304), _1487314), c_Orderings_Obot__class_Obot(tc_fun(_1487304, tc_HOL_Obool))))), _1487312) = hAPP(_1487312, _1487314))], (41962 ^ _779854) ^ [_1606152, _1606154] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606152, _1606152)), _1606154), c_Relation_OId(_1606152))), -(_1606154 = hAPP(hAPP(c_Product__Type_OPair(_1606152, _1606152), 41965 ^ [_1606152, _1606154]), 41965 ^ [_1606152, _1606154]))], (39264 ^ _779854) ^ [_1536309, _1536311, _1536313, _1536315] : [-(c_Nitpick_Oprod(_1536309, _1536311, _1536313, _1536315) = hAPP(c_Set_OCollect(tc_prod(_1536309, _1536311)), hAPP(c_Product__Type_Oprod_Oprod__case(_1536309, _1536311, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1536309, tc_fun(_1536311, tc_HOL_Obool), tc_fun(_1536311, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1536311, tc_HOL_Obool), tc_fun(_1536311, tc_HOL_Obool)), _1536309), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536311)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536309), c_fconj), hAPP(hAPP(c_COMBC(_1536309, tc_fun(_1536309, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536309)), _1536313)))), hAPP(hAPP(c_COMBC(_1536311, tc_fun(_1536311, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536311)), _1536315)))))], (31967 ^ _779854) ^ [_1354964, _1354966, _1354968] : [class_Groups_Oordered__ab__group__add__abs(_1354964), -(hAPP(c_Groups_Oabs__class_Oabs(_1354964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1354964), _1354966), _1354968)) = hAPP(c_Groups_Oabs__class_Oabs(_1354964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1354964), _1354968), _1354966)))], (18068 ^ _779854) ^ [_1106713] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1106713), hAPP(c_Nat_OSuc, _1106713)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1106713), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (30603 ^ _779854) ^ [_1332178, _1332180] : [-(_1332178 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332180), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1332178), _1332180))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332178, _1332180)))], (32818 ^ _779854) ^ [_1371021, _1371023, _1371025, _1371027] : [class_Groups_Oordered__ab__group__add__abs(_1371021), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371021), hAPP(c_Groups_Oabs__class_Oabs(_1371021), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371023, _1371021), _1371025), _1371027))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371023, _1371021), hAPP(hAPP(c_COMBB(_1371021, _1371021, _1371023), c_Groups_Oabs__class_Oabs(_1371021)), _1371025)), _1371027))))], (47596 ^ _779854) ^ [_1737030, _1737032, _1737034] : [47598 ^ _779854 : [(47601 ^ _779854) ^ [] : [hBOOL(hAPP(_1737032, 47597 ^ [_1737030, _1737032, _1737034]))], (47599 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737030), 47597 ^ [_1737030, _1737032, _1737034]), hAPP(c_List_Oset(_1737030), _1737034))))]], -(c_List_OtakeWhile(_1737030, _1737032, _1737034) = _1737034)], (17408 ^ _779854) ^ [_1094511, _1094513, _1094515] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094511), _1094513)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1094511, tc_HOL_Obool)), _1094515), _1094513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1094511), _1094515)), hAPP(c_Finite__Set_Ocard(_1094511), _1094513))))], (16982 ^ _779854) ^ [_1086255, _1086257, _1086259] : [class_Lattices_Oab__semigroup__idem__mult(_1086255), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086255), _1086257)), -(hAPP(c_Finite__Set_Ofold1(_1086255, c_Groups_Otimes__class_Otimes(_1086255)), hAPP(hAPP(c_Set_Oinsert(_1086255), _1086259), _1086257)) = hAPP(hAPP(c_Finite__Set_Ofold(_1086255, _1086255, c_Groups_Otimes__class_Otimes(_1086255)), _1086259), _1086257))], (51248 ^ _779854) ^ [_1817680, _1817682, _1817684, _1817686] : [51251 ^ _779854 : [(51254 ^ _779854) ^ [] : [hAPP(_1817684, 51249 ^ [_1817680, _1817682, _1817684, _1817686]) = hAPP(_1817684, 51250 ^ [_1817680, _1817682, _1817684, _1817686])], (51252 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817680, _1817680)), hAPP(hAPP(c_Product__Type_OPair(_1817680, _1817680), 51249 ^ [_1817680, _1817682, _1817684, _1817686]), 51250 ^ [_1817680, _1817682, _1817684, _1817686])), _1817682)))]], -(c_Equiv__Relations_Ocongruent(_1817680, _1817686, _1817682, _1817684))], (6405 ^ _779854) ^ [_881918, _881920, _881922] : [_881920 = _881922, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_881918, tc_HOL_Obool)), _881920) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_881918, tc_HOL_Obool)), _881922))], (34893 ^ _779854) ^ [_1428234, _1428236, _1428238, _1428240] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1428234, tc_fun(_1428236, tc_HOL_Obool))), _1428238), _1428240))], (20916 ^ _779854) ^ [_1156260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1156260)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1156260), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1156260)], (47780 ^ _779854) ^ [_1740811, _1740813, _1740815, _1740817, _1740819] : [-(c_List_OdropWhile(_1740811, _1740813, hAPP(hAPP(c_List_Omap(_1740815, _1740811), _1740817), _1740819)) = hAPP(hAPP(c_List_Omap(_1740815, _1740811), _1740817), c_List_OdropWhile(_1740815, hAPP(c_Fun_Ocomp(_1740811, tc_HOL_Obool, _1740815, _1740813), _1740817), _1740819)))], (7896 ^ _779854) ^ [_911894, _911896, _911898] : [class_Orderings_Oorder(_911894), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911894, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_911894), _911896)), c_SetInterval_Oord__class_OgreaterThanAtMost(_911894, _911896, _911898)) = c_Orderings_Obot__class_Obot(tc_fun(_911894, tc_HOL_Obool)))], (34749 ^ _779854) ^ [_1425684, _1425686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1425684)), 34752 ^ _779854 : [(34759 ^ _779854) ^ [] : [-(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), _1425686), _1425684)))), -(c_Divides_OnegDivAlg(_1425686, _1425684) = hAPP(c_Divides_Oadjust(_1425684), c_Divides_OnegDivAlg(_1425686, 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)))), _1425684))))], (34753 ^ _779854) ^ [] : [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), _1425686), _1425684))), -(c_Divides_OnegDivAlg(_1425686, _1425684) = 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), _1425686), _1425684)))]]], (33252 ^ _779854) ^ [_1383074, _1383076, _1383078, _1383080] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1383074, tc_HOL_Obool), tc_fun(_1383076, tc_HOL_Obool)), _1383078), hAPP(hAPP(c_COMBC(tc_fun(_1383074, tc_HOL_Obool), tc_fun(_1383074, tc_fun(_1383076, tc_HOL_Obool)), tc_fun(_1383076, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383074, tc_fun(_1383076, tc_HOL_Obool))), _1383080)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383074, tc_fun(_1383076, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1383074, tc_HOL_Obool), _1383078)), _1383080))], (36209 ^ _779854) ^ [_1455389, _1455391, _1455393] : [-(_1455389 = hAPP(hAPP(c_Product__Type_OPair(_1455391, _1455393), hAPP(c_Product__Type_Ofst(_1455391, _1455393), _1455389)), hAPP(c_Product__Type_Osnd(_1455391, _1455393), _1455389)))], (45160 ^ _779854) ^ [_1683904, _1683906, _1683908, _1683910, _1683912] : [class_Rings_Osemiring__0(_1683904), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1683904), hAPP(hAPP(c_List_Omap(_1683906, _1683904), hAPP(hAPP(c_COMBB(_1683904, _1683904, _1683906), hAPP(c_Groups_Otimes__class_Otimes(_1683904), _1683908)), _1683910)), _1683912)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1683904), _1683908), hAPP(c_List_Omonoid__add__class_Olistsum(_1683904), hAPP(hAPP(c_List_Omap(_1683906, _1683904), _1683910), _1683912))))], (15796 ^ _779854) ^ [_1062868, _1062870, _1062872, _1062874] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062868), _1062870)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062872), _1062870)), _1062874)) = 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), _1062868), _1062872)), _1062870)), _1062874))], (40940 ^ _779854) ^ [_1579628, _1579630, _1579632, _1579634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579628, _1579628)), hAPP(hAPP(c_Product__Type_OPair(_1579628, _1579628), _1579630), _1579632)), _1579634)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579628, _1579628)), hAPP(hAPP(c_Product__Type_OPair(_1579628, _1579628), _1579630), _1579632)), c_Transitive__Closure_Otrancl(_1579628, _1579634))))], (29549 ^ _779854) ^ [_1312847, _1312849] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1312847)), c_Int_OBit1(_1312849)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1312847), _1312849)))], (10381 ^ _779854) ^ [_955788, _955790, _955792, _955794, _955796] : [class_Lattices_Osemilattice__sup(_955788), class_Lattices_Osemilattice__sup(_955790), c_Orderings_Oorder__class_Omono(_955790, _955788, _955792), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955788), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955788), hAPP(_955792, _955794)), hAPP(_955792, _955796))), hAPP(_955792, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955790), _955794), _955796)))))], (14113 ^ _779854) ^ [_1028992, _1028994, _1028996, _1028998, _1029000, _1029002] : [-(_1028992 = _1028994), -(hAPP(c_Fun_Ofun__upd(_1028996, _1028998, _1029000, _1028994, _1029002), _1028992) = hAPP(_1029000, _1028992))], (5050 ^ _779854) ^ [_857022, _857024, _857026, _857028, _857030, _857032, _857034, _857036] : [-(c_Hilbert__Choice_Oinv__into(_857036, _857032, _857028, _857024) = c_Hilbert__Choice_Oinv__into(_857034, _857030, _857026, _857022)), _857036 = _857034, _857032 = _857030, _857028 = _857026, _857024 = _857022], (670 ^ _779854) ^ [_789953, _789955, _789957, _789959] : [-(c_FunDef_Ois__measure(_789957, _789953)), c_FunDef_Ois__measure(_789959, _789955), _789959 = _789957, _789955 = _789953], (16139 ^ _779854) ^ [_1069672, _1069674, _1069676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069672), _1069674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069674), _1069676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069672), _1069676)))], (42751 ^ _779854) ^ [_1628903, _1628905, _1628907, _1628909, _1628911] : [hBOOL(hAPP(hAPP(c_member(_1628903), _1628905), hAPP(c_List_Oset(_1628903), _1628907))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628909), hAPP(_1628911, _1628905))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628909), c_List_Olist_Olist__size(_1628903, _1628911, _1628907))))], (13199 ^ _779854) ^ [_1012703, _1012705] : [class_Lattices_Olattice(_1012703), -(c_Big__Operators_Olattice__class_OInf__fin(_1012703, hAPP(hAPP(c_Set_Oinsert(_1012703), _1012705), c_Orderings_Obot__class_Obot(tc_fun(_1012703, tc_HOL_Obool)))) = _1012705)], (12320 ^ _779854) ^ [_994723, _994725, _994727, _994729] : [hBOOL(hAPP(hAPP(c_member(_994723), _994725), _994727)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994723, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_994723), _994725), _994729)), _994727) = hAPP(hAPP(c_Set_Oinsert(_994723), _994725), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994723, tc_HOL_Obool)), _994729), _994727)))], (29379 ^ _779854) ^ [_1309847, _1309849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1309847)), c_Int_OBit0(_1309849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309847), _1309849)))], (52583 ^ _779854) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (48908 ^ _779854) ^ [_1765899, _1765901, _1765903, _1765905, _1765907] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765901, _1765899)), hAPP(hAPP(c_Product__Type_OPair(_1765901, _1765899), _1765905), _1765907)), hAPP(c_Relation_Oconverse(_1765899, _1765901), _1765903))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1765899, _1765901, hAPP(hAPP(c_COMBC(_1765899, tc_fun(tc_prod(_1765899, _1765901), tc_HOL_Obool), tc_fun(_1765901, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1765901, tc_fun(tc_fun(tc_prod(_1765899, _1765901), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1765899, _1765901), tc_HOL_Obool), tc_fun(_1765901, tc_HOL_Obool)), _1765899), c_COMBC(_1765901, tc_fun(tc_prod(_1765899, _1765901), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1765901, tc_prod(_1765899, _1765901)), tc_fun(_1765901, tc_fun(tc_fun(tc_prod(_1765899, _1765901), tc_HOL_Obool), tc_HOL_Obool)), _1765899), hAPP(c_COMBB(tc_prod(_1765899, _1765901), tc_fun(tc_fun(tc_prod(_1765899, _1765901), tc_HOL_Obool), tc_HOL_Obool), _1765901), c_member(tc_prod(_1765899, _1765901)))), c_Product__Type_OPair(_1765899, _1765901)))), _1765903)), _1765905), _1765907)))], (41168 ^ _779854) ^ [_1586057, _1586059] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1586057, _1586057, _1586057), c_Transitive__Closure_Ortrancl(_1586057, _1586059)), c_Transitive__Closure_Ortrancl(_1586057, _1586059)) = c_Transitive__Closure_Ortrancl(_1586057, _1586059))], (36201 ^ _779854) ^ [_1455252, _1455254] : [_1455252 = _1455254, -(hAPP(c_Int_ORep__Integ, _1455252) = hAPP(c_Int_ORep__Integ, _1455254))], (29797 ^ _779854) ^ [_1317184, _1317186] : [class_Rings_Olinordered__idom(_1317184), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317184), c_Groups_Ozero__class_Ozero(_1317184)), hAPP(hAPP(c_Power_Opower__class_Opower(_1317184), _1317186), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21208 ^ _779854) ^ [_1161770, _1161772] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1161770), _1161772)))), -(_1161772 = c_Orderings_Obot__class_Obot(tc_fun(_1161770, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1161770), _1161772))], (52667 ^ _779854) ^ [_1838640, _1838642] : [hBOOL(_1838640), hBOOL(_1838642), -(hBOOL(hAPP(hAPP(c_fconj, _1838640), _1838642)))], (38362 ^ _779854) ^ [_1507945, _1507947, _1507949, _1507951, _1507953] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507945, _1507947), _1507949), hAPP(hAPP(c_COMBS(_1507945, tc_fun(_1507947, tc_HOL_Obool), tc_fun(_1507947, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507947, tc_HOL_Obool), tc_fun(tc_fun(_1507947, tc_HOL_Obool), tc_fun(_1507947, tc_HOL_Obool)), _1507945), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507947, tc_HOL_Obool))), _1507951)), _1507953)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1507945, _1507947), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507945, _1507947), _1507949), _1507951)), hAPP(hAPP(c_Product__Type_OSigma(_1507945, _1507947), _1507949), _1507953)))], (15402 ^ _779854) ^ [_1054702, _1054704, _1054706] : [class_Groups_Ogroup__add(_1054702), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054702), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054702), _1054704), _1054706)), _1054706) = _1054704)], (35854 ^ _779854) ^ [_1447442, _1447444, _1447446, _1447448, _1447450] : [class_Orderings_Oorder(_1447442), c_Orderings_Oorder__class_Omono(_1447442, tc_fun(_1447444, tc_HOL_Obool), _1447446), -(c_Orderings_Oorder__class_Omono(_1447442, tc_fun(_1447444, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1447442, tc_fun(_1447444, tc_HOL_Obool), tc_fun(_1447444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447444, tc_HOL_Obool), tc_fun(tc_fun(_1447444, tc_HOL_Obool), tc_fun(_1447444, tc_HOL_Obool)), _1447442), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447444, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1447442, tc_fun(_1447444, tc_HOL_Obool), tc_fun(_1447444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447444, tc_HOL_Obool), tc_fun(tc_fun(_1447444, tc_HOL_Obool), tc_fun(_1447444, tc_HOL_Obool)), _1447442), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447444, tc_HOL_Obool))), _1447446)), _1447448))), _1447450)))], (41477 ^ _779854) ^ [_1593347, _1593349, _1593351, _1593353] : [-(hAPP(c_Relation_Oconverse(_1593347, _1593349), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593347, _1593349), tc_HOL_Obool)), _1593351), _1593353)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593349, _1593347), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1593347, _1593349), _1593351)), hAPP(c_Relation_Oconverse(_1593347, _1593349), _1593353)))], (2922 ^ _779854) ^ [_823378, _823380] : [_823380 = _823378, -(c_Int_Oring__1__class_Oof__int(_823380) = c_Int_Oring__1__class_Oof__int(_823378))], (11390 ^ _779854) ^ [_976611, _976613, _976615, _976617] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976611), hAPP(c_Set_Oimage(_976613, _976611, _976615), _976617))), c_Fun_Oinj__on(_976613, _976611, _976615, _976617), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976613), _976617)))], (2818 ^ _779854) ^ [_821784, _821786, _821788, _821790] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_821790, _821786) = c_Inductive_Ocomplete__lattice__class_Olfp(_821788, _821784)), _821790 = _821788, _821786 = _821784], (46623 ^ _779854) ^ [_1718094, _1718096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718094), _1718096)), -(c_List_Oupt(_1718094, hAPP(c_Nat_OSuc, _1718096)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1718094, _1718096)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1718096), c_List_Olist_ONil(tc_Nat_Onat))))], (27943 ^ _779854) ^ [_1285283, _1285285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285283)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285285)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1285283)), hAPP(c_Int_Onat, _1285285)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1285283), _1285285)))], (23834 ^ _779854) ^ [_1212047, _1212049, _1212051, _1212053] : [class_Rings_Olinordered__semidom(_1212047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212047), _1212049), _1212051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212047), c_Groups_Ozero__class_Ozero(_1212047)), _1212049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212047), hAPP(hAPP(c_Power_Opower__class_Opower(_1212047), _1212049), _1212053)), hAPP(hAPP(c_Power_Opower__class_Opower(_1212047), _1212051), _1212053))))], (18253 ^ _779854) ^ [_1110153, _1110155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110153), _1110155)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110155)), _1110153) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110155), _1110153)))], (16066 ^ _779854) ^ [_1068342, _1068344] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068342), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068344), _1068342))))], (52437 ^ _779854) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52381 ^ _779854) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (44570 ^ _779854) ^ [_1671385, _1671387, _1671389] : [-(hAPP(c_List_Orotate(_1671385, hAPP(c_Nat_OSuc, _1671387)), _1671389) = hAPP(c_List_Orotate1(_1671385), hAPP(c_List_Orotate(_1671385, _1671387), _1671389)))], (5160 ^ _779854) ^ [_858755, _858757] : [_858757 = _858755, -(c_Groups_Oplus__class_Oplus(_858757) = c_Groups_Oplus__class_Oplus(_858755))], (31961 ^ _779854) ^ [_1354817, _1354819, _1354821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1354819), 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), _1354819), _1354821))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1354817))), _1354821)))], (50120 ^ _779854) ^ [_1792915, _1792917] : [-(c_Relation_Osym(_1792915, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1792915, _1792915), tc_HOL_Obool)), _1792917), hAPP(c_Relation_Oconverse(_1792915, _1792915), _1792917))))], (51639 ^ _779854) ^ [_1825104, _1825106, _1825108, _1825110] : [class_Rings_Ocomm__ring__1(_1825104), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825104), _1825106), _1825108)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825104), _1825106), _1825110)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825104), _1825106), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1825104), _1825108), _1825110))))], (45276 ^ _779854) ^ [_1686693, _1686695, _1686697, _1686699] : [hBOOL(hAPP(c_List_Odistinct(_1686693), hAPP(hAPP(c_List_Omap(_1686695, _1686693), _1686697), _1686699))), 45279 ^ _779854 : [(45282 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_1686695, _1686693, _1686697, hAPP(c_List_Oset(_1686695), _1686699)))], (45280 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1686695), _1686699)))]]], (44127 ^ _779854) ^ [_1660845, _1660847, _1660849, _1660851, _1660853] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660845), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660847)), _1660849)))), -(hAPP(hAPP(c_List_Olist__update(_1660847, hAPP(hAPP(c_List_Oappend(_1660847), _1660849), _1660851)), _1660845), _1660853) = hAPP(hAPP(c_List_Oappend(_1660847), _1660849), hAPP(hAPP(c_List_Olist__update(_1660847, _1660851), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1660845), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660847)), _1660849))), _1660853)))], (16044 ^ _779854) ^ [_1068033, _1068035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068033), _1068035)), -(_1068033 = _1068035), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068033), _1068035)))], (25791 ^ _779854) ^ [_1248634] : [-(c_Int_Opred(_1248634) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1248634), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25013 ^ _779854) ^ [_1234021, _1234023, _1234025, _1234027] : [class_Fields_Olinordered__field__inverse__zero(_1234021), class_Int_Onumber(_1234021), 25020 ^ _779854 : [(25021 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234021), _1234023), _1234025)), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027))), 25024 ^ _779854 : [(25031 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), c_Groups_Ozero__class_Ozero(_1234021)), _1234025))), 25034 ^ _779854 : [(25041 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), _1234025), c_Groups_Ozero__class_Ozero(_1234021)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), c_Groups_Ozero__class_Ozero(_1234021)), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027))))], (25035 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), _1234025), c_Groups_Ozero__class_Ozero(_1234021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234021), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027)), _1234025)), _1234023)))]]], (25025 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), c_Groups_Ozero__class_Ozero(_1234021)), _1234025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), _1234023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234021), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027)), _1234025))))]]], (25047 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234021), _1234023), _1234025)), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027)))), 25050 ^ _779854 : [(25053 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), _1234023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234021), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027)), _1234025)))], (25051 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), c_Groups_Ozero__class_Ozero(_1234021)), _1234025)))]], 25054 ^ _779854 : [(25057 ^ _779854) ^ [] : [25058 ^ _779854 : [(25061 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234021), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027)), _1234025)), _1234023))], (25059 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), _1234025), c_Groups_Ozero__class_Ozero(_1234021))))]], 25062 ^ _779854 : [(25065 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), c_Groups_Ozero__class_Ozero(_1234021)), hAPP(c_Int_Onumber__class_Onumber__of(_1234021), _1234027)))], (25063 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), _1234025), c_Groups_Ozero__class_Ozero(_1234021)))]]], (25055 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234021), c_Groups_Ozero__class_Ozero(_1234021)), _1234025))]]]]], (15608 ^ _779854) ^ [_1058912, _1058914, _1058916] : [class_Lattices_Oab__semigroup__idem__mult(_1058912), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058912), _1058914)), -(_1058914 = c_Orderings_Obot__class_Obot(tc_fun(_1058912, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058912), _1058916)), -(_1058916 = c_Orderings_Obot__class_Obot(tc_fun(_1058912, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1058912, c_Groups_Otimes__class_Otimes(_1058912)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1058912, tc_HOL_Obool)), _1058914), _1058916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058912), hAPP(c_Finite__Set_Ofold1(_1058912, c_Groups_Otimes__class_Otimes(_1058912)), _1058914)), hAPP(c_Finite__Set_Ofold1(_1058912, c_Groups_Otimes__class_Otimes(_1058912)), _1058916)))], (42293 ^ _779854) ^ [_1616170, _1616172, _1616174, _1616176, _1616178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616170, _1616170)), hAPP(hAPP(c_Product__Type_OPair(_1616170, _1616170), _1616172), _1616174)), _1616176)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616170), tc_List_Olist(_1616170))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616170), tc_List_Olist(_1616170)), hAPP(hAPP(c_List_Olist_OCons(_1616170), _1616172), _1616178)), hAPP(hAPP(c_List_Olist_OCons(_1616170), _1616174), _1616178))), c_List_Olistrel1(_1616170, _1616176))))], (52327 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (46968 ^ _779854) ^ [_1724272, _1724274] : [class_Orderings_Olinorder(_1724272), c_List_Olinorder__class_Osorted(_1724272, _1724274), -(c_List_Olinorder__class_Osorted(_1724272, c_List_Oremdups(_1724272, _1724274)))], (36189 ^ _779854) ^ [_1455039, _1455041, _1455043, _1455045, _1455047] : [hAPP(c_Product__Type_Ofst(_1455039, _1455041), hAPP(hAPP(c_Product__Type_OPair(_1455039, _1455041), _1455043), _1455045)) = _1455047, -(_1455043 = _1455047)], (49687 ^ _779854) ^ [_1783071, _1783073] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1783071, tc_HOL_Obool), _1783073) = hAPP(c_Set_OCollect(_1783071), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1783071, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1783071), c_HOL_OEx(tc_fun(_1783071, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1783071, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1783071, tc_HOL_Obool), tc_HOL_Obool), _1783071), hAPP(c_COMBS(tc_fun(_1783071, 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(_1783071, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1783071, tc_HOL_Obool), tc_fun(tc_fun(_1783071, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1783071, tc_HOL_Obool))), _1783073)))), c_member(_1783071)))))], (43053 ^ _779854) ^ [_1637447, _1637449, _1637451, _1637453, _1637455, _1637457] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1637447, _1637449), hAPP(hAPP(c_List_Ozip(_1637447, _1637449), _1637451), _1637453)), _1637455), _1637457) = hAPP(hAPP(c_List_Ozip(_1637447, _1637449), hAPP(hAPP(c_List_Olist__update(_1637447, _1637451), _1637455), hAPP(c_Product__Type_Ofst(_1637447, _1637449), _1637457))), hAPP(hAPP(c_List_Olist__update(_1637449, _1637453), _1637455), hAPP(c_Product__Type_Osnd(_1637447, _1637449), _1637457))))], (15804 ^ _779854) ^ [_1063056, _1063058, _1063060] : [_1063056 = _1063060, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063056), _1063058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063060), _1063058))], (39520 ^ _779854) ^ [_1544644, _1544646, _1544648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544644, _1544644), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1544644, _1544644, _1544644), _1544646), _1544648)), _1544646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1544644, tc_HOL_Obool), tc_fun(_1544644, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1544644, tc_HOL_Obool), tc_fun(_1544644, tc_HOL_Obool), tc_fun(_1544644, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1544644, _1544646)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1544644, tc_HOL_Obool), tc_fun(_1544644, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1544644, _1544648)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1544644, tc_HOL_Obool), tc_fun(_1544644, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1544644, tc_HOL_Obool), tc_fun(_1544644, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1544644, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1544644, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1544644, tc_HOL_Obool), tc_fun(_1544644, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1544644, _1544646))))], (15542 ^ _779854) ^ [_1057488, _1057490, _1057492, _1057494] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1057488), _1057490)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057488), _1057492)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057488, tc_Nat_Onat), _1057494), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1057488, tc_HOL_Obool)), _1057490), _1057492)) = 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(_1057488, tc_Nat_Onat), _1057494), _1057490)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057488, tc_Nat_Onat), _1057494), _1057492))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057488, tc_Nat_Onat), _1057494), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057488, tc_HOL_Obool)), _1057490), _1057492))))], (18719 ^ _779854) ^ [_1118284, _1118286] : [class_Groups_Olinordered__ab__group__add(_1118284), 18722 ^ _779854 : [(18729 ^ _779854) ^ [] : [_1118286 = c_Groups_Ozero__class_Ozero(_1118284), -(_1118286 = hAPP(c_Groups_Ouminus__class_Ouminus(_1118284), _1118286))], (18723 ^ _779854) ^ [] : [_1118286 = hAPP(c_Groups_Ouminus__class_Ouminus(_1118284), _1118286), -(_1118286 = c_Groups_Ozero__class_Ozero(_1118284))]]], (43867 ^ _779854) ^ [_1655156, _1655158, _1655160, _1655162] : [hAPP(hAPP(c_List_Oappend(_1655156), _1655158), _1655160) = hAPP(hAPP(c_List_Oappend(_1655156), _1655158), _1655162), -(_1655160 = _1655162)], (23776 ^ _779854) ^ [_1210976, _1210978] : [class_Rings_Ocomm__semiring__1(_1210976), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210976), _1210978), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1210978)], (44705 ^ _779854) ^ [_1674242, _1674244, _1674246] : [class_Orderings_Olinorder(_1674242), -(c_Big__Operators_Olinorder__class_OMax(_1674242, hAPP(c_List_Oset(_1674242), hAPP(hAPP(c_List_Olist_OCons(_1674242), _1674244), _1674246))) = hAPP(c_List_Ofoldl(_1674242, _1674242, c_Orderings_Oord__class_Omax(_1674242), _1674244), _1674246))], (43414 ^ _779854) ^ [_1645380, _1645382] : [-(hAPP(hAPP(c_List_Otake(_1645380), _1645382), c_List_Olist_ONil(_1645380)) = c_List_Olist_ONil(_1645380))], (34823 ^ _779854) ^ [_1427020] : [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), _1427020))), 34826 ^ _779854 : [(34833 ^ _779854) ^ [] : [-(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), _1427020)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427020)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427020)), 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), _1427020)))))], (34827 ^ _779854) ^ [] : [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), _1427020))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427020)) = 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)))]]], (42169 ^ _779854) ^ [_1612361, _1612363, _1612365, _1612367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1612361), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1612363), _1612365))), -(hAPP(c_Random_Opick(_1612363, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1612363)), _1612365), _1612367)), _1612361) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1612363), _1612365))], (41523 ^ _779854) ^ [_1594628, _1594630, _1594632, _1594634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594628, _1594628)), hAPP(hAPP(c_Product__Type_OPair(_1594628, _1594628), _1594630), _1594632)), c_Transitive__Closure_Otrancl(_1594628, hAPP(c_Relation_Oconverse(_1594628, _1594628), _1594634)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594628, _1594628)), hAPP(hAPP(c_Product__Type_OPair(_1594628, _1594628), _1594630), _1594632)), hAPP(c_Relation_Oconverse(_1594628, _1594628), c_Transitive__Closure_Otrancl(_1594628, _1594634)))))], (2104 ^ _779854) ^ [_810471, _810473] : [_810473 = _810471, -(c_Int_Oring__1__class_OInts(_810473) = c_Int_Oring__1__class_OInts(_810471))], (1590 ^ _779854) ^ [_802681, _802683] : [-(class_Groups_Ocancel__ab__semigroup__add(_802681)), _802683 = _802681, class_Groups_Ocancel__ab__semigroup__add(_802683)], (45877 ^ _779854) ^ [_1700174, _1700176, _1700178, _1700180, _1700182, _1700184, _1700186] : [-(c_List_Olist__all2(_1700174, _1700176, _1700178, hAPP(hAPP(c_List_Olist_OCons(_1700174), _1700180), _1700182), hAPP(hAPP(c_List_Olist_OCons(_1700176), _1700184), _1700186))), hBOOL(hAPP(hAPP(_1700178, _1700180), _1700184)), c_List_Olist__all2(_1700174, _1700176, _1700178, _1700182, _1700186)], (18355 ^ _779854) ^ [_1112027, _1112029, _1112031] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1112027), _1112029)), 18358 ^ _779854 : [(18365 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112027), _1112031), _1112029))), -(hAPP(c_Finite__Set_Ocard(_1112027), hAPP(hAPP(c_Set_Oinsert(_1112027), _1112031), _1112029)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1112027), _1112029)))], (18359 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1112027), _1112031), _1112029)), -(hAPP(c_Finite__Set_Ocard(_1112027), hAPP(hAPP(c_Set_Oinsert(_1112027), _1112031), _1112029)) = hAPP(c_Finite__Set_Ocard(_1112027), _1112029))]]], (39148 ^ _779854) ^ [_1530893, _1530895, _1530897] : [class_Lattices_Odistrib__lattice(_1530893), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530893), _1530895)), -(_1530895 = c_Orderings_Obot__class_Obot(tc_fun(_1530893, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530893), _1530897)), -(_1530897 = c_Orderings_Obot__class_Obot(tc_fun(_1530893, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1530893), c_Big__Operators_Olattice__class_OInf__fin(_1530893, _1530895)), c_Big__Operators_Olattice__class_OInf__fin(_1530893, _1530897)) = c_Big__Operators_Olattice__class_OInf__fin(_1530893, hAPP(c_Set_OCollect(_1530893), hAPP(hAPP(c_COMBB(tc_fun(_1530893, tc_HOL_Obool), tc_HOL_Obool, _1530893), c_HOL_OEx(_1530893)), hAPP(hAPP(c_COMBB(tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool)), tc_fun(_1530893, tc_HOL_Obool), _1530893), hAPP(c_COMBB(tc_fun(_1530893, tc_HOL_Obool), tc_HOL_Obool, _1530893), c_HOL_OEx(_1530893))), hAPP(hAPP(c_COMBC(_1530893, tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool)), tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1530893, tc_fun(tc_fun(_1530893, tc_HOL_Obool), tc_fun(_1530893, tc_HOL_Obool))), tc_fun(tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool)), tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool))), _1530893), c_COMBS(_1530893, tc_fun(_1530893, tc_HOL_Obool), tc_fun(_1530893, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1530893, tc_fun(_1530893, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1530893, tc_fun(tc_fun(_1530893, tc_HOL_Obool), tc_fun(_1530893, tc_HOL_Obool))), _1530893), hAPP(c_COMBB(tc_fun(_1530893, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1530893, tc_HOL_Obool), tc_fun(_1530893, tc_HOL_Obool)), _1530893), c_COMBS(_1530893, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool)), tc_fun(_1530893, tc_fun(_1530893, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1530893), hAPP(c_COMBB(tc_fun(_1530893, tc_HOL_Obool), tc_fun(_1530893, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1530893), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530893), c_fconj))), hAPP(hAPP(c_COMBC(_1530893, tc_fun(_1530893, tc_fun(_1530893, _1530893)), tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1530893, _1530893), tc_fun(_1530893, tc_HOL_Obool)), tc_fun(tc_fun(_1530893, tc_fun(_1530893, _1530893)), tc_fun(_1530893, tc_fun(_1530893, tc_HOL_Obool))), _1530893), c_COMBB(tc_fun(_1530893, _1530893), tc_fun(_1530893, tc_HOL_Obool), _1530893)), hAPP(hAPP(c_COMBB(tc_fun(_1530893, tc_HOL_Obool), tc_fun(tc_fun(_1530893, _1530893), tc_fun(_1530893, tc_HOL_Obool)), _1530893), c_COMBB(_1530893, tc_HOL_Obool, _1530893)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1530893)))))), hAPP(hAPP(c_COMBC(_1530893, tc_fun(_1530893, tc_HOL_Obool), tc_fun(_1530893, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1530893, tc_HOL_Obool), tc_fun(_1530893, tc_HOL_Obool)), _1530893), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1530893)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530893), c_fconj), hAPP(hAPP(c_COMBC(_1530893, tc_fun(_1530893, tc_HOL_Obool), tc_HOL_Obool), c_member(_1530893)), _1530895)))), hAPP(hAPP(c_COMBC(_1530893, tc_fun(_1530893, tc_HOL_Obool), tc_HOL_Obool), c_member(_1530893)), _1530897))))))))], (44741 ^ _779854) ^ [_1675092, _1675094, _1675096] : [class_Orderings_Olinorder(_1675092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1675092), _1675094)), -(c_List_Olinorder__class_Osorted__list__of__set(_1675092, hAPP(hAPP(c_Set_Oinsert(_1675092), _1675096), _1675094)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675092, _1675092, c_COMBI(_1675092)), _1675096), c_List_Olinorder__class_Osorted__list__of__set(_1675092, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1675092, tc_HOL_Obool)), _1675094), hAPP(hAPP(c_Set_Oinsert(_1675092), _1675096), c_Orderings_Obot__class_Obot(tc_fun(_1675092, tc_HOL_Obool)))))))], (4534 ^ _779854) ^ [_848880, _848882, _848884, _848886, _848888, _848890] : [-(c_FunDef_OTHE__default(_848890, _848886, _848882) = c_FunDef_OTHE__default(_848888, _848884, _848880)), _848890 = _848888, _848886 = _848884, _848882 = _848880], (5392 ^ _779854) ^ [_862399, _862401] : [_862401 = _862399, -(c_Int_Onumber__class_Onumber__of(_862401) = c_Int_Onumber__class_Onumber__of(_862399))], (32748 ^ _779854) ^ [_1369491, _1369493, _1369495, _1369497, _1369499, _1369501, _1369503, _1369505] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369491, tc_fun(_1369493, tc_fun(_1369495, tc_HOL_Obool))), _1369497), _1369499), _1369501), _1369503)), hBOOL(hAPP(hAPP(c_member(_1369491), _1369505), _1369497)), -(hBOOL(hAPP(hAPP(hAPP(_1369499, _1369505), _1369501), _1369503)))], (46028 ^ _779854) ^ [_1703397, _1703399, _1703401] : [-(c_Enum_Osublists(_1703397, hAPP(hAPP(c_List_Olist_OCons(_1703397), _1703399), _1703401)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1703397)), tc_List_Olist(tc_List_Olist(_1703397))), c_Enum_Osublists(_1703397, _1703401)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1703397)), tc_List_Olist(tc_List_Olist(_1703397)), tc_List_Olist(tc_List_Olist(_1703397))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1703397)), tc_fun(tc_List_Olist(tc_List_Olist(_1703397)), tc_List_Olist(tc_List_Olist(_1703397))), tc_List_Olist(tc_List_Olist(_1703397))), c_List_Oappend(tc_List_Olist(_1703397))), hAPP(c_List_Omap(tc_List_Olist(_1703397), tc_List_Olist(_1703397)), hAPP(c_List_Olist_OCons(_1703397), _1703399)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1703397))))))], (28914 ^ _779854) ^ [_1301944, _1301946] : [-(hAPP(c_Int_Onat, _1301944) = _1301946), 28917 ^ _779854 : [(28920 ^ _779854) ^ [] : [_1301944 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1301946)], (28918 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301944)))]], 28921 ^ _779854 : [(28924 ^ _779854) ^ [] : [_1301946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28922 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301944))]]], (30029 ^ _779854) ^ [_1321435, _1321437] : [class_Rings_Oring__1(_1321435), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1321435), hAPP(c_Groups_Ouminus__class_Ouminus(_1321435), c_Groups_Oone__class_Oone(_1321435))), 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)))), _1321437)) = c_Groups_Oone__class_Oone(_1321435))], (51467 ^ _779854) ^ [_1822077, _1822079, _1822081] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822077), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1822079), _1822081))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822077), _1822081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1822081), _1822079)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822077), _1822079)))], (40867 ^ _779854) ^ [_1577894, _1577896, _1577898, _1577900, _1577902] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1577894, _1577896, _1577894, _1577898), hAPP(c_Product__Type_OPair(_1577896, _1577894), _1577900)), _1577902) = hAPP(_1577902, _1577900))], (31186 ^ _779854) ^ [_1342259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1342259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1342259)))], (31077 ^ _779854) ^ [_1340568, _1340570] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340568, _1340570) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1340568 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1340570), 31080 ^ [_1340568, _1340570]))], (20475 ^ _779854) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (39495 ^ _779854) ^ [_1543721, _1543723, _1543725, _1543727] : [hBOOL(hAPP(hAPP(c_member(_1543721), _1543723), hAPP(c_Relation_ORange(_1543725, _1543721), _1543727))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543725, _1543721)), hAPP(hAPP(c_Product__Type_OPair(_1543725, _1543721), 39498 ^ [_1543721, _1543723, _1543725, _1543727]), _1543723)), _1543727)))], (24244 ^ _779854) ^ [_1219572, _1219574] : [class_Power_Opower(_1219572), class_Rings_Osemiring__0(_1219572), 24251 ^ _779854 : [(24258 ^ _779854) ^ [] : [-(_1219574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219572), c_Groups_Ozero__class_Ozero(_1219572)), _1219574) = c_Groups_Ozero__class_Ozero(_1219572))], (24252 ^ _779854) ^ [] : [_1219574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219572), c_Groups_Ozero__class_Ozero(_1219572)), _1219574) = c_Groups_Oone__class_Oone(_1219572))]]], (9460 ^ _779854) ^ [_938032, _938034] : [class_Orderings_Olinorder(_938032), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938032), _938034), _938034) = _938034)], (51186 ^ _779854) ^ [_1814909, _1814911, _1814913, _1814915, _1814917, _1814919, _1814921] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814909, _1814911), tc_prod(_1814909, _1814911))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814909, _1814911), tc_prod(_1814909, _1814911)), hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), _1814913), _1814915)), hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), _1814917), _1814919))), c_Transitive__Closure_Ortrancl(tc_prod(_1814909, _1814911), _1814921))), -(hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), _1814913), _1814915) = hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), _1814917), _1814919)), 51195 ^ _779854 : [(51198 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814909, _1814911), tc_prod(_1814909, _1814911))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814909, _1814911), tc_prod(_1814909, _1814911)), hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), 51193 ^ [_1814909, _1814911, _1814913, _1814915, _1814917, _1814919, _1814921]), 51194 ^ [_1814909, _1814911, _1814913, _1814915, _1814917, _1814919, _1814921])), hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), _1814917), _1814919))), c_Transitive__Closure_Ortrancl(tc_prod(_1814909, _1814911), _1814921))))], (51196 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814909, _1814911), tc_prod(_1814909, _1814911))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814909, _1814911), tc_prod(_1814909, _1814911)), hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), _1814913), _1814915)), hAPP(hAPP(c_Product__Type_OPair(_1814909, _1814911), 51193 ^ [_1814909, _1814911, _1814913, _1814915, _1814917, _1814919, _1814921]), 51194 ^ [_1814909, _1814911, _1814913, _1814915, _1814917, _1814919, _1814921]))), _1814921)))]]], (3150 ^ _779854) ^ [_826912, _826914, _826916, _826918] : [-(c_Finite__Set_Ofold1(_826918, _826914) = c_Finite__Set_Ofold1(_826916, _826912)), _826918 = _826916, _826914 = _826912], (34363 ^ _779854) ^ [_1416791] : [-(c_Finite__Set_Ofun__left__comm__idem(_1416791, tc_fun(_1416791, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1416791, tc_HOL_Obool), tc_fun(tc_fun(_1416791, tc_HOL_Obool), tc_fun(_1416791, tc_HOL_Obool)), _1416791), hAPP(c_COMBC(tc_fun(_1416791, tc_HOL_Obool), tc_fun(_1416791, tc_HOL_Obool), tc_fun(_1416791, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1416791, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1416791, tc_fun(_1416791, tc_HOL_Obool), tc_fun(_1416791, tc_HOL_Obool)), c_Set_Oinsert(_1416791)), c_Orderings_Obot__class_Obot(tc_fun(_1416791, tc_HOL_Obool))))))], (39508 ^ _779854) ^ [_1544038, _1544040, _1544042, _1544044, _1544046] : [-(hAPP(c_Relation_ORange(_1544038, _1544040), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1544038, _1544040)), hAPP(hAPP(c_Product__Type_OPair(_1544038, _1544040), _1544042), _1544044)), _1544046)) = hAPP(hAPP(c_Set_Oinsert(_1544040), _1544044), hAPP(c_Relation_ORange(_1544038, _1544040), _1544046)))], (44063 ^ _779854) ^ [_1659206, _1659208, _1659210, _1659212, _1659214, _1659216] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659206), tc_List_Olist(_1659206))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659206), tc_List_Olist(_1659206)), hAPP(hAPP(c_List_Oappend(_1659206), _1659208), _1659214)), hAPP(hAPP(c_List_Oappend(_1659206), _1659210), _1659216))), c_List_Olistrel1(_1659206, _1659212)))), 44064 ^ _779854 : [(44071 ^ _779854) ^ [] : [_1659208 = _1659210, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659206), tc_List_Olist(_1659206))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659206), tc_List_Olist(_1659206)), _1659214), _1659216)), c_List_Olistrel1(_1659206, _1659212)))], (44065 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659206), tc_List_Olist(_1659206))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659206), tc_List_Olist(_1659206)), _1659208), _1659210)), c_List_Olistrel1(_1659206, _1659212))), _1659214 = _1659216]]], (35284 ^ _779854) ^ [_1437201, _1437203, _1437205] : [-(c_Fun_Oinj__on(tc_prod(_1437201, _1437203), tc_prod(_1437203, _1437201), hAPP(c_Product__Type_Oprod_Oprod__case(_1437201, _1437203, tc_prod(_1437203, _1437201)), hAPP(c_COMBC(_1437203, _1437201, tc_prod(_1437203, _1437201)), c_Product__Type_OPair(_1437203, _1437201))), _1437205))], (27261 ^ _779854) ^ [_1274055, _1274057, _1274059] : [-(hBOOL(hAPP(_1274055, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1274057), _1274059)))), 27264 ^ _779854 : [(27267 ^ _779854) ^ [] : [hBOOL(hAPP(_1274055, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27265 ^ _779854) ^ [] : [-(_1274059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 27270 ^ _779854 : [(27271 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1274059)))], (27277 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 27273 ^ [_1274055, _1274057, _1274059]), _1274059)))], (27281 ^ _779854) ^ [] : [hBOOL(hAPP(_1274055, 27272 ^ [_1274055, _1274057, _1274059]))], (27279 ^ _779854) ^ [] : [-(_1274057 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1274059), 27272 ^ [_1274055, _1274057, _1274059])), 27273 ^ [_1274055, _1274057, _1274059]))], (27275 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27273 ^ [_1274055, _1274057, _1274059])))]], 27282 ^ _779854 : [(27283 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274059), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27289 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 27285 ^ [_1274055, _1274057, _1274059]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27293 ^ _779854) ^ [] : [hBOOL(hAPP(_1274055, 27284 ^ [_1274055, _1274057, _1274059]))], (27291 ^ _779854) ^ [] : [-(_1274057 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1274059), 27284 ^ [_1274055, _1274057, _1274059])), 27285 ^ [_1274055, _1274057, _1274059]))], (27287 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274059), 27285 ^ [_1274055, _1274057, _1274059])))]]], (36401 ^ _779854) ^ [_1459300, _1459302, _1459304, _1459306] : [class_Orderings_Oorder(_1459300), class_Orderings_Oorder(_1459302), c_Orderings_Oorder__class_Omono(_1459302, _1459300, _1459304), -(c_Orderings_Oord__class_OLeast(_1459300, hAPP(hAPP(c_COMBC(_1459300, tc_fun(_1459300, tc_HOL_Obool), tc_HOL_Obool), c_member(_1459300)), hAPP(c_Set_Oimage(_1459302, _1459300, _1459304), _1459306))) = hAPP(_1459304, c_Orderings_Oord__class_OLeast(_1459302, hAPP(hAPP(c_COMBC(_1459302, tc_fun(_1459302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1459302)), _1459306)))), 36414 ^ _779854 : [(36415 ^ _779854) ^ [_1459584] : [hBOOL(hAPP(hAPP(c_member(_1459302), _1459584), _1459306)), 36419 ^ _779854 : [(36422 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459302), _1459584), 36418 ^ [_1459300, _1459302, _1459304, _1459306, _1459584]))], (36420 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459302), 36418 ^ [_1459300, _1459302, _1459304, _1459306, _1459584]), _1459306)))]]]]], (18333 ^ _779854) ^ [_1111571, _1111573, _1111575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111571), _1111573)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1111573), _1111571))), _1111575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111573)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111571), _1111575)))], (18020 ^ _779854) ^ [_1105957, _1105959, _1105961] : [_1105959 = _1105961, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105957)), _1105959) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105957)), _1105961))], (32886 ^ _779854) ^ [_1372879, _1372881, _1372883, _1372885, _1372887, _1372889] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372879, tc_fun(_1372881, tc_fun(_1372883, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1372879, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool), tc_fun(_1372881, tc_fun(_1372883, tc_HOL_Obool)), _1372879), hAPP(c_COMBC(_1372881, tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool), tc_fun(_1372883, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372883, tc_fun(tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool), tc_fun(_1372883, tc_HOL_Obool)), _1372881), c_COMBC(_1372883, tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372883, tc_prod(_1372881, _1372883)), tc_fun(_1372883, tc_fun(tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool), tc_HOL_Obool)), _1372881), hAPP(c_COMBB(tc_prod(_1372881, _1372883), tc_fun(tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool), tc_HOL_Obool), _1372883), c_member(tc_prod(_1372881, _1372883)))), c_Product__Type_OPair(_1372881, _1372883))))), _1372885)), _1372887), _1372889)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1372881, _1372883)), hAPP(hAPP(c_Product__Type_OPair(_1372881, _1372883), _1372887), _1372889)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372879, tc_fun(tc_prod(_1372881, _1372883), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1372879, tc_HOL_Obool))), _1372885))))], (18028 ^ _779854) ^ [_1106115, _1106117] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106115), _1106117), 18031 ^ _779854 : [(18034 ^ _779854) ^ [] : [-(_1106117 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18032 ^ _779854) ^ [] : [-(_1106115 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (46429 ^ _779854) ^ [_1712735, _1712737, _1712739, _1712741] : [-(hAPP(c_List_Ofilter(_1712735, _1712737), hAPP(c_List_Ofilter(_1712735, _1712739), _1712741)) = hAPP(c_List_Ofilter(_1712735, hAPP(hAPP(c_COMBS(_1712735, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1712735), c_fconj), _1712739)), _1712737)), _1712741))], (45131 ^ _779854) ^ [_1683088, _1683090, _1683092, _1683094, _1683096] : [45133 ^ _779854 : [(45136 ^ _779854) ^ [] : [hAPP(_1683092, 45132 ^ [_1683088, _1683090, _1683092, _1683094, _1683096]) = hAPP(_1683096, 45132 ^ [_1683088, _1683090, _1683092, _1683094, _1683096])], (45134 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1683088), 45132 ^ [_1683088, _1683090, _1683092, _1683094, _1683096]), hAPP(c_List_Oset(_1683088), _1683094))))]], -(hAPP(hAPP(c_List_Omap(_1683088, _1683090), _1683092), _1683094) = hAPP(hAPP(c_List_Omap(_1683088, _1683090), _1683096), _1683094))], (33246 ^ _779854) ^ [_1382891, _1382893, _1382895, _1382897, _1382899] : [class_Fields_Ofield(_1382891), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382891), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382893, _1382891), _1382895), _1382897)), _1382899) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382893, _1382891), hAPP(hAPP(c_COMBC(_1382893, _1382891, _1382891), hAPP(hAPP(c_COMBB(_1382891, tc_fun(_1382891, _1382891), _1382893), c_Rings_Oinverse__class_Odivide(_1382891)), _1382895)), _1382899)), _1382897))], (8248 ^ _779854) ^ [_918017, _918019, _918021] : [class_Orderings_Oorder(_918017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918017), _918019), _918021)), _918021 = _918019], (48656 ^ _779854) ^ [_1760069, _1760071, _1760073] : [48658 ^ _779854 : [(48661 ^ _779854) ^ [] : [hBOOL(hAPP(_1760073, 48657 ^ [_1760069, _1760071, _1760073]))], (48659 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760069), 48657 ^ [_1760069, _1760071, _1760073]), hAPP(c_List_Oset(_1760069), _1760071))))]], -(c_List_Olist__all(_1760069, _1760073, _1760071))], (31156 ^ _779854) ^ [_1341754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1341754), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1341754)), c_Int_OMin)))], (26609 ^ _779854) ^ [_1263436, _1263438] : [class_Divides_Osemiring__div(_1263436), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1263436), _1263438), c_Groups_Oone__class_Oone(_1263436)) = _1263438)], (48478 ^ _779854) ^ [_1756623, _1756625, _1756627] : [c_List_Olist__ex(_1756623, _1756625, hAPP(c_List_Orev(_1756623), _1756627)), -(c_List_Olist__ex(_1756623, _1756625, _1756627))], (34449 ^ _779854) ^ [_1418727, _1418729] : [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(_1418727))), 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)), _1418729))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418727) = hAPP(c_Nat_OSuc, _1418729))], (21224 ^ _779854) ^ [_1162053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162053)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1162053), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1162053)], (9971 ^ _779854) ^ [_948184, _948186, _948188] : [class_Orderings_Olinorder(_948184), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_948184), _948186), hAPP(hAPP(c_Orderings_Oord__class_Omin(_948184), _948186), _948188)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_948184), _948186), _948188))], (2416 ^ _779854) ^ [_815457, _815459] : [_815459 = _815457, -(c_Nat_Onat_Onat__size(_815459) = c_Nat_Onat_Onat__size(_815457))], (49032 ^ _779854) ^ [_1768476, _1768478, _1768480, _1768482] : [-(c_List_Oreplicate(_1768476, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1768478), _1768480), _1768482) = hAPP(hAPP(c_List_Oappend(_1768476), c_List_Oreplicate(_1768476, _1768478, _1768482)), c_List_Oreplicate(_1768476, _1768480, _1768482)))], (37139 ^ _779854) ^ [_1477774, _1477776] : [c_Relation_Oirrefl(_1477774, _1477776), 37142 ^ _779854 : [(37143 ^ _779854) ^ [_1477856] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477774, _1477774)), hAPP(hAPP(c_Product__Type_OPair(_1477774, _1477774), _1477856), _1477856)), _1477776))]]], (16722 ^ _779854) ^ [_1081068, _1081070, _1081072, _1081074] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1081068, _1081070, _1081072, _1081074, c_Orderings_Obot__class_Obot(tc_fun(_1081068, tc_HOL_Obool))), _1081074)))], (28834 ^ _779854) ^ [_1300669, _1300671] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300669), _1300671), hAPP(c_Int_Onumber__class_Onumber__of(_1300669), c_Int_OBit1(c_Int_OPls))) = _1300671), class_Fields_Ofield(_1300669), class_Int_Onumber__ring(_1300669)], (41074 ^ _779854) ^ [_1583747, _1583749] : [-(c_Transitive__Closure_Otrancl(_1583747, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583747, _1583747), tc_HOL_Obool)), _1583749), c_Relation_OId(_1583747))) = c_Transitive__Closure_Ortrancl(_1583747, _1583749))], (9811 ^ _779854) ^ [_944667] : [-(c_Lattices_Osemilattice__sup__class_Osup(_944667) = c_Orderings_Oord__class_Omax(_944667)), class_Lattices_Osemilattice__sup(_944667), class_Orderings_Olinorder(_944667)], (4060 ^ _779854) ^ [_841455, _841457, _841459, _841461, _841463, _841465, _841467, _841469] : [-(c_New__Random__Sequence_Oneg__bind(_841469, _841465, _841461, _841457) = c_New__Random__Sequence_Oneg__bind(_841467, _841463, _841459, _841455)), _841469 = _841467, _841465 = _841463, _841461 = _841459, _841457 = _841455], (52263 ^ _779854) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (18309 ^ _779854) ^ [_1111160, _1111162] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111160), _1111162))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1111160), hAPP(c_Nat_OSuc, _1111162)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34990 ^ _779854) ^ [_1430548, _1430550, _1430552, _1430554, _1430556, _1430558] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430548, tc_fun(_1430550, tc_HOL_Obool))), _1430552), _1430554), _1430556), _1430558)), -(hBOOL(hAPP(hAPP(_1430552, _1430556), _1430558)))], (9496 ^ _779854) ^ [_938682, _938684, _938686, _938688] : [class_Orderings_Olinorder(_938682), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938682), _938684), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938682), _938686), _938688)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_938682), _938686), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938682), _938684), _938688)))], (10989 ^ _779854) ^ [_968488, _968490, _968492, _968494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968488, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968488, tc_HOL_Obool)), _968490), _968492)), _968494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968488, tc_HOL_Obool)), _968490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_968488, tc_HOL_Obool)), _968492), _968494))))], (15088 ^ _779854) ^ [_1048120, _1048122, _1048124, _1048126] : [class_Groups_Ocancel__semigroup__add(_1048120), 15091 ^ _779854 : [(15098 ^ _779854) ^ [] : [_1048122 = _1048126, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048120), _1048122), _1048124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048120), _1048126), _1048124))], (15092 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048120), _1048122), _1048124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048120), _1048126), _1048124), -(_1048122 = _1048126)]]], (46024 ^ _779854) ^ [_1703306, _1703308] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703306))), c_Enum_Osublists(_1703306, _1703308)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703306)), _1703308)))], (29671 ^ _779854) ^ [_1315052, _1315054] : [class_Int_Onumber__ring(_1315052), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315052), _1315054), hAPP(c_Int_Onumber__class_Onumber__of(_1315052), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1315052), _1315054), _1315054))], (40879 ^ _779854) ^ [_1578189, _1578191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1578189), _1578191)), -(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), _1578189), _1578191)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (52209 ^ _779854) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (52677 ^ _779854) ^ [_1838779, _1838781] : [hBOOL(hAPP(hAPP(c_fconj, _1838779), _1838781)), -(hBOOL(_1838779))], (33569 ^ _779854) ^ [_1395389, _1395391, _1395393, _1395395, _1395397] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395389, tc_HOL_Obool)), _1395391), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395393, tc_fun(_1395389, tc_HOL_Obool)), _1395395), _1395397)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395393, tc_fun(_1395389, tc_HOL_Obool)), _1395395), hAPP(hAPP(c_COMBB(tc_fun(_1395389, tc_HOL_Obool), tc_fun(_1395389, tc_HOL_Obool), _1395393), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395389, tc_HOL_Obool)), _1395391)), _1395397)))], (43446 ^ _779854) ^ [_1645898, _1645900, _1645902] : [-(hAPP(hAPP(c_List_Ozip(_1645898, _1645900), _1645902), c_List_Olist_ONil(_1645900)) = c_List_Olist_ONil(tc_prod(_1645898, _1645900)))], (40054 ^ _779854) ^ [_1558111, _1558113, _1558115] : [c_Wellfounded_OwfP(_1558111, _1558113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558111, tc_fun(_1558111, tc_HOL_Obool))), _1558115), _1558113)), -(c_Wellfounded_OwfP(_1558111, _1558115))], (6197 ^ _779854) ^ [_878266, _878268, _878270] : [class_Orderings_Olinorder(_878266), 6200 ^ _779854 : [(6207 ^ _779854) ^ [] : [_878268 = _878270, -(hAPP(c_SetInterval_Oord__class_OatLeast(_878266), _878268) = hAPP(c_SetInterval_Oord__class_OatLeast(_878266), _878270))], (6201 ^ _779854) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_878266), _878268) = hAPP(c_SetInterval_Oord__class_OatLeast(_878266), _878270), -(_878268 = _878270)]]], (31518 ^ _779854) ^ [_1347906] : [-(_1347906 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 31521 ^ _779854 : [(31528 ^ _779854) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1347906, 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, _1347906) = 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), _1347906), 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)))], (31522 ^ _779854) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1347906, 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, _1347906) = 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), _1347906), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (30943 ^ _779854) ^ [_1338537] : [c_Nat__Transfer_Onat__set(_1338537), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1338537) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1338537)))], (46110 ^ _779854) ^ [_1705415, _1705417] : [c_List_Oremdups(_1705415, _1705417) = _1705417, -(hBOOL(hAPP(c_List_Odistinct(_1705415), _1705417)))], (46461 ^ _779854) ^ [_1713370, _1713372, _1713374, _1713376] : [hBOOL(hAPP(_1713370, _1713372)), -(hAPP(c_List_Ofilter(_1713374, _1713370), hAPP(hAPP(c_List_Olist_OCons(_1713374), _1713372), _1713376)) = hAPP(hAPP(c_List_Olist_OCons(_1713374), _1713372), hAPP(c_List_Ofilter(_1713374, _1713370), _1713376)))], (52233 ^ _779854) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (9320 ^ _779854) ^ [_935375, _935377, _935379] : [class_Complete__Lattice_Ocomplete__lattice(_935375), -(c_Complete__Lattice_OInf__class_OInf(_935375, hAPP(hAPP(c_Set_Oinsert(_935375), _935377), _935379)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935375), _935377), c_Complete__Lattice_OInf__class_OInf(_935375, _935379)))], (51294 ^ _779854) ^ [_1818923, _1818925, _1818927] : [c_List_Oall__interval__nat(_1818923, _1818925, _1818927), 51297 ^ _779854 : [(51298 ^ _779854) ^ [_1819003] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1819003), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1818925), _1818927))), -(hBOOL(hAPP(_1818923, _1819003)))]]], (19331 ^ _779854) ^ [_1128529, _1128531, _1128533] : [class_Rings_Oordered__cancel__semiring(_1128529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128529), _1128531), c_Groups_Ozero__class_Ozero(_1128529))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128529), c_Groups_Ozero__class_Ozero(_1128529)), _1128533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128529), _1128531), _1128533)), c_Groups_Ozero__class_Ozero(_1128529))))], (29971 ^ _779854) ^ [_1320119, _1320121, _1320123] : [class_Rings_Olinordered__idom(_1320119), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320119), c_Groups_Ozero__class_Ozero(_1320119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320119), hAPP(hAPP(c_Power_Opower__class_Opower(_1320119), _1320121), 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(_1320119), _1320123), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (27879 ^ _779854) ^ [_1284229, _1284231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284229)), 27882 ^ _779854 : [(27889 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284229), _1284231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1284229)), hAPP(c_Int_Onat, _1284231))))], (27883 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1284229)), hAPP(c_Int_Onat, _1284231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284229), _1284231)))]]], (17552 ^ _779854) ^ [_1097682, _1097684, _1097686, _1097688, _1097690] : [c_Fun_Oinj__on(_1097682, _1097684, _1097686, _1097688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097684, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1097682, _1097684, _1097686), _1097688)), _1097690)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097684), _1097690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1097682), _1097688)), hAPP(c_Finite__Set_Ocard(_1097684), _1097690))))], (5516 ^ _779854) ^ [_864315, _864317] : [_864317 = _864315, -(c_Divides_Odiv__class_Odiv(_864317) = c_Divides_Odiv__class_Odiv(_864315))], (5478 ^ _779854) ^ [_863754, _863756] : [_863756 = _863754, -(c_Orderings_Oord__class_Oless(_863756) = c_Orderings_Oord__class_Oless(_863754))], (18539 ^ _779854) ^ [_1115608, _1115610] : [class_Groups_Olinordered__ab__group__add(_1115608), 18542 ^ _779854 : [(18549 ^ _779854) ^ [] : [_1115610 = c_Groups_Ozero__class_Ozero(_1115608), -(c_Groups_Ozero__class_Ozero(_1115608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115608), _1115610), _1115610))], (18543 ^ _779854) ^ [] : [c_Groups_Ozero__class_Ozero(_1115608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115608), _1115610), _1115610), -(_1115610 = c_Groups_Ozero__class_Ozero(_1115608))]]], (1230 ^ _779854) ^ [_798181, _798183] : [-(class_Rings_Olinordered__idom(_798181)), _798183 = _798181, class_Rings_Olinordered__idom(_798183)], (52311 ^ _779854) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (46026 ^ _779854) ^ [_1703353] : [-(c_Enum_Osublists(_1703353, c_List_Olist_ONil(_1703353)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1703353)), c_List_Olist_ONil(_1703353)), c_List_Olist_ONil(tc_List_Olist(_1703353))))], (46048 ^ _779854) ^ [_1704005, _1704007] : [_1704005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1704007, _1704005, c_List_Olist_ONil(_1704007)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704007)), c_List_Olist_ONil(_1704007)), c_List_Olist_ONil(tc_List_Olist(_1704007))))], (25125 ^ _779854) ^ [_1236159, _1236161, _1236163, _1236165] : [class_Fields_Olinordered__field__inverse__zero(_1236159), class_Int_Onumber(_1236159), 25132 ^ _779854 : [(25133 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), _1236161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236159), _1236163), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)))), 25136 ^ _779854 : [(25143 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), c_Groups_Ozero__class_Ozero(_1236159)), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)))), 25146 ^ _779854 : [(25153 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)), c_Groups_Ozero__class_Ozero(_1236159)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), _1236161), c_Groups_Ozero__class_Ozero(_1236159))))], (25147 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)), c_Groups_Ozero__class_Ozero(_1236159))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), _1236163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236159), _1236161), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)))))]]], (25137 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), c_Groups_Ozero__class_Ozero(_1236159)), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236159), _1236161), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165))), _1236163)))]]], (25159 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), _1236161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236159), _1236163), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165))))), 25162 ^ _779854 : [(25165 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236159), _1236161), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165))), _1236163))], (25163 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), c_Groups_Ozero__class_Ozero(_1236159)), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165))))]], 25166 ^ _779854 : [(25169 ^ _779854) ^ [] : [25170 ^ _779854 : [(25173 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), _1236163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236159), _1236161), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165))))], (25171 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)), c_Groups_Ozero__class_Ozero(_1236159))))]], 25174 ^ _779854 : [(25177 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), _1236161), c_Groups_Ozero__class_Ozero(_1236159)))], (25175 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)), c_Groups_Ozero__class_Ozero(_1236159)))]]], (25167 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236159), c_Groups_Ozero__class_Ozero(_1236159)), hAPP(c_Int_Onumber__class_Onumber__of(_1236159), _1236165)))]]]]], (1640 ^ _779854) ^ [_803306, _803308] : [-(class_Rings_Olinordered__semidom(_803306)), _803308 = _803306, class_Rings_Olinordered__semidom(_803308)], (28944 ^ _779854) ^ [_1302375, _1302377] : [-(_1302375 = hAPP(c_Int_Onat, _1302377)), 28947 ^ _779854 : [(28950 ^ _779854) ^ [] : [_1302377 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1302375)], (28948 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302377)))]], 28951 ^ _779854 : [(28954 ^ _779854) ^ [] : [_1302375 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28952 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302377))]]], (15296 ^ _779854) ^ [_1052647, _1052649, _1052651, _1052653] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1052647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052647), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052647), _1052649), _1052651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052647), _1052653), _1052651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052647), _1052649), _1052653)))], (31683 ^ _779854) ^ [_1350317, _1350319] : [class_Rings_Oring__1(_1350317), 31686 ^ _779854 : [(31693 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350319), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1350317), _1350319) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1350317), hAPP(c_Int_Onat, _1350319)))], (31687 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350319), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1350317), _1350319) = hAPP(c_Groups_Ouminus__class_Ouminus(_1350317), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1350317), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1350319)))))]]], (43710 ^ _779854) ^ [_1651374, _1651376, _1651378, _1651380, _1651382] : [_1651374 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1651376, _1651378, _1651380), _1651374), _1651382) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651378), _1651376), c_List_Olist_ONil(_1651378)), _1651382))], (17052 ^ _779854) ^ [_1087572, _1087574, _1087576, _1087578, _1087580] : [c_Finite__Set_Ofolding__one(_1087572, _1087574, _1087576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087572), _1087578)), -(hBOOL(hAPP(hAPP(c_member(_1087572), _1087580), _1087578))), -(hAPP(_1087576, hAPP(hAPP(c_Set_Oinsert(_1087572), _1087580), _1087578)) = hAPP(hAPP(c_Finite__Set_Ofold(_1087572, _1087572, _1087574), _1087580), _1087578))], (35332 ^ _779854) ^ [_1437999, _1438001] : [_1437999 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1437999, _1438001) = 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)))], (20267 ^ _779854) ^ [_1144861, _1144863] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1144861), _1144863) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 20268 ^ _779854 : [(20275 ^ _779854) ^ [] : [_1144861 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1144863 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20269 ^ _779854) ^ [] : [_1144861 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (41064 ^ _779854) ^ [_1583496, _1583498, _1583500, _1583502] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583496, _1583496)), hAPP(hAPP(c_Product__Type_OPair(_1583496, _1583496), _1583498), _1583500)), c_Transitive__Closure_Otrancl(_1583496, _1583502))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583496, _1583496)), hAPP(hAPP(c_Product__Type_OPair(_1583496, _1583496), _1583498), _1583500)), c_Transitive__Closure_Ortrancl(_1583496, _1583502))))], (9953 ^ _779854) ^ [_947773, _947775, _947777, _947779] : [class_Orderings_Olinorder(_947773), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_947773), _947775), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947773), _947777), _947779)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_947773), _947777), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947773), _947775), _947779)))], (50332 ^ _779854) ^ [_1796698, _1796700, _1796702] : [c_Fun_Oinj__on(_1796698, _1796700, _1796702, c_Orderings_Otop__class_Otop(tc_fun(_1796698, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1796700, _1796698, _1796698, c_Hilbert__Choice_Oinv__into(_1796698, _1796700, c_Orderings_Otop__class_Otop(tc_fun(_1796698, tc_HOL_Obool)), _1796702)), _1796702) = c_Fun_Oid(_1796698))], (31705 ^ _779854) ^ [_1350665, _1350667] : [-(_1350665 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1350665, _1350667) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1350665), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1350667)))], (39134 ^ _779854) ^ [_1530407, _1530409, _1530411] : [class_Lattices_Odistrib__lattice(_1530407), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530407), _1530409)), -(_1530409 = c_Orderings_Obot__class_Obot(tc_fun(_1530407, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1530407), _1530411), c_Big__Operators_Olattice__class_OInf__fin(_1530407, _1530409)) = c_Big__Operators_Olattice__class_OInf__fin(_1530407, hAPP(c_Set_OCollect(_1530407), hAPP(hAPP(c_COMBB(tc_fun(_1530407, tc_HOL_Obool), tc_HOL_Obool, _1530407), c_HOL_OEx(_1530407)), hAPP(hAPP(c_COMBC(_1530407, tc_fun(_1530407, tc_HOL_Obool), tc_fun(_1530407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530407, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1530407, tc_HOL_Obool), tc_fun(_1530407, tc_HOL_Obool)), _1530407), c_COMBS(_1530407, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530407, tc_HOL_Obool), tc_fun(_1530407, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1530407), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530407), c_fconj)), hAPP(hAPP(c_COMBC(_1530407, tc_fun(_1530407, _1530407), tc_fun(_1530407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530407, tc_HOL_Obool), tc_fun(tc_fun(_1530407, _1530407), tc_fun(_1530407, tc_HOL_Obool)), _1530407), c_COMBB(_1530407, tc_HOL_Obool, _1530407)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1530407), _1530411))))), hAPP(hAPP(c_COMBC(_1530407, tc_fun(_1530407, tc_HOL_Obool), tc_HOL_Obool), c_member(_1530407)), _1530409))))))], (40531 ^ _779854) ^ [_1569970, _1569972] : [class_Complete__Lattice_Ocomplete__lattice(_1569970), c_Orderings_Oorder__class_Omono(_1569970, _1569970, _1569972), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1569970), hAPP(_1569972, c_Inductive_Ocomplete__lattice__class_Ogfp(_1569970, _1569972))), c_Inductive_Ocomplete__lattice__class_Ogfp(_1569970, _1569972))))], (9266 ^ _779854) ^ [_934534, _934536, _934538] : [class_Complete__Lattice_Ocomplete__lattice(_934534), -(c_Complete__Lattice_OSup__class_OSup(_934534, hAPP(hAPP(c_Set_Oinsert(_934534), _934536), _934538)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934534), _934536), c_Complete__Lattice_OSup__class_OSup(_934534, _934538)))], (3180 ^ _779854) ^ [_827359, _827361, _827363, _827365] : [-(c_Big__Operators_Olinorder__class_OMin(_827365, _827361) = c_Big__Operators_Olinorder__class_OMin(_827363, _827359)), _827365 = _827363, _827361 = _827359], (38070 ^ _779854) ^ [_1500073, _1500075, _1500077, _1500079] : [-(hAPP(c_Set_Ovimage(_1500073, _1500075, _1500077), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1500075, tc_HOL_Obool)), _1500079)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1500073, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1500073, _1500075, _1500077), _1500079)))], (38041 ^ _779854) ^ [_1499433] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1499433), c_Int_OInteg)), -(_1499433 = hAPP(c_Int_ORep__Integ, 38044 ^ [_1499433]))], (51258 ^ _779854) ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948] : [51261 ^ _779854 : [(51268 ^ _779854) ^ [] : [hAPP(hAPP(_1817946, 51259 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948]), 51263 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948]) = hAPP(hAPP(_1817946, 51260 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948]), 51264 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948])], (51266 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817942, _1817942)), hAPP(hAPP(c_Product__Type_OPair(_1817942, _1817942), 51263 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948]), 51264 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948])), _1817944)))], (51262 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817938, _1817938)), hAPP(hAPP(c_Product__Type_OPair(_1817938, _1817938), 51259 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948]), 51260 ^ [_1817938, _1817940, _1817942, _1817944, _1817946, _1817948])), _1817940)))]], -(c_Equiv__Relations_Ocongruent2(_1817938, _1817942, _1817948, _1817940, _1817944, _1817946))], (33084 ^ _779854) ^ [_1379206, _1379208, _1379210, _1379212, _1379214] : [-(_1379206 = c_Orderings_Obot__class_Obot(tc_fun(_1379208, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379210, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379208, tc_fun(_1379210, tc_HOL_Obool)), _1379206), _1379212)), _1379214) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379208, tc_fun(_1379210, tc_HOL_Obool)), _1379206), hAPP(hAPP(c_COMBC(_1379208, tc_fun(_1379210, tc_HOL_Obool), tc_fun(_1379210, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1379210, tc_HOL_Obool), tc_fun(tc_fun(_1379210, tc_HOL_Obool), tc_fun(_1379210, tc_HOL_Obool)), _1379208), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379210, tc_HOL_Obool))), _1379212)), _1379214)))], (39770 ^ _779854) ^ [_1551192, _1551194, _1551196] : [c_Wellfounded_Owf(_1551192, _1551194), -(hBOOL(hAPP(hAPP(c_member(_1551192), _1551196), c_Wellfounded_Oacc(_1551192, _1551194))))], (52313 ^ _779854) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (16559 ^ _779854) ^ [_1078300, _1078302, _1078304, _1078306, _1078308] : [class_Groups_Oab__semigroup__mult(_1078300), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1078300, _1078300, c_Groups_Otimes__class_Otimes(_1078300), _1078302, _1078304), _1078306)), hBOOL(hAPP(hAPP(c_member(_1078300), _1078308), _1078304)), -(hBOOL(hAPP(hAPP(c_member(_1078300), _1078302), _1078304))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1078300, _1078300, c_Groups_Otimes__class_Otimes(_1078300), _1078308, hAPP(hAPP(c_Set_Oinsert(_1078300), _1078302), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078300, tc_HOL_Obool)), _1078304), hAPP(hAPP(c_Set_Oinsert(_1078300), _1078308), c_Orderings_Obot__class_Obot(tc_fun(_1078300, tc_HOL_Obool)))))), _1078306)))], (28314 ^ _779854) ^ [_1291798] : [_1291798 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291798) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15124 ^ _779854) ^ [_1048719, _1048721, _1048723, _1048725] : [class_Groups_Ocancel__semigroup__add(_1048719), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048719), _1048721), _1048723) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048719), _1048725), _1048723), -(_1048721 = _1048725)], (1770 ^ _779854) ^ [_804931, _804933] : [-(class_Orderings_Opreorder(_804931)), _804933 = _804931, class_Orderings_Opreorder(_804933)], (46106 ^ _779854) ^ [_1705321, _1705323] : [-(hBOOL(hAPP(c_List_Odistinct(_1705321), c_List_Oremdups(_1705321, _1705323))))], (45222 ^ _779854) ^ [_1685416, _1685418, _1685420, _1685422, _1685424] : [-(hAPP(hAPP(c_List_Odrop(_1685416), _1685418), hAPP(hAPP(c_List_Omap(_1685420, _1685416), _1685422), _1685424)) = hAPP(hAPP(c_List_Omap(_1685420, _1685416), _1685422), hAPP(hAPP(c_List_Odrop(_1685420), _1685418), _1685424)))], (2134 ^ _779854) ^ [_810942, _810944, _810946, _810948] : [-(c_Nitpick_Onat__lcm(_810948, _810944) = c_Nitpick_Onat__lcm(_810946, _810942)), _810948 = _810946, _810944 = _810942], (38092 ^ _779854) ^ [_1500601, _1500603, _1500605, _1500607, _1500609, _1500611] : [-(hAPP(c_Set_Ovimage(_1500601, _1500603, _1500605), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500607, tc_fun(_1500603, tc_HOL_Obool)), _1500609), _1500611)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500607, tc_fun(_1500601, tc_HOL_Obool)), _1500609), hAPP(hAPP(c_COMBB(tc_fun(_1500603, tc_HOL_Obool), tc_fun(_1500601, tc_HOL_Obool), _1500607), c_Set_Ovimage(_1500601, _1500603, _1500605)), _1500611)))], (32830 ^ _779854) ^ [_1371323, _1371325, _1371327, _1371329] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1371323), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371325, tc_Int_Oint), _1371327), _1371329)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1371325, _1371323), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1371323, _1371325), c_Int_Oring__1__class_Oof__int(_1371323)), _1371327)), _1371329)), class_Groups_Ocomm__monoid__mult(_1371323), class_Rings_Oring__1(_1371323)], (45226 ^ _779854) ^ [_1685516] : [-(hAPP(c_List_Omap(_1685516, _1685516), c_Fun_Oid(_1685516)) = c_Fun_Oid(tc_List_Olist(_1685516)))], (38009 ^ _779854) ^ [_1498641, _1498643, _1498645, _1498647, _1498649] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1498641, _1498643, _1498645), _1498647), _1498649) = c_HOL_OThe(_1498643, c_Finite__Set_Ofold__graph(_1498641, _1498643, _1498645, _1498647, _1498649)))], (36100 ^ _779854) ^ [_1452946, _1452948, _1452950, _1452952, _1452954, _1452956] : [c_Finite__Set_Ofolding(_1452946, _1452948, _1452950, _1452952), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452946), _1452954)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452946), _1452956)), -(hAPP(c_Fun_Ocomp(_1452948, _1452948, _1452948, hAPP(_1452952, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452946, tc_HOL_Obool)), _1452954), _1452956))), hAPP(_1452952, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452946, tc_HOL_Obool)), _1452954), _1452956))) = hAPP(c_Fun_Ocomp(_1452948, _1452948, _1452948, hAPP(_1452952, _1452954)), hAPP(_1452952, _1452956)))], (51429 ^ _779854) ^ [_1821336, _1821338, _1821340, _1821342, _1821344] : [class_Rings_Ocomm__semiring__1(_1821336), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821336), hAPP(hAPP(c_Power_Opower__class_Opower(_1821336), _1821338), _1821340)), _1821342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1821344), _1821340)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821336), hAPP(hAPP(c_Power_Opower__class_Opower(_1821336), _1821338), _1821344)), _1821342)))], (37209 ^ _779854) ^ [_1479477, _1479479, _1479481] : [_1479479 = c_Orderings_Obot__class_Obot(tc_fun(_1479477, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479477), _1479479), _1479481) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1479477, tc_HOL_Obool), tc_HOL_Obool)))], (7990 ^ _779854) ^ [_913429, _913431, _913433] : [class_Orderings_Olinorder(_913429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913429), _913431), _913433)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913429, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_913429, _913431, _913433)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_913429), _913433)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_913429), _913431))], (11897 ^ _779854) ^ [_986560, _986562, _986564] : [-(hBOOL(hAPP(hAPP(c_member(_986560), _986562), hAPP(hAPP(c_Set_Oinsert(_986560), _986562), _986564))))], (45905 ^ _779854) ^ [_1700694, _1700696, _1700698, _1700700, _1700702] : [c_List_Olist__all2(_1700694, _1700696, _1700698, _1700700, _1700702), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700694)), _1700700) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700696)), _1700702))], (40704 ^ _779854) ^ [_1573818, _1573820, _1573822] : [class_Complete__Lattice_Ocomplete__lattice(_1573818), _1573820 = c_Inductive_Ocomplete__lattice__class_Olfp(_1573818, _1573822), c_Orderings_Oorder__class_Omono(_1573818, _1573818, _1573822), -(_1573820 = hAPP(_1573822, _1573820))], (52343 ^ _779854) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (12292 ^ _779854) ^ [_994093, _994095, _994097, _994099] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_994093, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_994093), _994095), _994097)), _994099))), hBOOL(hAPP(hAPP(c_member(_994093), _994095), _994099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_994093, tc_HOL_Obool)), _994097), _994099))], (38632 ^ _779854) ^ [_1515567, _1515569, _1515571, _1515573, _1515575, _1515577, _1515579] : [-(hAPP(c_Product__Type_Osnd(_1515567, _1515569), hAPP(c_Product__Type_Omap__pair(_1515571, _1515567, _1515573, _1515569, _1515575, _1515577), _1515579)) = hAPP(_1515577, hAPP(c_Product__Type_Osnd(_1515571, _1515573), _1515579)))], (30607 ^ _779854) ^ [_1332298, _1332300, _1332302] : [-(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), _1332298), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1332300), _1332298))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332300, _1332298))), _1332302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332300), _1332302))], (51048 ^ _779854) ^ [_1811979, _1811981, _1811983, _1811985, _1811987] : [hBOOL(hAPP(_1811979, hAPP(hAPP(c_Product__Type_OPair(_1811981, _1811983), _1811985), _1811987))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1811981, _1811983, tc_HOL_Obool, _1811979), _1811985), _1811987)))], (17917 ^ _779854) ^ [_1104179, _1104181] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104179)), _1104181) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1104179), _1104181)))], (3446 ^ _779854) ^ [_831506, _831508, _831510, _831512] : [-(c_List_OremoveAll(_831512, _831508) = c_List_OremoveAll(_831510, _831506)), _831512 = _831510, _831508 = _831506], (50589 ^ _779854) ^ [_1802823, _1802825] : [50591 ^ _779854 : [(50594 ^ _779854) ^ [] : [hBOOL(hAPP(_1802823, hAPP(c_Code__Numeral_Oof__nat, 50590 ^ [_1802823, _1802825])))], (50592 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50590 ^ [_1802823, _1802825]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1802823, _1802825)))], (1240 ^ _779854) ^ [_798306, _798308] : [-(class_Groups_Oab__group__add(_798306)), _798308 = _798306, class_Groups_Oab__group__add(_798308)], (37456 ^ _779854) ^ [_1485338, _1485340, _1485342, _1485344, _1485346] : [c_Equiv__Relations_Oequiv(_1485338, _1485340, _1485342), hBOOL(hAPP(hAPP(c_member(_1485338), _1485344), _1485340)), hBOOL(hAPP(hAPP(c_member(_1485338), _1485346), _1485340)), 37467 ^ _779854 : [(37474 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485338, _1485338)), hAPP(hAPP(c_Product__Type_OPair(_1485338, _1485338), _1485344), _1485346)), _1485342)), -(hAPP(c_Relation_OImage(_1485338, _1485338, _1485342), hAPP(hAPP(c_Set_Oinsert(_1485338), _1485344), c_Orderings_Obot__class_Obot(tc_fun(_1485338, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1485338, _1485338, _1485342), hAPP(hAPP(c_Set_Oinsert(_1485338), _1485346), c_Orderings_Obot__class_Obot(tc_fun(_1485338, tc_HOL_Obool)))))], (37468 ^ _779854) ^ [] : [hAPP(c_Relation_OImage(_1485338, _1485338, _1485342), hAPP(hAPP(c_Set_Oinsert(_1485338), _1485344), c_Orderings_Obot__class_Obot(tc_fun(_1485338, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1485338, _1485338, _1485342), hAPP(hAPP(c_Set_Oinsert(_1485338), _1485346), c_Orderings_Obot__class_Obot(tc_fun(_1485338, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1485338, _1485338)), hAPP(hAPP(c_Product__Type_OPair(_1485338, _1485338), _1485344), _1485346)), _1485342)))]]], (42761 ^ _779854) ^ [_1629102, _1629104, _1629106, _1629108, _1629110] : [hBOOL(hAPP(hAPP(c_member(_1629102), _1629104), hAPP(c_List_Oset(_1629102), _1629106))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1629108), hAPP(_1629110, _1629104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1629108), c_List_Olist_Olist__size(_1629102, _1629110, _1629106))))], (47949 ^ _779854) ^ [_1744409, _1744411, _1744413] : [-(c_List_Oinsert(_1744409, _1744411, c_List_Oremdups(_1744409, _1744413)) = c_List_Oremdups(_1744409, c_List_Oinsert(_1744409, _1744411, _1744413)))], (38887 ^ _779854) ^ [_1521988, _1521990, _1521992, _1521994] : [-(hAPP(c_Set_Ovimage(_1521988, _1521990, _1521992), _1521994) = hAPP(c_Set_OCollect(_1521988), hAPP(hAPP(c_COMBC(_1521988, tc_fun(_1521990, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1521990, tc_fun(tc_fun(_1521990, tc_HOL_Obool), tc_HOL_Obool), _1521988), c_member(_1521990)), _1521992)), _1521994)))], (46621 ^ _779854) ^ [_1718048, _1718050] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1718048), _1718050) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1718048, _1718050)))], (29059 ^ _779854) ^ [_1304368] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1304368))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1304368)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40631 ^ _779854) ^ [_1571922, _1571924, _1571926, _1571928] : [c_Orderings_Oorder__class_Omono(tc_fun(_1571922, tc_HOL_Obool), tc_fun(_1571922, tc_HOL_Obool), _1571924), hBOOL(hAPP(hAPP(c_member(_1571922), _1571926), _1571928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571922, tc_HOL_Obool)), _1571928), hAPP(_1571924, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1571922, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1571922, tc_HOL_Obool), tc_fun(_1571922, tc_HOL_Obool), tc_fun(_1571922, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571922, tc_HOL_Obool), tc_fun(tc_fun(_1571922, tc_HOL_Obool), tc_fun(_1571922, tc_HOL_Obool)), tc_fun(_1571922, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571922, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1571922, tc_HOL_Obool), tc_fun(_1571922, tc_HOL_Obool), tc_fun(_1571922, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571922, tc_HOL_Obool), tc_fun(tc_fun(_1571922, tc_HOL_Obool), tc_fun(_1571922, tc_HOL_Obool)), tc_fun(_1571922, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571922, tc_HOL_Obool))), _1571924)), _1571928))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1571922, tc_HOL_Obool), _1571924)))))), -(hBOOL(hAPP(hAPP(c_member(_1571922), _1571926), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1571922, tc_HOL_Obool), _1571924))))], (49541 ^ _779854) ^ [_1779910, _1779912] : [c_Relation_Otrans(_1779910, _1779912), 49544 ^ _779854 : [(49545 ^ _779854) ^ [_1780046, _1780048] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779910, _1779910)), hAPP(hAPP(c_Product__Type_OPair(_1779910, _1779910), _1780048), _1780046)), _1779912)), 49548 ^ _779854 : [(49549 ^ _779854) ^ [_1780189] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779910, _1779910)), hAPP(hAPP(c_Product__Type_OPair(_1779910, _1779910), _1780046), _1780189)), _1779912)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779910, _1779910)), hAPP(hAPP(c_Product__Type_OPair(_1779910, _1779910), _1780048), _1780189)), _1779912)))]]]]], (43211 ^ _779854) ^ [_1641130, _1641132, _1641134] : [-(hBOOL(hAPP(c_List_Odistinct(_1641130), hAPP(hAPP(c_List_Olist_OCons(_1641130), _1641132), _1641134)))), -(hBOOL(hAPP(hAPP(c_member(_1641130), _1641132), hAPP(c_List_Oset(_1641130), _1641134)))), hBOOL(hAPP(c_List_Odistinct(_1641130), _1641134))], (15794 ^ _779854) ^ [_1062837, _1062839] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1062837, _1062839))))], (17712 ^ _779854) ^ [_1100972, _1100974] : [_1100972 = _1100974, -(hAPP(c_Nat_OSuc, _1100972) = hAPP(c_Nat_OSuc, _1100974))], (35662 ^ _779854) ^ [_1444011, _1444013, _1444015] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444011), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444013)), _1444015)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1444011, _1444013), hAPP(c_Divides_OnegateSnd, _1444015))))], (10793 ^ _779854) ^ [_964165, _964167, _964169] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964165, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964165, tc_HOL_Obool)), _964167), _964169)), _964169) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964165, tc_HOL_Obool)), _964167), _964169))], (8586 ^ _779854) ^ [_923025, _923027, _923029] : [class_Orderings_Oorder(_923025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923025), _923027), _923029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923025), _923027), _923029))), -(_923027 = _923029)], (5721 ^ _779854) ^ [_870224, _870226, _870228, _870230] : [class_Orderings_Oord(_870224), 5724 ^ _779854 : [(5731 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870224), hAPP(_870228, 5732 ^ [_870224, _870226, _870228, _870230])), hAPP(_870230, 5732 ^ [_870224, _870226, _870228, _870230]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870226, _870224)), _870228), _870230)))], (5725 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870226, _870224)), _870228), _870230)), 5728 ^ _779854 : [(5729 ^ _779854) ^ [_870381] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870224), hAPP(_870228, _870381)), hAPP(_870230, _870381))))]]]]], (5036 ^ _779854) ^ [_856801, _856803, _856805, _856807, _856809, _856811] : [-(c_Set_Ovimage(_856811, _856807, _856803) = c_Set_Ovimage(_856809, _856805, _856801)), _856811 = _856809, _856807 = _856805, _856803 = _856801], (11129 ^ _779854) ^ [_971611, _971613, _971615] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_971611), _971613)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_971611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971611, tc_HOL_Obool)), _971613), _971615))))], (18861 ^ _779854) ^ [_1120292] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120292), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1120292)], (37075 ^ _779854) ^ [_1475791, _1475793, _1475795, _1475797] : [-(hAPP(c_Relation_OImage(_1475791, _1475793, _1475795), _1475797) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1475791, tc_fun(_1475793, tc_HOL_Obool)), _1475797), hAPP(hAPP(c_COMBB(tc_fun(_1475791, tc_HOL_Obool), tc_fun(_1475793, tc_HOL_Obool), _1475791), c_Relation_OImage(_1475791, _1475793, _1475795)), hAPP(hAPP(c_COMBC(_1475791, tc_fun(_1475791, tc_HOL_Obool), tc_fun(_1475791, tc_HOL_Obool)), c_Set_Oinsert(_1475791)), c_Orderings_Obot__class_Obot(tc_fun(_1475791, tc_HOL_Obool))))))], (1600 ^ _779854) ^ [_802806, _802808] : [-(class_Rings_Oordered__cancel__semiring(_802806)), _802808 = _802806, class_Rings_Oordered__cancel__semiring(_802808)], (8412 ^ _779854) ^ [_920200, _920202] : [class_Orderings_Opreorder(_920200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920200), _920202), _920202))], (31202 ^ _779854) ^ [] : [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)], (28513 ^ _779854) ^ [_1295360, _1295362] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295360), _1295362)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295360)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295362)))], (38298 ^ _779854) ^ [_1505921, _1505923, _1505925, _1505927] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505921, _1505923), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1505921, tc_HOL_Obool), _1505925)), _1505927) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1505921, tc_HOL_Obool), tc_fun(tc_prod(_1505921, _1505923), tc_HOL_Obool)), _1505925), hAPP(hAPP(c_COMBC(tc_fun(_1505921, tc_HOL_Obool), tc_fun(_1505921, tc_fun(_1505923, tc_HOL_Obool)), tc_fun(tc_prod(_1505921, _1505923), tc_HOL_Obool)), c_Product__Type_OSigma(_1505921, _1505923)), _1505927)))], (6721 ^ _779854) ^ [_887744, _887746, _887748] : [class_Lattices_Oboolean__algebra(_887744), -(hAPP(c_Groups_Ouminus__class_Ouminus(_887744), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_887744), _887746), _887748)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_887744), hAPP(c_Groups_Ouminus__class_Ouminus(_887744), _887746)), hAPP(c_Groups_Ouminus__class_Ouminus(_887744), _887748)))], (38 ^ _779854) ^ [_780383, _780385, _780387, _780389, _780391, _780393] : [-(c_Big__Operators_Osemilattice__big(_780391, _780387, _780383)), c_Big__Operators_Osemilattice__big(_780393, _780389, _780385), _780393 = _780391, _780389 = _780387, _780385 = _780383], (16103 ^ _779854) ^ [_1068994, _1068996] : [_1068994 = _1068996, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068994), _1068996)))], (43069 ^ _779854) ^ [_1637893, _1637895, _1637897] : [hBOOL(hAPP(hAPP(c_member(_1637893), _1637895), hAPP(c_List_Oset(_1637893), c_List_Obutlast(_1637893, _1637897)))), -(hBOOL(hAPP(hAPP(c_member(_1637893), _1637895), hAPP(c_List_Oset(_1637893), _1637897))))], (29385 ^ _779854) ^ [_1309948, _1309950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309948), _1309950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1309948)), c_Int_OBit0(_1309950))))], (46757 ^ _779854) ^ [_1720419] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1720419) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1720419)))], (19359 ^ _779854) ^ [_1129039, _1129041, _1129043] : [class_Rings_Oordered__cancel__semiring(_1129039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129039), c_Groups_Ozero__class_Ozero(_1129039)), _1129041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129039), _1129043), c_Groups_Ozero__class_Ozero(_1129039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129039), _1129041), _1129043)), c_Groups_Ozero__class_Ozero(_1129039))))], (41060 ^ _779854) ^ [_1583401, _1583403, _1583405] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583401, _1583401)), hAPP(hAPP(c_Product__Type_OPair(_1583401, _1583401), _1583403), _1583403)), c_Transitive__Closure_Ortrancl(_1583401, _1583405))))], (38937 ^ _779854) ^ [_1523570, _1523572, _1523574, _1523576] : [c_Relation_Orefl__on(_1523570, _1523572, _1523574), hBOOL(hAPP(hAPP(c_member(_1523570), _1523576), _1523572)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523570, _1523570)), hAPP(hAPP(c_Product__Type_OPair(_1523570, _1523570), _1523576), _1523576)), _1523574)))], (15894 ^ _779854) ^ [_1064874, _1064876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064874), _1064876)), _1064874))], (45929 ^ _779854) ^ [_1701132, _1701134, _1701136, _1701138] : [_1701138 = c_List_Olist_ONil(_1701134), -(c_List_Olist__all2(_1701132, _1701134, _1701136, c_List_Olist_ONil(_1701132), _1701138))], (44638 ^ _779854) ^ [_1672933] : [class_Groups_Omonoid__add(_1672933), -(c_List_Omonoid__add__class_Olistsum(_1672933) = c_List_Ofoldl(_1672933, _1672933, c_Groups_Oplus__class_Oplus(_1672933), c_Groups_Ozero__class_Ozero(_1672933)))], (39514 ^ _779854) ^ [_1544273, _1544275, _1544277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544273, _1544273), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1544273, _1544273, _1544273), _1544275), _1544277)), _1544275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1544273, tc_HOL_Obool), tc_fun(_1544273, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1544273, tc_HOL_Obool), tc_fun(_1544273, tc_HOL_Obool), tc_fun(_1544273, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1544273, _1544275)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1544273, tc_HOL_Obool), tc_fun(_1544273, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1544273, _1544277)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1544273, tc_HOL_Obool), tc_fun(_1544273, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1544273, tc_HOL_Obool), tc_fun(_1544273, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1544273, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1544273, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1544273, tc_HOL_Obool), tc_fun(_1544273, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1544273, _1544275))))], (37091 ^ _779854) ^ [_1476285, _1476287, _1476289] : [class_Rings_Oring__1(_1476285), -(hAPP(c_Int_Oring__1__class_Oof__int(_1476285), 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), _1476287), _1476289)), 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(_1476285), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1476285), _1476287)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1476285), _1476289)))], (6751 ^ _779854) ^ [_888542, _888544, _888546, _888548] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888542, tc_HOL_Obool)), _888544), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888542, tc_HOL_Obool)), _888546), _888548)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888542, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888542, tc_HOL_Obool)), _888544), _888546)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888542, tc_HOL_Obool)), _888544), _888548)))], (21851 ^ _779854) ^ [_1174613, _1174615] : [class_Rings_Odivision__ring(_1174613), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174613), c_Groups_Ozero__class_Ozero(_1174613)), _1174615) = c_Groups_Ozero__class_Ozero(_1174613))], (45462 ^ _779854) ^ [_1690603, _1690605, _1690607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1690603), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1690605), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1690605)), _1690607)))), -(hBOOL(hAPP(hAPP(c_member(_1690605), hAPP(c_Random_Opick(_1690605, _1690607), _1690603)), hAPP(c_List_Oset(_1690605), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1690605), _1690605), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1690605)), _1690607)))))], (42592 ^ _779854) ^ [_1624883, _1624885, _1624887] : [-(hAPP(hAPP(c_List_Onth(_1624883), hAPP(hAPP(c_List_Olist_OCons(_1624883), _1624885), _1624887)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1624885)], (44628 ^ _779854) ^ [_1672668, _1672670, _1672672] : [class_Groups_Omonoid__add(_1672668), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672668), _1672670), hAPP(c_List_Ofoldl(_1672668, _1672668, c_Groups_Oplus__class_Oplus(_1672668), c_Groups_Ozero__class_Ozero(_1672668)), _1672672)) = hAPP(c_List_Ofoldl(_1672668, _1672668, c_Groups_Oplus__class_Oplus(_1672668), _1672670), _1672672))], (31997 ^ _779854) ^ [_1355490, _1355492] : [class_Groups_Oordered__ab__group__add__abs(_1355490), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355490), _1355492), hAPP(c_Groups_Oabs__class_Oabs(_1355490), _1355492))))], (37030 ^ _779854) ^ [_1474559, _1474561, _1474563, _1474565, _1474567, _1474569] : [-(hAPP(c_Relation_OImage(_1474559, _1474561, _1474563), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474565, tc_fun(_1474559, tc_HOL_Obool)), _1474567), _1474569)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474565, tc_fun(_1474561, tc_HOL_Obool)), _1474567), hAPP(hAPP(c_COMBB(tc_fun(_1474559, tc_HOL_Obool), tc_fun(_1474561, tc_HOL_Obool), _1474565), c_Relation_OImage(_1474559, _1474561, _1474563)), _1474569)))], (35634 ^ _779854) ^ [_1443603, _1443605, _1443607, _1443609, _1443611, _1443613] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443603, _1443605), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443607), _1443609))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443603, _1443605), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443611), _1443613))), -(_1443605 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1443607 = _1443611)], (30135 ^ _779854) ^ [_1323612, _1323614] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323612, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1323614)) = 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), _1323612), _1323614)))], (36223 ^ _779854) ^ [_1455800, _1455802, _1455804, _1455806, _1455808, _1455810, _1455812] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1455800, _1455802, _1455804), hAPP(c_Fun_Ocomp(_1455806, tc_fun(_1455802, _1455804), _1455800, _1455808), _1455810)), _1455812) = hAPP(hAPP(_1455808, hAPP(_1455810, hAPP(c_Product__Type_Ofst(_1455800, _1455802), _1455812))), hAPP(c_Product__Type_Osnd(_1455800, _1455802), _1455812)))], (41062 ^ _779854) ^ [_1583450, _1583452] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583450, _1583450)), hAPP(hAPP(c_Product__Type_OPair(_1583450, _1583450), _1583452), _1583452)), c_Relation_OId(_1583450))))], (37624 ^ _779854) ^ [_1489385] : [-(c_Equiv__Relations_Oequivp(_1489385, c_fequal))], (39437 ^ _779854) ^ [_1542173, _1542175] : [-(hAPP(c_Relation_ORange(_1542173, _1542173), c_Relation_OId__on(_1542173, _1542175)) = _1542175)], (45238 ^ _779854) ^ [_1685885, _1685887, _1685889, _1685891, _1685893] : [hAPP(hAPP(c_List_Omap(_1685885, _1685887), _1685889), _1685891) = hAPP(hAPP(c_List_Omap(_1685885, _1685887), _1685889), _1685893), c_Fun_Oinj__on(_1685885, _1685887, _1685889, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1685885, tc_HOL_Obool)), hAPP(c_List_Oset(_1685885), _1685891)), hAPP(c_List_Oset(_1685885), _1685893))), -(_1685891 = _1685893)], (50252 ^ _779854) ^ [_1795028, _1795030] : [-(c_Equiv__Relations_Opart__equivp(_1795028, _1795030)), 50255 ^ _779854 : [(50256 ^ _779854) ^ [_1795148] : [hBOOL(hAPP(hAPP(_1795030, _1795148), _1795148))]], 50273 ^ _779854 : [(50276 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1795030, 50258 ^ [_1795028, _1795030]), 50258 ^ [_1795028, _1795030])))], (50278 ^ _779854) ^ [] : [-(hAPP(_1795030, 50257 ^ [_1795028, _1795030]) = hAPP(_1795030, 50258 ^ [_1795028, _1795030]))], (50280 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1795030, 50257 ^ [_1795028, _1795030]), 50258 ^ [_1795028, _1795030]))], (50274 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1795030, 50257 ^ [_1795028, _1795030]), 50257 ^ [_1795028, _1795030])))]], 50261 ^ _779854 : [(50264 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1795030, 50257 ^ [_1795028, _1795030]), 50257 ^ [_1795028, _1795030])), hBOOL(hAPP(hAPP(_1795030, 50258 ^ [_1795028, _1795030]), 50258 ^ [_1795028, _1795030])), hAPP(_1795030, 50257 ^ [_1795028, _1795030]) = hAPP(_1795030, 50258 ^ [_1795028, _1795030])], (50262 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1795030, 50257 ^ [_1795028, _1795030]), 50258 ^ [_1795028, _1795030])))]]], (49602 ^ _779854) ^ [_1781287, _1781289] : [c_Relation_Otrans(_1781287, hAPP(c_Relation_Oconverse(_1781287, _1781287), _1781289)), -(c_Relation_Otrans(_1781287, _1781289))], (46707 ^ _779854) ^ [_1719508, _1719510] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1719508, _1719510))))], (29879 ^ _779854) ^ [_1318572, _1318574] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1318572), hAPP(c_Int_Onumber__class_Onumber__of(_1318572), _1318574)), 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(_1318572), hAPP(c_Int_Onumber__class_Onumber__of(_1318572), _1318574)), hAPP(c_Int_Onumber__class_Onumber__of(_1318572), _1318574))), class_Groups_Omonoid__mult(_1318572), class_Int_Onumber(_1318572)], (10375 ^ _779854) ^ [_955609, _955611, _955613, _955615, _955617] : [c_Orderings_Oorder__class_Omono(tc_fun(_955609, tc_HOL_Obool), tc_fun(_955611, tc_HOL_Obool), _955613), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955611, tc_HOL_Obool)), hAPP(_955613, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955609, tc_HOL_Obool)), _955615), _955617))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955611, tc_HOL_Obool)), hAPP(_955613, _955615)), hAPP(_955613, _955617)))))], (33709 ^ _779854) ^ [_1399668, _1399670] : [-(hAPP(c_Finite__Set_Ocard(_1399668), _1399670) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399668, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1399668), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1399670))], (35115 ^ _779854) ^ [_1433275, _1433277, _1433279] : [-(hAPP(c_Nat_Onat_Onat__rec(_1433275, _1433277, _1433279), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1433277)], (2544 ^ _779854) ^ [_817539, _817541, _817543, _817545] : [-(c_Divides_Odivmod__nat(_817545, _817541) = c_Divides_Odivmod__nat(_817543, _817539)), _817545 = _817543, _817541 = _817539], (43536 ^ _779854) ^ [_1647538, _1647540, _1647542] : [-(hBOOL(hAPP(hAPP(c_member(_1647538), _1647540), hAPP(c_List_Oset(_1647538), _1647542)))), -(c_List_Oremove1(_1647538, _1647540, _1647542) = _1647542)], (35080 ^ _779854) ^ [_1432364, _1432366, _1432368, _1432370, _1432372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1432364, _1432366)), hAPP(hAPP(c_Product__Type_OPair(_1432364, _1432366), _1432370), _1432372)), _1432368)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1432364, _1432366, _1432368), _1432370), _1432372)))], (8640 ^ _779854) ^ [_923772, _923774, _923776] : [class_Orderings_Oorder(_923772), -(_923774 = _923776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923772), _923776), _923774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923772), _923776), _923774)))], (42596 ^ _779854) ^ [_1624996, _1624998, _1625000, _1625002] : [_1624996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1624998), hAPP(hAPP(c_List_Olist_OCons(_1624998), _1625000), _1625002)), _1624996) = _1625000)], (18407 ^ _779854) ^ [_1113114, _1113116, _1113118, _1113120, _1113122] : [class_Groups_Ocomm__monoid__add(_1113114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113116), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113118), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1113114), _1113120), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1113116, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113118), _1113122))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113114), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1113114), _1113120), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1113116, _1113118))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1113114), _1113120), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113118), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113118), _1113122)))))], (15134 ^ _779854) ^ [_1048886, _1048888, _1048890, _1048892] : [class_Rings_Ocomm__semiring(_1048886), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048886), _1048888), _1048890)), _1048892) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048886), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048886), _1048888), _1048892)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048886), _1048890), _1048892)))], (38011 ^ _779854) ^ [_1498691, _1498693] : [-(c_Divides_Odivmod__nat(_1498691, _1498693) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1498691, _1498693)))], (3746 ^ _779854) ^ [_836228, _836230, _836232, _836234] : [-(c_List_Olex(_836234, _836230) = c_List_Olex(_836232, _836228)), _836234 = _836232, _836230 = _836228], (20542 ^ _779854) ^ [_1149338, _1149340, _1149342] : [class_Groups_Oordered__comm__monoid__add(_1149338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149338), _1149340), c_Groups_Ozero__class_Ozero(_1149338))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149338), _1149342), c_Groups_Ozero__class_Ozero(_1149338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149338), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149338), _1149340), _1149342)), c_Groups_Ozero__class_Ozero(_1149338))))], (32073 ^ _779854) ^ [_1356911, _1356913] : [_1356911 = _1356913, -(c_Code__Numeral_OSuc__code__numeral(_1356911) = c_Code__Numeral_OSuc__code__numeral(_1356913))], (30969 ^ _779854) ^ [_1338940, _1338942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1338940)), -(c_SMT_Oz3mod(_1338942, _1338940) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1338942, _1338940))], (29761 ^ _779854) ^ [_1316558] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1316558), _1316558)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1316558)], (4830 ^ _779854) ^ [_853546, _853548, _853550, _853552, _853554, _853556, _853558, _853560, _853562, _853564, _853566, _853568] : [-(c_Partial__Function_Ofun__lub(_853568, _853564, _853560, _853556, _853552, _853548) = c_Partial__Function_Ofun__lub(_853566, _853562, _853558, _853554, _853550, _853546)), _853568 = _853566, _853564 = _853562, _853560 = _853558, _853556 = _853554, _853552 = _853550, _853548 = _853546], (33711 ^ _779854) ^ [_1399713, _1399715, _1399717, _1399719, _1399721] : [class_Groups_Oab__group__add(_1399713), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399715, _1399713), hAPP(hAPP(c_COMBS(_1399715, _1399713, _1399713), hAPP(hAPP(c_COMBB(_1399713, tc_fun(_1399713, _1399713), _1399715), c_Groups_Ominus__class_Ominus(_1399713)), _1399717)), _1399719)), _1399721) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1399713), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399715, _1399713), _1399717), _1399721)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399715, _1399713), _1399719), _1399721)))], (49178 ^ _779854) ^ [_1771304, _1771306] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1771304), _1771306))), 49181 ^ _779854 : [(49188 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1771304), _1771306))), -(c_Lazy__Sequence_Osmall__lazy_H(_1771304, _1771306) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1771306), c_Lazy__Sequence_Osmall__lazy_H(_1771304, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1771306), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49182 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1771304), _1771306)), -(c_Lazy__Sequence_Osmall__lazy_H(_1771304, _1771306) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (37771 ^ _779854) ^ [_1493123, _1493125, _1493127] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493123, _1493123)), _1493125), c_Relation_OId__on(_1493123, _1493127))), 37775 ^ _779854 : [(37778 ^ _779854) ^ [] : [-(_1493125 = hAPP(hAPP(c_Product__Type_OPair(_1493123, _1493123), 37774 ^ [_1493123, _1493125, _1493127]), 37774 ^ [_1493123, _1493125, _1493127]))], (37776 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493123), 37774 ^ [_1493123, _1493125, _1493127]), _1493127)))]]], (17811 ^ _779854) ^ [_1102544, _1102546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102544), hAPP(c_Nat_OSuc, _1102546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102544), _1102546))), -(_1102544 = _1102546)], (26735 ^ _779854) ^ [_1265306, _1265308, _1265310] : [class_Divides_Osemiring__div(_1265306), -(_1265308 = c_Groups_Ozero__class_Ozero(_1265306)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265306), _1265310), _1265308)), _1265308) = _1265310)], (23379 ^ _779854) ^ [_1203036, _1203038] : [class_Rings_Olinordered__idom(_1203036), 23382 ^ _779854 : [(23389 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203036), _1203038), c_Groups_Ozero__class_Ozero(_1203036))), -(c_Groups_Osgn__class_Osgn(_1203036, _1203038) = hAPP(c_Groups_Ouminus__class_Ouminus(_1203036), c_Groups_Oone__class_Oone(_1203036)))], (23383 ^ _779854) ^ [] : [c_Groups_Osgn__class_Osgn(_1203036, _1203038) = hAPP(c_Groups_Ouminus__class_Ouminus(_1203036), c_Groups_Oone__class_Oone(_1203036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203036), _1203038), c_Groups_Ozero__class_Ozero(_1203036))))]]], (46516 ^ _779854) ^ [_1714550, _1714552, _1714554] : [-(hAPP(c_List_Oset(_1714550), hAPP(c_List_Ofilter(_1714550, _1714552), _1714554)) = hAPP(c_Set_OCollect(_1714550), hAPP(hAPP(c_COMBS(_1714550, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1714550), c_fconj), hAPP(hAPP(c_COMBC(_1714550, tc_fun(_1714550, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714550)), hAPP(c_List_Oset(_1714550), _1714554)))), _1714552)))], (49483 ^ _779854) ^ [_1778438, _1778440, _1778442, _1778444] : [-(c_Random__Sequence_Omap(_1778438, _1778440, _1778442, _1778444) = c_Random__Sequence_Obind(_1778438, _1778440, _1778444, hAPP(c_Fun_Ocomp(_1778440, 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(_1778440)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1778438, c_Random__Sequence_Osingle(_1778440)), _1778442)))], (33102 ^ _779854) ^ [_1379610, _1379612, _1379614, _1379616, _1379618] : [_1379610 = c_Orderings_Obot__class_Obot(tc_fun(_1379612, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379612, tc_fun(_1379614, tc_HOL_Obool)), _1379610), hAPP(hAPP(c_COMBC(_1379612, tc_fun(_1379614, tc_HOL_Obool), tc_fun(_1379614, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1379614, tc_HOL_Obool), tc_fun(tc_fun(_1379614, tc_HOL_Obool), tc_fun(_1379614, tc_HOL_Obool)), _1379612), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379614, tc_HOL_Obool))), _1379616)), _1379618)) = c_Orderings_Obot__class_Obot(tc_fun(_1379614, tc_HOL_Obool)))], (4220 ^ _779854) ^ [_843973, _843975] : [_843975 = _843973, -(c_List_Odrop(_843975) = c_List_Odrop(_843973))], (25785 ^ _779854) ^ [_1248523, _1248525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248523), _1248525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248523), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1248525), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (52399 ^ _779854) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (3134 ^ _779854) ^ [_826678, _826680, _826682, _826684] : [-(c_Nat_Ocompow(_826684, _826680) = c_Nat_Ocompow(_826682, _826678)), _826684 = _826682, _826680 = _826678], (364 ^ _779854) ^ [_785430, _785432, _785434, _785436] : [-(c_Nitpick_Owf_H(_785434, _785430)), c_Nitpick_Owf_H(_785436, _785432), _785436 = _785434, _785432 = _785430], (23894 ^ _779854) ^ [_1213166, _1213168, _1213170, _1213172] : [class_Rings_Olinordered__semidom(_1213166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213166), c_Groups_Oone__class_Oone(_1213166)), _1213168)), 23901 ^ _779854 : [(23908 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213170), _1213172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213166), hAPP(hAPP(c_Power_Opower__class_Opower(_1213166), _1213168), _1213170)), hAPP(hAPP(c_Power_Opower__class_Opower(_1213166), _1213168), _1213172))))], (23902 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213166), hAPP(hAPP(c_Power_Opower__class_Opower(_1213166), _1213168), _1213170)), hAPP(hAPP(c_Power_Opower__class_Opower(_1213166), _1213168), _1213172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213170), _1213172)))]]], (28329 ^ _779854) ^ [_1292050] : [hBOOL(hAPP(_1292050, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28330 ^ [_1292050]))), 28333 ^ _779854 : [(28334 ^ _779854) ^ [_1292150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292150)), -(hBOOL(hAPP(_1292050, _1292150)))]]], (31146 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (42825 ^ _779854) ^ [_1630676, _1630678, _1630680] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1630676), _1630678)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1630676)), hAPP(c_Set_OCollect(tc_List_Olist(_1630676)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1630676), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1630676)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1630676), tc_fun(_1630676, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1630676, tc_HOL_Obool), tc_fun(tc_fun(_1630676, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1630676)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1630676, tc_HOL_Obool))), c_List_Oset(_1630676))), _1630678))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1630676), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1630676)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1630676)))), _1630680))))))], (11177 ^ _779854) ^ [_972535, _972537, _972539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972535), _972537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972535, tc_HOL_Obool)), hAPP(c_Set_Oimage(_972535, _972535, _972539), _972537)), _972537)), c_Fun_Oinj__on(_972535, _972535, _972539, _972537), -(hAPP(c_Set_Oimage(_972535, _972535, _972539), _972537) = _972537)], (33565 ^ _779854) ^ [_1395077, _1395079, _1395081, _1395083, _1395085, _1395087, _1395089] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395077, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395079, tc_fun(_1395077, tc_HOL_Obool)), _1395081), _1395083)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395085, tc_fun(_1395077, tc_HOL_Obool)), _1395087), _1395089)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395079, tc_fun(_1395077, tc_HOL_Obool)), _1395081), hAPP(hAPP(c_COMBB(tc_fun(_1395085, tc_fun(_1395077, tc_HOL_Obool)), tc_fun(_1395077, tc_HOL_Obool), _1395079), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395085, tc_fun(_1395077, tc_HOL_Obool)), _1395087)), hAPP(hAPP(c_COMBC(_1395079, tc_fun(_1395085, tc_fun(_1395077, tc_HOL_Obool)), tc_fun(_1395085, tc_fun(_1395077, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1395077, tc_HOL_Obool), tc_fun(_1395077, tc_HOL_Obool)), tc_fun(tc_fun(_1395085, tc_fun(_1395077, tc_HOL_Obool)), tc_fun(_1395085, tc_fun(_1395077, tc_HOL_Obool))), _1395079), c_COMBB(tc_fun(_1395077, tc_HOL_Obool), tc_fun(_1395077, tc_HOL_Obool), _1395085)), hAPP(hAPP(c_COMBB(tc_fun(_1395077, tc_HOL_Obool), tc_fun(tc_fun(_1395077, tc_HOL_Obool), tc_fun(_1395077, tc_HOL_Obool)), _1395079), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395077, tc_HOL_Obool))), _1395083))), _1395089))))], (51292 ^ _779854) ^ [_1818869, _1818871, _1818873] : [-(c_Lazy__Sequence_Omap(_1818869, _1818871, _1818873, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1818869)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1818871))], (5194 ^ _779854) ^ [_859290, _859292, _859294, _859296] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_859296, _859292) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_859294, _859290)), _859296 = _859294, _859292 = _859290], (9010 ^ _779854) ^ [_930114, _930116, _930118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_930114, tc_HOL_Obool)), _930116), _930118)), 9013 ^ _779854 : [(9016 ^ _779854) ^ [] : [_930116 = _930118], (9014 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930114, tc_HOL_Obool)), _930116), _930118)))]]], (28774 ^ _779854) ^ [_1299679, _1299681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1299679)), _1299681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1299679), hAPP(c_Int_Onat, _1299681))))], (9989 ^ _779854) ^ [_948527, _948529] : [class_Orderings_Olinorder(_948527), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_948527), _948529), _948529) = _948529)], (38400 ^ _779854) ^ [_1509118, _1509120, _1509122, _1509124, _1509126, _1509128] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509118, _1509120)), hAPP(hAPP(c_Product__Type_OPair(_1509118, _1509120), _1509122), _1509124)), hAPP(hAPP(c_Product__Type_OSigma(_1509118, _1509120), _1509126), _1509128)))), hBOOL(hAPP(hAPP(c_member(_1509118), _1509122), _1509126)), hBOOL(hAPP(hAPP(c_member(_1509120), _1509124), hAPP(_1509128, _1509122)))], (24623 ^ _779854) ^ [_1226482, _1226484, _1226486] : [class_Int_Onumber__ring(_1226482), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226482), hAPP(c_Int_Onumber__class_Onumber__of(_1226482), _1226484)), hAPP(c_Int_Onumber__class_Onumber__of(_1226482), _1226486)) = hAPP(c_Int_Onumber__class_Onumber__of(_1226482), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226484), _1226486)))], (43566 ^ _779854) ^ [_1648107, _1648109, _1648111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648107), tc_List_Olist(_1648107))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648107), tc_List_Olist(_1648107)), _1648109), c_List_Olist_ONil(_1648107))), c_List_Olexord(_1648107, _1648111)))], (32682 ^ _779854) ^ [_1368083, _1368085] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1368083), _1368085) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1368083), _1368085))], (10071 ^ _779854) ^ [_949959, _949961, _949963, _949965] : [class_Orderings_Olinorder(_949959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949959), _949961), _949963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949959), _949961), _949965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949959), _949961), hAPP(hAPP(c_Orderings_Oord__class_Omin(_949959), _949963), _949965))))], (9272 ^ _779854) ^ [_934655, _934657, _934659] : [class_Orderings_Oorder(_934655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934655), _934657), _934659)), -(c_SetInterval_Oord__class_OatLeastAtMost(_934655, _934659, _934657) = c_Orderings_Obot__class_Obot(tc_fun(_934655, tc_HOL_Obool)))], (12894 ^ _779854) ^ [_1006433, _1006435, _1006437, _1006439] : [hBOOL(hAPP(hAPP(_1006437, _1006439), _1006435)), -(hBOOL(hAPP(hAPP(c_member(_1006433), _1006435), c_SetInterval_Oord_OatLeast(_1006433, _1006437, _1006439))))], (45837 ^ _779854) ^ [_1699360, _1699362, _1699364, _1699366, _1699368, _1699370, _1699372] : [c_List_Olist__all2(_1699360, _1699362, _1699364, _1699366, _1699368), c_List_Olist__all2(_1699360, _1699362, _1699364, _1699370, _1699372), -(c_List_Olist__all2(_1699360, _1699362, _1699364, hAPP(hAPP(c_List_Oappend(_1699360), _1699366), _1699370), hAPP(hAPP(c_List_Oappend(_1699362), _1699368), _1699372)))], (12376 ^ _779854) ^ [_995952, _995954, _995956, _995958] : [-(hBOOL(hAPP(hAPP(c_member(_995952), _995954), _995956))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995952, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995952), _995954), _995958)), _995956) = hAPP(hAPP(c_Set_Oinsert(_995952), _995954), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995952, tc_HOL_Obool)), _995958), _995956)))], (33679 ^ _779854) ^ [_1398894, _1398896, _1398898, _1398900] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1398894, tc_HOL_Obool), hAPP(c_Set_Oimage(_1398896, tc_fun(_1398894, tc_HOL_Obool), _1398898), _1398900)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398896, tc_fun(_1398894, tc_HOL_Obool)), _1398900), _1398898))], (10971 ^ _779854) ^ [_968007, _968009] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968007, tc_HOL_Obool)), _968009), c_Orderings_Otop__class_Otop(tc_fun(_968007, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_968007, tc_HOL_Obool)))], (25729 ^ _779854) ^ [_1247549, _1247551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247549), _1247551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247549), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1247551)))], (1890 ^ _779854) ^ [_806431, _806433] : [-(class_Groups_Ozero(_806431)), _806433 = _806431, class_Groups_Ozero(_806433)], (28306 ^ _779854) ^ [] : [-(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))], (21793 ^ _779854) ^ [_1173330, _1173332, _1173334, _1173336, _1173338] : [class_Groups_Ocomm__monoid__mult(_1173330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173332), _1173334)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173332), _1173336)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1173332, tc_HOL_Obool)), _1173334), _1173336) = c_Orderings_Obot__class_Obot(tc_fun(_1173332, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1173330, _1173332, c_Groups_Otimes__class_Otimes(_1173330)), _1173338), c_Groups_Oone__class_Oone(_1173330)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1173332, tc_HOL_Obool)), _1173334), _1173336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173330), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1173330, _1173332, c_Groups_Otimes__class_Otimes(_1173330)), _1173338), c_Groups_Oone__class_Oone(_1173330)), _1173334)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1173330, _1173332, c_Groups_Otimes__class_Otimes(_1173330)), _1173338), c_Groups_Oone__class_Oone(_1173330)), _1173336)))], (4662 ^ _779854) ^ [_850946, _850948, _850950, _850952, _850954, _850956] : [-(c_Random__Sequence_Oempty(_850956, _850952, _850948) = c_Random__Sequence_Oempty(_850954, _850950, _850946)), _850956 = _850954, _850952 = _850950, _850948 = _850946], (15948 ^ _779854) ^ [_1065993, _1065995, _1065997, _1065999, _1066001] : [class_Rings_Ocomm__semiring__1(_1065993), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065993), _1065995), _1065997)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065993), _1065999), _1066001)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065993), _1065995), _1065999)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065993), _1065997), _1066001)))], (42364 ^ _779854) ^ [_1618277, _1618279] : [-(c_List_Olistrel(_1618277, c_Transitive__Closure_Ortrancl(_1618277, _1618279)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1618277), c_List_Olistrel1(_1618277, _1618279)))], (36175 ^ _779854) ^ [_1454759, _1454761, _1454763, _1454765] : [hAPP(c_Product__Type_Ofst(_1454759, _1454761), _1454763) = hAPP(c_Product__Type_Ofst(_1454759, _1454761), _1454765), hAPP(c_Product__Type_Osnd(_1454759, _1454761), _1454763) = hAPP(c_Product__Type_Osnd(_1454759, _1454761), _1454765), -(_1454763 = _1454765)], (16185 ^ _779854) ^ [_1070477, _1070479, _1070481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070477), _1070479)), _1070481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070477), _1070481)))], (41022 ^ _779854) ^ [_1581625, _1581627] : [-(c_Transitive__Closure_Otrancl(_1581625, _1581627) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1581625, _1581625), tc_HOL_Obool)), _1581627), hAPP(hAPP(c_Relation_Orel__comp(_1581625, _1581625, _1581625), c_Transitive__Closure_Otrancl(_1581625, _1581627)), _1581627)))], (35004 ^ _779854) ^ [_1430846, _1430848, _1430850, _1430852] : [-(c_Nat_Onat_Onat__case(_1430846, _1430848, _1430850, hAPP(c_Nat_OSuc, _1430852)) = hAPP(_1430850, _1430852))], (31571 ^ _779854) ^ [_1348859, _1348861] : [c_Nat__Transfer_Ois__nat(_1348859), c_Nat__Transfer_Ois__nat(_1348861), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1348859, _1348861) = 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, _1348859), hAPP(c_Int_Onat, _1348861))))], (11276 ^ _779854) ^ [_974332, _974334] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_974332, _974334)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_974332, _974334), tc_HOL_Obool)))), 11279 ^ _779854 : [(11282 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_974334), c_Orderings_Otop__class_Otop(tc_fun(_974334, tc_HOL_Obool)))))], (11280 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_974332), c_Orderings_Otop__class_Otop(tc_fun(_974332, tc_HOL_Obool)))))]]], (33677 ^ _779854) ^ [_1398837, _1398839, _1398841, _1398843] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398837, tc_fun(_1398839, tc_HOL_Obool)), _1398841), _1398843) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1398839, tc_HOL_Obool), hAPP(c_Set_Oimage(_1398837, tc_fun(_1398839, tc_HOL_Obool), _1398843), _1398841)))], (17324 ^ _779854) ^ [_1092883, _1092885, _1092887, _1092889] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1092883, _1092885, _1092887), _1092889)), _1092887 = c_Orderings_Obot__class_Obot(tc_fun(_1092883, tc_HOL_Obool))], (28481 ^ _779854) ^ [_1294813, _1294815] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1294813)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1294815), 28484 ^ _779854 : [(28487 ^ _779854) ^ [] : [-(_1294815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28485 ^ _779854) ^ [] : [-(_1294813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23395 ^ _779854) ^ [_1203298, _1203300] : [class_Groups_Osgn__if(_1203298), 23398 ^ _779854 : [(23405 ^ _779854) ^ [] : [-(_1203300 = c_Groups_Ozero__class_Ozero(_1203298)), 23408 ^ _779854 : [(23415 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203298), c_Groups_Ozero__class_Ozero(_1203298)), _1203300))), -(c_Groups_Osgn__class_Osgn(_1203298, _1203300) = hAPP(c_Groups_Ouminus__class_Ouminus(_1203298), c_Groups_Oone__class_Oone(_1203298)))], (23409 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203298), c_Groups_Ozero__class_Ozero(_1203298)), _1203300)), -(c_Groups_Osgn__class_Osgn(_1203298, _1203300) = c_Groups_Oone__class_Oone(_1203298))]]], (23399 ^ _779854) ^ [] : [_1203300 = c_Groups_Ozero__class_Ozero(_1203298), -(c_Groups_Osgn__class_Osgn(_1203298, _1203300) = c_Groups_Ozero__class_Ozero(_1203298))]]], (43684 ^ _779854) ^ [_1650772, _1650774, _1650776] : [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), _1650772), _1650774))), -(hBOOL(hAPP(hAPP(_1650776, _1650772), _1650774))), 43691 ^ _779854 : [(43694 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43689 ^ [_1650772, _1650774, _1650776]), 43690 ^ [_1650772, _1650774, _1650776])), -(hBOOL(hAPP(hAPP(_1650776, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43689 ^ [_1650772, _1650774, _1650776]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43690 ^ [_1650772, _1650774, _1650776])))], (43700 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1650776, 43689 ^ [_1650772, _1650774, _1650776]), 43690 ^ [_1650772, _1650774, _1650776]))], (43692 ^ _779854) ^ [] : [-(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), 43689 ^ [_1650772, _1650774, _1650776]), 43690 ^ [_1650772, _1650774, _1650776]))))]]], (5748 ^ _779854) ^ [_870755, _870757, _870759, _870761, _870763] : [class_Orderings_Oord(_870755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870757, _870755)), _870759), _870761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870755), hAPP(_870759, _870763)), hAPP(_870761, _870763))))], (11628 ^ _779854) ^ [_981478, _981480, _981482, _981484] : [hBOOL(hAPP(hAPP(c_member(_981478), _981480), hAPP(hAPP(c_Set_Oinsert(_981478), _981482), _981484))), -(_981480 = _981482), -(hBOOL(hAPP(hAPP(c_member(_981478), _981480), _981484)))], (21522 ^ _779854) ^ [_1168135, _1168137, _1168139] : [-(hAPP(c_Finite__Set_Ocard(_1168135), _1168137) = hAPP(c_Nat_OSuc, _1168139)), 21523 ^ _779854 : [(21524 ^ _779854) ^ [_1168235, _1168237] : [_1168137 = hAPP(hAPP(c_Set_Oinsert(_1168135), _1168237), _1168235), -(hBOOL(hAPP(hAPP(c_member(_1168135), _1168237), _1168235))), hAPP(c_Finite__Set_Ocard(_1168135), _1168235) = _1168139, 21535 ^ _779854 : [(21538 ^ _779854) ^ [] : [_1168235 = c_Orderings_Obot__class_Obot(tc_fun(_1168135, tc_HOL_Obool))], (21536 ^ _779854) ^ [] : [-(_1168139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (45726 ^ _779854) ^ [_1696605, _1696607, _1696609, _1696611] : [hBOOL(hAPP(c_List_Olistsp(_1696605, _1696607), hAPP(hAPP(c_List_Olist_OCons(_1696605), _1696609), _1696611))), 45729 ^ _779854 : [(45732 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1696605, _1696607), _1696611)))], (45730 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1696607, _1696609)))]]], (11250 ^ _779854) ^ [_973862, _973864, _973866] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_973862), _973864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973862, tc_HOL_Obool)), _973866), _973864)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973862), _973866)))], (51278 ^ _779854) ^ [_1818641, _1818643, _1818645] : [c_List_Olist__all(tc_Nat_Onat, _1818641, c_List_Oupt(_1818643, _1818645)), -(c_List_Oall__interval__nat(_1818641, _1818643, _1818645))], (42961 ^ _779854) ^ [_1635560] : [42963 ^ _779854 : [(42966 ^ _779854) ^ [] : [42962 ^ [_1635560] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42964 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42962 ^ [_1635560]), hAPP(c_List_Oset(tc_Nat_Onat), _1635560))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1635560) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46142 ^ _779854) ^ [_1705959, _1705961] : [c_List_Oremdups(_1705959, _1705961) = _1705961, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705959)), c_List_Oremdups(_1705959, _1705961)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705959)), _1705961))], (30131 ^ _779854) ^ [_1323527, _1323529] : [-(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, _1323527, _1323529)), _1323529) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1323527), _1323529))], (1740 ^ _779854) ^ [_804556, _804558] : [-(class_Rings_Ocomm__semiring(_804556)), _804558 = _804556, class_Rings_Ocomm__semiring(_804558)], (6464 ^ _779854) ^ [_883190, _883192, _883194] : [class_Complete__Lattice_Ocomplete__lattice(_883190), 6467 ^ _779854 : [(6468 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883190), _883192), c_Complete__Lattice_OInf__class_OInf(_883190, _883194))), 6471 ^ _779854 : [(6472 ^ _779854) ^ [_883348] : [hBOOL(hAPP(hAPP(c_member(_883190), _883348), _883194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883190), _883192), _883348)))]]], (6478 ^ _779854) ^ [] : [6480 ^ _779854 : [(6483 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883190), _883192), 6479 ^ [_883190, _883192, _883194]))], (6481 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_883190), 6479 ^ [_883190, _883192, _883194]), _883194)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883190), _883192), c_Complete__Lattice_OInf__class_OInf(_883190, _883194))))]]], (29545 ^ _779854) ^ [_1312771] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1312771)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1312771)))], (9064 ^ _779854) ^ [_931055, _931057, _931059, _931061, _931063] : [class_Orderings_Olinorder(_931055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931055), _931057), _931059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931055), _931061), _931063)), 9075 ^ _779854 : [(9084 ^ _779854) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_931055, _931057), _931059) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_931055, _931061), _931063)), _931057 = _931061, _931059 = _931063], (9076 ^ _779854) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_931055, _931057), _931059) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_931055, _931061), _931063), 9079 ^ _779854 : [(9082 ^ _779854) ^ [] : [-(_931059 = _931063)], (9080 ^ _779854) ^ [] : [-(_931057 = _931061)]]]]], (27959 ^ _779854) ^ [_1285585, _1285587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285587)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1285585)), hAPP(c_Int_Onat, _1285587)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1285585), _1285587)))], (16245 ^ _779854) ^ [_1071624, _1071626, _1071628] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071624), _1071626)), _1071628) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1071624), _1071628)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1071626), _1071628)))], (27053 ^ _779854) ^ [_1270412, _1270414] : [27054 ^ _779854 : [(27057 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1270412), c_Int_OPls))], (27055 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1270412), _1270414))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1270412)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1270414))))], (21689 ^ _779854) ^ [_1171264, _1171266, _1171268, _1171270] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1171264, _1171266)), c_Sum__Type_OPlus(_1171264, _1171266, _1171268, _1171270))), 21692 ^ _779854 : [(21695 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171266), _1171270)))], (21693 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171264), _1171268)))]]], (9002 ^ _779854) ^ [_929937, _929939, _929941] : [9003 ^ _779854 : [(9006 ^ _779854) ^ [] : [_929939 = _929941], (9004 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929937, tc_HOL_Obool)), _929939), _929941))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929937, tc_HOL_Obool)), _929939), _929941)))], (21875 ^ _779854) ^ [_1175113, _1175115, _1175117, _1175119] : [class_Rings_Odivision__ring(_1175113), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175113), _1175115), _1175117)), _1175119) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175113), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175113), _1175115), _1175119)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175113), _1175117), _1175119)))], (7137 ^ _779854) ^ [_897223, _897225, _897227] : [class_Lattices_Osemilattice__inf(_897223), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897223), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_897223), _897225), _897227)), _897225)))], (52613 ^ _779854) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (35893 ^ _779854) ^ [_1448473, _1448475, _1448477, _1448479, _1448481] : [-(hAPP(c_Product__Type_Osnd(_1448473, _1448475), hAPP(c_Product__Type_Oapsnd(_1448477, _1448475, _1448473, _1448479), _1448481)) = hAPP(_1448479, hAPP(c_Product__Type_Osnd(_1448473, _1448477), _1448481)))], (52255 ^ _779854) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (44360 ^ _779854) ^ [_1666886, _1666888, _1666890, _1666892, _1666894] : [hAPP(hAPP(c_List_Oappend(_1666886), _1666888), _1666890) = hAPP(hAPP(c_List_Oappend(_1666886), _1666892), _1666894), 44363 ^ _779854 : [(44372 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666888)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666892)))), 44375 ^ _779854 : [(44378 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1666886), hAPP(hAPP(c_List_Odrop(_1666886), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666892)), _1666888)), _1666890) = _1666894)], (44376 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1666886), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666892)), _1666888) = _1666892)]]], (44364 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666888)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666892))), 44367 ^ _779854 : [(44370 ^ _779854) ^ [] : [-(_1666890 = hAPP(hAPP(c_List_Oappend(_1666886), hAPP(hAPP(c_List_Odrop(_1666886), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666888)), _1666892)), _1666894))], (44368 ^ _779854) ^ [] : [-(_1666888 = hAPP(hAPP(c_List_Otake(_1666886), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666886)), _1666888)), _1666892))]]]]], (17206 ^ _779854) ^ [_1090517, _1090519, _1090521, _1090523, _1090525] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1090517, _1090517, _1090519, _1090521, _1090523), _1090525)), -(hBOOL(hAPP(hAPP(c_member(_1090517), _1090521), _1090523))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1090517, _1090519, hAPP(hAPP(c_Set_Oinsert(_1090517), _1090521), _1090523)), _1090525)))], (31262 ^ _779854) ^ [_1343483, _1343485] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343483), _1343485), hAPP(c_Int_Onumber__class_Onumber__of(_1343483), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1343483), _1343485)), class_Fields_Ofield__inverse__zero(_1343483), class_Int_Onumber__ring(_1343483)], (31554 ^ _779854) ^ [_1348469, _1348471, _1348473, _1348475, _1348477] : [class_Groups_Oordered__ab__semigroup__add(_1348469), class_Rings_Osemiring__1(_1348469), 31564 ^ _779854 : [(31567 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348469), hAPP(_1348475, 31563 ^ [_1348469, _1348471, _1348473, _1348475, _1348477])), _1348477))], (31565 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1348471), 31563 ^ [_1348469, _1348471, _1348473, _1348475, _1348477]), _1348473)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348469), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348471, _1348469), _1348475), _1348473)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348469), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1348469), hAPP(c_Finite__Set_Ocard(_1348471), _1348473))), _1348477))))], (39681 ^ _779854) ^ [_1549587, _1549589, _1549591, _1549593] : [c_Wellfounded_Owf(_1549587, _1549589), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549587, _1549587)), hAPP(hAPP(c_Product__Type_OPair(_1549587, _1549587), _1549591), _1549593)), _1549589)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549587, _1549587)), hAPP(hAPP(c_Product__Type_OPair(_1549587, _1549587), _1549593), _1549591)), _1549589))], (28804 ^ _779854) ^ [_1300197, _1300199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1300197)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1300199)))), 28807 ^ _779854 : [(28810 ^ _779854) ^ [] : [-(_1300199 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28808 ^ _779854) ^ [] : [-(_1300197 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (32704 ^ _779854) ^ [_1368559, _1368561, _1368563, _1368565, _1368567, _1368569, _1368571] : [class_Groups_Oab__semigroup__mult(_1368559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368561), _1368563)), c_Fun_Oinj__on(_1368561, _1368565, _1368567, _1368563), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1368559, _1368565, c_Groups_Otimes__class_Otimes(_1368559)), _1368569), _1368571), hAPP(c_Set_Oimage(_1368561, _1368565, _1368567), _1368563)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1368559, _1368561, c_Groups_Otimes__class_Otimes(_1368559)), hAPP(c_Fun_Ocomp(_1368565, _1368559, _1368561, _1368569), _1368567)), _1368571), _1368563))], (23535 ^ _779854) ^ [_1206088, _1206090] : [class_Rings_Olinordered__idom(_1206088), 23538 ^ _779854 : [(23545 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206088), c_Groups_Ozero__class_Ozero(_1206088)), _1206090)), -(c_Groups_Osgn__class_Osgn(_1206088, _1206090) = c_Groups_Oone__class_Oone(_1206088))], (23539 ^ _779854) ^ [] : [c_Groups_Osgn__class_Osgn(_1206088, _1206090) = c_Groups_Oone__class_Oone(_1206088), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206088), c_Groups_Ozero__class_Ozero(_1206088)), _1206090)))]]], (43546 ^ _779854) ^ [_1647689, _1647691] : [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(_1647689)), _1647691))), _1647691 = c_List_Olist_ONil(_1647689)], (11240 ^ _779854) ^ [_973693, _973695, _973697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973693, tc_HOL_Obool)), _973695), _973697)), hBOOL(hAPP(c_Finite__Set_Ofinite(_973693), _973697)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973693), _973695)))], (27633 ^ _779854) ^ [_1280009, _1280011] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1280009, _1280011)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1280011), _1280009)))], (21288 ^ _779854) ^ [_1163360, _1163362] : [21296 ^ _779854 : [(21299 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1163362, 21295 ^ [_1163360, _1163362])))], (21297 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 21295 ^ [_1163360, _1163362]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1163360))))]], 21289 ^ _779854 : [(21290 ^ _779854) ^ [_1163429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1163429), _1163360)), hBOOL(hAPP(_1163362, _1163429))]]], (6555 ^ _779854) ^ [_884767] : [class_Lattices_Oboolean__algebra(_884767), -(hAPP(c_Groups_Ouminus__class_Ouminus(_884767), c_Orderings_Obot__class_Obot(_884767)) = c_Orderings_Otop__class_Otop(_884767))], (50991 ^ _779854) ^ [_1810774, _1810776, _1810778, _1810780] : [c_Fun_Obij__betw(_1810774, _1810776, _1810778, c_Orderings_Otop__class_Otop(tc_fun(_1810774, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810776, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1810774, _1810776, _1810778), _1810780) = hAPP(c_Set_Oimage(_1810776, _1810774, c_Hilbert__Choice_Oinv__into(_1810774, _1810776, c_Orderings_Otop__class_Otop(tc_fun(_1810774, tc_HOL_Obool)), _1810778)), _1810780))], (27565 ^ _779854) ^ [_1278947] : [hBOOL(hAPP(_1278947, 27566 ^ [_1278947])), 27569 ^ _779854 : [(27570 ^ _779854) ^ [_1279041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1279041)), -(hBOOL(hAPP(_1278947, hAPP(c_Int_Onat, _1279041))))]]], (28671 ^ _779854) ^ [_1298001, _1298003] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1298001), _1298003) = 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)), _1298001)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1298003))))], (38182 ^ _779854) ^ [_1502783, _1502785, _1502787, _1502789] : [hBOOL(hAPP(hAPP(c_member(_1502783), _1502785), _1502787)), -(hAPP(c_Set_Ovimage(_1502789, _1502783, hAPP(c_COMBK(_1502783, _1502789), _1502785)), _1502787) = c_Orderings_Otop__class_Otop(tc_fun(_1502789, tc_HOL_Obool)))], (42988 ^ _779854) ^ [_1636079, _1636081] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1636079, _1636081) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1636079), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1636081)))], (45794 ^ _779854) ^ [_1698146, _1698148, _1698150, _1698152, _1698154] : [-(c_List_Olist__all2(_1698146, _1698148, _1698150, _1698152, _1698154)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698146)), _1698152) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698148)), _1698154), 45800 ^ _779854 : [(45803 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1698146, _1698148, tc_HOL_Obool), _1698150), 45799 ^ [_1698146, _1698148, _1698150, _1698152, _1698154]))], (45801 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1698146, _1698148)), 45799 ^ [_1698146, _1698148, _1698150, _1698152, _1698154]), hAPP(c_List_Oset(tc_prod(_1698146, _1698148)), hAPP(hAPP(c_List_Ozip(_1698146, _1698148), _1698152), _1698154)))))]]], (44574 ^ _779854) ^ [_1671518, _1671520, _1671522] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1671518, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671520)), _1671522)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1671520, _1671518), _1671522) = _1671522)], (4202 ^ _779854) ^ [_843718, _843720] : [_843720 = _843718, -(c_List_Otl(_843720) = c_List_Otl(_843718))], (21811 ^ _779854) ^ [_1173772, _1173774] : [-(hBOOL(hAPP(_1173772, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1173772, _1173774)), 21819 ^ _779854 : [(21822 ^ _779854) ^ [_1174010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174010), 21818 ^ [_1173772, _1173774])), hBOOL(hAPP(_1173772, _1174010))], (21828 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1173772, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21818 ^ [_1173772, _1173774]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (21820 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21818 ^ [_1173772, _1173774]), _1173774)))]]], (41944 ^ _779854) ^ [_1605632, _1605634, _1605636, _1605638] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605632, _1605632)), hAPP(hAPP(c_Product__Type_OPair(_1605632, _1605632), _1605634), _1605636)), c_Transitive__Closure_Otrancl(_1605632, _1605638))), 41948 ^ _779854 : [(41951 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605632, _1605632)), hAPP(hAPP(c_Product__Type_OPair(_1605632, _1605632), 41947 ^ [_1605632, _1605634, _1605636, _1605638]), _1605636)), _1605638)))], (41949 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605632, _1605632)), hAPP(hAPP(c_Product__Type_OPair(_1605632, _1605632), _1605634), 41947 ^ [_1605632, _1605634, _1605636, _1605638])), c_Transitive__Closure_Ortrancl(_1605632, _1605638))))]]], (17744 ^ _779854) ^ [_1101448] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101448)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1101448)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1101448), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (6069 ^ _779854) ^ [_876028, _876030, _876032] : [class_Orderings_Olinorder(_876028), 6072 ^ _779854 : [(6079 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876028), _876030), _876032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876028, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_876028), _876030)), hAPP(c_SetInterval_Oord__class_OlessThan(_876028), _876032))))], (6073 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876028, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_876028), _876030)), hAPP(c_SetInterval_Oord__class_OlessThan(_876028), _876032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876028), _876030), _876032)))]]], (2564 ^ _779854) ^ [_817837, _817839] : [_817839 = _817837, -(c_Nitpick_Oone__frac(_817839) = c_Nitpick_Oone__frac(_817837))], (50818 ^ _779854) ^ [_1807563, _1807565, _1807567, _1807569, _1807571, _1807573, _1807575] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1807563, tc_HOL_Obool)), _1807565), _1807567) = c_Orderings_Obot__class_Obot(tc_fun(_1807563, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1807569, tc_HOL_Obool)), _1807571), _1807573) = c_Orderings_Obot__class_Obot(tc_fun(_1807569, tc_HOL_Obool)), c_Fun_Obij__betw(_1807563, _1807569, _1807575, _1807565, _1807571), c_Fun_Obij__betw(_1807563, _1807569, _1807575, _1807567, _1807573), -(c_Fun_Obij__betw(_1807563, _1807569, _1807575, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1807563, tc_HOL_Obool)), _1807565), _1807567), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1807569, tc_HOL_Obool)), _1807571), _1807573)))], (45704 ^ _779854) ^ [_1696126, _1696128, _1696130, _1696132] : [-(hBOOL(hAPP(c_List_Olistsp(_1696126, hAPP(hAPP(c_COMBS(_1696126, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1696126), c_fconj), _1696128)), _1696130)), _1696132))), hBOOL(hAPP(c_List_Olistsp(_1696126, _1696128), _1696132)), hBOOL(hAPP(c_List_Olistsp(_1696126, _1696130), _1696132))], (36440 ^ _779854) ^ [_1460166] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1460166)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1460166)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47326 ^ _779854) ^ [_1731323] : [-(hAPP(c_List_Orev(_1731323), c_List_Olist_ONil(_1731323)) = c_List_Olist_ONil(_1731323))], (23421 ^ _779854) ^ [_1203719, _1203721, _1203723, _1203725, _1203727] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1203719, _1203721, hAPP(hAPP(c_Set_Oinsert(_1203719), _1203723), _1203725)), _1203727)), 23426 ^ _779854 : [(23431 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1203719), 23424 ^ [_1203719, _1203721, _1203723, _1203725, _1203727]), 23425 ^ [_1203719, _1203721, _1203723, _1203725, _1203727]))], (23429 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1203719, _1203719, _1203721, 23424 ^ [_1203719, _1203721, _1203723, _1203725, _1203727], 23425 ^ [_1203719, _1203721, _1203723, _1203725, _1203727]), _1203727)))], (23427 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1203719), _1203723), _1203725) = hAPP(hAPP(c_Set_Oinsert(_1203719), 23424 ^ [_1203719, _1203721, _1203723, _1203725, _1203727]), 23425 ^ [_1203719, _1203721, _1203723, _1203725, _1203727]))]]], (26265 ^ _779854) ^ [_1257297, _1257299, _1257301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257297)), 26268 ^ _779854 : [(26269 ^ _779854) ^ [_1257431] : [26271 ^ _779854 : [(26277 ^ _779854) ^ [] : [-(_1257431 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26273 ^ [_1257297, _1257299, _1257301, _1257431]), 26270 ^ [_1257297, _1257299, _1257301, _1257431]))], (26275 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26273 ^ [_1257297, _1257299, _1257301, _1257431]), _1257299)))], (26272 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26270 ^ [_1257297, _1257299, _1257301, _1257431]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1257297))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257301), _1257431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257301), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1257431), _1257297))))]]], (51521 ^ _779854) ^ [_1823047, _1823049] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1823047), 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)))), _1823049)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823049), _1823047)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823047), _1823049)))], (36675 ^ _779854) ^ [_1465747, _1465749, _1465751, _1465753, _1465755, _1465757] : [c_Finite__Set_Ofolding__idem(_1465747, _1465749, _1465751, _1465753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465747), _1465755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465747, tc_HOL_Obool)), _1465757), _1465755)), -(hAPP(c_Fun_Ocomp(_1465749, _1465749, _1465749, hAPP(_1465753, _1465755)), hAPP(_1465753, _1465757)) = hAPP(_1465753, _1465755))], (49194 ^ _779854) ^ [_1771560] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1771560) = c_Lazy__Sequence_Osmall__lazy_H(_1771560, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1771560)))], (45609 ^ _779854) ^ [_1693602, _1693604] : [-(c_Code__Numeral_Onat__of__aux(_1693602, _1693604) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693602)), _1693604))], (37083 ^ _779854) ^ [_1476077, _1476079, _1476081, _1476083, _1476085] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476081, _1476077)), hAPP(hAPP(c_Product__Type_OPair(_1476081, _1476077), _1476085), _1476079)), _1476083)), -(hBOOL(hAPP(hAPP(c_member(_1476077), _1476079), hAPP(c_Relation_OImage(_1476081, _1476077, _1476083), hAPP(hAPP(c_Set_Oinsert(_1476081), _1476085), c_Orderings_Obot__class_Obot(tc_fun(_1476081, tc_HOL_Obool)))))))], (36518 ^ _779854) ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514] : [class_Groups_Ocomm__monoid__add(_1461504), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461506), _1461508)), 36528 ^ _779854 : [(36529 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461506), 36527 ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514]), _1461508)))], (36534 ^ _779854) ^ [] : [36527 ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514] = 36530 ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514]], (36538 ^ _779854) ^ [] : [hAPP(_1461512, hAPP(_1461510, 36527 ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514])) = c_Groups_Ozero__class_Ozero(_1461504)], (36536 ^ _779854) ^ [] : [-(hAPP(_1461510, 36527 ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514]) = hAPP(_1461510, 36530 ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514]))], (36532 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461506), 36530 ^ [_1461504, _1461506, _1461508, _1461510, _1461512, _1461514]), _1461508)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461514, _1461504), _1461512), hAPP(c_Set_Oimage(_1461506, _1461514, _1461510), _1461508)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461506, _1461504), hAPP(c_Fun_Ocomp(_1461514, _1461504, _1461506, _1461512), _1461510)), _1461508))], (31462 ^ _779854) ^ [_1346983, _1346985] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1346983))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1346983), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1346985)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40758 ^ _779854) ^ [_1574681, _1574683, _1574685, _1574687] : [class_Complete__Lattice_Ocomplete__lattice(_1574681), _1574683 = c_Inductive_Ocomplete__lattice__class_Olfp(_1574681, _1574685), c_Orderings_Oorder__class_Omono(_1574681, _1574681, _1574685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574681), hAPP(_1574685, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1574681), _1574683), _1574687))), _1574687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574681), _1574683), _1574687)))], (29683 ^ _779854) ^ [_1315286] : [class_Int_Onumber__ring(_1315286), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1315286), c_Groups_Oone__class_Oone(_1315286)), c_Groups_Oone__class_Oone(_1315286)) = hAPP(c_Int_Onumber__class_Onumber__of(_1315286), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (44510 ^ _779854) ^ [_1670226, _1670228, _1670230] : [-(hAPP(c_List_Otl(_1670226), hAPP(hAPP(c_List_Olist_OCons(_1670226), _1670228), _1670230)) = _1670230)], (17012 ^ _779854) ^ [_1086820, _1086822, _1086824] : [class_Orderings_Olinorder(_1086820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086820), _1086822)), -(c_Big__Operators_Olinorder__class_OMin(_1086820, hAPP(hAPP(c_Set_Oinsert(_1086820), _1086824), _1086822)) = hAPP(hAPP(c_Finite__Set_Ofold(_1086820, _1086820, c_Orderings_Oord__class_Omin(_1086820)), _1086824), _1086822))], (46068 ^ _779854) ^ [_1704356, _1704358, _1704360, _1704362, _1704364] : [46070 ^ _779854 : [(46073 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1704356, _1704358, tc_HOL_Obool), _1704364), 46069 ^ [_1704356, _1704358, _1704360, _1704362, _1704364]))], (46071 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1704356, _1704358)), 46069 ^ [_1704356, _1704358, _1704360, _1704362, _1704364]), hAPP(c_List_Oset(tc_prod(_1704356, _1704358)), hAPP(hAPP(c_List_Ozip(_1704356, _1704358), _1704360), _1704362)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704356)), _1704360) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704358)), _1704362), -(c_List_Olist__all2(_1704356, _1704358, _1704364, _1704360, _1704362))], (43360 ^ _779854) ^ [_1644511, _1644513] : [-(_1644511 = c_List_Olist_ONil(_1644513)), hBOOL(hAPP(c_List_Odistinct(_1644513), _1644511)), -(hBOOL(hAPP(c_List_Odistinct(_1644513), c_List_Obutlast(_1644513, _1644511))))], (42972 ^ _779854) ^ [_1635751, _1635753] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1635751, _1635753) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1635751, _1635753)))], (35286 ^ _779854) ^ [_1437259, _1437261, _1437263, _1437265, _1437267, _1437269, _1437271, _1437273] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1437259, _1437261, _1437263), _1437265), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1437267, _1437269, tc_prod(_1437259, _1437261)), _1437271), _1437273)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1437267, _1437269, _1437263), hAPP(hAPP(c_COMBB(tc_fun(_1437269, tc_prod(_1437259, _1437261)), tc_fun(_1437269, _1437263), _1437267), hAPP(c_COMBB(tc_prod(_1437259, _1437261), _1437263, _1437269), hAPP(c_Product__Type_Oprod_Oprod__case(_1437259, _1437261, _1437263), _1437265))), _1437271)), _1437273))], (31922 ^ _779854) ^ [_1354224, _1354226] : [class_Rings_Olinordered__idom(_1354224), 31925 ^ _779854 : [(31932 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354224), c_Groups_Ozero__class_Ozero(_1354224)), hAPP(c_Int_Oring__1__class_Oof__int(_1354224), _1354226))))], (31926 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354224), c_Groups_Ozero__class_Ozero(_1354224)), hAPP(c_Int_Oring__1__class_Oof__int(_1354224), _1354226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354226)))]]], (33571 ^ _779854) ^ [_1395479, _1395481, _1395483, _1395485, _1395487] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395479, tc_HOL_Obool)), _1395481), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395483, tc_fun(_1395479, tc_HOL_Obool)), _1395485), _1395487)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395483, tc_fun(_1395479, tc_HOL_Obool)), _1395485), hAPP(hAPP(c_COMBB(tc_fun(_1395479, tc_HOL_Obool), tc_fun(_1395479, tc_HOL_Obool), _1395483), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395479, tc_HOL_Obool)), _1395481)), _1395487)))], (49388 ^ _779854) ^ [_1776304, _1776306, _1776308, _1776310, _1776312, _1776314, _1776316] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1776304, tc_fun(_1776306, tc_fun(_1776308, tc_HOL_Obool))), _1776310), _1776312), _1776314), _1776316)), 49392 ^ _779854 : [(49395 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1776312, 49391 ^ [_1776304, _1776306, _1776308, _1776310, _1776312, _1776314, _1776316]), _1776314), _1776316)))], (49393 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776304), 49391 ^ [_1776304, _1776306, _1776308, _1776310, _1776312, _1776314, _1776316]), _1776310)))]]], (7105 ^ _779854) ^ [_896608, _896610, _896612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896608, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_896608, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_896608, tc_HOL_Obool), tc_HOL_Obool)), _896610), _896612))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_896608, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_896608, tc_HOL_Obool), _896610)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_896608, tc_HOL_Obool), _896612)))))], (35282 ^ _779854) ^ [_1437133, _1437135, _1437137, _1437139] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1437133, _1437135, _1437137), hAPP(hAPP(c_COMBB(tc_fun(_1437135, tc_prod(_1437133, _1437135)), tc_fun(_1437135, _1437137), _1437133), hAPP(c_COMBB(tc_prod(_1437133, _1437135), _1437137, _1437135), _1437139)), c_Product__Type_OPair(_1437133, _1437135))) = _1437139)], (3292 ^ _779854) ^ [_829159, _829161] : [_829161 = _829159, -(c_Random_Orange(_829161) = c_Random_Orange(_829159))], (1680 ^ _779854) ^ [_803806, _803808] : [-(class_Rings_Oordered__semiring(_803806)), _803808 = _803806, class_Rings_Oordered__semiring(_803808)], (22095 ^ _779854) ^ [_1178809, _1178811, _1178813, _1178815] : [class_Groups_Ocomm__monoid__mult(_1178809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178811), _1178813)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1178811, _1178809), _1178815), _1178813) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1178809, _1178811, c_Groups_Otimes__class_Otimes(_1178809)), _1178815), c_Groups_Oone__class_Oone(_1178809)), _1178813))], (1490 ^ _779854) ^ [_801431, _801433] : [-(class_Lazy__Sequence_Osmall__lazy(_801431)), _801433 = _801431, class_Lazy__Sequence_Osmall__lazy(_801433)], (26697 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5656 ^ _779854) ^ [_866403, _866405, _866407, _866409] : [-(tc_fun(_866409, _866405) = tc_fun(_866407, _866403)), _866409 = _866407, _866405 = _866403], (8312 ^ _779854) ^ [_918910, _918912, _918914] : [class_Orderings_Olinorder(_918910), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918910), _918912), _918914))), 8319 ^ _779854 : [(8326 ^ _779854) ^ [] : [_918914 = _918912, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918910), _918914), _918912))], (8320 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918910), _918914), _918912))), -(_918914 = _918912)]]], (26887 ^ _779854) ^ [_1267642, _1267644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1267642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267642), _1267644)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267642), _1267644) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45194 ^ _779854) ^ [_1684814, _1684816, _1684818, _1684820, _1684822] : [hAPP(hAPP(c_List_Omap(_1684814, _1684816), _1684818), _1684820) = hAPP(hAPP(c_List_Omap(_1684814, _1684816), _1684818), _1684822), c_Fun_Oinj__on(_1684814, _1684816, _1684818, c_Orderings_Otop__class_Otop(tc_fun(_1684814, tc_HOL_Obool))), -(_1684820 = _1684822)], (40012 ^ _779854) ^ [_1557139, _1557141, _1557143, _1557145] : [40014 ^ _779854 : [(40017 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1557141, hAPP(_1557143, 40013 ^ [_1557139, _1557141, _1557143, _1557145]))), hAPP(_1557141, 40013 ^ [_1557139, _1557141, _1557143, _1557145])))], (40015 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1557139, 40013 ^ [_1557139, _1557141, _1557143, _1557145])))]], -(c_Wellfounded_Owf(_1557145, hAPP(c_Set_OCollect(tc_prod(_1557145, _1557145)), hAPP(c_Product__Type_Oprod_Oprod__case(_1557145, _1557145, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1557145, tc_HOL_Obool), tc_fun(_1557145, tc_HOL_Obool), _1557145), hAPP(c_COMBS(_1557145, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1557145), c_fconj), _1557139))), hAPP(hAPP(c_COMBC(_1557145, tc_fun(_1557145, _1557145), tc_fun(_1557145, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1557145, tc_HOL_Obool), tc_fun(tc_fun(_1557145, _1557145), tc_fun(_1557145, tc_HOL_Obool)), _1557145), c_COMBB(_1557145, tc_HOL_Obool, _1557145)), c_fequal)), _1557143))))))], (13365 ^ _779854) ^ [_1015301, _1015303] : [class_Complete__Lattice_Ocomplete__lattice(_1015301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015301), _1015303)), -(_1015303 = c_Orderings_Obot__class_Obot(tc_fun(_1015301, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1015301, _1015303) = c_Complete__Lattice_OInf__class_OInf(_1015301, _1015303))], (8258 ^ _779854) ^ [_918163, _918165, _918167] : [class_Orderings_Oorder(_918163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918163), _918165), _918167)), _918165 = _918167], (23788 ^ _779854) ^ [_1211198, _1211200, _1211202] : [class_Rings_Ocomm__semiring__1(_1211198), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211198), _1211200), hAPP(hAPP(c_Power_Opower__class_Opower(_1211198), _1211200), _1211202)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1211198), _1211200), hAPP(c_Nat_OSuc, _1211202)))], (11065 ^ _779854) ^ [_970232, _970234, _970236] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970232, tc_HOL_Obool)), _970234), _970236) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970232, tc_HOL_Obool)), _970234), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_970232, tc_HOL_Obool)), _970236)))], (24955 ^ _779854) ^ [_1232847, _1232849, _1232851, _1232853, _1232855] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1232847, _1232849, _1232851), _1232853), hAPP(c_Nat_OSuc, _1232855)) = hAPP(hAPP(_1232851, _1232853), hAPP(hAPP(c_Power_Opower_Opower(_1232847, _1232849, _1232851), _1232853), _1232855)))], (6427 ^ _779854) ^ [_882414, _882416, _882418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882414, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882414, tc_HOL_Obool)), _882416)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882414, tc_HOL_Obool)), _882418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882414, tc_HOL_Obool)), _882418), _882416)))], (13565 ^ _779854) ^ [_1018522, _1018524, _1018526] : [class_Lattices_Olattice(_1018522), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018522), _1018524)), -(_1018524 = c_Orderings_Obot__class_Obot(tc_fun(_1018522, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018522), _1018526)), -(_1018526 = c_Orderings_Obot__class_Obot(tc_fun(_1018522, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1018522, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018522, tc_HOL_Obool)), _1018524), _1018526)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1018522), c_Big__Operators_Olattice__class_OInf__fin(_1018522, _1018524)), c_Big__Operators_Olattice__class_OInf__fin(_1018522, _1018526)))], (29073 ^ _779854) ^ [_1304545, _1304547] : [class_Int_Onumber__ring(_1304545), class_Rings_Olinordered__idom(_1304545), 29080 ^ _779854 : [(29087 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1304547), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304545), hAPP(c_Int_Onumber__class_Onumber__of(_1304545), _1304547)), c_Groups_Oone__class_Oone(_1304545))))], (29081 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304545), hAPP(c_Int_Onumber__class_Onumber__of(_1304545), _1304547)), c_Groups_Oone__class_Oone(_1304545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1304547), c_Int_OBit1(c_Int_OPls))))]]], (8862 ^ _779854) ^ [_927270, _927272, _927274, _927276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927270, tc_HOL_Obool)), _927272), _927274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927270, tc_HOL_Obool)), _927272), hAPP(hAPP(c_Set_Oinsert(_927270), _927276), _927274))))], (18189 ^ _779854) ^ [_1108982, _1108984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1108982)), _1108984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108982), _1108984)))], (35668 ^ _779854) ^ [_1444124, _1444126] : [-(_1444124 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1444126, _1444124), c_Divides_Odivmod__int(_1444126, _1444124))))], (48589 ^ _779854) ^ [_1758839, _1758841] : [-(c_FunDef_Ois__measure(_1758839, _1758841))], (50892 ^ _779854) ^ [_1809007, _1809009, _1809011] : [c_Fun_Obij__betw(_1809007, _1809009, _1809011, c_Orderings_Otop__class_Otop(tc_fun(_1809007, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1809009, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1809007, _1809009, _1809011, c_Orderings_Otop__class_Otop(tc_fun(_1809007, tc_HOL_Obool))))], (45615 ^ _779854) ^ [_1693719] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1693719), 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, _1693719)) = _1693719)], (6931 ^ _779854) ^ [_892862, _892864, _892866, _892868] : [class_Lattices_Odistrib__lattice(_892862), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892862), _892864), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892862), _892866), _892868)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892862), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892862), _892864), _892866)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892862), _892864), _892868)))], (42895 ^ _779854) ^ [_1633890, _1633892, _1633894, _1633896] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633890, _1633890)), hAPP(hAPP(c_Product__Type_OPair(_1633890, _1633890), _1633892), _1633894)), hAPP(c_List_Oset(tc_prod(_1633890, _1633890)), hAPP(hAPP(c_List_Ozip(_1633890, _1633890), _1633896), _1633896)))), 42898 ^ _779854 : [(42901 ^ _779854) ^ [] : [-(_1633892 = _1633894)], (42899 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633890), _1633892), hAPP(c_List_Oset(_1633890), _1633896))))]]], (35836 ^ _779854) ^ [_1447188, _1447190] : [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), _1447188), _1447190))), 35839 ^ _779854 : [(35846 ^ _779854) ^ [] : [-(_1447190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1447188, _1447190) = c_Nitpick_Onat__gcd(_1447190, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1447188, _1447190)))], (35840 ^ _779854) ^ [] : [_1447190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1447188, _1447190) = _1447188)]]], (33723 ^ _779854) ^ [_1400051, _1400053, _1400055] : [class_Groups_Ocomm__monoid__mult(_1400051), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400053, _1400051), hAPP(c_COMBK(_1400051, _1400053), c_Groups_Oone__class_Oone(_1400051))), _1400055) = c_Groups_Oone__class_Oone(_1400051))], (30263 ^ _779854) ^ [_1326161, _1326163, _1326165] : [class_Divides_Osemiring__div(_1326161), -(c_Divides_Odiv__class_Omod(_1326161, c_Divides_Odiv__class_Omod(_1326161, _1326163, _1326165), _1326165) = c_Divides_Odiv__class_Omod(_1326161, _1326163, _1326165))], (6745 ^ _779854) ^ [_888312, _888314, _888316, _888318] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888312, tc_HOL_Obool)), _888314), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888312, tc_HOL_Obool)), _888316), _888318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888312, tc_HOL_Obool)), _888316), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888312, tc_HOL_Obool)), _888314), _888318)))], (36124 ^ _779854) ^ [_1453526, _1453528, _1453530, _1453532, _1453534, _1453536] : [c_Finite__Set_Ofolding(_1453526, _1453528, _1453530, _1453532), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453526), _1453534)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453526), _1453536)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453526, tc_HOL_Obool)), _1453534), _1453536) = c_Orderings_Obot__class_Obot(tc_fun(_1453526, tc_HOL_Obool)), -(hAPP(_1453532, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1453526, tc_HOL_Obool)), _1453534), _1453536)) = hAPP(c_Fun_Ocomp(_1453528, _1453528, _1453528, hAPP(_1453532, _1453534)), hAPP(_1453532, _1453536)))], (35010 ^ _779854) ^ [_1430960, _1430962] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1430960), hAPP(c_Nat_OSuc, _1430962)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1430962), 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)), _1430962)), _1430960))], (41076 ^ _779854) ^ [_1583794, _1583796] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583794, _1583794), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1583794, _1583796)), c_Relation_OId(_1583794)) = c_Transitive__Closure_Ortrancl(_1583794, _1583796))], (32864 ^ _779854) ^ [_1372110, _1372112, _1372114] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372110, tc_Nat_Onat), _1372112), _1372114) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372110, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1372110), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1372112)), _1372114)))], (35742 ^ _779854) ^ [_1445357, _1445359, _1445361, _1445363] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445357, _1445359), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445361), _1445363))), -(_1445359 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1445357), _1445359) = _1445361)], (20598 ^ _779854) ^ [_1150354, _1150356, _1150358] : [class_Groups_Oordered__comm__monoid__add(_1150354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150354), c_Groups_Ozero__class_Ozero(_1150354)), _1150356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150354), c_Groups_Ozero__class_Ozero(_1150354)), _1150358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150354), c_Groups_Ozero__class_Ozero(_1150354)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150354), _1150356), _1150358))))], (8100 ^ _779854) ^ [_915648, _915650] : [class_Orderings_Olinorder(_915648), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915648, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_915648), _915650)), hAPP(hAPP(c_Set_Oinsert(_915648), _915650), c_Orderings_Obot__class_Obot(tc_fun(_915648, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_915648), _915650))], (37055 ^ _779854) ^ [_1475300, _1475302, _1475304, _1475306, _1475308] : [-(hBOOL(hAPP(hAPP(c_member(_1475300), _1475302), hAPP(c_Relation_OImage(_1475304, _1475300, _1475306), _1475308)))), 37056 ^ _779854 : [(37057 ^ _779854) ^ [_1475386] : [hBOOL(hAPP(hAPP(c_member(_1475304), _1475386), _1475308)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475304, _1475300)), hAPP(hAPP(c_Product__Type_OPair(_1475304, _1475300), _1475386), _1475302)), _1475306))]]], (33681 ^ _779854) ^ [_1398951, _1398953, _1398955, _1398957, _1398959] : [class_Fields_Ofield__inverse__zero(_1398951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398953), _1398955)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398953, _1398951), hAPP(hAPP(c_COMBS(_1398953, _1398951, _1398951), hAPP(hAPP(c_COMBB(_1398951, tc_fun(_1398951, _1398951), _1398953), c_Rings_Oinverse__class_Odivide(_1398951)), _1398957)), _1398959)), _1398955) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1398951), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398953, _1398951), _1398957), _1398955)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398953, _1398951), _1398959), _1398955)))], (9742 ^ _779854) ^ [_943231, _943233, _943235, _943237] : [class_Orderings_Olinorder(_943231), 9745 ^ _779854 : [(9754 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943231), hAPP(hAPP(c_Orderings_Oord__class_Omax(_943231), _943233), _943235)), _943237))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943231), _943233), _943237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943231), _943235), _943237))], (9746 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943231), hAPP(hAPP(c_Orderings_Oord__class_Omax(_943231), _943233), _943235)), _943237)), 9749 ^ _779854 : [(9752 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943231), _943235), _943237)))], (9750 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943231), _943233), _943237)))]]]]], (38763 ^ _779854) ^ [_1519221, _1519223, _1519225] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1519221), hAPP(c_Set_OCollect(_1519221), hAPP(hAPP(c_COMBS(_1519221, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519221), c_fdisj), _1519223)), _1519225))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519221), hAPP(c_Set_OCollect(_1519221), _1519223))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519221), hAPP(c_Set_OCollect(_1519221), _1519225)))], (18841 ^ _779854) ^ [_1119998] : [_1119998 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119998), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17698 ^ _779854) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (35086 ^ _779854) ^ [_1432505, _1432507] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1432505, _1432507) = 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), _1432505), _1432507)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1432505, _1432507)))], (8986 ^ _779854) ^ [_929672, _929674, _929676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929672, tc_HOL_Obool)), _929674), _929676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929672, tc_HOL_Obool)), _929674), _929676)))], (46518 ^ _779854) ^ [_1714633, _1714635, _1714637, _1714639] : [hBOOL(hAPP(hAPP(c_member(_1714633), _1714635), hAPP(c_List_Oset(_1714633), _1714637))), -(hBOOL(hAPP(_1714639, _1714635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714633)), hAPP(c_List_Ofilter(_1714633, _1714639), _1714637))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714633)), _1714637))))], (10169 ^ _779854) ^ [_951631, _951633, _951635] : [class_Orderings_Olinorder(_951631), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951631), hAPP(hAPP(c_Orderings_Oord__class_Omin(_951631), _951633), _951635)), _951633)))], (7914 ^ _779854) ^ [_912275, _912277, _912279] : [class_Lattices_Oboolean__algebra(_912275), 7917 ^ _779854 : [(7924 ^ _779854) ^ [] : [_912277 = _912279, -(hAPP(c_Groups_Ouminus__class_Ouminus(_912275), _912277) = hAPP(c_Groups_Ouminus__class_Ouminus(_912275), _912279))], (7918 ^ _779854) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_912275), _912277) = hAPP(c_Groups_Ouminus__class_Ouminus(_912275), _912279), -(_912277 = _912279)]]], (7772 ^ _779854) ^ [_909298, _909300, _909302, _909304] : [class_Orderings_Olinorder(_909298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909298), _909300), _909302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909298), _909302), _909304)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909298, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_909298, _909300), _909302)), c_SetInterval_Oord__class_OatLeastAtMost(_909298, _909302, _909304)) = c_SetInterval_Oord__class_OatLeastAtMost(_909298, _909300, _909304))], (26699 ^ _779854) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46128 ^ _779854) ^ [_1705702, _1705704] : [hBOOL(hAPP(c_List_Odistinct(_1705702), _1705704)), -(c_List_Oremdups(_1705702, _1705704) = _1705704)], (49675 ^ _779854) ^ [_1782863, _1782865] : [c_Relation_Otrans(_1782863, _1782865), -(c_Relation_Otrans(_1782863, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1782863, _1782863), tc_HOL_Obool)), _1782865), c_Relation_OId(_1782863))))], (38885 ^ _779854) ^ [_1521925, _1521927] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1521925, tc_HOL_Obool)), _1521927) = hAPP(c_Set_OCollect(_1521925), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1521925), c_fNot), hAPP(hAPP(c_COMBC(_1521925, tc_fun(_1521925, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521925)), _1521927))))], (26467 ^ _779854) ^ [_1260731] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1260731)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1260731)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1260731)))], (15594 ^ _779854) ^ [_1058642, _1058644, _1058646] : [class_Lattices_Oab__semigroup__idem__mult(_1058642), -(_1058644 = c_Orderings_Obot__class_Obot(tc_fun(_1058642, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058642), _1058644)), -(hAPP(c_Finite__Set_Ofold1(_1058642, c_Groups_Otimes__class_Otimes(_1058642)), hAPP(hAPP(c_Set_Oinsert(_1058642), _1058646), _1058644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058642), _1058646), hAPP(c_Finite__Set_Ofold1(_1058642, c_Groups_Otimes__class_Otimes(_1058642)), _1058644)))], (39951 ^ _779854) ^ [_1556032, _1556034] : [c_Wellfounded_Owf(_1556032, _1556034), -(c_Wellfounded_Owf(tc_List_Olist(_1556032), c_List_Olenlex(_1556032, _1556034)))], (262 ^ _779854) ^ [_783963, _783965] : [-(class_Fields_Olinordered__field(_783963)), _783965 = _783963, class_Fields_Olinordered__field(_783965)], (38636 ^ _779854) ^ [_1515687, _1515689, _1515691, _1515693, _1515695, _1515697, _1515699, _1515701] : [-(hAPP(c_Product__Type_Omap__pair(_1515687, _1515689, _1515691, _1515693, _1515695, _1515697), hAPP(hAPP(c_Product__Type_OPair(_1515687, _1515691), _1515699), _1515701)) = hAPP(hAPP(c_Product__Type_OPair(_1515689, _1515693), hAPP(_1515695, _1515699)), hAPP(_1515697, _1515701)))], (32688 ^ _779854) ^ [_1368269] : [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), _1368269))), 32691 ^ _779854 : [(32698 ^ _779854) ^ [] : [-(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), _1368269))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1368269)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1368269)), 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), _1368269)))))], (32692 ^ _779854) ^ [] : [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), _1368269)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1368269)) = 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), _1368269))))]]], (10939 ^ _779854) ^ [_967239, _967241, _967243] : [-(hAPP(hAPP(c_Set_Oinsert(_967239), _967241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967239, tc_HOL_Obool)), _967243), hAPP(hAPP(c_Set_Oinsert(_967239), _967241), c_Orderings_Obot__class_Obot(tc_fun(_967239, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_967239), _967241), _967243))], (7752 ^ _779854) ^ [_908906, _908908, _908910, _908912] : [class_Orderings_Olinorder(_908906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908906), _908908), _908910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908906), _908910), _908912)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908906, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_908906, _908908, _908910)), c_SetInterval_Oord__class_OgreaterThanAtMost(_908906, _908910, _908912)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_908906, _908908, _908912))], (4188 ^ _779854) ^ [_843497, _843499, _843501, _843503, _843505, _843507] : [-(c_Predicate_Oconversep(_843507, _843503, _843499) = c_Predicate_Oconversep(_843505, _843501, _843497)), _843507 = _843505, _843503 = _843501, _843499 = _843497], (16646 ^ _779854) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (22275 ^ _779854) ^ [_1182472, _1182474, _1182476] : [class_Fields_Olinordered__field__inverse__zero(_1182472), 22278 ^ _779854 : [(22293 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182472), _1182474), _1182476)), c_Groups_Ozero__class_Ozero(_1182472)))), 22294 ^ _779854 : [(22301 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), _1182474), c_Groups_Ozero__class_Ozero(_1182472))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), c_Groups_Ozero__class_Ozero(_1182472)), _1182476))], (22295 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), c_Groups_Ozero__class_Ozero(_1182472)), _1182474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), _1182476), c_Groups_Ozero__class_Ozero(_1182472)))]]], (22279 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182472), _1182474), _1182476)), c_Groups_Ozero__class_Ozero(_1182472))), 22284 ^ _779854 : [(22287 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), _1182476), c_Groups_Ozero__class_Ozero(_1182472))))], (22285 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), c_Groups_Ozero__class_Ozero(_1182472)), _1182474)))]], 22288 ^ _779854 : [(22291 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), c_Groups_Ozero__class_Ozero(_1182472)), _1182476)))], (22289 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182472), _1182474), c_Groups_Ozero__class_Ozero(_1182472))))]]]]], (52625 ^ _779854) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (38827 ^ _779854) ^ [_1520637, _1520639, _1520641, _1520643] : [-(hBOOL(hAPP(hAPP(c_member(_1520637), _1520639), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520637, tc_HOL_Obool)), _1520641), hAPP(c_Set_OCollect(_1520637), _1520643))))), hBOOL(hAPP(hAPP(c_member(_1520637), _1520639), _1520641)), hBOOL(hAPP(_1520643, _1520639))], (41786 ^ _779854) ^ [_1600960, _1600962, _1600964] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600960, _1600960), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1600962)), _1600964) = hAPP(hAPP(c_Relation_Orel__comp(_1600960, _1600960, _1600960), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600960, _1600960), tc_HOL_Obool), _1600962), _1600964)), _1600964))], (4290 ^ _779854) ^ [_844994, _844996, _844998, _845000] : [-(c_List_Omap(_845000, _844996) = c_List_Omap(_844998, _844994)), _845000 = _844998, _844996 = _844994], (34885 ^ _779854) ^ [_1428043, _1428045, _1428047, _1428049, _1428051, _1428053] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428043, tc_fun(_1428045, tc_HOL_Obool))), _1428047), _1428049), _1428051), _1428053)), 34888 ^ _779854 : [(34891 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1428049, _1428051), _1428053)))], (34889 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1428047, _1428051), _1428053)))]]], (29635 ^ _779854) ^ [_1314393, _1314395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1314393)), c_Int_OBit1(_1314395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1314393), _1314395)))], (38114 ^ _779854) ^ [_1501172, _1501174, _1501176, _1501178, _1501180] : [hBOOL(hAPP(hAPP(c_member(_1501176), hAPP(_1501178, _1501174)), _1501180)), -(hBOOL(hAPP(hAPP(c_member(_1501172), _1501174), hAPP(c_Set_Ovimage(_1501172, _1501176, _1501178), _1501180))))], (45057 ^ _779854) ^ [_1680968, _1680970] : [-(_1680968 = c_List_Olist_ONil(_1680970)), -(c_Random_Oselect__weight(_1680970, hAPP(hAPP(c_List_Omap(_1680970, tc_prod(tc_Code__Numeral_Ocode__numeral, _1680970)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1680970), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1680968)) = c_Random_Oselect(_1680970, _1680968))], (2828 ^ _779854) ^ [_821933, _821935, _821937, _821939, _821941, _821943, _821945, _821947] : [-(c_Random_Oiterate(_821947, _821943, _821939, _821935) = c_Random_Oiterate(_821945, _821941, _821937, _821933)), _821947 = _821945, _821943 = _821941, _821939 = _821937, _821935 = _821933], (8730 ^ _779854) ^ [_925045, _925047, _925049] : [class_Orderings_Opreorder(_925045), 8733 ^ _779854 : [(8742 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925045), _925047), _925049))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925045), _925047), _925049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925045), _925049), _925047)))], (8734 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925045), _925047), _925049)), 8737 ^ _779854 : [(8740 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925045), _925049), _925047))], (8738 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925045), _925047), _925049)))]]]]], (49247 ^ _779854) ^ [_1773007, _1773009] : [hBOOL(hAPP(hAPP(c_List_Omember(_1773007), c_List_Olist_ONil(_1773007)), _1773009))], (16179 ^ _779854) ^ [_1070366, _1070368, _1070370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070366), _1070368)), _1070370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070368), _1070370)))], (40617 ^ _779854) ^ [_1571615, _1571617, _1571619, _1571621] : [c_Orderings_Oorder__class_Omono(tc_fun(_1571615, tc_HOL_Obool), tc_fun(_1571615, tc_HOL_Obool), _1571617), hBOOL(hAPP(hAPP(c_member(_1571615), _1571619), _1571621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571615, tc_HOL_Obool)), _1571621), hAPP(_1571617, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571615, tc_HOL_Obool)), _1571621), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1571615, tc_HOL_Obool), _1571617))))), -(hBOOL(hAPP(hAPP(c_member(_1571615), _1571619), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1571615, tc_HOL_Obool), _1571617))))], (7057 ^ _779854) ^ [_895501, _895503] : [class_Lattices_Osemilattice__sup(_895501), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895501), _895503), _895503) = _895503)], (33623 ^ _779854) ^ [_1397442, _1397444, _1397446, _1397448, _1397450] : [-(_1397442 = c_Orderings_Obot__class_Obot(tc_fun(_1397444, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397446, tc_HOL_Obool)), _1397448), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397444, tc_fun(_1397446, tc_HOL_Obool)), _1397442), _1397450)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397444, tc_fun(_1397446, tc_HOL_Obool)), _1397442), hAPP(hAPP(c_COMBB(tc_fun(_1397446, tc_HOL_Obool), tc_fun(_1397446, tc_HOL_Obool), _1397444), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397446, tc_HOL_Obool)), _1397448)), _1397450)))], (21038 ^ _779854) ^ [_1158420, _1158422, _1158424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158420)), 21041 ^ _779854 : [(21048 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158422), _1158424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158420), _1158422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158420), _1158424))))], (21042 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158420), _1158422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158420), _1158424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158422), _1158424)))]]], (3666 ^ _779854) ^ [_835004, _835006, _835008, _835010] : [-(c_List_Otranspose(_835010, _835006) = c_List_Otranspose(_835008, _835004)), _835010 = _835008, _835006 = _835004], (40249 ^ _779854) ^ [_1563633, _1563635] : [-(c_Nitpick_Owf_H(_1563633, _1563635)), c_Wellfounded_Oacyclic(_1563633, _1563635), 40254 ^ _779854 : [(40257 ^ _779854) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (40255 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1563633, _1563633)), _1563635))]]], (37191 ^ _779854) ^ [_1479102, _1479104, _1479106] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1479102, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479102), _1479104), _1479106), -(_1479104 = c_Orderings_Obot__class_Obot(tc_fun(_1479102, tc_HOL_Obool)))], (49481 ^ _779854) ^ [_1778377, _1778379, _1778381, _1778383] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1778377), _1778379), _1778381), _1778383) = 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(_1778377)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1778377), _1778379)))], (8654 ^ _779854) ^ [_923988, _923990, _923992] : [class_Orderings_Oorder(_923988), -(_923990 = _923992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923988), _923990), _923992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923988), _923990), _923992)))], (15954 ^ _779854) ^ [_1066170, _1066172, _1066174] : [class_Rings_Ocomm__semiring__1(_1066170), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066170), _1066172), _1066174) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066170), _1066174), _1066172))], (47139 ^ _779854) ^ [_1727410, _1727412, _1727414, _1727416, _1727418, _1727420] : [class_Orderings_Olinorder(_1727410), c_List_Olinorder__class_Osorted(_1727410, hAPP(hAPP(c_List_Omap(_1727412, _1727410), _1727414), _1727416)), hBOOL(hAPP(_1727418, _1727420)), -(hAPP(c_List_Ofilter(_1727412, _1727418), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727412, _1727410, _1727414), _1727420), _1727416)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727412, _1727410, _1727414), _1727420), hAPP(c_List_Ofilter(_1727412, _1727418), _1727416)))], (29345 ^ _779854) ^ [_1309286] : [c_Int_OPls = _1309286, -(c_Int_OPls = c_Int_OBit0(_1309286))], (25773 ^ _779854) ^ [_1248318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1248318)))], (33814 ^ _779854) ^ [_1402673, _1402675, _1402677, _1402679, _1402681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402673, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402675, tc_fun(_1402673, tc_HOL_Obool)), _1402677), _1402679)), _1402681)), 33817 ^ _779854 : [(33818 ^ _779854) ^ [_1402806] : [hBOOL(hAPP(hAPP(c_member(_1402675), _1402806), _1402677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402673, tc_HOL_Obool)), hAPP(_1402679, _1402806)), _1402681)))]]], (44771 ^ _779854) ^ [_1675839, _1675841, _1675843, _1675845, _1675847, _1675849] : [class_Orderings_Olinorder(_1675839), 44774 ^ _779854 : [(44781 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675839), hAPP(_1675841, _1675843)), hAPP(_1675841, _1675845)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675847, _1675839, _1675841), _1675843), hAPP(hAPP(c_List_Olist_OCons(_1675847), _1675845), _1675849)) = hAPP(hAPP(c_List_Olist_OCons(_1675847), _1675845), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675847, _1675839, _1675841), _1675843), _1675849)))], (44775 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675839), hAPP(_1675841, _1675843)), hAPP(_1675841, _1675845))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675847, _1675839, _1675841), _1675843), hAPP(hAPP(c_List_Olist_OCons(_1675847), _1675845), _1675849)) = hAPP(hAPP(c_List_Olist_OCons(_1675847), _1675843), hAPP(hAPP(c_List_Olist_OCons(_1675847), _1675845), _1675849)))]]], (38723 ^ _779854) ^ [_1518325, _1518327] : [-(hAPP(c_Set_OCollect(_1518325), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1518325), c_fNot), _1518327)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1518325, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1518325), _1518327)))], (41433 ^ _779854) ^ [_1592173, _1592175, _1592177, _1592179] : [-(hAPP(c_Relation_Oconverse(_1592173, _1592173), hAPP(hAPP(c_Relation_Oinv__image(_1592175, _1592173), _1592177), _1592179)) = hAPP(hAPP(c_Relation_Oinv__image(_1592175, _1592173), hAPP(c_Relation_Oconverse(_1592175, _1592175), _1592177)), _1592179))], (19225 ^ _779854) ^ [_1126506, _1126508, _1126510, _1126512, _1126514] : [class_Rings_Oordered__semiring(_1126506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126506), _1126508), _1126510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126506), _1126512), _1126514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126506), c_Groups_Ozero__class_Ozero(_1126506)), _1126508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126506), c_Groups_Ozero__class_Ozero(_1126506)), _1126512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126506), _1126508), _1126512)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126506), _1126510), _1126514))))], (4300 ^ _779854) ^ [_845143, _845145, _845147, _845149, _845151, _845153] : [-(c_List_Oreplicate(_845153, _845149, _845145) = c_List_Oreplicate(_845151, _845147, _845143)), _845153 = _845151, _845149 = _845147, _845145 = _845143], (36902 ^ _779854) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (17376 ^ _779854) ^ [_1093914, _1093916, _1093918, _1093920] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093914), _1093916)), 17379 ^ _779854 : [(17386 ^ _779854) ^ [] : [hAPP(c_Finite__Set_Ocard(_1093918), hAPP(c_Set_Oimage(_1093914, _1093918, _1093920), _1093916)) = hAPP(c_Finite__Set_Ocard(_1093914), _1093916), -(c_Fun_Oinj__on(_1093914, _1093918, _1093920, _1093916))], (17380 ^ _779854) ^ [] : [c_Fun_Oinj__on(_1093914, _1093918, _1093920, _1093916), -(hAPP(c_Finite__Set_Ocard(_1093918), hAPP(c_Set_Oimage(_1093914, _1093918, _1093920), _1093916)) = hAPP(c_Finite__Set_Ocard(_1093914), _1093916))]]], (5150 ^ _779854) ^ [_858606, _858608, _858610, _858612] : [-(c_Transitive__Closure_Otrancl(_858612, _858608) = c_Transitive__Closure_Otrancl(_858610, _858606)), _858612 = _858610, _858608 = _858606], (4428 ^ _779854) ^ [_847249, _847251, _847253, _847255] : [-(c_Lazy__Sequence_Osmall__lazy_H(_847255, _847251) = c_Lazy__Sequence_Osmall__lazy_H(_847253, _847249)), _847255 = _847253, _847251 = _847249], (35875 ^ _779854) ^ [_1448017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1448017)), 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), _1448017)) = 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), _1448017))))))], (48439 ^ _779854) ^ [_1755933, _1755935] : [c_List_Olist__ex(_1755933, _1755935, c_List_Olist_ONil(_1755933))], (29511 ^ _779854) ^ [_1312150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1312150)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1312150))))], (23203 ^ _779854) ^ [_1199353, _1199355, _1199357, _1199359] : [class_Fields_Olinordered__field(_1199353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199353), c_Groups_Ozero__class_Ozero(_1199353)), _1199355)), 23210 ^ _779854 : [(23217 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199353), _1199357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1199353), _1199359), _1199355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199353), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1199353), _1199357), _1199355)), _1199359)))], (23211 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199353), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1199353), _1199357), _1199355)), _1199359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199353), _1199357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1199353), _1199359), _1199355))))]]], (23025 ^ _779854) ^ [_1196033, _1196035, _1196037, _1196039] : [class_Fields_Ofield(_1196033), -(_1196035 = c_Groups_Ozero__class_Ozero(_1196033)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1196033), _1196037), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196033), _1196039), _1196035)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1196033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196033), _1196035), _1196037)), _1196039)), _1196035))], (30631 ^ _779854) ^ [_1332776, _1332778] : [c_Nat__Transfer_Onat__set(_1332776), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1332778), _1332776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332778)))], (41751 ^ _779854) ^ [_1600073, _1600075, _1600077, _1600079] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1600073, _1600075), tc_fun(_1600073, _1600075)), _1600077), c_Fun_Ocomp(_1600075, _1600075, _1600073, _1600079)) = c_Fun_Ocomp(_1600075, _1600075, _1600073, hAPP(hAPP(c_Nat_Ocompow(_1600075, _1600075), _1600077), _1600079)))], (24523 ^ _779854) ^ [_1224740, _1224742, _1224744] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1224740), _1224742)), _1224744) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224740), _1224744)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224742), _1224744)))], (43221 ^ _779854) ^ [_1641324, _1641326] : [hBOOL(hAPP(c_List_Odistinct(_1641324), _1641326)), -(hAPP(c_Finite__Set_Ocard(_1641324), hAPP(c_List_Oset(_1641324), _1641326)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641324)), _1641326))], (35929 ^ _779854) ^ [_1449267, _1449269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449269)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1449267, _1449269) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1449267, _1449269)))], (4274 ^ _779854) ^ [_844760, _844762, _844764, _844766] : [-(c_List_Oconcat(_844766, _844762) = c_List_Oconcat(_844764, _844760)), _844766 = _844764, _844762 = _844760], (52275 ^ _779854) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (24653 ^ _779854) ^ [_1227225, _1227227, _1227229] : [class_Int_Onumber__ring(_1227225), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227225), hAPP(c_Int_Onumber__class_Onumber__of(_1227225), _1227227)), hAPP(c_Int_Onumber__class_Onumber__of(_1227225), _1227229)) = hAPP(c_Int_Onumber__class_Onumber__of(_1227225), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1227227), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1227229))))], (3862 ^ _779854) ^ [_838046, _838048] : [_838048 = _838046, -(c_Enum_Oenum__class_Oenum__all(_838048) = c_Enum_Oenum__class_Oenum__all(_838046))], (35131 ^ _779854) ^ [_1433664, _1433666, _1433668, _1433670, _1433672, _1433674, _1433676] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1433664, _1433666)), hAPP(hAPP(c_Product__Type_OPair(_1433664, _1433666), _1433668), _1433670)), _1433672)), -(hBOOL(hAPP(hAPP(c_member(_1433674), hAPP(hAPP(_1433676, _1433668), _1433670)), hAPP(c_Set_Oimage(tc_prod(_1433664, _1433666), _1433674, hAPP(c_Product__Type_Oprod_Oprod__case(_1433664, _1433666, _1433674), _1433676)), _1433672))))], (33455 ^ _779854) ^ [_1389174, _1389176, _1389178, _1389180] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389174, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1389174, tc_fun(_1389174, tc_HOL_Obool), tc_HOL_Obool), c_member(_1389174)), _1389176)), hAPP(hAPP(c_COMBC(_1389174, tc_fun(_1389174, tc_HOL_Obool), tc_HOL_Obool), c_member(_1389174)), _1389178)), _1389180)), -(hBOOL(hAPP(hAPP(c_member(_1389174), _1389180), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389174, tc_HOL_Obool)), _1389176), _1389178))))], (51375 ^ _779854) ^ [_1820361, _1820363] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820361), _1820363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1820363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1820361), _1820363)))], (6747 ^ _779854) ^ [_888385, _888387, _888389, _888391] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888385, tc_HOL_Obool)), _888387), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888385, tc_HOL_Obool)), _888389), _888391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888385, tc_HOL_Obool)), _888389), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888385, tc_HOL_Obool)), _888387), _888391)))], (32461 ^ _779854) ^ [_1364000, _1364002] : [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), _1364000)), _1364002))), _1364000 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1364002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6985 ^ _779854) ^ [_894129, _894131, _894133] : [class_Lattices_Osemilattice__sup(_894129), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894129), _894131), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894129), _894131), _894133)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894129), _894131), _894133))], (28511 ^ _779854) ^ [_1295314, _1295316] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295314)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295314), _1295316)))], (49667 ^ _779854) ^ [_1782712] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1782712, tc_HOL_Obool) = c_Set_OBex(_1782712))], (29727 ^ _779854) ^ [] : [-(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))))))], (45661 ^ _779854) ^ [_1695053, _1695055, _1695057] : [-(c_List_Olistsp(_1695053, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1695053, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1695053, tc_fun(_1695053, tc_HOL_Obool), tc_HOL_Obool), c_member(_1695053)), _1695055)), hAPP(hAPP(c_COMBC(_1695053, tc_fun(_1695053, tc_HOL_Obool), tc_HOL_Obool), c_member(_1695053)), _1695057))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1695053), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695053), tc_fun(tc_List_Olist(_1695053), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1695053))), c_List_Olists(_1695053, _1695055))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695053), tc_fun(tc_List_Olist(_1695053), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1695053))), c_List_Olists(_1695053, _1695057))))], (45917 ^ _779854) ^ [_1700923, _1700925, _1700927, _1700929] : [_1700929 = c_List_Olist_ONil(_1700923), -(c_List_Olist__all2(_1700923, _1700925, _1700927, _1700929, c_List_Olist_ONil(_1700925)))], (7608 ^ _779854) ^ [_905810, _905812, _905814] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905810, tc_HOL_Obool)), _905812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905810, tc_HOL_Obool)), _905814), _905812))))], (48646 ^ _779854) ^ [_1759888, _1759890, _1759892, _1759894] : [-(c_List_Olist__all(_1759888, _1759890, hAPP(hAPP(c_List_Olist_OCons(_1759888), _1759892), _1759894))), hBOOL(hAPP(_1759890, _1759892)), c_List_Olist__all(_1759888, _1759890, _1759894)], (18703 ^ _779854) ^ [_1118052, _1118054] : [class_Groups_Ogroup__add(_1118052), 18706 ^ _779854 : [(18713 ^ _779854) ^ [] : [c_Groups_Ozero__class_Ozero(_1118052) = _1118054, -(c_Groups_Ozero__class_Ozero(_1118052) = hAPP(c_Groups_Ouminus__class_Ouminus(_1118052), _1118054))], (18707 ^ _779854) ^ [] : [c_Groups_Ozero__class_Ozero(_1118052) = hAPP(c_Groups_Ouminus__class_Ouminus(_1118052), _1118054), -(c_Groups_Ozero__class_Ozero(_1118052) = _1118054)]]], (28822 ^ _779854) ^ [_1300483] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1300483)) = 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), _1300483)))], (38532 ^ _779854) ^ [_1512915, _1512917, _1512919, _1512921] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512915), _1512917)), 38538 ^ _779854 : [(38541 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512919), hAPP(_1512921, 38537 ^ [_1512915, _1512917, _1512919, _1512921])))], (38539 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512915), 38537 ^ [_1512915, _1512917, _1512919, _1512921]), _1512917)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1512915, _1512919)), hAPP(hAPP(c_Product__Type_OSigma(_1512915, _1512919), _1512917), _1512921))))], (37576 ^ _779854) ^ [_1488497, _1488499, _1488501, _1488503] : [c_Equiv__Relations_Oequivp(_1488497, _1488499), hBOOL(hAPP(hAPP(_1488499, _1488501), _1488503)), -(hBOOL(hAPP(hAPP(_1488499, _1488503), _1488501)))], (51272 ^ _779854) ^ [_1818502, _1818504, _1818506] : [-(c_Lazy__Sequence_Oflat(_1818502, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1818502), _1818504, _1818506)) = c_Lazy__Sequence_Oappend(_1818502, _1818504, c_Lazy__Sequence_Oflat(_1818502, _1818506)))], (866 ^ _779854) ^ [_792817, _792819, _792821, _792823] : [-(c_Predicate_Otransp(_792821, _792817)), c_Predicate_Otransp(_792823, _792819), _792823 = _792821, _792819 = _792817], (49648 ^ _779854) ^ [_1782382, _1782384] : [49649 ^ _779854 : [(49650 ^ _779854) ^ [_1782448] : [hBOOL(hAPP(_1782384, _1782448))]], 49652 ^ _779854 : [(49655 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1782384, 49651 ^ [_1782382, _1782384])))], (49653 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1782382), 49651 ^ [_1782382, _1782384]), c_Orderings_Otop__class_Otop(tc_fun(_1782382, tc_HOL_Obool)))))]]], (20796 ^ _779854) ^ [_1154125, _1154127, _1154129, _1154131] : [class_Rings_Olinordered__semiring__strict(_1154125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154125), _1154127), _1154129)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154125), _1154127), _1154131))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154125), c_Groups_Ozero__class_Ozero(_1154125)), _1154127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154125), _1154129), _1154131)))], (49112 ^ _779854) ^ [_1769905, _1769907, _1769909] : [-(_1769905 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1769907), c_List_Oreplicate(_1769907, _1769905, _1769909)) = hAPP(hAPP(c_Set_Oinsert(_1769907), _1769909), c_Orderings_Obot__class_Obot(tc_fun(_1769907, tc_HOL_Obool))))], (44717 ^ _779854) ^ [_1674506, _1674508, _1674510] : [class_Orderings_Olinorder(_1674506), -(c_Big__Operators_Olattice_OSup__fin(_1674506, c_Orderings_Oord__class_Omax(_1674506), hAPP(c_List_Oset(_1674506), hAPP(hAPP(c_List_Olist_OCons(_1674506), _1674508), _1674510))) = hAPP(c_List_Ofoldl(_1674506, _1674506, c_Orderings_Oord__class_Omax(_1674506), _1674508), _1674510))], (48154 ^ _779854) ^ [_1749416, _1749418, _1749420, _1749422, _1749424] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749416)), _1749418) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749420)), _1749422), 48160 ^ _779854 : [(48163 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1749424, hAPP(hAPP(c_List_Onth(_1749416), _1749418), 48159 ^ [_1749416, _1749418, _1749420, _1749422, _1749424])), hAPP(hAPP(c_List_Onth(_1749420), _1749422), 48159 ^ [_1749416, _1749418, _1749420, _1749422, _1749424])))], (48161 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48159 ^ [_1749416, _1749418, _1749420, _1749422, _1749424]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749416)), _1749418))))]], -(c_List_Olist__all2(_1749416, _1749420, _1749424, _1749418, _1749422))], (42340 ^ _779854) ^ [_1617565, _1617567, _1617569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1617565, _1617565), tc_HOL_Obool)), _1617567), _1617569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1617565), tc_List_Olist(_1617565)), tc_HOL_Obool)), c_List_Olistrel(_1617565, _1617567)), c_List_Olistrel(_1617565, _1617569))))], (39104 ^ _779854) ^ [_1529394] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1529394) = 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), _1529394), c_Int_Onat)))))], (6181 ^ _779854) ^ [_878025, _878027, _878029] : [class_Orderings_Olinorder(_878025), 6184 ^ _779854 : [(6191 ^ _779854) ^ [] : [_878027 = _878029, -(hAPP(c_SetInterval_Oord__class_OlessThan(_878025), _878027) = hAPP(c_SetInterval_Oord__class_OlessThan(_878025), _878029))], (6185 ^ _779854) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_878025), _878027) = hAPP(c_SetInterval_Oord__class_OlessThan(_878025), _878029), -(_878027 = _878029)]]], (6889 ^ _779854) ^ [_891845, _891847, _891849, _891851] : [class_Lattices_Osemilattice__sup(_891845), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891845), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891845), _891847), _891849)), _891851) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891845), _891847), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891845), _891849), _891851)))], (44751 ^ _779854) ^ [_1675349, _1675351, _1675353] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675349), tc_List_Olist(_1675349))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675349), tc_List_Olist(_1675349)), c_List_Olist_ONil(_1675349)), _1675351)), c_List_Olexord(_1675349, _1675353))), -(_1675351 = hAPP(hAPP(c_List_Olist_OCons(_1675349), 44754 ^ [_1675349, _1675351, _1675353]), 44755 ^ [_1675349, _1675351, _1675353]))], (19817 ^ _779854) ^ [_1137381, _1137383, _1137385] : [class_Groups_Oordered__ab__group__add(_1137381), 19820 ^ _779854 : [(19827 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137381), _1137383), _1137385)), c_Groups_Ozero__class_Ozero(_1137381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137381), _1137383), _1137385)))], (19821 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137381), _1137383), _1137385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137381), _1137383), _1137385)), c_Groups_Ozero__class_Ozero(_1137381))))]]], (47691 ^ _779854) ^ [_1738998] : [c_List_Onat__list(_1738998), -(c_List_Oembed__list(c_List_Oreturn__list(_1738998)) = _1738998)], (3214 ^ _779854) ^ [_827878, _827880, _827882, _827884, _827886, _827888] : [-(c_Big__Operators_Olattice_OSup__fin(_827888, _827884, _827880) = c_Big__Operators_Olattice_OSup__fin(_827886, _827882, _827878)), _827888 = _827886, _827884 = _827882, _827880 = _827878], (23001 ^ _779854) ^ [_1195608, _1195610, _1195612, _1195614] : [class_Fields_Ofield(_1195608), -(_1195610 = c_Groups_Ozero__class_Ozero(_1195608)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195608), _1195612), _1195610)), _1195614) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195608), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195608), _1195612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195608), _1195610), _1195614))), _1195610))], (4320 ^ _779854) ^ [_845449, _845451] : [_845451 = _845449, -(c_If(_845451) = c_If(_845449))], (31055 ^ _779854) ^ [_1340235] : [c_Int_OBit0(_1340235) = c_Int_OMin], (27515 ^ _779854) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24224 ^ _779854) ^ [_1219162, _1219164, _1219166] : [class_Rings_Olinordered__semidom(_1219162), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219162), c_Groups_Oone__class_Oone(_1219162)), _1219164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219162), c_Groups_Oone__class_Oone(_1219162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219162), _1219164), hAPP(hAPP(c_Power_Opower__class_Opower(_1219162), _1219164), _1219166)))))], (37034 ^ _779854) ^ [_1474737, _1474739, _1474741, _1474743, _1474745] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474737, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474739, _1474737, _1474741), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474739, tc_HOL_Obool)), _1474743), _1474745))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474737, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474739, _1474737, _1474741), _1474743)), hAPP(c_Relation_OImage(_1474739, _1474737, _1474741), _1474745)))))], (29351 ^ _779854) ^ [_1309379] : [c_Int_OBit0(_1309379) = c_Int_OPls, -(_1309379 = c_Int_OPls)], (49216 ^ _779854) ^ [_1772044, _1772046] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1772044)), _1772046) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1772044, tc_Lazy__Sequence_Olazy__sequence(_1772044)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1772044, tc_Lazy__Sequence_Olazy__sequence(_1772044), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772044), tc_Nat_Onat), _1772044), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1772044), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1772044)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1772044)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1772044), _1772046)))], (35362 ^ _779854) ^ [_1438627, _1438629] : [-(c_Divides_Opdivmod(_1438627, _1438629) = 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), _1438627)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438629))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438627), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438629))))], (29301 ^ _779854) ^ [_1308583, _1308585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1308583), _1308585)), -(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)), _1308583)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1308585))))], (3072 ^ _779854) ^ [_825709, _825711, _825713, _825715] : [-(c_Nitpick_Ocard_H(_825715, _825711) = c_Nitpick_Ocard_H(_825713, _825709)), _825715 = _825713, _825711 = _825709], (30225 ^ _779854) ^ [_1325534, _1325536, _1325538] : [class_Divides_Oring__div(_1325534), -(c_Divides_Odiv__class_Omod(_1325534, hAPP(c_Groups_Ouminus__class_Ouminus(_1325534), _1325536), _1325538) = c_Divides_Odiv__class_Omod(_1325534, hAPP(c_Groups_Ouminus__class_Ouminus(_1325534), c_Divides_Odiv__class_Omod(_1325534, _1325536, _1325538)), _1325538))], (9526 ^ _779854) ^ [_939426, _939428, _939430, _939432] : [c_Orderings_Obot__class_Obot(tc_fun(_939426, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_939428, _939426, _939430), _939432), -(_939432 = c_Orderings_Obot__class_Obot(tc_fun(_939428, tc_HOL_Obool)))], (4392 ^ _779854) ^ [_846709, _846711, _846713, _846715, _846717, _846719] : [-(c_New__DSequence_Opos__union(_846719, _846715, _846711) = c_New__DSequence_Opos__union(_846717, _846713, _846709)), _846719 = _846717, _846715 = _846713, _846711 = _846709], (5640 ^ _779854) ^ [_866169, _866171, _866173, _866175] : [-(hAPP(_866175, _866171) = hAPP(_866173, _866169)), _866175 = _866173, _866171 = _866169], (18171 ^ _779854) ^ [_1108643, _1108645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1108643)), _1108645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108643), _1108645)))], (38660 ^ _779854) ^ [_1516603, _1516605, _1516607, _1516609, _1516611, _1516613, _1516615, _1516617] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516603, _1516605)), _1516607), hAPP(c_Set_Oimage(tc_prod(_1516609, _1516611), tc_prod(_1516603, _1516605), c_Product__Type_Omap__pair(_1516609, _1516603, _1516611, _1516605, _1516613, _1516615)), _1516617))), 38665 ^ _779854 : [(38668 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516609, _1516611)), hAPP(hAPP(c_Product__Type_OPair(_1516609, _1516611), 38663 ^ [_1516603, _1516605, _1516607, _1516609, _1516611, _1516613, _1516615, _1516617]), 38664 ^ [_1516603, _1516605, _1516607, _1516609, _1516611, _1516613, _1516615, _1516617])), _1516617)))], (38666 ^ _779854) ^ [] : [-(_1516607 = hAPP(hAPP(c_Product__Type_OPair(_1516603, _1516605), hAPP(_1516613, 38663 ^ [_1516603, _1516605, _1516607, _1516609, _1516611, _1516613, _1516615, _1516617])), hAPP(_1516615, 38664 ^ [_1516603, _1516605, _1516607, _1516609, _1516611, _1516613, _1516615, _1516617])))]]], (4596 ^ _779854) ^ [_849873, _849875] : [_849875 = _849873, -(c_Code__Numeral_OSuc__code__numeral(_849875) = c_Code__Numeral_OSuc__code__numeral(_849873))], (33911 ^ _779854) ^ [_1405962, _1405964, _1405966, _1405968, _1405970] : [class_Groups_Ocomm__monoid__add(_1405962), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405964, _1405962), hAPP(hAPP(c_COMBS(_1405964, _1405962, _1405962), hAPP(hAPP(c_COMBB(_1405962, tc_fun(_1405962, _1405962), _1405964), c_Groups_Oplus__class_Oplus(_1405962)), _1405966)), _1405968)), _1405970) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1405962), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405964, _1405962), _1405966), _1405970)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405964, _1405962), _1405968), _1405970)))], (18771 ^ _779854) ^ [_1119047] : [hAPP(c_Nat_OSuc, _1119047) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8600 ^ _779854) ^ [_923197, _923199, _923201] : [class_Orderings_Olinorder(_923197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923197), _923199), _923201)), 8607 ^ _779854 : [(8614 ^ _779854) ^ [] : [_923199 = _923201, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923197), _923199), _923201))], (8608 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923197), _923199), _923201))), -(_923199 = _923201)]]], (17676 ^ _779854) ^ [_1100340, _1100342, _1100344] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1100340), _1100342)), hBOOL(hAPP(hAPP(c_member(_1100340), _1100344), _1100342)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1100340), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100340, tc_HOL_Obool)), _1100342), hAPP(hAPP(c_Set_Oinsert(_1100340), _1100344), c_Orderings_Obot__class_Obot(tc_fun(_1100340, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1100340), _1100342))], (32061 ^ _779854) ^ [_1356724] : [class_Groups_Oordered__ab__group__add__abs(_1356724), -(hAPP(c_Groups_Oabs__class_Oabs(_1356724), c_Groups_Ozero__class_Ozero(_1356724)) = c_Groups_Ozero__class_Ozero(_1356724))], (9867 ^ _779854) ^ [_945985] : [class_Orderings_Oord(_945985), -(c_Orderings_Oord__class_Omax(_945985) = c_Orderings_Oord_Omax(_945985, c_Orderings_Oord__class_Oless__eq(_945985)))], (32359 ^ _779854) ^ [_1362300, _1362302] : [class_Groups_Oabs__if(_1362300), 32362 ^ _779854 : [(32369 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362300), _1362302), c_Groups_Ozero__class_Ozero(_1362300)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1362300), _1362302) = _1362302)], (32363 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362300), _1362302), c_Groups_Ozero__class_Ozero(_1362300))), -(hAPP(c_Groups_Oabs__class_Oabs(_1362300), _1362302) = hAPP(c_Groups_Ouminus__class_Ouminus(_1362300), _1362302))]]], (19117 ^ _779854) ^ [_1124510, _1124512, _1124514] : [class_Groups_Oordered__comm__monoid__add(_1124510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124510), c_Groups_Ozero__class_Ozero(_1124510)), _1124512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124510), c_Groups_Ozero__class_Ozero(_1124510)), _1124514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124510), c_Groups_Ozero__class_Ozero(_1124510)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124510), _1124512), _1124514))))], (45768 ^ _779854) ^ [_1697435, _1697437, _1697439] : [hBOOL(hAPP(c_List_Olistsp(_1697435, hAPP(hAPP(c_COMBC(_1697435, tc_fun(_1697435, tc_HOL_Obool), tc_HOL_Obool), c_member(_1697435)), _1697437)), _1697439)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697435)), _1697439), c_List_Olists(_1697435, _1697437))))], (49226 ^ _779854) ^ [_1772477, _1772479, _1772481, _1772483, _1772485] : [49228 ^ _779854 : [(49231 ^ _779854) ^ [] : [c_Relation_Orefl__on(_1772481, hAPP(_1772483, 49227 ^ [_1772477, _1772479, _1772481, _1772483, _1772485]), hAPP(_1772485, 49227 ^ [_1772477, _1772479, _1772481, _1772483, _1772485]))], (49229 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772477), 49227 ^ [_1772477, _1772479, _1772481, _1772483, _1772485]), _1772479)))]], -(c_Relation_Orefl__on(_1772481, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1772477, tc_fun(_1772481, tc_HOL_Obool)), _1772479), _1772483), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1772477, tc_fun(tc_prod(_1772481, _1772481), tc_HOL_Obool)), _1772479), _1772485)))], (46416 ^ _779854) ^ [_1712415, _1712417, _1712419] : [46418 ^ _779854 : [(46421 ^ _779854) ^ [] : [hBOOL(hAPP(_1712417, 46417 ^ [_1712415, _1712417, _1712419]))], (46419 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1712415), 46417 ^ [_1712415, _1712417, _1712419]), hAPP(c_List_Oset(_1712415), _1712419))))]], -(hAPP(c_List_Ofilter(_1712415, _1712417), _1712419) = _1712419)], (35181 ^ _779854) ^ [_1435147, _1435149, _1435151, _1435153, _1435155, _1435157, _1435159] : [hBOOL(hAPP(hAPP(c_member(_1435147), _1435149), hAPP(hAPP(_1435151, _1435153), _1435155))), -(hBOOL(hAPP(hAPP(c_member(_1435147), _1435149), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1435157, _1435159, tc_fun(_1435147, tc_HOL_Obool)), _1435151), hAPP(hAPP(c_Product__Type_OPair(_1435157, _1435159), _1435153), _1435155)))))], (31512 ^ _779854) ^ [_1347830] : [_1347830 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1347830) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51495 ^ _779854) ^ [_1822570, _1822572] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1822570), 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)))), _1822572))), 51498 ^ _779854 : [(51501 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822572), _1822570))], (51499 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822570), _1822572)))]]], (42468 ^ _779854) ^ [_1621666] : [-(c_List_Olists(_1621666, c_Orderings_Otop__class_Otop(tc_fun(_1621666, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1621666), tc_HOL_Obool)))], (27061 ^ _779854) ^ [_1270573, _1270575, _1270577, _1270579] : [class_Divides_Osemiring__div(_1270573), -(_1270575 = c_Groups_Ozero__class_Ozero(_1270573)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1270573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1270573), _1270577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270573), _1270575), _1270579))), _1270575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1270573), _1270579), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1270573), _1270577), _1270575)))], (33795 ^ _779854) ^ [_1402128, _1402130, _1402132, _1402134, _1402136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402128, tc_HOL_Obool)), _1402130), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1402132, tc_fun(_1402128, tc_HOL_Obool)), _1402134), _1402136))), 33798 ^ _779854 : [(33799 ^ _779854) ^ [_1402261] : [hBOOL(hAPP(hAPP(c_member(_1402132), _1402261), _1402134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402128, tc_HOL_Obool)), _1402130), hAPP(_1402136, _1402261))))]]], (46178 ^ _779854) ^ [_1706582, _1706584, _1706586, _1706588] : [_1706582 = _1706584, -(hAPP(c_List_OremoveAll(_1706586, _1706582), hAPP(hAPP(c_List_Olist_OCons(_1706586), _1706584), _1706588)) = hAPP(c_List_OremoveAll(_1706586, _1706582), _1706588))], (6701 ^ _779854) ^ [_887358, _887360, _887362, _887364] : [hBOOL(hAPP(_887358, _887360)), hBOOL(hAPP(_887362, _887360)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_887364, tc_HOL_Obool)), _887358), _887362), _887360)))], (49379 ^ _779854) ^ [_1776046, _1776048, _1776050, _1776052, _1776054, _1776056, _1776058] : [49381 ^ _779854 : [(49384 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1776050, 49380 ^ [_1776046, _1776048, _1776050, _1776052, _1776054, _1776056, _1776058]), _1776052), _1776054))], (49382 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776046), 49380 ^ [_1776046, _1776048, _1776050, _1776052, _1776054, _1776056, _1776058]), _1776048)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1776046, tc_fun(_1776056, tc_fun(_1776058, tc_HOL_Obool))), _1776048), _1776050), _1776052), _1776054)))], (2200 ^ _779854) ^ [_811999, _812001] : [_812001 = _811999, -(c_SetInterval_Oord__class_OatLeast(_812001) = c_SetInterval_Oord__class_OatLeast(_811999))], (38412 ^ _779854) ^ [_1509428, _1509430, _1509432, _1509434, _1509436, _1509438] : [hBOOL(hAPP(hAPP(c_member(_1509428), _1509430), _1509432)), 38415 ^ _779854 : [(38422 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509434, tc_HOL_Obool)), _1509436), _1509438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509434, _1509428), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1509434, _1509428), _1509436), hAPP(c_COMBK(tc_fun(_1509428, tc_HOL_Obool), _1509434), _1509432))), hAPP(hAPP(c_Product__Type_OSigma(_1509434, _1509428), _1509438), hAPP(c_COMBK(tc_fun(_1509428, tc_HOL_Obool), _1509434), _1509432)))))], (38416 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509434, _1509428), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1509434, _1509428), _1509436), hAPP(c_COMBK(tc_fun(_1509428, tc_HOL_Obool), _1509434), _1509432))), hAPP(hAPP(c_Product__Type_OSigma(_1509434, _1509428), _1509438), hAPP(c_COMBK(tc_fun(_1509428, tc_HOL_Obool), _1509434), _1509432)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509434, tc_HOL_Obool)), _1509436), _1509438)))]]], (15420 ^ _779854) ^ [_1055039, _1055041, _1055043] : [class_Groups_Ogroup__add(_1055039), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055039), _1055041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055039), hAPP(c_Groups_Ouminus__class_Ouminus(_1055039), _1055041)), _1055043)) = _1055043)], (31049 ^ _779854) ^ [] : [c_Int_OPls = c_Int_OMin], (11135 ^ _779854) ^ [_971728, _971730, _971732] : [11136 ^ _779854 : [(11139 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_971728), _971732))], (11137 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_971728), _971730))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_971728), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971728, tc_HOL_Obool)), _971730), _971732))))], (15580 ^ _779854) ^ [_1058281, _1058283, _1058285, _1058287, _1058289] : [class_Groups_Ocomm__monoid__add(_1058281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058283), _1058285)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058283), _1058287)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058281), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058283, _1058281), _1058289), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1058283, tc_HOL_Obool)), _1058285), _1058287))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058283, _1058281), _1058289), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1058283, tc_HOL_Obool)), _1058285), _1058287))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058281), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058283, _1058281), _1058289), _1058285)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058283, _1058281), _1058289), _1058287)))], (44294 ^ _779854) ^ [_1665317, _1665319] : [-(hAPP(hAPP(c_List_Odrop(_1665317), _1665319), c_List_Olist_ONil(_1665317)) = c_List_Olist_ONil(_1665317))], (35129 ^ _779854) ^ [_1433533, _1433535, _1433537, _1433539] : [-(hAPP(c_Nat_Onat_Onat__rec(_1433533, _1433535, _1433537), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433539)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1433533), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1433539))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1433533, _1433533), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1433533, tc_fun(_1433533, _1433533)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1433533, tc_fun(_1433533, _1433533)), tc_Int_Oint), c_If(_1433533)), c_Nat__Numeral_Oneg)), _1433535)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1433533, _1433533), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1433533, _1433533), tc_Int_Oint), _1433537), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1433533, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1433533, _1433535, _1433537)), c_Int_Onat)))))], (4502 ^ _779854) ^ [_848412, _848414] : [_848414 = _848412, -(c_List_Olist_OCons(_848414) = c_List_Olist_OCons(_848412))], (296 ^ _779854) ^ [_784406, _784408] : [-(c_Nat__Transfer_Ois__nat(_784406)), _784408 = _784406, c_Nat__Transfer_Ois__nat(_784408)], (39387 ^ _779854) ^ [_1540210, _1540212] : [39388 ^ _779854 : [(39389 ^ _779854) ^ [_1540274, _1540276] : [_1540212 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1540210, _1540274), 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)), _1540276)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540210), _1540212)))], (9893 ^ _779854) ^ [_946448, _946450, _946452, _946454] : [class_Orderings_Olinorder(_946448), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946448, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_946448), _946450)), c_SetInterval_Oord__class_OatLeastAtMost(_946448, _946452, _946454)) = c_SetInterval_Oord__class_OatLeastAtMost(_946448, _946452, hAPP(hAPP(c_Orderings_Oord__class_Omin(_946448), _946450), _946454)))], (52193 ^ _779854) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (34381 ^ _779854) ^ [_1417213, _1417215] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1417213))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1417215)), hAPP(c_Int_Onat, _1417213)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1417215), _1417213)), 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)))], (10757 ^ _779854) ^ [_963304, _963306, _963308, _963310] : [class_Groups_Oordered__ab__group__add(_963304), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963304), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963304), _963306), _963308)), _963310) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_963304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963304), _963306), _963310)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963304), _963308), _963310)))], (52531 ^ _779854) ^ [_1837179, _1837181] : [-(class_Nat_Osize(tc_prod(_1837179, _1837181)))], (48675 ^ _779854) ^ [_1760459, _1760461, _1760463] : [c_List_Olist__all(_1760459, _1760461, _1760463), 48678 ^ _779854 : [(48679 ^ _779854) ^ [_1760540] : [hBOOL(hAPP(hAPP(c_member(_1760459), _1760540), hAPP(c_List_Oset(_1760459), _1760463))), -(hBOOL(hAPP(_1760461, _1760540)))]]], (31599 ^ _779854) ^ [_1349232, _1349234] : [c_Nat__Transfer_Ois__nat(_1349232), c_Nat__Transfer_Ois__nat(_1349234), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1349232), _1349234)))], (37356 ^ _779854) ^ [_1483224, _1483226, _1483228, _1483230, _1483232, _1483234, _1483236] : [c_Equiv__Relations_Oequiv(_1483224, _1483226, _1483228), hBOOL(hAPP(hAPP(c_member(tc_fun(_1483224, tc_HOL_Obool)), _1483230), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483224), _1483226), _1483228))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1483224, tc_HOL_Obool)), _1483232), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483224), _1483226), _1483228))), hBOOL(hAPP(hAPP(c_member(_1483224), _1483234), _1483230)), hBOOL(hAPP(hAPP(c_member(_1483224), _1483236), _1483232)), 37375 ^ _779854 : [(37382 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1483224, _1483224)), hAPP(hAPP(c_Product__Type_OPair(_1483224, _1483224), _1483234), _1483236)), _1483228)), -(_1483230 = _1483232)], (37376 ^ _779854) ^ [] : [_1483230 = _1483232, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483224, _1483224)), hAPP(hAPP(c_Product__Type_OPair(_1483224, _1483224), _1483234), _1483236)), _1483228)))]]], (39094 ^ _779854) ^ [_1528804, _1528806] : [-(c_Fun_Oinj__on(tc_fun(_1528804, _1528806), tc_fun(tc_prod(_1528804, _1528806), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1528804, _1528806), tc_HOL_Obool), tc_fun(tc_prod(_1528804, _1528806), tc_HOL_Obool), tc_fun(_1528804, _1528806)), c_Set_OCollect(tc_prod(_1528804, _1528806))), hAPP(hAPP(c_COMBB(tc_fun(_1528804, tc_fun(_1528806, tc_HOL_Obool)), tc_fun(tc_prod(_1528804, _1528806), tc_HOL_Obool), tc_fun(_1528804, _1528806)), c_Product__Type_Oprod_Oprod__case(_1528804, _1528806, tc_HOL_Obool)), hAPP(c_COMBB(_1528806, tc_fun(_1528806, tc_HOL_Obool), _1528804), hAPP(c_COMBC(_1528806, _1528806, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1528804, _1528806), tc_HOL_Obool))))], (18849 ^ _779854) ^ [_1120110, _1120112] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120110), _1120112) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120112), _1120110) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1120110 = _1120112)], (28738 ^ _779854) ^ [_1299147] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299147))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1299147)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43087 ^ _779854) ^ [_1638325, _1638327, _1638329, _1638331, _1638333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638327)), _1638329))), 43090 ^ _779854 : [(43097 ^ _779854) ^ [] : [-(_1638325 = _1638331), -(hAPP(hAPP(c_List_Onth(_1638327), hAPP(hAPP(c_List_Olist__update(_1638327, _1638329), _1638325), _1638333)), _1638331) = hAPP(hAPP(c_List_Onth(_1638327), _1638329), _1638331))], (43091 ^ _779854) ^ [] : [_1638325 = _1638331, -(hAPP(hAPP(c_List_Onth(_1638327), hAPP(hAPP(c_List_Olist__update(_1638327, _1638329), _1638325), _1638333)), _1638331) = _1638333)]]], (37999 ^ _779854) ^ [_1498259] : [-(c_Nitpick_Ozero__frac(_1498259) = c_Nitpick_OAbs__Frac(_1498259, 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))))], (11820 ^ _779854) ^ [_984980, _984982, _984984, _984986] : [_984980 = _984982, hBOOL(hAPP(hAPP(c_member(_984984), _984982), _984986)), -(hBOOL(hAPP(hAPP(c_member(_984984), _984980), _984986)))], (52535 ^ _779854) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (20477 ^ _779854) ^ [_1148330, _1148332] : [_1148330 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1148330), _1148332), -(_1148332 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1148330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41505 ^ _779854) ^ [_1594073, _1594075, _1594077, _1594079] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594073, _1594073)), hAPP(hAPP(c_Product__Type_OPair(_1594073, _1594073), _1594075), _1594077)), c_Transitive__Closure_Ortrancl(_1594073, _1594079))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594073, _1594073)), hAPP(hAPP(c_Product__Type_OPair(_1594073, _1594073), _1594077), _1594075)), c_Transitive__Closure_Ortrancl(_1594073, hAPP(c_Relation_Oconverse(_1594073, _1594073), _1594079)))))], (32175 ^ _779854) ^ [_1358763, _1358765, _1358767] : [class_Groups_Oordered__ab__group__add__abs(_1358763), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358763), hAPP(c_Groups_Oabs__class_Oabs(_1358763), _1358765)), hAPP(c_Groups_Oabs__class_Oabs(_1358763), _1358767))), hAPP(c_Groups_Oabs__class_Oabs(_1358763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358763), _1358767), _1358765)))))], (39816 ^ _779854) ^ [_1552343, _1552345, _1552347] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1552343, _1552345)), _1552347)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1552343), hAPP(c_Relation_ODomain(_1552343, _1552345), _1552347))))], (44268 ^ _779854) ^ [_1664775, _1664777, _1664779] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664775)), hAPP(hAPP(c_List_Odrop(_1664775), _1664777), _1664779)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664775)), _1664779)), _1664777))], (38496 ^ _779854) ^ [_1511433, _1511435, _1511437, _1511439, _1511441, _1511443, _1511445, _1511447] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1511433, _1511435), tc_fun(tc_prod(_1511437, _1511439), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1511433, _1511435), _1511441), hAPP(c_COMBK(tc_fun(_1511435, tc_HOL_Obool), _1511433), _1511443))), hAPP(c_Product__Type_Oprod_Oprod__case(_1511433, _1511435, tc_fun(tc_prod(_1511437, _1511439), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1511433, tc_fun(_1511435, tc_fun(_1511437, tc_fun(_1511439, tc_HOL_Obool))), tc_fun(_1511435, tc_fun(tc_prod(_1511437, _1511439), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1511437, tc_fun(_1511439, tc_HOL_Obool)), tc_fun(tc_prod(_1511437, _1511439), tc_HOL_Obool)), tc_fun(tc_fun(_1511435, tc_fun(_1511437, tc_fun(_1511439, tc_HOL_Obool))), tc_fun(_1511435, tc_fun(tc_prod(_1511437, _1511439), tc_HOL_Obool))), _1511433), c_COMBB(tc_fun(_1511437, tc_fun(_1511439, tc_HOL_Obool)), tc_fun(tc_prod(_1511437, _1511439), tc_HOL_Obool), _1511435)), hAPP(hAPP(c_COMBB(tc_fun(_1511437, tc_HOL_Obool), tc_fun(tc_fun(_1511437, tc_fun(_1511439, tc_HOL_Obool)), tc_fun(tc_prod(_1511437, _1511439), tc_HOL_Obool)), _1511433), c_Product__Type_OSigma(_1511437, _1511439)), _1511445))), hAPP(hAPP(c_COMBB(tc_fun(_1511439, tc_HOL_Obool), tc_fun(_1511437, tc_fun(_1511439, tc_HOL_Obool)), _1511435), c_COMBK(tc_fun(_1511439, tc_HOL_Obool), _1511437)), _1511447)))) = hAPP(hAPP(c_Product__Type_OSigma(_1511437, _1511439), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511433, tc_fun(_1511437, tc_HOL_Obool)), _1511441), _1511445)), hAPP(c_COMBK(tc_fun(_1511439, tc_HOL_Obool), _1511437), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511435, tc_fun(_1511439, tc_HOL_Obool)), _1511443), _1511447))))], (42721 ^ _779854) ^ [_1628166, _1628168, _1628170] : [-(c_List_Osublist(_1628166, _1628168, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1628170)) = hAPP(hAPP(c_List_Otake(_1628166), _1628170), _1628168))], (39739 ^ _779854) ^ [_1550621] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1550621)))], (19203 ^ _779854) ^ [_1126083, _1126085, _1126087, _1126089, _1126091] : [class_Rings_Oordered__semiring(_1126083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126083), _1126085), _1126087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126083), _1126089), _1126091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126083), c_Groups_Ozero__class_Ozero(_1126083)), _1126087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126083), c_Groups_Ozero__class_Ozero(_1126083)), _1126089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126083), _1126085), _1126089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126083), _1126087), _1126091))))], (33335 ^ _779854) ^ [_1385843, _1385845] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1385843, tc_HOL_Obool), _1385845) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1385843, tc_HOL_Obool), tc_fun(_1385843, tc_HOL_Obool)), _1385845), c_COMBI(tc_fun(_1385843, tc_HOL_Obool))))], (46705 ^ _779854) ^ [_1719463, _1719465, _1719467] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1719463), c_List_Oupt(_1719465, _1719467)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1719465), _1719463), _1719467))], (6533 ^ _779854) ^ [_884437, _884439, _884441] : [class_Orderings_Oorder(_884437), 6536 ^ _779854 : [(6543 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884437), _884439), _884441))), -(c_Orderings_Obot__class_Obot(tc_fun(_884437, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_884437, _884439, _884441))], (6537 ^ _779854) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_884437, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_884437, _884439, _884441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884437), _884439), _884441))]]], (39266 ^ _779854) ^ [_1536437] : [-(c_Int_Oint__ge__less__than(_1536437) = 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), _1536437)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (25859 ^ _779854) ^ [_1249846, _1249848, _1249850, _1249852, _1249854] : [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), _1249846), _1249848)), _1249850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1249846), _1249852)), _1249854))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249854), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249846), _1249854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249846), _1249850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249852), _1249848)))], (28561 ^ _779854) ^ [_1296156, _1296158, _1296160] : [class_Rings_Olinordered__semidom(_1296156), 28564 ^ _779854 : [(28571 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1296158), _1296160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296156), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296156), _1296158)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296156), _1296160))))], (28565 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296156), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296156), _1296158)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296156), _1296160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1296158), _1296160)))]]], (38777 ^ _779854) ^ [_1519553, _1519555, _1519557] : [-(hAPP(c_Set_OCollect(_1519553), hAPP(hAPP(c_COMBS(_1519553, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519553), c_fdisj), _1519555)), _1519557)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1519553, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1519553), _1519555)), hAPP(c_Set_OCollect(_1519553), _1519557)))], (12476 ^ _779854) ^ [_997752, _997754, _997756] : [class_Orderings_Oord(_997752), 12479 ^ _779854 : [(12486 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997752), _997756), _997754)), -(hBOOL(hAPP(hAPP(c_member(_997752), _997754), hAPP(c_SetInterval_Oord__class_OgreaterThan(_997752), _997756))))], (12480 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_997752), _997754), hAPP(c_SetInterval_Oord__class_OgreaterThan(_997752), _997756))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997752), _997756), _997754)))]]], (39713 ^ _779854) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (16533 ^ _779854) ^ [_1077766, _1077768, _1077770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077766), _1077768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1077770), _1077768))))], (45398 ^ _779854) ^ [_1689369, _1689371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1689369)), hAPP(c_Code__Numeral_Oof__nat, _1689371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689369), _1689371)))], (30231 ^ _779854) ^ [_1325655, _1325657, _1325659, _1325661] : [class_Divides_Oring__div(_1325655), c_Divides_Odiv__class_Omod(_1325655, _1325657, _1325659) = c_Divides_Odiv__class_Omod(_1325655, _1325661, _1325659), -(c_Divides_Odiv__class_Omod(_1325655, hAPP(c_Groups_Ouminus__class_Ouminus(_1325655), _1325657), _1325659) = c_Divides_Odiv__class_Omod(_1325655, hAPP(c_Groups_Ouminus__class_Ouminus(_1325655), _1325661), _1325659))], (43939 ^ _779854) ^ [_1656736, _1656738, _1656740] : [hAPP(hAPP(c_List_Oappend(_1656736), _1656738), _1656740) = _1656738, -(_1656740 = c_List_Olist_ONil(_1656736))], (40176 ^ _779854) ^ [_1561595, _1561597, _1561599, _1561601] : [-(hAPP(c_Set_OCollect(_1561595), hAPP(hAPP(c_COMBB(tc_fun(_1561597, tc_HOL_Obool), tc_HOL_Obool, _1561595), c_HOL_OAll(_1561597)), hAPP(hAPP(c_COMBB(tc_fun(_1561597, tc_HOL_Obool), tc_fun(_1561597, tc_HOL_Obool), _1561595), hAPP(c_COMBS(_1561597, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1561597), c_fimplies), hAPP(hAPP(c_COMBC(_1561597, tc_fun(_1561597, tc_HOL_Obool), tc_HOL_Obool), c_member(_1561597)), _1561599)))), _1561601))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561597, tc_fun(_1561595, tc_HOL_Obool)), _1561599), hAPP(hAPP(c_COMBB(tc_fun(_1561595, tc_HOL_Obool), tc_fun(_1561595, tc_HOL_Obool), _1561597), c_Set_OCollect(_1561595)), hAPP(c_COMBC(_1561595, _1561597, tc_HOL_Obool), _1561601))))], (43141 ^ _779854) ^ [_1639460, _1639462, _1639464, _1639466] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639460), tc_List_Olist(_1639460))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639460), tc_List_Olist(_1639460)), _1639462), _1639464)), c_List_Olistrel1(_1639460, _1639466))), 43146 ^ _779854 : [(43151 ^ _779854) ^ [] : [-(_1639464 = hAPP(hAPP(c_List_Olist__update(_1639460, _1639462), 43145 ^ [_1639460, _1639462, _1639464, _1639466]), 43144 ^ [_1639460, _1639462, _1639464, _1639466]))], (43149 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43145 ^ [_1639460, _1639462, _1639464, _1639466]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639460)), _1639462))))], (43147 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639460, _1639460)), hAPP(hAPP(c_Product__Type_OPair(_1639460, _1639460), hAPP(hAPP(c_List_Onth(_1639460), _1639462), 43145 ^ [_1639460, _1639462, _1639464, _1639466])), 43144 ^ [_1639460, _1639462, _1639464, _1639466])), _1639466)))]]], (45625 ^ _779854) ^ [_1693908, _1693910] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1693908, _1693910) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1693908), hAPP(c_Code__Numeral_Onat__of, _1693910))))], (39323 ^ _779854) ^ [_1539029, _1539031] : [-(hAPP(c_Fun_Oid(_1539029), _1539031) = _1539031)], (15924 ^ _779854) ^ [_1065421, _1065423, _1065425, _1065427] : [class_Rings_Ocomm__semiring__1(_1065421), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065421), _1065423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065421), _1065425), _1065427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065421), _1065425), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065421), _1065423), _1065427)))], (11234 ^ _779854) ^ [_973580, _973582, _973584] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_973580), _973584)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973580), hAPP(hAPP(c_Set_Oinsert(_973580), _973582), _973584))))], (1630 ^ _779854) ^ [_803181, _803183] : [-(class_Rings_Olinordered__semiring(_803181)), _803183 = _803181, class_Rings_Olinordered__semiring(_803183)], (11067 ^ _779854) ^ [_970289, _970291, _970293] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970289, tc_HOL_Obool)), _970291), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_970289, tc_HOL_Obool)), _970293)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970289, tc_HOL_Obool)), _970291), _970293))], (13415 ^ _779854) ^ [_1016085, _1016087, _1016089] : [class_Lattices_Olattice(_1016085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016085), _1016087)), -(_1016087 = c_Orderings_Obot__class_Obot(tc_fun(_1016085, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1016085, hAPP(hAPP(c_Set_Oinsert(_1016085), _1016089), _1016087)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1016085), _1016089), c_Big__Operators_Olattice__class_OSup__fin(_1016085, _1016087)))], (5262 ^ _779854) ^ [_860328, _860330, _860332, _860334, _860336, _860338] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_860338, _860334, _860330) = c_Lazy__Sequence_Olazy__sequence_OInsert(_860336, _860332, _860328)), _860338 = _860336, _860334 = _860332, _860330 = _860328], (2554 ^ _779854) ^ [_817688, _817690, _817692, _817694] : [-(c_Divides_Odivmod__nat__rel(_817694, _817690) = c_Divides_Odivmod__nat__rel(_817692, _817688)), _817694 = _817692, _817690 = _817688], (15054 ^ _779854) ^ [_1047444, _1047446, _1047448] : [class_Lattices_Oab__semigroup__idem__mult(_1047444), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047444), _1047446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047444), _1047446), _1047448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047444), _1047446), _1047448))], (27639 ^ _779854) ^ [_1280106, _1280108, _1280110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1280106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1280106), _1280108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1280110), _1280108)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1280110), _1280106))))], (34433 ^ _779854) ^ [_1418376, _1418378, _1418380, _1418382, _1418384, _1418386] : [class_Groups_Ocomm__monoid__add(_1418376), c_Fun_Oinj__on(_1418378, _1418380, _1418382, _1418384), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418380, _1418376), _1418386), hAPP(c_Set_Oimage(_1418378, _1418380, _1418382), _1418384)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418378, _1418376), hAPP(c_Fun_Ocomp(_1418380, _1418376, _1418378, _1418386), _1418382)), _1418384))], (20409 ^ _779854) ^ [_1147139, _1147141, _1147143] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147139), _1147141)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147143), _1147141)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147139), _1147143))], (13309 ^ _779854) ^ [_1014424, _1014426, _1014428] : [class_Lattices_Olattice(_1014424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014424), _1014426)), hBOOL(hAPP(hAPP(c_member(_1014424), _1014428), _1014426)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1014424), _1014428), c_Big__Operators_Olattice__class_OInf__fin(_1014424, _1014426)) = c_Big__Operators_Olattice__class_OInf__fin(_1014424, _1014426))], (14484 ^ _779854) ^ [_1036240, _1036242, _1036244, _1036246, _1036248] : [class_Rings_Oring(_1036240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036242), _1036244)), hBOOL(hAPP(hAPP(c_member(_1036242), _1036246), _1036244)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1036242, _1036240), _1036248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1036242, tc_HOL_Obool)), _1036244), hAPP(hAPP(c_Set_Oinsert(_1036242), _1036246), c_Orderings_Obot__class_Obot(tc_fun(_1036242, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1036240), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1036242, _1036240), _1036248), _1036244)), hAPP(_1036248, _1036246)))], (42620 ^ _779854) ^ [_1625411, _1625413, _1625415, _1625417] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625411), tc_List_Olist(_1625411))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625411), tc_List_Olist(_1625411)), _1625413), _1625415)), c_List_Olexord(_1625411, _1625417))), 42625 ^ _779854 : [(42628 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1625411), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625411)), _1625413)), _1625415) = _1625413)], (42626 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625411)), _1625413)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625411)), _1625415))))]], 42630 ^ _779854 : [(42635 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625411, _1625411)), hAPP(hAPP(c_Product__Type_OPair(_1625411, _1625411), hAPP(hAPP(c_List_Onth(_1625411), _1625413), 42629 ^ [_1625411, _1625413, _1625415, _1625417])), hAPP(hAPP(c_List_Onth(_1625411), _1625415), 42629 ^ [_1625411, _1625413, _1625415, _1625417]))), _1625417)))], (42633 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1625411), 42629 ^ [_1625411, _1625413, _1625415, _1625417]), _1625413) = hAPP(hAPP(c_List_Otake(_1625411), 42629 ^ [_1625411, _1625413, _1625415, _1625417]), _1625415))], (42631 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42629 ^ [_1625411, _1625413, _1625415, _1625417]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625411)), _1625413)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625411)), _1625415)))))]]], (3698 ^ _779854) ^ [_835472, _835474] : [_835474 = _835472, -(c_List_Omonoid__add__class_Olistsum(_835474) = c_List_Omonoid__add__class_Olistsum(_835472))], (18635 ^ _779854) ^ [_1117026, _1117028] : [class_Rings_Omult__zero(_1117026), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117026), c_Groups_Ozero__class_Ozero(_1117026)), _1117028) = c_Groups_Ozero__class_Ozero(_1117026))], (48500 ^ _779854) ^ [_1756942, _1756944, _1756946, _1756948] : [48501 ^ _779854 : [(48504 ^ _779854) ^ [] : [c_List_Olist__ex(_1756942, _1756944, _1756948)], (48502 ^ _779854) ^ [] : [hBOOL(hAPP(_1756944, _1756946))]], -(c_List_Olist__ex(_1756942, _1756944, hAPP(hAPP(c_List_Olist_OCons(_1756942), _1756946), _1756948)))], (34587 ^ _779854) ^ [_1421848, _1421850] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421848)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421850)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1421850))), 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, _1421848))), 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), _1421848)), c_Int_Onat)))))], (17356 ^ _779854) ^ [_1093536, _1093538, _1093540] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093536), _1093538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1093536, tc_HOL_Obool)), _1093540), _1093538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1093536), _1093538)), hAPP(c_Finite__Set_Ocard(_1093536), _1093540))), -(_1093540 = _1093538)], (19131 ^ _779854) ^ [_1124765, _1124767] : [class_Groups_Olinordered__ab__group__add(_1124765), 19134 ^ _779854 : [(19141 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124765), _1124767), c_Groups_Ozero__class_Ozero(_1124765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124765), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124765), _1124767), _1124767)), c_Groups_Ozero__class_Ozero(_1124765))))], (19135 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124765), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124765), _1124767), _1124767)), c_Groups_Ozero__class_Ozero(_1124765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124765), _1124767), c_Groups_Ozero__class_Ozero(_1124765))))]]], (49786 ^ _779854) ^ [_1786704, _1786706] : [c_Relation_Otrans(_1786704, hAPP(c_Set_OCollect(tc_prod(_1786704, _1786704)), hAPP(c_Product__Type_Oprod_Oprod__case(_1786704, _1786704, tc_HOL_Obool), _1786706))), -(c_Predicate_Otransp(_1786704, _1786706))], (25683 ^ _779854) ^ [_1246754] : [-(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)), _1246754))))], (30283 ^ _779854) ^ [_1326545, _1326547, _1326549, _1326551] : [class_Divides_Osemiring__div(_1326545), -(c_Divides_Odiv__class_Omod(_1326545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326545), c_Divides_Odiv__class_Omod(_1326545, _1326547, _1326549)), _1326551), _1326549) = c_Divides_Odiv__class_Omod(_1326545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326545), _1326547), _1326551), _1326549))], (52587 ^ _779854) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (40133 ^ _779854) ^ [_1560843, _1560845, _1560847] : [hBOOL(hAPP(hAPP(c_member(_1560845), _1560843), c_Orderings_Obot__class_Obot(tc_fun(_1560845, tc_HOL_Obool)))), -(hBOOL(hAPP(_1560847, _1560843)))], (49936 ^ _779854) ^ [_1789202, _1789204, _1789206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1789202, _1789202), tc_HOL_Obool)), _1789204), _1789206)), c_Relation_Oantisym(_1789202, _1789206), -(c_Relation_Oantisym(_1789202, _1789204))], (35356 ^ _779854) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (31023 ^ _779854) ^ [_1339802] : [c_Int_OMin = c_Int_OBit1(_1339802), -(c_Int_OMin = _1339802)], (35440 ^ _779854) ^ [_1440100, _1440102] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1440100, _1440102), c_Divides_Odivmod__nat(_1440100, _1440102))))], (6255 ^ _779854) ^ [_879162, _879164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879162, tc_HOL_Obool)), _879164), c_Orderings_Obot__class_Obot(tc_fun(_879162, tc_HOL_Obool)))), -(_879164 = c_Orderings_Obot__class_Obot(tc_fun(_879162, tc_HOL_Obool)))], (46252 ^ _779854) ^ [_1708014, _1708016, _1708018, _1708020] : [class_Orderings_Olinorder(_1708014), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708016)), c_List_Olinorder__class_Osort__key(_1708016, _1708014, _1708018, _1708020)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708016)), _1708020))], (33467 ^ _779854) ^ [_1389578, _1389580, _1389582, _1389584, _1389586] : [hBOOL(hAPP(hAPP(c_member(_1389578), _1389580), _1389582)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389584, tc_HOL_Obool)), hAPP(_1389586, _1389580)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389578, tc_fun(_1389584, tc_HOL_Obool)), _1389582), _1389586)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389578, tc_fun(_1389584, tc_HOL_Obool)), _1389582), _1389586))], (46711 ^ _779854) ^ [_1719584, _1719586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719584)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719586))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719584), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719586)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719584)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719584)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719586))))], (38013 ^ _779854) ^ [_1498725, _1498727, _1498729] : [-(hAPP(c_Finite__Set_Ofold1(_1498725, _1498727), _1498729) = c_HOL_OThe(_1498725, c_Finite__Set_Ofold1Set(_1498725, _1498727, _1498729)))], (27655 ^ _779854) ^ [_1280392, _1280394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1280392)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1280394), _1280392)), _1280392) = _1280394)], (3418 ^ _779854) ^ [_831064, _831066, _831068, _831070, _831072, _831074] : [-(c_Enum_On__lists(_831074, _831070, _831066) = c_Enum_On__lists(_831072, _831068, _831064)), _831074 = _831072, _831070 = _831068, _831066 = _831064], (23866 ^ _779854) ^ [_1212660, _1212662, _1212664] : [class_Rings_Olinordered__semidom(_1212660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212660), c_Groups_Oone__class_Oone(_1212660)), _1212662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212660), c_Groups_Oone__class_Oone(_1212660)), hAPP(hAPP(c_Power_Opower__class_Opower(_1212660), _1212662), _1212664))))], (43580 ^ _779854) ^ [_1648529, _1648531] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1648529), _1648531))), -(c_List_Oupto(_1648529, _1648531) = c_List_Olist_ONil(tc_Int_Oint))], (44556 ^ _779854) ^ [_1671123, _1671125] : [-(c_List_Orotate(_1671123, _1671125) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1671123), tc_List_Olist(_1671123)), _1671125), c_List_Orotate1(_1671123)))], (5672 ^ _779854) ^ [_869423, _869425] : [hAPP(_869423, 5673 ^ [_869423, _869425]) = hAPP(_869425, 5673 ^ [_869423, _869425]), -(_869423 = _869425)], (26217 ^ _779854) ^ [_1256397, _1256399, _1256401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256397)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1256399), _1256401)), 26224 ^ _779854 : [(26225 ^ _779854) ^ [_1256587] : [26227 ^ _779854 : [(26233 ^ _779854) ^ [] : [-(_1256587 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26229 ^ [_1256397, _1256399, _1256401, _1256587]), 26226 ^ [_1256397, _1256399, _1256401, _1256587]))], (26231 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26229 ^ [_1256397, _1256399, _1256401, _1256587]), _1256401)))], (26228 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26226 ^ [_1256397, _1256399, _1256401, _1256587]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1256397))))]], -(_1256587 = _1256399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1256587), _1256397) = _1256399]]], (8872 ^ _779854) ^ [_927504, _927506, _927508, _927510] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927504, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_927504), _927506), _927508)), _927510) = hAPP(hAPP(c_Set_Oinsert(_927504), _927506), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927504, tc_HOL_Obool)), _927508), _927510)))], (49555 ^ _779854) ^ [_1780352, _1780354] : [49558 ^ _779854 : [(49564 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780352, _1780352)), hAPP(hAPP(c_Product__Type_OPair(_1780352, _1780352), 49556 ^ [_1780352, _1780354]), 49560 ^ [_1780352, _1780354])), _1780354))], (49562 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780352, _1780352)), hAPP(hAPP(c_Product__Type_OPair(_1780352, _1780352), 49557 ^ [_1780352, _1780354]), 49560 ^ [_1780352, _1780354])), _1780354)))], (49559 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780352, _1780352)), hAPP(hAPP(c_Product__Type_OPair(_1780352, _1780352), 49556 ^ [_1780352, _1780354]), 49557 ^ [_1780352, _1780354])), _1780354)))]], -(c_Relation_Otrans(_1780352, _1780354))], (12146 ^ _779854) ^ [_991459, _991461, _991463, _991465, _991467, _991469] : [c_Fun_Oinj__on(_991459, _991461, _991463, _991465), hAPP(_991463, _991467) = hAPP(_991463, _991469), hBOOL(hAPP(hAPP(c_member(_991459), _991467), _991465)), hBOOL(hAPP(hAPP(c_member(_991459), _991469), _991465)), -(_991467 = _991469)], (43067 ^ _779854) ^ [_1637839, _1637841, _1637843, _1637845] : [-(hAPP(hAPP(c_List_Olist__update(_1637839, hAPP(hAPP(c_List_Olist_OCons(_1637839), _1637841), _1637843)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1637845) = hAPP(hAPP(c_List_Olist_OCons(_1637839), _1637845), _1637843))], (40487 ^ _779854) ^ [_1569250, _1569252, _1569254] : [class_Complete__Lattice_Ocomplete__lattice(_1569250), _1569252 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1569250, _1569254), c_Orderings_Oorder__class_Omono(_1569250, _1569250, _1569254), -(_1569252 = hAPP(_1569254, _1569252))], (26591 ^ _779854) ^ [_1263165, _1263167] : [class_Divides_Osemiring__div(_1263165), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1263165), c_Groups_Ozero__class_Ozero(_1263165)), _1263167) = c_Groups_Ozero__class_Ozero(_1263165))], (44308 ^ _779854) ^ [_1665658, _1665660, _1665662] : [hAPP(hAPP(c_List_Odrop(_1665658), _1665660), _1665662) = c_List_Olist_ONil(_1665658), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665658)), _1665662)), _1665660)))], (30615 ^ _779854) ^ [_1332514, _1332516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332514), _1332516)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332514, _1332516) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332514), _1332516))], (38392 ^ _779854) ^ [_1508921, _1508923, _1508925, _1508927, _1508929, _1508931] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508921, _1508923)), hAPP(hAPP(c_Product__Type_OPair(_1508921, _1508923), _1508925), _1508927)), hAPP(hAPP(c_Product__Type_OSigma(_1508921, _1508923), _1508929), _1508931))), 38395 ^ _779854 : [(38398 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508923), _1508927), hAPP(_1508931, _1508925))))], (38396 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508921), _1508925), _1508929)))]]], (36235 ^ _779854) ^ [_1456044, _1456046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456046)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1456044), _1456046) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1456044, _1456046)))], (18475 ^ _779854) ^ [_1114671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114671), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24160 ^ _779854) ^ [_1217967, _1217969] : [24161 ^ _779854 : [(24164 ^ _779854) ^ [] : [_1217969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24162 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217967))]], -(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), _1217967), _1217969))))], (48788 ^ _779854) ^ [_1762720, _1762722, _1762724, _1762726, _1762728] : [-(_1762720 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1762722, _1762724, _1762726, _1762728), _1762720) = c_Lazy__Sequence_Ohb__bind(_1762722, _1762724, hAPP(_1762726, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1762720), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1762722, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1762724))), _1762728), _1762720)))], (14990 ^ _779854) ^ [_1045984, _1045986, _1045988, _1045990, _1045992] : [class_Groups_Ocomm__monoid__add(_1045984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045986), _1045988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045988), _1045990)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045984), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1045984), _1045992), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1045986), _1045988))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1045984), _1045992), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1045988), _1045990))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1045984), _1045992), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1045986), _1045990)))], (38007 ^ _779854) ^ [_1498541, _1498543, _1498545, _1498547, _1498549] : [-(hAPP(c_Fun_Othe__inv__into(_1498541, _1498543, _1498545, _1498547), _1498549) = c_HOL_OThe(_1498541, hAPP(hAPP(c_COMBS(_1498541, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498541), c_fconj), hAPP(hAPP(c_COMBC(_1498541, tc_fun(_1498541, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498541)), _1498545))), hAPP(hAPP(c_COMBC(_1498541, _1498543, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1498543, tc_fun(_1498543, tc_HOL_Obool), _1498541), c_fequal), _1498547)), _1498549))))], (14215 ^ _779854) ^ [_1030737, _1030739, _1030741] : [class_Lattices_Olattice(_1030737), hAPP(_1030739, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1030737), 14220 ^ [_1030737, _1030739, _1030741]), 14221 ^ [_1030737, _1030739, _1030741])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1030737), hAPP(_1030739, 14220 ^ [_1030737, _1030739, _1030741])), hAPP(_1030739, 14221 ^ [_1030737, _1030739, _1030741])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030737), _1030741)), -(_1030741 = c_Orderings_Obot__class_Obot(tc_fun(_1030737, tc_HOL_Obool))), -(hAPP(_1030739, c_Big__Operators_Olattice__class_OInf__fin(_1030737, _1030741)) = c_Big__Operators_Olattice__class_OInf__fin(_1030737, hAPP(c_Set_Oimage(_1030737, _1030737, _1030739), _1030741)))], (31308 ^ _779854) ^ [_1344340] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1344340)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1344340)))], (30035 ^ _779854) ^ [_1321559, _1321561] : [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), _1321559))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1321561))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1321559))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1321561)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1321559)))], (29977 ^ _779854) ^ [_1320262, _1320264, _1320266] : [class_Rings_Olinordered__idom(_1320262), 29980 ^ _779854 : [(29981 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320262), c_Groups_Ozero__class_Ozero(_1320262)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320262), hAPP(hAPP(c_Power_Opower__class_Opower(_1320262), _1320264), 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(_1320262), _1320266), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1320264 = c_Groups_Ozero__class_Ozero(_1320262), _1320266 = c_Groups_Ozero__class_Ozero(_1320262)], (29991 ^ _779854) ^ [] : [29992 ^ _779854 : [(29995 ^ _779854) ^ [] : [-(_1320266 = c_Groups_Ozero__class_Ozero(_1320262))], (29993 ^ _779854) ^ [] : [-(_1320264 = c_Groups_Ozero__class_Ozero(_1320262))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320262), c_Groups_Ozero__class_Ozero(_1320262)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320262), hAPP(hAPP(c_Power_Opower__class_Opower(_1320262), _1320264), 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(_1320262), _1320266), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (39063 ^ _779854) ^ [_1527736, _1527738] : [-(hAPP(c_Set_OPow(_1527736), _1527738) = hAPP(c_Set_OCollect(tc_fun(_1527736, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1527736, tc_HOL_Obool), tc_fun(_1527736, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1527736, tc_HOL_Obool))), _1527738)))], (46896 ^ _779854) ^ [_1723117, _1723119, _1723121] : [class_Orderings_Olinorder(_1723117), 46899 ^ _779854 : [(46906 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1723117, _1723121), -(c_List_Olinorder__class_Osorted(_1723117, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723117, _1723117, c_COMBI(_1723117)), _1723119), _1723121)))], (46900 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1723117, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723117, _1723117, c_COMBI(_1723117)), _1723119), _1723121)), -(c_List_Olinorder__class_Osorted(_1723117, _1723121))]]], (52453 ^ _779854) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (36008 ^ _779854) ^ [_1450925, _1450927, _1450929, _1450931, _1450933, _1450935, _1450937, _1450939] : [c_Finite__Set_Ofolding(_1450925, _1450927, _1450929, _1450931), -(hAPP(c_Fun_Ocomp(_1450927, _1450927, _1450933, hAPP(_1450929, _1450935)), hAPP(c_Fun_Ocomp(_1450927, _1450927, _1450933, hAPP(_1450929, _1450937)), _1450939)) = hAPP(c_Fun_Ocomp(_1450927, _1450927, _1450933, hAPP(_1450929, _1450937)), hAPP(c_Fun_Ocomp(_1450927, _1450927, _1450933, hAPP(_1450929, _1450935)), _1450939)))], (11001 ^ _779854) ^ [_968816, _968818, _968820, _968822] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968816, tc_HOL_Obool)), _968818), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968816, tc_HOL_Obool)), _968820), _968822)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_968816, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968816, tc_HOL_Obool)), _968818), _968820)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968816, tc_HOL_Obool)), _968818), _968822)))], (29541 ^ _779854) ^ [_1312685, _1312687] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1312685)), c_Int_OBit1(_1312687)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1312685), _1312687)))], (1260 ^ _779854) ^ [_798556, _798558] : [-(class_Rings_Ocomm__ring__1(_798556)), _798558 = _798556, class_Rings_Ocomm__ring__1(_798558)], (45591 ^ _779854) ^ [_1693292] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1693292)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1693292))], (48167 ^ _779854) ^ [_1749774, _1749776] : [class_Orderings_Olinorder(_1749774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1749774), _1749776)), 48175 ^ _779854 : [(48178 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1749774, 48174 ^ [_1749774, _1749776]))], (48180 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1749774), 48174 ^ [_1749774, _1749776])))], (48182 ^ _779854) ^ [_1750100] : [-(_1750100 = 48174 ^ [_1749774, _1749776]), hAPP(c_List_Oset(_1749774), _1750100) = _1749776, c_List_Olinorder__class_Osorted(_1749774, _1750100), hBOOL(hAPP(c_List_Odistinct(_1749774), _1750100))], (48176 ^ _779854) ^ [] : [-(hAPP(c_List_Oset(_1749774), 48174 ^ [_1749774, _1749776]) = _1749776)]]], (52261 ^ _779854) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (7069 ^ _779854) ^ [_895683, _895685] : [class_Lattices_Osemilattice__inf(_895683), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895683), _895685), _895685) = _895685)], (3368 ^ _779854) ^ [_830311, _830313] : [_830313 = _830311, -(c_Set_OPow(_830313) = c_Set_OPow(_830311))], (29365 ^ _779854) ^ [_1309566, _1309568] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1309566)), c_Int_OBit0(_1309568)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309566), _1309568)))], (18010 ^ _779854) ^ [_1105728, _1105730] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105728)), hAPP(c_Nat_OSuc, _1105730)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1105728), _1105730))], (29065 ^ _779854) ^ [_1304459] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1304459)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1304459)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1304459))], (52429 ^ _779854) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (48196 ^ _779854) ^ [_1750331, _1750333, _1750335, _1750337] : [48198 ^ _779854 : [(48201 ^ _779854) ^ [] : [hBOOL(hAPP(_1750335, 48197 ^ [_1750331, _1750333, _1750335, _1750337]))], (48199 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750331), 48197 ^ [_1750331, _1750333, _1750335, _1750337]), hAPP(c_List_Oset(_1750331), _1750333))))]], -(c_List_OtakeWhile(_1750331, _1750335, hAPP(hAPP(c_List_Oappend(_1750331), _1750333), _1750337)) = hAPP(hAPP(c_List_Oappend(_1750331), _1750333), c_List_OtakeWhile(_1750331, _1750335, _1750337)))], (12882 ^ _779854) ^ [_1006188, _1006190, _1006192, _1006194] : [hBOOL(hAPP(hAPP(_1006192, _1006190), _1006194)), -(hBOOL(hAPP(hAPP(c_member(_1006188), _1006190), c_SetInterval_Oord_OatMost(_1006188, _1006192, _1006194))))], (8530 ^ _779854) ^ [_922211, _922213, _922215, _922217] : [class_Orderings_Oorder(_922211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922211), _922213), _922215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922211), _922217), _922213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922211), _922217), _922215)))], (15426 ^ _779854) ^ [_1055158, _1055160, _1055162] : [class_Groups_Ogroup__add(_1055158), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1055158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055158), _1055160), _1055162)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055158), hAPP(c_Groups_Ouminus__class_Ouminus(_1055158), _1055162)), hAPP(c_Groups_Ouminus__class_Ouminus(_1055158), _1055160)))], (10547 ^ _779854) ^ [_959038, _959040] : [class_Groups_Oordered__ab__group__add(_959038), -(c_Fun_Oinj__on(_959038, _959038, c_Groups_Ouminus__class_Ouminus(_959038), _959040))], (30301 ^ _779854) ^ [_1326966, _1326968, _1326970, _1326972] : [class_Divides_Osemiring__div(_1326966), -(c_Divides_Odiv__class_Omod(_1326966, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326966), _1326968), _1326970), _1326972) = c_Divides_Odiv__class_Omod(_1326966, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326966), c_Divides_Odiv__class_Omod(_1326966, _1326968, _1326972)), c_Divides_Odiv__class_Omod(_1326966, _1326970, _1326972)), _1326972))], (45780 ^ _779854) ^ [_1697719, _1697721, _1697723, _1697725, _1697727] : [-(c_Enum_Oproduct(_1697719, _1697721, hAPP(hAPP(c_List_Olist_OCons(_1697719), _1697723), _1697725), _1697727) = hAPP(hAPP(c_List_Oappend(tc_prod(_1697719, _1697721)), hAPP(hAPP(c_List_Omap(_1697721, tc_prod(_1697719, _1697721)), hAPP(c_Product__Type_OPair(_1697719, _1697721), _1697723)), _1697727)), c_Enum_Oproduct(_1697719, _1697721, _1697725, _1697727)))], (11882 ^ _779854) ^ [_986350, _986352] : [-(_986352 = c_Orderings_Obot__class_Obot(tc_fun(_986350, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_986350), 11885 ^ [_986350, _986352]), _986352)))], (10751 ^ _779854) ^ [_963145, _963147, _963149, _963151] : [class_Groups_Oordered__ab__group__add(_963145), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963145), hAPP(hAPP(c_Orderings_Oord__class_Omin(_963145), _963147), _963149)), _963151) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_963145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963145), _963147), _963151)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963145), _963149), _963151)))], (5598 ^ _779854) ^ [_865506, _865508, _865510, _865512, _865514, _865516] : [-(c_COMBB(_865516, _865512, _865508) = c_COMBB(_865514, _865510, _865506)), _865516 = _865514, _865512 = _865510, _865508 = _865506], (28390 ^ _779854) ^ [_1293142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1293142)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293142), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37807 ^ _779854) ^ [] : [-(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))], (11149 ^ _779854) ^ [_972002, _972004, _972006] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972002), _972004)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_972002), hAPP(hAPP(c_Set_Oinsert(_972002), _972006), _972004))))], (43334 ^ _779854) ^ [_1643967, _1643969, _1643971, _1643973] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643967) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1643969), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643967)), hAPP(hAPP(c_List_Olist_OCons(_1643969), _1643971), _1643973)) = c_List_Olist_ONil(_1643969))], (29729 ^ _779854) ^ [_1315999] : [-(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)))), _1315999) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1315999)))], (30219 ^ _779854) ^ [_1325425, _1325427, _1325429] : [class_Divides_Osemiring__div(_1325425), -(c_Divides_Odiv__class_Omod(_1325425, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325425), _1325427), _1325429), _1325429) = c_Divides_Odiv__class_Omod(_1325425, _1325427, _1325429))], (6677 ^ _779854) ^ [_886946, _886948, _886950] : [class_Orderings_Oorder(_886946), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_886946, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_886946, _886948, _886950)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_886946), _886950)) = c_Orderings_Obot__class_Obot(tc_fun(_886946, tc_HOL_Obool)))], (45893 ^ _779854) ^ [_1700526, _1700528, _1700530] : [_1700526 = _1700528, -(c_List_Olist__all2(_1700530, _1700530, c_fequal, _1700526, _1700528))], (48409 ^ _779854) ^ [_1755145, _1755147, _1755149] : [-(c_List_Olist__ex(_1755145, _1755147, _1755149)), 48410 ^ _779854 : [(48411 ^ _779854) ^ [_1755210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755210), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755145)), _1755149))), hBOOL(hAPP(_1755147, hAPP(hAPP(c_List_Onth(_1755145), _1755149), _1755210)))]]], (10851 ^ _779854) ^ [_965383, _965385, _965387] : [class_Orderings_Olinorder(_965383), hBOOL(hAPP(c_Finite__Set_Ofinite(_965383), _965385)), -(_965385 = c_Orderings_Obot__class_Obot(tc_fun(_965383, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_965383), _965387)), -(_965387 = c_Orderings_Obot__class_Obot(tc_fun(_965383, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_965383, c_Orderings_Oord__class_Omin(_965383), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965383, tc_HOL_Obool)), _965385), _965387)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_965383), c_Big__Operators_Olattice_OInf__fin(_965383, c_Orderings_Oord__class_Omin(_965383), _965385)), c_Big__Operators_Olattice_OInf__fin(_965383, c_Orderings_Oord__class_Omin(_965383), _965387)))], (10175 ^ _779854) ^ [_951738, _951740, _951742, _951744] : [class_Orderings_Olinorder(_951738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951738), _951740), _951742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951738), hAPP(hAPP(c_Orderings_Oord__class_Omin(_951738), _951744), _951740)), _951742)))], (34715 ^ _779854) ^ [_1424785, _1424787] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424785)), hAPP(c_Nat_OSuc, _1424787)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1424785))), 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)), _1424787)))))], (14626 ^ _779854) ^ [_1039144, _1039146] : [class_Orderings_Olinorder(_1039144), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039144), _1039146)), -(c_Big__Operators_Olinorder__class_OMax(_1039144, _1039146) = hAPP(c_Finite__Set_Ofold1(_1039144, c_Orderings_Oord__class_Omax(_1039144)), _1039146))], (11007 ^ _779854) ^ [_969044, _969046, _969048, _969050] : [class_Orderings_Olinorder(_969044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969044), _969046), _969048)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969044, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_969044, _969046), _969050)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_969044, _969046), _969048)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_969044, _969048), _969050))], (47625 ^ _779854) ^ [_1737677, _1737679, _1737681, _1737683] : [hBOOL(hAPP(_1737677, _1737679)), -(c_List_OtakeWhile(_1737681, _1737677, hAPP(hAPP(c_List_Olist_OCons(_1737681), _1737679), _1737683)) = hAPP(hAPP(c_List_Olist_OCons(_1737681), _1737679), c_List_OtakeWhile(_1737681, _1737677, _1737683)))], (48022 ^ _779854) ^ [_1746325, _1746327, _1746329, _1746331, _1746333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1746325, _1746325)), hAPP(hAPP(c_Product__Type_OPair(_1746325, _1746325), _1746327), _1746329)), c_List_Omeasures(_1746325, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1746325, tc_Nat_Onat)), _1746331), _1746333)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1746331, _1746327)), hAPP(_1746331, _1746329)))), 48029 ^ _779854 : [(48032 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1746325, _1746325)), hAPP(hAPP(c_Product__Type_OPair(_1746325, _1746325), _1746327), _1746329)), c_List_Omeasures(_1746325, _1746333))))], (48030 ^ _779854) ^ [] : [-(hAPP(_1746331, _1746327) = hAPP(_1746331, _1746329))]]], (44989 ^ _779854) ^ [_1679656, _1679658, _1679660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679658)), _1679660))), -(c_List_Olast(_1679658, hAPP(hAPP(c_List_Odrop(_1679658), _1679656), _1679660)) = c_List_Olast(_1679658, _1679660))], (45744 ^ _779854) ^ [_1696948, _1696950, _1696952, _1696954] : [hBOOL(hAPP(c_List_Olistsp(_1696948, _1696950), hAPP(hAPP(c_List_Oappend(_1696948), _1696952), _1696954))), 45747 ^ _779854 : [(45750 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1696948, _1696950), _1696954)))], (45748 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1696948, _1696950), _1696952)))]]], (42565 ^ _779854) ^ [_1624225, _1624227, _1624229] : [_1624225 = _1624227, 42568 ^ _779854 : [(42571 ^ _779854) ^ [_1624373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624373), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624229)), _1624225))), -(hAPP(hAPP(c_List_Onth(_1624229), _1624225), _1624373) = hAPP(hAPP(c_List_Onth(_1624229), _1624227), _1624373))], (42569 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624229)), _1624225) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624229)), _1624227))]]], (40273 ^ _779854) ^ [_1564005] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40269 ^ [_1564005]), c_Int_OInteg)))], (31645 ^ _779854) ^ [_1349859] : [c_Nat__Transfer_Ois__nat(_1349859), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1349859)))], (37480 ^ _779854) ^ [_1485886, _1485888, _1485890, _1485892, _1485894] : [c_Equiv__Relations_Oequiv(_1485886, _1485888, _1485890), hBOOL(hAPP(hAPP(c_member(tc_prod(_1485886, _1485886)), hAPP(hAPP(c_Product__Type_OPair(_1485886, _1485886), _1485892), _1485894)), _1485890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1485886, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1485886, _1485886, _1485890), hAPP(hAPP(c_Set_Oinsert(_1485886), _1485892), c_Orderings_Obot__class_Obot(tc_fun(_1485886, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1485886, _1485886, _1485890), hAPP(hAPP(c_Set_Oinsert(_1485886), _1485894), c_Orderings_Obot__class_Obot(tc_fun(_1485886, tc_HOL_Obool)))))))], (20303 ^ _779854) ^ [_1145382, _1145384] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1145382), _1145384))), -(hAPP(c_Finite__Set_Ocard(_1145382), _1145384) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19247 ^ _779854) ^ [_1126929, _1126931, _1126933, _1126935] : [class_Rings_Oordered__ring(_1126929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126929), _1126931), _1126933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126929), _1126935), c_Groups_Ozero__class_Ozero(_1126929))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126929), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126929), _1126935), _1126933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126929), _1126935), _1126931))))], (37310 ^ _779854) ^ [] : [-(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))], (42707 ^ _779854) ^ [_1627811, _1627813, _1627815, _1627817] : [-(hBOOL(hAPP(hAPP(c_member(_1627811), _1627813), hAPP(c_List_Oset(_1627811), _1627815)))), hBOOL(hAPP(hAPP(c_member(_1627811), _1627813), hAPP(c_List_Oset(_1627811), c_List_Osublist(_1627811, _1627815, _1627817))))], (30513 ^ _779854) ^ [_1330844, _1330846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330844), 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, _1330846, _1330844)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39510 ^ _779854) ^ [_1544109, _1544111, _1544113, _1544115] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544109, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544111, _1544109), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1544111, _1544109), tc_HOL_Obool)), _1544113), _1544115))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1544109, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544111, _1544109), _1544113)), hAPP(c_Relation_ORange(_1544111, _1544109), _1544115)))))], (8698 ^ _779854) ^ [_924627, _924629, _924631] : [class_Orderings_Olinorder(_924627), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924627), _924629), _924631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924627), _924631), _924629)))], (44596 ^ _779854) ^ [_1671928, _1671930, _1671932] : [-(hAPP(c_List_Orotate(_1671928, _1671930), _1671932) = hAPP(hAPP(c_List_Oappend(_1671928), hAPP(hAPP(c_List_Odrop(_1671928), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1671930, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671928)), _1671932))), _1671932)), hAPP(hAPP(c_List_Otake(_1671928), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1671930, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671928)), _1671932))), _1671932)))], (37490 ^ _779854) ^ [_1486167, _1486169, _1486171, _1486173, _1486175] : [c_Equiv__Relations_Oequiv(_1486167, _1486169, _1486171), hBOOL(hAPP(hAPP(c_member(_1486167), _1486173), _1486169)), hBOOL(hAPP(hAPP(c_member(_1486167), _1486175), _1486169)), 37501 ^ _779854 : [(37508 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486167, _1486167)), hAPP(hAPP(c_Product__Type_OPair(_1486167, _1486167), _1486173), _1486175)), _1486171)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486167), hAPP(hAPP(c_Set_Oinsert(_1486167), _1486173), c_Orderings_Obot__class_Obot(tc_fun(_1486167, tc_HOL_Obool)))), _1486171) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486167), hAPP(hAPP(c_Set_Oinsert(_1486167), _1486175), c_Orderings_Obot__class_Obot(tc_fun(_1486167, tc_HOL_Obool)))), _1486171))], (37502 ^ _779854) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486167), hAPP(hAPP(c_Set_Oinsert(_1486167), _1486173), c_Orderings_Obot__class_Obot(tc_fun(_1486167, tc_HOL_Obool)))), _1486171) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486167), hAPP(hAPP(c_Set_Oinsert(_1486167), _1486175), c_Orderings_Obot__class_Obot(tc_fun(_1486167, tc_HOL_Obool)))), _1486171), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486167, _1486167)), hAPP(hAPP(c_Product__Type_OPair(_1486167, _1486167), _1486173), _1486175)), _1486171)))]]], (36930 ^ _779854) ^ [_1471691, _1471693, _1471695, _1471697] : [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), _1471691), _1471693)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1471695), _1471697))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1471691), _1471697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1471695), _1471693))], (36746 ^ _779854) ^ [_1467269, _1467271, _1467273, _1467275, _1467277, _1467279, _1467281] : [-(hAPP(c_Product__Type_Oapsnd(_1467269, _1467271, _1467273, _1467275), hAPP(c_Product__Type_Oapfst(_1467277, _1467273, _1467269, _1467279), _1467281)) = hAPP(hAPP(c_Product__Type_OPair(_1467273, _1467271), hAPP(_1467279, hAPP(c_Product__Type_Ofst(_1467277, _1467269), _1467281))), hAPP(_1467275, hAPP(c_Product__Type_Osnd(_1467277, _1467269), _1467281))))], (45085 ^ _779854) ^ [_1681672, _1681674, _1681676, _1681678, _1681680, _1681682] : [-(hAPP(hAPP(c_List_Ozip(_1681672, _1681674), hAPP(hAPP(c_List_Omap(_1681676, _1681672), _1681678), _1681680)), _1681682) = hAPP(hAPP(c_List_Omap(tc_prod(_1681676, _1681674), tc_prod(_1681672, _1681674)), hAPP(c_Product__Type_Oprod_Oprod__case(_1681676, _1681674, tc_prod(_1681672, _1681674)), hAPP(hAPP(c_COMBB(_1681672, tc_fun(_1681674, tc_prod(_1681672, _1681674)), _1681676), c_Product__Type_OPair(_1681672, _1681674)), _1681678))), hAPP(hAPP(c_List_Ozip(_1681676, _1681674), _1681680), _1681682)))], (41072 ^ _779854) ^ [_1583706, _1583708] : [-(c_Transitive__Closure_Otrancl(_1583706, _1583708) = hAPP(hAPP(c_Relation_Orel__comp(_1583706, _1583706, _1583706), c_Transitive__Closure_Ortrancl(_1583706, _1583708)), _1583708))], (2978 ^ _779854) ^ [_824216, _824218] : [_824218 = _824216, -(c_Nitpick_Odenom(_824218) = c_Nitpick_Odenom(_824216))], (42913 ^ _779854) ^ [_1634324, _1634326, _1634328, _1634330, _1634332, _1634334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634324, _1634326)), hAPP(hAPP(c_Product__Type_OPair(_1634324, _1634326), _1634328), _1634330)), hAPP(c_List_Oset(tc_prod(_1634324, _1634326)), hAPP(hAPP(c_List_Ozip(_1634324, _1634326), _1634332), _1634334)))), -(hBOOL(hAPP(hAPP(c_member(_1634324), _1634328), hAPP(c_List_Oset(_1634324), _1634332))))], (2580 ^ _779854) ^ [_818071, _818073, _818075, _818077] : [-(c_Nitpick_Onorm__frac(_818077, _818073) = c_Nitpick_Onorm__frac(_818075, _818071)), _818077 = _818075, _818073 = _818071], (43436 ^ _779854) ^ [_1645725, _1645727] : [-(c_List_Osublist(_1645725, c_List_Olist_ONil(_1645725), _1645727) = c_List_Olist_ONil(_1645725))], (3404 ^ _779854) ^ [_830843, _830845, _830847, _830849, _830851, _830853] : [-(c_Finite__Set_Ofold(_830853, _830849, _830845) = c_Finite__Set_Ofold(_830851, _830847, _830843)), _830853 = _830851, _830849 = _830847, _830845 = _830843], (18777 ^ _779854) ^ [_1119152] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1119152)], (32291 ^ _779854) ^ [_1360862] : [c_Code__Numeral_OSuc__code__numeral(_1360862) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (12628 ^ _779854) ^ [_1000800, _1000802, _1000804, _1000806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000800, tc_HOL_Obool)), _1000802), hAPP(hAPP(c_Set_Oinsert(_1000800), _1000804), _1000806))), 12631 ^ _779854 : [(12638 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1000800), _1000804), _1000802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000800, tc_HOL_Obool)), _1000802), _1000806)))], (12632 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1000800), _1000804), _1000802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000800, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1000800, tc_HOL_Obool)), _1000802), hAPP(hAPP(c_Set_Oinsert(_1000800), _1000804), c_Orderings_Obot__class_Obot(tc_fun(_1000800, tc_HOL_Obool))))), _1000806)))]]], (9774 ^ _779854) ^ [_943790, _943792, _943794, _943796] : [class_Orderings_Olinorder(_943790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943790), _943792), _943794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943790), _943792), hAPP(hAPP(c_Orderings_Oord__class_Omax(_943790), _943796), _943794))))], (31326 ^ _779854) ^ [_1344590, _1344592] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1344590), _1344592) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 31327 ^ _779854 : [(31334 ^ _779854) ^ [] : [_1344590 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1344592 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (31328 ^ _779854) ^ [] : [_1344590 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1344592 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (27895 ^ _779854) ^ [_1284488, _1284490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284490)), 27902 ^ _779854 : [(27909 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284488), _1284490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1284488)), hAPP(c_Int_Onat, _1284490))))], (27903 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1284488)), hAPP(c_Int_Onat, _1284490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284488), _1284490)))]]], (42235 ^ _779854) ^ [_1614292, _1614294, _1614296, _1614298] : [-(c_List_Olist_Olist__size(_1614292, _1614294, hAPP(hAPP(c_List_Olist_OCons(_1614292), _1614296), _1614298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1614294, _1614296)), c_List_Olist_Olist__size(_1614292, _1614294, _1614298))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9859 ^ _779854) ^ [_945732, _945734, _945736, _945738] : [hAPP(c_Set_Oimage(_945732, _945734, _945736), c_Orderings_Otop__class_Otop(tc_fun(_945732, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_945734, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945734, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945734, tc_HOL_Obool)), hAPP(c_Set_Oimage(_945732, _945734, _945736), _945738))), hAPP(c_Set_Oimage(_945732, _945734, _945736), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945732, tc_HOL_Obool)), _945738)))))], (27751 ^ _779854) ^ [_1281979] : [class_Int_Onumber__ring(_1281979), -(c_Int_Oiszero(_1281979, hAPP(c_Int_Onumber__class_Onumber__of(_1281979), c_Int_OPls)))], (45819 ^ _779854) ^ [_1698831, _1698833, _1698835, _1698837, _1698839, _1698841, _1698843] : [c_List_Olist__all2(_1698831, _1698833, _1698835, _1698837, hAPP(hAPP(c_List_Omap(_1698839, _1698833), _1698841), _1698843)), -(c_List_Olist__all2(_1698831, _1698839, hAPP(hAPP(c_COMBC(_1698831, tc_fun(_1698839, _1698833), tc_fun(_1698839, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1698833, tc_HOL_Obool), tc_fun(tc_fun(_1698839, _1698833), tc_fun(_1698839, tc_HOL_Obool)), _1698831), c_COMBB(_1698833, tc_HOL_Obool, _1698839)), _1698835)), _1698841), _1698837, _1698843))], (24915 ^ _779854) ^ [_1232198, _1232200, _1232202, _1232204] : [class_Fields_Ofield__inverse__zero(_1232198), class_Int_Onumber(_1232198), 24922 ^ _779854 : [(24923 ^ _779854) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232198), _1232200), hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202)) = _1232204, 24926 ^ _779854 : [(24933 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202) = c_Groups_Ozero__class_Ozero(_1232198), -(_1232204 = c_Groups_Ozero__class_Ozero(_1232198))], (24927 ^ _779854) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202) = c_Groups_Ozero__class_Ozero(_1232198)), -(_1232200 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232198), _1232204), hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202)))]]], (24939 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232198), _1232200), hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202)) = _1232204), 24942 ^ _779854 : [(24945 ^ _779854) ^ [] : [_1232200 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232198), _1232204), hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202))], (24943 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202) = c_Groups_Ozero__class_Ozero(_1232198)]], 24946 ^ _779854 : [(24949 ^ _779854) ^ [] : [_1232204 = c_Groups_Ozero__class_Ozero(_1232198)], (24947 ^ _779854) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1232198), _1232202) = c_Groups_Ozero__class_Ozero(_1232198))]]]]], (34787 ^ _779854) ^ [_1426416, _1426418] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426416), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426418)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426416)) = 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), _1426418), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426416)))), 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)))], (33307 ^ _779854) ^ [_1385028, _1385030, _1385032, _1385034, _1385036] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385028, tc_fun(_1385030, tc_HOL_Obool)), _1385032), _1385034), _1385036))), 33308 ^ _779854 : [(33309 ^ _779854) ^ [_1385100] : [hBOOL(hAPP(hAPP(c_member(_1385028), _1385100), _1385032)), hBOOL(hAPP(hAPP(_1385034, _1385100), _1385036))]]], (5715 ^ _779854) ^ [_870135, _870137] : [class_Orderings_Opreorder(_870135), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870135), _870137), _870137)))], (20 ^ _779854) ^ [_780114, _780116, _780118, _780120, _780122, _780124] : [-(c_Orderings_Oorder__class_Ostrict__mono(_780122, _780118, _780114)), c_Orderings_Oorder__class_Ostrict__mono(_780124, _780120, _780116), _780124 = _780122, _780120 = _780118, _780116 = _780114], (28308 ^ _779854) ^ [_1291721] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1291721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14195 ^ _779854) ^ [_1030394, _1030396, _1030398, _1030400, _1030402, _1030404] : [c_Fun_Oinj__on(_1030394, _1030396, _1030398, _1030400), -(hBOOL(hAPP(hAPP(c_member(_1030396), _1030402), hAPP(c_Set_Oimage(_1030394, _1030396, _1030398), _1030400)))), -(c_Fun_Oinj__on(_1030394, _1030396, c_Fun_Ofun__upd(_1030394, _1030396, _1030398, _1030404, _1030402), _1030400))], (16830 ^ _779854) ^ [_1083290, _1083292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083290), _1083292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1083290), _1083292)))], (37964 ^ _779854) ^ [_1497451, _1497453, _1497455, _1497457, _1497459, _1497461] : [c_Typedef_Otype__definition(_1497451, _1497453, _1497455, _1497457, _1497459), hBOOL(hAPP(hAPP(c_member(_1497453), _1497461), _1497459)), -(hAPP(_1497455, hAPP(_1497457, _1497461)) = _1497461)], (29239 ^ _779854) ^ [_1307338, _1307340] : [class_Int_Onumber__ring(_1307338), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1307338), c_Groups_Oone__class_Oone(_1307338)), hAPP(c_Int_Onumber__class_Onumber__of(_1307338), _1307340)) = hAPP(c_Int_Onumber__class_Onumber__of(_1307338), 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), _1307340))))], (32067 ^ _779854) ^ [_1356830, _1356832] : [c_Code__Numeral_OSuc__code__numeral(_1356830) = c_Code__Numeral_OSuc__code__numeral(_1356832), -(_1356830 = _1356832)], (50794 ^ _779854) ^ [_1807051, _1807053, _1807055] : [c_Fun_Oinj__on(_1807051, _1807053, _1807055, c_Orderings_Otop__class_Otop(tc_fun(_1807051, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1807051, _1807053, _1807055), c_Orderings_Otop__class_Otop(tc_fun(_1807051, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1807053, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1807051, _1807053, _1807055, c_Orderings_Otop__class_Otop(tc_fun(_1807051, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1807053, tc_HOL_Obool))))], (20487 ^ _779854) ^ [_1148432, _1148434] : [hAPP(_1148432, 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), _1148432), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1148434)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1148432), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1148434)))], (52259 ^ _779854) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (44546 ^ _779854) ^ [_1670941, _1670943, _1670945] : [_1670945 = c_List_Olist_ONil(_1670941), -(hAPP(c_List_Orotate(_1670941, _1670943), _1670945) = c_List_Olist_ONil(_1670941))], (8502 ^ _779854) ^ [_921745, _921747, _921749, _921751] : [class_Orderings_Oorder(_921745), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921745), _921747), _921749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921745), _921751), _921747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921745), _921751), _921749)))], (45234 ^ _779854) ^ [_1685758, _1685760, _1685762, _1685764, _1685766] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1685758), tc_List_Olist(_1685760), tc_List_Olist(_1685762), hAPP(c_List_Omap(_1685758, _1685760), _1685764)), hAPP(c_List_Omap(_1685762, _1685758), _1685766)) = hAPP(c_List_Omap(_1685762, _1685760), hAPP(c_Fun_Ocomp(_1685758, _1685760, _1685762, _1685764), _1685766)))], (17981 ^ _779854) ^ [_1105205, _1105207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105205)), _1105207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1105205), _1105207)))], (4326 ^ _779854) ^ [_845534, _845536, _845538, _845540, _845542, _845544, _845546, _845548, _845550, _845552] : [-(c_Predicate_Opred__comp(_845552, _845548, _845544, _845540, _845536) = c_Predicate_Opred__comp(_845550, _845546, _845542, _845538, _845534)), _845552 = _845550, _845548 = _845546, _845544 = _845542, _845540 = _845538, _845536 = _845534], (24529 ^ _779854) ^ [_1224905, _1224907, _1224909] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224907), _1224909)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224905), _1224907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224905), _1224909)))], (23914 ^ _779854) ^ [_1213541, _1213543, _1213545, _1213547] : [class_Rings_Olinordered__semidom(_1213541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213543), _1213545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213541), c_Groups_Ozero__class_Ozero(_1213541)), _1213547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213541), _1213547), c_Groups_Oone__class_Oone(_1213541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213541), hAPP(hAPP(c_Power_Opower__class_Opower(_1213541), _1213547), _1213545)), hAPP(hAPP(c_Power_Opower__class_Opower(_1213541), _1213547), _1213543))))], (17857 ^ _779854) ^ [_1103262, _1103264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103262), _1103264))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103262), hAPP(c_Nat_OSuc, _1103264))), -(_1103264 = _1103262)], (21669 ^ _779854) ^ [_1170932, _1170934] : [class_Int_Oring__char__0(_1170932), hBOOL(hAPP(hAPP(c_member(_1170932), _1170934), c_Int_Oring__1__class_OInts(_1170932))), 21676 ^ _779854 : [(21683 ^ _779854) ^ [] : [_1170934 = c_Groups_Ozero__class_Ozero(_1170932), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170932), _1170934), _1170934) = c_Groups_Ozero__class_Ozero(_1170932))], (21677 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170932), _1170934), _1170934) = c_Groups_Ozero__class_Ozero(_1170932), -(_1170934 = c_Groups_Ozero__class_Ozero(_1170932))]]], (50314 ^ _779854) ^ [_1796159, _1796161] : [c_Equiv__Relations_Opart__equivp(_1796159, _1796161), 50318 ^ _779854 : [(50323 ^ _779854) ^ [] : [-(c_Predicate_Otransp(_1796159, _1796161))], (50321 ^ _779854) ^ [] : [-(c_Predicate_Osymp(_1796159, _1796161))], (50319 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1796161, 50317 ^ [_1796159, _1796161]), 50317 ^ [_1796159, _1796161])))]]], (38290 ^ _779854) ^ [_1505564, _1505566, _1505568, _1505570, _1505572] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505564, _1505566), _1505568), hAPP(hAPP(c_COMBS(_1505564, tc_fun(_1505566, tc_HOL_Obool), tc_fun(_1505566, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505566, tc_HOL_Obool), tc_fun(tc_fun(_1505566, tc_HOL_Obool), tc_fun(_1505566, tc_HOL_Obool)), _1505564), c_Groups_Ominus__class_Ominus(tc_fun(_1505566, tc_HOL_Obool))), _1505570)), _1505572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1505564, _1505566), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505564, _1505566), _1505568), _1505570)), hAPP(hAPP(c_Product__Type_OSigma(_1505564, _1505566), _1505568), _1505572)))], (26003 ^ _779854) ^ [_1252297, _1252299, _1252301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252297)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1252299), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1252301)), 26010 ^ _779854 : [(26011 ^ _779854) ^ [_1252505] : [26013 ^ _779854 : [(26019 ^ _779854) ^ [] : [-(_1252505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26015 ^ [_1252297, _1252299, _1252301, _1252505]), 26012 ^ [_1252297, _1252299, _1252301, _1252505]))], (26017 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26015 ^ [_1252297, _1252299, _1252301, _1252505]), _1252301)))], (26014 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26012 ^ [_1252297, _1252299, _1252301, _1252505]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1252297))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252299), _1252505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1252505), _1252297))))]]], (26957 ^ _779854) ^ [_1268805, _1268807, _1268809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268805), _1268807)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1268809), 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), _1268807), _1268809)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268805), _1268809))))], (29559 ^ _779854) ^ [_1313050] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1313050))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1313050)))))], (10659 ^ _779854) ^ [_961548, _961550, _961552, _961554, _961556] : [class_Groups_Oordered__ab__group__add(_961548), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961548), _961550), _961552) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961548), _961554), _961556), 10666 ^ _779854 : [(10673 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961548), _961554), _961556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961548), _961550), _961552)))], (10667 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961548), _961550), _961552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961548), _961554), _961556)))]]], (41048 ^ _779854) ^ [_1582849, _1582851, _1582853, _1582855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582849, _1582849)), hAPP(hAPP(c_Product__Type_OPair(_1582849, _1582849), _1582853), _1582855)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582849, _1582849), tc_HOL_Obool)), _1582851), c_Relation_OId(_1582849)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1582849, tc_fun(_1582849, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1582849, tc_fun(tc_prod(_1582849, _1582849), tc_HOL_Obool), tc_fun(_1582849, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582849, tc_fun(tc_fun(tc_prod(_1582849, _1582849), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1582849, _1582849), tc_HOL_Obool), tc_fun(_1582849, tc_HOL_Obool)), _1582849), c_COMBC(_1582849, tc_fun(tc_prod(_1582849, _1582849), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582849, tc_prod(_1582849, _1582849)), tc_fun(_1582849, tc_fun(tc_fun(tc_prod(_1582849, _1582849), tc_HOL_Obool), tc_HOL_Obool)), _1582849), hAPP(c_COMBB(tc_prod(_1582849, _1582849), tc_fun(tc_fun(tc_prod(_1582849, _1582849), tc_HOL_Obool), tc_HOL_Obool), _1582849), c_member(tc_prod(_1582849, _1582849)))), c_Product__Type_OPair(_1582849, _1582849)))), _1582851)), c_fequal), _1582853), _1582855)))], (19087 ^ _779854) ^ [_1124039, _1124041, _1124043] : [class_Groups_Oordered__comm__monoid__add(_1124039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124039), c_Groups_Ozero__class_Ozero(_1124039)), _1124041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124039), c_Groups_Ozero__class_Ozero(_1124039)), _1124043)), 19098 ^ _779854 : [(19107 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124039), _1124041), _1124043) = c_Groups_Ozero__class_Ozero(_1124039)), _1124041 = c_Groups_Ozero__class_Ozero(_1124039), _1124043 = c_Groups_Ozero__class_Ozero(_1124039)], (19099 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124039), _1124041), _1124043) = c_Groups_Ozero__class_Ozero(_1124039), 19102 ^ _779854 : [(19105 ^ _779854) ^ [] : [-(_1124043 = c_Groups_Ozero__class_Ozero(_1124039))], (19103 ^ _779854) ^ [] : [-(_1124041 = c_Groups_Ozero__class_Ozero(_1124039))]]]]], (43370 ^ _779854) ^ [_1644662] : [-(hBOOL(hAPP(c_List_Odistinct(_1644662), c_List_Olist_ONil(_1644662))))], (3320 ^ _779854) ^ [_829563, _829565, _829567, _829569] : [-(c_List_Olistsp(_829569, _829565) = c_List_Olistsp(_829567, _829563)), _829569 = _829567, _829565 = _829563], (21090 ^ _779854) ^ [_1159417, _1159419, _1159421] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1159417), _1159419)), 21093 ^ _779854 : [(21113 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1159417, tc_Nat_Onat), _1159421), _1159419) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 21114 ^ _779854 : [(21115 ^ _779854) ^ [_1159898] : [hBOOL(hAPP(hAPP(c_member(_1159417), _1159898), _1159419)), hAPP(_1159421, _1159898) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21123 ^ _779854 : [(21128 ^ _779854) ^ [] : [hAPP(_1159421, 21122 ^ [_1159417, _1159419, _1159421, _1159898]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21126 ^ _779854) ^ [] : [_1159898 = 21122 ^ [_1159417, _1159419, _1159421, _1159898]], (21124 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1159417), 21122 ^ [_1159417, _1159419, _1159421, _1159898]), _1159419)))]]]]], (21094 ^ _779854) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1159417, tc_Nat_Onat), _1159421), _1159419) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21098 ^ _779854 : [(21103 ^ _779854) ^ [_1159737] : [hBOOL(hAPP(hAPP(c_member(_1159417), _1159737), _1159419)), -(21097 ^ [_1159417, _1159419, _1159421] = _1159737), -(hAPP(_1159421, _1159737) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21101 ^ _779854) ^ [] : [-(hAPP(_1159421, 21097 ^ [_1159417, _1159419, _1159421]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21099 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1159417), 21097 ^ [_1159417, _1159419, _1159421]), _1159419)))]]]]], (45324 ^ _779854) ^ [_1687762, _1687764, _1687766] : [c_Fun_Oinj__on(_1687762, _1687764, _1687766, c_Orderings_Otop__class_Otop(tc_fun(_1687762, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1687762), tc_List_Olist(_1687764), hAPP(c_List_Omap(_1687762, _1687764), _1687766), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1687762), tc_HOL_Obool))))], (2322 ^ _779854) ^ [_813910, _813912, _813914, _813916, _813918, _813920, _813922, _813924, _813926, _813928] : [-(c_Nitpick_Opair__box_Opair__box__case(_813928, _813924, _813920, _813916, _813912) = c_Nitpick_Opair__box_Opair__box__case(_813926, _813922, _813918, _813914, _813910)), _813928 = _813926, _813924 = _813922, _813920 = _813918, _813916 = _813914, _813912 = _813910], (15020 ^ _779854) ^ [_1046704, _1046706, _1046708, _1046710, _1046712, _1046714] : [class_Rings_Oring(_1046704), 15023 ^ _779854 : [(15030 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046704), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046704), _1046706), _1046712)), _1046708)), _1046710) = _1046714, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046704), _1046706), _1046708)), _1046710) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046704), _1046712), _1046708)), _1046714))], (15024 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046704), _1046706), _1046708)), _1046710) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046704), _1046712), _1046708)), _1046714), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046704), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046704), _1046706), _1046712)), _1046708)), _1046710) = _1046714)]]], (31468 ^ _779854) ^ [_1347085, _1347087] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1347085)))), 31471 ^ _779854 : [(31478 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1347087)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1347085), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1347087)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1347085), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1347087))))], (31472 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1347087))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1347085), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1347087)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1347085))]]], (50660 ^ _779854) ^ [_1804099, _1804101, _1804103, _1804105, _1804107, _1804109] : [c_Fun_Obij__betw(_1804099, _1804101, _1804103, _1804105, _1804107), hBOOL(hAPP(hAPP(c_member(_1804099), _1804109), _1804105)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1804101, _1804099, _1804107, c_Hilbert__Choice_Oinv__into(_1804099, _1804101, _1804105, _1804103)), _1804109) = hAPP(_1804103, _1804109))], (12522 ^ _779854) ^ [_998673, _998675, _998677, _998679, _998681, _998683, _998685, _998687] : [c_Finite__Set_Ofolding__image__simple(_998673, _998675, _998677, _998679, _998681, _998683), hBOOL(hAPP(c_Finite__Set_Ofinite(_998675), _998685)), hBOOL(hAPP(hAPP(c_member(_998675), _998687), _998685)), -(hAPP(_998683, _998685) = hAPP(hAPP(_998677, hAPP(_998681, _998687)), hAPP(_998683, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998675, tc_HOL_Obool)), _998685), hAPP(hAPP(c_Set_Oinsert(_998675), _998687), c_Orderings_Obot__class_Obot(tc_fun(_998675, tc_HOL_Obool)))))))], (52655 ^ _779854) ^ [_1838529] : [hBOOL(hAPP(c_fNot, _1838529)), hBOOL(_1838529)], (39617 ^ _779854) ^ [_1548498, _1548500] : [-(c_HOL_OThe(_1548498, hAPP(hAPP(c_COMBC(_1548498, _1548498, tc_HOL_Obool), c_fequal), _1548500)) = _1548500)], (42986 ^ _779854) ^ [_1636036, _1636038] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1636036), _1636038) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1636036, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1636038), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45394 ^ _779854) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (29439 ^ _779854) ^ [_1310908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310908), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1310908)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43125 ^ _779854) ^ [_1639054, _1639056, _1639058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639054), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639056)), _1639058))), -(hAPP(hAPP(c_List_Otake(_1639056), _1639054), c_List_Obutlast(_1639056, _1639058)) = hAPP(hAPP(c_List_Otake(_1639056), _1639054), _1639058))], (46226 ^ _779854) ^ [_1707416, _1707418, _1707420, _1707422, _1707424] : [c_Fun_Oinj__on(_1707416, _1707418, _1707420, c_Orderings_Otop__class_Otop(tc_fun(_1707416, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1707416, _1707418), _1707420), hAPP(c_List_OremoveAll(_1707416, _1707422), _1707424)) = hAPP(c_List_OremoveAll(_1707418, hAPP(_1707420, _1707422)), hAPP(hAPP(c_List_Omap(_1707416, _1707418), _1707420), _1707424)))], (3594 ^ _779854) ^ [_833862, _833864, _833866, _833868] : [-(c_List_Olinorder__class_Osorted__list__of__set(_833868, _833864) = c_List_Olinorder__class_Osorted__list__of__set(_833866, _833862)), _833868 = _833866, _833864 = _833862], (526 ^ _779854) ^ [_787729, _787731, _787733, _787735, _787737, _787739, _787741, _787743] : [-(c_List_Olistrelp(_787741, _787737, _787733, _787729)), c_List_Olistrelp(_787743, _787739, _787735, _787731), _787743 = _787741, _787739 = _787737, _787735 = _787733, _787731 = _787729], (15166 ^ _779854) ^ [_1049616, _1049618, _1049620, _1049622, _1049624, _1049626] : [class_Rings_Oordered__ring(_1049616), 15169 ^ _779854 : [(15176 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049616), _1049622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049616), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049616), _1049624), _1049618)), _1049620)), _1049626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049616), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049616), _1049618), _1049620)), _1049622)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049616), _1049624), _1049620)), _1049626))))], (15170 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049616), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049616), _1049618), _1049620)), _1049622)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049616), _1049624), _1049620)), _1049626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049616), _1049622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049616), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049616), _1049624), _1049618)), _1049620)), _1049626))))]]], (45627 ^ _779854) ^ [_1693946] : [-(_1693946 = 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, _1693946)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1693946))))], (7509 ^ _779854) ^ [_903637, _903639] : [class_Lattices_Obounded__lattice__top(_903637), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903637), c_Orderings_Otop__class_Otop(_903637)), _903639) = c_Orderings_Otop__class_Otop(_903637))], (22523 ^ _779854) ^ [_1186832, _1186834, _1186836, _1186838] : [class_Fields_Ofield__inverse__zero(_1186832), 22526 ^ _779854 : [(22527 ^ _779854) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186832), _1186834), _1186836) = _1186838, 22530 ^ _779854 : [(22537 ^ _779854) ^ [] : [_1186836 = c_Groups_Ozero__class_Ozero(_1186832), -(_1186838 = c_Groups_Ozero__class_Ozero(_1186832))], (22531 ^ _779854) ^ [] : [-(_1186836 = c_Groups_Ozero__class_Ozero(_1186832)), -(_1186834 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186832), _1186838), _1186836))]]], (22543 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186832), _1186834), _1186836) = _1186838), 22546 ^ _779854 : [(22549 ^ _779854) ^ [] : [_1186834 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186832), _1186838), _1186836)], (22547 ^ _779854) ^ [] : [_1186836 = c_Groups_Ozero__class_Ozero(_1186832)]], 22550 ^ _779854 : [(22553 ^ _779854) ^ [] : [_1186838 = c_Groups_Ozero__class_Ozero(_1186832)], (22551 ^ _779854) ^ [] : [-(_1186836 = c_Groups_Ozero__class_Ozero(_1186832))]]]]], (32333 ^ _779854) ^ [_1361857, _1361859] : [class_Groups_Oordered__ab__group__add__abs(_1361857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361857), _1361859), c_Groups_Ozero__class_Ozero(_1361857))), -(hAPP(c_Groups_Oabs__class_Oabs(_1361857), _1361859) = hAPP(c_Groups_Ouminus__class_Ouminus(_1361857), _1361859))], (29605 ^ _779854) ^ [_1313825, _1313827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1313825), _1313827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1313825)), c_Int_OBit0(_1313827))))], (14107 ^ _779854) ^ [_1028895, _1028897, _1028899, _1028901, _1028903] : [hAPP(_1028895, _1028897) = _1028899, -(c_Fun_Ofun__upd(_1028901, _1028903, _1028895, _1028897, _1028899) = _1028895)], (10031 ^ _779854) ^ [_949216, _949218, _949220, _949222] : [class_Orderings_Olinorder(_949216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949216), _949218), hAPP(hAPP(c_Orderings_Oord__class_Omin(_949216), _949220), _949222))), 10038 ^ _779854 : [(10041 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949216), _949218), _949222)))], (10039 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949216), _949218), _949220)))]]], (18048 ^ _779854) ^ [_1106413, _1106415] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106413), _1106415) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 18051 ^ _779854 : [(18054 ^ _779854) ^ [] : [-(_1106415 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18052 ^ _779854) ^ [] : [-(_1106413 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (42657 ^ _779854) ^ [_1626612, _1626614, _1626616] : [-(hAPP(c_List_Oset(_1626612), c_List_Osublist(_1626612, _1626614, _1626616)) = hAPP(c_Set_OCollect(_1626612), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1626612), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1626612, 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)), _1626612), 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)), _1626612), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1626612, tc_fun(tc_Nat_Onat, _1626612), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626612, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1626612), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1626612), c_COMBB(_1626612, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1626612), _1626614))))), 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(_1626612)), _1626614)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1626616))))))], (4508 ^ _779854) ^ [_848497, _848499] : [_848499 = _848497, -(c_List_Omember(_848499) = c_List_Omember(_848497))], (18805 ^ _779854) ^ [_1119464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119464), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41517 ^ _779854) ^ [_1594435, _1594437, _1594439, _1594441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594435, _1594435)), hAPP(hAPP(c_Product__Type_OPair(_1594435, _1594435), _1594437), _1594439)), hAPP(c_Relation_Oconverse(_1594435, _1594435), c_Transitive__Closure_Otrancl(_1594435, _1594441)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594435, _1594435)), hAPP(hAPP(c_Product__Type_OPair(_1594435, _1594435), _1594437), _1594439)), c_Transitive__Closure_Otrancl(_1594435, hAPP(c_Relation_Oconverse(_1594435, _1594435), _1594441)))))], (7075 ^ _779854) ^ [_895774, _895776] : [class_Lattices_Osemilattice__inf(_895774), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895774), _895776), _895776) = _895776)], (42725 ^ _779854) ^ [_1628273, _1628275, _1628277] : [42727 ^ _779854 : [(42730 ^ _779854) ^ [] : [hBOOL(hAPP(_1628277, 42726 ^ [_1628273, _1628275, _1628277]))], (42728 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1628273), 42726 ^ [_1628273, _1628275, _1628277]), hAPP(c_List_Oset(_1628273), _1628275))))]], 42731 ^ _779854 : [(42732 ^ _779854) ^ [_1628457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628457), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628273)), _1628275))), -(hBOOL(hAPP(_1628277, hAPP(hAPP(c_List_Onth(_1628273), _1628275), _1628457))))]]], (45105 ^ _779854) ^ [_1682475, _1682477, _1682479] : [-(hAPP(hAPP(c_List_Omap(_1682475, _1682477), _1682479), c_List_Olist_ONil(_1682475)) = c_List_Olist_ONil(_1682477))], (44981 ^ _779854) ^ [_1679555, _1679557] : [-(_1679555 = c_List_Olist_ONil(_1679557)), -(hBOOL(hAPP(hAPP(c_member(_1679557), c_List_Olast(_1679557, _1679555)), hAPP(c_List_Oset(_1679557), _1679555))))], (19163 ^ _779854) ^ [_1125331, _1125333, _1125335] : [class_Rings_Oordered__cancel__semiring(_1125331), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125331), _1125333), _1125335)), c_Groups_Ozero__class_Ozero(_1125331)))), 19168 ^ _779854 : [(19175 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125331), _1125333), c_Groups_Ozero__class_Ozero(_1125331))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125331), c_Groups_Ozero__class_Ozero(_1125331)), _1125335))], (19169 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125331), c_Groups_Ozero__class_Ozero(_1125331)), _1125333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125331), _1125335), c_Groups_Ozero__class_Ozero(_1125331)))]]], (49501 ^ _779854) ^ [_1779032, _1779034, _1779036, _1779038, _1779040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1779032), tc_List_Olist(_1779032))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1779032), tc_List_Olist(_1779032)), _1779034), _1779036)), c_List_Olexord(_1779032, _1779038))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1779032), tc_List_Olist(_1779032))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1779032), tc_List_Olist(_1779032)), _1779036), _1779040)), c_List_Olexord(_1779032, _1779038))), c_Relation_Otrans(_1779032, _1779038), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1779032), tc_List_Olist(_1779032))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1779032), tc_List_Olist(_1779032)), _1779034), _1779040)), c_List_Olexord(_1779032, _1779038))))], (44566 ^ _779854) ^ [_1671284, _1671286, _1671288] : [-(hAPP(c_List_Orotate(_1671284, _1671286), _1671288) = hAPP(c_List_Orotate(_1671284, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1671286, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671284)), _1671288))), _1671288))], (11638 ^ _779854) ^ [_981618, _981620, _981622, _981624] : [11639 ^ _779854 : [(11642 ^ _779854) ^ [] : [_981620 = _981624], (11640 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_981618), _981620), _981622))]], -(hBOOL(hAPP(hAPP(c_member(_981618), _981620), hAPP(hAPP(c_Set_Oinsert(_981618), _981624), _981622))))], (35008 ^ _779854) ^ [_1430912, _1430914] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1430912)), _1430914) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1430912), 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), _1430912)), _1430914))], (41042 ^ _779854) ^ [_1582428, _1582430, _1582432, _1582434] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1582428, tc_fun(_1582428, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1582428, tc_fun(tc_prod(_1582428, _1582428), tc_HOL_Obool), tc_fun(_1582428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582428, tc_fun(tc_fun(tc_prod(_1582428, _1582428), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1582428, _1582428), tc_HOL_Obool), tc_fun(_1582428, tc_HOL_Obool)), _1582428), c_COMBC(_1582428, tc_fun(tc_prod(_1582428, _1582428), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582428, tc_prod(_1582428, _1582428)), tc_fun(_1582428, tc_fun(tc_fun(tc_prod(_1582428, _1582428), tc_HOL_Obool), tc_HOL_Obool)), _1582428), hAPP(c_COMBB(tc_prod(_1582428, _1582428), tc_fun(tc_fun(tc_prod(_1582428, _1582428), tc_HOL_Obool), tc_HOL_Obool), _1582428), c_member(tc_prod(_1582428, _1582428)))), c_Product__Type_OPair(_1582428, _1582428)))), _1582430)), c_fequal), _1582432), _1582434)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582428, _1582428)), hAPP(hAPP(c_Product__Type_OPair(_1582428, _1582428), _1582432), _1582434)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582428, _1582428), tc_HOL_Obool)), _1582430), c_Relation_OId(_1582428)))))], (10415 ^ _779854) ^ [_956473, _956475, _956477, _956479, _956481] : [class_Orderings_Olinorder(_956473), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956473, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_956473, _956475), _956477)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_956473, _956479), _956481)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_956473, hAPP(hAPP(c_Orderings_Oord__class_Omax(_956473), _956475), _956479)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_956473), _956477), _956481)))], (16748 ^ _779854) ^ [_1081613, _1081615, _1081617, _1081619] : [class_Lattices_Osemilattice__sup(_1081613), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081613), _1081615)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1081613, _1081613, c_Lattices_Osemilattice__sup__class_Osup(_1081613)), _1081617), hAPP(hAPP(c_Set_Oinsert(_1081613), _1081619), _1081615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1081613), _1081619), hAPP(hAPP(c_Finite__Set_Ofold(_1081613, _1081613, c_Lattices_Osemilattice__sup__class_Osup(_1081613)), _1081617), _1081615)))], (28613 ^ _779854) ^ [_1297036] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1297036)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1297036))))], (23045 ^ _779854) ^ [_1196389, _1196391, _1196393, _1196395, _1196397] : [class_Fields_Ofield(_1196389), -(_1196391 = c_Groups_Ozero__class_Ozero(_1196389)), -(_1196393 = c_Groups_Ozero__class_Ozero(_1196389)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1196389), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196389), _1196395), _1196391)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196389), _1196397), _1196393)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196389), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1196389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196389), _1196395), _1196393)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196389), _1196397), _1196391))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196389), _1196391), _1196393)))], (44536 ^ _779854) ^ [_1670738, _1670740, _1670742] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670738)), hAPP(c_List_Orotate(_1670738, _1670740), _1670742)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670738)), _1670742))], (28768 ^ _779854) ^ [_1299574, _1299576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1299574), hAPP(c_Int_Onat, _1299576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1299574)), _1299576)))], (35193 ^ _779854) ^ [_1435447, _1435449, _1435451, _1435453, _1435455, _1435457, _1435459] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1435447, _1435449, tc_fun(_1435451, tc_HOL_Obool)), _1435453), hAPP(hAPP(c_Product__Type_OPair(_1435447, _1435449), _1435455), _1435457)), _1435459)), -(hBOOL(hAPP(hAPP(hAPP(_1435453, _1435455), _1435457), _1435459)))], (43498 ^ _779854) ^ [_1646827, _1646829, _1646831, _1646833] : [hAPP(hAPP(c_List_Olist__update(_1646827, _1646829), _1646831), _1646833) = c_List_Olist_ONil(_1646827), -(_1646829 = c_List_Olist_ONil(_1646827))], (42530 ^ _779854) ^ [_1623171, _1623173, _1623175, _1623177] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623171), tc_List_Olist(_1623171))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623171), tc_List_Olist(_1623171)), _1623173), _1623175)), c_List_Olistrel(_1623171, _1623177)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623171)), _1623173) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623171)), _1623175), 42536 ^ _779854 : [(42539 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623171, _1623171)), hAPP(hAPP(c_Product__Type_OPair(_1623171, _1623171), hAPP(hAPP(c_List_Onth(_1623171), _1623173), 42535 ^ [_1623171, _1623173, _1623175, _1623177])), hAPP(hAPP(c_List_Onth(_1623171), _1623175), 42535 ^ [_1623171, _1623173, _1623175, _1623177]))), _1623177))], (42537 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42535 ^ [_1623171, _1623173, _1623175, _1623177]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623171)), _1623173))))]]], (52001 ^ _779854) ^ [_1831225, _1831227] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831225), _1831227)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831227), _1831225)), -(_1831225 = _1831227)], (18499 ^ _779854) ^ [_1114987, _1114989, _1114991] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1114987), 18502 ^ _779854 : [(18509 ^ _779854) ^ [] : [_1114991 = c_Groups_Ozero__class_Ozero(_1114987), -(_1114989 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114987), _1114989), _1114991))], (18503 ^ _779854) ^ [] : [_1114989 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114987), _1114989), _1114991), -(_1114991 = c_Groups_Ozero__class_Ozero(_1114987))]]], (27873 ^ _779854) ^ [_1284138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1284138))))], (41078 ^ _779854) ^ [_1583841, _1583843] : [-(c_Transitive__Closure_Otrancl(_1583841, c_Transitive__Closure_Ortrancl(_1583841, _1583843)) = c_Transitive__Closure_Ortrancl(_1583841, _1583843))], (42087 ^ _779854) ^ [_1609096, _1609098, _1609100, _1609102, _1609104] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609096), tc_List_Olist(_1609096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609096), tc_List_Olist(_1609096)), _1609098), _1609100)), hAPP(c_List_Olexn(_1609096, _1609102), _1609104))), 42090 ^ _779854 : [(42093 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609096)), _1609100) = _1609104)], (42091 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609096)), _1609098) = _1609104)]]], (8836 ^ _779854) ^ [_926691, _926693, _926695, _926697, _926699] : [-(hAPP(hAPP(c_Set_Oinsert(_926691), _926693), hAPP(hAPP(c_Set_Oinsert(_926691), _926695), c_Orderings_Obot__class_Obot(tc_fun(_926691, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_926691), _926697), hAPP(hAPP(c_Set_Oinsert(_926691), _926699), c_Orderings_Obot__class_Obot(tc_fun(_926691, tc_HOL_Obool))))), 8837 ^ _779854 : [(8844 ^ _779854) ^ [] : [_926693 = _926699, _926695 = _926697], (8838 ^ _779854) ^ [] : [_926693 = _926697, _926695 = _926699]]], (43732 ^ _779854) ^ [_1652079, _1652081, _1652083, _1652085, _1652087] : [-(hAPP(hAPP(c_List_Oappend(_1652079), _1652081), hAPP(hAPP(c_List_Olist_OCons(_1652079), _1652083), c_List_Olist_ONil(_1652079))) = hAPP(hAPP(c_List_Oappend(_1652079), _1652085), hAPP(hAPP(c_List_Olist_OCons(_1652079), _1652087), c_List_Olist_ONil(_1652079)))), _1652081 = _1652085, _1652083 = _1652087], (49319 ^ _779854) ^ [_1774518, _1774520, _1774522, _1774524] : [class_Groups_Ocomm__monoid__add(_1774518), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1774520, tc_HOL_Obool)), _1774522)), 49329 ^ _779854 : [(49332 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1774520), 49328 ^ [_1774518, _1774520, _1774522, _1774524]))], (49330 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1774520, tc_HOL_Obool)), 49328 ^ [_1774518, _1774520, _1774522, _1774524]), _1774522)))]], 49336 ^ _779854 : [(49340 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1774520, tc_HOL_Obool)), 49338 ^ [_1774518, _1774520, _1774522, _1774524]), _1774522)))], (49337 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1774520, tc_HOL_Obool)), 49335 ^ [_1774518, _1774520, _1774522, _1774524]), _1774522)))], (49349 ^ _779854) ^ [] : [hAPP(_1774524, 49343 ^ [_1774518, _1774520, _1774522, _1774524]) = c_Groups_Ozero__class_Ozero(_1774518)], (49345 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774520), 49343 ^ [_1774518, _1774520, _1774522, _1774524]), 49335 ^ [_1774518, _1774520, _1774522, _1774524])))], (49347 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774520), 49343 ^ [_1774518, _1774520, _1774522, _1774524]), 49338 ^ [_1774518, _1774520, _1774522, _1774524])))], (49342 ^ _779854) ^ [] : [49335 ^ [_1774518, _1774520, _1774522, _1774524] = 49338 ^ [_1774518, _1774520, _1774522, _1774524]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1774520, _1774518), _1774524), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1774520, tc_HOL_Obool), _1774522)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1774520, tc_HOL_Obool), _1774518), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1774520, _1774518), _1774524)), _1774522))], (34285 ^ _779854) ^ [_1414900, _1414902] : [-(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)), _1414900)), 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), _1414902), _1414900))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1414900), _1414902))], (14888 ^ _779854) ^ [_1043956, _1043958, _1043960, _1043962, _1043964] : [class_Groups_Ocomm__monoid__add(_1043956), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043958), _1043960)), hBOOL(hAPP(hAPP(c_member(_1043958), _1043962), _1043960)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043958, _1043956), _1043964), _1043960) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043956), hAPP(_1043964, _1043962)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043958, _1043956), _1043964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043958, tc_HOL_Obool)), _1043960), hAPP(hAPP(c_Set_Oinsert(_1043958), _1043962), c_Orderings_Obot__class_Obot(tc_fun(_1043958, tc_HOL_Obool)))))))], (23677 ^ _779854) ^ [_1208877, _1208879] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208877), _1208879)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1208877, tc_HOL_Obool)), hAPP(c_Set_OPow(_1208877), _1208879)) = 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(_1208877), _1208879)))], (48808 ^ _779854) ^ [_1763341, _1763343, _1763345, _1763347] : [-(c_New__Random__Sequence_Oneg__map(_1763341, _1763343, _1763345, _1763347) = c_New__Random__Sequence_Oneg__bind(_1763341, _1763343, _1763347, hAPP(c_Fun_Ocomp(_1763343, 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(_1763343)))))), _1763341, c_New__Random__Sequence_Oneg__single(_1763343)), _1763345)))], (14372 ^ _779854) ^ [_1033904, _1033906, _1033908, _1033910] : [c_Finite__Set_Ofolding__one__idem(_1033904, _1033906, _1033908), -(hAPP(hAPP(_1033906, _1033910), _1033910) = _1033910)], (43586 ^ _779854) ^ [_1648587, _1648589, _1648591] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1648587)), -(c_List_Osublist(_1648589, hAPP(hAPP(c_List_Olist_OCons(_1648589), _1648591), c_List_Olist_ONil(_1648589)), _1648587) = hAPP(hAPP(c_List_Olist_OCons(_1648589), _1648591), c_List_Olist_ONil(_1648589)))], (50603 ^ _779854) ^ [_1803053, _1803055, _1803057, _1803059] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1803053, _1803055, _1803057, _1803059, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1803055)) = _1803057)], (2110 ^ _779854) ^ [_810556, _810558] : [_810558 = _810556, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_810558) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_810556))], (18975 ^ _779854) ^ [_1121984] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1121984), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1121984)], (11157 ^ _779854) ^ [_972145, _972147] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972145), c_Orderings_Otop__class_Otop(tc_fun(_972145, tc_HOL_Obool)))), c_Fun_Oinj__on(_972145, _972145, _972147, c_Orderings_Otop__class_Otop(tc_fun(_972145, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_972145, _972145, _972147), c_Orderings_Otop__class_Otop(tc_fun(_972145, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_972145, tc_HOL_Obool)))], (46536 ^ _779854) ^ [_1715064, _1715066] : [c_List_Otranspose(_1715064, _1715066) = c_List_Olist_ONil(tc_List_Olist(_1715064)), 46539 ^ _779854 : [(46540 ^ _779854) ^ [_1715159] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1715064)), _1715159), hAPP(c_List_Oset(tc_List_Olist(_1715064)), _1715066))), -(_1715159 = c_List_Olist_ONil(_1715064))]]], (10599 ^ _779854) ^ [_960229, _960231, _960233, _960235, _960237] : [class_Groups_Oab__group__add(_960229), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960229), _960231), _960233) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960229), _960235), _960237), 10606 ^ _779854 : [(10613 ^ _779854) ^ [] : [_960235 = _960237, -(_960231 = _960233)], (10607 ^ _779854) ^ [] : [_960231 = _960233, -(_960235 = _960237)]]], (52617 ^ _779854) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (22079 ^ _779854) ^ [_1178537, _1178539, _1178541, _1178543] : [class_Groups_Ocomm__monoid__mult(_1178537), 22082 ^ _779854 : [(22089 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1178539), _1178541))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1178539, _1178537), _1178543), _1178541) = c_Groups_Oone__class_Oone(_1178537))], (22083 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1178539), _1178541)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1178539, _1178537), _1178543), _1178541) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1178537, _1178539, c_Groups_Otimes__class_Otimes(_1178537)), _1178543), c_Groups_Oone__class_Oone(_1178537)), _1178541))]]], (40589 ^ _779854) ^ [_1571073, _1571075, _1571077] : [class_Complete__Lattice_Ocomplete__lattice(_1571073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1571073), _1571075), hAPP(_1571077, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1571073), _1571075), c_Inductive_Ocomplete__lattice__class_Ogfp(_1571073, _1571077))))), c_Orderings_Oorder__class_Omono(_1571073, _1571073, _1571077), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1571073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1571073), _1571075), c_Inductive_Ocomplete__lattice__class_Ogfp(_1571073, _1571077))), hAPP(_1571077, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1571073), _1571075), c_Inductive_Ocomplete__lattice__class_Ogfp(_1571073, _1571077))))))], (4232 ^ _779854) ^ [_844143, _844145, _844147, _844149] : [-(c_List_Olast(_844149, _844145) = c_List_Olast(_844147, _844143)), _844149 = _844147, _844145 = _844143], (15438 ^ _779854) ^ [_1055436, _1055438, _1055440] : [class_Rings_Oidom(_1055436), 15441 ^ _779854 : [(15442 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055436), _1055438), _1055438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055436), _1055440), _1055440), -(_1055438 = _1055440), -(_1055438 = hAPP(c_Groups_Ouminus__class_Ouminus(_1055436), _1055440))], (15452 ^ _779854) ^ [] : [15453 ^ _779854 : [(15456 ^ _779854) ^ [] : [_1055438 = hAPP(c_Groups_Ouminus__class_Ouminus(_1055436), _1055440)], (15454 ^ _779854) ^ [] : [_1055438 = _1055440]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055436), _1055438), _1055438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055436), _1055440), _1055440))]]], (43885 ^ _779854) ^ [_1655510, _1655512, _1655514, _1655516] : [_1655512 = _1655516, -(hAPP(hAPP(c_List_Oappend(_1655510), _1655512), _1655514) = hAPP(hAPP(c_List_Oappend(_1655510), _1655516), _1655514))], (11959 ^ _779854) ^ [_987685, _987687, _987689, _987691] : [hBOOL(hAPP(hAPP(c_member(_987685), _987687), _987689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987685, tc_HOL_Obool)), _987689), _987691)), -(hBOOL(hAPP(hAPP(c_member(_987685), _987687), _987691)))], (6739 ^ _779854) ^ [_888143, _888145, _888147] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888143, tc_HOL_Obool)), _888145), _888147) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888143, tc_HOL_Obool)), _888147), _888145))], (20437 ^ _779854) ^ [_1147687, _1147689] : [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), _1147687), _1147689))), 20440 ^ _779854 : [(20443 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147689)))], (20441 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147687)))]]], (38999 ^ _779854) ^ [_1525457, _1525459] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1525457)), -(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)), _1525457))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1525459))))) = 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)), _1525457))), 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, _1525459))))))], (39055 ^ _779854) ^ [_1527299, _1527301] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527299), _1527301)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1527299, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1527299, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1527299, tc_HOL_Obool), tc_fun(_1527299, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1527299, tc_HOL_Obool))), _1527301)))))], (50132 ^ _779854) ^ [_1793097, _1793099, _1793101] : [c_Relation_Orefl__on(_1793097, _1793099, _1793101), c_Relation_Osym(_1793097, _1793101), c_Relation_Otrans(_1793097, _1793101), -(c_Equiv__Relations_Oequiv(_1793097, _1793099, _1793101))], (34283 ^ _779854) ^ [_1414771, _1414773, _1414775, _1414777, _1414779] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414771, tc_fun(_1414773, tc_HOL_Obool)), _1414775), hAPP(hAPP(c_COMBS(_1414771, tc_fun(_1414773, tc_HOL_Obool), tc_fun(_1414773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414773, tc_HOL_Obool), tc_fun(tc_fun(_1414773, tc_HOL_Obool), tc_fun(_1414773, tc_HOL_Obool)), _1414771), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414773, tc_HOL_Obool))), _1414777)), _1414779)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414773, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1414773, tc_HOL_Obool), hAPP(c_Set_Oimage(_1414771, tc_fun(_1414773, tc_HOL_Obool), _1414777), _1414775))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1414773, tc_HOL_Obool), hAPP(c_Set_Oimage(_1414771, tc_fun(_1414773, tc_HOL_Obool), _1414779), _1414775))))], (11422 ^ _779854) ^ [_977185, _977187, _977189] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977185), _977187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977185, tc_HOL_Obool)), _977187), hAPP(c_Set_Oimage(_977185, _977185, _977189), _977187))), -(c_Fun_Oinj__on(_977185, _977185, _977189, _977187))], (28037 ^ _779854) ^ [_1287037, _1287039, _1287041] : [hBOOL(hAPP(_1287037, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1287039), _1287041))), 28042 ^ _779854 : [(28045 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1287037, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28043 ^ _779854) ^ [] : [-(_1287041 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 28047 ^ _779854 : [(28052 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1287037, 28046 ^ [_1287037, _1287039, _1287041])))], (28050 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1287039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1287041), hAPP(c_Nat_OSuc, 28046 ^ [_1287037, _1287039, _1287041])))))], (28048 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1287041), 28046 ^ [_1287037, _1287039, _1287041])), _1287039)))]]], (52577 ^ _779854) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (33641 ^ _779854) ^ [_1397828, _1397830, _1397832, _1397834, _1397836] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397828, tc_fun(_1397830, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1397828), _1397832), _1397834)), _1397836) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397830, tc_HOL_Obool)), hAPP(_1397836, _1397832)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397828, tc_fun(_1397830, tc_HOL_Obool)), _1397834), _1397836)))], (28120 ^ _779854) ^ [_1288568, _1288570] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1288568)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1288568)), _1288570) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1288568)), _1288570)))], (21625 ^ _779854) ^ [_1170154, _1170156, _1170158] : [class_Rings_Oring__1(_1170154), hBOOL(hAPP(hAPP(c_member(_1170154), _1170156), c_Int_Oring__1__class_OInts(_1170154))), hBOOL(hAPP(hAPP(c_member(_1170154), _1170158), c_Int_Oring__1__class_OInts(_1170154))), -(hBOOL(hAPP(hAPP(c_member(_1170154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170154), _1170156), _1170158)), c_Int_Oring__1__class_OInts(_1170154))))], (6511 ^ _779854) ^ [_884069, _884071, _884073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_884069, tc_HOL_Obool), tc_HOL_Obool)), _884071), _884073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884069, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_884069, tc_HOL_Obool), _884071)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_884069, tc_HOL_Obool), _884073))))], (37237 ^ _779854) ^ [_1480419, _1480421, _1480423, _1480425] : [_1480419 = _1480421, hBOOL(hAPP(hAPP(c_member(_1480423), _1480419), _1480425)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1480423, _1480423)), hAPP(hAPP(c_Product__Type_OPair(_1480423, _1480423), _1480419), _1480421)), c_Relation_OId__on(_1480423, _1480425))))], (112 ^ _779854) ^ [_781440, _781442, _781444, _781446, _781448, _781450, _781452, _781454, _781456, _781458, _781460, _781462] : [-(c_Finite__Set_Ofolding__image__simple(_781460, _781456, _781452, _781448, _781444, _781440)), c_Finite__Set_Ofolding__image__simple(_781462, _781458, _781454, _781450, _781446, _781442), _781462 = _781460, _781458 = _781456, _781454 = _781452, _781450 = _781448, _781446 = _781444, _781442 = _781440], (11300 ^ _779854) ^ [_974821] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_974821), c_Orderings_Otop__class_Otop(tc_fun(_974821, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_974821)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_974821), tc_HOL_Obool)))))], (12032 ^ _779854) ^ [_989165, _989167, _989169, _989171] : [hBOOL(hAPP(hAPP(c_member(_989165), _989167), _989169)), -(hBOOL(hAPP(hAPP(c_member(_989165), _989167), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989165, tc_HOL_Obool)), _989169), _989171))))], (44462 ^ _779854) ^ [_1669610, _1669612, _1669614] : [-(hAPP(c_List_Ohd(_1669610), hAPP(hAPP(c_List_Olist_OCons(_1669610), _1669612), _1669614)) = _1669612)], (41082 ^ _779854) ^ [_1583909, _1583911] : [-(hAPP(c_Relation_ODomain(_1583909, _1583909), c_Transitive__Closure_Ortrancl(_1583909, _1583911)) = c_Orderings_Otop__class_Otop(tc_fun(_1583909, tc_HOL_Obool)))], (45075 ^ _779854) ^ [_1681217, _1681219, _1681221, _1681223, _1681225, _1681227, _1681229] : [-(hAPP(c_List_Ofoldl(_1681217, _1681219, _1681221, _1681223), hAPP(hAPP(c_List_Omap(_1681225, _1681219), _1681227), _1681229)) = hAPP(c_List_Ofoldl(_1681217, _1681225, hAPP(hAPP(c_COMBC(_1681217, tc_fun(_1681225, _1681219), tc_fun(_1681225, _1681217)), hAPP(hAPP(c_COMBB(tc_fun(_1681219, _1681217), tc_fun(tc_fun(_1681225, _1681219), tc_fun(_1681225, _1681217)), _1681217), c_COMBB(_1681219, _1681217, _1681225)), _1681221)), _1681227), _1681223), _1681229))], (52109 ^ _779854) ^ [_1832790, _1832792] : [class_Lattices_Oboolean__algebra(_1832790), -(class_Lattices_Oboolean__algebra(tc_fun(_1832792, _1832790)))], (33000 ^ _779854) ^ [_1376960, _1376962, _1376964, _1376966] : [hBOOL(hAPP(hAPP(c_member(_1376962), _1376966), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376960, tc_fun(_1376962, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376960, tc_HOL_Obool))), _1376964))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376960, tc_fun(_1376962, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376960, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1376962, tc_HOL_Obool), tc_fun(_1376962, tc_HOL_Obool), _1376960), hAPP(c_COMBC(_1376962, tc_fun(_1376962, tc_HOL_Obool), tc_HOL_Obool), c_member(_1376962))), _1376964)), _1376966)))], (9947 ^ _779854) ^ [_947630, _947632, _947634, _947636] : [class_Orderings_Olinorder(_947630), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_947630), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947630), _947632), _947634)), _947636) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_947630), _947632), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947630), _947634), _947636)))], (10913 ^ _779854) ^ [_966661, _966663, _966665, _966667, _966669] : [c_Fun_Oinj__on(_966661, _966663, _966665, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_966661, tc_HOL_Obool)), _966667), _966669)), 10916 ^ _779854 : [(10923 ^ _779854) ^ [] : [_966667 = _966669, -(hAPP(c_Set_Oimage(_966661, _966663, _966665), _966667) = hAPP(c_Set_Oimage(_966661, _966663, _966665), _966669))], (10917 ^ _779854) ^ [] : [hAPP(c_Set_Oimage(_966661, _966663, _966665), _966667) = hAPP(c_Set_Oimage(_966661, _966663, _966665), _966669), -(_966667 = _966669)]]], (43836 ^ _779854) ^ [_1654416, _1654418, _1654420, _1654422, _1654424] : [hAPP(hAPP(c_List_Oappend(_1654416), _1654418), _1654420) = hAPP(hAPP(c_List_Oappend(_1654416), _1654422), _1654424), 43842 ^ _779854 : [(43845 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1654416), 43839 ^ [_1654416, _1654418, _1654420, _1654422, _1654424]), _1654420) = _1654424)], (43843 ^ _779854) ^ [] : [-(_1654418 = hAPP(hAPP(c_List_Oappend(_1654416), _1654422), 43839 ^ [_1654416, _1654418, _1654420, _1654422, _1654424]))]], 43846 ^ _779854 : [(43849 ^ _779854) ^ [] : [-(_1654420 = hAPP(hAPP(c_List_Oappend(_1654416), 43839 ^ [_1654416, _1654418, _1654420, _1654422, _1654424]), _1654424))], (43847 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1654416), _1654418), 43839 ^ [_1654416, _1654418, _1654420, _1654422, _1654424]) = _1654422)]]], (46150 ^ _779854) ^ [_1706112] : [-(c_List_Oremdups(_1706112, c_List_Olist_ONil(_1706112)) = c_List_Olist_ONil(_1706112))], (20186 ^ _779854) ^ [_1143652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143652), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1143652 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12924 ^ _779854) ^ [_1007062, _1007064, _1007066, _1007068, _1007070] : [hBOOL(hAPP(hAPP(c_member(_1007062), _1007064), c_SetInterval_Oord_OatLeastAtMost(_1007062, _1007066, _1007068, _1007070))), 12927 ^ _779854 : [(12930 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1007066, _1007064), _1007070)))], (12928 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1007066, _1007068), _1007064)))]]], (3358 ^ _779854) ^ [_830162, _830164, _830166, _830168] : [-(c_Product__Type_OSigma(_830168, _830164) = c_Product__Type_OSigma(_830166, _830162)), _830168 = _830166, _830164 = _830162], (39796 ^ _779854) ^ [_1551888, _1551890, _1551892] : [hAPP(c_Relation_ODomain(_1551888, _1551890), _1551892) = c_Orderings_Obot__class_Obot(tc_fun(_1551888, tc_HOL_Obool)), -(_1551892 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551888, _1551890), tc_HOL_Obool)))], (38701 ^ _779854) ^ [_1517699, _1517701, _1517703] : [hBOOL(hAPP(_1517699, _1517701)), -(hBOOL(hAPP(hAPP(c_member(_1517703), _1517701), hAPP(c_Set_OCollect(_1517703), _1517699))))], (36639 ^ _779854) ^ [_1464997, _1464999, _1465001, _1465003, _1465005] : [c_Finite__Set_Ofolding__idem(_1464997, _1464999, _1465001, _1465003), -(hAPP(c_Fun_Ocomp(_1464999, _1464999, _1464999, hAPP(_1465001, _1465005)), hAPP(_1465001, _1465005)) = hAPP(_1465001, _1465005))], (38977 ^ _779854) ^ [_1524560, _1524562, _1524564, _1524566, _1524568, _1524570] : [class_Groups_Ocomm__monoid__add(_1524560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524562), _1524564)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524562, _1524560), _1524566), _1524564) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524568, _1524560), hAPP(hAPP(c_COMBB(tc_fun(_1524562, tc_HOL_Obool), _1524560, _1524568), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524562, _1524560), _1524566)), hAPP(hAPP(c_COMBB(tc_fun(_1524562, tc_HOL_Obool), tc_fun(_1524562, tc_HOL_Obool), _1524568), c_Set_OCollect(_1524562)), hAPP(hAPP(c_COMBB(tc_fun(_1524562, tc_HOL_Obool), tc_fun(_1524562, tc_HOL_Obool), _1524568), hAPP(c_COMBS(_1524562, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524562), c_fconj), hAPP(hAPP(c_COMBC(_1524562, tc_fun(_1524562, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524562)), _1524564)))), hAPP(c_COMBC(_1524562, _1524568, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1524568, tc_fun(_1524568, tc_HOL_Obool), _1524562), c_fequal), _1524570)))))), hAPP(c_Set_Oimage(_1524562, _1524568, _1524570), _1524564)))], (14670 ^ _779854) ^ [_1039864, _1039866, _1039868] : [class_Lattices_Osemilattice__inf(_1039864), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039864), _1039866)), -(_1039866 = c_Orderings_Obot__class_Obot(tc_fun(_1039864, tc_HOL_Obool))), 14681 ^ _779854 : [(14682 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039864), _1039868), hAPP(c_Finite__Set_Ofold1(_1039864, c_Lattices_Osemilattice__inf__class_Oinf(_1039864)), _1039866))), 14685 ^ _779854 : [(14686 ^ _779854) ^ [_1040157] : [hBOOL(hAPP(hAPP(c_member(_1039864), _1040157), _1039866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039864), _1039868), _1040157)))]]], (14692 ^ _779854) ^ [] : [14694 ^ _779854 : [(14697 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039864), _1039868), 14693 ^ [_1039864, _1039866, _1039868]))], (14695 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039864), 14693 ^ [_1039864, _1039866, _1039868]), _1039866)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039864), _1039868), hAPP(c_Finite__Set_Ofold1(_1039864, c_Lattices_Osemilattice__inf__class_Oinf(_1039864)), _1039866))))]]], (16091 ^ _779854) ^ [_1068750, _1068752, _1068754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068750), _1068752)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068750), _1068754))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068752), _1068754)))], (33659 ^ _779854) ^ [_1398224, _1398226, _1398228, _1398230, _1398232, _1398234] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398224, tc_fun(_1398226, tc_HOL_Obool)), _1398228), hAPP(hAPP(c_COMBB(_1398230, tc_fun(_1398226, tc_HOL_Obool), _1398224), _1398232), _1398234)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398230, tc_fun(_1398226, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398224, _1398230, _1398234), _1398228)), _1398232))], (36788 ^ _779854) ^ [_1468397, _1468399, _1468401, _1468403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1468397), _1468399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1468401), _1468403)), -(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), _1468397), _1468401)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1468399), _1468403))), c_FunDef_Opair__leq)))], (44342 ^ _779854) ^ [_1666490, _1666492, _1666494, _1666496] : [_1666490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1666492), _1666490), hAPP(hAPP(c_List_Olist_OCons(_1666492), _1666494), _1666496)) = hAPP(hAPP(c_List_Olist_OCons(_1666492), _1666494), _1666496))], (43909 ^ _779854) ^ [_1656035, _1656037, _1656039, _1656041, _1656043, _1656045] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656035)), _1656037) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656039)), _1656041), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656035)), _1656043) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656039)), _1656045), -(hAPP(hAPP(c_List_Ozip(_1656035, _1656039), hAPP(hAPP(c_List_Oappend(_1656035), _1656037), _1656043)), hAPP(hAPP(c_List_Oappend(_1656039), _1656041), _1656045)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1656035, _1656039)), hAPP(hAPP(c_List_Ozip(_1656035, _1656039), _1656037), _1656041)), hAPP(hAPP(c_List_Ozip(_1656035, _1656039), _1656043), _1656045)))], (8200 ^ _779854) ^ [_917259, _917261, _917263, _917265] : [class_Orderings_Oorder(_917259), _917261 = _917263, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917259), _917265), _917263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917259), _917265), _917261)))], (31699 ^ _779854) ^ [_1350588, _1350590] : [_1350588 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1350588, _1350590) = _1350590)], (49142 ^ _779854) ^ [_1770675, _1770677, _1770679, _1770681] : [-(c_Lazy__Sequence_Oappend(_1770675, c_Lazy__Sequence_Olazy__sequence_OInsert(_1770675, _1770677, _1770679), _1770681) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1770675, _1770677, c_Lazy__Sequence_Oappend(_1770675, _1770679, _1770681)))], (7503 ^ _779854) ^ [_903542, _903544] : [class_Lattices_Obounded__lattice__top(_903542), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903542), c_Orderings_Otop__class_Otop(_903542)), _903544) = _903544)], (33419 ^ _779854) ^ [_1388165, _1388167, _1388169, _1388171] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1388165, tc_fun(_1388167, tc_HOL_Obool))), _1388169), _1388171)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1388165, _1388167)), hAPP(hAPP(c_Product__Type_OPair(_1388165, _1388167), _1388169), _1388171)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1388165, _1388167), tc_HOL_Obool)))))], (49934 ^ _779854) ^ [_1789177] : [-(c_Relation_Oantisym(_1789177, c_Relation_OId(_1789177)))], (39011 ^ _779854) ^ [_1525764, _1525766, _1525768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1525764, _1525764), tc_HOL_Obool)), _1525766), hAPP(hAPP(c_Product__Type_OSigma(_1525764, _1525764), _1525768), hAPP(c_COMBK(tc_fun(_1525764, tc_HOL_Obool), _1525764), _1525768)))), 39017 ^ _779854 : [(39020 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525764, _1525764)), hAPP(hAPP(c_Product__Type_OPair(_1525764, _1525764), 39016 ^ [_1525764, _1525766, _1525768]), 39016 ^ [_1525764, _1525766, _1525768])), _1525766))], (39018 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525764), 39016 ^ [_1525764, _1525766, _1525768]), _1525768)))]], -(c_Relation_Orefl__on(_1525764, _1525768, _1525766))], (49414 ^ _779854) ^ [_1776881, _1776883, _1776885] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1776881, _1776883, _1776885) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1776881)], (45677 ^ _779854) ^ [_1695544, _1695546, _1695548] : [hBOOL(hAPP(c_List_Olistsp(_1695544, _1695546), _1695548)), 45680 ^ _779854 : [(45681 ^ _779854) ^ [_1695633] : [hBOOL(hAPP(hAPP(c_member(_1695544), _1695633), hAPP(c_List_Oset(_1695544), _1695548))), -(hBOOL(hAPP(_1695546, _1695633)))]]], (7497 ^ _779854) ^ [_903443, _903445] : [class_Lattices_Obounded__lattice__top(_903443), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903443), _903445), c_Orderings_Otop__class_Otop(_903443)) = c_Orderings_Otop__class_Otop(_903443))], (37099 ^ _779854) ^ [_1476462, _1476464, _1476466, _1476468] : [-(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), _1476462), _1476464)), 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), _1476466), _1476468)), 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), _1476462), _1476466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1476464), _1476468))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1476462), _1476468)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1476464), _1476466)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (35648 ^ _779854) ^ [_1443807, _1443809, _1443811, _1443813, _1443815, _1443817] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443807, _1443809), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443811), _1443813))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443807, _1443809), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443815), _1443817))), -(_1443809 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1443813 = _1443817)], (49002 ^ _779854) ^ [_1768026, _1768028, _1768030, _1768032, _1768034] : [c_List_Oreplicate(_1768026, _1768028, _1768030) = c_List_Oreplicate(_1768026, _1768032, _1768034), 49005 ^ _779854 : [(49008 ^ _779854) ^ [] : [-(_1768028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1768030 = _1768034)], (49006 ^ _779854) ^ [] : [-(_1768028 = _1768032)]]], (45847 ^ _779854) ^ [_1699559, _1699561, _1699563, _1699565, _1699567, _1699569, _1699571] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699559)), _1699561) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699563)), _1699565), 45850 ^ _779854 : [(45859 ^ _779854) ^ [] : [-(c_List_Olist__all2(_1699559, _1699563, _1699567, hAPP(hAPP(c_List_Oappend(_1699559), _1699561), _1699569), hAPP(hAPP(c_List_Oappend(_1699563), _1699565), _1699571))), c_List_Olist__all2(_1699559, _1699563, _1699567, _1699561, _1699565), c_List_Olist__all2(_1699559, _1699563, _1699567, _1699569, _1699571)], (45851 ^ _779854) ^ [] : [c_List_Olist__all2(_1699559, _1699563, _1699567, hAPP(hAPP(c_List_Oappend(_1699559), _1699561), _1699569), hAPP(hAPP(c_List_Oappend(_1699563), _1699565), _1699571)), 45854 ^ _779854 : [(45857 ^ _779854) ^ [] : [-(c_List_Olist__all2(_1699559, _1699563, _1699567, _1699569, _1699571))], (45855 ^ _779854) ^ [] : [-(c_List_Olist__all2(_1699559, _1699563, _1699567, _1699561, _1699565))]]]]], (29391 ^ _779854) ^ [_1310070, _1310072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1310070)), c_Int_OBit0(_1310072))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310070), _1310072)))], (40033 ^ _779854) ^ [_1557759] : [-(c_Wellfounded_OwfP(_1557759, hAPP(c_COMBK(tc_fun(_1557759, tc_HOL_Obool), _1557759), hAPP(c_COMBK(tc_HOL_Obool, _1557759), c_fFalse))))], (35398 ^ _779854) ^ [_1439230, _1439232, _1439234, _1439236, _1439238] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1439230, _1439232), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1439234), _1439236))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1439232)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439238), _1439230), _1439232), 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), _1439238), _1439234)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439238), _1439236)), _1439232))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439238), _1439236), _1439232)))))], (47671 ^ _779854) ^ [_1738554, _1738556] : [-(_1738554 = c_List_Olist_ONil(_1738556)), hBOOL(hAPP(c_List_Odistinct(_1738556), _1738554)), -(c_List_OtakeWhile(_1738556, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1738556), c_fNot), hAPP(hAPP(c_COMBC(_1738556, _1738556, tc_HOL_Obool), c_fequal), c_List_Olast(_1738556, _1738554))), _1738554) = c_List_Obutlast(_1738556, _1738554))], (49128 ^ _779854) ^ [_1770415, _1770417, _1770419] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1770415, _1770417), _1770419) = c_Lazy__Sequence_Oproduct(_1770415, _1770417, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1770415, _1770419), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1770417, _1770419))), class_Lazy__Sequence_Osmall__lazy(_1770415), class_Lazy__Sequence_Osmall__lazy(_1770417)], (27441 ^ _779854) ^ [_1277019, _1277021] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1277019)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277019)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277021)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1277019)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277021))))], (47422 ^ _779854) ^ [_1733369, _1733371, _1733373] : [_1733371 = _1733373, -(hAPP(c_List_Orev(_1733369), _1733371) = hAPP(c_List_Orev(_1733369), _1733373))], (29611 ^ _779854) ^ [_1313947, _1313949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1313947)), c_Int_OBit0(_1313949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1313947), _1313949)))], (25519 ^ _779854) ^ [_1244125, _1244127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244125)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244125), _1244127)))], (7561 ^ _779854) ^ [_904738, _904740, _904742] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904738, tc_HOL_Obool)), _904740), _904742) = c_Orderings_Obot__class_Obot(tc_fun(_904738, tc_HOL_Obool)), 7564 ^ _779854 : [(7565 ^ _779854) ^ [_904862] : [hBOOL(hAPP(hAPP(c_member(_904738), _904862), _904740)), 7568 ^ _779854 : [(7569 ^ _779854) ^ [_904952] : [hBOOL(hAPP(hAPP(c_member(_904738), _904952), _904742)), _904862 = _904952]]]]], (16892 ^ _779854) ^ [_1084609, _1084611, _1084613, _1084615, _1084617] : [class_Groups_Oab__semigroup__mult(_1084609), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1084609, _1084609, c_Groups_Otimes__class_Otimes(_1084609), _1084611, _1084613), _1084615)), -(hBOOL(hAPP(hAPP(c_member(_1084609), _1084611), _1084613))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1084609, _1084609, c_Groups_Otimes__class_Otimes(_1084609), _1084617, hAPP(hAPP(c_Set_Oinsert(_1084609), _1084611), _1084613)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084609), _1084617), _1084615))))], (45154 ^ _779854) ^ [_1683779, _1683781, _1683783] : [class_Groups_Omonoid__add(_1683779), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1683779), hAPP(hAPP(c_List_Omap(_1683781, _1683779), hAPP(c_COMBK(_1683779, _1683781), c_Groups_Ozero__class_Ozero(_1683779))), _1683783)) = c_Groups_Ozero__class_Ozero(_1683779))], (32381 ^ _779854) ^ [_1362661, _1362663, _1362665] : [class_Fields_Olinordered__field__inverse__zero(_1362661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362661), c_Groups_Ozero__class_Ozero(_1362661)), _1362663)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362661), hAPP(c_Groups_Oabs__class_Oabs(_1362661), _1362665)), _1362663) = hAPP(c_Groups_Oabs__class_Oabs(_1362661), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362661), _1362665), _1362663)))], (47352 ^ _779854) ^ [_1731779, _1731781, _1731783] : [hAPP(c_List_Orev(_1731779), _1731781) = hAPP(hAPP(c_List_Olist_OCons(_1731779), _1731783), c_List_Olist_ONil(_1731779)), -(_1731781 = hAPP(hAPP(c_List_Olist_OCons(_1731779), _1731783), c_List_Olist_ONil(_1731779)))], (41792 ^ _779854) ^ [_1601144, _1601146, _1601148, _1601150] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601144, _1601144)), hAPP(hAPP(c_Product__Type_OPair(_1601144, _1601144), _1601146), _1601148)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601144, _1601144), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1601150))), -(_1601146 = _1601148)], (28577 ^ _779854) ^ [_1296433, _1296435, _1296437] : [class_Rings_Osemiring__1(_1296433), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296433), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1296435), _1296437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1296433), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296433), _1296435)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296433), _1296437)))], (23782 ^ _779854) ^ [_1211067, _1211069, _1211071] : [class_Rings_Ocomm__semiring__1(_1211067), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1211067), _1211069), hAPP(c_Nat_OSuc, _1211071)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211067), _1211069), hAPP(hAPP(c_Power_Opower__class_Opower(_1211067), _1211069), _1211071)))], (16020 ^ _779854) ^ [_1067693, _1067695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067693), _1067695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067693), _1067695))), -(_1067693 = _1067695)], (41425 ^ _779854) ^ [_1592039, _1592041, _1592043] : [c_Relation_Orefl__on(_1592039, _1592041, _1592043), -(c_Relation_Orefl__on(_1592039, _1592041, hAPP(c_Relation_Oconverse(_1592039, _1592039), _1592043)))], (34865 ^ _779854) ^ [_1427682, _1427684, _1427686, _1427688, _1427690, _1427692] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427682, tc_fun(_1427684, tc_HOL_Obool))), _1427686), _1427688), _1427690), _1427692)), -(hBOOL(hAPP(hAPP(_1427686, _1427690), _1427692))), -(hBOOL(hAPP(hAPP(_1427688, _1427690), _1427692)))], (25645 ^ _779854) ^ [_1246174, _1246176, _1246178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246174), _1246176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246174), _1246178)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246176), _1246178))))], (46030 ^ _779854) ^ [_1703531, _1703533] : [hBOOL(hAPP(c_List_Odistinct(_1703531), _1703533)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1703531, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1703531), tc_fun(_1703531, tc_HOL_Obool)), c_List_Oset(_1703531)), c_Enum_Osublists(_1703531, _1703533)))))], (41487 ^ _779854) ^ [_1593718, _1593720] : [c_Wellfounded_Owf(_1593718, hAPP(c_Relation_Oconverse(_1593718, _1593718), _1593720)), -(c_Wellfounded_Owf(_1593718, hAPP(c_Relation_Oconverse(_1593718, _1593718), c_Transitive__Closure_Otrancl(_1593718, _1593720))))], (16377 ^ _779854) ^ [_1074469, _1074471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074469), _1074471)), _1074469)))], (16347 ^ _779854) ^ [_1073929, _1073931, _1073933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073929), _1073931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073933), _1073929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073929), _1073933)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073931), _1073933))))], (38206 ^ _779854) ^ [_1503310, _1503312, _1503314, _1503316, _1503318, _1503320] : [hBOOL(hAPP(hAPP(c_member(_1503310), _1503312), _1503314)), 38209 ^ _779854 : [(38216 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503310), _1503316), _1503314))), -(hAPP(c_Set_Ovimage(_1503318, _1503310, hAPP(hAPP(c_COMBC(_1503318, _1503310, _1503310), hAPP(hAPP(c_COMBC(_1503318, _1503310, tc_fun(_1503310, _1503310)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1503310, tc_fun(_1503310, _1503310)), _1503318), c_If(_1503310)), hAPP(hAPP(c_COMBC(_1503318, tc_fun(_1503318, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503318)), _1503320))), _1503312)), _1503316)), _1503314) = _1503320)], (38210 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1503310), _1503316), _1503314)), -(hAPP(c_Set_Ovimage(_1503318, _1503310, hAPP(hAPP(c_COMBC(_1503318, _1503310, _1503310), hAPP(hAPP(c_COMBC(_1503318, _1503310, tc_fun(_1503310, _1503310)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1503310, tc_fun(_1503310, _1503310)), _1503318), c_If(_1503310)), hAPP(hAPP(c_COMBC(_1503318, tc_fun(_1503318, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503318)), _1503320))), _1503312)), _1503316)), _1503314) = c_Orderings_Otop__class_Otop(tc_fun(_1503318, tc_HOL_Obool)))]]], (5962 ^ _779854) ^ [_874222, _874224, _874226] : [class_Orderings_Opreorder(_874222), _874224 = _874226, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874222), _874224), _874226)))], (25779 ^ _779854) ^ [_1248418, _1248420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1248420), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248418), _1248420)))], (46152 ^ _779854) ^ [_1706157, _1706159] : [c_List_Olist_ONil(_1706157) = c_List_Oremdups(_1706157, _1706159), -(_1706159 = c_List_Olist_ONil(_1706157))], (7009 ^ _779854) ^ [_894629, _894631, _894633] : [class_Lattices_Olattice(_894629), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894629), _894631), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894629), _894631), _894633)) = _894631)], (14378 ^ _779854) ^ [_1033999, _1034001, _1034003, _1034005, _1034007] : [c_Finite__Set_Ofolding__one__idem(_1033999, _1034001, _1034003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033999), _1034005)), hBOOL(hAPP(hAPP(c_member(_1033999), _1034007), _1034005)), -(hAPP(hAPP(_1034001, _1034007), hAPP(_1034003, _1034005)) = hAPP(_1034003, _1034005))], (18108 ^ _779854) ^ [_1107505, _1107507, _1107509] : [class_Rings_Ocomm__semiring__1(_1107505), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107505), _1107507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107505), _1107509), _1107507)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107505), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107505), _1107509), c_Groups_Oone__class_Oone(_1107505))), _1107507))], (49098 ^ _779854) ^ [_1769685, _1769687, _1769689] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1769685), hAPP(c_COMBK(_1769685, tc_Nat_Onat), _1769687)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1769689)) = c_List_Oreplicate(_1769685, _1769689, _1769687))], (27297 ^ _779854) ^ [_1274769, _1274771, _1274773, _1274775] : [_1274769 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1274771), _1274773)), _1274775), -(_1274771 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1274769), _1274771) = _1274773), 27304 ^ _779854 : [(27307 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1274775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274775), _1274771))], (27305 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1274771)))]], 27312 ^ _779854 : [(27315 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274771), _1274775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1274775), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27313 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1274771))]]], (35988 ^ _779854) ^ [_1450452, _1450454, _1450456] : [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), _1450452), _1450454))), -(hBOOL(hAPP(hAPP(_1450456, _1450452), _1450454))), 35995 ^ _779854 : [(35998 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 35994 ^ [_1450452, _1450454, _1450456]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1450456, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 35993 ^ [_1450452, _1450454, _1450456])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 35994 ^ [_1450452, _1450454, _1450456]))))], (36004 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1450456, 35993 ^ [_1450452, _1450454, _1450456]), 35994 ^ [_1450452, _1450454, _1450456]))], (35996 ^ _779854) ^ [] : [-(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), 35993 ^ [_1450452, _1450454, _1450456]), 35994 ^ [_1450452, _1450454, _1450456]))))]]], (30345 ^ _779854) ^ [_1327894, _1327896] : [class_Divides_Osemiring__div(_1327894), -(c_Divides_Odiv__class_Omod(_1327894, _1327896, c_Groups_Oone__class_Oone(_1327894)) = c_Groups_Ozero__class_Ozero(_1327894))], (20732 ^ _779854) ^ [_1152895, _1152897, _1152899, _1152901, _1152903] : [class_Rings_Olinordered__semiring__strict(_1152895), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152895), _1152897), _1152899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152895), _1152901), _1152903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152895), c_Groups_Ozero__class_Ozero(_1152895)), _1152897)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152895), c_Groups_Ozero__class_Ozero(_1152895)), _1152901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152895), _1152897), _1152901)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152895), _1152899), _1152903))))], (16191 ^ _779854) ^ [_1070588, _1070590, _1070592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070588), _1070590)), _1070592)), 16194 ^ _779854 : [(16197 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070590), _1070592)))], (16195 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070588), _1070592)))]]], (31838 ^ _779854) ^ [_1352779, _1352781, _1352783] : [class_Rings_Oring__1(_1352779), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1352781), _1352783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1352779), hAPP(c_Int_Oring__1__class_Oof__int(_1352779), _1352781)), hAPP(c_Int_Oring__1__class_Oof__int(_1352779), _1352783)))], (43492 ^ _779854) ^ [_1646703, _1646705] : [_1646705 = c_List_Olist_ONil(_1646703), -(hAPP(c_List_Oset(_1646703), _1646705) = c_Orderings_Obot__class_Obot(tc_fun(_1646703, tc_HOL_Obool)))], (36293 ^ _779854) ^ [_1457228, _1457230, _1457232] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1457228, _1457230), _1457232)), 36296 ^ _779854 : [(36305 ^ _779854) ^ [] : [-(_1457230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36308 ^ _779854 : [(36317 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457230))), 36320 ^ _779854 : [(36323 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457232)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36321 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1457230), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457232))))]]], (36309 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457230)), 36312 ^ _779854 : [(36315 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457232)), _1457230)))], (36313 ^ _779854) ^ [] : [-(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), _1457232))))]]]]], (36299 ^ _779854) ^ [] : [_1457230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1457232) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36297 ^ _779854) ^ [] : [-(_1457228 = 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), _1457232)), _1457230)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457232)))]]], (31412 ^ _779854) ^ [_1346081, _1346083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1346081)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1346081), _1346083)), _1346081) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7465 ^ _779854) ^ [_902875, _902877, _902879] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_902875, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_902875, tc_HOL_Obool)), _902877), _902879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902875, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_902875, tc_HOL_Obool)), _902877)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_902875, tc_HOL_Obool)), _902879)))], (15764 ^ _779854) ^ [_1062157, _1062159, _1062161, _1062163, _1062165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062157), _1062159)), -(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), _1062159), _1062161)), _1062163)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062157), _1062161)), _1062165)) = 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), _1062159), _1062157)), _1062161)), _1062163)), _1062165))], (47364 ^ _779854) ^ [_1732053, _1732055, _1732057] : [hAPP(hAPP(c_List_Olist_OCons(_1732053), _1732055), c_List_Olist_ONil(_1732053)) = hAPP(c_List_Orev(_1732053), _1732057), -(_1732057 = hAPP(hAPP(c_List_Olist_OCons(_1732053), _1732055), c_List_Olist_ONil(_1732053)))], (49590 ^ _779854) ^ [_1781079, _1781081] : [c_Relation_Otrans(_1781079, _1781081), -(c_Relation_Otrans(tc_List_Olist(_1781079), c_List_Olistrel(_1781079, _1781081)))], (8908 ^ _779854) ^ [_928250, _928252, _928254, _928256] : [class_Lattices_Osemilattice__inf(_928250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928250), _928252), _928254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928250), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928250), _928256), _928252)), _928254)))], (48490 ^ _779854) ^ [_1756828, _1756830, _1756832, _1756834] : [c_List_Olist__ex(_1756828, _1756830, hAPP(hAPP(c_List_Olist_OCons(_1756828), _1756832), _1756834)), -(hBOOL(hAPP(_1756830, _1756832))), -(c_List_Olist__ex(_1756828, _1756830, _1756834))], (43851 ^ _779854) ^ [_1654747, _1654749, _1654751, _1654753, _1654755] : [-(hAPP(hAPP(c_List_Oappend(_1654747), _1654749), _1654751) = hAPP(hAPP(c_List_Oappend(_1654747), _1654753), _1654755)), 43852 ^ _779854 : [(43859 ^ _779854) ^ [_1654971] : [hAPP(hAPP(c_List_Oappend(_1654747), _1654749), _1654971) = _1654753, _1654751 = hAPP(hAPP(c_List_Oappend(_1654747), _1654971), _1654755)], (43853 ^ _779854) ^ [_1654859] : [_1654749 = hAPP(hAPP(c_List_Oappend(_1654747), _1654753), _1654859), hAPP(hAPP(c_List_Oappend(_1654747), _1654859), _1654751) = _1654755]]], (30465 ^ _779854) ^ [_1329863, _1329865, _1329867] : [class_Divides_Osemiring__div(_1329863), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329863), _1329865), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1329863), _1329867), _1329865))), c_Divides_Odiv__class_Omod(_1329863, _1329867, _1329865)) = _1329867)], (20025 ^ _779854) ^ [_1140940, _1140942, _1140944] : [class_Groups_Ogroup__add(_1140940), 20028 ^ _779854 : [(20035 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140940), _1140942), _1140944) = c_Groups_Ozero__class_Ozero(_1140940), -(_1140942 = hAPP(c_Groups_Ouminus__class_Ouminus(_1140940), _1140944))], (20029 ^ _779854) ^ [] : [_1140942 = hAPP(c_Groups_Ouminus__class_Ouminus(_1140940), _1140944), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140940), _1140942), _1140944) = c_Groups_Ozero__class_Ozero(_1140940))]]], (40501 ^ _779854) ^ [_1569449, _1569451] : [class_Complete__Lattice_Ocomplete__lattice(_1569449), c_Orderings_Oorder__class_Omono(_1569449, _1569449, _1569451), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_1569449, _1569451) = hAPP(_1569451, c_Inductive_Ocomplete__lattice__class_Ogfp(_1569449, _1569451)))], (30295 ^ _779854) ^ [_1326823, _1326825, _1326827, _1326829] : [class_Divides_Osemiring__div(_1326823), -(c_Divides_Odiv__class_Omod(_1326823, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326823), _1326825), _1326827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326823), _1326825), _1326829)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326823), _1326825), c_Divides_Odiv__class_Omod(_1326823, _1326827, _1326829)))], (30751 ^ _779854) ^ [_1335036, _1335038, _1335040, _1335042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335038), _1335040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335040), 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), _1335038), _1335036)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1335038), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1335042, _1335036))), _1335040))))], (44532 ^ _779854) ^ [_1670629, _1670631, _1670633, _1670635] : [-(hAPP(c_List_Orotate(_1670629, _1670631), hAPP(c_List_Orotate(_1670629, _1670633), _1670635)) = hAPP(c_List_Orotate(_1670629, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1670631), _1670633)), _1670635))], (29651 ^ _779854) ^ [_1314666, _1314668] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1314666)), c_Int_OBit1(_1314668)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1314666)), _1314668)))], (6973 ^ _779854) ^ [_893879, _893881, _893883] : [class_Lattices_Osemilattice__sup(_893879), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893879), _893881), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893879), _893881), _893883)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893879), _893881), _893883))], (39502 ^ _779854) ^ [_1543878, _1543880, _1543882, _1543884] : [39503 ^ _779854 : [(39504 ^ _779854) ^ [_1543953] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1543882, _1543878)), hAPP(hAPP(c_Product__Type_OPair(_1543882, _1543878), _1543953), _1543880)), _1543884))]], -(hBOOL(hAPP(hAPP(c_member(_1543878), _1543880), hAPP(c_Relation_ORange(_1543882, _1543878), _1543884))))], (6609 ^ _779854) ^ [_885707, _885709, _885711] : [class_Groups_Oordered__ab__group__add(_885707), 6612 ^ _779854 : [(6619 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885707), _885711), _885709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885707), hAPP(c_Groups_Ouminus__class_Ouminus(_885707), _885709)), hAPP(c_Groups_Ouminus__class_Ouminus(_885707), _885711))))], (6613 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885707), hAPP(c_Groups_Ouminus__class_Ouminus(_885707), _885709)), hAPP(c_Groups_Ouminus__class_Ouminus(_885707), _885711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885707), _885711), _885709)))]]], (11863 ^ _779854) ^ [_986059, _986061] : [-(hBOOL(hAPP(hAPP(c_member(_986059), 11864 ^ [_986059, _986061]), _986061))), -(_986061 = c_Orderings_Obot__class_Obot(tc_fun(_986059, tc_HOL_Obool)))], (34984 ^ _779854) ^ [_1430415, _1430417, _1430419, _1430421, _1430423, _1430425] : [hBOOL(hAPP(hAPP(_1430415, _1430417), _1430419)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430421, tc_fun(_1430423, tc_HOL_Obool))), _1430415), _1430425), _1430417), _1430419)))], (42388 ^ _779854) ^ [_1618951, _1618953, _1618955, _1618957, _1618959, _1618961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618951, _1618951)), hAPP(hAPP(c_Product__Type_OPair(_1618951, _1618951), _1618953), _1618955)), _1618957)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618951), tc_List_Olist(_1618951))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618951), tc_List_Olist(_1618951)), _1618959), _1618961)), c_List_Olistrel(_1618951, _1618957))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618951), tc_List_Olist(_1618951))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618951), tc_List_Olist(_1618951)), hAPP(hAPP(c_List_Olist_OCons(_1618951), _1618953), _1618959)), hAPP(hAPP(c_List_Olist_OCons(_1618951), _1618955), _1618961))), c_List_Olistrel(_1618951, _1618957))))], (30641 ^ _779854) ^ [_1332935, _1332937, _1332939] : [hBOOL(hAPP(_1332935, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332937, _1332939))), 30644 ^ _779854 : [(30669 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332939), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30672 ^ _779854 : [(30673 ^ _779854) ^ [_1333557, _1333559] : [-(hBOOL(hAPP(_1332935, _1333557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332939), _1333557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1333557), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1332937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332939), _1333559)), _1333557)]]], (30651 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332939)), 30654 ^ _779854 : [(30655 ^ _779854) ^ [_1333265, _1333267] : [-(hBOOL(hAPP(_1332935, _1333265))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333265), _1332939)), _1332937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332939), _1333267)), _1333265)]]], (30645 ^ _779854) ^ [] : [_1332939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1332935, _1332937)))]]], (35370 ^ _779854) ^ [_1438781, _1438783] : [-(_1438781 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1438783, _1438781) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438783), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438781)))], (45547 ^ _779854) ^ [_1692555] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1692555)) = _1692555)], (10493 ^ _779854) ^ [_957965, _957967, _957969] : [class_Orderings_Olinorder(_957965), hBOOL(hAPP(c_Finite__Set_Ofinite(_957965), _957967)), -(_957969 = c_Orderings_Obot__class_Obot(tc_fun(_957965, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957965, tc_HOL_Obool)), _957969), _957967)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_957965), c_Big__Operators_Olattice_OSup__fin(_957965, c_Orderings_Oord__class_Omax(_957965), _957969)), c_Big__Operators_Olattice_OSup__fin(_957965, c_Orderings_Oord__class_Omax(_957965), _957967)) = c_Big__Operators_Olattice_OSup__fin(_957965, c_Orderings_Oord__class_Omax(_957965), _957967))], (1840 ^ _779854) ^ [_805806, _805808] : [-(class_Orderings_Oorder(_805806)), _805808 = _805806, class_Orderings_Oorder(_805808)], (37277 ^ _779854) ^ [_1481429, _1481431, _1481433, _1481435, _1481437, _1481439] : [c_Equiv__Relations_Oequiv(_1481429, _1481431, _1481433), hBOOL(hAPP(hAPP(c_member(_1481429), _1481435), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481429, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1481429, _1481429, _1481433), hAPP(hAPP(c_Set_Oinsert(_1481429), _1481437), c_Orderings_Obot__class_Obot(tc_fun(_1481429, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1481429, _1481429, _1481433), hAPP(hAPP(c_Set_Oinsert(_1481429), _1481439), c_Orderings_Obot__class_Obot(tc_fun(_1481429, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1481429, _1481429)), hAPP(hAPP(c_Product__Type_OPair(_1481429, _1481429), _1481437), _1481439)), _1481433)))], (33407 ^ _779854) ^ [_1387798, _1387800, _1387802, _1387804, _1387806] : [c_Finite__Set_Ofun__left__comm(_1387798, _1387800, _1387802), -(hAPP(c_Fun_Ocomp(_1387800, _1387800, _1387800, hAPP(_1387802, _1387804)), hAPP(_1387802, _1387806)) = hAPP(c_Fun_Ocomp(_1387800, _1387800, _1387800, hAPP(_1387802, _1387806)), hAPP(_1387802, _1387804)))], (9935 ^ _779854) ^ [_947396, _947398] : [class_Orderings_Olinorder(_947396), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_947396), _947398), _947398) = _947398)], (8120 ^ _779854) ^ [_916060, _916062, _916064] : [class_Orderings_Olinorder(_916060), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916060), _916062), _916064))), -(_916062 = _916064), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916060), _916064), _916062)))], (16030 ^ _779854) ^ [_1067799, _1067801] : [16031 ^ _779854 : [(16034 ^ _779854) ^ [] : [_1067799 = _1067801], (16032 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067799), _1067801))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067799), _1067801)))], (29661 ^ _779854) ^ [_1314895] : [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), _1314895))), 29664 ^ _779854 : [(29667 ^ _779854) ^ [] : [-(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(_1314895)))))], (29665 ^ _779854) ^ [] : [-(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(_1314895)))))]]], (33749 ^ _779854) ^ [_1400841, _1400843, _1400845, _1400847, _1400849] : [_1400841 = c_Orderings_Obot__class_Obot(tc_fun(_1400843, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400845, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400843, tc_fun(_1400845, tc_HOL_Obool)), _1400841), _1400847)), _1400849) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400845, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1400845, tc_HOL_Obool))), _1400849))], (41591 ^ _779854) ^ [_1596354] : [-(c_Relation_Osingle__valued(_1596354, _1596354, c_Relation_OId(_1596354)))], (48828 ^ _779854) ^ [_1763909, _1763911, _1763913] : [-(c_List_Osplice(_1763909, hAPP(hAPP(c_List_Olist_OCons(_1763909), _1763911), _1763913), c_List_Olist_ONil(_1763909)) = hAPP(hAPP(c_List_Olist_OCons(_1763909), _1763911), _1763913))], (31744 ^ _779854) ^ [_1351228, _1351230] : [class_Int_Oring__char__0(_1351228), 31747 ^ _779854 : [(31754 ^ _779854) ^ [] : [_1351230 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1351228), _1351230) = c_Groups_Ozero__class_Ozero(_1351228))], (31748 ^ _779854) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1351228), _1351230) = c_Groups_Ozero__class_Ozero(_1351228), -(_1351230 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (3052 ^ _779854) ^ [_825411, _825413, _825415, _825417] : [-(c_List_Olexn(_825417, _825413) = c_List_Olexn(_825415, _825411)), _825417 = _825415, _825413 = _825411], (43406 ^ _779854) ^ [_1645250, _1645252, _1645254] : [c_List_Olist_ONil(_1645250) = hAPP(hAPP(c_List_Olist_OCons(_1645250), _1645252), _1645254)], (44236 ^ _779854) ^ [_1664060, _1664062] : [hBOOL(hAPP(c_List_Odistinct(_1664060), hAPP(c_List_Orotate1(_1664060), _1664062))), -(hBOOL(hAPP(c_List_Odistinct(_1664060), _1664062)))], (10591 ^ _779854) ^ [_960032, _960034, _960036] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960032, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960032, tc_HOL_Obool)), _960034), _960036)), _960036) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960032, tc_HOL_Obool)), _960034), _960036))], (31950 ^ _779854) ^ [] : [-(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))], (32233 ^ _779854) ^ [_1359829, _1359831, _1359833] : [class_Rings_Olinordered__idom(_1359829), 32236 ^ _779854 : [(32245 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359829), hAPP(c_Groups_Oabs__class_Oabs(_1359829), _1359831)), _1359833))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359829), _1359831), _1359833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359829), hAPP(c_Groups_Ouminus__class_Ouminus(_1359829), _1359831)), _1359833))], (32237 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359829), hAPP(c_Groups_Oabs__class_Oabs(_1359829), _1359831)), _1359833)), 32240 ^ _779854 : [(32243 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359829), hAPP(c_Groups_Ouminus__class_Ouminus(_1359829), _1359831)), _1359833)))], (32241 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359829), _1359831), _1359833)))]]]]], (29617 ^ _779854) ^ [_1314048, _1314050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314048), _1314050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1314048)), c_Int_OBit0(_1314050))))], (17518 ^ _779854) ^ [_1096953, _1096955, _1096957] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096953), _1096955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1096953, tc_HOL_Obool)), _1096957), _1096955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1096953), _1096957)), hAPP(c_Finite__Set_Ocard(_1096953), _1096955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1096953, tc_HOL_Obool)), _1096957), _1096955)))], (22119 ^ _779854) ^ [_1179429, _1179431, _1179433, _1179435] : [class_Fields_Olinordered__field__inverse__zero(_1179429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179429), _1179431), _1179433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179429), _1179435), c_Groups_Ozero__class_Ozero(_1179429))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179429), c_Groups_Ozero__class_Ozero(_1179429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179429), _1179431), _1179433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179429), _1179435), _1179431)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179429), _1179435), _1179433))))], (45526 ^ _779854) ^ [_1692073, _1692075, _1692077, _1692079, _1692081] : [class_Groups_Omonoid__add(_1692073), class_Groups_Oordered__ab__semigroup__add(_1692073), 45536 ^ _779854 : [(45539 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1692073), hAPP(_1692079, 45535 ^ [_1692073, _1692075, _1692077, _1692079, _1692081])), hAPP(_1692081, 45535 ^ [_1692073, _1692075, _1692077, _1692079, _1692081])))], (45537 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1692075), 45535 ^ [_1692073, _1692075, _1692077, _1692079, _1692081]), hAPP(c_List_Oset(_1692075), _1692077))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1692073), hAPP(c_List_Omonoid__add__class_Olistsum(_1692073), hAPP(hAPP(c_List_Omap(_1692075, _1692073), _1692079), _1692077))), hAPP(c_List_Omonoid__add__class_Olistsum(_1692073), hAPP(hAPP(c_List_Omap(_1692075, _1692073), _1692081), _1692077)))))], (38019 ^ _779854) ^ [_1498874, _1498876] : [-(c_Nitpick_Onumber__of__frac(_1498874, _1498876) = c_Nitpick_OAbs__Frac(_1498874, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1498876), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (27199 ^ _779854) ^ [_1272804, _1272806] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272804), c_Int_OPls))), 27202 ^ _779854 : [(27209 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272806), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272804)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272806)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1272804), _1272806)))], (27203 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272806), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272804)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272806)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272804))]]], (12402 ^ _779854) ^ [_996369, _996371, _996373] : [class_Orderings_Oord(_996369), 12405 ^ _779854 : [(12412 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996369), _996371), _996373)), -(hBOOL(hAPP(hAPP(c_member(_996369), _996371), hAPP(c_SetInterval_Oord__class_OlessThan(_996369), _996373))))], (12406 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_996369), _996371), hAPP(c_SetInterval_Oord__class_OlessThan(_996369), _996373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996369), _996371), _996373)))]]], (25635 ^ _779854) ^ [_1245983, _1245985, _1245987, _1245989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245983), _1245985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245987), _1245989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245983), _1245987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245985), _1245989))))], (4638 ^ _779854) ^ [_850560, _850562] : [_850562 = _850560, -(c_DSequence_Ounion(_850562) = c_DSequence_Ounion(_850560))], (45593 ^ _779854) ^ [] : [-(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))], (49418 ^ _779854) ^ [_1776962, _1776964, _1776966, _1776968] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1776962, _1776964, _1776966, _1776968, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1776964)) = _1776966)], (24577 ^ _779854) ^ [_1225685, _1225687, _1225689] : [class_Int_Onumber__ring(_1225685), class_Rings_Olinordered__idom(_1225685), 24584 ^ _779854 : [(24591 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225687), _1225689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225685), hAPP(c_Int_Onumber__class_Onumber__of(_1225685), _1225687)), hAPP(c_Int_Onumber__class_Onumber__of(_1225685), _1225689))))], (24585 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225685), hAPP(c_Int_Onumber__class_Onumber__of(_1225685), _1225687)), hAPP(c_Int_Onumber__class_Onumber__of(_1225685), _1225689))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225687), _1225689)))]]], (3384 ^ _779854) ^ [_830545, _830547, _830549, _830551] : [-(c_Enum_Osublists(_830551, _830547) = c_Enum_Osublists(_830549, _830545)), _830551 = _830549, _830547 = _830545], (43340 ^ _779854) ^ [_1644090, _1644092, _1644094, _1644096] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1644090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1644092), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1644090)), hAPP(hAPP(c_List_Olist_OCons(_1644092), _1644094), _1644096)) = hAPP(hAPP(c_List_Olist_OCons(_1644092), _1644094), hAPP(hAPP(c_List_Otake(_1644092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1644090)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1644096)))], (47631 ^ _779854) ^ [_1737804, _1737806, _1737808, _1737810] : [-(hBOOL(hAPP(_1737804, _1737806))), -(c_List_OtakeWhile(_1737808, _1737804, hAPP(hAPP(c_List_Olist_OCons(_1737808), _1737806), _1737810)) = c_List_Olist_ONil(_1737808))], (48316 ^ _779854) ^ [_1753410, _1753412] : [class_Enum_Oenum(_1753410), 48319 ^ _779854 : [(48326 ^ _779854) ^ [] : [hBOOL(hAPP(_1753412, 48327 ^ [_1753410, _1753412])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753410), _1753412)))], (48320 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753410), _1753412)), 48323 ^ _779854 : [(48324 ^ _779854) ^ [_1753536] : [-(hBOOL(hAPP(_1753412, _1753536)))]]]]], (17775 ^ _779854) ^ [_1101989, _1101991] : [class_Groups_Omonoid__mult(_1101989), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101989), _1101991), c_Groups_Oone__class_Oone(_1101989)) = _1101991)], (46406 ^ _779854) ^ [_1712215, _1712217, _1712219] : [hAPP(c_List_Ofilter(_1712215, _1712217), _1712219) = _1712219, 46409 ^ _779854 : [(46410 ^ _779854) ^ [_1712306] : [hBOOL(hAPP(hAPP(c_member(_1712215), _1712306), hAPP(c_List_Oset(_1712215), _1712219))), -(hBOOL(hAPP(_1712217, _1712306)))]]], (12548 ^ _779854) ^ [_999228, _999230, _999232, _999234] : [c_Fun_Oinj__on(_999228, _999230, _999232, c_Orderings_Otop__class_Otop(tc_fun(_999228, tc_HOL_Obool))), 12551 ^ _779854 : [(12565 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_999230), _999234), hAPP(c_Set_Oimage(_999228, _999230, _999232), c_Orderings_Otop__class_Otop(tc_fun(_999228, tc_HOL_Obool)))))), 12566 ^ _779854 : [(12567 ^ _779854) ^ [_999631] : [_999234 = hAPP(_999232, _999631), 12571 ^ _779854 : [(12574 ^ _779854) ^ [] : [12570 ^ [_999228, _999230, _999232, _999234, _999631] = _999631], (12572 ^ _779854) ^ [] : [-(_999234 = hAPP(_999232, 12570 ^ [_999228, _999230, _999232, _999234, _999631]))]]]]], (12552 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_999230), _999234), hAPP(c_Set_Oimage(_999228, _999230, _999232), c_Orderings_Otop__class_Otop(tc_fun(_999228, tc_HOL_Obool))))), 12556 ^ _779854 : [(12559 ^ _779854) ^ [_999493] : [_999234 = hAPP(_999232, _999493), -(_999493 = 12555 ^ [_999228, _999230, _999232, _999234])], (12557 ^ _779854) ^ [] : [-(_999234 = hAPP(_999232, 12555 ^ [_999228, _999230, _999232, _999234]))]]]]], (39369 ^ _779854) ^ [_1539871, _1539873, _1539875, _1539877] : [class_Groups_Ocomm__monoid__mult(_1539871), c_Fun_Oinj__on(_1539873, _1539871, _1539875, _1539877), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1539873, _1539871), _1539875), _1539877) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1539871, _1539871), c_Fun_Oid(_1539871)), hAPP(c_Set_Oimage(_1539873, _1539871, _1539875), _1539877)))], (30613 ^ _779854) ^ [_1332467, _1332469] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332467, _1332469) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1332467), _1332469)), _1332469)))], (20427 ^ _779854) ^ [_1147489, _1147491, _1147493] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147489), _1147491)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147489), _1147493)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147491), _1147493))], (46641 ^ _779854) ^ [_1718395, _1718397, _1718399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718395), _1718397)), -(c_List_Oupt(_1718395, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1718397), _1718399)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1718395, _1718397)), c_List_Oupt(_1718397, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1718397), _1718399))))], (30117 ^ _779854) ^ [_1323196, _1323198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1323196)), -(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)))), _1323198)), 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)))), _1323196)) = 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, _1323198, _1323196))))], (39983 ^ _779854) ^ [] : [-(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))))], (41088 ^ _779854) ^ [_1584021, _1584023] : [-(c_Transitive__Closure_Ortrancl(_1584021, c_Transitive__Closure_Ortrancl(_1584021, _1584023)) = c_Transitive__Closure_Ortrancl(_1584021, _1584023))], (14596 ^ _779854) ^ [_1038579, _1038581, _1038583, _1038585] : [-(hBOOL(hAPP(hAPP(c_member(_1038579), _1038581), _1038583))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038579, tc_Nat_Onat), _1038585), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038579, tc_HOL_Obool)), _1038583), hAPP(hAPP(c_Set_Oinsert(_1038579), _1038581), c_Orderings_Obot__class_Obot(tc_fun(_1038579, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038579, tc_Nat_Onat), _1038585), _1038583))], (16511 ^ _779854) ^ [_1077264, _1077266, _1077268, _1077270, _1077272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077264), _1077266)), 16514 ^ _779854 : [(16521 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077270), 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), _1077266), _1077264)), _1077268)), _1077272))), -(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), _1077264), _1077268)), _1077270)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077266), _1077268)), _1077272))))], (16515 ^ _779854) ^ [] : [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), _1077264), _1077268)), _1077270)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077266), _1077268)), _1077272))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077270), 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), _1077266), _1077264)), _1077268)), _1077272))))]]], (48333 ^ _779854) ^ [_1753663, _1753665] : [class_Enum_Oenum(_1753663), 48336 ^ _779854 : [(48344 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753663), _1753665)), 48347 ^ _779854 : [(48348 ^ _779854) ^ [_1753881] : [-(hBOOL(hAPP(_1753665, _1753881)))]]], (48337 ^ _779854) ^ [] : [hBOOL(hAPP(_1753665, 48338 ^ [_1753663, _1753665])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753663), _1753665)))]]], (7539 ^ _779854) ^ [_904288, _904290, _904292] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904288, tc_HOL_Obool)), _904290), _904292) = c_Orderings_Obot__class_Obot(tc_fun(_904288, tc_HOL_Obool)), 7542 ^ _779854 : [(7545 ^ _779854) ^ [] : [-(_904292 = c_Orderings_Obot__class_Obot(tc_fun(_904288, tc_HOL_Obool)))], (7543 ^ _779854) ^ [] : [-(_904290 = c_Orderings_Obot__class_Obot(tc_fun(_904288, tc_HOL_Obool)))]]], (15048 ^ _779854) ^ [_1047353, _1047355] : [class_Lattices_Oab__semigroup__idem__mult(_1047353), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047353), _1047355), _1047355) = _1047355)], (36185 ^ _779854) ^ [_1454944, _1454946, _1454948, _1454950, _1454952] : [-(hAPP(c_Product__Type_Ofst(_1454944, _1454946), hAPP(c_Product__Type_Oapsnd(_1454948, _1454946, _1454944, _1454950), _1454952)) = hAPP(c_Product__Type_Ofst(_1454944, _1454948), _1454952))], (42496 ^ _779854) ^ [_1622239, _1622241, _1622243, _1622245] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622239)), hAPP(hAPP(c_List_Olist_OCons(_1622239), _1622241), _1622243)), c_List_Olists(_1622239, _1622245)))), hBOOL(hAPP(hAPP(c_member(_1622239), _1622241), _1622245)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622239)), _1622243), c_List_Olists(_1622239, _1622245)))], (9873 ^ _779854) ^ [_946072, _946074, _946076, _946078, _946080] : [class_Lattices_Osemilattice__sup(_946072), class_Orderings_Olinorder(_946074), c_Orderings_Oorder__class_Omono(_946074, _946072, _946076), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946072), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_946072), hAPP(_946076, _946078)), hAPP(_946076, _946080))), hAPP(_946076, hAPP(hAPP(c_Orderings_Oord__class_Omax(_946074), _946078), _946080)))))], (50804 ^ _779854) ^ [_1807258, _1807260, _1807262, _1807264, _1807266, _1807268, _1807270] : [c_Fun_Obij__betw(_1807258, _1807260, _1807262, _1807264, _1807266), c_Fun_Obij__betw(_1807258, _1807260, _1807262, _1807268, _1807270), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1807260, tc_HOL_Obool)), _1807266), _1807270) = c_Orderings_Obot__class_Obot(tc_fun(_1807260, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1807258, _1807260, _1807262, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1807258, tc_HOL_Obool)), _1807264), _1807268), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1807260, tc_HOL_Obool)), _1807266), _1807270)))], (32637 ^ _779854) ^ [_1367339, _1367341, _1367343] : [class_Divides_Osemiring__div(_1367339), -(_1367341 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1367339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367339), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367339), _1367341), _1367343)), _1367343)), c_Divides_Odiv__class_Omod(_1367339, _1367341, _1367343)))], (46322 ^ _779854) ^ [_1709403, _1709405, _1709407, _1709409] : [-(hAPP(hAPP(c_List_Omap(_1709403, _1709405), _1709407), c_List_Oconcat(_1709403, _1709409)) = c_List_Oconcat(_1709405, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1709403), tc_List_Olist(_1709405)), hAPP(c_List_Omap(_1709403, _1709405), _1709407)), _1709409)))], (36379 ^ _779854) ^ [_1458795, _1458797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1458795)), -(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(_1458795), _1458797))), _1458795)))], (38444 ^ _779854) ^ [_1510195, _1510197, _1510199, _1510201] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1510195, _1510197)), hAPP(hAPP(c_Product__Type_OSigma(_1510195, _1510197), _1510199), hAPP(c_COMBK(tc_fun(_1510197, tc_HOL_Obool), _1510195), _1510201)))), -(_1510199 = c_Orderings_Obot__class_Obot(tc_fun(_1510195, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1510197), _1510201)))], (17883 ^ _779854) ^ [_1103637, _1103639, _1103641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103637), _1103639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103639), _1103641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103637)), _1103641)))], (52215 ^ _779854) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (42482 ^ _779854) ^ [_1621938, _1621940, _1621942] : [c_Relation_Orefl__on(_1621938, _1621940, _1621942), -(c_Relation_Orefl__on(tc_List_Olist(_1621938), c_List_Olists(_1621938, _1621940), c_List_Olistrel(_1621938, _1621942)))], (20838 ^ _779854) ^ [_1154941, _1154943] : [_1154941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1154941), _1154943) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37821 ^ _779854) ^ [_1494561, _1494563, _1494565, _1494567] : [c_Wellfounded_Omax__extp(_1494561, _1494563, _1494565, _1494567), 37824 ^ _779854 : [(37827 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1494561), _1494567)))], (37829 ^ _779854) ^ [] : [_1494567 = c_Orderings_Obot__class_Obot(tc_fun(_1494561, tc_HOL_Obool))], (37831 ^ _779854) ^ [_1494777] : [hBOOL(hAPP(hAPP(c_member(_1494561), _1494777), _1494565)), 37835 ^ _779854 : [(37838 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1494563, _1494777), 37834 ^ [_1494561, _1494563, _1494565, _1494567, _1494777])))], (37836 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494561), 37834 ^ [_1494561, _1494563, _1494565, _1494567, _1494777]), _1494567)))]]], (37825 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1494561), _1494565)))]]], (1280 ^ _779854) ^ [_798806, _798808] : [-(class_Divides_Oring__div(_798806)), _798808 = _798806, class_Divides_Oring__div(_798808)], (52627 ^ _779854) ^ [_1838058] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1838058)))], (1390 ^ _779854) ^ [_800181, _800183] : [-(class_Lattices_Obounded__lattice__top(_800181)), _800183 = _800181, class_Lattices_Obounded__lattice__top(_800183)], (18579 ^ _779854) ^ [_1116237, _1116239, _1116241] : [class_Rings_Ono__zero__divisors(_1116237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116237), _1116239), _1116241) = c_Groups_Ozero__class_Ozero(_1116237), -(_1116239 = c_Groups_Ozero__class_Ozero(_1116237)), -(_1116241 = c_Groups_Ozero__class_Ozero(_1116237))], (35408 ^ _779854) ^ [_1439499, _1439501, _1439503, _1439505, _1439507] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1439499, _1439501), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1439503), _1439505))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1439501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1439507)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1439499, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439501), _1439507)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1439503), _1439507)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1439501), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1439503, _1439507))), _1439505)))))], (39701 ^ _779854) ^ [_1550015, _1550017, _1550019] : [c_Wellfounded_Owf(_1550015, _1550017), hBOOL(hAPP(hAPP(c_member(tc_prod(_1550015, _1550015)), hAPP(hAPP(c_Product__Type_OPair(_1550015, _1550015), _1550019), _1550019)), _1550017))], (16471 ^ _779854) ^ [_1076291, _1076293, _1076295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076291), _1076293)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076295), _1076293)), _1076291) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076295), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076293), _1076291)))], (516 ^ _779854) ^ [_787604, _787606] : [-(c_Nat__Transfer_Onat__set(_787604)), _787606 = _787604, c_Nat__Transfer_Onat__set(_787606)], (48862 ^ _779854) ^ [_1764682, _1764684, _1764686, _1764688, _1764690] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1764682, _1764684, _1764686), _1764688), _1764690)), -(hBOOL(hAPP(hAPP(_1764686, _1764690), _1764688)))], (50469 ^ _779854) ^ [_1799798, _1799800, _1799802, _1799804] : [c_Fun_Oinj__on(_1799798, _1799800, _1799802, c_Orderings_Otop__class_Otop(tc_fun(_1799798, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1799800, _1799798, c_Hilbert__Choice_Oinv__into(_1799798, _1799800, c_Orderings_Otop__class_Otop(tc_fun(_1799798, tc_HOL_Obool)), _1799802)), hAPP(c_Set_Oimage(_1799798, _1799800, _1799802), _1799804)) = _1799804)], (42068 ^ _779854) ^ [_1608664] : [-(c_Nitpick_Onum(_1608664) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1608664, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1608664)))], (2754 ^ _779854) ^ [_820810, _820812, _820814, _820816] : [-(c_Predicate_OPowp(_820816, _820812) = c_Predicate_OPowp(_820814, _820810)), _820816 = _820814, _820812 = _820810], (39605 ^ _779854) ^ [_1548209, _1548211, _1548213] : [c_Wellfounded_Owf(_1548209, _1548211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1548209, _1548209), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1548209, _1548209, _1548209), _1548211), _1548213)), _1548211)), -(c_FunDef_Oreduction__pair(_1548209, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1548209, _1548209), tc_HOL_Obool), tc_fun(tc_prod(_1548209, _1548209), tc_HOL_Obool)), _1548211), _1548213)))], (41348 ^ _779854) ^ [_1590236, _1590238, _1590240, _1590242] : [-(c_Wellfounded_Oacyclic(_1590236, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1590236, _1590236)), hAPP(hAPP(c_Product__Type_OPair(_1590236, _1590236), _1590238), _1590240)), _1590242))), c_Wellfounded_Oacyclic(_1590236, _1590242), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590236, _1590236)), hAPP(hAPP(c_Product__Type_OPair(_1590236, _1590236), _1590240), _1590238)), c_Transitive__Closure_Ortrancl(_1590236, _1590242))))], (21597 ^ _779854) ^ [_1169704, _1169706, _1169708, _1169710] : [21598 ^ _779854 : [(21601 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1169708), _1169710)))], (21599 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1169704), _1169706)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1169704, _1169708)), c_Sum__Type_OPlus(_1169704, _1169708, _1169706, _1169710)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14560 ^ _779854) ^ [_1037894, _1037896, _1037898, _1037900] : [c_Finite__Set_Ofolding__one(_1037894, _1037896, _1037898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037894), _1037900)), -(hAPP(_1037898, _1037900) = hAPP(c_Finite__Set_Ofold1(_1037894, _1037896), _1037900))], (33449 ^ _779854) ^ [_1388948, _1388950, _1388952, _1388954] : [hBOOL(hAPP(hAPP(c_member(_1388948), _1388954), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388948, tc_HOL_Obool)), _1388950), _1388952))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388948, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1388948, tc_fun(_1388948, tc_HOL_Obool), tc_HOL_Obool), c_member(_1388948)), _1388950)), hAPP(hAPP(c_COMBC(_1388948, tc_fun(_1388948, tc_HOL_Obool), tc_HOL_Obool), c_member(_1388948)), _1388952)), _1388954)))], (48880 ^ _779854) ^ [_1765033, _1765035, _1765037, _1765039, _1765041] : [hBOOL(hAPP(hAPP(_1765037, _1765041), _1765039)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1765033, _1765035, _1765037), _1765039), _1765041)))], (19261 ^ _779854) ^ [_1127198, _1127200, _1127202, _1127204] : [class_Rings_Oordered__ring(_1127198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127198), _1127200), _1127202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127198), _1127204), c_Groups_Ozero__class_Ozero(_1127198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127198), _1127202), _1127204)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127198), _1127200), _1127204))))], (42101 ^ _779854) ^ [_1609390, _1609392] : [-(c_List_Olenlex(_1609390, _1609392) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1609390), tc_List_Olist(_1609390), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1609390), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1609390), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), tc_List_Olist(_1609390)), c_COMBS(tc_List_Olist(_1609390), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1609390)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1609390)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1609390), tc_fun(tc_List_Olist(_1609390), tc_Nat_Onat), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1609390), tc_Nat_Onat), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), tc_List_Olist(_1609390)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1609390))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1609390)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1609390))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1609390)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1609390), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1609390), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), tc_List_Olist(_1609390)), c_COMBS(tc_List_Olist(_1609390), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1609390)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1609390)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1609390), tc_fun(tc_List_Olist(_1609390), tc_Nat_Onat), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1609390), tc_Nat_Onat), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), tc_List_Olist(_1609390)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1609390))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1609390)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1609390))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1609390)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1609390), tc_fun(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1609390), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1609390), tc_HOL_Obool)), tc_List_Olist(_1609390)), c_COMBC(tc_List_Olist(_1609390), tc_fun(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1609390), tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390))), tc_fun(tc_List_Olist(_1609390), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1609390)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1609390)), c_member(tc_prod(tc_List_Olist(_1609390), tc_List_Olist(_1609390))))), c_Product__Type_OPair(tc_List_Olist(_1609390), tc_List_Olist(_1609390))))), c_List_Olex(_1609390, _1609392)))))))], (44218 ^ _779854) ^ [_1663571, _1663573, _1663575, _1663577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663571), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663573)), _1663575))), -(hAPP(hAPP(c_List_Olist__update(_1663573, _1663575), _1663571), _1663577) = hAPP(hAPP(c_List_Oappend(_1663573), hAPP(hAPP(c_List_Otake(_1663573), _1663571), _1663575)), hAPP(hAPP(c_List_Olist_OCons(_1663573), _1663577), hAPP(hAPP(c_List_Odrop(_1663573), hAPP(c_Nat_OSuc, _1663571)), _1663575))))], (35113 ^ _779854) ^ [_1433123, _1433125, _1433127, _1433129, _1433131] : [-(hAPP(c_Nat_Onat_Onat__rec(_1433123, _1433125, _1433127), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433129)), _1433131)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1433123), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1433129))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1433123, _1433123), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1433123, tc_fun(_1433123, _1433123)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1433123, tc_fun(_1433123, _1433123)), tc_Int_Oint), c_If(_1433123)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1433123, _1433125, _1433127), _1433131))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1433123, _1433123), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1433123, _1433123), tc_Int_Oint), _1433127), 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)), _1433131))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1433123, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1433123, _1433125, _1433127)), 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)), _1433131))))))], (20301 ^ _779854) ^ [_1145353] : [-(hAPP(c_Finite__Set_Ocard(_1145353), c_Orderings_Obot__class_Obot(tc_fun(_1145353, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6165 ^ _779854) ^ [_877784, _877786, _877788] : [class_Orderings_Olinorder(_877784), 6168 ^ _779854 : [(6175 ^ _779854) ^ [] : [_877786 = _877788, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_877784), _877786) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_877784), _877788))], (6169 ^ _779854) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_877784), _877786) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_877784), _877788), -(_877786 = _877788)]]], (2264 ^ _779854) ^ [_813005, _813007] : [_813007 = _813005, -(c_Int_Opred(_813007) = c_Int_Opred(_813005))], (21064 ^ _779854) ^ [_1158898, _1158900, _1158902] : [21065 ^ _779854 : [(21068 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158898), _1158902))], (21066 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158900)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158898), _1158900)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158902), _1158900))))], (9720 ^ _779854) ^ [_942882, _942884, _942886, _942888] : [class_Orderings_Olinorder(_942882), 9723 ^ _779854 : [(9724 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942882), _942884), hAPP(hAPP(c_Orderings_Oord__class_Omax(_942882), _942886), _942888))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942882), _942884), _942886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942882), _942884), _942888)))], (9734 ^ _779854) ^ [] : [9735 ^ _779854 : [(9738 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942882), _942884), _942888))], (9736 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942882), _942884), _942886))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942882), _942884), hAPP(hAPP(c_Orderings_Oord__class_Omax(_942882), _942886), _942888))))]]], (6759 ^ _779854) ^ [_888856, _888858, _888860, _888862] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888856, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888856, tc_HOL_Obool)), _888858), _888860)), _888862) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888856, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888856, tc_HOL_Obool)), _888858), _888862)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888856, tc_HOL_Obool)), _888860), _888862)))], (50308 ^ _779854) ^ [_1796082, _1796084] : [c_Equiv__Relations_Oequivp(_1796082, _1796084), -(c_Equiv__Relations_Opart__equivp(_1796082, _1796084))], (37974 ^ _779854) ^ [_1497628, _1497630, _1497632, _1497634] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497628), _1497630)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497628), _1497632)), -(_1497632 = c_Orderings_Obot__class_Obot(tc_fun(_1497628, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1497628, tc_HOL_Obool), tc_fun(_1497628, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1497628, tc_HOL_Obool), tc_fun(_1497628, tc_HOL_Obool)), _1497630), _1497632)), c_Wellfounded_Omax__ext(_1497628, _1497634)))), 37988 ^ _779854 : [(37991 ^ _779854) ^ [_1498033] : [hBOOL(hAPP(hAPP(c_member(_1497628), _1498033), _1497632)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1497628, _1497628)), hAPP(hAPP(c_Product__Type_OPair(_1497628, _1497628), 37987 ^ [_1497628, _1497630, _1497632, _1497634]), _1498033)), _1497634))], (37989 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497628), 37987 ^ [_1497628, _1497630, _1497632, _1497634]), _1497630)))]]], (8134 ^ _779854) ^ [_916195, _916197, _916199] : [class_Orderings_Opreorder(_916195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916195), _916197), _916199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916195), _916199), _916197))], (16483 ^ _779854) ^ [_1076565, _1076567, _1076569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076565), _1076567)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076567), _1076569)), _1076565) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076567), _1076565)), _1076569))], (12464 ^ _779854) ^ [_997496, _997498, _997500] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997496, tc_HOL_Obool)), _997498), hAPP(c_Set_OPow(_997496), _997500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997496, tc_HOL_Obool)), _997498), _997500)))], (29363 ^ _779854) ^ [_1309535] : [-(c_Int_OBit0(_1309535) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309535), _1309535))], (9210 ^ _779854) ^ [_933541, _933543, _933545] : [-(hAPP(hAPP(c_Set_Oinsert(_933541), _933543), _933545) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933541, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_933541), _933543), c_Orderings_Obot__class_Obot(tc_fun(_933541, tc_HOL_Obool)))), _933545))], (17769 ^ _779854) ^ [_1101894, _1101896] : [class_Groups_Ocomm__monoid__mult(_1101894), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101894), c_Groups_Oone__class_Oone(_1101894)), _1101896) = _1101896)], (7519 ^ _779854) ^ [_903873, _903875, _903877] : [class_Lattices_Oboolean__algebra(_903873), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903873), _903875), _903877) = c_Orderings_Obot__class_Obot(_903873), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903873), _903875), _903877) = c_Orderings_Otop__class_Otop(_903873), -(hAPP(c_Groups_Ouminus__class_Ouminus(_903873), _903875) = _903877)], (27381 ^ _779854) ^ [_1276068, _1276070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1276068)), -(c_SMT_Oz3div(_1276070, _1276068) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1276070), _1276068))], (34972 ^ _779854) ^ [_1430161, _1430163, _1430165] : [_1430161 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1430163, _1430163), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1430163, _1430163), tc_HOL_Obool)), _1430161), _1430165)))], (44155 ^ _779854) ^ [_1661655, _1661657, _1661659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661655), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661657)), _1661659))), -(hAPP(hAPP(c_List_Otake(_1661657), hAPP(c_Nat_OSuc, _1661655)), _1661659) = hAPP(hAPP(c_List_Oappend(_1661657), hAPP(hAPP(c_List_Otake(_1661657), _1661655), _1661659)), hAPP(hAPP(c_List_Olist_OCons(_1661657), hAPP(hAPP(c_List_Onth(_1661657), _1661659), _1661655)), c_List_Olist_ONil(_1661657))))], (52733 ^ _779854) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts))], (9582 ^ _779854) ^ [_940481, _940483, _940485, _940487] : [class_Orderings_Olinorder(_940481), 9585 ^ _779854 : [(9594 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940481), hAPP(hAPP(c_Orderings_Oord__class_Omax(_940481), _940483), _940485)), _940487))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940481), _940483), _940487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940481), _940485), _940487))], (9586 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940481), hAPP(hAPP(c_Orderings_Oord__class_Omax(_940481), _940483), _940485)), _940487)), 9589 ^ _779854 : [(9592 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940481), _940485), _940487)))], (9590 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940481), _940483), _940487)))]]]]], (17987 ^ _779854) ^ [_1105308, _1105310, _1105312] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1105308), _1105310)), 17990 ^ _779854 : [(17991 ^ _779854) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1105308, tc_Nat_Onat), _1105312), _1105310) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17994 ^ _779854 : [(17995 ^ _779854) ^ [_1105470] : [hBOOL(hAPP(hAPP(c_member(_1105308), _1105470), _1105310)), -(hAPP(_1105312, _1105470) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (18001 ^ _779854) ^ [] : [18003 ^ _779854 : [(18006 ^ _779854) ^ [] : [hAPP(_1105312, 18002 ^ [_1105308, _1105310, _1105312]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (18004 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105308), 18002 ^ [_1105308, _1105310, _1105312]), _1105310)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1105308, tc_Nat_Onat), _1105312), _1105310) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (50776 ^ _779854) ^ [_1806667, _1806669, _1806671] : [c_Fun_Obij__betw(_1806667, _1806669, _1806671, c_Orderings_Otop__class_Otop(tc_fun(_1806667, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1806669, tc_HOL_Obool))), 50779 ^ _779854 : [(50782 ^ _779854) ^ [] : [-(hAPP(c_Set_Oimage(_1806667, _1806669, _1806671), c_Orderings_Otop__class_Otop(tc_fun(_1806667, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1806669, tc_HOL_Obool)))], (50780 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_1806667, _1806669, _1806671, c_Orderings_Otop__class_Otop(tc_fun(_1806667, tc_HOL_Obool))))]]], (142 ^ _779854) ^ [_781985, _781987, _781989, _781991, _781993, _781995, _781997, _781999, _782001, _782003] : [-(c_Big__Operators_Ocomm__monoid__big(_782001, _781997, _781993, _781989, _781985)), c_Big__Operators_Ocomm__monoid__big(_782003, _781999, _781995, _781991, _781987), _782003 = _782001, _781999 = _781997, _781995 = _781993, _781991 = _781989, _781987 = _781985], (6411 ^ _779854) ^ [_882031, _882033] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882031, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882031, tc_HOL_Obool)), _882033)) = _882033)], (36484 ^ _779854) ^ [_1460840, _1460842, _1460844, _1460846, _1460848, _1460850, _1460852, _1460854] : [c_Finite__Set_Ofolding__image(_1460840, _1460842, _1460844, _1460846, _1460848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460842), _1460850)), -(hAPP(hAPP(_1460848, hAPP(hAPP(c_COMBS(_1460842, _1460840, _1460840), hAPP(hAPP(c_COMBB(_1460840, tc_fun(_1460840, _1460840), _1460842), _1460844), _1460852)), _1460854)), _1460850) = hAPP(hAPP(_1460844, hAPP(hAPP(_1460848, _1460852), _1460850)), hAPP(hAPP(_1460848, _1460854), _1460850)))], (49034 ^ _779854) ^ [_1768531, _1768533, _1768535, _1768537] : [-(hAPP(hAPP(c_List_Oappend(_1768531), c_List_Oreplicate(_1768531, _1768533, _1768535)), c_List_Oreplicate(_1768531, _1768537, _1768535)) = hAPP(hAPP(c_List_Oappend(_1768531), c_List_Oreplicate(_1768531, _1768537, _1768535)), c_List_Oreplicate(_1768531, _1768533, _1768535)))], (46583 ^ _779854) ^ [_1716789, _1716791] : [-(c_List_Ofoldr(tc_List_Olist(_1716789), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1716789)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1716789))), c_List_Otranspose(_1716789, _1716791), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1716789))), hAPP(c_List_Ofilter(tc_List_Olist(_1716789), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1716789)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1716789), tc_List_Olist(_1716789), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1716789)))), _1716791)))], (46425 ^ _779854) ^ [_1712607, _1712609, _1712611] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712607)), hAPP(c_List_Ofilter(_1712607, _1712609), _1712611))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712607)), hAPP(c_List_Ofilter(_1712607, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1712607), c_fNot), _1712609)), _1712611))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712607)), _1712611))], (50294 ^ _779854) ^ [_1795853, _1795855, _1795857, _1795859, _1795861] : [c_Equiv__Relations_Opart__equivp(_1795853, _1795855), hBOOL(hAPP(hAPP(_1795855, _1795857), _1795859)), hBOOL(hAPP(hAPP(_1795855, _1795859), _1795861)), -(hBOOL(hAPP(hAPP(_1795855, _1795857), _1795861)))], (23958 ^ _779854) ^ [_1214447, _1214449] : [class_Groups_Omonoid__mult(_1214447), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214447), c_Groups_Oone__class_Oone(_1214447)), _1214449) = c_Groups_Oone__class_Oone(_1214447))], (23551 ^ _779854) ^ [_1206335, _1206337, _1206339] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1206335), _1206337)), 23557 ^ _779854 : [(23560 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1206339, 23556 ^ [_1206335, _1206337, _1206339])))], (23558 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1206335), 23556 ^ [_1206335, _1206337, _1206339]), _1206337)))]], -(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(_1206335, tc_Nat_Onat), _1206339), _1206337))))], (33329 ^ _779854) ^ [_1385634, _1385636, _1385638, _1385640, _1385642, _1385644] : [class_Complete__Lattice_Ocomplete__lattice(_1385634), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385636, _1385634), _1385638), hAPP(hAPP(c_COMBB(tc_fun(_1385640, _1385634), _1385634, _1385636), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385640, _1385634), _1385642)), _1385644)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385640, _1385634), _1385642), hAPP(hAPP(c_COMBB(tc_fun(_1385636, _1385634), _1385634, _1385640), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385636, _1385634), _1385638)), hAPP(c_COMBC(_1385636, _1385640, _1385634), _1385644))))], (24416 ^ _779854) ^ [_1222725] : [class_Power_Opower(_1222725), -(c_Power_Opower__class_Opower(_1222725) = c_Power_Opower_Opower(_1222725, c_Groups_Oone__class_Oone(_1222725), c_Groups_Otimes__class_Otimes(_1222725)))], (17945 ^ _779854) ^ [_1104598, _1104600] : [17946 ^ _779854 : [(17949 ^ _779854) ^ [] : [_1104598 = hAPP(c_Nat_OSuc, _1104600)], (17947 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104598), _1104600))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104598), hAPP(c_Nat_OSuc, _1104600))))], (6743 ^ _779854) ^ [_888252, _888254, _888256] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888252, tc_HOL_Obool)), _888254), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888252, tc_HOL_Obool)), _888254), _888256)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888252, tc_HOL_Obool)), _888254), _888256))], (23747 ^ _779854) ^ [_1210273, _1210275, _1210277, _1210279, _1210281, _1210283] : [class_Groups_Oab__semigroup__mult(_1210273), hBOOL(hAPP(c_Finite__Set_Ofinite(_1210275), _1210277)), 23757 ^ _779854 : [(23760 ^ _779854) ^ [] : [hAPP(_1210279, 23756 ^ [_1210273, _1210275, _1210277, _1210279, _1210281, _1210283]) = hAPP(_1210281, 23756 ^ [_1210273, _1210275, _1210277, _1210279, _1210281, _1210283])], (23758 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1210275), 23756 ^ [_1210273, _1210275, _1210277, _1210279, _1210281, _1210283]), _1210277)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1210273, _1210275, c_Groups_Otimes__class_Otimes(_1210273)), _1210279), _1210283), _1210277) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1210273, _1210275, c_Groups_Otimes__class_Otimes(_1210273)), _1210281), _1210283), _1210277))], (48451 ^ _779854) ^ [_1756094, _1756096, _1756098, _1756100] : [48452 ^ _779854 : [(48455 ^ _779854) ^ [] : [c_List_Olist__ex(_1756094, _1756096, _1756100)], (48453 ^ _779854) ^ [] : [c_List_Olist__ex(_1756094, _1756096, _1756098)]], -(c_List_Olist__ex(_1756094, _1756096, hAPP(hAPP(c_List_Oappend(_1756094), _1756098), _1756100)))], (34235 ^ _779854) ^ [_1413819, _1413821, _1413823, _1413825, _1413827, _1413829] : [c_Fun_Oinj__on(_1413819, _1413821, _1413823, _1413825), 34238 ^ _779854 : [(34245 ^ _779854) ^ [] : [c_Fun_Oinj__on(_1413819, _1413827, hAPP(c_Fun_Ocomp(_1413821, _1413827, _1413819, _1413829), _1413823), _1413825), -(c_Fun_Oinj__on(_1413821, _1413827, _1413829, hAPP(c_Set_Oimage(_1413819, _1413821, _1413823), _1413825)))], (34239 ^ _779854) ^ [] : [c_Fun_Oinj__on(_1413821, _1413827, _1413829, hAPP(c_Set_Oimage(_1413819, _1413821, _1413823), _1413825)), -(c_Fun_Oinj__on(_1413819, _1413827, hAPP(c_Fun_Ocomp(_1413821, _1413827, _1413819, _1413829), _1413823), _1413825))]]], (40861 ^ _779854) ^ [_1577648, _1577650, _1577652, _1577654, _1577656, _1577658, _1577660] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1577648, _1577650, _1577652, _1577654), _1577656), _1577658), _1577660) = hAPP(hAPP(_1577658, hAPP(c_Product__Type_Ofst(_1577650, _1577652), hAPP(_1577656, _1577660))), hAPP(c_Product__Type_Osnd(_1577650, _1577652), hAPP(_1577656, _1577660))))], (8006 ^ _779854) ^ [_913751, _913753, _913755, _913757] : [class_Orderings_Olinorder(_913751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913751), _913753), _913755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913751), _913755), _913757)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913751, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_913751, _913753, _913755)), c_SetInterval_Oord__class_OatLeastAtMost(_913751, _913755, _913757)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_913751, _913753, _913757))], (24016 ^ _779854) ^ [_1215570, _1215572, _1215574] : [class_Power_Opower(_1215570), class_Rings_Omult__zero(_1215570), class_Rings_Ono__zero__divisors(_1215570), class_Rings_Ozero__neq__one(_1215570), 24031 ^ _779854 : [(24040 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1215570), _1215572), _1215574) = c_Groups_Ozero__class_Ozero(_1215570)), _1215572 = c_Groups_Ozero__class_Ozero(_1215570), -(_1215574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24032 ^ _779854) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1215570), _1215572), _1215574) = c_Groups_Ozero__class_Ozero(_1215570), 24035 ^ _779854 : [(24038 ^ _779854) ^ [] : [_1215574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24036 ^ _779854) ^ [] : [-(_1215572 = c_Groups_Ozero__class_Ozero(_1215570))]]]]], (8352 ^ _779854) ^ [_919510, _919512, _919514] : [-(hAPP(hAPP(c_Set_Oinsert(_919510), _919512), hAPP(hAPP(c_Set_Oinsert(_919510), _919512), _919514)) = hAPP(hAPP(c_Set_Oinsert(_919510), _919512), _919514))], (9390 ^ _779854) ^ [_936740, _936742] : [-(c_Set_Othe__elem(_936740, hAPP(hAPP(c_Set_Oinsert(_936740), _936742), c_Orderings_Obot__class_Obot(tc_fun(_936740, tc_HOL_Obool)))) = _936742)], (29543 ^ _779854) ^ [_1312728, _1312730] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1312728)), c_Int_OBit0(_1312730)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1312728), _1312730)))], (47496 ^ _779854) ^ [_1734947, _1734949, _1734951, _1734953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734947), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734949)), _1734951))), -(hAPP(c_List_Orev(_1734949), hAPP(hAPP(c_List_Olist__update(_1734949, _1734951), _1734947), _1734953)) = hAPP(hAPP(c_List_Olist__update(_1734949, hAPP(c_List_Orev(_1734949), _1734951)), 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(_1734949)), _1734951)), _1734947)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1734953))], (32619 ^ _779854) ^ [_1367134, _1367136] : [32620 ^ _779854 : [(32623 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1367136), _1367134))], (32621 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1367134), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1367134, _1367136) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (3474 ^ _779854) ^ [_831956, _831958, _831960, _831962] : [-(c_Random_Oselect__weight(_831962, _831958) = c_Random_Oselect__weight(_831960, _831956)), _831962 = _831960, _831958 = _831956], (47572 ^ _779854) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (26703 ^ _779854) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (49281 ^ _779854) ^ [_1773656, _1773658, _1773660] : [c_List_Olist__ex1(_1773656, _1773658, _1773660), 49285 ^ _779854 : [(49290 ^ _779854) ^ [_1773902] : [-(_1773902 = 49284 ^ [_1773656, _1773658, _1773660]), hBOOL(hAPP(hAPP(c_member(_1773656), _1773902), hAPP(c_List_Oset(_1773656), _1773660))), hBOOL(hAPP(_1773658, _1773902))], (49288 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1773658, 49284 ^ [_1773656, _1773658, _1773660])))], (49286 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773656), 49284 ^ [_1773656, _1773658, _1773660]), hAPP(c_List_Oset(_1773656), _1773660))))]]], (6417 ^ _779854) ^ [_882162] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882162, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_882162, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_882162, tc_HOL_Obool)))], (28856 ^ _779854) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (47442 ^ _779854) ^ [_1733719, _1733721] : [class_Groups_Ocomm__monoid__add(_1733719), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1733719), hAPP(c_List_Orev(_1733719), _1733721)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1733719), _1733721))], (31206 ^ _779854) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26603 ^ _779854) ^ [_1263363] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1263363) = c_Int_OPls)], (33502 ^ _779854) ^ [_1390499, _1390501, _1390503, _1390505, _1390507] : [33504 ^ _779854 : [(33507 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1390499), _1390501), hAPP(_1390507, 33503 ^ [_1390499, _1390501, _1390503, _1390505, _1390507])))], (33505 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390503), 33503 ^ [_1390499, _1390501, _1390503, _1390505, _1390507]), _1390505)))]], -(hBOOL(hAPP(hAPP(c_member(_1390499), _1390501), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390503, tc_fun(_1390499, tc_HOL_Obool)), _1390505), _1390507))))], (6961 ^ _779854) ^ [_893593, _893595, _893597, _893599] : [class_Lattices_Olattice(_893593), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893593), _893595), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893593), _893597), _893599)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893593), _893597), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893593), _893595), _893599)))], (27497 ^ _779854) ^ [_1277918, _1277920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1277918), _1277920)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1277918), _1277920) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37748 ^ _779854) ^ [_1492594, _1492596, _1492598, _1492600, _1492602, _1492604, _1492606] : [c_Equiv__Relations_Oequiv(_1492594, _1492596, _1492598), c_Equiv__Relations_Ocongruent(_1492594, tc_fun(_1492600, tc_HOL_Obool), _1492598, _1492602), hBOOL(hAPP(hAPP(c_member(tc_fun(_1492594, tc_HOL_Obool)), _1492604), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1492594), _1492596), _1492598))), 37762 ^ _779854 : [(37765 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1492600, tc_HOL_Obool)), hAPP(_1492602, 37761 ^ [_1492594, _1492596, _1492598, _1492600, _1492602, _1492604, _1492606])), _1492606))], (37763 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492594), 37761 ^ [_1492594, _1492596, _1492598, _1492600, _1492602, _1492604, _1492606]), _1492596)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1492600, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1492594, tc_fun(_1492600, tc_HOL_Obool)), _1492604), _1492602)), _1492606)))], (42608 ^ _779854) ^ [_1625190, _1625192, _1625194, _1625196] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1625190) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1625192), hAPP(hAPP(c_List_Olist_OCons(_1625192), _1625194), _1625196)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1625190)) = _1625194)], (18641 ^ _779854) ^ [_1117125, _1117127, _1117129] : [class_Groups_Ogroup__add(_1117125), 18644 ^ _779854 : [(18651 ^ _779854) ^ [] : [_1117127 = _1117129, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117125), _1117127), _1117129) = c_Groups_Ozero__class_Ozero(_1117125))], (18645 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117125), _1117127), _1117129) = c_Groups_Ozero__class_Ozero(_1117125), -(_1117127 = _1117129)]]], (32487 ^ _779854) ^ [_1364433, _1364435] : [class_Rings_Olinordered__idom(_1364433), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1364433), hAPP(c_Groups_Oabs__class_Oabs(_1364433), _1364435)), 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(_1364433), _1364435), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (5942 ^ _779854) ^ [_873922, _873924, _873926] : [class_Orderings_Oorder(_873922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873922), _873924), _873926)), 5949 ^ _779854 : [(5956 ^ _779854) ^ [] : [_873926 = _873924, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873922), _873926), _873924)))], (5950 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873922), _873926), _873924)), -(_873926 = _873924)]]], (43305 ^ _779854) ^ [_1643327, _1643329] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1643327), _1643329))), -(c_Nitpick_Ocard_H(_1643327, _1643329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16070 ^ _779854) ^ [_1068414] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1068414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1068414), _1068414)))))], (27611 ^ _779854) ^ [_1279665] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1279665)), -(hAPP(c_Int_Onat, _1279665) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1750 ^ _779854) ^ [_804681, _804683] : [-(class_Nat_Osemiring__char__0(_804681)), _804683 = _804681, class_Nat_Osemiring__char__0(_804683)], (42701 ^ _779854) ^ [_1627667, _1627669, _1627671, _1627673] : [hBOOL(hAPP(hAPP(c_member(_1627667), _1627669), hAPP(c_List_Oset(_1627667), hAPP(hAPP(c_List_Otake(_1627667), _1627671), _1627673)))), -(hBOOL(hAPP(hAPP(c_member(_1627667), _1627669), hAPP(c_List_Oset(_1627667), _1627673))))], (29023 ^ _779854) ^ [_1303793, _1303795] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1303793) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1303795), 29026 ^ _779854 : [(29029 ^ _779854) ^ [] : [-(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), _1303795))))], (29027 ^ _779854) ^ [] : [-(_1303793 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1303795)))]]], (49596 ^ _779854) ^ [_1781166, _1781168, _1781170] : [hBOOL(hAPP(hAPP(c_member(_1781168), _1781166), c_Orderings_Obot__class_Obot(tc_fun(_1781168, tc_HOL_Obool)))), hBOOL(hAPP(_1781170, _1781166))], (37682 ^ _779854) ^ [_1490622, _1490624, _1490626, _1490628, _1490630, _1490632, _1490634] : [c_Equiv__Relations_Oequiv(_1490622, _1490624, _1490626), c_Equiv__Relations_Ocongruent(_1490622, tc_fun(_1490628, tc_HOL_Obool), _1490626, _1490630), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490622, tc_fun(_1490628, tc_HOL_Obool)), _1490632), _1490630) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490622, tc_fun(_1490628, tc_HOL_Obool)), _1490634), _1490630), hBOOL(hAPP(hAPP(c_member(tc_fun(_1490622, tc_HOL_Obool)), _1490632), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490622), _1490624), _1490626))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1490622, tc_HOL_Obool)), _1490634), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490622), _1490624), _1490626))), 37704 ^ _779854 : [(37708 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490622), 37706 ^ [_1490622, _1490624, _1490626, _1490628, _1490630, _1490632, _1490634]), _1490624)))], (37710 ^ _779854) ^ [] : [-(hAPP(_1490630, 37703 ^ [_1490622, _1490624, _1490626, _1490628, _1490630, _1490632, _1490634]) = hAPP(_1490630, 37706 ^ [_1490622, _1490624, _1490626, _1490628, _1490630, _1490632, _1490634]))], (37712 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1490622, _1490622)), hAPP(hAPP(c_Product__Type_OPair(_1490622, _1490622), 37703 ^ [_1490622, _1490624, _1490626, _1490628, _1490630, _1490632, _1490634]), 37706 ^ [_1490622, _1490624, _1490626, _1490628, _1490630, _1490632, _1490634])), _1490626))], (37705 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490622), 37703 ^ [_1490622, _1490624, _1490626, _1490628, _1490630, _1490632, _1490634]), _1490624)))]], -(_1490632 = _1490634)], (16159 ^ _779854) ^ [_1069984, _1069986, _1069988, _1069990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069984), _1069986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069988), _1069990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1069984), _1069988)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1069986), _1069990))))], (52203 ^ _779854) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (1710 ^ _779854) ^ [_804181, _804183] : [-(class_Rings_Ocomm__semiring__1(_804181)), _804183 = _804181, class_Rings_Ocomm__semiring__1(_804183)], (22309 ^ _779854) ^ [_1183062, _1183064, _1183066, _1183068] : [class_Fields_Olinordered__field__inverse__zero(_1183062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183062), _1183064), _1183066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183062), c_Groups_Ozero__class_Ozero(_1183062)), _1183068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183062), _1183064), _1183068)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183062), _1183066), _1183068))))], (18697 ^ _779854) ^ [_1117961] : [class_Groups_Ogroup__add(_1117961), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1117961), c_Groups_Ozero__class_Ozero(_1117961)) = c_Groups_Ozero__class_Ozero(_1117961))], (39623 ^ _779854) ^ [_1548585, _1548587, _1548589, _1548591] : [c_Wellfounded_Owf(_1548585, _1548587), -(c_Wellfounded_Owf(_1548589, hAPP(hAPP(c_Relation_Oinv__image(_1548585, _1548589), _1548587), _1548591)))], (27545 ^ _779854) ^ [_1278613] : [27546 ^ _779854 : [(27547 ^ _779854) ^ [_1278670] : [hBOOL(hAPP(_1278613, _1278670))]], 27549 ^ _779854 : [(27552 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1278613, hAPP(c_Int_Onat, 27548 ^ [_1278613]))))], (27550 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27548 ^ [_1278613])))]]], (35674 ^ _779854) ^ [_1444168, _1444170, _1444172, _1444174] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1444168, _1444170), _1444172)), hBOOL(hAPP(hAPP(_1444170, _1444174), _1444172)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1444168, _1444170), _1444174)))], (26761 ^ _779854) ^ [_1265740, _1265742] : [class_Divides_Osemiring__div(_1265740), -(_1265742 = c_Groups_Ozero__class_Ozero(_1265740)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265740), _1265742), _1265742) = c_Groups_Oone__class_Oone(_1265740))], (11678 ^ _779854) ^ [_982358, _982360, _982362, _982364] : [11679 ^ _779854 : [(11682 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_982358), _982360), _982364))], (11680 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_982358), _982360), _982362))]], -(hBOOL(hAPP(hAPP(c_member(_982358), _982360), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982358, tc_HOL_Obool)), _982364), _982362))))], (16235 ^ _779854) ^ [_1071391, _1071393, _1071395] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1071391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071393), _1071395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1071391), _1071393)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1071391), _1071395)))], (49064 ^ _779854) ^ [_1769055, _1769057, _1769059] : [c_List_Oreplicate(_1769055, _1769057, _1769059) = c_List_Olist_ONil(_1769055), -(_1769057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5582 ^ _779854) ^ [_865272, _865274] : [_865274 = _865272, -(c_COMBI(_865274) = c_COMBI(_865272))], (36890 ^ _779854) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (40139 ^ _779854) ^ [_1560950, _1560952] : [c_Wellfounded_Owf(_1560950, _1560952), -(c_Wellfounded_Oacyclic(_1560950, _1560952))], (1860 ^ _779854) ^ [_806056, _806058] : [-(class_Orderings_Oord(_806056)), _806058 = _806056, class_Orderings_Oord(_806058)], (1800 ^ _779854) ^ [_805306, _805308] : [-(class_Groups_Omonoid__add(_805306)), _805308 = _805306, class_Groups_Omonoid__add(_805308)], (39848 ^ _779854) ^ [_1552998, _1553000, _1553002] : [c_Wellfounded_Owf(_1552998, _1553000), c_Wellfounded_Owf(_1552998, _1553002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552998, _1552998), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552998, _1552998, _1552998), _1553000), _1553002)), _1553000)), -(c_Wellfounded_Owf(_1552998, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552998, _1552998), tc_HOL_Obool)), _1553000), _1553002)))], (45230 ^ _779854) ^ [_1685619, _1685621, _1685623, _1685625, _1685627, _1685629] : [-(hAPP(hAPP(c_List_Omap(_1685619, _1685621), _1685623), hAPP(hAPP(c_List_Omap(_1685625, _1685619), _1685627), _1685629)) = hAPP(hAPP(c_List_Omap(_1685625, _1685621), hAPP(c_Fun_Ocomp(_1685619, _1685621, _1685625, _1685623), _1685627)), _1685629))], (47812 ^ _779854) ^ [_1741519, _1741521, _1741523, _1741525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741519), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741521)), c_List_OdropWhile(_1741521, _1741523, _1741525)))), -(hAPP(hAPP(c_List_Onth(_1741521), c_List_OdropWhile(_1741521, _1741523, _1741525)), _1741519) = hAPP(hAPP(c_List_Onth(_1741521), _1741525), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1741519), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741521)), c_List_OtakeWhile(_1741521, _1741523, _1741525)))))], (4682 ^ _779854) ^ [_851252, _851254] : [_851254 = _851252, -(c_DSequence_Osingle(_851254) = c_DSequence_Osingle(_851252))], (19609 ^ _779854) ^ [_1133489, _1133491, _1133493, _1133495] : [class_Rings_Olinordered__ring__strict(_1133489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133489), c_Groups_Ozero__class_Ozero(_1133489)), _1133491)), 19616 ^ _779854 : [(19623 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133489), _1133493), _1133495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133489), _1133491), _1133493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133489), _1133491), _1133495))))], (19617 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133489), _1133491), _1133493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133489), _1133491), _1133495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133489), _1133493), _1133495)))]]], (47774 ^ _779854) ^ [_1740705, _1740707, _1740709] : [-(c_List_OdropWhile(_1740705, _1740707, _1740709) = c_List_Olist_ONil(_1740705)), hBOOL(hAPP(_1740707, hAPP(c_List_Ohd(_1740705), c_List_OdropWhile(_1740705, _1740707, _1740709))))], (34021 ^ _779854) ^ [_1408466, _1408468, _1408470, _1408472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1408466, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408468, tc_fun(tc_fun(_1408466, tc_HOL_Obool), tc_HOL_Obool)), _1408470), hAPP(hAPP(c_COMBB(tc_fun(_1408466, tc_HOL_Obool), tc_fun(tc_fun(_1408466, tc_HOL_Obool), tc_HOL_Obool), _1408468), c_Set_OPow(_1408466)), _1408472))), hAPP(c_Set_OPow(_1408466), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408468, tc_fun(_1408466, tc_HOL_Obool)), _1408470), _1408472)))))], (6299 ^ _779854) ^ [_879954, _879956, _879958] : [class_Orderings_Oorder(_879954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879954), _879956), _879958)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_879954, _879958, _879956) = c_Orderings_Obot__class_Obot(tc_fun(_879954, tc_HOL_Obool)))], (33345 ^ _779854) ^ [_1386130, _1386132, _1386134, _1386136, _1386138, _1386140, _1386142, _1386144, _1386146] : [hAPP(c_Fun_Ocomp(_1386130, _1386132, _1386134, _1386136), _1386138) = hAPP(c_Fun_Ocomp(_1386140, _1386132, _1386134, _1386142), _1386144), -(hAPP(_1386136, hAPP(_1386138, _1386146)) = hAPP(_1386142, hAPP(_1386144, _1386146)))], (34551 ^ _779854) ^ [_1420966, _1420968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1420966)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420968))), -(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(_1420968))), 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), _1420966)), c_Int_Onat))))))], (16233 ^ _779854) ^ [_1071348, _1071350] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071348), _1071350)), _1071350) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1071348), _1071350))], (16239 ^ _779854) ^ [_1071485, _1071487] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071485), _1071487)), _1071485) = _1071487)], (48977 ^ _779854) ^ [_1767543, _1767545, _1767547, _1767549] : [48979 ^ _779854 : [(48982 ^ _779854) ^ [] : [hBOOL(hAPP(_1767549, 48978 ^ [_1767543, _1767545, _1767547, _1767549]))], (48980 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767543), 48978 ^ [_1767543, _1767545, _1767547, _1767549]), hAPP(c_List_Oset(_1767543), c_List_Oreplicate(_1767543, _1767545, _1767547)))))]], -(hBOOL(hAPP(_1767549, _1767547))), -(_1767545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37197 ^ _779854) ^ [_1479219, _1479221, _1479223] : [_1479221 = c_Orderings_Obot__class_Obot(tc_fun(_1479219, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1479219, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479219), _1479221), _1479223))], (51513 ^ _779854) ^ [_1822902, _1822904] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1822902), 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)))), _1822904))), 51516 ^ _779854 : [(51519 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822902), _1822904))], (51517 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822904), _1822902)))]]], (1010 ^ _779854) ^ [_795009, _795011, _795013, _795015, _795017, _795019, _795021, _795023, _795025, _795027, _795029, _795031] : [-(c_Equiv__Relations_Ocongruent2(_795029, _795025, _795021, _795017, _795013, _795009)), c_Equiv__Relations_Ocongruent2(_795031, _795027, _795023, _795019, _795015, _795011), _795031 = _795029, _795027 = _795025, _795023 = _795021, _795019 = _795017, _795015 = _795013, _795011 = _795009], (35618 ^ _779854) ^ [_1443448] : [-(_1443448 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1443448), 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)))))], (7587 ^ _779854) ^ [_905231, _905233, _905235] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905231, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_905231, tc_HOL_Obool), _905233)), _905235) = c_Orderings_Obot__class_Obot(tc_fun(_905231, tc_HOL_Obool)), 7590 ^ _779854 : [(7591 ^ _779854) ^ [_905366] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_905231, tc_HOL_Obool)), _905366), _905233)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905231, tc_HOL_Obool)), _905366), _905235) = c_Orderings_Obot__class_Obot(tc_fun(_905231, tc_HOL_Obool)))]]], (50652 ^ _779854) ^ [_1803964, _1803966] : [-(c_Fun_Obij__betw(_1803964, _1803964, c_Fun_Oid(_1803964), _1803966, _1803966))], (34455 ^ _779854) ^ [_1418871, _1418873] : [hAPP(c_Nat_OSuc, _1418871) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418873), -(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(_1418873))), 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)), _1418871))))))], (27763 ^ _779854) ^ [_1282157, _1282159, _1282161] : [class_Rings_Osemiring__1(_1282157), hBOOL(hAPP(hAPP(c_member(_1282157), _1282159), c_Nat_Osemiring__1__class_ONats(_1282157))), hBOOL(hAPP(hAPP(c_member(_1282157), _1282161), c_Nat_Osemiring__1__class_ONats(_1282157))), -(hBOOL(hAPP(hAPP(c_member(_1282157), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1282157), _1282159), _1282161)), c_Nat_Osemiring__1__class_ONats(_1282157))))], (29677 ^ _779854) ^ [_1315169, _1315171] : [class_Int_Onumber__ring(_1315169), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315169), hAPP(c_Int_Onumber__class_Onumber__of(_1315169), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1315171) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1315169), _1315171), _1315171))], (45210 ^ _779854) ^ [_1685159, _1685161, _1685163, _1685165] : [-(hAPP(c_List_Oset(_1685159), hAPP(hAPP(c_List_Omap(_1685161, _1685159), _1685163), _1685165)) = hAPP(c_Set_Oimage(_1685161, _1685159, _1685163), hAPP(c_List_Oset(_1685161), _1685165)))], (1160 ^ _779854) ^ [_797306, _797308] : [-(class_Rings_Oring__1__no__zero__divisors(_797306)), _797308 = _797306, class_Rings_Oring__1__no__zero__divisors(_797308)], (31278 ^ _779854) ^ [_1343751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343751), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1343751)), c_Int_OMin)))], (35376 ^ _779854) ^ [_1438840, _1438842] : [_1438840 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1438840, _1438842) = 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)))], (23932 ^ _779854) ^ [_1213880, _1213882, _1213884] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1213880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213882), _1213884)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1213880), _1213882)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1213880), _1213884)))], (49042 ^ _779854) ^ [_1768714, _1768716, _1768718, _1768720] : [-(hBOOL(hAPP(_1768714, _1768716))), -(hAPP(c_List_Ofilter(_1768718, _1768714), c_List_Oreplicate(_1768718, _1768720, _1768716)) = c_List_Olist_ONil(_1768718))], (52551 ^ _779854) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (48593 ^ _779854) ^ [_1758889, _1758891] : [-(c_FunDef_Ois__measure(_1758889, _1758891))], (30559 ^ _779854) ^ [_1331583, _1331585] : [c_Nat__Transfer_Onat__set(_1331583), c_Nat__Transfer_Onat__set(_1331585), 30566 ^ _779854 : [(30573 ^ _779854) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1331583) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1331585), -(_1331583 = _1331585)], (30567 ^ _779854) ^ [] : [_1331583 = _1331585, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1331583) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1331585))]]], (50344 ^ _779854) ^ [_1796962, _1796964, _1796966] : [c_Fun_Oinj__on(_1796962, _1796964, _1796966, c_Orderings_Otop__class_Otop(tc_fun(_1796962, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1796964, _1796962, _1796962, c_Hilbert__Choice_Oinv__into(_1796962, _1796964, c_Orderings_Otop__class_Otop(tc_fun(_1796962, tc_HOL_Obool)), _1796966)), _1796966) = c_Fun_Oid(_1796962))], (306 ^ _779854) ^ [_784531, _784533, _784535, _784537, _784539, _784541, _784543, _784545] : [-(c_Finite__Set_Ofolding__idem(_784543, _784539, _784535, _784531)), c_Finite__Set_Ofolding__idem(_784545, _784541, _784537, _784533), _784545 = _784543, _784541 = _784539, _784537 = _784535, _784533 = _784531], (21653 ^ _779854) ^ [_1170664] : [class_Rings_Oring__1(_1170664), -(hBOOL(hAPP(hAPP(c_member(_1170664), c_Groups_Oone__class_Oone(_1170664)), c_Int_Oring__1__class_OInts(_1170664))))], (27495 ^ _779854) ^ [_1277889] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1277889), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1277889)], (25819 ^ _779854) ^ [_1249112, _1249114, _1249116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249112)), _1249112 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1249114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1249112), _1249116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249116), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (51555 ^ _779854) ^ [_1823677] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823677), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1823677 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (168 ^ _779854) ^ [_782430, _782432, _782434, _782436, _782438, _782440, _782442, _782444, _782446, _782448, _782450, _782452] : [-(c_Finite__Set_Ofolding__image__simple__idem(_782450, _782446, _782442, _782438, _782434, _782430)), c_Finite__Set_Ofolding__image__simple__idem(_782452, _782448, _782444, _782440, _782436, _782432), _782452 = _782450, _782448 = _782446, _782444 = _782442, _782440 = _782438, _782436 = _782434, _782432 = _782430], (18995 ^ _779854) ^ [_1122363, _1122365, _1122367] : [class_Rings_Olinordered__ring__strict(_1122363), 18998 ^ _779854 : [(19007 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122363), _1122365), _1122365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122363), _1122367), _1122367))), c_Groups_Ozero__class_Ozero(_1122363)))), _1122365 = c_Groups_Ozero__class_Ozero(_1122363), _1122367 = c_Groups_Ozero__class_Ozero(_1122363)], (18999 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122363), _1122365), _1122365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122363), _1122367), _1122367))), c_Groups_Ozero__class_Ozero(_1122363))), 19002 ^ _779854 : [(19005 ^ _779854) ^ [] : [-(_1122367 = c_Groups_Ozero__class_Ozero(_1122363))], (19003 ^ _779854) ^ [] : [-(_1122365 = c_Groups_Ozero__class_Ozero(_1122363))]]]]], (7271 ^ _779854) ^ [_899532, _899534, _899536] : [class_Lattices_Osemilattice__inf(_899532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899532), _899534), _899536)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_899532), _899534), _899536) = _899534)], (52205 ^ _779854) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (24485 ^ _779854) ^ [_1224146] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224146), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1224146)], (8544 ^ _779854) ^ [_922444, _922446, _922448, _922450] : [class_Orderings_Opreorder(_922444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922444), _922446), _922448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922444), _922448), _922450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922444), _922446), _922450)))], (12470 ^ _779854) ^ [_997621, _997623, _997625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997621, tc_HOL_Obool)), _997623), _997625)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_997621, tc_HOL_Obool)), _997623), hAPP(c_Set_OPow(_997621), _997625))))], (39005 ^ _779854) ^ [_1525634, _1525636] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1525634)), 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)), _1525634))), 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, _1525636))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6919 ^ _779854) ^ [_892560, _892562, _892564, _892566] : [class_Lattices_Osemilattice__inf(_892560), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892560), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892560), _892562), _892564)), _892566) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892560), _892562), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892560), _892564), _892566)))], (32910 ^ _779854) ^ [] : [-(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)))], (45869 ^ _779854) ^ [_1700011, _1700013, _1700015, _1700017, _1700019, _1700021, _1700023] : [c_List_Olist__all2(_1700011, _1700013, _1700015, hAPP(hAPP(c_List_Olist_OCons(_1700011), _1700017), _1700019), hAPP(hAPP(c_List_Olist_OCons(_1700013), _1700021), _1700023)), 45872 ^ _779854 : [(45875 ^ _779854) ^ [] : [-(c_List_Olist__all2(_1700011, _1700013, _1700015, _1700019, _1700023))], (45873 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1700015, _1700017), _1700021)))]]], (13941 ^ _779854) ^ [_1025349, _1025351, _1025353] : [class_Orderings_Olinorder(_1025349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025349), _1025351)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025349), _1025353)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025349, tc_HOL_Obool)), _1025351), _1025353) = c_Orderings_Obot__class_Obot(tc_fun(_1025349, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1025349), c_Big__Operators_Olinorder__class_OMax(_1025349, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025349, tc_HOL_Obool)), _1025351), _1025353))), c_Big__Operators_Olinorder__class_OMax(_1025349, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025349, tc_HOL_Obool)), _1025351), _1025353))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1025349), c_Big__Operators_Olinorder__class_OMax(_1025349, _1025351)), c_Big__Operators_Olinorder__class_OMax(_1025349, _1025353)))], (7367 ^ _779854) ^ [_901172, _901174, _901176, _901178, _901180] : [class_Lattices_Osemilattice__inf(_901172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901172), _901174), _901176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901172), _901178), _901180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901172), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_901172), _901174), _901178)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_901172), _901176), _901180))))], (52269 ^ _779854) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (10819 ^ _779854) ^ [_964831, _964833, _964835] : [class_Orderings_Olinorder(_964831), hBOOL(hAPP(c_Finite__Set_Ofinite(_964831), _964833)), -(_964833 = c_Orderings_Obot__class_Obot(tc_fun(_964831, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_964831, c_Orderings_Oord__class_Omin(_964831), hAPP(hAPP(c_Set_Oinsert(_964831), _964835), _964833)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_964831), _964835), c_Big__Operators_Olattice_OInf__fin(_964831, c_Orderings_Oord__class_Omin(_964831), _964833)))], (41376 ^ _779854) ^ [_1590910, _1590912, _1590914, _1590916, _1590918] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590910, _1590910)), hAPP(hAPP(c_Product__Type_OPair(_1590910, _1590910), _1590912), _1590914)), c_Transitive__Closure_Ortrancl(_1590910, _1590916))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590910, _1590910), tc_HOL_Obool)), _1590916), hAPP(hAPP(c_Product__Type_OSigma(_1590910, _1590910), _1590918), hAPP(c_COMBK(tc_fun(_1590910, tc_HOL_Obool), _1590910), _1590918)))), -(_1590912 = _1590914), -(hBOOL(hAPP(hAPP(c_member(_1590910), _1590912), _1590918)))], (18971 ^ _779854) ^ [] : [-(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)))], (18979 ^ _779854) ^ [_1122031, _1122033, _1122035] : [class_Groups_Ocomm__monoid__add(_1122031), hAPP(_1122033, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1122031), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1122031), _1122033), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1122035)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1122031), _1122033), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122035)))], (28445 ^ _779854) ^ [_1294212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1294212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1294212)))], (27345 ^ _779854) ^ [_1275561, _1275563] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275561), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275561)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275563)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1275561), _1275563)))], (32680 ^ _779854) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (52339 ^ _779854) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11518 ^ _779854) ^ [_979067, _979069, _979071, _979073, _979075] : [c_Finite__Set_Ofolding__one(_979067, _979069, _979071), hBOOL(hAPP(c_Finite__Set_Ofinite(_979067), _979073)), 11525 ^ _779854 : [(11532 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979067, tc_HOL_Obool)), _979073), hAPP(hAPP(c_Set_Oinsert(_979067), _979075), c_Orderings_Obot__class_Obot(tc_fun(_979067, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_979067, tc_HOL_Obool))), -(hAPP(_979071, hAPP(hAPP(c_Set_Oinsert(_979067), _979075), _979073)) = hAPP(hAPP(_979069, _979075), hAPP(_979071, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979067, tc_HOL_Obool)), _979073), hAPP(hAPP(c_Set_Oinsert(_979067), _979075), c_Orderings_Obot__class_Obot(tc_fun(_979067, tc_HOL_Obool)))))))], (11526 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979067, tc_HOL_Obool)), _979073), hAPP(hAPP(c_Set_Oinsert(_979067), _979075), c_Orderings_Obot__class_Obot(tc_fun(_979067, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_979067, tc_HOL_Obool)), -(hAPP(_979071, hAPP(hAPP(c_Set_Oinsert(_979067), _979075), _979073)) = _979075)]]], (35434 ^ _779854) ^ [_1440005, _1440007, _1440009] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1440005, _1440007), _1440009)), -(c_Divides_Odivmod__nat(_1440005, _1440007) = _1440009)], (50392 ^ _779854) ^ [_1797872, _1797874, _1797876, _1797878, _1797880] : [hBOOL(hAPP(hAPP(c_member(_1797872), _1797874), hAPP(c_Set_Oimage(_1797876, _1797872, _1797878), _1797880))), -(hAPP(_1797878, hAPP(c_Hilbert__Choice_Oinv__into(_1797876, _1797872, _1797880, _1797878), _1797874)) = _1797874)], (51561 ^ _779854) ^ [_1823758] : [_1823758 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823758), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (35442 ^ _779854) ^ [_1440133, _1440135, _1440137, _1440139] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1440133, _1440135), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1440137), _1440139))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440133, _1440135) = _1440139)], (52359 ^ _779854) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (17284 ^ _779854) ^ [_1092171] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1092171)) = _1092171)], (21425 ^ _779854) ^ [_1165982, _1165984, _1165986, _1165988, _1165990] : [class_Groups_Oordered__comm__monoid__add(_1165982), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165984), _1165986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1165984, tc_HOL_Obool)), _1165988), _1165986)), 21439 ^ _779854 : [(21442 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165982), c_Groups_Ozero__class_Ozero(_1165982)), hAPP(_1165990, 21438 ^ [_1165982, _1165984, _1165986, _1165988, _1165990])))], (21440 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1165984), 21438 ^ [_1165982, _1165984, _1165986, _1165988, _1165990]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1165984, tc_HOL_Obool)), _1165986), _1165988))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165982), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165984, _1165982), _1165990), _1165988)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165984, _1165982), _1165990), _1165986))))], (24192 ^ _779854) ^ [_1218554, _1218556, _1218558, _1218560] : [class_Rings_Olinordered__semidom(_1218554), hAPP(hAPP(c_Power_Opower__class_Opower(_1218554), _1218556), hAPP(c_Nat_OSuc, _1218558)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1218554), _1218560), hAPP(c_Nat_OSuc, _1218558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218554), c_Groups_Ozero__class_Ozero(_1218554)), _1218556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218554), c_Groups_Ozero__class_Ozero(_1218554)), _1218560)), -(_1218556 = _1218560)], (27455 ^ _779854) ^ [_1277248, _1277250, _1277252] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1277248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1277250), _1277252)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1277248), _1277250)), _1277252))], (44975 ^ _779854) ^ [_1679503, _1679505, _1679507] : [-(_1679503 = c_List_Olist_ONil(_1679505)), -(c_List_Olast(_1679505, hAPP(hAPP(c_List_Oappend(_1679505), _1679507), _1679503)) = c_List_Olast(_1679505, _1679503))], (28126 ^ _779854) ^ [_1288632, _1288634] : [-(c_Int_Onat__aux(_1288632, _1288634) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1288632)), _1288634))], (52257 ^ _779854) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (1300 ^ _779854) ^ [_799056, _799058] : [-(class_Int_Onumber__ring(_799056)), _799058 = _799056, class_Int_Onumber__ring(_799058)], (32668 ^ _779854) ^ [_1367941, _1367943] : [_1367941 = _1367943, -(c_Random_Oinc__shift(_1367941, _1367943) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (28290 ^ _779854) ^ [] : [-(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)))))], (34267 ^ _779854) ^ [_1414421, _1414423, _1414425] : [class_Groups_Ocomm__monoid__add(_1414421), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414421), _1414423), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1414425))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414421), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414421), _1414423), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1414425))), hAPP(_1414423, hAPP(c_Nat_OSuc, _1414425))))], (39822 ^ _779854) ^ [_1552456, _1552458, _1552460] : [-(hAPP(c_Set_Oimage(tc_prod(_1552456, _1552458), _1552456, c_Product__Type_Ofst(_1552456, _1552458)), _1552460) = hAPP(c_Relation_ODomain(_1552456, _1552458), _1552460))], (52253 ^ _779854) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (23800 ^ _779854) ^ [_1211460, _1211462] : [class_Rings_Ocomm__semiring__1(_1211460), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1211460), _1211462), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1211460))], (12262 ^ _779854) ^ [_993473, _993475, _993477] : [hBOOL(hAPP(hAPP(c_member(_993473), _993475), hAPP(hAPP(c_Set_Oinsert(_993473), _993477), c_Orderings_Obot__class_Obot(tc_fun(_993473, tc_HOL_Obool))))), -(_993475 = _993477)], (18243 ^ _779854) ^ [_1109924, _1109926, _1109928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109926), _1109928)), -(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, _1109924)), _1109926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1109924)), _1109928))))], (33036 ^ _779854) ^ [_1378045, _1378047, _1378049, _1378051, _1378053] : [-(_1378045 = c_Orderings_Obot__class_Obot(tc_fun(_1378047, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1378047, tc_fun(_1378049, tc_HOL_Obool)), _1378045), hAPP(hAPP(c_COMBC(_1378047, tc_fun(_1378049, tc_HOL_Obool), tc_fun(_1378049, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378049, tc_HOL_Obool), tc_fun(tc_fun(_1378049, tc_HOL_Obool), tc_fun(_1378049, tc_HOL_Obool)), _1378047), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378049, tc_HOL_Obool))), _1378051)), _1378053)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378049, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1378047, tc_fun(_1378049, tc_HOL_Obool)), _1378045), _1378051)), _1378053))], (16920 ^ _779854) ^ [_1085116, _1085118, _1085120, _1085122] : [class_Lattices_Osemilattice__inf(_1085116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085116), _1085118)), hBOOL(hAPP(hAPP(c_member(_1085116), _1085120), _1085118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085116), hAPP(hAPP(c_Finite__Set_Ofold(_1085116, _1085116, c_Lattices_Osemilattice__inf__class_Oinf(_1085116)), _1085122), _1085118)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1085116), _1085120), _1085122))))], (48296 ^ _779854) ^ [_1753020, _1753022, _1753024, _1753026] : [class_Orderings_Oorder(_1753020), class_Enum_Oenum(_1753022), 48303 ^ _779854 : [(48310 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753022), hAPP(hAPP(c_COMBS(_1753022, _1753020, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1753020, tc_fun(_1753020, tc_HOL_Obool), _1753022), c_Orderings_Oord__class_Oless__eq(_1753020)), _1753024)), _1753026))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1753022, _1753020)), _1753024), _1753026)))], (48304 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1753022, _1753020)), _1753024), _1753026)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753022), hAPP(hAPP(c_COMBS(_1753022, _1753020, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1753020, tc_fun(_1753020, tc_HOL_Obool), _1753022), c_Orderings_Oord__class_Oless__eq(_1753020)), _1753024)), _1753026))))]]], (16331 ^ _779854) ^ [_1073538, _1073540, _1073542, _1073544, _1073546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073538), _1073540)), 16334 ^ _779854 : [(16341 ^ _779854) ^ [] : [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), _1073540), _1073538)), _1073542)), _1073544)), _1073546)), -(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), _1073540), _1073542)), _1073544)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073538), _1073542)), _1073546))))], (16335 ^ _779854) ^ [] : [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), _1073540), _1073542)), _1073544)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073538), _1073542)), _1073546))), -(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), _1073540), _1073538)), _1073542)), _1073544)), _1073546)))]]], (23059 ^ _779854) ^ [_1196636, _1196638, _1196640] : [class_Fields_Olinordered__field(_1196636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196636), _1196638), _1196640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196636), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196636), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196636), _1196638), _1196640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196636), c_Groups_Oone__class_Oone(_1196636)), c_Groups_Oone__class_Oone(_1196636)))), _1196640)))], (45935 ^ _779854) ^ [_1701229, _1701231, _1701233] : [-(c_Enum_Oproduct(_1701229, _1701231, c_List_Olist_ONil(_1701229), _1701233) = c_List_Olist_ONil(tc_prod(_1701229, _1701231)))], (6877 ^ _779854) ^ [_891527, _891529, _891531, _891533] : [class_Lattices_Odistrib__lattice(_891527), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891527), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_891527), _891529), _891531)), _891533) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_891527), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891527), _891529), _891533)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891527), _891531), _891533)))], (24775 ^ _779854) ^ [_1229903, _1229905, _1229907] : [class_Int_Onumber(_1229903), class_Orderings_Oord(_1229903), 24782 ^ _779854 : [(24789 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229903), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229905)), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229907)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1229903), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229905)), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229907)) = hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229905))], (24783 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229903), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229905)), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229907))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1229903), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229905)), hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229907)) = hAPP(c_Int_Onumber__class_Onumber__of(_1229903), _1229907))]]], (49681 ^ _779854) ^ [_1782972, _1782974, _1782976, _1782978] : [c_Relation_Otrans(_1782972, _1782974), -(c_Relation_Otrans(_1782976, hAPP(hAPP(c_Relation_Oinv__image(_1782972, _1782976), _1782974), _1782978)))], (40299 ^ _779854) ^ [_1564630, _1564632, _1564634] : [c_Wellfounded_OwfP(_1564630, hAPP(_1564632, 40300 ^ [_1564630, _1564632, _1564634])), 40307 ^ _779854 : [(40310 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1564630, tc_HOL_Obool)), c_Predicate_ODomainP(_1564630, _1564630, hAPP(_1564632, 40305 ^ [_1564630, _1564632, _1564634]))), c_Predicate_ORangeP(_1564630, _1564630, hAPP(_1564632, 40306 ^ [_1564630, _1564632, _1564634]))) = c_Orderings_Obot__class_Obot(tc_fun(_1564630, tc_HOL_Obool))], (40308 ^ _779854) ^ [] : [hAPP(_1564632, 40305 ^ [_1564630, _1564632, _1564634]) = hAPP(_1564632, 40306 ^ [_1564630, _1564632, _1564634])]], -(c_Wellfounded_OwfP(_1564630, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1564634, tc_fun(_1564630, tc_fun(_1564630, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1564634, tc_HOL_Obool))), _1564632)))], (29451 ^ _779854) ^ [_1311104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1311104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1311104))))], (5430 ^ _779854) ^ [_863006, _863008, _863010, _863012, _863014, _863016] : [-(c_SetInterval_Oord_OgreaterThan(_863016, _863012, _863008) = c_SetInterval_Oord_OgreaterThan(_863014, _863010, _863006)), _863016 = _863014, _863012 = _863010, _863008 = _863006], (52191 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (47480 ^ _779854) ^ [_1734464, _1734466] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1734464), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1734464))), c_List_Otranspose(_1734464, _1734466)))))], (48936 ^ _779854) ^ [_1766817, _1766819, _1766821, _1766823] : [-(hAPP(hAPP(c_List_Odrop(_1766817), _1766819), c_List_Oreplicate(_1766817, _1766821, _1766823)) = c_List_Oreplicate(_1766817, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1766821), _1766819), _1766823))], (28250 ^ _779854) ^ [_1290684, _1290686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290684), _1290686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1290684)), c_Int_OBit1(_1290686))))], (42410 ^ _779854) ^ [_1620067, _1620069, _1620071, _1620073, _1620075] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1620067), tc_List_Olist(_1620067))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1620067), tc_List_Olist(_1620067)), _1620069), hAPP(hAPP(c_List_Olist_OCons(_1620067), _1620071), _1620073))), c_List_Olistrel(_1620067, _1620075))), 42415 ^ _779854 : [(42420 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1620067), tc_List_Olist(_1620067))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1620067), tc_List_Olist(_1620067)), 42414 ^ [_1620067, _1620069, _1620071, _1620073, _1620075]), _1620073)), c_List_Olistrel(_1620067, _1620075))))], (42418 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620067, _1620067)), hAPP(hAPP(c_Product__Type_OPair(_1620067, _1620067), 42413 ^ [_1620067, _1620069, _1620071, _1620073, _1620075]), _1620071)), _1620075)))], (42416 ^ _779854) ^ [] : [-(_1620069 = hAPP(hAPP(c_List_Olist_OCons(_1620067), 42413 ^ [_1620067, _1620069, _1620071, _1620073, _1620075]), 42414 ^ [_1620067, _1620069, _1620071, _1620073, _1620075]))]]], (13525 ^ _779854) ^ [_1017859, _1017861, _1017863] : [class_Lattices_Olattice(_1017859), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017859), _1017861)), -(_1017861 = c_Orderings_Obot__class_Obot(tc_fun(_1017859, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017859), _1017863)), -(_1017863 = c_Orderings_Obot__class_Obot(tc_fun(_1017859, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1017859, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017859, tc_HOL_Obool)), _1017861), _1017863)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1017859), c_Big__Operators_Olattice__class_OSup__fin(_1017859, _1017861)), c_Big__Operators_Olattice__class_OSup__fin(_1017859, _1017863)))], (33581 ^ _779854) ^ [_1395918, _1395920, _1395922, _1395924, _1395926] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395918, tc_fun(_1395920, tc_HOL_Obool)), _1395922), hAPP(hAPP(c_COMBB(tc_fun(_1395920, tc_HOL_Obool), tc_fun(_1395920, tc_HOL_Obool), _1395918), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395920, tc_HOL_Obool)), _1395924)), _1395926)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395920, tc_HOL_Obool)), _1395924), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395918, tc_fun(_1395920, tc_HOL_Obool)), _1395922), _1395926)))], (48383 ^ _779854) ^ [_1754641, _1754643, _1754645] : [class_Orderings_Olinorder(_1754641), 48389 ^ _779854 : [(48392 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754641), _1754645), 48388 ^ [_1754641, _1754643, _1754645]))], (48390 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754641), 48388 ^ [_1754641, _1754643, _1754645]), hAPP(c_List_Oset(_1754641), _1754643))))]], c_List_Olinorder__class_Osorted(_1754641, _1754643), -(c_List_Olinorder__class_Osorted(_1754641, hAPP(hAPP(c_List_Olist_OCons(_1754641), _1754645), _1754643)))], (16415 ^ _779854) ^ [_1075273, _1075275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075273), _1075275)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075275), _1075273)) = _1075273)], (37105 ^ _779854) ^ [] : [-(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))))))], (43426 ^ _779854) ^ [_1645547, _1645549, _1645551] : [43427 ^ _779854 : [(43430 ^ _779854) ^ [] : [_1645551 = c_List_Olist_ONil(_1645547)], (43428 ^ _779854) ^ [] : [_1645549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1645547), _1645549), _1645551) = c_List_Olist_ONil(_1645547))], (11686 ^ _779854) ^ [_982543, _982545, _982547, _982549] : [hBOOL(hAPP(hAPP(c_member(_982543), _982545), _982547)), hBOOL(hAPP(hAPP(c_member(_982543), _982545), _982549)), -(hBOOL(hAPP(hAPP(c_member(_982543), _982545), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982543, tc_HOL_Obool)), _982547), _982549))))], (15182 ^ _779854) ^ [_1050055, _1050057, _1050059, _1050061, _1050063, _1050065] : [class_Rings_Oordered__ring(_1050055), 15185 ^ _779854 : [(15192 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050055), _1050057), _1050063)), _1050059)), _1050061)), _1050065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050055), _1050057), _1050059)), _1050061)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050055), _1050063), _1050059)), _1050065))))], (15186 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050055), _1050057), _1050059)), _1050061)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050055), _1050063), _1050059)), _1050065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050055), _1050057), _1050063)), _1050059)), _1050061)), _1050065)))]]], (21893 ^ _779854) ^ [_1175496, _1175498, _1175500, _1175502, _1175504] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1175496, _1175498, _1175500), _1175502), _1175504), c_Orderings_Obot__class_Obot(tc_fun(_1175498, tc_HOL_Obool))) = _1175504)], (46864 ^ _779854) ^ [_1722666, _1722668] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1722666, _1722668)))], (2422 ^ _779854) ^ [_815542, _815544, _815546, _815548] : [-(c_Divides_Odivmod__int(_815548, _815544) = c_Divides_Odivmod__int(_815546, _815542)), _815548 = _815546, _815544 = _815542], (14548 ^ _779854) ^ [_1037595, _1037597, _1037599] : [-(hAPP(c_Finite__Set_Ofold1(_1037595, _1037597), hAPP(hAPP(c_Set_Oinsert(_1037595), _1037599), c_Orderings_Obot__class_Obot(tc_fun(_1037595, tc_HOL_Obool)))) = _1037599)], (29591 ^ _779854) ^ [_1313533] : [-(c_Int_Osucc(c_Int_OBit1(_1313533)) = c_Int_OBit0(c_Int_Osucc(_1313533)))], (28005 ^ _779854) ^ [_1286450, _1286452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1286450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1286450), _1286452)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1286452), _1286450) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1286452), _1286450)), _1286450)))], (42078 ^ _779854) ^ [_1608828, _1608830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 42079 ^ [_1608828, _1608830]), hAPP(_1608828, 42079 ^ [_1608828, _1608830]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1608828)), _1608830)))))], (16249 ^ _779854) ^ [_1071732, _1071734, _1071736] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071732), _1071734)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071736), _1071734)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071732), _1071736))], (45264 ^ _779854) ^ [_1686433, _1686435, _1686437, _1686439, _1686441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686433), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686435)), _1686437))), -(hAPP(hAPP(c_List_Onth(_1686439), hAPP(hAPP(c_List_Omap(_1686435, _1686439), _1686441), _1686437)), _1686433) = hAPP(_1686441, hAPP(hAPP(c_List_Onth(_1686435), _1686437), _1686433)))], (43919 ^ _779854) ^ [_1656344, _1656346, _1656348] : [-(hAPP(c_List_Oset(_1656344), hAPP(hAPP(c_List_Oappend(_1656344), _1656346), _1656348)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1656344, tc_HOL_Obool)), hAPP(c_List_Oset(_1656344), _1656346)), hAPP(c_List_Oset(_1656344), _1656348)))], (38905 ^ _779854) ^ [_1522417, _1522419, _1522421, _1522423, _1522425] : [c_Relation_Orefl__on(_1522417, _1522419, _1522421), c_Relation_Orefl__on(_1522417, _1522423, _1522425), -(c_Relation_Orefl__on(_1522417, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522417, tc_HOL_Obool)), _1522419), _1522423), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522417, _1522417), tc_HOL_Obool)), _1522421), _1522425)))], (24677 ^ _779854) ^ [_1227723, _1227725, _1227727] : [class_Int_Onumber(_1227723), class_Orderings_Olinorder(_1227723), 24684 ^ _779854 : [(24691 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1227723), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227727)), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227725)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1227723), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227725)), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227727))))], (24685 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1227723), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227725)), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227727))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1227723), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227727)), hAPP(c_Int_Onumber__class_Onumber__of(_1227723), _1227725)))]]], (49471 ^ _779854) ^ [_1777917, _1777919, _1777921, _1777923] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1777917), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1777919, _1777921, _1777917, _1777923) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1777919, 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(_1777919)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1777921, _1777923)), 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(_1777919)))), 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(_1777919)))), 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(_1777919)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1777919, 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(_1777919)))), 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(_1777919)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1777919, _1777921, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1777917), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1777923))), 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(_1777919)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1777919))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1777919)))), 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(_1777919)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1777919, 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(_1777919)))), 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(_1777919)))), 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(_1777919))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1777919)))), 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(_1777919)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1777919)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1777919))))), tc_prod(_1777919, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1777919)), hAPP(hAPP(c_COMBB(_1777919, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1777919)))), tc_prod(_1777919, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1777919)), c_Product__Type_Ofst(_1777919, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (25419 ^ _779854) ^ [_1241916, _1241918, _1241920, _1241922, _1241924, _1241926, _1241928, _1241930] : [c_Finite__Set_Ofolding__image__simple__idem(_1241916, _1241918, _1241920, _1241922, _1241924, _1241926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1241918), _1241928)), -(hAPP(_1241926, hAPP(hAPP(c_Set_Oinsert(_1241918), _1241930), _1241928)) = hAPP(hAPP(_1241920, hAPP(_1241924, _1241930)), hAPP(_1241926, _1241928)))], (33128 ^ _779854) ^ [_1380316, _1380318, _1380320, _1380322, _1380324] : [-(hAPP(hAPP(c_Set_Oinsert(_1380316), _1380318), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380320, tc_fun(_1380316, tc_HOL_Obool)), _1380322), _1380324)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380320, tc_fun(_1380316, tc_HOL_Obool)), _1380322), hAPP(hAPP(c_COMBB(tc_fun(_1380316, tc_HOL_Obool), tc_fun(_1380316, tc_HOL_Obool), _1380320), hAPP(c_Set_Oinsert(_1380316), _1380318)), _1380324)))], (48730 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12750 ^ _779854) ^ [_1003235, _1003237, _1003239, _1003241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1003235, tc_HOL_Obool)), _1003237), hAPP(hAPP(c_Set_Oinsert(_1003235), _1003239), _1003241))), 12753 ^ _779854 : [(12760 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003235), _1003239), _1003241))), 12763 ^ _779854 : [(12770 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003235), _1003239), _1003237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1003235, tc_HOL_Obool)), _1003237), _1003241)))], (12764 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1003235), _1003239), _1003237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1003235, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003235, tc_HOL_Obool)), _1003237), hAPP(hAPP(c_Set_Oinsert(_1003235), _1003239), c_Orderings_Obot__class_Obot(tc_fun(_1003235, tc_HOL_Obool))))), _1003241)))]]], (12754 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1003235), _1003239), _1003241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1003235, tc_HOL_Obool)), _1003237), _1003241)))]]], (18381 ^ _779854) ^ [_1112554, _1112556, _1112558, _1112560] : [class_Groups_Ocomm__monoid__add(_1112554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112556), _1112558)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1112554), _1112560), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1112556, _1112558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112554), hAPP(_1112560, _1112556)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1112554), _1112560), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1112556), _1112558))))], (1720 ^ _779854) ^ [_804306, _804308] : [-(class_Groups_Osemigroup__add(_804306)), _804308 = _804306, class_Groups_Osemigroup__add(_804308)], (44031 ^ _779854) ^ [_1658357, _1658359, _1658361, _1658363] : [-(hAPP(hAPP(c_List_Otake(_1658357), _1658359), hAPP(hAPP(c_List_Oappend(_1658357), _1658361), _1658363)) = hAPP(hAPP(c_List_Oappend(_1658357), hAPP(hAPP(c_List_Otake(_1658357), _1658359), _1658361)), hAPP(hAPP(c_List_Otake(_1658357), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1658359), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658357)), _1658361))), _1658363)))], (30585 ^ _779854) ^ [_1331958, _1331960] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331958, _1331960) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331958, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1331960)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331958, _1331960)), _1331960))], (51567 ^ _779854) ^ [_1823845, _1823847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1823845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1823845), _1823847)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823847), _1823845))], (38072 ^ _779854) ^ [_1500156, _1500158, _1500160, _1500162, _1500164] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1500156, _1500158, _1500160), _1500162), _1500164)), -(hBOOL(hAPP(_1500162, hAPP(_1500160, _1500164))))], (38891 ^ _779854) ^ [_1522141, _1522143] : [-(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), _1522141)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1522143))))))], (46242 ^ _779854) ^ [_1707823, _1707825, _1707827] : [class_Orderings_Olinorder(_1707823), -(c_List_Olinorder__class_Osort__key(_1707825, _1707823, _1707827, c_List_Olist_ONil(_1707825)) = c_List_Olist_ONil(_1707825))], (44282 ^ _779854) ^ [_1665129, _1665131] : [hAPP(c_List_Orotate1(_1665129), _1665131) = c_List_Olist_ONil(_1665129), -(_1665131 = c_List_Olist_ONil(_1665129))], (39757 ^ _779854) ^ [_1550957, _1550959] : [c_Wellfounded_Owf(_1550957, _1550959), 39760 ^ _779854 : [(39761 ^ _779854) ^ [_1551026] : [-(hBOOL(hAPP(hAPP(c_member(_1550957), _1551026), c_Wellfounded_Oacc(_1550957, _1550959))))]]], (44438 ^ _779854) ^ [_1668913, _1668915, _1668917, _1668919, _1668921] : [-(hAPP(hAPP(c_List_Ozip(_1668913, _1668915), hAPP(hAPP(c_List_Oappend(_1668913), _1668917), _1668919)), _1668921) = hAPP(hAPP(c_List_Oappend(tc_prod(_1668913, _1668915)), hAPP(hAPP(c_List_Ozip(_1668913, _1668915), _1668917), hAPP(hAPP(c_List_Otake(_1668915), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668913)), _1668917)), _1668921))), hAPP(hAPP(c_List_Ozip(_1668913, _1668915), _1668919), hAPP(hAPP(c_List_Odrop(_1668915), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668913)), _1668917)), _1668921))))], (7852 ^ _779854) ^ [_910984, _910986, _910988, _910990] : [class_Orderings_Oorder(_910984), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_910984, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_910984, _910986, _910988)), c_SetInterval_Oord__class_OatLeastAtMost(_910984, _910988, _910990)) = c_Orderings_Obot__class_Obot(tc_fun(_910984, tc_HOL_Obool)))], (35448 ^ _779854) ^ [_1440244, _1440246, _1440248, _1440250] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1440244, _1440246), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1440248), _1440250))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440244), _1440246) = _1440248)], (43480 ^ _779854) ^ [_1646488, _1646490] : [_1646490 = c_List_Olist_ONil(_1646488), -(c_Orderings_Obot__class_Obot(tc_fun(_1646488, tc_HOL_Obool)) = hAPP(c_List_Oset(_1646488), _1646490))], (28878 ^ _779854) ^ [_1301423] : [class_Int_Onumber__ring(_1301423), c_Int_Oiszero(_1301423, hAPP(c_Int_Onumber__class_Onumber__of(_1301423), c_Int_OBit1(c_Int_OPls)))], (51152 ^ _779854) ^ [_1814035, _1814037, _1814039, _1814041] : [c_Equiv__Relations_Oequivp(_1814035, _1814037), -(c_Quotient_OBabs(_1814035, _1814039, c_Quotient_ORespects(_1814035, _1814037), _1814041) = _1814041)], (27987 ^ _779854) ^ [_1286113, _1286115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1286113)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1286113), _1286115)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1286113)), _1286115))], (3728 ^ _779854) ^ [_835927, _835929, _835931, _835933, _835935, _835937, _835939, _835941] : [-(c_List_Omaps(_835941, _835937, _835933, _835929) = c_List_Omaps(_835939, _835935, _835931, _835927)), _835941 = _835939, _835937 = _835935, _835933 = _835931, _835929 = _835927], (1610 ^ _779854) ^ [_802931, _802933] : [-(class_Rings_Oordered__comm__semiring(_802931)), _802933 = _802931, class_Rings_Oordered__comm__semiring(_802933)], (30477 ^ _779854) ^ [_1330129, _1330131, _1330133, _1330135] : [class_Divides_Osemiring__div(_1330129), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330129), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330129), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330129), _1330131), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1330129), _1330133), _1330131))), c_Divides_Odiv__class_Omod(_1330129, _1330133, _1330131))), _1330135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330129), _1330133), _1330135))], (4706 ^ _779854) ^ [_851638, _851640, _851642, _851644, _851646, _851648, _851650, _851652] : [-(c_Random__Sequence_Obind(_851652, _851648, _851644, _851640) = c_Random__Sequence_Obind(_851650, _851646, _851642, _851638)), _851652 = _851650, _851648 = _851646, _851644 = _851642, _851640 = _851638], (38604 ^ _779854) ^ [_1514795, _1514797, _1514799, _1514801, _1514803, _1514805] : [hAPP(c_Set_Oimage(_1514795, _1514797, _1514799), c_Orderings_Otop__class_Otop(tc_fun(_1514795, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1514797, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1514801, _1514803, _1514805), c_Orderings_Otop__class_Otop(tc_fun(_1514801, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1514803, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1514795, _1514801), tc_prod(_1514797, _1514803), c_Product__Type_Omap__pair(_1514795, _1514797, _1514801, _1514803, _1514799, _1514805)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1514795, _1514801), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1514797, _1514803), tc_HOL_Obool)))], (31200 ^ _779854) ^ [_1342473, _1342475] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1342473, _1342475)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1342473), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1342475)))], (34205 ^ _779854) ^ [_1413082, _1413084] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1413082), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1413084))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1413082), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413084))), 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))))], (47298 ^ _779854) ^ [_1730648, _1730650, _1730652, _1730654] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1730648), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1730648))), _1730650))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730652), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1730648))), c_List_Otranspose(_1730648, _1730650)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730654), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1730648))), hAPP(c_List_Ofilter(tc_List_Olist(_1730648), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1730648)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730652)), c_Nat_Osize__class_Osize(tc_List_Olist(_1730648)))), _1730650)))), -(hAPP(hAPP(c_List_Onth(_1730648), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1730648)), c_List_Otranspose(_1730648, _1730650)), _1730652)), _1730654) = hAPP(hAPP(c_List_Onth(_1730648), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1730648)), _1730650), _1730654)), _1730652))], (8876 ^ _779854) ^ [_927638, _927640, _927642, _927644] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927638, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_927638), _927640), _927642)), hAPP(hAPP(c_Set_Oinsert(_927638), _927640), _927644)) = hAPP(hAPP(c_Set_Oinsert(_927638), _927640), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927638, tc_HOL_Obool)), _927642), _927644)))], (30993 ^ _779854) ^ [_1339319] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1339319))), -(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), _1339319)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17460 ^ _779854) ^ [_1095618, _1095620, _1095622] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1095618), _1095620)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095618), _1095622)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095618), _1095620)), hAPP(c_Finite__Set_Ocard(_1095618), _1095622)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095618), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095618, tc_HOL_Obool)), _1095620), _1095622))), hAPP(c_Finite__Set_Ocard(_1095618), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095618, tc_HOL_Obool)), _1095620), _1095622))))], (40776 ^ _779854) ^ [_1574986, _1574988, _1574990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1574986, tc_HOL_Obool)), _1574988), hAPP(_1574990, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1574986, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574986, tc_HOL_Obool), tc_fun(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), tc_fun(_1574986, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574986, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574986, tc_HOL_Obool), tc_fun(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), tc_fun(_1574986, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574986, tc_HOL_Obool))), _1574990)), _1574988))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1574986, tc_HOL_Obool), _1574990)))))), c_Orderings_Oorder__class_Omono(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool), _1574990), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1574986, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1574986, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574986, tc_HOL_Obool), tc_fun(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), tc_fun(_1574986, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574986, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574986, tc_HOL_Obool), tc_fun(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), tc_fun(_1574986, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574986, tc_HOL_Obool))), _1574990)), _1574988))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1574986, tc_HOL_Obool), _1574990)))), hAPP(_1574990, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1574986, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574986, tc_HOL_Obool), tc_fun(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), tc_fun(_1574986, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574986, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574986, tc_HOL_Obool), tc_fun(tc_fun(_1574986, tc_HOL_Obool), tc_fun(_1574986, tc_HOL_Obool)), tc_fun(_1574986, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574986, tc_HOL_Obool))), _1574990)), _1574988))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1574986, tc_HOL_Obool), _1574990)))))))], (18076 ^ _779854) ^ [_1106877, _1106879] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1106877)), hAPP(c_Nat_OSuc, _1106879)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1106877), _1106879)))], (20081 ^ _779854) ^ [_1141890, _1141892, _1141894, _1141896] : [class_Groups_Ocomm__monoid__add(_1141890), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1141892), _1141894))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1141892, _1141890), _1141896), _1141894) = c_Groups_Ozero__class_Ozero(_1141890))], (19507 ^ _779854) ^ [_1131657, _1131659, _1131661] : [class_Groups_Oordered__comm__monoid__add(_1131657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131657), c_Groups_Ozero__class_Ozero(_1131657)), _1131659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131657), c_Groups_Ozero__class_Ozero(_1131657)), _1131661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131657), c_Groups_Ozero__class_Ozero(_1131657)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131657), _1131659), _1131661))))], (17793 ^ _779854) ^ [_1102274, _1102276] : [class_Rings_Ocomm__semiring__1(_1102274), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102274), _1102276), c_Groups_Oone__class_Oone(_1102274)) = _1102276)], (11804 ^ _779854) ^ [_984719, _984721, _984723, _984725] : [_984719 = _984721, 11807 ^ _779854 : [(11814 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_984723), _984721), _984725)), -(hBOOL(hAPP(hAPP(c_member(_984723), _984719), _984725)))], (11808 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_984723), _984719), _984725)), -(hBOOL(hAPP(hAPP(c_member(_984723), _984721), _984725)))]]], (1570 ^ _779854) ^ [_802431, _802433] : [-(class_Groups_Oordered__ab__semigroup__add(_802431)), _802433 = _802431, class_Groups_Oordered__ab__semigroup__add(_802433)], (24439 ^ _779854) ^ [_1223182, _1223184, _1223186, _1223188] : [class_Lattices_Osemilattice__sup(_1223182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1223182), _1223184)), 24449 ^ _779854 : [(24452 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223182), 24448 ^ [_1223182, _1223184, _1223186, _1223188]), _1223186))], (24450 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1223182), 24448 ^ [_1223182, _1223184, _1223186, _1223188]), _1223184)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223182), hAPP(hAPP(c_Finite__Set_Ofold(_1223182, _1223182, c_Lattices_Osemilattice__sup__class_Osup(_1223182)), _1223188), _1223184)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1223182), _1223186), _1223188))))], (17226 ^ _779854) ^ [_1090944, _1090946, _1090948, _1090950, _1090952, _1090954] : [c_Finite__Set_Ofun__left__comm(_1090944, _1090946, _1090948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090944), _1090950)), -(hBOOL(hAPP(hAPP(c_member(_1090944), _1090952), _1090950))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1090944, _1090946, _1090948), _1090954), hAPP(hAPP(c_Set_Oinsert(_1090944), _1090952), _1090950)) = hAPP(hAPP(_1090948, _1090952), hAPP(hAPP(c_Finite__Set_Ofold(_1090944, _1090946, _1090948), _1090954), _1090950)))], (41122 ^ _779854) ^ [_1584909, _1584911, _1584913, _1584915] : [41123 ^ _779854 : [(41126 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584909, _1584909)), _1584911), c_Transitive__Closure_Ortrancl(_1584909, _1584915)))], (41124 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584909, _1584909)), _1584911), c_Transitive__Closure_Ortrancl(_1584909, _1584913)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584909, _1584909)), _1584911), c_Transitive__Closure_Ortrancl(_1584909, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584909, _1584909), tc_HOL_Obool)), _1584913), _1584915)))))], (6667 ^ _779854) ^ [_886751, _886753, _886755] : [class_Orderings_Olinorder(_886751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886751), _886753), _886755)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886751, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_886751), _886753)), c_SetInterval_Oord__class_OatLeastAtMost(_886751, _886753, _886755)) = hAPP(c_SetInterval_Oord__class_OatMost(_886751), _886755))], (46978 ^ _779854) ^ [_1724405, _1724407, _1724409] : [class_Orderings_Olinorder(_1724405), c_List_Olinorder__class_Osorted(_1724405, _1724407), hBOOL(hAPP(c_List_Odistinct(_1724405), _1724407)), c_List_Olinorder__class_Osorted(_1724405, _1724409), hBOOL(hAPP(c_List_Odistinct(_1724405), _1724409)), hAPP(c_List_Oset(_1724405), _1724407) = hAPP(c_List_Oset(_1724405), _1724409), -(_1724407 = _1724409)], (25515 ^ _779854) ^ [_1244029, _1244031] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244029)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244031)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244029), _1244031)))], (30017 ^ _779854) ^ [_1321113, _1321115, _1321117] : [class_Rings_Ocomm__semiring__1(_1321113), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1321113), _1321115), 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)))), _1321117))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321113), _1321115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321113), hAPP(hAPP(c_Power_Opower__class_Opower(_1321113), _1321115), _1321117)), hAPP(hAPP(c_Power_Opower__class_Opower(_1321113), _1321115), _1321117))))], (26715 ^ _779854) ^ [_1265016, _1265018, _1265020, _1265022] : [class_Divides_Osemiring__div(_1265016), -(_1265018 = c_Groups_Ozero__class_Ozero(_1265016)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265016), _1265020), _1265018)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265016), _1265022), _1265018)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265016), _1265020), _1265022))], (41186 ^ _779854) ^ [_1586502, _1586504, _1586506] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1586502, _1586502, _1586504), c_Relation_OId(_1586502)), _1586506) = _1586506)], (39421 ^ _779854) ^ [_1541649, _1541651, _1541653, _1541655, _1541657, _1541659] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541649, _1541651, _1541653), _1541655), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541651, _1541653), tc_HOL_Obool)), _1541657), _1541659)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541649, _1541653), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541649, _1541651, _1541653), _1541655), _1541657)), hAPP(hAPP(c_Relation_Orel__comp(_1541649, _1541651, _1541653), _1541655), _1541659)))], (27071 ^ _779854) ^ [_1270751, _1270753, _1270755, _1270757] : [class_Divides_Osemiring__div(_1270751), -(_1270753 = c_Groups_Ozero__class_Ozero(_1270751)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1270751), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1270751), _1270755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270751), _1270757), _1270753))), _1270753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1270751), _1270757), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1270751), _1270755), _1270753)))], (26455 ^ _779854) ^ [_1260529, _1260531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1260529), _1260531)), -(c_Nat__Transfer_Otsub(_1260531, _1260529) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1260531), _1260529))], (36812 ^ _779854) ^ [_1468881, _1468883, _1468885, _1468887] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1468881), _1468883)), 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)), _1468885), _1468881)), 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)), _1468887), _1468883)), 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)), _1468885), _1468887)), _1468883)), c_FunDef_Omax__strict)))], (27425 ^ _779854) ^ [_1276734, _1276736] : [class_Int_Onumber__ring(_1276734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1276736)), -(hBOOL(hAPP(hAPP(c_member(_1276734), hAPP(c_Int_Onumber__class_Onumber__of(_1276734), _1276736)), c_Nat_Osemiring__1__class_ONats(_1276734))))], (48014 ^ _779854) ^ [_1746033, _1746035] : [-(c_List_Omeasures(_1746033, _1746035) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1746033), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1746033, tc_List_Olist(tc_fun(_1746033, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1746033, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1746033, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1746033), c_List_Omap(tc_fun(_1746033, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1746033, tc_Nat_Onat), _1746033, tc_Nat_Onat), c_COMBI(tc_fun(_1746033, tc_Nat_Onat))))), _1746035)))], (21993 ^ _779854) ^ [_1177077, _1177079] : [class_Rings_Odivision__ring__inverse__zero(_1177077), 21996 ^ _779854 : [(22003 ^ _779854) ^ [] : [-(_1177079 = c_Groups_Ozero__class_Ozero(_1177077)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177077), _1177079), _1177079) = c_Groups_Oone__class_Oone(_1177077))], (21997 ^ _779854) ^ [] : [_1177079 = c_Groups_Ozero__class_Ozero(_1177077), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177077), _1177079), _1177079) = c_Groups_Ozero__class_Ozero(_1177077))]]], (26491 ^ _779854) ^ [_1261250, _1261252, _1261254, _1261256, _1261258, _1261260, _1261262] : [-(c_Nitpick_Ofold__graph_H(_1261250, _1261252, _1261254, _1261256, _1261258, hAPP(hAPP(_1261254, _1261260), _1261262))), 26492 ^ _779854 : [(26499 ^ _779854) ^ [_1261479, _1261481] : [hAPP(hAPP(_1261254, _1261260), _1261262) = hAPP(hAPP(_1261254, _1261481), _1261479), hBOOL(hAPP(hAPP(c_member(_1261250), _1261481), _1261258)), c_Nitpick_Ofold__graph_H(_1261250, _1261252, _1261254, _1261256, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261250, tc_HOL_Obool)), _1261258), hAPP(hAPP(c_Set_Oinsert(_1261250), _1261481), c_Orderings_Obot__class_Obot(tc_fun(_1261250, tc_HOL_Obool)))), _1261479)], (26493 ^ _779854) ^ [] : [_1261258 = c_Orderings_Obot__class_Obot(tc_fun(_1261250, tc_HOL_Obool)), hAPP(hAPP(_1261254, _1261260), _1261262) = _1261256]]], (42811 ^ _779854) ^ [_1630236, _1630238, _1630240] : [-(hBOOL(hAPP(hAPP(c_member(_1630236), _1630238), hAPP(c_List_Oset(_1630236), _1630240)))), 42812 ^ _779854 : [(42813 ^ _779854) ^ [_1630310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630310), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630236)), _1630240))), hAPP(hAPP(c_List_Onth(_1630236), _1630240), _1630310) = _1630238]]], (48732 ^ _779854) ^ [_1761548, _1761550, _1761552] : [c_List_Olist__ex1(_1761548, _1761550, _1761552), 48736 ^ _779854 : [(48741 ^ _779854) ^ [_1761794] : [-(_1761794 = 48735 ^ [_1761548, _1761550, _1761552]), hBOOL(hAPP(hAPP(c_member(_1761548), _1761794), hAPP(c_List_Oset(_1761548), _1761552))), hBOOL(hAPP(_1761550, _1761794))], (48739 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1761550, 48735 ^ [_1761548, _1761550, _1761552])))], (48737 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761548), 48735 ^ [_1761548, _1761550, _1761552]), hAPP(c_List_Oset(_1761548), _1761552))))]]], (50862 ^ _779854) ^ [_1808489, _1808491, _1808493, _1808495] : [c_Fun_Oinj__on(_1808489, _1808491, _1808493, _1808495), -(c_Fun_Obij__betw(_1808489, _1808491, _1808493, _1808495, hAPP(c_Set_Oimage(_1808489, _1808491, _1808493), _1808495)))], (20768 ^ _779854) ^ [_1153587, _1153589, _1153591, _1153593] : [class_Rings_Olinordered__semiring__strict(_1153587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153587), _1153589), _1153591)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153587), _1153593), _1153591))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153587), c_Groups_Ozero__class_Ozero(_1153587)), _1153591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153587), _1153589), _1153593)))], (47760 ^ _779854) ^ [_1740506, _1740508, _1740510, _1740512] : [-(hBOOL(hAPP(_1740506, _1740508))), -(c_List_OdropWhile(_1740510, _1740506, hAPP(hAPP(c_List_Olist_OCons(_1740510), _1740508), _1740512)) = hAPP(hAPP(c_List_Olist_OCons(_1740510), _1740508), _1740512))], (5366 ^ _779854) ^ [_862008, _862010] : [_862010 = _862008, -(c_Finite__Set_Ofinite(_862010) = c_Finite__Set_Ofinite(_862008))], (27387 ^ _779854) ^ [_1276161, _1276163] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1276161))), -(c_SMT_Oz3div(_1276163, _1276161) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1276163), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1276161))))], (6137 ^ _779854) ^ [_877322, _877324] : [class_Orderings_Otop(_877322), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877322), _877324), c_Orderings_Otop__class_Otop(_877322))))], (52213 ^ _779854) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (12536 ^ _779854) ^ [_998998, _999000, _999002] : [hBOOL(hAPP(hAPP(c_member(_998998), _999000), _999002)), -(hAPP(hAPP(c_Set_Oinsert(_998998), _999000), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998998, tc_HOL_Obool)), _999002), hAPP(hAPP(c_Set_Oinsert(_998998), _999000), c_Orderings_Obot__class_Obot(tc_fun(_998998, tc_HOL_Obool))))) = _999002)], (41370 ^ _779854) ^ [_1590799, _1590801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1590799), _1590801)), -(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), _1590799), _1590801)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (23822 ^ _779854) ^ [_1211902, _1211904] : [_1211902 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211904), _1211902) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (40064 ^ _779854) ^ [_1558270, _1558272] : [c_Wellfounded_Owf(_1558270, _1558272), -(c_Wellfounded_OwfP(_1558270, c_FunDef_Oin__rel(_1558270, _1558270, _1558272)))], (5320 ^ _779854) ^ [_861233, _861235, _861237, _861239, _861241, _861243, _861245, _861247, _861249, _861251] : [-(c_New__DSequence_Opos__map(_861251, _861247, _861243, _861239, _861235) = c_New__DSequence_Opos__map(_861249, _861245, _861241, _861237, _861233)), _861251 = _861249, _861247 = _861245, _861243 = _861241, _861239 = _861237, _861235 = _861233], (52335 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11324 ^ _779854) ^ [_975288, _975290, _975292] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975288), _975290)), hBOOL(hAPP(c_Finite__Set_Ofinite(_975288), _975292)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_975288), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_975288, tc_HOL_Obool)), _975290), _975292))))], (17700 ^ _779854) ^ [_1100777] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1100777))], (43757 ^ _779854) ^ [_1652611, _1652613, _1652615, _1652617, _1652619] : [-(hAPP(hAPP(c_List_Olist_OCons(_1652611), _1652613), _1652615) = hAPP(hAPP(c_List_Oappend(_1652611), _1652617), _1652619)), 43758 ^ _779854 : [(43765 ^ _779854) ^ [_1652794] : [hAPP(hAPP(c_List_Olist_OCons(_1652611), _1652613), _1652794) = _1652617, _1652615 = hAPP(hAPP(c_List_Oappend(_1652611), _1652794), _1652619)], (43759 ^ _779854) ^ [] : [_1652617 = c_List_Olist_ONil(_1652611), hAPP(hAPP(c_List_Olist_OCons(_1652611), _1652613), _1652615) = _1652619]]], (31814 ^ _779854) ^ [_1352321, _1352323, _1352325] : [class_Rings_Oring__1(_1352321), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352321), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1352323), _1352325)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352321), hAPP(c_Int_Oring__1__class_Oof__int(_1352321), _1352323)), hAPP(c_Int_Oring__1__class_Oof__int(_1352321), _1352325)))], (17496 ^ _779854) ^ [_1096372, _1096374, _1096376] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096372), _1096374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1096372, tc_HOL_Obool)), _1096374), _1096376)), -(hAPP(c_Finite__Set_Ocard(_1096372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096372, tc_HOL_Obool)), _1096376), _1096374)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1096372), _1096376)), hAPP(c_Finite__Set_Ocard(_1096372), _1096374)))], (52307 ^ _779854) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (21881 ^ _779854) ^ [_1175272, _1175274] : [class_Rings_Odivision__ring(_1175272), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175272), _1175274), c_Groups_Oone__class_Oone(_1175272)) = _1175274)], (6387 ^ _779854) ^ [_881550, _881552] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_881550, tc_HOL_Obool)), _881552)))], (1920 ^ _779854) ^ [_806806, _806808] : [-(class_Nat_Osize(_806806)), _806808 = _806806, class_Nat_Osize(_806808)], (33945 ^ _779854) ^ [_1406800, _1406802, _1406804, _1406806, _1406808] : [class_Complete__Lattice_Ocomplete__lattice(_1406800), hBOOL(hAPP(hAPP(c_member(_1406802), _1406804), _1406806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406800), hAPP(_1406808, _1406804)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406802, _1406800), _1406806), _1406808))))], (20522 ^ _779854) ^ [_1149060] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1149060) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1149060))], (41407 ^ _779854) ^ [_1591754, _1591756] : [c_Wellfounded_Oacyclic(_1591754, hAPP(c_Relation_Oconverse(_1591754, _1591754), _1591756)), -(c_Wellfounded_Oacyclic(_1591754, _1591756))], (38849 ^ _779854) ^ [_1521119, _1521121, _1521123] : [hBOOL(hAPP(_1521119, _1521121)), -(hAPP(c_Set_OCollect(_1521123), hAPP(hAPP(c_COMBS(_1521123, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521123), c_fconj), hAPP(c_fequal, _1521121))), _1521119)) = hAPP(hAPP(c_Set_Oinsert(_1521123), _1521121), c_Orderings_Obot__class_Obot(tc_fun(_1521123, tc_HOL_Obool))))], (8228 ^ _779854) ^ [_917697, _917699, _917701] : [class_Orderings_Oorder(_917697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917697), _917699), _917701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917697), _917701), _917699))], (42663 ^ _779854) ^ [_1626845, _1626847, _1626849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626845)), _1626847)), _1626849)), -(hAPP(hAPP(c_List_Otake(_1626845), _1626849), _1626847) = _1626847)], (30127 ^ _779854) ^ [_1323425, _1323427, _1323429] : [-(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, _1323425, _1323427)), _1323429), _1323427) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1323425), _1323429), _1323427))], (7187 ^ _779854) ^ [_898056, _898058, _898060, _898062] : [class_Lattices_Osemilattice__inf(_898056), 7190 ^ _779854 : [(7199 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898056), _898058), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_898056), _898060), _898062)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898056), _898058), _898060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898056), _898058), _898062))], (7191 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898056), _898058), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_898056), _898060), _898062))), 7194 ^ _779854 : [(7197 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898056), _898058), _898062)))], (7195 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898056), _898058), _898060)))]]]]], (38861 ^ _779854) ^ [_1521353, _1521355] : [-(hAPP(c_Set_OCollect(_1521353), hAPP(hAPP(c_COMBC(_1521353, _1521353, tc_HOL_Obool), c_fequal), _1521355)) = hAPP(hAPP(c_Set_Oinsert(_1521353), _1521355), c_Orderings_Obot__class_Obot(tc_fun(_1521353, tc_HOL_Obool))))], (45673 ^ _779854) ^ [_1695462, _1695464] : [-(hBOOL(hAPP(c_List_Olistsp(_1695462, _1695464), c_List_Olist_ONil(_1695462))))], (38130 ^ _779854) ^ [_1501586, _1501588, _1501590, _1501592, _1501594] : [hBOOL(hAPP(hAPP(c_member(_1501586), _1501588), hAPP(c_Set_Ovimage(_1501586, _1501590, _1501592), hAPP(hAPP(c_Set_Oinsert(_1501590), _1501594), c_Orderings_Obot__class_Obot(tc_fun(_1501590, tc_HOL_Obool)))))), -(hAPP(_1501592, _1501588) = _1501594)], (30416 ^ _779854) ^ [_1329042, _1329044, _1329046] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329042), _1329044)), _1329046) = 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), _1329042), _1329046)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329044), _1329046))), 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, _1329042, _1329046)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329044, _1329046))), _1329046)))], (52131 ^ _779854) ^ [_1833077, _1833079] : [class_Lattices_Olattice(_1833077), -(class_Lattices_Olattice(tc_fun(_1833079, _1833077)))], (31198 ^ _779854) ^ [_1342431, _1342433] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1342431), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1342433)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1342431, _1342433)))], (22615 ^ _779854) ^ [_1188354, _1188356, _1188358] : [class_Fields_Olinordered__field(_1188354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188354), c_Groups_Ozero__class_Ozero(_1188354)), _1188356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188354), _1188358), c_Groups_Ozero__class_Ozero(_1188354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188354), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188354), _1188356), _1188358)), c_Groups_Ozero__class_Ozero(_1188354))))], (50967 ^ _779854) ^ [_1810292, _1810294, _1810296] : [_1810294 = _1810296, -(c_Fun_Obij__betw(_1810292, _1810292, c_Fun_Oid(_1810292), _1810294, _1810296))], (36549 ^ _779854) ^ [_1462521, _1462523, _1462525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462521, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1462521, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36550 ^ [_1462521, _1462523, _1462525])), _1462523)), _1462525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462521, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1462521, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1462523)), _1462525)))], (28824 ^ _779854) ^ [_1300518, _1300520] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300518), _1300520), hAPP(c_Int_Onumber__class_Onumber__of(_1300518), c_Int_OBit1(c_Int_OPls))) = _1300520), class_Fields_Ofield(_1300518), class_Int_Onumber__ring(_1300518)], (25069 ^ _779854) ^ [_1235090, _1235092, _1235094, _1235096] : [class_Fields_Olinordered__field__inverse__zero(_1235090), class_Int_Onumber(_1235090), 25076 ^ _779854 : [(25077 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1235090), _1235094), _1235096))), 25080 ^ _779854 : [(25087 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), c_Groups_Ozero__class_Ozero(_1235090)), _1235096))), 25090 ^ _779854 : [(25097 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), _1235096), c_Groups_Ozero__class_Ozero(_1235090)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), c_Groups_Ozero__class_Ozero(_1235090))))], (25091 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), _1235096), c_Groups_Ozero__class_Ozero(_1235090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), _1235094), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), _1235096))))]]], (25081 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), c_Groups_Ozero__class_Ozero(_1235090)), _1235096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), _1235096)), _1235094)))]]], (25103 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1235090), _1235094), _1235096)))), 25106 ^ _779854 : [(25109 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), _1235096)), _1235094))], (25107 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), c_Groups_Ozero__class_Ozero(_1235090)), _1235096)))]], 25110 ^ _779854 : [(25113 ^ _779854) ^ [] : [25114 ^ _779854 : [(25117 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), _1235094), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), _1235096)))], (25115 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), _1235096), c_Groups_Ozero__class_Ozero(_1235090))))]], 25118 ^ _779854 : [(25121 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), hAPP(c_Int_Onumber__class_Onumber__of(_1235090), _1235092)), c_Groups_Ozero__class_Ozero(_1235090)))], (25119 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), _1235096), c_Groups_Ozero__class_Ozero(_1235090)))]]], (25111 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235090), c_Groups_Ozero__class_Ozero(_1235090)), _1235096))]]]]], (33667 ^ _779854) ^ [_1398523, _1398525, _1398527, _1398529, _1398531, _1398533] : [-(hAPP(c_Set_Oimage(_1398523, _1398525, _1398527), hAPP(c_Set_Oimage(_1398529, _1398523, _1398531), _1398533)) = hAPP(c_Set_Oimage(_1398529, _1398525, hAPP(hAPP(c_COMBB(_1398523, _1398525, _1398529), _1398527), _1398531)), _1398533))], (52407 ^ _779854) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (33296 ^ _779854) ^ [_1384697, _1384699, _1384701, _1384703, _1384705, _1384707] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384697, tc_fun(_1384699, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384701, tc_fun(_1384697, tc_HOL_Obool)), _1384703), _1384705)), _1384707) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384701, tc_fun(_1384699, tc_HOL_Obool)), _1384703), hAPP(hAPP(c_COMBC(_1384701, tc_fun(_1384697, tc_fun(_1384699, tc_HOL_Obool)), tc_fun(_1384699, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384697, tc_HOL_Obool), tc_fun(tc_fun(_1384697, tc_fun(_1384699, tc_HOL_Obool)), tc_fun(_1384699, tc_HOL_Obool)), _1384701), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384697, tc_fun(_1384699, tc_HOL_Obool))), _1384705)), _1384707)))], (15792 ^ _779854) ^ [_1062806, _1062808] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1062806, _1062808))))], (22991 ^ _779854) ^ [_1195430, _1195432, _1195434, _1195436] : [class_Fields_Ofield__inverse__zero(_1195430), -(_1195432 = c_Groups_Ozero__class_Ozero(_1195430)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195430), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195430), _1195434), _1195432)), _1195436) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195430), _1195434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195430), _1195436), _1195432))), _1195432))], (9166 ^ _779854) ^ [_932753, _932755, _932757, _932759, _932761] : [class_Orderings_Oorder(_932753), class_Orderings_Olinorder(_932755), c_Orderings_Oorder__class_Ostrict__mono(_932755, _932753, _932757), 9177 ^ _779854 : [(9184 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932755), _932759), _932761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932753), hAPP(_932757, _932759)), hAPP(_932757, _932761))))], (9178 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932753), hAPP(_932757, _932759)), hAPP(_932757, _932761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932755), _932759), _932761)))]]], (6493 ^ _779854) ^ [_883717] : [class_Complete__Lattice_Ocomplete__lattice(_883717), -(c_Complete__Lattice_OSup__class_OSup(_883717, c_Orderings_Otop__class_Otop(tc_fun(_883717, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_883717))], (2590 ^ _779854) ^ [_818220, _818222, _818224, _818226, _818228, _818230] : [-(c_Partial__Function_Oflat__lub(_818230, _818226, _818222) = c_Partial__Function_Oflat__lub(_818228, _818224, _818220)), _818230 = _818228, _818226 = _818224, _818222 = _818220], (43386 ^ _779854) ^ [_1644939, _1644941, _1644943] : [-(_1644939 = c_List_Olist_ONil(_1644941)), -(c_List_Obutlast(_1644941, hAPP(hAPP(c_List_Olist_OCons(_1644941), _1644943), _1644939)) = hAPP(hAPP(c_List_Olist_OCons(_1644941), _1644943), c_List_Obutlast(_1644941, _1644939)))], (33232 ^ _779854) ^ [_1382572, _1382574, _1382576, _1382578] : [class_Groups_Ouminus(_1382572), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1382574, _1382572)), _1382576), _1382578) = hAPP(c_Groups_Ouminus__class_Ouminus(_1382572), hAPP(_1382576, _1382578)))], (51811 ^ _779854) ^ [_1828098, _1828100] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828098), _1828100)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828100), _1828098))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828100), _1828098)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828098), _1828100)))], (33575 ^ _779854) ^ [_1395678, _1395680, _1395682, _1395684, _1395686] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395678, tc_fun(_1395680, tc_HOL_Obool)), _1395682), hAPP(hAPP(c_COMBB(tc_fun(_1395680, tc_HOL_Obool), tc_fun(_1395680, tc_HOL_Obool), _1395678), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395680, tc_HOL_Obool)), _1395684)), _1395686)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395680, tc_HOL_Obool)), _1395684), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395678, tc_fun(_1395680, tc_HOL_Obool)), _1395682), _1395686)))], (44039 ^ _779854) ^ [_1658614, _1658616, _1658618, _1658620, _1658622] : [-(hAPP(hAPP(c_List_Olist__update(_1658614, hAPP(hAPP(c_List_Oappend(_1658614), _1658616), hAPP(hAPP(c_List_Olist_OCons(_1658614), _1658618), _1658620))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658614)), _1658616)), _1658622) = hAPP(hAPP(c_List_Oappend(_1658614), _1658616), hAPP(hAPP(c_List_Olist_OCons(_1658614), _1658622), _1658620)))], (11191 ^ _779854) ^ [_972782, _972784, _972786, _972788] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972782), _972784)), 11194 ^ _779854 : [(11195 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972786), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_972782, tc_fun(_972786, tc_HOL_Obool)), _972784), _972788))), 11198 ^ _779854 : [(11199 ^ _779854) ^ [_972966] : [hBOOL(hAPP(hAPP(c_member(_972782), _972966), _972784)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_972786), hAPP(_972788, _972966))))]]], (11205 ^ _779854) ^ [] : [11207 ^ _779854 : [(11210 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972786), hAPP(_972788, 11206 ^ [_972782, _972784, _972786, _972788])))], (11208 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972782), 11206 ^ [_972782, _972784, _972786, _972788]), _972784)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_972786), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_972782, tc_fun(_972786, tc_HOL_Obool)), _972784), _972788))))]]], (9604 ^ _779854) ^ [_940861, _940863, _940865, _940867] : [class_Orderings_Olinorder(_940861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940861), _940863), _940865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940861), _940863), hAPP(hAPP(c_Orderings_Oord__class_Omax(_940861), _940865), _940867))))], (49235 ^ _779854) ^ [_1772763, _1772765, _1772767] : [hBOOL(hAPP(hAPP(c_member(_1772763), _1772765), hAPP(c_List_Oset(_1772763), _1772767))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1772763), _1772767), _1772765)))], (34895 ^ _779854) ^ [_1428306, _1428308, _1428310, _1428312, _1428314, _1428316, _1428318] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428306, tc_fun(_1428308, tc_fun(_1428310, tc_HOL_Obool))), _1428312), _1428314), _1428316), _1428318)), 34899 ^ _779854 : [(34902 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1428314, 34898 ^ [_1428306, _1428308, _1428310, _1428312, _1428314, _1428316, _1428318]), _1428316), _1428318)))], (34900 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1428306), 34898 ^ [_1428306, _1428308, _1428310, _1428312, _1428314, _1428316, _1428318]), _1428312)))]]], (47721 ^ _779854) ^ [_1739738, _1739740, _1739742] : [-(hAPP(hAPP(c_List_Oappend(_1739738), c_List_OtakeWhile(_1739738, _1739740, _1739742)), c_List_OdropWhile(_1739738, _1739740, _1739742)) = _1739742)], (12082 ^ _779854) ^ [_990276, _990278, _990280, _990282] : [-(hBOOL(hAPP(hAPP(c_member(_990276), _990278), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990276, tc_HOL_Obool)), _990280), _990282)))), hBOOL(hAPP(hAPP(c_member(_990276), _990278), _990280)), -(hBOOL(hAPP(hAPP(c_member(_990276), _990278), _990282)))], (41885 ^ _779854) ^ [_1603582, _1603584, _1603586, _1603588, _1603590] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603582, _1603582)), hAPP(hAPP(c_Product__Type_OPair(_1603582, _1603582), _1603584), _1603586)), c_Transitive__Closure_Ortrancl(_1603582, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1603582, _1603582), tc_HOL_Obool)), _1603588), _1603590)))), 41891 ^ _779854 : [(41897 ^ _779854) ^ [] : [41890 ^ [_1603582, _1603584, _1603586, _1603588, _1603590] = 41893 ^ [_1603582, _1603584, _1603586, _1603588, _1603590]], (41895 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603582, _1603582)), hAPP(hAPP(c_Product__Type_OPair(_1603582, _1603582), 41890 ^ [_1603582, _1603584, _1603586, _1603588, _1603590]), 41893 ^ [_1603582, _1603584, _1603586, _1603588, _1603590])), _1603590)))], (41892 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603582, _1603582)), hAPP(hAPP(c_Product__Type_OPair(_1603582, _1603582), _1603584), 41890 ^ [_1603582, _1603584, _1603586, _1603588, _1603590])), c_Transitive__Closure_Ortrancl(_1603582, _1603588))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603582, _1603582)), hAPP(hAPP(c_Product__Type_OPair(_1603582, _1603582), _1603584), _1603586)), c_Transitive__Closure_Ortrancl(_1603582, _1603588))))], (15972 ^ _779854) ^ [_1066565, _1066567, _1066569, _1066571] : [class_Rings_Ocomm__semiring__1(_1066565), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066565), _1066567), _1066569)), _1066571) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066565), _1066567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066565), _1066569), _1066571)))], (5534 ^ _779854) ^ [_864570, _864572] : [_864572 = _864570, -(tc_List_Olist(_864572) = tc_List_Olist(_864570))], (5276 ^ _779854) ^ [_860549, _860551] : [_860551 = _860549, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_860551) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_860549))], (50605 ^ _779854) ^ [_1803090, _1803092, _1803094, _1803096] : [hBOOL(hAPP(_1803090, _1803092)), hBOOL(hAPP(_1803094, _1803096)), -(hBOOL(hAPP(_1803090, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1803090) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1803094))), 50621 ^ _779854 : [(50624 ^ _779854) ^ [] : [hBOOL(hAPP(_1803094, 50618 ^ [_1803090, _1803092, _1803094, _1803096]))], (50622 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1803090, hAPP(c_Nat_OSuc, 50618 ^ [_1803090, _1803092, _1803094, _1803096]))))]], 50625 ^ _779854 : [(50628 ^ _779854) ^ [] : [hBOOL(hAPP(_1803090, hAPP(c_Nat_OSuc, 50618 ^ [_1803090, _1803092, _1803094, _1803096])))], (50626 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1803094, 50618 ^ [_1803090, _1803092, _1803094, _1803096])))]]], (38066 ^ _779854) ^ [_1499977, _1499979, _1499981, _1499983, _1499985, _1499987] : [-(hAPP(c_Set_Ovimage(_1499977, _1499979, hAPP(c_Fun_Ocomp(_1499981, _1499979, _1499977, _1499983), _1499985)), _1499987) = hAPP(c_Set_Ovimage(_1499977, _1499981, _1499985), hAPP(c_Set_Ovimage(_1499981, _1499979, _1499983), _1499987)))], (46303 ^ _779854) ^ [_1709006, _1709008] : [c_List_Oconcat(_1709006, _1709008) = c_List_Olist_ONil(_1709006), 46306 ^ _779854 : [(46307 ^ _779854) ^ [_1709097] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709006)), _1709097), hAPP(c_List_Oset(tc_List_Olist(_1709006)), _1709008))), -(_1709097 = c_List_Olist_ONil(_1709006))]]], (3116 ^ _779854) ^ [_826377, _826379, _826381, _826383, _826385, _826387, _826389, _826391] : [-(c_Nat_Onat_Onat__case(_826391, _826387, _826383, _826379) = c_Nat_Onat_Onat__case(_826389, _826385, _826381, _826377)), _826391 = _826389, _826387 = _826385, _826383 = _826381, _826379 = _826377], (3096 ^ _779854) ^ [_826079, _826081, _826083, _826085] : [-(c_List_Olistset(_826085, _826081) = c_List_Olistset(_826083, _826079)), _826085 = _826083, _826081 = _826079], (35768 ^ _779854) ^ [_1445699, _1445701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1445699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1445701)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445699, _1445701), c_Divides_OposDivAlg(_1445699, _1445701))))], (7171 ^ _779854) ^ [_897800, _897802, _897804] : [class_Lattices_Osemilattice__sup(_897800), 7174 ^ _779854 : [(7181 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897800), _897802), _897804) = _897804, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897800), _897802), _897804)))], (7175 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897800), _897802), _897804)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897800), _897802), _897804) = _897804)]]], (14928 ^ _779854) ^ [_1044788, _1044790, _1044792] : [class_Groups_Oab__semigroup__mult(_1044788), -(_1044790 = c_Orderings_Obot__class_Obot(tc_fun(_1044788, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044788), _1044790)), -(hBOOL(hAPP(hAPP(c_member(_1044788), _1044792), _1044790))), -(hAPP(c_Finite__Set_Ofold1(_1044788, c_Groups_Otimes__class_Otimes(_1044788)), hAPP(hAPP(c_Set_Oinsert(_1044788), _1044792), _1044790)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044788), _1044792), hAPP(c_Finite__Set_Ofold1(_1044788, c_Groups_Otimes__class_Otimes(_1044788)), _1044790)))], (26351 ^ _779854) ^ [_1258724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1258724)))], (41086 ^ _779854) ^ [_1583987, _1583989] : [-(c_Relation_Orefl__on(_1583987, c_Orderings_Otop__class_Otop(tc_fun(_1583987, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1583987, _1583989)))], (51991 ^ _779854) ^ [_1831062, _1831064, _1831066] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831062), _1831064)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831064), _1831066)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831062), _1831066)))], (48838 ^ _779854) ^ [_1764152, _1764154] : [c_Wellfounded_Oacyclic(_1764152, hAPP(c_Set_OCollect(tc_prod(_1764152, _1764152)), hAPP(c_Product__Type_Oprod_Oprod__case(_1764152, _1764152, tc_HOL_Obool), _1764154))), -(c_Wellfounded_Oacyclic(_1764152, hAPP(c_Set_OCollect(tc_prod(_1764152, _1764152)), hAPP(c_Product__Type_Oprod_Oprod__case(_1764152, _1764152, tc_HOL_Obool), c_Predicate_Oconversep(_1764152, _1764152, _1764154)))))], (2506 ^ _779854) ^ [_816916, _816918] : [_816918 = _816916, -(c_Nitpick_Ozero__frac(_816918) = c_Nitpick_Ozero__frac(_816916))], (38707 ^ _779854) ^ [_1517806, _1517808, _1517810] : [38708 ^ _779854 : [(38711 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517806), hAPP(c_Set_OCollect(_1517806), _1517810)))], (38709 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517806), hAPP(c_Set_OCollect(_1517806), _1517808)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1517806), hAPP(c_Set_OCollect(_1517806), hAPP(hAPP(c_COMBS(_1517806, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517806), c_fconj), _1517808)), _1517810)))))], (10 ^ _779854) ^ [_779977, _779979, _779981] : [-(_779981 = _779977), _779981 = _779979, _779979 = _779977], (25795 ^ _779854) ^ [_1248698] : [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)), _1248698)), _1248698) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19421 ^ _779854) ^ [_1130139, _1130141, _1130143] : [class_Rings_Olinordered__ring__strict(_1130139), 19424 ^ _779854 : [(19439 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), c_Groups_Ozero__class_Ozero(_1130139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130139), _1130141), _1130143)))), 19440 ^ _779854 : [(19447 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), _1130141), c_Groups_Ozero__class_Ozero(_1130139))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), _1130143), c_Groups_Ozero__class_Ozero(_1130139)))], (19441 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), c_Groups_Ozero__class_Ozero(_1130139)), _1130141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), c_Groups_Ozero__class_Ozero(_1130139)), _1130143))]]], (19425 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), c_Groups_Ozero__class_Ozero(_1130139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130139), _1130141), _1130143))), 19430 ^ _779854 : [(19433 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), c_Groups_Ozero__class_Ozero(_1130139)), _1130143)))], (19431 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), c_Groups_Ozero__class_Ozero(_1130139)), _1130141)))]], 19434 ^ _779854 : [(19437 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), _1130143), c_Groups_Ozero__class_Ozero(_1130139))))], (19435 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130139), _1130141), c_Groups_Ozero__class_Ozero(_1130139))))]]]]], (50221 ^ _779854) ^ [_1794447, _1794449] : [c_Equiv__Relations_Opart__equivp(_1794447, _1794449), 50225 ^ _779854 : [(50238 ^ _779854) ^ [_1794789, _1794791] : [-(hBOOL(hAPP(hAPP(_1794449, _1794791), _1794789))), hBOOL(hAPP(hAPP(_1794449, _1794791), _1794791)), hBOOL(hAPP(hAPP(_1794449, _1794789), _1794789)), hAPP(_1794449, _1794791) = hAPP(_1794449, _1794789)], (50228 ^ _779854) ^ [_1794620, _1794622] : [hBOOL(hAPP(hAPP(_1794449, _1794622), _1794620)), 50231 ^ _779854 : [(50236 ^ _779854) ^ [] : [-(hAPP(_1794449, _1794622) = hAPP(_1794449, _1794620))], (50234 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1794449, _1794620), _1794620)))], (50232 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1794449, _1794622), _1794622)))]]], (50226 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1794449, 50224 ^ [_1794447, _1794449]), 50224 ^ [_1794447, _1794449])))]]], (20928 ^ _779854) ^ [_1156466, _1156468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1156466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1156468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156468), _1156466))))], (14550 ^ _779854) ^ [_1037641, _1037643, _1037645, _1037647] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037641), _1037643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1037641, tc_HOL_Obool)), _1037643), _1037645)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1037641, tc_Nat_Onat), _1037647), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1037641, tc_HOL_Obool)), _1037645), _1037643)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1037641, tc_Nat_Onat), _1037647), _1037645)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1037641, tc_Nat_Onat), _1037647), _1037643)))], (49014 ^ _779854) ^ [_1768162, _1768164, _1768166, _1768168, _1768170] : [-(c_List_Oreplicate(_1768162, _1768164, _1768166) = c_List_Oreplicate(_1768162, _1768168, _1768170)), _1768164 = _1768168, 49019 ^ _779854 : [(49022 ^ _779854) ^ [] : [_1768166 = _1768170], (49020 ^ _779854) ^ [] : [_1768164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23610 ^ _779854) ^ [_1207550, _1207552, _1207554] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1207550, tc_HOL_Obool)), _1207552)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1207550), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1207550, tc_HOL_Obool), _1207552))), 23620 ^ _779854 : [(23623 ^ _779854) ^ [] : [hAPP(c_Finite__Set_Ocard(_1207550), 23619 ^ [_1207550, _1207552, _1207554]) = _1207554], (23621 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1207550, tc_HOL_Obool)), 23619 ^ [_1207550, _1207552, _1207554]), _1207552)))]], 23627 ^ _779854 : [(23631 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1207550, tc_HOL_Obool)), 23629 ^ [_1207550, _1207552, _1207554]), _1207552)))], (23633 ^ _779854) ^ [] : [23626 ^ [_1207550, _1207552, _1207554] = 23629 ^ [_1207550, _1207552, _1207554]], (23635 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1207550, tc_HOL_Obool)), 23626 ^ [_1207550, _1207552, _1207554]), 23629 ^ [_1207550, _1207552, _1207554]) = c_Orderings_Obot__class_Obot(tc_fun(_1207550, tc_HOL_Obool))], (23628 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1207550, tc_HOL_Obool)), 23626 ^ [_1207550, _1207552, _1207554]), _1207552)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207554), hAPP(c_Finite__Set_Ocard(tc_fun(_1207550, tc_HOL_Obool)), _1207552)) = hAPP(c_Finite__Set_Ocard(_1207550), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1207550, tc_HOL_Obool), _1207552)))], (50542 ^ _779854) ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586] : [class_Groups_Ocomm__monoid__mult(_1801576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1801578), _1801580)), 50552 ^ _779854 : [(50555 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1801582), hAPP(_1801584, 50551 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586])))], (50553 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801578), 50551 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586]), _1801580)))]], 50559 ^ _779854 : [(50563 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801578), 50561 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586]), _1801580)))], (50565 ^ _779854) ^ [] : [50558 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586] = 50561 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586]], (50567 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1801582, tc_HOL_Obool)), hAPP(_1801584, 50558 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586])), hAPP(_1801584, 50561 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586])) = c_Orderings_Obot__class_Obot(tc_fun(_1801582, tc_HOL_Obool))], (50560 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801578), 50558 ^ [_1801576, _1801578, _1801580, _1801582, _1801584, _1801586]), _1801580)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1801576, _1801582, c_Groups_Otimes__class_Otimes(_1801576)), _1801586), c_Groups_Oone__class_Oone(_1801576)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1801578, tc_fun(_1801582, tc_HOL_Obool)), _1801580), _1801584)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1801576, _1801578, c_Groups_Otimes__class_Otimes(_1801576)), hAPP(hAPP(c_COMBB(tc_fun(_1801582, tc_HOL_Obool), _1801576, _1801578), hAPP(hAPP(c_Finite__Set_Ofold__image(_1801576, _1801582, c_Groups_Otimes__class_Otimes(_1801576)), _1801586), c_Groups_Oone__class_Oone(_1801576))), _1801584)), c_Groups_Oone__class_Oone(_1801576)), _1801580))], (33288 ^ _779854) ^ [_1384221, _1384223, _1384225, _1384227, _1384229, _1384231] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384221, tc_fun(_1384223, tc_HOL_Obool)), _1384225), hAPP(hAPP(c_COMBC(_1384221, tc_fun(_1384227, tc_fun(_1384223, tc_HOL_Obool)), tc_fun(_1384223, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384227, tc_HOL_Obool), tc_fun(tc_fun(_1384227, tc_fun(_1384223, tc_HOL_Obool)), tc_fun(_1384223, tc_HOL_Obool)), _1384221), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384227, tc_fun(_1384223, tc_HOL_Obool))), _1384229)), _1384231)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384227, tc_fun(_1384223, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384221, tc_fun(_1384227, tc_HOL_Obool)), _1384225), _1384229)), _1384231))], (31460 ^ _779854) ^ [_1346937] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1346937)), 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, _1346937, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (20317 ^ _779854) ^ [_1145553, _1145555] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145553), _1145555) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1145553 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145555 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40145 ^ _779854) ^ [_1561027, _1561029, _1561031] : [c_Wellfounded_Oacyclic(_1561027, _1561029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561027, _1561027), tc_HOL_Obool)), _1561031), _1561029)), -(c_Wellfounded_Oacyclic(_1561027, _1561031))], (38739 ^ _779854) ^ [_1518666, _1518668, _1518670] : [hBOOL(hAPP(hAPP(c_member(_1518666), _1518668), hAPP(c_Set_OCollect(_1518666), _1518670))), -(hBOOL(hAPP(_1518670, _1518668)))], (16379 ^ _779854) ^ [_1074505, _1074507, _1074509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074505), _1074507)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074509), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074507), _1074505)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074509), _1074505)), _1074507))], (44518 ^ _779854) ^ [_1670387, _1670389, _1670391] : [hBOOL(hAPP(c_List_Odistinct(_1670387), _1670391)), -(hBOOL(hAPP(c_List_Odistinct(_1670387), hAPP(c_List_Orotate(_1670387, _1670389), _1670391))))], (39493 ^ _779854) ^ [_1543654, _1543656, _1543658] : [-(hAPP(c_Set_Oimage(tc_prod(_1543654, _1543656), _1543656, c_Product__Type_Osnd(_1543654, _1543656)), _1543658) = hAPP(c_Relation_ORange(_1543654, _1543656), _1543658))], (10299 ^ _779854) ^ [_954071, _954073, _954075, _954077, _954079] : [class_Orderings_Oorder(_954071), class_Orderings_Oorder(_954073), c_Orderings_Oorder__class_Omono(_954073, _954071, _954075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954073), _954077), _954079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954071), hAPP(_954075, _954077)), hAPP(_954075, _954079))))], (5566 ^ _779854) ^ [_865038, _865040, _865042, _865044] : [-(tc_prod(_865044, _865040) = tc_prod(_865042, _865038)), _865044 = _865042, _865040 = _865038], (33729 ^ _779854) ^ [_1400166, _1400168, _1400170, _1400172, _1400174] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400166, tc_fun(_1400168, tc_HOL_Obool)), _1400170), hAPP(hAPP(c_COMBB(tc_fun(_1400168, tc_HOL_Obool), tc_fun(_1400168, tc_HOL_Obool), _1400166), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400168, tc_HOL_Obool)), _1400172)), _1400174)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400168, tc_HOL_Obool)), _1400172), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400166, tc_fun(_1400168, tc_HOL_Obool)), _1400170), _1400174)))], (33290 ^ _779854) ^ [_1384340, _1384342, _1384344, _1384346, _1384348, _1384350] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384340, tc_fun(_1384342, tc_HOL_Obool)), _1384344), hAPP(hAPP(c_COMBC(_1384340, tc_fun(_1384346, tc_fun(_1384342, tc_HOL_Obool)), tc_fun(_1384342, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384346, tc_HOL_Obool), tc_fun(tc_fun(_1384346, tc_fun(_1384342, tc_HOL_Obool)), tc_fun(_1384342, tc_HOL_Obool)), _1384340), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384346, tc_fun(_1384342, tc_HOL_Obool))), _1384348)), _1384350)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384346, tc_fun(_1384342, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384340, tc_fun(_1384346, tc_HOL_Obool)), _1384344), _1384348)), _1384350))], (3200 ^ _779854) ^ [_827657, _827659, _827661, _827663, _827665, _827667] : [-(c_Big__Operators_Olattice_OInf__fin(_827667, _827663, _827659) = c_Big__Operators_Olattice_OInf__fin(_827665, _827661, _827657)), _827667 = _827665, _827663 = _827661, _827659 = _827657], (23323 ^ _779854) ^ [_1201943, _1201945, _1201947, _1201949, _1201951] : [class_Groups_Ocomm__monoid__add(_1201943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201945), _1201947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201945, tc_HOL_Obool)), _1201949), _1201947)), 23337 ^ _779854 : [(23340 ^ _779854) ^ [] : [hAPP(_1201951, 23336 ^ [_1201943, _1201945, _1201947, _1201949, _1201951]) = c_Groups_Ozero__class_Ozero(_1201943)], (23338 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201945), 23336 ^ [_1201943, _1201945, _1201947, _1201949, _1201951]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201945, tc_HOL_Obool)), _1201947), _1201949))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201945, _1201943), _1201951), _1201949) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201945, _1201943), _1201951), _1201947))], (21504 ^ _779854) ^ [_1167717, _1167719, _1167721] : [hAPP(c_Finite__Set_Ocard(_1167717), _1167719) = hAPP(c_Nat_OSuc, _1167721), 21509 ^ _779854 : [(21512 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1167717), 21507 ^ [_1167717, _1167719, _1167721]), 21508 ^ [_1167717, _1167719, _1167721]))], (21514 ^ _779854) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1167717), 21508 ^ [_1167717, _1167719, _1167721]) = _1167721)], (21516 ^ _779854) ^ [] : [_1167721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(21508 ^ [_1167717, _1167719, _1167721] = c_Orderings_Obot__class_Obot(tc_fun(_1167717, tc_HOL_Obool)))], (21510 ^ _779854) ^ [] : [-(_1167719 = hAPP(hAPP(c_Set_Oinsert(_1167717), 21507 ^ [_1167717, _1167719, _1167721]), 21508 ^ [_1167717, _1167719, _1167721]))]]], (44258 ^ _779854) ^ [_1664473, _1664475, _1664477, _1664479] : [-(hAPP(hAPP(c_List_Otake(_1664473), _1664475), hAPP(hAPP(c_List_Odrop(_1664473), _1664477), _1664479)) = hAPP(hAPP(c_List_Odrop(_1664473), _1664477), hAPP(hAPP(c_List_Otake(_1664473), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1664475), _1664477)), _1664479)))], (37514 ^ _779854) ^ [_1486721, _1486723, _1486725, _1486727, _1486729, _1486731, _1486733, _1486735, _1486737, _1486739] : [c_Equiv__Relations_Oequiv(_1486721, _1486723, _1486725), c_Equiv__Relations_Oequiv(_1486727, _1486729, _1486731), c_Equiv__Relations_Ocongruent2(_1486721, _1486727, tc_fun(_1486733, tc_HOL_Obool), _1486725, _1486731, _1486735), hBOOL(hAPP(hAPP(c_member(_1486721), _1486737), _1486723)), hBOOL(hAPP(hAPP(c_member(_1486727), _1486739), _1486729)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486721, tc_fun(_1486733, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1486721, _1486721, _1486725), hAPP(hAPP(c_Set_Oinsert(_1486721), _1486737), c_Orderings_Obot__class_Obot(tc_fun(_1486721, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1486727, tc_fun(_1486733, tc_HOL_Obool)), tc_fun(_1486733, tc_HOL_Obool), _1486721), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486727, tc_fun(_1486733, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1486727, _1486727, _1486731), hAPP(hAPP(c_Set_Oinsert(_1486727), _1486739), c_Orderings_Obot__class_Obot(tc_fun(_1486727, tc_HOL_Obool)))))), _1486735)) = hAPP(hAPP(_1486735, _1486737), _1486739))], (39487 ^ _779854) ^ [_1543541, _1543543, _1543545] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1543541, _1543543)), _1543545)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543543), hAPP(c_Relation_ORange(_1543541, _1543543), _1543545))))], (4242 ^ _779854) ^ [_844292, _844294, _844296, _844298] : [-(c_List_Ozip(_844298, _844294) = c_List_Ozip(_844296, _844292)), _844298 = _844296, _844294 = _844292], (40966 ^ _779854) ^ [_1580229, _1580231] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580229, _1580229)), _1580231)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580229, _1580229)), c_Transitive__Closure_Otrancl(_1580229, _1580231))))], (49269 ^ _779854) ^ [_1773406, _1773408, _1773410] : [hBOOL(hAPP(hAPP(c_List_Omember(_1773406), _1773408), _1773410)), -(hBOOL(hAPP(hAPP(c_member(_1773406), _1773410), hAPP(c_List_Oset(_1773406), _1773408))))], (49410 ^ _779854) ^ [_1776802, _1776804] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1776802, _1776804), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1776802)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18555 ^ _779854) ^ [_1115849, _1115851] : [class_Groups_Ocomm__monoid__add(_1115849), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115849), c_Groups_Ozero__class_Ozero(_1115849)), _1115851) = _1115851)], (45549 ^ _779854) ^ [_1692584, _1692586] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1692584), _1692586) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1692584)), hAPP(c_Code__Numeral_Onat__of, _1692586))))], (16692 ^ _779854) ^ [_1080551, _1080553, _1080555] : [16693 ^ _779854 : [(16696 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1080555, _1080553), _1080551))], (16694 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080551), _1080553)))]], 16699 ^ _779854 : [(16702 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1080555, _1080553), _1080551))], (16700 ^ _779854) ^ [] : [-(_1080551 = _1080553)]], 16705 ^ _779854 : [(16708 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1080555, _1080553), _1080551))], (16706 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080553), _1080551)))]], -(hBOOL(hAPP(hAPP(_1080555, _1080553), _1080551)))], (34175 ^ _779854) ^ [_1412421, _1412423, _1412425, _1412427] : [class_Groups_Ocomm__monoid__mult(_1412421), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412423), _1412425)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1412423, _1412421), hAPP(c_COMBK(_1412421, _1412423), _1412427)), _1412425) = hAPP(hAPP(c_Power_Opower__class_Opower(_1412421), _1412427), hAPP(c_Finite__Set_Ocard(_1412423), _1412425)))], (21949 ^ _779854) ^ [_1176431, _1176433, _1176435, _1176437] : [class_Rings_Odivision__ring(_1176431), -(_1176433 = c_Groups_Ozero__class_Ozero(_1176431)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176431), _1176435), _1176433) = _1176437, -(_1176435 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176431), _1176437), _1176433))], (45121 ^ _779854) ^ [_1682844, _1682846, _1682848, _1682850, _1682852] : [hAPP(hAPP(c_List_Omap(_1682844, _1682846), _1682848), _1682850) = hAPP(hAPP(c_List_Omap(_1682844, _1682846), _1682852), _1682850), 45124 ^ _779854 : [(45125 ^ _779854) ^ [_1682967] : [hBOOL(hAPP(hAPP(c_member(_1682844), _1682967), hAPP(c_List_Oset(_1682844), _1682850))), -(hAPP(_1682848, _1682967) = hAPP(_1682852, _1682967))]]], (42263 ^ _779854) ^ [_1615102, _1615104, _1615106, _1615108, _1615110] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615102), tc_List_Olist(_1615102))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615102), tc_List_Olist(_1615102)), _1615104), _1615106)), c_List_Olistrel1(_1615102, _1615108))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615102), tc_List_Olist(_1615102))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615102), tc_List_Olist(_1615102)), hAPP(hAPP(c_List_Olist_OCons(_1615102), _1615110), _1615104)), hAPP(hAPP(c_List_Olist_OCons(_1615102), _1615110), _1615106))), c_List_Olistrel1(_1615102, _1615108))))], (5088 ^ _779854) ^ [_857629, _857631, _857633, _857635, _857637, _857639] : [-(c_Set_Oimage(_857639, _857635, _857631) = c_Set_Oimage(_857637, _857633, _857629)), _857639 = _857637, _857635 = _857633, _857631 = _857629], (2154 ^ _779854) ^ [_811240, _811242, _811244, _811246, _811248, _811250] : [-(c_Random_Ominus__shift(_811250, _811246, _811242) = c_Random_Ominus__shift(_811248, _811244, _811240)), _811250 = _811248, _811246 = _811244, _811242 = _811240], (52447 ^ _779854) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (30339 ^ _779854) ^ [_1327767, _1327769, _1327771, _1327773] : [class_Divides_Osemiring__div(_1327767), -(c_Divides_Odiv__class_Omod(_1327767, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327767), _1327769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327767), _1327771), _1327773)), _1327771) = c_Divides_Odiv__class_Omod(_1327767, _1327769, _1327771))], (2522 ^ _779854) ^ [_817150, _817152, _817154, _817156, _817158, _817160, _817162, _817164, _817166, _817168] : [-(c_Finite__Set_Ofold__graph(_817168, _817164, _817160, _817156, _817152) = c_Finite__Set_Ofold__graph(_817166, _817162, _817158, _817154, _817150)), _817168 = _817166, _817164 = _817162, _817160 = _817158, _817156 = _817154, _817152 = _817150], (51781 ^ _779854) ^ [_1827581, _1827583, _1827585, _1827587] : [class_Rings_Ocomm__semiring__1(_1827581), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827581), _1827583), _1827585)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827581), hAPP(hAPP(c_Power_Opower__class_Opower(_1827581), _1827583), _1827587)), hAPP(hAPP(c_Power_Opower__class_Opower(_1827581), _1827585), _1827587))))], (46635 ^ _779854) ^ [_1718266, _1718268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718266), _1718268)), -(c_List_Oupt(_1718266, hAPP(c_Nat_OSuc, _1718268)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1718266, _1718268)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1718268), c_List_Olist_ONil(tc_Nat_Onat))))], (36884 ^ _779854) ^ [] : [-(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)))))], (18293 ^ _779854) ^ [_1110904, _1110906, _1110908, _1110910] : [class_Groups_Ocomm__monoid__mult(_1110904), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110906), _1110908))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1110906, _1110904), _1110910), _1110908) = c_Groups_Oone__class_Oone(_1110904))], (37815 ^ _779854) ^ [_1494193, _1494195, _1494197] : [hBOOL(hAPP(hAPP(c_member(_1494193), _1494197), c_Wellfounded_Oacc(_1494193, _1494195))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1494193, hAPP(hAPP(c_COMBC(_1494193, tc_fun(tc_prod(_1494193, _1494193), tc_HOL_Obool), tc_fun(_1494193, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494193, tc_fun(tc_fun(tc_prod(_1494193, _1494193), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1494193, _1494193), tc_HOL_Obool), tc_fun(_1494193, tc_HOL_Obool)), _1494193), c_COMBC(_1494193, tc_fun(tc_prod(_1494193, _1494193), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494193, tc_prod(_1494193, _1494193)), tc_fun(_1494193, tc_fun(tc_fun(tc_prod(_1494193, _1494193), tc_HOL_Obool), tc_HOL_Obool)), _1494193), hAPP(c_COMBB(tc_prod(_1494193, _1494193), tc_fun(tc_fun(tc_prod(_1494193, _1494193), tc_HOL_Obool), tc_HOL_Obool), _1494193), c_member(tc_prod(_1494193, _1494193)))), c_Product__Type_OPair(_1494193, _1494193)))), _1494195)), _1494197)))], (6573 ^ _779854) ^ [_885066, _885068, _885070] : [class_Lattices_Oboolean__algebra(_885066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885066), _885068), _885070)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885066), hAPP(c_Groups_Ouminus__class_Ouminus(_885066), _885070)), hAPP(c_Groups_Ouminus__class_Ouminus(_885066), _885068))))], (24456 ^ _779854) ^ [_1223546] : [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), _1223546))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223546) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223546)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (6781 ^ _779854) ^ [_889360, _889362, _889364, _889366] : [6795 ^ _779854 : [(6798 ^ _779854) ^ [] : [-(hBOOL(hAPP(_889366, 6794 ^ [_889360, _889362, _889364, _889366])))], (6796 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889360), 6794 ^ [_889360, _889362, _889364, _889366]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889360, tc_HOL_Obool)), _889362), _889364))))]], 6782 ^ _779854 : [(6789 ^ _779854) ^ [_889569] : [hBOOL(hAPP(hAPP(c_member(_889360), _889569), _889364)), hBOOL(hAPP(_889366, _889569))], (6783 ^ _779854) ^ [_889473] : [hBOOL(hAPP(hAPP(c_member(_889360), _889473), _889362)), hBOOL(hAPP(_889366, _889473))]]], (6397 ^ _779854) ^ [_881751] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_881751, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_881751, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_881751, tc_HOL_Obool)))], (23770 ^ _779854) ^ [_1210837, _1210839, _1210841, _1210843] : [class_Rings_Ocomm__semiring__1(_1210837), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210837), hAPP(hAPP(c_Power_Opower__class_Opower(_1210837), _1210839), _1210841)), _1210843) = hAPP(hAPP(c_Power_Opower__class_Opower(_1210837), _1210839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210841), _1210843)))], (45516 ^ _779854) ^ [_1691704, _1691706, _1691708] : [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, _1691704), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1691704)), _1691706)))), -(hBOOL(hAPP(hAPP(c_member(_1691704), hAPP(c_Product__Type_Ofst(_1691704, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1691704, _1691706), _1691708))), hAPP(c_List_Oset(_1691704), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1691704), _1691704), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1691704)), _1691706)))))], (27463 ^ _779854) ^ [_1277422, _1277424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277424)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1277422)), hAPP(c_Int_Onat, _1277424)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1277422), _1277424)))], (52315 ^ _779854) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (41431 ^ _779854) ^ [_1592136, _1592138] : [-(hAPP(c_Relation_Oconverse(_1592136, _1592136), c_Relation_OId__on(_1592136, _1592138)) = c_Relation_OId__on(_1592136, _1592138))], (27525 ^ _779854) ^ [_1278316, _1278318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1278316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1278318)), 27532 ^ _779854 : [(27539 ^ _779854) ^ [] : [_1278316 = _1278318, -(hAPP(c_Int_Onat, _1278316) = hAPP(c_Int_Onat, _1278318))], (27533 ^ _779854) ^ [] : [hAPP(c_Int_Onat, _1278316) = hAPP(c_Int_Onat, _1278318), -(_1278316 = _1278318)]]], (974 ^ _779854) ^ [_794463, _794465, _794467, _794469] : [-(c_Equiv__Relations_Oequivp(_794467, _794463)), c_Equiv__Relations_Oequivp(_794469, _794465), _794469 = _794467, _794465 = _794463], (4896 ^ _779854) ^ [_854635, _854637, _854639, _854641] : [-(c_Relation_Oinv__image(_854641, _854637) = c_Relation_Oinv__image(_854639, _854635)), _854641 = _854639, _854637 = _854635], (50836 ^ _779854) ^ [_1807962, _1807964, _1807966, _1807968, _1807970, _1807972, _1807974] : [c_Fun_Obij__betw(_1807962, _1807964, _1807966, _1807968, _1807970), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1807962, tc_HOL_Obool)), _1807972), _1807968)), hAPP(c_Set_Oimage(_1807962, _1807964, _1807966), _1807972) = _1807974, -(c_Fun_Obij__betw(_1807962, _1807964, _1807966, _1807972, _1807974))], (49574 ^ _779854) ^ [_1780853, _1780855] : [c_Relation_Otrans(_1780853, _1780855), -(c_Transitive__Closure_Otrancl(_1780853, _1780855) = _1780855)], (37156 ^ _779854) ^ [_1478018, _1478020, _1478022, _1478024] : [-(hAPP(c_Relation_OField(_1478018), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1478018, _1478018)), hAPP(hAPP(c_Product__Type_OPair(_1478018, _1478018), _1478020), _1478022)), _1478024)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478018, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1478018), _1478020), hAPP(hAPP(c_Set_Oinsert(_1478018), _1478022), c_Orderings_Obot__class_Obot(tc_fun(_1478018, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1478018), _1478024)))], (45378 ^ _779854) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (28653 ^ _779854) ^ [_1297744] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1297744)), -(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)), _1297744))))], (28744 ^ _779854) ^ [_1299206, _1299208] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1299206) = _1299208, 28747 ^ _779854 : [(28750 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299208)))], (28748 ^ _779854) ^ [] : [-(_1299206 = hAPP(c_Int_Onat, _1299208))]]], (51200 ^ _779854) ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1815490, _1815492), tc_prod(_1815490, _1815492))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1815490, _1815492), tc_prod(_1815490, _1815492)), hAPP(hAPP(c_Product__Type_OPair(_1815490, _1815492), _1815494), _1815496)), hAPP(hAPP(c_Product__Type_OPair(_1815490, _1815492), _1815498), _1815500))), c_Transitive__Closure_Ortrancl(tc_prod(_1815490, _1815492), _1815502))), hBOOL(hAPP(hAPP(_1815504, _1815498), _1815500)), 51213 ^ _779854 : [(51216 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1815490, _1815492), tc_prod(_1815490, _1815492))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1815490, _1815492), tc_prod(_1815490, _1815492)), hAPP(hAPP(c_Product__Type_OPair(_1815490, _1815492), 51211 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504]), 51212 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504])), hAPP(hAPP(c_Product__Type_OPair(_1815490, _1815492), _1815498), _1815500))), c_Transitive__Closure_Ortrancl(tc_prod(_1815490, _1815492), _1815502))))], (51218 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1815504, 51211 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504]), 51212 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504])))], (51220 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1815504, 51209 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504]), 51210 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504]))], (51214 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1815490, _1815492), tc_prod(_1815490, _1815492))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1815490, _1815492), tc_prod(_1815490, _1815492)), hAPP(hAPP(c_Product__Type_OPair(_1815490, _1815492), 51209 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504]), 51210 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504])), hAPP(hAPP(c_Product__Type_OPair(_1815490, _1815492), 51211 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504]), 51212 ^ [_1815490, _1815492, _1815494, _1815496, _1815498, _1815500, _1815502, _1815504]))), _1815502)))]], -(hBOOL(hAPP(hAPP(_1815504, _1815494), _1815496)))], (7616 ^ _779854) ^ [_905993, _905995, _905997] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905993, tc_HOL_Obool)), _905995), _905997) = _905997, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905993, tc_HOL_Obool)), _905995), _905997)))], (41160 ^ _779854) ^ [_1585867, _1585869, _1585871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1585867, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1585867, _1585867, _1585869), _1585871)), _1585871)), -(hAPP(c_Relation_OImage(_1585867, _1585867, c_Transitive__Closure_Ortrancl(_1585867, _1585869)), _1585871) = _1585871)], (27479 ^ _779854) ^ [_1277678, _1277680] : [class_Rings_Osemiring__1(_1277678), 27482 ^ _779854 : [(27489 ^ _779854) ^ [] : [_1277680 = c_Groups_Ozero__class_Ozero(_1277678), -(c_Int_Oiszero(_1277678, _1277680))], (27483 ^ _779854) ^ [] : [c_Int_Oiszero(_1277678, _1277680), -(_1277680 = c_Groups_Ozero__class_Ozero(_1277678))]]], (10531 ^ _779854) ^ [_958692, _958694] : [class_Orderings_Olinorder(_958692), -(c_Big__Operators_Olattice_OInf__fin(_958692, c_Orderings_Oord__class_Omin(_958692), hAPP(hAPP(c_Set_Oinsert(_958692), _958694), c_Orderings_Obot__class_Obot(tc_fun(_958692, tc_HOL_Obool)))) = _958694)], (46779 ^ _779854) ^ [_1720888, _1720890, _1720892, _1720894] : [class_Groups_Ocomm__monoid__add(_1720888), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1720888), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1720888), _1720890), c_List_Oupt(_1720892, _1720894))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1720888), _1720890), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1720892, _1720894))))], (38102 ^ _779854) ^ [_1500890, _1500892, _1500894, _1500896, _1500898] : [hBOOL(hAPP(hAPP(c_member(_1500890), _1500892), hAPP(c_Set_Ovimage(_1500890, _1500894, _1500896), _1500898))), -(hBOOL(hAPP(hAPP(c_member(_1500894), hAPP(_1500896, _1500892)), _1500898)))], (52389 ^ _779854) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (33437 ^ _779854) ^ [_1388611, _1388613] : [hBOOL(hAPP(hAPP(c_member(_1388611), _1388613), c_Orderings_Obot__class_Obot(tc_fun(_1388611, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1388611, tc_HOL_Obool)), _1388613)))], (42175 ^ _779854) ^ [_1612504, _1612506, _1612508, _1612510] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1612504), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1612506), _1612508)))), -(hAPP(c_Random_Opick(_1612506, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1612506)), _1612508), _1612510)), _1612504) = hAPP(c_Random_Opick(_1612506, _1612510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1612504), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1612506), _1612508))))], (19289 ^ _779854) ^ [_1127736, _1127738, _1127740, _1127742] : [class_Rings_Oordered__semiring(_1127736), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127736), _1127738), _1127740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127736), c_Groups_Ozero__class_Ozero(_1127736)), _1127742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127736), _1127742), _1127738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127736), _1127742), _1127740))))], (11776 ^ _779854) ^ [_984262, _984264, _984266] : [hBOOL(hAPP(hAPP(c_member(_984262), _984264), hAPP(c_fequal, _984266))), -(_984264 = _984266)], (18833 ^ _779854) ^ [_1119879] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119879) = _1119879)], (4178 ^ _779854) ^ [_843348, _843350, _843352, _843354] : [-(c_New__DSequence_Opos__single(_843354, _843350) = c_New__DSequence_Opos__single(_843352, _843348)), _843354 = _843352, _843350 = _843348], (10833 ^ _779854) ^ [_965051, _965053, _965055] : [class_Orderings_Olinorder(_965051), hBOOL(hAPP(c_Finite__Set_Ofinite(_965051), _965053)), -(_965055 = c_Orderings_Obot__class_Obot(tc_fun(_965051, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965051, tc_HOL_Obool)), _965055), _965053)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_965051), c_Big__Operators_Olattice_OInf__fin(_965051, c_Orderings_Oord__class_Omin(_965051), _965055)), c_Big__Operators_Olattice_OInf__fin(_965051, c_Orderings_Oord__class_Omin(_965051), _965053)) = c_Big__Operators_Olattice_OInf__fin(_965051, c_Orderings_Oord__class_Omin(_965051), _965053))], (26339 ^ _779854) ^ [_1258541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258541)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1258541))], (37145 ^ _779854) ^ [_1477896, _1477898] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477896, _1477896)), hAPP(hAPP(c_Product__Type_OPair(_1477896, _1477896), 37146 ^ [_1477896, _1477898]), 37146 ^ [_1477896, _1477898])), _1477898))), -(c_Relation_Oirrefl(_1477896, _1477898))], (52425 ^ _779854) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (32718 ^ _779854) ^ [_1368870, _1368872, _1368874, _1368876, _1368878, _1368880, _1368882, _1368884] : [hBOOL(hAPP(hAPP(c_member(_1368870), _1368872), _1368874)), hBOOL(hAPP(hAPP(hAPP(_1368876, _1368872), _1368878), _1368880)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368870, tc_fun(_1368882, tc_fun(_1368884, tc_HOL_Obool))), _1368874), _1368876), _1368878), _1368880)))], (13703 ^ _779854) ^ [_1020517, _1020519, _1020521] : [class_Lattices_Olattice(_1020517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020517), _1020519)), 13710 ^ _779854 : [(13717 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020517, tc_HOL_Obool)), _1020519), hAPP(hAPP(c_Set_Oinsert(_1020517), _1020521), c_Orderings_Obot__class_Obot(tc_fun(_1020517, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1020517, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1020517, hAPP(hAPP(c_Set_Oinsert(_1020517), _1020521), _1020519)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1020517), _1020521), c_Big__Operators_Olattice__class_OSup__fin(_1020517, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020517, tc_HOL_Obool)), _1020519), hAPP(hAPP(c_Set_Oinsert(_1020517), _1020521), c_Orderings_Obot__class_Obot(tc_fun(_1020517, tc_HOL_Obool)))))))], (13711 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020517, tc_HOL_Obool)), _1020519), hAPP(hAPP(c_Set_Oinsert(_1020517), _1020521), c_Orderings_Obot__class_Obot(tc_fun(_1020517, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1020517, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1020517, hAPP(hAPP(c_Set_Oinsert(_1020517), _1020521), _1020519)) = _1020521)]]], (33387 ^ _779854) ^ [_1387047, _1387049, _1387051, _1387053, _1387055] : [class_Rings_Osemiring__0(_1387047), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387047), _1387049), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387051, _1387047), _1387053), _1387055)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387051, _1387047), hAPP(hAPP(c_COMBB(_1387047, _1387047, _1387051), hAPP(c_Groups_Otimes__class_Otimes(_1387047), _1387049)), _1387053)), _1387055))], (44053 ^ _779854) ^ [_1658933, _1658935, _1658937, _1658939] : [44054 ^ _779854 : [(44057 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1658933), _1658935), hAPP(c_List_Oset(_1658933), c_List_Obutlast(_1658933, _1658939))))], (44055 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1658933), _1658935), hAPP(c_List_Oset(_1658933), c_List_Obutlast(_1658933, _1658937))))]], -(hBOOL(hAPP(hAPP(c_member(_1658933), _1658935), hAPP(c_List_Oset(_1658933), c_List_Obutlast(_1658933, hAPP(hAPP(c_List_Oappend(_1658933), _1658937), _1658939))))))], (18120 ^ _779854) ^ [_1107781, _1107783] : [class_Rings_Oring__1__no__zero__divisors(_1107781), 18123 ^ _779854 : [(18124 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107781), _1107783), _1107783) = c_Groups_Oone__class_Oone(_1107781), -(_1107783 = c_Groups_Oone__class_Oone(_1107781)), -(_1107783 = hAPP(c_Groups_Ouminus__class_Ouminus(_1107781), c_Groups_Oone__class_Oone(_1107781)))], (18134 ^ _779854) ^ [] : [18135 ^ _779854 : [(18138 ^ _779854) ^ [] : [_1107783 = hAPP(c_Groups_Ouminus__class_Ouminus(_1107781), c_Groups_Oone__class_Oone(_1107781))], (18136 ^ _779854) ^ [] : [_1107783 = c_Groups_Oone__class_Oone(_1107781)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107781), _1107783), _1107783) = c_Groups_Oone__class_Oone(_1107781))]]], (7738 ^ _779854) ^ [_908575, _908577, _908579, _908581] : [class_Orderings_Oorder(_908575), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_908575, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_908575, _908577), _908579)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_908575, _908579), _908581)) = c_Orderings_Obot__class_Obot(tc_fun(_908575, tc_HOL_Obool)))], (37871 ^ _779854) ^ [_1495611, _1495613, _1495615, _1495617] : [hBOOL(hAPP(hAPP(c_member(_1495611), _1495613), c_Wellfounded_Oacc(_1495611, _1495615))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1495611, _1495611)), hAPP(hAPP(c_Product__Type_OPair(_1495611, _1495611), _1495617), _1495613)), _1495615)), -(hBOOL(hAPP(hAPP(c_member(_1495611), _1495617), c_Wellfounded_Oacc(_1495611, _1495615))))], (4112 ^ _779854) ^ [_842291, _842293, _842295, _842297] : [-(c_Lazy__Sequence_Ohb__single(_842297, _842293) = c_Lazy__Sequence_Ohb__single(_842295, _842291)), _842297 = _842295, _842293 = _842291], (31428 ^ _779854) ^ [_1346359, _1346361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346361)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1346359), hAPP(c_Int_Onat, _1346361)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1346359, _1346361)))], (13853 ^ _779854) ^ [_1023699, _1023701, _1023703] : [class_Lattices_Olattice(_1023699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023699), _1023701)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023699), _1023703)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1023699, tc_HOL_Obool)), _1023701), _1023703) = c_Orderings_Obot__class_Obot(tc_fun(_1023699, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1023699), c_Big__Operators_Olattice__class_OInf__fin(_1023699, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1023699, tc_HOL_Obool)), _1023701), _1023703))), c_Big__Operators_Olattice__class_OInf__fin(_1023699, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1023699, tc_HOL_Obool)), _1023701), _1023703))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1023699), c_Big__Operators_Olattice__class_OInf__fin(_1023699, _1023701)), c_Big__Operators_Olattice__class_OInf__fin(_1023699, _1023703)))], (43634 ^ _779854) ^ [_1649561, _1649563, _1649565] : [-(hBOOL(hAPP(hAPP(c_member(_1649561), _1649563), hAPP(c_List_Oset(_1649561), _1649565)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649561)), c_List_Oremove1(_1649561, _1649563, _1649565)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649561)), _1649565))], (26597 ^ _779854) ^ [_1263264, _1263266] : [class_Divides_Osemiring__div(_1263264), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1263264), _1263266), c_Groups_Ozero__class_Ozero(_1263264)) = c_Groups_Ozero__class_Ozero(_1263264))], (35518 ^ _779854) ^ [_1441536, _1441538] : [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), _1441536), _1441538))), 35521 ^ _779854 : [(35528 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441538), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 35531 ^ _779854 : [(35540 ^ _779854) ^ [] : [-(c_Nitpick_Onorm__frac(_1441536, _1441538) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1441536), _1441538)), 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), _1441536))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1441538)))), -(_1441536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1441538 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35532 ^ _779854) ^ [] : [35533 ^ _779854 : [(35536 ^ _779854) ^ [] : [_1441538 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35534 ^ _779854) ^ [] : [_1441536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1441536, _1441538) = 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)))]]], (35522 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441538), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1441536, _1441538) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1441536), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1441538)))]]], (27607 ^ _779854) ^ [_1279615] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1279615)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279615))], (48605 ^ _779854) ^ [_1759122, _1759124, _1759126] : [48607 ^ _779854 : [(48610 ^ _779854) ^ [] : [hBOOL(hAPP(_1759124, 48606 ^ [_1759122, _1759124, _1759126]))], (48608 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759122), 48606 ^ [_1759122, _1759124, _1759126]), hAPP(c_List_Oset(_1759122), _1759126))))]], -(c_List_Olist__all(_1759122, _1759124, _1759126))], (43065 ^ _779854) ^ [_1637771, _1637773, _1637775, _1637777, _1637779] : [-(hAPP(hAPP(c_List_Olist__update(_1637771, hAPP(hAPP(c_List_Olist_OCons(_1637771), _1637773), _1637775)), hAPP(c_Nat_OSuc, _1637777)), _1637779) = hAPP(hAPP(c_List_Olist_OCons(_1637771), _1637773), hAPP(hAPP(c_List_Olist__update(_1637771, _1637775), _1637777), _1637779)))], (36516 ^ _779854) ^ [_1461450, _1461452, _1461454, _1461456, _1461458, _1461460] : [-(c_Product__Type_Oprod_Oprod__rec(_1461450, _1461452, _1461454, _1461456, hAPP(hAPP(c_Product__Type_OPair(_1461450, _1461452), _1461458), _1461460)) = hAPP(hAPP(_1461456, _1461458), _1461460))], (30023 ^ _779854) ^ [_1321282, _1321284, _1321286] : [class_Groups_Omonoid__mult(_1321282), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1321282), _1321284), 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)))), _1321286))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321282), _1321284), hAPP(hAPP(c_Power_Opower__class_Opower(_1321282), hAPP(hAPP(c_Power_Opower__class_Opower(_1321282), _1321284), _1321286)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (52553 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (30047 ^ _779854) ^ [_1321773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1321773)), -(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), _1321773), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (44191 ^ _779854) ^ [_1662753, _1662755, _1662757, _1662759] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662753), tc_List_Olist(_1662753))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662753), tc_List_Olist(_1662753)), _1662755), _1662757)), c_List_Olistrel1(_1662753, _1662759))), 44196 ^ _779854 : [(44203 ^ _779854) ^ [] : [-(_1662757 = hAPP(hAPP(c_List_Oappend(_1662753), 44198 ^ [_1662753, _1662755, _1662757, _1662759]), hAPP(hAPP(c_List_Olist_OCons(_1662753), 44195 ^ [_1662753, _1662755, _1662757, _1662759]), 44199 ^ [_1662753, _1662755, _1662757, _1662759])))], (44201 ^ _779854) ^ [] : [-(_1662755 = hAPP(hAPP(c_List_Oappend(_1662753), 44198 ^ [_1662753, _1662755, _1662757, _1662759]), hAPP(hAPP(c_List_Olist_OCons(_1662753), 44194 ^ [_1662753, _1662755, _1662757, _1662759]), 44199 ^ [_1662753, _1662755, _1662757, _1662759])))], (44197 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662753, _1662753)), hAPP(hAPP(c_Product__Type_OPair(_1662753, _1662753), 44194 ^ [_1662753, _1662755, _1662757, _1662759]), 44195 ^ [_1662753, _1662755, _1662757, _1662759])), _1662759)))]]], (31724 ^ _779854) ^ [_1350926] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1350926) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1350926))], (1500 ^ _779854) ^ [_801556, _801558] : [-(class_Finite__Set_Ofinite(_801556)), _801558 = _801556, class_Finite__Set_Ofinite(_801558)], (40865 ^ _779854) ^ [_1577848, _1577850, _1577852, _1577854] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1577848, _1577850, _1577852, tc_prod(_1577850, _1577852)), _1577854), c_Product__Type_OPair(_1577850, _1577852)) = _1577854)], (41266 ^ _779854) ^ [_1588454, _1588456, _1588458, _1588460] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588454, _1588454)), hAPP(hAPP(c_Product__Type_OPair(_1588454, _1588454), _1588456), _1588458)), c_Transitive__Closure_Ortrancl(_1588454, _1588460)))), 41267 ^ _779854 : [(41270 ^ _779854) ^ [] : [-(_1588456 = _1588458), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588454, _1588454)), hAPP(hAPP(c_Product__Type_OPair(_1588454, _1588454), _1588456), _1588458)), c_Transitive__Closure_Otrancl(_1588454, _1588460)))], (41268 ^ _779854) ^ [] : [_1588456 = _1588458]]], (37881 ^ _779854) ^ [_1495844, _1495846, _1495848] : [hBOOL(hAPP(hAPP(c_member(_1495844), _1495846), c_Wellfounded_Oacc(_1495844, _1495848))), 37884 ^ _779854 : [(37885 ^ _779854) ^ [_1495958] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495844, _1495844)), hAPP(hAPP(c_Product__Type_OPair(_1495844, _1495844), _1495958), _1495846)), _1495848)), -(hBOOL(hAPP(hAPP(c_member(_1495844), _1495958), c_Wellfounded_Oacc(_1495844, _1495848))))]]], (13253 ^ _779854) ^ [_1013551, _1013553] : [class_Orderings_Olinorder(_1013551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013551), _1013553)), -(_1013553 = c_Orderings_Obot__class_Obot(tc_fun(_1013551, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1013551), c_Big__Operators_Olinorder__class_OMax(_1013551, _1013553)), _1013553)))], (38545 ^ _779854) ^ [_1513202, _1513204, _1513206, _1513208, _1513210, _1513212] : [class_Groups_Ocomm__monoid__mult(_1513202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513204), _1513206)), 38555 ^ _779854 : [(38558 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513208), hAPP(_1513210, 38554 ^ [_1513202, _1513204, _1513206, _1513208, _1513210, _1513212])))], (38556 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513204), 38554 ^ [_1513202, _1513204, _1513206, _1513208, _1513210, _1513212]), _1513206)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1513204, _1513202), hAPP(hAPP(c_COMBS(_1513204, tc_fun(_1513208, tc_HOL_Obool), _1513202), hAPP(hAPP(c_COMBB(tc_fun(_1513208, _1513202), tc_fun(tc_fun(_1513208, tc_HOL_Obool), _1513202), _1513204), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1513208, _1513202)), _1513212)), _1513210)), _1513206) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1513204, _1513208), _1513202), hAPP(c_Product__Type_Oprod_Oprod__case(_1513204, _1513208, _1513202), _1513212)), hAPP(hAPP(c_Product__Type_OSigma(_1513204, _1513208), _1513206), _1513210)))], (47875 ^ _779854) ^ [_1742993, _1742995, _1742997, _1742999] : [47877 ^ _779854 : [(47880 ^ _779854) ^ [] : [hBOOL(hAPP(_1742995, hAPP(hAPP(c_List_Onth(_1742997), _1742999), 47876 ^ [_1742993, _1742995, _1742997, _1742999])))], (47878 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47876 ^ [_1742993, _1742995, _1742997, _1742999]), _1742993)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1742993), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742997)), _1742999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1742993), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742997)), c_List_OtakeWhile(_1742997, _1742995, _1742999)))))], (35792 ^ _779854) ^ [_1446162, _1446164, _1446166, _1446168] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1446162, _1446164), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1446166), _1446168))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1446162), _1446164), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1446168), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1446166)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1446166)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1446168), 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), _1446164), _1446168))))))], (28362 ^ _779854) ^ [_1292600] : [-(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), _1292600))))], (52543 ^ _779854) ^ [_1837296] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1837296)))], (41603 ^ _779854) ^ [_1596547, _1596549, _1596551, _1596553, _1596555] : [c_Relation_Osingle__valued(_1596547, _1596549, _1596551), c_Relation_Osingle__valued(_1596549, _1596553, _1596555), -(c_Relation_Osingle__valued(_1596547, _1596553, hAPP(hAPP(c_Relation_Orel__comp(_1596547, _1596549, _1596553), _1596551), _1596555)))], (26417 ^ _779854) ^ [_1259857, _1259859, _1259861] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259857)))), 26420 ^ _779854 : [(26427 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259859)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259859)), _1259861)) = 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), _1259857), _1259859))), _1259861))], (26421 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259859))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259859)), _1259861)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259857)), _1259861))]]], (12178 ^ _779854) ^ [_992030, _992032, _992034] : [hBOOL(hAPP(hAPP(c_member(_992030), _992032), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_992030, tc_HOL_Obool)), _992034))), hBOOL(hAPP(hAPP(c_member(_992030), _992032), _992034))], (19575 ^ _779854) ^ [_1132883, _1132885, _1132887, _1132889] : [class_Rings_Olinordered__ring__strict(_1132883), 19578 ^ _779854 : [(19593 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132883), _1132885), _1132887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132883), _1132885), _1132889)))), 19594 ^ _779854 : [(19601 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), _1132885), c_Groups_Ozero__class_Ozero(_1132883))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), _1132889), _1132887))], (19595 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), c_Groups_Ozero__class_Ozero(_1132883)), _1132885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), _1132887), _1132889))]]], (19579 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132883), _1132885), _1132887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132883), _1132885), _1132889))), 19584 ^ _779854 : [(19587 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), _1132887), _1132889)))], (19585 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), c_Groups_Ozero__class_Ozero(_1132883)), _1132885)))]], 19588 ^ _779854 : [(19591 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), _1132889), _1132887)))], (19589 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132883), _1132885), c_Groups_Ozero__class_Ozero(_1132883))))]]]]], (6711 ^ _779854) ^ [_887529, _887531, _887533, _887535] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_887529, tc_HOL_Obool)), _887531), _887533), _887535)), 6714 ^ _779854 : [(6717 ^ _779854) ^ [] : [-(hBOOL(hAPP(_887533, _887535)))], (6715 ^ _779854) ^ [] : [-(hBOOL(hAPP(_887531, _887535)))]]], (18965 ^ _779854) ^ [] : [-(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)))], (18283 ^ _779854) ^ [_1110780, _1110782, _1110784, _1110786] : [class_Groups_Ocomm__monoid__mult(_1110780), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110782), _1110784))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1110782, _1110780), _1110786), _1110784) = c_Groups_Oone__class_Oone(_1110780))], (3026 ^ _779854) ^ [_824926, _824928, _824930, _824932, _824934, _824936, _824938, _824940, _824942, _824944, _824946, _824948] : [-(c_Product__Type_Omap__pair(_824948, _824944, _824940, _824936, _824932, _824928) = c_Product__Type_Omap__pair(_824946, _824942, _824938, _824934, _824930, _824926)), _824948 = _824946, _824944 = _824942, _824940 = _824938, _824936 = _824934, _824932 = _824930, _824928 = _824926], (37891 ^ _779854) ^ [_1496097, _1496099, _1496101] : [37893 ^ _779854 : [(37896 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1496097), 37892 ^ [_1496097, _1496099, _1496101]), c_Wellfounded_Oacc(_1496097, _1496101)))], (37894 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1496097, _1496097)), hAPP(hAPP(c_Product__Type_OPair(_1496097, _1496097), 37892 ^ [_1496097, _1496099, _1496101]), _1496099)), _1496101)))]], -(hBOOL(hAPP(hAPP(c_member(_1496097), _1496099), c_Wellfounded_Oacc(_1496097, _1496101))))], (29181 ^ _779854) ^ [_1306290, _1306292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1306290)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1306292)), _1306290) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1306292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1306290), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (11356 ^ _779854) ^ [_975871, _975873] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_975871, tc_HOL_Obool)), hAPP(c_Set_OPow(_975871), _975873))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_975871), _975873)))], (10343 ^ _779854) ^ [_954963, _954965, _954967] : [class_Groups_Olinordered__ab__group__add(_954963), -(hAPP(c_Groups_Ouminus__class_Ouminus(_954963), hAPP(hAPP(c_Orderings_Oord__class_Omax(_954963), _954965), _954967)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_954963), hAPP(c_Groups_Ouminus__class_Ouminus(_954963), _954965)), hAPP(c_Groups_Ouminus__class_Ouminus(_954963), _954967)))], (47488 ^ _779854) ^ [_1734697, _1734699, _1734701] : [-(hAPP(c_List_Orotate(_1734697, _1734699), hAPP(c_List_Orev(_1734697), _1734701)) = hAPP(c_List_Orev(_1734697), hAPP(c_List_Orotate(_1734697, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734697)), _1734701)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1734699, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734697)), _1734701)))), _1734701)))], (39824 ^ _779854) ^ [_1552517, _1552519] : [c_Wellfounded_Owf(_1552517, _1552519), 39828 ^ _779854 : [(39829 ^ _779854) ^ [_1552653] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1552517, _1552517)), hAPP(hAPP(c_Product__Type_OPair(_1552517, _1552517), hAPP(_1552653, hAPP(c_Nat_OSuc, 39827 ^ [_1552517, _1552519, _1552653]))), hAPP(_1552653, 39827 ^ [_1552517, _1552519, _1552653]))), _1552519))]]], (10293 ^ _779854) ^ [_953962, _953964, _953966] : [class_Orderings_Olinorder(_953962), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_953962), _953964), hAPP(hAPP(c_Orderings_Oord__class_Omin(_953962), _953964), _953966)) = _953964)], (35218 ^ _779854) ^ [_1435961, _1435963, _1435965] : [hBOOL(hAPP(_1435961, hAPP(hAPP(c_Product__Type_OPair(_1435963, _1435965), 35219 ^ [_1435961, _1435963, _1435965]), 35220 ^ [_1435961, _1435963, _1435965]))), 35223 ^ _779854 : [(35224 ^ _779854) ^ [_1436108] : [-(hBOOL(hAPP(_1435961, _1436108)))]]], (38855 ^ _779854) ^ [_1521278, _1521280, _1521282] : [-(hBOOL(hAPP(_1521278, _1521280))), -(hAPP(c_Set_OCollect(_1521282), hAPP(hAPP(c_COMBS(_1521282, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521282), c_fconj), hAPP(c_fequal, _1521280))), _1521278)) = c_Orderings_Obot__class_Obot(tc_fun(_1521282, tc_HOL_Obool)))], (5830 ^ _779854) ^ [_872154, _872156, _872158, _872160] : [class_Orderings_Oorder(_872154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872154), _872156), _872158)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872154), _872160), _872156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872154), _872160), _872158)))], (50654 ^ _779854) ^ [_1803994, _1803996, _1803998, _1804000, _1804002] : [c_Fun_Obij__betw(_1803994, _1803996, _1803998, _1804000, _1804002), -(c_Fun_Obij__betw(_1803996, _1803994, c_Hilbert__Choice_Oinv__into(_1803994, _1803996, _1804000, _1803998), _1804002, _1804000))], (47448 ^ _779854) ^ [_1733824, _1733826] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733824)), hAPP(c_List_Orev(_1733824), _1733826)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733824)), _1733826))], (15214 ^ _779854) ^ [_1050933, _1050935, _1050937, _1050939, _1050941, _1050943] : [class_Rings_Oordered__ring(_1050933), 15217 ^ _779854 : [(15224 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050933), _1050939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050933), _1050941), _1050935)), _1050937)), _1050943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050933), _1050935), _1050937)), _1050939)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050933), _1050941), _1050937)), _1050943))))], (15218 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050933), _1050935), _1050937)), _1050939)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050933), _1050941), _1050937)), _1050943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050933), _1050939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050933), _1050941), _1050935)), _1050937)), _1050943))))]]], (15282 ^ _779854) ^ [_1052376, _1052378, _1052380, _1052382, _1052384] : [class_Groups_Oordered__ab__semigroup__add(_1052376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052376), _1052378), _1052380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052376), _1052382), _1052384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052376), _1052378), _1052382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052376), _1052380), _1052384))))], (30367 ^ _779854) ^ [_1328239, _1328241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328239, _1328241)), _1328239)))], (44270 ^ _779854) ^ [_1664830, _1664832] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664830)), hAPP(c_List_Orotate1(_1664830), _1664832)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664830)), _1664832))], (27005 ^ _779854) ^ [_1269641] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1269641), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269641), c_Int_OPls)))], (18397 ^ _779854) ^ [_1112956, _1112958, _1112960] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1112956), _1112958)), -(hBOOL(hAPP(hAPP(c_member(_1112956), _1112960), _1112958))), -(hAPP(c_Finite__Set_Ocard(_1112956), hAPP(hAPP(c_Set_Oinsert(_1112956), _1112960), _1112958)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1112956), _1112958)))], (41170 ^ _779854) ^ [_1586101, _1586103] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1586101, _1586101, _1586101), _1586103), c_Transitive__Closure_Ortrancl(_1586101, _1586103)) = hAPP(hAPP(c_Relation_Orel__comp(_1586101, _1586101, _1586101), c_Transitive__Closure_Ortrancl(_1586101, _1586103)), _1586103))], (41284 ^ _779854) ^ [] : [-(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))))], (15036 ^ _779854) ^ [_1047101, _1047103, _1047105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047101), _1047103)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1047101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047103), _1047105)) = 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, _1047101), _1047103)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1047103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047103), _1047105))))], (16409 ^ _779854) ^ [_1075150, _1075152, _1075154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075150), _1075152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075150), _1075154)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075152), _1075154))))], (50378 ^ _779854) ^ [_1797627, _1797629, _1797631, _1797633, _1797635, _1797637] : [c_Fun_Oinj__on(_1797627, _1797629, _1797631, _1797633), hBOOL(hAPP(hAPP(c_member(_1797627), _1797635), _1797633)), hAPP(_1797631, _1797635) = _1797637, -(hAPP(c_Hilbert__Choice_Oinv__into(_1797627, _1797629, _1797633, _1797631), _1797637) = _1797635)], (31985 ^ _779854) ^ [_1355289] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1355289)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1355289))], (31776 ^ _779854) ^ [_1351680] : [class_Rings_Oring__1(_1351680), -(hAPP(c_Int_Oring__1__class_Oof__int(_1351680), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1351680))], (51037 ^ _779854) ^ [_1811655, _1811657, _1811659, _1811661, _1811663, _1811665] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1811655, _1811657, _1811659, _1811661), _1811663), _1811665) = hAPP(_1811661, hAPP(hAPP(c_Product__Type_OPair(_1811655, _1811657), _1811663), _1811665)))], (5166 ^ _779854) ^ [_858840, _858842, _858844, _858846] : [-(c_Quotient_ORespects(_858846, _858842) = c_Quotient_ORespects(_858844, _858840)), _858846 = _858844, _858842 = _858840], (36444 ^ _779854) ^ [_1460230, _1460232] : [class_Orderings_Owellorder(_1460230), 36449 ^ _779854 : [(36450 ^ _779854) ^ [_1460324] : [hBOOL(hAPP(_1460232, _1460324))]], -(hBOOL(hAPP(_1460232, c_Orderings_Oord__class_OLeast(_1460230, _1460232))))], (42121 ^ _779854) ^ [_1610600, _1610602, _1610604, _1610606, _1610608] : [-(hAPP(hAPP(c_List_Olist_OCons(_1610600), _1610602), _1610604) = hAPP(hAPP(c_List_Olist_OCons(_1610600), _1610606), _1610608)), _1610602 = _1610606, _1610604 = _1610608], (25767 ^ _779854) ^ [_1248239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1248239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248239)))], (38798 ^ _779854) ^ [_1519929, _1519931] : [-(hBOOL(hAPP(_1519931, 38799 ^ [_1519929, _1519931]))), -(hAPP(c_Set_OCollect(_1519929), _1519931) = c_Orderings_Obot__class_Obot(tc_fun(_1519929, tc_HOL_Obool)))], (4870 ^ _779854) ^ [_854252, _854254] : [_854254 = _854252, -(c_Relation_OId(_854254) = c_Relation_OId(_854252))], (11949 ^ _779854) ^ [_987500, _987502, _987504, _987506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987500, tc_HOL_Obool)), _987502), _987504)), hBOOL(hAPP(hAPP(c_member(_987500), _987506), _987502)), -(hBOOL(hAPP(hAPP(c_member(_987500), _987506), _987504)))], (18148 ^ _779854) ^ [_1108203, _1108205] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108203), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108203), _1108205)))))], (32643 ^ _779854) ^ [_1367472, _1367474, _1367476] : [class_Fields_Olinordered__field(_1367472), 32649 ^ _779854 : [(32652 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367472), _1367474), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1367472), _1367476), 32648 ^ [_1367472, _1367474, _1367476])))], (32650 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367472), c_Groups_Ozero__class_Ozero(_1367472)), 32648 ^ [_1367472, _1367474, _1367476])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367472), _1367474), _1367476)))], (43075 ^ _779854) ^ [_1638026, _1638028, _1638030, _1638032, _1638034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638026, tc_HOL_Obool)), hAPP(c_List_Oset(_1638026), _1638028)), _1638030)), hBOOL(hAPP(hAPP(c_member(_1638026), _1638032), _1638030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638026, tc_HOL_Obool)), hAPP(c_List_Oset(_1638026), hAPP(hAPP(c_List_Olist__update(_1638026, _1638028), _1638034), _1638032))), _1638030)))], (7469 ^ _779854) ^ [_903021, _903023, _903025] : [class_Lattices_Obounded__lattice__top(_903021), 7472 ^ _779854 : [(7481 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903021), _903023), _903025) = c_Orderings_Otop__class_Otop(_903021)), _903023 = c_Orderings_Otop__class_Otop(_903021), _903025 = c_Orderings_Otop__class_Otop(_903021)], (7473 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903021), _903023), _903025) = c_Orderings_Otop__class_Otop(_903021), 7476 ^ _779854 : [(7479 ^ _779854) ^ [] : [-(_903025 = c_Orderings_Otop__class_Otop(_903021))], (7477 ^ _779854) ^ [] : [-(_903023 = c_Orderings_Otop__class_Otop(_903021))]]]]], (2984 ^ _779854) ^ [_824301, _824303] : [_824303 = _824301, -(c_Nitpick_Onum(_824303) = c_Nitpick_Onum(_824301))], (43592 ^ _779854) ^ [_1648712, _1648714, _1648716] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1648712))), -(c_List_Osublist(_1648714, hAPP(hAPP(c_List_Olist_OCons(_1648714), _1648716), c_List_Olist_ONil(_1648714)), _1648712) = c_List_Olist_ONil(_1648714))], (35117 ^ _779854) ^ [_1433309, _1433311, _1433313, _1433315] : [-(hAPP(c_Nat_Onat_Onat__rec(_1433309, _1433311, _1433313), hAPP(c_Nat_OSuc, _1433315)) = hAPP(hAPP(_1433313, _1433315), hAPP(c_Nat_Onat_Onat__rec(_1433309, _1433311, _1433313), _1433315)))], (17718 ^ _779854) ^ [_1101063, _1101065] : [hAPP(c_Nat_OSuc, _1101063) = hAPP(c_Nat_OSuc, _1101065), -(_1101063 = _1101065)], (27791 ^ _779854) ^ [_1282667] : [class_Rings_Osemiring__1(_1282667), -(hBOOL(hAPP(hAPP(c_member(_1282667), c_Groups_Oone__class_Oone(_1282667)), c_Nat_Osemiring__1__class_ONats(_1282667))))], (27339 ^ _779854) ^ [_1275456, _1275458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275456), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275456)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275458)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52575 ^ _779854) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (40383 ^ _779854) ^ [_1566573, _1566575, _1566577, _1566579] : [-(c_Hilbert__Choice_OEps(tc_prod(_1566573, _1566575), hAPP(c_Product__Type_Oprod_Oprod__case(_1566573, _1566575, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1566573, tc_fun(_1566575, tc_HOL_Obool), tc_fun(_1566575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1566575, tc_HOL_Obool), tc_fun(_1566575, tc_HOL_Obool)), _1566573), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1566575)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566573), c_fconj), hAPP(c_fequal, _1566577)))), hAPP(c_fequal, _1566579)))) = hAPP(hAPP(c_Product__Type_OPair(_1566573, _1566575), _1566577), _1566579))], (13397 ^ _779854) ^ [_1015779, _1015781, _1015783] : [class_Orderings_Olinorder(_1015779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015779, tc_HOL_Obool)), _1015781), _1015783)), -(_1015781 = c_Orderings_Obot__class_Obot(tc_fun(_1015779, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015779), _1015783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015779), c_Big__Operators_Olinorder__class_OMin(_1015779, _1015783)), c_Big__Operators_Olinorder__class_OMin(_1015779, _1015781))))], (47384 ^ _779854) ^ [_1732531, _1732533, _1732535, _1732537] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732531)), _1732533) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732535)), _1732537), -(hAPP(hAPP(c_List_Ozip(_1732531, _1732535), hAPP(c_List_Orev(_1732531), _1732533)), hAPP(c_List_Orev(_1732535), _1732537)) = hAPP(c_List_Orev(tc_prod(_1732531, _1732535)), hAPP(hAPP(c_List_Ozip(_1732531, _1732535), _1732533), _1732537)))], (46010 ^ _779854) ^ [_1703000, _1703002, _1703004, _1703006] : [hBOOL(hAPP(c_List_Odistinct(_1703000), _1703002)), hBOOL(hAPP(c_List_Odistinct(_1703004), _1703006)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1703000, _1703004)), c_Enum_Oproduct(_1703000, _1703004, _1703002, _1703006))))], (41969 ^ _779854) ^ [_1606294, _1606296] : [-(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)))), _1606294)) = 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)))), _1606296))), 41971 ^ _779854 : [(41974 ^ _779854) ^ [] : [41975 ^ _779854 : [(41978 ^ _779854) ^ [] : [hBOOL(hAPP(_1606296, 41970 ^ [_1606294, _1606296]))], (41976 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1606294, 41970 ^ [_1606294, _1606296])))]], 41979 ^ _779854 : [(41982 ^ _779854) ^ [] : [hBOOL(hAPP(_1606294, 41970 ^ [_1606294, _1606296]))], (41980 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1606296, 41970 ^ [_1606294, _1606296])))]]], (41972 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41970 ^ [_1606294, _1606296])))]]], (29013 ^ _779854) ^ [] : [-(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))))))], (50006 ^ _779854) ^ [_1790818, _1790820] : [c_Relation_Osym(_1790818, _1790820), c_Relation_Otrans(_1790818, _1790820), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1790818, _1790818), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1790818, _1790818, _1790818), hAPP(c_Relation_Oconverse(_1790818, _1790818), _1790820)), _1790820)), _1790820)))], (21082 ^ _779854) ^ [_1159255, _1159257, _1159259] : [21083 ^ _779854 : [(21086 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159257), _1159259))], (21084 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159255)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159255), _1159257)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159255), _1159259))))], (20041 ^ _779854) ^ [_1141196, _1141198] : [class_Groups_Ogroup__add(_1141196), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141196), hAPP(c_Groups_Ouminus__class_Ouminus(_1141196), _1141198)), _1141198) = c_Groups_Ozero__class_Ozero(_1141196))], (27689 ^ _779854) ^ [_1280977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1280977), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1280977) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49300 ^ _779854) ^ [_1774089, _1774091, _1774093] : [-(c_List_Olist__ex1(_1774089, _1774091, _1774093)), 49301 ^ _779854 : [(49302 ^ _779854) ^ [_1774183] : [hBOOL(hAPP(hAPP(c_member(_1774089), _1774183), hAPP(c_List_Oset(_1774089), _1774093))), hBOOL(hAPP(_1774091, _1774183)), 49310 ^ _779854 : [(49315 ^ _779854) ^ [] : [49309 ^ [_1774089, _1774091, _1774093, _1774183] = _1774183], (49313 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1774091, 49309 ^ [_1774089, _1774091, _1774093, _1774183])))], (49311 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774089), 49309 ^ [_1774089, _1774091, _1774093, _1774183]), hAPP(c_List_Oset(_1774089), _1774093))))]]]]], (7902 ^ _779854) ^ [_912021, _912023, _912025] : [class_Orderings_Oorder(_912021), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912021, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_912021), _912023)), c_SetInterval_Oord__class_OgreaterThanLessThan(_912021, _912023, _912025)) = c_Orderings_Obot__class_Obot(tc_fun(_912021, tc_HOL_Obool)))], (33054 ^ _779854) ^ [_1378455, _1378457] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378455, tc_fun(_1378455, tc_HOL_Obool)), _1378457), hAPP(hAPP(c_COMBC(_1378455, tc_fun(_1378455, tc_HOL_Obool), tc_fun(_1378455, tc_HOL_Obool)), c_Set_Oinsert(_1378455)), c_Orderings_Obot__class_Obot(tc_fun(_1378455, tc_HOL_Obool)))) = _1378457)], (9532 ^ _779854) ^ [_939537, _939539, _939541, _939543] : [_939543 = c_Orderings_Obot__class_Obot(tc_fun(_939539, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_939537, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_939539, _939537, _939541), _939543))], (33169 ^ _779854) ^ [_1381268, _1381270, _1381272, _1381274] : [_1381268 = c_Orderings_Obot__class_Obot(tc_fun(_1381270, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381270, tc_fun(_1381272, tc_HOL_Obool)), _1381268), hAPP(c_COMBK(tc_fun(_1381272, tc_HOL_Obool), _1381270), _1381274)) = c_Orderings_Obot__class_Obot(tc_fun(_1381272, tc_HOL_Obool)))], (44033 ^ _779854) ^ [_1658439, _1658441, _1658443, _1658445, _1658447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658439), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658441)), _1658443))), -(hAPP(hAPP(c_List_Olist__update(_1658441, hAPP(hAPP(c_List_Oappend(_1658441), _1658443), _1658445)), _1658439), _1658447) = hAPP(hAPP(c_List_Oappend(_1658441), hAPP(hAPP(c_List_Olist__update(_1658441, _1658443), _1658439), _1658447)), _1658445))], (1510 ^ _779854) ^ [_801681, _801683] : [-(class_Enum_Oenum(_801681)), _801683 = _801681, class_Enum_Oenum(_801683)], (7628 ^ _779854) ^ [_906237, _906239, _906241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906237, tc_HOL_Obool)), _906239), _906241)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906237, tc_HOL_Obool)), _906241), _906239) = _906241)], (38058 ^ _779854) ^ [_1499731, _1499733, _1499735] : [-(hAPP(c_Set_Ovimage(_1499731, _1499733, _1499735), c_Orderings_Otop__class_Otop(tc_fun(_1499733, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1499731, tc_HOL_Obool)))], (39327 ^ _779854) ^ [_1539096, _1539098, _1539100] : [c_Predicate_Oreflp(_1539096, _1539098), -(hBOOL(hAPP(hAPP(_1539098, _1539100), _1539100)))], (18074 ^ _779854) ^ [_1106839] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1106839)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1106839), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1106839)))], (28304 ^ _779854) ^ [] : [-(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)))], (43945 ^ _779854) ^ [_1656831, _1656833, _1656835] : [_1656835 = c_List_Olist_ONil(_1656831), -(hAPP(hAPP(c_List_Oappend(_1656831), _1656833), _1656835) = _1656833)], (29493 ^ _779854) ^ [_1311859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1311859)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311859), c_Int_OPls)))], (12912 ^ _779854) ^ [_1006814, _1006816, _1006818, _1006820] : [hBOOL(hAPP(hAPP(c_member(_1006814), _1006816), c_SetInterval_Oord_OgreaterThan(_1006814, _1006818, _1006820))), -(hBOOL(hAPP(hAPP(_1006818, _1006820), _1006816)))], (43572 ^ _779854) ^ [_1648314, _1648316, _1648318, _1648320] : [-(hAPP(hAPP(c_List_Otake(_1648314), _1648316), hAPP(hAPP(c_List_Olist_OCons(_1648314), _1648318), _1648320)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1648314), c_List_Olist_ONil(_1648314), hAPP(hAPP(c_COMBB(tc_List_Olist(_1648314), tc_List_Olist(_1648314), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1648314), _1648318)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1648314), tc_List_Olist(_1648314)), c_List_Otake(_1648314)), _1648320)), _1648316))], (19491 ^ _779854) ^ [_1131374, _1131376] : [class_Groups_Olinordered__ab__group__add(_1131374), 19494 ^ _779854 : [(19501 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131374), _1131376), c_Groups_Ozero__class_Ozero(_1131374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131374), _1131376), _1131376)), c_Groups_Ozero__class_Ozero(_1131374))))], (19495 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131374), _1131376), _1131376)), c_Groups_Ozero__class_Ozero(_1131374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131374), _1131376), c_Groups_Ozero__class_Ozero(_1131374))))]]], (26771 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (40178 ^ _779854) ^ [_1561750, _1561752, _1561754, _1561756] : [c_Equiv__Relations_Ocongruent(_1561750, _1561752, _1561754, _1561756), 40181 ^ _779854 : [(40182 ^ _779854) ^ [_1561895] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561750, _1561750)), _1561895), _1561754)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561750, _1561750, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1561750, tc_fun(_1561750, _1561752), tc_fun(_1561750, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1561752, tc_HOL_Obool), tc_fun(tc_fun(_1561750, _1561752), tc_fun(_1561750, tc_HOL_Obool)), _1561750), c_COMBB(_1561752, tc_HOL_Obool, _1561750)), hAPP(hAPP(c_COMBB(_1561752, tc_fun(_1561752, tc_HOL_Obool), _1561750), c_fequal), _1561756))), _1561756)), _1561895)))]]], (39359 ^ _779854) ^ [_1539678, _1539680, _1539682, _1539684] : [class_Groups_Ocomm__monoid__add(_1539678), c_Fun_Oinj__on(_1539680, _1539678, _1539682, _1539684), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539680, _1539678), _1539682), _1539684) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539678, _1539678), c_Fun_Oid(_1539678)), hAPP(c_Set_Oimage(_1539680, _1539678, _1539682), _1539684)))], (41824 ^ _779854) ^ [_1602097, _1602099] : [-(hAPP(hAPP(c_Nat_Ocompow(_1602097, _1602097), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1602099) = c_Fun_Oid(_1602097))], (24342 ^ _779854) ^ [_1221370, _1221372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1221370)), -(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), _1221370), _1221372))))], (30125 ^ _779854) ^ [_1323374, _1323376, _1323378] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323374), _1323376), _1323378) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323374), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323376, _1323378)), _1323378))], (47810 ^ _779854) ^ [_1741469, _1741471, _1741473] : [-(c_List_OdropWhile(_1741469, _1741471, _1741473) = hAPP(hAPP(c_List_Odrop(_1741469), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741469)), c_List_OtakeWhile(_1741469, _1741471, _1741473))), _1741473))], (18785 ^ _779854) ^ [_1119210, _1119212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119210), _1119212)), _1119212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47659 ^ _779854) ^ [_1738234, _1738236, _1738238, _1738240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738234), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738236)), c_List_OtakeWhile(_1738236, _1738238, _1738240)))), -(hAPP(hAPP(c_List_Onth(_1738236), c_List_OtakeWhile(_1738236, _1738238, _1738240)), _1738234) = hAPP(hAPP(c_List_Onth(_1738236), _1738240), _1738234))], (15788 ^ _779854) ^ [_1062747] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1062747))))], (15816 ^ _779854) ^ [_1063278, _1063280, _1063282] : [_1063280 = _1063282, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063278), _1063280) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063278), _1063282))], (32429 ^ _779854) ^ [_1363432, _1363434] : [-(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), _1363432)), _1363434))))], (21218 ^ _779854) ^ [_1161936] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1161936), c_Orderings_Otop__class_Otop(tc_fun(_1161936, 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(_1161936), c_Orderings_Otop__class_Otop(tc_fun(_1161936, tc_HOL_Obool))))))], (48950 ^ _779854) ^ [_1766952, _1766954, _1766956, _1766958, _1766960, _1766962] : [-(hAPP(hAPP(c_List_Ozip(_1766952, _1766954), c_List_Oreplicate(_1766952, _1766956, _1766958)), c_List_Oreplicate(_1766954, _1766960, _1766962)) = c_List_Oreplicate(tc_prod(_1766952, _1766954), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1766956), _1766960), hAPP(hAPP(c_Product__Type_OPair(_1766952, _1766954), _1766958), _1766962)))], (9634 ^ _779854) ^ [_941380, _941382, _941384] : [class_Orderings_Olinorder(_941380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941380), _941382), _941384)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_941380), _941384), _941382) = _941384)], (2902 ^ _779854) ^ [_823072, _823074, _823076, _823078, _823080, _823082] : [-(c_Nitpick_Oof__frac(_823082, _823078, _823074) = c_Nitpick_Oof__frac(_823080, _823076, _823072)), _823082 = _823080, _823078 = _823076, _823074 = _823072], (33167 ^ _779854) ^ [_1381195, _1381197, _1381199] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381195, tc_fun(_1381197, tc_HOL_Obool)), _1381199), hAPP(c_COMBK(tc_fun(_1381197, tc_HOL_Obool), _1381195), c_Orderings_Obot__class_Obot(tc_fun(_1381197, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1381197, tc_HOL_Obool)))], (8816 ^ _779854) ^ [_926274, _926276, _926278] : [hAPP(hAPP(c_Set_Oinsert(_926274), _926276), c_Orderings_Obot__class_Obot(tc_fun(_926274, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_926274), _926278), c_Orderings_Obot__class_Obot(tc_fun(_926274, tc_HOL_Obool))), -(_926276 = _926278)], (32471 ^ _779854) ^ [_1364149, _1364151] : [32472 ^ _779854 : [(32475 ^ _779854) ^ [] : [_1364151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (32473 ^ _779854) ^ [] : [-(_1364149 = 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), _1364149)), _1364151))))], (37716 ^ _779854) ^ [_1491592, _1491594, _1491596, _1491598, _1491600, _1491602, _1491604, _1491606, _1491608, _1491610, _1491612] : [c_Equiv__Relations_Oequiv(_1491592, _1491594, _1491596), c_Equiv__Relations_Oequiv(_1491598, _1491600, _1491602), c_Equiv__Relations_Ocongruent2(_1491592, _1491598, tc_fun(_1491604, tc_HOL_Obool), _1491596, _1491602, _1491606), hBOOL(hAPP(hAPP(c_member(tc_fun(_1491592, tc_HOL_Obool)), _1491608), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1491592), _1491594), _1491596))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1491598, tc_HOL_Obool)), _1491610), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1491598), _1491600), _1491602))), 37738 ^ _779854 : [(37744 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1491604, tc_HOL_Obool)), hAPP(hAPP(_1491606, 37737 ^ [_1491592, _1491594, _1491596, _1491598, _1491600, _1491602, _1491604, _1491606, _1491608, _1491610, _1491612]), 37740 ^ [_1491592, _1491594, _1491596, _1491598, _1491600, _1491602, _1491604, _1491606, _1491608, _1491610, _1491612])), _1491612))], (37742 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491598), 37740 ^ [_1491592, _1491594, _1491596, _1491598, _1491600, _1491602, _1491604, _1491606, _1491608, _1491610, _1491612]), _1491600)))], (37739 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491592), 37737 ^ [_1491592, _1491594, _1491596, _1491598, _1491600, _1491602, _1491604, _1491606, _1491608, _1491610, _1491612]), _1491594)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1491604, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1491592, tc_fun(_1491604, tc_HOL_Obool)), _1491608), hAPP(hAPP(c_COMBB(tc_fun(_1491598, tc_fun(_1491604, tc_HOL_Obool)), tc_fun(_1491604, tc_HOL_Obool), _1491592), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1491598, tc_fun(_1491604, tc_HOL_Obool)), _1491610)), _1491606))), _1491612)))], (45224 ^ _779854) ^ [_1685481] : [-(hAPP(c_List_Omap(_1685481, _1685481), c_COMBI(_1685481)) = c_Fun_Oid(tc_List_Olist(_1685481)))], (9995 ^ _779854) ^ [_948618, _948620, _948622, _948624, _948626] : [class_Orderings_Olinorder(_948618), class_Orderings_Olinorder(_948620), c_Orderings_Oorder__class_Omono(_948620, _948618, _948622), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_948618), hAPP(_948622, _948624)), hAPP(_948622, _948626)) = hAPP(_948622, hAPP(hAPP(c_Orderings_Oord__class_Omin(_948620), _948624), _948626)))], (44608 ^ _779854) ^ [_1672167, _1672169, _1672171, _1672173] : [44609 ^ _779854 : [(44610 ^ _779854) ^ [_1672264, _1672266] : [_1672167 = hAPP(hAPP(c_List_Olist_OCons(_1672169), _1672266), _1672264)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672169), tc_List_Olist(_1672169))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672169), tc_List_Olist(_1672169)), _1672171), hAPP(hAPP(c_List_Oappend(_1672169), _1672171), _1672167))), c_List_Olexord(_1672169, _1672173))))], (10355 ^ _779854) ^ [_955241, _955243, _955245] : [class_Orderings_Oorder(_955241), class_Orderings_Oorder(_955243), c_Orderings_Oorder__class_Ostrict__mono(_955243, _955241, _955245), -(c_Orderings_Oorder__class_Omono(_955243, _955241, _955245))], (44588 ^ _779854) ^ [_1671796, _1671798, _1671800] : [-(hAPP(c_List_Otl(_1671796), hAPP(hAPP(c_List_Otake(_1671796), _1671798), _1671800)) = hAPP(hAPP(c_List_Otake(_1671796), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1671798), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1671796), _1671800)))], (44380 ^ _779854) ^ [_1667399, _1667401, _1667403, _1667405, _1667407] : [-(hAPP(hAPP(c_List_Oappend(_1667399), _1667401), _1667403) = hAPP(hAPP(c_List_Oappend(_1667399), _1667405), _1667407)), 44383 ^ _779854 : [(44386 ^ _779854) ^ [] : [_1667401 = hAPP(hAPP(c_List_Otake(_1667399), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667401)), _1667405), _1667403 = hAPP(hAPP(c_List_Oappend(_1667399), hAPP(hAPP(c_List_Odrop(_1667399), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667401)), _1667405)), _1667407)], (44384 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667401)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667405))))]], 44391 ^ _779854 : [(44394 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Otake(_1667399), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667405)), _1667401) = _1667405, hAPP(hAPP(c_List_Oappend(_1667399), hAPP(hAPP(c_List_Odrop(_1667399), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667405)), _1667401)), _1667403) = _1667407], (44392 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667401)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667399)), _1667405)))]]], (31651 ^ _779854) ^ [_1349932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1349932)), -(c_Nat__Transfer_Ois__nat(_1349932))], (42796 ^ _779854) ^ [_1629887, _1629889, _1629891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629887), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629889)), _1629891))), -(hBOOL(hAPP(hAPP(c_member(_1629889), hAPP(hAPP(c_List_Onth(_1629889), _1629891), _1629887)), hAPP(c_List_Oset(_1629889), _1629891))))], (40919 ^ _779854) ^ [_1579310, _1579312] : [c_Wellfounded_Owf(_1579310, _1579312), -(c_Wellfounded_Owf(_1579310, c_Transitive__Closure_Otrancl(_1579310, _1579312)))], (28639 ^ _779854) ^ [_1297457, _1297459] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297457)), _1297459) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1297457), _1297459)))], (30257 ^ _779854) ^ [_1326070, _1326072] : [class_Divides_Osemiring__div(_1326070), -(c_Divides_Odiv__class_Omod(_1326070, c_Groups_Ozero__class_Ozero(_1326070), _1326072) = c_Groups_Ozero__class_Ozero(_1326070))], (20850 ^ _779854) ^ [_1155086, _1155088, _1155090] : [class_Rings_Olinordered__idom(_1155086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155086), c_Groups_Ozero__class_Ozero(_1155086)), _1155088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155086), c_Groups_Ozero__class_Ozero(_1155086)), _1155090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155086), _1155090), c_Groups_Oone__class_Oone(_1155086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155086), _1155090), _1155088)), _1155088)))], (35030 ^ _779854) ^ [_1431370, _1431372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431372)), -(c_Divides_OposDivAlg(_1431370, _1431372) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1431370), _1431372)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1431370, _1431372)))], (42366 ^ _779854) ^ [_1618316, _1618318, _1618320, _1618322] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618316), tc_List_Olist(_1618316))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618316), tc_List_Olist(_1618316)), _1618318), _1618320)), c_List_Olistrel1(_1618316, _1618322))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618316), tc_List_Olist(_1618316))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618316), tc_List_Olist(_1618316)), _1618318), _1618320)), c_List_Olistrel(_1618316, c_Transitive__Closure_Ortrancl(_1618316, _1618322)))))], (17799 ^ _779854) ^ [_1102378, _1102380] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102378), _1102380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102380), hAPP(c_Nat_OSuc, _1102378))))], (41763 ^ _779854) ^ [_1600360, _1600362, _1600364] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1600360, _1600360, _1600360), _1600362), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600360, _1600360), tc_HOL_Obool), _1600364), _1600362)) = hAPP(hAPP(c_Relation_Orel__comp(_1600360, _1600360, _1600360), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600360, _1600360), tc_HOL_Obool), _1600364), _1600362)), _1600362))], (10619 ^ _779854) ^ [_960542, _960544, _960546, _960548, _960550, _960552] : [c_Fun_Oinj__on(_960542, _960544, _960546, _960548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960542, tc_HOL_Obool)), _960550), _960548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960542, tc_HOL_Obool)), _960552), _960548)), -(hAPP(c_Set_Oimage(_960542, _960544, _960546), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960542, tc_HOL_Obool)), _960550), _960552)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960544, tc_HOL_Obool)), hAPP(c_Set_Oimage(_960542, _960544, _960546), _960550)), hAPP(c_Set_Oimage(_960542, _960544, _960546), _960552)))], (21132 ^ _779854) ^ [_1160251, _1160253, _1160255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1160251), _1160253)), 21135 ^ _779854 : [(21155 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1160251, tc_Nat_Onat), _1160255), _1160253) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 21156 ^ _779854 : [(21157 ^ _779854) ^ [_1160732] : [hBOOL(hAPP(hAPP(c_member(_1160251), _1160732), _1160253)), hAPP(_1160255, _1160732) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21165 ^ _779854 : [(21170 ^ _779854) ^ [] : [hAPP(_1160255, 21164 ^ [_1160251, _1160253, _1160255, _1160732]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21168 ^ _779854) ^ [] : [_1160732 = 21164 ^ [_1160251, _1160253, _1160255, _1160732]], (21166 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1160251), 21164 ^ [_1160251, _1160253, _1160255, _1160732]), _1160253)))]]]]], (21136 ^ _779854) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1160251, tc_Nat_Onat), _1160255), _1160253) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21140 ^ _779854 : [(21145 ^ _779854) ^ [_1160571] : [hBOOL(hAPP(hAPP(c_member(_1160251), _1160571), _1160253)), -(21139 ^ [_1160251, _1160253, _1160255] = _1160571), -(hAPP(_1160255, _1160571) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21143 ^ _779854) ^ [] : [-(hAPP(_1160255, 21139 ^ [_1160251, _1160253, _1160255]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21141 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1160251), 21139 ^ [_1160251, _1160253, _1160255]), _1160253)))]]]]], (14039 ^ _779854) ^ [_1027494, _1027496, _1027498, _1027500, _1027502, _1027504] : [hBOOL(hAPP(hAPP(c_member(_1027494), _1027496), _1027498)), -(hAPP(c_Set_Oimage(_1027494, _1027500, c_Fun_Ofun__upd(_1027494, _1027500, _1027502, _1027496, _1027504)), _1027498) = hAPP(hAPP(c_Set_Oinsert(_1027500), _1027504), hAPP(c_Set_Oimage(_1027494, _1027500, _1027502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1027494, tc_HOL_Obool)), _1027498), hAPP(hAPP(c_Set_Oinsert(_1027494), _1027496), c_Orderings_Obot__class_Obot(tc_fun(_1027494, tc_HOL_Obool)))))))], (44340 ^ _779854) ^ [_1666399, _1666401, _1666403, _1666405] : [-(hAPP(hAPP(c_List_Odrop(_1666399), _1666401), hAPP(hAPP(c_List_Olist_OCons(_1666399), _1666403), _1666405)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1666399), hAPP(hAPP(c_List_Olist_OCons(_1666399), _1666403), _1666405), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1666399), tc_List_Olist(_1666399)), c_List_Odrop(_1666399)), _1666405), _1666401))], (5458 ^ _779854) ^ [_863448, _863450] : [_863450 = _863448, -(c_member(_863450) = c_member(_863448))], (15408 ^ _779854) ^ [_1054811, _1054813, _1054815] : [class_Groups_Ogroup__add(_1054811), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1054811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054811), _1054813), _1054815)), _1054815) = _1054813)], (30687 ^ _779854) ^ [_1333812, _1333814, _1333816] : [-(hBOOL(hAPP(_1333812, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333814, _1333816)))), 30690 ^ _779854 : [(30693 ^ _779854) ^ [] : [hBOOL(hAPP(_1333812, _1333814))], (30691 ^ _779854) ^ [] : [-(_1333816 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 30696 ^ _779854 : [(30697 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333816)))], (30703 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 30699 ^ [_1333812, _1333814, _1333816]), _1333816)))], (30707 ^ _779854) ^ [] : [hBOOL(hAPP(_1333812, 30699 ^ [_1333812, _1333814, _1333816]))], (30705 ^ _779854) ^ [] : [-(_1333814 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1333816), 30698 ^ [_1333812, _1333814, _1333816])), 30699 ^ [_1333812, _1333814, _1333816]))], (30701 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30699 ^ [_1333812, _1333814, _1333816])))]], 30708 ^ _779854 : [(30709 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333816), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30715 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30711 ^ [_1333812, _1333814, _1333816]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30719 ^ _779854) ^ [] : [hBOOL(hAPP(_1333812, 30711 ^ [_1333812, _1333814, _1333816]))], (30717 ^ _779854) ^ [] : [-(_1333814 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1333816), 30710 ^ [_1333812, _1333814, _1333816])), 30711 ^ [_1333812, _1333814, _1333816]))], (30713 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333816), 30711 ^ [_1333812, _1333814, _1333816])))]]], (4810 ^ _779854) ^ [_853248, _853250, _853252, _853254] : [-(c_Complete__Lattice_OSup__class_OSup(_853254, _853250) = c_Complete__Lattice_OSup__class_OSup(_853252, _853248)), _853254 = _853252, _853250 = _853248], (33006 ^ _779854) ^ [_1377185, _1377187, _1377189, _1377191, _1377193] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1377185), hAPP(c_Set_Oimage(_1377187, _1377185, _1377189), c_Orderings_Otop__class_Otop(tc_fun(_1377187, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1377191), hAPP(c_Set_Oimage(_1377187, _1377191, hAPP(hAPP(c_COMBB(_1377185, _1377191, _1377187), _1377193), _1377189)), c_Orderings_Otop__class_Otop(tc_fun(_1377187, tc_HOL_Obool))))))], (18679 ^ _779854) ^ [_1117702, _1117704] : [class_Groups_Ogroup__add(_1117702), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117702), _1117704), c_Groups_Ozero__class_Ozero(_1117702)) = _1117704)], (45663 ^ _779854) ^ [_1695185, _1695187, _1695189, _1695191] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1695185)), _1695187), c_List_Olists(_1695185, _1695189))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1695185)), _1695187), c_List_Olists(_1695185, _1695191))), -(hBOOL(hAPP(c_List_Olistsp(_1695185, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1695185, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1695185, tc_fun(_1695185, tc_HOL_Obool), tc_HOL_Obool), c_member(_1695185)), _1695189)), hAPP(hAPP(c_COMBC(_1695185, tc_fun(_1695185, tc_HOL_Obool), tc_HOL_Obool), c_member(_1695185)), _1695191))), _1695187)))], (43824 ^ _779854) ^ [_1654104, _1654106, _1654108, _1654110] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1654104)), hAPP(hAPP(c_List_Oappend(_1654104), _1654106), _1654108)), c_List_Olists(_1654104, _1654110)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1654104)), _1654106), c_List_Olists(_1654104, _1654110))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1654104)), _1654108), c_List_Olists(_1654104, _1654110)))], (42329 ^ _779854) ^ [_1617208, _1617210, _1617212, _1617214] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1617208), tc_List_Olist(_1617208), c_List_Olistrel(_1617208, _1617210)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1617208)), hAPP(hAPP(c_List_Olist_OCons(_1617208), _1617212), _1617214)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1617208), tc_HOL_Obool)))) = c_List_Oset__Cons(_1617208, hAPP(c_Relation_OImage(_1617208, _1617208, _1617210), hAPP(hAPP(c_Set_Oinsert(_1617208), _1617212), c_Orderings_Obot__class_Obot(tc_fun(_1617208, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1617208), tc_List_Olist(_1617208), c_List_Olistrel(_1617208, _1617210)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1617208)), _1617214), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1617208), tc_HOL_Obool))))))], (17506 ^ _779854) ^ [_1096597, _1096599, _1096601] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096597), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1096597, tc_HOL_Obool)), _1096599), _1096601))), -(hAPP(c_Finite__Set_Ocard(_1096597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096597, tc_HOL_Obool)), _1096599), _1096601)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1096597), _1096599)), hAPP(c_Finite__Set_Ocard(_1096597), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1096597, tc_HOL_Obool)), _1096599), _1096601))))], (46388 ^ _779854) ^ [_1711714, _1711716] : [-(c_List_Oconcat(_1711714, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711714), tc_List_Olist(_1711714)), c_List_Olist_Olist__case(tc_List_Olist(_1711714), _1711714, c_List_Olist_ONil(_1711714), hAPP(hAPP(c_COMBB(tc_List_Olist(_1711714), tc_fun(tc_List_Olist(_1711714), tc_List_Olist(_1711714)), _1711714), c_COMBK(tc_List_Olist(_1711714), tc_List_Olist(_1711714))), hAPP(hAPP(c_COMBC(_1711714, tc_List_Olist(_1711714), tc_List_Olist(_1711714)), c_List_Olist_OCons(_1711714)), c_List_Olist_ONil(_1711714))))), _1711716)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711714), _1711714), c_List_Ohd(_1711714)), hAPP(c_List_Ofilter(tc_List_Olist(_1711714), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1711714)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711714), tc_List_Olist(_1711714), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1711714)))), _1711716)))], (13187 ^ _779854) ^ [_1012489, _1012491] : [class_Orderings_Olinorder(_1012489), -(c_Big__Operators_Olinorder__class_OMax(_1012489, hAPP(hAPP(c_Set_Oinsert(_1012489), _1012491), c_Orderings_Obot__class_Obot(tc_fun(_1012489, tc_HOL_Obool)))) = _1012491)], (36848 ^ _779854) ^ [_1469450, _1469452, _1469454, _1469456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1469450), _1469452)), 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)), _1469454), _1469450)), 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)), _1469456), _1469452)), 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)), _1469454), _1469456)), _1469452)), c_FunDef_Omax__weak)))], (620 ^ _779854) ^ [_789190, _789192] : [-(c_List_Onat__list(_789190)), _789192 = _789190, c_List_Onat__list(_789192)], (28557 ^ _779854) ^ [] : [-(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)))], (12014 ^ _779854) ^ [_988826, _988828, _988830, _988832] : [hBOOL(hAPP(hAPP(c_member(_988826), _988828), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988826, tc_HOL_Obool)), _988830), _988832))), -(hBOOL(hAPP(hAPP(c_member(_988826), _988828), _988830))), -(hBOOL(hAPP(hAPP(c_member(_988826), _988828), _988832)))], (42512 ^ _779854) ^ [_1622599, _1622601, _1622603] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622599)), _1622601), c_List_Olists(_1622599, c_Wellfounded_Oacc(_1622599, _1622603)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622599)), _1622601), c_Wellfounded_Oacc(tc_List_Olist(_1622599), c_List_Olistrel1(_1622599, _1622603)))))], (9282 ^ _779854) ^ [_934818, _934820, _934822] : [class_Orderings_Oorder(_934818), 9285 ^ _779854 : [(9292 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934818), _934820), _934822))), -(c_Orderings_Obot__class_Obot(tc_fun(_934818, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_934818, _934820), _934822))], (9286 ^ _779854) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_934818, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_934818, _934820), _934822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934818), _934820), _934822))]]], (11656 ^ _779854) ^ [_981968, _981970] : [-(hBOOL(hAPP(hAPP(c_member(_981968), _981970), c_Orderings_Otop__class_Otop(tc_fun(_981968, tc_HOL_Obool)))))], (36750 ^ _779854) ^ [_1467425, _1467427, _1467429, _1467431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1467425), _1467427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1467429), _1467431)), -(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), _1467425), _1467429)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1467427), _1467431))), c_FunDef_Opair__less)))], (31041 ^ _779854) ^ [_1340045] : [_1340045 = c_Int_OMin, -(c_Int_OBit1(_1340045) = c_Int_OMin)], (17909 ^ _779854) ^ [_1104027, _1104029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104027)), hAPP(c_Nat_OSuc, _1104029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1104027), _1104029)))], (32976 ^ _779854) ^ [_1376306, _1376308, _1376310, _1376312, _1376314, _1376316] : [hBOOL(hAPP(hAPP(c_member(_1376306), _1376308), _1376310)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376306, tc_fun(_1376312, tc_HOL_Obool)), _1376310), hAPP(hAPP(c_COMBB(tc_fun(_1376312, tc_HOL_Obool), tc_fun(_1376312, tc_HOL_Obool), _1376306), hAPP(c_Set_Oinsert(_1376312), _1376314)), _1376316)) = hAPP(hAPP(c_Set_Oinsert(_1376312), _1376314), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376306, tc_fun(_1376312, tc_HOL_Obool)), _1376310), _1376316)))], (34127 ^ _779854) ^ [_1411203, _1411205, _1411207, _1411209] : [-(hAPP(c_Set_Oimage(_1411203, _1411205, _1411207), _1411209) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411203, tc_fun(_1411205, tc_HOL_Obool)), _1411209), hAPP(hAPP(c_COMBC(_1411203, tc_fun(_1411205, tc_HOL_Obool), tc_fun(_1411205, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1411205, tc_fun(tc_fun(_1411205, tc_HOL_Obool), tc_fun(_1411205, tc_HOL_Obool)), _1411203), c_Set_Oinsert(_1411205)), _1411207)), c_Orderings_Obot__class_Obot(tc_fun(_1411205, tc_HOL_Obool)))))], (51158 ^ _779854) ^ [_1814132, _1814134, _1814136, _1814138, _1814140] : [hBOOL(hAPP(hAPP(c_member(_1814132), _1814134), _1814136)), -(hAPP(c_Quotient_OBabs(_1814132, _1814138, _1814136, _1814140), _1814134) = hAPP(_1814140, _1814134))], (15060 ^ _779854) ^ [_1047569, _1047571, _1047573, _1047575] : [class_Groups_Oab__semigroup__add(_1047569), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047569), _1047571), _1047573)), _1047575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047569), _1047571), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047569), _1047573), _1047575)))], (44027 ^ _779854) ^ [_1658231, _1658233, _1658235, _1658237] : [-(hAPP(hAPP(c_List_Onth(_1658231), hAPP(hAPP(c_List_Oappend(_1658231), _1658233), hAPP(hAPP(c_List_Olist_OCons(_1658231), _1658235), _1658237))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658231)), _1658233)) = _1658235)], (272 ^ _779854) ^ [_784088, _784090] : [-(class_Fields_Ofield(_784088)), _784090 = _784088, class_Fields_Ofield(_784090)], (18229 ^ _779854) ^ [_1109633, _1109635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1109633)), _1109635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109633), _1109635)))], (7606 ^ _779854) ^ [_905762, _905764, _905766] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905762, tc_HOL_Obool)), _905764), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905762, tc_HOL_Obool)), _905764), _905766))))], (51859 ^ _779854) ^ [_1828901, _1828903, _1828905] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828901), _1828903)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828903), _1828901))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828903), _1828905)), 51870 ^ _779854 : [(51873 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828905), _1828901))], (51871 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828901), _1828905)))]]], (15990 ^ _779854) ^ [_1067028, _1067030, _1067032, _1067034, _1067036] : [class_Rings_Ocomm__semiring__1(_1067028), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067028), _1067030), _1067032)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067028), _1067034), _1067036)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067028), _1067034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067028), _1067030), _1067032)), _1067036)))], (33274 ^ _779854) ^ [_1383841, _1383843, _1383845, _1383847, _1383849, _1383851, _1383853] : [hAPP(c_Fun_Ocomp(_1383841, _1383843, _1383845, _1383847), _1383849) = _1383851, -(hAPP(_1383847, hAPP(_1383849, _1383853)) = hAPP(_1383851, _1383853))], (52423 ^ _779854) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (49727 ^ _779854) ^ [_1783935, _1783937, _1783939, _1783941] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1783935, tc_fun(_1783937, tc_HOL_Obool)), _1783939), _1783941) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1783937, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1783937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1783935, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1783937, tc_HOL_Obool)), c_HOL_OEx(_1783935)), hAPP(hAPP(c_COMBB(tc_fun(_1783935, tc_HOL_Obool), tc_fun(_1783935, tc_HOL_Obool), tc_fun(_1783937, tc_HOL_Obool)), hAPP(c_COMBS(_1783935, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1783935), c_fconj), hAPP(hAPP(c_COMBC(_1783935, tc_fun(_1783935, tc_HOL_Obool), tc_HOL_Obool), c_member(_1783935)), _1783939)))), hAPP(hAPP(c_COMBC(tc_fun(_1783937, tc_HOL_Obool), tc_fun(_1783935, tc_fun(_1783937, tc_HOL_Obool)), tc_fun(_1783935, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1783937, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1783935, tc_fun(_1783937, tc_HOL_Obool)), tc_fun(_1783935, tc_HOL_Obool)), tc_fun(_1783937, tc_HOL_Obool)), c_COMBB(tc_fun(_1783937, tc_HOL_Obool), tc_HOL_Obool, _1783935)), c_fequal)), _1783941))))))], (24178 ^ _779854) ^ [_1218285, _1218287, _1218289, _1218291] : [class_Rings_Olinordered__semidom(_1218285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218285), hAPP(hAPP(c_Power_Opower__class_Opower(_1218285), _1218287), _1218289)), hAPP(hAPP(c_Power_Opower__class_Opower(_1218285), _1218291), _1218289))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218285), c_Groups_Ozero__class_Ozero(_1218285)), _1218291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218285), _1218287), _1218291)))], (31296 ^ _779854) ^ [_1344036, _1344038, _1344040] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1344036, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344038), _1344040)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344038), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344036), _1344038), _1344040))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1344036, _1344038)))], (25237 ^ _779854) ^ [_1238387, _1238389, _1238391, _1238393] : [class_Fields_Olinordered__field__inverse__zero(_1238387), class_Int_Onumber(_1238387), 25244 ^ _779854 : [(25245 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238387), _1238391), _1238393))), 25248 ^ _779854 : [(25255 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), c_Groups_Ozero__class_Ozero(_1238387)), _1238393))), 25258 ^ _779854 : [(25265 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), _1238393), c_Groups_Ozero__class_Ozero(_1238387)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), c_Groups_Ozero__class_Ozero(_1238387))))], (25259 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), _1238393), c_Groups_Ozero__class_Ozero(_1238387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), _1238391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), _1238393))))]]], (25249 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), c_Groups_Ozero__class_Ozero(_1238387)), _1238393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), _1238393)), _1238391)))]]], (25271 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238387), _1238391), _1238393)))), 25274 ^ _779854 : [(25277 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), _1238393)), _1238391))], (25275 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), c_Groups_Ozero__class_Ozero(_1238387)), _1238393)))]], 25278 ^ _779854 : [(25281 ^ _779854) ^ [] : [25282 ^ _779854 : [(25285 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), _1238391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), _1238393)))], (25283 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), _1238393), c_Groups_Ozero__class_Ozero(_1238387))))]], 25286 ^ _779854 : [(25289 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238387), hAPP(c_Int_Onumber__class_Onumber__of(_1238387), _1238389)), c_Groups_Ozero__class_Ozero(_1238387)))], (25287 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), _1238393), c_Groups_Ozero__class_Ozero(_1238387)))]]], (25279 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238387), c_Groups_Ozero__class_Ozero(_1238387)), _1238393))]]]]], (41330 ^ _779854) ^ [_1589794, _1589796, _1589798, _1589800] : [-(c_Wellfounded_Owf(_1589794, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1589794, _1589794)), hAPP(hAPP(c_Product__Type_OPair(_1589794, _1589794), _1589796), _1589798)), _1589800))), c_Wellfounded_Owf(_1589794, _1589800), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589794, _1589794)), hAPP(hAPP(c_Product__Type_OPair(_1589794, _1589794), _1589798), _1589796)), c_Transitive__Closure_Ortrancl(_1589794, _1589800))))], (28384 ^ _779854) ^ [_1293019, _1293021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1293019), _1293021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293019)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293021))))], (34695 ^ _779854) ^ [_1424491, _1424493] : [34696 ^ _779854 : [(34699 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424493), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34697 ^ _779854) ^ [] : [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), _1424491), _1424493)))]], -(c_Divides_OnegDivAlg(_1424491, _1424493) = 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), _1424491), _1424493)))], (7634 ^ _779854) ^ [_906358, _906360, _906362, _906364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906358, tc_HOL_Obool)), _906360), _906362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906358, tc_HOL_Obool)), _906364), _906362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906358, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906358, tc_HOL_Obool)), _906360), _906364)), _906362)))], (13009 ^ _779854) ^ [_1008763, _1008765, _1008767] : [class_Lattices_Olattice(_1008763), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008763), _1008765)), hBOOL(hAPP(hAPP(c_member(_1008763), _1008767), _1008765)), 13020 ^ _779854 : [(13027 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008763, tc_HOL_Obool)), _1008765), hAPP(hAPP(c_Set_Oinsert(_1008763), _1008767), c_Orderings_Obot__class_Obot(tc_fun(_1008763, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1008763, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1008763, _1008765) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1008763), _1008767), c_Big__Operators_Olattice__class_OInf__fin(_1008763, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008763, tc_HOL_Obool)), _1008765), hAPP(hAPP(c_Set_Oinsert(_1008763), _1008767), c_Orderings_Obot__class_Obot(tc_fun(_1008763, tc_HOL_Obool)))))))], (13021 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008763, tc_HOL_Obool)), _1008765), hAPP(hAPP(c_Set_Oinsert(_1008763), _1008767), c_Orderings_Obot__class_Obot(tc_fun(_1008763, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1008763, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1008763, _1008765) = _1008767)]]], (44586 ^ _779854) ^ [_1671746, _1671748] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671746)), hAPP(c_List_Otl(_1671746), _1671748)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671746)), _1671748)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (17066 ^ _779854) ^ [_1087794, _1087796, _1087798, _1087800, _1087802] : [class_Groups_Ocomm__monoid__mult(_1087794), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087796), _1087798)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1087796, _1087794), _1087800), hAPP(hAPP(c_Set_Oinsert(_1087796), _1087802), _1087798)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087794), hAPP(_1087800, _1087802)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1087796, _1087794), _1087800), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1087796, tc_HOL_Obool)), _1087798), hAPP(hAPP(c_Set_Oinsert(_1087796), _1087802), c_Orderings_Obot__class_Obot(tc_fun(_1087796, tc_HOL_Obool)))))))], (2716 ^ _779854) ^ [_820203, _820205, _820207, _820209, _820211, _820213, _820215, _820217] : [-(c_Recdef_Osame__fst(_820217, _820213, _820209, _820205) = c_Recdef_Osame__fst(_820215, _820211, _820207, _820203)), _820217 = _820215, _820213 = _820211, _820209 = _820207, _820205 = _820203], (20253 ^ _779854) ^ [_1144677, _1144679] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1144677), _1144679) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20258 ^ _779854 : [(20261 ^ _779854) ^ [] : [-(_1144679 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20259 ^ _779854) ^ [] : [-(_1144677 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20262 ^ _779854 : [(20265 ^ _779854) ^ [] : [-(_1144679 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20263 ^ _779854) ^ [] : [-(_1144677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (33529 ^ _779854) ^ [_1391611, _1391613, _1391615, _1391617] : [_1391615 = _1391617, -(hAPP(hAPP(c_COMBC(_1391611, tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_fun(_1391613, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391613, tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_fun(_1391613, tc_HOL_Obool)), _1391611), c_COMBC(_1391613, tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391613, tc_prod(_1391611, _1391613)), tc_fun(_1391613, tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool)), _1391611), hAPP(c_COMBB(tc_prod(_1391611, _1391613), tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool), _1391613), c_member(tc_prod(_1391611, _1391613)))), c_Product__Type_OPair(_1391611, _1391613)))), _1391615) = hAPP(hAPP(c_COMBC(_1391611, tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_fun(_1391613, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391613, tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_fun(_1391613, tc_HOL_Obool)), _1391611), c_COMBC(_1391613, tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391613, tc_prod(_1391611, _1391613)), tc_fun(_1391613, tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool)), _1391611), hAPP(c_COMBB(tc_prod(_1391611, _1391613), tc_fun(tc_fun(tc_prod(_1391611, _1391613), tc_HOL_Obool), tc_HOL_Obool), _1391613), c_member(tc_prod(_1391611, _1391613)))), c_Product__Type_OPair(_1391611, _1391613)))), _1391617))], (15978 ^ _779854) ^ [_1066708, _1066710, _1066712, _1066714] : [class_Rings_Ocomm__semiring__1(_1066708), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066708), _1066710), _1066712)), _1066714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066708), _1066710), _1066714)), _1066712))], (1250 ^ _779854) ^ [_798431, _798433] : [-(class_Rings_Oordered__ring(_798431)), _798433 = _798431, class_Rings_Oordered__ring(_798433)], (46455 ^ _779854) ^ [_1713217, _1713219, _1713221, _1713223, _1713225] : [-(hAPP(c_List_Ofilter(_1713217, _1713219), hAPP(hAPP(c_List_Omap(_1713221, _1713217), _1713223), _1713225)) = hAPP(hAPP(c_List_Omap(_1713221, _1713217), _1713223), hAPP(c_List_Ofilter(_1713221, hAPP(c_Fun_Ocomp(_1713217, tc_HOL_Obool, _1713221, _1713219), _1713223)), _1713225)))], (12214 ^ _779854) ^ [_992679, _992681, _992683, _992685, _992687, _992689] : [-(hBOOL(hAPP(hAPP(c_member(_992679), _992681), _992683))), -(hAPP(c_Fun_Ooverride__on(_992679, _992685, _992687, _992689, _992683), _992681) = hAPP(_992687, _992681))], (52385 ^ _779854) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (40001 ^ _779854) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (52221 ^ _779854) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (24308 ^ _779854) ^ [_1220675, _1220677, _1220679, _1220681] : [class_Rings_Olinordered__semidom(_1220675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220677), _1220679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220675), c_Groups_Oone__class_Oone(_1220675)), _1220681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220675), hAPP(hAPP(c_Power_Opower__class_Opower(_1220675), _1220681), _1220677)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220675), _1220681), _1220679))))], (20349 ^ _779854) ^ [_1146074, _1146076, _1146078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146074), _1146076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146078), _1146074)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146078), _1146076))))], (28270 ^ _779854) ^ [_1291060, _1291062] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1291060), _1291062)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291060)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291062)))], (5679 ^ _779854) ^ [_869549, _869551, _869553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_869549), tc_HOL_Obool)), _869551), _869553)), -(c_Hoare__Mirabelle_Ohoare__derivs(_869549, _869553, _869551))], (2312 ^ _779854) ^ [_813761, _813763, _813765, _813767] : [-(c_Divides_Opdivmod(_813767, _813763) = c_Divides_Opdivmod(_813765, _813761)), _813767 = _813765, _813763 = _813761], (44021 ^ _779854) ^ [_1658167, _1658169, _1658171] : [-(_1658167 = c_List_Olist_ONil(_1658169)), -(c_List_Obutlast(_1658169, hAPP(hAPP(c_List_Oappend(_1658169), _1658171), _1658167)) = hAPP(hAPP(c_List_Oappend(_1658169), _1658171), c_List_Obutlast(_1658169, _1658167)))], (52103 ^ _779854) ^ [_1832711, _1832713] : [class_Lattices_Odistrib__lattice(_1832711), -(class_Lattices_Odistrib__lattice(tc_fun(_1832713, _1832711)))], (31609 ^ _779854) ^ [_1349367, _1349369] : [c_Nat__Transfer_Ois__nat(_1349367), c_Nat__Transfer_Ois__nat(_1349369), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1349367, _1349369)))], (4406 ^ _779854) ^ [_846930, _846932] : [_846932 = _846930, -(c_Lazy__Sequence_Oempty(_846932) = c_Lazy__Sequence_Oempty(_846930))], (47440 ^ _779854) ^ [_1733684, _1733686] : [-(hAPP(c_List_Orev(_1733684), hAPP(c_List_Orev(_1733684), _1733686)) = _1733686)], (49657 ^ _779854) ^ [_1782551, _1782553, _1782555] : [c_Relation_Otrans(_1782551, _1782553), c_Relation_Otrans(_1782551, _1782555), -(c_Relation_Otrans(_1782551, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1782551, _1782551), tc_HOL_Obool)), _1782553), _1782555)))], (49052 ^ _779854) ^ [_1768857, _1768859, _1768861] : [c_List_Olist_ONil(_1768857) = c_List_Oreplicate(_1768857, _1768859, _1768861), -(_1768859 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39538 ^ _779854) ^ [_1545744, _1545746, _1545748, _1545750] : [hBOOL(hAPP(hAPP(c_member(_1545744), _1545746), hAPP(c_Relation_ORange(_1545748, _1545744), _1545750))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545748, _1545744)), hAPP(hAPP(c_Product__Type_OPair(_1545748, _1545744), 39541 ^ [_1545744, _1545746, _1545748, _1545750]), _1545746)), _1545750)))], (16742 ^ _779854) ^ [_1081474, _1081476, _1081478] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1081474), _1081476)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1081474, tc_HOL_Obool)), _1081476), _1081478) = hAPP(hAPP(c_Finite__Set_Ofold(_1081474, tc_fun(_1081474, tc_HOL_Obool), c_Set_Oinsert(_1081474)), _1081478), _1081476))], (18012 ^ _779854) ^ [_1105771, _1105773, _1105775] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105771)), _1105773)), hAPP(c_Nat_OSuc, _1105775)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1105771), _1105773)), _1105775))], (14542 ^ _779854) ^ [_1037476, _1037478, _1037480, _1037482] : [_1037476 = c_Finite__Set_Ofold1(_1037478, _1037480), -(hAPP(_1037476, hAPP(hAPP(c_Set_Oinsert(_1037478), _1037482), c_Orderings_Obot__class_Obot(tc_fun(_1037478, tc_HOL_Obool)))) = _1037482)], (35598 ^ _779854) ^ [_1443009, _1443011, _1443013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443009, tc_fun(_1443009, tc_HOL_Obool))), _1443011), _1443013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443009, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1443009, _1443013)), c_Wellfounded_Oaccp(_1443009, _1443011))))], (39325 ^ _779854) ^ [_1539059, _1539061] : [-(c_Product__Type_Oapsnd(_1539059, _1539059, _1539061, c_Fun_Oid(_1539059)) = c_Fun_Oid(tc_prod(_1539061, _1539059)))], (36325 ^ _779854) ^ [_1457764, _1457766, _1457768] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1457764, _1457766), _1457768))), _1457764 = 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), _1457768)), _1457766)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457768)), 36332 ^ _779854 : [(36335 ^ _779854) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1457768) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36333 ^ _779854) ^ [] : [-(_1457766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 36336 ^ _779854 : [(36339 ^ _779854) ^ [] : [36340 ^ _779854 : [(36343 ^ _779854) ^ [] : [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), _1457768))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457768)), _1457766))], (36341 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457766)))]], 36348 ^ _779854 : [(36351 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1457766), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457768))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1457768)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36349 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457766))]]], (36337 ^ _779854) ^ [] : [_1457766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (35364 ^ _779854) ^ [_1438692, _1438694] : [_1438692 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1438694, _1438692) = 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), _1438694)))], (27457 ^ _779854) ^ [_1277299, _1277301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277299)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1277299), _1277301)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1277299)), hAPP(c_Int_Onat, _1277301)))], (47380 ^ _779854) ^ [_1732425, _1732427, _1732429, _1732431] : [-(hAPP(c_List_Orev(_1732425), hAPP(hAPP(c_List_Omap(_1732427, _1732425), _1732429), _1732431)) = hAPP(hAPP(c_List_Omap(_1732427, _1732425), _1732429), hAPP(c_List_Orev(_1732427), _1732431)))], (50898 ^ _779854) ^ [_1809126, _1809128, _1809130, _1809132, _1809134] : [c_Fun_Obij__betw(_1809126, _1809128, _1809130, _1809132, _1809134), -(hAPP(c_Finite__Set_Ocard(_1809126), _1809132) = hAPP(c_Finite__Set_Ocard(_1809128), _1809134))], (40824 ^ _779854) ^ [_1576669, _1576671, _1576673, _1576675, _1576677, _1576679] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576669, _1576671)), hAPP(hAPP(c_Product__Type_OPair(_1576669, _1576671), _1576673), _1576675)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1576669, _1576671), tc_HOL_Obool), _1576677))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1576669, _1576671), tc_HOL_Obool), tc_fun(tc_prod(_1576669, _1576671), tc_HOL_Obool), _1576677), 40835 ^ _779854 : [(40838 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1576679, 40833 ^ [_1576669, _1576671, _1576673, _1576675, _1576677, _1576679]), 40834 ^ [_1576669, _1576671, _1576673, _1576675, _1576677, _1576679]))], (40836 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576669, _1576671)), hAPP(hAPP(c_Product__Type_OPair(_1576669, _1576671), 40833 ^ [_1576669, _1576671, _1576673, _1576675, _1576677, _1576679]), 40834 ^ [_1576669, _1576671, _1576673, _1576675, _1576677, _1576679])), hAPP(_1576677, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1576669, _1576671), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1576669, _1576671), tc_HOL_Obool), _1576677)), hAPP(c_Set_OCollect(tc_prod(_1576669, _1576671)), hAPP(c_Product__Type_Oprod_Oprod__case(_1576669, _1576671, tc_HOL_Obool), _1576679)))))))]], -(hBOOL(hAPP(hAPP(_1576679, _1576673), _1576675)))], (33030 ^ _779854) ^ [_1377838, _1377840, _1377842, _1377844, _1377846] : [_1377838 = c_Orderings_Obot__class_Obot(tc_fun(_1377840, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377840, tc_fun(_1377842, tc_HOL_Obool)), _1377838), hAPP(hAPP(c_COMBC(_1377840, tc_fun(_1377842, tc_HOL_Obool), tc_fun(_1377842, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377842, tc_HOL_Obool), tc_fun(tc_fun(_1377842, tc_HOL_Obool), tc_fun(_1377842, tc_HOL_Obool)), _1377840), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377842, tc_HOL_Obool))), _1377844)), _1377846)) = c_Orderings_Otop__class_Otop(tc_fun(_1377842, tc_HOL_Obool)))], (50868 ^ _779854) ^ [_1808618, _1808620, _1808622, _1808624, _1808626] : [c_Fun_Obij__betw(_1808618, _1808620, _1808622, _1808624, _1808626), 50871 ^ _779854 : [(50874 ^ _779854) ^ [] : [-(hAPP(c_Set_Oimage(_1808618, _1808620, _1808622), _1808624) = _1808626)], (50872 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_1808618, _1808620, _1808622, _1808624))]]], (36157 ^ _779854) ^ [_1454421, _1454423, _1454425, _1454427] : [_1454421 = _1454423, 36160 ^ _779854 : [(36163 ^ _779854) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1454425, _1454427), _1454421) = hAPP(c_Product__Type_Osnd(_1454425, _1454427), _1454423))], (36161 ^ _779854) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1454425, _1454427), _1454421) = hAPP(c_Product__Type_Ofst(_1454425, _1454427), _1454423))]]], (44115 ^ _779854) ^ [_1660567, _1660569, _1660571, _1660573] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660567), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660569)), _1660571)))), -(hAPP(hAPP(c_List_Onth(_1660569), hAPP(hAPP(c_List_Oappend(_1660569), _1660571), _1660573)), _1660567) = hAPP(hAPP(c_List_Onth(_1660569), _1660573), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1660567), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660569)), _1660571))))], (16850 ^ _779854) ^ [_1083637, _1083639, _1083641, _1083643, _1083645] : [class_Groups_Ocomm__monoid__mult(_1083637), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083639), _1083641)), -(hBOOL(hAPP(hAPP(c_member(_1083639), _1083643), _1083641))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083639, _1083637), _1083645), hAPP(hAPP(c_Set_Oinsert(_1083639), _1083643), _1083641)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083637), hAPP(_1083645, _1083643)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083639, _1083637), _1083645), _1083641)))], (31021 ^ _779854) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (46559 ^ _779854) ^ [_1715701, _1715703, _1715705, _1715707] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1715701)), c_List_Otranspose__rel(_1715701)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1715701)), hAPP(hAPP(c_List_Olist_OCons(_1715701), _1715703), _1715705)), _1715707))), -(c_List_Otranspose(_1715701, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1715701)), hAPP(hAPP(c_List_Olist_OCons(_1715701), _1715703), _1715705)), _1715707)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1715701)), hAPP(hAPP(c_List_Olist_OCons(_1715701), _1715703), c_List_Oconcat(_1715701, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715701), tc_List_Olist(_1715701)), c_List_Olist_Olist__case(tc_List_Olist(_1715701), _1715701, c_List_Olist_ONil(_1715701), hAPP(hAPP(c_COMBB(tc_List_Olist(_1715701), tc_fun(tc_List_Olist(_1715701), tc_List_Olist(_1715701)), _1715701), c_COMBK(tc_List_Olist(_1715701), tc_List_Olist(_1715701))), hAPP(hAPP(c_COMBC(_1715701, tc_List_Olist(_1715701), tc_List_Olist(_1715701)), c_List_Olist_OCons(_1715701)), c_List_Olist_ONil(_1715701))))), _1715707)))), c_List_Otranspose(_1715701, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1715701)), _1715705), c_List_Oconcat(tc_List_Olist(_1715701), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715701), tc_List_Olist(tc_List_Olist(_1715701))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1715701)), _1715701, c_List_Olist_ONil(tc_List_Olist(_1715701)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1715701), tc_List_Olist(tc_List_Olist(_1715701))), _1715701), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715701), tc_List_Olist(tc_List_Olist(_1715701)), tc_List_Olist(tc_List_Olist(_1715701))), c_List_Olist_OCons(tc_List_Olist(_1715701))), c_List_Olist_ONil(tc_List_Olist(_1715701)))))), _1715707))))))], (33673 ^ _779854) ^ [_1398698, _1398700, _1398702, _1398704, _1398706, _1398708] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398698, tc_fun(_1398700, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398702, _1398698, _1398704), _1398706)), _1398708) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398702, tc_fun(_1398700, tc_HOL_Obool)), _1398706), hAPP(hAPP(c_COMBB(_1398698, tc_fun(_1398700, tc_HOL_Obool), _1398702), _1398708), _1398704)))], (52599 ^ _779854) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (29523 ^ _779854) ^ [_1312355, _1312357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1312355), _1312357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1312355)), c_Int_OBit0(_1312357))))], (51673 ^ _779854) ^ [_1825739, _1825741, _1825743] : [class_Divides_Osemiring__div(_1825739), 51676 ^ _779854 : [(51683 ^ _779854) ^ [] : [c_Divides_Odiv__class_Omod(_1825739, _1825743, _1825741) = c_Groups_Ozero__class_Ozero(_1825739), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825739), _1825741), _1825743)))], (51677 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825739), _1825741), _1825743)), -(c_Divides_Odiv__class_Omod(_1825739, _1825743, _1825741) = c_Groups_Ozero__class_Ozero(_1825739))]]], (49717 ^ _779854) ^ [_1783739, _1783741, _1783743] : [-(c_List_Olist__ex(_1783739, _1783741, _1783743)), 49718 ^ _779854 : [(49719 ^ _779854) ^ [_1783796] : [hBOOL(hAPP(hAPP(c_member(_1783739), _1783796), hAPP(c_List_Oset(_1783739), _1783743))), hBOOL(hAPP(_1783741, _1783796))]]], (6761 ^ _779854) ^ [_888961, _888963, _888965, _888967] : [6762 ^ _779854 : [(6763 ^ _779854) ^ [_889071] : [hBOOL(hAPP(hAPP(c_member(_888961), _889071), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888961, tc_HOL_Obool)), _888963), _888965))), hBOOL(hAPP(_888967, _889071))]], 6771 ^ _779854 : [(6774 ^ _779854) ^ [] : [-(hBOOL(hAPP(_888967, 6770 ^ [_888961, _888963, _888965, _888967])))], (6772 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_888961), 6770 ^ [_888961, _888963, _888965, _888967]), _888963)))]], 6776 ^ _779854 : [(6779 ^ _779854) ^ [] : [-(hBOOL(hAPP(_888967, 6775 ^ [_888961, _888963, _888965, _888967])))], (6777 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_888961), 6775 ^ [_888961, _888963, _888965, _888967]), _888965)))]]], (32427 ^ _779854) ^ [_1363395] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1363395)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1363395)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36651 ^ _779854) ^ [_1465275, _1465277, _1465279, _1465281, _1465283, _1465285] : [c_Finite__Set_Ofolding__idem(_1465275, _1465277, _1465279, _1465281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465275), _1465283)), hBOOL(hAPP(hAPP(c_member(_1465275), _1465285), _1465283)), -(hAPP(c_Fun_Ocomp(_1465277, _1465277, _1465277, hAPP(_1465281, _1465283)), hAPP(_1465279, _1465285)) = hAPP(_1465281, _1465283))], (3268 ^ _779854) ^ [_828789, _828791, _828793, _828795, _828797, _828799] : [-(c_List_Olist_Olist__size(_828799, _828795, _828791) = c_List_Olist_Olist__size(_828797, _828793, _828789)), _828799 = _828797, _828795 = _828793, _828791 = _828789], (45442 ^ _779854) ^ [] : [-(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))], (13057 ^ _779854) ^ [_1009775, _1009777, _1009779] : [class_Orderings_Olinorder(_1009775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009775), _1009777)), hBOOL(hAPP(hAPP(c_member(_1009775), _1009779), _1009777)), 13068 ^ _779854 : [(13075 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009775, tc_HOL_Obool)), _1009777), hAPP(hAPP(c_Set_Oinsert(_1009775), _1009779), c_Orderings_Obot__class_Obot(tc_fun(_1009775, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1009775, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1009775, _1009777) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1009775), _1009779), c_Big__Operators_Olinorder__class_OMax(_1009775, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009775, tc_HOL_Obool)), _1009777), hAPP(hAPP(c_Set_Oinsert(_1009775), _1009779), c_Orderings_Obot__class_Obot(tc_fun(_1009775, tc_HOL_Obool)))))))], (13069 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009775, tc_HOL_Obool)), _1009777), hAPP(hAPP(c_Set_Oinsert(_1009775), _1009779), c_Orderings_Obot__class_Obot(tc_fun(_1009775, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1009775, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1009775, _1009777) = _1009779)]]], (47574 ^ _779854) ^ [_1736627, _1736629, _1736631] : [class_Orderings_Olinorder(_1736627), c_List_Olinorder__class_Osorted(_1736627, _1736629), -(c_List_Olinorder__class_Osorted(_1736627, c_List_OtakeWhile(_1736627, _1736631, _1736629)))], (28190 ^ _779854) ^ [_1289673] : [c_Int_OPls = c_Int_OBit1(_1289673)], (51747 ^ _779854) ^ [_1826985, _1826987] : [class_Rings_Ocomm__semiring__1(_1826985), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826985), c_Groups_Ozero__class_Ozero(_1826985)), _1826987)), -(_1826987 = c_Groups_Ozero__class_Ozero(_1826985))], (10799 ^ _779854) ^ [_964393, _964395, _964397, _964399] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964393, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964393, tc_HOL_Obool)), _964395), _964397)), _964399) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964393, tc_HOL_Obool)), _964395), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964393, tc_HOL_Obool)), _964397), _964399)))], (38264 ^ _779854) ^ [_1504976, _1504978, _1504980, _1504982, _1504984, _1504986] : [hBOOL(hAPP(hAPP(c_member(_1504976), _1504978), _1504980)), hBOOL(hAPP(hAPP(c_member(_1504982), _1504984), hAPP(_1504986, _1504978))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504976, _1504982)), hAPP(hAPP(c_Product__Type_OPair(_1504976, _1504982), _1504978), _1504984)), hAPP(hAPP(c_Product__Type_OSigma(_1504976, _1504982), _1504980), _1504986))))], (1340 ^ _779854) ^ [_799556, _799558] : [-(class_Rings_Oring(_799556)), _799558 = _799556, class_Rings_Oring(_799558)], (51023 ^ _779854) ^ [_1811417, _1811419] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1811417), _1811419)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1811417, 51026 ^ [_1811417, _1811419], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1811417), _1811419)), _1811419))], (38515 ^ _779854) ^ [_1512358, _1512360, _1512362, _1512364, _1512366, _1512368] : [class_Groups_Ocomm__monoid__mult(_1512358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512360), _1512362)), 38525 ^ _779854 : [(38528 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512364), hAPP(_1512366, 38524 ^ [_1512358, _1512360, _1512362, _1512364, _1512366, _1512368])))], (38526 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512360), 38524 ^ [_1512358, _1512360, _1512362, _1512364, _1512366, _1512368]), _1512362)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1512358, _1512360, c_Groups_Otimes__class_Otimes(_1512358)), hAPP(hAPP(c_COMBS(_1512360, tc_fun(_1512364, tc_HOL_Obool), _1512358), hAPP(hAPP(c_COMBC(_1512360, _1512358, tc_fun(tc_fun(_1512364, tc_HOL_Obool), _1512358)), hAPP(hAPP(c_COMBB(tc_fun(_1512364, _1512358), tc_fun(_1512358, tc_fun(tc_fun(_1512364, tc_HOL_Obool), _1512358)), _1512360), c_Finite__Set_Ofold__image(_1512358, _1512364, c_Groups_Otimes__class_Otimes(_1512358))), _1512368)), c_Groups_Oone__class_Oone(_1512358))), _1512366)), c_Groups_Oone__class_Oone(_1512358)), _1512362) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1512358, tc_prod(_1512360, _1512364), c_Groups_Otimes__class_Otimes(_1512358)), hAPP(c_Product__Type_Oprod_Oprod__case(_1512360, _1512364, _1512358), _1512368)), c_Groups_Oone__class_Oone(_1512358)), hAPP(hAPP(c_Product__Type_OSigma(_1512360, _1512364), _1512362), _1512366)))], (33473 ^ _779854) ^ [_1389775, _1389777, _1389779, _1389781, _1389783] : [hBOOL(hAPP(hAPP(c_member(_1389775), _1389777), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389779, tc_fun(_1389775, tc_HOL_Obool)), _1389781), _1389783))), 33477 ^ _779854 : [(33480 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389775), _1389777), hAPP(_1389783, 33476 ^ [_1389775, _1389777, _1389779, _1389781, _1389783]))))], (33478 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389779), 33476 ^ [_1389775, _1389777, _1389779, _1389781, _1389783]), _1389781)))]]], (29287 ^ _779854) ^ [_1308348, _1308350] : [c_Int_OBit1(_1308348) = c_Int_OBit0(_1308350)], (28681 ^ _779854) ^ [_1298210, _1298212] : [class_Int_Onumber__ring(_1298210), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298210), hAPP(c_Int_Onumber__class_Onumber__of(_1298210), c_Int_OBit1(c_Int_OPls))), _1298212) = _1298212)], (36912 ^ _779854) ^ [_1471048, _1471050, _1471052, _1471054] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1471048, tc_HOL_Obool), tc_fun(_1471048, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1471048, tc_HOL_Obool), tc_fun(_1471048, tc_HOL_Obool)), _1471052), _1471054)), c_Wellfounded_Omax__ext(_1471048, _1471050))), -(c_Wellfounded_Omax__extp(_1471048, hAPP(hAPP(c_COMBC(_1471048, tc_fun(tc_prod(_1471048, _1471048), tc_HOL_Obool), tc_fun(_1471048, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471048, tc_fun(tc_fun(tc_prod(_1471048, _1471048), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471048, _1471048), tc_HOL_Obool), tc_fun(_1471048, tc_HOL_Obool)), _1471048), c_COMBC(_1471048, tc_fun(tc_prod(_1471048, _1471048), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471048, tc_prod(_1471048, _1471048)), tc_fun(_1471048, tc_fun(tc_fun(tc_prod(_1471048, _1471048), tc_HOL_Obool), tc_HOL_Obool)), _1471048), hAPP(c_COMBB(tc_prod(_1471048, _1471048), tc_fun(tc_fun(tc_prod(_1471048, _1471048), tc_HOL_Obool), tc_HOL_Obool), _1471048), c_member(tc_prod(_1471048, _1471048)))), c_Product__Type_OPair(_1471048, _1471048)))), _1471050), _1471052, _1471054))], (7535 ^ _779854) ^ [_904188, _904190] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904188, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_904188, tc_HOL_Obool))), _904190) = _904190)], (30385 ^ _779854) ^ [_1328557, _1328559] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328557, _1328559) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1328557 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1328559), 30388 ^ [_1328557, _1328559]))], (1180 ^ _779854) ^ [_797556, _797558] : [-(class_Rings_Oring__no__zero__divisors(_797556)), _797558 = _797556, class_Rings_Oring__no__zero__divisors(_797558)], (16385 ^ _779854) ^ [_1074660, _1074662, _1074664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074660), _1074662)), _1074664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074664), _1074662))))], (36273 ^ _779854) ^ [_1456763, _1456765, _1456767, _1456769, _1456771] : [hBOOL(hAPP(hAPP(_1456763, _1456765), _1456767)), -(hBOOL(hAPP(hAPP(_1456763, hAPP(c_Product__Type_Osnd(_1456769, _1456771), hAPP(hAPP(c_Product__Type_OPair(_1456769, _1456771), _1456767), _1456765))), hAPP(c_Product__Type_Ofst(_1456769, _1456771), hAPP(hAPP(c_Product__Type_OPair(_1456769, _1456771), _1456767), _1456765)))))], (42996 ^ _779854) ^ [_1636205] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1636205)), -(c_List_Onat__list(_1636205))], (52021 ^ _779854) ^ [_1831523, _1831525, _1831527] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831523), _1831525)), _1831525 = _1831527, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831523), _1831527)))], (27393 ^ _779854) ^ [_1276216, _1276218] : [class_Int_Onumber__ring(_1276216), 27396 ^ _779854 : [(27403 ^ _779854) ^ [] : [c_Int_Oiszero(_1276216, hAPP(c_Int_Onumber__class_Onumber__of(_1276216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1276218), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1276216), _1276218) = c_Groups_Ozero__class_Ozero(_1276216))], (27397 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1276216), _1276218) = c_Groups_Ozero__class_Ozero(_1276216), -(c_Int_Oiszero(_1276216, hAPP(c_Int_Onumber__class_Onumber__of(_1276216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1276218), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (38326 ^ _779854) ^ [_1506703, _1506705, _1506707] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1506703, _1506705), _1506707), hAPP(c_COMBK(tc_fun(_1506705, tc_HOL_Obool), _1506703), c_Orderings_Obot__class_Obot(tc_fun(_1506705, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1506703, _1506705), tc_HOL_Obool)))], (41579 ^ _779854) ^ [_1596126, _1596128, _1596130] : [c_Relation_Ototal__on(_1596126, _1596128, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1596126, _1596126), tc_HOL_Obool)), _1596130), c_Relation_OId(_1596126))), -(c_Relation_Ototal__on(_1596126, _1596128, _1596130))], (24957 ^ _779854) ^ [_1232907, _1232909, _1232911, _1232913] : [class_Fields_Olinordered__field__inverse__zero(_1232907), class_Int_Onumber(_1232907), 24964 ^ _779854 : [(24965 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232907), _1232909), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911))), _1232913)), 24968 ^ _779854 : [(24975 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), c_Groups_Ozero__class_Ozero(_1232907)), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911)))), 24978 ^ _779854 : [(24985 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911)), c_Groups_Ozero__class_Ozero(_1232907)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), c_Groups_Ozero__class_Ozero(_1232907)), _1232913)))], (24979 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911)), c_Groups_Ozero__class_Ozero(_1232907))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232907), _1232913), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911))), _1232909)))]]], (24969 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), c_Groups_Ozero__class_Ozero(_1232907)), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), _1232909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232907), _1232913), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911)))))]]], (24991 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232907), _1232909), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911))), _1232913))), 24994 ^ _779854 : [(24997 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), _1232909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232907), _1232913), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911))))], (24995 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), c_Groups_Ozero__class_Ozero(_1232907)), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911))))]], 24998 ^ _779854 : [(25001 ^ _779854) ^ [] : [25002 ^ _779854 : [(25005 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232907), _1232913), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911))), _1232909))], (25003 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911)), c_Groups_Ozero__class_Ozero(_1232907))))]], 25006 ^ _779854 : [(25009 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), c_Groups_Ozero__class_Ozero(_1232907)), _1232913))], (25007 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911)), c_Groups_Ozero__class_Ozero(_1232907)))]]], (24999 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232907), c_Groups_Ozero__class_Ozero(_1232907)), hAPP(c_Int_Onumber__class_Onumber__of(_1232907), _1232911)))]]]]], (32003 ^ _779854) ^ [_1355589, _1355591, _1355593] : [class_Fields_Olinordered__field__inverse__zero(_1355589), -(hAPP(c_Groups_Oabs__class_Oabs(_1355589), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355589), _1355591), _1355593)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355589), hAPP(c_Groups_Oabs__class_Oabs(_1355589), _1355591)), hAPP(c_Groups_Oabs__class_Oabs(_1355589), _1355593)))], (41184 ^ _779854) ^ [_1586463, _1586465, _1586467] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1586463, _1586465, _1586465), _1586467), c_Relation_OId(_1586465)) = _1586467)], (29339 ^ _779854) ^ [_1309211] : [c_Int_OPls = c_Int_OBit0(_1309211), -(c_Int_OPls = _1309211)], (7792 ^ _779854) ^ [_909728, _909730, _909732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909728, tc_HOL_Obool)), _909730), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_909728, tc_HOL_Obool)), _909732))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909728, tc_HOL_Obool)), _909730), _909732) = c_Orderings_Obot__class_Obot(tc_fun(_909728, tc_HOL_Obool)))], (52541 ^ _779854) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (28633 ^ _779854) ^ [_1297332, _1297334, _1297336] : [class_Rings_Osemiring__1(_1297332), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1297332), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1297334), _1297336)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1297332), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1297332), _1297334)), _1297336))], (7840 ^ _779854) ^ [_910730, _910732, _910734, _910736] : [class_Orderings_Oorder(_910730), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_910730, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_910730, _910732, _910734)), c_SetInterval_Oord__class_OgreaterThanAtMost(_910730, _910734, _910736)) = c_Orderings_Obot__class_Obot(tc_fun(_910730, tc_HOL_Obool)))], (16650 ^ _779854) ^ [_1080102, _1080104] : [-(_1080102 = _1080104), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080102), _1080104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080104), _1080102)))], (24795 ^ _779854) ^ [_1230295, _1230297] : [class_Int_Onumber__ring(_1230295), -(hBOOL(hAPP(hAPP(c_member(_1230295), hAPP(c_Int_Onumber__class_Onumber__of(_1230295), _1230297)), c_Int_Oring__1__class_OInts(_1230295))))], (19643 ^ _779854) ^ [_1134125, _1134127, _1134129] : [class_Rings_Olinordered__semiring__strict(_1134125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134125), c_Groups_Ozero__class_Ozero(_1134125)), _1134127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134125), _1134129), c_Groups_Ozero__class_Ozero(_1134125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134125), _1134127), _1134129)), c_Groups_Ozero__class_Ozero(_1134125))))], (30855 ^ _779854) ^ [_1336869, _1336871, _1336873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336869)), 30858 ^ _779854 : [(30859 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1336871, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336873), _1336869)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336873, _1336869))), 30862 ^ _779854 : [(30863 ^ _779854) ^ [_1337070, _1337072] : [-(hBOOL(hAPP(hAPP(_1336871, _1337072), _1337070))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337070), _1336869)), _1336873 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1336869), _1337072)), _1337070)]]], (30877 ^ _779854) ^ [] : [30880 ^ _779854 : [(30883 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 30879 ^ [_1336869, _1336871, _1336873]), _1336869)))], (30885 ^ _779854) ^ [] : [-(_1336873 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1336869), 30878 ^ [_1336869, _1336871, _1336873])), 30879 ^ [_1336869, _1336871, _1336873]))], (30887 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1336871, 30878 ^ [_1336869, _1336871, _1336873]), 30879 ^ [_1336869, _1336871, _1336873]))], (30881 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30879 ^ [_1336869, _1336871, _1336873])))]], -(hBOOL(hAPP(hAPP(_1336871, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336873), _1336869)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336873, _1336869))))]]], (52581 ^ _779854) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (29295 ^ _779854) ^ [_1308477, _1308479] : [_1308477 = _1308479, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308477) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308479))], (44723 ^ _779854) ^ [_1674641, _1674643, _1674645, _1674647] : [class_Complete__Lattice_Ocomplete__lattice(_1674641), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1674643, _1674641), hAPP(c_List_Oset(_1674643), _1674645)), _1674647) = hAPP(c_List_Ofoldl(_1674641, _1674643, hAPP(c_COMBC(_1674643, _1674641, _1674641), hAPP(hAPP(c_COMBB(_1674641, tc_fun(_1674641, _1674641), _1674643), c_Lattices_Osemilattice__sup__class_Osup(_1674641)), _1674647)), c_Orderings_Obot__class_Obot(_1674641)), _1674645))], (6859 ^ _779854) ^ [_891142, _891144, _891146, _891148] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_891142, tc_HOL_Obool)), _891144), _891146), _891148)), -(hBOOL(hAPP(_891146, _891148)))], (32401 ^ _779854) ^ [_1363019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1363019)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1363019 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44787 ^ _779854) ^ [_1676221, _1676223, _1676225, _1676227, _1676229] : [class_Orderings_Olinorder(_1676221), -(hAPP(c_List_Oset(_1676223), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676223, _1676221, _1676225), _1676227), _1676229)) = hAPP(hAPP(c_Set_Oinsert(_1676223), _1676227), hAPP(c_List_Oset(_1676223), _1676229)))], (39862 ^ _779854) ^ [_1553280, _1553282, _1553284, _1553286] : [hBOOL(hAPP(hAPP(c_member(_1553280), _1553282), hAPP(c_Relation_ODomain(_1553280, _1553284), _1553286))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553280, _1553284)), hAPP(hAPP(c_Product__Type_OPair(_1553280, _1553284), _1553282), 39865 ^ [_1553280, _1553282, _1553284, _1553286])), _1553286)))], (52279 ^ _779854) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (2496 ^ _779854) ^ [_816767, _816769, _816771, _816773] : [-(c_FunDef_Orp__inv__image(_816773, _816769) = c_FunDef_Orp__inv__image(_816771, _816767)), _816773 = _816771, _816769 = _816767], (3628 ^ _779854) ^ [_834381, _834383, _834385, _834387] : [-(c_List_Olist__update(_834387, _834383) = c_List_Olist__update(_834385, _834381)), _834387 = _834385, _834383 = _834381], (37318 ^ _779854) ^ [_1482438, _1482440, _1482442, _1482444] : [c_Equiv__Relations_Oequiv(_1482438, _1482440, _1482442), hBOOL(hAPP(hAPP(c_member(_1482438), _1482444), _1482440)), -(hBOOL(hAPP(hAPP(c_member(_1482438), _1482444), hAPP(c_Relation_OImage(_1482438, _1482438, _1482442), hAPP(hAPP(c_Set_Oinsert(_1482438), _1482444), c_Orderings_Obot__class_Obot(tc_fun(_1482438, tc_HOL_Obool)))))))], (47931 ^ _779854) ^ [_1744166, _1744168, _1744170] : [-(hBOOL(hAPP(hAPP(c_member(_1744166), _1744168), hAPP(c_List_Oset(_1744166), _1744170)))), -(c_List_Oinsert(_1744166, _1744168, _1744170) = hAPP(hAPP(c_List_Olist_OCons(_1744166), _1744168), _1744170))], (52309 ^ _779854) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (6841 ^ _779854) ^ [_890809, _890811, _890813, _890815] : [hBOOL(hAPP(_890809, _890811)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890813, tc_HOL_Obool)), _890809), _890815), _890811)))], (40948 ^ _779854) ^ [_1579860, _1579862, _1579864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579860, _1579860)), _1579862), _1579864)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579860, _1579860)), _1579862), c_Transitive__Closure_Otrancl(_1579860, _1579864))))], (23639 ^ _779854) ^ [_1208332, _1208334, _1208336, _1208338, _1208340] : [c_Finite__Set_Ofun__left__comm__idem(_1208332, _1208334, _1208336), -(hAPP(hAPP(_1208336, _1208338), hAPP(hAPP(_1208336, _1208338), _1208340)) = hAPP(hAPP(_1208336, _1208338), _1208340))], (32375 ^ _779854) ^ [_1362540, _1362542, _1362544] : [class_Rings_Olinordered__idom(_1362540), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362540), c_Groups_Ozero__class_Ozero(_1362540)), hAPP(hAPP(c_Power_Opower__class_Opower(_1362540), hAPP(c_Groups_Oabs__class_Oabs(_1362540), _1362542)), _1362544))))], (4524 ^ _779854) ^ [_848731, _848733, _848735, _848737] : [-(c_HOL_OThe(_848737, _848733) = c_HOL_OThe(_848735, _848731)), _848737 = _848735, _848733 = _848731], (29749 ^ _779854) ^ [_1316347, _1316349, _1316351] : [class_Groups_Omonoid__mult(_1316347), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1316347), _1316349), 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)))), _1316351)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1316347), hAPP(hAPP(c_Power_Opower__class_Opower(_1316347), _1316349), _1316351)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (32191 ^ _779854) ^ [_1359095, _1359097, _1359099] : [class_Groups_Oordered__ab__group__add__abs(_1359095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359095), _1359097), _1359099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359095), hAPP(c_Groups_Ouminus__class_Ouminus(_1359095), _1359097)), _1359099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359095), hAPP(c_Groups_Oabs__class_Oabs(_1359095), _1359097)), _1359099)))], (39901 ^ _779854) ^ [_1554400, _1554402, _1554404, _1554406] : [c_FunDef_Oreduction__pair(_1554400, _1554402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1554400, _1554400), tc_HOL_Obool)), _1554404), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1554400, _1554400), tc_HOL_Obool), tc_fun(tc_prod(_1554400, _1554400), tc_HOL_Obool)), _1554402))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1554400, _1554400), tc_HOL_Obool)), _1554406), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1554400, _1554400), tc_HOL_Obool), tc_fun(tc_prod(_1554400, _1554400), tc_HOL_Obool)), _1554402))), c_Wellfounded_Owf(_1554400, _1554406), -(c_Wellfounded_Owf(_1554400, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554400, _1554400), tc_HOL_Obool)), _1554404), _1554406)))], (12492 ^ _779854) ^ [_998020, _998022, _998024] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_998020, tc_HOL_Obool)), _998022), _998024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998020, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_998020, tc_HOL_Obool), _998024)), _998022)))], (48898 ^ _779854) ^ [_1765368, _1765370, _1765372, _1765374, _1765376] : [-(c_Predicate_Oconversep(_1765368, _1765370, c_Predicate_Opred__comp(_1765368, _1765372, _1765370, _1765374, _1765376)) = c_Predicate_Opred__comp(_1765370, _1765372, _1765368, c_Predicate_Oconversep(_1765372, _1765370, _1765376), c_Predicate_Oconversep(_1765368, _1765372, _1765374)))], (43404 ^ _779854) ^ [_1645198, _1645200, _1645202] : [hAPP(hAPP(c_List_Olist_OCons(_1645198), _1645200), _1645202) = c_List_Olist_ONil(_1645198)], (2452 ^ _779854) ^ [_815989, _815991, _815993, _815995, _815997, _815999, _816001, _816003, _816005, _816007] : [-(c_Product__Type_Oprod_Oprod__size(_816007, _816003, _815999, _815995, _815991) = c_Product__Type_Oprod_Oprod__size(_816005, _816001, _815997, _815993, _815989)), _816007 = _816005, _816003 = _816001, _815999 = _815997, _815995 = _815993, _815991 = _815989], (45696 ^ _779854) ^ [_1695953, _1695955, _1695957, _1695959] : [hBOOL(hAPP(c_List_Olistsp(_1695953, hAPP(hAPP(c_COMBS(_1695953, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1695953), c_fconj), _1695955)), _1695957)), _1695959)), 45699 ^ _779854 : [(45702 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1695953, _1695957), _1695959)))], (45700 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1695953, _1695955), _1695959)))]]], (7149 ^ _779854) ^ [_897437, _897439, _897441] : [class_Lattices_Osemilattice__inf(_897437), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897437), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_897437), _897439), _897441)), _897441)))], (7113 ^ _779854) ^ [_896795, _896797, _896799] : [class_Lattices_Osemilattice__sup(_896795), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896795), _896797), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896795), _896797), _896799))))], (15368 ^ _779854) ^ [_1054041, _1054043, _1054045, _1054047, _1054049] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1054041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054041), _1054043), _1054045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054041), _1054047), _1054049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054041), _1054043), _1054047)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054041), _1054045), _1054049))))], (12658 ^ _779854) ^ [_1001496, _1001498, _1001500, _1001502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001496, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1001496, tc_HOL_Obool)), _1001498), hAPP(hAPP(c_Set_Oinsert(_1001496), _1001500), c_Orderings_Obot__class_Obot(tc_fun(_1001496, tc_HOL_Obool))))), _1001502)), hBOOL(hAPP(hAPP(c_member(_1001496), _1001500), _1001498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001496, tc_HOL_Obool)), _1001498), hAPP(hAPP(c_Set_Oinsert(_1001496), _1001500), _1001502))))], (18070 ^ _779854) ^ [_1106751, _1106753] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1106751, _1106753)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1106751), hAPP(c_Nat_OSuc, _1106753)))], (33789 ^ _779854) ^ [_1401921, _1401923, _1401925, _1401927, _1401929] : [class_Groups_Ocomm__monoid__add(_1401921), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1401921), _1401923), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1401925), _1401927), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1401929), _1401927))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1401921), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1401921, tc_Nat_Onat), _1401923), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1401927))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1401925, _1401929)))], (17702 ^ _779854) ^ [_1100811] : [_1100811 = hAPP(c_Nat_OSuc, _1100811)], (1270 ^ _779854) ^ [_798681, _798683] : [-(class_Groups_Ogroup__add(_798681)), _798683 = _798681, class_Groups_Ogroup__add(_798683)], (17286 ^ _779854) ^ [_1092200] : [class_Groups_Oab__semigroup__mult(_1092200), -(c_Finite__Set_Ofun__left__comm(_1092200, _1092200, c_Groups_Otimes__class_Otimes(_1092200)))], (6004 ^ _779854) ^ [_874812, _874814, _874816] : [_874812 = _874814, 6007 ^ _779854 : [(6010 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874816, tc_HOL_Obool)), _874814), _874812)))], (6008 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874816, tc_HOL_Obool)), _874812), _874814)))]]], (29745 ^ _779854) ^ [_1316280] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1316280), 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), _1316280), _1316280))], (45623 ^ _779854) ^ [_1693862, _1693864] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1693862), _1693864) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693862)), hAPP(c_Code__Numeral_Onat__of, _1693864))))], (52555 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (38695 ^ _779854) ^ [_1517616, _1517618] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1517616))), -(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)), _1517616))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1517618)))) = 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)), _1517616))), 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, _1517618))))))], (52569 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (18259 ^ _779854) ^ [_1110294, _1110296, _1110298] : [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, _1110294)), _1110296)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110294)), _1110298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110296), _1110298)))], (25991 ^ _779854) ^ [_1252126, _1252128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252128)), -(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), _1252126), _1252128))))], (28272 ^ _779854) ^ [_1291115] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291115)))], (39675 ^ _779854) ^ [_1549469, _1549471, _1549473] : [c_Wellfounded_Owf(_1549469, _1549471), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549469, _1549469)), hAPP(hAPP(c_Product__Type_OPair(_1549469, _1549469), _1549473), _1549473)), _1549471))], (35187 ^ _779854) ^ [_1435318, _1435320, _1435322, _1435324, _1435326] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1435318, _1435320, tc_HOL_Obool), _1435322), hAPP(hAPP(c_Product__Type_OPair(_1435318, _1435320), _1435324), _1435326))), -(hBOOL(hAPP(hAPP(_1435322, _1435324), _1435326)))], (32009 ^ _779854) ^ [_1355728, _1355730] : [class_Rings_Olinordered__idom(_1355728), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355728), hAPP(c_Groups_Oabs__class_Oabs(_1355728), _1355730)), hAPP(c_Groups_Oabs__class_Oabs(_1355728), _1355730)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355728), _1355730), _1355730))], (41024 ^ _779854) ^ [_1581680, _1581682, _1581684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581680, _1581680), tc_HOL_Obool)), _1581682), hAPP(hAPP(c_Product__Type_OSigma(_1581680, _1581680), _1581684), hAPP(c_COMBK(tc_fun(_1581680, tc_HOL_Obool), _1581680), _1581684)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581680, _1581680), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1581680, _1581682)), hAPP(hAPP(c_Product__Type_OSigma(_1581680, _1581680), _1581684), hAPP(c_COMBK(tc_fun(_1581680, tc_HOL_Obool), _1581680), _1581684)))))], (42195 ^ _779854) ^ [_1612999, _1613001, _1613003, _1613005, _1613007, _1613009] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612999), tc_List_Olist(_1612999))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612999), tc_List_Olist(_1612999)), hAPP(hAPP(c_List_Olist_OCons(_1612999), _1613001), _1613003)), hAPP(hAPP(c_List_Olist_OCons(_1612999), _1613005), _1613007))), c_List_Olexord(_1612999, _1613009)))), 42196 ^ _779854 : [(42199 ^ _779854) ^ [] : [_1613001 = _1613005, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612999), tc_List_Olist(_1612999))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612999), tc_List_Olist(_1612999)), _1613003), _1613007)), c_List_Olexord(_1612999, _1613009)))], (42197 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612999, _1612999)), hAPP(hAPP(c_Product__Type_OPair(_1612999, _1612999), _1613001), _1613005)), _1613009))]]], (9624 ^ _779854) ^ [_941219, _941221, _941223] : [class_Orderings_Olinorder(_941219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941219), _941221), _941223)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_941219), _941221), _941223) = _941223)], (39357 ^ _779854) ^ [_1539635, _1539637] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1539635, _1539637, tc_prod(_1539635, _1539637)), c_Product__Type_OPair(_1539635, _1539637)) = c_Fun_Oid(tc_prod(_1539635, _1539637)))], (44821 ^ _779854) ^ [_1676949, _1676951, _1676953] : [class_Orderings_Olinorder(_1676949), -(c_List_Oremove1(_1676949, _1676951, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676949, _1676949, c_COMBI(_1676949)), _1676951), _1676953)) = _1676953)], (52591 ^ _779854) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (46334 ^ _779854) ^ [_1709712, _1709714, _1709716] : [-(c_List_Oconcat(_1709712, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1709712)), _1709714), _1709716)) = hAPP(hAPP(c_List_Oappend(_1709712), c_List_Oconcat(_1709712, _1709714)), c_List_Oconcat(_1709712, _1709716)))], (23465 ^ _779854) ^ [_1204957, _1204959] : [class_Rings_Olinordered__idom(_1204957), 23468 ^ _779854 : [(23475 ^ _779854) ^ [] : [_1204959 = c_Groups_Ozero__class_Ozero(_1204957), -(c_Groups_Osgn__class_Osgn(_1204957, _1204959) = c_Groups_Ozero__class_Ozero(_1204957))], (23469 ^ _779854) ^ [] : [c_Groups_Osgn__class_Osgn(_1204957, _1204959) = c_Groups_Ozero__class_Ozero(_1204957), -(_1204959 = c_Groups_Ozero__class_Ozero(_1204957))]]], (52379 ^ _779854) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (45657 ^ _779854) ^ [_1694586, _1694588] : [-(c_List_Opartition(_1694586, _1694588, c_List_Olist_ONil(_1694586)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694586), tc_List_Olist(_1694586)), c_List_Olist_ONil(_1694586)), c_List_Olist_ONil(_1694586)))], (16259 ^ _779854) ^ [_1071999, _1072001, _1072003, _1072005, _1072007] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1071999), 16262 ^ _779854 : [(16263 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072001), _1072005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072003), _1072007)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072001), _1072007)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072003), _1072005)), -(_1072001 = _1072003), -(_1072005 = _1072007)], (16273 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072001), _1072005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072003), _1072007)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072001), _1072007)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071999), _1072003), _1072005))), 16276 ^ _779854 : [(16279 ^ _779854) ^ [] : [_1072005 = _1072007], (16277 ^ _779854) ^ [] : [_1072001 = _1072003]]]]], (4820 ^ _779854) ^ [_853397, _853399, _853401, _853403] : [-(c_Complete__Lattice_OInf__class_OInf(_853403, _853399) = c_Complete__Lattice_OInf__class_OInf(_853401, _853397)), _853403 = _853401, _853399 = _853397], (40385 ^ _779854) ^ [_1566679, _1566681] : [40387 ^ _779854 : [(40390 ^ _779854) ^ [] : [40386 ^ [_1566679, _1566681] = c_Orderings_Obot__class_Obot(tc_fun(_1566679, tc_HOL_Obool))], (40388 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566679, tc_HOL_Obool)), 40386 ^ [_1566679, _1566681]), hAPP(c_Relation_OImage(_1566679, _1566679, _1566681), 40386 ^ [_1566679, _1566681]))))]], -(c_Wellfounded_Owf(_1566679, _1566681))], (47428 ^ _779854) ^ [_1733488, _1733490, _1733492] : [hAPP(c_List_Orev(_1733488), _1733490) = _1733492, -(_1733490 = hAPP(c_List_Orev(_1733488), _1733492))], (34569 ^ _779854) ^ [_1421404, _1421406] : [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(_1421404))), 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)), _1421406)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421404)), hAPP(c_Nat_OSuc, _1421406))))], (27631 ^ _779854) ^ [_1279966, _1279968] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1279966), _1279968)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1279968), _1279966)))], (38023 ^ _779854) ^ [_1498964, _1498966, _1498968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498964, tc_HOL_Obool)), _1498966), hAPP(hAPP(c_Set_Oinsert(_1498964), _1498968), c_Orderings_Obot__class_Obot(tc_fun(_1498964, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1498964, _1498968, _1498966) = _1498968)], (30379 ^ _779854) ^ [_1328437, _1328439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328437), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328437), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328439, _1328437))))], (6213 ^ _779854) ^ [_878507, _878509, _878511] : [class_Orderings_Olinorder(_878507), 6216 ^ _779854 : [(6223 ^ _779854) ^ [] : [_878509 = _878511, -(hAPP(c_SetInterval_Oord__class_OatMost(_878507), _878509) = hAPP(c_SetInterval_Oord__class_OatMost(_878507), _878511))], (6217 ^ _779854) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_878507), _878509) = hAPP(c_SetInterval_Oord__class_OatMost(_878507), _878511), -(_878509 = _878511)]]], (17308 ^ _779854) ^ [_1092585, _1092587, _1092589, _1092591, _1092593, _1092595, _1092597] : [c_Finite__Set_Ofun__left__comm(_1092585, _1092587, _1092589), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1092585, _1092587, _1092589, _1092591, _1092593), _1092595)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1092585, _1092587, _1092589, _1092591, _1092593), _1092597)), -(_1092597 = _1092595)], (5214 ^ _779854) ^ [_859588, _859590, _859592, _859594] : [-(c_Product__Type_OPair(_859594, _859590) = c_Product__Type_OPair(_859592, _859588)), _859594 = _859592, _859590 = _859588], (3160 ^ _779854) ^ [_827061, _827063, _827065, _827067] : [-(c_Big__Operators_Olattice__class_OSup__fin(_827067, _827063) = c_Big__Operators_Olattice__class_OSup__fin(_827065, _827061)), _827067 = _827065, _827063 = _827061], (28798 ^ _779854) ^ [_1300081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1300081), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1300081)), c_Int_OPls)))], (38166 ^ _779854) ^ [_1502464, _1502466, _1502468, _1502470] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502464), _1502466)), c_Fun_Oinj__on(_1502468, _1502464, _1502470, c_Orderings_Otop__class_Otop(tc_fun(_1502468, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1502468), hAPP(c_Set_Ovimage(_1502468, _1502464, _1502470), _1502466))))], (21028 ^ _779854) ^ [_1158265, _1158267] : [-(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), _1158265), _1158267)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1158265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1158267))], (19775 ^ _779854) ^ [_1136574, _1136576, _1136578, _1136580] : [class_Rings_Olinordered__comm__semiring__strict(_1136574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136574), _1136576), _1136578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136574), c_Groups_Ozero__class_Ozero(_1136574)), _1136580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136574), _1136580), _1136576)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136574), _1136580), _1136578))))], (7684 ^ _779854) ^ [_907471, _907473, _907475, _907477, _907479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907471, tc_HOL_Obool)), _907473), _907475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907471, tc_HOL_Obool)), _907477), _907479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907471, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907471, tc_HOL_Obool)), _907473), _907477)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907471, tc_HOL_Obool)), _907475), _907479))))], (45595 ^ _779854) ^ [_1693357, _1693359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1693357), _1693359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693357)), hAPP(c_Code__Numeral_Onat__of, _1693359))))], (47030 ^ _779854) ^ [_1725265, _1725267, _1725269, _1725271, _1725273] : [class_Orderings_Olinorder(_1725265), 47033 ^ _779854 : [(47040 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1725265, hAPP(hAPP(c_List_Omap(_1725267, _1725265), _1725269), _1725273)), -(c_List_Olinorder__class_Osorted(_1725265, hAPP(hAPP(c_List_Omap(_1725267, _1725265), _1725269), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1725267, _1725265, _1725269), _1725271), _1725273))))], (47034 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1725265, hAPP(hAPP(c_List_Omap(_1725267, _1725265), _1725269), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1725267, _1725265, _1725269), _1725271), _1725273))), -(c_List_Olinorder__class_Osorted(_1725265, hAPP(hAPP(c_List_Omap(_1725267, _1725265), _1725269), _1725273)))]]], (18479 ^ _779854) ^ [_1114724] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1114724))))], (28848 ^ _779854) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (47641 ^ _779854) ^ [_1737945, _1737947, _1737949] : [hBOOL(hAPP(c_List_Odistinct(_1737945), _1737947)), -(hBOOL(hAPP(c_List_Odistinct(_1737945), c_List_OtakeWhile(_1737945, _1737949, _1737947))))], (34713 ^ _779854) ^ [_1424722, _1424724] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1424722)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424724)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1424724))), 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), _1424722)), c_Int_Onat)))))], (33583 ^ _779854) ^ [_1396008, _1396010, _1396012, _1396014, _1396016] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396008, tc_fun(_1396010, tc_HOL_Obool)), _1396012), hAPP(hAPP(c_COMBC(_1396008, tc_fun(_1396010, tc_HOL_Obool), tc_fun(_1396010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396010, tc_HOL_Obool), tc_fun(tc_fun(_1396010, tc_HOL_Obool), tc_fun(_1396010, tc_HOL_Obool)), _1396008), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396010, tc_HOL_Obool))), _1396014)), _1396016)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396010, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396008, tc_fun(_1396010, tc_HOL_Obool)), _1396012), _1396014)), _1396016))], (51689 ^ _779854) ^ [_1825989, _1825991, _1825993, _1825995] : [class_Divides_Osemiring__div(_1825989), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825989), _1825991), _1825993)), 51696 ^ _779854 : [(51703 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825989), _1825991), _1825995)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825989), _1825991), c_Divides_Odiv__class_Omod(_1825989, _1825995, _1825993))))], (51697 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825989), _1825991), c_Divides_Odiv__class_Omod(_1825989, _1825995, _1825993))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825989), _1825991), _1825995)))]]], (38466 ^ _779854) ^ [_1510624, _1510626, _1510628, _1510630] : [_1510624 = c_Orderings_Obot__class_Obot(tc_fun(_1510626, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1510626, _1510628), _1510628, c_Product__Type_Osnd(_1510626, _1510628)), hAPP(hAPP(c_Product__Type_OSigma(_1510626, _1510628), _1510624), hAPP(c_COMBK(tc_fun(_1510628, tc_HOL_Obool), _1510626), _1510630))) = c_Orderings_Obot__class_Obot(tc_fun(_1510628, tc_HOL_Obool)))], (12370 ^ _779854) ^ [_995803, _995805, _995807, _995809] : [hBOOL(hAPP(hAPP(c_member(_995803), _995805), _995807)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995803, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995803), _995805), _995809)), _995807) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995803, tc_HOL_Obool)), _995809), _995807))], (47586 ^ _779854) ^ [_1736834, _1736836, _1736838] : [c_List_OtakeWhile(_1736834, _1736836, _1736838) = _1736838, 47589 ^ _779854 : [(47590 ^ _779854) ^ [_1736921] : [hBOOL(hAPP(hAPP(c_member(_1736834), _1736921), hAPP(c_List_Oset(_1736834), _1736838))), -(hBOOL(hAPP(_1736836, _1736921)))]]], (32912 ^ _779854) ^ [] : [-(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)))], (11432 ^ _779854) ^ [_977363, _977365, _977367, _977369] : [-(_977363 = c_Orderings_Obot__class_Obot(tc_fun(_977365, tc_HOL_Obool))), 11435 ^ _779854 : [(11436 ^ _779854) ^ [] : [-(hAPP(c_Set_Oimage(_977367, _977365, 11443 ^ [_977363, _977365, _977367, _977369]), _977369) = _977363), 11437 ^ _779854 : [(11438 ^ _779854) ^ [_977504] : [c_Fun_Oinj__on(_977365, _977367, _977504, _977363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977367, tc_HOL_Obool)), hAPP(c_Set_Oimage(_977365, _977367, _977504), _977363)), _977369))]]], (11447 ^ _779854) ^ [] : [11448 ^ _779854 : [(11449 ^ _779854) ^ [_977696] : [hAPP(c_Set_Oimage(_977367, _977365, _977696), _977369) = _977363]], 11451 ^ _779854 : [(11454 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977367, tc_HOL_Obool)), hAPP(c_Set_Oimage(_977365, _977367, 11450 ^ [_977363, _977365, _977367, _977369]), _977363)), _977369)))], (11452 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_977365, _977367, 11450 ^ [_977363, _977365, _977367, _977369], _977363))]]]]], (25349 ^ _779854) ^ [_1240525, _1240527, _1240529, _1240531] : [class_Fields_Olinordered__field__inverse__zero(_1240525), class_Int_Onumber(_1240525), 25356 ^ _779854 : [(25357 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240525), _1240527), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529))), _1240531)), 25360 ^ _779854 : [(25367 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), c_Groups_Ozero__class_Ozero(_1240525)), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529)))), 25370 ^ _779854 : [(25377 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529)), c_Groups_Ozero__class_Ozero(_1240525)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), c_Groups_Ozero__class_Ozero(_1240525)), _1240531)))], (25371 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529)), c_Groups_Ozero__class_Ozero(_1240525))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240525), _1240531), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529))), _1240527)))]]], (25361 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), c_Groups_Ozero__class_Ozero(_1240525)), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), _1240527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240525), _1240531), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529)))))]]], (25383 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240525), _1240527), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529))), _1240531))), 25386 ^ _779854 : [(25389 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), _1240527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240525), _1240531), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529))))], (25387 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), c_Groups_Ozero__class_Ozero(_1240525)), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529))))]], 25390 ^ _779854 : [(25393 ^ _779854) ^ [] : [25394 ^ _779854 : [(25397 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240525), _1240531), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529))), _1240527))], (25395 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529)), c_Groups_Ozero__class_Ozero(_1240525))))]], 25398 ^ _779854 : [(25401 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240525), c_Groups_Ozero__class_Ozero(_1240525)), _1240531))], (25399 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529)), c_Groups_Ozero__class_Ozero(_1240525)))]]], (25391 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240525), c_Groups_Ozero__class_Ozero(_1240525)), hAPP(c_Int_Onumber__class_Onumber__of(_1240525), _1240529)))]]]]], (12714 ^ _779854) ^ [_1002716, _1002718, _1002720] : [class_Orderings_Olinorder(_1002716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002716), _1002718)), -(hBOOL(hAPP(hAPP(c_member(_1002716), _1002720), _1002718))), -(_1002718 = c_Orderings_Obot__class_Obot(tc_fun(_1002716, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1002716, c_Orderings_Oord__class_Omin(_1002716), hAPP(hAPP(c_Set_Oinsert(_1002716), _1002720), _1002718)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1002716), _1002720), c_Big__Operators_Olattice_OInf__fin(_1002716, c_Orderings_Oord__class_Omin(_1002716), _1002718)))], (44135 ^ _779854) ^ [_1661027, _1661029, _1661031, _1661033, _1661035, _1661037, _1661039, _1661041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1661027, _1661027)), hAPP(hAPP(c_Product__Type_OPair(_1661027, _1661027), _1661029), _1661031)), _1661033)), _1661035 = hAPP(hAPP(c_List_Oappend(_1661027), _1661037), hAPP(hAPP(c_List_Olist_OCons(_1661027), _1661029), _1661039)), _1661041 = hAPP(hAPP(c_List_Oappend(_1661027), _1661037), hAPP(hAPP(c_List_Olist_OCons(_1661027), _1661031), _1661039)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661027), tc_List_Olist(_1661027))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661027), tc_List_Olist(_1661027)), _1661035), _1661041)), c_List_Olistrel1(_1661027, _1661033))))], (41212 ^ _779854) ^ [_1587106, _1587108, _1587110, _1587112, _1587114] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587106, _1587106)), hAPP(hAPP(c_Product__Type_OPair(_1587106, _1587106), _1587108), _1587110)), c_Transitive__Closure_Otrancl(_1587106, _1587112))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587106, _1587106)), hAPP(hAPP(c_Product__Type_OPair(_1587106, _1587106), _1587110), _1587114)), c_Transitive__Closure_Ortrancl(_1587106, _1587112))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587106, _1587106)), hAPP(hAPP(c_Product__Type_OPair(_1587106, _1587106), _1587108), _1587114)), c_Transitive__Closure_Otrancl(_1587106, _1587112))))], (19147 ^ _779854) ^ [_1125048, _1125050] : [class_Groups_Olinordered__ab__group__add(_1125048), 19150 ^ _779854 : [(19157 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125048), c_Groups_Ozero__class_Ozero(_1125048)), _1125050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125048), c_Groups_Ozero__class_Ozero(_1125048)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125048), _1125050), _1125050))))], (19151 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125048), c_Groups_Ozero__class_Ozero(_1125048)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125048), _1125050), _1125050))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125048), c_Groups_Ozero__class_Ozero(_1125048)), _1125050)))]]], (22029 ^ _779854) ^ [_1177595, _1177597, _1177599, _1177601, _1177603, _1177605, _1177607] : [c_Finite__Set_Ofolding__image__simple(_1177595, _1177597, _1177599, _1177601, _1177603, _1177605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177597), _1177607)), -(hAPP(_1177605, _1177607) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1177595, _1177597, _1177599), _1177603), _1177601), _1177607))], (50362 ^ _779854) ^ [_1797319, _1797321, _1797323, _1797325] : [c_Fun_Oinj__on(_1797319, _1797321, _1797323, c_Orderings_Otop__class_Otop(tc_fun(_1797319, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1797319, _1797321, c_Orderings_Otop__class_Otop(tc_fun(_1797319, tc_HOL_Obool)), _1797323), hAPP(_1797323, _1797325)) = _1797325)], (41617 ^ _779854) ^ [_1596792, _1596794, _1596796] : [c_Relation_Ototal__on(_1596792, _1596794, hAPP(c_Relation_Oconverse(_1596792, _1596792), _1596796)), -(c_Relation_Ototal__on(_1596792, _1596794, _1596796))], (27729 ^ _779854) ^ [_1281646, _1281648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281648)), 27736 ^ _779854 : [(27743 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1281646), _1281648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1281646)), hAPP(c_Int_Onat, _1281648))))], (27737 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1281646)), hAPP(c_Int_Onat, _1281648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1281646), _1281648)))]]], (960 ^ _779854) ^ [_794270, _794272, _794274, _794276] : [-(c_Wellfounded_Owf(_794274, _794270)), c_Wellfounded_Owf(_794276, _794272), _794276 = _794274, _794272 = _794270], (11226 ^ _779854) ^ [_973423] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_973423), c_Orderings_Obot__class_Obot(tc_fun(_973423, tc_HOL_Obool)))))], (36607 ^ _779854) ^ [_1464292, _1464294, _1464296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1464292, tc_HOL_Obool), tc_fun(_1464292, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1464292, tc_HOL_Obool), tc_fun(_1464292, tc_HOL_Obool)), _1464294), _1464296)), c_Wellfounded_Ofinite__psubset(_1464292))), 36610 ^ _779854 : [(36613 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1464292), _1464296)))], (36611 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1464292, tc_HOL_Obool)), _1464294), _1464296)))]]], (30053 ^ _779854) ^ [_1321868, _1321870, _1321872] : [class_Int_Onumber__ring(_1321868), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1321868), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321868), _1321870), _1321872)), 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(_1321868), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321868), hAPP(hAPP(c_Power_Opower__class_Opower(_1321868), _1321870), 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(_1321868), _1321872), 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(_1321868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321868), hAPP(c_Int_Onumber__class_Onumber__of(_1321868), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1321870)), _1321872)))], (44348 ^ _779854) ^ [_1666613, _1666615, _1666617, _1666619] : [-(_1666613 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1666615), _1666613), hAPP(hAPP(c_List_Olist_OCons(_1666615), _1666617), _1666619)) = hAPP(hAPP(c_List_Odrop(_1666615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1666613), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1666619))], (9298 ^ _779854) ^ [_935043, _935045, _935047] : [class_Orderings_Oorder(_935043), 9301 ^ _779854 : [(9308 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935043), _935045), _935047))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_935043, _935045), _935047) = c_Orderings_Obot__class_Obot(tc_fun(_935043, tc_HOL_Obool)))], (9302 ^ _779854) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_935043, _935045), _935047) = c_Orderings_Obot__class_Obot(tc_fun(_935043, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935043), _935045), _935047))]]], (7547 ^ _779854) ^ [_904441, _904443, _904445] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904441, tc_HOL_Obool)), _904443), _904445) = c_Orderings_Obot__class_Obot(tc_fun(_904441, tc_HOL_Obool))), _904443 = c_Orderings_Obot__class_Obot(tc_fun(_904441, tc_HOL_Obool)), _904445 = c_Orderings_Obot__class_Obot(tc_fun(_904441, tc_HOL_Obool))], (1200 ^ _779854) ^ [_797806, _797808] : [-(class_Groups_Oordered__ab__group__add(_797806)), _797808 = _797806, class_Groups_Oordered__ab__group__add(_797808)], (33511 ^ _779854) ^ [_1390765, _1390767, _1390769] : [hAPP(hAPP(c_COMBC(_1390765, tc_fun(_1390765, tc_HOL_Obool), tc_HOL_Obool), c_member(_1390765)), _1390767) = hAPP(hAPP(c_COMBC(_1390765, tc_fun(_1390765, tc_HOL_Obool), tc_HOL_Obool), c_member(_1390765)), _1390769), -(_1390767 = _1390769)], (41282 ^ _779854) ^ [_1588792] : [-(c_Relation_Orefl__on(_1588792, c_Orderings_Otop__class_Otop(tc_fun(_1588792, tc_HOL_Obool)), c_Relation_OId(_1588792)))], (39567 ^ _779854) ^ [_1547410, _1547412, _1547414, _1547416, _1547418] : [hBOOL(hAPP(hAPP(_1547410, _1547412), _1547414)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1547416, _1547418, _1547410), _1547414)))], (42026 ^ _779854) ^ [_1607777, _1607779, _1607781] : [-(c_Nitpick_Otimes__frac(_1607777, _1607779, _1607781) = hAPP(hAPP(c_Nitpick_Ofrac(_1607777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1607777), _1607779)), hAPP(c_Nitpick_Onum(_1607777), _1607781))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1607777), _1607779)), hAPP(c_Nitpick_Odenom(_1607777), _1607781))))], (43233 ^ _779854) ^ [_1641577, _1641579] : [hBOOL(hAPP(c_List_Odistinct(_1641577), _1641579)), 43236 ^ _779854 : [(43237 ^ _779854) ^ [_1641709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641709), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641577)), _1641579))), 43240 ^ _779854 : [(43241 ^ _779854) ^ [_1641836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641836), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641577)), _1641579))), -(_1641709 = _1641836), hAPP(hAPP(c_List_Onth(_1641577), _1641579), _1641709) = hAPP(hAPP(c_List_Onth(_1641577), _1641579), _1641836)]]]]], (49737 ^ _779854) ^ [_1784746, _1784748, _1784750, _1784752] : [class_Complete__Lattice_Ocomplete__lattice(_1784746), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1784748, _1784746), _1784750), _1784752) = c_Complete__Lattice_OSup__class_OSup(_1784746, hAPP(c_Set_OCollect(_1784746), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784748, _1784746), tc_HOL_Obool), tc_HOL_Obool, _1784746), c_HOL_OEx(tc_fun(_1784748, _1784746))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784748, _1784746), tc_HOL_Obool), tc_fun(tc_fun(_1784748, _1784746), tc_HOL_Obool), _1784746), hAPP(c_COMBS(tc_fun(_1784748, _1784746), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1784748, _1784746)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1784748, _1784746), tc_fun(tc_fun(_1784748, _1784746), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1784748, _1784746))), _1784750)))), hAPP(hAPP(c_COMBC(_1784746, tc_fun(tc_fun(_1784748, _1784746), _1784746), tc_fun(tc_fun(_1784748, _1784746), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1784746, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1784748, _1784746), _1784746), tc_fun(tc_fun(_1784748, _1784746), tc_HOL_Obool)), _1784746), c_COMBB(_1784746, tc_HOL_Obool, tc_fun(_1784748, _1784746))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1784748, _1784746), _1784748, _1784746), c_COMBI(tc_fun(_1784748, _1784746))), _1784752)))))))], (36918 ^ _779854) ^ [_1471454, _1471456] : [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), _1471454), _1471456)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1471454), _1471456)))], (9121 ^ _779854) ^ [_931996, _931998, _932000] : [class_Complete__Lattice_Ocomplete__lattice(_931996), class_Orderings_Olinorder(_931996), 9128 ^ _779854 : [(9138 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931996), c_Complete__Lattice_OInf__class_OInf(_931996, _931998)), _932000))), 9139 ^ _779854 : [(9140 ^ _779854) ^ [_932302] : [hBOOL(hAPP(hAPP(c_member(_931996), _932302), _931998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931996), _932302), _932000))]]], (9129 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931996), c_Complete__Lattice_OInf__class_OInf(_931996, _931998)), _932000)), 9133 ^ _779854 : [(9136 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931996), 9132 ^ [_931996, _931998, _932000]), _932000)))], (9134 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_931996), 9132 ^ [_931996, _931998, _932000]), _931998)))]]]]], (41090 ^ _779854) ^ [_1584055, _1584057, _1584059, _1584061, _1584063] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584055, _1584055)), hAPP(hAPP(c_Product__Type_OPair(_1584055, _1584055), _1584057), _1584059)), c_Transitive__Closure_Ortrancl(_1584055, _1584061))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584055, _1584055)), hAPP(hAPP(c_Product__Type_OPair(_1584055, _1584055), _1584059), _1584063)), c_Transitive__Closure_Ortrancl(_1584055, _1584061))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584055, _1584055)), hAPP(hAPP(c_Product__Type_OPair(_1584055, _1584055), _1584057), _1584063)), c_Transitive__Closure_Ortrancl(_1584055, _1584061))))], (50026 ^ _779854) ^ [_1791233, _1791235] : [c_Relation_Osym(_1791233, _1791235), 50029 ^ _779854 : [(50030 ^ _779854) ^ [_1791339, _1791341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1791233, _1791233)), hAPP(hAPP(c_Product__Type_OPair(_1791233, _1791233), _1791341), _1791339)), _1791235)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1791233, _1791233)), hAPP(hAPP(c_Product__Type_OPair(_1791233, _1791233), _1791339), _1791341)), _1791235)))]]], (32892 ^ _779854) ^ [_1373362, _1373364, _1373366, _1373368, _1373370, _1373372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1373364, _1373366)), hAPP(hAPP(c_Product__Type_OPair(_1373364, _1373366), _1373370), _1373372)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1373362, tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1373362, tc_HOL_Obool))), _1373368))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1373362, tc_fun(_1373364, tc_fun(_1373366, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1373362, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool), tc_fun(_1373364, tc_fun(_1373366, tc_HOL_Obool)), _1373362), hAPP(c_COMBC(_1373364, tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool), tc_fun(_1373366, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373366, tc_fun(tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool), tc_fun(_1373366, tc_HOL_Obool)), _1373364), c_COMBC(_1373366, tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373366, tc_prod(_1373364, _1373366)), tc_fun(_1373366, tc_fun(tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool), tc_HOL_Obool)), _1373364), hAPP(c_COMBB(tc_prod(_1373364, _1373366), tc_fun(tc_fun(tc_prod(_1373364, _1373366), tc_HOL_Obool), tc_HOL_Obool), _1373366), c_member(tc_prod(_1373364, _1373366)))), c_Product__Type_OPair(_1373364, _1373366))))), _1373368)), _1373370), _1373372)))], (47957 ^ _779854) ^ [_1744553, _1744555, _1744557] : [hBOOL(hAPP(hAPP(c_member(_1744553), _1744555), hAPP(c_List_Oset(_1744553), _1744557))), -(c_List_Oinsert(_1744553, _1744555, _1744557) = _1744557)], (34943 ^ _779854) ^ [_1429519, _1429521, _1429523, _1429525, _1429527, _1429529, _1429531] : [34945 ^ _779854 : [(34948 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1429527, 34944 ^ [_1429519, _1429521, _1429523, _1429525, _1429527, _1429529, _1429531]), _1429529), _1429531))], (34946 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429519), 34944 ^ [_1429519, _1429521, _1429523, _1429525, _1429527, _1429529, _1429531]), _1429525)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429519, tc_fun(_1429521, tc_fun(_1429523, tc_HOL_Obool))), _1429525), _1429527), _1429529), _1429531)))], (21729 ^ _779854) ^ [_1171989, _1171991, _1171993, _1171995] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1171989), _1171991)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171993), _1171995)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1171989, _1171993)), c_Sum__Type_OPlus(_1171989, _1171993, _1171991, _1171995)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1171989), _1171991)), hAPP(c_Finite__Set_Ocard(_1171993), _1171995)))], (47745 ^ _779854) ^ [_1740188, _1740190, _1740192] : [47747 ^ _779854 : [(47750 ^ _779854) ^ [] : [hBOOL(hAPP(_1740190, 47746 ^ [_1740188, _1740190, _1740192]))], (47748 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740188), 47746 ^ [_1740188, _1740190, _1740192]), hAPP(c_List_Oset(_1740188), _1740192))))]], -(c_List_OdropWhile(_1740188, _1740190, _1740192) = c_List_Olist_ONil(_1740188))], (40842 ^ _779854) ^ [_1577244, _1577246, _1577248] : [c_Wellfounded_Owf(_1577244, _1577246), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577244, _1577244)), hAPP(hAPP(c_Product__Type_OPair(_1577244, _1577244), hAPP(_1577248, hAPP(c_Nat_OSuc, 40845 ^ [_1577244, _1577246, _1577248]))), hAPP(_1577248, 40845 ^ [_1577244, _1577246, _1577248]))), _1577246))], (46328 ^ _779854) ^ [_1709575, _1709577, _1709579, _1709581, _1709583] : [class_Orderings_Olinorder(_1709575), -(c_List_Olinorder__class_Osort__key(_1709577, _1709575, _1709579, hAPP(hAPP(c_List_Olist_OCons(_1709577), _1709581), _1709583)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1709577, _1709575, _1709579), _1709581), c_List_Olinorder__class_Osort__key(_1709577, _1709575, _1709579, _1709583)))], (42945 ^ _779854) ^ [_1635247, _1635249] : [class_Groups_Ocomm__monoid__add(_1635247), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1635247), _1635249) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1635247), hAPP(c_List_Onth(_1635247), _1635249)), 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(_1635247)), _1635249))))], (32758 ^ _779854) ^ [_1369714, _1369716, _1369718, _1369720, _1369722, _1369724, _1369726, _1369728] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369714, tc_fun(_1369716, tc_fun(_1369718, tc_HOL_Obool))), _1369720), _1369722), _1369724), _1369726)), -(hBOOL(hAPP(hAPP(hAPP(_1369722, _1369728), _1369724), _1369726))), hBOOL(hAPP(hAPP(c_member(_1369714), _1369728), _1369720))], (24641 ^ _779854) ^ [_1226921, _1226923, _1226925] : [class_Int_Onumber__ring(_1226921), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226921), hAPP(c_Int_Onumber__class_Onumber__of(_1226921), _1226923)), hAPP(c_Int_Onumber__class_Onumber__of(_1226921), _1226925)) = hAPP(c_Int_Onumber__class_Onumber__of(_1226921), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226923), _1226925)))], (38136 ^ _779854) ^ [_1501725, _1501727, _1501729, _1501731, _1501733] : [hAPP(_1501731, _1501727) = _1501733, -(hBOOL(hAPP(hAPP(c_member(_1501725), _1501727), hAPP(c_Set_Ovimage(_1501725, _1501729, _1501731), hAPP(hAPP(c_Set_Oinsert(_1501729), _1501733), c_Orderings_Obot__class_Obot(tc_fun(_1501729, tc_HOL_Obool)))))))], (3062 ^ _779854) ^ [_825560, _825562, _825564, _825566] : [-(c_Wellfounded_Oacc(_825566, _825562) = c_Wellfounded_Oacc(_825564, _825560)), _825566 = _825564, _825562 = _825560], (18847 ^ _779854) ^ [_1120085] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1120085)))], (50961 ^ _779854) ^ [_1810207, _1810209, _1810211] : [c_Fun_Obij__betw(_1810207, _1810207, c_Fun_Oid(_1810207), _1810209, _1810211), -(_1810209 = _1810211)], (20003 ^ _779854) ^ [_1140567, _1140569] : [class_Rings_Olinordered__idom(_1140567), 20006 ^ _779854 : [(20013 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140567), _1140569), c_Groups_Ozero__class_Ozero(_1140567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140567), _1140569), hAPP(c_Groups_Ouminus__class_Ouminus(_1140567), _1140569))))], (20007 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140567), _1140569), hAPP(c_Groups_Ouminus__class_Ouminus(_1140567), _1140569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140567), _1140569), c_Groups_Ozero__class_Ozero(_1140567))))]]], (28732 ^ _779854) ^ [_1299062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299062)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1299062)) = _1299062)], (38650 ^ _779854) ^ [_1516302, _1516304, _1516306, _1516308, _1516310, _1516312, _1516314, _1516316, _1516318, _1516320] : [hAPP(c_Set_Oimage(_1516302, _1516304, _1516306), _1516308) = _1516310, hAPP(c_Set_Oimage(_1516312, _1516314, _1516316), _1516318) = _1516320, -(hAPP(c_Set_Oimage(tc_prod(_1516302, _1516312), tc_prod(_1516304, _1516314), c_Product__Type_Omap__pair(_1516302, _1516304, _1516312, _1516314, _1516306, _1516316)), hAPP(hAPP(c_Product__Type_OSigma(_1516302, _1516312), _1516308), hAPP(c_COMBK(tc_fun(_1516312, tc_HOL_Obool), _1516302), _1516318))) = hAPP(hAPP(c_Product__Type_OSigma(_1516304, _1516314), _1516310), hAPP(c_COMBK(tc_fun(_1516314, tc_HOL_Obool), _1516304), _1516320)))], (36714 ^ _779854) ^ [_1466538, _1466540, _1466542, _1466544, _1466546] : [class_Groups_Oordered__ab__group__add(_1466538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466540), _1466542)), 36724 ^ _779854 : [(36727 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1466538), c_Groups_Ozero__class_Ozero(_1466538)), hAPP(_1466544, 36723 ^ [_1466538, _1466540, _1466542, _1466544, _1466546])))], (36725 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466540), 36723 ^ [_1466538, _1466540, _1466542, _1466544, _1466546]), _1466542)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466540, _1466538), _1466544), _1466542) = c_Groups_Ozero__class_Ozero(_1466538), hBOOL(hAPP(hAPP(c_member(_1466540), _1466546), _1466542)), -(hAPP(_1466544, _1466546) = c_Groups_Ozero__class_Ozero(_1466538))], (33735 ^ _779854) ^ [_1400455, _1400457, _1400459, _1400461, _1400463] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400455, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400457, tc_fun(_1400455, tc_HOL_Obool)), _1400459), _1400461)), _1400463) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400457, tc_fun(_1400455, tc_HOL_Obool)), _1400459), hAPP(hAPP(c_COMBC(_1400457, tc_fun(_1400455, tc_HOL_Obool), tc_fun(_1400455, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1400455, tc_HOL_Obool), tc_fun(tc_fun(_1400455, tc_HOL_Obool), tc_fun(_1400455, tc_HOL_Obool)), _1400457), c_Groups_Ominus__class_Ominus(tc_fun(_1400455, tc_HOL_Obool))), _1400461)), _1400463)))], (14392 ^ _779854) ^ [_1034246, _1034248, _1034250] : [14394 ^ _779854 : [(14397 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1034246, tc_HOL_Obool)), 14393 ^ [_1034246, _1034248, _1034250]), _1034250))], (14395 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1034246, tc_HOL_Obool)), 14393 ^ [_1034246, _1034248, _1034250]), _1034248)))]], -(_1034248 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1034246, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1034246, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1034246, tc_HOL_Obool), _1034248)), _1034250)))], (35895 ^ _779854) ^ [_1448554, _1448556, _1448558, _1448560, _1448562, _1448564] : [hAPP(c_Product__Type_Oapsnd(_1448554, _1448556, _1448558, _1448560), _1448562) = hAPP(c_Product__Type_Oapsnd(_1448554, _1448556, _1448558, _1448564), _1448562), -(hAPP(_1448560, hAPP(c_Product__Type_Osnd(_1448558, _1448554), _1448562)) = hAPP(_1448564, hAPP(c_Product__Type_Osnd(_1448558, _1448554), _1448562)))], (48964 ^ _779854) ^ [_1767287, _1767289, _1767291, _1767293] : [48972 ^ _779854 : [(48975 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1767293, 48971 ^ [_1767287, _1767289, _1767291, _1767293])))], (48973 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767287), 48971 ^ [_1767287, _1767289, _1767291, _1767293]), hAPP(c_List_Oset(_1767287), c_List_Oreplicate(_1767287, _1767289, _1767291)))))]], hBOOL(hAPP(_1767293, _1767291)), -(_1767289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34195 ^ _779854) ^ [_1412851, _1412853, _1412855, _1412857, _1412859] : [class_Complete__Lattice_Ocomplete__lattice(_1412851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412853), _1412855)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412851), _1412857), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412853, _1412851), _1412855), _1412859)) = hAPP(hAPP(c_Finite__Set_Ofold(_1412853, _1412851, hAPP(hAPP(c_COMBB(_1412851, tc_fun(_1412851, _1412851), _1412853), c_Lattices_Osemilattice__inf__class_Oinf(_1412851)), _1412859)), _1412857), _1412855))], (32169 ^ _779854) ^ [_1358610, _1358612, _1358614] : [class_Groups_Oordered__ab__group__add__abs(_1358610), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358610), hAPP(c_Groups_Oabs__class_Oabs(_1358610), _1358612)), hAPP(c_Groups_Oabs__class_Oabs(_1358610), _1358614))), hAPP(c_Groups_Oabs__class_Oabs(_1358610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358610), _1358612), _1358614)))))], (48824 ^ _779854) ^ [_1763847, _1763849] : [-(c_List_Osplice(_1763847, _1763849, c_List_Olist_ONil(_1763847)) = _1763849)], (47735 ^ _779854) ^ [_1739988, _1739990, _1739992] : [c_List_OdropWhile(_1739988, _1739990, _1739992) = c_List_Olist_ONil(_1739988), 47738 ^ _779854 : [(47739 ^ _779854) ^ [_1740079] : [hBOOL(hAPP(hAPP(c_member(_1739988), _1740079), hAPP(c_List_Oset(_1739988), _1739992))), -(hBOOL(hAPP(_1739990, _1740079)))]]], (23683 ^ _779854) ^ [_1209004, _1209006, _1209008, _1209010] : [class_Groups_Ocomm__monoid__mult(_1209004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209006), _1209008)), 23693 ^ _779854 : [(23696 ^ _779854) ^ [] : [hAPP(_1209010, 23692 ^ [_1209004, _1209006, _1209008, _1209010]) = c_Groups_Oone__class_Oone(_1209004)], (23694 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1209006), 23692 ^ [_1209004, _1209006, _1209008, _1209010]), _1209008)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1209004, _1209006, c_Groups_Otimes__class_Otimes(_1209004)), _1209010), c_Groups_Oone__class_Oone(_1209004)), _1209008) = c_Groups_Oone__class_Oone(_1209004))], (49162 ^ _779854) ^ [_1771024, _1771026, _1771028, _1771030, _1771032, _1771034] : [-(c_New__Random__Sequence_Opos__union(_1771024, _1771026, _1771028, _1771030, _1771032, _1771034) = c_New__DSequence_Opos__union(_1771024, hAPP(hAPP(hAPP(_1771026, _1771030), _1771032), _1771034), hAPP(hAPP(hAPP(_1771028, _1771030), _1771032), _1771034)))], (40684 ^ _779854) ^ [_1573500, _1573502, _1573504] : [class_Complete__Lattice_Ocomplete__lattice(_1573500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573500), hAPP(_1573502, _1573504)), _1573504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573500), c_Inductive_Ocomplete__lattice__class_Olfp(_1573500, _1573502)), _1573504)))], (10593 ^ _779854) ^ [_960092, _960094, _960096, _960098, _960100] : [class_Groups_Ominus(_960092), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960094, _960092)), _960096), _960098), _960100) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960092), hAPP(_960096, _960100)), hAPP(_960098, _960100)))], (28475 ^ _779854) ^ [_1294695, _1294697] : [class_Rings_Olinordered__semidom(_1294695), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294695), c_Groups_Ozero__class_Ozero(_1294695)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294695), _1294697))))], (37101 ^ _779854) ^ [_1476587] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1476587)) = _1476587)], (34545 ^ _779854) ^ [_1420818, _1420820] : [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(_1420818))), 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)), _1420820)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420818)), hAPP(c_Nat_OSuc, _1420820))))], (15672 ^ _779854) ^ [_1060316, _1060318, _1060320] : [class_Rings_Ocomm__ring__1(_1060316), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060316), _1060318), _1060320) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060316), _1060318), hAPP(c_Groups_Ouminus__class_Ouminus(_1060316), _1060320)))], (25671 ^ _779854) ^ [_1246536, _1246538, _1246540] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246536), _1246538)), _1246540) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246536), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246538), _1246540)))], (5464 ^ _779854) ^ [_863533, _863535, _863537, _863539, _863541, _863543] : [-(c_SetInterval_Oord_OatMost(_863543, _863539, _863535) = c_SetInterval_Oord_OatMost(_863541, _863537, _863533)), _863543 = _863541, _863539 = _863537, _863535 = _863533], (32181 ^ _779854) ^ [_1358916, _1358918, _1358920] : [class_Groups_Oordered__ab__group__add__abs(_1358916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358916), hAPP(c_Groups_Oabs__class_Oabs(_1358916), _1358918)), _1358920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358916), hAPP(c_Groups_Ouminus__class_Ouminus(_1358916), _1358918)), _1358920)))], (30410 ^ _779854) ^ [_1328954, _1328956] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328954, _1328956)), _1328956) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12052 ^ _779854) ^ [_989615, _989617, _989619, _989621] : [-(hBOOL(hAPP(hAPP(c_member(_989615), _989617), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989615, tc_HOL_Obool)), _989619), _989621)))), hBOOL(hAPP(hAPP(c_member(_989615), _989617), _989619)), hBOOL(hAPP(hAPP(c_member(_989615), _989617), _989621))], (46164 ^ _779854) ^ [_1706337, _1706339] : [-(hAPP(c_List_OremoveAll(_1706337, _1706339), c_List_Olist_ONil(_1706337)) = c_List_Olist_ONil(_1706337))], (10427 ^ _779854) ^ [_956731, _956733, _956735] : [class_Orderings_Olinorder(_956731), hBOOL(hAPP(c_Finite__Set_Ofinite(_956731), _956733)), hBOOL(hAPP(c_Finite__Set_Ofinite(_956731), _956735)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956731, tc_HOL_Obool)), _956733), _956735) = c_Orderings_Obot__class_Obot(tc_fun(_956731, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_956731), c_Big__Operators_Olattice_OSup__fin(_956731, c_Orderings_Oord__class_Omax(_956731), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_956731, tc_HOL_Obool)), _956733), _956735))), c_Big__Operators_Olattice_OSup__fin(_956731, c_Orderings_Oord__class_Omax(_956731), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956731, tc_HOL_Obool)), _956733), _956735))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_956731), c_Big__Operators_Olattice_OSup__fin(_956731, c_Orderings_Oord__class_Omax(_956731), _956733)), c_Big__Operators_Olattice_OSup__fin(_956731, c_Orderings_Oord__class_Omax(_956731), _956735)))], (36225 ^ _779854) ^ [_1455877, _1455879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1455877), 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)), _1455879)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1455877), _1455879) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1455877, _1455879)))], (26977 ^ _779854) ^ [_1269151, _1269153, _1269155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269151)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1269153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1269155), _1269151)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1269153), _1269155)), _1269151))], (30440 ^ _779854) ^ [_1329425] : [c_Nat__Transfer_Onat__set(_1329425), 30443 ^ _779854 : [(30444 ^ _779854) ^ [_1329491] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1329491), _1329425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329491)))]]], (25711 ^ _779854) ^ [_1247282, _1247284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247282), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247284), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247282), _1247284))), -(_1247282 = _1247284)], (21327 ^ _779854) ^ [_1164099, _1164101] : [21329 ^ _779854 : [(21332 ^ _779854) ^ [] : [hBOOL(hAPP(_1164101, 21328 ^ [_1164099, _1164101]))], (21330 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 21328 ^ [_1164099, _1164101]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1164099))))]], 21333 ^ _779854 : [(21334 ^ _779854) ^ [_1164254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1164254), _1164099)), -(hBOOL(hAPP(_1164101, _1164254)))]]], (52401 ^ _779854) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (43816 ^ _779854) ^ [_1653913, _1653915, _1653917, _1653919] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653913)), hAPP(hAPP(c_List_Oappend(_1653913), _1653915), _1653917)), c_List_Olists(_1653913, _1653919))), 43819 ^ _779854 : [(43822 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653913)), _1653917), c_List_Olists(_1653913, _1653919))))], (43820 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653913)), _1653915), c_List_Olists(_1653913, _1653919))))]]], (14167 ^ _779854) ^ [_1029850, _1029852, _1029854, _1029856, _1029858] : [c_Fun_Oinj__on(_1029850, _1029852, _1029854, _1029856), hBOOL(hAPP(hAPP(c_member(_1029850), _1029858), _1029856)), -(hAPP(c_Fun_Othe__inv__into(_1029850, _1029852, _1029856, _1029854), hAPP(_1029854, _1029858)) = _1029858)], (39939 ^ _779854) ^ [_1555324, _1555326, _1555328, _1555330] : [hBOOL(hAPP(c_Predicate_ODomainP(_1555324, _1555326, hAPP(hAPP(c_COMBC(_1555324, tc_fun(tc_prod(_1555324, _1555326), tc_HOL_Obool), tc_fun(_1555326, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555326, tc_fun(tc_fun(tc_prod(_1555324, _1555326), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555324, _1555326), tc_HOL_Obool), tc_fun(_1555326, tc_HOL_Obool)), _1555324), c_COMBC(_1555326, tc_fun(tc_prod(_1555324, _1555326), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555326, tc_prod(_1555324, _1555326)), tc_fun(_1555326, tc_fun(tc_fun(tc_prod(_1555324, _1555326), tc_HOL_Obool), tc_HOL_Obool)), _1555324), hAPP(c_COMBB(tc_prod(_1555324, _1555326), tc_fun(tc_fun(tc_prod(_1555324, _1555326), tc_HOL_Obool), tc_HOL_Obool), _1555326), c_member(tc_prod(_1555324, _1555326)))), c_Product__Type_OPair(_1555324, _1555326)))), _1555328)), _1555330)), -(hBOOL(hAPP(hAPP(c_member(_1555324), _1555330), hAPP(c_Relation_ODomain(_1555324, _1555326), _1555328))))], (1150 ^ _779854) ^ [_797181, _797183] : [-(class_Groups_Olinordered__ab__group__add(_797181)), _797183 = _797181, class_Groups_Olinordered__ab__group__add(_797183)], (49729 ^ _779854) ^ [_1784119, _1784121, _1784123, _1784125] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1784119, tc_fun(_1784121, tc_HOL_Obool)), _1784123), _1784125) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1784121, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1784121, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1784119, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1784121, tc_HOL_Obool)), c_HOL_OEx(_1784119)), hAPP(hAPP(c_COMBB(tc_fun(_1784119, tc_HOL_Obool), tc_fun(_1784119, tc_HOL_Obool), tc_fun(_1784121, tc_HOL_Obool)), hAPP(c_COMBS(_1784119, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1784119), c_fconj), hAPP(hAPP(c_COMBC(_1784119, tc_fun(_1784119, tc_HOL_Obool), tc_HOL_Obool), c_member(_1784119)), _1784123)))), hAPP(hAPP(c_COMBC(tc_fun(_1784121, tc_HOL_Obool), tc_fun(_1784119, tc_fun(_1784121, tc_HOL_Obool)), tc_fun(_1784119, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784121, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1784119, tc_fun(_1784121, tc_HOL_Obool)), tc_fun(_1784119, tc_HOL_Obool)), tc_fun(_1784121, tc_HOL_Obool)), c_COMBB(tc_fun(_1784121, tc_HOL_Obool), tc_HOL_Obool, _1784119)), c_fequal)), _1784125))))))], (47410 ^ _779854) ^ [_1733139, _1733141, _1733143, _1733145, _1733147] : [c_List_Olist__all2(_1733139, _1733141, _1733143, _1733145, _1733147), -(c_List_Olist__all2(_1733139, _1733141, _1733143, hAPP(c_List_Orev(_1733139), _1733145), hAPP(c_List_Orev(_1733141), _1733147)))], (29427 ^ _779854) ^ [_1310684] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1310684)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1310684)))], (32808 ^ _779854) ^ [_1370824, _1370826, _1370828, _1370830, _1370832, _1370834] : [hBOOL(hAPP(hAPP(c_member(_1370824), _1370826), _1370828)), hBOOL(hAPP(hAPP(_1370830, _1370826), _1370832)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1370824, tc_fun(_1370834, tc_HOL_Obool)), _1370828), _1370830), _1370832)))], (40663 ^ _779854) ^ [_1572960, _1572962, _1572964, _1572966, _1572968] : [_1572960 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1572962, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1572962, tc_HOL_Obool), tc_fun(_1572962, tc_HOL_Obool), tc_fun(_1572962, tc_HOL_Obool)), c_Set_OCollect(_1572962)), _1572964)), c_Orderings_Oorder__class_Omono(tc_fun(_1572962, tc_HOL_Obool), tc_fun(_1572962, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1572962, tc_HOL_Obool), tc_fun(_1572962, tc_HOL_Obool), tc_fun(_1572962, tc_HOL_Obool)), c_Set_OCollect(_1572962)), _1572964)), hBOOL(hAPP(hAPP(c_member(_1572962), _1572966), _1572968)), 40677 ^ _779854 : [(40680 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1572964, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572962, tc_HOL_Obool)), _1572968), _1572960)), 40676 ^ [_1572960, _1572962, _1572964, _1572966, _1572968]))], (40678 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572962), 40676 ^ [_1572960, _1572962, _1572964, _1572966, _1572968]), _1572968)))]], -(hBOOL(hAPP(hAPP(c_member(_1572962), _1572966), _1572960)))], (44827 ^ _779854) ^ [_1677058, _1677060, _1677062, _1677064, _1677066] : [class_Orderings_Olinorder(_1677058), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1677060, _1677058, _1677062), _1677064), _1677066) = c_List_Olist_ONil(_1677060)], (25967 ^ _779854) ^ [_1251795, _1251797] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251795), _1251797))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1251797, _1251795) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1251797), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1251797), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1251795)))], (34273 ^ _779854) ^ [_1414580, _1414582, _1414584] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414580), _1414582), _1414584) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1414580), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1414580, tc_Int_Oint), _1414582), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1414584))), class_Groups_Ocomm__monoid__add(_1414580), class_Groups_Ocomm__monoid__mult(_1414580)], (20910 ^ _779854) ^ [_1156161, _1156163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1156161), _1156163))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1156161), _1156163)))], (49275 ^ _779854) ^ [_1773519, _1773521, _1773523] : [hBOOL(hAPP(hAPP(c_member(_1773519), _1773523), hAPP(c_List_Oset(_1773519), _1773521))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1773519), _1773521), _1773523)))], (3144 ^ _779854) ^ [_826827, _826829] : [_826829 = _826827, -(c_List_Orotate1(_826829) = c_List_Orotate1(_826827))], (34017 ^ _779854) ^ [_1408255, _1408257, _1408259, _1408261, _1408263] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408255, tc_fun(_1408257, tc_HOL_Obool)), _1408259), hAPP(hAPP(c_COMBS(_1408255, tc_fun(_1408257, tc_HOL_Obool), tc_fun(_1408257, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408257, tc_HOL_Obool), tc_fun(tc_fun(_1408257, tc_HOL_Obool), tc_fun(_1408257, tc_HOL_Obool)), _1408255), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408257, tc_HOL_Obool))), _1408261)), _1408263)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408257, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1408257, tc_HOL_Obool), hAPP(c_Set_Oimage(_1408255, tc_fun(_1408257, tc_HOL_Obool), _1408261), _1408259))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1408257, tc_HOL_Obool), hAPP(c_Set_Oimage(_1408255, tc_fun(_1408257, tc_HOL_Obool), _1408263), _1408259))))], (7119 ^ _779854) ^ [_896902, _896904, _896906] : [class_Lattices_Olattice(_896902), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896902), _896904), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896902), _896906), _896904))))], (24124 ^ _779854) ^ [_1217429, _1217431, _1217433] : [class_Fields_Ofield__inverse__zero(_1217429), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217429), c_Groups_Oone__class_Oone(_1217429)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217429), _1217431), _1217433)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1217429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217429), c_Groups_Oone__class_Oone(_1217429)), _1217431)), _1217433))], (38017 ^ _779854) ^ [_1498846] : [-(c_Nitpick_Oone__frac(_1498846) = c_Nitpick_OAbs__Frac(_1498846, 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))))], (2062 ^ _779854) ^ [_809854, _809856, _809858, _809860] : [-(c_Int_Onat__aux(_809860, _809856) = c_Int_Onat__aux(_809858, _809854)), _809860 = _809858, _809856 = _809854], (36748 ^ _779854) ^ [_1467347, _1467349, _1467351, _1467353, _1467355, _1467357, _1467359] : [-(hAPP(c_Product__Type_Oapfst(_1467347, _1467349, _1467351, _1467353), hAPP(c_Product__Type_Oapsnd(_1467355, _1467351, _1467347, _1467357), _1467359)) = hAPP(hAPP(c_Product__Type_OPair(_1467349, _1467351), hAPP(_1467353, hAPP(c_Product__Type_Ofst(_1467347, _1467355), _1467359))), hAPP(_1467357, hAPP(c_Product__Type_Osnd(_1467347, _1467355), _1467359))))], (47649 ^ _779854) ^ [_1738076, _1738078, _1738080, _1738082, _1738084] : [hBOOL(hAPP(hAPP(c_member(_1738076), _1738078), hAPP(c_List_Oset(_1738076), _1738080))), -(hBOOL(hAPP(_1738082, _1738078))), -(c_List_OtakeWhile(_1738076, _1738082, hAPP(hAPP(c_List_Oappend(_1738076), _1738080), _1738084)) = c_List_OtakeWhile(_1738076, _1738082, _1738080))], (10639 ^ _779854) ^ [_961060, _961062, _961064] : [class_Orderings_Olinorder(_961060), hBOOL(hAPP(c_Finite__Set_Ofinite(_961060), _961062)), 10646 ^ _779854 : [(10653 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961060, tc_HOL_Obool)), _961062), hAPP(hAPP(c_Set_Oinsert(_961060), _961064), c_Orderings_Obot__class_Obot(tc_fun(_961060, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_961060, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_961060, c_Orderings_Oord__class_Omin(_961060), hAPP(hAPP(c_Set_Oinsert(_961060), _961064), _961062)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_961060), _961064), c_Big__Operators_Olattice_OInf__fin(_961060, c_Orderings_Oord__class_Omin(_961060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961060, tc_HOL_Obool)), _961062), hAPP(hAPP(c_Set_Oinsert(_961060), _961064), c_Orderings_Obot__class_Obot(tc_fun(_961060, tc_HOL_Obool)))))))], (10647 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961060, tc_HOL_Obool)), _961062), hAPP(hAPP(c_Set_Oinsert(_961060), _961064), c_Orderings_Obot__class_Obot(tc_fun(_961060, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_961060, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_961060, c_Orderings_Oord__class_Omin(_961060), hAPP(hAPP(c_Set_Oinsert(_961060), _961064), _961062)) = _961064)]]], (23302 ^ _779854) ^ [_1201492, _1201494, _1201496, _1201498, _1201500] : [class_Groups_Ocomm__monoid__add(_1201492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201494), _1201496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201494, tc_HOL_Obool)), _1201498), _1201496)), 23316 ^ _779854 : [(23319 ^ _779854) ^ [] : [hAPP(_1201500, 23315 ^ [_1201492, _1201494, _1201496, _1201498, _1201500]) = c_Groups_Ozero__class_Ozero(_1201492)], (23317 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201494), 23315 ^ [_1201492, _1201494, _1201496, _1201498, _1201500]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201494, tc_HOL_Obool)), _1201496), _1201498))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201494, _1201492), _1201500), _1201496) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201494, _1201492), _1201500), _1201498))], (52645 ^ _779854) ^ [_1838398, _1838400] : [_1838398 = _1838400, -(hBOOL(hAPP(hAPP(c_fequal, _1838398), _1838400)))], (31890 ^ _779854) ^ [_1353700, _1353702] : [class_Rings_Olinordered__idom(_1353700), 31893 ^ _779854 : [(31900 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1353702), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353700), hAPP(c_Int_Oring__1__class_Oof__int(_1353700), _1353702)), c_Groups_Ozero__class_Ozero(_1353700))))], (31894 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353700), hAPP(c_Int_Oring__1__class_Oof__int(_1353700), _1353702)), c_Groups_Ozero__class_Ozero(_1353700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1353702), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (42215 ^ _779854) ^ [_1613644, _1613646, _1613648, _1613650] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613644), tc_List_Olist(_1613644))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613644), tc_List_Olist(_1613644)), _1613646), _1613648)), c_List_Olex(_1613644, _1613650)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613644), tc_List_Olist(_1613644))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613644), tc_List_Olist(_1613644)), _1613646), _1613648)), c_List_Olexord(_1613644, _1613650))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613644)), _1613646) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613644)), _1613648)], (39449 ^ _779854) ^ [_1542480, _1542482, _1542484, _1542486] : [hAPP(hAPP(c_Relation_Orel__comp(_1542480, _1542480, _1542480), _1542482), _1542484) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542480, _1542480), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1542480, _1542480, _1542480), _1542486), _1542484) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542480, _1542480), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1542480, _1542480, _1542480), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1542480, _1542480), tc_HOL_Obool)), _1542482), _1542486)), _1542484) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542480, _1542480), tc_HOL_Obool)))], (6505 ^ _779854) ^ [_883944, _883946] : [_883946 = c_Orderings_Obot__class_Obot(tc_fun(_883944, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883944, tc_HOL_Obool)), _883946), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_883944, tc_HOL_Obool)), _883946))))], (5372 ^ _779854) ^ [_862093, _862095] : [_862095 = _862093, -(c_Orderings_Obot__class_Obot(_862095) = c_Orderings_Obot__class_Obot(_862093))], (38480 ^ _779854) ^ [_1511012, _1511014, _1511016, _1511018] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511012), _1511014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511012, _1511012), tc_HOL_Obool)), _1511016), hAPP(hAPP(c_Product__Type_OSigma(_1511012, _1511012), _1511014), hAPP(c_COMBK(tc_fun(_1511012, tc_HOL_Obool), _1511012), _1511014)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1511012, tc_HOL_Obool)), _1511018), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1511012), _1511014), _1511016))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1511012), _1511018)))], (19387 ^ _779854) ^ [_1129549, _1129551, _1129553] : [class_Rings_Olinordered__ring__strict(_1129549), 19390 ^ _779854 : [(19405 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129549), _1129551), _1129553)), c_Groups_Ozero__class_Ozero(_1129549)))), 19406 ^ _779854 : [(19413 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), _1129551), c_Groups_Ozero__class_Ozero(_1129549))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), c_Groups_Ozero__class_Ozero(_1129549)), _1129553))], (19407 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), c_Groups_Ozero__class_Ozero(_1129549)), _1129551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), _1129553), c_Groups_Ozero__class_Ozero(_1129549)))]]], (19391 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129549), _1129551), _1129553)), c_Groups_Ozero__class_Ozero(_1129549))), 19396 ^ _779854 : [(19399 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), _1129553), c_Groups_Ozero__class_Ozero(_1129549))))], (19397 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), c_Groups_Ozero__class_Ozero(_1129549)), _1129551)))]], 19400 ^ _779854 : [(19403 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), c_Groups_Ozero__class_Ozero(_1129549)), _1129553)))], (19401 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129549), _1129551), c_Groups_Ozero__class_Ozero(_1129549))))]]]]], (17724 ^ _779854) ^ [_1101152] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101152)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1101152))], (44079 ^ _779854) ^ [_1659654, _1659656, _1659658, _1659660, _1659662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659654), tc_List_Olist(_1659654))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659654), tc_List_Olist(_1659654)), _1659656), _1659658)), c_List_Olexord(_1659654, _1659660))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659654), tc_List_Olist(_1659654))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659654), tc_List_Olist(_1659654)), hAPP(hAPP(c_List_Oappend(_1659654), _1659662), _1659656)), hAPP(hAPP(c_List_Oappend(_1659654), _1659662), _1659658))), c_List_Olexord(_1659654, _1659660))))], (34589 ^ _779854) ^ [_1421920, _1421922] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421920)), hAPP(c_Nat_OSuc, _1421922)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1421920))), 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, _1421922))), 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)), _1421922)))))], (45172 ^ _779854) ^ [_1684290, _1684292, _1684294, _1684296, _1684298] : [class_Groups_Ocomm__monoid__add(_1684290), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1684290), hAPP(hAPP(c_List_Omap(_1684292, _1684290), hAPP(hAPP(c_COMBS(_1684292, _1684290, _1684290), hAPP(hAPP(c_COMBB(_1684290, tc_fun(_1684290, _1684290), _1684292), c_Groups_Oplus__class_Oplus(_1684290)), _1684294)), _1684296)), _1684298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1684290), hAPP(c_List_Omonoid__add__class_Olistsum(_1684290), hAPP(hAPP(c_List_Omap(_1684292, _1684290), _1684294), _1684298))), hAPP(c_List_Omonoid__add__class_Olistsum(_1684290), hAPP(hAPP(c_List_Omap(_1684292, _1684290), _1684296), _1684298))))], (44470 ^ _779854) ^ [_1669775, _1669777, _1669779] : [-(_1669775 = c_List_Olist_ONil(_1669777)), -(hAPP(c_List_Ohd(_1669777), hAPP(hAPP(c_List_Oappend(_1669777), _1669775), _1669779)) = hAPP(c_List_Ohd(_1669777), _1669775))], (18477 ^ _779854) ^ [_1114699] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1114699)))], (34765 ^ _779854) ^ [_1425948, _1425950] : [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), _1425948))), 34768 ^ _779854 : [(34775 ^ _779854) ^ [] : [-(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), _1425950)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425948))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425950), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425948)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425948)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425950), 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), _1425948)))))], (34769 ^ _779854) ^ [] : [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), _1425950)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425948)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425950), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425948)) = 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), _1425950)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425948))))]]], (28186 ^ _779854) ^ [_1289601] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1289601)) = _1289601)], (37065 ^ _779854) ^ [_1475566, _1475568, _1475570, _1475572, _1475574, _1475576] : [hBOOL(hAPP(hAPP(c_member(_1475566), _1475568), _1475570)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475566, _1475572)), hAPP(hAPP(c_Product__Type_OPair(_1475566, _1475572), _1475568), _1475574)), _1475576)), -(hBOOL(hAPP(hAPP(c_member(_1475572), _1475574), hAPP(c_Relation_OImage(_1475566, _1475572, _1475576), _1475570))))], (15698 ^ _779854) ^ [_1060889, _1060891, _1060893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060889), _1060891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060889), _1060893)), 15705 ^ _779854 : [(15712 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060891), _1060893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060891), _1060889)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060893), _1060889))))], (15706 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060891), _1060889)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060893), _1060889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060891), _1060893)))]]], (15810 ^ _779854) ^ [_1063179, _1063181, _1063183] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063179), _1063181) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063179), _1063183), -(_1063181 = _1063183)], (49463 ^ _779854) ^ [_1777724, _1777726, _1777728, _1777730] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1777724, _1777726, _1777728, c_Code__Numeral_OSuc__code__numeral(_1777730)) = hAPP(hAPP(_1777728, _1777730), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1777724, _1777726, _1777728, _1777730)))], (2234 ^ _779854) ^ [_812558, _812560, _812562, _812564] : [-(c_Orderings_Oord_Omax(_812564, _812560) = c_Orderings_Oord_Omax(_812562, _812558)), _812564 = _812562, _812560 = _812558], (45025 ^ _779854) ^ [_1680323, _1680325, _1680327] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680323)), _1680325), c_List_Olists(_1680323, _1680327))), -(_1680325 = c_List_Olist_ONil(_1680323)), 45034 ^ _779854 : [(45039 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680323)), 45033 ^ [_1680323, _1680325, _1680327]), c_List_Olists(_1680323, _1680327))))], (45037 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1680323), 45032 ^ [_1680323, _1680325, _1680327]), _1680327)))], (45035 ^ _779854) ^ [] : [-(_1680325 = hAPP(hAPP(c_List_Olist_OCons(_1680323), 45032 ^ [_1680323, _1680325, _1680327]), 45033 ^ [_1680323, _1680325, _1680327]))]]], (47486 ^ _779854) ^ [_1734631, _1734633, _1734635] : [-(hAPP(c_List_Orev(_1734631), hAPP(hAPP(c_List_Otake(_1734631), _1734633), _1734635)) = hAPP(hAPP(c_List_Odrop(_1734631), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734631)), _1734635)), _1734633)), hAPP(c_List_Orev(_1734631), _1734635)))], (32227 ^ _779854) ^ [_1359720, _1359722] : [class_Groups_Oordered__ab__group__add__abs(_1359720), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359720), hAPP(c_Groups_Ouminus__class_Ouminus(_1359720), _1359722)), hAPP(c_Groups_Oabs__class_Oabs(_1359720), _1359722))))], (33761 ^ _779854) ^ [_1401151, _1401153, _1401155, _1401157, _1401159] : [_1401151 = c_Orderings_Obot__class_Obot(tc_fun(_1401153, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401153, tc_fun(_1401155, tc_HOL_Obool)), _1401151), hAPP(hAPP(c_COMBC(_1401153, tc_fun(_1401155, tc_HOL_Obool), tc_fun(_1401155, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401155, tc_HOL_Obool), tc_fun(tc_fun(_1401155, tc_HOL_Obool), tc_fun(_1401155, tc_HOL_Obool)), _1401153), c_Groups_Ominus__class_Ominus(tc_fun(_1401155, tc_HOL_Obool))), _1401157)), _1401159)) = c_Orderings_Otop__class_Otop(tc_fun(_1401155, tc_HOL_Obool)))], (46046 ^ _779854) ^ [_1703951, _1703953] : [-(c_Enum_On__lists(_1703951, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1703953) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1703951)), c_List_Olist_ONil(_1703951)), c_List_Olist_ONil(tc_List_Olist(_1703951))))], (25877 ^ _779854) ^ [_1250201, _1250203, _1250205, _1250207, _1250209, _1250211] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1250201), _1250203)), _1250205) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1250207), _1250209)), _1250211), 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), _1250207), _1250209)), _1250211))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250211), _1250207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250207), _1250201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250203), _1250209)))], (37608 ^ _779854) ^ [_1489056, _1489058] : [-(c_Equiv__Relations_Oequivp(_1489056, _1489058)), 37613 ^ _779854 : [(37616 ^ _779854) ^ [] : [hAPP(_1489058, 37609 ^ [_1489056, _1489058]) = hAPP(_1489058, 37610 ^ [_1489056, _1489058])], (37614 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1489058, 37609 ^ [_1489056, _1489058]), 37610 ^ [_1489056, _1489058])))]], 37617 ^ _779854 : [(37620 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1489058, 37609 ^ [_1489056, _1489058]), 37610 ^ [_1489056, _1489058]))], (37618 ^ _779854) ^ [] : [-(hAPP(_1489058, 37609 ^ [_1489056, _1489058]) = hAPP(_1489058, 37610 ^ [_1489056, _1489058]))]]], (23976 ^ _779854) ^ [_1214844, _1214846] : [class_Groups_Omonoid__mult(_1214844), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214844), _1214846), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1214846)], (12226 ^ _779854) ^ [_992865, _992867, _992869, _992871, _992873] : [c_Finite__Set_Ofolding__one(_992865, _992867, _992869), hBOOL(hAPP(c_Finite__Set_Ofinite(_992865), _992871)), -(hBOOL(hAPP(hAPP(c_member(_992865), _992873), _992871))), -(_992871 = c_Orderings_Obot__class_Obot(tc_fun(_992865, tc_HOL_Obool))), -(hAPP(_992869, hAPP(hAPP(c_Set_Oinsert(_992865), _992873), _992871)) = hAPP(hAPP(_992867, _992873), hAPP(_992869, _992871)))], (12932 ^ _779854) ^ [_1007211, _1007213, _1007215, _1007217, _1007219] : [-(hBOOL(hAPP(hAPP(c_member(_1007211), _1007213), c_SetInterval_Oord_OatLeastAtMost(_1007211, _1007215, _1007217, _1007219)))), hBOOL(hAPP(hAPP(_1007215, _1007217), _1007213)), hBOOL(hAPP(hAPP(_1007215, _1007213), _1007219))], (42281 ^ _779854) ^ [_1615706, _1615708, _1615710, _1615712] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615706), tc_List_Olist(_1615706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615706), tc_List_Olist(_1615706)), _1615708), _1615710)), c_List_Olistrel1(_1615706, hAPP(c_Relation_Oconverse(_1615706, _1615706), _1615712)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615706), tc_List_Olist(_1615706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615706), tc_List_Olist(_1615706)), _1615708), _1615710)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1615706), tc_List_Olist(_1615706)), c_List_Olistrel1(_1615706, _1615712)))))], (7886 ^ _779854) ^ [_911699, _911701, _911703] : [class_Orderings_Olinorder(_911699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911699), _911701), _911703)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911699, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_911699), _911701)), c_SetInterval_Oord__class_OgreaterThanAtMost(_911699, _911701, _911703)) = hAPP(c_SetInterval_Oord__class_OatMost(_911699), _911703))], (10897 ^ _779854) ^ [_966380, _966382, _966384, _966386, _966388] : [c_Fun_Oinj__on(_966380, _966382, _966384, c_Orderings_Otop__class_Otop(tc_fun(_966380, tc_HOL_Obool))), 10900 ^ _779854 : [(10907 ^ _779854) ^ [] : [_966386 = _966388, -(hAPP(c_Set_Oimage(_966380, _966382, _966384), _966386) = hAPP(c_Set_Oimage(_966380, _966382, _966384), _966388))], (10901 ^ _779854) ^ [] : [hAPP(c_Set_Oimage(_966380, _966382, _966384), _966386) = hAPP(c_Set_Oimage(_966380, _966382, _966384), _966388), -(_966386 = _966388)]]], (35909 ^ _779854) ^ [_1448902, _1448904, _1448906, _1448908, _1448910] : [hAPP(c_Product__Type_Osnd(_1448902, _1448904), hAPP(hAPP(c_Product__Type_OPair(_1448902, _1448904), _1448906), _1448908)) = _1448910, -(_1448908 = _1448910)], (1550 ^ _779854) ^ [_802181, _802183] : [-(class_Groups_Olinordered__ab__semigroup__add(_802181)), _802183 = _802181, class_Groups_Olinordered__ab__semigroup__add(_802183)], (48800 ^ _779854) ^ [_1763089, _1763091] : [-(hAPP(c_New__DSequence_Opos__empty(_1763089), _1763091) = c_Lazy__Sequence_Oempty(_1763089))], (45166 ^ _779854) ^ [_1684087, _1684089, _1684091, _1684093, _1684095] : [class_Rings_Osemiring__0(_1684087), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1684087), hAPP(hAPP(c_List_Omap(_1684089, _1684087), hAPP(hAPP(c_COMBC(_1684089, _1684087, _1684087), hAPP(hAPP(c_COMBB(_1684087, tc_fun(_1684087, _1684087), _1684089), c_Groups_Otimes__class_Otimes(_1684087)), _1684091)), _1684093)), _1684095)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1684087), hAPP(c_List_Omonoid__add__class_Olistsum(_1684087), hAPP(hAPP(c_List_Omap(_1684089, _1684087), _1684091), _1684095))), _1684093))], (17662 ^ _779854) ^ [_1100060, _1100062, _1100064, _1100066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1100060), _1100062)), hBOOL(hAPP(hAPP(c_member(_1100060), _1100064), _1100062)), -(hBOOL(hAPP(hAPP(c_member(_1100060), _1100064), _1100066))), -(hAPP(c_Finite__Set_Ocard(_1100060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100060, tc_HOL_Obool)), _1100062), hAPP(hAPP(c_Set_Oinsert(_1100060), _1100064), _1100066))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1100060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100060, tc_HOL_Obool)), _1100062), _1100066))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45146 ^ _779854) ^ [_1683496, _1683498, _1683500, _1683502] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683496)), hAPP(hAPP(c_List_Omap(_1683498, _1683496), _1683500), _1683502)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683498)), _1683502))], (29649 ^ _779854) ^ [_1314619, _1314621] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1314619)), _1314621) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1314619), _1314621))), _1314621))], (49218 ^ _779854) ^ [_1772140, _1772142, _1772144] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1772140, _1772142), _1772144) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1772140, tc_Lazy__Sequence_Olazy__sequence(_1772140)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1772140, tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1772140, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat)), _1772140), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1772140), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1772140)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1772140, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1772140), tc_Nat_Onat)), _1772140), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1772140))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1772140), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1772142))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1772140, _1772142))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1772140), _1772144)))], (46629 ^ _779854) ^ [_1718217, _1718219] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718217), _1718219))), -(c_List_Oupt(_1718217, hAPP(c_Nat_OSuc, _1718219)) = c_List_Olist_ONil(tc_Nat_Onat))], (16591 ^ _779854) ^ [_1078969, _1078971, _1078973, _1078975, _1078977, _1078979, _1078981, _1078983] : [class_Groups_Ocomm__monoid__add(_1078969), class_Orderings_Oord(_1078971), _1078973 = _1078975, _1078977 = _1078979, 16609 ^ _779854 : [(16614 ^ _779854) ^ [] : [hAPP(_1078981, 16608 ^ [_1078969, _1078971, _1078973, _1078975, _1078977, _1078979, _1078981, _1078983]) = hAPP(_1078983, 16608 ^ [_1078969, _1078971, _1078973, _1078975, _1078977, _1078979, _1078981, _1078983])], (16612 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078971), 16608 ^ [_1078969, _1078971, _1078973, _1078975, _1078977, _1078979, _1078981, _1078983]), _1078979)))], (16610 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078971), _1078975), 16608 ^ [_1078969, _1078971, _1078973, _1078975, _1078977, _1078979, _1078981, _1078983])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1078971, _1078969), _1078981), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1078971, _1078973), _1078977)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1078971, _1078969), _1078983), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1078971, _1078975), _1078979)))], (11400 ^ _779854) ^ [_976782, _976784] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976782), _976784)), 11403 ^ _779854 : [(11410 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976782), c_Orderings_Otop__class_Otop(tc_fun(_976782, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976782), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_976782, tc_HOL_Obool)), _976784))))], (11404 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976782), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_976782, tc_HOL_Obool)), _976784))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976782), c_Orderings_Otop__class_Otop(tc_fun(_976782, tc_HOL_Obool)))))]]], (7696 ^ _779854) ^ [_907757, _907759] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907757, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_907757, tc_HOL_Obool))), _907759) = _907759)], (52121 ^ _779854) ^ [_1832948, _1832950] : [-(class_Finite__Set_Ofinite(tc_fun(_1832948, _1832950))), class_Finite__Set_Ofinite(_1832948), class_Finite__Set_Ofinite(_1832950)], (38947 ^ _779854) ^ [_1523761, _1523763, _1523765, _1523767, _1523769] : [c_Relation_Orefl__on(_1523761, _1523763, _1523765), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523761, _1523761)), hAPP(hAPP(c_Product__Type_OPair(_1523761, _1523761), _1523767), _1523769)), _1523765)), -(hBOOL(hAPP(hAPP(c_member(_1523761), _1523767), _1523763)))], (35042 ^ _779854) ^ [_1431647, _1431649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431647)), 35045 ^ _779854 : [(35052 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431649), _1431647))), -(c_Divides_OposDivAlg(_1431649, _1431647) = hAPP(c_Divides_Oadjust(_1431647), c_Divides_OposDivAlg(_1431649, 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)))), _1431647))))], (35046 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431649), _1431647)), -(c_Divides_OposDivAlg(_1431649, _1431647) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431649))]]], (36842 ^ _779854) ^ [_1469313, _1469315, _1469317, _1469319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1469313), _1469315)), -(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), _1469313), _1469317)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1469315), _1469319))), c_FunDef_Opair__leq)))], (20053 ^ _779854) ^ [_1141406, _1141408, _1141410] : [class_Groups_Ogroup__add(_1141406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141406), _1141408), _1141410) = c_Groups_Ozero__class_Ozero(_1141406), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1141406), _1141408) = _1141410)], (19747 ^ _779854) ^ [_1136036, _1136038, _1136040, _1136042] : [class_Rings_Olinordered__semiring__strict(_1136036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136036), _1136038), _1136040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136036), c_Groups_Ozero__class_Ozero(_1136036)), _1136042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136036), _1136038), _1136042)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136036), _1136040), _1136042))))], (15432 ^ _779854) ^ [_1055297, _1055299, _1055301] : [class_Groups_Oab__group__add(_1055297), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1055297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055297), _1055299), _1055301)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055297), hAPP(c_Groups_Ouminus__class_Ouminus(_1055297), _1055299)), hAPP(c_Groups_Ouminus__class_Ouminus(_1055297), _1055301)))], (30483 ^ _779854) ^ [_1330296, _1330298, _1330300, _1330302] : [class_Divides_Osemiring__div(_1330296), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330296), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1330296), _1330298), _1330300)), _1330300)), c_Divides_Odiv__class_Omod(_1330296, _1330298, _1330300))), _1330302) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330296), _1330298), _1330302))], (36207 ^ _779854) ^ [_1455343, _1455345, _1455347] : [-(hAPP(c_Product__Type_Ofst(_1455343, _1455345), _1455347) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1455343, _1455345, _1455343), c_COMBK(_1455343, _1455345)), _1455347))], (28086 ^ _779854) ^ [_1287927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1287927)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1287927)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1287927)))], (39469 ^ _779854) ^ [_1542991, _1542993, _1542995] : [_1542995 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542991, _1542993), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1542991, _1542993), _1542995) = c_Orderings_Obot__class_Obot(tc_fun(_1542993, tc_HOL_Obool)))], (37028 ^ _779854) ^ [_1474485, _1474487, _1474489, _1474491, _1474493] : [-(hAPP(c_Relation_OImage(_1474485, _1474487, _1474489), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474485, tc_HOL_Obool)), _1474491), _1474493)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474487, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474485, _1474487, _1474489), _1474491)), hAPP(c_Relation_OImage(_1474485, _1474487, _1474489), _1474493)))], (35713 ^ _779854) ^ [_1444929, _1444931, _1444933] : [35715 ^ _779854 : [(35718 ^ _779854) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1444929, _1444931), 35714 ^ [_1444929, _1444931, _1444933]))], (35716 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1444931, 35714 ^ [_1444929, _1444931, _1444933]), _1444933)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1444929, _1444931), _1444933)))], (35040 ^ _779854) ^ [_1431545, _1431547, _1431549, _1431551] : [-(c_Nat_Onat_Onat__case(_1431545, _1431547, _1431549, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431551)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1431545), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431551))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1431545, _1431545), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1431545, tc_fun(_1431545, _1431545)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1431545, tc_fun(_1431545, _1431545)), tc_Int_Oint), c_If(_1431545)), c_Nat__Numeral_Oneg)), _1431547)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1431545, tc_Int_Oint), _1431549), c_Int_Onat))))], (38893 ^ _779854) ^ [_1522183] : [-(c_Relation_Orefl__on(_1522183, c_Orderings_Obot__class_Obot(tc_fun(_1522183, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1522183, _1522183), tc_HOL_Obool))))], (41152 ^ _779854) ^ [_1585629, _1585631] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585629, _1585629), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1585629, _1585631)), c_Relation_OId(_1585629)) = c_Transitive__Closure_Ortrancl(_1585629, _1585631))], (52411 ^ _779854) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (18807 ^ _779854) ^ [_1119492, _1119494] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119492), _1119494) = _1119492, -(_1119494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37247 ^ _779854) ^ [_1480635, _1480637, _1480639, _1480641] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1480635, _1480635)), hAPP(hAPP(c_Product__Type_OPair(_1480635, _1480635), _1480637), _1480639)), c_Relation_OId__on(_1480635, _1480641))), 37250 ^ _779854 : [(37253 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480635), _1480637), _1480641)))], (37251 ^ _779854) ^ [] : [-(_1480637 = _1480639)]]], (52593 ^ _779854) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (28651 ^ _779854) ^ [_1297689, _1297691] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297689), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297691)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1297689), _1297691)))], (17829 ^ _779854) ^ [_1102814, _1102816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1102814)), hAPP(c_Nat_OSuc, _1102816))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102814), _1102816)))], (43901 ^ _779854) ^ [_1655834, _1655836, _1655838] : [class_Groups_Omonoid__add(_1655834), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1655834), hAPP(hAPP(c_List_Oappend(_1655834), _1655836), _1655838)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655834), hAPP(c_List_Omonoid__add__class_Olistsum(_1655834), _1655836)), hAPP(c_List_Omonoid__add__class_Olistsum(_1655834), _1655838)))], (24489 ^ _779854) ^ [_1224201, _1224203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224201)), 24492 ^ _779854 : [(24501 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224201), _1224203) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1224201 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1224203 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (24493 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224201), _1224203) = c_Groups_Oone__class_Oone(tc_Int_Oint), 24496 ^ _779854 : [(24499 ^ _779854) ^ [] : [-(_1224203 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (24497 ^ _779854) ^ [] : [-(_1224201 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (11696 ^ _779854) ^ [_982744, _982746, _982748, _982750] : [hBOOL(hAPP(hAPP(c_member(_982744), _982746), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982744, tc_HOL_Obool)), _982748), _982750))), 11699 ^ _779854 : [(11702 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_982744), _982746), _982750)))], (11700 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_982744), _982746), _982748)))]]], (50975 ^ _779854) ^ [_1810421, _1810423, _1810425, _1810427, _1810429] : [c_Fun_Obij__betw(_1810421, _1810423, _1810425, c_Orderings_Otop__class_Otop(tc_fun(_1810421, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810423, tc_HOL_Obool))), 50978 ^ _779854 : [(50985 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1810423, tc_HOL_Obool)), _1810427), hAPP(c_Set_Oimage(_1810421, _1810423, _1810425), _1810429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1810421, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1810421, _1810423, _1810425), _1810427)), _1810429)))], (50979 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1810421, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1810421, _1810423, _1810425), _1810427)), _1810429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1810423, tc_HOL_Obool)), _1810427), hAPP(c_Set_Oimage(_1810421, _1810423, _1810425), _1810429))))]]], (45454 ^ _779854) ^ [_1690446, _1690448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1690446), _1690448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1690446)), hAPP(c_Code__Numeral_Oof__nat, _1690448))))], (30169 ^ _779854) ^ [_1324350, _1324352, _1324354, _1324356, _1324358, _1324360] : [class_Divides_Osemiring__div(_1324350), c_Divides_Odiv__class_Omod(_1324350, _1324352, _1324354) = c_Divides_Odiv__class_Omod(_1324350, _1324356, _1324354), c_Divides_Odiv__class_Omod(_1324350, _1324358, _1324354) = c_Divides_Odiv__class_Omod(_1324350, _1324360, _1324354), -(c_Divides_Odiv__class_Omod(_1324350, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324350), _1324352), _1324358), _1324354) = c_Divides_Odiv__class_Omod(_1324350, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324350), _1324356), _1324360), _1324354))], (10935 ^ _779854) ^ [_967073, _967075, _967077, _967079] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967073, tc_HOL_Obool)), _967075), hAPP(hAPP(c_Set_Oinsert(_967073), _967077), _967079)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967073, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967073, tc_HOL_Obool)), _967075), _967079)), hAPP(hAPP(c_Set_Oinsert(_967073), _967077), c_Orderings_Obot__class_Obot(tc_fun(_967073, tc_HOL_Obool)))))], (47416 ^ _779854) ^ [_1733274, _1733276, _1733278] : [hAPP(c_List_Orev(_1733274), _1733276) = hAPP(c_List_Orev(_1733274), _1733278), -(_1733276 = _1733278)], (26863 ^ _779854) ^ [_1267238, _1267240, _1267242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1267238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1267240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267240), _1267242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267238), _1267242)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267238), _1267240))))], (41182 ^ _779854) ^ [_1586427] : [-(c_Transitive__Closure_Ortrancl(_1586427, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1586427, _1586427), tc_HOL_Obool))) = c_Relation_OId(_1586427))], (32778 ^ _779854) ^ [_1370162, _1370164, _1370166, _1370168, _1370170, _1370172] : [hBOOL(hAPP(hAPP(c_member(_1370162), _1370164), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370166, tc_fun(_1370162, tc_HOL_Obool)), _1370168), _1370170))), hBOOL(hAPP(hAPP(c_member(_1370166), _1370172), _1370168)), -(hBOOL(hAPP(hAPP(c_member(_1370162), _1370164), hAPP(_1370170, _1370172))))], (48858 ^ _779854) ^ [_1764596] : [-(c_Predicate_Oconversep(_1764596, _1764596, c_fequal) = c_fequal)], (40157 ^ _779854) ^ [_1561232, _1561234, _1561236] : [hBOOL(hAPP(c_Predicate_OPowp(_1561232, _1561234), _1561236)), 40160 ^ _779854 : [(40161 ^ _779854) ^ [_1561316] : [hBOOL(hAPP(hAPP(c_member(_1561232), _1561316), _1561236)), -(hBOOL(hAPP(_1561234, _1561316)))]]], (50090 ^ _779854) ^ [_1792434, _1792436] : [c_Relation_Osym(_1792434, _1792436), -(hAPP(c_Relation_Oconverse(_1792434, _1792434), _1792436) = _1792436)], (30079 ^ _779854) ^ [_1322473, _1322475] : [c_Nat__Transfer_Onat__set(_1322473), c_Nat__Transfer_Onat__set(_1322475), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1322473), _1322475) = 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), _1322473)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1322475))))], (29257 ^ _779854) ^ [_1307715, _1307717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1307715), 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)))), _1307717))), 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)))), _1307715)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1307717), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1307715))], (6625 ^ _779854) ^ [_885990, _885992, _885994] : [class_Groups_Oordered__ab__group__add(_885990), 6628 ^ _779854 : [(6635 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885990), hAPP(c_Groups_Ouminus__class_Ouminus(_885990), _885994)), _885992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885990), hAPP(c_Groups_Ouminus__class_Ouminus(_885990), _885992)), _885994)))], (6629 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885990), hAPP(c_Groups_Ouminus__class_Ouminus(_885990), _885992)), _885994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885990), hAPP(c_Groups_Ouminus__class_Ouminus(_885990), _885994)), _885992)))]]], (41156 ^ _779854) ^ [_1585743, _1585745] : [-(c_Transitive__Closure_Ortrancl(_1585743, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585743, _1585743), tc_HOL_Obool)), _1585745), c_Relation_OId(_1585743))) = c_Transitive__Closure_Ortrancl(_1585743, _1585745))], (11889 ^ _779854) ^ [_986419, _986421] : [hBOOL(hAPP(hAPP(c_member(_986419), _986421), c_Orderings_Obot__class_Obot(tc_fun(_986419, tc_HOL_Obool))))], (43804 ^ _779854) ^ [_1653622, _1653624, _1653626, _1653628, _1653630, _1653632] : [hAPP(hAPP(c_List_Olist_OCons(_1653622), _1653624), _1653626) = _1653628, _1653630 = hAPP(hAPP(c_List_Oappend(_1653622), _1653626), _1653632), -(hAPP(hAPP(c_List_Olist_OCons(_1653622), _1653624), _1653630) = hAPP(hAPP(c_List_Oappend(_1653622), _1653628), _1653632))], (41054 ^ _779854) ^ [_1583276, _1583278, _1583280] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583276, _1583276)), _1583278), _1583280)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583276, _1583276)), _1583278), c_Transitive__Closure_Ortrancl(_1583276, _1583280))))], (27043 ^ _779854) ^ [_1270282, _1270284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1270282)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1270284))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1270282), _1270284))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1270282), c_Int_OPls)))], (38364 ^ _779854) ^ [_1508060, _1508062, _1508064, _1508066, _1508068] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1508060, _1508062), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1508060, tc_HOL_Obool)), _1508064), _1508066)), hAPP(c_COMBK(tc_fun(_1508062, tc_HOL_Obool), _1508060), _1508068)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1508060, _1508062), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1508060, _1508062), _1508064), hAPP(c_COMBK(tc_fun(_1508062, tc_HOL_Obool), _1508060), _1508068))), hAPP(hAPP(c_Product__Type_OSigma(_1508060, _1508062), _1508066), hAPP(c_COMBK(tc_fun(_1508062, tc_HOL_Obool), _1508060), _1508068))))], (30313 ^ _779854) ^ [_1327244, _1327246, _1327248, _1327250] : [class_Divides_Osemiring__div(_1327244), -(c_Divides_Odiv__class_Omod(_1327244, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327244), _1327246), _1327248), _1327250) = c_Divides_Odiv__class_Omod(_1327244, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327244), _1327246), c_Divides_Odiv__class_Omod(_1327244, _1327248, _1327250)), _1327250))], (37113 ^ _779854) ^ [_1476895] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1476895) = 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, _1476895)), 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))))))))], (37089 ^ _779854) ^ [_1476254] : [-(c_Wellfounded_Omeasure(_1476254) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1476254), c_Wellfounded_Oless__than))], (2954 ^ _779854) ^ [_823846, _823848, _823850, _823852, _823854, _823856] : [-(c_Nitpick_Oplus__frac(_823856, _823852, _823848) = c_Nitpick_Oplus__frac(_823854, _823850, _823846)), _823856 = _823854, _823852 = _823850, _823848 = _823846], (27517 ^ _779854) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (44616 ^ _779854) ^ [_1672402, _1672404, _1672406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1672402), _1672404)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1672402), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1672404), _1672406))))], (26679 ^ _779854) ^ [_1264487] : [class_Int_Onumber__ring(_1264487), -(c_Groups_Ozero__class_Ozero(_1264487) = hAPP(c_Int_Onumber__class_Onumber__of(_1264487), c_Int_OPls))], (10765 ^ _779854) ^ [_963509, _963511] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963509, tc_HOL_Obool)), _963511), c_Orderings_Obot__class_Obot(tc_fun(_963509, tc_HOL_Obool))) = _963511)], (1410 ^ _779854) ^ [_800431, _800433] : [-(class_Lattices_Osemilattice__sup(_800431)), _800433 = _800431, class_Lattices_Osemilattice__sup(_800433)], (16149 ^ _779854) ^ [_1069835, _1069837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069835), _1069837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069837), _1069835)), -(_1069835 = _1069837)], (22651 ^ _779854) ^ [_1189032, _1189034, _1189036, _1189038, _1189040] : [class_Fields_Olinordered__field(_1189032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189032), c_Groups_Ozero__class_Ozero(_1189032)), _1189034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189032), _1189034), _1189036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189032), c_Groups_Ozero__class_Ozero(_1189032)), _1189038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189032), _1189038), _1189040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189032), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189032), _1189034), _1189040)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189032), _1189036), _1189038))))], (3874 ^ _779854) ^ [_838216, _838218] : [_838218 = _838216, -(c_Nat_Osemiring__1__class_Oof__nat(_838218) = c_Nat_Osemiring__1__class_Oof__nat(_838216))], (40047 ^ _779854) ^ [_1557993, _1557995] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1557993, _1557995), 40048 ^ [_1557993, _1557995])), -(c_Wellfounded_OwfP(_1557993, _1557995))], (19535 ^ _779854) ^ [_1132167, _1132169] : [class_Rings_Olinordered__ring(_1132167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132167), _1132169), _1132169)), c_Groups_Ozero__class_Ozero(_1132167)))], (6839 ^ _779854) ^ [_890670, _890672, _890674, _890676] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890670, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890670, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_890670, tc_HOL_Obool)), _890672), _890674)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_890670, tc_HOL_Obool)), _890674), _890676))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_890670, tc_HOL_Obool)), _890676), _890672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_890670, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_890670, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890670, tc_HOL_Obool)), _890672), _890674)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890670, tc_HOL_Obool)), _890674), _890676))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890670, tc_HOL_Obool)), _890676), _890672)))], (47701 ^ _779854) ^ [_1739150, _1739152, _1739154] : [hBOOL(hAPP(c_List_Odistinct(_1739150), _1739152)), hBOOL(hAPP(hAPP(c_member(_1739150), _1739154), hAPP(c_List_Oset(_1739150), _1739152))), -(c_List_OtakeWhile(_1739150, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1739150), c_fNot), hAPP(hAPP(c_COMBC(_1739150, _1739150, tc_HOL_Obool), c_fequal), _1739154)), hAPP(c_List_Orev(_1739150), _1739152)) = hAPP(c_List_Orev(_1739150), hAPP(c_List_Otl(_1739150), c_List_OdropWhile(_1739150, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1739150), c_fNot), hAPP(hAPP(c_COMBC(_1739150, _1739150, tc_HOL_Obool), c_fequal), _1739154)), _1739152))))], (46094 ^ _779854) ^ [_1704991, _1704993, _1704995, _1704997, _1704999] : [c_Finite__Set_Ofun__left__comm(_1704991, _1704993, _1704995), -(hAPP(hAPP(c_Finite__Set_Ofold(_1704991, _1704993, _1704995), _1704997), hAPP(c_List_Oset(_1704991), _1704999)) = hAPP(c_List_Ofoldl(_1704993, _1704991, hAPP(c_COMBC(_1704991, _1704993, _1704993), _1704995), _1704997), c_List_Oremdups(_1704991, _1704999)))], (20810 ^ _779854) ^ [_1154394, _1154396, _1154398, _1154400] : [class_Rings_Olinordered__semiring__strict(_1154394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154394), _1154396), _1154398)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154394), _1154400), _1154398))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154394), c_Groups_Ozero__class_Ozero(_1154394)), _1154398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154394), _1154396), _1154400)))], (6641 ^ _779854) ^ [_886273, _886275, _886277] : [class_Groups_Oordered__ab__group__add(_886273), 6644 ^ _779854 : [(6651 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886273), _886277), hAPP(c_Groups_Ouminus__class_Ouminus(_886273), _886275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886273), _886275), hAPP(c_Groups_Ouminus__class_Ouminus(_886273), _886277))))], (6645 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886273), _886275), hAPP(c_Groups_Ouminus__class_Ouminus(_886273), _886277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886273), _886277), hAPP(c_Groups_Ouminus__class_Ouminus(_886273), _886275))))]]], (35137 ^ _779854) ^ [_1433849, _1433851] : [class_Rings_Oring__1(_1433849), 35140 ^ _779854 : [(35147 ^ _779854) ^ [] : [-(_1433851 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35150 ^ _779854 : [(35157 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433851), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1433849), _1433851) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1433849), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1433849, _1433849)), tc_fun(tc_Int_Oint, _1433849)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1433849, _1433849), _1433849), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1433849, _1433849)), tc_fun(tc_Int_Oint, _1433849)), tc_Int_Oint), c_COMBB(tc_fun(_1433849, _1433849), _1433849, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1433849, tc_fun(tc_fun(_1433849, _1433849), _1433849), tc_Int_Oint), c_HOL_OLet(_1433849, _1433849)), c_Int_Oring__1__class_Oof__int(_1433849)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1433849, _1433849), tc_fun(_1433849, _1433849)), hAPP(hAPP(c_COMBB(tc_fun(_1433849, tc_fun(_1433849, _1433849)), tc_fun(tc_fun(_1433849, _1433849), tc_fun(_1433849, _1433849)), tc_Int_Oint), c_COMBS(_1433849, _1433849, _1433849)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1433849, _1433849), tc_fun(_1433849, tc_fun(_1433849, _1433849))), hAPP(hAPP(c_COMBB(tc_fun(_1433849, tc_fun(_1433849, _1433849)), tc_fun(tc_fun(_1433849, _1433849), tc_fun(_1433849, tc_fun(_1433849, _1433849))), tc_Int_Oint), c_COMBB(_1433849, tc_fun(_1433849, _1433849), _1433849)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1433849, tc_fun(_1433849, _1433849)), tc_Int_Oint), c_If(_1433849)), 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(_1433849, _1433849, _1433849), c_Groups_Oplus__class_Oplus(_1433849)), c_COMBI(_1433849))))), hAPP(hAPP(c_COMBC(_1433849, _1433849, _1433849), hAPP(hAPP(c_COMBB(_1433849, tc_fun(_1433849, _1433849), _1433849), c_Groups_Oplus__class_Oplus(_1433849)), hAPP(hAPP(c_COMBS(_1433849, _1433849, _1433849), c_Groups_Oplus__class_Oplus(_1433849)), c_COMBI(_1433849)))), c_Groups_Oone__class_Oone(_1433849))))), c_Divides_Odivmod__int(_1433851, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35151 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433851), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1433849), _1433851) = hAPP(c_Groups_Ouminus__class_Ouminus(_1433849), hAPP(c_Int_Oring__1__class_Oof__int(_1433849), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1433851))))]]], (35141 ^ _779854) ^ [] : [_1433851 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1433849), _1433851) = c_Groups_Ozero__class_Ozero(_1433849))]]], (27777 ^ _779854) ^ [_1282412, _1282414, _1282416] : [class_Rings_Osemiring__1(_1282412), hBOOL(hAPP(hAPP(c_member(_1282412), _1282414), c_Nat_Osemiring__1__class_ONats(_1282412))), hBOOL(hAPP(hAPP(c_member(_1282412), _1282416), c_Nat_Osemiring__1__class_ONats(_1282412))), -(hBOOL(hAPP(hAPP(c_member(_1282412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282412), _1282414), _1282416)), c_Nat_Osemiring__1__class_ONats(_1282412))))], (28439 ^ _779854) ^ [_1294080, _1294082] : [28440 ^ _779854 : [(28441 ^ _779854) ^ [_1294133] : [_1294082 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1294080), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1294133))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1294080), _1294082)))], (17418 ^ _779854) ^ [_1094702, _1094704, _1094706, _1094708, _1094710, _1094712] : [c_Finite__Set_Ofun__left__comm(_1094702, _1094704, _1094706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094702), _1094708)), -(hAPP(hAPP(_1094706, _1094710), hAPP(hAPP(c_Finite__Set_Ofold(_1094702, _1094704, _1094706), _1094712), _1094708)) = hAPP(hAPP(c_Finite__Set_Ofold(_1094702, _1094704, _1094706), hAPP(hAPP(_1094706, _1094710), _1094712)), _1094708))], (34914 ^ _779854) ^ [_1428801, _1428803, _1428805, _1428807, _1428809] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428801, tc_fun(_1428803, tc_HOL_Obool)), _1428805), _1428807), _1428809)), 34917 ^ _779854 : [(34918 ^ _779854) ^ [_1428910] : [hBOOL(hAPP(hAPP(c_member(_1428801), _1428910), _1428805)), -(hBOOL(hAPP(hAPP(_1428807, _1428910), _1428809)))]]], (6979 ^ _779854) ^ [_894004, _894006, _894008] : [class_Lattices_Olattice(_894004), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894004), _894006), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894004), _894006), _894008)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894004), _894006), _894008))], (50054 ^ _779854) ^ [_1791869, _1791871, _1791873] : [c_Relation_Osym(_1791869, _1791871), c_Relation_Osym(_1791869, _1791873), -(c_Relation_Osym(_1791869, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1791869, _1791869), tc_HOL_Obool)), _1791871), _1791873)))], (33701 ^ _779854) ^ [_1399409, _1399411, _1399413, _1399415] : [class_Groups_Ocomm__monoid__add(_1399409), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1399409), _1399411), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1399413), hAPP(c_Nat_OSuc, _1399415))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1399409), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1399409, tc_Nat_Onat), _1399411), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1399413, _1399415)))], (36776 ^ _779854) ^ [_1468080, _1468082, _1468084, _1468086, _1468088, _1468090] : [-(hAPP(c_Product__Type_Oapfst(_1468080, _1468082, _1468084, _1468086), hAPP(hAPP(c_Product__Type_OPair(_1468080, _1468084), _1468088), _1468090)) = hAPP(hAPP(c_Product__Type_OPair(_1468082, _1468084), hAPP(_1468086, _1468088)), _1468090))], (42715 ^ _779854) ^ [_1627999, _1628001, _1628003] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627999)), hAPP(hAPP(c_List_Otake(_1627999), _1628001), _1628003)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627999)), _1628003)), _1628001))], (16241 ^ _779854) ^ [_1071522, _1071524, _1071526] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071522), _1071524)), _1071526) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071522), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071524), _1071526)))], (36876 ^ _779854) ^ [_1470012] : [-(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)), _1470012), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (3686 ^ _779854) ^ [_835302, _835304] : [_835304 = _835302, -(c_List_Oreturn__list(_835304) = c_List_Oreturn__list(_835302))], (46709 ^ _779854) ^ [_1719538, _1719540] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1719538, _1719540)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1719540), _1719538))], (6737 ^ _779854) ^ [_888094, _888096, _888098] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888094, tc_HOL_Obool)), _888096), _888098) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888094, tc_HOL_Obool)), _888098), _888096))], (7241 ^ _779854) ^ [_898995, _898997, _898999, _899001] : [class_Lattices_Osemilattice__sup(_898995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898995), _898997), _898999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898995), _898997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898995), _899001), _898999))))], (17254 ^ _779854) ^ [_1091448, _1091450, _1091452] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1091448), _1091450)), hBOOL(hAPP(hAPP(c_member(_1091448), _1091452), _1091450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1091448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1091448, tc_HOL_Obool)), _1091450), hAPP(hAPP(c_Set_Oinsert(_1091448), _1091452), c_Orderings_Obot__class_Obot(tc_fun(_1091448, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1091448), _1091450))))], (52611 ^ _779854) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (38579 ^ _779854) ^ [_1514156, _1514158, _1514160, _1514162] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514156), _1514158)), 38585 ^ _779854 : [(38588 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514160), hAPP(_1514162, 38584 ^ [_1514156, _1514158, _1514160, _1514162])))], (38586 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514156), 38584 ^ [_1514156, _1514158, _1514160, _1514162]), _1514158)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1514156, _1514160)), hAPP(hAPP(c_Product__Type_OSigma(_1514156, _1514160), _1514158), _1514162)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514156, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1514160, tc_HOL_Obool), tc_Nat_Onat, _1514156), c_Finite__Set_Ocard(_1514160)), _1514162)), _1514158))], (9865 ^ _779854) ^ [_945943, _945945, _945947] : [hAPP(c_Set_Oimage(_945945, tc_fun(_945945, tc_HOL_Obool), _945943), _945947) = hAPP(c_Set_OPow(_945945), _945947)], (1210 ^ _779854) ^ [_797931, _797933] : [-(class_Rings_Oordered__ring__abs(_797931)), _797933 = _797931, class_Rings_Oordered__ring__abs(_797933)], (7087 ^ _779854) ^ [_896038, _896040, _896042, _896044] : [class_Lattices_Olattice(_896038), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896038), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896038), _896040), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_896038), _896042), _896044))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_896038), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896038), _896040), _896042)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896038), _896040), _896044)))))], (15836 ^ _779854) ^ [_1063724, _1063726, _1063728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063724), _1063726)), _1063728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063724), _1063728)))], (30137 ^ _779854) ^ [_1323654, _1323656, _1323658, _1323660, _1323662, _1323664] : [class_Divides_Oring__div(_1323654), c_Divides_Odiv__class_Omod(_1323654, _1323656, _1323658) = c_Divides_Odiv__class_Omod(_1323654, _1323660, _1323658), c_Divides_Odiv__class_Omod(_1323654, _1323662, _1323658) = c_Divides_Odiv__class_Omod(_1323654, _1323664, _1323658), -(c_Divides_Odiv__class_Omod(_1323654, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1323654), _1323656), _1323662), _1323658) = c_Divides_Odiv__class_Omod(_1323654, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1323654), _1323660), _1323664), _1323658))], (52143 ^ _779854) ^ [_1833235, _1833237] : [class_Orderings_Otop(_1833235), -(class_Orderings_Otop(tc_fun(_1833237, _1833235)))], (48484 ^ _779854) ^ [_1756712, _1756714, _1756716] : [c_List_Olist__ex(_1756712, _1756714, _1756716), -(c_List_Olist__ex(_1756712, _1756714, hAPP(c_List_Orev(_1756712), _1756716)))], (29003 ^ _779854) ^ [_1303378] : [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, _1303378)))))], (4798 ^ _779854) ^ [_853078, _853080] : [_853080 = _853078, -(c_Set_OBex(_853080) = c_Set_OBex(_853078))], (23996 ^ _779854) ^ [_1215204, _1215206, _1215208] : [class_Rings_Olinordered__semidom(_1215204), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215204), c_Groups_Ozero__class_Ozero(_1215204)), _1215206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215204), c_Groups_Ozero__class_Ozero(_1215204)), hAPP(hAPP(c_Power_Opower__class_Opower(_1215204), _1215206), _1215208))))], (38989 ^ _779854) ^ [_1525074, _1525076, _1525078, _1525080, _1525082, _1525084] : [class_Groups_Ocomm__monoid__add(_1525074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525076), _1525078)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525076, _1525074), hAPP(hAPP(c_COMBS(_1525076, _1525074, _1525074), hAPP(hAPP(c_COMBS(_1525076, _1525074, tc_fun(_1525074, _1525074)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525074, tc_fun(_1525074, _1525074)), _1525076), c_If(_1525074)), _1525080)), _1525082)), _1525084)), _1525078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1525074), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525076, _1525074), _1525082), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1525076, tc_HOL_Obool)), _1525078), hAPP(c_Set_OCollect(_1525076), _1525080)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525076, _1525074), _1525084), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1525076, tc_HOL_Obool)), _1525078), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1525076, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1525076), _1525080))))))], (42677 ^ _779854) ^ [_1627182, _1627184, _1627186] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627182, tc_HOL_Obool)), hAPP(c_List_Oset(_1627182), c_List_Osublist(_1627182, _1627184, _1627186))), hAPP(c_List_Oset(_1627182), _1627184))))], (34417 ^ _779854) ^ [_1417890, _1417892, _1417894, _1417896] : [class_Groups_Ocomm__monoid__add(_1417890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1417892), _1417894)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1417890), _1417896), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1417892, _1417894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1417890), hAPP(_1417896, _1417892)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1417890), _1417896), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1417892, _1417894))))], (49353 ^ _779854) ^ [_1775527, _1775529, _1775531] : [-(c_FunDef_OTHE__default(_1775529, _1775531, _1775527) = c_HOL_OThe(_1775529, _1775527)), 49354 ^ _779854 : [(49355 ^ _779854) ^ [_1775591] : [hBOOL(hAPP(_1775527, _1775591)), 49359 ^ _779854 : [(49362 ^ _779854) ^ [] : [49358 ^ [_1775527, _1775529, _1775531, _1775591] = _1775591], (49360 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1775527, 49358 ^ [_1775527, _1775529, _1775531, _1775591])))]]]]], (43037 ^ _779854) ^ [_1637078, _1637080, _1637082, _1637084] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637078)), hAPP(hAPP(c_List_Olist__update(_1637078, _1637080), _1637082), _1637084)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637078)), _1637080))], (37115 ^ _779854) ^ [_1476954, _1476956, _1476958, _1476960] : [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), _1476954), _1476956)), 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), _1476958), _1476960)), 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), _1476954), _1476960)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1476958), _1476956))))], (35684 ^ _779854) ^ [_1444353, _1444355, _1444357] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1444353, _1444355), _1444357)), 35687 ^ _779854 : [(35688 ^ _779854) ^ [_1444438] : [hBOOL(hAPP(hAPP(_1444355, _1444438), _1444357)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1444353, _1444355), _1444438)))]]], (9190 ^ _779854) ^ [_933154, _933156, _933158] : [class_Orderings_Olinorder(_933154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933154), _933156), _933158)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933154, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_933154), _933156), c_Orderings_Obot__class_Obot(tc_fun(_933154, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_933154, _933156, _933158)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_933154, _933156), _933158))], (38003 ^ _779854) ^ [_1498357, _1498359, _1498361, _1498363] : [-(c_HOL_OThe(tc_prod(_1498357, _1498359), hAPP(c_Product__Type_Oprod_Oprod__case(_1498357, _1498359, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1498357, tc_fun(_1498359, tc_HOL_Obool), tc_fun(_1498359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1498359, tc_HOL_Obool), tc_fun(_1498359, tc_HOL_Obool)), _1498357), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1498359)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498357), c_fconj), hAPP(c_fequal, _1498361)))), hAPP(c_fequal, _1498363)))) = hAPP(hAPP(c_Product__Type_OPair(_1498357, _1498359), _1498361), _1498363))], (12622 ^ _779854) ^ [_1000664, _1000666, _1000668, _1000670] : [c_Finite__Set_Ofolding__one(_1000664, _1000666, _1000668), -(hAPP(_1000668, hAPP(hAPP(c_Set_Oinsert(_1000664), _1000670), c_Orderings_Obot__class_Obot(tc_fun(_1000664, tc_HOL_Obool)))) = _1000670)], (35094 ^ _779854) ^ [_1432684, _1432686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1432684, _1432684)), hAPP(hAPP(c_Product__Type_OPair(_1432684, _1432684), 35095 ^ [_1432684, _1432686]), 35095 ^ [_1432684, _1432686])), _1432686)), -(c_Nitpick_Orefl_H(_1432684, _1432686))], (6277 ^ _779854) ^ [_879553] : [class_Complete__Lattice_Ocomplete__lattice(_879553), -(c_Complete__Lattice_OSup__class_OSup(_879553, c_Orderings_Obot__class_Obot(tc_fun(_879553, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_879553))], (2270 ^ _779854) ^ [_813090, _813092, _813094, _813096, _813098, _813100] : [-(c_Nat_Onat_Onat__rec(_813100, _813096, _813092) = c_Nat_Onat_Onat__rec(_813098, _813094, _813090)), _813100 = _813098, _813096 = _813094, _813092 = _813090], (26331 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (988 ^ _779854) ^ [_794656, _794658, _794660, _794662, _794664, _794666, _794668, _794670] : [-(c_Equiv__Relations_Ocongruent(_794668, _794664, _794660, _794656)), c_Equiv__Relations_Ocongruent(_794670, _794666, _794662, _794658), _794670 = _794668, _794666 = _794664, _794662 = _794660, _794658 = _794656], (30157 ^ _779854) ^ [_1324080, _1324082, _1324084, _1324086] : [class_Divides_Oring__div(_1324080), -(c_Divides_Odiv__class_Omod(_1324080, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1324080), _1324082), _1324084), _1324086) = c_Divides_Odiv__class_Omod(_1324080, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1324080), c_Divides_Odiv__class_Omod(_1324080, _1324082, _1324086)), _1324084), _1324086))], (34733 ^ _779854) ^ [_1425286, _1425288, _1425290] : [class_Int_Onumber__ring(_1425286), 34736 ^ _779854 : [(34743 ^ _779854) ^ [] : [-(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), _1425288)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1425286), hAPP(c_Int_Onumber__class_Onumber__of(_1425286), _1425290)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1425288))) = c_Groups_Oone__class_Oone(_1425286))], (34737 ^ _779854) ^ [] : [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), _1425288))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1425286), hAPP(c_Int_Onumber__class_Onumber__of(_1425286), _1425290)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1425288))) = hAPP(hAPP(c_HOL_OLet(_1425286, _1425286), hAPP(hAPP(c_Power_Opower__class_Opower(_1425286), hAPP(c_Int_Onumber__class_Onumber__of(_1425286), _1425290)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425288))), hAPP(hAPP(c_COMBS(_1425286, _1425286, _1425286), hAPP(hAPP(c_COMBB(_1425286, tc_fun(_1425286, _1425286), _1425286), c_Groups_Otimes__class_Otimes(_1425286)), hAPP(c_Groups_Otimes__class_Otimes(_1425286), hAPP(c_Int_Onumber__class_Onumber__of(_1425286), _1425290)))), c_COMBI(_1425286))))]]], (35199 ^ _779854) ^ [_1435598, _1435600, _1435602] : [class_Rings_Osemiring__1(_1435598), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1435598, _1435600, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1435602) = _1435602)], (34087 ^ _779854) ^ [_1410155, _1410157, _1410159, _1410161, _1410163] : [class_Groups_Ocomm__monoid__mult(_1410155), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410157), _1410159)), 34094 ^ _779854 : [(34101 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410157), _1410161), _1410159))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410157, _1410155), hAPP(hAPP(c_COMBC(_1410157, _1410155, _1410155), hAPP(hAPP(c_COMBS(_1410157, _1410155, tc_fun(_1410155, _1410155)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1410155, tc_fun(_1410155, _1410155)), _1410157), c_If(_1410155)), hAPP(hAPP(c_COMBC(_1410157, _1410157, tc_HOL_Obool), c_fequal), _1410161))), _1410163)), c_Groups_Oone__class_Oone(_1410155))), _1410159) = c_Groups_Oone__class_Oone(_1410155))], (34095 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1410157), _1410161), _1410159)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410157, _1410155), hAPP(hAPP(c_COMBC(_1410157, _1410155, _1410155), hAPP(hAPP(c_COMBS(_1410157, _1410155, tc_fun(_1410155, _1410155)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1410155, tc_fun(_1410155, _1410155)), _1410157), c_If(_1410155)), hAPP(hAPP(c_COMBC(_1410157, _1410157, tc_HOL_Obool), c_fequal), _1410161))), _1410163)), c_Groups_Oone__class_Oone(_1410155))), _1410159) = hAPP(_1410163, _1410161))]]], (15552 ^ _779854) ^ [_1057781, _1057783, _1057785, _1057787, _1057789] : [class_Groups_Ocomm__monoid__add(_1057781), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057783), _1057785)), -(hBOOL(hAPP(hAPP(c_member(_1057783), _1057787), _1057785))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057783, _1057781), _1057789), hAPP(hAPP(c_Set_Oinsert(_1057783), _1057787), _1057785)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057781), hAPP(_1057789, _1057787)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057783, _1057781), _1057789), _1057785)))], (7858 ^ _779854) ^ [_911111, _911113, _911115] : [class_Orderings_Olinorder(_911111), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911111), _911113), _911115)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911111, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_911111, _911113), _911115)), hAPP(c_SetInterval_Oord__class_OatLeast(_911111), _911115)) = hAPP(c_SetInterval_Oord__class_OatLeast(_911111), _911113))], (25462 ^ _779854) ^ [_1242839, _1242841, _1242843, _1242845] : [class_Rings_Olinordered__semidom(_1242839), 25468 ^ _779854 : [(25471 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242839), c_Groups_Ozero__class_Ozero(_1242839)), hAPP(_1242845, 25467 ^ [_1242839, _1242841, _1242843, _1242845])))], (25469 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1242841), 25467 ^ [_1242839, _1242841, _1242843, _1242845]), _1242843)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242839), c_Groups_Ozero__class_Ozero(_1242839)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1242841, _1242839), _1242845), _1242843))))], (36944 ^ _779854) ^ [_1472009, _1472011, _1472013] : [-(c_Wellfounded_Omlex__prod(_1472009, _1472011, _1472013) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1472009), _1472009), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1472009, c_Wellfounded_Oless__than, _1472013)), hAPP(hAPP(c_COMBS(_1472009, _1472009, tc_prod(tc_Nat_Onat, _1472009)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1472009, tc_prod(tc_Nat_Onat, _1472009)), _1472009), c_Product__Type_OPair(tc_Nat_Onat, _1472009)), _1472011)), c_COMBI(_1472009))))], (15826 ^ _779854) ^ [_1063491, _1063493, _1063495] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063491), _1063493)), _1063495) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063493), _1063495)))], (32543 ^ _779854) ^ [_1365682, _1365684, _1365686] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1365682, _1365684, _1365686, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1365684)], (27011 ^ _779854) ^ [_1269728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269728), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1269728))], (48886 ^ _779854) ^ [_1765146, _1765148, _1765150, _1765152, _1765154] : [hBOOL(hAPP(hAPP(_1765146, _1765148), _1765150)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1765152, _1765154, _1765146), _1765150), _1765148)))], (21983 ^ _779854) ^ [_1176963, _1176965] : [class_Rings_Odivision__ring(_1176963), -(_1176965 = c_Groups_Ozero__class_Ozero(_1176963)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176963), _1176965), _1176965) = c_Groups_Oone__class_Oone(_1176963))], (41822 ^ _779854) ^ [_1602027, _1602029, _1602031, _1602033] : [-(hAPP(hAPP(c_Nat_Ocompow(_1602027, _1602027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1602029), _1602031)), _1602033) = hAPP(c_Fun_Ocomp(_1602027, _1602027, _1602027, hAPP(hAPP(c_Nat_Ocompow(_1602027, _1602027), _1602029), _1602033)), hAPP(hAPP(c_Nat_Ocompow(_1602027, _1602027), _1602031), _1602033)))], (9432 ^ _779854) ^ [_937466, _937468] : [class_Groups_Oordered__ab__group__add(_937466), -(hAPP(c_Set_Oimage(_937466, _937466, c_Groups_Ouminus__class_Ouminus(_937466)), hAPP(c_SetInterval_Oord__class_OatMost(_937466), _937468)) = hAPP(c_SetInterval_Oord__class_OatLeast(_937466), hAPP(c_Groups_Ouminus__class_Ouminus(_937466), _937468)))], (18835 ^ _779854) ^ [_1119917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119917), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1119917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6593 ^ _779854) ^ [_885424, _885426, _885428] : [class_Lattices_Oboolean__algebra(_885424), 6596 ^ _779854 : [(6603 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885424), _885428), _885426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885424), hAPP(c_Groups_Ouminus__class_Ouminus(_885424), _885426)), hAPP(c_Groups_Ouminus__class_Ouminus(_885424), _885428))))], (6597 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885424), hAPP(c_Groups_Ouminus__class_Ouminus(_885424), _885426)), hAPP(c_Groups_Ouminus__class_Ouminus(_885424), _885428))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885424), _885428), _885426)))]]], (44885 ^ _779854) ^ [_1678061, _1678063, _1678065] : [class_Orderings_Olinorder(_1678061), hBOOL(hAPP(hAPP(c_member(_1678061), _1678063), hAPP(c_List_Oset(_1678061), _1678065))), -(c_List_Olinorder__class_Oinsort__insert__key(_1678061, _1678061, c_COMBI(_1678061), _1678063, _1678065) = _1678065)], (31017 ^ _779854) ^ [_1339666, _1339668, _1339670] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1339666, _1339668)), _1339670) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339666), _1339670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339668), _1339670)))], (13267 ^ _779854) ^ [_1013731, _1013733, _1013735] : [class_Lattices_Olattice(_1013731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013731), _1013733)), hBOOL(hAPP(hAPP(c_member(_1013731), _1013735), _1013733)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1013731), _1013735), c_Big__Operators_Olattice__class_OInf__fin(_1013731, _1013733)) = _1013735)], (41244 ^ _779854) ^ [_1587908, _1587910, _1587912, _1587914, _1587916] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587908, _1587908)), hAPP(hAPP(c_Product__Type_OPair(_1587908, _1587908), _1587910), _1587912)), _1587914)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587908, _1587908)), hAPP(hAPP(c_Product__Type_OPair(_1587908, _1587908), _1587912), _1587916)), c_Transitive__Closure_Ortrancl(_1587908, _1587914))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587908, _1587908)), hAPP(hAPP(c_Product__Type_OPair(_1587908, _1587908), _1587910), _1587916)), c_Transitive__Closure_Otrancl(_1587908, _1587914))))], (12440 ^ _779854) ^ [_997036, _997038] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_997036, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_997036, tc_HOL_Obool))), hAPP(c_Set_OPow(_997036), _997038))))], (23069 ^ _779854) ^ [_1196851, _1196853, _1196855] : [class_Fields_Olinordered__field(_1196851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196851), _1196853), _1196855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196851), _1196853), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196851), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196851), _1196853), _1196855)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196851), c_Groups_Oone__class_Oone(_1196851)), c_Groups_Oone__class_Oone(_1196851))))))], (20688 ^ _779854) ^ [_1152049, _1152051, _1152053, _1152055, _1152057] : [class_Rings_Olinordered__semiring__strict(_1152049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152049), _1152051), _1152053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152049), _1152055), _1152057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152049), c_Groups_Ozero__class_Ozero(_1152049)), _1152051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152049), c_Groups_Ozero__class_Ozero(_1152049)), _1152055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152049), _1152051), _1152055)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152049), _1152053), _1152057))))], (52427 ^ _779854) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (17112 ^ _779854) ^ [_1088853, _1088855, _1088857, _1088859, _1088861, _1088863, _1088865] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1088853, _1088855, _1088857, _1088859, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088853, tc_HOL_Obool)), _1088861), hAPP(hAPP(c_Set_Oinsert(_1088853), _1088863), c_Orderings_Obot__class_Obot(tc_fun(_1088853, tc_HOL_Obool))))), _1088865)), hBOOL(hAPP(hAPP(c_member(_1088853), _1088863), _1088861)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1088853, _1088855, _1088857, _1088859, _1088861), hAPP(hAPP(_1088857, _1088863), _1088865))))], (7748 ^ _779854) ^ [_908808, _908810] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908808, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_908808, tc_HOL_Obool)), _908810)), _908810) = c_Orderings_Otop__class_Otop(tc_fun(_908808, tc_HOL_Obool)))], (16712 ^ _779854) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (602 ^ _779854) ^ [_788921, _788923, _788925, _788927, _788929, _788931] : [-(c_Finite__Set_Ofun__left__comm(_788929, _788925, _788921)), c_Finite__Set_Ofun__left__comm(_788931, _788927, _788923), _788931 = _788929, _788927 = _788925, _788923 = _788921], (11003 ^ _779854) ^ [_968900, _968902, _968904, _968906] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968900, tc_HOL_Obool)), _968902), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_968900, tc_HOL_Obool)), _968904), _968906)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968900, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968900, tc_HOL_Obool)), _968902), _968904)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968900, tc_HOL_Obool)), _968902), _968906)))], (38642 ^ _779854) ^ [_1515924, _1515926, _1515928, _1515930, _1515932, _1515934, _1515936, _1515938, _1515940, _1515942] : [-(c_Product__Type_Omap__pair(_1515924, _1515926, _1515928, _1515930, hAPP(c_Fun_Ocomp(_1515932, _1515926, _1515924, _1515934), _1515936), hAPP(c_Fun_Ocomp(_1515938, _1515930, _1515928, _1515940), _1515942)) = hAPP(c_Fun_Ocomp(tc_prod(_1515932, _1515938), tc_prod(_1515926, _1515930), tc_prod(_1515924, _1515928), c_Product__Type_Omap__pair(_1515932, _1515926, _1515938, _1515930, _1515934, _1515940)), c_Product__Type_Omap__pair(_1515924, _1515932, _1515928, _1515938, _1515936, _1515942)))], (31306 ^ _779854) ^ [_1344313] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1344313, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37168 ^ _779854) ^ [_1478358, _1478360, _1478362] : [-(hAPP(c_Relation_OField(_1478358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1478358, _1478358), tc_HOL_Obool)), _1478360), _1478362)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478358, tc_HOL_Obool)), hAPP(c_Relation_OField(_1478358), _1478360)), hAPP(c_Relation_OField(_1478358), _1478362)))], (31216 ^ _779854) ^ [_1342736] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1342736) = c_Int_Opred(_1342736))], (36213 ^ _779854) ^ [_1455485, _1455487, _1455489, _1455491, _1455493] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1455485, _1455487, _1455489), _1455491), _1455493) = hAPP(hAPP(_1455491, hAPP(c_Product__Type_Ofst(_1455485, _1455487), _1455493)), hAPP(c_Product__Type_Osnd(_1455485, _1455487), _1455493)))], (28780 ^ _779854) ^ [_1299802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1299802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1299802)))], (2390 ^ _779854) ^ [_815074, _815076] : [_815076 = _815074, -(c_Int_OBit0(_815076) = c_Int_OBit0(_815074))], (23344 ^ _779854) ^ [_1202394, _1202396, _1202398, _1202400, _1202402, _1202404, _1202406] : [c_Big__Operators_Ocomm__monoid__big(_1202394, _1202396, _1202398, _1202400, _1202402), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1202396), _1202404))), -(hAPP(hAPP(_1202402, _1202406), _1202404) = _1202400)], (20419 ^ _779854) ^ [_1147340, _1147342, _1147344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147340), _1147342)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147340), _1147344))), 20422 ^ _779854 : [(20425 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147342), _1147344)))], (20423 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147340)))]]], (20445 ^ _779854) ^ [_1147810, _1147812] : [-(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), _1147810), _1147812)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147812))], (44320 ^ _779854) ^ [_1665902, _1665904, _1665906, _1665908] : [-(hAPP(hAPP(c_List_Odrop(_1665902), _1665904), hAPP(hAPP(c_List_Oappend(_1665902), _1665906), _1665908)) = hAPP(hAPP(c_List_Oappend(_1665902), hAPP(hAPP(c_List_Odrop(_1665902), _1665904), _1665906)), hAPP(hAPP(c_List_Odrop(_1665902), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1665904), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665902)), _1665906))), _1665908)))], (4804 ^ _779854) ^ [_853163, _853165] : [_853165 = _853163, -(c_List_Oset(_853165) = c_List_Oset(_853163))], (10105 ^ _779854) ^ [_950530, _950532, _950534, _950536] : [class_Orderings_Olinorder(_950530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950530), _950532), _950534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950530), hAPP(hAPP(c_Orderings_Oord__class_Omin(_950530), _950536), _950532)), _950534)))], (252 ^ _779854) ^ [_783838, _783840] : [-(class_Fields_Ofield__inverse__zero(_783838)), _783840 = _783838, class_Fields_Ofield__inverse__zero(_783840)], (17178 ^ _779854) ^ [_1089974, _1089976, _1089978] : [class_Orderings_Olinorder(_1089974), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089974), _1089976)), -(hBOOL(hAPP(hAPP(c_member(_1089974), _1089978), _1089976))), -(c_Big__Operators_Olinorder__class_OMax(_1089974, hAPP(hAPP(c_Set_Oinsert(_1089974), _1089978), _1089976)) = hAPP(hAPP(c_Finite__Set_Ofold(_1089974, _1089974, c_Orderings_Oord__class_Omax(_1089974)), _1089978), _1089976))], (7209 ^ _779854) ^ [_898436, _898438, _898440, _898442] : [class_Lattices_Osemilattice__sup(_898436), 7212 ^ _779854 : [(7221 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898436), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898436), _898438), _898440)), _898442))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898436), _898438), _898442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898436), _898440), _898442))], (7213 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898436), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898436), _898438), _898440)), _898442)), 7216 ^ _779854 : [(7219 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898436), _898440), _898442)))], (7217 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898436), _898438), _898442)))]]]]], (41070 ^ _779854) ^ [_1583665, _1583667] : [-(c_Transitive__Closure_Otrancl(_1583665, _1583667) = hAPP(hAPP(c_Relation_Orel__comp(_1583665, _1583665, _1583665), _1583667), c_Transitive__Closure_Ortrancl(_1583665, _1583667)))], (37158 ^ _779854) ^ [_1478109, _1478111] : [-(hAPP(c_Relation_OField(_1478109), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1478109, _1478109), tc_HOL_Obool), _1478111)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1478109, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1478109, _1478109), tc_HOL_Obool), tc_fun(_1478109, tc_HOL_Obool), c_Relation_OField(_1478109)), _1478111)))], (2710 ^ _779854) ^ [_820118, _820120] : [_820120 = _820118, -(c_Int_Oint__ge__less__than(_820120) = c_Int_Oint__ge__less__than(_820118))], (44554 ^ _779854) ^ [_1671074, _1671076, _1671078] : [-(hAPP(c_List_Orotate1(_1671074), hAPP(c_List_Orotate(_1671074, _1671076), _1671078)) = hAPP(c_List_Orotate(_1671074, _1671076), hAPP(c_List_Orotate1(_1671074), _1671078)))], (42738 ^ _779854) ^ [_1628584, _1628586, _1628588] : [42740 ^ _779854 : [(42743 ^ _779854) ^ [] : [hBOOL(hAPP(_1628588, hAPP(hAPP(c_List_Onth(_1628584), _1628586), 42739 ^ [_1628584, _1628586, _1628588])))], (42741 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42739 ^ [_1628584, _1628586, _1628588]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628584)), _1628586))))]], 42744 ^ _779854 : [(42745 ^ _779854) ^ [_1628786] : [hBOOL(hAPP(hAPP(c_member(_1628584), _1628786), hAPP(c_List_Oset(_1628584), _1628586))), -(hBOOL(hAPP(_1628588, _1628786)))]]], (30255 ^ _779854) ^ [_1326043] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1326043) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25613 ^ _779854) ^ [_1245614, _1245616] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245614), _1245616))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245614), _1245616)), -(_1245614 = _1245616)], (3308 ^ _779854) ^ [_829393, _829395] : [_829395 = _829393, -(c_Lazy__Sequence_Ohb__not__seq(_829395) = c_Lazy__Sequence_Ohb__not__seq(_829393))], (33230 ^ _779854) ^ [_1382490, _1382492, _1382494, _1382496] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1382490, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382492, tc_fun(_1382490, tc_HOL_Obool)), _1382494), _1382496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382492, tc_fun(_1382490, tc_HOL_Obool)), _1382494), hAPP(hAPP(c_COMBB(tc_fun(_1382490, tc_HOL_Obool), tc_fun(_1382490, tc_HOL_Obool), _1382492), c_Groups_Ouminus__class_Ouminus(tc_fun(_1382490, tc_HOL_Obool))), _1382496)))], (15382 ^ _779854) ^ [_1054312, _1054314, _1054316, _1054318] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1054312), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054312), _1054314), _1054316)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054312), _1054318), _1054316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054312), _1054314), _1054318)))], (10511 ^ _779854) ^ [_958297, _958299, _958301] : [class_Orderings_Olinorder(_958297), hBOOL(hAPP(c_Finite__Set_Ofinite(_958297), _958299)), -(_958299 = c_Orderings_Obot__class_Obot(tc_fun(_958297, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_958297, c_Orderings_Oord__class_Omax(_958297), hAPP(hAPP(c_Set_Oinsert(_958297), _958301), _958299)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_958297), _958301), c_Big__Operators_Olattice_OSup__fin(_958297, c_Orderings_Oord__class_Omax(_958297), _958299)))], (52201 ^ _779854) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (21717 ^ _779854) ^ [_1171763, _1171765, _1171767, _1171769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1171763, _1171765)), c_Sum__Type_OPlus(_1171763, _1171765, _1171767, _1171769))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171763), _1171767)))], (3010 ^ _779854) ^ [_824692, _824694] : [_824694 = _824692, -(c_HOL_Obool_Obool__size(_824694) = c_HOL_Obool_Obool__size(_824692))], (49438 ^ _779854) ^ [_1777301, _1777303, _1777305] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1777301), _1777303, _1777305)), -(c_List_Olist__ex(tc_Int_Oint, _1777301, c_List_Oupto(_1777303, _1777305)))], (36542 ^ _779854) ^ [_1462241, _1462243, _1462245, _1462247] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1462241, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36543 ^ [_1462241, _1462243, _1462245, _1462247])), _1462243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1462241, 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), 36543 ^ [_1462241, _1462243, _1462245, _1462247]), _1462245))), _1462247), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1462241, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1462243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1462241, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1462247))], (40101 ^ _779854) ^ [_1559583, _1559585, _1559587] : [c_Relation_Orefl__on(_1559583, _1559585, _1559587), 40104 ^ _779854 : [(40111 ^ _779854) ^ [_1560067] : [hBOOL(hAPP(hAPP(c_member(_1559583), _1560067), _1559585)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559583, _1559583)), hAPP(hAPP(c_Product__Type_OPair(_1559583, _1559583), _1560067), _1560067)), _1559587)))], (40105 ^ _779854) ^ [_1559794] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559583, _1559583)), _1559794), _1559587)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559583, _1559583, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1559583, tc_fun(_1559583, tc_HOL_Obool), tc_fun(_1559583, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1559583, tc_HOL_Obool), tc_fun(_1559583, tc_HOL_Obool)), _1559583), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1559583)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559583), c_fconj), hAPP(hAPP(c_COMBC(_1559583, tc_fun(_1559583, tc_HOL_Obool), tc_HOL_Obool), c_member(_1559583)), _1559585)))), hAPP(hAPP(c_COMBC(_1559583, tc_fun(_1559583, tc_HOL_Obool), tc_HOL_Obool), c_member(_1559583)), _1559585))), _1559794)))]]], (42719 ^ _779854) ^ [_1628113, _1628115, _1628117] : [-(hAPP(c_List_Oset(_1628113), hAPP(hAPP(c_List_Olist_OCons(_1628113), _1628115), _1628117)) = hAPP(hAPP(c_Set_Oinsert(_1628113), _1628115), hAPP(c_List_Oset(_1628113), _1628117)))], (15936 ^ _779854) ^ [_1065707, _1065709, _1065711, _1065713] : [class_Rings_Ocomm__semiring__1(_1065707), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065707), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065707), _1065709), _1065711)), _1065713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065707), _1065709), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065707), _1065711), _1065713)))], (15909 ^ _779854) ^ [_1065133] : [15911 ^ _779854 : [(15914 ^ _779854) ^ [_1065243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15910 ^ [_1065133, _1065243]), _1065243))], (15912 ^ _779854) ^ [_1065209] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 15910 ^ [_1065133, _1065209]), _1065133)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1065133)))], (16062 ^ _779854) ^ [_1068280] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068280), _1068280)))], (16115 ^ _779854) ^ [_1069192, _1069194, _1069196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069192), _1069194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1069196), _1069194))))], (45551 ^ _779854) ^ [_1692645, _1692647] : [hAPP(c_Code__Numeral_Onat__of, _1692645) = hAPP(c_Code__Numeral_Onat__of, _1692647), -(_1692645 = _1692647)], (792 ^ _779854) ^ [_791776, _791778, _791780, _791782] : [-(c_Relation_Oantisym(_791780, _791776)), c_Relation_Oantisym(_791782, _791778), _791782 = _791780, _791778 = _791776], (45543 ^ _779854) ^ [_1692497] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1692497)) = _1692497)], (52435 ^ _779854) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52405 ^ _779854) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (38142 ^ _779854) ^ [_1501870, _1501872, _1501874, _1501876, _1501878] : [-(hAPP(c_Set_Ovimage(_1501870, _1501872, _1501874), hAPP(hAPP(c_Set_Oinsert(_1501872), _1501876), _1501878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501870, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1501870, _1501872, _1501874), hAPP(hAPP(c_Set_Oinsert(_1501872), _1501876), c_Orderings_Obot__class_Obot(tc_fun(_1501872, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1501870, _1501872, _1501874), _1501878)))], (52289 ^ _779854) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (52219 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (12392 ^ _779854) ^ [_996204, _996206, _996208] : [class_Complete__Lattice_Ocomplete__lattice(_996204), hBOOL(hAPP(hAPP(c_member(_996204), _996206), _996208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996204), c_Complete__Lattice_OInf__class_OInf(_996204, _996208)), _996206)))], (33593 ^ _779854) ^ [_1396609, _1396611, _1396613, _1396615, _1396617] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396609, tc_fun(_1396611, tc_HOL_Obool)), _1396613), hAPP(hAPP(c_COMBS(_1396609, tc_fun(_1396611, tc_HOL_Obool), tc_fun(_1396611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396611, tc_HOL_Obool), tc_fun(tc_fun(_1396611, tc_HOL_Obool), tc_fun(_1396611, tc_HOL_Obool)), _1396609), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396611, tc_HOL_Obool))), _1396615)), _1396617)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396611, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396609, tc_fun(_1396611, tc_HOL_Obool)), _1396613), _1396615)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396609, tc_fun(_1396611, tc_HOL_Obool)), _1396613), _1396617)))], (7155 ^ _779854) ^ [_897544, _897546, _897548] : [class_Lattices_Osemilattice__inf(_897544), 7158 ^ _779854 : [(7165 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_897544), _897546), _897548) = _897546, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897544), _897546), _897548)))], (7159 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897544), _897546), _897548)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_897544), _897546), _897548) = _897546)]]], (37865 ^ _779854) ^ [_1495474, _1495476, _1495478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495474, _1495474), tc_HOL_Obool)), _1495476), _1495478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495474, tc_HOL_Obool)), c_Wellfounded_Oacc(_1495474, _1495478)), c_Wellfounded_Oacc(_1495474, _1495476))))], (35316 ^ _779854) ^ [_1437762, _1437764] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437762))), 35319 ^ _779854 : [(35326 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437764))), -(c_Divides_Odivmod__int(_1437762, _1437764) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1437762), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1437764))))], (35320 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437764)), -(c_Divides_Odivmod__int(_1437762, _1437764) = c_Divides_OnegDivAlg(_1437762, _1437764))]]], (39615 ^ _779854) ^ [_1548430, _1548432, _1548434] : [-(hAPP(c_Relation_ODomain(_1548430, _1548432), hAPP(c_Set_OCollect(tc_prod(_1548430, _1548432)), hAPP(c_Product__Type_Oprod_Oprod__case(_1548430, _1548432, tc_HOL_Obool), _1548434))) = hAPP(c_Set_OCollect(_1548430), hAPP(hAPP(c_COMBB(tc_fun(_1548432, tc_HOL_Obool), tc_HOL_Obool, _1548430), c_HOL_OEx(_1548432)), _1548434)))], (10043 ^ _779854) ^ [_949439, _949441, _949443, _949445, _949447] : [class_Orderings_Olinorder(_949439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949439), _949441), _949443)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949439), _949445), _949447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949439), hAPP(hAPP(c_Orderings_Oord__class_Omin(_949439), _949441), _949445)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_949439), _949443), _949447))))], (24839 ^ _779854) ^ [_1231008, _1231010, _1231012, _1231014] : [class_Fields_Ofield__inverse__zero(_1231008), class_Int_Onumber(_1231008), 24846 ^ _779854 : [(24847 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1231008), _1231010) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1231008), _1231012), _1231014), 24850 ^ _779854 : [(24857 ^ _779854) ^ [] : [_1231014 = c_Groups_Ozero__class_Ozero(_1231008), -(hAPP(c_Int_Onumber__class_Onumber__of(_1231008), _1231010) = c_Groups_Ozero__class_Ozero(_1231008))], (24851 ^ _779854) ^ [] : [-(_1231014 = c_Groups_Ozero__class_Ozero(_1231008)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231008), hAPP(c_Int_Onumber__class_Onumber__of(_1231008), _1231010)), _1231014) = _1231012)]]], (24863 ^ _779854) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1231008), _1231010) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1231008), _1231012), _1231014)), 24866 ^ _779854 : [(24869 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231008), hAPP(c_Int_Onumber__class_Onumber__of(_1231008), _1231010)), _1231014) = _1231012], (24867 ^ _779854) ^ [] : [_1231014 = c_Groups_Ozero__class_Ozero(_1231008)]], 24870 ^ _779854 : [(24873 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1231008), _1231010) = c_Groups_Ozero__class_Ozero(_1231008)], (24871 ^ _779854) ^ [] : [-(_1231014 = c_Groups_Ozero__class_Ozero(_1231008))]]]]], (38294 ^ _779854) ^ [_1505789, _1505791, _1505793, _1505795, _1505797] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505789, _1505791), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1505789, tc_HOL_Obool)), _1505793), _1505795)), _1505797) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1505789, _1505791), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505789, _1505791), _1505793), _1505797)), hAPP(hAPP(c_Product__Type_OSigma(_1505789, _1505791), _1505795), _1505797)))], (35604 ^ _779854) ^ [_1443146, _1443148, _1443150, _1443152, _1443154] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443146, _1443148), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443150), _1443152))), -(_1443148 = 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)), _1443154)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1443148), _1443154)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1443150), _1443154)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1443148), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1443150, _1443154))), _1443152)))))], (33587 ^ _779854) ^ [_1396207, _1396209, _1396211, _1396213, _1396215] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396207, tc_HOL_Obool)), _1396209), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396211, tc_fun(_1396207, tc_HOL_Obool)), _1396213), _1396215)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396211, tc_fun(_1396207, tc_HOL_Obool)), _1396213), hAPP(hAPP(c_COMBB(tc_fun(_1396207, tc_HOL_Obool), tc_fun(_1396207, tc_HOL_Obool), _1396211), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396207, tc_HOL_Obool)), _1396209)), _1396215)))], (47937 ^ _779854) ^ [_1744240, _1744242, _1744244] : [hBOOL(hAPP(hAPP(c_member(_1744240), _1744242), hAPP(c_List_Oset(_1744240), _1744244))), -(c_List_Oinsert(_1744240, _1744242, _1744244) = _1744244)], (228 ^ _779854) ^ [_783520, _783522, _783524, _783526] : [-(c_Int_Oiszero(_783524, _783520)), c_Int_Oiszero(_783526, _783522), _783526 = _783524, _783522 = _783520], (48081 ^ _779854) ^ [_1747816, _1747818, _1747820] : [class_Enum_Oenum(_1747816), class_Enum_Oenum(_1747818), 48088 ^ _779854 : [(48095 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1747818), hAPP(hAPP(c_COMBB(tc_fun(_1747816, tc_HOL_Obool), tc_HOL_Obool, _1747818), c_Enum_Oenum__class_Oenum__ex(_1747816)), hAPP(hAPP(c_COMBB(tc_fun(_1747816, tc_prod(_1747818, _1747816)), tc_fun(_1747816, tc_HOL_Obool), _1747818), hAPP(c_COMBB(tc_prod(_1747818, _1747816), tc_HOL_Obool, _1747816), _1747820)), c_Product__Type_OPair(_1747818, _1747816))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1747818, _1747816)), _1747820)))], (48089 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1747818, _1747816)), _1747820)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1747818), hAPP(hAPP(c_COMBB(tc_fun(_1747816, tc_HOL_Obool), tc_HOL_Obool, _1747818), c_Enum_Oenum__class_Oenum__ex(_1747816)), hAPP(hAPP(c_COMBB(tc_fun(_1747816, tc_prod(_1747818, _1747816)), tc_fun(_1747816, tc_HOL_Obool), _1747818), hAPP(c_COMBB(tc_prod(_1747818, _1747816), tc_HOL_Obool, _1747816), _1747820)), c_Product__Type_OPair(_1747818, _1747816))))))]]], (52433 ^ _779854) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (50064 ^ _779854) ^ [_1792030, _1792032] : [c_Relation_Osym(_1792030, _1792032), -(c_Relation_Osym(_1792030, c_Transitive__Closure_Otrancl(_1792030, _1792032)))], (41745 ^ _779854) ^ [_1599966, _1599968, _1599970] : [c_Relation_Osingle__valued(_1599966, _1599966, _1599968), -(c_Relation_Osingle__valued(_1599966, _1599966, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1599966, _1599966), tc_HOL_Obool), _1599970), _1599968)))], (52345 ^ _779854) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (33078 ^ _779854) ^ [_1379073, _1379075, _1379077, _1379079, _1379081] : [_1379073 = c_Orderings_Obot__class_Obot(tc_fun(_1379075, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379077, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379075, tc_fun(_1379077, tc_HOL_Obool)), _1379073), _1379079)), _1379081) = _1379081)], (48770 ^ _779854) ^ [_1762428, _1762430, _1762432, _1762434, _1762436] : [_1762428 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1762430, _1762432, _1762434, _1762436), _1762428) = c_Lazy__Sequence_Oempty(_1762432))], (18773 ^ _779854) ^ [_1119082] : [hAPP(c_Nat_OSuc, _1119082) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41222 ^ _779854) ^ [_1587379, _1587381, _1587383, _1587385, _1587387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587379, _1587379)), hAPP(hAPP(c_Product__Type_OPair(_1587379, _1587379), _1587381), _1587383)), c_Transitive__Closure_Ortrancl(_1587379, _1587385))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587379, _1587379)), hAPP(hAPP(c_Product__Type_OPair(_1587379, _1587379), _1587383), _1587387)), _1587385)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587379, _1587379)), hAPP(hAPP(c_Product__Type_OPair(_1587379, _1587379), _1587381), _1587387)), c_Transitive__Closure_Otrancl(_1587379, _1587385))))], (45392 ^ _779854) ^ [_1689272, _1689274] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1689272)), hAPP(c_Code__Numeral_Oof__nat, _1689274)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1689272), _1689274)))], (38292 ^ _779854) ^ [_1505679, _1505681, _1505683, _1505685, _1505687] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505679, _1505681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1505679, tc_HOL_Obool)), _1505683), _1505685)), hAPP(c_COMBK(tc_fun(_1505681, tc_HOL_Obool), _1505679), _1505687)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1505679, _1505681), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1505679, _1505681), _1505683), hAPP(c_COMBK(tc_fun(_1505681, tc_HOL_Obool), _1505679), _1505687))), hAPP(hAPP(c_Product__Type_OSigma(_1505679, _1505681), _1505685), hAPP(c_COMBK(tc_fun(_1505681, tc_HOL_Obool), _1505679), _1505687))))], (29043 ^ _779854) ^ [_1304109, _1304111] : [class_Rings_Olinordered__semidom(_1304109), 29046 ^ _779854 : [(29053 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1304111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304109), c_Groups_Ozero__class_Ozero(_1304109)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1304109), _1304111))))], (29047 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304109), c_Groups_Ozero__class_Ozero(_1304109)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1304109), _1304111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1304111)))]]], (5820 ^ _779854) ^ [_872034, _872036, _872038] : [class_Orderings_Olinorder(_872034), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872034), _872036), _872038))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872034), _872038), _872036)))], (3868 ^ _779854) ^ [_838131, _838133] : [_838133 = _838131, -(c_Groups_Oabs__class_Oabs(_838133) = c_Groups_Oabs__class_Oabs(_838131))], (33339 ^ _779854) ^ [_1385976, _1385978, _1385980, _1385982, _1385984, _1385986, _1385988, _1385990] : [hAPP(c_Fun_Ocomp(_1385976, _1385978, _1385980, _1385982), _1385984) = hAPP(c_Fun_Ocomp(_1385986, _1385978, _1385980, _1385988), _1385990), 33342 ^ _779854 : [(33343 ^ _779854) ^ [_1386091] : [-(hAPP(_1385982, hAPP(_1385984, _1386091)) = hAPP(_1385988, hAPP(_1385990, _1386091)))]]], (39311 ^ _779854) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (35454 ^ _779854) ^ [_1440359, _1440361] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1440359, _1440361), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440359), _1440361)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440359, _1440361)))))], (5576 ^ _779854) ^ [_865187, _865189] : [_865189 = _865187, -(tc_Lazy__Sequence_Olazy__sequence(_865189) = tc_Lazy__Sequence_Olazy__sequence(_865187))], (20524 ^ _779854) ^ [_1149090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1149090)), -(_1149090 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1149090), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (45621 ^ _779854) ^ [_1693816, _1693818] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1693816), _1693818) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693816)), hAPP(c_Code__Numeral_Onat__of, _1693818))))], (29233 ^ _779854) ^ [_1307235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307235)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307235) = 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, _1307235))))], (42450 ^ _779854) ^ [_1621032, _1621034, _1621036, _1621038, _1621040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621032), tc_List_Olist(_1621032))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621032), tc_List_Olist(_1621032)), hAPP(hAPP(c_List_Olist_OCons(_1621032), _1621034), _1621036)), _1621038)), c_List_Olistrel(_1621032, _1621040))), 42455 ^ _779854 : [(42460 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621032), tc_List_Olist(_1621032))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621032), tc_List_Olist(_1621032)), _1621036), 42454 ^ [_1621032, _1621034, _1621036, _1621038, _1621040])), c_List_Olistrel(_1621032, _1621040))))], (42458 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621032, _1621032)), hAPP(hAPP(c_Product__Type_OPair(_1621032, _1621032), _1621034), 42453 ^ [_1621032, _1621034, _1621036, _1621038, _1621040])), _1621040)))], (42456 ^ _779854) ^ [] : [-(_1621038 = hAPP(hAPP(c_List_Olist_OCons(_1621032), 42453 ^ [_1621032, _1621034, _1621036, _1621038, _1621040]), 42454 ^ [_1621032, _1621034, _1621036, _1621038, _1621040]))]]], (25543 ^ _779854) ^ [_1244578] : [_1244578 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1244578) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35852 ^ _779854) ^ [_1447406] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1447406)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1447406)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32349 ^ _779854) ^ [_1362135, _1362137] : [class_Groups_Oordered__ab__group__add__abs(_1362135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362135), _1362137), c_Groups_Ozero__class_Ozero(_1362135))), -(hAPP(c_Groups_Oabs__class_Oabs(_1362135), _1362137) = hAPP(c_Groups_Ouminus__class_Ouminus(_1362135), _1362137))], (4078 ^ _779854) ^ [_841756, _841758] : [_841758 = _841756, -(c_New__Random__Sequence_Oneg__single(_841758) = c_New__Random__Sequence_Oneg__single(_841756))], (41322 ^ _779854) ^ [_1589599, _1589601, _1589603, _1589605] : [c_Wellfounded_Owf(_1589599, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1589599, _1589599)), hAPP(hAPP(c_Product__Type_OPair(_1589599, _1589599), _1589601), _1589603)), _1589605)), 41325 ^ _779854 : [(41328 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589599, _1589599)), hAPP(hAPP(c_Product__Type_OPair(_1589599, _1589599), _1589603), _1589601)), c_Transitive__Closure_Ortrancl(_1589599, _1589605)))], (41326 ^ _779854) ^ [] : [-(c_Wellfounded_Owf(_1589599, _1589605))]]], (49220 ^ _779854) ^ [_1772333, _1772335, _1772337, _1772339, _1772341] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1772333, _1772335, _1772337, _1772339, _1772341) = c_Option_Ooption_Ooption__case(_1772333, tc_prod(_1772335, tc_Lazy__Sequence_Olazy__sequence(_1772335)), _1772337, hAPP(c_Product__Type_Oprod_Oprod__case(_1772335, tc_Lazy__Sequence_Olazy__sequence(_1772335), _1772333), _1772339), hAPP(c_Lazy__Sequence_Oyield(_1772335), _1772341)))], (47967 ^ _779854) ^ [_1744754, _1744756, _1744758, _1744760] : [-(c_List_Oconcat(_1744754, hAPP(hAPP(c_List_Omap(_1744756, tc_List_Olist(_1744754)), _1744758), _1744760)) = c_List_Omaps(_1744756, _1744754, _1744758, _1744760))], (25565 ^ _779854) ^ [_1244846, _1244848] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1244846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244848), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1244846, _1244848))], (8332 ^ _779854) ^ [_919190, _919192, _919194, _919196] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_919190), _919192), _919194), _919196)), -(_919192 = _919196), -(hBOOL(hAPP(_919194, _919196)))], (1930 ^ _779854) ^ [_806931, _806933] : [-(hBOOL(_806931)), _806933 = _806931, hBOOL(_806933)], (7339 ^ _779854) ^ [_900674, _900676, _900678, _900680] : [class_Lattices_Osemilattice__sup(_900674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900674), _900676), _900678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900674), _900680), _900678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900674), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900674), _900676), _900680)), _900678)))], (5282 ^ _779854) ^ [_860634, _860636, _860638, _860640] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_860640, _860636) = c_SetInterval_Oord__class_OatLeastLessThan(_860638, _860634)), _860640 = _860638, _860636 = _860634], (35574 ^ _779854) ^ [_1442523, _1442525, _1442527] : [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), _1442523), _1442525))), -(hBOOL(hAPP(hAPP(_1442527, _1442523), _1442525))), 35581 ^ _779854 : [(35584 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1442527, 35579 ^ [_1442523, _1442525, _1442527]), 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)))), 35580 ^ [_1442523, _1442525, _1442527])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 35579 ^ [_1442523, _1442525, _1442527]), 35580 ^ [_1442523, _1442525, _1442527]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 35580 ^ [_1442523, _1442525, _1442527]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35594 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1442527, 35579 ^ [_1442523, _1442525, _1442527]), 35580 ^ [_1442523, _1442525, _1442527]))], (35582 ^ _779854) ^ [] : [-(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), 35579 ^ [_1442523, _1442525, _1442527]), 35580 ^ [_1442523, _1442525, _1442527]))))]]], (42225 ^ _779854) ^ [_1613931, _1613933, _1613935, _1613937, _1613939, _1613941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613931, _1613931)), hAPP(hAPP(c_Product__Type_OPair(_1613931, _1613931), _1613933), _1613935)), c_Transitive__Closure_Ortrancl(_1613931, _1613937))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613931), tc_List_Olist(_1613931))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613931), tc_List_Olist(_1613931)), _1613939), _1613941)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1613931), c_List_Olistrel1(_1613931, _1613937)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613931), tc_List_Olist(_1613931))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613931), tc_List_Olist(_1613931)), hAPP(hAPP(c_List_Olist_OCons(_1613931), _1613933), _1613939)), hAPP(hAPP(c_List_Olist_OCons(_1613931), _1613935), _1613941))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1613931), c_List_Olistrel1(_1613931, _1613937)))))], (52533 ^ _779854) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (46571 ^ _779854) ^ [_1716393, _1716395, _1716397, _1716399] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1716393, tc_Nat_Onat), _1716393), c_Product__Type_Ofst(_1716393, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1716393, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1716393, tc_Nat_Onat)), _1716395), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1716393, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1716393, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1716393, tc_Nat_Onat), _1716397), _1716399))) = hAPP(hAPP(c_List_Omap(tc_prod(_1716393, tc_Nat_Onat), _1716393), c_Product__Type_Ofst(_1716393, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1716393, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1716393, tc_Nat_Onat)), _1716395), c_Product__Type_Osnd(_1716393, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1716393, tc_Nat_Onat), _1716397), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1716399)))))], (41798 ^ _779854) ^ [_1601287, _1601289, _1601291] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601287, _1601287)), hAPP(hAPP(c_Product__Type_OPair(_1601287, _1601287), _1601289), _1601289)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601287, _1601287), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1601291))))], (42462 ^ _779854) ^ [_1621421, _1621423, _1621425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1621421, _1621421), tc_HOL_Obool)), _1621423), hAPP(hAPP(c_Product__Type_OSigma(_1621421, _1621421), _1621425), hAPP(c_COMBK(tc_fun(_1621421, tc_HOL_Obool), _1621421), _1621425)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1621421), tc_List_Olist(_1621421)), tc_HOL_Obool)), c_List_Olistrel(_1621421, _1621423)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1621421), tc_List_Olist(_1621421)), c_List_Olists(_1621421, _1621425)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1621421), tc_HOL_Obool), tc_List_Olist(_1621421)), c_List_Olists(_1621421, _1621425))))))], (11167 ^ _779854) ^ [_972340, _972342] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972340), c_Orderings_Otop__class_Otop(tc_fun(_972340, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_972340, _972340, _972342), c_Orderings_Otop__class_Otop(tc_fun(_972340, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_972340, tc_HOL_Obool)), -(c_Fun_Oinj__on(_972340, _972340, _972342, c_Orderings_Otop__class_Otop(tc_fun(_972340, tc_HOL_Obool))))], (38122 ^ _779854) ^ [_1501358, _1501360, _1501362, _1501364] : [hAPP(c_Set_Oimage(_1501358, _1501360, _1501362), c_Orderings_Otop__class_Otop(tc_fun(_1501358, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1501360, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1501358, _1501360, _1501362), hAPP(c_Set_Ovimage(_1501358, _1501360, _1501362), _1501364)) = _1501364)], (20124 ^ _779854) ^ [_1142574, _1142576, _1142578, _1142580] : [class_Rings_Ocomm__semiring__1(_1142574), class_Rings_Ono__zero__divisors(_1142574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1142576), _1142578)), 20135 ^ _779854 : [(20145 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1142576, _1142574), _1142580), _1142578) = c_Groups_Ozero__class_Ozero(_1142574)), 20146 ^ _779854 : [(20147 ^ _779854) ^ [_1142952] : [hBOOL(hAPP(hAPP(c_member(_1142576), _1142952), _1142578)), hAPP(_1142580, _1142952) = c_Groups_Ozero__class_Ozero(_1142574)]]], (20136 ^ _779854) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1142576, _1142574), _1142580), _1142578) = c_Groups_Ozero__class_Ozero(_1142574), 20140 ^ _779854 : [(20143 ^ _779854) ^ [] : [-(hAPP(_1142580, 20139 ^ [_1142574, _1142576, _1142578, _1142580]) = c_Groups_Ozero__class_Ozero(_1142574))], (20141 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1142576), 20139 ^ [_1142574, _1142576, _1142578, _1142580]), _1142578)))]]]]], (1700 ^ _779854) ^ [_804056, _804058] : [-(class_Groups_Ocomm__monoid__add(_804056)), _804058 = _804056, class_Groups_Ocomm__monoid__add(_804058)], (33731 ^ _779854) ^ [_1400256, _1400258, _1400260, _1400262, _1400264] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400256, tc_fun(_1400258, tc_HOL_Obool)), _1400260), hAPP(hAPP(c_COMBC(_1400256, tc_fun(_1400258, tc_HOL_Obool), tc_fun(_1400258, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1400258, tc_HOL_Obool), tc_fun(tc_fun(_1400258, tc_HOL_Obool), tc_fun(_1400258, tc_HOL_Obool)), _1400256), c_Groups_Ominus__class_Ominus(tc_fun(_1400258, tc_HOL_Obool))), _1400262)), _1400264)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400258, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400256, tc_fun(_1400258, tc_HOL_Obool)), _1400260), _1400262)), _1400264))], (24142 ^ _779854) ^ [_1217717, _1217719] : [24143 ^ _779854 : [(24146 ^ _779854) ^ [] : [_1217717 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24144 ^ _779854) ^ [] : [_1217719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217717), _1217719) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15918 ^ _779854) ^ [_1065312, _1065314, _1065316] : [class_Rings_Ocomm__semiring__1(_1065312), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065312), _1065314), _1065316) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065312), _1065316), _1065314))], (40849 ^ _779854) ^ [_1577463, _1577465, _1577467, _1577469, _1577471] : [_1577463 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1577465, _1577467, _1577463, _1577469), _1577471) = hAPP(c_Product__Type_OPair(_1577465, _1577467), _1577471))], (35163 ^ _779854) ^ [_1434762, _1434764] : [class_Rings_Osemiring__1(_1434762), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434762), _1434764) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1434762, hAPP(hAPP(c_COMBC(_1434762, _1434762, _1434762), c_Groups_Oplus__class_Oplus(_1434762)), c_Groups_Oone__class_Oone(_1434762)), _1434764, c_Groups_Ozero__class_Ozero(_1434762)))], (47210 ^ _779854) ^ [_1728687, _1728689] : [class_Orderings_Olinorder(_1728687), 47213 ^ _779854 : [(47214 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1728687, _1728689), 47217 ^ _779854 : [(47218 ^ _779854) ^ [_1728858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728858), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728687)), _1728689))), 47221 ^ _779854 : [(47222 ^ _779854) ^ [_1728975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1728975), _1728858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1728687), hAPP(hAPP(c_List_Onth(_1728687), _1728689), _1728975)), hAPP(hAPP(c_List_Onth(_1728687), _1728689), _1728858))))]]]]], (47228 ^ _779854) ^ [] : [47230 ^ _779854 : [(47236 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1728687), hAPP(hAPP(c_List_Onth(_1728687), _1728689), 47232 ^ [_1728687, _1728689])), hAPP(hAPP(c_List_Onth(_1728687), _1728689), 47229 ^ [_1728687, _1728689])))], (47234 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47232 ^ [_1728687, _1728689]), 47229 ^ [_1728687, _1728689])))], (47231 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47229 ^ [_1728687, _1728689]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728687)), _1728689))))]], -(c_List_Olinorder__class_Osorted(_1728687, _1728689))]]], (40718 ^ _779854) ^ [_1574017, _1574019] : [class_Complete__Lattice_Ocomplete__lattice(_1574017), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1574017, hAPP(c_COMBK(_1574017, _1574017), _1574019)) = _1574019)], (26725 ^ _779854) ^ [_1265178, _1265180, _1265182] : [class_Divides_Osemiring__div(_1265178), -(_1265180 = c_Groups_Ozero__class_Ozero(_1265178)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265178), _1265180), _1265182)), _1265180) = _1265182)], (31228 ^ _779854) ^ [_1342884] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1342884), c_Int_OMin) = c_Int_Osucc(_1342884))], (20198 ^ _779854) ^ [_1143835, _1143837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143835), hAPP(c_Nat_OSuc, _1143837))), -(_1143835 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20206 ^ _779854 : [(20209 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20205 ^ [_1143835, _1143837]), _1143837)))], (20207 ^ _779854) ^ [] : [-(_1143835 = hAPP(c_Nat_OSuc, 20205 ^ [_1143835, _1143837]))]]], (38454 ^ _779854) ^ [_1510374, _1510376, _1510378, _1510380] : [_1510374 = c_Orderings_Obot__class_Obot(tc_fun(_1510376, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1510378, _1510376), _1510378, c_Product__Type_Ofst(_1510378, _1510376)), hAPP(hAPP(c_Product__Type_OSigma(_1510378, _1510376), _1510380), hAPP(c_COMBK(tc_fun(_1510376, tc_HOL_Obool), _1510378), _1510374))) = c_Orderings_Obot__class_Obot(tc_fun(_1510378, tc_HOL_Obool)))], (1170 ^ _779854) ^ [_797431, _797433] : [-(class_Rings_Olinordered__ring__strict(_797431)), _797433 = _797431, class_Rings_Olinordered__ring__strict(_797433)], (36496 ^ _779854) ^ [_1461119, _1461121] : [hBOOL(hAPP(_1461119, _1461121)), -(hBOOL(hAPP(_1461119, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1461119) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat), _1461119), c_Nat_OSuc))))], (45270 ^ _779854) ^ [_1686592, _1686594, _1686596, _1686598, _1686600, _1686602] : [-(hBOOL(hAPP(hAPP(c_member(_1686592), _1686594), hAPP(c_List_Oset(_1686592), _1686596)))), -(hAPP(hAPP(c_List_Omap(_1686592, _1686598), c_Fun_Ofun__upd(_1686592, _1686598, _1686600, _1686594, _1686602)), _1686596) = hAPP(hAPP(c_List_Omap(_1686592, _1686598), _1686600), _1686596))], (42135 ^ _779854) ^ [_1610875, _1610877, _1610879] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610875)), hAPP(hAPP(c_List_Olist_OCons(_1610875), _1610877), _1610879)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610875)), _1610879)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30987 ^ _779854) ^ [_1339202, _1339204] : [class_Int_Onumber__ring(_1339202), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339202), hAPP(c_Int_Onumber__class_Onumber__of(_1339202), 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)))), _1339204)) = c_Groups_Oone__class_Oone(_1339202))], (35915 ^ _779854) ^ [_1449015, _1449017, _1449019] : [-(hAPP(c_Product__Type_Osnd(_1449015, _1449017), _1449019) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1449015, _1449017, _1449017), hAPP(c_COMBK(tc_fun(_1449017, _1449017), _1449015), c_COMBI(_1449017))), _1449019))], (40956 ^ _779854) ^ [_1580027, _1580029] : [-(hAPP(c_Relation_ODomain(_1580027, _1580027), c_Transitive__Closure_Otrancl(_1580027, _1580029)) = hAPP(c_Relation_ODomain(_1580027, _1580027), _1580029))], (19303 ^ _779854) ^ [_1128005, _1128007, _1128009, _1128011] : [class_Rings_Oordered__semiring(_1128005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128005), _1128007), _1128009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128005), c_Groups_Ozero__class_Ozero(_1128005)), _1128011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128005), _1128007), _1128011)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128005), _1128009), _1128011))))], (44230 ^ _779854) ^ [_1663914, _1663916, _1663918, _1663920, _1663922] : [hAPP(hAPP(c_List_Odrop(_1663914), _1663916), _1663918) = hAPP(hAPP(c_List_Olist_OCons(_1663914), _1663920), _1663922), -(hAPP(hAPP(c_List_Onth(_1663914), _1663918), _1663916) = _1663920)], (43724 ^ _779854) ^ [_1651902, _1651904, _1651906, _1651908, _1651910] : [hAPP(hAPP(c_List_Oappend(_1651902), _1651904), hAPP(hAPP(c_List_Olist_OCons(_1651902), _1651906), c_List_Olist_ONil(_1651902))) = hAPP(hAPP(c_List_Oappend(_1651902), _1651908), hAPP(hAPP(c_List_Olist_OCons(_1651902), _1651910), c_List_Olist_ONil(_1651902))), 43727 ^ _779854 : [(43730 ^ _779854) ^ [] : [-(_1651906 = _1651910)], (43728 ^ _779854) ^ [] : [-(_1651904 = _1651908)]]], (28892 ^ _779854) ^ [_1301646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1301646)), -(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), _1301646))))], (5900 ^ _779854) ^ [_873265, _873267, _873269, _873271] : [class_Orderings_Oord(_873265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873265), _873267), _873269)), _873269 = _873271, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873265), _873267), _873271)))], (24729 ^ _779854) ^ [_1228880, _1228882, _1228884, _1228886] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228880), hAPP(c_Int_Onumber__class_Onumber__of(_1228880), _1228882)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1228880), _1228884), _1228886)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1228880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228880), hAPP(c_Int_Onumber__class_Onumber__of(_1228880), _1228882)), _1228884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228880), hAPP(c_Int_Onumber__class_Onumber__of(_1228880), _1228882)), _1228886))), class_Int_Onumber(_1228880), class_Rings_Oring(_1228880)], (25805 ^ _779854) ^ [_1248883, _1248885, _1248887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248883)), _1248883 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1248885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1248883), _1248887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248885), _1248883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1248887)))], (46473 ^ _779854) ^ [_1713569, _1713571, _1713573, _1713575] : [-(hAPP(c_List_Ofilter(_1713569, _1713571), hAPP(hAPP(c_List_Oappend(_1713569), _1713573), _1713575)) = hAPP(hAPP(c_List_Oappend(_1713569), hAPP(c_List_Ofilter(_1713569, _1713571), _1713573)), hAPP(c_List_Ofilter(_1713569, _1713571), _1713575)))], (31973 ^ _779854) ^ [_1355093] : [class_Rings_Olinordered__idom(_1355093), -(hAPP(c_Groups_Oabs__class_Oabs(_1355093), c_Groups_Oone__class_Oone(_1355093)) = c_Groups_Oone__class_Oone(_1355093))], (52601 ^ _779854) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (2344 ^ _779854) ^ [_814299, _814301, _814303, _814305, _814307, _814309, _814311, _814313, _814315, _814317] : [-(c_Nitpick_Opair__box_Opair__box__rec(_814317, _814313, _814309, _814305, _814301) = c_Nitpick_Opair__box_Opair__box__rec(_814315, _814311, _814307, _814303, _814299)), _814317 = _814315, _814313 = _814311, _814309 = _814307, _814305 = _814303, _814301 = _814299], (45436 ^ _779854) ^ [_1690039, _1690041, _1690043, _1690045] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690039)), _1690041) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690043)), _1690045), -(hAPP(hAPP(c_List_Omap(tc_prod(_1690039, _1690043), _1690043), c_Product__Type_Osnd(_1690039, _1690043)), hAPP(hAPP(c_List_Ozip(_1690039, _1690043), _1690041), _1690045)) = _1690045)], (49908 ^ _779854) ^ [_1788766, _1788768] : [c_Relation_Otrans(_1788766, _1788768), c_Relation_Oantisym(_1788766, _1788768), -(c_Relation_Otrans(_1788766, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1788766, _1788766), tc_HOL_Obool)), _1788768), c_Relation_OId(_1788766))))], (49614 ^ _779854) ^ [_1781463, _1781465, _1781467, _1781469] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1781463), _1781465)), 49617 ^ _779854 : [(49618 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1781467), hAPP(c_Set_OCollect(_1781467), hAPP(hAPP(c_COMBB(tc_fun(_1781463, tc_HOL_Obool), tc_HOL_Obool, _1781467), c_HOL_OEx(_1781463)), hAPP(hAPP(c_COMBB(tc_fun(_1781463, tc_HOL_Obool), tc_fun(_1781463, tc_HOL_Obool), _1781467), hAPP(c_COMBS(_1781463, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1781463), c_fconj), hAPP(hAPP(c_COMBC(_1781463, tc_fun(_1781463, tc_HOL_Obool), tc_HOL_Obool), c_member(_1781463)), _1781465)))), _1781469))))), 49621 ^ _779854 : [(49622 ^ _779854) ^ [_1781771] : [hBOOL(hAPP(hAPP(c_member(_1781463), _1781771), _1781465)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1781467), hAPP(c_Set_OCollect(_1781467), hAPP(hAPP(c_COMBC(_1781467, _1781463, tc_HOL_Obool), _1781469), _1781771)))))]]], (49628 ^ _779854) ^ [] : [49630 ^ _779854 : [(49633 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1781467), hAPP(c_Set_OCollect(_1781467), hAPP(hAPP(c_COMBC(_1781467, _1781463, tc_HOL_Obool), _1781469), 49629 ^ [_1781463, _1781465, _1781467, _1781469]))))], (49631 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781463), 49629 ^ [_1781463, _1781465, _1781467, _1781469]), _1781465)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1781467), hAPP(c_Set_OCollect(_1781467), hAPP(hAPP(c_COMBB(tc_fun(_1781463, tc_HOL_Obool), tc_HOL_Obool, _1781467), c_HOL_OEx(_1781463)), hAPP(hAPP(c_COMBB(tc_fun(_1781463, tc_HOL_Obool), tc_fun(_1781463, tc_HOL_Obool), _1781467), hAPP(c_COMBS(_1781463, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1781463), c_fconj), hAPP(hAPP(c_COMBC(_1781463, tc_fun(_1781463, tc_HOL_Obool), tc_HOL_Obool), c_member(_1781463)), _1781465)))), _1781469))))))]]], (15566 ^ _779854) ^ [_1058031, _1058033, _1058035, _1058037, _1058039] : [class_Groups_Ocomm__monoid__add(_1058031), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058033), _1058035)), -(hBOOL(hAPP(hAPP(c_member(_1058033), _1058037), _1058035))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058033, _1058031), _1058039), hAPP(hAPP(c_Set_Oinsert(_1058033), _1058037), _1058035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058031), hAPP(_1058039, _1058037)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058033, _1058031), _1058039), _1058035)))], (41585 ^ _779854) ^ [_1596237, _1596239, _1596241] : [c_Relation_Ototal__on(_1596237, _1596239, _1596241), -(c_Relation_Ototal__on(_1596237, _1596239, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1596237, _1596237), tc_HOL_Obool)), _1596241), c_Relation_OId(_1596237))))], (10317 ^ _779854) ^ [_954368, _954370, _954372, _954374, _954376] : [class_Orderings_Olinorder(_954368), class_Orderings_Olinorder(_954370), c_Orderings_Oorder__class_Omono(_954370, _954368, _954372), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_954368), hAPP(_954372, _954374)), hAPP(_954372, _954376)) = hAPP(_954372, hAPP(hAPP(c_Orderings_Oord__class_Omax(_954370), _954374), _954376)))], (16577 ^ _779854) ^ [_1078644, _1078646, _1078648, _1078650, _1078652] : [class_Groups_Ocomm__monoid__mult(_1078644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078646), _1078648)), hBOOL(hAPP(hAPP(c_member(_1078646), _1078650), _1078648)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1078646, _1078644), _1078652), _1078648) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078644), hAPP(_1078652, _1078650)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1078646, _1078644), _1078652), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078646, tc_HOL_Obool)), _1078648), hAPP(hAPP(c_Set_Oinsert(_1078646), _1078650), c_Orderings_Obot__class_Obot(tc_fun(_1078646, tc_HOL_Obool)))))))], (20530 ^ _779854) ^ [_1149196, _1149198] : [_1149196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1149196), _1149198) = _1149198)], (14443 ^ _779854) ^ [_1035269, _1035271, _1035273, _1035275, _1035277, _1035279, _1035281, _1035283] : [c_Finite__Set_Ofolding__image__simple(_1035269, _1035271, _1035273, _1035275, _1035277, _1035279), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035271), _1035281)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035271), _1035283)), 14457 ^ _779854 : [(14460 ^ _779854) ^ [] : [hAPP(_1035277, 14456 ^ [_1035269, _1035271, _1035273, _1035275, _1035277, _1035279, _1035281, _1035283]) = _1035275], (14458 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1035271), 14456 ^ [_1035269, _1035271, _1035273, _1035275, _1035277, _1035279, _1035281, _1035283]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035271, tc_HOL_Obool)), _1035281), _1035283))))]], -(hAPP(_1035279, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1035271, tc_HOL_Obool)), _1035281), _1035283)) = hAPP(hAPP(_1035273, hAPP(_1035279, _1035281)), hAPP(_1035279, _1035283)))], (39485 ^ _779854) ^ [_1543469, _1543471, _1543473, _1543475] : [-(hAPP(c_Relation_ORange(_1543469, _1543471), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543469, _1543471), tc_HOL_Obool)), _1543473), _1543475)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543471, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1543469, _1543471), _1543473)), hAPP(c_Relation_ORange(_1543469, _1543471), _1543475)))], (18165 ^ _779854) ^ [_1108544, _1108546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108544), _1108546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1108544)), _1108546)))], (12362 ^ _779854) ^ [_995582, _995584, _995586, _995588] : [-(hBOOL(hAPP(hAPP(c_member(_995582), hAPP(_995584, _995586)), hAPP(c_Set_Oimage(_995588, _995582, _995584), c_Orderings_Otop__class_Otop(tc_fun(_995588, tc_HOL_Obool))))))], (13107 ^ _779854) ^ [_1010823, _1010825, _1010827] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1010823, tc_HOL_Obool)), _1010825), _1010827))), 13113 ^ _779854 : [(13117 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1010823, tc_HOL_Obool)), 13115 ^ [_1010823, _1010825, _1010827]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1010823, tc_HOL_Obool)), _1010825), _1010827))))], (13119 ^ _779854) ^ [] : [13112 ^ [_1010823, _1010825, _1010827] = 13115 ^ [_1010823, _1010825, _1010827]], (13121 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1010823, tc_HOL_Obool)), 13112 ^ [_1010823, _1010825, _1010827]), 13115 ^ [_1010823, _1010825, _1010827]) = c_Orderings_Obot__class_Obot(tc_fun(_1010823, tc_HOL_Obool))], (13114 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1010823, tc_HOL_Obool)), 13112 ^ [_1010823, _1010825, _1010827]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1010823, tc_HOL_Obool)), _1010825), _1010827))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1010823, tc_HOL_Obool)), _1010825), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1010823, tc_HOL_Obool), _1010827)) = c_Orderings_Obot__class_Obot(tc_fun(_1010823, tc_HOL_Obool)))], (27823 ^ _779854) ^ [_1283182, _1283184, _1283186] : [hBOOL(hAPP(_1283182, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1283184), _1283186))), 27826 ^ _779854 : [(27833 ^ _779854) ^ [] : [-(_1283186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 27836 ^ _779854 : [(27837 ^ _779854) ^ [_1283434, _1283436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1283434), _1283186)), _1283184 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1283186), _1283436)), _1283434), -(hBOOL(hAPP(_1283182, _1283436)))]]], (27827 ^ _779854) ^ [] : [_1283186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1283182, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (30539 ^ _779854) ^ [_1331280, _1331282] : [c_Nat__Transfer_Onat__set(_1331280), c_Nat__Transfer_Onat__set(_1331282), 30546 ^ _779854 : [(30553 ^ _779854) ^ [] : [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), _1331280)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1331282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1331280), _1331282)))], (30547 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1331280), _1331282)), -(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), _1331280)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1331282))))]]], (40167 ^ _779854) ^ [_1561415, _1561417, _1561419] : [40169 ^ _779854 : [(40172 ^ _779854) ^ [] : [hBOOL(hAPP(_1561417, 40168 ^ [_1561415, _1561417, _1561419]))], (40170 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561415), 40168 ^ [_1561415, _1561417, _1561419]), _1561419)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1561415, _1561417), _1561419)))], (6800 ^ _779854) ^ [_889784, _889786, _889788, _889790] : [6802 ^ _779854 : [(6805 ^ _779854) ^ [] : [hBOOL(hAPP(_889790, 6801 ^ [_889784, _889786, _889788, _889790]))], (6803 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889784), 6801 ^ [_889784, _889786, _889788, _889790]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889784, tc_HOL_Obool)), _889786), _889788))))]], 6806 ^ _779854 : [(6813 ^ _779854) ^ [_890101] : [hBOOL(hAPP(hAPP(c_member(_889784), _890101), _889788)), -(hBOOL(hAPP(_889790, _890101)))], (6807 ^ _779854) ^ [_890004] : [hBOOL(hAPP(hAPP(c_member(_889784), _890004), _889786)), -(hBOOL(hAPP(_889790, _890004)))]]], (42790 ^ _779854) ^ [_1629766, _1629768, _1629770] : [hBOOL(hAPP(hAPP(c_member(_1629766), _1629768), hAPP(c_List_Oset(_1629766), _1629770))), -(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(_1629766)), _1629770))))], (29367 ^ _779854) ^ [_1309624, _1309626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1309624)), c_Int_OBit0(_1309626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309624), _1309626)))], (27453 ^ _779854) ^ [_1277212, _1277214] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1277212), _1277214)), _1277212)))], (50325 ^ _779854) ^ [_1796319, _1796321] : [c_Equiv__Relations_Opart__equivp(_1796319, _1796321), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1796319, tc_HOL_Obool)), 50328 ^ [_1796319, _1796321]), hAPP(hAPP(c_COMBB(tc_fun(_1796319, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1796319, tc_HOL_Obool)), c_HOL_OEx(_1796319)), hAPP(hAPP(c_COMBB(tc_fun(_1796319, tc_HOL_Obool), tc_fun(_1796319, tc_HOL_Obool), tc_fun(_1796319, tc_HOL_Obool)), hAPP(c_COMBS(_1796319, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1796319), c_fconj), hAPP(hAPP(c_COMBS(_1796319, _1796319, tc_HOL_Obool), _1796321), c_COMBI(_1796319))))), hAPP(hAPP(c_COMBC(tc_fun(_1796319, tc_HOL_Obool), tc_fun(_1796319, tc_fun(_1796319, tc_HOL_Obool)), tc_fun(_1796319, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1796319, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1796319, tc_fun(_1796319, tc_HOL_Obool)), tc_fun(_1796319, tc_HOL_Obool)), tc_fun(_1796319, tc_HOL_Obool)), c_COMBB(tc_fun(_1796319, tc_HOL_Obool), tc_HOL_Obool, _1796319)), c_fequal)), _1796321))))))], (16002 ^ _779854) ^ [_1067397, _1067399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067397), _1067399)), 16005 ^ _779854 : [(16008 ^ _779854) ^ [] : [_1067397 = _1067399], (16006 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067397), _1067399)))]]], (16648 ^ _779854) ^ [_1080065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080065), _1080065))], (41820 ^ _779854) ^ [_1601971, _1601973, _1601975] : [-(hAPP(hAPP(c_Nat_Ocompow(_1601971, _1601971), hAPP(c_Nat_OSuc, _1601973)), _1601975) = hAPP(c_Fun_Ocomp(_1601971, _1601971, _1601971, _1601975), hAPP(hAPP(c_Nat_Ocompow(_1601971, _1601971), _1601973), _1601975)))], (41278 ^ _779854) ^ [_1588720] : [-(hAPP(c_Relation_ODomain(_1588720, _1588720), c_Relation_OId(_1588720)) = c_Orderings_Otop__class_Otop(tc_fun(_1588720, tc_HOL_Obool)))], (41593 ^ _779854) ^ [_1596380, _1596382, _1596384, _1596386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1596380, _1596382), tc_HOL_Obool)), _1596384), _1596386)), c_Relation_Osingle__valued(_1596380, _1596382, _1596386), -(c_Relation_Osingle__valued(_1596380, _1596382, _1596384))], (47965 ^ _779854) ^ [_1744713, _1744715] : [-(c_List_Oinsert(_1744713, _1744715, c_List_Olist_ONil(_1744713)) = hAPP(hAPP(c_List_Olist_OCons(_1744713), _1744715), c_List_Olist_ONil(_1744713)))], (46546 ^ _779854) ^ [_1715274, _1715276] : [46548 ^ _779854 : [(46551 ^ _779854) ^ [] : [46547 ^ [_1715274, _1715276] = c_List_Olist_ONil(_1715274)], (46549 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1715274)), 46547 ^ [_1715274, _1715276]), hAPP(c_List_Oset(tc_List_Olist(_1715274)), _1715276))))]], -(c_List_Otranspose(_1715274, _1715276) = c_List_Olist_ONil(tc_List_Olist(_1715274)))], (33244 ^ _779854) ^ [_1382838, _1382840, _1382842, _1382844] : [-(hAPP(c_Finite__Set_Ofold__image(_1382838, _1382840, _1382842), _1382844) = c_Finite__Set_Ofold(_1382840, _1382838, hAPP(hAPP(c_COMBB(_1382838, tc_fun(_1382838, _1382838), _1382840), _1382842), _1382844)))], (52299 ^ _779854) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (26389 ^ _779854) ^ [_1259306, _1259308] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259306) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259308)), 26392 ^ _779854 : [(26395 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259308)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26393 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259306))))]], 26396 ^ _779854 : [(26399 ^ _779854) ^ [] : [26400 ^ _779854 : [(26403 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259306) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (26401 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259308))))]], 26404 ^ _779854 : [(26407 ^ _779854) ^ [] : [_1259306 = _1259308], (26405 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259308)))]]], (26397 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259306)))]]], (41780 ^ _779854) ^ [_1600809, _1600811, _1600813, _1600815] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600809, _1600809)), _1600811), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600809, _1600809), tc_HOL_Obool), _1600813), _1600815))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600809, _1600809)), _1600811), c_Transitive__Closure_Ortrancl(_1600809, _1600815))))], (51949 ^ _779854) ^ [_1830371, _1830373] : [_1830371 = _1830373, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830371), _1830373)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830373), _1830371)))], (49477 ^ _779854) ^ [_1778296, _1778298, _1778300] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1778296, _1778298, _1778300, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1778298)], (45306 ^ _779854) ^ [_1687337, _1687339, _1687341, _1687343] : [c_Fun_Oinj__on(_1687337, _1687339, _1687341, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1687337, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1687337), tc_fun(_1687337, tc_HOL_Obool), c_List_Oset(_1687337)), _1687343))), -(c_Fun_Oinj__on(tc_List_Olist(_1687337), tc_List_Olist(_1687339), hAPP(c_List_Omap(_1687337, _1687339), _1687341), _1687343))], (21272 ^ _779854) ^ [_1163009, _1163011, _1163013, _1163015] : [class_Groups_Ocomm__monoid__add(_1163009), 21275 ^ _779854 : [(21282 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163011)), _1163013))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1163009), _1163015), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1163013, hAPP(c_Nat_OSuc, _1163011))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163009), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1163009), _1163015), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1163013, _1163011))), hAPP(_1163015, hAPP(c_Nat_OSuc, _1163011))))], (21276 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1163011)), _1163013)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1163009), _1163015), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1163013, hAPP(c_Nat_OSuc, _1163011))) = c_Groups_Ozero__class_Ozero(_1163009))]]], (49584 ^ _779854) ^ [_1780992, _1780994] : [c_Relation_Otrans(_1780992, _1780994), -(c_Relation_Otrans(tc_List_Olist(_1780992), c_List_Olexord(_1780992, _1780994)))], (11728 ^ _779854) ^ [_983314, _983316, _983318, _983320] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_983314, tc_HOL_Obool)), _983316), _983318)), hBOOL(hAPP(hAPP(c_member(_983314), _983320), _983316)), -(hBOOL(hAPP(hAPP(c_member(_983314), _983320), c_Complete__Lattice_OSup__class_OSup(tc_fun(_983314, tc_HOL_Obool), _983318))))], (33909 ^ _779854) ^ [_1405932, _1405934] : [-(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)), _1405932), _1405934))], (29273 ^ _779854) ^ [_1308057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1308057)), -(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), _1308057), 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)))))))], (3880 ^ _779854) ^ [_838301, _838303] : [_838303 = _838301, -(c_Lazy__Sequence_Ohit__bound(_838303) = c_Lazy__Sequence_Ohit__bound(_838301))], (3618 ^ _779854) ^ [_834232, _834234, _834236, _834238] : [-(c_List_Orotate(_834238, _834234) = c_List_Orotate(_834236, _834232)), _834238 = _834236, _834234 = _834232], (37032 ^ _779854) ^ [_1474643, _1474645, _1474647, _1474649, _1474651, _1474653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474643, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474645, _1474643, _1474647), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1474649, tc_fun(_1474645, tc_HOL_Obool)), _1474651), _1474653))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1474649, tc_fun(_1474643, tc_HOL_Obool)), _1474651), hAPP(hAPP(c_COMBB(tc_fun(_1474645, tc_HOL_Obool), tc_fun(_1474643, tc_HOL_Obool), _1474649), c_Relation_OImage(_1474645, _1474643, _1474647)), _1474653)))))], (42338 ^ _779854) ^ [_1617505, _1617507, _1617509] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617505), tc_List_Olist(_1617505))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617505), tc_List_Olist(_1617505)), _1617507), _1617507)), c_List_Olistrel(_1617505, c_Transitive__Closure_Ortrancl(_1617505, _1617509)))))], (43119 ^ _779854) ^ [_1638915, _1638917, _1638919, _1638921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638915), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638917)), _1638919))), -(hAPP(hAPP(c_List_Onth(_1638917), hAPP(hAPP(c_List_Olist__update(_1638917, _1638919), _1638915), _1638921)), _1638915) = _1638921)], (47733 ^ _779854) ^ [_1739920, _1739922, _1739924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739920)), c_List_OdropWhile(_1739920, _1739922, _1739924))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739920)), _1739924))))], (16934 ^ _779854) ^ [_1085383, _1085385, _1085387, _1085389] : [class_Orderings_Olinorder(_1085383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085383), _1085385)), hBOOL(hAPP(hAPP(c_member(_1085383), _1085387), _1085385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085383), hAPP(hAPP(c_Finite__Set_Ofold(_1085383, _1085383, c_Orderings_Oord__class_Omin(_1085383)), _1085389), _1085385)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1085383), _1085387), _1085389))))], (29517 ^ _779854) ^ [_1312254, _1312256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1312254)), c_Int_OBit0(_1312256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1312254), _1312256)))], (18779 ^ _779854) ^ [_1119174] : [-(_1119174 = 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)), _1119174)))], (44440 ^ _779854) ^ [_1669020, _1669022, _1669024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669020), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669022)), _1669024))), -(_1669024 = hAPP(hAPP(c_List_Oappend(_1669022), hAPP(hAPP(c_List_Otake(_1669022), _1669020), _1669024)), hAPP(hAPP(c_List_Olist_OCons(_1669022), hAPP(hAPP(c_List_Onth(_1669022), _1669024), _1669020)), hAPP(hAPP(c_List_Odrop(_1669022), hAPP(c_Nat_OSuc, _1669020)), _1669024))))], (43029 ^ _779854) ^ [_1636971, _1636973, _1636975] : [-(hAPP(hAPP(c_List_Olist__update(_1636971, _1636973), _1636975), hAPP(hAPP(c_List_Onth(_1636971), _1636973), _1636975)) = _1636973)], (39717 ^ _779854) ^ [_1550268, _1550270, _1550272] : [c_Wellfounded_Owf(_1550268, _1550270), -(c_Wellfounded_Owf(_1550268, c_Wellfounded_Omlex__prod(_1550268, _1550272, _1550270)))], (6733 ^ _779854) ^ [_888022, _888024] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888022, tc_HOL_Obool)), _888024), _888024) = _888024)], (31226 ^ _779854) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (11099 ^ _779854) ^ [_970885, _970887, _970889, _970891, _970893, _970895] : [c_Fun_Oinj__on(_970885, _970887, _970889, _970891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970885, tc_HOL_Obool)), _970893), _970891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970885, tc_HOL_Obool)), _970895), _970891)), -(hAPP(c_Set_Oimage(_970885, _970887, _970889), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970885, tc_HOL_Obool)), _970893), _970895)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970887, tc_HOL_Obool)), hAPP(c_Set_Oimage(_970885, _970887, _970889), _970893)), hAPP(c_Set_Oimage(_970885, _970887, _970889), _970895)))], (35018 ^ _779854) ^ [_1431126, _1431128] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1431126), _1431128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431126)), _1431128)))], (30133 ^ _779854) ^ [_1323570, _1323572] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1323570), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1323572)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323570, _1323572)))], (37626 ^ _779854) ^ [_1489408, _1489410, _1489412, _1489414, _1489416, _1489418, _1489420, _1489422] : [c_Equiv__Relations_Oequiv(_1489408, _1489410, _1489412), c_Equiv__Relations_Ocongruent2(_1489408, _1489414, _1489416, _1489412, _1489418, _1489420), hBOOL(hAPP(hAPP(c_member(_1489408), _1489422), _1489410)), -(c_Equiv__Relations_Ocongruent(_1489414, _1489416, _1489418, hAPP(_1489420, _1489422)))], (28420 ^ _779854) ^ [_1293689, _1293691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1293689), _1293691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293689)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293691))))], (31148 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (44109 ^ _779854) ^ [_1660420, _1660422, _1660424, _1660426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660420), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660422)), _1660424))), -(hAPP(hAPP(c_List_Onth(_1660422), hAPP(hAPP(c_List_Oappend(_1660422), _1660424), _1660426)), _1660420) = hAPP(hAPP(c_List_Onth(_1660422), _1660424), _1660420))], (33399 ^ _779854) ^ [_1387393, _1387395, _1387397, _1387399, _1387401, _1387403, _1387405] : [class_Rings_Osemiring__0(_1387393), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387393), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387395, _1387393), _1387397), _1387399)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387401, _1387393), _1387403), _1387405)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387395, _1387393), hAPP(hAPP(c_COMBC(_1387395, tc_fun(_1387401, tc_HOL_Obool), _1387393), hAPP(hAPP(c_COMBB(tc_fun(_1387401, _1387393), tc_fun(tc_fun(_1387401, tc_HOL_Obool), _1387393), _1387395), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387401, _1387393)), hAPP(hAPP(c_COMBC(_1387395, tc_fun(_1387401, _1387393), tc_fun(_1387401, _1387393)), hAPP(hAPP(c_COMBB(tc_fun(_1387393, _1387393), tc_fun(tc_fun(_1387401, _1387393), tc_fun(_1387401, _1387393)), _1387395), c_COMBB(_1387393, _1387393, _1387401)), hAPP(hAPP(c_COMBB(_1387393, tc_fun(_1387393, _1387393), _1387395), c_Groups_Otimes__class_Otimes(_1387393)), _1387397))), _1387403))), _1387405)), _1387399))], (42970 ^ _779854) ^ [_1635716, _1635718] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1635716, _1635718)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1635716, _1635718))], (28372 ^ _779854) ^ [_1292788, _1292790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1292788), _1292790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292788)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292790))))], (48794 ^ _779854) ^ [_1762800, _1762802, _1762804, _1762806, _1762808, _1762810, _1762812] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1762800, _1762802, _1762804, _1762806, _1762808, _1762810, _1762812) = c_New__DSequence_Oneg__decr__bind(_1762800, _1762802, hAPP(hAPP(hAPP(_1762804, _1762808), _1762810), _1762812), hAPP(hAPP(c_COMBC(_1762800, 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(_1762802)))), hAPP(hAPP(c_COMBC(_1762800, 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(_1762802))))), hAPP(hAPP(c_COMBC(_1762800, 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(_1762802)))))), _1762806), _1762808)), _1762810)), _1762812)))], (37077 ^ _779854) ^ [_1475906, _1475908, _1475910, _1475912, _1475914] : [hBOOL(hAPP(hAPP(c_member(_1475906), _1475908), hAPP(c_Relation_OImage(_1475910, _1475906, _1475912), hAPP(hAPP(c_Set_Oinsert(_1475910), _1475914), c_Orderings_Obot__class_Obot(tc_fun(_1475910, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475910, _1475906)), hAPP(hAPP(c_Product__Type_OPair(_1475910, _1475906), _1475914), _1475908)), _1475912)))], (37958 ^ _779854) ^ [_1497340, _1497342, _1497344, _1497346, _1497348, _1497350] : [c_Typedef_Otype__definition(_1497340, _1497342, _1497344, _1497346, _1497348), -(hBOOL(hAPP(hAPP(c_member(_1497342), hAPP(_1497344, _1497350)), _1497348)))], (5650 ^ _779854) ^ [_866318, _866320] : [_866320 = _866318, -(c_Orderings_Oord__class_Oless__eq(_866320) = c_Orderings_Oord__class_Oless__eq(_866318))], (51959 ^ _779854) ^ [_1830524, _1830526, _1830528] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830524), _1830526)), 51970 ^ _779854 : [(51973 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830528), _1830524))], (51971 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830524), _1830528)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830526), _1830528)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830528), _1830526)))], (44452 ^ _779854) ^ [_1669411, _1669413, _1669415] : [-(_1669411 = c_List_Olist_ONil(_1669413)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669415), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669413)), _1669411))), -(hAPP(c_List_Ohd(_1669413), hAPP(hAPP(c_List_Odrop(_1669413), _1669415), _1669411)) = hAPP(hAPP(c_List_Onth(_1669413), _1669411), _1669415))], (47020 ^ _779854) ^ [_1725082, _1725084, _1725086, _1725088, _1725090] : [class_Orderings_Olinorder(_1725082), c_List_Olinorder__class_Osorted(_1725082, hAPP(hAPP(c_List_Omap(_1725084, _1725082), _1725086), _1725088)), -(c_List_Olinorder__class_Osorted(_1725082, hAPP(hAPP(c_List_Omap(_1725084, _1725082), _1725086), c_List_Oremove1(_1725084, _1725090, _1725088))))], (30089 ^ _779854) ^ [_1322640, _1322642] : [c_Nat__Transfer_Onat__set(_1322640), c_Nat__Transfer_Onat__set(_1322642), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1322640), _1322642) = 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), _1322640)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1322642))))], (38889 ^ _779854) ^ [_1522060, _1522062, _1522064] : [-(hAPP(c_Set_OCollect(_1522060), hAPP(hAPP(c_COMBS(_1522060, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522060), c_fimplies), _1522062)), _1522064)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1522060, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1522060, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1522060), _1522062))), hAPP(c_Set_OCollect(_1522060), _1522064)))], (18821 ^ _779854) ^ [_1119707, _1119709] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119707), _1119709) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1119709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20646 ^ _779854) ^ [_1151245, _1151247, _1151249, _1151251] : [class_Rings_Olinordered__ring__strict(_1151245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151245), _1151247), c_Groups_Ozero__class_Ozero(_1151245))), 20653 ^ _779854 : [(20660 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151245), _1151251), _1151249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151245), _1151247), _1151249)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151245), _1151247), _1151251))))], (20654 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151245), _1151247), _1151249)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151245), _1151247), _1151251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151245), _1151251), _1151249)))]]], (22695 ^ _779854) ^ [_1189878, _1189880, _1189882] : [class_Fields_Olinordered__field(_1189878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189878), _1189880), c_Groups_Ozero__class_Ozero(_1189878))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189878), c_Groups_Ozero__class_Ozero(_1189878)), _1189882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189878), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189878), _1189880), _1189882)), c_Groups_Ozero__class_Ozero(_1189878))))], (13351 ^ _779854) ^ [_1015129, _1015131] : [class_Complete__Lattice_Ocomplete__lattice(_1015129), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015129), _1015131)), -(_1015131 = c_Orderings_Obot__class_Obot(tc_fun(_1015129, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1015129, _1015131) = c_Complete__Lattice_OSup__class_OSup(_1015129, _1015131))], (12434 ^ _779854) ^ [_996905, _996907, _996909] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_996905, tc_HOL_Obool)), _996907), _996909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_996905, tc_HOL_Obool)), _996907), c_Complete__Lattice_OSup__class_OSup(tc_fun(_996905, tc_HOL_Obool), _996909))))], (49946 ^ _779854) ^ [_1789376, _1789378] : [c_Relation_Oantisym(_1789376, _1789378), 49949 ^ _779854 : [(49950 ^ _779854) ^ [_1789488, _1789490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1789376, _1789376)), hAPP(hAPP(c_Product__Type_OPair(_1789376, _1789376), _1789490), _1789488)), _1789378)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1789376, _1789376)), hAPP(hAPP(c_Product__Type_OPair(_1789376, _1789376), _1789488), _1789490)), _1789378)), -(_1789490 = _1789488)]]], (46467 ^ _779854) ^ [_1713505, _1713507, _1713509, _1713511] : [-(hBOOL(hAPP(_1713505, _1713507))), -(hAPP(c_List_Ofilter(_1713509, _1713505), hAPP(hAPP(c_List_Olist_OCons(_1713509), _1713507), _1713511)) = hAPP(c_List_Ofilter(_1713509, _1713505), _1713511))], (37103 ^ _779854) ^ [_1476616, _1476618] : [-(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), _1476616), _1476618)), 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), _1476618), _1476616)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (7291 ^ _779854) ^ [_899854, _899856, _899858] : [class_Lattices_Osemilattice__inf(_899854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899854), _899856), _899858)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_899854), _899858), _899856) = _899856)], (27181 ^ _779854) ^ [_1272507] : [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), _1272507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1272507)))], (20223 ^ _779854) ^ [_1144252, _1144254] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1144252), _1144254), 20228 ^ _779854 : [(20231 ^ _779854) ^ [] : [-(_1144254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20229 ^ _779854) ^ [] : [-(_1144252 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20232 ^ _779854 : [(20235 ^ _779854) ^ [] : [-(_1144254 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20233 ^ _779854) ^ [] : [-(_1144252 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6749 ^ _779854) ^ [_888458, _888460, _888462, _888464] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888458, tc_HOL_Obool)), _888460), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888458, tc_HOL_Obool)), _888462), _888464)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888458, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888458, tc_HOL_Obool)), _888460), _888462)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888458, tc_HOL_Obool)), _888460), _888464)))], (40873 ^ _779854) ^ [_1578084, _1578086] : [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), _1578084), _1578086)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1578084), _1578086)))], (5118 ^ _779854) ^ [_858084, _858086, _858088, _858090, _858092, _858094] : [-(c_Product__Type_Oprod_Oprod__case(_858094, _858090, _858086) = c_Product__Type_Oprod_Oprod__case(_858092, _858088, _858084)), _858094 = _858092, _858090 = _858088, _858086 = _858084], (16064 ^ _779854) ^ [_1068308] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1068308), _1068308))))], (33663 ^ _779854) ^ [_1398385, _1398387, _1398389, _1398391, _1398393, _1398395] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398385, tc_fun(_1398387, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398389, _1398385, _1398391), _1398393)), _1398395) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398389, tc_fun(_1398387, tc_HOL_Obool)), _1398393), hAPP(hAPP(c_COMBB(_1398385, tc_fun(_1398387, tc_HOL_Obool), _1398389), _1398395), _1398391)))], (29475 ^ _779854) ^ [_1311517, _1311519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311517), _1311519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1311517)), c_Int_OBit1(_1311519))))], (32523 ^ _779854) ^ [_1365232, _1365234, _1365236] : [32525 ^ _779854 : [(32528 ^ _779854) ^ [] : [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(_1365234, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 32524 ^ [_1365232, _1365234, _1365236]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1365234, 32524 ^ [_1365232, _1365234, _1365236])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32526 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32524 ^ [_1365232, _1365234, _1365236]), _1365232)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1365234, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1365236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1365236), hAPP(_1365234, _1365232))), 32538 ^ _779854 : [(32541 ^ _779854) ^ [] : [-(hAPP(_1365234, 32537 ^ [_1365232, _1365234, _1365236]) = _1365236)], (32539 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 32537 ^ [_1365232, _1365234, _1365236]), _1365232)))]]], (20493 ^ _779854) ^ [_1148555, _1148557, _1148559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1148555), _1148557)), 20496 ^ _779854 : [(20497 ^ _779854) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1148555, tc_Nat_Onat), _1148559), _1148557) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 20500 ^ _779854 : [(20501 ^ _779854) ^ [_1148717] : [hBOOL(hAPP(hAPP(c_member(_1148555), _1148717), _1148557)), -(hAPP(_1148559, _1148717) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20507 ^ _779854) ^ [] : [20509 ^ _779854 : [(20512 ^ _779854) ^ [] : [hAPP(_1148559, 20508 ^ [_1148555, _1148557, _1148559]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20510 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1148555), 20508 ^ [_1148555, _1148557, _1148559]), _1148557)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1148555, tc_Nat_Onat), _1148559), _1148557) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (34345 ^ _779854) ^ [_1416484, _1416486] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1416484), _1416486)), -(hAPP(c_Finite__Set_Ocard(_1416484), _1416486) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1416484, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1416484), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1416486))], (2384 ^ _779854) ^ [_814989, _814991] : [_814991 = _814989, -(c_Divides_Oadjust(_814991) = c_Divides_Oadjust(_814989))], (13457 ^ _779854) ^ [_1016709, _1016711, _1016713] : [class_Lattices_Olattice(_1016709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016709), _1016711)), -(_1016713 = c_Orderings_Obot__class_Obot(tc_fun(_1016709, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016709, tc_HOL_Obool)), _1016713), _1016711)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1016709), c_Big__Operators_Olattice__class_OSup__fin(_1016709, _1016713)), c_Big__Operators_Olattice__class_OSup__fin(_1016709, _1016711)) = c_Big__Operators_Olattice__class_OSup__fin(_1016709, _1016711))], (48620 ^ _779854) ^ [_1759421, _1759423, _1759425] : [c_FunDef_Ois__measure(_1759421, _1759423), -(c_FunDef_Ois__measure(tc_prod(_1759425, _1759421), hAPP(hAPP(c_COMBB(_1759421, tc_Nat_Onat, tc_prod(_1759425, _1759421)), _1759423), c_Product__Type_Osnd(_1759425, _1759421))))], (28958 ^ _779854) ^ [_1302614, _1302616] : [hBOOL(hAPP(_1302614, hAPP(c_Int_Onat, _1302616))), 28961 ^ _779854 : [(28968 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302616), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1302614, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28962 ^ _779854) ^ [_1302714] : [_1302616 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1302714), -(hBOOL(hAPP(_1302614, _1302714)))]]], (12704 ^ _779854) ^ [_1002464, _1002466, _1002468, _1002470, _1002472] : [-(c_Fun_Oinj__on(_1002464, _1002466, _1002468, hAPP(hAPP(c_Set_Oinsert(_1002464), _1002470), _1002472))), c_Fun_Oinj__on(_1002464, _1002466, _1002468, _1002472), -(hBOOL(hAPP(hAPP(c_member(_1002466), hAPP(_1002468, _1002470)), hAPP(c_Set_Oimage(_1002464, _1002466, _1002468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002464, tc_HOL_Obool)), _1002472), hAPP(hAPP(c_Set_Oinsert(_1002464), _1002470), c_Orderings_Obot__class_Obot(tc_fun(_1002464, tc_HOL_Obool))))))))], (15748 ^ _779854) ^ [_1061766, _1061768, _1061770, _1061772, _1061774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061766), _1061768)), 15751 ^ _779854 : [(15758 ^ _779854) ^ [] : [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), _1061768), _1061766)), _1061770)), _1061772)), _1061774)), -(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), _1061768), _1061770)), _1061772)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061766), _1061770)), _1061774))))], (15752 ^ _779854) ^ [] : [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), _1061768), _1061770)), _1061772)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061766), _1061770)), _1061774))), -(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), _1061768), _1061766)), _1061770)), _1061772)), _1061774)))]]], (40933 ^ _779854) ^ [_1579554, _1579556] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579554, _1579554)), hAPP(hAPP(c_Product__Type_OPair(_1579554, _1579554), 40934 ^ [_1579554, _1579556]), 40934 ^ [_1579554, _1579556])), c_Transitive__Closure_Otrancl(_1579554, _1579556)))), -(c_Wellfounded_Oacyclic(_1579554, _1579556))], (44175 ^ _779854) ^ [_1662285, _1662287, _1662289, _1662291, _1662293, _1662295] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662285), tc_List_Olist(_1662285))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662285), tc_List_Olist(_1662285)), hAPP(hAPP(c_List_Oappend(_1662285), _1662287), hAPP(hAPP(c_List_Olist_OCons(_1662285), _1662289), c_List_Olist_ONil(_1662285)))), hAPP(hAPP(c_List_Oappend(_1662285), _1662291), hAPP(hAPP(c_List_Olist_OCons(_1662285), _1662293), c_List_Olist_ONil(_1662285))))), c_List_Olistrel1(_1662285, _1662295)))), 44176 ^ _779854 : [(44183 ^ _779854) ^ [] : [_1662287 = _1662291, hBOOL(hAPP(hAPP(c_member(tc_prod(_1662285, _1662285)), hAPP(hAPP(c_Product__Type_OPair(_1662285, _1662285), _1662289), _1662293)), _1662295))], (44177 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662285), tc_List_Olist(_1662285))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662285), tc_List_Olist(_1662285)), _1662287), _1662291)), c_List_Olistrel1(_1662285, _1662295))), _1662289 = _1662293]]], (20754 ^ _779854) ^ [_1153318, _1153320, _1153322, _1153324] : [class_Rings_Olinordered__semiring(_1153318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153318), _1153320), _1153322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153318), _1153324), _1153322))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153318), c_Groups_Ozero__class_Ozero(_1153318)), _1153322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), _1153320), _1153324)))], (45204 ^ _779854) ^ [_1685005, _1685007] : [-(hAPP(hAPP(c_List_Omap(_1685005, _1685005), c_COMBI(_1685005)), _1685007) = _1685007)], (36993 ^ _779854) ^ [_1473764, _1473766] : [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)), _1473764), _1473766)), 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)), _1473764), 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)), _1473766), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (28184 ^ _779854) ^ [_1289555, _1289557] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1289555), _1289557) = 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)), _1289555)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1289557))))], (18026 ^ _779854) ^ [_1106074] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1106074) = _1106074)], (20293 ^ _779854) ^ [_1145212, _1145214] : [20294 ^ _779854 : [(20297 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145214))], (20295 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145212))]], -(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), _1145212), _1145214))))], (42287 ^ _779854) ^ [_1615935, _1615937, _1615939, _1615941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615935), tc_List_Olist(_1615935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615935), tc_List_Olist(_1615935)), _1615937), _1615939)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1615935), tc_List_Olist(_1615935)), c_List_Olistrel1(_1615935, _1615941)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615935), tc_List_Olist(_1615935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615935), tc_List_Olist(_1615935)), _1615937), _1615939)), c_List_Olistrel1(_1615935, hAPP(c_Relation_Oconverse(_1615935, _1615935), _1615941)))))], (46313 ^ _779854) ^ [_1709212, _1709214] : [46315 ^ _779854 : [(46318 ^ _779854) ^ [] : [46314 ^ [_1709212, _1709214] = c_List_Olist_ONil(_1709212)], (46316 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709212)), 46314 ^ [_1709212, _1709214]), hAPP(c_List_Oset(tc_List_Olist(_1709212)), _1709214))))]], -(c_List_Oconcat(_1709212, _1709214) = c_List_Olist_ONil(_1709212))], (45208 ^ _779854) ^ [_1685106, _1685108, _1685110, _1685112] : [-(hAPP(hAPP(c_List_Omap(_1685106, _1685108), _1685110), c_List_Obutlast(_1685106, _1685112)) = c_List_Obutlast(_1685108, hAPP(hAPP(c_List_Omap(_1685106, _1685108), _1685110), _1685112)))], (45782 ^ _779854) ^ [_1697821, _1697823, _1697825, _1697827, _1697829] : [c_List_Olist__all2(_1697821, _1697823, _1697825, _1697827, _1697829), 45785 ^ _779854 : [(45788 ^ _779854) ^ [_1697987] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1697821, _1697823)), _1697987), hAPP(c_List_Oset(tc_prod(_1697821, _1697823)), hAPP(hAPP(c_List_Ozip(_1697821, _1697823), _1697827), _1697829)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1697821, _1697823, tc_HOL_Obool), _1697825), _1697987)))], (45786 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697821)), _1697827) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697823)), _1697829))]]], (47370 ^ _779854) ^ [_1732178, _1732180, _1732182] : [_1732182 = hAPP(hAPP(c_List_Olist_OCons(_1732178), _1732180), c_List_Olist_ONil(_1732178)), -(hAPP(hAPP(c_List_Olist_OCons(_1732178), _1732180), c_List_Olist_ONil(_1732178)) = hAPP(c_List_Orev(_1732178), _1732182))], (23433 ^ _779854) ^ [_1204110, _1204112, _1204114, _1204116, _1204118] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1204110, _1204112, hAPP(hAPP(c_Set_Oinsert(_1204110), _1204114), _1204116)), _1204118))), 23434 ^ _779854 : [(23435 ^ _779854) ^ [_1204214, _1204216] : [hAPP(hAPP(c_Set_Oinsert(_1204110), _1204114), _1204116) = hAPP(hAPP(c_Set_Oinsert(_1204110), _1204216), _1204214), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1204110, _1204110, _1204112, _1204216, _1204214), _1204118)), -(hBOOL(hAPP(hAPP(c_member(_1204110), _1204216), _1204214)))]]], (8630 ^ _779854) ^ [_923612, _923614, _923616] : [class_Orderings_Olinorder(_923612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923612), _923614), _923616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923612), _923616), _923614))], (50924 ^ _779854) ^ [_1809580, _1809582, _1809584, _1809586, _1809588] : [c_Fun_Obij__betw(_1809580, _1809582, _1809584, _1809586, _1809588), 50927 ^ _779854 : [(50934 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1809582), _1809588)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1809580), _1809586)))], (50928 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1809580), _1809586)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1809582), _1809588)))]]], (18323 ^ _779854) ^ [_1111386, _1111388] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1111386), hAPP(c_Nat_OSuc, _1111388)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1111386, _1111388))], (16253 ^ _779854) ^ [_1071840, _1071842, _1071844, _1071846] : [class_Rings_Ocomm__semiring__1(_1071840), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071840), _1071842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071840), _1071844), _1071846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071840), _1071842), _1071844)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071840), _1071842), _1071846)))], (29757 ^ _779854) ^ [] : [-(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))))], (52409 ^ _779854) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (40261 ^ _779854) ^ [_1563810, _1563812] : [40263 ^ _779854 : [(40266 ^ _779854) ^ [] : [hBOOL(hAPP(_1563810, hAPP(c_Int_OAbs__Integ, 40262 ^ [_1563810, _1563812])))], (40264 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40262 ^ [_1563810, _1563812]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1563810, _1563812)))], (45641 ^ _779854) ^ [_1694204, _1694206, _1694208, _1694210, _1694212] : [c_List_Opartition(_1694204, _1694206, _1694208) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694204), tc_List_Olist(_1694204)), _1694210), _1694212), 45644 ^ _779854 : [(45651 ^ _779854) ^ [_1694466] : [hBOOL(hAPP(hAPP(c_member(_1694204), _1694466), hAPP(c_List_Oset(_1694204), _1694212))), hBOOL(hAPP(_1694206, _1694466))], (45645 ^ _779854) ^ [_1694357] : [hBOOL(hAPP(hAPP(c_member(_1694204), _1694357), hAPP(c_List_Oset(_1694204), _1694210))), -(hBOOL(hAPP(_1694206, _1694357)))]]], (46836 ^ _779854) ^ [_1722255, _1722257] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1722255, _1722257)))], (26579 ^ _779854) ^ [_1263007, _1263009] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1263007)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1263009)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1263007), _1263009))], (3520 ^ _779854) ^ [_832645, _832647, _832649, _832651, _832653, _832655] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_832655, _832651, _832647) = c_SetInterval_Oord__class_OgreaterThanAtMost(_832653, _832649, _832645)), _832655 = _832653, _832651 = _832649, _832647 = _832645], (45430 ^ _779854) ^ [_1689882, _1689884, _1689886, _1689888] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689882)), _1689884) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689886)), _1689888), -(hAPP(hAPP(c_List_Omap(tc_prod(_1689882, _1689886), _1689882), c_Product__Type_Ofst(_1689882, _1689886)), hAPP(hAPP(c_List_Ozip(_1689882, _1689886), _1689884), _1689888)) = _1689884)], (31140 ^ _779854) ^ [_1341504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1341504), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1341504)), c_Int_OMin)))], (25667 ^ _779854) ^ [_1246448, _1246450] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246448), _1246450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246450), _1246448))], (43185 ^ _779854) ^ [_1640600, _1640602, _1640604] : [hBOOL(hAPP(c_List_Odistinct(_1640600), _1640602)), -(hBOOL(hAPP(c_List_Odistinct(_1640600), c_List_Osublist(_1640600, _1640602, _1640604))))], (24877 ^ _779854) ^ [_1231603, _1231605, _1231607, _1231609] : [class_Fields_Ofield__inverse__zero(_1231603), class_Int_Onumber(_1231603), 24884 ^ _779854 : [(24885 ^ _779854) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1231603), _1231605), _1231607) = hAPP(c_Int_Onumber__class_Onumber__of(_1231603), _1231609), 24888 ^ _779854 : [(24895 ^ _779854) ^ [] : [_1231607 = c_Groups_Ozero__class_Ozero(_1231603), -(hAPP(c_Int_Onumber__class_Onumber__of(_1231603), _1231609) = c_Groups_Ozero__class_Ozero(_1231603))], (24889 ^ _779854) ^ [] : [-(_1231607 = c_Groups_Ozero__class_Ozero(_1231603)), -(_1231605 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231603), hAPP(c_Int_Onumber__class_Onumber__of(_1231603), _1231609)), _1231607))]]], (24901 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1231603), _1231605), _1231607) = hAPP(c_Int_Onumber__class_Onumber__of(_1231603), _1231609)), 24904 ^ _779854 : [(24907 ^ _779854) ^ [] : [_1231605 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231603), hAPP(c_Int_Onumber__class_Onumber__of(_1231603), _1231609)), _1231607)], (24905 ^ _779854) ^ [] : [_1231607 = c_Groups_Ozero__class_Ozero(_1231603)]], 24908 ^ _779854 : [(24911 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1231603), _1231609) = c_Groups_Ozero__class_Ozero(_1231603)], (24909 ^ _779854) ^ [] : [-(_1231607 = c_Groups_Ozero__class_Ozero(_1231603))]]]]], (35121 ^ _779854) ^ [_1433390, _1433392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1433390), _1433392)), -(c_Divides_Odivmod__nat(_1433390, _1433392) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1433390))], (20047 ^ _779854) ^ [_1141301, _1141303] : [class_Groups_Oab__group__add(_1141301), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141301), hAPP(c_Groups_Ouminus__class_Ouminus(_1141301), _1141303)), _1141303) = c_Groups_Ozero__class_Ozero(_1141301))], (2474 ^ _779854) ^ [_816378, _816380, _816382, _816384, _816386, _816388, _816390, _816392, _816394, _816396] : [-(c_Product__Type_Oprod_Oprod__rec(_816396, _816392, _816388, _816384, _816380) = c_Product__Type_Oprod_Oprod__rec(_816394, _816390, _816386, _816382, _816378)), _816396 = _816394, _816392 = _816390, _816388 = _816386, _816384 = _816382, _816380 = _816378], (44266 ^ _779854) ^ [_1664699, _1664701, _1664703, _1664705, _1664707] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1664699, _1664701)), _1664703), hAPP(hAPP(c_List_Ozip(_1664699, _1664701), _1664705), _1664707)) = hAPP(hAPP(c_List_Ozip(_1664699, _1664701), hAPP(hAPP(c_List_Odrop(_1664699), _1664703), _1664705)), hAPP(hAPP(c_List_Odrop(_1664701), _1664703), _1664707)))], (39921 ^ _779854) ^ [_1554883, _1554885, _1554887, _1554889] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554883, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1554883, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1554883, _1554885), _1554887)), hAPP(c_Relation_ODomain(_1554883, _1554885), _1554889))), hAPP(c_Relation_ODomain(_1554883, _1554885), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1554883, _1554885), tc_HOL_Obool)), _1554887), _1554889)))))], (46236 ^ _779854) ^ [_1707712, _1707714] : [class_Orderings_Olinorder(_1707712), -(c_List_Olinorder__class_Osorted__list__of__set(_1707712, hAPP(c_List_Oset(_1707712), _1707714)) = c_List_Olinorder__class_Osort__key(_1707712, _1707712, c_COMBI(_1707712), c_List_Oremdups(_1707712, _1707714)))], (39098 ^ _779854) ^ [_1528952] : [-(c_Wellfounded_Ofinite__psubset(_1528952) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1528952, tc_HOL_Obool), tc_fun(_1528952, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1528952, tc_HOL_Obool), tc_fun(_1528952, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1528952, tc_HOL_Obool), tc_fun(tc_fun(_1528952, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1528952, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1528952, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1528952, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1528952, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1528952, tc_HOL_Obool)), c_COMBS(tc_fun(_1528952, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1528952, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1528952, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1528952, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1528952, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1528952, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1528952)))))], (24659 ^ _779854) ^ [_1227366, _1227368, _1227370] : [class_Int_Onumber__ring(_1227366), -(hAPP(c_Int_Onumber__class_Onumber__of(_1227366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1227368), _1227370)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227366), hAPP(c_Int_Onumber__class_Onumber__of(_1227366), _1227368)), hAPP(c_Int_Onumber__class_Onumber__of(_1227366), _1227370)))], (15104 ^ _779854) ^ [_1048385, _1048387, _1048389, _1048391] : [class_Groups_Ocancel__semigroup__add(_1048385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048385), _1048387), _1048389) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048385), _1048387), _1048391), -(_1048389 = _1048391)], (42011 ^ _779854) ^ [_1607268, _1607270, _1607272, _1607274, _1607276, _1607278] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607268, _1607270)), _1607272), hAPP(hAPP(c_Relation_Orel__comp(_1607268, _1607274, _1607270), _1607276), _1607278))), 42017 ^ _779854 : [(42022 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607274, _1607270)), hAPP(hAPP(c_Product__Type_OPair(_1607274, _1607270), 42015 ^ [_1607268, _1607270, _1607272, _1607274, _1607276, _1607278]), 42016 ^ [_1607268, _1607270, _1607272, _1607274, _1607276, _1607278])), _1607278)))], (42020 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607268, _1607274)), hAPP(hAPP(c_Product__Type_OPair(_1607268, _1607274), 42014 ^ [_1607268, _1607270, _1607272, _1607274, _1607276, _1607278]), 42015 ^ [_1607268, _1607270, _1607272, _1607274, _1607276, _1607278])), _1607276)))], (42018 ^ _779854) ^ [] : [-(_1607272 = hAPP(hAPP(c_Product__Type_OPair(_1607268, _1607270), 42014 ^ [_1607268, _1607270, _1607272, _1607274, _1607276, _1607278]), 42016 ^ [_1607268, _1607270, _1607272, _1607274, _1607276, _1607278]))]]], (49830 ^ _779854) ^ [_1787363, _1787365] : [c_Predicate_Oreflp(_1787363, _1787365), c_Predicate_Osymp(_1787363, _1787365), c_Predicate_Otransp(_1787363, _1787365), -(c_Equiv__Relations_Oequivp(_1787363, _1787365))], (48010 ^ _779854) ^ [_1745936, _1745938] : [-(c_Wellfounded_Owf(_1745936, c_List_Omeasures(_1745936, _1745938)))], (47849 ^ _779854) ^ [_1742468, _1742470, _1742472] : [47851 ^ _779854 : [(47854 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1742470, 47850 ^ [_1742468, _1742470, _1742472])))], (47852 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742468), 47850 ^ [_1742468, _1742470, _1742472]), hAPP(c_List_Oset(_1742468), c_List_OdropWhile(_1742468, _1742470, _1742472)))))]], -(c_List_OtakeWhile(_1742468, _1742470, _1742472) = hAPP(c_List_Ofilter(_1742468, _1742470), _1742472))], (47046 ^ _779854) ^ [_1725572, _1725574, _1725576, _1725578, _1725580] : [class_Orderings_Olinorder(_1725572), c_List_Olinorder__class_Osorted(_1725572, hAPP(hAPP(c_List_Omap(_1725574, _1725572), _1725576), _1725578)), -(c_List_Olinorder__class_Osorted(_1725572, hAPP(hAPP(c_List_Omap(_1725574, _1725572), _1725576), hAPP(c_List_Ofilter(_1725574, _1725580), _1725578))))], (45300 ^ _779854) ^ [_1687172, _1687174, _1687176, _1687178] : [class_Groups_Oab__group__add(_1687172), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1687172), hAPP(c_List_Omonoid__add__class_Olistsum(_1687172), hAPP(hAPP(c_List_Omap(_1687174, _1687172), _1687176), _1687178))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1687172), hAPP(hAPP(c_List_Omap(_1687174, _1687172), hAPP(c_Fun_Ocomp(_1687172, _1687172, _1687174, c_Groups_Ouminus__class_Ouminus(_1687172)), _1687176)), _1687178)))], (44205 ^ _779854) ^ [_1663158, _1663160, _1663162, _1663164, _1663166] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663158), tc_List_Olist(_1663158))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663158), tc_List_Olist(_1663158)), hAPP(hAPP(c_List_Oappend(_1663158), _1663160), _1663162)), hAPP(hAPP(c_List_Oappend(_1663158), _1663160), _1663164))), c_List_Olexord(_1663158, _1663166))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1663158, _1663158)), hAPP(hAPP(c_Product__Type_OPair(_1663158, _1663158), 44210 ^ [_1663158, _1663160, _1663162, _1663164, _1663166]), 44210 ^ [_1663158, _1663160, _1663162, _1663164, _1663166])), _1663166))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663158), tc_List_Olist(_1663158))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663158), tc_List_Olist(_1663158)), _1663162), _1663164)), c_List_Olexord(_1663158, _1663166))))], (26363 ^ _779854) ^ [_1258921, _1258923] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1258921) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1258923), 26366 ^ _779854 : [(26373 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258921)))), 26376 ^ _779854 : [(26383 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258923)))), -(_1258921 = _1258923)], (26377 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258923))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258921) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (26367 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258923)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (47943 ^ _779854) ^ [_1744345, _1744347, _1744349] : [-(hBOOL(hAPP(hAPP(c_member(_1744345), _1744347), hAPP(c_List_Oset(_1744345), _1744349)))), -(c_List_Oinsert(_1744345, _1744347, _1744349) = hAPP(hAPP(c_List_Olist_OCons(_1744345), _1744347), _1744349))], (46824 ^ _779854) ^ [_1722083] : [class_Orderings_Olinorder(_1722083), -(c_List_Olinorder__class_Osorted(_1722083, c_List_Olist_ONil(_1722083)))], (17438 ^ _779854) ^ [_1095125, _1095127, _1095129, _1095131] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1095125, _1095127, hAPP(hAPP(c_Set_Oinsert(_1095125), _1095129), c_Orderings_Obot__class_Obot(tc_fun(_1095125, tc_HOL_Obool)))), _1095131)), -(_1095129 = _1095131)], (39347 ^ _779854) ^ [_1539444, _1539446, _1539448, _1539450] : [c_Finite__Set_Ofolding(_1539444, _1539446, _1539448, _1539450), -(hAPP(_1539450, c_Orderings_Obot__class_Obot(tc_fun(_1539444, tc_HOL_Obool))) = c_Fun_Oid(_1539446))], (43562 ^ _779854) ^ [_1647974, _1647976, _1647978] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647974), tc_List_Olist(_1647974))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647974), tc_List_Olist(_1647974)), _1647976), c_List_Olist_ONil(_1647974))), c_List_Olistrel1(_1647974, _1647978)))], (35211 ^ _779854) ^ [_1435814, _1435816, _1435818] : [hBOOL(hAPP(_1435814, 35212 ^ [_1435814, _1435816, _1435818])), 35215 ^ _779854 : [(35216 ^ _779854) ^ [_1435925, _1435927] : [-(hBOOL(hAPP(_1435814, hAPP(hAPP(c_Product__Type_OPair(_1435816, _1435818), _1435927), _1435925))))]]], (52239 ^ _779854) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (52623 ^ _779854) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52265 ^ _779854) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11876 ^ _779854) ^ [_986241, _986243] : [11877 ^ _779854 : [(11878 ^ _779854) ^ [_986294] : [hBOOL(hAPP(hAPP(c_member(_986241), _986294), _986243))]], _986243 = c_Orderings_Obot__class_Obot(tc_fun(_986241, tc_HOL_Obool))], (48852 ^ _779854) ^ [_1764524, _1764526, _1764528] : [-(_1764526 = _1764528), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1764524, _1764524, hAPP(hAPP(c_COMBB(tc_fun(_1764524, tc_HOL_Obool), tc_fun(_1764524, tc_HOL_Obool), _1764524), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1764524), c_fNot)), c_fequal)), _1764526), _1764528)))], (38372 ^ _779854) ^ [_1508373, _1508375, _1508377, _1508379, _1508381, _1508383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508373, _1508375)), hAPP(hAPP(c_Product__Type_OPair(_1508373, _1508375), _1508377), _1508379)), hAPP(hAPP(c_Product__Type_OSigma(_1508373, _1508375), _1508381), _1508383))), 38375 ^ _779854 : [(38378 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508375), _1508379), hAPP(_1508383, _1508377))))], (38376 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508373), _1508377), _1508381)))]]], (6567 ^ _779854) ^ [_884949, _884951, _884953, _884955] : [class_Groups_Ouminus(_884949), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_884951, _884949)), _884953), _884955) = hAPP(c_Groups_Ouminus__class_Ouminus(_884949), hAPP(_884953, _884955)))], (33657 ^ _779854) ^ [_1398166, _1398168, _1398170] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398166, tc_Nat_Onat), _1398168), _1398170)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398166, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1398166), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1398168)), _1398170))], (28098 ^ _779854) ^ [_1288171, _1288173, _1288175] : [class_Int_Onumber__ring(_1288171), 28101 ^ _779854 : [(28108 ^ _779854) ^ [] : [c_Int_Oiszero(_1288171, hAPP(c_Int_Onumber__class_Onumber__of(_1288171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1288173), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1288175)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1288171), _1288173) = hAPP(c_Int_Onumber__class_Onumber__of(_1288171), _1288175))], (28102 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1288171), _1288173) = hAPP(c_Int_Onumber__class_Onumber__of(_1288171), _1288175), -(c_Int_Oiszero(_1288171, hAPP(c_Int_Onumber__class_Onumber__of(_1288171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1288173), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1288175)))))]]], (28898 ^ _779854) ^ [_1301752, _1301754] : [hAPP(c_Int_Onat, _1301752) = _1301754, 28901 ^ _779854 : [(28908 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301752))), -(_1301754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28902 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301752)), -(_1301752 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1301754))]]], (41110 ^ _779854) ^ [_1584595, _1584597, _1584599, _1584601, _1584603] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584595, _1584595)), hAPP(hAPP(c_Product__Type_OPair(_1584595, _1584595), _1584597), _1584599)), _1584601)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584595, _1584595)), hAPP(hAPP(c_Product__Type_OPair(_1584595, _1584595), _1584599), _1584603)), c_Transitive__Closure_Ortrancl(_1584595, _1584601))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584595, _1584595)), hAPP(hAPP(c_Product__Type_OPair(_1584595, _1584595), _1584597), _1584603)), c_Transitive__Closure_Ortrancl(_1584595, _1584601))))], (5844 ^ _779854) ^ [_872387, _872389, _872391] : [class_Orderings_Oorder(_872387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872387), _872389), _872391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872387), _872391), _872389)), -(_872391 = _872389)], (31250 ^ _779854) ^ [_1343289] : [class_Int_Onumber__ring(_1343289), -(hAPP(c_Int_Onumber__class_Onumber__of(_1343289), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1343289), c_Groups_Oone__class_Oone(_1343289)))], (3170 ^ _779854) ^ [_827210, _827212, _827214, _827216] : [-(c_Big__Operators_Olattice__class_OInf__fin(_827216, _827212) = c_Big__Operators_Olattice__class_OInf__fin(_827214, _827210)), _827216 = _827214, _827212 = _827210], (52603 ^ _779854) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (2628 ^ _779854) ^ [_818827, _818829, _818831, _818833, _818835, _818837, _818839, _818841] : [-(c_Product__Type_Oapsnd(_818841, _818837, _818833, _818829) = c_Product__Type_Oapsnd(_818839, _818835, _818831, _818827)), _818841 = _818839, _818837 = _818835, _818833 = _818831, _818829 = _818827], (43378 ^ _779854) ^ [_1644794] : [-(c_List_Obutlast(_1644794, c_List_Olist_ONil(_1644794)) = c_List_Olist_ONil(_1644794))], (46192 ^ _779854) ^ [_1706830, _1706832, _1706834, _1706836] : [-(c_List_Oremdups(_1706830, hAPP(hAPP(c_List_Omap(_1706832, _1706830), _1706834), c_List_Oremdups(_1706832, _1706836))) = c_List_Oremdups(_1706830, hAPP(hAPP(c_List_Omap(_1706832, _1706830), _1706834), _1706836)))], (45807 ^ _779854) ^ [_1698517, _1698519, _1698521, _1698523, _1698525, _1698527, _1698529] : [c_List_Olist__all2(_1698517, _1698519, _1698521, hAPP(hAPP(c_List_Omap(_1698523, _1698517), _1698525), _1698527), _1698529), -(c_List_Olist__all2(_1698523, _1698519, hAPP(hAPP(c_COMBB(_1698517, tc_fun(_1698519, tc_HOL_Obool), _1698523), _1698521), _1698525), _1698527, _1698529))], (29623 ^ _779854) ^ [_1314170, _1314172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1314170)), c_Int_OBit1(_1314172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1314170), _1314172)))], (28092 ^ _779854) ^ [_1288030, _1288032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1288030), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1288030), _1288032)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1288030))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1288032))))], (33068 ^ _779854) ^ [_1378788, _1378790, _1378792, _1378794, _1378796] : [class_Groups_Ocomm__monoid__mult(_1378788), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378790), _1378792)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378790, _1378788), hAPP(hAPP(c_COMBS(_1378790, _1378788, _1378788), hAPP(hAPP(c_COMBB(_1378788, tc_fun(_1378788, _1378788), _1378790), c_Groups_Otimes__class_Otimes(_1378788)), _1378794)), _1378796)), _1378792) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378788), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378790, _1378788), _1378794), _1378792)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378790, _1378788), _1378796), _1378792)))], (30321 ^ _779854) ^ [_1327430, _1327432, _1327434] : [class_Divides_Osemiring__div(_1327430), -(c_Divides_Odiv__class_Omod(_1327430, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327430), _1327432), _1327434), _1327432) = c_Groups_Ozero__class_Ozero(_1327430))], (10745 ^ _779854) ^ [_963026, _963028, _963030] : [class_Groups_Oab__group__add(_963026), -(hAPP(c_Groups_Ouminus__class_Ouminus(_963026), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963026), _963028), _963030)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_963026), _963030), _963028))], (40041 ^ _779854) ^ [_1557901, _1557903] : [c_Wellfounded_OwfP(_1557901, _1557903), 40044 ^ _779854 : [(40045 ^ _779854) ^ [_1557965] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1557901, _1557903), _1557965)))]]], (6997 ^ _779854) ^ [_894379, _894381, _894383] : [class_Lattices_Olattice(_894379), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894379), _894381), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894379), _894381), _894383)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894379), _894381), _894383))], (22759 ^ _779854) ^ [_1191106, _1191108, _1191110, _1191112] : [class_Fields_Olinordered__field(_1191106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191106), _1191108), c_Groups_Ozero__class_Ozero(_1191106))), 22766 ^ _779854 : [(22773 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191106), _1191112), _1191108)), _1191110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191106), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191106), _1191110), _1191108)), _1191112)))], (22767 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191106), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191106), _1191110), _1191108)), _1191112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191106), _1191112), _1191108)), _1191110)))]]], (43773 ^ _779854) ^ [_1652982, _1652984, _1652986, _1652988, _1652990] : [hAPP(hAPP(c_List_Oappend(_1652982), _1652984), _1652986) = hAPP(hAPP(c_List_Olist_OCons(_1652982), _1652988), _1652990), 43778 ^ _779854 : [(43781 ^ _779854) ^ [] : [-(_1652986 = hAPP(hAPP(c_List_Olist_OCons(_1652982), _1652988), _1652990))], (43779 ^ _779854) ^ [] : [-(_1652984 = c_List_Olist_ONil(_1652982))]], 43783 ^ _779854 : [(43786 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1652982), 43782 ^ [_1652982, _1652984, _1652986, _1652988, _1652990]), _1652986) = _1652990)], (43784 ^ _779854) ^ [] : [-(_1652984 = hAPP(hAPP(c_List_Olist_OCons(_1652982), _1652988), 43782 ^ [_1652982, _1652984, _1652986, _1652988, _1652990]))]]], (47800 ^ _779854) ^ [_1741255, _1741257, _1741259, _1741261, _1741263] : [-(c_List_OdropWhile(_1741255, _1741257, _1741259) = hAPP(hAPP(c_List_Olist_OCons(_1741255), _1741261), _1741263)), _1741259 = hAPP(hAPP(c_List_Oappend(_1741255), c_List_OtakeWhile(_1741255, _1741257, _1741259)), hAPP(hAPP(c_List_Olist_OCons(_1741255), _1741261), _1741263)), -(hBOOL(hAPP(_1741257, _1741261)))], (4514 ^ _779854) ^ [_848582, _848584, _848586, _848588] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_848588, _848584) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_848586, _848582)), _848588 = _848586, _848584 = _848582], (18423 ^ _779854) ^ [_1113512, _1113514, _1113516, _1113518, _1113520] : [class_Groups_Ocomm__monoid__mult(_1113512), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113514), _1113516)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113514), _1113518)), 18437 ^ _779854 : [(18440 ^ _779854) ^ [] : [hAPP(_1113520, 18436 ^ [_1113512, _1113514, _1113516, _1113518, _1113520]) = c_Groups_Oone__class_Oone(_1113512)], (18438 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113514), 18436 ^ [_1113512, _1113514, _1113516, _1113518, _1113520]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1113514, tc_HOL_Obool)), _1113516), _1113518))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1113514, _1113512), _1113520), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1113514, tc_HOL_Obool)), _1113516), _1113518)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113512), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1113514, _1113512), _1113520), _1113516)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1113514, _1113512), _1113520), _1113518)))], (29739 ^ _779854) ^ [_1316163, _1316165] : [class_Rings_Oring__1(_1316163), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1316163), hAPP(c_Groups_Ouminus__class_Ouminus(_1316163), _1316165)), 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(_1316163), _1316165), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (24476 ^ _779854) ^ [_1223954, _1223956, _1223958] : [hBOOL(hAPP(hAPP(c_member(_1223954), _1223956), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1223954, tc_HOL_Obool), _1223958))), 24480 ^ _779854 : [(24483 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1223954, tc_HOL_Obool)), 24479 ^ [_1223954, _1223956, _1223958]), _1223958)))], (24481 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1223954), _1223956), 24479 ^ [_1223954, _1223956, _1223958])))]]], (5510 ^ _779854) ^ [_864230, _864232] : [_864232 = _864230, -(c_Groups_Ozero__class_Ozero(_864232) = c_Groups_Ozero__class_Ozero(_864230))], (1670 ^ _779854) ^ [_803681, _803683] : [-(class_Groups_Oab__semigroup__add(_803681)), _803683 = _803681, class_Groups_Oab__semigroup__add(_803683)], (18195 ^ _779854) ^ [_1109081, _1109083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109081), _1109083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1109081)), _1109083)))], (43002 ^ _779854) ^ [_1636284, _1636286, _1636288, _1636290] : [43004 ^ _779854 : [(43007 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1636288, 43003 ^ [_1636284, _1636286, _1636288, _1636290])), hAPP(_1636290, 43003 ^ [_1636284, _1636286, _1636288, _1636290])))], (43005 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1636284), 43003 ^ [_1636284, _1636286, _1636288, _1636290]), hAPP(c_List_Oset(_1636284), _1636286))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1636284, _1636288, _1636286)), c_List_Olist_Olist__size(_1636284, _1636290, _1636286))))], (6693 ^ _779854) ^ [_887203, _887205, _887207, _887209] : [6694 ^ _779854 : [(6697 ^ _779854) ^ [] : [hBOOL(hAPP(_887207, _887205))], (6695 ^ _779854) ^ [] : [hBOOL(hAPP(_887203, _887205))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887209, tc_HOL_Obool)), _887207), _887203), _887205)))], (31782 ^ _779854) ^ [_1351767, _1351769, _1351771] : [class_Rings_Olinordered__idom(_1351767), 31785 ^ _779854 : [(31792 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351769), _1351771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351767), hAPP(c_Int_Oring__1__class_Oof__int(_1351767), _1351769)), hAPP(c_Int_Oring__1__class_Oof__int(_1351767), _1351771))))], (31786 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351767), hAPP(c_Int_Oring__1__class_Oof__int(_1351767), _1351769)), hAPP(c_Int_Oring__1__class_Oof__int(_1351767), _1351771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351769), _1351771)))]]], (23665 ^ _779854) ^ [_1208719] : [class_Orderings_Olinorder(_1208719), -(c_Finite__Set_Ofun__left__comm__idem(_1208719, _1208719, c_Orderings_Oord__class_Omin(_1208719)))], (11017 ^ _779854) ^ [_969251, _969253, _969255] : [class_Orderings_Olinorder(_969251), hBOOL(hAPP(c_Finite__Set_Ofinite(_969251), _969253)), -(_969253 = c_Orderings_Obot__class_Obot(tc_fun(_969251, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_969251), _969255)), -(_969255 = c_Orderings_Obot__class_Obot(tc_fun(_969251, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969251, tc_HOL_Obool)), _969253), _969255) = c_Orderings_Obot__class_Obot(tc_fun(_969251, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_969251, c_Orderings_Oord__class_Omin(_969251), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_969251, tc_HOL_Obool)), _969253), _969255)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_969251), c_Big__Operators_Olattice_OInf__fin(_969251, c_Orderings_Oord__class_Omin(_969251), _969253)), c_Big__Operators_Olattice_OInf__fin(_969251, c_Orderings_Oord__class_Omin(_969251), _969255)))], (39659 ^ _779854) ^ [_1549221, _1549223] : [c_Wellfounded_Owf(_1549221, _1549223), -(c_Wellfounded_Owf(tc_fun(_1549221, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1549221, _1549223)))], (38494 ^ _779854) ^ [_1511319, _1511321, _1511323, _1511325, _1511327, _1511329] : [-(hAPP(c_Set_Ovimage(_1511319, tc_prod(_1511321, _1511323), _1511325), hAPP(hAPP(c_Product__Type_OSigma(_1511321, _1511323), _1511327), hAPP(c_COMBK(tc_fun(_1511323, tc_HOL_Obool), _1511321), _1511329))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511319, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1511319, _1511321, hAPP(c_Fun_Ocomp(tc_prod(_1511321, _1511323), _1511321, _1511319, c_Product__Type_Ofst(_1511321, _1511323)), _1511325)), _1511327)), hAPP(c_Set_Ovimage(_1511319, _1511323, hAPP(c_Fun_Ocomp(tc_prod(_1511321, _1511323), _1511323, _1511319, c_Product__Type_Osnd(_1511321, _1511323)), _1511325)), _1511329)))], (35244 ^ _779854) ^ [_1436492, _1436494, _1436496, _1436498, _1436500, _1436502] : [hAPP(hAPP(c_Product__Type_OPair(_1436492, _1436494), _1436496), _1436498) = hAPP(hAPP(c_Product__Type_OPair(_1436492, _1436494), _1436500), _1436502), 35247 ^ _779854 : [(35250 ^ _779854) ^ [] : [-(_1436498 = _1436502)], (35248 ^ _779854) ^ [] : [-(_1436496 = _1436500)]]], (42440 ^ _779854) ^ [_1620837, _1620839, _1620841, _1620843, _1620845, _1620847] : [hBOOL(hAPP(hAPP(_1620837, _1620839), _1620841)), c_List_Olistrelp(_1620843, _1620837, _1620845, _1620847), -(c_List_Olistrelp(_1620843, _1620837, hAPP(hAPP(c_List_Olist_OCons(_1620843), _1620839), _1620845), hAPP(hAPP(c_List_Olist_OCons(_1620843), _1620841), _1620847)))], (8934 ^ _779854) ^ [_928712, _928714, _928716] : [class_Groups_Oordered__ab__group__add(_928712), 8937 ^ _779854 : [(8944 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928712), hAPP(c_Groups_Ouminus__class_Ouminus(_928712), _928716)), _928714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928712), hAPP(c_Groups_Ouminus__class_Ouminus(_928712), _928714)), _928716)))], (8938 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928712), hAPP(c_Groups_Ouminus__class_Ouminus(_928712), _928714)), _928716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928712), hAPP(c_Groups_Ouminus__class_Ouminus(_928712), _928716)), _928714)))]]], (32577 ^ _779854) ^ [_1366316, _1366318, _1366320, _1366322] : [32579 ^ _779854 : [(32584 ^ _779854) ^ [] : [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(_1366320, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 32578 ^ [_1366316, _1366318, _1366320, _1366322]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1366320, 32578 ^ [_1366316, _1366318, _1366320, _1366322])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32582 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32578 ^ [_1366316, _1366318, _1366320, _1366322]), _1366318)))], (32580 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1366316), 32578 ^ [_1366316, _1366318, _1366320, _1366322])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1366316), _1366318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1366320, _1366316)), _1366322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1366322), hAPP(_1366320, _1366318))), 32598 ^ _779854 : [(32603 ^ _779854) ^ [] : [-(hAPP(_1366320, 32597 ^ [_1366316, _1366318, _1366320, _1366322]) = _1366322)], (32601 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 32597 ^ [_1366316, _1366318, _1366320, _1366322]), _1366318)))], (32599 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1366316), 32597 ^ [_1366316, _1366318, _1366320, _1366322])))]]], (10337 ^ _779854) ^ [_954790, _954792, _954794, _954796] : [class_Orderings_Olinorder(_954790), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954790), hAPP(hAPP(c_Orderings_Oord__class_Omax(_954790), _954792), hAPP(hAPP(c_Orderings_Oord__class_Omin(_954790), _954794), _954796))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_954790), hAPP(hAPP(c_Orderings_Oord__class_Omax(_954790), _954792), _954794)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_954790), _954792), _954796)))))], (33321 ^ _779854) ^ [_1385393, _1385395, _1385397, _1385399] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1385393, tc_HOL_Obool), tc_fun(_1385395, tc_HOL_Obool)), _1385397), hAPP(hAPP(c_COMBC(tc_fun(_1385393, tc_HOL_Obool), tc_fun(_1385393, tc_fun(_1385395, tc_HOL_Obool)), tc_fun(_1385395, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385393, tc_fun(_1385395, tc_HOL_Obool))), _1385399)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385393, tc_fun(_1385395, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385393, tc_HOL_Obool), _1385397)), _1385399))], (44911 ^ _779854) ^ [_1678555, _1678557, _1678559, _1678561] : [-(_1678555 = c_List_Olist_ONil(_1678557)), 44914 ^ _779854 : [(44921 ^ _779854) ^ [] : [-(_1678559 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678557)), _1678555)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1678557, hAPP(hAPP(c_List_Olist__update(_1678557, _1678555), _1678559), _1678561)) = c_List_Olast(_1678557, _1678555))], (44915 ^ _779854) ^ [] : [_1678559 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678557)), _1678555)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1678557, hAPP(hAPP(c_List_Olist__update(_1678557, _1678555), _1678559), _1678561)) = _1678561)]]], (26701 ^ _779854) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (52377 ^ _779854) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (36952 ^ _779854) ^ [_1472190, _1472192, _1472194, _1472196, _1472198, _1472200, _1472202, _1472204] : [class_Groups_Ocomm__monoid__mult(_1472190), c_Fun_Oinj__on(_1472192, _1472194, _1472196, _1472198), _1472200 = hAPP(c_Set_Oimage(_1472192, _1472194, _1472196), _1472198), 36966 ^ _779854 : [(36969 ^ _779854) ^ [] : [hAPP(_1472202, 36965 ^ [_1472190, _1472192, _1472194, _1472196, _1472198, _1472200, _1472202, _1472204]) = hAPP(hAPP(c_Fun_Ocomp(_1472194, _1472190, _1472192, _1472204), _1472196), 36965 ^ [_1472190, _1472192, _1472194, _1472196, _1472198, _1472200, _1472202, _1472204])], (36967 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472192), 36965 ^ [_1472190, _1472192, _1472194, _1472196, _1472198, _1472200, _1472202, _1472204]), _1472198)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1472194, _1472190), _1472204), _1472200) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1472192, _1472190), _1472202), _1472198))], (44464 ^ _779854) ^ [_1669662, _1669664, _1669666] : [_1669662 = c_List_Olist_ONil(_1669664), -(hAPP(c_List_Ohd(_1669664), hAPP(hAPP(c_List_Oappend(_1669664), _1669662), _1669666)) = hAPP(c_List_Ohd(_1669664), _1669666))], (50455 ^ _779854) ^ [_1799434, _1799436, _1799438, _1799440] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1799434, _1799436, c_Orderings_Otop__class_Otop(tc_fun(_1799434, tc_HOL_Obool)), _1799438), _1799440) = c_Hilbert__Choice_OEps(_1799434, hAPP(hAPP(c_COMBC(_1799434, _1799436, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1799436, tc_fun(_1799436, tc_HOL_Obool), _1799434), c_fequal), _1799438)), _1799440)))], (31102 ^ _779854) ^ [_1340934, _1340936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1340934), _1340936))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340934, _1340936) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1340934), _1340936), _1340936))], (34035 ^ _779854) ^ [_1408822, _1408824, _1408826] : [-(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)), _1408822)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408824), _1408826)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408824), _1408822)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408826), _1408822)))], (48814 ^ _779854) ^ [_1763571, _1763573, _1763575] : [-(hAPP(c_New__DSequence_Oneg__single(_1763571, _1763573), _1763575) = c_Lazy__Sequence_Ohb__single(_1763571, _1763573))], (18875 ^ _779854) ^ [_1120477, _1120479, _1120481] : [18876 ^ _779854 : [(18879 ^ _779854) ^ [] : [_1120479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18877 ^ _779854) ^ [] : [_1120477 = _1120481]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120477), _1120479) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120481), _1120479))], (28846 ^ _779854) ^ [_1300854] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1300854))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10269 ^ _779854) ^ [_953376, _953378, _953380, _953382] : [class_Orderings_Olinorder(_953376), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_953376), hAPP(hAPP(c_Orderings_Oord__class_Omin(_953376), _953378), _953380)), _953382) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_953376), hAPP(hAPP(c_Orderings_Oord__class_Omax(_953376), _953378), _953382)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_953376), _953380), _953382)))], (38342 ^ _779854) ^ [_1507383, _1507385, _1507387, _1507389, _1507391] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507383, _1507385), _1507387), hAPP(hAPP(c_COMBS(_1507383, tc_fun(_1507385, tc_HOL_Obool), tc_fun(_1507385, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507385, tc_HOL_Obool), tc_fun(tc_fun(_1507385, tc_HOL_Obool), tc_fun(_1507385, tc_HOL_Obool)), _1507383), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507385, tc_HOL_Obool))), _1507389)), _1507391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507383, _1507385), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507383, _1507385), _1507387), _1507389)), hAPP(hAPP(c_Product__Type_OSigma(_1507383, _1507385), _1507387), _1507391)))], (15852 ^ _779854) ^ [_1064016, _1064018, _1064020, _1064022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064016), _1064018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064020), _1064022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064016), _1064020)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064018), _1064022))))], (31718 ^ _779854) ^ [_1350831, _1350833] : [class_Int_Onumber__ring(_1350831), -(hAPP(c_Int_Onumber__class_Onumber__of(_1350831), _1350833) = hAPP(c_Int_Oring__1__class_Oof__int(_1350831), _1350833))], (11704 ^ _779854) ^ [_982919, _982921, _982923, _982925] : [hBOOL(hAPP(hAPP(c_member(_982919), _982921), _982923)), -(hBOOL(hAPP(hAPP(c_member(_982919), _982921), _982925))), -(hBOOL(hAPP(hAPP(c_member(_982919), _982921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982919, tc_HOL_Obool)), _982923), _982925))))], (33181 ^ _779854) ^ [_1381494, _1381496, _1381498, _1381500] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381494, tc_fun(_1381496, tc_HOL_Obool)), _1381498), _1381500) = c_Orderings_Obot__class_Obot(tc_fun(_1381496, tc_HOL_Obool)), 33184 ^ _779854 : [(33185 ^ _779854) ^ [_1381610] : [hBOOL(hAPP(hAPP(c_member(_1381494), _1381610), _1381498)), -(hAPP(_1381500, _1381610) = c_Orderings_Obot__class_Obot(tc_fun(_1381496, tc_HOL_Obool)))]]], (29165 ^ _779854) ^ [_1306031, _1306033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1306031)), 29168 ^ _779854 : [(29175 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306031), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306033))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1306031)), _1306033)))], (29169 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1306031)), _1306033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306031), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306033))))]]], (5204 ^ _779854) ^ [_859439, _859441, _859443, _859445] : [-(c_Transitive__Closure_Ortrancl(_859445, _859441) = c_Transitive__Closure_Ortrancl(_859443, _859439)), _859445 = _859443, _859441 = _859439], (37231 ^ _779854) ^ [_1480248, _1480250, _1480252, _1480254] : [hBOOL(hAPP(hAPP(c_member(_1480248), _1480250), _1480252)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1480248, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1480248, _1480248, _1480254), hAPP(hAPP(c_Set_Oinsert(_1480248), _1480250), c_Orderings_Obot__class_Obot(tc_fun(_1480248, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1480248), _1480252), _1480254))))], (41670 ^ _779854) ^ [_1598043, _1598045, _1598047] : [c_Relation_Ototal__on(_1598043, _1598045, _1598047), 41673 ^ _779854 : [(41674 ^ _779854) ^ [_1598187] : [hBOOL(hAPP(hAPP(c_member(_1598043), _1598187), _1598045)), 41677 ^ _779854 : [(41678 ^ _779854) ^ [_1598327] : [hBOOL(hAPP(hAPP(c_member(_1598043), _1598327), _1598045)), -(_1598187 = _1598327), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598043, _1598043)), hAPP(hAPP(c_Product__Type_OPair(_1598043, _1598043), _1598187), _1598327)), _1598047))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598043, _1598043)), hAPP(hAPP(c_Product__Type_OPair(_1598043, _1598043), _1598327), _1598187)), _1598047)))]]]]], (6741 ^ _779854) ^ [_888192, _888194, _888196] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888192, tc_HOL_Obool)), _888194), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888192, tc_HOL_Obool)), _888194), _888196)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888192, tc_HOL_Obool)), _888194), _888196))], (44322 ^ _779854) ^ [_1666005, _1666007, _1666009, _1666011] : [hAPP(hAPP(c_List_Oappend(_1666005), _1666007), _1666009) = _1666011, 44325 ^ _779854 : [(44328 ^ _779854) ^ [] : [-(_1666009 = hAPP(hAPP(c_List_Odrop(_1666005), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666005)), _1666007)), _1666011))], (44326 ^ _779854) ^ [] : [-(_1666007 = hAPP(hAPP(c_List_Otake(_1666005), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666005)), _1666007)), _1666011))]]], (2680 ^ _779854) ^ [_819663, _819665, _819667, _819669] : [-(c_Wellfounded_Omin__ext(_819669, _819665) = c_Wellfounded_Omin__ext(_819667, _819663)), _819669 = _819667, _819665 = _819663], (46747 ^ _779854) ^ [_1720230, _1720232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720230), _1720232)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1720230, _1720232)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1720232), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (48930 ^ _779854) ^ [_1766680, _1766682, _1766684] : [-(c_List_Oreplicate(_1766680, hAPP(c_Nat_OSuc, _1766682), _1766684) = hAPP(hAPP(c_List_Olist_OCons(_1766680), _1766684), c_List_Oreplicate(_1766680, _1766682, _1766684)))], (8992 ^ _779854) ^ [_929809, _929811, _929813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929809, tc_HOL_Obool)), _929811), _929813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929809, tc_HOL_Obool)), _929811), _929813))), -(_929811 = _929813)], (7419 ^ _779854) ^ [_902160, _902162, _902164] : [class_Lattices_Obounded__lattice__bot(_902160), 7422 ^ _779854 : [(7431 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902160), _902162), _902164) = c_Orderings_Obot__class_Obot(_902160)), _902162 = c_Orderings_Obot__class_Obot(_902160), _902164 = c_Orderings_Obot__class_Obot(_902160)], (7423 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902160), _902162), _902164) = c_Orderings_Obot__class_Obot(_902160), 7426 ^ _779854 : [(7429 ^ _779854) ^ [] : [-(_902164 = c_Orderings_Obot__class_Obot(_902160))], (7427 ^ _779854) ^ [] : [-(_902162 = c_Orderings_Obot__class_Obot(_902160))]]]]], (44687 ^ _779854) ^ [_1673855, _1673857, _1673859] : [class_Lattices_Olattice(_1673855), -(c_Big__Operators_Olattice__class_OSup__fin(_1673855, hAPP(c_List_Oset(_1673855), hAPP(hAPP(c_List_Olist_OCons(_1673855), _1673857), _1673859))) = hAPP(c_List_Ofoldl(_1673855, _1673855, c_Lattices_Osemilattice__sup__class_Osup(_1673855), _1673857), _1673859))], (1810 ^ _779854) ^ [_805431, _805433] : [-(class_Rings_Osemiring__1(_805431)), _805433 = _805431, class_Rings_Osemiring__1(_805433)], (42001 ^ _779854) ^ [_1607015, _1607017, _1607019, _1607021] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607015, _1607017)), _1607019), hAPP(c_Relation_Oconverse(_1607017, _1607015), _1607021))), 42006 ^ _779854 : [(42009 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607017, _1607015)), hAPP(hAPP(c_Product__Type_OPair(_1607017, _1607015), 42004 ^ [_1607015, _1607017, _1607019, _1607021]), 42005 ^ [_1607015, _1607017, _1607019, _1607021])), _1607021)))], (42007 ^ _779854) ^ [] : [-(_1607019 = hAPP(hAPP(c_Product__Type_OPair(_1607015, _1607017), 42005 ^ [_1607015, _1607017, _1607019, _1607021]), 42004 ^ [_1607015, _1607017, _1607019, _1607021]))]]], (49689 ^ _779854) ^ [_1783217, _1783219, _1783221] : [-(c_List_Olist__ex(_1783217, _1783221, _1783219)), 49690 ^ _779854 : [(49691 ^ _779854) ^ [_1783274] : [hBOOL(hAPP(hAPP(c_member(_1783217), _1783274), hAPP(c_List_Oset(_1783217), _1783219))), hBOOL(hAPP(_1783221, _1783274))]]], (47484 ^ _779854) ^ [_1734565, _1734567, _1734569] : [-(hAPP(c_List_Orev(_1734565), hAPP(hAPP(c_List_Odrop(_1734565), _1734567), _1734569)) = hAPP(hAPP(c_List_Otake(_1734565), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734565)), _1734569)), _1734567)), hAPP(c_List_Orev(_1734565), _1734569)))], (38630 ^ _779854) ^ [_1515526, _1515528, _1515530] : [-(hAPP(c_Product__Type_Omap__pair(_1515526, _1515526, _1515528, _1515528, c_COMBI(_1515526), c_COMBI(_1515528)), _1515530) = _1515530)], (31090 ^ _779854) ^ [_1340781, _1340783] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1340781), _1340783))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340781, _1340783) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1340781), _1340783), _1340783))], (6517 ^ _779854) ^ [_884218, _884220, _884222] : [class_Orderings_Oorder(_884218), 6520 ^ _779854 : [(6527 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884218), _884220), _884222))), -(c_SetInterval_Oord__class_OatLeastAtMost(_884218, _884220, _884222) = c_Orderings_Obot__class_Obot(tc_fun(_884218, tc_HOL_Obool)))], (6521 ^ _779854) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_884218, _884220, _884222) = c_Orderings_Obot__class_Obot(tc_fun(_884218, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884218), _884220), _884222))]]], (40346 ^ _779854) ^ [_1565905, _1565907] : [-(c_Hilbert__Choice_OEps(_1565905, hAPP(c_fequal, _1565907)) = _1565907)], (12220 ^ _779854) ^ [_992742, _992744, _992746, _992748, _992750, _992752] : [hBOOL(hAPP(hAPP(c_member(_992742), _992744), _992746)), -(hAPP(c_Fun_Ooverride__on(_992742, _992748, _992750, _992752, _992746), _992744) = hAPP(_992752, _992744))], (31204 ^ _779854) ^ [_1342539, _1342541, _1342543] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1342539), _1342541)), _1342543) = 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), _1342539), _1342543)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1342541), _1342543))), 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, _1342539, _1342543)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1342541, _1342543))), _1342543)))], (41986 ^ _779854) ^ [_1606615, _1606617, _1606619, _1606621, _1606623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606615, tc_HOL_Obool)), _1606617), _1606619)), 41992 ^ _779854 : [(41997 ^ _779854) ^ [] : [hBOOL(hAPP(_1606623, 41991 ^ [_1606615, _1606617, _1606619, _1606621, _1606623]))], (41995 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1606621, 41991 ^ [_1606615, _1606617, _1606619, _1606621, _1606623])))], (41993 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606615), 41991 ^ [_1606615, _1606617, _1606619, _1606621, _1606623]), _1606617)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606615, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606615, tc_HOL_Obool)), _1606617), hAPP(c_Set_OCollect(_1606615), _1606621))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606615, tc_HOL_Obool)), _1606619), hAPP(c_Set_OCollect(_1606615), _1606623)))))], (42802 ^ _779854) ^ [_1630048, _1630050, _1630052] : [hBOOL(hAPP(hAPP(c_member(_1630048), _1630050), hAPP(c_List_Oset(_1630048), _1630052))), 42806 ^ _779854 : [(42809 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1630048), _1630052), 42805 ^ [_1630048, _1630050, _1630052]) = _1630050)], (42807 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42805 ^ [_1630048, _1630050, _1630052]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630048)), _1630052))))]]], (49026 ^ _779854) ^ [_1768361, _1768363, _1768365, _1768367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768361), _1768363)), -(hAPP(hAPP(c_List_Onth(_1768365), c_List_Oreplicate(_1768365, _1768363, _1768367)), _1768361) = _1768367)], (50418 ^ _779854) ^ [_1798439, _1798441, _1798443, _1798445] : [hAPP(c_Set_Oimage(_1798439, _1798441, _1798443), c_Orderings_Otop__class_Otop(tc_fun(_1798439, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1798441, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1798439, _1798441, _1798443), hAPP(c_Set_Oimage(_1798441, _1798439, c_Hilbert__Choice_Oinv__into(_1798439, _1798441, c_Orderings_Otop__class_Otop(tc_fun(_1798439, tc_HOL_Obool)), _1798443)), _1798445)) = _1798445)], (46224 ^ _779854) ^ [_1707371, _1707373] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707371)), c_List_Oremdups(_1707371, _1707373)) = hAPP(c_Finite__Set_Ocard(_1707371), hAPP(c_List_Oset(_1707371), _1707373)))], (17688 ^ _779854) ^ [_1100600, _1100602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100600), _1100602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1100600)), hAPP(c_Nat_OSuc, _1100602))))], (28659 ^ _779854) ^ [_1297829] : [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)), _1297829))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1297829)))], (36904 ^ _779854) ^ [] : [-(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)))], (42821 ^ _779854) ^ [_1630472, _1630474] : [-(c_List_Olists(_1630472, _1630474) = hAPP(c_Set_OCollect(tc_List_Olist(_1630472)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1630472), tc_fun(_1630472, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1630472, tc_HOL_Obool), tc_fun(tc_fun(_1630472, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1630472)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1630472, tc_HOL_Obool))), c_List_Oset(_1630472))), _1630474)))], (42095 ^ _779854) ^ [_1609298, _1609300, _1609302] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609298)), _1609300) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609298)), _1609302)), _1609300 = _1609302], (38895 ^ _779854) ^ [_1522220, _1522222, _1522224, _1522226, _1522228] : [c_Relation_Orefl__on(_1522220, _1522222, _1522224), c_Relation_Orefl__on(_1522220, _1522226, _1522228), -(c_Relation_Orefl__on(_1522220, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1522220, tc_HOL_Obool)), _1522222), _1522226), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1522220, _1522220), tc_HOL_Obool)), _1522224), _1522228)))], (8064 ^ _779854) ^ [_914902, _914904, _914906] : [class_Orderings_Olinorder(_914902), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914902), _914904), _914906)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914902, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_914902), _914904)), c_SetInterval_Oord__class_OgreaterThanLessThan(_914902, _914904, _914906)) = hAPP(c_SetInterval_Oord__class_OlessThan(_914902), _914906))], (1880 ^ _779854) ^ [_806306, _806308] : [-(class_Power_Opower(_806306)), _806308 = _806306, class_Power_Opower(_806308)], (16237 ^ _779854) ^ [_1071448, _1071450] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071448), _1071450)), _1071450) = _1071448)], (1976 ^ _779854) ^ [_808405, _808407, _808409, _808411, _808413, _808415, _808417, _808419, _808421, _808423] : [-(c_SetInterval_Oord_OatLeastLessThan(_808423, _808419, _808415, _808411, _808407) = c_SetInterval_Oord_OatLeastLessThan(_808421, _808417, _808413, _808409, _808405)), _808423 = _808421, _808419 = _808417, _808415 = _808413, _808411 = _808409, _808407 = _808405], (3692 ^ _779854) ^ [_835387, _835389] : [_835389 = _835387, -(c_List_Oembed__list(_835389) = c_List_Oembed__list(_835387))], (31850 ^ _779854) ^ [_1353015, _1353017] : [class_Rings_Oring__1(_1353015), -(hAPP(c_Int_Oring__1__class_Oof__int(_1353015), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1353017)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1353015), hAPP(c_Int_Oring__1__class_Oof__int(_1353015), _1353017)))], (9911 ^ _779854) ^ [_946893, _946895, _946897] : [class_Orderings_Oorder(_946893), class_Orderings_Oorder(_946895), 9922 ^ _779854 : [(9925 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946893), hAPP(_946897, 9920 ^ [_946893, _946895, _946897])), hAPP(_946897, 9921 ^ [_946893, _946895, _946897])))], (9923 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946895), 9920 ^ [_946893, _946895, _946897]), 9921 ^ [_946893, _946895, _946897])))]], -(c_Orderings_Oorder__class_Ostrict__mono(_946895, _946893, _946897))], (52333 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (28505 ^ _779854) ^ [_1295183] : [-(c_Int_OBit1(_1295183) = 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)), _1295183)), _1295183))], (12978 ^ _779854) ^ [_1008158, _1008160, _1008162, _1008164, _1008166, _1008168] : [hBOOL(hAPP(hAPP(c_member(_1008158), _1008160), c_SetInterval_Oord_OgreaterThanAtMost(_1008158, _1008162, _1008164, _1008166, _1008168))), 12981 ^ _779854 : [(12984 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1008162, _1008160), _1008168)))], (12982 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1008164, _1008166), _1008160)))]]], (25585 ^ _779854) ^ [_1245160, _1245162, _1245164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245160), _1245162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245162), _1245164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245160), _1245164)))], (1330 ^ _779854) ^ [_799431, _799433] : [-(class_Rings_Oring__1(_799431)), _799433 = _799431, class_Rings_Oring__1(_799433)], (12968 ^ _779854) ^ [_1007938, _1007940, _1007942, _1007944, _1007946, _1007948] : [-(hBOOL(hAPP(hAPP(c_member(_1007938), _1007940), c_SetInterval_Oord_OatLeastLessThan(_1007938, _1007942, _1007944, _1007946, _1007948)))), hBOOL(hAPP(hAPP(_1007942, _1007946), _1007940)), hBOOL(hAPP(hAPP(_1007944, _1007940), _1007948))], (12542 ^ _779854) ^ [_999151, _999153, _999155] : [-(hBOOL(hAPP(hAPP(c_member(_999151), _999153), _999155))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_999151, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_999151), _999153), _999155)), hAPP(hAPP(c_Set_Oinsert(_999151), _999153), c_Orderings_Obot__class_Obot(tc_fun(_999151, tc_HOL_Obool)))) = _999155)], (7766 ^ _779854) ^ [_909171, _909173, _909175, _909177] : [class_Orderings_Oorder(_909171), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909171, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_909171, _909173, _909175)), c_SetInterval_Oord__class_OgreaterThanAtMost(_909171, _909175, _909177)) = c_Orderings_Obot__class_Obot(tc_fun(_909171, tc_HOL_Obool)))], (26027 ^ _779854) ^ [_1252781, _1252783, _1252785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252781)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252783), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1252785)), 26034 ^ _779854 : [(26035 ^ _779854) ^ [_1252989] : [26037 ^ _779854 : [(26043 ^ _779854) ^ [] : [-(_1252989 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26039 ^ [_1252781, _1252783, _1252785, _1252989]), 26036 ^ [_1252781, _1252783, _1252785, _1252989]))], (26041 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26039 ^ [_1252781, _1252783, _1252785, _1252989]), _1252785)))], (26038 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26036 ^ [_1252781, _1252783, _1252785, _1252989]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1252781))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252989), _1252783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252989), _1252781)), _1252783)))]]], (24114 ^ _779854) ^ [_1217251, _1217253, _1217255, _1217257] : [class_Fields_Ofield(_1217251), -(_1217253 = c_Groups_Ozero__class_Ozero(_1217251)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217251), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217251), _1217255), _1217253)), _1217257) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217251), hAPP(hAPP(c_Power_Opower__class_Opower(_1217251), _1217255), _1217257)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217251), _1217253), _1217257)))], (31150 ^ _779854) ^ [_1341659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1341659)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1341659), c_Int_OMin)))], (18929 ^ _779854) ^ [_1121279, _1121281] : [18930 ^ _779854 : [(18933 ^ _779854) ^ [] : [_1121281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18931 ^ _779854) ^ [] : [_1121279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1121279), _1121281) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32840 ^ _779854) ^ [_1371526, _1371528, _1371530, _1371532] : [class_Rings_Oring__1(_1371526), -(hAPP(c_Int_Oring__1__class_Oof__int(_1371526), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371528, tc_Int_Oint), _1371530), _1371532)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371528, _1371526), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1371526, _1371528), c_Int_Oring__1__class_Oof__int(_1371526)), _1371530)), _1371532))], (27619 ^ _779854) ^ [_1279791, _1279793] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1279791))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279791)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279793)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44759 ^ _779854) ^ [_1675532, _1675534, _1675536] : [44760 ^ _779854 : [(44761 ^ _779854) ^ [_1675621, _1675623] : [_1675534 = hAPP(hAPP(c_List_Olist_OCons(_1675532), _1675623), _1675621)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675532), tc_List_Olist(_1675532))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675532), tc_List_Olist(_1675532)), c_List_Olist_ONil(_1675532)), _1675534)), c_List_Olexord(_1675532, _1675536))))], (38719 ^ _779854) ^ [_1518079, _1518081, _1518083, _1518085] : [-(hAPP(c_Set_OCollect(tc_prod(_1518079, _1518081)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518079, _1518081, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1518079, tc_fun(_1518081, tc_HOL_Obool), tc_fun(_1518081, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1518081, tc_HOL_Obool), tc_fun(_1518081, tc_HOL_Obool)), _1518079), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1518081)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518079), c_fconj), _1518083))), _1518085))) = hAPP(hAPP(c_Product__Type_OSigma(_1518079, _1518081), hAPP(c_Set_OCollect(_1518079), _1518083)), hAPP(c_COMBK(tc_fun(_1518081, tc_HOL_Obool), _1518079), hAPP(c_Set_OCollect(_1518081), _1518085))))], (52637 ^ _779854) ^ [_1838254, _1838256, _1838258, _1838260, _1838262, _1838264] : [-(hAPP(hAPP(hAPP(c_COMBS(_1838254, _1838256, _1838258), _1838260), _1838262), _1838264) = hAPP(hAPP(_1838260, _1838264), hAPP(_1838262, _1838264)))], (47482 ^ _779854) ^ [_1734510, _1734512] : [-(hAPP(c_List_Orev(_1734510), _1734512) = hAPP(c_List_Ofoldl(tc_List_Olist(_1734510), _1734510, hAPP(c_COMBC(_1734510, tc_List_Olist(_1734510), tc_List_Olist(_1734510)), c_List_Olist_OCons(_1734510)), c_List_Olist_ONil(_1734510)), _1734512))], (33919 ^ _779854) ^ [_1406195, _1406197, _1406199, _1406201, _1406203] : [hBOOL(hAPP(hAPP(c_member(_1406195), _1406197), _1406199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1406201, tc_HOL_Obool)), hAPP(_1406203, _1406197)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406195, tc_fun(_1406201, tc_HOL_Obool)), _1406199), _1406203))))], (45041 ^ _779854) ^ [_1680606, _1680608, _1680610] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680606)), _1680608), c_List_Olists(_1680606, _1680610)))), 45042 ^ _779854 : [(45045 ^ _779854) ^ [_1680734, _1680736] : [_1680608 = hAPP(hAPP(c_List_Olist_OCons(_1680606), _1680736), _1680734), hBOOL(hAPP(hAPP(c_member(_1680606), _1680736), _1680610)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680606)), _1680734), c_List_Olists(_1680606, _1680610)))], (45043 ^ _779854) ^ [] : [_1680608 = c_List_Olist_ONil(_1680606)]]], (51319 ^ _779854) ^ [_1819398, _1819400, _1819402] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1819398), _1819400, _1819402)), -(c_List_Olist__ex(tc_Nat_Onat, _1819398, c_List_Oupt(_1819400, _1819402)))], (50904 ^ _779854) ^ [_1809235] : [-(c_Quickcheck_Obeyond(_1809235, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (48205 ^ _779854) ^ [_1750565, _1750567, _1750569, _1750571, _1750573] : [class_Orderings_Olinorder(_1750565), 48211 ^ _779854 : [(48214 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750565), hAPP(_1750571, _1750573)), hAPP(_1750571, 48210 ^ [_1750565, _1750567, _1750569, _1750571, _1750573])))], (48212 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750567), 48210 ^ [_1750565, _1750567, _1750569, _1750571, _1750573]), hAPP(c_List_Oset(_1750567), _1750569))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1750567, _1750565, _1750571), _1750573), _1750569) = hAPP(hAPP(c_List_Olist_OCons(_1750567), _1750573), _1750569))], (15728 ^ _779854) ^ [_1061443, _1061445, _1061447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061443), _1061445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061443), _1061447)), 15735 ^ _779854 : [(15742 ^ _779854) ^ [] : [_1061445 = _1061447, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061445), _1061443) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061447), _1061443))], (15736 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061445), _1061443) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061447), _1061443), -(_1061445 = _1061447)]]], (33210 ^ _779854) ^ [_1382114, _1382116, _1382118, _1382120, _1382122, _1382124] : [c_Nitpick_Opair__box_OPairBox(_1382114, _1382116, _1382118, _1382120) = c_Nitpick_Opair__box_OPairBox(_1382114, _1382116, _1382122, _1382124), 33213 ^ _779854 : [(33216 ^ _779854) ^ [] : [-(_1382120 = _1382124)], (33214 ^ _779854) ^ [] : [-(_1382118 = _1382122)]]], (51709 ^ _779854) ^ [_1826330, _1826332, _1826334, _1826336] : [class_Divides_Osemiring__div(_1826330), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826330), _1826332), _1826334)), -(c_Divides_Odiv__class_Omod(_1826330, c_Divides_Odiv__class_Omod(_1826330, _1826336, _1826334), _1826332) = c_Divides_Odiv__class_Omod(_1826330, _1826336, _1826332))], (43993 ^ _779854) ^ [_1657670, _1657672] : [-(hAPP(hAPP(c_List_Oappend(_1657670), _1657672), c_List_Olist_ONil(_1657670)) = _1657672)], (45563 ^ _779854) ^ [_1692836, _1692838] : [hAPP(c_Code__Numeral_Onat__of, _1692836) = hAPP(c_Code__Numeral_Onat__of, _1692838), -(_1692836 = _1692838)], (1580 ^ _779854) ^ [_802556, _802558] : [-(class_Groups_Oordered__comm__monoid__add(_802556)), _802558 = _802556, class_Groups_Oordered__comm__monoid__add(_802558)], (52361 ^ _779854) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (47699 ^ _779854) ^ [_1739122] : [-(c_List_Oembed__list(_1739122) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1739122))], (29325 ^ _779854) ^ [_1309005, _1309007] : [_1309005 = _1309007, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1309005) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1309007))], (42348 ^ _779854) ^ [_1617769, _1617771, _1617773, _1617775] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617769), tc_List_Olist(_1617769))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617769), tc_List_Olist(_1617769)), _1617771), _1617773)), c_List_Olistrel(_1617769, _1617775))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617769)), _1617771) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617769)), _1617773))], (16778 ^ _779854) ^ [_1082282, _1082284, _1082286, _1082288] : [class_Orderings_Olinorder(_1082282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082282), _1082284)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1082282, _1082282, c_Orderings_Oord__class_Omax(_1082282)), _1082286), hAPP(hAPP(c_Set_Oinsert(_1082282), _1082288), _1082284)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1082282), _1082288), hAPP(hAPP(c_Finite__Set_Ofold(_1082282, _1082282, c_Orderings_Oord__class_Omax(_1082282)), _1082286), _1082284)))], (32321 ^ _779854) ^ [_1361483, _1361485, _1361487] : [class_Groups_Oordered__ab__group__add__abs(_1361483), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361483), hAPP(c_Groups_Oabs__class_Oabs(_1361483), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1361483), _1361485), _1361487))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361483), hAPP(c_Groups_Oabs__class_Oabs(_1361483), _1361485)), hAPP(c_Groups_Oabs__class_Oabs(_1361483), _1361487)))))], (40992 ^ _779854) ^ [_1580882, _1580884, _1580886, _1580888, _1580890] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580882, _1580882)), hAPP(hAPP(c_Product__Type_OPair(_1580882, _1580882), _1580884), _1580886)), _1580888)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580882, _1580882)), hAPP(hAPP(c_Product__Type_OPair(_1580882, _1580882), _1580886), _1580890)), c_Transitive__Closure_Otrancl(_1580882, _1580888))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580882, _1580882)), hAPP(hAPP(c_Product__Type_OPair(_1580882, _1580882), _1580884), _1580890)), c_Transitive__Closure_Otrancl(_1580882, _1580888))))], (27447 ^ _779854) ^ [_1277089, _1277091, _1277093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1277089), _1277091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1277089), _1277093)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1277091), _1277093))))], (27605 ^ _779854) ^ [_1279583] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279583) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1279583)))], (3340 ^ _779854) ^ [_829861, _829863, _829865, _829867, _829869, _829871, _829873, _829875] : [-(c_Enum_Oproduct(_829875, _829871, _829867, _829863) = c_Enum_Oproduct(_829873, _829869, _829865, _829861)), _829875 = _829873, _829871 = _829869, _829867 = _829865, _829863 = _829861], (23880 ^ _779854) ^ [_1212901, _1212903, _1212905, _1212907] : [class_Rings_Olinordered__semidom(_1212901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212901), c_Groups_Oone__class_Oone(_1212901)), _1212903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212901), hAPP(hAPP(c_Power_Opower__class_Opower(_1212901), _1212903), _1212905)), hAPP(hAPP(c_Power_Opower__class_Opower(_1212901), _1212903), _1212907))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212905), _1212907)))], (17746 ^ _779854) ^ [_1101492, _1101494] : [class_Orderings_Oorder(_1101492), 17749 ^ _779854 : [(17756 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101492), hAPP(_1101494, 17757 ^ [_1101492, _1101494])), hAPP(_1101494, hAPP(c_Nat_OSuc, 17757 ^ [_1101492, _1101494])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1101492, _1101494))], (17750 ^ _779854) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1101492, _1101494), 17753 ^ _779854 : [(17754 ^ _779854) ^ [_1101626] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101492), hAPP(_1101494, _1101626)), hAPP(_1101494, hAPP(c_Nat_OSuc, _1101626)))))]]]]], (29763 ^ _779854) ^ [_1316593, _1316595] : [class_Fields_Olinordered__field__inverse__zero(_1316593), class_Int_Onumber__ring(_1316593), 29770 ^ _779854 : [(29777 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316593), c_Groups_Ozero__class_Ozero(_1316593)), _1316595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316593), c_Groups_Ozero__class_Ozero(_1316593)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316593), _1316595), hAPP(c_Int_Onumber__class_Onumber__of(_1316593), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29771 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316593), c_Groups_Ozero__class_Ozero(_1316593)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316593), _1316595), hAPP(c_Int_Onumber__class_Onumber__of(_1316593), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316593), c_Groups_Ozero__class_Ozero(_1316593)), _1316595)))]]], (23581 ^ _779854) ^ [_1206922, _1206924, _1206926, _1206928, _1206930, _1206932] : [c_Finite__Set_Ofun__left__comm__idem(_1206922, _1206924, _1206926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1206922), _1206928)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1206922, _1206924, _1206926), _1206930), hAPP(hAPP(c_Set_Oinsert(_1206922), _1206932), _1206928)) = hAPP(hAPP(_1206926, _1206932), hAPP(hAPP(c_Finite__Set_Ofold(_1206922, _1206924, _1206926), _1206930), _1206928)))], (32968 ^ _779854) ^ [_1376133, _1376135, _1376137, _1376139] : [c_Finite__Set_Ofun__left__comm__idem(_1376133, _1376135, _1376137), -(hAPP(c_Fun_Ocomp(_1376135, _1376135, _1376135, hAPP(_1376137, _1376139)), hAPP(_1376137, _1376139)) = hAPP(_1376137, _1376139))], (46158 ^ _779854) ^ [_1706244, _1706246] : [_1706246 = c_List_Olist_ONil(_1706244), -(c_List_Olist_ONil(_1706244) = c_List_Oremdups(_1706244, _1706246))], (10763 ^ _779854) ^ [_963463, _963465] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963463, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_963463, tc_HOL_Obool))), _963465) = c_Orderings_Obot__class_Obot(tc_fun(_963463, tc_HOL_Obool)))], (15042 ^ _779854) ^ [_1047262, _1047264] : [class_Lattices_Oab__semigroup__idem__mult(_1047262), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047262), _1047264), _1047264) = _1047264)], (42299 ^ _779854) ^ [_1616410, _1616412, _1616414, _1616416, _1616418, _1616420] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616410), tc_List_Olist(_1616410))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616410), tc_List_Olist(_1616410)), hAPP(hAPP(c_List_Olist_OCons(_1616410), _1616412), _1616414)), hAPP(hAPP(c_List_Olist_OCons(_1616410), _1616416), _1616418))), c_List_Olistrel1(_1616410, _1616420))), 42304 ^ _779854 : [(42307 ^ _779854) ^ [] : [-(_1616414 = _1616418)], (42305 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616410, _1616410)), hAPP(hAPP(c_Product__Type_OPair(_1616410, _1616410), _1616412), _1616416)), _1616420)))]], 42308 ^ _779854 : [(42311 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616410), tc_List_Olist(_1616410))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616410), tc_List_Olist(_1616410)), _1616414), _1616418)), c_List_Olistrel1(_1616410, _1616420))))], (42309 ^ _779854) ^ [] : [-(_1616412 = _1616416)]]], (46912 ^ _779854) ^ [_1723364, _1723366] : [class_Orderings_Olinorder(_1723364), -(_1723366 = c_List_Olist_ONil(_1723364)), c_List_Olinorder__class_Osorted(_1723364, _1723366), -(c_List_Olinorder__class_Osorted(_1723364, c_List_Obutlast(_1723364, _1723366)))], (3298 ^ _779854) ^ [_829244, _829246, _829248, _829250] : [-(c_Code__Numeral_Onat__of__aux(_829250, _829246) = c_Code__Numeral_Onat__of__aux(_829248, _829244)), _829250 = _829248, _829246 = _829244], (6289 ^ _779854) ^ [_879791, _879793, _879795] : [class_Orderings_Oorder(_879791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879791), _879793), _879795)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_879791, _879795, _879793) = c_Orderings_Obot__class_Obot(tc_fun(_879791, tc_HOL_Obool)))], (29415 ^ _779854) ^ [_1310516, _1310518] : [c_Int_OBit0(_1310516) = c_Int_OBit0(_1310518), -(_1310516 = _1310518)], (49932 ^ _779854) ^ [_1789146] : [-(c_Relation_Oantisym(_1789146, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1789146, _1789146), tc_HOL_Obool))))], (23509 ^ _779854) ^ [_1205665, _1205667] : [class_Rings_Olinordered__idom(_1205665), 23512 ^ _779854 : [(23519 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205665), c_Groups_Ozero__class_Ozero(_1205665)), _1205667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205665), c_Groups_Ozero__class_Ozero(_1205665)), c_Groups_Osgn__class_Osgn(_1205665, _1205667))))], (23513 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205665), c_Groups_Ozero__class_Ozero(_1205665)), c_Groups_Osgn__class_Osgn(_1205665, _1205667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205665), c_Groups_Ozero__class_Ozero(_1205665)), _1205667)))]]], (16680 ^ _779854) ^ [_1080375, _1080377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080375), _1080377)), _1080377 = _1080375], (6991 ^ _779854) ^ [_894254, _894256, _894258] : [class_Lattices_Osemilattice__inf(_894254), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894254), _894256), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894254), _894256), _894258)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894254), _894256), _894258))], (15306 ^ _779854) ^ [_1052842, _1052844, _1052846, _1052848] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1052842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052842), _1052844), _1052846)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052842), _1052844), _1052848))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052842), _1052846), _1052848)))], (1310 ^ _779854) ^ [_799181, _799183] : [-(class_Groups_Osgn__if(_799181)), _799183 = _799181, class_Groups_Osgn__if(_799183)], (27609 ^ _779854) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26967 ^ _779854) ^ [_1268992, _1268994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1268994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268992), _1268994)), _1268992)))], (28463 ^ _779854) ^ [_1294491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294491), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1294491)), c_Int_OPls)))], (28192 ^ _779854) ^ [_1289698, _1289700, _1289702] : [class_Nat_Osemiring__char__0(_1289698), 28195 ^ _779854 : [(28202 ^ _779854) ^ [] : [_1289700 = _1289702, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289698), _1289700) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289698), _1289702))], (28196 ^ _779854) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289698), _1289700) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289698), _1289702), -(_1289700 = _1289702)]]], (38094 ^ _779854) ^ [_1500685, _1500687, _1500689, _1500691, _1500693] : [-(hAPP(c_Set_Ovimage(_1500685, _1500687, _1500689), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1500687, tc_HOL_Obool)), _1500691), _1500693)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1500685, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1500685, _1500687, _1500689), _1500691)), hAPP(c_Set_Ovimage(_1500685, _1500687, _1500689), _1500693)))], (35119 ^ _779854) ^ [_1433361] : [-(c_Divides_Odivmod__nat(_1433361, 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)), _1433361))], (11764 ^ _779854) ^ [_984052, _984054, _984056] : [hBOOL(hAPP(hAPP(c_member(_984052), _984054), _984056)), -(hBOOL(hAPP(_984056, _984054)))], (20584 ^ _779854) ^ [_1150101, _1150103, _1150105, _1150107] : [class_Groups_Oordered__comm__monoid__add(_1150101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), c_Groups_Ozero__class_Ozero(_1150101)), _1150103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150101), _1150105), _1150107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150101), _1150103), _1150107))))], (15272 ^ _779854) ^ [_1052181, _1052183, _1052185, _1052187] : [class_Groups_Oordered__ab__semigroup__add(_1052181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052181), _1052183), _1052185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052181), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052181), _1052187), _1052183)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052181), _1052187), _1052185))))], (28182 ^ _779854) ^ [_1289526] : [-(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)), _1289526)) = _1289526)], (198 ^ _779854) ^ [_782975, _782977, _782979, _782981, _782983, _782985, _782987, _782989, _782991, _782993, _782995, _782997] : [-(c_Nitpick_Ofold__graph_H(_782995, _782991, _782987, _782983, _782979, _782975)), c_Nitpick_Ofold__graph_H(_782997, _782993, _782989, _782985, _782981, _782977), _782997 = _782995, _782993 = _782991, _782989 = _782987, _782985 = _782983, _782981 = _782979, _782977 = _782975], (44260 ^ _779854) ^ [_1664540, _1664542, _1664544, _1664546] : [-(hAPP(hAPP(c_List_Odrop(_1664540), _1664542), hAPP(hAPP(c_List_Otake(_1664540), _1664544), _1664546)) = hAPP(hAPP(c_List_Otake(_1664540), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1664544), _1664542)), hAPP(hAPP(c_List_Odrop(_1664540), _1664542), _1664546)))], (36973 ^ _779854) ^ [_1472698, _1472700] : [-(c_FunDef_Orp__inv__image(_1472698, _1472700) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool), tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool), tc_fun(tc_fun(_1472700, _1472698), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool), tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool), tc_fun(tc_fun(_1472700, _1472698), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)), tc_fun(tc_fun(_1472700, _1472698), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool), tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool), tc_fun(tc_fun(_1472700, _1472698), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool))))), tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)), tc_fun(tc_fun(_1472700, _1472698), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool))), tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)), tc_fun(tc_fun(_1472700, _1472698), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)))), tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool)), c_COMBS(tc_fun(_1472700, _1472698), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)), tc_fun(tc_fun(_1472700, _1472698), tc_fun(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)))), tc_fun(tc_prod(_1472698, _1472698), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool))), tc_fun(_1472700, _1472698)), c_Product__Type_OPair(tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool), tc_fun(tc_prod(_1472700, _1472700), tc_HOL_Obool)))), c_Relation_Oinv__image(_1472698, _1472700))))), c_Relation_Oinv__image(_1472698, _1472700))))], (47639 ^ _779854) ^ [_1737895, _1737897, _1737899] : [-(c_List_OtakeWhile(_1737895, _1737897, _1737899) = hAPP(hAPP(c_List_Otake(_1737895), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737895)), c_List_OtakeWhile(_1737895, _1737897, _1737899))), _1737899))], (756 ^ _779854) ^ [_791230, _791232, _791234, _791236, _791238, _791240, _791242, _791244] : [-(c_Wellfounded_Omax__extp(_791242, _791238, _791234, _791230)), c_Wellfounded_Omax__extp(_791244, _791240, _791236, _791232), _791244 = _791242, _791240 = _791238, _791236 = _791234, _791232 = _791230], (52341 ^ _779854) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (48626 ^ _779854) ^ [_1759556, _1759558, _1759560] : [c_List_Olist__all(_1759556, _1759558, hAPP(c_List_Orev(_1759556), _1759560)), -(c_List_Olist__all(_1759556, _1759558, _1759560))], (18521 ^ _779854) ^ [_1115323, _1115325] : [class_Rings_Ocomm__semiring__1(_1115323), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115323), c_Groups_Ozero__class_Ozero(_1115323)), _1115325) = _1115325)], (20710 ^ _779854) ^ [_1152472, _1152474, _1152476, _1152478, _1152480] : [class_Rings_Olinordered__semiring__strict(_1152472), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152472), _1152474), _1152476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152472), _1152478), _1152480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152472), c_Groups_Ozero__class_Ozero(_1152472)), _1152474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152472), c_Groups_Ozero__class_Ozero(_1152472)), _1152478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152472), _1152474), _1152478)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152472), _1152476), _1152480))))], (3790 ^ _779854) ^ [_836912, _836914, _836916, _836918, _836920, _836922, _836924, _836926] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_836926, _836922, _836918, _836914) = c_New__Random__Sequence_Opos__not__random__dseq(_836924, _836920, _836916, _836912)), _836926 = _836924, _836922 = _836920, _836918 = _836916, _836914 = _836912], (51096 ^ _779854) ^ [_1812890, _1812892, _1812894] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1812890, _1812890)), hAPP(hAPP(c_Product__Type_OPair(_1812890, _1812890), hAPP(_1812892, hAPP(c_Nat_OSuc, 51097 ^ [_1812890, _1812892, _1812894]))), hAPP(_1812892, 51097 ^ [_1812890, _1812892, _1812894]))), c_Transitive__Closure_Ortrancl(_1812890, _1812894))), c_Wellfounded_Owf(_1812890, c_Transitive__Closure_Otrancl(_1812890, _1812894)), 51105 ^ _779854 : [(51106 ^ _779854) ^ [_1813156] : [-(hAPP(_1812892, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 51104 ^ [_1812890, _1812892, _1812894]), _1813156)) = hAPP(_1812892, 51104 ^ [_1812890, _1812892, _1812894]))]]], (39653 ^ _779854) ^ [_1549122, _1549124] : [c_Wellfounded_Owf(_1549122, hAPP(hAPP(c_Relation_Orel__comp(_1549122, _1549122, _1549122), _1549124), _1549124)), -(c_Wellfounded_Owf(_1549122, _1549124))], (11119 ^ _779854) ^ [_971403, _971405] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_971403), c_Complete__Lattice_OInf__class_OInf(tc_fun(_971403, tc_HOL_Obool), _971405)))), 11120 ^ _779854 : [(11121 ^ _779854) ^ [_971467] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_971403, tc_HOL_Obool)), _971467), _971405)), hBOOL(hAPP(c_Finite__Set_Ofinite(_971403), _971467))]]], (42870 ^ _779854) ^ [_1633244, _1633246, _1633248] : [_1633244 = _1633246, 42873 ^ _779854 : [(42876 ^ _779854) ^ [_1633400] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633248, _1633248)), _1633400), hAPP(c_List_Oset(tc_prod(_1633248, _1633248)), hAPP(hAPP(c_List_Ozip(_1633248, _1633248), _1633244), _1633246)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1633248, _1633248, tc_HOL_Obool), c_fequal), _1633400)))], (42874 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633248)), _1633244) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633248)), _1633246))]]], (21759 ^ _779854) ^ [_1172604, _1172606, _1172608, _1172610] : [-(c_Sum__Type_OPlus(_1172604, _1172606, _1172608, _1172610) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1172604, _1172606), tc_HOL_Obool))), _1172608 = c_Orderings_Obot__class_Obot(tc_fun(_1172604, tc_HOL_Obool)), _1172610 = c_Orderings_Obot__class_Obot(tc_fun(_1172606, tc_HOL_Obool))], (30597 ^ _779854) ^ [_1332119, _1332121] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332119, _1332121) = 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), _1332119), _1332121) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332121), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332119, _1332121)))], (35264 ^ _779854) ^ [_1436937, _1436939] : [35265 ^ _779854 : [(35268 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1436939), _1436937))], (35266 ^ _779854) ^ [] : [_1436937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1436939, _1436937) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1436939))], (20457 ^ _779854) ^ [_1148017, _1148019] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1148017), _1148019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148017), _1148019)))], (29747 ^ _779854) ^ [_1316315] : [-(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)))), _1316315) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1316315), _1316315))], (29001 ^ _779854) ^ [] : [-(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)))))], (52549 ^ _779854) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (18201 ^ _779854) ^ [_1109186, _1109188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109186), _1109188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109186), hAPP(c_Nat_OSuc, _1109188))))], (12876 ^ _779854) ^ [_1006079, _1006081, _1006083, _1006085] : [hBOOL(hAPP(hAPP(c_member(_1006079), _1006081), c_SetInterval_Oord_OatMost(_1006079, _1006083, _1006085))), -(hBOOL(hAPP(hAPP(_1006083, _1006081), _1006085)))], (46172 ^ _779854) ^ [_1706474, _1706476] : [_1706476 = c_List_Olist_ONil(_1706474), -(c_List_Oremdups(_1706474, _1706476) = c_List_Olist_ONil(_1706474))], (30289 ^ _779854) ^ [_1326680, _1326682, _1326684, _1326686] : [class_Divides_Osemiring__div(_1326680), -(c_Divides_Odiv__class_Omod(_1326680, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326680), _1326682), _1326684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326680), _1326686), _1326684)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326680), c_Divides_Odiv__class_Omod(_1326680, _1326682, _1326686)), _1326684))], (18941 ^ _779854) ^ [_1121463, _1121465, _1121467] : [class_Rings_Olinordered__ring__strict(_1121463), 18944 ^ _779854 : [(18953 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121463), _1121465), _1121465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121463), _1121467), _1121467)) = c_Groups_Ozero__class_Ozero(_1121463)), _1121465 = c_Groups_Ozero__class_Ozero(_1121463), _1121467 = c_Groups_Ozero__class_Ozero(_1121463)], (18945 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121463), _1121465), _1121465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121463), _1121467), _1121467)) = c_Groups_Ozero__class_Ozero(_1121463), 18948 ^ _779854 : [(18951 ^ _779854) ^ [] : [-(_1121467 = c_Groups_Ozero__class_Ozero(_1121463))], (18949 ^ _779854) ^ [] : [-(_1121465 = c_Groups_Ozero__class_Ozero(_1121463))]]]]], (11416 ^ _779854) ^ [_977060, _977062] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_977060, _977062)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_977060, _977062), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977062), c_Orderings_Otop__class_Otop(tc_fun(_977062, tc_HOL_Obool)))))], (30591 ^ _779854) ^ [_1332026, _1332028] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332026, _1332028) = 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), _1332026), _1332028) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4688 ^ _779854) ^ [_851337, _851339, _851341, _851343, _851345, _851347, _851349, _851351] : [-(c_Random__Sequence_Omap(_851351, _851347, _851343, _851339) = c_Random__Sequence_Omap(_851349, _851345, _851341, _851337)), _851351 = _851349, _851347 = _851345, _851343 = _851341, _851339 = _851337], (31122 ^ _779854) ^ [_1341225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1341225))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1341225)))], (40444 ^ _779854) ^ [_1568258, _1568260, _1568262, _1568264] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1568258, tc_HOL_Obool), tc_fun(_1568258, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1568258, tc_HOL_Obool), tc_fun(_1568258, tc_HOL_Obool)), _1568260), _1568262)), c_Wellfounded_Omax__ext(_1568258, _1568264)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1568258), _1568260)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1568258), _1568262)), -(_1568262 = c_Orderings_Obot__class_Obot(tc_fun(_1568258, tc_HOL_Obool))), 40458 ^ _779854 : [(40461 ^ _779854) ^ [_1568663] : [hBOOL(hAPP(hAPP(c_member(_1568258), _1568663), _1568262)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568258, _1568258)), hAPP(hAPP(c_Product__Type_OPair(_1568258, _1568258), 40457 ^ [_1568258, _1568260, _1568262, _1568264]), _1568663)), _1568264))], (40459 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568258), 40457 ^ [_1568258, _1568260, _1568262, _1568264]), _1568260)))]]], (29713 ^ _779854) ^ [] : [-(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))))], (19879 ^ _779854) ^ [_1138476] : [class_Rings_Olinordered__semidom(_1138476), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138476), c_Groups_Ozero__class_Ozero(_1138476)), c_Groups_Oone__class_Oone(_1138476))))], (31284 ^ _779854) ^ [_1343864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1343864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1343864)))], (47520 ^ _779854) ^ [_1735483, _1735485, _1735487] : [class_Orderings_Olinorder(_1735483), c_List_Olinorder__class_Osorted(_1735483, hAPP(c_List_Orev(_1735483), _1735485)), 47527 ^ _779854 : [(47534 ^ _779854) ^ [] : [-(_1735485 = c_List_Olist_ONil(_1735483)), -(c_List_Ofoldr(_1735483, _1735483, c_Orderings_Oord__class_Omax(_1735483), _1735485, _1735487) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1735483), hAPP(hAPP(c_List_Onth(_1735483), _1735485), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1735487))], (47528 ^ _779854) ^ [] : [_1735485 = c_List_Olist_ONil(_1735483), -(c_List_Ofoldr(_1735483, _1735483, c_Orderings_Oord__class_Omax(_1735483), _1735485, _1735487) = _1735487)]]], (43464 ^ _779854) ^ [_1646212, _1646214] : [_1646214 = c_List_Olist_ONil(_1646212), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646212)), _1646214) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26521 ^ _779854) ^ [_1261962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261962), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1261962)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40082 ^ _779854) ^ [_1558994, _1558996] : [c_Wellfounded_OwfP(_1558994, _1558996), -(c_Wellfounded_Oacyclic(_1558994, hAPP(c_Set_OCollect(tc_prod(_1558994, _1558994)), hAPP(c_Product__Type_Oprod_Oprod__case(_1558994, _1558994, tc_HOL_Obool), _1558996))))], (47454 ^ _779854) ^ [_1733982, _1733984, _1733986] : [-(hAPP(c_List_Orev(_1733982), hAPP(hAPP(c_List_Olist_OCons(_1733982), _1733984), _1733986)) = hAPP(hAPP(c_List_Oappend(_1733982), hAPP(c_List_Orev(_1733982), _1733986)), hAPP(hAPP(c_List_Olist_OCons(_1733982), _1733984), c_List_Olist_ONil(_1733982))))], (4164 ^ _779854) ^ [_843127, _843129, _843131, _843133, _843135, _843137] : [-(c_List_Osplice(_843137, _843133, _843129) = c_List_Osplice(_843135, _843131, _843127)), _843137 = _843135, _843133 = _843131, _843129 = _843127], (31726 ^ _779854) ^ [_1350955] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1350955)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1350955))], (32289 ^ _779854) ^ [_1360828] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1360828)], (28559 ^ _779854) ^ [] : [-(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))], (36385 ^ _779854) ^ [_1458902, _1458904, _1458906, _1458908, _1458910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1458902, _1458904)), hAPP(_1458902, _1458906))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1458908, _1458908)), hAPP(hAPP(c_Product__Type_OPair(_1458908, _1458908), _1458904), _1458906)), _1458910)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1458908, _1458908)), hAPP(hAPP(c_Product__Type_OPair(_1458908, _1458908), _1458904), _1458906)), c_Wellfounded_Omlex__prod(_1458908, _1458902, _1458910))))], (3554 ^ _779854) ^ [_833172, _833174, _833176, _833178, _833180, _833182, _833184, _833186] : [-(c_List_Olinorder__class_Osort__key(_833186, _833182, _833178, _833174) = c_List_Olinorder__class_Osort__key(_833184, _833180, _833176, _833172)), _833186 = _833184, _833182 = _833180, _833178 = _833176, _833174 = _833172], (36739 ^ _779854) ^ [_1467036, _1467038, _1467040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1467036, 36740 ^ [_1467036, _1467038, _1467040])), hAPP(_1467038, 36740 ^ [_1467036, _1467038, _1467040]))), -(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), _1467038), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1467040))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1467036), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1467040))) = 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)), _1467038)), _1467036)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1467040)))], (34952 ^ _779854) ^ [_1429779, _1429781, _1429783, _1429785, _1429787, _1429789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429779, tc_fun(_1429781, tc_HOL_Obool))), _1429783), _1429785)), hBOOL(hAPP(hAPP(_1429783, _1429787), _1429789)), -(hBOOL(hAPP(hAPP(_1429785, _1429787), _1429789)))], (52155 ^ _779854) ^ [_1833393, _1833395] : [class_Orderings_Obot(_1833393), -(class_Orderings_Obot(tc_fun(_1833395, _1833393)))], (45019 ^ _779854) ^ [_1680243, _1680245] : [-(_1680243 = c_List_Olist_ONil(_1680245)), -(hAPP(hAPP(c_List_Oappend(_1680245), c_List_Obutlast(_1680245, _1680243)), hAPP(hAPP(c_List_Olist_OCons(_1680245), c_List_Olast(_1680245, _1680243)), c_List_Olist_ONil(_1680245))) = _1680243)], (28130 ^ _779854) ^ [_1288687, _1288689] : [class_Int_Onumber__ring(_1288687), 28133 ^ _779854 : [(28140 ^ _779854) ^ [] : [c_Int_Oiszero(_1288687, hAPP(c_Int_Onumber__class_Onumber__of(_1288687), 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), _1288689)))), -(c_Groups_Oone__class_Oone(_1288687) = hAPP(c_Int_Onumber__class_Onumber__of(_1288687), _1288689))], (28134 ^ _779854) ^ [] : [c_Groups_Oone__class_Oone(_1288687) = hAPP(c_Int_Onumber__class_Onumber__of(_1288687), _1288689), -(c_Int_Oiszero(_1288687, hAPP(c_Int_Onumber__class_Onumber__of(_1288687), 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), _1288689)))))]]], (29569 ^ _779854) ^ [_1313211, _1313213] : [class_Int_Onumber__ring(_1313211), class_Int_Oring__char__0(_1313211), 29576 ^ _779854 : [(29583 ^ _779854) ^ [] : [c_Int_Oiszero(_1313211, hAPP(c_Int_Onumber__class_Onumber__of(_1313211), _1313213)), -(c_Int_Oiszero(_1313211, hAPP(c_Int_Onumber__class_Onumber__of(_1313211), c_Int_OBit0(_1313213))))], (29577 ^ _779854) ^ [] : [c_Int_Oiszero(_1313211, hAPP(c_Int_Onumber__class_Onumber__of(_1313211), c_Int_OBit0(_1313213))), -(c_Int_Oiszero(_1313211, hAPP(c_Int_Onumber__class_Onumber__of(_1313211), _1313213)))]]], (9841 ^ _779854) ^ [_945339, _945341, _945343] : [class_Groups_Oordered__ab__group__add(_945339), -(hAPP(c_Set_Oimage(_945339, _945339, c_Groups_Ouminus__class_Ouminus(_945339)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_945339, _945341), _945343)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_945339, hAPP(c_Groups_Ouminus__class_Ouminus(_945339), _945343), hAPP(c_Groups_Ouminus__class_Ouminus(_945339), _945341)))], (40855 ^ _779854) ^ [_1577568, _1577570, _1577572, _1577574, _1577576] : [-(_1577568 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1577570, _1577572, _1577568, _1577574), _1577576) = hAPP(hAPP(c_Product__Type_Oscomp(_1577572, _1577570, _1577572, tc_prod(_1577570, _1577572)), hAPP(_1577574, _1577576)), c_Random_Oiterate(_1577570, _1577572, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1577568), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1577574)))], (48236 ^ _779854) ^ [_1751426, _1751428, _1751430, _1751432, _1751434] : [-(hAPP(c_List_Ofilter(_1751426, _1751428), _1751430) = hAPP(hAPP(c_List_Olist_OCons(_1751426), _1751432), _1751434)), 48237 ^ _779854 : [(48238 ^ _779854) ^ [_1751554, _1751556] : [_1751430 = hAPP(hAPP(c_List_Oappend(_1751426), _1751556), hAPP(hAPP(c_List_Olist_OCons(_1751426), _1751432), _1751554)), 48244 ^ _779854 : [(48247 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1751428, 48243 ^ [_1751426, _1751428, _1751430, _1751432, _1751434, _1751554, _1751556])))], (48245 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751426), 48243 ^ [_1751426, _1751428, _1751430, _1751432, _1751434, _1751554, _1751556]), hAPP(c_List_Oset(_1751426), _1751556))))]], hBOOL(hAPP(_1751428, _1751432)), _1751434 = hAPP(c_List_Ofilter(_1751426, _1751428), _1751554)]]], (41471 ^ _779854) ^ [_1593176, _1593178, _1593180, _1593182, _1593184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593176, _1593178)), hAPP(hAPP(c_Product__Type_OPair(_1593176, _1593178), _1593180), _1593182)), hAPP(c_Relation_Oconverse(_1593178, _1593176), _1593184))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593178, _1593176)), hAPP(hAPP(c_Product__Type_OPair(_1593178, _1593176), _1593182), _1593180)), _1593184)))], (33824 ^ _779854) ^ [_1402931, _1402933, _1402935, _1402937, _1402939] : [33826 ^ _779854 : [(33829 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402931, tc_HOL_Obool)), hAPP(_1402937, 33825 ^ [_1402931, _1402933, _1402935, _1402937, _1402939])), _1402939))], (33827 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1402933), 33825 ^ [_1402931, _1402933, _1402935, _1402937, _1402939]), _1402935)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402931, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402933, tc_fun(_1402931, tc_HOL_Obool)), _1402935), _1402937)), _1402939)))], (46530 ^ _779854) ^ [_1714894, _1714896, _1714898] : [hBOOL(hAPP(c_List_Odistinct(_1714894), _1714896)), -(hAPP(c_List_Ofilter(_1714894, hAPP(hAPP(c_COMBC(_1714894, tc_fun(_1714894, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714894)), hAPP(c_List_Oset(_1714894), c_List_Osublist(_1714894, _1714896, _1714898)))), _1714896) = c_List_Osublist(_1714894, _1714896, _1714898))], (12798 ^ _779854) ^ [_1004301, _1004303, _1004305, _1004307, _1004309, _1004311, _1004313, _1004315] : [c_Finite__Set_Ofolding__image__simple(_1004301, _1004303, _1004305, _1004307, _1004309, _1004311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004303), _1004313)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004303), _1004315)), -(hAPP(hAPP(_1004305, hAPP(_1004311, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004303, tc_HOL_Obool)), _1004313), _1004315))), hAPP(_1004311, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004303, tc_HOL_Obool)), _1004313), _1004315))) = hAPP(hAPP(_1004305, hAPP(_1004311, _1004313)), hAPP(_1004311, _1004315)))], (49249 ^ _779854) ^ [_1773041] : [-(c_List_Omember(_1773041) = c_List_Oset(_1773041))], (17546 ^ _779854) ^ [_1097517, _1097519, _1097521] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097517), _1097519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1097517), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1097517, tc_HOL_Obool)), _1097519), hAPP(hAPP(c_Set_Oinsert(_1097517), _1097521), c_Orderings_Obot__class_Obot(tc_fun(_1097517, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1097517), _1097519))))], (52267 ^ _779854) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (5695 ^ _779854) ^ [_869819, _869821, _869823, _869825] : [c_Hoare__Mirabelle_Ohoare__derivs(_869819, _869821, _869823), c_Hoare__Mirabelle_Ohoare__derivs(_869819, _869825, _869821), -(c_Hoare__Mirabelle_Ohoare__derivs(_869819, _869825, _869823))], (39427 ^ _779854) ^ [_1541906, _1541908, _1541910, _1541912, _1541914, _1541916, _1541918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541906, _1541908), tc_HOL_Obool)), _1541910), _1541912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541908, _1541914), tc_HOL_Obool)), _1541916), _1541918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541906, _1541914), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541906, _1541908, _1541914), _1541910), _1541916)), hAPP(hAPP(c_Relation_Orel__comp(_1541906, _1541908, _1541914), _1541912), _1541918))))], (7311 ^ _779854) ^ [_900176, _900178, _900180, _900182] : [class_Lattices_Osemilattice__inf(_900176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900176), _900178), _900180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900176), _900178), _900182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900176), _900178), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_900176), _900180), _900182))))], (31116 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36056 ^ _779854) ^ [_1452055, _1452057, _1452059, _1452061, _1452063, _1452065, _1452067, _1452069] : [c_Finite__Set_Ofolding(_1452055, _1452057, _1452059, _1452061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452055), _1452063)), -(hAPP(c_Fun_Ocomp(_1452057, _1452057, _1452065, hAPP(_1452059, _1452067)), hAPP(c_Fun_Ocomp(_1452057, _1452057, _1452065, hAPP(_1452061, _1452063)), _1452069)) = hAPP(c_Fun_Ocomp(_1452057, _1452057, _1452065, hAPP(_1452061, _1452063)), hAPP(c_Fun_Ocomp(_1452057, _1452057, _1452065, hAPP(_1452059, _1452067)), _1452069)))], (25673 ^ _779854) ^ [_1246587, _1246589] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246587), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246589)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246587), _1246589))], (35338 ^ _779854) ^ [_1438077, _1438079] : [-(_1438077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35341 ^ _779854 : [(35348 ^ _779854) ^ [] : [-(_1438079 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1438077, _1438079) = 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, _1438079))), 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)), _1438079)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1438077))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1438079), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1438077), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1438077, _1438079)), 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), _1438079))))), c_Divides_Opdivmod(_1438077, _1438079)))))], (35342 ^ _779854) ^ [] : [_1438079 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1438077, _1438079) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1438077))]]], (9983 ^ _779854) ^ [_948418, _948420, _948422] : [class_Orderings_Olinorder(_948418), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_948418), _948420), _948422) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_948418), _948422), _948420))], (35474 ^ _779854) ^ [_1440866, _1440868] : [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), _1440866), _1440868))), 35477 ^ _779854 : [(35486 ^ _779854) ^ [] : [-(c_Divides_OnegDivAlg(_1440866, _1440868) = hAPP(c_Divides_Oadjust(_1440868), c_Divides_OnegDivAlg(_1440866, 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)))), _1440868)))), -(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), _1440866), _1440868)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1440868), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35478 ^ _779854) ^ [] : [35479 ^ _779854 : [(35482 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1440868), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35480 ^ _779854) ^ [] : [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), _1440866), _1440868)))]], -(c_Divides_OnegDivAlg(_1440866, _1440868) = 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), _1440866), _1440868)))]]], (6149 ^ _779854) ^ [_877508, _877510] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877508, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_877508, tc_HOL_Obool))), _877510)))], (46830 ^ _779854) ^ [_1722160, _1722162] : [class_Orderings_Olinorder(_1722160), -(c_List_Olinorder__class_Osorted(_1722160, hAPP(hAPP(c_List_Olist_OCons(_1722160), _1722162), c_List_Olist_ONil(_1722160))))], (28162 ^ _779854) ^ [_1289205, _1289207] : [class_Int_Onumber__ring(_1289205), 28165 ^ _779854 : [(28172 ^ _779854) ^ [] : [-(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), _1289207)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289205), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1289207)) = c_Groups_Ozero__class_Ozero(_1289205))], (28166 ^ _779854) ^ [] : [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), _1289207))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289205), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1289207)) = hAPP(c_Int_Onumber__class_Onumber__of(_1289205), _1289207))]]], (18735 ^ _779854) ^ [_1118510, _1118512] : [class_Groups_Ogroup__add(_1118510), 18738 ^ _779854 : [(18745 ^ _779854) ^ [] : [_1118512 = c_Groups_Ozero__class_Ozero(_1118510), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1118510), _1118512) = c_Groups_Ozero__class_Ozero(_1118510))], (18739 ^ _779854) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1118510), _1118512) = c_Groups_Ozero__class_Ozero(_1118510), -(_1118512 = c_Groups_Ozero__class_Ozero(_1118510))]]], (46431 ^ _779854) ^ [_1712798, _1712800, _1712802, _1712804] : [-(hBOOL(hAPP(_1712798, _1712800))), -(c_List_Oremove1(_1712802, _1712800, hAPP(c_List_Ofilter(_1712802, _1712798), _1712804)) = hAPP(c_List_Ofilter(_1712802, _1712798), _1712804))], (44957 ^ _779854) ^ [_1679225, _1679227, _1679229] : [_1679225 = c_List_Olist_ONil(_1679227), -(c_List_Olast(_1679227, hAPP(hAPP(c_List_Oappend(_1679227), _1679229), _1679225)) = c_List_Olast(_1679227, _1679229))], (44482 ^ _779854) ^ [_1669885, _1669887] : [-(_1669885 = c_List_Olist_ONil(_1669887)), -(hBOOL(hAPP(hAPP(c_member(_1669887), hAPP(c_List_Ohd(_1669887), _1669885)), hAPP(c_List_Oset(_1669887), _1669885))))], (29285 ^ _779854) ^ [_1308307, _1308309] : [c_Int_OBit0(_1308307) = c_Int_OBit1(_1308309)], (30459 ^ _779854) ^ [_1329730, _1329732, _1329734] : [class_Divides_Osemiring__div(_1329730), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329730), c_Divides_Odiv__class_Omod(_1329730, _1329732, _1329734)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329730), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1329730), _1329732), _1329734)), _1329734)) = _1329732)], (45448 ^ _779854) ^ [_1690341, _1690343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1690341)), hAPP(c_Code__Numeral_Oof__nat, _1690343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1690341), _1690343)))], (52073 ^ _779854) ^ [_1832316, _1832318] : [class_Complete__Lattice_Ocomplete__lattice(_1832316), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1832318, _1832316)))], (44524 ^ _779854) ^ [_1670496, _1670498] : [hBOOL(hAPP(c_List_Odistinct(_1670496), _1670498)), -(hBOOL(hAPP(c_List_Odistinct(_1670496), hAPP(c_List_Otl(_1670496), _1670498))))], (29431 ^ _779854) ^ [_1310760, _1310762] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1310760)), _1310762) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1310760), _1310762)))], (37562 ^ _779854) ^ [_1488268, _1488270, _1488272, _1488274, _1488276] : [c_Equiv__Relations_Oequivp(_1488268, _1488270), hBOOL(hAPP(hAPP(_1488270, _1488272), _1488274)), hBOOL(hAPP(hAPP(_1488270, _1488274), _1488276)), -(hBOOL(hAPP(hAPP(_1488270, _1488272), _1488276)))], (52237 ^ _779854) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (47378 ^ _779854) ^ [_1732367, _1732369] : [-(hAPP(c_List_Orev(_1732367), c_List_Oconcat(_1732367, _1732369)) = c_List_Oconcat(_1732367, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732367), tc_List_Olist(_1732367)), c_List_Orev(_1732367)), hAPP(c_List_Orev(tc_List_Olist(_1732367)), _1732369))))], (29721 ^ _779854) ^ [_1315874, _1315876] : [class_Rings_Ocomm__semiring__1(_1315874), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315874), _1315876), _1315876) = hAPP(hAPP(c_Power_Opower__class_Opower(_1315874), _1315876), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (31174 ^ _779854) ^ [_1342051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1342051)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342051), c_Int_OMin)))], (15874 ^ _779854) ^ [_1064441, _1064443, _1064445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064441), _1064443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064441), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064443), _1064445))))], (30243 ^ _779854) ^ [_1325869, _1325871] : [class_Divides_Osemiring__div(_1325869), -(c_Divides_Odiv__class_Omod(_1325869, _1325871, _1325871) = c_Groups_Ozero__class_Ozero(_1325869))], (17032 ^ _779854) ^ [_1087190, _1087192, _1087194] : [class_Orderings_Olinorder(_1087190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087190), _1087192)), -(c_Big__Operators_Olattice_OInf__fin(_1087190, c_Orderings_Oord__class_Omin(_1087190), hAPP(hAPP(c_Set_Oinsert(_1087190), _1087194), _1087192)) = hAPP(hAPP(c_Finite__Set_Ofold(_1087190, _1087190, c_Orderings_Oord__class_Omin(_1087190)), _1087194), _1087192))], (7874 ^ _779854) ^ [_911441, _911443, _911445] : [class_Orderings_Oorder(_911441), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911441, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_911441, _911443), _911445)), hAPP(c_SetInterval_Oord__class_OatLeast(_911441), _911445)) = c_Orderings_Obot__class_Obot(tc_fun(_911441, tc_HOL_Obool)))], (38592 ^ _779854) ^ [_1514493, _1514495, _1514497, _1514499, _1514501] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1514493, _1514495)), _1514497), hAPP(hAPP(c_Product__Type_OSigma(_1514493, _1514495), _1514499), _1514501))), 38596 ^ _779854 : [(38602 ^ _779854) ^ [] : [-(_1514497 = hAPP(hAPP(c_Product__Type_OPair(_1514493, _1514495), 38595 ^ [_1514493, _1514495, _1514497, _1514499, _1514501]), 38598 ^ [_1514493, _1514495, _1514497, _1514499, _1514501]))], (38600 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514495), 38598 ^ [_1514493, _1514495, _1514497, _1514499, _1514501]), hAPP(_1514501, 38595 ^ [_1514493, _1514495, _1514497, _1514499, _1514501]))))], (38597 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514493), 38595 ^ [_1514493, _1514495, _1514497, _1514499, _1514501]), _1514499)))]]], (50718 ^ _779854) ^ [_1805479, _1805481, _1805483, _1805485, _1805487, _1805489, _1805491, _1805493] : [c_Fun_Obij__betw(_1805479, _1805481, _1805483, _1805485, _1805487), 50721 ^ _779854 : [(50728 ^ _779854) ^ [] : [c_Fun_Obij__betw(_1805479, _1805489, hAPP(c_Fun_Ocomp(_1805481, _1805489, _1805479, _1805491), _1805483), _1805485, _1805493), -(c_Fun_Obij__betw(_1805481, _1805489, _1805491, _1805487, _1805493))], (50722 ^ _779854) ^ [] : [c_Fun_Obij__betw(_1805481, _1805489, _1805491, _1805487, _1805493), -(c_Fun_Obij__betw(_1805479, _1805489, hAPP(c_Fun_Ocomp(_1805481, _1805489, _1805479, _1805491), _1805483), _1805485, _1805493))]]], (36886 ^ _779854) ^ [] : [-(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)))))], (43600 ^ _779854) ^ [_1648835, _1648837, _1648839, _1648841] : [_1648835 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1648837), _1648835), hAPP(hAPP(c_List_Olist_OCons(_1648837), _1648839), _1648841)) = c_List_Olist_ONil(_1648837))], (37287 ^ _779854) ^ [_1481730, _1481732, _1481734, _1481736, _1481738] : [c_Equiv__Relations_Oequiv(_1481730, _1481732, _1481734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481730, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1481730, _1481730, _1481734), hAPP(hAPP(c_Set_Oinsert(_1481730), _1481736), c_Orderings_Obot__class_Obot(tc_fun(_1481730, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1481730, _1481730, _1481734), hAPP(hAPP(c_Set_Oinsert(_1481730), _1481738), c_Orderings_Obot__class_Obot(tc_fun(_1481730, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1481730), _1481736), _1481732)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1481730, _1481730)), hAPP(hAPP(c_Product__Type_OPair(_1481730, _1481730), _1481738), _1481736)), _1481734)))], (41030 ^ _779854) ^ [_1581889, _1581891, _1581893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581889, _1581889), tc_HOL_Obool)), _1581891), _1581893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581889, _1581889), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1581889, _1581889, _1581889), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1581889, _1581889), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1581889, _1581891)), _1581893)), _1581891)), _1581893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581889, _1581889), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1581889, _1581891)), _1581893)))], (51276 ^ _779854) ^ [_1818577, _1818579, _1818581, _1818583] : [-(hAPP(c_Lazy__Sequence_Obind(_1818577, _1818579, _1818581), _1818583) = c_Lazy__Sequence_Oflat(_1818579, c_Lazy__Sequence_Omap(_1818577, tc_Lazy__Sequence_Olazy__sequence(_1818579), _1818583, _1818581)))], (26625 ^ _779854) ^ [_1263684, _1263686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263684)), 26628 ^ _779854 : [(26635 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1263686), 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), _1263686), _1263684)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26629 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1263686), _1263684)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1263686), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (19849 ^ _779854) ^ [_1137947, _1137949, _1137951, _1137953, _1137955, _1137957] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1137947), -(_1137949 = c_Groups_Ozero__class_Ozero(_1137947)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137947), _1137951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137947), _1137949), _1137955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137947), _1137953), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137947), _1137949), _1137957)), _1137951 = _1137953, -(_1137955 = _1137957)], (5398 ^ _779854) ^ [_862484, _862486, _862488, _862490, _862492, _862494, _862496, _862498] : [-(c_SetInterval_Oord_OatLeastAtMost(_862498, _862494, _862490, _862486) = c_SetInterval_Oord_OatLeastAtMost(_862496, _862492, _862488, _862484)), _862498 = _862496, _862494 = _862492, _862490 = _862488, _862486 = _862484], (14177 ^ _779854) ^ [_1030031, _1030033, _1030035, _1030037] : [c_Fun_Oinj__on(_1030031, _1030033, _1030035, c_Orderings_Otop__class_Otop(tc_fun(_1030031, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1030031, _1030033, c_Orderings_Otop__class_Otop(tc_fun(_1030031, tc_HOL_Obool)), _1030035), hAPP(_1030035, _1030037)) = _1030037)], (30891 ^ _779854) ^ [_1337584, _1337586, _1337588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337584), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30894 ^ _779854 : [(30895 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1337586, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1337588), _1337584)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1337588, _1337584))), 30898 ^ _779854 : [(30899 ^ _779854) ^ [_1337794, _1337796] : [-(hBOOL(hAPP(hAPP(_1337586, _1337796), _1337794))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337584), _1337794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337794), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1337588 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1337584), _1337796)), _1337794)]]], (30913 ^ _779854) ^ [] : [30916 ^ _779854 : [(30919 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30915 ^ [_1337584, _1337586, _1337588]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30921 ^ _779854) ^ [] : [-(_1337588 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1337584), 30914 ^ [_1337584, _1337586, _1337588])), 30915 ^ [_1337584, _1337586, _1337588]))], (30923 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1337586, 30914 ^ [_1337584, _1337586, _1337588]), 30915 ^ [_1337584, _1337586, _1337588]))], (30917 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337584), 30915 ^ [_1337584, _1337586, _1337588])))]], -(hBOOL(hAPP(hAPP(_1337586, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1337588), _1337584)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1337588, _1337584))))]]], (7143 ^ _779854) ^ [_897330, _897332, _897334] : [class_Lattices_Olattice(_897330), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897330), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_897330), _897332), _897334)), _897334)))], (36585 ^ _779854) ^ [_1463594, _1463596, _1463598, _1463600, _1463602, _1463604, _1463606, _1463608] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1463594, _1463596), tc_prod(_1463594, _1463596))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1463594, _1463596), tc_prod(_1463594, _1463596)), hAPP(hAPP(c_Product__Type_OPair(_1463594, _1463596), _1463598), _1463600)), hAPP(hAPP(c_Product__Type_OPair(_1463594, _1463596), _1463602), _1463604))), c_Wellfounded_Olex__prod(_1463594, _1463596, _1463606, _1463608)))), 36586 ^ _779854 : [(36589 ^ _779854) ^ [] : [_1463598 = _1463602, hBOOL(hAPP(hAPP(c_member(tc_prod(_1463596, _1463596)), hAPP(hAPP(c_Product__Type_OPair(_1463596, _1463596), _1463600), _1463604)), _1463608))], (36587 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1463594, _1463594)), hAPP(hAPP(c_Product__Type_OPair(_1463594, _1463594), _1463598), _1463602)), _1463606))]]], (4962 ^ _779854) ^ [_855622, _855624, _855626, _855628, _855630, _855632, _855634, _855636, _855638, _855640] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_855640, _855636, _855632, _855628, _855624) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_855638, _855634, _855630, _855626, _855622)), _855640 = _855638, _855636 = _855634, _855632 = _855630, _855628 = _855626, _855624 = _855622], (39881 ^ _779854) ^ [_1553704, _1553706, _1553708, _1553710, _1553712] : [-(hAPP(c_Relation_ODomain(_1553704, _1553706), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1553704, _1553706)), hAPP(hAPP(c_Product__Type_OPair(_1553704, _1553706), _1553708), _1553710)), _1553712)) = hAPP(hAPP(c_Set_Oinsert(_1553704), _1553708), hAPP(c_Relation_ODomain(_1553704, _1553706), _1553712)))], (3394 ^ _779854) ^ [_830694, _830696, _830698, _830700] : [-(c_Enum_Oenum__the(_830700, _830696) = c_Enum_Oenum__the(_830698, _830694)), _830700 = _830698, _830696 = _830694], (9018 ^ _779854) ^ [_930263, _930265, _930267] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_930263, tc_HOL_Obool)), _930265), _930267))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930263, tc_HOL_Obool)), _930265), _930267)), -(_930265 = _930267)], (7744 ^ _779854) ^ [_908710, _908712] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_908710, tc_HOL_Obool)), _908712), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_908710, tc_HOL_Obool)), _908712)) = c_Orderings_Obot__class_Obot(tc_fun(_908710, tc_HOL_Obool)))], (28643 ^ _779854) ^ [_1297543, _1297545] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1297543), _1297545)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297543)), _1297545))], (50453 ^ _779854) ^ [_1799334, _1799336, _1799338, _1799340, _1799342] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1799334, _1799336, _1799338, _1799340), _1799342) = c_Hilbert__Choice_OEps(_1799334, hAPP(hAPP(c_COMBS(_1799334, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1799334), c_fconj), hAPP(hAPP(c_COMBC(_1799334, tc_fun(_1799334, tc_HOL_Obool), tc_HOL_Obool), c_member(_1799334)), _1799338))), hAPP(hAPP(c_COMBC(_1799334, _1799336, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1799336, tc_fun(_1799336, tc_HOL_Obool), _1799334), c_fequal), _1799340)), _1799342))))], (17042 ^ _779854) ^ [_1087381, _1087383, _1087385] : [class_Orderings_Olinorder(_1087381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087381), _1087383)), -(c_Big__Operators_Olattice_OSup__fin(_1087381, c_Orderings_Oord__class_Omax(_1087381), hAPP(hAPP(c_Set_Oinsert(_1087381), _1087385), _1087383)) = hAPP(hAPP(c_Finite__Set_Ofold(_1087381, _1087381, c_Orderings_Oord__class_Omax(_1087381)), _1087385), _1087383))], (38562 ^ _779854) ^ [_1513679, _1513681, _1513683, _1513685, _1513687, _1513689] : [class_Groups_Ocomm__monoid__add(_1513679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513681), _1513683)), 38572 ^ _779854 : [(38575 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513685), hAPP(_1513687, 38571 ^ [_1513679, _1513681, _1513683, _1513685, _1513687, _1513689])))], (38573 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513681), 38571 ^ [_1513679, _1513681, _1513683, _1513685, _1513687, _1513689]), _1513683)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513681, _1513679), hAPP(hAPP(c_COMBS(_1513681, tc_fun(_1513685, tc_HOL_Obool), _1513679), hAPP(hAPP(c_COMBB(tc_fun(_1513685, _1513679), tc_fun(tc_fun(_1513685, tc_HOL_Obool), _1513679), _1513681), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513685, _1513679)), _1513689)), _1513687)), _1513683) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1513681, _1513685), _1513679), hAPP(c_Product__Type_Oprod_Oprod__case(_1513681, _1513685, _1513679), _1513689)), hAPP(hAPP(c_Product__Type_OSigma(_1513681, _1513685), _1513683), _1513687)))], (22919 ^ _779854) ^ [_1194121, _1194123, _1194125, _1194127] : [class_Fields_Olinordered__field__inverse__zero(_1194121), 22922 ^ _779854 : [(22923 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1194121), _1194125), _1194127))), 22926 ^ _779854 : [(22933 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), c_Groups_Ozero__class_Ozero(_1194121)), _1194127))), 22936 ^ _779854 : [(22943 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194127), c_Groups_Ozero__class_Ozero(_1194121)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194123), c_Groups_Ozero__class_Ozero(_1194121))))], (22937 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194127), c_Groups_Ozero__class_Ozero(_1194121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194121), _1194123), _1194127))))]]], (22927 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), c_Groups_Ozero__class_Ozero(_1194121)), _1194127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194121), _1194123), _1194127)), _1194125)))]]], (22949 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194123), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1194121), _1194125), _1194127)))), 22952 ^ _779854 : [(22955 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194121), _1194123), _1194127)), _1194125))], (22953 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), c_Groups_Ozero__class_Ozero(_1194121)), _1194127)))]], 22956 ^ _779854 : [(22959 ^ _779854) ^ [] : [22960 ^ _779854 : [(22963 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194121), _1194123), _1194127)))], (22961 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194127), c_Groups_Ozero__class_Ozero(_1194121))))]], 22964 ^ _779854 : [(22967 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194123), c_Groups_Ozero__class_Ozero(_1194121)))], (22965 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), _1194127), c_Groups_Ozero__class_Ozero(_1194121)))]]], (22957 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194121), c_Groups_Ozero__class_Ozero(_1194121)), _1194127))]]]]], (42614 ^ _779854) ^ [_1625309, _1625311, _1625313, _1625315] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1625309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1625311), hAPP(hAPP(c_List_Olist_OCons(_1625311), _1625313), _1625315)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1625309)) = hAPP(hAPP(c_List_Onth(_1625311), _1625315), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1625309)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (38108 ^ _779854) ^ [_1501045, _1501047, _1501049, _1501051, _1501053] : [hBOOL(hAPP(hAPP(c_member(_1501045), _1501047), hAPP(c_Set_Ovimage(_1501045, _1501049, _1501051), _1501053))), -(hBOOL(hAPP(hAPP(c_member(_1501049), hAPP(_1501051, _1501047)), _1501053)))], (38733 ^ _779854) ^ [_1518541, _1518543, _1518545] : [hBOOL(hAPP(hAPP(c_member(_1518541), _1518543), hAPP(c_Set_OCollect(_1518541), _1518545))), -(hBOOL(hAPP(_1518545, _1518543)))], (47723 ^ _779854) ^ [_1739781, _1739783, _1739785] : [class_Orderings_Olinorder(_1739781), c_List_Olinorder__class_Osorted(_1739781, _1739783), -(c_List_Olinorder__class_Osorted(_1739781, c_List_OdropWhile(_1739781, _1739785, _1739783)))], (38062 ^ _779854) ^ [_1499819, _1499821, _1499823, _1499825, _1499827] : [-(hAPP(c_Set_Ovimage(_1499819, _1499821, _1499823), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499821, tc_HOL_Obool)), _1499825), _1499827)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499819, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1499819, _1499821, _1499823), _1499825)), hAPP(c_Set_Ovimage(_1499819, _1499821, _1499823), _1499827)))], (49078 ^ _779854) ^ [_1769307, _1769309, _1769311, _1769313] : [hBOOL(hAPP(hAPP(c_member(_1769307), _1769309), hAPP(c_List_Oset(_1769307), c_List_Oreplicate(_1769307, _1769311, _1769313)))), 49081 ^ _779854 : [(49084 ^ _779854) ^ [] : [_1769311 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49082 ^ _779854) ^ [] : [-(_1769309 = _1769313)]]], (45063 ^ _779854) ^ [_1681030, _1681032, _1681034] : [c_Fun_Oinj__on(_1681030, _1681032, _1681034, c_Orderings_Otop__class_Otop(tc_fun(_1681030, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1681030), tc_List_Olist(_1681032), hAPP(c_List_Omap(_1681030, _1681032), _1681034), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1681030), tc_HOL_Obool))))], (38755 ^ _779854) ^ [_1519026, _1519028, _1519030] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519026), hAPP(c_Set_OCollect(_1519026), hAPP(hAPP(c_COMBS(_1519026, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519026), c_fdisj), _1519028)), _1519030)))), 38758 ^ _779854 : [(38761 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1519026), hAPP(c_Set_OCollect(_1519026), _1519030))))], (38759 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1519026), hAPP(c_Set_OCollect(_1519026), _1519028))))]]], (10125 ^ _779854) ^ [_950888, _950890, _950892, _950894] : [class_Orderings_Olinorder(_950888), 10128 ^ _779854 : [(10137 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950888), _950890), hAPP(hAPP(c_Orderings_Oord__class_Omin(_950888), _950892), _950894)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950888), _950890), _950892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950888), _950890), _950894))], (10129 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950888), _950890), hAPP(hAPP(c_Orderings_Oord__class_Omin(_950888), _950892), _950894))), 10132 ^ _779854 : [(10135 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950888), _950890), _950894)))], (10133 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950888), _950890), _950892)))]]]]], (30420 ^ _779854) ^ [_1329143, _1329145] : [c_Nat__Transfer_Onat__set(_1329143), c_Nat__Transfer_Onat__set(_1329145), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1329143), _1329145)))], (15898 ^ _779854) ^ [_1064946] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1064946)), 15902 ^ _779854 : [(15903 ^ _779854) ^ [_1065026] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1065026), _1064946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065026), 15901 ^ [_1064946])))]]], (41753 ^ _779854) ^ [_1600136, _1600138, _1600140, _1600142] : [-(hAPP(_1600136, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1600138, _1600138), _1600140), _1600136), _1600142)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1600138, _1600138), _1600140), _1600136), hAPP(_1600136, _1600142)))], (12024 ^ _779854) ^ [_988980, _988982, _988984, _988986] : [12025 ^ _779854 : [(12028 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_988980), _988982), _988986))], (12026 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_988980), _988982), _988984))]], -(hBOOL(hAPP(hAPP(c_member(_988980), _988982), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988980, tc_HOL_Obool)), _988984), _988986))))], (8480 ^ _779854) ^ [_921353, _921355, _921357, _921359] : [class_Orderings_Oord(_921353), 8483 ^ _779854 : [(8492 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921355, _921353)), _921357), _921359))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921355, _921353)), _921357), _921359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921355, _921353)), _921359), _921357)))], (8484 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921355, _921353)), _921357), _921359)), 8487 ^ _779854 : [(8490 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921355, _921353)), _921359), _921357))], (8488 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921355, _921353)), _921357), _921359)))]]]]], (13211 ^ _779854) ^ [_1012917, _1012919, _1012921] : [class_Orderings_Olinorder(_1012917), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012917), _1012919)), hBOOL(hAPP(hAPP(c_member(_1012917), _1012921), _1012919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012917), _1012921), c_Big__Operators_Olinorder__class_OMax(_1012917, _1012919))))], (16788 ^ _779854) ^ [_1082505, _1082507, _1082509] : [class_Complete__Lattice_Ocomplete__lattice(_1082505), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082505), _1082507)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1082505), _1082509), c_Complete__Lattice_OSup__class_OSup(_1082505, _1082507)) = hAPP(hAPP(c_Finite__Set_Ofold(_1082505, _1082505, c_Lattices_Osemilattice__sup__class_Osup(_1082505)), _1082509), _1082507))], (43704 ^ _779854) ^ [_1651263] : [class_Orderings_Olinorder(_1651263), -(c_List_Olinorder__class_Osorted__list__of__set(_1651263, c_Orderings_Obot__class_Obot(tc_fun(_1651263, tc_HOL_Obool))) = c_List_Olist_ONil(_1651263))], (17893 ^ _779854) ^ [_1103806, _1103808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103806), hAPP(c_Nat_OSuc, _1103808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103806), _1103808))), -(_1103806 = _1103808)], (46122 ^ _779854) ^ [_1705595, _1705597, _1705599] : [hBOOL(hAPP(c_List_Odistinct(_1705595), _1705597)), -(hBOOL(hAPP(c_List_Odistinct(_1705595), hAPP(c_List_OremoveAll(_1705595, _1705599), _1705597))))], (16085 ^ _779854) ^ [_1068686, _1068688] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068686), _1068688))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068688), _1068686)))], (2996 ^ _779854) ^ [_824471, _824473, _824475, _824477, _824479, _824481] : [-(c_Product__Type_Ointernal__split(_824481, _824477, _824473) = c_Product__Type_Ointernal__split(_824479, _824475, _824471)), _824481 = _824479, _824477 = _824475, _824473 = _824471], (20902 ^ _779854) ^ [_1156017, _1156019] : [20903 ^ _779854 : [(20906 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1156017), _1156019)))], (20904 ^ _779854) ^ [] : [_1156019 = c_Orderings_Obot__class_Obot(tc_fun(_1156017, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1156017), _1156019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16732 ^ _779854) ^ [_1081260, _1081262, _1081264, _1081266, _1081268, _1081270, _1081272] : [-(hBOOL(hAPP(hAPP(c_member(_1081260), _1081262), _1081264))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1081260, _1081266, _1081268, _1081270, _1081264), _1081272)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1081260, _1081266, _1081268, _1081270, hAPP(hAPP(c_Set_Oinsert(_1081260), _1081262), _1081264)), hAPP(hAPP(_1081268, _1081262), _1081272))))], (2116 ^ _779854) ^ [_810641, _810643, _810645, _810647, _810649, _810651, _810653, _810655] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810655, _810651, _810647, _810643) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810653, _810649, _810645, _810641)), _810655 = _810653, _810651 = _810649, _810647 = _810645, _810643 = _810641], (52563 ^ _779854) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (33903 ^ _779854) ^ [_1405325, _1405327, _1405329, _1405331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool)), _1405329), _1405331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1405325, tc_fun(_1405327, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1405325, tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_fun(_1405327, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405327, tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_fun(_1405327, tc_HOL_Obool)), _1405325), c_COMBC(_1405327, tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405327, tc_prod(_1405325, _1405327)), tc_fun(_1405327, tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool)), _1405325), hAPP(c_COMBB(tc_prod(_1405325, _1405327), tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool), _1405327), c_member(tc_prod(_1405325, _1405327)))), c_Product__Type_OPair(_1405325, _1405327)))), _1405329)), hAPP(hAPP(c_COMBC(_1405325, tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_fun(_1405327, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405327, tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_fun(_1405327, tc_HOL_Obool)), _1405325), c_COMBC(_1405327, tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405327, tc_prod(_1405325, _1405327)), tc_fun(_1405327, tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool)), _1405325), hAPP(c_COMBB(tc_prod(_1405325, _1405327), tc_fun(tc_fun(tc_prod(_1405325, _1405327), tc_HOL_Obool), tc_HOL_Obool), _1405327), c_member(tc_prod(_1405325, _1405327)))), c_Product__Type_OPair(_1405325, _1405327)))), _1405331))))], (11714 ^ _779854) ^ [_983079, _983081, _983083, _983085] : [hBOOL(hAPP(hAPP(c_member(_983079), _983081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983079, tc_HOL_Obool)), _983083), _983085))), 11717 ^ _779854 : [(11720 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_983079), _983081), _983085))], (11718 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_983079), _983081), _983083)))]]], (31679 ^ _779854) ^ [] : [-(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)))], (35258 ^ _779854) ^ [_1436768, _1436770] : [-(c_Divides_Odivmod__int(_1436768, _1436770) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1436768), _1436770)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1436768, _1436770)))], (26585 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (39184 ^ _779854) ^ [_1532478, _1532480, _1532482] : [class_Lattices_Odistrib__lattice(_1532478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532478), _1532480)), -(_1532480 = c_Orderings_Obot__class_Obot(tc_fun(_1532478, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532478), _1532482)), -(_1532482 = c_Orderings_Obot__class_Obot(tc_fun(_1532478, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1532478), c_Big__Operators_Olattice__class_OSup__fin(_1532478, _1532480)), c_Big__Operators_Olattice__class_OSup__fin(_1532478, _1532482)) = c_Big__Operators_Olattice__class_OSup__fin(_1532478, hAPP(c_Set_OCollect(_1532478), hAPP(hAPP(c_COMBB(tc_fun(_1532478, tc_HOL_Obool), tc_HOL_Obool, _1532478), c_HOL_OEx(_1532478)), hAPP(hAPP(c_COMBB(tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool)), tc_fun(_1532478, tc_HOL_Obool), _1532478), hAPP(c_COMBB(tc_fun(_1532478, tc_HOL_Obool), tc_HOL_Obool, _1532478), c_HOL_OEx(_1532478))), hAPP(hAPP(c_COMBC(_1532478, tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool)), tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1532478, tc_fun(tc_fun(_1532478, tc_HOL_Obool), tc_fun(_1532478, tc_HOL_Obool))), tc_fun(tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool)), tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool))), _1532478), c_COMBS(_1532478, tc_fun(_1532478, tc_HOL_Obool), tc_fun(_1532478, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1532478, tc_fun(_1532478, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1532478, tc_fun(tc_fun(_1532478, tc_HOL_Obool), tc_fun(_1532478, tc_HOL_Obool))), _1532478), hAPP(c_COMBB(tc_fun(_1532478, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1532478, tc_HOL_Obool), tc_fun(_1532478, tc_HOL_Obool)), _1532478), c_COMBS(_1532478, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool)), tc_fun(_1532478, tc_fun(_1532478, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1532478), hAPP(c_COMBB(tc_fun(_1532478, tc_HOL_Obool), tc_fun(_1532478, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1532478), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532478), c_fconj))), hAPP(hAPP(c_COMBC(_1532478, tc_fun(_1532478, tc_fun(_1532478, _1532478)), tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1532478, _1532478), tc_fun(_1532478, tc_HOL_Obool)), tc_fun(tc_fun(_1532478, tc_fun(_1532478, _1532478)), tc_fun(_1532478, tc_fun(_1532478, tc_HOL_Obool))), _1532478), c_COMBB(tc_fun(_1532478, _1532478), tc_fun(_1532478, tc_HOL_Obool), _1532478)), hAPP(hAPP(c_COMBB(tc_fun(_1532478, tc_HOL_Obool), tc_fun(tc_fun(_1532478, _1532478), tc_fun(_1532478, tc_HOL_Obool)), _1532478), c_COMBB(_1532478, tc_HOL_Obool, _1532478)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1532478)))))), hAPP(hAPP(c_COMBC(_1532478, tc_fun(_1532478, tc_HOL_Obool), tc_fun(_1532478, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532478, tc_HOL_Obool), tc_fun(_1532478, tc_HOL_Obool)), _1532478), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532478)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532478), c_fconj), hAPP(hAPP(c_COMBC(_1532478, tc_fun(_1532478, tc_HOL_Obool), tc_HOL_Obool), c_member(_1532478)), _1532480)))), hAPP(hAPP(c_COMBC(_1532478, tc_fun(_1532478, tc_HOL_Obool), tc_HOL_Obool), c_member(_1532478)), _1532482))))))))], (35006 ^ _779854) ^ [_1430886] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1430886) = 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)))], (42181 ^ _779854) ^ [_1612592, _1612594, _1612596] : [-(c_Random_Oselect__weight(_1612592, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1612592)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1612592), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1612594)), _1612596)) = c_Random_Oselect__weight(_1612592, _1612596))], (44242 ^ _779854) ^ [_1664159, _1664161] : [hBOOL(hAPP(c_List_Odistinct(_1664159), _1664161)), -(hBOOL(hAPP(c_List_Odistinct(_1664159), hAPP(c_List_Orotate1(_1664159), _1664161))))], (28509 ^ _779854) ^ [_1295268, _1295270] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295268)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295270)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295268), _1295270)))], (39417 ^ _779854) ^ [_1541539, _1541541, _1541543, _1541545] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541539, _1541541, _1541543), _1541545), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1541541, _1541543), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1541539, _1541543), tc_HOL_Obool)))], (14988 ^ _779854) ^ [_1045951, _1045953] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1045951), _1045953))))], (46284 ^ _779854) ^ [_1708594, _1708596] : [c_List_Olist_ONil(_1708594) = c_List_Oconcat(_1708594, _1708596), 46287 ^ _779854 : [(46288 ^ _779854) ^ [_1708685] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1708594)), _1708685), hAPP(c_List_Oset(tc_List_Olist(_1708594)), _1708596))), -(_1708685 = c_List_Olist_ONil(_1708594))]]], (39741 ^ _779854) ^ [_1550646] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1550646)))], (52417 ^ _779854) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (46591 ^ _779854) ^ [_1717151, _1717153, _1717155, _1717157, _1717159, _1717161] : [-(c_List_Ofoldr(_1717151, _1717153, _1717155, hAPP(hAPP(c_List_Oappend(_1717151), _1717157), _1717159), _1717161) = c_List_Ofoldr(_1717151, _1717153, _1717155, _1717157, c_List_Ofoldr(_1717151, _1717153, _1717155, _1717159, _1717161)))], (38753 ^ _779854) ^ [_1518923, _1518925, _1518927] : [-(hAPP(hAPP(c_Set_Oinsert(_1518923), _1518925), hAPP(c_Set_OCollect(_1518923), _1518927)) = hAPP(c_Set_OCollect(_1518923), hAPP(hAPP(c_COMBS(_1518923, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518923), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1518923), c_fNot), hAPP(hAPP(c_COMBC(_1518923, _1518923, tc_HOL_Obool), c_fequal), _1518925)))), _1518927)))], (7622 ^ _779854) ^ [_906116, _906118, _906120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906116, tc_HOL_Obool)), _906118), _906120)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906116, tc_HOL_Obool)), _906118), _906120) = _906120)], (14019 ^ _779854) ^ [_1027029, _1027031] : [class_Lattices_Olattice(_1027029), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027029), _1027031)), -(_1027031 = c_Orderings_Obot__class_Obot(tc_fun(_1027029, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1027029), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1027029), 14032 ^ [_1027029, _1027031]), 14033 ^ [_1027029, _1027031])), hAPP(hAPP(c_Set_Oinsert(_1027029), 14032 ^ [_1027029, _1027031]), hAPP(hAPP(c_Set_Oinsert(_1027029), 14033 ^ [_1027029, _1027031]), c_Orderings_Obot__class_Obot(tc_fun(_1027029, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1027029), c_Big__Operators_Olattice__class_OSup__fin(_1027029, _1027031)), _1027031)))], (22601 ^ _779854) ^ [_1188099, _1188101, _1188103] : [class_Fields_Olinordered__field(_1188099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188099), c_Groups_Ozero__class_Ozero(_1188099)), _1188101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188099), c_Groups_Ozero__class_Ozero(_1188099)), _1188103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188099), c_Groups_Ozero__class_Ozero(_1188099)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188099), _1188101), _1188103))))], (52337 ^ _779854) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (21707 ^ _779854) ^ [_1171586, _1171588, _1171590, _1171592] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1171586), _1171588)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171590), _1171592)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1171586, _1171590)), c_Sum__Type_OPlus(_1171586, _1171590, _1171588, _1171592))))], (46665 ^ _779854) ^ [_1718821, _1718823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718821), _1718823)), -(c_List_Oupt(_1718823, _1718821) = c_List_Olist_ONil(tc_Nat_Onat))], (17706 ^ _779854) ^ [_1100887, _1100889] : [hAPP(c_Nat_OSuc, _1100887) = hAPP(c_Nat_OSuc, _1100889), -(_1100887 = _1100889)], (6895 ^ _779854) ^ [_891988, _891990, _891992, _891994] : [class_Lattices_Olattice(_891988), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891988), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891988), _891990), _891992)), _891994) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891988), _891990), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891988), _891992), _891994)))], (20173 ^ _779854) ^ [_1143449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143449)), -(_1143449 = hAPP(c_Nat_OSuc, 20176 ^ [_1143449]))], (40334 ^ _779854) ^ [_1565664, _1565666, _1565668] : [-(c_Hilbert__Choice_OEps(tc_prod(_1565664, _1565666), hAPP(c_Product__Type_Oprod_Oprod__case(_1565664, _1565666, tc_HOL_Obool), _1565668)) = c_Hilbert__Choice_OEps(tc_prod(_1565664, _1565666), hAPP(hAPP(c_COMBS(tc_prod(_1565664, _1565666), _1565666, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1565664, tc_fun(_1565666, tc_HOL_Obool), tc_prod(_1565664, _1565666)), _1565668), c_Product__Type_Ofst(_1565664, _1565666))), c_Product__Type_Osnd(_1565664, _1565666))))], (39729 ^ _779854) ^ [_1550462, _1550464, _1550466] : [c_Wellfounded_Owf(_1550462, _1550464), -(c_Wellfounded_Owf(_1550462, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1550462, _1550462), tc_HOL_Obool)), _1550466), _1550464)))], (44412 ^ _779854) ^ [_1668270, _1668272, _1668274, _1668276] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668270) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1668272), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668270)), hAPP(hAPP(c_List_Olist_OCons(_1668272), _1668274), _1668276)) = hAPP(hAPP(c_List_Olist_OCons(_1668272), _1668274), _1668276))], (18533 ^ _779854) ^ [_1115513, _1115515] : [class_Groups_Omonoid__add(_1115513), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115513), _1115515), c_Groups_Ozero__class_Ozero(_1115513)) = _1115515)], (29731 ^ _779854) ^ [_1316031] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1316031), 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, _1316031)))], (28792 ^ _779854) ^ [_1299986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299986)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299986), c_Int_OPls)))], (29935 ^ _779854) ^ [_1319460, _1319462, _1319464] : [class_Rings_Olinordered__semidom(_1319460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319460), hAPP(hAPP(c_Power_Opower__class_Opower(_1319460), _1319462), 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(_1319460), _1319464), 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(_1319460), c_Groups_Ozero__class_Ozero(_1319460)), _1319464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319460), _1319462), _1319464)))], (52085 ^ _779854) ^ [_1832474, _1832476] : [class_Lattices_Obounded__lattice(_1832474), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1832476, _1832474)))], (46723 ^ _779854) ^ [_1719816, _1719818, _1719820, _1719822] : [c_List_Oupt(_1719816, _1719818) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1719820), _1719822), 46726 ^ _779854 : [(46731 ^ _779854) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1719816), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1719818) = _1719822)], (46729 ^ _779854) ^ [] : [-(_1719816 = _1719820)], (46727 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719816), _1719818)))]]], (7946 ^ _779854) ^ [_912757, _912759, _912761] : [class_Groups_Ogroup__add(_912757), 7949 ^ _779854 : [(7956 ^ _779854) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_912757), _912761) = _912759, -(hAPP(c_Groups_Ouminus__class_Ouminus(_912757), _912759) = _912761)], (7950 ^ _779854) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_912757), _912759) = _912761, -(hAPP(c_Groups_Ouminus__class_Ouminus(_912757), _912761) = _912759)]]], (32431 ^ _779854) ^ [_1363468, _1363470] : [class_Int_Onumber__ring(_1363468), class_Rings_Olinordered__idom(_1363468), 32438 ^ _779854 : [(32445 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363468), hAPP(c_Int_Onumber__class_Onumber__of(_1363468), _1363470)), c_Groups_Ozero__class_Ozero(_1363468)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1363468), hAPP(c_Int_Onumber__class_Onumber__of(_1363468), _1363470)) = hAPP(c_Int_Onumber__class_Onumber__of(_1363468), _1363470))], (32439 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363468), hAPP(c_Int_Onumber__class_Onumber__of(_1363468), _1363470)), c_Groups_Ozero__class_Ozero(_1363468))), -(hAPP(c_Groups_Oabs__class_Oabs(_1363468), hAPP(c_Int_Onumber__class_Onumber__of(_1363468), _1363470)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1363468), hAPP(c_Int_Onumber__class_Onumber__of(_1363468), _1363470)))]]], (46166 ^ _779854) ^ [_1706387, _1706389] : [c_List_Oremdups(_1706387, _1706389) = c_List_Olist_ONil(_1706387), -(_1706389 = c_List_Olist_ONil(_1706387))], (49140 ^ _779854) ^ [_1770624, _1770626, _1770628] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1770624)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1770624, _1770626, _1770628)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1770624)), _1770628)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29715 ^ _779854) ^ [_1315767, _1315769] : [class_Groups_Omonoid__mult(_1315767), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1315767), _1315769), 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(_1315767), _1315769), _1315769))], (12418 ^ _779854) ^ [_996637, _996639, _996641] : [class_Orderings_Oord(_996637), 12421 ^ _779854 : [(12428 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996637), _996639), _996641)), -(hBOOL(hAPP(hAPP(c_member(_996637), _996639), hAPP(c_SetInterval_Oord__class_OatMost(_996637), _996641))))], (12422 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_996637), _996639), hAPP(c_SetInterval_Oord__class_OatMost(_996637), _996641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996637), _996639), _996641)))]]], (22799 ^ _779854) ^ [_1191868, _1191870, _1191872, _1191874] : [class_Fields_Olinordered__field(_1191868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191868), c_Groups_Ozero__class_Ozero(_1191868)), _1191870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191868), _1191872), _1191870)), _1191874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191868), _1191872), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191868), _1191874), _1191870))))], (45206 ^ _779854) ^ [_1685041, _1685043, _1685045, _1685047, _1685049] : [-(hAPP(hAPP(c_List_Otake(_1685041), _1685043), hAPP(hAPP(c_List_Omap(_1685045, _1685041), _1685047), _1685049)) = hAPP(hAPP(c_List_Omap(_1685045, _1685041), _1685047), hAPP(hAPP(c_List_Otake(_1685045), _1685043), _1685049)))], (15718 ^ _779854) ^ [_1061242, _1061244, _1061246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061242), _1061244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061242), _1061246)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061244), _1061242)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061246), _1061242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061244), _1061246))], (10983 ^ _779854) ^ [_968324, _968326, _968328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968324, tc_HOL_Obool)), _968326), _968328)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_968324, tc_HOL_Obool)), _968326), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968324, tc_HOL_Obool)), _968328), _968326)) = _968328)], (44430 ^ _779854) ^ [_1668695, _1668697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668695)), _1668697)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1668695), _1668697) = _1668697)], (15316 ^ _779854) ^ [_1053037, _1053039, _1053041, _1053043] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1053037), 15319 ^ _779854 : [(15326 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053037), _1053039), _1053043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053037), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053037), _1053039), _1053041)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053037), _1053043), _1053041))))], (15320 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053037), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053037), _1053039), _1053041)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053037), _1053043), _1053041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053037), _1053039), _1053043)))]]], (11113 ^ _779854) ^ [_971220, _971222, _971224, _971226, _971228] : [c_Fun_Oinj__on(_971220, _971222, _971224, c_Orderings_Otop__class_Otop(tc_fun(_971220, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_971220, _971222, _971224), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971220, tc_HOL_Obool)), _971226), _971228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971222, tc_HOL_Obool)), hAPP(c_Set_Oimage(_971220, _971222, _971224), _971226)), hAPP(c_Set_Oimage(_971220, _971222, _971224), _971228)))], (9260 ^ _779854) ^ [_934427, _934429] : [class_Complete__Lattice_Ocomplete__lattice(_934427), -(c_Complete__Lattice_OSup__class_OSup(_934427, hAPP(hAPP(c_Set_Oinsert(_934427), _934429), c_Orderings_Obot__class_Obot(tc_fun(_934427, tc_HOL_Obool)))) = _934429)], (14507 ^ _779854) ^ [_1036781, _1036783, _1036785] : [class_Orderings_Olinorder(_1036781), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036781), _1036783)), 14517 ^ _779854 : [(14520 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036781), _1036785), 14516 ^ [_1036781, _1036783, _1036785]))], (14518 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036781), 14516 ^ [_1036781, _1036783, _1036785]), _1036783)))]], hBOOL(hAPP(hAPP(c_member(_1036781), _1036785), _1036783)), -(c_Big__Operators_Olinorder__class_OMin(_1036781, _1036783) = _1036785)], (3374 ^ _779854) ^ [_830396, _830398, _830400, _830402] : [-(c_HOL_OLet(_830402, _830398) = c_HOL_OLet(_830400, _830396)), _830402 = _830400, _830398 = _830396], (34978 ^ _779854) ^ [_1430282, _1430284, _1430286, _1430288, _1430290, _1430292] : [hBOOL(hAPP(hAPP(_1430282, _1430284), _1430286)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430288, tc_fun(_1430290, tc_HOL_Obool))), _1430292), _1430282), _1430284), _1430286)))], (4000 ^ _779854) ^ [_840467, _840469, _840471, _840473, _840475, _840477, _840479, _840481] : [-(c_New__Random__Sequence_Opos__empty(_840481, _840477, _840473, _840469) = c_New__Random__Sequence_Opos__empty(_840479, _840475, _840471, _840467)), _840481 = _840479, _840477 = _840475, _840473 = _840471, _840469 = _840467], (46148 ^ _779854) ^ [_1706078, _1706080] : [-(c_List_Oremdups(_1706078, c_List_Oremdups(_1706078, _1706080)) = c_List_Oremdups(_1706078, _1706080))], (32605 ^ _779854) ^ [_1366951, _1366953] : [_1366951 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1366953, _1366951) = _1366953)], (7984 ^ _779854) ^ [_913334, _913336] : [class_Groups_Ogroup__add(_913334), -(hAPP(c_Groups_Ouminus__class_Ouminus(_913334), hAPP(c_Groups_Ouminus__class_Ouminus(_913334), _913336)) = _913336)], (46589 ^ _779854) ^ [_1717092, _1717094, _1717096, _1717098, _1717100, _1717102] : [-(c_List_Ofoldr(_1717092, _1717094, _1717096, hAPP(hAPP(c_List_Olist_OCons(_1717092), _1717098), _1717100), _1717102) = hAPP(hAPP(_1717096, _1717098), c_List_Ofoldr(_1717092, _1717094, _1717096, _1717100, _1717102)))], (402 ^ _779854) ^ [_785941, _785943, _785945, _785947, _785949, _785951] : [-(c_Orderings_Oorder__class_Omono(_785949, _785945, _785941)), c_Orderings_Oorder__class_Omono(_785951, _785947, _785943), _785951 = _785949, _785947 = _785945, _785943 = _785941], (52431 ^ _779854) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (51304 ^ _779854) ^ [_1819110, _1819112, _1819114] : [51306 ^ _779854 : [(51309 ^ _779854) ^ [] : [hBOOL(hAPP(_1819110, 51305 ^ [_1819110, _1819112, _1819114]))], (51307 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51305 ^ [_1819110, _1819112, _1819114]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1819112), _1819114))))]], -(c_List_Oall__interval__nat(_1819110, _1819112, _1819114))], (2088 ^ _779854) ^ [_810237, _810239] : [_810239 = _810237, -(c_Int_Osucc(_810239) = c_Int_Osucc(_810237))], (24755 ^ _779854) ^ [_1229511, _1229513, _1229515] : [class_Int_Onumber(_1229511), class_Orderings_Oord(_1229511), 24762 ^ _779854 : [(24769 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229511), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229513)), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229515)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1229511), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229513)), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229515)) = hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229515))], (24763 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229511), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229513)), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229515))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1229511), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229513)), hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229515)) = hAPP(c_Int_Onumber__class_Onumber__of(_1229511), _1229513))]]], (6085 ^ _779854) ^ [_876320, _876322, _876324] : [class_Orderings_Oorder(_876320), 6088 ^ _779854 : [(6095 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876320), _876324), _876322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876320, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_876320), _876322)), hAPP(c_SetInterval_Oord__class_OatLeast(_876320), _876324))))], (6089 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876320, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_876320), _876322)), hAPP(c_SetInterval_Oord__class_OatLeast(_876320), _876324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876320), _876324), _876322)))]]], (40225 ^ _779854) ^ [_1563030, _1563032] : [class_Complete__Lattice_Ocomplete__lattice(_1563030), -(c_Complete__Lattice_OSup__class_OSup(_1563030, _1563032) = c_Complete__Lattice_OInf__class_OInf(_1563030, hAPP(c_Set_OCollect(_1563030), hAPP(hAPP(c_COMBB(tc_fun(_1563030, tc_HOL_Obool), tc_HOL_Obool, _1563030), c_HOL_OAll(_1563030)), hAPP(hAPP(c_COMBB(tc_fun(_1563030, tc_HOL_Obool), tc_fun(_1563030, tc_HOL_Obool), _1563030), hAPP(c_COMBS(_1563030, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563030), c_fimplies), hAPP(hAPP(c_COMBC(_1563030, tc_fun(_1563030, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563030)), _1563032)))), hAPP(c_COMBC(_1563030, _1563030, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1563030)))))))], (28402 ^ _779854) ^ [_1293353, _1293355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293353)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1293353), _1293355)))], (41481 ^ _779854) ^ [_1593491, _1593493, _1593495, _1593497, _1593499] : [-(hAPP(c_Relation_Oconverse(_1593491, _1593493), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1593495, tc_fun(tc_prod(_1593491, _1593493), tc_HOL_Obool)), _1593497), _1593499)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1593495, tc_fun(tc_prod(_1593493, _1593491), tc_HOL_Obool)), _1593497), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1593491, _1593493), tc_HOL_Obool), tc_fun(tc_prod(_1593493, _1593491), tc_HOL_Obool), _1593495), c_Relation_Oconverse(_1593491, _1593493)), _1593499)))], (12256 ^ _779854) ^ [_993352, _993354, _993356] : [_993354 = _993356, -(hBOOL(hAPP(hAPP(c_member(_993352), _993354), hAPP(hAPP(c_Set_Oinsert(_993352), _993356), c_Orderings_Obot__class_Obot(tc_fun(_993352, tc_HOL_Obool))))))], (44494 ^ _779854) ^ [_1669983, _1669985] : [-(_1669983 = c_List_Olist_ONil(_1669985)), -(hAPP(c_List_Orotate1(_1669985), _1669983) = hAPP(hAPP(c_List_Oappend(_1669985), hAPP(c_List_Otl(_1669985), _1669983)), hAPP(hAPP(c_List_Olist_OCons(_1669985), hAPP(c_List_Ohd(_1669985), _1669983)), c_List_Olist_ONil(_1669985))))], (34563 ^ _779854) ^ [_1421277, _1421279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421277)), hAPP(c_Nat_OSuc, _1421279))), -(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(_1421277))), 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)), _1421279)))))], (31120 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (11937 ^ _779854) ^ [_987266, _987268, _987270, _987272] : [hBOOL(hAPP(hAPP(c_member(_987266), _987268), _987270)), -(hBOOL(hAPP(hAPP(c_member(_987266), _987268), hAPP(hAPP(c_Set_Oinsert(_987266), _987272), _987270))))], (10445 ^ _779854) ^ [_957103, _957105, _957107] : [class_Orderings_Olinorder(_957103), hBOOL(hAPP(c_Finite__Set_Ofinite(_957103), _957105)), -(_957105 = c_Orderings_Obot__class_Obot(tc_fun(_957103, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_957103), _957107)), -(_957107 = c_Orderings_Obot__class_Obot(tc_fun(_957103, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957103, tc_HOL_Obool)), _957105), _957107) = c_Orderings_Obot__class_Obot(tc_fun(_957103, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_957103, c_Orderings_Oord__class_Omax(_957103), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_957103, tc_HOL_Obool)), _957105), _957107)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_957103), c_Big__Operators_Olattice_OSup__fin(_957103, c_Orderings_Oord__class_Omax(_957103), _957105)), c_Big__Operators_Olattice_OSup__fin(_957103, c_Orderings_Oord__class_Omax(_957103), _957107)))], (31300 ^ _779854) ^ [_1344172, _1344174] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344172), _1344174)), _1344174) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1344172), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1344172, _1344174)))], (40237 ^ _779854) ^ [_1563513, _1563515] : [c_Nitpick_Owf_H(_1563513, _1563515), 40240 ^ _779854 : [(40243 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1563513, _1563513)), _1563515))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (40241 ^ _779854) ^ [] : [-(c_Wellfounded_Oacyclic(_1563513, _1563515))]]], (39423 ^ _779854) ^ [_1541740, _1541742, _1541744, _1541746, _1541748, _1541750] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541740, _1541742, _1541744), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541740, _1541742), tc_HOL_Obool)), _1541746), _1541748)), _1541750) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541740, _1541744), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541740, _1541742, _1541744), _1541746), _1541750)), hAPP(hAPP(c_Relation_Orel__comp(_1541740, _1541742, _1541744), _1541748), _1541750)))], (32293 ^ _779854) ^ [_1360887, _1360889, _1360891] : [class_Rings_Olinordered__idom(_1360887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360887), c_Groups_Ozero__class_Ozero(_1360887)), _1360889)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360887), hAPP(c_Groups_Oabs__class_Oabs(_1360887), _1360891)), _1360889) = hAPP(c_Groups_Oabs__class_Oabs(_1360887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360887), _1360891), _1360889)))], (33649 ^ _779854) ^ [_1398043, _1398045, _1398047, _1398049, _1398051, _1398053] : [-(hBOOL(hAPP(hAPP(c_member(_1398043), _1398045), _1398047))), -(hAPP(c_Fun_Ooverride__on(_1398043, _1398049, _1398051, _1398053, _1398047), _1398045) = hAPP(_1398051, _1398045))], (51663 ^ _779854) ^ [_1825582, _1825584, _1825586] : [class_Divides_Osemiring__div(_1825582), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825582), _1825584), _1825586)), -(c_Divides_Odiv__class_Omod(_1825582, _1825586, _1825584) = c_Groups_Ozero__class_Ozero(_1825582))], (42723 ^ _779854) ^ [_1628208, _1628210] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1628208), hAPP(c_List_Oset(_1628208), _1628210))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628208)), _1628210))))], (13587 ^ _779854) ^ [_1018871, _1018873, _1018875] : [class_Orderings_Olinorder(_1018871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018871), _1018873)), -(_1018873 = c_Orderings_Obot__class_Obot(tc_fun(_1018871, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018871), _1018875)), -(_1018875 = c_Orderings_Obot__class_Obot(tc_fun(_1018871, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1018871, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018871, tc_HOL_Obool)), _1018873), _1018875)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1018871), c_Big__Operators_Olinorder__class_OMin(_1018871, _1018873)), c_Big__Operators_Olinorder__class_OMin(_1018871, _1018875)))], (26691 ^ _779854) ^ [_1264675, _1264677] : [class_Int_Onumber__ring(_1264675), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264675), hAPP(c_Int_Onumber__class_Onumber__of(_1264675), c_Int_OPls)), _1264677) = _1264677)], (52353 ^ _779854) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (13295 ^ _779854) ^ [_1014195, _1014197, _1014199] : [class_Lattices_Olattice(_1014195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014195), _1014197)), hBOOL(hAPP(hAPP(c_member(_1014195), _1014199), _1014197)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1014195), _1014199), c_Big__Operators_Olattice__class_OSup__fin(_1014195, _1014197)) = _1014199)], (44095 ^ _779854) ^ [_1660124, _1660126, _1660128] : [-(hBOOL(hAPP(c_List_Odistinct(_1660124), hAPP(hAPP(c_List_Oappend(_1660124), _1660126), _1660128)))), hBOOL(hAPP(c_List_Odistinct(_1660124), _1660126)), hBOOL(hAPP(c_List_Odistinct(_1660124), _1660128)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660124, tc_HOL_Obool)), hAPP(c_List_Oset(_1660124), _1660126)), hAPP(c_List_Oset(_1660124), _1660128)) = c_Orderings_Obot__class_Obot(tc_fun(_1660124, tc_HOL_Obool))], (28366 ^ _779854) ^ [_1292683, _1292685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292683)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1292683), _1292685)))], (742 ^ _779854) ^ [_791037, _791039, _791041, _791043] : [-(c_Predicate_Oreflp(_791041, _791037)), c_Predicate_Oreflp(_791043, _791039), _791043 = _791041, _791039 = _791037], (42831 ^ _779854) ^ [_1630979, _1630981, _1630983] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1630979), _1630981)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1630979)), hAPP(c_Set_OCollect(tc_List_Olist(_1630979)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1630979), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1630979)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1630979), tc_fun(_1630979, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1630979, tc_HOL_Obool), tc_fun(tc_fun(_1630979, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1630979)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1630979, tc_HOL_Obool))), c_List_Oset(_1630979))), _1630981))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1630979), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1630979)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1630979)))), _1630983))))))], (30414 ^ _779854) ^ [_1329013] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329013, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1329013)], (33256 ^ _779854) ^ [_1383254, _1383256, _1383258, _1383260, _1383262, _1383264] : [class_Groups_Ocomm__monoid__add(_1383254), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1383256, _1383254), hAPP(hAPP(c_COMBC(_1383256, tc_fun(_1383258, tc_HOL_Obool), _1383254), hAPP(hAPP(c_COMBB(tc_fun(_1383258, _1383254), tc_fun(tc_fun(_1383258, tc_HOL_Obool), _1383254), _1383256), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1383258, _1383254)), _1383260)), _1383262)), _1383264) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1383258, _1383254), hAPP(hAPP(c_COMBC(_1383258, tc_fun(_1383256, tc_HOL_Obool), _1383254), hAPP(hAPP(c_COMBB(tc_fun(_1383256, _1383254), tc_fun(tc_fun(_1383256, tc_HOL_Obool), _1383254), _1383258), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1383256, _1383254)), hAPP(c_COMBC(_1383256, _1383258, _1383254), _1383260))), _1383264)), _1383262))], (44622 ^ _779854) ^ [_1672517, _1672519, _1672521, _1672523] : [class_Groups_Osemigroup__add(_1672517), -(hAPP(c_List_Ofoldl(_1672517, _1672517, c_Groups_Oplus__class_Oplus(_1672517), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672517), _1672519), _1672521)), _1672523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672517), _1672519), hAPP(c_List_Ofoldl(_1672517, _1672517, c_Groups_Oplus__class_Oplus(_1672517), _1672521), _1672523)))], (51365 ^ _779854) ^ [_1820215] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820215), _1820215)))], (17593 ^ _779854) ^ [_1098484, _1098486, _1098488, _1098490, _1098492] : [c_Finite__Set_Ofun__left__comm(_1098484, _1098486, _1098488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098484), _1098490)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1098484, _1098486, _1098488, _1098492, _1098490), hAPP(hAPP(c_Finite__Set_Ofold(_1098484, _1098486, _1098488), _1098492), _1098490))))], (7718 ^ _779854) ^ [_908193, _908195] : [class_Lattices_Oboolean__algebra(_908193), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908193), hAPP(c_Groups_Ouminus__class_Ouminus(_908193), _908195)), _908195) = c_Orderings_Otop__class_Otop(_908193))], (36942 ^ _779854) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (14189 ^ _779854) ^ [_1030281, _1030283, _1030285, _1030287] : [c_Fun_Oinj__on(_1030281, _1030283, _1030285, _1030287), -(c_Fun_Oinj__on(_1030283, _1030281, c_Fun_Othe__inv__into(_1030281, _1030283, _1030287, _1030285), hAPP(c_Set_Oimage(_1030281, _1030283, _1030285), _1030287)))], (6419 ^ _779854) ^ [_882203] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_882203, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_882203, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_882203, tc_HOL_Obool)))], (13999 ^ _779854) ^ [_1026585, _1026587] : [class_Lattices_Olattice(_1026585), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026585), _1026587)), -(_1026587 = c_Orderings_Obot__class_Obot(tc_fun(_1026585, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1026585), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1026585), 14012 ^ [_1026585, _1026587]), 14013 ^ [_1026585, _1026587])), hAPP(hAPP(c_Set_Oinsert(_1026585), 14012 ^ [_1026585, _1026587]), hAPP(hAPP(c_Set_Oinsert(_1026585), 14013 ^ [_1026585, _1026587]), c_Orderings_Obot__class_Obot(tc_fun(_1026585, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1026585), c_Big__Operators_Olattice__class_OInf__fin(_1026585, _1026587)), _1026587)))], (43434 ^ _779854) ^ [_1645690, _1645692] : [-(hAPP(hAPP(c_List_Otake(_1645690), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1645692) = c_List_Olist_ONil(_1645690))], (42107 ^ _779854) ^ [_1610303, _1610305, _1610307, _1610309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610303)), _1610305)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610303)), _1610307))), _1610305 = hAPP(hAPP(c_List_Olist_OCons(_1610303), _1610309), _1610307)], (23852 ^ _779854) ^ [_1212376, _1212378, _1212380, _1212382] : [class_Fields_Ofield(_1212376), -(_1212378 = c_Groups_Ozero__class_Ozero(_1212376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212380), _1212382)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1212376), _1212378), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212382), _1212380)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212376), hAPP(hAPP(c_Power_Opower__class_Opower(_1212376), _1212378), _1212382)), hAPP(hAPP(c_Power_Opower__class_Opower(_1212376), _1212378), _1212380)))], (46876 ^ _779854) ^ [_1722841, _1722843, _1722845] : [class_Orderings_Olinorder(_1722841), c_List_Olinorder__class_Osorted(_1722841, _1722843), -(c_List_Olinorder__class_Osorted(_1722841, c_List_Oremove1(_1722841, _1722845, _1722843)))], (46557 ^ _779854) ^ [_1715549, _1715551] : [-(c_List_Oconcat(tc_List_Olist(_1715549), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715549), tc_List_Olist(tc_List_Olist(_1715549))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1715549)), _1715549, c_List_Olist_ONil(tc_List_Olist(_1715549)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1715549), tc_List_Olist(tc_List_Olist(_1715549))), _1715549), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715549), tc_List_Olist(tc_List_Olist(_1715549)), tc_List_Olist(tc_List_Olist(_1715549))), c_List_Olist_OCons(tc_List_Olist(_1715549))), c_List_Olist_ONil(tc_List_Olist(_1715549)))))), _1715551)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715549), tc_List_Olist(_1715549)), c_List_Otl(_1715549)), hAPP(c_List_Ofilter(tc_List_Olist(_1715549), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1715549)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715549), tc_List_Olist(_1715549), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1715549)))), _1715551)))], (29589 ^ _779854) ^ [_1313504] : [-(c_Int_Osucc(c_Int_OBit0(_1313504)) = c_Int_OBit1(_1313504))], (48916 ^ _779854) ^ [_1766405, _1766407, _1766409] : [-(_1766405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1766407), c_List_Oreplicate(_1766407, _1766405, _1766409)) = c_List_Oreplicate(_1766407, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1766405), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1766409))], (46218 ^ _779854) ^ [_1707297, _1707299, _1707301] : [-(hBOOL(hAPP(hAPP(c_member(_1707297), _1707299), hAPP(c_List_Oset(_1707297), _1707301)))), -(c_List_Oremdups(_1707297, hAPP(hAPP(c_List_Olist_OCons(_1707297), _1707299), _1707301)) = hAPP(hAPP(c_List_Olist_OCons(_1707297), _1707299), c_List_Oremdups(_1707297, _1707301)))], (33669 ^ _779854) ^ [_1398587, _1398589] : [-(hAPP(c_Set_Oimage(_1398587, _1398587, c_COMBI(_1398587)), _1398589) = _1398589)], (43879 ^ _779854) ^ [_1655401, _1655403, _1655405, _1655407] : [hAPP(hAPP(c_List_Oappend(_1655401), _1655403), _1655405) = hAPP(hAPP(c_List_Oappend(_1655401), _1655407), _1655405), -(_1655403 = _1655407)], (35762 ^ _779854) ^ [_1445642, _1445644] : [-(_1445642 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445644, _1445642), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1445644), _1445642)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1445644, _1445642)))))], (42470 ^ _779854) ^ [_1621704, _1621706, _1621708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621704, tc_HOL_Obool)), _1621706), _1621708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1621704), tc_HOL_Obool)), c_List_Olists(_1621704, _1621706)), c_List_Olists(_1621704, _1621708))))], (24102 ^ _779854) ^ [_1217001, _1217003] : [class_Power_Opower(_1217001), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217001), _1217003), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1217001))], (46619 ^ _779854) ^ [_1718011, _1718013] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1718011, _1718013)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1718011), _1718013))], (16864 ^ _779854) ^ [_1083887, _1083889, _1083891, _1083893, _1083895] : [class_Groups_Ocomm__monoid__mult(_1083887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083889), _1083891)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083889), _1083893)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083887), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083889, _1083887), _1083895), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083889, tc_HOL_Obool)), _1083891), _1083893))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083889, _1083887), _1083895), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1083889, tc_HOL_Obool)), _1083891), _1083893))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083887), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083889, _1083887), _1083895), _1083891)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083889, _1083887), _1083895), _1083893)))], (33585 ^ _779854) ^ [_1396117, _1396119, _1396121, _1396123, _1396125] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396117, tc_HOL_Obool)), _1396119), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396121, tc_fun(_1396117, tc_HOL_Obool)), _1396123), _1396125)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396121, tc_fun(_1396117, tc_HOL_Obool)), _1396123), hAPP(hAPP(c_COMBB(tc_fun(_1396117, tc_HOL_Obool), tc_fun(_1396117, tc_HOL_Obool), _1396121), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396117, tc_HOL_Obool)), _1396119)), _1396125)))], (26615 ^ _779854) ^ [_1263531, _1263533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263533)), -(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), _1263531), _1263533))))], (51481 ^ _779854) ^ [_1822316, _1822318, _1822320] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822316), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1822318), _1822320))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822316), _1822318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1822320), _1822318)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822316), _1822320)))], (49637 ^ _779854) ^ [_1782182, _1782184] : [-(hBOOL(hAPP(_1782184, 49644 ^ [_1782182, _1782184]))), 49638 ^ _779854 : [(49639 ^ _779854) ^ [_1782243] : [hBOOL(hAPP(hAPP(c_member(_1782182), _1782243), c_Orderings_Otop__class_Otop(tc_fun(_1782182, tc_HOL_Obool)))), hBOOL(hAPP(_1782184, _1782243))]]], (48101 ^ _779854) ^ [_1748255, _1748257] : [class_Enum_Oenum(_1748255), 48104 ^ _779854 : [(48111 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1748255), _1748257)), -(hBOOL(hAPP(_1748257, 48114 ^ [_1748255, _1748257])))], (48105 ^ _779854) ^ [] : [48106 ^ _779854 : [(48107 ^ _779854) ^ [_1748357] : [hBOOL(hAPP(_1748257, _1748357))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1748255), _1748257)))]]], (41360 ^ _779854) ^ [_1590509] : [-(c_Relation_OId(_1590509) = hAPP(c_Set_OCollect(tc_prod(_1590509, _1590509)), hAPP(hAPP(c_COMBB(tc_fun(_1590509, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1590509, _1590509)), c_HOL_OEx(_1590509)), hAPP(hAPP(c_COMBC(tc_prod(_1590509, _1590509), tc_fun(_1590509, tc_prod(_1590509, _1590509)), tc_fun(_1590509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1590509, _1590509), tc_HOL_Obool), tc_fun(tc_fun(_1590509, tc_prod(_1590509, _1590509)), tc_fun(_1590509, tc_HOL_Obool)), tc_prod(_1590509, _1590509)), c_COMBB(tc_prod(_1590509, _1590509), tc_HOL_Obool, _1590509)), c_fequal)), hAPP(hAPP(c_COMBS(_1590509, _1590509, tc_prod(_1590509, _1590509)), c_Product__Type_OPair(_1590509, _1590509)), c_COMBI(_1590509))))))], (48561 ^ _779854) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (25679 ^ _779854) ^ [_1246696] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246696) = _1246696)], (29403 ^ _779854) ^ [_1310293, _1310295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1310293)), c_Int_OBit0(_1310295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310293), _1310295)))], (52391 ^ _779854) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (44614 ^ _779854) ^ [_1672363, _1672365, _1672367, _1672369] : [-(hAPP(c_List_Ofoldl(_1672363, _1672365, _1672367, _1672369), c_List_Olist_ONil(_1672365)) = _1672369)], (25681 ^ _779854) ^ [_1246722] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246722)), _1246722) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31210 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (40215 ^ _779854) ^ [_1562887, _1562889] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562887, _1562887)), _1562889)), c_Wellfounded_Oacyclic(_1562887, _1562889), -(c_Wellfounded_Owf(_1562887, _1562889))], (5914 ^ _779854) ^ [_873484, _873486, _873488, _873490] : [class_Orderings_Oorder(_873484), _873486 = _873488, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873484), _873490), _873488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873484), _873490), _873486)))], (15930 ^ _779854) ^ [_1065564, _1065566, _1065568, _1065570] : [class_Rings_Ocomm__semiring__1(_1065564), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065564), _1065566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065564), _1065568), _1065570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065564), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065564), _1065566), _1065568)), _1065570))], (23764 ^ _779854) ^ [_1210678, _1210680, _1210682, _1210684] : [class_Rings_Ocomm__semiring__1(_1210678), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210678), _1210680), _1210682)), _1210684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210678), hAPP(hAPP(c_Power_Opower__class_Opower(_1210678), _1210680), _1210684)), hAPP(hAPP(c_Power_Opower__class_Opower(_1210678), _1210682), _1210684)))], (38967 ^ _779854) ^ [_1524151, _1524153, _1524155, _1524157, _1524159] : [class_Groups_Ocomm__monoid__add(_1524151), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524153), _1524155)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524153, _1524151), _1524157), hAPP(c_Set_OCollect(_1524153), hAPP(hAPP(c_COMBS(_1524153, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524153), c_fconj), hAPP(hAPP(c_COMBC(_1524153, tc_fun(_1524153, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524153)), _1524155))), hAPP(hAPP(c_COMBC(_1524153, tc_fun(_1524153, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524153)), _1524159)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524153, _1524151), hAPP(hAPP(c_COMBC(_1524153, _1524151, _1524151), hAPP(hAPP(c_COMBS(_1524153, _1524151, tc_fun(_1524151, _1524151)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1524151, tc_fun(_1524151, _1524151)), _1524153), c_If(_1524151)), hAPP(hAPP(c_COMBC(_1524153, tc_fun(_1524153, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524153)), _1524159))), _1524157)), c_Groups_Ozero__class_Ozero(_1524151))), _1524155))], (37267 ^ _779854) ^ [_1481080, _1481082, _1481084] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1481080), _1481082)), c_Fun_Oinj__on(_1481080, tc_fun(tc_fun(_1481080, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1481080, tc_fun(tc_prod(_1481080, _1481080), tc_HOL_Obool), tc_fun(tc_fun(_1481080, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481080, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1481080, _1481080), tc_HOL_Obool), tc_fun(tc_fun(_1481080, tc_HOL_Obool), tc_HOL_Obool)), _1481080), c_Equiv__Relations_Oquotient(_1481080)), hAPP(hAPP(c_COMBC(_1481080, tc_fun(_1481080, tc_HOL_Obool), tc_fun(_1481080, tc_HOL_Obool)), c_Set_Oinsert(_1481080)), c_Orderings_Obot__class_Obot(tc_fun(_1481080, tc_HOL_Obool))))), _1481084), _1481082), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1481080, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481080), _1481082), _1481084)) = hAPP(c_Finite__Set_Ocard(_1481080), _1481082))], (45396 ^ _779854) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (21392 ^ _779854) ^ [_1165355, _1165357] : [class_Rings_Olinordered__idom(_1165355), 21395 ^ _779854 : [(21402 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165355), _1165357), c_Groups_Ozero__class_Ozero(_1165355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165355), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165355), _1165357), _1165357)), c_Groups_Ozero__class_Ozero(_1165355))))], (21396 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165355), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165355), _1165357), _1165357)), c_Groups_Ozero__class_Ozero(_1165355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165355), _1165357), c_Groups_Ozero__class_Ozero(_1165355))))]]], (43670 ^ _779854) ^ [_1650290, _1650292, _1650294] : [-(c_List_Olistset(_1650290, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1650290, tc_HOL_Obool)), _1650292), _1650294)) = c_List_Oset__Cons(_1650290, _1650292, c_List_Olistset(_1650290, _1650294)))], (1450 ^ _779854) ^ [_800931, _800933] : [-(class_Lattices_Olattice(_800931)), _800933 = _800931, class_Lattices_Olattice(_800933)], (9444 ^ _779854) ^ [_937712, _937714] : [class_Groups_Oordered__ab__group__add(_937712), -(hAPP(c_Set_Oimage(_937712, _937712, c_Groups_Ouminus__class_Ouminus(_937712)), hAPP(c_SetInterval_Oord__class_OlessThan(_937712), _937714)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_937712), hAPP(c_Groups_Ouminus__class_Ouminus(_937712), _937714)))], (4932 ^ _779854) ^ [_855167, _855169, _855171, _855173, _855175, _855177] : [-(c_Finite__Set_Ofold__image(_855177, _855173, _855169) = c_Finite__Set_Ofold__image(_855175, _855171, _855167)), _855177 = _855175, _855173 = _855171, _855169 = _855167], (33018 ^ _779854) ^ [_1377543, _1377545, _1377547, _1377549, _1377551] : [_1377543 = c_Orderings_Obot__class_Obot(tc_fun(_1377545, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377545, tc_fun(_1377547, tc_HOL_Obool)), _1377543), hAPP(hAPP(c_COMBB(tc_fun(_1377547, tc_HOL_Obool), tc_fun(_1377547, tc_HOL_Obool), _1377545), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377547, tc_HOL_Obool)), _1377549)), _1377551)) = c_Orderings_Otop__class_Otop(tc_fun(_1377547, tc_HOL_Obool)))], (18497 ^ _779854) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47452 ^ _779854) ^ [_1733925, _1733927, _1733929, _1733931, _1733933] : [-(hAPP(c_List_Ofoldl(_1733925, _1733927, _1733929, _1733931), _1733933) = c_List_Ofoldr(_1733927, _1733925, hAPP(c_COMBC(_1733925, _1733927, _1733925), _1733929), hAPP(c_List_Orev(_1733927), _1733933), _1733931))], (46248 ^ _779854) ^ [_1707918, _1707920, _1707922] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1707918), tc_List_Olist(_1707918), c_List_Oappend(_1707918), _1707920), _1707922) = hAPP(hAPP(c_List_Oappend(_1707918), _1707920), c_List_Oconcat(_1707918, _1707922)))], (38296 ^ _779854) ^ [_1505872, _1505874, _1505876] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1505872, _1505874), c_Orderings_Obot__class_Obot(tc_fun(_1505872, tc_HOL_Obool))), _1505876) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1505872, _1505874), tc_HOL_Obool)))], (25569 ^ _779854) ^ [_1244926, _1244928] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244926), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1244928) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1244926, _1244928))], (52281 ^ _779854) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (45148 ^ _779854) ^ [_1683548, _1683550, _1683552, _1683554, _1683556] : [class_Groups_Oab__group__add(_1683548), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1683548), hAPP(hAPP(c_List_Omap(_1683550, _1683548), hAPP(hAPP(c_COMBS(_1683550, _1683548, _1683548), hAPP(hAPP(c_COMBB(_1683548, tc_fun(_1683548, _1683548), _1683550), c_Groups_Ominus__class_Ominus(_1683548)), _1683552)), _1683554)), _1683556)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1683548), hAPP(c_List_Omonoid__add__class_Olistsum(_1683548), hAPP(hAPP(c_List_Omap(_1683550, _1683548), _1683552), _1683556))), hAPP(c_List_Omonoid__add__class_Olistsum(_1683548), hAPP(hAPP(c_List_Omap(_1683550, _1683548), _1683554), _1683556))))], (34015 ^ _779854) ^ [_1408218] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1408218)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408218)), 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))))], (51030 ^ _779854) ^ [_1811536, _1811538] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1811536), _1811538)), -(c_Fun_Obij__betw(_1811536, tc_Nat_Onat, 51033 ^ [_1811536, _1811538], _1811538, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1811536), _1811538))))], (35088 ^ _779854) ^ [_1432564, _1432566] : [c_Nitpick_Orefl_H(_1432564, _1432566), 35091 ^ _779854 : [(35092 ^ _779854) ^ [_1432642] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1432564, _1432564)), hAPP(hAPP(c_Product__Type_OPair(_1432564, _1432564), _1432642), _1432642)), _1432566)))]]], (39723 ^ _779854) ^ [_1550355, _1550357, _1550359] : [c_Wellfounded_Owf(_1550355, _1550357), -(c_Wellfounded_Owf(_1550355, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1550355, _1550355), tc_HOL_Obool)), _1550357), _1550359)))], (39313 ^ _779854) ^ [_1538814, _1538816, _1538818, _1538820, _1538822, _1538824, _1538826] : [hAPP(c_Fun_Ocomp(_1538814, _1538816, _1538818, _1538820), _1538822) = hAPP(c_Fun_Ocomp(_1538816, _1538816, _1538818, c_Fun_Oid(_1538816)), _1538824), -(hAPP(_1538820, hAPP(_1538822, _1538826)) = hAPP(_1538824, _1538826))], (41002 ^ _779854) ^ [_1581149, _1581151, _1581153, _1581155, _1581157] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581149, _1581149)), hAPP(hAPP(c_Product__Type_OPair(_1581149, _1581149), _1581151), _1581153)), _1581155)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1581149, _1581149)), hAPP(hAPP(c_Product__Type_OPair(_1581149, _1581149), _1581153), _1581157)), _1581155)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581149, _1581149)), hAPP(hAPP(c_Product__Type_OPair(_1581149, _1581149), _1581151), _1581157)), c_Transitive__Closure_Otrancl(_1581149, _1581155))))], (4226 ^ _779854) ^ [_844058, _844060] : [_844060 = _844058, -(c_List_Ohd(_844060) = c_List_Ohd(_844058))], (49416 ^ _779854) ^ [_1776929, _1776931, _1776933] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1776929) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1776929, _1776931, _1776933)], (34607 ^ _779854) ^ [_1422344, _1422346, _1422348, _1422350, _1422352, _1422354] : [class_Groups_Ocomm__monoid__mult(_1422344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422346), _1422348)), 34614 ^ _779854 : [(34621 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1422346), _1422350), _1422348))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422346, _1422344), hAPP(hAPP(c_COMBC(_1422346, _1422344, _1422344), hAPP(hAPP(c_COMBS(_1422346, _1422344, tc_fun(_1422344, _1422344)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1422344, tc_fun(_1422344, _1422344)), _1422346), c_If(_1422344)), hAPP(hAPP(c_COMBC(_1422346, _1422346, tc_HOL_Obool), c_fequal), _1422350))), _1422352)), _1422354)), _1422348) = hAPP(hAPP(c_Power_Opower__class_Opower(_1422344), _1422354), hAPP(c_Finite__Set_Ocard(_1422346), _1422348)))], (34615 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1422346), _1422350), _1422348)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422346, _1422344), hAPP(hAPP(c_COMBC(_1422346, _1422344, _1422344), hAPP(hAPP(c_COMBS(_1422346, _1422344, tc_fun(_1422344, _1422344)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1422344, tc_fun(_1422344, _1422344)), _1422346), c_If(_1422344)), hAPP(hAPP(c_COMBC(_1422346, _1422346, tc_HOL_Obool), c_fequal), _1422350))), _1422352)), _1422354)), _1422348) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422344), hAPP(_1422352, _1422350)), hAPP(hAPP(c_Power_Opower__class_Opower(_1422344), _1422354), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1422346), _1422348)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (46294 ^ _779854) ^ [_1708800, _1708802] : [46296 ^ _779854 : [(46299 ^ _779854) ^ [] : [46295 ^ [_1708800, _1708802] = c_List_Olist_ONil(_1708800)], (46297 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1708800)), 46295 ^ [_1708800, _1708802]), hAPP(c_List_Oset(tc_List_Olist(_1708800)), _1708802))))]], -(c_List_Olist_ONil(_1708800) = c_List_Oconcat(_1708800, _1708802))], (27847 ^ _779854) ^ [_1283619, _1283621, _1283623] : [-(hBOOL(hAPP(_1283619, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1283621), _1283623)))), 27850 ^ _779854 : [(27853 ^ _779854) ^ [] : [hBOOL(hAPP(_1283619, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27851 ^ _779854) ^ [] : [-(_1283623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 27854 ^ _779854 : [(27859 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27857 ^ [_1283619, _1283621, _1283623]), _1283623)))], (27861 ^ _779854) ^ [] : [-(_1283621 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1283623), 27856 ^ [_1283619, _1283621, _1283623])), 27857 ^ [_1283619, _1283621, _1283623]))], (27863 ^ _779854) ^ [] : [hBOOL(hAPP(_1283619, 27856 ^ [_1283619, _1283621, _1283623]))], (27855 ^ _779854) ^ [] : [_1283623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (1320 ^ _779854) ^ [_799306, _799308] : [-(class_Groups_Oabs__if(_799306)), _799308 = _799306, class_Groups_Oabs__if(_799308)], (50754 ^ _779854) ^ [_1806192, _1806194, _1806196, _1806198] : [c_Fun_Obij__betw(_1806192, _1806194, _1806196, c_Orderings_Otop__class_Otop(tc_fun(_1806192, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1806194, tc_HOL_Obool))), 50757 ^ _779854 : [(50764 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1806194), _1806198)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1806192), hAPP(c_Set_Ovimage(_1806192, _1806194, _1806196), _1806198))))], (50758 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1806192), hAPP(c_Set_Ovimage(_1806192, _1806194, _1806196), _1806198))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1806194), _1806198)))]]], (15140 ^ _779854) ^ [_1049045, _1049047, _1049049, _1049051, _1049053] : [class_Rings_Osemiring(_1049045), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049045), _1049047), _1049049)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049045), _1049051), _1049049)), _1049053)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049045), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049045), _1049047), _1049051)), _1049049)), _1049053))], (38624 ^ _779854) ^ [_1515307, _1515309, _1515311, _1515313, _1515315, _1515317, _1515319, _1515321, _1515323] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515307, _1515309)), hAPP(hAPP(c_Product__Type_OPair(_1515307, _1515309), _1515311), _1515313)), _1515315)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515317, _1515319)), hAPP(hAPP(c_Product__Type_OPair(_1515317, _1515319), hAPP(_1515321, _1515311)), hAPP(_1515323, _1515313))), hAPP(c_Set_Oimage(tc_prod(_1515307, _1515309), tc_prod(_1515317, _1515319), c_Product__Type_Omap__pair(_1515307, _1515317, _1515309, _1515319, _1515321, _1515323)), _1515315))))], (36862 ^ _779854) ^ [_1469731, _1469733, _1469735, _1469737] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1469731), _1469733)), 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)), _1469731), _1469735)), 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)), _1469733), _1469737)), 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)), _1469733), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1469735), _1469737))), c_FunDef_Omin__weak)))], (32085 ^ _779854) ^ [_1357101, _1357103] : [class_Groups_Oordered__ab__group__add__abs(_1357101), 32088 ^ _779854 : [(32095 ^ _779854) ^ [] : [_1357103 = c_Groups_Ozero__class_Ozero(_1357101), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357101), hAPP(c_Groups_Oabs__class_Oabs(_1357101), _1357103)), c_Groups_Ozero__class_Ozero(_1357101))))], (32089 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357101), hAPP(c_Groups_Oabs__class_Oabs(_1357101), _1357103)), c_Groups_Ozero__class_Ozero(_1357101))), -(_1357103 = c_Groups_Ozero__class_Ozero(_1357101))]]], (11063 ^ _779854) ^ [_970167, _970169, _970171] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_970167, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970167, tc_HOL_Obool)), _970169), _970171)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_970167, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_970167, tc_HOL_Obool)), _970169)), _970171))], (10941 ^ _779854) ^ [_967306, _967308, _967310, _967312, _967314] : [c_Fun_Oinj__on(_967306, _967308, _967310, _967312), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_967306, tc_HOL_Obool)), _967314), _967312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_967308, tc_HOL_Obool)), hAPP(c_Set_Oimage(_967306, _967308, _967310), _967314)), hAPP(c_Set_Oimage(_967306, _967308, _967310), _967312))))], (50046 ^ _779854) ^ [_1791761, _1791763] : [c_Relation_Osym(_1791761, _1791763), -(c_Relation_Osym(_1791761, c_Transitive__Closure_Ortrancl(_1791761, _1791763)))], (9384 ^ _779854) ^ [_936535, _936537, _936539] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936535, tc_HOL_Obool)), _936537), _936539) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_936535, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_936535, tc_HOL_Obool)), _936537), hAPP(hAPP(c_Set_Oinsert(tc_fun(_936535, tc_HOL_Obool)), _936539), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_936535, tc_HOL_Obool), tc_HOL_Obool))))))], (50906 ^ _779854) ^ [_1809261, _1809263, _1809265, _1809267, _1809269] : [c_Fun_Obij__betw(_1809261, _1809263, _1809265, _1809267, _1809269), -(c_Fun_Obij__betw(_1809263, _1809261, c_Fun_Othe__inv__into(_1809261, _1809263, _1809267, _1809265), _1809269, _1809267))], (35866 ^ _779854) ^ [_1447787, _1447789, _1447791] : [35868 ^ _779854 : [(35871 ^ _779854) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1447791, 35867 ^ [_1447787, _1447789, _1447791]))], (35869 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447787), 35867 ^ [_1447787, _1447789, _1447791]), _1447789)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1447787, tc_Int_Oint), _1447791), _1447789) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1447787, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1447787), c_Int_Onat), _1447791)), _1447789)))], (22723 ^ _779854) ^ [_1190388, _1190390, _1190392, _1190394] : [class_Fields_Olinordered__field(_1190388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190388), _1190390), _1190392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190388), _1190394), c_Groups_Ozero__class_Ozero(_1190388))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190388), c_Groups_Ozero__class_Ozero(_1190388)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190388), _1190390), _1190392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190388), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1190388), _1190394), _1190390)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1190388), _1190394), _1190392))))], (30333 ^ _779854) ^ [_1327640, _1327642, _1327644, _1327646] : [class_Divides_Osemiring__div(_1327640), -(c_Divides_Odiv__class_Omod(_1327640, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327640), _1327642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327640), _1327644), _1327646)), _1327646) = c_Divides_Odiv__class_Omod(_1327640, _1327642, _1327646))], (52365 ^ _779854) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (27979 ^ _779854) ^ [_1285949, _1285951] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1285949, _1285951)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1285951), _1285949)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (33935 ^ _779854) ^ [_1406609, _1406611, _1406613, _1406615, _1406617] : [class_Complete__Lattice_Ocomplete__lattice(_1406609), hBOOL(hAPP(hAPP(c_member(_1406611), _1406613), _1406615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1406611, _1406609), _1406615), _1406617)), hAPP(_1406617, _1406613))))], (24801 ^ _779854) ^ [_1230398, _1230400, _1230402, _1230404] : [class_Fields_Ofield__inverse__zero(_1230398), class_Int_Onumber(_1230398), 24808 ^ _779854 : [(24809 ^ _779854) ^ [] : [_1230400 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1230398), _1230402), hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404)), 24812 ^ _779854 : [(24819 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404) = c_Groups_Ozero__class_Ozero(_1230398), -(_1230400 = c_Groups_Ozero__class_Ozero(_1230398))], (24813 ^ _779854) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404) = c_Groups_Ozero__class_Ozero(_1230398)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230398), _1230400), hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404)) = _1230402)]]], (24825 ^ _779854) ^ [] : [-(_1230400 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1230398), _1230402), hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404))), 24828 ^ _779854 : [(24831 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230398), _1230400), hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404)) = _1230402], (24829 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404) = c_Groups_Ozero__class_Ozero(_1230398)]], 24832 ^ _779854 : [(24835 ^ _779854) ^ [] : [_1230400 = c_Groups_Ozero__class_Ozero(_1230398)], (24833 ^ _779854) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1230398), _1230404) = c_Groups_Ozero__class_Ozero(_1230398))]]]]], (19657 ^ _779854) ^ [_1134380, _1134382, _1134384] : [class_Rings_Olinordered__semiring__strict(_1134380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134380), c_Groups_Ozero__class_Ozero(_1134380)), _1134382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134380), _1134384), c_Groups_Ozero__class_Ozero(_1134380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134380), _1134384), _1134382)), c_Groups_Ozero__class_Ozero(_1134380))))], (39419 ^ _779854) ^ [_1541594, _1541596, _1541598, _1541600] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541594, _1541596, _1541598), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1541594, _1541596), tc_HOL_Obool))), _1541600) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1541594, _1541598), tc_HOL_Obool)))], (35103 ^ _779854) ^ [_1432912, _1432914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1432912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1432912), _1432914)), -(c_Divides_Odivmod__nat(_1432914, _1432912) = 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), _1432914), _1432912)), _1432912))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1432914), _1432912), _1432912)))], (684 ^ _779854) ^ [_790146, _790148, _790150, _790152, _790154, _790156, _790158, _790160] : [-(c_Nat__Transfer_Otransfer__morphism(_790158, _790154, _790150, _790146)), c_Nat__Transfer_Otransfer__morphism(_790160, _790156, _790152, _790148), _790160 = _790158, _790156 = _790154, _790152 = _790150, _790148 = _790146], (9388 ^ _779854) ^ [_936666, _936668, _936670] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936666, tc_HOL_Obool)), _936668), _936670) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_936666, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_936666, tc_HOL_Obool)), _936668), hAPP(hAPP(c_Set_Oinsert(tc_fun(_936666, tc_HOL_Obool)), _936670), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_936666, tc_HOL_Obool), tc_HOL_Obool))))))], (7654 ^ _779854) ^ [_906822, _906824] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906822, tc_HOL_Obool)), _906824), c_Orderings_Otop__class_Otop(tc_fun(_906822, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_906822, tc_HOL_Obool)))], (35354 ^ _779854) ^ [_1438437, _1438439, _1438441, _1438443, _1438445, _1438447] : [-(hAPP(c_Product__Type_Oapsnd(_1438437, _1438439, _1438441, _1438443), hAPP(hAPP(c_Product__Type_OPair(_1438441, _1438437), _1438445), _1438447)) = hAPP(hAPP(c_Product__Type_OPair(_1438441, _1438439), _1438445), hAPP(_1438443, _1438447)))], (30041 ^ _779854) ^ [_1321696, _1321698] : [-(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), _1321696)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1321698))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1321696))) = 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), _1321698)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1321696)))], (26791 ^ _779854) ^ [_1266124, _1266126] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1266124), _1266126) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26792 ^ _779854 : [(26801 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1266124), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266126), _1266124))], (26795 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266124), _1266126))], (26793 ^ _779854) ^ [] : [_1266126 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (18657 ^ _779854) ^ [_1117366, _1117368, _1117370] : [class_Groups_Oab__group__add(_1117366), 18660 ^ _779854 : [(18667 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117366), _1117368), _1117370) = c_Groups_Ozero__class_Ozero(_1117366), -(_1117368 = _1117370)], (18661 ^ _779854) ^ [] : [_1117368 = _1117370, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117366), _1117368), _1117370) = c_Groups_Ozero__class_Ozero(_1117366))]]], (31084 ^ _779854) ^ [_1340673, _1340675] : [31085 ^ _779854 : [(31086 ^ _779854) ^ [_1340722] : [_1340673 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1340675), _1340722)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340673, _1340675) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43514 ^ _779854) ^ [_1647118, _1647120, _1647122, _1647124] : [-(_1647118 = _1647120), 43517 ^ _779854 : [(43524 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1647122), _1647118), hAPP(c_List_Oset(_1647122), _1647124))), -(hBOOL(hAPP(hAPP(c_member(_1647122), _1647118), hAPP(c_List_Oset(_1647122), c_List_Oremove1(_1647122, _1647120, _1647124)))))], (43518 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1647122), _1647118), hAPP(c_List_Oset(_1647122), c_List_Oremove1(_1647122, _1647120, _1647124)))), -(hBOOL(hAPP(hAPP(c_member(_1647122), _1647118), hAPP(c_List_Oset(_1647122), _1647124))))]]], (31484 ^ _779854) ^ [_1347358, _1347360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1347358), _1347360)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1347358), _1347360) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (51405 ^ _779854) ^ [_1820878, _1820880, _1820882, _1820884] : [class_Rings_Ocomm__semiring__1(_1820878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1820880), _1820882)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820878), hAPP(hAPP(c_Power_Opower__class_Opower(_1820878), _1820884), _1820880)), hAPP(hAPP(c_Power_Opower__class_Opower(_1820878), _1820884), _1820882))))], (39997 ^ _779854) ^ [_1556843, _1556845] : [-(c_List_Olex(_1556843, _1556845) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1556843), tc_List_Olist(_1556843)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1556843, _1556845)))], (33891 ^ _779854) ^ [_1404522, _1404524, _1404526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404522, tc_HOL_Obool)), _1404524), _1404526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404522, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1404522, tc_fun(_1404522, tc_HOL_Obool), tc_HOL_Obool), c_member(_1404522)), _1404524)), hAPP(hAPP(c_COMBC(_1404522, tc_fun(_1404522, tc_HOL_Obool), tc_HOL_Obool), c_member(_1404522)), _1404526))))], (38498 ^ _779854) ^ [_1511707, _1511709, _1511711, _1511713] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1511707, _1511709), _1511711), _1511713) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511707, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool)), _1511711), hAPP(hAPP(c_COMBS(_1511707, tc_fun(_1511709, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool)), tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511709, tc_HOL_Obool), tc_fun(tc_fun(_1511709, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool)), tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool)), _1511707), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511709, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool))), _1511713)), hAPP(hAPP(c_COMBC(_1511707, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool), tc_fun(_1511709, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511709, tc_fun(tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool), tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool), tc_fun(_1511709, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool))), _1511707), c_COMBC(_1511709, tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool), tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511709, tc_prod(_1511707, _1511709)), tc_fun(_1511709, tc_fun(tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool), tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool))), _1511707), hAPP(c_COMBB(tc_prod(_1511707, _1511709), tc_fun(tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool), tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool)), _1511709), c_Set_Oinsert(tc_prod(_1511707, _1511709)))), c_Product__Type_OPair(_1511707, _1511709)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1511707, _1511709), tc_HOL_Obool))))))], (22971 ^ _779854) ^ [_1195074, _1195076, _1195078, _1195080] : [class_Fields_Ofield__inverse__zero(_1195074), -(_1195076 = c_Groups_Ozero__class_Ozero(_1195074)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195074), _1195078), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195074), _1195080), _1195076)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195074), _1195080), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195074), _1195078), _1195076))), _1195076))], (7459 ^ _779854) ^ [_902776, _902778] : [class_Lattices_Obounded__lattice__bot(_902776), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_902776), c_Orderings_Obot__class_Obot(_902776)), _902778) = c_Orderings_Obot__class_Obot(_902776))], (29553 ^ _779854) ^ [_1312955] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1312955)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312955))))], (39106 ^ _779854) ^ [_1529435, _1529437, _1529439] : [class_Groups_Olinordered__ab__semigroup__add(_1529435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529435), _1529437)), -(_1529437 = c_Orderings_Obot__class_Obot(tc_fun(_1529435, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1529435), _1529439), c_Big__Operators_Olinorder__class_OMin(_1529435, _1529437)) = c_Big__Operators_Olinorder__class_OMin(_1529435, hAPP(c_Set_OCollect(_1529435), hAPP(hAPP(c_COMBB(tc_fun(_1529435, tc_HOL_Obool), tc_HOL_Obool, _1529435), c_HOL_OEx(_1529435)), hAPP(hAPP(c_COMBC(_1529435, tc_fun(_1529435, tc_HOL_Obool), tc_fun(_1529435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529435, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1529435, tc_HOL_Obool), tc_fun(_1529435, tc_HOL_Obool)), _1529435), c_COMBS(_1529435, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529435, tc_HOL_Obool), tc_fun(_1529435, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1529435), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529435), c_fconj)), hAPP(hAPP(c_COMBC(_1529435, tc_fun(_1529435, _1529435), tc_fun(_1529435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529435, tc_HOL_Obool), tc_fun(tc_fun(_1529435, _1529435), tc_fun(_1529435, tc_HOL_Obool)), _1529435), c_COMBB(_1529435, tc_HOL_Obool, _1529435)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1529435), _1529439))))), hAPP(hAPP(c_COMBC(_1529435, tc_fun(_1529435, tc_HOL_Obool), tc_HOL_Obool), c_member(_1529435)), _1529437))))))], (26193 ^ _779854) ^ [_1255925, _1255927, _1255929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255925)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1255927), _1255929)), 26200 ^ _779854 : [(26201 ^ _779854) ^ [_1256121] : [26203 ^ _779854 : [(26209 ^ _779854) ^ [] : [-(_1256121 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26205 ^ [_1255925, _1255927, _1255929, _1256121]), 26202 ^ [_1255925, _1255927, _1255929, _1256121]))], (26207 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26205 ^ [_1255925, _1255927, _1255929, _1256121]), _1255929)))], (26204 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26202 ^ [_1255925, _1255927, _1255929, _1256121]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1255925))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255927), _1256121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255927), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1256121), _1255925))))]]], (50646 ^ _779854) ^ [_1803783, _1803785, _1803787, _1803789] : [c_Fun_Obij__betw(_1803783, _1803785, _1803787, c_Orderings_Otop__class_Otop(tc_fun(_1803783, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1803785, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1803783, _1803785, _1803787), hAPP(c_Set_OCollect(_1803783), _1803789)) = hAPP(c_Set_OCollect(_1803785), hAPP(hAPP(c_COMBB(_1803783, tc_HOL_Obool, _1803785), _1803789), c_Hilbert__Choice_Oinv__into(_1803783, _1803785, c_Orderings_Otop__class_Otop(tc_fun(_1803783, tc_HOL_Obool)), _1803787))))], (1076 ^ _779854) ^ [_796092, _796094, _796096, _796098, _796100, _796102] : [-(c_List_Oall__interval__nat(_796100, _796096, _796092)), c_List_Oall__interval__nat(_796102, _796098, _796094), _796102 = _796100, _796098 = _796096, _796094 = _796092], (46504 ^ _779854) ^ [_1714147, _1714149] : [-(c_List_OremoveAll(_1714147, _1714149) = c_List_Ofilter(_1714147, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1714147), c_fNot), hAPP(c_fequal, _1714149))))], (44003 ^ _779854) ^ [_1657852, _1657854, _1657856] : [-(c_List_Olist_ONil(_1657852) = hAPP(hAPP(c_List_Oappend(_1657852), _1657854), _1657856)), _1657854 = c_List_Olist_ONil(_1657852), _1657856 = c_List_Olist_ONil(_1657852)], (37442 ^ _779854) ^ [_1485005, _1485007, _1485009, _1485011, _1485013] : [hAPP(c_Relation_OImage(_1485005, _1485005, _1485007), hAPP(hAPP(c_Set_Oinsert(_1485005), _1485009), c_Orderings_Obot__class_Obot(tc_fun(_1485005, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1485005, _1485005, _1485007), hAPP(hAPP(c_Set_Oinsert(_1485005), _1485011), c_Orderings_Obot__class_Obot(tc_fun(_1485005, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1485005, _1485013, _1485007), hBOOL(hAPP(hAPP(c_member(_1485005), _1485011), _1485013)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1485005, _1485005)), hAPP(hAPP(c_Product__Type_OPair(_1485005, _1485005), _1485009), _1485011)), _1485007)))], (42048 ^ _779854) ^ [_1608266, _1608268, _1608270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1608266), c_Nitpick_Oplus__frac(_1608266, _1608268, c_Nitpick_Ouminus__frac(_1608266, _1608270)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1608266, _1608268, _1608270))], (51224 ^ _779854) ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1816550, _1816552), tc_prod(_1816550, _1816552))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1816550, _1816552), tc_prod(_1816550, _1816552)), hAPP(hAPP(c_Product__Type_OPair(_1816550, _1816552), _1816554), _1816556)), hAPP(hAPP(c_Product__Type_OPair(_1816550, _1816552), _1816558), _1816560))), c_Transitive__Closure_Ortrancl(tc_prod(_1816550, _1816552), _1816562))), hBOOL(hAPP(hAPP(_1816564, _1816554), _1816556)), 51235 ^ _779854 : [(51240 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1816550, _1816552), tc_prod(_1816550, _1816552))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1816550, _1816552), tc_prod(_1816550, _1816552)), hAPP(hAPP(c_Product__Type_OPair(_1816550, _1816552), 51233 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]), 51234 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564])), hAPP(hAPP(c_Product__Type_OPair(_1816550, _1816552), 51237 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]), 51238 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]))), _1816562)))], (51242 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1816564, 51233 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]), 51234 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564])))], (51244 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1816564, 51237 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]), 51238 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]))], (51236 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1816550, _1816552), tc_prod(_1816550, _1816552))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1816550, _1816552), tc_prod(_1816550, _1816552)), hAPP(hAPP(c_Product__Type_OPair(_1816550, _1816552), _1816554), _1816556)), hAPP(hAPP(c_Product__Type_OPair(_1816550, _1816552), 51233 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]), 51234 ^ [_1816550, _1816552, _1816554, _1816556, _1816558, _1816560, _1816562, _1816564]))), c_Transitive__Closure_Ortrancl(tc_prod(_1816550, _1816552), _1816562))))]], -(hBOOL(hAPP(hAPP(_1816564, _1816558), _1816560)))], (2764 ^ _779854) ^ [_820959, _820961] : [_820961 = _820959, -(c_HOL_OAll(_820961) = c_HOL_OAll(_820959))], (45119 ^ _779854) ^ [_1682748, _1682750, _1682752, _1682754, _1682756, _1682758] : [-(hAPP(hAPP(c_List_Omap(_1682748, _1682750), _1682752), hAPP(hAPP(c_List_Olist__update(_1682748, _1682754), _1682756), _1682758)) = hAPP(hAPP(c_List_Olist__update(_1682750, hAPP(hAPP(c_List_Omap(_1682748, _1682750), _1682752), _1682754)), _1682756), hAPP(_1682752, _1682758)))], (43167 ^ _779854) ^ [_1640241, _1640243, _1640245, _1640247] : [hBOOL(hAPP(c_List_Odistinct(_1640241), _1640243)), -(hBOOL(hAPP(hAPP(c_member(_1640241), _1640245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640241, tc_HOL_Obool)), hAPP(c_List_Oset(_1640241), _1640243)), hAPP(hAPP(c_Set_Oinsert(_1640241), hAPP(hAPP(c_List_Onth(_1640241), _1640243), _1640247)), c_Orderings_Obot__class_Obot(tc_fun(_1640241, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1640241), hAPP(hAPP(c_List_Olist__update(_1640241, _1640243), _1640247), _1640245))))], (40350 ^ _779854) ^ [_1565989, _1565991] : [hBOOL(hAPP(_1565989, c_Hilbert__Choice_OEps(_1565991, _1565989))), -(hBOOL(hAPP(_1565989, 40353 ^ [_1565989, _1565991])))], (31168 ^ _779854) ^ [_1341950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1341950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1341950))))], (50122 ^ _779854) ^ [_1792960, _1792962, _1792964] : [c_Equiv__Relations_Oequiv(_1792960, _1792962, _1792964), 50125 ^ _779854 : [(50130 ^ _779854) ^ [] : [-(c_Relation_Otrans(_1792960, _1792964))], (50128 ^ _779854) ^ [] : [-(c_Relation_Osym(_1792960, _1792964))], (50126 ^ _779854) ^ [] : [-(c_Relation_Orefl__on(_1792960, _1792962, _1792964))]]], (10525 ^ _779854) ^ [_958517, _958519, _958521, _958523] : [c_Fun_Oinj__on(_958517, _958519, _958521, c_Orderings_Otop__class_Otop(tc_fun(_958517, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958519, tc_HOL_Obool)), hAPP(c_Set_Oimage(_958517, _958519, _958521), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_958517, tc_HOL_Obool)), _958523))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_958519, tc_HOL_Obool)), hAPP(c_Set_Oimage(_958517, _958519, _958521), _958523)))))], (10973 ^ _779854) ^ [_968053, _968055, _968057] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968053, tc_HOL_Obool)), _968055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968053, tc_HOL_Obool)), _968057), _968055)) = c_Orderings_Obot__class_Obot(tc_fun(_968053, tc_HOL_Obool)))], (49454 ^ _779854) ^ [_1777548, _1777550, _1777552] : [49456 ^ _779854 : [(49459 ^ _779854) ^ [] : [hBOOL(hAPP(_1777548, 49455 ^ [_1777548, _1777550, _1777552]))], (49457 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49455 ^ [_1777548, _1777550, _1777552]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1777550, _1777552))))]], -(c_List_Oall__interval__int(_1777548, _1777550, _1777552))], (29901 ^ _779854) ^ [_1318875, _1318877] : [class_Rings_Oring__1__no__zero__divisors(_1318875), 29904 ^ _779854 : [(29905 ^ _779854) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1318875), _1318877), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1318875), -(_1318877 = c_Groups_Oone__class_Oone(_1318875)), -(_1318877 = hAPP(c_Groups_Ouminus__class_Ouminus(_1318875), c_Groups_Oone__class_Oone(_1318875)))], (29915 ^ _779854) ^ [] : [29916 ^ _779854 : [(29919 ^ _779854) ^ [] : [_1318877 = hAPP(c_Groups_Ouminus__class_Ouminus(_1318875), c_Groups_Oone__class_Oone(_1318875))], (29917 ^ _779854) ^ [] : [_1318877 = c_Groups_Oone__class_Oone(_1318875)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1318875), _1318877), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1318875))]]], (11612 ^ _779854) ^ [_981166, _981168, _981170, _981172] : [_981166 = _981168, 11617 ^ _779854 : [(11620 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_981170), _981172), _981168)))], (11618 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_981170), _981172), _981166)))]], 11621 ^ _779854 : [(11624 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_981170), _981172), _981168))], (11622 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_981170), _981172), _981166))]]], (8342 ^ _779854) ^ [_919304, _919306, _919308, _919310] : [8343 ^ _779854 : [(8346 ^ _779854) ^ [] : [hBOOL(hAPP(_919308, _919310))], (8344 ^ _779854) ^ [] : [_919306 = _919310]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_919304), _919306), _919308), _919310)))], (27503 ^ _779854) ^ [_1278029, _1278031, _1278033] : [_1278029 = 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), _1278029), _1278031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1278029), _1278033)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32163 ^ _779854) ^ [_1358447, _1358449, _1358451] : [class_Groups_Oordered__ab__group__add__abs(_1358447), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358447), hAPP(c_Groups_Oabs__class_Oabs(_1358447), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358447), hAPP(c_Groups_Oabs__class_Oabs(_1358447), _1358449)), hAPP(c_Groups_Oabs__class_Oabs(_1358447), _1358451)))), hAPP(c_Groups_Oabs__class_Oabs(_1358447), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358447), _1358449), _1358451)))))], (21751 ^ _779854) ^ [_1172455, _1172457, _1172459, _1172461] : [c_Sum__Type_OPlus(_1172455, _1172457, _1172459, _1172461) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1172455, _1172457), tc_HOL_Obool)), 21754 ^ _779854 : [(21757 ^ _779854) ^ [] : [-(_1172461 = c_Orderings_Obot__class_Obot(tc_fun(_1172457, tc_HOL_Obool)))], (21755 ^ _779854) ^ [] : [-(_1172459 = c_Orderings_Obot__class_Obot(tc_fun(_1172455, tc_HOL_Obool)))]]], (41120 ^ _779854) ^ [_1584862, _1584864] : [-(c_Transitive__Closure_Ortrancl(_1584862, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1584862, _1584862), tc_HOL_Obool)), _1584864), c_Relation_OId(_1584862))) = c_Transitive__Closure_Ortrancl(_1584862, _1584864))], (34023 ^ _779854) ^ [_1408561, _1408563, _1408565, _1408567] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1408561), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408563, tc_Nat_Onat), _1408565), _1408567)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408563, _1408561), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1408561, _1408563), c_Nat_Osemiring__1__class_Oof__nat(_1408561)), _1408565)), _1408567)), class_Groups_Ocomm__monoid__mult(_1408561), class_Rings_Osemiring__1(_1408561)], (33357 ^ _779854) ^ [_1386465, _1386467, _1386469, _1386471, _1386473, _1386475] : [_1386465 = _1386467, -(hAPP(c_Fun_Ofun__upd(_1386469, _1386471, _1386473, _1386467, _1386475), _1386465) = _1386475)], (7015 ^ _779854) ^ [_894738, _894740, _894742] : [class_Lattices_Olattice(_894738), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894738), _894740), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894738), _894740), _894742)) = _894740)], (10409 ^ _779854) ^ [_956314, _956316, _956318, _956320, _956322] : [class_Orderings_Olinorder(_956314), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956314, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_956314, _956316, _956318)), c_SetInterval_Oord__class_OatLeastAtMost(_956314, _956320, _956322)) = c_SetInterval_Oord__class_OatLeastAtMost(_956314, hAPP(hAPP(c_Orderings_Oord__class_Omax(_956314), _956316), _956320), hAPP(hAPP(c_Orderings_Oord__class_Omin(_956314), _956318), _956322)))], (14746 ^ _779854) ^ [_1041257, _1041259, _1041261] : [class_Orderings_Olinorder(_1041257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041257), _1041259)), -(_1041259 = c_Orderings_Obot__class_Obot(tc_fun(_1041257, tc_HOL_Obool))), 14757 ^ _779854 : [(14767 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041257), hAPP(c_Finite__Set_Ofold1(_1041257, c_Orderings_Oord__class_Omin(_1041257)), _1041259)), _1041261))), 14768 ^ _779854 : [(14769 ^ _779854) ^ [_1041646] : [hBOOL(hAPP(hAPP(c_member(_1041257), _1041646), _1041259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041257), _1041646), _1041261))]]], (14758 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041257), hAPP(c_Finite__Set_Ofold1(_1041257, c_Orderings_Oord__class_Omin(_1041257)), _1041259)), _1041261)), 14762 ^ _779854 : [(14765 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041257), 14761 ^ [_1041257, _1041259, _1041261]), _1041261)))], (14763 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041257), 14761 ^ [_1041257, _1041259, _1041261]), _1041259)))]]]]], (52241 ^ _779854) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (24060 ^ _779854) ^ [_1216245, _1216247] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1216245), c_Groups_Ozero__class_Ozero(_1216245)), hAPP(c_Nat_OSuc, _1216247)) = c_Groups_Ozero__class_Ozero(_1216245)), class_Power_Opower(_1216245), class_Rings_Osemiring__0(_1216245)], (47450 ^ _779854) ^ [_1733868, _1733870, _1733872, _1733874, _1733876] : [-(c_List_Ofoldr(_1733868, _1733870, _1733872, _1733874, _1733876) = hAPP(c_List_Ofoldl(_1733870, _1733868, hAPP(c_COMBC(_1733868, _1733870, _1733870), _1733872), _1733876), hAPP(c_List_Orev(_1733868), _1733874)))], (20091 ^ _779854) ^ [_1142014, _1142016, _1142018, _1142020] : [class_Groups_Ocomm__monoid__add(_1142014), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1142016), _1142018))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1142016, _1142014), _1142020), _1142018) = c_Groups_Ozero__class_Ozero(_1142014))], (1910 ^ _779854) ^ [_806681, _806683] : [-(class_Groups_Oone(_806681)), _806683 = _806681, class_Groups_Oone(_806683)], (33405 ^ _779854) ^ [_1387732, _1387734, _1387736, _1387738, _1387740, _1387742, _1387744] : [-(hAPP(c_Fun_Ocomp(_1387732, _1387734, _1387736, _1387738), c_Fun_Ofun__upd(_1387736, _1387732, _1387740, _1387742, _1387744)) = c_Fun_Ofun__upd(_1387736, _1387734, hAPP(c_Fun_Ocomp(_1387732, _1387734, _1387736, _1387738), _1387740), _1387742, hAPP(_1387738, _1387744)))], (11043 ^ _779854) ^ [_969746, _969748, _969750] : [class_Orderings_Olinorder(_969746), hBOOL(hAPP(c_Finite__Set_Ofinite(_969746), _969748)), hBOOL(hAPP(c_Finite__Set_Ofinite(_969746), _969750)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969746, tc_HOL_Obool)), _969748), _969750) = c_Orderings_Obot__class_Obot(tc_fun(_969746, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_969746), c_Big__Operators_Olattice_OInf__fin(_969746, c_Orderings_Oord__class_Omin(_969746), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_969746, tc_HOL_Obool)), _969748), _969750))), c_Big__Operators_Olattice_OInf__fin(_969746, c_Orderings_Oord__class_Omin(_969746), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969746, tc_HOL_Obool)), _969748), _969750))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_969746), c_Big__Operators_Olattice_OInf__fin(_969746, c_Orderings_Oord__class_Omin(_969746), _969748)), c_Big__Operators_Olattice_OInf__fin(_969746, c_Orderings_Oord__class_Omin(_969746), _969750)))], (46699 ^ _779854) ^ [_1719364, _1719366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719364), _1719366)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1719364, _1719366)) = _1719364)], (17402 ^ _779854) ^ [_1094381, _1094383, _1094385, _1094387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1094381), hAPP(c_Set_Oimage(_1094383, _1094381, _1094385), _1094387))), hAPP(c_Finite__Set_Ocard(_1094383), _1094387))), c_Fun_Oinj__on(_1094383, _1094381, _1094385, _1094387)], (30398 ^ _779854) ^ [_1328773, _1328775] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1328773), _1328775) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328773, _1328775) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (46587 ^ _779854) ^ [_1717055, _1717057, _1717059, _1717061] : [-(c_List_Ofoldr(_1717055, _1717057, _1717059, c_List_Olist_ONil(_1717055), _1717061) = _1717061)], (27661 ^ _779854) ^ [_1280497, _1280499, _1280501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1280497)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1280497), _1280499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1280497), _1280501)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1280499), _1280501))], (42943 ^ _779854) ^ [_1635200, _1635202] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1635200, _1635202) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1635200), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1635202), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51108 ^ _779854) ^ [_1813233, _1813235, _1813237] : [hBOOL(hAPP(c_Quotient_ORespects(_1813233, _1813235), _1813237)), -(hBOOL(hAPP(hAPP(_1813235, _1813237), _1813237)))], (41547 ^ _779854) ^ [_1595372, _1595374, _1595376] : [hAPP(hAPP(c_Relation_Orel__comp(_1595372, _1595372, _1595372), hAPP(c_Relation_Oconverse(_1595372, _1595372), _1595374)), _1595374) = _1595374, hAPP(c_Relation_ODomain(_1595372, _1595372), _1595374) = _1595376, -(c_Equiv__Relations_Oequiv(_1595372, _1595376, _1595374))], (7698 ^ _779854) ^ [_907798, _907800, _907802] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_907798, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_907798, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_907798), _907800)), hAPP(c_Set_OPow(_907798), _907802))), hAPP(c_Set_OPow(_907798), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907798, tc_HOL_Obool)), _907800), _907802)))))], (25567 ^ _779854) ^ [_1244887, _1244889] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244887), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1244889) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1244887, _1244889))], (45813 ^ _779854) ^ [_1698656, _1698658, _1698660, _1698662, _1698664, _1698666, _1698668] : [c_List_Olist__all2(_1698662, _1698658, hAPP(hAPP(c_COMBB(_1698656, tc_fun(_1698658, tc_HOL_Obool), _1698662), _1698660), _1698664), _1698666, _1698668), -(c_List_Olist__all2(_1698656, _1698658, _1698660, hAPP(hAPP(c_List_Omap(_1698662, _1698656), _1698664), _1698666), _1698668))], (33955 ^ _779854) ^ [_1406991, _1406993, _1406995, _1406997, _1406999] : [class_Complete__Lattice_Ocomplete__lattice(_1406991), class_Orderings_Olinorder(_1406991), 33962 ^ _779854 : [(33972 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406991), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1406993, _1406991), _1406995), _1406997)), _1406999))), 33973 ^ _779854 : [(33974 ^ _779854) ^ [_1407339] : [hBOOL(hAPP(hAPP(c_member(_1406993), _1407339), _1406995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406991), hAPP(_1406997, _1407339)), _1406999))]]], (33963 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406991), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1406993, _1406991), _1406995), _1406997)), _1406999)), 33967 ^ _779854 : [(33970 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406991), hAPP(_1406997, 33966 ^ [_1406991, _1406993, _1406995, _1406997, _1406999])), _1406999)))], (33968 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406993), 33966 ^ [_1406991, _1406993, _1406995, _1406997, _1406999]), _1406995)))]]]]], (25833 ^ _779854) ^ [_1249341, _1249343, _1249345, _1249347, _1249349, _1249351] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1249341), _1249343)), _1249345) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1249347), _1249349)), _1249351), 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), _1249347), _1249349)), _1249351)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249345), _1249341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249347), _1249341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249349), _1249343)))], (36150 ^ _779854) ^ [_1454070, _1454072, _1454074, _1454076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454070, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1454070, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36151 ^ [_1454070, _1454072, _1454074, _1454076])), _1454072)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1454070, 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), 36151 ^ [_1454070, _1454072, _1454074, _1454076]), _1454074))), _1454076))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454070, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1454070, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1454072)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1454070, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1454076))))], (24006 ^ _779854) ^ [_1215387, _1215389, _1215391] : [class_Rings_Olinordered__semidom(_1215387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215387), c_Groups_Ozero__class_Ozero(_1215387)), _1215389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215387), c_Groups_Ozero__class_Ozero(_1215387)), hAPP(hAPP(c_Power_Opower__class_Opower(_1215387), _1215389), _1215391))))], (25747 ^ _779854) ^ [_1247867, _1247869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247867), _1247869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247867), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1247869)))], (9941 ^ _779854) ^ [_947487, _947489, _947491, _947493] : [class_Orderings_Olinorder(_947487), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_947487), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947487), _947489), _947491)), _947493) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_947487), _947489), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947487), _947491), _947493)))], (47963 ^ _779854) ^ [_1744664, _1744666, _1744668] : [-(hAPP(c_List_Oset(_1744664), c_List_Oinsert(_1744664, _1744666, _1744668)) = hAPP(hAPP(c_Set_Oinsert(_1744664), _1744666), hAPP(c_List_Oset(_1744664), _1744668)))], (27993 ^ _779854) ^ [_1286230, _1286232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1286230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1286232)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1286230)), hAPP(c_Int_Onat, _1286232)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1286230, _1286232)))], (27193 ^ _779854) ^ [_1272692, _1272694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272692), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272692)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272694)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1272694))], (22455 ^ _779854) ^ [_1185748, _1185750, _1185752] : [class_Fields_Olinordered__field__inverse__zero(_1185748), 22458 ^ _779854 : [(22473 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), c_Groups_Ozero__class_Ozero(_1185748)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185748), _1185750), _1185752)))), 22474 ^ _779854 : [(22481 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), _1185750), c_Groups_Ozero__class_Ozero(_1185748))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), _1185752), c_Groups_Ozero__class_Ozero(_1185748)))], (22475 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), c_Groups_Ozero__class_Ozero(_1185748)), _1185750)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), c_Groups_Ozero__class_Ozero(_1185748)), _1185752))]]], (22459 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), c_Groups_Ozero__class_Ozero(_1185748)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185748), _1185750), _1185752))), 22464 ^ _779854 : [(22467 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), c_Groups_Ozero__class_Ozero(_1185748)), _1185752)))], (22465 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), c_Groups_Ozero__class_Ozero(_1185748)), _1185750)))]], 22468 ^ _779854 : [(22471 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), _1185752), c_Groups_Ozero__class_Ozero(_1185748))))], (22469 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185748), _1185750), c_Groups_Ozero__class_Ozero(_1185748))))]]]]], (74 ^ _779854) ^ [_780921, _780923, _780925, _780927, _780929, _780931] : [-(c_Finite__Set_Ofolding__one(_780929, _780925, _780921)), c_Finite__Set_Ofolding__one(_780931, _780927, _780923), _780931 = _780929, _780927 = _780925, _780923 = _780921], (46753 ^ _779854) ^ [_1720341, _1720343] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1720341, _1720343)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1720341), hAPP(c_Nat_OSuc, _1720343)))], (52347 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (49086 ^ _779854) ^ [_1769450, _1769452, _1769454, _1769456] : [-(hBOOL(hAPP(hAPP(c_member(_1769450), _1769452), hAPP(c_List_Oset(_1769450), c_List_Oreplicate(_1769450, _1769454, _1769456))))), _1769452 = _1769456, -(_1769454 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32205 ^ _779854) ^ [_1359342, _1359344, _1359346] : [class_Groups_Oordered__ab__group__add__abs(_1359342), 32208 ^ _779854 : [(32217 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359342), hAPP(c_Groups_Oabs__class_Oabs(_1359342), _1359344)), _1359346))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359342), _1359344), _1359346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359342), hAPP(c_Groups_Ouminus__class_Ouminus(_1359342), _1359344)), _1359346))], (32209 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359342), hAPP(c_Groups_Oabs__class_Oabs(_1359342), _1359344)), _1359346)), 32212 ^ _779854 : [(32215 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359342), hAPP(c_Groups_Ouminus__class_Ouminus(_1359342), _1359344)), _1359346)))], (32213 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359342), _1359344), _1359346)))]]]]], (11770 ^ _779854) ^ [_984145, _984147, _984149] : [hBOOL(hAPP(_984149, _984147)), -(hBOOL(hAPP(hAPP(c_member(_984145), _984147), _984149)))], (24362 ^ _779854) ^ [_1221750, _1221752, _1221754, _1221756] : [class_Rings_Olinordered__semidom(_1221750), hAPP(hAPP(c_Power_Opower__class_Opower(_1221750), _1221752), _1221754) = hAPP(hAPP(c_Power_Opower__class_Opower(_1221750), _1221756), _1221754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221750), c_Groups_Ozero__class_Ozero(_1221750)), _1221752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221750), c_Groups_Ozero__class_Ozero(_1221750)), _1221756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1221754)), -(_1221752 = _1221756)], (52395 ^ _779854) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (12578 ^ _779854) ^ [_999859, _999861, _999863, _999865, _999867] : [c_Fun_Oinj__on(_999859, _999861, _999863, c_Orderings_Otop__class_Otop(tc_fun(_999859, tc_HOL_Obool))), 12581 ^ _779854 : [(12588 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_999859), _999865), _999867)), -(hBOOL(hAPP(hAPP(c_member(_999861), hAPP(_999863, _999865)), hAPP(c_Set_Oimage(_999859, _999861, _999863), _999867))))], (12582 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_999861), hAPP(_999863, _999865)), hAPP(c_Set_Oimage(_999859, _999861, _999863), _999867))), -(hBOOL(hAPP(hAPP(c_member(_999859), _999865), _999867)))]]], (28999 ^ _779854) ^ [] : [-(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)))], (7033 ^ _779854) ^ [_895065, _895067, _895069] : [class_Lattices_Osemilattice__sup(_895065), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895065), _895067), _895069) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895065), _895069), _895067))], (14137 ^ _779854) ^ [_1029290, _1029292, _1029294, _1029296, _1029298] : [-(hAPP(c_Fun_Ofun__upd(_1029290, _1029292, _1029294, _1029296, _1029298), _1029296) = _1029298)], (43458 ^ _779854) ^ [_1646121, _1646123] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646121)), _1646123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1646123 = c_List_Olist_ONil(_1646121))], (1520 ^ _779854) ^ [_801806, _801808] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801806)), _801808 = _801806, class_Groups_Oordered__cancel__ab__semigroup__add(_801808)], (1660 ^ _779854) ^ [_803556, _803558] : [-(class_Groups_Ocomm__monoid__mult(_803556)), _803558 = _803556, class_Groups_Ocomm__monoid__mult(_803558)], (17302 ^ _779854) ^ [_1092466, _1092468, _1092470, _1092472] : [c_Fun_Oinj__on(_1092466, _1092468, _1092470, _1092472), -(hAPP(c_Finite__Set_Ocard(_1092468), hAPP(c_Set_Oimage(_1092466, _1092468, _1092470), _1092472)) = hAPP(c_Finite__Set_Ocard(_1092466), _1092472))], (27333 ^ _779854) ^ [_1275369, _1275371, _1275373] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275369), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275369)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275371)), _1275373)) = 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), _1275369), _1275371))), _1275373))], (29711 ^ _779854) ^ [] : [-(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))))], (40416 ^ _779854) ^ [_1567493, _1567495, _1567497] : [40418 ^ _779854 : [(40421 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1567493), 40417 ^ [_1567493, _1567495, _1567497]), c_Wellfounded_Oacc(_1567493, _1567497)))], (40419 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567493, _1567493)), hAPP(hAPP(c_Product__Type_OPair(_1567493, _1567493), 40417 ^ [_1567493, _1567495, _1567497]), _1567495)), _1567497)))]], -(hBOOL(hAPP(hAPP(c_member(_1567493), _1567495), c_Wellfounded_Oacc(_1567493, _1567497))))], (41146 ^ _779854) ^ [_1585480, _1585482, _1585484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585480, _1585480), tc_HOL_Obool)), _1585482), c_Transitive__Closure_Ortrancl(_1585480, _1585484))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585480, _1585480), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1585480, _1585482)), c_Transitive__Closure_Ortrancl(_1585480, _1585484))))], (42113 ^ _779854) ^ [_1610463, _1610465, _1610467, _1610469, _1610471] : [hAPP(hAPP(c_List_Olist_OCons(_1610463), _1610465), _1610467) = hAPP(hAPP(c_List_Olist_OCons(_1610463), _1610469), _1610471), 42116 ^ _779854 : [(42119 ^ _779854) ^ [] : [-(_1610467 = _1610471)], (42117 ^ _779854) ^ [] : [-(_1610465 = _1610469)]]], (51313 ^ _779854) ^ [_1819308, _1819310, _1819312] : [c_List_Olist__ex(tc_Nat_Onat, _1819308, c_List_Oupt(_1819310, _1819312)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1819308), _1819310, _1819312)], (29653 ^ _779854) ^ [_1314711, _1314713] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1314711)), c_Int_OBit1(_1314713)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1314711), c_Int_Osucc(_1314713))))], (18150 ^ _779854) ^ [_1108242, _1108244] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108242), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108244), _1108242)))))], (48776 ^ _779854) ^ [_1762525, _1762527, _1762529, _1762531, _1762533] : [-(_1762525 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1762527, _1762529, _1762531, _1762533), _1762525) = hAPP(c_Lazy__Sequence_Obind(_1762527, _1762529, hAPP(_1762531, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1762525), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1762527, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1762529)), _1762533), _1762525)))], (16878 ^ _779854) ^ [_1084248, _1084250, _1084252, _1084254, _1084256] : [class_Groups_Ocomm__monoid__mult(_1084248), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084250), _1084252)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084250), _1084254)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084248), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084250, _1084248), _1084256), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1084250, tc_HOL_Obool)), _1084252), _1084254))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084250, _1084248), _1084256), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1084250, tc_HOL_Obool)), _1084252), _1084254))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084248), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084250, _1084248), _1084256), _1084252)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084250, _1084248), _1084256), _1084254)))], (51925 ^ _779854) ^ [_1829979, _1829981] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829979), _1829981))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829979), _1829981)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829981), _1829979)))], (5972 ^ _779854) ^ [_874367, _874369, _874371] : [class_Orderings_Oorder(_874367), 5975 ^ _779854 : [(5984 ^ _779854) ^ [] : [-(_874369 = _874371), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874367), _874369), _874371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874367), _874371), _874369))], (5976 ^ _779854) ^ [] : [_874369 = _874371, 5979 ^ _779854 : [(5982 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874367), _874371), _874369)))], (5980 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874367), _874369), _874371)))]]]]], (35127 ^ _779854) ^ [_1433489, _1433491] : [-(c_Divides_Odivmod__nat(_1433489, _1433491) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1433489), _1433491)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1433489, _1433491)))], (49568 ^ _779854) ^ [_1780772, _1780774] : [-(c_Relation_Otrans(_1780772, c_Transitive__Closure_Ortrancl(_1780772, _1780774)))], (3756 ^ _779854) ^ [_836377, _836379, _836381, _836383] : [-(c_List_Omeasures(_836383, _836379) = c_List_Omeasures(_836381, _836377)), _836383 = _836381, _836379 = _836377], (51537 ^ _779854) ^ [_1823335, _1823337] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823337), _1823335)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1823335), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823337))))], (14570 ^ _779854) ^ [_1038059, _1038061] : [class_Lattices_Olattice(_1038059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038059), _1038061)), -(c_Big__Operators_Olattice__class_OSup__fin(_1038059, _1038061) = hAPP(c_Finite__Set_Ofold1(_1038059, c_Lattices_Osemilattice__sup__class_Osup(_1038059)), _1038061))], (36981 ^ _779854) ^ [_1473425, _1473427, _1473429, _1473431, _1473433, _1473435] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473431, _1473431)), hAPP(hAPP(c_Product__Type_OPair(_1473431, _1473431), hAPP(_1473435, _1473427)), hAPP(_1473435, _1473429))), _1473433)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473425, _1473425)), hAPP(hAPP(c_Product__Type_OPair(_1473425, _1473425), _1473427), _1473429)), hAPP(hAPP(c_Relation_Oinv__image(_1473431, _1473425), _1473433), _1473435))))], (15230 ^ _779854) ^ [_1051372, _1051374, _1051376, _1051378] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1051372), 15233 ^ _779854 : [(15240 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051372), _1051374), _1051378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051372), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051372), _1051374), _1051376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051372), _1051378), _1051376))))], (15234 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051372), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051372), _1051374), _1051376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051372), _1051378), _1051376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051372), _1051374), _1051378)))]]], (27473 ^ _779854) ^ [_1277601] : [class_Rings_Osemiring__1(_1277601), -(c_Int_Oiszero(_1277601, c_Groups_Ozero__class_Ozero(_1277601)))], (12644 ^ _779854) ^ [_1001132, _1001134, _1001136, _1001138] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001132, tc_HOL_Obool)), _1001134), hAPP(hAPP(c_Set_Oinsert(_1001132), _1001136), _1001138)))), 12647 ^ _779854 : [(12650 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001132, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1001132, tc_HOL_Obool)), _1001134), hAPP(hAPP(c_Set_Oinsert(_1001132), _1001136), c_Orderings_Obot__class_Obot(tc_fun(_1001132, tc_HOL_Obool))))), _1001138))], (12648 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001132), _1001136), _1001134)))]], 12651 ^ _779854 : [(12654 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001132, tc_HOL_Obool)), _1001134), _1001138))], (12652 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1001132), _1001136), _1001134))]]], (1430 ^ _779854) ^ [_800681, _800683] : [-(class_Lattices_Odistrib__lattice(_800681)), _800683 = _800681, class_Lattices_Odistrib__lattice(_800683)], (22709 ^ _779854) ^ [_1190133, _1190135, _1190137] : [class_Fields_Olinordered__field(_1190133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190133), _1190135), c_Groups_Ozero__class_Ozero(_1190133))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190133), _1190137), c_Groups_Ozero__class_Ozero(_1190133))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190133), c_Groups_Ozero__class_Ozero(_1190133)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1190133), _1190135), _1190137))))], (42054 ^ _779854) ^ [_1608401, _1608403, _1608405] : [c_Nitpick_Oless__eq__frac(_1608401, _1608403, _1608405), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1608401), c_Nitpick_Oplus__frac(_1608401, _1608403, c_Nitpick_Ouminus__frac(_1608401, _1608405)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7668 ^ _779854) ^ [_907131, _907133, _907135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907131, tc_HOL_Obool)), _907133), _907135)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907131, tc_HOL_Obool)), _907135), _907133) = _907133)], (26937 ^ _779854) ^ [_1268463, _1268465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268463), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1268465), _1268463)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268463), _1268465) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25973 ^ _779854) ^ [_1251858, _1251860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251858)), -(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), _1251858), _1251860))))], (42868 ^ _779854) ^ [_1633139, _1633141, _1633143, _1633145, _1633147, _1633149] : [-(hAPP(hAPP(c_List_Ozip(_1633139, _1633141), hAPP(hAPP(c_List_Olist_OCons(_1633139), _1633143), _1633145)), hAPP(hAPP(c_List_Olist_OCons(_1633141), _1633147), _1633149)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1633139, _1633141)), hAPP(hAPP(c_Product__Type_OPair(_1633139, _1633141), _1633143), _1633147)), hAPP(hAPP(c_List_Ozip(_1633139, _1633141), _1633145), _1633149)))], (26051 ^ _779854) ^ [_1253265, _1253267, _1253269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253265)), 26054 ^ _779854 : [(26055 ^ _779854) ^ [_1253399] : [26057 ^ _779854 : [(26063 ^ _779854) ^ [] : [-(_1253399 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26059 ^ [_1253265, _1253267, _1253269, _1253399]), 26056 ^ [_1253265, _1253267, _1253269, _1253399]))], (26061 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26059 ^ [_1253265, _1253267, _1253269, _1253399]), _1253267)))], (26058 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26056 ^ [_1253265, _1253267, _1253269, _1253399]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1253265))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1253269), _1253399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1253269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1253399), _1253265))))]]], (9362 ^ _779854) ^ [_936056, _936058, _936060, _936062] : [c_Hoare__Mirabelle_Ohoare__derivs(_936056, _936058, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_936056)), _936060), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_936056), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_936056, _936058, _936062), -(c_Hoare__Mirabelle_Ohoare__derivs(_936056, _936058, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_936056)), _936060), _936062)))], (5108 ^ _779854) ^ [_857935, _857937, _857939, _857941] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_857941, _857937) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_857939, _857935)), _857941 = _857939, _857937 = _857935], (37178 ^ _779854) ^ [_1478658, _1478660, _1478662] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1478658), _1478660), _1478662) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478658, tc_fun(tc_fun(_1478658, tc_HOL_Obool), tc_HOL_Obool)), _1478660), hAPP(hAPP(c_COMBC(_1478658, tc_fun(tc_fun(_1478658, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1478658, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478658, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1478658, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1478658, tc_HOL_Obool), tc_HOL_Obool)), _1478658), c_Set_Oinsert(tc_fun(_1478658, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1478658, tc_HOL_Obool), tc_fun(_1478658, tc_HOL_Obool), _1478658), c_Relation_OImage(_1478658, _1478658, _1478662)), hAPP(hAPP(c_COMBC(_1478658, tc_fun(_1478658, tc_HOL_Obool), tc_fun(_1478658, tc_HOL_Obool)), c_Set_Oinsert(_1478658)), c_Orderings_Obot__class_Obot(tc_fun(_1478658, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1478658, tc_HOL_Obool), tc_HOL_Obool)))))], (16798 ^ _779854) ^ [_1082690, _1082692, _1082694] : [class_Complete__Lattice_Ocomplete__lattice(_1082690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082690), _1082692)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1082690), _1082694), c_Complete__Lattice_OInf__class_OInf(_1082690, _1082692)) = hAPP(hAPP(c_Finite__Set_Ofold(_1082690, _1082690, c_Lattices_Osemilattice__inf__class_Oinf(_1082690)), _1082694), _1082692))], (7027 ^ _779854) ^ [_894956, _894958, _894960] : [class_Lattices_Olattice(_894956), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894956), _894958), _894960) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894956), _894960), _894958))], (33982 ^ _779854) ^ [_1407509, _1407511, _1407513, _1407515, _1407517] : [class_Complete__Lattice_Ocomplete__lattice(_1407509), class_Orderings_Olinorder(_1407509), 33989 ^ _779854 : [(33999 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407509), _1407511), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407513, _1407509), _1407515), _1407517)))), 34000 ^ _779854 : [(34001 ^ _779854) ^ [_1407857] : [hBOOL(hAPP(hAPP(c_member(_1407513), _1407857), _1407515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407509), _1407511), hAPP(_1407517, _1407857)))]]], (33990 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407509), _1407511), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407513, _1407509), _1407515), _1407517))), 33994 ^ _779854 : [(33997 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407509), _1407511), hAPP(_1407517, 33993 ^ [_1407509, _1407511, _1407513, _1407515, _1407517]))))], (33995 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407513), 33993 ^ [_1407509, _1407511, _1407513, _1407515, _1407517]), _1407515)))]]]]], (23447 ^ _779854) ^ [_1204471, _1204473, _1204475, _1204477, _1204479] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1204471, _1204473, hAPP(hAPP(c_Set_Oinsert(_1204471), _1204475), _1204477)), _1204479)), 23452 ^ _779854 : [(23457 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1204471), 23450 ^ [_1204471, _1204473, _1204475, _1204477, _1204479]), 23451 ^ [_1204471, _1204473, _1204475, _1204477, _1204479]))], (23455 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1204471, _1204471, _1204473, 23450 ^ [_1204471, _1204473, _1204475, _1204477, _1204479], 23451 ^ [_1204471, _1204473, _1204475, _1204477, _1204479]), _1204479)))], (23453 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1204471), _1204475), _1204477) = hAPP(hAPP(c_Set_Oinsert(_1204471), 23450 ^ [_1204471, _1204473, _1204475, _1204477, _1204479]), 23451 ^ [_1204471, _1204473, _1204475, _1204477, _1204479]))]]], (576 ^ _779854) ^ [_788476, _788478, _788480, _788482, _788484, _788486, _788488, _788490, _788492, _788494] : [-(c_Typedef_Otype__definition(_788492, _788488, _788484, _788480, _788476)), c_Typedef_Otype__definition(_788494, _788490, _788486, _788482, _788478), _788494 = _788492, _788490 = _788488, _788486 = _788484, _788482 = _788480, _788478 = _788476], (8856 ^ _779854) ^ [_927117, _927119, _927121, _927123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927117, tc_HOL_Obool)), _927119), _927121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927117, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_927117), _927123), _927119)), hAPP(hAPP(c_Set_Oinsert(_927117), _927123), _927121))))], (41012 ^ _779854) ^ [_1581410, _1581412, _1581414, _1581416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581410, _1581410)), _1581412), c_Transitive__Closure_Otrancl(_1581410, _1581414))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581410, _1581410), tc_HOL_Obool)), _1581414), _1581416)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581410, _1581410)), _1581412), c_Transitive__Closure_Otrancl(_1581410, _1581416))))], (39321 ^ _779854) ^ [_1538992, _1538994, _1538996] : [-(hAPP(c_Fun_Ocomp(_1538992, _1538992, _1538994, c_Fun_Oid(_1538992)), _1538996) = _1538996)], (2944 ^ _779854) ^ [_823697, _823699, _823701, _823703] : [-(c_Nitpick_OAbs__Frac(_823703, _823699) = c_Nitpick_OAbs__Frac(_823701, _823697)), _823703 = _823701, _823699 = _823697], (46806 ^ _779854) ^ [_1721704, _1721706, _1721708, _1721710, _1721712] : [class_Orderings_Olinorder(_1721704), hBOOL(hAPP(hAPP(c_member(_1721706), _1721708), hAPP(c_List_Oset(_1721706), _1721710))), c_List_Olinorder__class_Osorted(_1721704, hAPP(hAPP(c_List_Omap(_1721706, _1721704), _1721712), _1721710)), hAPP(c_List_Ohd(_1721706), hAPP(c_List_Ofilter(_1721706, hAPP(hAPP(c_COMBB(_1721704, tc_HOL_Obool, _1721706), hAPP(c_fequal, hAPP(_1721712, _1721708))), _1721712)), _1721710)) = _1721708, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721706, _1721704, _1721712), _1721708), c_List_Oremove1(_1721706, _1721708, _1721710)) = _1721710)], (17646 ^ _779854) ^ [_1099654, _1099656, _1099658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099654), _1099656)), hBOOL(hAPP(hAPP(c_member(_1099654), _1099658), _1099656)), -(hAPP(c_Finite__Set_Ocard(_1099654), _1099656) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1099654), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099654, tc_HOL_Obool)), _1099656), hAPP(hAPP(c_Set_Oinsert(_1099654), _1099658), c_Orderings_Obot__class_Obot(tc_fun(_1099654, tc_HOL_Obool)))))))], (22421 ^ _779854) ^ [_1185158, _1185160, _1185162] : [class_Fields_Olinordered__field__inverse__zero(_1185158), 22424 ^ _779854 : [(22439 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185158), _1185160), _1185162)), c_Groups_Ozero__class_Ozero(_1185158)))), 22440 ^ _779854 : [(22447 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), _1185160), c_Groups_Ozero__class_Ozero(_1185158))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), c_Groups_Ozero__class_Ozero(_1185158)), _1185162))], (22441 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), c_Groups_Ozero__class_Ozero(_1185158)), _1185160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), _1185162), c_Groups_Ozero__class_Ozero(_1185158)))]]], (22425 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185158), _1185160), _1185162)), c_Groups_Ozero__class_Ozero(_1185158))), 22430 ^ _779854 : [(22433 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), _1185162), c_Groups_Ozero__class_Ozero(_1185158))))], (22431 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), c_Groups_Ozero__class_Ozero(_1185158)), _1185160)))]], 22434 ^ _779854 : [(22437 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), c_Groups_Ozero__class_Ozero(_1185158)), _1185162)))], (22435 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185158), _1185160), c_Groups_Ozero__class_Ozero(_1185158))))]]]]], (49164 ^ _779854) ^ [_1771086, _1771088, _1771090, _1771092] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1771086, _1771088), c_Lazy__Sequence_Olazy__sequence_OInsert(_1771086, _1771090, _1771092)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1771088, _1771090)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1771086, _1771088), _1771092))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43560 ^ _779854) ^ [_1647900, _1647902, _1647904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647900), tc_List_Olist(_1647900))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647900), tc_List_Olist(_1647900)), c_List_Olist_ONil(_1647900)), _1647902)), c_List_Olistrel1(_1647900, _1647904)))], (52635 ^ _779854) ^ [_1838202, _1838204, _1838206, _1838208, _1838210, _1838212] : [-(hAPP(hAPP(hAPP(c_COMBC(_1838202, _1838204, _1838206), _1838208), _1838210), _1838212) = hAPP(hAPP(_1838208, _1838212), _1838210))], (38644 ^ _779854) ^ [_1516019, _1516021, _1516023, _1516025, _1516027, _1516029, _1516031, _1516033, _1516035, _1516037, _1516039] : [-(hAPP(c_Product__Type_Omap__pair(_1516019, _1516021, _1516023, _1516025, _1516027, _1516029), hAPP(c_Product__Type_Omap__pair(_1516031, _1516019, _1516033, _1516023, _1516035, _1516037), _1516039)) = hAPP(c_Product__Type_Omap__pair(_1516031, _1516021, _1516033, _1516025, hAPP(c_Fun_Ocomp(_1516019, _1516021, _1516031, _1516027), _1516035), hAPP(c_Fun_Ocomp(_1516023, _1516025, _1516033, _1516029), _1516037)), _1516039))], (20343 ^ _779854) ^ [_1145969, _1145971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145971), _1145969)), -(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), _1145969), _1145971))))], (8278 ^ _779854) ^ [_918469, _918471, _918473] : [class_Orderings_Opreorder(_918469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918469), _918471), _918473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918469), _918473), _918471))], (46020 ^ _779854) ^ [_1703177, _1703179, _1703181, _1703183] : [-(hAPP(c_List_Oset(tc_prod(_1703177, _1703179)), c_Enum_Oproduct(_1703177, _1703179, _1703181, _1703183)) = hAPP(hAPP(c_Product__Type_OSigma(_1703177, _1703179), hAPP(c_List_Oset(_1703177), _1703181)), hAPP(c_COMBK(tc_fun(_1703179, tc_HOL_Obool), _1703177), hAPP(c_List_Oset(_1703179), _1703183))))], (38318 ^ _779854) ^ [_1506510, _1506512, _1506514, _1506516] : [38319 ^ _779854 : [(38322 ^ _779854) ^ [] : [_1506516 = c_Orderings_Obot__class_Obot(tc_fun(_1506512, tc_HOL_Obool))], (38320 ^ _779854) ^ [] : [_1506514 = c_Orderings_Obot__class_Obot(tc_fun(_1506510, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1506510, _1506512), _1506514), hAPP(c_COMBK(tc_fun(_1506512, tc_HOL_Obool), _1506510), _1506516)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1506510, _1506512), tc_HOL_Obool)))], (38648 ^ _779854) ^ [_1516179, _1516181, _1516183, _1516185, _1516187, _1516189] : [-(c_Product__Type_Omap__pair(_1516179, _1516181, _1516183, _1516185, _1516187, _1516189) = hAPP(c_Product__Type_Oprod_Oprod__case(_1516179, _1516183, tc_prod(_1516181, _1516185)), hAPP(hAPP(c_COMBC(_1516179, tc_fun(_1516183, _1516185), tc_fun(_1516183, tc_prod(_1516181, _1516185))), hAPP(hAPP(c_COMBB(tc_fun(_1516185, tc_prod(_1516181, _1516185)), tc_fun(tc_fun(_1516183, _1516185), tc_fun(_1516183, tc_prod(_1516181, _1516185))), _1516179), c_COMBB(_1516185, tc_prod(_1516181, _1516185), _1516183)), hAPP(hAPP(c_COMBB(_1516181, tc_fun(_1516185, tc_prod(_1516181, _1516185)), _1516179), c_Product__Type_OPair(_1516181, _1516185)), _1516187))), _1516189)))], (44262 ^ _779854) ^ [_1664607, _1664609, _1664611, _1664613] : [-(hAPP(hAPP(c_List_Odrop(_1664607), _1664609), hAPP(hAPP(c_List_Odrop(_1664607), _1664611), _1664613)) = hAPP(hAPP(c_List_Odrop(_1664607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1664609), _1664611)), _1664613))], (39345 ^ _779854) ^ [_1539402] : [-(hAPP(c_Set_Oimage(_1539402, _1539402, c_Fun_Oid(_1539402)), c_Orderings_Otop__class_Otop(tc_fun(_1539402, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1539402, tc_HOL_Obool)))], (7610 ^ _779854) ^ [_905876, _905878, _905880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905876, tc_HOL_Obool)), _905878), _905880)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905876, tc_HOL_Obool)), _905878), _905880) = _905880)], (42038 ^ _779854) ^ [_1608041, _1608043] : [-(c_Nitpick_Oinverse__frac(_1608041, _1608043) = hAPP(hAPP(c_Nitpick_Ofrac(_1608041), hAPP(c_Nitpick_Odenom(_1608041), _1608043)), hAPP(c_Nitpick_Onum(_1608041), _1608043)))], (37127 ^ _779854) ^ [_1477367, _1477369, _1477371, _1477373] : [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), _1477367), _1477369)), 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), _1477371), _1477373)), 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), _1477367), _1477373)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1477371), _1477369))))], (5378 ^ _779854) ^ [_862178, _862180, _862182, _862184, _862186, _862188] : [-(c_Finite__Set_Ofold1Set(_862188, _862184, _862180) = c_Finite__Set_Ofold1Set(_862186, _862182, _862178)), _862188 = _862186, _862184 = _862182, _862180 = _862178], (12350 ^ _779854) ^ [_995284, _995286, _995288, _995290] : [hBOOL(hAPP(hAPP(c_member(_995284), _995286), _995288)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995284, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995284), _995286), _995290)), _995288) = hAPP(hAPP(c_Set_Oinsert(_995284), _995286), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995284, tc_HOL_Obool)), _995290), _995288)))], (26605 ^ _779854) ^ [_1263389] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1263389), c_Int_OPls) = _1263389)], (41280 ^ _779854) ^ [_1588756] : [-(hAPP(c_Relation_ORange(_1588756, _1588756), c_Relation_OId(_1588756)) = c_Orderings_Otop__class_Otop(tc_fun(_1588756, tc_HOL_Obool)))], (28601 ^ _779854) ^ [_1296907] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1296907))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1296907)) = _1296907)], (32143 ^ _779854) ^ [_1357983, _1357985, _1357987] : [class_Groups_Oordered__ab__group__add__abs(_1357983), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357983), hAPP(c_Groups_Oabs__class_Oabs(_1357983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357983), _1357985), _1357987))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357983), hAPP(c_Groups_Oabs__class_Oabs(_1357983), _1357985)), hAPP(c_Groups_Oabs__class_Oabs(_1357983), _1357987)))))], (40425 ^ _779854) ^ [_1567752, _1567754, _1567756, _1567758] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1567752, tc_HOL_Obool), tc_fun(_1567752, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1567752, tc_HOL_Obool), tc_fun(_1567752, tc_HOL_Obool)), _1567754), _1567756)), c_Wellfounded_Omax__ext(_1567752, _1567758))), 40428 ^ _779854 : [(40431 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1567752), _1567756)))], (40433 ^ _779854) ^ [] : [_1567756 = c_Orderings_Obot__class_Obot(tc_fun(_1567752, tc_HOL_Obool))], (40435 ^ _779854) ^ [_1568046] : [hBOOL(hAPP(hAPP(c_member(_1567752), _1568046), _1567754)), 40439 ^ _779854 : [(40442 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567752, _1567752)), hAPP(hAPP(c_Product__Type_OPair(_1567752, _1567752), _1568046), 40438 ^ [_1567752, _1567754, _1567756, _1567758, _1568046])), _1567758)))], (40440 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567752), 40438 ^ [_1567752, _1567754, _1567756, _1567758, _1568046]), _1567756)))]]], (40429 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1567752), _1567754)))]]], (48665 ^ _779854) ^ [_1760245, _1760247, _1760249] : [c_List_Olist__all(_1760245, _1760249, _1760247), 48668 ^ _779854 : [(48669 ^ _779854) ^ [_1760326] : [hBOOL(hAPP(hAPP(c_member(_1760245), _1760326), hAPP(c_List_Oset(_1760245), _1760247))), -(hBOOL(hAPP(_1760249, _1760326)))]]], (16808 ^ _779854) ^ [_1082875, _1082877, _1082879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082875), _1082877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082875), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1082877), _1082879))))], (3082 ^ _779854) ^ [_825858, _825860, _825862, _825864, _825866, _825868] : [-(c_List_Oset__Cons(_825868, _825864, _825860) = c_List_Oset__Cons(_825866, _825862, _825858)), _825868 = _825866, _825864 = _825862, _825860 = _825858], (26473 ^ _779854) ^ [_1260813, _1260815, _1260817, _1260819, _1260821, _1260823, _1260825] : [c_Nitpick_Ofold__graph_H(_1260813, _1260815, _1260817, _1260819, _1260821, hAPP(hAPP(_1260817, _1260823), _1260825)), 26478 ^ _779854 : [(26481 ^ _779854) ^ [] : [-(hAPP(hAPP(_1260817, _1260823), _1260825) = _1260819)], (26479 ^ _779854) ^ [] : [-(_1260821 = c_Orderings_Obot__class_Obot(tc_fun(_1260813, tc_HOL_Obool)))]], 26484 ^ _779854 : [(26489 ^ _779854) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1260813, _1260815, _1260817, _1260819, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260813, tc_HOL_Obool)), _1260821), hAPP(hAPP(c_Set_Oinsert(_1260813), 26482 ^ [_1260813, _1260815, _1260817, _1260819, _1260821, _1260823, _1260825]), c_Orderings_Obot__class_Obot(tc_fun(_1260813, tc_HOL_Obool)))), 26483 ^ [_1260813, _1260815, _1260817, _1260819, _1260821, _1260823, _1260825]))], (26487 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260813), 26482 ^ [_1260813, _1260815, _1260817, _1260819, _1260821, _1260823, _1260825]), _1260821)))], (26485 ^ _779854) ^ [] : [-(hAPP(hAPP(_1260817, _1260823), _1260825) = hAPP(hAPP(_1260817, 26482 ^ [_1260813, _1260815, _1260817, _1260819, _1260821, _1260823, _1260825]), 26483 ^ [_1260813, _1260815, _1260817, _1260819, _1260821, _1260823, _1260825]))]]], (36359 ^ _779854) ^ [_1458373, _1458375, _1458377] : [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), _1458373), _1458375))), -(hBOOL(hAPP(hAPP(_1458377, _1458373), _1458375))), 36366 ^ _779854 : [(36369 ^ _779854) ^ [] : [-(36365 ^ [_1458373, _1458375, _1458377] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1458377, 36365 ^ [_1458373, _1458375, _1458377]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 36364 ^ [_1458373, _1458375, _1458377], 36365 ^ [_1458373, _1458375, _1458377]))))], (36375 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1458377, 36364 ^ [_1458373, _1458375, _1458377]), 36365 ^ [_1458373, _1458375, _1458377]))], (36367 ^ _779854) ^ [] : [-(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), 36364 ^ [_1458373, _1458375, _1458377]), 36365 ^ [_1458373, _1458375, _1458377]))))]]], (40314 ^ _779854) ^ [_1565070, _1565072, _1565074, _1565076, _1565078, _1565080] : [40317 ^ _779854 : [(40320 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1565076), _1565078), hAPP(hAPP(_1565080, 40315 ^ [_1565070, _1565072, _1565074, _1565076, _1565078, _1565080]), 40316 ^ [_1565070, _1565072, _1565074, _1565076, _1565078, _1565080])))], (40318 ^ _779854) ^ [] : [-(_1565070 = hAPP(hAPP(c_Product__Type_OPair(_1565072, _1565074), 40315 ^ [_1565070, _1565072, _1565074, _1565076, _1565078, _1565080]), 40316 ^ [_1565070, _1565072, _1565074, _1565076, _1565078, _1565080]))]], -(hBOOL(hAPP(hAPP(c_member(_1565076), _1565078), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1565072, _1565074, tc_fun(_1565076, tc_HOL_Obool)), _1565080), _1565070))))], (5738 ^ _779854) ^ [_870570, _870572, _870574, _870576, _870578] : [class_Orderings_Oord(_870570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870572, _870570)), _870574), _870576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870570), hAPP(_870574, _870578)), hAPP(_870576, _870578))))], (19541 ^ _779854) ^ [_1132277, _1132279, _1132281, _1132283] : [class_Rings_Olinordered__ring__strict(_1132277), 19544 ^ _779854 : [(19559 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132277), _1132279), _1132281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132277), _1132283), _1132281)))), 19560 ^ _779854 : [(19567 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), _1132281), c_Groups_Ozero__class_Ozero(_1132277))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), _1132283), _1132279))], (19561 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), c_Groups_Ozero__class_Ozero(_1132277)), _1132281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), _1132279), _1132283))]]], (19545 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132277), _1132279), _1132281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132277), _1132283), _1132281))), 19550 ^ _779854 : [(19553 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), _1132279), _1132283)))], (19551 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), c_Groups_Ozero__class_Ozero(_1132277)), _1132281)))]], 19554 ^ _779854 : [(19557 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), _1132283), _1132279)))], (19555 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132277), _1132281), c_Groups_Ozero__class_Ozero(_1132277))))]]]]], (49050 ^ _779854) ^ [_1768808, _1768810] : [-(c_List_Oreplicate(_1768808, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1768810) = c_List_Olist_ONil(_1768808))], (48522 ^ _779854) ^ [_1757442, _1757444, _1757446] : [hBOOL(hAPP(hAPP(c_member(_1757442), _1757444), hAPP(c_List_Oset(_1757442), _1757446))), 48527 ^ _779854 : [(48530 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1757442), _1757444), hAPP(c_List_Oset(_1757442), 48526 ^ [_1757442, _1757444, _1757446])))], (48528 ^ _779854) ^ [] : [-(_1757446 = hAPP(hAPP(c_List_Oappend(_1757442), 48525 ^ [_1757442, _1757444, _1757446]), hAPP(hAPP(c_List_Olist_OCons(_1757442), _1757444), 48526 ^ [_1757442, _1757444, _1757446])))]]], (43981 ^ _779854) ^ [_1657474, _1657476, _1657478] : [_1657474 = hAPP(hAPP(c_List_Oappend(_1657476), _1657474), _1657478), -(_1657478 = c_List_Olist_ONil(_1657476))], (41953 ^ _779854) ^ [_1605892, _1605894, _1605896, _1605898] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605892, _1605892)), hAPP(hAPP(c_Product__Type_OPair(_1605892, _1605892), _1605894), _1605896)), c_Transitive__Closure_Otrancl(_1605892, _1605898))), 41957 ^ _779854 : [(41960 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605892, _1605892)), hAPP(hAPP(c_Product__Type_OPair(_1605892, _1605892), 41956 ^ [_1605892, _1605894, _1605896, _1605898]), _1605896)), c_Transitive__Closure_Ortrancl(_1605892, _1605898))))], (41958 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605892, _1605892)), hAPP(hAPP(c_Product__Type_OPair(_1605892, _1605892), _1605894), 41956 ^ [_1605892, _1605894, _1605896, _1605898])), _1605898)))]]], (47973 ^ _779854) ^ [_1744886, _1744888, _1744890, _1744892, _1744894] : [-(c_List_Omaps(_1744886, _1744888, _1744890, hAPP(hAPP(c_List_Olist_OCons(_1744886), _1744892), _1744894)) = hAPP(hAPP(c_List_Oappend(_1744888), hAPP(_1744890, _1744892)), c_List_Omaps(_1744886, _1744888, _1744890, _1744894)))], (34523 ^ _779854) ^ [_1420238, _1420240, _1420242, _1420244] : [class_Groups_Oab__group__add(_1420238), 34526 ^ _779854 : [(34533 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1420240), _1420242))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420238), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1420238, _1420238), hAPP(hAPP(c_COMBB(_1420238, tc_fun(_1420238, _1420238), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1420238)), _1420244)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1420238, tc_Nat_Onat), _1420244), 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, _1420240, _1420242)) = c_Groups_Ozero__class_Ozero(_1420238))], (34527 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1420240), _1420242)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420238), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1420238, _1420238), hAPP(hAPP(c_COMBB(_1420238, tc_fun(_1420238, _1420238), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1420238)), _1420244)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1420238, tc_Nat_Onat), _1420244), 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, _1420240, _1420242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1420238), hAPP(_1420244, _1420240)), hAPP(_1420244, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1420242), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (11988 ^ _779854) ^ [_988263, _988265, _988267, _988269, _988271] : [-(hBOOL(hAPP(hAPP(c_member(_988263), _988265), hAPP(c_Set_Oimage(_988267, _988263, _988269), _988271)))), 11989 ^ _779854 : [(11990 ^ _779854) ^ [_988333] : [hBOOL(hAPP(hAPP(c_member(_988267), _988333), _988271)), _988265 = hAPP(_988269, _988333)]]], (43612 ^ _779854) ^ [_1649035, _1649037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649035)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649037))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649035), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649037)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649035)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649035)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649037))))], (31681 ^ _779854) ^ [] : [-(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))], (30537 ^ _779854) ^ [_1331255] : [-(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)), _1331255)))], (46326 ^ _779854) ^ [_1709519, _1709521] : [-(hAPP(c_List_Oset(_1709519), c_List_Oconcat(_1709519, _1709521)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1709519), tc_fun(_1709519, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1709519)), _1709521)), c_List_Oset(_1709519)))], (40511 ^ _779854) ^ [_1569596, _1569598, _1569600] : [class_Complete__Lattice_Ocomplete__lattice(_1569596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1569596), _1569598), hAPP(_1569600, _1569598))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1569596), _1569598), c_Inductive_Ocomplete__lattice__class_Ogfp(_1569596, _1569600))))], (35456 ^ _779854) ^ [_1440405, _1440407, _1440409, _1440411, _1440413, _1440415, _1440417] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1440405, _1440407), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1440409), _1440411))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1440413, _1440407), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1440415), _1440417))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1440407)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440405), _1440413), _1440407), 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), _1440409), _1440415)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440411), _1440417)), _1440407))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1440411), _1440417), _1440407)))))], (38428 ^ _779854) ^ [_1509850, _1509852, _1509854, _1509856, _1509858, _1509860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509850, _1509852), tc_HOL_Obool)), _1509854), hAPP(hAPP(c_Product__Type_OSigma(_1509850, _1509852), _1509856), hAPP(c_COMBK(tc_fun(_1509852, tc_HOL_Obool), _1509850), _1509858)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509852, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1509850, _1509852, _1509854), _1509860)), _1509858)))], (48928 ^ _779854) ^ [_1766611, _1766613, _1766615, _1766617] : [-(hAPP(hAPP(c_List_Oappend(_1766611), c_List_Oreplicate(_1766611, _1766613, _1766615)), hAPP(hAPP(c_List_Olist_OCons(_1766611), _1766615), _1766617)) = hAPP(hAPP(c_List_Olist_OCons(_1766611), _1766615), hAPP(hAPP(c_List_Oappend(_1766611), c_List_Oreplicate(_1766611, _1766613, _1766615)), _1766617)))], (38883 ^ _779854) ^ [_1521864, _1521866, _1521868] : [-(hAPP(hAPP(c_Set_Oinsert(_1521864), _1521866), _1521868) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521864, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1521864), hAPP(hAPP(c_COMBC(_1521864, _1521864, tc_HOL_Obool), c_fequal), _1521866))), _1521868))], (46453 ^ _779854) ^ [_1713153, _1713155, _1713157] : [-(c_List_Opartition(_1713153, _1713155, _1713157) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713153), tc_List_Olist(_1713153)), hAPP(c_List_Ofilter(_1713153, _1713155), _1713157)), hAPP(c_List_Ofilter(_1713153, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1713153, c_fNot), _1713155)), _1713157)))], (28408 ^ _779854) ^ [_1293458, _1293460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1293458), _1293460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293458)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293460))))], (44995 ^ _779854) ^ [_1679808, _1679810, _1679812, _1679814] : [hAPP(hAPP(c_List_Oappend(_1679808), _1679810), hAPP(hAPP(c_List_Olist_OCons(_1679808), _1679812), c_List_Olist_ONil(_1679808))) = _1679814, 44998 ^ _779854 : [(45003 ^ _779854) ^ [] : [-(c_List_Olast(_1679808, _1679814) = _1679812)], (45001 ^ _779854) ^ [] : [-(c_List_Obutlast(_1679808, _1679814) = _1679810)], (44999 ^ _779854) ^ [] : [_1679814 = c_List_Olist_ONil(_1679808)]]], (26449 ^ _779854) ^ [_1260432] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1260432) = 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(_1260432)))))], (43251 ^ _779854) ^ [_1642037, _1642039] : [43253 ^ _779854 : [(43257 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43255 ^ [_1642037, _1642039]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642037)), _1642039))))], (43259 ^ _779854) ^ [] : [43252 ^ [_1642037, _1642039] = 43255 ^ [_1642037, _1642039]], (43261 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1642037), _1642039), 43252 ^ [_1642037, _1642039]) = hAPP(hAPP(c_List_Onth(_1642037), _1642039), 43255 ^ [_1642037, _1642039]))], (43254 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43252 ^ [_1642037, _1642039]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642037)), _1642039))))]], -(hBOOL(hAPP(c_List_Odistinct(_1642037), _1642039)))], (36772 ^ _779854) ^ [_1467959, _1467961, _1467963, _1467965, _1467967] : [-(hAPP(c_Product__Type_Ofst(_1467959, _1467961), hAPP(c_Product__Type_Oapfst(_1467963, _1467959, _1467961, _1467965), _1467967)) = hAPP(_1467965, hAPP(c_Product__Type_Ofst(_1467963, _1467961), _1467967)))], (43179 ^ _779854) ^ [_1640489, _1640491, _1640493] : [hBOOL(hAPP(c_List_Odistinct(_1640489), _1640491)), -(hBOOL(hAPP(c_List_Odistinct(_1640489), hAPP(hAPP(c_List_Otake(_1640489), _1640493), _1640491))))], (39883 ^ _779854) ^ [_1553790, _1553792] : [c_FunDef_Oreduction__pair(_1553790, _1553792), 39886 ^ _779854 : [(39889 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1553790, _1553790, _1553790), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool), tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool)), _1553792)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool), tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool)), _1553792))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool), tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool)), _1553792))))], (39887 ^ _779854) ^ [] : [-(c_Wellfounded_Owf(_1553790, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool), tc_fun(tc_prod(_1553790, _1553790), tc_HOL_Obool)), _1553792)))]]], (50997 ^ _779854) ^ [_1810929, _1810931] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1810929), _1810931)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1810929, 51000 ^ [_1810929, _1810931], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1810929), _1810931)), _1810931))], (41459 ^ _779854) ^ [_1592832, _1592834, _1592836, _1592838, _1592840] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592834, _1592832)), hAPP(hAPP(c_Product__Type_OPair(_1592834, _1592832), _1592838), _1592836)), _1592840)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592832, _1592834)), hAPP(hAPP(c_Product__Type_OPair(_1592832, _1592834), _1592836), _1592838)), hAPP(c_Relation_Oconverse(_1592834, _1592832), _1592840))))], (41535 ^ _779854) ^ [_1595036, _1595038, _1595040, _1595042, _1595044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1595038, tc_HOL_Obool)), _1595042), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1595038, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1595036, _1595038, hAPP(c_Relation_Oconverse(_1595038, _1595036), _1595040)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1595036, tc_HOL_Obool)), _1595044))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1595036, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1595038, _1595036, _1595040), _1595042)), _1595044)))], (49479 ^ _779854) ^ [_1778328, _1778330, _1778332] : [-(c_Random__Sequence_Oempty(_1778328, _1778330, _1778332) = 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(_1778328)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1778328)))], (47474 ^ _779854) ^ [_1734413, _1734415] : [-(_1734413 = c_List_Olist_ONil(_1734415)), -(hAPP(c_List_Ohd(_1734415), hAPP(c_List_Orev(_1734415), _1734413)) = c_List_Olast(_1734415, _1734413))], (48532 ^ _779854) ^ [_1757697, _1757699, _1757701] : [-(hBOOL(hAPP(hAPP(c_member(_1757697), _1757699), hAPP(c_List_Oset(_1757697), _1757701)))), 48533 ^ _779854 : [(48534 ^ _779854) ^ [_1757786, _1757788] : [_1757701 = hAPP(hAPP(c_List_Oappend(_1757697), _1757788), hAPP(hAPP(c_List_Olist_OCons(_1757697), _1757699), _1757786)), -(hBOOL(hAPP(hAPP(c_member(_1757697), _1757699), hAPP(c_List_Oset(_1757697), _1757786))))]]], (52589 ^ _779854) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (42028 ^ _779854) ^ [_1607848, _1607850, _1607852] : [-(c_Nitpick_Oof__frac(_1607850, _1607848, _1607852) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1607848), hAPP(c_Int_Oring__1__class_Oof__int(_1607848), hAPP(c_Nitpick_Onum(_1607850), _1607852))), hAPP(c_Int_Oring__1__class_Oof__int(_1607848), hAPP(c_Nitpick_Odenom(_1607850), _1607852)))), class_Rings_Oinverse(_1607848), class_Rings_Oring__1(_1607848)], (31862 ^ _779854) ^ [_1353229, _1353231, _1353233] : [class_Rings_Oring__1(_1353229), -(hAPP(c_Int_Oring__1__class_Oof__int(_1353229), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1353231), _1353233)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1353229), hAPP(c_Int_Oring__1__class_Oof__int(_1353229), _1353231)), _1353233))], (34399 ^ _779854) ^ [_1417493, _1417495, _1417497] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1417493, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1417495)), _1417497) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417493, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1417493, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1417495)), _1417497)), hAPP(_1417497, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48595 ^ _779854) ^ [_1758932, _1758934, _1758936] : [c_List_Olist__all(_1758932, _1758934, _1758936), 48598 ^ _779854 : [(48599 ^ _779854) ^ [_1759013] : [hBOOL(hAPP(hAPP(c_member(_1758932), _1759013), hAPP(c_List_Oset(_1758932), _1758936))), -(hBOOL(hAPP(_1758934, _1759013)))]]], (5626 ^ _779854) ^ [_865948, _865950, _865952, _865954, _865956, _865958] : [-(c_COMBS(_865958, _865954, _865950) = c_COMBS(_865956, _865952, _865948)), _865958 = _865956, _865954 = _865952, _865950 = _865948], (48914 ^ _779854) ^ [_1766288, _1766290, _1766292, _1766294] : [-(c_Lazy__Sequence_Oproduct(_1766288, _1766290, _1766292, _1766294) = hAPP(c_Lazy__Sequence_Obind(_1766288, tc_prod(_1766288, _1766290), _1766292), hAPP(hAPP(c_COMBB(tc_fun(_1766290, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1766288, _1766290))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1766288, _1766290)), _1766288), c_Lazy__Sequence_Obind(_1766290, tc_prod(_1766288, _1766290), _1766294)), hAPP(hAPP(c_COMBB(tc_fun(_1766290, tc_prod(_1766288, _1766290)), tc_fun(_1766290, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1766288, _1766290))), _1766288), hAPP(c_COMBB(tc_prod(_1766288, _1766290), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1766288, _1766290)), _1766290), c_Lazy__Sequence_Osingle(tc_prod(_1766288, _1766290)))), c_Product__Type_OPair(_1766288, _1766290)))))], (46653 ^ _779854) ^ [_1718658, _1718660] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718658), _1718660))), -(c_List_Oupt(_1718658, _1718660) = c_List_Olist_ONil(tc_Nat_Onat))], (5994 ^ _779854) ^ [_874694, _874696, _874698] : [class_Orderings_Olinorder(_874694), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874694), _874696), _874698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874694), _874698), _874696)))], (16243 ^ _779854) ^ [_1071573, _1071575, _1071577] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071573), _1071575)), _1071577) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071573), _1071577)), _1071575))], (35026 ^ _779854) ^ [_1431280, _1431282] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431280)), _1431282) = 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), _1431280)), _1431282))], (41692 ^ _779854) ^ [_1598532, _1598534, _1598536] : [41694 ^ _779854 : [(41695 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1598532), 41693 ^ [_1598532, _1598534, _1598536]), _1598534)))], (41700 ^ _779854) ^ [] : [41693 ^ [_1598532, _1598534, _1598536] = 41696 ^ [_1598532, _1598534, _1598536]], (41704 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598532, _1598532)), hAPP(hAPP(c_Product__Type_OPair(_1598532, _1598532), 41696 ^ [_1598532, _1598534, _1598536]), 41693 ^ [_1598532, _1598534, _1598536])), _1598536))], (41702 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598532, _1598532)), hAPP(hAPP(c_Product__Type_OPair(_1598532, _1598532), 41693 ^ [_1598532, _1598534, _1598536]), 41696 ^ [_1598532, _1598534, _1598536])), _1598536))], (41698 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1598532), 41696 ^ [_1598532, _1598534, _1598536]), _1598534)))]], -(c_Relation_Ototal__on(_1598532, _1598534, _1598536))], (19719 ^ _779854) ^ [_1135526, _1135528, _1135530] : [class_Rings_Olinordered__semiring__strict(_1135526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135526), _1135528), c_Groups_Ozero__class_Ozero(_1135526))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135526), c_Groups_Ozero__class_Ozero(_1135526)), _1135530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135526), _1135528), _1135530)), c_Groups_Ozero__class_Ozero(_1135526))))], (37654 ^ _779854) ^ [_1489996, _1489998, _1490000, _1490002, _1490004, _1490006] : [c_Equiv__Relations_Ocongruent(_1489996, _1489998, _1490000, _1490002), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489996, _1489996)), hAPP(hAPP(c_Product__Type_OPair(_1489996, _1489996), _1490004), _1490006)), _1490000)), -(hAPP(_1490002, _1490004) = hAPP(_1490002, _1490006))], (47392 ^ _779854) ^ [_1732776, _1732778, _1732780, _1732782, _1732784] : [c_List_Olist__all2(_1732776, _1732778, _1732780, hAPP(c_List_Orev(_1732776), _1732782), _1732784), -(c_List_Olist__all2(_1732776, _1732778, _1732780, _1732782, hAPP(c_List_Orev(_1732778), _1732784)))], (39923 ^ _779854) ^ [_1554965, _1554967] : [-(hAPP(c_Relation_OField(_1554965), _1554967) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1554965, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1554965, _1554965), _1554967)), hAPP(c_Relation_ORange(_1554965, _1554965), _1554967)))], (24274 ^ _779854) ^ [_1220035, _1220037, _1220039, _1220041] : [class_Rings_Olinordered__semidom(_1220035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220035), c_Groups_Oone__class_Oone(_1220035)), _1220037)), 24281 ^ _779854 : [(24288 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220039), _1220041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220035), hAPP(hAPP(c_Power_Opower__class_Opower(_1220035), _1220037), _1220039)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220035), _1220037), _1220041))))], (24282 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220035), hAPP(hAPP(c_Power_Opower__class_Opower(_1220035), _1220037), _1220039)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220035), _1220037), _1220041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220039), _1220041)))]]], (38015 ^ _779854) ^ [_1498765, _1498767, _1498769] : [-(c_HOL_OThe(tc_prod(_1498765, _1498767), hAPP(c_Product__Type_Oprod_Oprod__case(_1498765, _1498767, tc_HOL_Obool), _1498769)) = c_HOL_OThe(tc_prod(_1498765, _1498767), hAPP(hAPP(c_COMBS(tc_prod(_1498765, _1498767), _1498767, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1498765, tc_fun(_1498767, tc_HOL_Obool), tc_prod(_1498765, _1498767)), _1498769), c_Product__Type_Ofst(_1498765, _1498767))), c_Product__Type_Osnd(_1498765, _1498767))))], (38005 ^ _779854) ^ [_1498463, _1498465, _1498467] : [-(c_HOL_OThe(tc_prod(_1498463, _1498465), _1498467) = c_HOL_OThe(tc_prod(_1498463, _1498465), hAPP(c_Product__Type_Oprod_Oprod__case(_1498463, _1498465, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1498465, tc_prod(_1498463, _1498465)), tc_fun(_1498465, tc_HOL_Obool), _1498463), hAPP(c_COMBB(tc_prod(_1498463, _1498465), tc_HOL_Obool, _1498465), _1498467)), c_Product__Type_OPair(_1498463, _1498465)))))], (6907 ^ _779854) ^ [_892274, _892276, _892278, _892280] : [class_Lattices_Osemilattice__inf(_892274), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892274), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892274), _892276), _892278)), _892280) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892274), _892276), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892274), _892278), _892280)))], (22741 ^ _779854) ^ [_1190747, _1190749, _1190751, _1190753] : [class_Fields_Olinordered__field(_1190747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190747), _1190749), _1190751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190747), c_Groups_Ozero__class_Ozero(_1190747)), _1190753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190747), c_Groups_Ozero__class_Ozero(_1190747)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190747), _1190751), _1190749))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190747), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1190747), _1190753), _1190751)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1190747), _1190753), _1190749))))], (17240 ^ _779854) ^ [_1091196, _1091198, _1091200, _1091202, _1091204, _1091206] : [c_Finite__Set_Ofun__left__comm(_1091196, _1091198, _1091200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091196), _1091202)), -(hBOOL(hAPP(hAPP(c_member(_1091196), _1091204), _1091202))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1091196, _1091198, _1091200), _1091206), hAPP(hAPP(c_Set_Oinsert(_1091196), _1091204), _1091202)) = hAPP(hAPP(c_Finite__Set_Ofold(_1091196, _1091198, _1091200), hAPP(hAPP(_1091200, _1091204), _1091206)), _1091202))], (92 ^ _779854) ^ [_781190, _781192] : [-(class_Rings_Odivision__ring__inverse__zero(_781190)), _781192 = _781190, class_Rings_Odivision__ring__inverse__zero(_781192)], (31663 ^ _779854) ^ [_1350092, _1350094] : [c_Nat__Transfer_Onat__set(_1350092), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1350094), _1350092)), -(c_Nat__Transfer_Ois__nat(_1350094))], (9228 ^ _779854) ^ [_933918, _933920, _933922, _933924] : [class_Orderings_Oorder(_933918), 9231 ^ _779854 : [(9240 ^ _779854) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_933918, _933920, _933922) = hAPP(hAPP(c_Set_Oinsert(_933918), _933924), c_Orderings_Obot__class_Obot(tc_fun(_933918, tc_HOL_Obool)))), _933920 = _933922, _933922 = _933924], (9232 ^ _779854) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_933918, _933920, _933922) = hAPP(hAPP(c_Set_Oinsert(_933918), _933924), c_Orderings_Obot__class_Obot(tc_fun(_933918, tc_HOL_Obool))), 9235 ^ _779854 : [(9238 ^ _779854) ^ [] : [-(_933922 = _933924)], (9236 ^ _779854) ^ [] : [-(_933920 = _933922)]]]]], (30213 ^ _779854) ^ [_1325316, _1325318, _1325320] : [class_Divides_Osemiring__div(_1325316), -(c_Divides_Odiv__class_Omod(_1325316, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325316), _1325318), _1325320), _1325318) = c_Divides_Odiv__class_Omod(_1325316, _1325320, _1325318))], (35024 ^ _779854) ^ [_1431235, _1431237] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1431235), hAPP(c_Nat_OSuc, _1431237)) = 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), _1431235), _1431237)))], (2512 ^ _779854) ^ [_817001, _817003, _817005, _817007] : [-(c_Set_Othe__elem(_817007, _817003) = c_Set_Othe__elem(_817005, _817001)), _817007 = _817005, _817003 = _817001], (5484 ^ _779854) ^ [_863839, _863841] : [_863841 = _863839, -(c_Groups_Ouminus__class_Ouminus(_863841) = c_Groups_Ouminus__class_Ouminus(_863839))], (24665 ^ _779854) ^ [_1227501, _1227503] : [class_Int_Onumber__ring(_1227501), -(hAPP(c_Int_Onumber__class_Onumber__of(_1227501), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1227503)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1227501), hAPP(c_Int_Onumber__class_Onumber__of(_1227501), _1227503)))], (15478 ^ _779854) ^ [_1056142, _1056144, _1056146] : [class_Rings_Oring(_1056142), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1056142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056142), _1056144), _1056146)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056142), _1056144), hAPP(c_Groups_Ouminus__class_Ouminus(_1056142), _1056146)))], (10543 ^ _779854) ^ [_958964, _958966, _958968, _958970] : [-(c_Fun_Ooverride__on(_958964, _958966, _958968, _958970, c_Orderings_Obot__class_Obot(tc_fun(_958964, tc_HOL_Obool))) = _958968)], (26999 ^ _779854) ^ [_1269536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269536), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1269536) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31342 ^ _779854) ^ [_1344816, _1344818] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1344816), _1344818) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1344816 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1344816 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (28589 ^ _779854) ^ [_1296715] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1296715)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1296715))))], (19317 ^ _779854) ^ [_1128274, _1128276, _1128278] : [class_Rings_Oordered__ring(_1128274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128274), _1128276), c_Groups_Ozero__class_Ozero(_1128274))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128274), _1128278), c_Groups_Ozero__class_Ozero(_1128274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128274), c_Groups_Ozero__class_Ozero(_1128274)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128274), _1128276), _1128278))))], (42105 ^ _779854) ^ [_1610012, _1610014, _1610016] : [-(hAPP(c_List_Olexn(_1610012, _1610014), hAPP(c_Nat_OSuc, _1610016)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1610012), tc_List_Olist(_1610012)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1610012, tc_List_Olist(_1610012)), tc_prod(_1610012, tc_List_Olist(_1610012))), tc_prod(tc_List_Olist(_1610012), tc_List_Olist(_1610012)), c_Product__Type_Omap__pair(tc_prod(_1610012, tc_List_Olist(_1610012)), tc_List_Olist(_1610012), tc_prod(_1610012, tc_List_Olist(_1610012)), tc_List_Olist(_1610012), hAPP(c_Product__Type_Oprod_Oprod__case(_1610012, tc_List_Olist(_1610012), tc_List_Olist(_1610012)), c_List_Olist_OCons(_1610012)), hAPP(c_Product__Type_Oprod_Oprod__case(_1610012, tc_List_Olist(_1610012), tc_List_Olist(_1610012)), c_List_Olist_OCons(_1610012)))), c_Wellfounded_Olex__prod(_1610012, tc_List_Olist(_1610012), _1610014, hAPP(c_List_Olexn(_1610012, _1610014), _1610016)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1610012), tc_List_Olist(_1610012))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1610012), tc_List_Olist(_1610012), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1610012), tc_fun(tc_List_Olist(_1610012), tc_HOL_Obool), tc_fun(tc_List_Olist(_1610012), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1610012), tc_HOL_Obool), tc_fun(tc_List_Olist(_1610012), tc_HOL_Obool)), tc_List_Olist(_1610012)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1610012))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1610012)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1610012), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1610012)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1610012)))), hAPP(c_Nat_OSuc, _1610016))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1610012), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1610012)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1610012)))), hAPP(c_Nat_OSuc, _1610016)))))))], (50070 ^ _779854) ^ [_1792113, _1792115] : [-(c_Relation_Osym(_1792113, c_Relation_OId__on(_1792113, _1792115)))], (16724 ^ _779854) ^ [_1081110, _1081112, _1081114, _1081116] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1081110, _1081112, _1081114, _1081116, c_Orderings_Obot__class_Obot(tc_fun(_1081110, tc_HOL_Obool))), _1081116)))], (43530 ^ _779854) ^ [_1647418, _1647420, _1647422, _1647424] : [-(hBOOL(hAPP(hAPP(c_member(_1647418), _1647420), hAPP(c_List_Oset(_1647418), _1647422)))), hBOOL(hAPP(hAPP(c_member(_1647418), _1647420), hAPP(c_List_Oset(_1647418), c_List_Oremove1(_1647418, _1647424, _1647422))))], (30981 ^ _779854) ^ [_1339079, _1339081] : [class_Int_Onumber__ring(_1339079), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339079), hAPP(c_Int_Onumber__class_Onumber__of(_1339079), 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)))), _1339081))) = hAPP(c_Int_Onumber__class_Onumber__of(_1339079), c_Int_OMin))], (20180 ^ _779854) ^ [_1143540] : [20181 ^ _779854 : [(20182 ^ _779854) ^ [_1143582] : [_1143540 = hAPP(c_Nat_OSuc, _1143582)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143540)))], (21340 ^ _779854) ^ [_1164370, _1164372] : [21342 ^ _779854 : [(21345 ^ _779854) ^ [] : [hBOOL(hAPP(_1164372, 21341 ^ [_1164370, _1164372]))], (21343 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21341 ^ [_1164370, _1164372]), _1164370)))]], 21346 ^ _779854 : [(21347 ^ _779854) ^ [_1164520] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1164520), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1164370))), -(hBOOL(hAPP(_1164372, _1164520)))]]], (47792 ^ _779854) ^ [_1741074, _1741076, _1741078, _1741080, _1741082] : [c_List_OdropWhile(_1741074, _1741076, _1741078) = hAPP(hAPP(c_List_Olist_OCons(_1741074), _1741080), _1741082), 47795 ^ _779854 : [(47798 ^ _779854) ^ [] : [hBOOL(hAPP(_1741076, _1741080))], (47796 ^ _779854) ^ [] : [-(_1741078 = hAPP(hAPP(c_List_Oappend(_1741074), c_List_OtakeWhile(_1741074, _1741076, _1741078)), hAPP(hAPP(c_List_Olist_OCons(_1741074), _1741080), _1741082)))]]], (102 ^ _779854) ^ [_781315, _781317] : [-(class_Rings_Odivision__ring(_781315)), _781317 = _781315, class_Rings_Odivision__ring(_781317)], (26685 ^ _779854) ^ [_1264574, _1264576] : [class_Int_Onumber__ring(_1264574), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264574), _1264576), hAPP(c_Int_Onumber__class_Onumber__of(_1264574), c_Int_OPls)) = _1264576)], (42659 ^ _779854) ^ [_1626756, _1626758] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1626756), hAPP(c_List_Oset(_1626756), _1626758))))], (26345 ^ _779854) ^ [_1258639] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1258639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258639), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (2748 ^ _779854) ^ [_820725, _820727] : [_820727 = _820725, -(c_Set_OBall(_820727) = c_Set_OBall(_820725))], (9490 ^ _779854) ^ [_938557, _938559, _938561] : [class_Orderings_Olinorder(_938557), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938557), _938559), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938557), _938559), _938561)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_938557), _938559), _938561))], (16948 ^ _779854) ^ [_1085650, _1085652, _1085654, _1085656] : [class_Orderings_Olinorder(_1085650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085650), _1085652)), hBOOL(hAPP(hAPP(c_member(_1085650), _1085654), _1085652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085650), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1085650), _1085654), _1085656)), hAPP(hAPP(c_Finite__Set_Ofold(_1085650, _1085650, c_Orderings_Oord__class_Omax(_1085650)), _1085656), _1085652))))], (9372 ^ _779854) ^ [_936253, _936255, _936257] : [class_Complete__Lattice_Ocomplete__lattice(_936253), -(c_Complete__Lattice_OSup__class_OSup(_936253, hAPP(hAPP(c_Set_Oinsert(_936253), _936255), hAPP(hAPP(c_Set_Oinsert(_936253), _936257), c_Orderings_Obot__class_Obot(tc_fun(_936253, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936253), _936255), _936257))], (16527 ^ _779854) ^ [_1077655, _1077657, _1077659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077655), _1077657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1077657), _1077659))))], (24336 ^ _779854) ^ [_1221205, _1221207, _1221209] : [class_Rings_Oring__1(_1221205), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221205), hAPP(c_Groups_Ouminus__class_Ouminus(_1221205), _1221207)), _1221209) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221205), hAPP(hAPP(c_Power_Opower__class_Opower(_1221205), hAPP(c_Groups_Ouminus__class_Ouminus(_1221205), c_Groups_Oone__class_Oone(_1221205))), _1221209)), hAPP(hAPP(c_Power_Opower__class_Opower(_1221205), _1221207), _1221209)))], (43628 ^ _779854) ^ [_1649416, _1649418, _1649420] : [hBOOL(hAPP(hAPP(c_member(_1649416), _1649418), hAPP(c_List_Oset(_1649416), _1649420))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649416)), c_List_Oremove1(_1649416, _1649418, _1649420)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649416)), _1649420)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (26913 ^ _779854) ^ [_1268053, _1268055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268053), 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)), _1268055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268053), _1268055)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41447 ^ _779854) ^ [_1592486, _1592488, _1592490, _1592492] : [-(hAPP(c_Relation_Oconverse(_1592486, _1592488), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1592486, _1592488), tc_HOL_Obool)), _1592490), _1592492)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1592488, _1592486), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1592486, _1592488), _1592490)), hAPP(c_Relation_Oconverse(_1592486, _1592488), _1592492)))], (7381 ^ _779854) ^ [_901443, _901445, _901447, _901449, _901451] : [class_Lattices_Osemilattice__sup(_901443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901443), _901445), _901447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901443), _901449), _901451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901443), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901443), _901445), _901449)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901443), _901447), _901451))))], (30201 ^ _779854) ^ [_1325046, _1325048, _1325050, _1325052] : [class_Divides_Osemiring__div(_1325046), -(c_Divides_Odiv__class_Omod(_1325046, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325046), _1325048), _1325050), _1325052) = c_Divides_Odiv__class_Omod(_1325046, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325046), c_Divides_Odiv__class_Omod(_1325046, _1325048, _1325052)), _1325050), _1325052))], (22137 ^ _779854) ^ [_1179788, _1179790, _1179792, _1179794] : [class_Fields_Olinordered__field(_1179788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179788), _1179790), _1179792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179788), c_Groups_Ozero__class_Ozero(_1179788)), _1179794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179788), c_Groups_Ozero__class_Ozero(_1179788)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179788), _1179792), _1179790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179788), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179788), _1179794), _1179792)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179788), _1179794), _1179790))))], (20824 ^ _779854) ^ [_1154663, _1154665, _1154667, _1154669] : [class_Rings_Olinordered__semiring__strict(_1154663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154663), _1154665), _1154667)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154663), _1154665), _1154669))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154663), c_Groups_Ozero__class_Ozero(_1154663)), _1154665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154663), _1154667), _1154669)))], (25735 ^ _779854) ^ [_1247658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247658)), -(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)), _1247658))))], (6399 ^ _779854) ^ [_881811, _881813, _881815] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_881811, tc_HOL_Obool)), _881813) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_881811, tc_HOL_Obool)), _881815), -(_881813 = _881815)], (52441 ^ _779854) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (24130 ^ _779854) ^ [_1217578] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1217578) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (42685 ^ _779854) ^ [_1627372, _1627374, _1627376, _1627378] : [hBOOL(hAPP(hAPP(c_member(_1627372), _1627374), hAPP(c_List_Oset(_1627372), hAPP(hAPP(c_List_Olist_OCons(_1627372), _1627376), _1627378)))), -(_1627374 = _1627376), -(hBOOL(hAPP(hAPP(c_member(_1627372), _1627374), hAPP(c_List_Oset(_1627372), _1627378))))], (39061 ^ _779854) ^ [_1527456, _1527458] : [-(hAPP(c_Set_OPow(_1527456), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1527456, tc_HOL_Obool)), _1527458)) = hAPP(c_Set_OCollect(tc_fun(_1527456, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1527456, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1527456, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1527456, tc_HOL_Obool), tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1527456, tc_HOL_Obool)), c_COMBS(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1527456, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1527456, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1527456, tc_HOL_Obool), tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_fun(_1527456, tc_HOL_Obool)), tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_fun(_1527456, tc_HOL_Obool)), tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1527456, tc_HOL_Obool)), c_COMBB(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1527456, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1527456, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1527456, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1527456, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1527456, tc_HOL_Obool)), _1527458)), c_Set_OPow(_1527456))))))], (40021 ^ _779854) ^ [_1557547, _1557549] : [c_Wellfounded_OwfP(_1557547, _1557549), -(c_Wellfounded_Owf(_1557547, hAPP(c_Set_OCollect(tc_prod(_1557547, _1557547)), hAPP(c_Product__Type_Oprod_Oprod__case(_1557547, _1557547, tc_HOL_Obool), _1557549))))], (32425 ^ _779854) ^ [_1363340, _1363342] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1363340), _1363342))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1363340))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1363342))))], (39096 ^ _779854) ^ [_1528924] : [-(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)))), _1528924))))], (50182 ^ _779854) ^ [_1793870, _1793872] : [c_Equiv__Relations_Opart__equivp(_1793870, _1793872), 50186 ^ _779854 : [(50191 ^ _779854) ^ [] : [-(c_Predicate_Otransp(_1793870, _1793872))], (50189 ^ _779854) ^ [] : [-(c_Predicate_Osymp(_1793870, _1793872))], (50187 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1793872, 50185 ^ [_1793870, _1793872]), 50185 ^ [_1793870, _1793872])))]]], (25699 ^ _779854) ^ [_1247043] : [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)), _1247043)), _1247043)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247043), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35919 ^ _779854) ^ [_1449104, _1449106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449104), 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)), _1449106)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1449104, _1449106) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1449104, _1449106)))], (29015 ^ _779854) ^ [_1303590] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1303590))) = 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)))), _1303590))], (33132 ^ _779854) ^ [_1380484, _1380486, _1380488] : [class_Orderings_Obot(_1380484), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1380486, _1380484)), _1380488) = c_Orderings_Obot__class_Obot(_1380484))], (32503 ^ _779854) ^ [_1364782, _1364784, _1364786] : [32505 ^ _779854 : [(32508 ^ _779854) ^ [] : [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(_1364784, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 32504 ^ [_1364782, _1364784, _1364786]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1364784, 32504 ^ [_1364782, _1364784, _1364786])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32506 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32504 ^ [_1364782, _1364784, _1364786]), _1364782)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1364784, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1364786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1364786), hAPP(_1364784, _1364782))), 32518 ^ _779854 : [(32521 ^ _779854) ^ [] : [-(hAPP(_1364784, 32517 ^ [_1364782, _1364784, _1364786]) = _1364786)], (32519 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 32517 ^ [_1364782, _1364784, _1364786]), _1364782)))]]], (28858 ^ _779854) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8000 ^ _779854) ^ [_913624, _913626, _913628] : [class_Orderings_Oorder(_913624), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913624, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_913624, _913626, _913628)), hAPP(c_SetInterval_Oord__class_OatLeast(_913624), _913628)) = c_Orderings_Obot__class_Obot(tc_fun(_913624, tc_HOL_Obool)))], (48143 ^ _779854) ^ [_1749153, _1749155, _1749157, _1749159] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1749153, _1749155, _1749157, _1749159) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1749153, _1749155), _1749157), _1749159)))], (3548 ^ _779854) ^ [_833087, _833089] : [_833089 = _833087, -(c_SetInterval_Oord__class_OatMost(_833089) = c_SetInterval_Oord__class_OatMost(_833087))], (18893 ^ _779854) ^ [_1120750, _1120752, _1120754] : [18894 ^ _779854 : [(18897 ^ _779854) ^ [] : [_1120750 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18895 ^ _779854) ^ [] : [_1120752 = _1120754]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120750), _1120752) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120750), _1120754))], (51975 ^ _779854) ^ [_1830798, _1830800, _1830802] : [_1830798 = _1830800, 51986 ^ _779854 : [(51989 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830802), _1830798))], (51987 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830798), _1830802)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830800), _1830802)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830802), _1830800)))], (25907 ^ _779854) ^ [_1250764, _1250766] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1250764, _1250766))))], (46585 ^ _779854) ^ [_1716886, _1716888, _1716890, _1716892] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716886)), _1716888))), c_List_Ofoldr(tc_List_Olist(_1716890), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1716890)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1716890))), _1716892, 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(_1716886)), _1716888)), c_List_Ofoldr(tc_List_Olist(_1716890), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1716890)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1716890), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1716890)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1716890)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1716890), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1716890)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1716890), tc_List_Olist(_1716890), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1716890)))), _1716892), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (33443 ^ _779854) ^ [_1388749, _1388751, _1388753, _1388755] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388749, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1388749, tc_fun(_1388749, tc_HOL_Obool), tc_HOL_Obool), c_member(_1388749)), _1388751)), hAPP(hAPP(c_COMBC(_1388749, tc_fun(_1388749, tc_HOL_Obool), tc_HOL_Obool), c_member(_1388749)), _1388753)), _1388755)), -(hBOOL(hAPP(hAPP(c_member(_1388749), _1388755), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388749, tc_HOL_Obool)), _1388751), _1388753))))], (2664 ^ _779854) ^ [_819429, _819431, _819433, _819435] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_819435, _819431) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_819433, _819429)), _819435 = _819433, _819431 = _819429], (8034 ^ _779854) ^ [_914285, _914287, _914289] : [class_Orderings_Olinorder(_914285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914285), _914287), _914289)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914285, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_914285), _914287), c_Orderings_Obot__class_Obot(tc_fun(_914285, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_914285, _914287, _914289)) = c_SetInterval_Oord__class_OatLeastAtMost(_914285, _914287, _914289))], (38987 ^ _779854) ^ [_1524971, _1524973, _1524975, _1524977] : [-(hAPP(c_Relation_OImage(_1524971, _1524973, _1524975), hAPP(hAPP(c_Set_Oinsert(_1524971), _1524977), c_Orderings_Obot__class_Obot(tc_fun(_1524971, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1524973), hAPP(hAPP(c_COMBC(_1524973, tc_fun(tc_prod(_1524971, _1524973), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1524971, _1524973), tc_fun(tc_fun(tc_prod(_1524971, _1524973), tc_HOL_Obool), tc_HOL_Obool), _1524973), c_member(tc_prod(_1524971, _1524973))), hAPP(c_Product__Type_OPair(_1524971, _1524973), _1524977))), _1524975)))], (30357 ^ _779854) ^ [_1328090, _1328092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328092)), -(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, _1328090, _1328092))))], (18751 ^ _779854) ^ [_1118742, _1118744] : [class_Groups_Olinordered__ab__group__add(_1118742), 18754 ^ _779854 : [(18761 ^ _779854) ^ [] : [_1118744 = c_Groups_Ozero__class_Ozero(_1118742), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1118742), _1118744) = _1118744)], (18755 ^ _779854) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1118742), _1118744) = _1118744, -(_1118744 = c_Groups_Ozero__class_Ozero(_1118742))]]], (29899 ^ _779854) ^ [] : [-(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))))], (38715 ^ _779854) ^ [_1518017] : [-(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)), _1518017)))))], (28860 ^ _779854) ^ [_1301069, _1301071] : [class_Rings_Osemiring__1(_1301069), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1301069), hAPP(c_Nat_OSuc, _1301071)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301069), c_Groups_Oone__class_Oone(_1301069)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1301069), _1301071)))], (44280 ^ _779854) ^ [_1665059, _1665061, _1665063] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1665059, tc_HOL_Obool)), hAPP(c_List_Oset(_1665059), hAPP(hAPP(c_List_Odrop(_1665059), _1665061), _1665063))), hAPP(c_List_Oset(_1665059), _1665063))))], (6757 ^ _779854) ^ [_888772, _888774, _888776, _888778] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888772, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888772, tc_HOL_Obool)), _888774), _888776)), _888778) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888772, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888772, tc_HOL_Obool)), _888774), _888778)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888772, tc_HOL_Obool)), _888776), _888778)))], (47711 ^ _779854) ^ [_1739441, _1739443, _1739445] : [hBOOL(hAPP(c_List_Odistinct(_1739441), _1739443)), hBOOL(hAPP(hAPP(c_member(_1739441), _1739445), hAPP(c_List_Oset(_1739441), _1739443))), -(c_List_OdropWhile(_1739441, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1739441), c_fNot), hAPP(hAPP(c_COMBC(_1739441, _1739441, tc_HOL_Obool), c_fequal), _1739445)), hAPP(c_List_Orev(_1739441), _1739443)) = hAPP(hAPP(c_List_Olist_OCons(_1739441), _1739445), hAPP(c_List_Orev(_1739441), c_List_OtakeWhile(_1739441, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1739441), c_fNot), hAPP(hAPP(c_COMBC(_1739441, _1739441, tc_HOL_Obool), c_fequal), _1739445)), _1739443))))], (8868 ^ _779854) ^ [_927407, _927409, _927411] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927407, tc_HOL_Obool)), _927409), hAPP(hAPP(c_Set_Oinsert(_927407), _927411), _927409))))], (48573 ^ _779854) ^ [_1758601, _1758603, _1758605, _1758607] : [-(c_List_Olist__all(_1758601, _1758603, hAPP(hAPP(c_List_Oappend(_1758601), _1758605), _1758607))), c_List_Olist__all(_1758601, _1758603, _1758605), c_List_Olist__all(_1758601, _1758603, _1758607)], (4018 ^ _779854) ^ [_840768, _840770] : [_840770 = _840768, -(c_New__DSequence_Opos__empty(_840770) = c_New__DSequence_Opos__empty(_840768))], (6117 ^ _779854) ^ [_876904, _876906, _876908, _876910, _876912] : [class_Complete__Lattice_Ocomplete__lattice(_876904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876906, tc_HOL_Obool)), _876908), _876910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876904), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_876906, _876904), _876908), _876912)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_876906, _876904), _876910), _876912))))], (46844 ^ _779854) ^ [_1722372, _1722374, _1722376] : [class_Orderings_Olinorder(_1722372), c_List_Olinorder__class_Osorted(_1722372, _1722374), -(c_List_Olinorder__class_Osorted(_1722372, c_List_Olinorder__class_Oinsort__insert__key(_1722372, _1722372, c_COMBI(_1722372), _1722376, _1722374)))], (28015 ^ _779854) ^ [_1286635, _1286637, _1286639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1286635)), 28018 ^ _779854 : [(28019 ^ _779854) ^ [] : [-(_1286637 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1286639), _1286635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1286635), _1286637)), _1286639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1286639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1286635), hAPP(c_Nat_OSuc, _1286637))))], (28029 ^ _779854) ^ [] : [_1286637 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1286639), _1286635), 28032 ^ _779854 : [(28035 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1286639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1286635), hAPP(c_Nat_OSuc, _1286637)))))], (28033 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1286635), _1286637)), _1286639)))]]]]], (14528 ^ _779854) ^ [_1037153, _1037155, _1037157, _1037159, _1037161] : [class_Groups_Oab__group__add(_1037153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037155), _1037157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037157), _1037159)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1037153), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1037153), _1037161), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1037155), _1037159))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1037153), _1037161), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1037155), _1037157))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1037153), _1037161), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1037157), _1037159)))], (48782 ^ _779854) ^ [_1762623, _1762625, _1762627, _1762629, _1762631] : [_1762623 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1762625, _1762627, _1762629, _1762631), _1762623) = c_Lazy__Sequence_Ohit__bound(_1762627))], (36454 ^ _779854) ^ [_1460384, _1460386, _1460388] : [class_Orderings_Owellorder(_1460384), hBOOL(hAPP(_1460386, _1460388)), -(hBOOL(hAPP(_1460386, c_Orderings_Oord__class_OLeast(_1460384, _1460386))))], (32846 ^ _779854) ^ [_1371675, _1371677, _1371679] : [class_Groups_Ocomm__monoid__add(_1371675), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371677, _1371675), hAPP(c_COMBK(_1371675, _1371677), c_Groups_Ozero__class_Ozero(_1371675))), _1371679) = c_Groups_Ozero__class_Ozero(_1371675))], (8080 ^ _779854) ^ [_915240, _915242, _915244, _915246] : [class_Orderings_Olinorder(_915240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915240), _915242), _915244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915240), _915244), _915246)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915240, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_915240, _915242, _915244)), c_SetInterval_Oord__class_OgreaterThanLessThan(_915240, _915244, _915246)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_915240, _915242, _915246))], (47462 ^ _779854) ^ [_1734215, _1734217, _1734219, _1734221] : [_1734217 = hAPP(hAPP(c_List_Oappend(_1734215), hAPP(c_List_Orev(_1734215), _1734221)), hAPP(hAPP(c_List_Olist_OCons(_1734215), _1734219), c_List_Olist_ONil(_1734215))), -(hAPP(c_List_Orev(_1734215), _1734217) = hAPP(hAPP(c_List_Olist_OCons(_1734215), _1734219), _1734221))], (27649 ^ _779854) ^ [_1280287, _1280289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1280287)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1280287), _1280289)), _1280287) = _1280289)], (38222 ^ _779854) ^ [_1503801, _1503803, _1503805, _1503807, _1503809, _1503811] : [-(hBOOL(hAPP(hAPP(c_member(_1503801), _1503803), _1503805))), 38225 ^ _779854 : [(38232 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503801), _1503807), _1503805))), -(hAPP(c_Set_Ovimage(_1503809, _1503801, hAPP(hAPP(c_COMBC(_1503809, _1503801, _1503801), hAPP(hAPP(c_COMBC(_1503809, _1503801, tc_fun(_1503801, _1503801)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1503801, tc_fun(_1503801, _1503801)), _1503809), c_If(_1503801)), hAPP(hAPP(c_COMBC(_1503809, tc_fun(_1503809, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503809)), _1503811))), _1503803)), _1503807)), _1503805) = c_Orderings_Obot__class_Obot(tc_fun(_1503809, tc_HOL_Obool)))], (38226 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1503801), _1503807), _1503805)), -(hAPP(c_Set_Ovimage(_1503809, _1503801, hAPP(hAPP(c_COMBC(_1503809, _1503801, _1503801), hAPP(hAPP(c_COMBC(_1503809, _1503801, tc_fun(_1503801, _1503801)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1503801, tc_fun(_1503801, _1503801)), _1503809), c_If(_1503801)), hAPP(hAPP(c_COMBC(_1503809, tc_fun(_1503809, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503809)), _1503811))), _1503803)), _1503807)), _1503805) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1503809, tc_HOL_Obool)), _1503811))]]], (3534 ^ _779854) ^ [_832866, _832868, _832870, _832872, _832874, _832876] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_832876, _832872, _832868) = c_SetInterval_Oord__class_OgreaterThanLessThan(_832874, _832870, _832866)), _832876 = _832874, _832872 = _832870, _832868 = _832866], (32674 ^ _779854) ^ [_1368018, _1368020] : [-(_1368018 = _1368020), -(c_Random_Oinc__shift(_1368018, _1368020) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1368020), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (44302 ^ _779854) ^ [_1665517, _1665519, _1665521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665517)), _1665519)), _1665521)), -(hAPP(hAPP(c_List_Odrop(_1665517), _1665521), _1665519) = c_List_Olist_ONil(_1665517))], (1094 ^ _779854) ^ [_796361, _796363, _796365, _796367, _796369, _796371, _796373, _796375, _796377, _796379] : [-(c_Finite__Set_Ofolding__image(_796377, _796373, _796369, _796365, _796361)), c_Finite__Set_Ofolding__image(_796379, _796375, _796371, _796367, _796363), _796379 = _796377, _796375 = _796373, _796371 = _796369, _796367 = _796365, _796363 = _796361], (14616 ^ _779854) ^ [_1038987, _1038989] : [class_Orderings_Olinorder(_1038987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038987), _1038989)), -(c_Big__Operators_Olinorder__class_OMin(_1038987, _1038989) = hAPP(c_Finite__Set_Ofold1(_1038987, c_Orderings_Oord__class_Omin(_1038987)), _1038989))], (18345 ^ _779854) ^ [_1111869, _1111871, _1111873] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1111869), _1111871)), -(hBOOL(hAPP(hAPP(c_member(_1111869), _1111873), _1111871))), -(hAPP(c_Finite__Set_Ocard(_1111869), hAPP(hAPP(c_Set_Oinsert(_1111869), _1111873), _1111871)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1111869), _1111871)))], (20283 ^ _779854) ^ [_1145102, _1145104] : [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), _1145102), _1145104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145102))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145104)))], (40885 ^ _779854) ^ [_1578315, _1578317] : [c_Wellfounded_Owf(_1578315, _1578317), 40888 ^ _779854 : [(40889 ^ _779854) ^ [_1578447] : [40890 ^ _779854 : [(40891 ^ _779854) ^ [_1578552] : [hBOOL(hAPP(hAPP(c_member(_1578315), _1578552), _1578447))]], 40893 ^ _779854 : [(40896 ^ _779854) ^ [_1578674] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578315, _1578315)), hAPP(hAPP(c_Product__Type_OPair(_1578315, _1578315), _1578674), 40892 ^ [_1578315, _1578317, _1578447])), _1578317)), hBOOL(hAPP(hAPP(c_member(_1578315), _1578674), _1578447))], (40894 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578315), 40892 ^ [_1578315, _1578317, _1578447]), _1578447)))]]]]], (6101 ^ _779854) ^ [_876612, _876614, _876616] : [class_Orderings_Oorder(_876612), 6104 ^ _779854 : [(6111 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876612), _876614), _876616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876612, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_876612), _876614)), hAPP(c_SetInterval_Oord__class_OatMost(_876612), _876616))))], (6105 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876612, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_876612), _876614)), hAPP(c_SetInterval_Oord__class_OatMost(_876612), _876616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876612), _876614), _876616)))]]], (7467 ^ _779854) ^ [_902948, _902950, _902952] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_902948, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902948, tc_HOL_Obool)), _902950), _902952)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_902948, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_902948, tc_HOL_Obool)), _902950)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_902948, tc_HOL_Obool)), _902952)))], (7834 ^ _779854) ^ [_910599, _910601, _910603] : [class_Orderings_Oorder(_910599), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_910599, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_910599), _910601)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_910599, _910601), _910603)) = c_Orderings_Obot__class_Obot(tc_fun(_910599, tc_HOL_Obool)))], (52195 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11870 ^ _779854) ^ [_986110, _986112] : [_986112 = c_Orderings_Obot__class_Obot(tc_fun(_986110, tc_HOL_Obool)), 11873 ^ _779854 : [(11874 ^ _779854) ^ [_986190] : [hBOOL(hAPP(hAPP(c_member(_986110), _986190), _986112))]]], (38308 ^ _779854) ^ [_1506348, _1506350, _1506352, _1506354] : [hAPP(hAPP(c_Product__Type_OSigma(_1506348, _1506350), _1506352), hAPP(c_COMBK(tc_fun(_1506350, tc_HOL_Obool), _1506348), _1506354)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1506348, _1506350), tc_HOL_Obool)), -(_1506352 = c_Orderings_Obot__class_Obot(tc_fun(_1506348, tc_HOL_Obool))), -(_1506354 = c_Orderings_Obot__class_Obot(tc_fun(_1506350, tc_HOL_Obool)))], (39309 ^ _779854) ^ [_1538767, _1538769] : [-(c_Fun_Oinj__on(_1538767, _1538767, c_Fun_Oid(_1538767), _1538769))], (35422 ^ _779854) ^ [_1439806, _1439808, _1439810, _1439812] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1439806, _1439808)), c_Nitpick_Opair__box_OPairBox(_1439806, _1439808, _1439810, _1439812)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44408 ^ _779854) ^ [_1668158, _1668160, _1668162, _1668164] : [-(hAPP(c_List_Orotate1(_1668158), c_List_Olist_ONil(_1668158)) = c_List_Olist_ONil(_1668158))], (9540 ^ _779854) ^ [_939719, _939721, _939723, _939725] : [hAPP(c_Set_Oimage(_939719, _939721, _939723), _939725) = c_Orderings_Obot__class_Obot(tc_fun(_939721, tc_HOL_Obool)), -(_939725 = c_Orderings_Obot__class_Obot(tc_fun(_939719, tc_HOL_Obool)))], (45093 ^ _779854) ^ [_1682263, _1682265, _1682267, _1682269] : [c_List_Olist_ONil(_1682263) = hAPP(hAPP(c_List_Omap(_1682265, _1682263), _1682267), _1682269), -(_1682269 = c_List_Olist_ONil(_1682265))], (39461 ^ _779854) ^ [_1542816, _1542818] : [-(hAPP(c_Relation_ORange(_1542816, _1542818), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542816, _1542818), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1542818, tc_HOL_Obool)))], (34821 ^ _779854) ^ [_1426902, _1426904, _1426906, _1426908, _1426910] : [-(c_Nat_Onat_Onat__case(_1426902, _1426904, _1426906, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426908)), _1426910)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1426902), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1426908))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1426902, _1426902), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1426902, tc_fun(_1426902, _1426902)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1426902, tc_fun(_1426902, _1426902)), tc_Int_Oint), c_If(_1426902)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1426902, _1426904, _1426906, _1426910))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1426902, tc_Int_Oint), _1426906), 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)), _1426910)))))], (11748 ^ _779854) ^ [_983708, _983710, _983712, _983714] : [hBOOL(hAPP(hAPP(c_member(_983708), _983710), c_Complete__Lattice_OInf__class_OInf(tc_fun(_983708, tc_HOL_Obool), _983712))), hBOOL(hAPP(hAPP(c_member(tc_fun(_983708, tc_HOL_Obool)), _983714), _983712)), -(hBOOL(hAPP(hAPP(c_member(_983708), _983710), _983714)))], (34501 ^ _779854) ^ [_1419780] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419780)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419780)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419780)), 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)))))], (32898 ^ _779854) ^ [_1373878, _1373880, _1373882, _1373884, _1373886, _1373888] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1373878, tc_fun(_1373880, tc_fun(_1373882, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1373878, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool), tc_fun(_1373880, tc_fun(_1373882, tc_HOL_Obool)), _1373878), hAPP(c_COMBC(_1373880, tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool), tc_fun(_1373882, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373882, tc_fun(tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool), tc_fun(_1373882, tc_HOL_Obool)), _1373880), c_COMBC(_1373882, tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373882, tc_prod(_1373880, _1373882)), tc_fun(_1373882, tc_fun(tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool), tc_HOL_Obool)), _1373880), hAPP(c_COMBB(tc_prod(_1373880, _1373882), tc_fun(tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool), tc_HOL_Obool), _1373882), c_member(tc_prod(_1373880, _1373882)))), c_Product__Type_OPair(_1373880, _1373882))))), _1373884)), _1373886), _1373888)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1373880, _1373882)), hAPP(hAPP(c_Product__Type_OPair(_1373880, _1373882), _1373886), _1373888)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1373878, tc_fun(tc_prod(_1373880, _1373882), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1373878, tc_HOL_Obool))), _1373884))))], (33108 ^ _779854) ^ [_1379817, _1379819, _1379821, _1379823, _1379825] : [-(_1379817 = c_Orderings_Obot__class_Obot(tc_fun(_1379819, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379819, tc_fun(_1379821, tc_HOL_Obool)), _1379817), hAPP(hAPP(c_COMBC(_1379819, tc_fun(_1379821, tc_HOL_Obool), tc_fun(_1379821, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1379821, tc_HOL_Obool), tc_fun(tc_fun(_1379821, tc_HOL_Obool), tc_fun(_1379821, tc_HOL_Obool)), _1379819), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379821, tc_HOL_Obool))), _1379823)), _1379825)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379821, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379819, tc_fun(_1379821, tc_HOL_Obool)), _1379817), _1379823)), _1379825))], (33553 ^ _779854) ^ [_1394197, _1394199, _1394201, _1394203, _1394205, _1394207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1394197, _1394199)), hAPP(hAPP(c_Product__Type_OPair(_1394197, _1394199), _1394205), _1394207)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool)), _1394201), _1394203))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394197, tc_fun(_1394199, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1394197, tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_fun(_1394199, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1394199, tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_fun(_1394199, tc_HOL_Obool)), _1394197), c_COMBC(_1394199, tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1394199, tc_prod(_1394197, _1394199)), tc_fun(_1394199, tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool)), _1394197), hAPP(c_COMBB(tc_prod(_1394197, _1394199), tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool), _1394199), c_member(tc_prod(_1394197, _1394199)))), c_Product__Type_OPair(_1394197, _1394199)))), _1394201)), hAPP(hAPP(c_COMBC(_1394197, tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_fun(_1394199, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1394199, tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_fun(_1394199, tc_HOL_Obool)), _1394197), c_COMBC(_1394199, tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1394199, tc_prod(_1394197, _1394199)), tc_fun(_1394199, tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool)), _1394197), hAPP(c_COMBB(tc_prod(_1394197, _1394199), tc_fun(tc_fun(tc_prod(_1394197, _1394199), tc_HOL_Obool), tc_HOL_Obool), _1394199), c_member(tc_prod(_1394197, _1394199)))), c_Product__Type_OPair(_1394197, _1394199)))), _1394203)), _1394205), _1394207)))], (52701 ^ _779854) ^ [_1839127, _1839129] : [hBOOL(hAPP(hAPP(c_fdisj, _1839127), _1839129)), -(hBOOL(_1839127)), -(hBOOL(_1839129))], (480 ^ _779854) ^ [_787066, _787068, _787070, _787072, _787074, _787076] : [-(c_Nitpick_Oless__frac(_787074, _787070, _787066)), c_Nitpick_Oless__frac(_787076, _787072, _787068), _787076 = _787074, _787072 = _787070, _787068 = _787066], (33126 ^ _779854) ^ [_1380239, _1380241, _1380243, _1380245, _1380247] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380239, tc_fun(_1380241, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1380239), _1380243), _1380245)), _1380247) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380241, tc_HOL_Obool)), hAPP(_1380247, _1380243)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380239, tc_fun(_1380241, tc_HOL_Obool)), _1380245), _1380247)))], (18939 ^ _779854) ^ [_1121437] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1121437) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43346 ^ _779854) ^ [_1644179, _1644181] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1644179)), c_List_Olist_ONil(_1644179)), c_List_Olists(_1644179, _1644181))))], (38478 ^ _779854) ^ [_1510859, _1510861, _1510863, _1510865, _1510867, _1510869] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1510859, _1510861), hAPP(hAPP(c_Set_Oinsert(_1510859), _1510863), _1510865)), hAPP(c_COMBK(tc_fun(_1510861, tc_HOL_Obool), _1510859), hAPP(hAPP(c_Set_Oinsert(_1510861), _1510867), _1510869))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1510859, _1510861)), hAPP(hAPP(c_Product__Type_OPair(_1510859, _1510861), _1510863), _1510867)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510859, _1510861), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1510859, _1510861), _1510865), hAPP(c_COMBK(tc_fun(_1510861, tc_HOL_Obool), _1510859), hAPP(hAPP(c_Set_Oinsert(_1510861), _1510867), _1510869)))), hAPP(hAPP(c_Product__Type_OSigma(_1510859, _1510861), hAPP(hAPP(c_Set_Oinsert(_1510859), _1510863), _1510865)), hAPP(c_COMBK(tc_fun(_1510861, tc_HOL_Obool), _1510859), _1510869)))))], (39407 ^ _779854) ^ [_1541156, _1541158, _1541160, _1541162, _1541164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541156, _1541158)), hAPP(hAPP(c_Product__Type_OPair(_1541156, _1541158), _1541160), _1541162)), _1541164)), -(hBOOL(hAPP(hAPP(c_member(_1541158), _1541162), hAPP(c_Relation_ORange(_1541156, _1541158), _1541164))))], (21605 ^ _779854) ^ [_1169804] : [class_Rings_Oring__1(_1169804), -(hBOOL(hAPP(hAPP(c_member(_1169804), c_Groups_Ozero__class_Ozero(_1169804)), c_Int_Oring__1__class_OInts(_1169804))))], (51531 ^ _779854) ^ [_1823234, _1823236] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1823234), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823236))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823236), _1823234)))], (39545 ^ _779854) ^ [_1545939, _1545941, _1545943, _1545945, _1545947, _1545949, _1545951] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1545939, _1545941, _1545943, hAPP(hAPP(c_COMBC(_1545939, tc_fun(tc_prod(_1545939, _1545941), tc_HOL_Obool), tc_fun(_1545941, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545941, tc_fun(tc_fun(tc_prod(_1545939, _1545941), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545939, _1545941), tc_HOL_Obool), tc_fun(_1545941, tc_HOL_Obool)), _1545939), c_COMBC(_1545941, tc_fun(tc_prod(_1545939, _1545941), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545941, tc_prod(_1545939, _1545941)), tc_fun(_1545941, tc_fun(tc_fun(tc_prod(_1545939, _1545941), tc_HOL_Obool), tc_HOL_Obool)), _1545939), hAPP(c_COMBB(tc_prod(_1545939, _1545941), tc_fun(tc_fun(tc_prod(_1545939, _1545941), tc_HOL_Obool), tc_HOL_Obool), _1545941), c_member(tc_prod(_1545939, _1545941)))), c_Product__Type_OPair(_1545939, _1545941)))), _1545945), hAPP(hAPP(c_COMBC(_1545941, tc_fun(tc_prod(_1545941, _1545943), tc_HOL_Obool), tc_fun(_1545943, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545943, tc_fun(tc_fun(tc_prod(_1545941, _1545943), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545941, _1545943), tc_HOL_Obool), tc_fun(_1545943, tc_HOL_Obool)), _1545941), c_COMBC(_1545943, tc_fun(tc_prod(_1545941, _1545943), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545943, tc_prod(_1545941, _1545943)), tc_fun(_1545943, tc_fun(tc_fun(tc_prod(_1545941, _1545943), tc_HOL_Obool), tc_HOL_Obool)), _1545941), hAPP(c_COMBB(tc_prod(_1545941, _1545943), tc_fun(tc_fun(tc_prod(_1545941, _1545943), tc_HOL_Obool), tc_HOL_Obool), _1545943), c_member(tc_prod(_1545941, _1545943)))), c_Product__Type_OPair(_1545941, _1545943)))), _1545947)), _1545949), _1545951)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545939, _1545943)), hAPP(hAPP(c_Product__Type_OPair(_1545939, _1545943), _1545949), _1545951)), hAPP(hAPP(c_Relation_Orel__comp(_1545939, _1545941, _1545943), _1545945), _1545947))))], (23601 ^ _779854) ^ [_1207368, _1207370, _1207372, _1207374] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1207368, tc_Nat_Onat), _1207370), _1207372) = hAPP(c_Nat_OSuc, _1207374), 23605 ^ _779854 : [(23608 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1207370, 23604 ^ [_1207368, _1207370, _1207372, _1207374]))))], (23606 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1207368), 23604 ^ [_1207368, _1207370, _1207372, _1207374]), _1207372)))]]], (14839 ^ _779854) ^ [_1042935, _1042937, _1042939, _1042941] : [c_Big__Operators_Osemilattice__big(_1042935, _1042937, _1042939), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042935), _1042941)), -(hAPP(_1042939, _1042941) = hAPP(c_Finite__Set_Ofold1(_1042935, _1042937), _1042941))], (22235 ^ _779854) ^ [_1181753, _1181755, _1181757] : [class_Fields_Ofield__inverse__zero(_1181753), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1181753), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181753), _1181755), _1181757)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181753), _1181755), hAPP(c_Groups_Ouminus__class_Ouminus(_1181753), _1181757)))], (27101 ^ _779854) ^ [_1271257, _1271259] : [class_Int_Onumber__ring(_1271257), class_Rings_Olinordered__idom(_1271257), 27108 ^ _779854 : [(27115 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271259), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271257), hAPP(c_Int_Onumber__class_Onumber__of(_1271257), _1271259)), c_Groups_Ozero__class_Ozero(_1271257))))], (27109 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271257), hAPP(c_Int_Onumber__class_Onumber__of(_1271257), _1271259)), c_Groups_Ozero__class_Ozero(_1271257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271259), c_Int_OPls)))]]], (28489 ^ _779854) ^ [_1294930, _1294932] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1294930)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1294932)), _1294930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1294932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14967 ^ _779854) ^ [_1045459, _1045461, _1045463, _1045465, _1045467, _1045469, _1045471, _1045473] : [class_Groups_Ocomm__monoid__add(_1045459), c_Fun_Oinj__on(_1045461, _1045463, _1045465, _1045467), _1045469 = hAPP(c_Set_Oimage(_1045461, _1045463, _1045465), _1045467), 14981 ^ _779854 : [(14984 ^ _779854) ^ [] : [hAPP(_1045471, 14980 ^ [_1045459, _1045461, _1045463, _1045465, _1045467, _1045469, _1045471, _1045473]) = hAPP(_1045473, hAPP(_1045465, 14980 ^ [_1045459, _1045461, _1045463, _1045465, _1045467, _1045469, _1045471, _1045473]))], (14982 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1045461), 14980 ^ [_1045459, _1045461, _1045463, _1045465, _1045467, _1045469, _1045471, _1045473]), _1045467)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1045463, _1045459), _1045473), _1045469) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1045461, _1045459), _1045471), _1045467))], (48000 ^ _779854) ^ [_1745663, _1745665, _1745667, _1745669, _1745671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1745663, _1745665)), hAPP(_1745663, _1745667))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1745669, _1745669)), hAPP(hAPP(c_Product__Type_OPair(_1745669, _1745669), _1745665), _1745667)), c_List_Omeasures(_1745669, _1745671))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1745669, _1745669)), hAPP(hAPP(c_Product__Type_OPair(_1745669, _1745669), _1745665), _1745667)), c_List_Omeasures(_1745669, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1745669, tc_Nat_Onat)), _1745663), _1745671)))))], (46336 ^ _779854) ^ [_1709766, _1709768] : [class_Orderings_Olinorder(_1709766), -(c_List_Olinorder__class_Osort__key(_1709766, _1709766, c_COMBI(_1709766), _1709768) = hAPP(c_List_Ofoldl(tc_List_Olist(_1709766), _1709766, hAPP(c_COMBC(_1709766, tc_List_Olist(_1709766), tc_List_Olist(_1709766)), c_List_Olinorder__class_Oinsort__key(_1709766, _1709766, c_COMBI(_1709766))), c_List_Olist_ONil(_1709766)), _1709768))], (29469 ^ _779854) ^ [_1311416, _1311418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1311416)), c_Int_OBit1(_1311418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311416), _1311418)))], (41453 ^ _779854) ^ [_1592665, _1592667, _1592669, _1592671, _1592673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592665, _1592667)), hAPP(hAPP(c_Product__Type_OPair(_1592665, _1592667), _1592669), _1592671)), hAPP(c_Relation_Oconverse(_1592667, _1592665), _1592673))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592667, _1592665)), hAPP(hAPP(c_Product__Type_OPair(_1592667, _1592665), _1592671), _1592669)), _1592673)))], (6871 ^ _779854) ^ [_891390, _891392, _891394, _891396, _891398] : [class_Lattices_Olattice(_891390), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_891392, _891390)), _891394), _891396), _891398) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_891390), hAPP(_891394, _891398)), hAPP(_891396, _891398)))], (33012 ^ _779854) ^ [_1377352, _1377354, _1377356, _1377358, _1377360] : [hBOOL(hAPP(hAPP(c_member(_1377352), _1377354), _1377356)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377358, tc_HOL_Obool)), hAPP(_1377360, _1377354)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377352, tc_fun(_1377358, tc_HOL_Obool)), _1377356), _1377360)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377352, tc_fun(_1377358, tc_HOL_Obool)), _1377356), _1377360))], (45504 ^ _779854) ^ [_1691418, _1691420, _1691422, _1691424] : [class_Groups_Ocomm__monoid__add(_1691418), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1691418), _1691420), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1691422, _1691424))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1691418), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1691418), _1691420), c_List_Oupto(_1691422, _1691424))))], (45752 ^ _779854) ^ [_1697097, _1697099, _1697101, _1697103] : [-(hBOOL(hAPP(c_List_Olistsp(_1697097, _1697099), hAPP(hAPP(c_List_Oappend(_1697097), _1697101), _1697103)))), hBOOL(hAPP(c_List_Olistsp(_1697097, _1697099), _1697101)), hBOOL(hAPP(c_List_Olistsp(_1697097, _1697099), _1697103))], (9326 ^ _779854) ^ [_935496, _935498, _935500] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_935496, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_935496, tc_HOL_Obool)), _935498), _935500)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_935496, tc_HOL_Obool)), _935498), c_Complete__Lattice_OSup__class_OSup(tc_fun(_935496, tc_HOL_Obool), _935500)))], (26587 ^ _779854) ^ [_1263110] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1263110) = _1263110)], (39838 ^ _779854) ^ [_1552821, _1552823, _1552825] : [c_Wellfounded_Owf(_1552821, _1552823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552821, tc_HOL_Obool)), _1552825), hAPP(c_Relation_OImage(_1552821, _1552821, _1552823), _1552825))), -(_1552825 = c_Orderings_Obot__class_Obot(tc_fun(_1552821, tc_HOL_Obool)))], (35470 ^ _779854) ^ [_1440766, _1440768, _1440770, _1440772, _1440774, _1440776] : [-(c_Nitpick_Opair__box_Opair__box__case(_1440766, _1440768, _1440770, _1440772, c_Nitpick_Opair__box_OPairBox(_1440766, _1440768, _1440774, _1440776)) = hAPP(hAPP(_1440772, _1440774), _1440776))], (18036 ^ _779854) ^ [_1106226, _1106228] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106226), _1106228)), _1106226 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1106228 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (52651 ^ _779854) ^ [] : [hBOOL(c_fFalse)], (32419 ^ _779854) ^ [_1363296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1363296), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1363296) = _1363296)], (42903 ^ _779854) ^ [_1634089, _1634091, _1634093, _1634095] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634089, _1634089)), hAPP(hAPP(c_Product__Type_OPair(_1634089, _1634089), _1634091), _1634093)), hAPP(c_List_Oset(tc_prod(_1634089, _1634089)), hAPP(hAPP(c_List_Ozip(_1634089, _1634089), _1634095), _1634095))))), hBOOL(hAPP(hAPP(c_member(_1634089), _1634091), hAPP(c_List_Oset(_1634089), _1634095))), _1634091 = _1634093], (45774 ^ _779854) ^ [_1697574, _1697576, _1697578] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697574)), _1697578), c_List_Olists(_1697574, _1697576))), -(hBOOL(hAPP(c_List_Olistsp(_1697574, hAPP(hAPP(c_COMBC(_1697574, tc_fun(_1697574, tc_HOL_Obool), tc_HOL_Obool), c_member(_1697574)), _1697576)), _1697578)))], (42862 ^ _779854) ^ [_1632770, _1632772, _1632774, _1632776] : [-(hAPP(c_List_Oset(tc_prod(_1632770, _1632772)), hAPP(hAPP(c_List_Ozip(_1632770, _1632772), _1632774), _1632776)) = hAPP(c_Set_OCollect(tc_prod(_1632770, _1632772)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1632770, _1632772)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1632770, _1632772), 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(_1632770, _1632772)), 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(_1632770, _1632772)), 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(_1632770, _1632772), tc_fun(tc_Nat_Onat, tc_prod(_1632770, _1632772)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1632770, _1632772), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1632770, _1632772)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1632770, _1632772)), c_COMBB(tc_prod(_1632770, _1632772), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1632772, tc_prod(_1632770, _1632772)), hAPP(hAPP(c_COMBB(_1632770, tc_fun(_1632772, tc_prod(_1632770, _1632772)), tc_Nat_Onat), c_Product__Type_OPair(_1632770, _1632772)), hAPP(c_List_Onth(_1632770), _1632774))), hAPP(c_List_Onth(_1632772), _1632776)))))), 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(_1632770)), _1632774)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632772)), _1632776)))))))], (52683 ^ _779854) ^ [_1838866, _1838868] : [hBOOL(hAPP(hAPP(c_fconj, _1838866), _1838868)), -(hBOOL(_1838868))], (22407 ^ _779854) ^ [_1184903, _1184905, _1184907] : [class_Fields_Olinordered__field(_1184903), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184903), c_Groups_Ozero__class_Ozero(_1184903)), _1184905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184903), c_Groups_Ozero__class_Ozero(_1184903)), _1184907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184903), c_Groups_Ozero__class_Ozero(_1184903)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184903), _1184905), _1184907))))], (26129 ^ _779854) ^ [_1254775, _1254777, _1254779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254775)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1254777), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1254779)), 26139 ^ _779854 : [(26145 ^ _779854) ^ [] : [-(_1254777 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26141 ^ [_1254775, _1254777, _1254779]), 26138 ^ [_1254775, _1254777, _1254779]))], (26143 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26141 ^ [_1254775, _1254777, _1254779]), _1254779)))], (26140 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26138 ^ [_1254775, _1254777, _1254779]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1254775))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1254777), _1254775) = _1254777)], (51577 ^ _779854) ^ [_1823999, _1824001, _1824003] : [class_Divides_Oring__div(_1823999), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823999), _1824001), _1824003)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823999), _1824003), hAPP(c_Groups_Ouminus__class_Ouminus(_1823999), _1824001)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1823999), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823999), _1824003), _1824001)))], (45318 ^ _779854) ^ [_1687635, _1687637, _1687639] : [c_Fun_Oinj__on(tc_List_Olist(_1687635), tc_List_Olist(_1687637), hAPP(c_List_Omap(_1687635, _1687637), _1687639), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1687635), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1687635, _1687637, _1687639, c_Orderings_Otop__class_Otop(tc_fun(_1687635, tc_HOL_Obool))))], (21749 ^ _779854) ^ [_1172386, _1172388] : [-(c_Sum__Type_OPlus(_1172386, _1172388, c_Orderings_Otop__class_Otop(tc_fun(_1172386, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1172388, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1172386, _1172388), tc_HOL_Obool)))], (39814 ^ _779854) ^ [_1552271, _1552273, _1552275, _1552277] : [-(hAPP(c_Relation_ODomain(_1552271, _1552273), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552271, _1552273), tc_HOL_Obool)), _1552275), _1552277)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552271, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1552271, _1552273), _1552275)), hAPP(c_Relation_ODomain(_1552271, _1552273), _1552277)))], (14125 ^ _779854) ^ [_1029135, _1029137, _1029139, _1029141, _1029143, _1029145] : [_1029135 = _1029137, -(hAPP(c_Fun_Ofun__upd(_1029139, _1029141, _1029143, _1029137, _1029145), _1029135) = _1029145)], (30249 ^ _779854) ^ [_1325956, _1325958] : [class_Divides_Osemiring__div(_1325956), -(c_Divides_Odiv__class_Omod(_1325956, _1325958, c_Groups_Ozero__class_Ozero(_1325956)) = _1325958)], (21020 ^ _779854) ^ [_1158142, _1158144] : [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), _1158142), _1158144))), 21023 ^ _779854 : [(21026 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1158144)))], (21024 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1158142)))]]], (41130 ^ _779854) ^ [_1585134, _1585136, _1585138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585134, _1585134), tc_HOL_Obool)), _1585136), _1585138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585134, _1585134), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1585134, _1585136)), c_Transitive__Closure_Ortrancl(_1585134, _1585138))))], (21567 ^ _779854) ^ [_1169101, _1169103] : [class_Rings_Olinordered__idom(_1169101), hBOOL(hAPP(hAPP(c_member(_1169101), _1169103), c_Int_Oring__1__class_OInts(_1169101))), 21574 ^ _779854 : [(21581 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169101), _1169103), c_Groups_Ozero__class_Ozero(_1169101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169101), c_Groups_Oone__class_Oone(_1169101)), _1169103)), _1169103)), c_Groups_Ozero__class_Ozero(_1169101))))], (21575 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169101), c_Groups_Oone__class_Oone(_1169101)), _1169103)), _1169103)), c_Groups_Ozero__class_Ozero(_1169101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169101), _1169103), c_Groups_Ozero__class_Ozero(_1169101))))]]], (21611 ^ _779854) ^ [_1169899, _1169901, _1169903] : [class_Rings_Oring__1(_1169899), hBOOL(hAPP(hAPP(c_member(_1169899), _1169901), c_Int_Oring__1__class_OInts(_1169899))), hBOOL(hAPP(hAPP(c_member(_1169899), _1169903), c_Int_Oring__1__class_OInts(_1169899))), -(hBOOL(hAPP(hAPP(c_member(_1169899), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169899), _1169901), _1169903)), c_Int_Oring__1__class_OInts(_1169899))))], (18799 ^ _779854) ^ [_1119373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119373)), _1119373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (38188 ^ _779854) ^ [_1502908, _1502910, _1502912, _1502914] : [-(hBOOL(hAPP(hAPP(c_member(_1502908), _1502910), _1502912))), -(hAPP(c_Set_Ovimage(_1502914, _1502908, hAPP(c_COMBK(_1502908, _1502914), _1502910)), _1502912) = c_Orderings_Obot__class_Obot(tc_fun(_1502914, tc_HOL_Obool)))], (9829 ^ _779854) ^ [_945077, _945079, _945081] : [class_Groups_Oordered__ab__group__add(_945077), -(hAPP(c_Set_Oimage(_945077, _945077, c_Groups_Ouminus__class_Ouminus(_945077)), c_SetInterval_Oord__class_OatLeastAtMost(_945077, _945079, _945081)) = c_SetInterval_Oord__class_OatLeastAtMost(_945077, hAPP(c_Groups_Ouminus__class_Ouminus(_945077), _945081), hAPP(c_Groups_Ouminus__class_Ouminus(_945077), _945079)))], (21935 ^ _779854) ^ [_1176201, _1176203, _1176205, _1176207] : [class_Rings_Odivision__ring(_1176201), -(_1176203 = c_Groups_Ozero__class_Ozero(_1176201)), _1176205 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176201), _1176207), _1176203), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176201), _1176205), _1176203) = _1176207)], (35864 ^ _779854) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16992 ^ _779854) ^ [_1086450, _1086452, _1086454] : [class_Lattices_Olattice(_1086450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086450), _1086452)), -(c_Big__Operators_Olattice__class_OSup__fin(_1086450, hAPP(hAPP(c_Set_Oinsert(_1086450), _1086454), _1086452)) = hAPP(hAPP(c_Finite__Set_Ofold(_1086450, _1086450, c_Lattices_Osemilattice__sup__class_Osup(_1086450)), _1086454), _1086452))], (35798 ^ _779854) ^ [_1446389, _1446391, _1446393, _1446395] : [_1446389 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1446391), _1446393)), _1446395), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1446389, _1446391), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1446393), _1446395)))), 35805 ^ _779854 : [(35808 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1446395)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446395), _1446391))], (35806 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1446391)))]], 35813 ^ _779854 : [(35816 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446391), _1446395)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446395), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35814 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1446391))]]], (45079 ^ _779854) ^ [_1681376, _1681378, _1681380, _1681382, _1681384] : [-(hAPP(c_List_Orotate(_1681376, _1681378), hAPP(hAPP(c_List_Omap(_1681380, _1681376), _1681382), _1681384)) = hAPP(hAPP(c_List_Omap(_1681380, _1681376), _1681382), hAPP(c_List_Orotate(_1681380, _1681378), _1681384)))], (11909 ^ _779854) ^ [_986757, _986759, _986761, _986763] : [11910 ^ _779854 : [(11913 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_986757), _986759), _986763))], (11911 ^ _779854) ^ [] : [_986759 = _986761]], -(hBOOL(hAPP(hAPP(c_member(_986757), _986759), hAPP(hAPP(c_Set_Oinsert(_986757), _986761), _986763))))], (8708 ^ _779854) ^ [_924747, _924749, _924751] : [class_Orderings_Oorder(_924747), 8711 ^ _779854 : [(8712 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924747), _924749), _924751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924747), _924749), _924751))), -(_924749 = _924751)], (8722 ^ _779854) ^ [] : [8723 ^ _779854 : [(8726 ^ _779854) ^ [] : [_924749 = _924751], (8724 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924747), _924749), _924751))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924747), _924749), _924751)))]]], (7039 ^ _779854) ^ [_895174, _895176, _895178] : [class_Lattices_Osemilattice__inf(_895174), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895174), _895176), _895178) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895174), _895178), _895176))], (28364 ^ _779854) ^ [_1292637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292637)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9835 ^ _779854) ^ [_945208, _945210, _945212] : [class_Groups_Oordered__ab__group__add(_945208), -(hAPP(c_Set_Oimage(_945208, _945208, c_Groups_Ouminus__class_Ouminus(_945208)), c_SetInterval_Oord__class_OgreaterThanLessThan(_945208, _945210, _945212)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_945208, hAPP(c_Groups_Ouminus__class_Ouminus(_945208), _945212), hAPP(c_Groups_Ouminus__class_Ouminus(_945208), _945210)))], (18561 ^ _779854) ^ [_1115944, _1115946] : [class_Groups_Omonoid__add(_1115944), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115944), c_Groups_Ozero__class_Ozero(_1115944)), _1115946) = _1115946)], (28850 ^ _779854) ^ [_1300904, _1300906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1300904), _1300906)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1300906)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1300904)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1300906), _1300904)))], (10263 ^ _779854) ^ [_953217, _953219, _953221, _953223] : [class_Orderings_Olinorder(_953217), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_953217), hAPP(hAPP(c_Orderings_Oord__class_Omax(_953217), _953219), _953221)), _953223) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_953217), hAPP(hAPP(c_Orderings_Oord__class_Omin(_953217), _953219), _953223)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_953217), _953221), _953223)))], (32481 ^ _779854) ^ [_1364316, _1364318] : [class_Rings_Olinordered__idom(_1364316), -(hAPP(c_Groups_Oabs__class_Oabs(_1364316), hAPP(hAPP(c_Power_Opower__class_Opower(_1364316), _1364318), 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(_1364316), _1364318), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (48944 ^ _779854) ^ [_1766907, _1766909, _1766911] : [-(_1766907 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1766909, c_List_Oreplicate(_1766909, _1766907, _1766911)) = _1766911)], (32866 ^ _779854) ^ [_1372168, _1372170, _1372172, _1372174, _1372176] : [-(hAPP(c_Set_Oimage(_1372168, _1372170, hAPP(hAPP(c_COMBB(_1372172, _1372170, _1372168), _1372174), _1372176)), c_Orderings_Otop__class_Otop(tc_fun(_1372168, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1372172, _1372170, _1372174), hAPP(c_Set_Oimage(_1372168, _1372172, _1372176), c_Orderings_Otop__class_Otop(tc_fun(_1372168, tc_HOL_Obool)))))], (50571 ^ _779854) ^ [_1802536, _1802538] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1802536), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1802538, hAPP(c_Code__Numeral_Onat__of, 50576 ^ [_1802536, _1802538]))), -(hBOOL(hAPP(_1802538, _1802536)))], (11143 ^ _779854) ^ [_971891, _971893, _971895, _971897] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_971891), _971893)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_971895), hAPP(c_Set_Oimage(_971891, _971895, _971897), _971893))))], (50784 ^ _779854) ^ [_1806842, _1806844, _1806846] : [-(c_Fun_Obij__betw(_1806842, _1806844, _1806846, c_Orderings_Otop__class_Otop(tc_fun(_1806842, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1806844, tc_HOL_Obool)))), c_Fun_Oinj__on(_1806842, _1806844, _1806846, c_Orderings_Otop__class_Otop(tc_fun(_1806842, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1806842, _1806844, _1806846), c_Orderings_Otop__class_Otop(tc_fun(_1806842, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1806844, tc_HOL_Obool))], (23564 ^ _779854) ^ [_1206596, _1206598, _1206600, _1206602, _1206604, _1206606, _1206608] : [c_Finite__Set_Ofun__left__comm(_1206596, _1206598, _1206600), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1206596, _1206598, _1206600, _1206602, hAPP(hAPP(c_Set_Oinsert(_1206596), _1206604), _1206606)), _1206608)), -(hBOOL(hAPP(hAPP(c_member(_1206596), _1206604), _1206606))), 23576 ^ _779854 : [(23579 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1206596, _1206598, _1206600, _1206602, _1206606), 23575 ^ [_1206596, _1206598, _1206600, _1206602, _1206604, _1206606, _1206608])))], (23577 ^ _779854) ^ [] : [-(_1206608 = hAPP(hAPP(_1206600, _1206604), 23575 ^ [_1206596, _1206598, _1206600, _1206602, _1206604, _1206606, _1206608]))]]], (13145 ^ _779854) ^ [_1011903, _1011905] : [class_Lattices_Olattice(_1011903), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011903), _1011905)), -(_1011905 = c_Orderings_Obot__class_Obot(tc_fun(_1011903, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011903), c_Big__Operators_Olattice__class_OInf__fin(_1011903, _1011905)), c_Big__Operators_Olattice__class_OSup__fin(_1011903, _1011905))))], (47196 ^ _779854) ^ [_1728446, _1728448, _1728450] : [class_Orderings_Olinorder(_1728446), hBOOL(hAPP(hAPP(c_member(_1728446), _1728448), hAPP(c_List_Oset(_1728446), _1728450))), c_List_Olinorder__class_Osorted(_1728446, _1728450), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1728446, _1728446, c_COMBI(_1728446)), _1728448), c_List_Oremove1(_1728446, _1728448, _1728450)) = _1728450)], (38086 ^ _779854) ^ [_1500450, _1500452, _1500454, _1500456, _1500458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500450, tc_HOL_Obool)), _1500452), _1500454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500456, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1500456, _1500450, _1500458), _1500452)), hAPP(c_Set_Ovimage(_1500456, _1500450, _1500458), _1500454))))], (18102 ^ _779854) ^ [_1107360, _1107362, _1107364] : [class_Rings_Ocomm__semiring__1(_1107360), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107360), _1107362), _1107364)), _1107364) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107360), _1107362), c_Groups_Oone__class_Oone(_1107360))), _1107364))], (48926 ^ _779854) ^ [_1766556, _1766558, _1766560, _1766562] : [-(hAPP(hAPP(c_List_Omap(_1766556, _1766558), hAPP(c_COMBK(_1766558, _1766556), _1766560)), _1766562) = c_List_Oreplicate(_1766558, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766556)), _1766562), _1766560))], (25595 ^ _779854) ^ [_1245323, _1245325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245323), _1245325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245325), _1245323)), -(_1245323 = _1245325)], (4448 ^ _779854) ^ [_847547, _847549, _847551, _847553, _847555, _847557, _847559, _847561, _847563, _847565] : [-(c_Option_Ooption_Ooption__case(_847565, _847561, _847557, _847553, _847549) = c_Option_Ooption_Ooption__case(_847563, _847559, _847555, _847551, _847547)), _847565 = _847563, _847561 = _847559, _847557 = _847555, _847553 = _847551, _847549 = _847547], (40407 ^ _779854) ^ [_1567266, _1567268, _1567270] : [-(hBOOL(hAPP(hAPP(c_member(_1567266), _1567268), c_Wellfounded_Oacc(_1567266, _1567270)))), 40411 ^ _779854 : [(40414 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1567266), 40410 ^ [_1567266, _1567268, _1567270]), c_Wellfounded_Oacc(_1567266, _1567270)))], (40412 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567266, _1567266)), hAPP(hAPP(c_Product__Type_OPair(_1567266, _1567266), 40410 ^ [_1567266, _1567268, _1567270]), _1567268)), _1567270)))]]], (46615 ^ _779854) ^ [_1717703, _1717705, _1717707] : [-(c_List_Osublist(_1717703, _1717705, _1717707) = hAPP(hAPP(c_List_Omap(tc_prod(_1717703, tc_Nat_Onat), _1717703), c_Product__Type_Ofst(_1717703, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1717703, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1717703, 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(_1717703, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1717703, tc_Nat_Onat))), _1717707)), hAPP(hAPP(c_List_Ozip(_1717703, tc_Nat_Onat), _1717705), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717703)), _1717705))))))], (12856 ^ _779854) ^ [_1005608, _1005610] : [class_Orderings_Olinorder(_1005608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005608), _1005610)), -(_1005610 = c_Orderings_Obot__class_Obot(tc_fun(_1005608, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1005608), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1005608), 12869 ^ [_1005608, _1005610]), 12870 ^ [_1005608, _1005610])), hAPP(hAPP(c_Set_Oinsert(_1005608), 12869 ^ [_1005608, _1005610]), hAPP(hAPP(c_Set_Oinsert(_1005608), 12870 ^ [_1005608, _1005610]), c_Orderings_Obot__class_Obot(tc_fun(_1005608, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1005608), c_Big__Operators_Olattice_OInf__fin(_1005608, c_Orderings_Oord__class_Omin(_1005608), _1005610)), _1005610)))], (5302 ^ _779854) ^ [_860932, _860934, _860936, _860938, _860940, _860942, _860944, _860946] : [-(c_Fun_Ocomp(_860946, _860942, _860938, _860934) = c_Fun_Ocomp(_860944, _860940, _860936, _860932)), _860946 = _860944, _860942 = _860940, _860938 = _860936, _860934 = _860932], (15824 ^ _779854) ^ [_1063440, _1063442, _1063444] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063440), _1063442)), _1063444) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063442), _1063444)))], (38614 ^ _779854) ^ [_1515080, _1515082, _1515084, _1515086, _1515088, _1515090, _1515092, _1515094] : [c_Fun_Oinj__on(_1515080, _1515082, _1515084, _1515086), c_Fun_Oinj__on(_1515088, _1515090, _1515092, _1515094), -(c_Fun_Oinj__on(tc_prod(_1515080, _1515088), tc_prod(_1515082, _1515090), c_Product__Type_Omap__pair(_1515080, _1515082, _1515088, _1515090, _1515084, _1515092), hAPP(hAPP(c_Product__Type_OSigma(_1515080, _1515088), _1515086), hAPP(c_COMBK(tc_fun(_1515088, tc_HOL_Obool), _1515080), _1515094))))], (26323 ^ _779854) ^ [_1258407, _1258409] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258407), _1258409))), -(c_Nat__Transfer_Otsub(_1258409, _1258407) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17603 ^ _779854) ^ [_1098671, _1098673, _1098675, _1098677, _1098679, _1098681, _1098683] : [c_Finite__Set_Ofun__left__comm(_1098671, _1098673, _1098675), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1098671, _1098673, _1098675, _1098677, _1098679), _1098681)), hBOOL(hAPP(hAPP(c_member(_1098671), _1098683), _1098679)), 17615 ^ _779854 : [(17618 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1098671, _1098673, _1098675, _1098677, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1098671, tc_HOL_Obool)), _1098679), hAPP(hAPP(c_Set_Oinsert(_1098671), _1098683), c_Orderings_Obot__class_Obot(tc_fun(_1098671, tc_HOL_Obool))))), 17614 ^ [_1098671, _1098673, _1098675, _1098677, _1098679, _1098681, _1098683])))], (17616 ^ _779854) ^ [] : [-(_1098681 = hAPP(hAPP(_1098675, _1098683), 17614 ^ [_1098671, _1098673, _1098675, _1098677, _1098679, _1098681, _1098683]))]]], (5074 ^ _779854) ^ [_857408, _857410, _857412, _857414, _857416, _857418] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_857418, _857414, _857410) = c_SetInterval_Oord__class_OatLeastAtMost(_857416, _857412, _857408)), _857418 = _857416, _857414 = _857412, _857410 = _857408], (39592 ^ _779854) ^ [_1547976, _1547978, _1547980, _1547982] : [hBOOL(hAPP(c_Predicate_ORangeP(_1547976, _1547978, _1547980), _1547982)), -(hBOOL(hAPP(hAPP(_1547980, 39595 ^ [_1547976, _1547978, _1547980, _1547982]), _1547982)))], (42275 ^ _779854) ^ [_1615516, _1615518, _1615520, _1615522] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615516), tc_List_Olist(_1615516))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615516), tc_List_Olist(_1615516)), _1615518), _1615520)), c_List_Olistrel1(_1615516, _1615522))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615516)), _1615518) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615516)), _1615520))], (44534 ^ _779854) ^ [_1670682, _1670684, _1670686] : [-(c_List_Orotate(_1670682, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1670684), _1670686)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1670682), tc_List_Olist(_1670682), tc_List_Olist(_1670682), c_List_Orotate(_1670682, _1670684)), c_List_Orotate(_1670682, _1670686)))], (498 ^ _779854) ^ [_787335, _787337, _787339, _787341, _787343, _787345] : [-(c_Nitpick_Oless__eq__frac(_787343, _787339, _787335)), c_Nitpick_Oless__eq__frac(_787345, _787341, _787337), _787345 = _787343, _787341 = _787339, _787337 = _787335], (12204 ^ _779854) ^ [_992498, _992500, _992502, _992504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_992498, tc_HOL_Obool)), _992500), _992502)), hBOOL(hAPP(hAPP(c_member(_992498), _992504), _992500)), -(hBOOL(hAPP(hAPP(c_member(_992498), _992504), _992502)))], (34261 ^ _779854) ^ [_1414298, _1414300, _1414302, _1414304, _1414306, _1414308] : [c_Fun_Oinj__on(_1414298, _1414300, hAPP(c_Fun_Ocomp(_1414302, _1414300, _1414298, _1414304), _1414306), _1414308), -(c_Fun_Oinj__on(_1414302, _1414300, _1414304, hAPP(c_Set_Oimage(_1414298, _1414302, _1414306), _1414308)))], (30207 ^ _779854) ^ [_1325181, _1325183, _1325185, _1325187] : [class_Divides_Osemiring__div(_1325181), -(c_Divides_Odiv__class_Omod(_1325181, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325181), _1325183), _1325185), _1325187) = c_Divides_Odiv__class_Omod(_1325181, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325181), _1325183), c_Divides_Odiv__class_Omod(_1325181, _1325185, _1325187)), _1325187))], (46528 ^ _779854) ^ [_1714807, _1714809, _1714811] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1714807, tc_HOL_Obool)), hAPP(c_List_Oset(_1714807), _1714809)), hAPP(hAPP(c_Set_Oinsert(_1714807), _1714811), c_Orderings_Obot__class_Obot(tc_fun(_1714807, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1714807), hAPP(c_List_Ofilter(_1714807, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1714807), c_fNot), hAPP(hAPP(c_COMBC(_1714807, _1714807, tc_HOL_Obool), c_fequal), _1714811))), _1714809)))], (41364 ^ _779854) ^ [_1590694, _1590696] : [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), _1590694), _1590696)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1590694), _1590696)))], (28146 ^ _779854) ^ [_1288946, _1288948] : [class_Int_Onumber__ring(_1288946), 28149 ^ _779854 : [(28156 ^ _779854) ^ [] : [c_Int_Oiszero(_1288946, hAPP(c_Int_Onumber__class_Onumber__of(_1288946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1288948), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1288946), _1288948) = c_Groups_Oone__class_Oone(_1288946))], (28150 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1288946), _1288948) = c_Groups_Oone__class_Oone(_1288946), -(c_Int_Oiszero(_1288946, hAPP(c_Int_Onumber__class_Onumber__of(_1288946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1288948), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (4470 ^ _779854) ^ [_847936, _847938] : [_847938 = _847936, -(c_Lazy__Sequence_Oyieldn(_847938) = c_Lazy__Sequence_Oyieldn(_847936))], (43177 ^ _779854) ^ [_1640459, _1640461] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1640459, _1640461))))], (41529 ^ _779854) ^ [_1594845, _1594847, _1594849, _1594851, _1594853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1594845, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1594847, _1594845, _1594849), _1594851)), _1594853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1594847, tc_HOL_Obool)), _1594851), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1594847, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1594845, _1594847, hAPP(c_Relation_Oconverse(_1594847, _1594845), _1594849)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1594845, tc_HOL_Obool)), _1594853))))))], (17340 ^ _779854) ^ [_1093212, _1093214, _1093216] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093212), _1093214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1093212), _1093214)), hAPP(c_Finite__Set_Ocard(_1093212), hAPP(hAPP(c_Set_Oinsert(_1093212), _1093216), _1093214)))))], (31581 ^ _779854) ^ [] : [-(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))], (48370 ^ _779854) ^ [_1754355, _1754357, _1754359, _1754361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754355), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754357)), _1754359))), 48376 ^ _779854 : [(48379 ^ _779854) ^ [] : [hBOOL(hAPP(_1754361, 48375 ^ [_1754355, _1754357, _1754359, _1754361]))], (48377 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754357), 48375 ^ [_1754355, _1754357, _1754359, _1754361]), hAPP(c_List_Oset(_1754357), _1754359))))]], -(hBOOL(hAPP(_1754361, hAPP(hAPP(c_List_Onth(_1754357), _1754359), _1754355))))], (18901 ^ _779854) ^ [_1120911, _1120913, _1120915] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120911), _1120913) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120911), _1120915), -(_1120911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1120913 = _1120915)], (47768 ^ _779854) ^ [_1740603, _1740605, _1740607] : [hBOOL(hAPP(c_List_Odistinct(_1740603), _1740605)), -(hBOOL(hAPP(c_List_Odistinct(_1740603), c_List_OdropWhile(_1740603, _1740607, _1740605))))], (34649 ^ _779854) ^ [_1423389, _1423391, _1423393, _1423395, _1423397] : [class_Groups_Ocomm__monoid__add(_1423389), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423391), _1423393)), c_Fun_Oinj__on(_1423391, _1423391, _1423395, _1423393), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423391, _1423389), _1423397), hAPP(c_Set_Oimage(_1423391, _1423391, _1423395), _1423393)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423391, _1423389), hAPP(c_Fun_Ocomp(_1423391, _1423389, _1423391, _1423397), _1423395)), _1423393))], (21256 ^ _779854) ^ [_1162679, _1162681, _1162683, _1162685] : [class_Groups_Ocomm__monoid__add(_1162679), 21259 ^ _779854 : [(21266 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162681), _1162683))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1162679), _1162685), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1162683), hAPP(c_Nat_OSuc, _1162681))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162679), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1162679), _1162685), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1162683), _1162681))), hAPP(_1162685, _1162681)))], (21260 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162681), _1162683)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1162679), _1162685), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1162683), hAPP(c_Nat_OSuc, _1162681))) = c_Groups_Ozero__class_Ozero(_1162679))]]], (15798 ^ _779854) ^ [_1062957, _1062959, _1062961] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1062957), _1062959) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1062961), _1062959), -(_1062957 = _1062961)], (52449 ^ _779854) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (46184 ^ _779854) ^ [_1706697, _1706699, _1706701, _1706703] : [-(_1706697 = _1706699), -(hAPP(c_List_OremoveAll(_1706701, _1706697), hAPP(hAPP(c_List_Olist_OCons(_1706701), _1706699), _1706703)) = hAPP(hAPP(c_List_Olist_OCons(_1706701), _1706699), hAPP(c_List_OremoveAll(_1706701, _1706697), _1706703)))], (19373 ^ _779854) ^ [_1129294, _1129296, _1129298] : [class_Rings_Oordered__cancel__semiring(_1129294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129294), c_Groups_Ozero__class_Ozero(_1129294)), _1129296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129294), c_Groups_Ozero__class_Ozero(_1129294)), _1129298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129294), c_Groups_Ozero__class_Ozero(_1129294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129294), _1129296), _1129298))))], (12888 ^ _779854) ^ [_1006324, _1006326, _1006328, _1006330] : [hBOOL(hAPP(hAPP(c_member(_1006324), _1006326), c_SetInterval_Oord_OatLeast(_1006324, _1006328, _1006330))), -(hBOOL(hAPP(hAPP(_1006328, _1006330), _1006326)))], (48934 ^ _779854) ^ [_1766766, _1766768, _1766770, _1766772] : [-(hAPP(hAPP(c_List_Otake(_1766766), _1766768), c_List_Oreplicate(_1766766, _1766770, _1766772)) = c_List_Oreplicate(_1766766, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1766768), _1766770), _1766772))], (33282 ^ _779854) ^ [_1384012, _1384014, _1384016, _1384018, _1384020, _1384022] : [class_Complete__Lattice_Ocomplete__lattice(_1384012), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384014, _1384012), _1384016), hAPP(hAPP(c_COMBB(tc_fun(_1384018, _1384012), _1384012, _1384014), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384018, _1384012), _1384020)), _1384022)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384018, _1384012), _1384020), hAPP(hAPP(c_COMBB(tc_fun(_1384014, _1384012), _1384012, _1384018), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384014, _1384012), _1384016)), hAPP(c_COMBC(_1384014, _1384018, _1384012), _1384022))))], (21863 ^ _779854) ^ [_1174811, _1174813, _1174815, _1174817] : [class_Rings_Odivision__ring(_1174811), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1174811), _1174813), _1174815)), _1174817) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1174811), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174811), _1174813), _1174817)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174811), _1174815), _1174817)))], (50443 ^ _779854) ^ [_1799117, _1799119, _1799121, _1799123, _1799125, _1799127] : [hAPP(c_Set_Oimage(_1799117, _1799119, _1799121), _1799123) = _1799125, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799119, tc_HOL_Obool)), _1799127), _1799125)), -(hAPP(c_Set_Oimage(_1799117, _1799119, _1799121), hAPP(c_Set_Oimage(_1799119, _1799117, c_Hilbert__Choice_Oinv__into(_1799117, _1799119, _1799123, _1799121)), _1799127)) = _1799127)], (1820 ^ _779854) ^ [_805556, _805558] : [-(class_Rings_Osemiring__0(_805556)), _805558 = _805556, class_Rings_Osemiring__0(_805558)], (33130 ^ _779854) ^ [_1380400, _1380402, _1380404, _1380406, _1380408] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380400, tc_fun(_1380402, tc_HOL_Obool)), _1380404), hAPP(hAPP(c_COMBB(tc_fun(_1380402, tc_HOL_Obool), tc_fun(_1380402, tc_HOL_Obool), _1380400), hAPP(c_Set_Oinsert(_1380402), _1380406)), _1380408)) = hAPP(hAPP(c_Set_Oinsert(_1380402), _1380406), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380400, tc_fun(_1380402, tc_HOL_Obool)), _1380404), _1380408)))], (8094 ^ _779854) ^ [_915505, _915507] : [class_Orderings_Oorder(_915505), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915505, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_915505), _915507)), hAPP(c_SetInterval_Oord__class_OatLeast(_915505), _915507)) = hAPP(hAPP(c_Set_Oinsert(_915505), _915507), c_Orderings_Obot__class_Obot(tc_fun(_915505, tc_HOL_Obool))))], (14131 ^ _779854) ^ [_1029232, _1029234, _1029236, _1029238, _1029240, _1029242] : [-(_1029232 = _1029234), -(hAPP(c_Fun_Ofun__upd(_1029236, _1029238, _1029240, _1029234, _1029242), _1029232) = hAPP(_1029240, _1029232))], (27813 ^ _779854) ^ [_1283016, _1283018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1283016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1283018), _1283016))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1283018), _1283016) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1283018), _1283016)), _1283016)))], (50481 ^ _779854) ^ [_1800084, _1800086, _1800088] : [c_Fun_Oinj__on(_1800084, _1800086, _1800088, c_Orderings_Otop__class_Otop(tc_fun(_1800084, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1800086, _1800084, c_Hilbert__Choice_Oinv__into(_1800084, _1800086, c_Orderings_Otop__class_Otop(tc_fun(_1800084, tc_HOL_Obool)), _1800088)), c_Orderings_Otop__class_Otop(tc_fun(_1800086, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1800084, tc_HOL_Obool)))], (18014 ^ _779854) ^ [_1105846, _1105848, _1105850] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105846)), _1105848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105846)), _1105850), -(_1105848 = _1105850)], (48924 ^ _779854) ^ [_1766518, _1766520, _1766522] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766518)), c_List_Oreplicate(_1766518, _1766520, _1766522)) = _1766520)], (29337 ^ _779854) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (52229 ^ _779854) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (29093 ^ _779854) ^ [_1304859, _1304861] : [class_Int_Onumber__ring(_1304859), class_Rings_Olinordered__idom(_1304859), 29100 ^ _779854 : [(29107 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1304861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304859), c_Groups_Oone__class_Oone(_1304859)), hAPP(c_Int_Onumber__class_Onumber__of(_1304859), _1304861))))], (29101 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304859), c_Groups_Oone__class_Oone(_1304859)), hAPP(c_Int_Onumber__class_Onumber__of(_1304859), _1304861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1304861)))]]], (42398 ^ _779854) ^ [_1619307, _1619309, _1619311, _1619313] : [c_List_Olistrelp(_1619307, hAPP(hAPP(c_COMBC(_1619307, tc_fun(tc_prod(_1619307, _1619307), tc_HOL_Obool), tc_fun(_1619307, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619307, tc_fun(tc_fun(tc_prod(_1619307, _1619307), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1619307, _1619307), tc_HOL_Obool), tc_fun(_1619307, tc_HOL_Obool)), _1619307), c_COMBC(_1619307, tc_fun(tc_prod(_1619307, _1619307), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619307, tc_prod(_1619307, _1619307)), tc_fun(_1619307, tc_fun(tc_fun(tc_prod(_1619307, _1619307), tc_HOL_Obool), tc_HOL_Obool)), _1619307), hAPP(c_COMBB(tc_prod(_1619307, _1619307), tc_fun(tc_fun(tc_prod(_1619307, _1619307), tc_HOL_Obool), tc_HOL_Obool), _1619307), c_member(tc_prod(_1619307, _1619307)))), c_Product__Type_OPair(_1619307, _1619307)))), _1619309), _1619311, _1619313), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619307), tc_List_Olist(_1619307))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619307), tc_List_Olist(_1619307)), _1619311), _1619313)), c_List_Olistrel(_1619307, _1619309))))], (26071 ^ _779854) ^ [_1253673, _1253675, _1253677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253673)), 26074 ^ _779854 : [(26075 ^ _779854) ^ [_1253807] : [26077 ^ _779854 : [(26083 ^ _779854) ^ [] : [-(_1253807 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26079 ^ [_1253673, _1253675, _1253677, _1253807]), 26076 ^ [_1253673, _1253675, _1253677, _1253807]))], (26081 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26079 ^ [_1253673, _1253675, _1253677, _1253807]), _1253675)))], (26078 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26076 ^ [_1253673, _1253675, _1253677, _1253807]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1253673))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1253807), _1253677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1253807), _1253673)), _1253677)))]]], (51385 ^ _779854) ^ [_1820514, _1820516, _1820518] : [class_Divides_Osemiring__div(_1820514), class_Int_Onumber(_1820514), 51392 ^ _779854 : [(51399 ^ _779854) ^ [] : [c_Divides_Odiv__class_Omod(_1820514, hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820518), hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820516)) = c_Groups_Ozero__class_Ozero(_1820514), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820514), hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820516)), hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820518))))], (51393 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820514), hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820516)), hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820518))), -(c_Divides_Odiv__class_Omod(_1820514, hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820518), hAPP(c_Int_Onumber__class_Onumber__of(_1820514), _1820516)) = c_Groups_Ozero__class_Ozero(_1820514))]]], (6735 ^ _779854) ^ [_888058, _888060] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888058, tc_HOL_Obool)), _888060), _888060) = _888060)], (14874 ^ _779854) ^ [_1043631, _1043633, _1043635, _1043637, _1043639] : [class_Groups_Ocomm__monoid__add(_1043631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043633), _1043635)), hBOOL(hAPP(hAPP(c_member(_1043633), _1043637), _1043635)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043633, _1043631), _1043639), _1043635) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043631), hAPP(_1043639, _1043637)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043633, _1043631), _1043639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043633, tc_HOL_Obool)), _1043635), hAPP(hAPP(c_Set_Oinsert(_1043633), _1043637), c_Orderings_Obot__class_Obot(tc_fun(_1043633, tc_HOL_Obool)))))))], (33605 ^ _779854) ^ [_1397045, _1397047, _1397049, _1397051, _1397053] : [class_Lattices_Olattice(_1397045), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397047, _1397045)), _1397049), _1397051), _1397053) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1397045), hAPP(_1397049, _1397053)), hAPP(_1397051, _1397053)))], (15466 ^ _779854) ^ [_1055884, _1055886, _1055888] : [class_Rings_Oring(_1055884), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055884), hAPP(c_Groups_Ouminus__class_Ouminus(_1055884), _1055886)), _1055888) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055884), _1055886), hAPP(c_Groups_Ouminus__class_Ouminus(_1055884), _1055888)))], (9965 ^ _779854) ^ [_948059, _948061, _948063] : [class_Orderings_Olinorder(_948059), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_948059), _948061), hAPP(hAPP(c_Orderings_Oord__class_Omin(_948059), _948061), _948063)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_948059), _948061), _948063))], (45557 ^ _779854) ^ [_1692730, _1692732] : [_1692730 = _1692732, -(hAPP(c_Code__Numeral_Onat__of, _1692730) = hAPP(c_Code__Numeral_Onat__of, _1692732))], (12812 ^ _779854) ^ [_1004634, _1004636, _1004638] : [class_Orderings_Olinorder(_1004634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004634), _1004636)), hBOOL(hAPP(hAPP(c_member(_1004634), _1004638), _1004636)), 12823 ^ _779854 : [(12830 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1004634, tc_HOL_Obool)), _1004636), hAPP(hAPP(c_Set_Oinsert(_1004634), _1004638), c_Orderings_Obot__class_Obot(tc_fun(_1004634, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1004634, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1004634, c_Orderings_Oord__class_Omin(_1004634), _1004636) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1004634), _1004638), c_Big__Operators_Olattice_OInf__fin(_1004634, c_Orderings_Oord__class_Omin(_1004634), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1004634, tc_HOL_Obool)), _1004636), hAPP(hAPP(c_Set_Oinsert(_1004634), _1004638), c_Orderings_Obot__class_Obot(tc_fun(_1004634, tc_HOL_Obool)))))))], (12824 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1004634, tc_HOL_Obool)), _1004636), hAPP(hAPP(c_Set_Oinsert(_1004634), _1004638), c_Orderings_Obot__class_Obot(tc_fun(_1004634, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1004634, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1004634, c_Orderings_Oord__class_Omin(_1004634), _1004636) = _1004638)]]], (28762 ^ _779854) ^ [_1299468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299468)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1299468)) = _1299468)], (49144 ^ _779854) ^ [_1770744, _1770746, _1770748, _1770750, _1770752] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1770744, _1770746, _1770748) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1770744, _1770750, _1770752), 49147 ^ _779854 : [(49150 ^ _779854) ^ [] : [-(_1770748 = _1770752)], (49148 ^ _779854) ^ [] : [-(_1770746 = _1770750)]]], (18371 ^ _779854) ^ [_1112321, _1112323, _1112325, _1112327] : [class_Groups_Ocomm__monoid__add(_1112321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112323), _1112325)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1112321), _1112327), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1112323), _1112325)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112321), hAPP(_1112327, _1112323)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1112321), _1112327), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1112323)), _1112325))))], (6413 ^ _779854) ^ [_882072, _882074] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_882072, tc_HOL_Obool), tc_HOL_Obool)), _882074), hAPP(c_Set_OPow(_882072), c_Complete__Lattice_OSup__class_OSup(tc_fun(_882072, tc_HOL_Obool), _882074)))))], (52303 ^ _779854) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (34163 ^ _779854) ^ [_1412219] : [class_Orderings_Olinorder(_1412219), -(c_Orderings_Oord_Omax(_1412219, hAPP(c_COMBC(_1412219, _1412219, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1412219))) = c_Orderings_Oord__class_Omin(_1412219))], (31118 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (47888 ^ _779854) ^ [_1743301, _1743303] : [class_Orderings_Olinorder(_1743301), 47891 ^ _779854 : [(47912 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743301, _1743303)), 47913 ^ _779854 : [(47916 ^ _779854) ^ [_1743861, _1743863] : [_1743303 = hAPP(hAPP(c_List_Olist_OCons(_1743301), _1743861), _1743863), 47922 ^ _779854 : [(47925 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743301), _1743861), 47921 ^ [_1743301, _1743303, _1743861, _1743863]))], (47923 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743301), 47921 ^ [_1743301, _1743303, _1743861, _1743863]), hAPP(c_List_Oset(_1743301), _1743863))))]], c_List_Olinorder__class_Osorted(_1743301, _1743863)], (47914 ^ _779854) ^ [] : [_1743303 = c_List_Olist_ONil(_1743301)]]], (47892 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1743301, _1743303), -(_1743303 = c_List_Olist_ONil(_1743301)), 47901 ^ _779854 : [(47904 ^ _779854) ^ [_1743635] : [hBOOL(hAPP(hAPP(c_member(_1743301), _1743635), hAPP(c_List_Oset(_1743301), 47899 ^ [_1743301, _1743303]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743301), 47900 ^ [_1743301, _1743303]), _1743635)))], (47910 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743301, 47899 ^ [_1743301, _1743303]))], (47902 ^ _779854) ^ [] : [-(_1743303 = hAPP(hAPP(c_List_Olist_OCons(_1743301), 47900 ^ [_1743301, _1743303]), 47899 ^ [_1743301, _1743303]))]]]]], (35002 ^ _779854) ^ [_1430814, _1430816, _1430818] : [-(c_Nat_Onat_Onat__case(_1430814, _1430816, _1430818, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1430816)], (31053 ^ _779854) ^ [_1340201] : [c_Int_OMin = c_Int_OBit0(_1340201)], (46496 ^ _779854) ^ [_1714042, _1714044, _1714046, _1714048] : [-(hBOOL(hAPP(_1714042, _1714044))), -(hAPP(c_List_OremoveAll(_1714046, _1714044), hAPP(c_List_Ofilter(_1714046, _1714042), _1714048)) = hAPP(c_List_Ofilter(_1714046, _1714042), _1714048))], (49408 ^ _779854) ^ [_1776770] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1776770)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1776770)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47376 ^ _779854) ^ [_1732309, _1732311, _1732313] : [-(hAPP(c_List_Orev(_1732309), hAPP(hAPP(c_List_Oappend(_1732309), _1732311), _1732313)) = hAPP(hAPP(c_List_Oappend(_1732309), hAPP(c_List_Orev(_1732309), _1732313)), hAPP(c_List_Orev(_1732309), _1732311)))], (5810 ^ _779854) ^ [_871837, _871839, _871841, _871843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871837, tc_HOL_Obool)), _871839), _871841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871837, tc_HOL_Obool)), _871841), _871843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871837, tc_HOL_Obool)), _871839), _871843)))], (42669 ^ _779854) ^ [_1626964, _1626966, _1626968] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1626964, tc_HOL_Obool)), hAPP(c_List_Oset(_1626964), hAPP(hAPP(c_List_Otake(_1626964), _1626966), _1626968))), hAPP(c_List_Oset(_1626964), _1626968))))], (52573 ^ _779854) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (13281 ^ _779854) ^ [_1013960, _1013962, _1013964] : [class_Lattices_Olattice(_1013960), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013960), _1013962)), hBOOL(hAPP(hAPP(c_member(_1013960), _1013964), _1013962)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1013960), _1013964), c_Big__Operators_Olattice__class_OSup__fin(_1013960, _1013962)) = c_Big__Operators_Olattice__class_OSup__fin(_1013960, _1013962))], (16205 ^ _779854) ^ [_1070876, _1070878, _1070880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070876), _1070880)), _1070878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070878), _1070880))))], (37217 ^ _779854) ^ [_1479694] : [-(c_Relation_OId__on(_1479694, c_Orderings_Obot__class_Obot(tc_fun(_1479694, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479694, _1479694), tc_HOL_Obool)))], (10771 ^ _779854) ^ [_963639, _963641, _963643, _963645, _963647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963639, tc_HOL_Obool)), _963641), _963643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963639, tc_HOL_Obool)), _963645), _963647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963639, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963639, tc_HOL_Obool)), _963641), _963647)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963639, tc_HOL_Obool)), _963643), _963645))))], (15862 ^ _779854) ^ [_1064207, _1064209, _1064211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064207), _1064209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064207), _1064211)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064209), _1064211))))], (47328 ^ _779854) ^ [_1731370, _1731372] : [c_List_Olist_ONil(_1731370) = hAPP(c_List_Orev(_1731370), _1731372), -(_1731372 = c_List_Olist_ONil(_1731370))], (51443 ^ _779854) ^ [_1821624, _1821626, _1821628, _1821630] : [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), _1821624, _1821626)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821628, _1821630))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821624), _1821626)), 51450 ^ _779854 : [(51453 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821626), _1821630)))], (51451 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821628), _1821624)))]]], (17370 ^ _779854) ^ [_1093781, _1093783, _1093785, _1093787] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093781), _1093783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1093785), hAPP(c_Set_Oimage(_1093781, _1093785, _1093787), _1093783))), hAPP(c_Finite__Set_Ocard(_1093781), _1093783))))], (52247 ^ _779854) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (46565 ^ _779854) ^ [_1716234, _1716236] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1716234)), c_List_Otranspose__rel(_1716234)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1716234)), c_List_Olist_ONil(_1716234)), _1716236))), -(c_List_Otranspose(_1716234, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1716234)), c_List_Olist_ONil(_1716234)), _1716236)) = c_List_Otranspose(_1716234, _1716236))], (48798 ^ _779854) ^ [_1763028, _1763030, _1763032, _1763034, _1763036] : [-(hAPP(c_New__DSequence_Oneg__bind(_1763028, _1763030, _1763032, _1763034), _1763036) = c_Lazy__Sequence_Ohb__bind(_1763028, _1763030, hAPP(_1763032, _1763036), hAPP(hAPP(c_COMBC(_1763028, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1763030))), _1763034), _1763036)))], (12442 ^ _779854) ^ [_997081, _997083, _997085] : [class_Orderings_Oord(_997081), 12445 ^ _779854 : [(12452 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997081), _997085), _997083)), -(hBOOL(hAPP(hAPP(c_member(_997081), _997083), hAPP(c_SetInterval_Oord__class_OatLeast(_997081), _997085))))], (12446 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_997081), _997083), hAPP(c_SetInterval_Oord__class_OatLeast(_997081), _997085))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997081), _997085), _997083)))]]], (15246 ^ _779854) ^ [_1051679, _1051681, _1051683, _1051685] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1051679), 15249 ^ _779854 : [(15256 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051679), _1051683), _1051685)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051679), _1051681), _1051683)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051679), _1051681), _1051685))))], (15250 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051679), _1051681), _1051683)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051679), _1051681), _1051685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051679), _1051683), _1051685)))]]], (43788 ^ _779854) ^ [_1653275, _1653277, _1653279, _1653281, _1653283] : [-(hAPP(hAPP(c_List_Oappend(_1653275), _1653277), _1653279) = hAPP(hAPP(c_List_Olist_OCons(_1653275), _1653281), _1653283)), 43789 ^ _779854 : [(43796 ^ _779854) ^ [_1653458] : [_1653277 = hAPP(hAPP(c_List_Olist_OCons(_1653275), _1653281), _1653458), hAPP(hAPP(c_List_Oappend(_1653275), _1653458), _1653279) = _1653283], (43790 ^ _779854) ^ [] : [_1653277 = c_List_Olist_ONil(_1653275), _1653279 = hAPP(hAPP(c_List_Olist_OCons(_1653275), _1653281), _1653283)]]], (50436 ^ _779854) ^ [_1798917, _1798919, _1798921] : [hAPP(_1798921, hAPP(c_Hilbert__Choice_Oinv__into(_1798917, _1798919, c_Orderings_Otop__class_Otop(tc_fun(_1798917, tc_HOL_Obool)), _1798921), 50437 ^ [_1798917, _1798919, _1798921])) = 50437 ^ [_1798917, _1798919, _1798921], -(hAPP(c_Set_Oimage(_1798917, _1798919, _1798921), c_Orderings_Otop__class_Otop(tc_fun(_1798917, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1798919, tc_HOL_Obool)))], (37900 ^ _779854) ^ [_1496337, _1496339, _1496341, _1496343, _1496345] : [c_Typedef_Otype__definition(_1496337, _1496339, _1496341, _1496343, _1496345), -(hAPP(c_Set_Oimage(_1496337, _1496339, _1496341), c_Orderings_Otop__class_Otop(tc_fun(_1496337, tc_HOL_Obool))) = _1496345)], (46280 ^ _779854) ^ [_1708496] : [-(c_List_Oconcat(_1708496, c_List_Olist_ONil(tc_List_Olist(_1708496))) = c_List_Olist_ONil(_1708496))], (14255 ^ _779854) ^ [_1031543, _1031545, _1031547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031543), _1031545)), hBOOL(hAPP(_1031547, _1031545)), 14266 ^ _779854 : [(14269 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1031543), 14264 ^ [_1031543, _1031545, _1031547]), 14265 ^ [_1031543, _1031545, _1031547])))], (14271 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1031547, 14265 ^ [_1031543, _1031545, _1031547])))], (14273 ^ _779854) ^ [] : [hBOOL(hAPP(_1031547, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031543, tc_HOL_Obool)), 14265 ^ [_1031543, _1031545, _1031547]), hAPP(hAPP(c_Set_Oinsert(_1031543), 14264 ^ [_1031543, _1031545, _1031547]), c_Orderings_Obot__class_Obot(tc_fun(_1031543, tc_HOL_Obool))))))], (14267 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031543), 14265 ^ [_1031543, _1031545, _1031547])))]], -(hBOOL(hAPP(_1031547, c_Orderings_Obot__class_Obot(tc_fun(_1031543, tc_HOL_Obool)))))], (47818 ^ _779854) ^ [_1741706, _1741708, _1741710, _1741712, _1741714] : [class_Groups_Omonoid__add(_1741706), 47824 ^ _779854 : [(47829 ^ _779854) ^ [] : [hAPP(_1741714, 47823 ^ [_1741706, _1741708, _1741710, _1741712, _1741714]) = c_Groups_Ozero__class_Ozero(_1741706)], (47827 ^ _779854) ^ [] : [hBOOL(hAPP(_1741712, 47823 ^ [_1741706, _1741708, _1741710, _1741712, _1741714]))], (47825 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741708), 47823 ^ [_1741706, _1741708, _1741710, _1741712, _1741714]), hAPP(c_List_Oset(_1741708), _1741710))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1741706), hAPP(hAPP(c_List_Omap(_1741708, _1741706), _1741714), hAPP(c_List_Ofilter(_1741708, _1741712), _1741710))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1741706), hAPP(hAPP(c_List_Omap(_1741708, _1741706), _1741714), _1741710)))], (45069 ^ _779854) ^ [_1681157, _1681159, _1681161, _1681163] : [-(_1681157 = c_List_Olist_ONil(_1681159)), -(c_List_Olast(_1681161, hAPP(hAPP(c_List_Omap(_1681159, _1681161), _1681163), _1681157)) = hAPP(_1681163, c_List_Olast(_1681159, _1681157)))], (42506 ^ _779854) ^ [_1622456, _1622458, _1622460] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622456)), _1622458), c_Wellfounded_Oacc(tc_List_Olist(_1622456), c_List_Olistrel1(_1622456, _1622460)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622456)), _1622458), c_List_Olists(_1622456, c_Wellfounded_Oacc(_1622456, _1622460)))))], (34019 ^ _779854) ^ [_1408384, _1408386, _1408388, _1408390] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1408384, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1408386)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1408384, tc_HOL_Obool), tc_Nat_Onat), _1408388), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1408390))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1408384, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1408390, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408386), _1408390))), _1408388))], (48441 ^ _779854) ^ [_1755982, _1755984, _1755986, _1755988] : [c_List_Olist__ex(_1755982, _1755984, hAPP(hAPP(c_List_Oappend(_1755982), _1755986), _1755988)), -(c_List_Olist__ex(_1755982, _1755984, _1755986)), -(c_List_Olist__ex(_1755982, _1755984, _1755988))], (32728 ^ _779854) ^ [_1369093, _1369095, _1369097, _1369099, _1369101, _1369103] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369093, tc_fun(_1369095, tc_HOL_Obool)), _1369097), _1369099), _1369101)), hBOOL(hAPP(hAPP(c_member(_1369093), _1369103), _1369097)), -(hBOOL(hAPP(hAPP(_1369099, _1369103), _1369101)))], (40869 ^ _779854) ^ [_1577945, _1577947, _1577949, _1577951, _1577953, _1577955, _1577957] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1577945, _1577947, _1577949, _1577951), _1577953), _1577955), _1577957) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1577947, _1577949, _1577951), _1577955), hAPP(_1577953, _1577957)))], (40197 ^ _779854) ^ [_1562501, _1562503, _1562505, _1562507] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562501, tc_fun(_1562503, tc_HOL_Obool)), _1562505), _1562507) = hAPP(c_Set_OCollect(_1562503), hAPP(hAPP(c_COMBB(tc_fun(_1562501, tc_HOL_Obool), tc_HOL_Obool, _1562503), c_HOL_OAll(_1562501)), hAPP(hAPP(c_COMBB(tc_fun(_1562501, tc_HOL_Obool), tc_fun(_1562501, tc_HOL_Obool), _1562503), hAPP(c_COMBS(_1562501, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562501), c_fimplies), hAPP(hAPP(c_COMBC(_1562501, tc_fun(_1562501, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562501)), _1562505)))), hAPP(hAPP(c_COMBC(_1562503, tc_fun(_1562501, tc_fun(_1562503, tc_HOL_Obool)), tc_fun(_1562501, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1562503, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1562501, tc_fun(_1562503, tc_HOL_Obool)), tc_fun(_1562501, tc_HOL_Obool)), _1562503), c_COMBB(tc_fun(_1562503, tc_HOL_Obool), tc_HOL_Obool, _1562501)), c_member(_1562503))), _1562507)))))], (7846 ^ _779854) ^ [_910857, _910859, _910861, _910863] : [class_Orderings_Oorder(_910857), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_910857, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_910857, _910859, _910861)), c_SetInterval_Oord__class_OgreaterThanLessThan(_910857, _910861, _910863)) = c_Orderings_Obot__class_Obot(tc_fun(_910857, tc_HOL_Obool)))], (4906 ^ _779854) ^ [_854784, _854786, _854788, _854790] : [-(c_Relation_Oconverse(_854790, _854786) = c_Relation_Oconverse(_854788, _854784)), _854790 = _854788, _854786 = _854784], (8434 ^ _779854) ^ [_920582, _920584, _920586, _920588, _920590] : [class_Orderings_Oorder(_920582), 8437 ^ _779854 : [(8458 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920582, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_920582, _920584, _920586)), c_SetInterval_Oord__class_OatLeastAtMost(_920582, _920588, _920590)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920588), _920590)), 8461 ^ _779854 : [(8464 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920588), _920584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920586), _920590)), 8471 ^ _779854 : [(8474 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920582), _920586), _920590))], (8472 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920582), _920588), _920584))]]], (8462 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920584), _920586)))]]], (8438 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920582, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_920582, _920584, _920586)), c_SetInterval_Oord__class_OatLeastAtMost(_920582, _920588, _920590))), 8441 ^ _779854 : [(8442 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920584), _920586)), 8445 ^ _779854 : [(8450 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920582), _920588), _920584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920582), _920586), _920590)))], (8448 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920586), _920590)))], (8446 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920588), _920584)))]]], (8456 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920582), _920588), _920590)))]]]]], (34107 ^ _779854) ^ [_1410693, _1410695, _1410697, _1410699, _1410701] : [class_Groups_Ocomm__monoid__mult(_1410693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410695), _1410697)), 34114 ^ _779854 : [(34121 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410695), _1410699), _1410697))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410695, _1410693), hAPP(hAPP(c_COMBC(_1410695, _1410693, _1410693), hAPP(hAPP(c_COMBS(_1410695, _1410693, tc_fun(_1410693, _1410693)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1410693, tc_fun(_1410693, _1410693)), _1410695), c_If(_1410693)), hAPP(c_fequal, _1410699))), _1410701)), c_Groups_Oone__class_Oone(_1410693))), _1410697) = c_Groups_Oone__class_Oone(_1410693))], (34115 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1410695), _1410699), _1410697)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410695, _1410693), hAPP(hAPP(c_COMBC(_1410695, _1410693, _1410693), hAPP(hAPP(c_COMBS(_1410695, _1410693, tc_fun(_1410693, _1410693)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1410693, tc_fun(_1410693, _1410693)), _1410695), c_If(_1410693)), hAPP(c_fequal, _1410699))), _1410701)), c_Groups_Oone__class_Oone(_1410693))), _1410697) = hAPP(_1410701, _1410699))]]], (31402 ^ _779854) ^ [_1345876, _1345878, _1345880, _1345882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1345876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345878), _1345880)), -(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), _1345880), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1345882, _1345876))), _1345878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1345880), _1345876))))], (50146 ^ _779854) ^ [_1793306, _1793308, _1793310] : [c_Equiv__Relations_Oequiv(_1793306, _1793308, _1793310), 50149 ^ _779854 : [(50154 ^ _779854) ^ [] : [-(c_Relation_Otrans(_1793306, _1793310))], (50152 ^ _779854) ^ [] : [-(c_Relation_Osym(_1793306, _1793310))], (50150 ^ _779854) ^ [] : [-(c_Relation_Orefl__on(_1793306, _1793308, _1793310))]]], (3808 ^ _779854) ^ [_837213, _837215] : [_837215 = _837213, -(c_New__DSequence_Opos__not__seq(_837215) = c_New__DSequence_Opos__not__seq(_837213))], (38196 ^ _779854) ^ [_1503066, _1503068, _1503070, _1503072, _1503074] : [c_Fun_Oinj__on(_1503066, _1503068, _1503070, c_Orderings_Otop__class_Otop(tc_fun(_1503066, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503068, tc_HOL_Obool)), _1503072), hAPP(c_Set_Oimage(_1503066, _1503068, _1503070), _1503074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503066, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1503066, _1503068, _1503070), _1503072)), _1503074)))], (11214 ^ _779854) ^ [_973257, _973259] : [class_Finite__Set_Ofinite(_973257), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973257), _973259)))], (44085 ^ _779854) ^ [_1659907, _1659909, _1659911] : [hBOOL(hAPP(c_List_Odistinct(_1659907), hAPP(hAPP(c_List_Oappend(_1659907), _1659909), _1659911))), 44088 ^ _779854 : [(44093 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659907, tc_HOL_Obool)), hAPP(c_List_Oset(_1659907), _1659909)), hAPP(c_List_Oset(_1659907), _1659911)) = c_Orderings_Obot__class_Obot(tc_fun(_1659907, tc_HOL_Obool)))], (44091 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1659907), _1659911)))], (44089 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1659907), _1659909)))]]], (40275 ^ _779854) ^ [_1564040, _1564042] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1564040, tc_HOL_Obool), _1564042) = hAPP(c_Set_OCollect(_1564040), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1564040, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1564040), c_HOL_OAll(tc_fun(_1564040, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1564040, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1564040, tc_HOL_Obool), tc_HOL_Obool), _1564040), hAPP(c_COMBS(tc_fun(_1564040, 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(_1564040, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1564040, tc_HOL_Obool), tc_fun(tc_fun(_1564040, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1564040, tc_HOL_Obool))), _1564042)))), c_member(_1564040)))))], (656 ^ _779854) ^ [_789760, _789762, _789764, _789766] : [-(c_List_Olinorder__class_Osorted(_789764, _789760)), c_List_Olinorder__class_Osorted(_789766, _789762), _789766 = _789764, _789762 = _789760], (7107 ^ _779854) ^ [_896688, _896690, _896692] : [class_Lattices_Olattice(_896688), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896688), _896690), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896688), _896690), _896692))))], (27017 ^ _779854) ^ [] : [-(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))))], (51177 ^ _779854) ^ [_1814648, _1814650, _1814652, _1814654, _1814656] : [51179 ^ _779854 : [(51182 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814652, tc_HOL_Obool)), _1814654), hAPP(_1814656, 51178 ^ [_1814648, _1814650, _1814652, _1814654, _1814656])))], (51180 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1814648), 51178 ^ [_1814648, _1814650, _1814652, _1814654, _1814656]), _1814650)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814652, tc_HOL_Obool)), _1814654), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1814648, tc_fun(_1814652, tc_HOL_Obool)), _1814650), _1814656))))], (48257 ^ _779854) ^ [_1751976, _1751978, _1751980, _1751982, _1751984] : [hAPP(hAPP(c_List_Olist_OCons(_1751976), _1751978), _1751980) = hAPP(c_List_Ofilter(_1751976, _1751982), _1751984), 48262 ^ _779854 : [(48271 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1751982, _1751978)))], (48273 ^ _779854) ^ [] : [-(_1751980 = hAPP(c_List_Ofilter(_1751976, _1751982), 48261 ^ [_1751976, _1751978, _1751980, _1751982, _1751984]))], (48265 ^ _779854) ^ [_1752290] : [hBOOL(hAPP(hAPP(c_member(_1751976), _1752290), hAPP(c_List_Oset(_1751976), 48260 ^ [_1751976, _1751978, _1751980, _1751982, _1751984]))), hBOOL(hAPP(_1751982, _1752290))], (48263 ^ _779854) ^ [] : [-(_1751984 = hAPP(hAPP(c_List_Oappend(_1751976), 48260 ^ [_1751976, _1751978, _1751980, _1751982, _1751984]), hAPP(hAPP(c_List_Olist_OCons(_1751976), _1751978), 48261 ^ [_1751976, _1751978, _1751980, _1751982, _1751984])))]]], (25623 ^ _779854) ^ [_1245783, _1245785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245783), _1245785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1245783)), _1245785)))], (52717 ^ _779854) ^ [_1839261, _1839263] : [hBOOL(_1839261), -(hBOOL(hAPP(hAPP(c_fimplies, _1839263), _1839261)))], (44296 ^ _779854) ^ [_1665354, _1665356, _1665358, _1665360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1665354), _1665356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1665358, tc_HOL_Obool)), hAPP(c_List_Oset(_1665358), hAPP(hAPP(c_List_Odrop(_1665358), _1665356), _1665360))), hAPP(c_List_Oset(_1665358), hAPP(hAPP(c_List_Odrop(_1665358), _1665354), _1665360)))))], (17915 ^ _779854) ^ [_1104136, _1104138] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1104136), hAPP(c_Nat_OSuc, _1104138)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1104136), _1104138)))], (10975 ^ _779854) ^ [_968107, _968109, _968111] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968107, tc_HOL_Obool)), _968109), _968111) = c_Orderings_Obot__class_Obot(tc_fun(_968107, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968107, tc_HOL_Obool)), _968109), _968111) = _968109)], (43568 ^ _779854) ^ [_1648181, _1648183, _1648185] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648181), tc_List_Olist(_1648181))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648181), tc_List_Olist(_1648181)), c_List_Olist_ONil(_1648181)), _1648183)), c_List_Olex(_1648181, _1648185)))], (41100 ^ _779854) ^ [_1584328, _1584330, _1584332, _1584334, _1584336] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584328, _1584328)), hAPP(hAPP(c_Product__Type_OPair(_1584328, _1584328), _1584330), _1584332)), c_Transitive__Closure_Ortrancl(_1584328, _1584334))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584328, _1584328)), hAPP(hAPP(c_Product__Type_OPair(_1584328, _1584328), _1584332), _1584336)), _1584334)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584328, _1584328)), hAPP(hAPP(c_Product__Type_OPair(_1584328, _1584328), _1584330), _1584336)), c_Transitive__Closure_Ortrancl(_1584328, _1584334))))], (44799 ^ _779854) ^ [_1676493, _1676495, _1676497, _1676499] : [class_Orderings_Olinorder(_1676493), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676493, _1676493, c_COMBI(_1676493)), _1676495), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676493, _1676493, c_COMBI(_1676493)), _1676497), _1676499)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676493, _1676493, c_COMBI(_1676493)), _1676497), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676493, _1676493, c_COMBI(_1676493)), _1676495), _1676499)))], (37809 ^ _779854) ^ [_1493852, _1493854, _1493856] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1493852, hAPP(hAPP(c_COMBC(_1493852, tc_fun(tc_prod(_1493852, _1493852), tc_HOL_Obool), tc_fun(_1493852, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493852, tc_fun(tc_fun(tc_prod(_1493852, _1493852), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1493852, _1493852), tc_HOL_Obool), tc_fun(_1493852, tc_HOL_Obool)), _1493852), c_COMBC(_1493852, tc_fun(tc_prod(_1493852, _1493852), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493852, tc_prod(_1493852, _1493852)), tc_fun(_1493852, tc_fun(tc_fun(tc_prod(_1493852, _1493852), tc_HOL_Obool), tc_HOL_Obool)), _1493852), hAPP(c_COMBB(tc_prod(_1493852, _1493852), tc_fun(tc_fun(tc_prod(_1493852, _1493852), tc_HOL_Obool), tc_HOL_Obool), _1493852), c_member(tc_prod(_1493852, _1493852)))), c_Product__Type_OPair(_1493852, _1493852)))), _1493854)), _1493856)), -(hBOOL(hAPP(hAPP(c_member(_1493852), _1493856), c_Wellfounded_Oacc(_1493852, _1493854))))], (43624 ^ _779854) ^ [_1649252, _1649254] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1649252), tc_List_Olist(_1649252), c_List_Olistrel(_1649252, _1649254)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1649252)), c_List_Olist_ONil(_1649252)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1649252), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1649252)), c_List_Olist_ONil(_1649252)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1649252), tc_HOL_Obool))))], (1998 ^ _779854) ^ [_808794, _808796, _808798, _808800, _808802, _808804, _808806, _808808, _808810, _808812] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_808812, _808808, _808804, _808800, _808796) = c_SetInterval_Oord_OgreaterThanAtMost(_808810, _808806, _808802, _808798, _808794)), _808812 = _808810, _808808 = _808806, _808804 = _808802, _808800 = _808798, _808796 = _808794], (9658 ^ _779854) ^ [_941790, _941792, _941794, _941796] : [class_Orderings_Olinorder(_941790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941790), _941792), _941794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941790), _941796), _941794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941790), hAPP(hAPP(c_Orderings_Oord__class_Omax(_941790), _941792), _941796)), _941794)))], (48055 ^ _779854) ^ [_1747296, _1747298, _1747300, _1747302] : [class_Orderings_Oorder(_1747296), class_Enum_Oenum(_1747298), 48062 ^ _779854 : [(48071 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1747298, _1747296)), _1747300), _1747302))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1747298, _1747296)), _1747300), _1747302)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1747298), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1747298), c_fNot), hAPP(hAPP(c_COMBS(_1747298, _1747296, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1747296, tc_fun(_1747296, tc_HOL_Obool), _1747298), c_fequal), _1747300)), _1747302))))], (48063 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1747298, _1747296)), _1747300), _1747302)), 48066 ^ _779854 : [(48069 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1747298), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1747298), c_fNot), hAPP(hAPP(c_COMBS(_1747298, _1747296, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1747296, tc_fun(_1747296, tc_HOL_Obool), _1747298), c_fequal), _1747300)), _1747302)))))], (48067 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1747298, _1747296)), _1747300), _1747302)))]]]]], (52537 ^ _779854) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (24697 ^ _779854) ^ [_1228050, _1228052, _1228054, _1228056] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228050), hAPP(c_Int_Onumber__class_Onumber__of(_1228050), _1228052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228050), _1228054), _1228056)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228050), hAPP(c_Int_Onumber__class_Onumber__of(_1228050), _1228052)), _1228054)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228050), hAPP(c_Int_Onumber__class_Onumber__of(_1228050), _1228052)), _1228056))), class_Int_Onumber(_1228050), class_Rings_Osemiring(_1228050)], (29433 ^ _779854) ^ [_1310813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1310813)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310813), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (38670 ^ _779854) ^ [_1516954, _1516956, _1516958] : [c_Relation_Orefl__on(_1516954, _1516956, _1516958), 38673 ^ _779854 : [(38676 ^ _779854) ^ [_1517136] : [hBOOL(hAPP(hAPP(c_member(_1516954), _1517136), _1516956)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516954, _1516954)), hAPP(hAPP(c_Product__Type_OPair(_1516954, _1516954), _1517136), _1517136)), _1516958)))], (38674 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1516954, _1516954), tc_HOL_Obool)), _1516958), hAPP(hAPP(c_Product__Type_OSigma(_1516954, _1516954), _1516956), hAPP(c_COMBK(tc_fun(_1516954, tc_HOL_Obool), _1516954), _1516956)))))]]], (42637 ^ _779854) ^ [_1625951, _1625953, _1625955, _1625957] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625951), tc_List_Olist(_1625951))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625951), tc_List_Olist(_1625951)), _1625953), _1625955)), c_List_Olexord(_1625951, _1625957)))), 42638 ^ _779854 : [(42645 ^ _779854) ^ [_1626258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626258), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625951)), _1625953)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625951)), _1625955)))), hAPP(hAPP(c_List_Otake(_1625951), _1626258), _1625953) = hAPP(hAPP(c_List_Otake(_1625951), _1626258), _1625955), hBOOL(hAPP(hAPP(c_member(tc_prod(_1625951, _1625951)), hAPP(hAPP(c_Product__Type_OPair(_1625951, _1625951), hAPP(hAPP(c_List_Onth(_1625951), _1625953), _1626258)), hAPP(hAPP(c_List_Onth(_1625951), _1625955), _1626258))), _1625957))], (42639 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625951)), _1625953)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625951)), _1625955))), hAPP(hAPP(c_List_Otake(_1625951), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625951)), _1625953)), _1625955) = _1625953]]], (12122 ^ _779854) ^ [_991058, _991060, _991062, _991064, _991066, _991068] : [c_Fun_Oinj__on(_991058, _991060, _991062, _991064), hBOOL(hAPP(hAPP(c_member(_991058), _991066), _991064)), hBOOL(hAPP(hAPP(c_member(_991058), _991068), _991064)), 12133 ^ _779854 : [(12140 ^ _779854) ^ [] : [_991066 = _991068, -(hAPP(_991062, _991066) = hAPP(_991062, _991068))], (12134 ^ _779854) ^ [] : [hAPP(_991062, _991066) = hAPP(_991062, _991068), -(_991066 = _991068)]]], (49412 ^ _779854) ^ [_1776835, _1776837] : [-(c_Lazy__Sequence_Oappend(_1776835, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1776835), _1776837) = _1776837)], (46437 ^ _779854) ^ [_1712856, _1712858, _1712860, _1712862] : [-(hAPP(c_List_Ofilter(_1712856, _1712858), c_List_Oremove1(_1712856, _1712860, _1712862)) = c_List_Oremove1(_1712856, _1712860, hAPP(c_List_Ofilter(_1712856, _1712858), _1712862)))], (20369 ^ _779854) ^ [_1146436, _1146438, _1146440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146436)), 20372 ^ _779854 : [(20379 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146438), _1146440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146436), _1146438)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146436), _1146440))))], (20373 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146436), _1146438)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146436), _1146440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146438), _1146440)))]]], (14636 ^ _779854) ^ [_1039301, _1039303] : [class_Orderings_Olinorder(_1039301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039301), _1039303)), -(c_Big__Operators_Olattice_OInf__fin(_1039301, c_Orderings_Oord__class_Omin(_1039301), _1039303) = hAPP(c_Finite__Set_Ofold1(_1039301, c_Orderings_Oord__class_Omin(_1039301)), _1039303))], (20520 ^ _779854) ^ [_1149031] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1149031) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1149031))], (29551 ^ _779854) ^ [_1312890, _1312892] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1312890))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1312892))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312890)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312892)))], (18249 ^ _779854) ^ [_1110061, _1110063] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110061), hAPP(c_Nat_OSuc, _1110063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110061), _1110063)))], (41867 ^ _779854) ^ [_1603140, _1603142, _1603144, _1603146, _1603148] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603140, _1603140)), hAPP(hAPP(c_Product__Type_OPair(_1603140, _1603140), _1603142), _1603144)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603140, _1603140), tc_HOL_Obool), _1603146), _1603148))), 41872 ^ _779854 : [(41875 ^ _779854) ^ [] : [-(_1603142 = _1603144)], (41873 ^ _779854) ^ [] : [-(_1603146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41878 ^ _779854 : [(41883 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603140, _1603140)), hAPP(hAPP(c_Product__Type_OPair(_1603140, _1603140), 41876 ^ [_1603140, _1603142, _1603144, _1603146, _1603148]), _1603144)), _1603148)))], (41881 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603140, _1603140)), hAPP(hAPP(c_Product__Type_OPair(_1603140, _1603140), _1603142), 41876 ^ [_1603140, _1603142, _1603144, _1603146, _1603148])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603140, _1603140), tc_HOL_Obool), 41877 ^ [_1603140, _1603142, _1603144, _1603146, _1603148]), _1603148))))], (41879 ^ _779854) ^ [] : [-(_1603146 = hAPP(c_Nat_OSuc, 41877 ^ [_1603140, _1603142, _1603144, _1603146, _1603148]))]]], (33158 ^ _779854) ^ [_1380965, _1380967, _1380969, _1380971] : [33160 ^ _779854 : [(33163 ^ _779854) ^ [] : [hAPP(_1380971, 33159 ^ [_1380965, _1380967, _1380969, _1380971]) = c_Orderings_Obot__class_Obot(tc_fun(_1380965, tc_HOL_Obool))], (33161 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380967), 33159 ^ [_1380965, _1380967, _1380969, _1380971]), _1380969)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1380965, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380967, tc_fun(_1380965, tc_HOL_Obool)), _1380969), _1380971))], (39794 ^ _779854) ^ [_1551826, _1551828] : [-(hAPP(c_Relation_ODomain(_1551826, _1551828), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551826, _1551828), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1551826, tc_HOL_Obool)))], (32966 ^ _779854) ^ [] : [-(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)))], (36086 ^ _779854) ^ [_1452710, _1452712, _1452714, _1452716, _1452718, _1452720] : [c_Finite__Set_Ofolding(_1452710, _1452712, _1452714, _1452716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452710), _1452718)), -(hBOOL(hAPP(hAPP(c_member(_1452710), _1452720), _1452718))), -(hAPP(_1452716, hAPP(hAPP(c_Set_Oinsert(_1452710), _1452720), _1452718)) = hAPP(c_Fun_Ocomp(_1452712, _1452712, _1452712, hAPP(_1452716, _1452718)), hAPP(_1452714, _1452720)))], (32914 ^ _779854) ^ [_1374886, _1374888, _1374890] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1374886, tc_fun(_1374888, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1374886, tc_HOL_Obool))), _1374890) = c_Orderings_Otop__class_Otop(tc_fun(_1374888, tc_HOL_Obool)))], (41166 ^ _779854) ^ [_1586000, _1586002] : [-(c_Transitive__Closure_Ortrancl(_1586000, _1586002) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586000, _1586000), tc_HOL_Obool)), c_Relation_OId(_1586000)), hAPP(hAPP(c_Relation_Orel__comp(_1586000, _1586000, _1586000), c_Transitive__Closure_Ortrancl(_1586000, _1586002)), _1586002)))], (44418 ^ _779854) ^ [_1668405, _1668407, _1668409, _1668411] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668405) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1668407), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668405)), hAPP(hAPP(c_List_Olist_OCons(_1668407), _1668409), _1668411)) = hAPP(hAPP(c_List_Odrop(_1668407), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668405)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1668411))], (28641 ^ _779854) ^ [_1297500, _1297502] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297500)), _1297502) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1297500), _1297502)))], (6229 ^ _779854) ^ [_878748, _878750, _878752, _878754, _878756] : [class_Orderings_Oorder(_878748), class_Orderings_Olinorder(_878750), c_Orderings_Oorder__class_Ostrict__mono(_878750, _878748, _878752), 6240 ^ _779854 : [(6247 ^ _779854) ^ [] : [_878754 = _878756, -(hAPP(_878752, _878754) = hAPP(_878752, _878756))], (6241 ^ _779854) ^ [] : [hAPP(_878752, _878754) = hAPP(_878752, _878756), -(_878754 = _878756)]]], (31356 ^ _779854) ^ [_1344984] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1344984), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1344984))], (34461 ^ _779854) ^ [_1418994, _1418996] : [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(_1418996))), 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)), _1418994))))), -(hAPP(c_Nat_OSuc, _1418994) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418996))], (10471 ^ _779854) ^ [_957598, _957600, _957602] : [class_Orderings_Olinorder(_957598), hBOOL(hAPP(c_Finite__Set_Ofinite(_957598), _957600)), -(_957600 = c_Orderings_Obot__class_Obot(tc_fun(_957598, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_957598), _957602)), -(_957602 = c_Orderings_Obot__class_Obot(tc_fun(_957598, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_957598, c_Orderings_Oord__class_Omax(_957598), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_957598, tc_HOL_Obool)), _957600), _957602)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_957598), c_Big__Operators_Olattice_OSup__fin(_957598, c_Orderings_Oord__class_Omax(_957598), _957600)), c_Big__Operators_Olattice_OSup__fin(_957598, c_Orderings_Oord__class_Omax(_957598), _957602)))], (50096 ^ _779854) ^ [_1792519, _1792521] : [hAPP(c_Relation_Oconverse(_1792519, _1792519), _1792521) = _1792521, -(c_Relation_Osym(_1792519, _1792521))], (43203 ^ _779854) ^ [_1640963, _1640965, _1640967] : [hBOOL(hAPP(c_List_Odistinct(_1640963), hAPP(hAPP(c_List_Olist_OCons(_1640963), _1640965), _1640967))), 43206 ^ _779854 : [(43209 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1640963), _1640967)))], (43207 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1640963), _1640965), hAPP(c_List_Oset(_1640963), _1640967)))]]], (40348 ^ _779854) ^ [_1565936, _1565938] : [-(c_Hilbert__Choice_OEps(_1565936, hAPP(hAPP(c_COMBC(_1565936, _1565936, tc_HOL_Obool), c_fequal), _1565938)) = _1565938)], (13649 ^ _779854) ^ [_1019806, _1019808, _1019810] : [class_Lattices_Olattice(_1019806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019806), _1019808)), -(hBOOL(hAPP(hAPP(c_member(_1019806), _1019810), _1019808))), -(_1019808 = c_Orderings_Obot__class_Obot(tc_fun(_1019806, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1019806, hAPP(hAPP(c_Set_Oinsert(_1019806), _1019810), _1019808)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1019806), _1019810), c_Big__Operators_Olattice__class_OInf__fin(_1019806, _1019808)))], (13723 ^ _779854) ^ [_1020987, _1020989, _1020991] : [class_Lattices_Olattice(_1020987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020987), _1020989)), 13730 ^ _779854 : [(13737 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020987, tc_HOL_Obool)), _1020989), hAPP(hAPP(c_Set_Oinsert(_1020987), _1020991), c_Orderings_Obot__class_Obot(tc_fun(_1020987, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1020987, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1020987, hAPP(hAPP(c_Set_Oinsert(_1020987), _1020991), _1020989)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1020987), _1020991), c_Big__Operators_Olattice__class_OInf__fin(_1020987, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020987, tc_HOL_Obool)), _1020989), hAPP(hAPP(c_Set_Oinsert(_1020987), _1020991), c_Orderings_Obot__class_Obot(tc_fun(_1020987, tc_HOL_Obool)))))))], (13731 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020987, tc_HOL_Obool)), _1020989), hAPP(hAPP(c_Set_Oinsert(_1020987), _1020991), c_Orderings_Obot__class_Obot(tc_fun(_1020987, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1020987, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1020987, hAPP(hAPP(c_Set_Oinsert(_1020987), _1020991), _1020989)) = _1020991)]]], (28378 ^ _779854) ^ [_1292914, _1292916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292914)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1292914), _1292916)))], (43474 ^ _779854) ^ [_1646391, _1646393] : [c_Orderings_Obot__class_Obot(tc_fun(_1646391, tc_HOL_Obool)) = hAPP(c_List_Oset(_1646391), _1646393), -(_1646393 = c_List_Olist_ONil(_1646391))], (52387 ^ _779854) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (13871 ^ _779854) ^ [_1024047, _1024049, _1024051] : [class_Orderings_Olinorder(_1024047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024047), _1024049)), -(_1024049 = c_Orderings_Obot__class_Obot(tc_fun(_1024047, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024047), _1024051)), -(_1024051 = c_Orderings_Obot__class_Obot(tc_fun(_1024047, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024047, tc_HOL_Obool)), _1024049), _1024051) = c_Orderings_Obot__class_Obot(tc_fun(_1024047, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1024047, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024047, tc_HOL_Obool)), _1024049), _1024051)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1024047), c_Big__Operators_Olinorder__class_OMin(_1024047, _1024049)), c_Big__Operators_Olinorder__class_OMin(_1024047, _1024051)))], (5858 ^ _779854) ^ [_872600, _872602, _872604, _872606] : [class_Orderings_Opreorder(_872600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872600), _872602), _872604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872600), _872604), _872606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872600), _872602), _872606)))], (16072 ^ _779854) ^ [_1068469, _1068471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068469), _1068471)), -(_1068471 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068469), 16075 ^ [_1068469, _1068471]))], (17805 ^ _779854) ^ [_1102423, _1102425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102425), hAPP(c_Nat_OSuc, _1102423))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102423), _1102425))], (40231 ^ _779854) ^ [_1563271, _1563273] : [class_Complete__Lattice_Ocomplete__lattice(_1563271), -(c_Complete__Lattice_OInf__class_OInf(_1563271, _1563273) = c_Complete__Lattice_OSup__class_OSup(_1563271, hAPP(c_Set_OCollect(_1563271), hAPP(hAPP(c_COMBB(tc_fun(_1563271, tc_HOL_Obool), tc_HOL_Obool, _1563271), c_HOL_OAll(_1563271)), hAPP(hAPP(c_COMBB(tc_fun(_1563271, tc_HOL_Obool), tc_fun(_1563271, tc_HOL_Obool), _1563271), hAPP(c_COMBS(_1563271, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563271), c_fimplies), hAPP(hAPP(c_COMBC(_1563271, tc_fun(_1563271, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563271)), _1563273)))), c_Orderings_Oord__class_Oless__eq(_1563271))))))], (35722 ^ _779854) ^ [_1445115, _1445117, _1445119] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445115, _1445115), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445117), _1445119))), -(_1445115 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1445117 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (49570 ^ _779854) ^ [_1780800] : [-(c_Relation_Otrans(_1780800, c_Relation_OId(_1780800)))], (45178 ^ _779854) ^ [_1684521, _1684523, _1684525, _1684527, _1684529] : [c_Fun_Oinj__on(_1684521, _1684523, _1684525, c_Orderings_Otop__class_Otop(tc_fun(_1684521, tc_HOL_Obool))), 45181 ^ _779854 : [(45188 ^ _779854) ^ [] : [_1684527 = _1684529, -(hAPP(hAPP(c_List_Omap(_1684521, _1684523), _1684525), _1684527) = hAPP(hAPP(c_List_Omap(_1684521, _1684523), _1684525), _1684529))], (45182 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Omap(_1684521, _1684523), _1684525), _1684527) = hAPP(hAPP(c_List_Omap(_1684521, _1684523), _1684525), _1684529), -(_1684527 = _1684529)]]], (4 ^ _779854) ^ [_779904, _779906] : [_779906 = _779904, -(_779904 = _779906)], (3106 ^ _779854) ^ [_826228, _826230, _826232, _826234] : [-(c_List_Olistrel1(_826234, _826230) = c_List_Olistrel1(_826232, _826228)), _826234 = _826232, _826230 = _826228], (7575 ^ _779854) ^ [_905052, _905054, _905056] : [7577 ^ _779854 : [(7583 ^ _779854) ^ [] : [-(7576 ^ [_905052, _905054, _905056] = 7579 ^ [_905052, _905054, _905056])], (7581 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_905052), 7579 ^ [_905052, _905054, _905056]), _905056)))], (7578 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_905052), 7576 ^ [_905052, _905054, _905056]), _905054)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905052, tc_HOL_Obool)), _905054), _905056) = c_Orderings_Obot__class_Obot(tc_fun(_905052, tc_HOL_Obool)))], (8688 ^ _779854) ^ [_924507, _924509, _924511] : [class_Orderings_Olinorder(_924507), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924507), _924509), _924511))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924507), _924511), _924509)))], (35703 ^ _779854) ^ [_1444743, _1444745, _1444747] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1444743, _1444745), _1444747)), 35706 ^ _779854 : [(35707 ^ _779854) ^ [_1444828] : [hBOOL(hAPP(hAPP(_1444745, _1444828), _1444747)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1444743, _1444745), _1444828)))]]], (47566 ^ _779854) ^ [_1736416, _1736418] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736416), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1736416))), _1736418))), -(c_List_Otranspose(_1736416, c_List_Otranspose(_1736416, _1736418)) = c_List_OtakeWhile(tc_List_Olist(_1736416), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1736416)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736416), tc_List_Olist(_1736416), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1736416))), _1736418))], (28615 ^ _779854) ^ [_1297071, _1297073] : [c_Int_Oiszero(_1297071, hAPP(c_Int_Onumber__class_Onumber__of(_1297071), c_Int_OBit1(_1297073))), class_Int_Onumber__ring(_1297071), class_Int_Oring__char__0(_1297071)], (6029 ^ _779854) ^ [_875335, _875337, _875339, _875341, _875343] : [class_Orderings_Oorder(_875335), class_Orderings_Olinorder(_875337), c_Orderings_Oorder__class_Ostrict__mono(_875337, _875335, _875339), 6040 ^ _779854 : [(6047 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875337), _875341), _875343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875335), hAPP(_875339, _875341)), hAPP(_875339, _875343))))], (6041 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875335), hAPP(_875339, _875341)), hAPP(_875339, _875343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875337), _875341), _875343)))]]], (45611 ^ _779854) ^ [_1693639] : [-(c_Code__Numeral_OSuc__code__numeral(_1693639) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1693639))))], (10185 ^ _779854) ^ [_951917, _951919, _951921, _951923] : [class_Orderings_Olinorder(_951917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951917), _951919), _951921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951917), hAPP(hAPP(c_Orderings_Oord__class_Omin(_951917), _951919), _951923)), _951921)))], (46264 ^ _779854) ^ [_1708240, _1708242, _1708244, _1708246] : [class_Orderings_Olinorder(_1708240), 46267 ^ _779854 : [(46274 ^ _779854) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1708242), _1708246)), -(hBOOL(hAPP(c_List_Odistinct(_1708242), c_List_Olinorder__class_Osort__key(_1708242, _1708240, _1708244, _1708246))))], (46268 ^ _779854) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1708242), c_List_Olinorder__class_Osort__key(_1708242, _1708240, _1708244, _1708246))), -(hBOOL(hAPP(c_List_Odistinct(_1708242), _1708246)))]]], (41790 ^ _779854) ^ [_1601105, _1601107] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601105, _1601105), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1601107) = c_Relation_OId(_1601105))], (35901 ^ _779854) ^ [_1448703, _1448705, _1448707, _1448709, _1448711, _1448713] : [hAPP(_1448709, hAPP(c_Product__Type_Osnd(_1448707, _1448703), _1448711)) = hAPP(_1448713, hAPP(c_Product__Type_Osnd(_1448707, _1448703), _1448711)), -(hAPP(c_Product__Type_Oapsnd(_1448703, _1448705, _1448707, _1448709), _1448711) = hAPP(c_Product__Type_Oapsnd(_1448703, _1448705, _1448707, _1448713), _1448711))], (28360 ^ _779854) ^ [_1292572] : [-(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), _1292572))))], (25793 ^ _779854) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (30412 ^ _779854) ^ [_1328987] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1328987), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33737 ^ _779854) ^ [_1400582, _1400584, _1400586, _1400588, _1400590] : [_1400582 = c_Orderings_Obot__class_Obot(tc_fun(_1400584, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400586, tc_HOL_Obool)), _1400588), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400584, tc_fun(_1400586, tc_HOL_Obool)), _1400582), _1400590)) = _1400588)], (29397 ^ _779854) ^ [_1310171, _1310173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310171), _1310173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1310171)), c_Int_OBit0(_1310173))))], (5102 ^ _779854) ^ [_857850, _857852] : [_857852 = _857850, -(c_Finite__Set_Ocard(_857852) = c_Finite__Set_Ocard(_857850))], (21072 ^ _779854) ^ [_1159078, _1159080, _1159082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159078), _1159080)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159078), _1159082))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159080), _1159082)))], (23730 ^ _779854) ^ [_1209909, _1209911, _1209913, _1209915] : [class_Orderings_Olinorder(_1209909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209909), _1209911)), 23740 ^ _779854 : [(23743 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209909), _1209913), 23739 ^ [_1209909, _1209911, _1209913, _1209915]))], (23741 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1209909), 23739 ^ [_1209909, _1209911, _1209913, _1209915]), _1209911)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209909), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1209909), _1209913), _1209915)), hAPP(hAPP(c_Finite__Set_Ofold(_1209909, _1209909, c_Orderings_Oord__class_Omin(_1209909)), _1209915), _1209911))))], (49986 ^ _779854) ^ [_1790306, _1790308] : [c_Relation_Oantisym(_1790306, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1790306, _1790306), tc_HOL_Obool)), _1790308), c_Relation_OId(_1790306))), -(c_Relation_Oantisym(_1790306, _1790308))], (28786 ^ _779854) ^ [_1299885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1299885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1299885))))], (5292 ^ _779854) ^ [_860783, _860785, _860787, _860789] : [-(c_List_Oupt(_860789, _860785) = c_List_Oupt(_860787, _860783)), _860789 = _860787, _860785 = _860783], (44500 ^ _779854) ^ [_1670050, _1670052, _1670054] : [-(_1670050 = c_List_Olist_ONil(_1670052)), -(hAPP(c_List_Ohd(_1670052), hAPP(c_List_Orotate(_1670052, _1670054), _1670050)) = hAPP(hAPP(c_List_Onth(_1670052), _1670050), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1670054, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670052)), _1670050))))], (46717 ^ _779854) ^ [_1719737, _1719739] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719737)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719739)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719737), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719739)) = c_List_Olist_ONil(tc_Nat_Onat))], (9686 ^ _779854) ^ [_942310, _942312, _942314, _942316] : [class_Orderings_Olinorder(_942310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942310), hAPP(hAPP(c_Orderings_Oord__class_Omax(_942310), _942312), _942314)), _942316)), 9693 ^ _779854 : [(9696 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942310), _942314), _942316)))], (9694 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942310), _942312), _942316)))]]], (14065 ^ _779854) ^ [_1028051, _1028053, _1028055] : [class_Orderings_Olinorder(_1028051), hAPP(_1028053, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1028051), 14070 ^ [_1028051, _1028053, _1028055]), 14071 ^ [_1028051, _1028053, _1028055])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1028051), hAPP(_1028053, 14070 ^ [_1028051, _1028053, _1028055])), hAPP(_1028053, 14071 ^ [_1028051, _1028053, _1028055])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028051), _1028055)), -(_1028055 = c_Orderings_Obot__class_Obot(tc_fun(_1028051, tc_HOL_Obool))), -(hAPP(_1028053, c_Big__Operators_Olinorder__class_OMax(_1028051, _1028055)) = c_Big__Operators_Olinorder__class_OMax(_1028051, hAPP(c_Set_Oimage(_1028051, _1028051, _1028053), _1028055)))], (46427 ^ _779854) ^ [_1712683, _1712685, _1712687] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712683)), hAPP(c_List_Ofilter(_1712683, _1712685), _1712687))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712683)), _1712687))))], (43873 ^ _779854) ^ [_1655265, _1655267, _1655269, _1655271] : [_1655269 = _1655271, -(hAPP(hAPP(c_List_Oappend(_1655265), _1655267), _1655269) = hAPP(hAPP(c_List_Oappend(_1655265), _1655267), _1655271))], (9328 ^ _779854) ^ [_935557, _935559, _935561] : [class_Orderings_Oorder(_935557), 9331 ^ _779854 : [(9338 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935557), _935559), _935561))), -(c_Orderings_Obot__class_Obot(tc_fun(_935557, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_935557, _935559, _935561))], (9332 ^ _779854) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_935557, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_935557, _935559, _935561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935557), _935559), _935561))]]], (7231 ^ _779854) ^ [_898816, _898818, _898820, _898822] : [class_Lattices_Osemilattice__sup(_898816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898816), _898818), _898820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898816), _898818), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898816), _898820), _898822))))], (37780 ^ _779854) ^ [_1493322, _1493324, _1493326, _1493328, _1493330] : [class_Groups_Ocomm__monoid__add(_1493322), class_Groups_Ocomm__monoid__mult(_1493322), _1493324 = _1493326, c_Nat__Transfer_Onat__set(_1493326), 37798 ^ _779854 : [(37801 ^ _779854) ^ [] : [hAPP(_1493328, 37797 ^ [_1493322, _1493324, _1493326, _1493328, _1493330]) = hAPP(_1493330, 37797 ^ [_1493322, _1493324, _1493326, _1493328, _1493330])], (37799 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37797 ^ [_1493322, _1493324, _1493326, _1493328, _1493330])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1493322), _1493328), _1493324) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1493322), _1493330), _1493326))], (18417 ^ _779854) ^ [_1113405, _1113407] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1113405), hAPP(c_Nat_OSuc, _1113407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1113405), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1113407))], (46838 ^ _779854) ^ [_1722283, _1722285] : [class_Orderings_Olinorder(_1722283), -(c_List_Olinorder__class_Osorted(_1722283, c_List_Olinorder__class_Osort__key(_1722283, _1722283, c_COMBI(_1722283), _1722285)))], (31675 ^ _779854) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (37936 ^ _779854) ^ [_1496976, _1496978, _1496980, _1496982, _1496984, _1496986] : [c_Typedef_Otype__definition(_1496976, _1496978, _1496980, _1496982, _1496984), -(hAPP(_1496982, hAPP(_1496980, _1496986)) = _1496986)], (47502 ^ _779854) ^ [_1735146, _1735148, _1735150, _1735152] : [class_Orderings_Olinorder(_1735146), c_List_Olinorder__class_Osorted(_1735146, hAPP(c_List_Orev(_1735146), _1735148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735150), _1735152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735152), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735146)), _1735148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1735146), hAPP(hAPP(c_List_Onth(_1735146), _1735148), _1735152)), hAPP(hAPP(c_List_Onth(_1735146), _1735148), _1735150))))], (8752 ^ _779854) ^ [_925402, _925404, _925406] : [class_Orderings_Oorder(_925402), 8755 ^ _779854 : [(8764 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925402), _925404), _925406))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925402), _925404), _925406)), -(_925404 = _925406)], (8756 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925402), _925404), _925406)), 8759 ^ _779854 : [(8762 ^ _779854) ^ [] : [_925404 = _925406], (8760 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925402), _925404), _925406)))]]]]], (31256 ^ _779854) ^ [_1343386] : [class_Int_Onumber__ring(_1343386), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1343386), c_Groups_Oone__class_Oone(_1343386)) = hAPP(c_Int_Onumber__class_Onumber__of(_1343386), c_Int_OMin))], (49058 ^ _779854) ^ [_1768944, _1768946, _1768948] : [_1768946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1768944) = c_List_Oreplicate(_1768944, _1768946, _1768948))], (39268 ^ _779854) ^ [_1536483] : [-(c_Int_Oint__ge__less__than2(_1536483) = 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), _1536483)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (50463 ^ _779854) ^ [_1799651, _1799653, _1799655] : [hAPP(c_Set_Oimage(_1799651, _1799653, _1799655), c_Orderings_Otop__class_Otop(tc_fun(_1799651, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799653, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1799653, _1799651, c_Hilbert__Choice_Oinv__into(_1799651, _1799653, c_Orderings_Otop__class_Otop(tc_fun(_1799651, tc_HOL_Obool)), _1799655), c_Orderings_Otop__class_Otop(tc_fun(_1799653, tc_HOL_Obool))))], (26809 ^ _779854) ^ [_1266419, _1266421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266419)), 26812 ^ _779854 : [(26819 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266421)), -(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), _1266421), _1266419))))], (26813 ^ _779854) ^ [] : [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), _1266421), _1266419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266421)))]]], (34307 ^ _779854) ^ [_1415358, _1415360, _1415362] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1415358, tc_HOL_Obool)), _1415362), hAPP(c_Set_OPow(_1415358), _1415360))), -(hBOOL(hAPP(c_Predicate_OPowp(_1415358, hAPP(hAPP(c_COMBC(_1415358, tc_fun(_1415358, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415358)), _1415360)), _1415362)))], (5778 ^ _779854) ^ [_871309, _871311, _871313, _871315] : [hBOOL(hAPP(_871309, _871311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871313, tc_HOL_Obool)), _871309), _871315)), -(hBOOL(hAPP(_871315, _871311)))], (35496 ^ _779854) ^ [_1441213, _1441215] : [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), _1441213), _1441215))), 35499 ^ _779854 : [(35508 ^ _779854) ^ [] : [-(c_Divides_OposDivAlg(_1441213, _1441215) = hAPP(c_Divides_Oadjust(_1441215), c_Divides_OposDivAlg(_1441213, 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)))), _1441215)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441213), _1441215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1441215), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35500 ^ _779854) ^ [] : [35501 ^ _779854 : [(35504 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1441215), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35502 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441213), _1441215))]], -(c_Divides_OposDivAlg(_1441213, _1441215) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1441213))]]], (44951 ^ _779854) ^ [_1679169, _1679171, _1679173] : [-(_1679169 = c_List_Olist_ONil(_1679171)), -(c_List_Olast(_1679171, hAPP(hAPP(c_List_Olist_OCons(_1679171), _1679173), _1679169)) = c_List_Olast(_1679171, _1679169))], (12776 ^ _779854) ^ [_1003762, _1003764, _1003766, _1003768] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1003762, tc_HOL_Obool)), _1003764), hAPP(hAPP(c_Set_Oinsert(_1003762), _1003766), _1003768)))), 12779 ^ _779854 : [(12782 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1003762, tc_HOL_Obool)), _1003764), _1003768))], (12780 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003762), _1003766), _1003768)))]], 12783 ^ _779854 : [(12786 ^ _779854) ^ [] : [12787 ^ _779854 : [(12790 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1003762, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003762, tc_HOL_Obool)), _1003764), hAPP(hAPP(c_Set_Oinsert(_1003762), _1003766), c_Orderings_Obot__class_Obot(tc_fun(_1003762, tc_HOL_Obool))))), _1003768))], (12788 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003762), _1003766), _1003764)))]], 12791 ^ _779854 : [(12794 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1003762, tc_HOL_Obool)), _1003764), _1003768))], (12792 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1003762), _1003766), _1003764))]]], (12784 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1003762), _1003766), _1003768))]]], (10395 ^ _779854) ^ [_956051, _956053, _956055, _956057, _956059] : [class_Lattices_Osemilattice__inf(_956051), class_Lattices_Osemilattice__inf(_956053), c_Orderings_Oorder__class_Omono(_956053, _956051, _956055), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956051), hAPP(_956055, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956053), _956057), _956059))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956051), hAPP(_956055, _956057)), hAPP(_956055, _956059)))))], (28989 ^ _779854) ^ [_1303140, _1303142, _1303144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303140), _1303142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1303144)), -(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), _1303144)), _1303140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1303144)), _1303142))))], (9672 ^ _779854) ^ [_942039, _942041, _942043, _942045, _942047] : [class_Orderings_Olinorder(_942039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942039), _942041), _942043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942039), _942045), _942047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942039), hAPP(hAPP(c_Orderings_Oord__class_Omax(_942039), _942041), _942045)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_942039), _942043), _942047))))], (52293 ^ _779854) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (13959 ^ _779854) ^ [_1025697, _1025699] : [class_Orderings_Olinorder(_1025697), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025697), _1025699)), -(_1025699 = c_Orderings_Obot__class_Obot(tc_fun(_1025697, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1025697), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1025697), 13972 ^ [_1025697, _1025699]), 13973 ^ [_1025697, _1025699])), hAPP(hAPP(c_Set_Oinsert(_1025697), 13972 ^ [_1025697, _1025699]), hAPP(hAPP(c_Set_Oinsert(_1025697), 13973 ^ [_1025697, _1025699]), c_Orderings_Obot__class_Obot(tc_fun(_1025697, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1025697), c_Big__Operators_Olinorder__class_OMax(_1025697, _1025699)), _1025699)))], (39551 ^ _779854) ^ [_1546574, _1546576, _1546578, _1546580, _1546582, _1546584, _1546586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546574, _1546578)), hAPP(hAPP(c_Product__Type_OPair(_1546574, _1546578), _1546584), _1546586)), hAPP(hAPP(c_Relation_Orel__comp(_1546574, _1546576, _1546578), _1546580), _1546582))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1546574, _1546576, _1546578, hAPP(hAPP(c_COMBC(_1546574, tc_fun(tc_prod(_1546574, _1546576), tc_HOL_Obool), tc_fun(_1546576, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546576, tc_fun(tc_fun(tc_prod(_1546574, _1546576), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1546574, _1546576), tc_HOL_Obool), tc_fun(_1546576, tc_HOL_Obool)), _1546574), c_COMBC(_1546576, tc_fun(tc_prod(_1546574, _1546576), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546576, tc_prod(_1546574, _1546576)), tc_fun(_1546576, tc_fun(tc_fun(tc_prod(_1546574, _1546576), tc_HOL_Obool), tc_HOL_Obool)), _1546574), hAPP(c_COMBB(tc_prod(_1546574, _1546576), tc_fun(tc_fun(tc_prod(_1546574, _1546576), tc_HOL_Obool), tc_HOL_Obool), _1546576), c_member(tc_prod(_1546574, _1546576)))), c_Product__Type_OPair(_1546574, _1546576)))), _1546580), hAPP(hAPP(c_COMBC(_1546576, tc_fun(tc_prod(_1546576, _1546578), tc_HOL_Obool), tc_fun(_1546578, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546578, tc_fun(tc_fun(tc_prod(_1546576, _1546578), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1546576, _1546578), tc_HOL_Obool), tc_fun(_1546578, tc_HOL_Obool)), _1546576), c_COMBC(_1546578, tc_fun(tc_prod(_1546576, _1546578), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546578, tc_prod(_1546576, _1546578)), tc_fun(_1546578, tc_fun(tc_fun(tc_prod(_1546576, _1546578), tc_HOL_Obool), tc_HOL_Obool)), _1546576), hAPP(c_COMBB(tc_prod(_1546576, _1546578), tc_fun(tc_fun(tc_prod(_1546576, _1546578), tc_HOL_Obool), tc_HOL_Obool), _1546578), c_member(tc_prod(_1546576, _1546578)))), c_Product__Type_OPair(_1546576, _1546578)))), _1546582)), _1546584), _1546586)))], (41613 ^ _779854) ^ [_1596714, _1596716] : [-(c_Relation_Osingle__valued(_1596714, _1596714, c_Relation_OId__on(_1596714, _1596716)))], (48016 ^ _779854) ^ [_1746130, _1746132, _1746134, _1746136, _1746138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1746130, _1746132)), hAPP(_1746130, _1746134))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1746136, _1746136)), hAPP(hAPP(c_Product__Type_OPair(_1746136, _1746136), _1746132), _1746134)), c_List_Omeasures(_1746136, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1746136, tc_Nat_Onat)), _1746130), _1746138)))))], (37097 ^ _779854) ^ [] : [-(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))))))], (6883 ^ _779854) ^ [_891686, _891688, _891690, _891692] : [class_Lattices_Odistrib__lattice(_891686), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_891686), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891686), _891688), _891690)), _891692) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891686), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_891686), _891688), _891692)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_891686), _891690), _891692)))], (48846 ^ _779854) ^ [_1764386, _1764388, _1764390] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1764386, _1764386, hAPP(hAPP(c_COMBB(tc_fun(_1764386, tc_HOL_Obool), tc_fun(_1764386, tc_HOL_Obool), _1764386), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1764386), c_fNot)), c_fequal)), _1764388), _1764390)), _1764388 = _1764390], (46100 ^ _779854) ^ [_1705142, _1705144, _1705146, _1705148, _1705150] : [c_Fun_Oinj__on(_1705142, _1705144, _1705146, hAPP(hAPP(c_Set_Oinsert(_1705142), _1705148), hAPP(c_List_Oset(_1705142), _1705150))), -(hAPP(hAPP(c_List_Omap(_1705142, _1705144), _1705146), hAPP(c_List_OremoveAll(_1705142, _1705148), _1705150)) = hAPP(c_List_OremoveAll(_1705144, hAPP(_1705146, _1705148)), hAPP(hAPP(c_List_Omap(_1705142, _1705144), _1705146), _1705150)))], (18251 ^ _779854) ^ [_1110107, _1110109] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110107)), _1110109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110107), _1110109)))], (42864 ^ _779854) ^ [_1632995, _1632997, _1632999, _1633001, _1633003] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1632995, _1632997)), _1632999), hAPP(hAPP(c_List_Ozip(_1632995, _1632997), _1633001), _1633003)) = hAPP(hAPP(c_List_Ozip(_1632995, _1632997), hAPP(hAPP(c_List_Otake(_1632995), _1632999), _1633001)), hAPP(hAPP(c_List_Otake(_1632997), _1632999), _1633003)))], (5012 ^ _779854) ^ [_856415, _856417, _856419, _856421, _856423, _856425, _856427, _856429] : [-(c_Fun_Othe__inv__into(_856429, _856425, _856421, _856417) = c_Fun_Othe__inv__into(_856427, _856423, _856419, _856415)), _856429 = _856427, _856425 = _856423, _856421 = _856419, _856417 = _856415], (33191 ^ _779854) ^ [_1381723, _1381725, _1381727, _1381729] : [33193 ^ _779854 : [(33196 ^ _779854) ^ [] : [hAPP(_1381729, 33192 ^ [_1381723, _1381725, _1381727, _1381729]) = c_Orderings_Obot__class_Obot(tc_fun(_1381725, tc_HOL_Obool))], (33194 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381723), 33192 ^ [_1381723, _1381725, _1381727, _1381729]), _1381727)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381723, tc_fun(_1381725, tc_HOL_Obool)), _1381727), _1381729) = c_Orderings_Obot__class_Obot(tc_fun(_1381725, tc_HOL_Obool)))], (17929 ^ _779854) ^ [_1104359, _1104361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104361)), _1104359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104359), _1104361))], (24527 ^ _779854) ^ [_1224854, _1224856, _1224858] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224854), _1224856)), _1224858) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224856), _1224858)))], (37640 ^ _779854) ^ [_1489659, _1489661, _1489663, _1489665, _1489667, _1489669, _1489671, _1489673, _1489675, _1489677] : [c_Equiv__Relations_Ocongruent2(_1489659, _1489661, _1489663, _1489665, _1489667, _1489669), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489659, _1489659)), hAPP(hAPP(c_Product__Type_OPair(_1489659, _1489659), _1489671), _1489673)), _1489665)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489661, _1489661)), hAPP(hAPP(c_Product__Type_OPair(_1489661, _1489661), _1489675), _1489677)), _1489667)), -(hAPP(hAPP(_1489669, _1489671), _1489675) = hAPP(hAPP(_1489669, _1489673), _1489677))], (47665 ^ _779854) ^ [_1738387, _1738389, _1738391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738387)), c_List_OtakeWhile(_1738387, _1738389, _1738391))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738387)), _1738391))), hBOOL(hAPP(_1738389, hAPP(hAPP(c_List_Onth(_1738387), _1738391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738387)), c_List_OtakeWhile(_1738387, _1738389, _1738391)))))], (14580 ^ _779854) ^ [_1038216, _1038218] : [class_Lattices_Olattice(_1038216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038216), _1038218)), -(c_Big__Operators_Olattice__class_OInf__fin(_1038216, _1038218) = hAPP(c_Finite__Set_Ofold1(_1038216, c_Lattices_Osemilattice__inf__class_Oinf(_1038216)), _1038218))], (30833 ^ _779854) ^ [_1336510, _1336512] : [-(_1336510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30836 ^ _779854 : [(30843 ^ _779854) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336512, _1336510) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336512), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1336510)) = 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), _1336512), _1336510))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30837 ^ _779854) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336512, _1336510) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336512), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1336510)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336512), _1336510)))]]], (50744 ^ _779854) ^ [_1805957, _1805959, _1805961, _1805963, _1805965] : [c_Fun_Obij__betw(_1805957, _1805959, _1805961, c_Orderings_Otop__class_Otop(tc_fun(_1805957, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1805959, tc_HOL_Obool))), c_Fun_Obij__betw(_1805959, _1805963, _1805965, c_Orderings_Otop__class_Otop(tc_fun(_1805959, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1805963, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1805957, _1805963, hAPP(c_Fun_Ocomp(_1805959, _1805963, _1805957, _1805965), _1805961), c_Orderings_Otop__class_Otop(tc_fun(_1805957, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1805963, tc_HOL_Obool))))], (27933 ^ _779854) ^ [_1285104, _1285106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285106)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1285104), _1285106)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1285104)), hAPP(c_Int_Onat, _1285106)))], (36211 ^ _779854) ^ [_1455437, _1455439, _1455441] : [-(hAPP(hAPP(c_Product__Type_OPair(_1455437, _1455439), hAPP(c_Product__Type_Ofst(_1455437, _1455439), _1455441)), hAPP(c_Product__Type_Osnd(_1455437, _1455439), _1455441)) = _1455441)], (49844 ^ _779854) ^ [_1787544, _1787546, _1787548, _1787550] : [c_Predicate_Osymp(_1787544, _1787546), hBOOL(hAPP(hAPP(_1787546, _1787548), _1787550)), -(hBOOL(hAPP(hAPP(_1787546, _1787550), _1787548)))], (46282 ^ _779854) ^ [_1708528, _1708530, _1708532] : [-(c_List_Oconcat(_1708528, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708528)), _1708530), _1708532)) = hAPP(hAPP(c_List_Oappend(_1708528), _1708530), c_List_Oconcat(_1708528, _1708532)))], (2916 ^ _779854) ^ [_823293, _823295] : [_823295 = _823293, -(c_Rings_Oinverse__class_Odivide(_823295) = c_Rings_Oinverse__class_Odivide(_823293))], (16660 ^ _779854) ^ [_1080151, _1080153] : [16661 ^ _779854 : [(16664 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080153), _1080151))], (16662 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080151), _1080153))]], _1080151 = _1080153], (24749 ^ _779854) ^ [_1229366, _1229368, _1229370] : [class_Int_Onumber__ring(_1229366), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229366), hAPP(c_Groups_Ouminus__class_Ouminus(_1229366), hAPP(c_Int_Onumber__class_Onumber__of(_1229366), _1229368))), _1229370) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229366), hAPP(c_Int_Onumber__class_Onumber__of(_1229366), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1229368))), _1229370))], (37805 ^ _779854) ^ [_1493785] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1493785)), c_Int_OInteg)))], (45687 ^ _779854) ^ [_1695742, _1695744, _1695746] : [45689 ^ _779854 : [(45692 ^ _779854) ^ [] : [hBOOL(hAPP(_1695744, 45688 ^ [_1695742, _1695744, _1695746]))], (45690 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1695742), 45688 ^ [_1695742, _1695744, _1695746]), hAPP(c_List_Oset(_1695742), _1695746))))]], -(hBOOL(hAPP(c_List_Olistsp(_1695742, _1695744), _1695746)))], (33114 ^ _779854) ^ [_1379962, _1379964, _1379966, _1379968, _1379970] : [_1379962 = c_Orderings_Obot__class_Obot(tc_fun(_1379964, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379964, tc_fun(_1379966, tc_HOL_Obool)), _1379962), hAPP(hAPP(c_COMBB(tc_fun(_1379966, tc_HOL_Obool), tc_fun(_1379966, tc_HOL_Obool), _1379964), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379966, tc_HOL_Obool)), _1379968)), _1379970)) = c_Orderings_Obot__class_Obot(tc_fun(_1379966, tc_HOL_Obool)))], (51597 ^ _779854) ^ [_1824393, _1824395, _1824397] : [class_Rings_Ocomm__ring__1(_1824393), 51600 ^ _779854 : [(51607 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824393), _1824395), _1824397)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824393), _1824395), hAPP(c_Groups_Ouminus__class_Ouminus(_1824393), _1824397))))], (51601 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824393), _1824395), hAPP(c_Groups_Ouminus__class_Ouminus(_1824393), _1824397))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824393), _1824395), _1824397)))]]], (37586 ^ _779854) ^ [_1488654, _1488656, _1488658] : [c_Equiv__Relations_Oequivp(_1488654, _1488656), -(hBOOL(hAPP(hAPP(_1488656, _1488658), _1488658)))], (26673 ^ _779854) ^ [_1264400] : [class_Int_Onumber__ring(_1264400), -(hAPP(c_Int_Onumber__class_Onumber__of(_1264400), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1264400))], (21830 ^ _779854) ^ [_1174162, _1174164, _1174166, _1174168, _1174170] : [class_Groups_Ocomm__monoid__mult(_1174162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174164), _1174166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174164, tc_HOL_Obool)), _1174168), _1174166)), 21844 ^ _779854 : [(21847 ^ _779854) ^ [] : [hAPP(_1174170, 21843 ^ [_1174162, _1174164, _1174166, _1174168, _1174170]) = c_Groups_Oone__class_Oone(_1174162)], (21845 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1174164), 21843 ^ [_1174162, _1174164, _1174166, _1174168, _1174170]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1174164, tc_HOL_Obool)), _1174166), _1174168))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1174164, _1174162), _1174170), _1174166) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1174164, _1174162), _1174170), _1174168))], (36291 ^ _779854) ^ [_1457173, _1457175] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1457173), _1457175) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1457173, _1457175)))], (49918 ^ _779854) ^ [_1788927, _1788929] : [-(c_Relation_Oantisym(_1788927, c_Relation_OId__on(_1788927, _1788929)))], (36261 ^ _779854) ^ [_1456505, _1456507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1456505), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1456507), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1456505), _1456507) = 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), _1456505), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1456507)))))], (27667 ^ _779854) ^ [_1280628, _1280630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1280628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1280630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1280630), _1280628)), _1280630)))], (47833 ^ _779854) ^ [_1742097, _1742099] : [class_Orderings_Olinorder(_1742097), 47840 ^ _779854 : [(47845 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1742097), hAPP(hAPP(c_List_Onth(_1742097), _1742099), 47838 ^ [_1742097, _1742099])), hAPP(hAPP(c_List_Onth(_1742097), _1742099), 47839 ^ [_1742097, _1742099])))], (47843 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47839 ^ [_1742097, _1742099]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742097)), _1742099))))], (47841 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47838 ^ [_1742097, _1742099]), 47839 ^ [_1742097, _1742099])))]], -(c_List_Olinorder__class_Osorted(_1742097, _1742099))], (45490 ^ _779854) ^ [_1691242, _1691244, _1691246] : [-(c_List_Olist_Olist__size(_1691242, _1691244, _1691246) = 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(_1691242, tc_Nat_Onat), _1691244), _1691246))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691242)), _1691246)))], (2808 ^ _779854) ^ [_821635, _821637, _821639, _821641] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_821641, _821637) = c_Inductive_Ocomplete__lattice__class_Ogfp(_821639, _821635)), _821641 = _821639, _821637 = _821635], (5788 ^ _779854) ^ [_871474, _871476, _871478] : [_871474 = _871476, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871478, tc_HOL_Obool)), _871474), _871476)))], (14849 ^ _779854) ^ [_1043100, _1043102, _1043104, _1043106, _1043108] : [class_Groups_Ocomm__monoid__add(_1043100), class_Groups_Oordered__cancel__ab__semigroup__add(_1043100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043102), _1043104)), -(_1043104 = c_Orderings_Obot__class_Obot(tc_fun(_1043102, tc_HOL_Obool))), 14867 ^ _779854 : [(14870 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043100), hAPP(_1043106, 14866 ^ [_1043100, _1043102, _1043104, _1043106, _1043108])), hAPP(_1043108, 14866 ^ [_1043100, _1043102, _1043104, _1043106, _1043108])))], (14868 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043102), 14866 ^ [_1043100, _1043102, _1043104, _1043106, _1043108]), _1043104)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043100), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043102, _1043100), _1043106), _1043104)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043102, _1043100), _1043108), _1043104))))], (48118 ^ _779854) ^ [_1748498, _1748500] : [class_Enum_Oenum(_1748498), 48121 ^ _779854 : [(48129 ^ _779854) ^ [] : [48130 ^ _779854 : [(48131 ^ _779854) ^ [_1748678] : [hBOOL(hAPP(_1748500, _1748678))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1748498), _1748500)))], (48122 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1748498), _1748500)), -(hBOOL(hAPP(_1748500, 48125 ^ [_1748498, _1748500])))]]], (49166 ^ _779854) ^ [_1771155, _1771157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1771155), _1771157)), -(c_Lazy__Sequence_Osmall__lazy_H(_1771155, _1771157) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (44933 ^ _779854) ^ [_1678903, _1678905, _1678907] : [_1678903 = c_List_Olist_ONil(_1678905), -(c_List_Olast(_1678905, hAPP(hAPP(c_List_Olist_OCons(_1678905), _1678907), _1678903)) = _1678907)], (25989 ^ _779854) ^ [] : [-(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))))], (52227 ^ _779854) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (43450 ^ _779854) ^ [_1645984, _1645986] : [-(c_List_Olist_Olist__size(_1645984, _1645986, c_List_Olist_ONil(_1645984)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38302 ^ _779854) ^ [_1506082, _1506084, _1506086, _1506088, _1506090, _1506092] : [class_Groups_Ocomm__monoid__add(_1506082), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1506084, _1506082), hAPP(hAPP(c_COMBC(_1506084, tc_fun(_1506086, tc_HOL_Obool), _1506082), hAPP(hAPP(c_COMBB(tc_fun(_1506086, _1506082), tc_fun(tc_fun(_1506086, tc_HOL_Obool), _1506082), _1506084), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1506086, _1506082)), _1506088)), _1506090)), _1506092) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1506084, _1506086), _1506082), hAPP(c_Product__Type_Oprod_Oprod__case(_1506084, _1506086, _1506082), _1506088)), hAPP(hAPP(c_Product__Type_OSigma(_1506084, _1506086), _1506092), hAPP(c_COMBK(tc_fun(_1506086, tc_HOL_Obool), _1506084), _1506090))))], (51072 ^ _779854) ^ [_1812492, _1812494, _1812496] : [c_Equiv__Relations_Oequivp(_1812492, _1812494), 51075 ^ _779854 : [(51076 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1812496, 51083 ^ [_1812492, _1812494, _1812496]))), 51077 ^ _779854 : [(51078 ^ _779854) ^ [_1812614] : [hBOOL(hAPP(hAPP(c_member(_1812492), _1812614), c_Quotient_ORespects(_1812492, _1812494))), hBOOL(hAPP(_1812496, _1812614))]]], (51087 ^ _779854) ^ [] : [51088 ^ _779854 : [(51089 ^ _779854) ^ [_1812781] : [hBOOL(hAPP(_1812496, _1812781))]], 51091 ^ _779854 : [(51094 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1812496, 51090 ^ [_1812492, _1812494, _1812496])))], (51092 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812492), 51090 ^ [_1812492, _1812494, _1812496]), c_Quotient_ORespects(_1812492, _1812494))))]]]]], (44506 ^ _779854) ^ [_1670120, _1670122, _1670124] : [-(hAPP(c_List_Otl(_1670120), hAPP(hAPP(c_List_Odrop(_1670120), _1670122), _1670124)) = hAPP(hAPP(c_List_Odrop(_1670120), _1670122), hAPP(c_List_Otl(_1670120), _1670124)))], (33323 ^ _779854) ^ [_1385483, _1385485, _1385487, _1385489, _1385491, _1385493] : [class_Complete__Lattice_Ocomplete__lattice(_1385483), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385485, tc_fun(_1385487, _1385483)), _1385489), _1385491), _1385493) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385485, _1385483), _1385489), hAPP(hAPP(c_COMBC(_1385485, _1385487, _1385483), _1385491), _1385493)))], (28717 ^ _779854) ^ [] : [-(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))], (14085 ^ _779854) ^ [_1028454, _1028456, _1028458] : [class_Orderings_Olinorder(_1028454), hAPP(_1028456, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1028454), 14090 ^ [_1028454, _1028456, _1028458]), 14091 ^ [_1028454, _1028456, _1028458])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1028454), hAPP(_1028456, 14090 ^ [_1028454, _1028456, _1028458])), hAPP(_1028456, 14091 ^ [_1028454, _1028456, _1028458])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028454), _1028458)), -(_1028458 = c_Orderings_Obot__class_Obot(tc_fun(_1028454, tc_HOL_Obool))), -(hAPP(_1028456, c_Big__Operators_Olinorder__class_OMin(_1028454, _1028458)) = c_Big__Operators_Olinorder__class_OMin(_1028454, hAPP(c_Set_Oimage(_1028454, _1028454, _1028456), _1028458)))], (16293 ^ _779854) ^ [_1072735, _1072737, _1072739, _1072741, _1072743] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1072735), 16296 ^ _779854 : [(16297 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072737), _1072739)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072741), _1072743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072737), _1072743)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072741), _1072739)), -(_1072737 = _1072741), -(_1072739 = _1072743)], (16307 ^ _779854) ^ [] : [16308 ^ _779854 : [(16311 ^ _779854) ^ [] : [_1072739 = _1072743], (16309 ^ _779854) ^ [] : [_1072737 = _1072741]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072737), _1072739)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072741), _1072743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072737), _1072743)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072735), _1072741), _1072739)))]]], (16972 ^ _779854) ^ [_1086086, _1086088] : [class_Complete__Lattice_Ocomplete__lattice(_1086086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086086), _1086088)), -(c_Complete__Lattice_OInf__class_OInf(_1086086, _1086088) = hAPP(hAPP(c_Finite__Set_Ofold(_1086086, _1086086, c_Lattices_Osemilattice__inf__class_Oinf(_1086086)), c_Orderings_Otop__class_Otop(_1086086)), _1086088))], (25517 ^ _779854) ^ [_1244075] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244075)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1244075)))], (52225 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (6395 ^ _779854) ^ [_881709] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_881709, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_881709, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_881709, tc_HOL_Obool)))], (34663 ^ _779854) ^ [_1423673, _1423675] : [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), _1423673))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1423675), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1423673))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1423675), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423673))), 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), _1423675))), c_COMBI(tc_Int_Oint))))], (15072 ^ _779854) ^ [_1047855, _1047857, _1047859, _1047861] : [class_Groups_Ocancel__semigroup__add(_1047855), 15075 ^ _779854 : [(15082 ^ _779854) ^ [] : [_1047859 = _1047861, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047855), _1047857), _1047859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047855), _1047857), _1047861))], (15076 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047855), _1047857), _1047859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047855), _1047857), _1047861), -(_1047859 = _1047861)]]], (31019 ^ _779854) ^ [_1339719, _1339721, _1339723] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339719), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1339721, _1339723)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339719), _1339721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339719), _1339723)))], (51875 ^ _779854) ^ [_1829177, _1829179, _1829181] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829177), _1829179)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829179), _1829177))), _1829179 = _1829181, 51886 ^ _779854 : [(51889 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829181), _1829177))], (51887 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829177), _1829181)))]]], (1360 ^ _779854) ^ [_799806, _799808] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799806)), _799808 = _799806, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799808)], (31456 ^ _779854) ^ [_1346841, _1346843] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1346841))), _1346843) = 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)))), _1346841), _1346843))], (11668 ^ _779854) ^ [_982198, _982200, _982202, _982204] : [hBOOL(hAPP(hAPP(c_member(_982198), _982200), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982198, tc_HOL_Obool)), _982202), _982204))), -(hBOOL(hAPP(hAPP(c_member(_982198), _982200), _982202))), -(hBOOL(hAPP(hAPP(c_member(_982198), _982200), _982204)))], (4554 ^ _779854) ^ [_849186, _849188, _849190, _849192] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_849192, _849188) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_849190, _849186)), _849192 = _849190, _849188 = _849186], (52605 ^ _779854) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (32277 ^ _779854) ^ [_1360605, _1360607] : [class_Rings_Olinordered__idom(_1360605), -(hAPP(c_Groups_Oabs__class_Oabs(_1360605), _1360607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360605), _1360607), c_Groups_Osgn__class_Osgn(_1360605, _1360607)))], (13379 ^ _779854) ^ [_1015473, _1015475, _1015477] : [class_Orderings_Olinorder(_1015473), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015473, tc_HOL_Obool)), _1015475), _1015477)), -(_1015475 = c_Orderings_Obot__class_Obot(tc_fun(_1015473, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015473), _1015477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015473), c_Big__Operators_Olinorder__class_OMax(_1015473, _1015475)), c_Big__Operators_Olinorder__class_OMax(_1015473, _1015477))))], (45404 ^ _779854) ^ [_1689474, _1689476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689474), _1689476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1689474)), hAPP(c_Code__Numeral_Oof__nat, _1689476))))], (7051 ^ _779854) ^ [_895392, _895394, _895396] : [class_Lattices_Osemilattice__inf(_895392), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895392), _895394), _895396) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895392), _895396), _895394))], (49864 ^ _779854) ^ [_1787853, _1787855, _1787857, _1787859] : [c_Wellfounded_Omax__extp(_1787853, _1787855, _1787857, _1787859), 49867 ^ _779854 : [(49870 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1787853), _1787859)))], (49872 ^ _779854) ^ [] : [_1787859 = c_Orderings_Obot__class_Obot(tc_fun(_1787853, tc_HOL_Obool))], (49874 ^ _779854) ^ [_1788069] : [hBOOL(hAPP(hAPP(c_member(_1787853), _1788069), _1787857)), 49878 ^ _779854 : [(49881 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1787855, _1788069), 49877 ^ [_1787853, _1787855, _1787857, _1787859, _1788069])))], (49879 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1787853), 49877 ^ [_1787853, _1787855, _1787857, _1787859, _1788069]), _1787859)))]]], (49868 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1787853), _1787857)))]]], (44047 ^ _779854) ^ [_1658855, _1658857, _1658859, _1658861] : [-(hBOOL(hAPP(hAPP(c_member(_1658855), _1658857), hAPP(c_List_Oset(_1658855), _1658859)))), -(c_List_Oremove1(_1658855, _1658857, hAPP(hAPP(c_List_Oappend(_1658855), _1658859), _1658861)) = hAPP(hAPP(c_List_Oappend(_1658855), _1658859), c_List_Oremove1(_1658855, _1658857, _1658861)))], (1470 ^ _779854) ^ [_801181, _801183] : [-(class_Orderings_Obot(_801181)), _801183 = _801181, class_Orderings_Obot(_801183)], (12498 ^ _779854) ^ [_998151, _998153, _998155, _998157, _998159] : [c_Finite__Set_Ofolding__one(_998151, _998153, _998155), hBOOL(hAPP(c_Finite__Set_Ofinite(_998151), _998157)), hBOOL(hAPP(hAPP(c_member(_998151), _998159), _998157)), 12509 ^ _779854 : [(12516 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998151, tc_HOL_Obool)), _998157), hAPP(hAPP(c_Set_Oinsert(_998151), _998159), c_Orderings_Obot__class_Obot(tc_fun(_998151, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_998151, tc_HOL_Obool))), -(hAPP(_998155, _998157) = hAPP(hAPP(_998153, _998159), hAPP(_998155, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998151, tc_HOL_Obool)), _998157), hAPP(hAPP(c_Set_Oinsert(_998151), _998159), c_Orderings_Obot__class_Obot(tc_fun(_998151, tc_HOL_Obool)))))))], (12510 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998151, tc_HOL_Obool)), _998157), hAPP(hAPP(c_Set_Oinsert(_998151), _998159), c_Orderings_Obot__class_Obot(tc_fun(_998151, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_998151, tc_HOL_Obool)), -(hAPP(_998155, _998157) = _998159)]]], (52197 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (24671 ^ _779854) ^ [_1227612, _1227614] : [class_Int_Onumber__ring(_1227612), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1227612), hAPP(c_Int_Onumber__class_Onumber__of(_1227612), _1227614)) = hAPP(c_Int_Onumber__class_Onumber__of(_1227612), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1227614)))], (21200 ^ _779854) ^ [_1161629, _1161631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1161629), _1161631))), 21203 ^ _779854 : [(21206 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1161629), _1161631)))], (21204 ^ _779854) ^ [] : [_1161631 = c_Orderings_Obot__class_Obot(tc_fun(_1161629, tc_HOL_Obool))]]], (17841 ^ _779854) ^ [_1103029, _1103031] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103029), _1103031))), 17844 ^ _779854 : [(17851 ^ _779854) ^ [] : [_1103029 = _1103031, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103029), hAPP(c_Nat_OSuc, _1103031))))], (17845 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103029), hAPP(c_Nat_OSuc, _1103031))), -(_1103029 = _1103031)]]], (19885 ^ _779854) ^ [_1138571] : [class_Rings_Olinordered__semidom(_1138571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138571), c_Groups_Oone__class_Oone(_1138571)), c_Groups_Ozero__class_Ozero(_1138571)))], (48751 ^ _779854) ^ [_1761981, _1761983, _1761985] : [-(c_List_Olist__ex1(_1761981, _1761983, _1761985)), 48752 ^ _779854 : [(48753 ^ _779854) ^ [_1762075] : [hBOOL(hAPP(hAPP(c_member(_1761981), _1762075), hAPP(c_List_Oset(_1761981), _1761985))), hBOOL(hAPP(_1761983, _1762075)), 48761 ^ _779854 : [(48766 ^ _779854) ^ [] : [48760 ^ [_1761981, _1761983, _1761985, _1762075] = _1762075], (48764 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1761983, 48760 ^ [_1761981, _1761983, _1761985, _1762075])))], (48762 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761981), 48760 ^ [_1761981, _1761983, _1761985, _1762075]), hAPP(c_List_Oset(_1761981), _1761985))))]]]]], (43265 ^ _779854) ^ [_1642469, _1642471, _1642473, _1642475] : [hBOOL(hAPP(c_List_Odistinct(_1642469), _1642471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642473), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642469)), _1642471))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642475), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642469)), _1642471))), 43276 ^ _779854 : [(43283 ^ _779854) ^ [] : [_1642473 = _1642475, -(hAPP(hAPP(c_List_Onth(_1642469), _1642471), _1642473) = hAPP(hAPP(c_List_Onth(_1642469), _1642471), _1642475))], (43277 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Onth(_1642469), _1642471), _1642473) = hAPP(hAPP(c_List_Onth(_1642469), _1642471), _1642475), -(_1642473 = _1642475)]]], (11588 ^ _779854) ^ [_980642, _980644, _980646] : [class_Orderings_Olinorder(_980642), hBOOL(hAPP(c_Finite__Set_Ofinite(_980642), _980644)), hBOOL(hAPP(hAPP(c_member(_980642), _980646), _980644)), 11599 ^ _779854 : [(11606 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980642, tc_HOL_Obool)), _980644), hAPP(hAPP(c_Set_Oinsert(_980642), _980646), c_Orderings_Obot__class_Obot(tc_fun(_980642, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_980642, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_980642, c_Orderings_Oord__class_Omax(_980642), _980644) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_980642), _980646), c_Big__Operators_Olattice_OSup__fin(_980642, c_Orderings_Oord__class_Omax(_980642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980642, tc_HOL_Obool)), _980644), hAPP(hAPP(c_Set_Oinsert(_980642), _980646), c_Orderings_Obot__class_Obot(tc_fun(_980642, tc_HOL_Obool)))))))], (11600 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980642, tc_HOL_Obool)), _980644), hAPP(hAPP(c_Set_Oinsert(_980642), _980646), c_Orderings_Obot__class_Obot(tc_fun(_980642, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_980642, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_980642, c_Orderings_Oord__class_Omax(_980642), _980644) = _980646)]]], (18969 ^ _779854) ^ [_1121911] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1121911), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38817 ^ _779854) ^ [_1520356, _1520358, _1520360] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520356, tc_HOL_Obool)), _1520358), _1520360) = hAPP(c_Set_OCollect(_1520356), hAPP(hAPP(c_COMBS(_1520356, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520356), c_fconj), hAPP(hAPP(c_COMBC(_1520356, tc_fun(_1520356, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520356)), _1520358))), hAPP(hAPP(c_COMBC(_1520356, tc_fun(_1520356, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520356)), _1520360))))], (34037 ^ _779854) ^ [_1408883, _1408885, _1408887] : [-(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)), _1408883)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1408885, _1408887)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408885), _1408883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408887), _1408883)))], (16199 ^ _779854) ^ [_1070757, _1070759, _1070761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070759), _1070761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070757), _1070761)), _1070759)))], (31826 ^ _779854) ^ [_1352557, _1352559, _1352561] : [class_Rings_Oring__1(_1352557), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1352559), _1352561)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352557), hAPP(c_Int_Oring__1__class_Oof__int(_1352557), _1352559)), hAPP(c_Int_Oring__1__class_Oof__int(_1352557), _1352561)))], (30099 ^ _779854) ^ [_1322816, _1322818] : [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), _1322816))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1322818)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1322816))) = 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), _1322818), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1322816)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (44833 ^ _779854) ^ [_1677164, _1677166, _1677168, _1677170, _1677172] : [class_Orderings_Olinorder(_1677164), 44836 ^ _779854 : [(44845 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1677166), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1677166, _1677164, _1677168), _1677170), _1677172)))), -(hBOOL(hAPP(hAPP(c_member(_1677166), _1677170), hAPP(c_List_Oset(_1677166), _1677172)))), hBOOL(hAPP(c_List_Odistinct(_1677166), _1677172))], (44837 ^ _779854) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1677166), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1677166, _1677164, _1677168), _1677170), _1677172))), 44840 ^ _779854 : [(44843 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1677166), _1677172)))], (44841 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1677166), _1677170), hAPP(c_List_Oset(_1677166), _1677172)))]]]]], (38410 ^ _779854) ^ [_1509355, _1509357, _1509359, _1509361] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1509355, _1509357)), hAPP(hAPP(c_Product__Type_OSigma(_1509355, _1509357), hAPP(hAPP(c_Set_Oinsert(_1509355), _1509359), c_Orderings_Obot__class_Obot(tc_fun(_1509355, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1509357, tc_HOL_Obool), _1509355), _1509361))) = hAPP(c_Finite__Set_Ocard(_1509357), _1509361))], (29187 ^ _779854) ^ [_1306431, _1306433, _1306435] : [hBOOL(hAPP(_1306431, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1306433), _1306435)))), 29190 ^ _779854 : [(29197 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306433), _1306435)), -(hBOOL(hAPP(_1306431, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29191 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1306435), _1306433)), -(hBOOL(hAPP(_1306431, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306433)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306435)))))]]], (27187 ^ _779854) ^ [_1272592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1272592)), -(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), _1272592))))], (6753 ^ _779854) ^ [_888626, _888628, _888630, _888632] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888626, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888626, tc_HOL_Obool)), _888628), _888630)), _888632) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888626, tc_HOL_Obool)), _888628), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_888626, tc_HOL_Obool)), _888630), _888632)))], (45569 ^ _779854) ^ [_1692921, _1692923] : [_1692921 = _1692923, -(hAPP(c_Code__Numeral_Onat__of, _1692921) = hAPP(c_Code__Numeral_Onat__of, _1692923))], (43299 ^ _779854) ^ [_1643090, _1643092] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1643090), _1643092)), -(c_Nitpick_Ocard_H(_1643090, _1643092) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643090)), c_Hilbert__Choice_OEps(tc_List_Olist(_1643090), hAPP(hAPP(c_COMBS(tc_List_Olist(_1643090), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1643090)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1643090), tc_fun(_1643090, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1643090, tc_HOL_Obool), tc_fun(tc_fun(_1643090, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1643090)), c_fequal), c_List_Oset(_1643090))), _1643092))), c_List_Odistinct(_1643090)))))], (12196 ^ _779854) ^ [_992334, _992336, _992338] : [hBOOL(hAPP(hAPP(c_member(_992334), _992336), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_992334, tc_HOL_Obool)), _992338))), hBOOL(hAPP(hAPP(c_member(_992334), _992336), _992338))], (39691 ^ _779854) ^ [_1549801, _1549803, _1549805, _1549807] : [c_Wellfounded_Owf(_1549801, _1549803), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549801, _1549801)), hAPP(hAPP(c_Product__Type_OPair(_1549801, _1549801), _1549805), _1549807)), _1549803)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549801, _1549801)), hAPP(hAPP(c_Product__Type_OPair(_1549801, _1549801), _1549807), _1549805)), _1549803))], (1560 ^ _779854) ^ [_802306, _802308] : [-(class_Rings_Olinordered__semiring__strict(_802306)), _802308 = _802306, class_Rings_Olinordered__semiring__strict(_802308)], (27031 ^ _779854) ^ [_1270057, _1270059] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1270057)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1270059)))), 27034 ^ _779854 : [(27037 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1270059))], (27035 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270057), _1270059)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270057), _1270059))], (20844 ^ _779854) ^ [_1155024, _1155026] : [-(_1155024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155024), _1155026) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1155026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1155024), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1155026)))], (10791 ^ _779854) ^ [_964105, _964107, _964109] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964105, tc_HOL_Obool)), _964107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964105, tc_HOL_Obool)), _964109), _964107)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964105, tc_HOL_Obool)), _964107), _964109))], (31595 ^ _779854) ^ [_1349189] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1349189)))], (37346 ^ _779854) ^ [_1482963, _1482965, _1482967, _1482969, _1482971] : [c_Equiv__Relations_Oequiv(_1482963, _1482965, _1482967), hBOOL(hAPP(hAPP(c_member(tc_prod(_1482963, _1482963)), hAPP(hAPP(c_Product__Type_OPair(_1482963, _1482963), _1482969), _1482971)), _1482967)), -(hAPP(c_Relation_OImage(_1482963, _1482963, _1482967), hAPP(hAPP(c_Set_Oinsert(_1482963), _1482969), c_Orderings_Obot__class_Obot(tc_fun(_1482963, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1482963, _1482963, _1482967), hAPP(hAPP(c_Set_Oinsert(_1482963), _1482971), c_Orderings_Obot__class_Obot(tc_fun(_1482963, tc_HOL_Obool)))))], (38931 ^ _779854) ^ [_1523455, _1523457, _1523459, _1523461] : [_1523455 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1523457, _1523459), 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)), _1523461))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523457), _1523455)))], (30495 ^ _779854) ^ [_1330556, _1330558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330556)), 30498 ^ _779854 : [(30501 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330558, _1330556)), _1330556)))], (30499 ^ _779854) ^ [] : [-(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, _1330558, _1330556))))]]], (20516 ^ _779854) ^ [] : [-(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))))], (42781 ^ _779854) ^ [_1629546, _1629548, _1629550] : [42783 ^ _779854 : [(42786 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1629546), 42782 ^ [_1629546, _1629548, _1629550]), _1629550))], (42784 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629546), 42782 ^ [_1629546, _1629548, _1629550]), hAPP(c_List_Oset(_1629546), _1629548))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1629546)), _1629548), c_List_Olists(_1629546, _1629550))))], (52187 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (38035 ^ _779854) ^ [_1499200, _1499202, _1499204, _1499206] : [c_Fun_Oinj__on(_1499200, _1499202, _1499204, c_Orderings_Otop__class_Otop(tc_fun(_1499200, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1499200, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1499200, _1499202, _1499204), hAPP(hAPP(c_Set_Oinsert(_1499202), _1499206), c_Orderings_Obot__class_Obot(tc_fun(_1499202, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1499200), c_HOL_OThe(_1499200, hAPP(hAPP(c_COMBC(_1499200, _1499202, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1499202, tc_fun(_1499202, tc_HOL_Obool), _1499200), c_fequal), _1499204)), _1499206))), c_Orderings_Obot__class_Obot(tc_fun(_1499200, tc_HOL_Obool))))))], (22351 ^ _779854) ^ [_1183869, _1183871, _1183873, _1183875] : [class_Fields_Olinordered__field(_1183869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183869), _1183871), _1183873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183869), c_Groups_Ozero__class_Ozero(_1183869)), _1183875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183869), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183869), _1183871), _1183875)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183869), _1183873), _1183875))))], (36114 ^ _779854) ^ [_1453271, _1453273, _1453275, _1453277, _1453279, _1453281] : [c_Finite__Set_Ofolding(_1453271, _1453273, _1453275, _1453277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453271), _1453279)), -(hAPP(_1453277, hAPP(hAPP(c_Set_Oinsert(_1453271), _1453281), _1453279)) = hAPP(c_Fun_Ocomp(_1453273, _1453273, _1453273, hAPP(_1453277, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1453271, tc_HOL_Obool)), _1453279), hAPP(hAPP(c_Set_Oinsert(_1453271), _1453281), c_Orderings_Obot__class_Obot(tc_fun(_1453271, tc_HOL_Obool)))))), hAPP(_1453275, _1453281)))], (34129 ^ _779854) ^ [_1411311, _1411313, _1411315, _1411317, _1411319] : [_1411311 = c_Orderings_Obot__class_Obot(tc_fun(_1411313, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411313, tc_fun(_1411315, tc_HOL_Obool)), _1411311), hAPP(hAPP(c_COMBB(tc_fun(_1411315, tc_HOL_Obool), tc_fun(_1411315, tc_HOL_Obool), _1411313), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411315, tc_HOL_Obool)), _1411317)), _1411319)) = c_Orderings_Otop__class_Otop(tc_fun(_1411315, tc_HOL_Obool)))], (52369 ^ _779854) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (39459 ^ _779854) ^ [_1542753, _1542755, _1542757] : [-(hAPP(c_Relation_ORange(_1542753, _1542755), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1542753, _1542755), tc_HOL_Obool), _1542757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1542753, _1542755), tc_HOL_Obool), tc_fun(_1542755, tc_HOL_Obool)), _1542757), c_Relation_ORange(_1542753, _1542755)))], (19671 ^ _779854) ^ [_1134635, _1134637, _1134639] : [class_Rings_Olinordered__semiring__strict(_1134635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134635), c_Groups_Ozero__class_Ozero(_1134635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134635), _1134637), _1134639))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134635), c_Groups_Ozero__class_Ozero(_1134635)), _1134637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134635), c_Groups_Ozero__class_Ozero(_1134635)), _1134639)))], (46134 ^ _779854) ^ [_1705793, _1705795] : [-(hAPP(c_List_Oset(_1705793), c_List_Oremdups(_1705793, _1705795)) = hAPP(c_List_Oset(_1705793), _1705795))], (42042 ^ _779854) ^ [_1608155, _1608157, _1608159] : [c_Nitpick_Oless__frac(_1608155, _1608157, _1608159), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1608155), c_Nitpick_Oplus__frac(_1608155, _1608157, c_Nitpick_Ouminus__frac(_1608155, _1608159)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52367 ^ _779854) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (27953 ^ _779854) ^ [_1285462, _1285464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285462)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1285462), _1285464)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1285462)), hAPP(c_Int_Onat, _1285464)))], (32858 ^ _779854) ^ [_1371939, _1371941, _1371943, _1371945] : [class_Groups_Ocomm__monoid__add(_1371939), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1371939), _1371941), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1371943)), hAPP(c_Nat_OSuc, _1371945))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1371939), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1371939, tc_Nat_Onat), _1371941), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1371943), _1371945)))], (46190 ^ _779854) ^ [_1706767, _1706769, _1706771, _1706773] : [-(hAPP(c_List_OremoveAll(_1706767, _1706769), hAPP(hAPP(c_List_Oappend(_1706767), _1706771), _1706773)) = hAPP(hAPP(c_List_Oappend(_1706767), hAPP(c_List_OremoveAll(_1706767, _1706769), _1706771)), hAPP(c_List_OremoveAll(_1706767, _1706769), _1706773)))], (34401 ^ _779854) ^ [_1417565, _1417567, _1417569] : [class_Groups_Ocomm__monoid__add(_1417565), class_Groups_Ocomm__monoid__mult(_1417565), c_Nat__Transfer_Onat__set(_1417567), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1417565), _1417569), _1417567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1417565), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1417565, tc_Nat_Onat), _1417569), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1417567)))], (44855 ^ _779854) ^ [_1677566, _1677568, _1677570, _1677572, _1677574] : [class_Orderings_Olinorder(_1677566), -(hBOOL(hAPP(hAPP(c_member(_1677566), hAPP(_1677568, _1677570)), hAPP(c_Set_Oimage(_1677572, _1677566, _1677568), hAPP(c_List_Oset(_1677572), _1677574))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1677572, _1677566, _1677568, _1677570, _1677574) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1677572, _1677566, _1677568), _1677570), _1677574))], (52319 ^ _779854) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (9378 ^ _779854) ^ [_936394, _936396, _936398] : [class_Complete__Lattice_Ocomplete__lattice(_936394), -(c_Complete__Lattice_OInf__class_OInf(_936394, hAPP(hAPP(c_Set_Oinsert(_936394), _936396), hAPP(hAPP(c_Set_Oinsert(_936394), _936398), c_Orderings_Obot__class_Obot(tc_fun(_936394, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936394), _936396), _936398))], (1380 ^ _779854) ^ [_800056, _800058] : [-(class_Complete__Lattice_Ocomplete__lattice(_800056)), _800058 = _800056, class_Complete__Lattice_Ocomplete__lattice(_800058)], (44568 ^ _779854) ^ [_1671334, _1671336, _1671338] : [-(hAPP(hAPP(c_List_Odrop(_1671334), hAPP(c_Nat_OSuc, _1671336)), _1671338) = hAPP(hAPP(c_List_Odrop(_1671334), _1671336), hAPP(c_List_Otl(_1671334), _1671338)))], (17867 ^ _779854) ^ [_1103410, _1103412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103410), _1103412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103410), hAPP(c_Nat_OSuc, _1103412))))], (25929 ^ _779854) ^ [_1251109, _1251111, _1251113] : [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), _1251109), _1251111)), _1251113)), 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)), _1251113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251111), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28226 ^ _779854) ^ [_1290238, _1290240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1290238), _1290240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1290238)), c_Int_OBit1(_1290240))))], (51114 ^ _779854) ^ [_1813328, _1813330, _1813332] : [hBOOL(hAPP(hAPP(_1813330, _1813332), _1813332)), -(hBOOL(hAPP(c_Quotient_ORespects(_1813328, _1813330), _1813332)))], (39206 ^ _779854) ^ [_1533577, _1533579, _1533581] : [class_Orderings_Olinorder(_1533577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533577), _1533579)), -(_1533579 = c_Orderings_Obot__class_Obot(tc_fun(_1533577, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1533577), _1533581), c_Big__Operators_Olattice_OSup__fin(_1533577, c_Orderings_Oord__class_Omax(_1533577), _1533579)) = c_Big__Operators_Olattice_OSup__fin(_1533577, c_Orderings_Oord__class_Omax(_1533577), hAPP(c_Set_OCollect(_1533577), hAPP(hAPP(c_COMBB(tc_fun(_1533577, tc_HOL_Obool), tc_HOL_Obool, _1533577), c_HOL_OEx(_1533577)), hAPP(hAPP(c_COMBC(_1533577, tc_fun(_1533577, tc_HOL_Obool), tc_fun(_1533577, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533577, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1533577, tc_HOL_Obool), tc_fun(_1533577, tc_HOL_Obool)), _1533577), c_COMBS(_1533577, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533577, tc_HOL_Obool), tc_fun(_1533577, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1533577), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533577), c_fconj)), hAPP(hAPP(c_COMBC(_1533577, tc_fun(_1533577, _1533577), tc_fun(_1533577, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533577, tc_HOL_Obool), tc_fun(tc_fun(_1533577, _1533577), tc_fun(_1533577, tc_HOL_Obool)), _1533577), c_COMBB(_1533577, tc_HOL_Obool, _1533577)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1533577), _1533581))))), hAPP(hAPP(c_COMBC(_1533577, tc_fun(_1533577, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533577)), _1533579))))))], (12906 ^ _779854) ^ [_1006678, _1006680, _1006682, _1006684] : [hBOOL(hAPP(hAPP(_1006682, _1006680), _1006684)), -(hBOOL(hAPP(hAPP(c_member(_1006678), _1006680), c_SetInterval_Oord_OlessThan(_1006678, _1006682, _1006684))))], (50698 ^ _779854) ^ [_1805090, _1805092, _1805094, _1805096, _1805098, _1805100, _1805102, _1805104] : [c_Fun_Obij__betw(_1805090, _1805092, _1805094, _1805096, _1805098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1805090, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1805100, _1805090, _1805102), _1805104)), _1805096)), 50705 ^ _779854 : [(50712 ^ _779854) ^ [] : [c_Fun_Obij__betw(_1805100, _1805092, hAPP(c_Fun_Ocomp(_1805090, _1805092, _1805100, _1805094), _1805102), _1805104, _1805098), -(c_Fun_Obij__betw(_1805100, _1805090, _1805102, _1805104, _1805096))], (50706 ^ _779854) ^ [] : [c_Fun_Obij__betw(_1805100, _1805090, _1805102, _1805104, _1805096), -(c_Fun_Obij__betw(_1805100, _1805092, hAPP(c_Fun_Ocomp(_1805090, _1805092, _1805100, _1805094), _1805102), _1805104, _1805098))]]], (14602 ^ _779854) ^ [_1038670, _1038672, _1038674, _1038676, _1038678] : [class_Groups_Oab__group__add(_1038670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038672), _1038674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038672, tc_HOL_Obool)), _1038676), _1038674)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038672, _1038670), _1038678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038672, tc_HOL_Obool)), _1038674), _1038676)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038670), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038672, _1038670), _1038678), _1038674)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038672, _1038670), _1038678), _1038676)))], (49972 ^ _779854) ^ [_1790022, _1790024, _1790026, _1790028] : [c_Relation_Oantisym(_1790022, _1790024), hBOOL(hAPP(hAPP(c_member(tc_prod(_1790022, _1790022)), hAPP(hAPP(c_Product__Type_OPair(_1790022, _1790022), _1790026), _1790028)), _1790024)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1790022, _1790022)), hAPP(hAPP(c_Product__Type_OPair(_1790022, _1790022), _1790028), _1790026)), _1790024)), -(_1790026 = _1790028)], (50640 ^ _779854) ^ [_1803737, _1803739] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1803737), _1803739))), -(c_Quickcheck_Obeyond(_1803737, _1803739) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (46116 ^ _779854) ^ [_1705502, _1705504] : [hBOOL(hAPP(c_List_Odistinct(_1705502), _1705504)), -(c_List_Oremdups(_1705502, _1705504) = _1705504)], (44402 ^ _779854) ^ [_1667987, _1667989, _1667991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1667987), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667989)), _1667991))), -(hAPP(hAPP(c_List_Olist_OCons(_1667989), hAPP(hAPP(c_List_Onth(_1667989), _1667991), _1667987)), hAPP(hAPP(c_List_Odrop(_1667989), hAPP(c_Nat_OSuc, _1667987)), _1667991)) = hAPP(hAPP(c_List_Odrop(_1667989), _1667987), _1667991))], (42990 ^ _779854) ^ [_1636132] : [c_List_Onat__list(_1636132), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1636132)))], (48542 ^ _779854) ^ [_1757987, _1757989, _1757991] : [c_List_Olist__all(_1757987, _1757989, _1757991), 48545 ^ _779854 : [(48546 ^ _779854) ^ [_1758076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758076), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757987)), _1757991))), -(hBOOL(hAPP(_1757989, hAPP(hAPP(c_List_Onth(_1757987), _1757991), _1758076))))]]], (34351 ^ _779854) ^ [_1416611, _1416613] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1416611), _1416613))), -(hAPP(c_Finite__Set_Ocard(_1416611), _1416613) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44865 ^ _779854) ^ [_1677738, _1677740, _1677742] : [class_Orderings_Olinorder(_1677738), -(hBOOL(hAPP(hAPP(c_member(_1677738), _1677740), hAPP(c_List_Oset(_1677738), _1677742)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1677738, _1677738, c_COMBI(_1677738), _1677740, _1677742) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1677738, _1677738, c_COMBI(_1677738)), _1677740), _1677742))], (38001 ^ _779854) ^ [_1498287, _1498289] : [-(c_Set_Othe__elem(_1498287, _1498289) = c_HOL_OThe(_1498287, hAPP(hAPP(c_COMBB(tc_fun(_1498287, tc_HOL_Obool), tc_HOL_Obool, _1498287), hAPP(c_fequal, _1498289)), hAPP(hAPP(c_COMBC(_1498287, tc_fun(_1498287, tc_HOL_Obool), tc_fun(_1498287, tc_HOL_Obool)), c_Set_Oinsert(_1498287)), c_Orderings_Obot__class_Obot(tc_fun(_1498287, tc_HOL_Obool))))))], (44508 ^ _779854) ^ [_1670173, _1670175, _1670177] : [-(hAPP(hAPP(c_List_Odrop(_1670173), _1670175), hAPP(c_List_Otl(_1670173), _1670177)) = hAPP(c_List_Otl(_1670173), hAPP(hAPP(c_List_Odrop(_1670173), _1670175), _1670177)))], (24090 ^ _779854) ^ [_1216739, _1216741, _1216743] : [class_Groups_Omonoid__mult(_1216739), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1216739), _1216741), hAPP(c_Nat_OSuc, _1216743)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216739), hAPP(hAPP(c_Power_Opower__class_Opower(_1216739), _1216741), _1216743)), _1216741))], (20892 ^ _779854) ^ [_1155862, _1155864] : [hAPP(c_Finite__Set_Ocard(_1155862), _1155864) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1155864 = c_Orderings_Obot__class_Obot(tc_fun(_1155862, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1155862), _1155864))], (4548 ^ _779854) ^ [_849101, _849103] : [_849103 = _849101, -(c_Nat_Osize__class_Osize(_849103) = c_Nat_Osize__class_Osize(_849101))], (39343 ^ _779854) ^ [_1539368, _1539370] : [-(hAPP(c_Set_Oimage(_1539368, _1539368, c_Fun_Oid(_1539368)), _1539370) = _1539370)], (40188 ^ _779854) ^ [_1562126, _1562128, _1562130, _1562132] : [40190 ^ _779854 : [(40193 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1562126, _1562126, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1562126, tc_fun(_1562126, _1562128), tc_fun(_1562126, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562128, tc_HOL_Obool), tc_fun(tc_fun(_1562126, _1562128), tc_fun(_1562126, tc_HOL_Obool)), _1562126), c_COMBB(_1562128, tc_HOL_Obool, _1562126)), hAPP(hAPP(c_COMBB(_1562128, tc_fun(_1562128, tc_HOL_Obool), _1562126), c_fequal), _1562132))), _1562132)), 40189 ^ [_1562126, _1562128, _1562130, _1562132]))], (40191 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562126, _1562126)), 40189 ^ [_1562126, _1562128, _1562130, _1562132]), _1562130)))]], -(c_Equiv__Relations_Ocongruent(_1562126, _1562128, _1562130, _1562132))], (16632 ^ _779854) ^ [_1079818, _1079820, _1079822] : [class_Orderings_Olinorder(_1079818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079818), _1079820)), -(hBOOL(hAPP(hAPP(c_member(_1079818), _1079822), _1079820))), -(c_Big__Operators_Olattice_OInf__fin(_1079818, c_Orderings_Oord__class_Omin(_1079818), hAPP(hAPP(c_Set_Oinsert(_1079818), _1079822), _1079820)) = hAPP(hAPP(c_Finite__Set_Ofold(_1079818, _1079818, c_Orderings_Oord__class_Omin(_1079818)), _1079822), _1079820))], (14045 ^ _779854) ^ [_1027691, _1027693, _1027695, _1027697, _1027699, _1027701] : [-(hBOOL(hAPP(hAPP(c_member(_1027691), _1027693), _1027695))), -(hAPP(c_Set_Oimage(_1027691, _1027697, c_Fun_Ofun__upd(_1027691, _1027697, _1027699, _1027693, _1027701)), _1027695) = hAPP(c_Set_Oimage(_1027691, _1027697, _1027699), _1027695))], (50634 ^ _779854) ^ [_1803650, _1803652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1803650), _1803652)), -(c_Quickcheck_Obeyond(_1803650, _1803652) = _1803652)], (4676 ^ _779854) ^ [_851167, _851169] : [_851169 = _851167, -(c_DSequence_Oempty(_851169) = c_DSequence_Oempty(_851167))], (15510 ^ _779854) ^ [_1056860, _1056862, _1056864, _1056866, _1056868] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1056860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056860), _1056862), _1056864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056860), _1056866), _1056868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056860), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056860), _1056862), _1056866)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056860), _1056864), _1056868))))], (22365 ^ _779854) ^ [_1184138, _1184140, _1184142] : [class_Fields_Olinordered__field(_1184138), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184138), _1184140), c_Groups_Ozero__class_Ozero(_1184138))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184138), _1184142), c_Groups_Ozero__class_Ozero(_1184138))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184138), c_Groups_Ozero__class_Ozero(_1184138)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184138), _1184140), _1184142))))], (44634 ^ _779854) ^ [_1672805, _1672807, _1672809, _1672811, _1672813, _1672815] : [-(hAPP(c_List_Ofoldl(_1672805, _1672807, _1672809, _1672811), hAPP(hAPP(c_List_Olist_OCons(_1672807), _1672813), _1672815)) = hAPP(c_List_Ofoldl(_1672805, _1672807, _1672809, hAPP(hAPP(_1672809, _1672811), _1672813)), _1672815))], (27585 ^ _779854) ^ [_1279298, _1279300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1279298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1279300)), 27592 ^ _779854 : [(27599 ^ _779854) ^ [] : [_1279298 = _1279300, -(hAPP(c_Int_Onat, _1279298) = hAPP(c_Int_Onat, _1279300))], (27593 ^ _779854) ^ [] : [hAPP(c_Int_Onat, _1279298) = hAPP(c_Int_Onat, _1279300), -(_1279298 = _1279300)]]], (17346 ^ _779854) ^ [_1093345, _1093347, _1093349] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093345), _1093347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1093345, tc_HOL_Obool)), _1093349), _1093347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1093345), _1093349)), hAPP(c_Finite__Set_Ocard(_1093345), _1093347))))], (45589 ^ _779854) ^ [_1693261] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693261)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (46681 ^ _779854) ^ [_1719031, _1719033] : [46682 ^ _779854 : [(46685 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1719033), _1719031))], (46683 ^ _779854) ^ [] : [_1719033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1719031, _1719033) = c_List_Olist_ONil(tc_Nat_Onat))], (45510 ^ _779854) ^ [_1691561, _1691563, _1691565, _1691567] : [class_Groups_Ocomm__monoid__add(_1691561), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1691561), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1691561), _1691563), c_List_Oupto(_1691565, _1691567))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1691561), _1691563), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1691565, _1691567))))], (15834 ^ _779854) ^ [_1063687, _1063689] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063687), _1063689) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063689), _1063687))], (28320 ^ _779854) ^ [_1291893] : [28322 ^ _779854 : [(28325 ^ _779854) ^ [] : [hBOOL(hAPP(_1291893, 28321 ^ [_1291893]))], (28323 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28321 ^ [_1291893])))]], 28326 ^ _779854 : [(28327 ^ _779854) ^ [_1292020] : [-(hBOOL(hAPP(_1291893, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292020))))]]], (36506 ^ _779854) ^ [_1461249, _1461251, _1461253, _1461255, _1461257, _1461259, _1461261] : [c_Finite__Set_Ofolding__image(_1461249, _1461251, _1461253, _1461255, _1461257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461251), _1461259)), -(hAPP(hAPP(_1461257, _1461261), _1461259) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1461249, _1461251, _1461253), _1461261), _1461255), _1461259))], (49126 ^ _779854) ^ [_1770378, _1770380] : [-(c_Predicate_Opred__comp(_1770378, _1770378, _1770378, c_fequal, c_Predicate_Opred__comp(_1770378, _1770378, _1770378, _1770380, c_fequal)) = _1770380)], (34085 ^ _779854) ^ [] : [-(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)))], (49731 ^ _779854) ^ [_1784303, _1784305, _1784307, _1784309] : [class_Complete__Lattice_Ocomplete__lattice(_1784303), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1784305, _1784303), _1784307), _1784309) = c_Complete__Lattice_OSup__class_OSup(_1784303, hAPP(c_Set_OCollect(_1784303), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784305, _1784303), tc_HOL_Obool), tc_HOL_Obool, _1784303), c_HOL_OEx(tc_fun(_1784305, _1784303))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784305, _1784303), tc_HOL_Obool), tc_fun(tc_fun(_1784305, _1784303), tc_HOL_Obool), _1784303), hAPP(c_COMBS(tc_fun(_1784305, _1784303), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1784305, _1784303)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1784305, _1784303), tc_fun(tc_fun(_1784305, _1784303), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1784305, _1784303))), _1784307)))), hAPP(hAPP(c_COMBC(_1784303, tc_fun(tc_fun(_1784305, _1784303), _1784303), tc_fun(tc_fun(_1784305, _1784303), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1784303, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1784305, _1784303), _1784303), tc_fun(tc_fun(_1784305, _1784303), tc_HOL_Obool)), _1784303), c_COMBB(_1784303, tc_HOL_Obool, tc_fun(_1784305, _1784303))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1784305, _1784303), _1784305, _1784303), c_COMBI(tc_fun(_1784305, _1784303))), _1784309)))))))], (916 ^ _779854) ^ [_793556, _793558, _793560, _793562, _793564, _793566, _793568, _793570, _793572, _793574] : [-(c_Fun_Obij__betw(_793572, _793568, _793564, _793560, _793556)), c_Fun_Obij__betw(_793574, _793570, _793566, _793562, _793558), _793574 = _793572, _793570 = _793568, _793566 = _793564, _793562 = _793560, _793558 = _793556], (41188 ^ _779854) ^ [_1586541, _1586543] : [-(hAPP(c_Relation_OImage(_1586541, _1586541, c_Relation_OId(_1586541)), _1586543) = _1586543)], (42488 ^ _779854) ^ [_1622058, _1622060, _1622062, _1622064] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622058)), hAPP(hAPP(c_List_Olist_OCons(_1622058), _1622060), _1622062)), c_List_Olists(_1622058, _1622064))), 42491 ^ _779854 : [(42494 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622058)), _1622062), c_List_Olists(_1622058, _1622064))))], (42492 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622058), _1622060), _1622064)))]]], (37840 ^ _779854) ^ [_1494961, _1494963, _1494965, _1494967] : [-(c_Wellfounded_Omax__extp(_1494961, _1494963, _1494965, _1494967)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494961), _1494965)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494961), _1494967)), -(_1494967 = c_Orderings_Obot__class_Obot(tc_fun(_1494961, tc_HOL_Obool))), 37854 ^ _779854 : [(37857 ^ _779854) ^ [_1495306] : [hBOOL(hAPP(hAPP(c_member(_1494961), _1495306), _1494967)), hBOOL(hAPP(hAPP(_1494963, 37853 ^ [_1494961, _1494963, _1494965, _1494967]), _1495306))], (37855 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494961), 37853 ^ [_1494961, _1494963, _1494965, _1494967]), _1494965)))]]], (52271 ^ _779854) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (420 ^ _779854) ^ [_786210, _786212, _786214, _786216] : [-(c_Relation_Oirrefl(_786214, _786210)), c_Relation_Oirrefl(_786216, _786212), _786216 = _786214, _786212 = _786210], (10217 ^ _779854) ^ [_952445, _952447, _952449, _952451] : [class_Orderings_Olinorder(_952445), 10220 ^ _779854 : [(10229 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952445), _952447), hAPP(hAPP(c_Orderings_Oord__class_Omin(_952445), _952449), _952451)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952445), _952447), _952449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952445), _952447), _952451))], (10221 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952445), _952447), hAPP(hAPP(c_Orderings_Oord__class_Omin(_952445), _952449), _952451))), 10224 ^ _779854 : [(10227 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952445), _952447), _952451)))], (10225 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952445), _952447), _952449)))]]]]], (40324 ^ _779854) ^ [_1565395, _1565397, _1565399, _1565401, _1565403, _1565405] : [hBOOL(hAPP(hAPP(c_member(_1565395), _1565397), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1565399, _1565401, tc_fun(_1565395, tc_HOL_Obool)), _1565403), _1565405))), 40329 ^ _779854 : [(40332 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565395), _1565397), hAPP(hAPP(_1565403, 40327 ^ [_1565395, _1565397, _1565399, _1565401, _1565403, _1565405]), 40328 ^ [_1565395, _1565397, _1565399, _1565401, _1565403, _1565405]))))], (40330 ^ _779854) ^ [] : [-(_1565405 = hAPP(hAPP(c_Product__Type_OPair(_1565399, _1565401), 40327 ^ [_1565395, _1565397, _1565399, _1565401, _1565403, _1565405]), 40328 ^ [_1565395, _1565397, _1565399, _1565401, _1565403, _1565405]))]]], (38366 ^ _779854) ^ [_1508170, _1508172, _1508174, _1508176, _1508178] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1508170, _1508172), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1508170, tc_HOL_Obool)), _1508174), _1508176)), _1508178) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1508170, _1508172), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1508170, _1508172), _1508174), _1508178)), hAPP(hAPP(c_Product__Type_OSigma(_1508170, _1508172), _1508176), _1508178)))], (32149 ^ _779854) ^ [_1358136, _1358138, _1358140, _1358142, _1358144] : [class_Rings_Olinordered__idom(_1358136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358136), hAPP(c_Groups_Oabs__class_Oabs(_1358136), _1358138)), _1358140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358136), hAPP(c_Groups_Oabs__class_Oabs(_1358136), _1358142)), _1358144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358136), hAPP(c_Groups_Oabs__class_Oabs(_1358136), _1358138)), hAPP(c_Groups_Oabs__class_Oabs(_1358136), _1358142))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358136), _1358140), _1358144))))], (46038 ^ _779854) ^ [_1703813, _1703815] : [-(c_Enum_Oenum__the(_1703813, _1703815) = c_HOL_OThe(_1703813, _1703815))], (32994 ^ _779854) ^ [_1376741, _1376743, _1376745, _1376747] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376741, tc_fun(_1376743, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376741, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1376743, tc_HOL_Obool), tc_fun(_1376743, tc_HOL_Obool), _1376741), hAPP(c_COMBC(_1376743, tc_fun(_1376743, tc_HOL_Obool), tc_HOL_Obool), c_member(_1376743))), _1376745)), _1376747)), -(hBOOL(hAPP(hAPP(c_member(_1376743), _1376747), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376741, tc_fun(_1376743, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1376741, tc_HOL_Obool))), _1376745))))], (17392 ^ _779854) ^ [_1094198, _1094200, _1094202, _1094204] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094198), _1094200)), hAPP(c_Finite__Set_Ocard(_1094202), hAPP(c_Set_Oimage(_1094198, _1094202, _1094204), _1094200)) = hAPP(c_Finite__Set_Ocard(_1094198), _1094200), -(c_Fun_Oinj__on(_1094198, _1094202, _1094204, _1094200))], (46250 ^ _779854) ^ [_1707970, _1707972] : [-(c_List_Oconcat(_1707970, _1707972) = hAPP(c_List_Ofoldl(tc_List_Olist(_1707970), tc_List_Olist(_1707970), c_List_Oappend(_1707970), c_List_Olist_ONil(_1707970)), _1707972))], (36014 ^ _779854) ^ [_1451106, _1451108, _1451110, _1451112, _1451114, _1451116] : [c_Finite__Set_Ofolding(_1451106, _1451108, _1451110, _1451112), -(hAPP(c_Fun_Ocomp(_1451108, _1451108, _1451108, hAPP(_1451110, _1451114)), hAPP(_1451110, _1451116)) = hAPP(c_Fun_Ocomp(_1451108, _1451108, _1451108, hAPP(_1451110, _1451116)), hAPP(_1451110, _1451114)))], (44488 ^ _779854) ^ [_1669936, _1669938] : [-(_1669936 = c_List_Olist_ONil(_1669938)), -(hAPP(c_List_Ohd(_1669938), _1669936) = hAPP(hAPP(c_List_Onth(_1669938), _1669936), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18315 ^ _779854) ^ [_1111212, _1111214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111212), hAPP(c_Nat_OSuc, _1111214))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1111212, hAPP(c_Nat_OSuc, _1111214)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111214)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1111212, _1111214)))], (41040 ^ _779854) ^ [_1582160, _1582162, _1582164, _1582166] : [-(c_Transitive__Closure_Otrancl(_1582160, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1582160, _1582160)), hAPP(hAPP(c_Product__Type_OPair(_1582160, _1582160), _1582162), _1582164)), _1582166)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582160, _1582160), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1582160, _1582166)), hAPP(c_Set_OCollect(tc_prod(_1582160, _1582160)), hAPP(c_Product__Type_Oprod_Oprod__case(_1582160, _1582160, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1582160, tc_fun(_1582160, tc_HOL_Obool), tc_fun(_1582160, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1582160, tc_HOL_Obool), tc_fun(_1582160, tc_HOL_Obool)), _1582160), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1582160)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1582160), c_fconj), hAPP(hAPP(c_COMBC(_1582160, tc_fun(tc_prod(_1582160, _1582160), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1582160, _1582160), tc_fun(tc_fun(tc_prod(_1582160, _1582160), tc_HOL_Obool), tc_HOL_Obool), _1582160), c_member(tc_prod(_1582160, _1582160))), hAPP(hAPP(c_COMBC(_1582160, _1582160, tc_prod(_1582160, _1582160)), c_Product__Type_OPair(_1582160, _1582160)), _1582162))), c_Transitive__Closure_Ortrancl(_1582160, _1582166))))), hAPP(hAPP(c_COMBC(_1582160, tc_fun(tc_prod(_1582160, _1582160), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1582160, _1582160), tc_fun(tc_fun(tc_prod(_1582160, _1582160), tc_HOL_Obool), tc_HOL_Obool), _1582160), c_member(tc_prod(_1582160, _1582160))), hAPP(c_Product__Type_OPair(_1582160, _1582160), _1582164))), c_Transitive__Closure_Ortrancl(_1582160, _1582166)))))))], (41826 ^ _779854) ^ [_1602151, _1602153, _1602155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602151, _1602151)), _1602153), c_Transitive__Closure_Otrancl(_1602151, _1602155))), 41830 ^ _779854 : [(41833 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602151, _1602151)), _1602153), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1602151, _1602151), tc_HOL_Obool), 41829 ^ [_1602151, _1602153, _1602155]), _1602155))))], (41831 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41829 ^ [_1602151, _1602153, _1602155])))]]], (5705 ^ _779854) ^ [_869962, _869964, _869966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869962, tc_HOL_Obool)), _869964), _869966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869962, tc_HOL_Obool)), _869966), _869964)), -(_869964 = _869966)], (15678 ^ _779854) ^ [_1060435, _1060437] : [class_Groups_Oab__semigroup__mult(_1060435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060435), _1060437)), -(_1060437 = c_Orderings_Obot__class_Obot(tc_fun(_1060435, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1060435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060435), 15691 ^ [_1060435, _1060437]), 15692 ^ [_1060435, _1060437])), hAPP(hAPP(c_Set_Oinsert(_1060435), 15691 ^ [_1060435, _1060437]), hAPP(hAPP(c_Set_Oinsert(_1060435), 15692 ^ [_1060435, _1060437]), c_Orderings_Obot__class_Obot(tc_fun(_1060435, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1060435), hAPP(c_Finite__Set_Ofold1(_1060435, c_Groups_Otimes__class_Otimes(_1060435)), _1060437)), _1060437)))], (35907 ^ _779854) ^ [_1448858, _1448860, _1448862, _1448864] : [-(hAPP(c_Product__Type_Osnd(_1448858, _1448860), hAPP(hAPP(c_Product__Type_OPair(_1448858, _1448860), _1448862), _1448864)) = _1448864)], (47004 ^ _779854) ^ [_1724788, _1724790, _1724792, _1724794] : [class_Orderings_Olinorder(_1724788), -(c_List_Olinorder__class_Osorted(_1724788, hAPP(hAPP(c_List_Omap(_1724790, _1724788), _1724792), c_List_Olinorder__class_Osort__key(_1724790, _1724788, _1724792, _1724794))))], (28884 ^ _779854) ^ [_1301507, _1301509] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1301507, _1301509) = 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), _1301507), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1301509))))], (20069 ^ _779854) ^ [_1141672, _1141674, _1141676] : [class_Groups_Ocomm__monoid__add(_1141672), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1141674, _1141672), _1141676), c_Orderings_Obot__class_Obot(tc_fun(_1141674, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1141672))], (7962 ^ _779854) ^ [_912998, _913000, _913002] : [class_Groups_Ogroup__add(_912998), 7965 ^ _779854 : [(7972 ^ _779854) ^ [] : [_913002 = hAPP(c_Groups_Ouminus__class_Ouminus(_912998), _913000), -(_913000 = hAPP(c_Groups_Ouminus__class_Ouminus(_912998), _913002))], (7966 ^ _779854) ^ [] : [_913000 = hAPP(c_Groups_Ouminus__class_Ouminus(_912998), _913002), -(_913002 = hAPP(c_Groups_Ouminus__class_Ouminus(_912998), _913000))]]], (33375 ^ _779854) ^ [_1386733, _1386735, _1386737, _1386739, _1386741] : [c_Finite__Set_Ofun__left__comm__idem(_1386733, _1386735, _1386737), -(c_Finite__Set_Ofun__left__comm__idem(_1386739, _1386735, hAPP(hAPP(c_COMBB(_1386733, tc_fun(_1386735, _1386735), _1386739), _1386737), _1386741)))], (37301 ^ _779854) ^ [_1482083, _1482085, _1482087, _1482089] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1482083, tc_HOL_Obool)), _1482085), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482083), _1482087), _1482089))), 37305 ^ _779854 : [(37308 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482083), 37304 ^ [_1482083, _1482085, _1482087, _1482089]), _1482087)))], (37306 ^ _779854) ^ [] : [-(_1482085 = hAPP(c_Relation_OImage(_1482083, _1482083, _1482089), hAPP(hAPP(c_Set_Oinsert(_1482083), 37304 ^ [_1482083, _1482085, _1482087, _1482089]), c_Orderings_Obot__class_Obot(tc_fun(_1482083, tc_HOL_Obool)))))]]], (7325 ^ _779854) ^ [_900425, _900427, _900429, _900431] : [class_Lattices_Osemilattice__inf(_900425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900425), _900427), _900429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900425), _900427), _900431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900425), _900427), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_900425), _900429), _900431))))], (46200 ^ _779854) ^ [_1706997, _1706999, _1707001] : [-(hBOOL(hAPP(hAPP(c_member(_1706997), _1706999), hAPP(c_List_Oset(_1706997), _1707001)))), -(hAPP(c_List_OremoveAll(_1706997, _1706999), _1707001) = _1707001)], (14147 ^ _779854) ^ [_1029502, _1029504, _1029506, _1029508, _1029510] : [hAPP(_1029506, _1029508) = _1029510, -(c_Fun_Ofun__upd(_1029502, _1029504, _1029506, _1029508, _1029510) = _1029506)], (3934 ^ _779854) ^ [_839276, _839278, _839280, _839282, _839284, _839286, _839288, _839290, _839292, _839294, _839296, _839298, _839300, _839302] : [-(c_New__Random__Sequence_Opos__decr__bind(_839302, _839298, _839294, _839290, _839286, _839282, _839278) = c_New__Random__Sequence_Opos__decr__bind(_839300, _839296, _839292, _839288, _839284, _839280, _839276)), _839302 = _839300, _839298 = _839296, _839294 = _839292, _839290 = _839288, _839286 = _839284, _839282 = _839280, _839278 = _839276], (14423 ^ _779854) ^ [_1034834, _1034836, _1034838, _1034840, _1034842] : [c_Finite__Set_Ofolding__one__idem(_1034834, _1034836, _1034838), hAPP(_1034840, hAPP(hAPP(_1034836, 14428 ^ [_1034834, _1034836, _1034838, _1034840, _1034842]), 14429 ^ [_1034834, _1034836, _1034838, _1034840, _1034842])) = hAPP(hAPP(_1034836, hAPP(_1034840, 14428 ^ [_1034834, _1034836, _1034838, _1034840, _1034842])), hAPP(_1034840, 14429 ^ [_1034834, _1034836, _1034838, _1034840, _1034842])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034834), _1034842)), -(_1034842 = c_Orderings_Obot__class_Obot(tc_fun(_1034834, tc_HOL_Obool))), -(hAPP(_1034840, hAPP(_1034838, _1034842)) = hAPP(_1034838, hAPP(c_Set_Oimage(_1034834, _1034834, _1034840), _1034842)))], (31007 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (33775 ^ _779854) ^ [_1401542, _1401544, _1401546, _1401548] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401542, tc_fun(_1401544, tc_HOL_Obool)), _1401546), _1401548) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1401544, tc_HOL_Obool), hAPP(c_Set_Oimage(_1401542, tc_fun(_1401544, tc_HOL_Obool), _1401548), _1401546)))], (30123 ^ _779854) ^ [_1323323, _1323325, _1323327] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323323), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323325, _1323327)), _1323327) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323323), _1323325), _1323327))], (17696 ^ _779854) ^ [_1100727] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1100727)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1100727)], (32874 ^ _779854) ^ [_1372408, _1372410, _1372412, _1372414] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372408, tc_fun(_1372410, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1372408, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1372410, tc_HOL_Obool), tc_fun(_1372410, tc_HOL_Obool), _1372408), hAPP(c_COMBC(_1372410, tc_fun(_1372410, tc_HOL_Obool), tc_HOL_Obool), c_member(_1372410))), _1372412)), _1372414)), -(hBOOL(hAPP(hAPP(c_member(_1372410), _1372414), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372408, tc_fun(_1372410, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1372408, tc_HOL_Obool))), _1372412))))], (15358 ^ _779854) ^ [_1053846, _1053848, _1053850, _1053852] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1053846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053846), _1053848), _1053850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053846), _1053852), _1053848)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053846), _1053852), _1053850))))], (15892 ^ _779854) ^ [_1064826, _1064828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064826), _1064828)), _1064828))], (7660 ^ _779854) ^ [_906962, _906964, _906966] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906962, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906962, tc_HOL_Obool)), _906964), _906966)), _906966)))], (17444 ^ _779854) ^ [_1095240, _1095242, _1095244, _1095246] : [_1095244 = _1095246, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1095240, _1095242, hAPP(hAPP(c_Set_Oinsert(_1095240), _1095244), c_Orderings_Obot__class_Obot(tc_fun(_1095240, tc_HOL_Obool)))), _1095246)))], (37414 ^ _779854) ^ [_1484405, _1484407, _1484409, _1484411, _1484413] : [c_Equiv__Relations_Oequiv(_1484405, _1484407, _1484409), 37417 ^ _779854 : [(37428 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484405, _1484405)), hAPP(hAPP(c_Product__Type_OPair(_1484405, _1484405), _1484411), _1484413)), _1484409))), hAPP(c_Relation_OImage(_1484405, _1484405, _1484409), hAPP(hAPP(c_Set_Oinsert(_1484405), _1484411), c_Orderings_Obot__class_Obot(tc_fun(_1484405, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1484405, _1484405, _1484409), hAPP(hAPP(c_Set_Oinsert(_1484405), _1484413), c_Orderings_Obot__class_Obot(tc_fun(_1484405, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1484405), _1484411), _1484407)), hBOOL(hAPP(hAPP(c_member(_1484405), _1484413), _1484407))], (37418 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484405, _1484405)), hAPP(hAPP(c_Product__Type_OPair(_1484405, _1484405), _1484411), _1484413)), _1484409)), 37421 ^ _779854 : [(37426 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484405), _1484413), _1484407)))], (37424 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484405), _1484411), _1484407)))], (37422 ^ _779854) ^ [] : [-(hAPP(c_Relation_OImage(_1484405, _1484405, _1484409), hAPP(hAPP(c_Set_Oinsert(_1484405), _1484411), c_Orderings_Obot__class_Obot(tc_fun(_1484405, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1484405, _1484405, _1484409), hAPP(hAPP(c_Set_Oinsert(_1484405), _1484413), c_Orderings_Obot__class_Obot(tc_fun(_1484405, tc_HOL_Obool)))))]]]]], (41657 ^ _779854) ^ [_1597655, _1597657, _1597659] : [41660 ^ _779854 : [(41666 ^ _779854) ^ [] : [41659 ^ [_1597655, _1597657, _1597659] = 41662 ^ [_1597655, _1597657, _1597659]], (41664 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597655, _1597657)), hAPP(hAPP(c_Product__Type_OPair(_1597655, _1597657), 41658 ^ [_1597655, _1597657, _1597659]), 41662 ^ [_1597655, _1597657, _1597659])), _1597659)))], (41661 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597655, _1597657)), hAPP(hAPP(c_Product__Type_OPair(_1597655, _1597657), 41658 ^ [_1597655, _1597657, _1597659]), 41659 ^ [_1597655, _1597657, _1597659])), _1597659)))]], -(c_Relation_Osingle__valued(_1597655, _1597657, _1597659))], (39333 ^ _779854) ^ [_1539185, _1539187] : [-(hAPP(c_Fun_Oid(_1539185), _1539187) = _1539187)], (44530 ^ _779854) ^ [_1670599] : [-(c_List_Orotate(_1670599, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1670599)))], (31856 ^ _779854) ^ [_1353126, _1353128] : [class_Rings_Oring__1(_1353126), -(hBOOL(hAPP(hAPP(c_member(_1353126), hAPP(c_Int_Oring__1__class_Oof__int(_1353126), _1353128)), c_Int_Oring__1__class_OInts(_1353126))))], (47390 ^ _779854) ^ [_1732712, _1732714] : [-(hAPP(c_List_Oset(_1732712), hAPP(c_List_Orev(_1732712), _1732714)) = hAPP(c_List_Oset(_1732712), _1732714))], (41465 ^ _779854) ^ [_1593005, _1593007, _1593009, _1593011, _1593013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593005, _1593007)), hAPP(hAPP(c_Product__Type_OPair(_1593005, _1593007), _1593009), _1593011)), _1593013)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593007, _1593005)), hAPP(hAPP(c_Product__Type_OPair(_1593007, _1593005), _1593011), _1593009)), hAPP(c_Relation_Oconverse(_1593005, _1593007), _1593013))))], (40199 ^ _779854) ^ [_1562666, _1562668] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562666, _1562666)), _1562668)), 40202 ^ _779854 : [(40209 ^ _779854) ^ [] : [c_Wellfounded_Oacyclic(_1562666, _1562668), -(c_Wellfounded_Owf(_1562666, _1562668))], (40203 ^ _779854) ^ [] : [c_Wellfounded_Owf(_1562666, _1562668), -(c_Wellfounded_Oacyclic(_1562666, _1562668))]]], (25801 ^ _779854) ^ [_1248799, _1248801, _1248803, _1248805] : [-(c_Nitpick_Ofold__graph_H(_1248799, _1248801, _1248803, _1248805, c_Orderings_Obot__class_Obot(tc_fun(_1248799, tc_HOL_Obool)), _1248805))], (11005 ^ _779854) ^ [_968984, _968986, _968988] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_968984, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968984, tc_HOL_Obool)), _968986), _968988)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_968984, tc_HOL_Obool)), _968986), _968988)) = _968986)], (35058 ^ _779854) ^ [_1431887, _1431889] : [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), _1431887))), 35061 ^ _779854 : [(35068 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431889)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431887)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431889), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431887)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431887)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431889), 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), _1431887)))))], (35062 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431889)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431887))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431889), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431887)) = 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), _1431889)))]]], (42247 ^ _779854) ^ [_1614593, _1614595, _1614597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1614593, _1614593), tc_HOL_Obool)), _1614595), _1614597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1614593), tc_List_Olist(_1614593)), tc_HOL_Obool)), c_List_Olistrel1(_1614593, _1614595)), c_List_Olistrel1(_1614593, _1614597))))], (1400 ^ _779854) ^ [_800306, _800308] : [-(class_Lattices_Obounded__lattice__bot(_800306)), _800308 = _800306, class_Lattices_Obounded__lattice__bot(_800308)], (30392 ^ _779854) ^ [_1328662, _1328664] : [30393 ^ _779854 : [(30394 ^ _779854) ^ [_1328711] : [_1328662 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1328664), _1328711)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328662, _1328664) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38338 ^ _779854) ^ [_1507190, _1507192, _1507194, _1507196, _1507198] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1507190, _1507192), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507190, tc_HOL_Obool)), _1507194), _1507196)), _1507198) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507190, _1507192), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1507190, _1507192), _1507194), _1507198)), hAPP(hAPP(c_Product__Type_OSigma(_1507190, _1507192), _1507196), _1507198)))], (49608 ^ _779854) ^ [_1781372, _1781374] : [c_Relation_Otrans(_1781372, _1781374), -(c_Relation_Otrans(_1781372, hAPP(c_Relation_Oconverse(_1781372, _1781372), _1781374)))], (46759 ^ _779854) ^ [_1720451, _1720453, _1720455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720451), _1720453)), _1720455)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1720451, _1720455)), _1720453) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720451), _1720453))], (24597 ^ _779854) ^ [_1226016, _1226018, _1226020] : [class_Int_Onumber__ring(_1226016), class_Rings_Olinordered__idom(_1226016), 24604 ^ _779854 : [(24611 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226018), _1226020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226016), hAPP(c_Int_Onumber__class_Onumber__of(_1226016), _1226018)), hAPP(c_Int_Onumber__class_Onumber__of(_1226016), _1226020))))], (24605 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226016), hAPP(c_Int_Onumber__class_Onumber__of(_1226016), _1226018)), hAPP(c_Int_Onumber__class_Onumber__of(_1226016), _1226020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226018), _1226020)))]]], (4996 ^ _779854) ^ [_856181, _856183] : [_856183 = _856181, -(c_Lattices_Osemilattice__sup__class_Osup(_856183) = c_Lattices_Osemilattice__sup__class_Osup(_856181))], (12202 ^ _779854) ^ [_992458, _992460] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_992458, tc_HOL_Obool)), _992460), hAPP(c_Set_OPow(_992458), _992460))))], (22827 ^ _779854) ^ [_1192406, _1192408, _1192410, _1192412] : [class_Fields_Olinordered__field(_1192406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192406), c_Groups_Ozero__class_Ozero(_1192406)), _1192408)), 22834 ^ _779854 : [(22841 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192406), _1192410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192406), _1192412), _1192408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192406), _1192410), _1192408)), _1192412)))], (22835 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192406), _1192410), _1192408)), _1192412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192406), _1192410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192406), _1192412), _1192408))))]]], (46194 ^ _779854) ^ [_1706886, _1706888, _1706890] : [hBOOL(hAPP(c_List_Odistinct(_1706886), _1706888)), -(c_List_Oremove1(_1706886, _1706890, c_List_Oremdups(_1706886, _1706888)) = c_List_Oremdups(_1706886, c_List_Oremove1(_1706886, _1706890, _1706888)))], (24521 ^ _779854) ^ [_1224683, _1224685, _1224687] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224683), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1224685), _1224687)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224683), _1224685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224683), _1224687)))], (350 ^ _779854) ^ [_785237, _785239, _785241, _785243] : [-(c_FunDef_Oreduction__pair(_785241, _785237)), c_FunDef_Oreduction__pair(_785243, _785239), _785243 = _785241, _785239 = _785237], (13081 ^ _779854) ^ [_1010281, _1010283, _1010285] : [class_Orderings_Olinorder(_1010281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010281), _1010283)), hBOOL(hAPP(hAPP(c_member(_1010281), _1010285), _1010283)), 13092 ^ _779854 : [(13099 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010281, tc_HOL_Obool)), _1010283), hAPP(hAPP(c_Set_Oinsert(_1010281), _1010285), c_Orderings_Obot__class_Obot(tc_fun(_1010281, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1010281, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1010281, _1010283) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1010281), _1010285), c_Big__Operators_Olinorder__class_OMin(_1010281, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010281, tc_HOL_Obool)), _1010283), hAPP(hAPP(c_Set_Oinsert(_1010281), _1010285), c_Orderings_Obot__class_Obot(tc_fun(_1010281, tc_HOL_Obool)))))))], (13093 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010281, tc_HOL_Obool)), _1010283), hAPP(hAPP(c_Set_Oinsert(_1010281), _1010285), c_Orderings_Obot__class_Obot(tc_fun(_1010281, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1010281, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1010281, _1010283) = _1010285)]]], (31938 ^ _779854) ^ [_1354477, _1354479] : [class_Rings_Oring__1(_1354477), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354479)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1354477), hAPP(c_Int_Onat, _1354479)) = hAPP(c_Int_Oring__1__class_Oof__int(_1354477), _1354479))], (17292 ^ _779854) ^ [_1092279, _1092281] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1092279), c_Orderings_Otop__class_Otop(tc_fun(_1092279, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1092279), _1092281) = hAPP(c_Finite__Set_Ocard(_1092279), c_Orderings_Otop__class_Otop(tc_fun(_1092279, tc_HOL_Obool))), -(_1092281 = c_Orderings_Otop__class_Otop(tc_fun(_1092279, tc_HOL_Obool)))], (14205 ^ _779854) ^ [_1030542, _1030544, _1030546, _1030548, _1030550] : [c_Fun_Oinj__on(_1030542, _1030544, _1030546, _1030548), hBOOL(hAPP(hAPP(c_member(_1030544), _1030550), hAPP(c_Set_Oimage(_1030542, _1030544, _1030546), _1030548))), -(hAPP(_1030546, hAPP(c_Fun_Othe__inv__into(_1030542, _1030544, _1030548, _1030546), _1030550)) = _1030550)], (45232 ^ _779854) ^ [_1685687, _1685689, _1685691, _1685693, _1685695] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1685687), tc_List_Olist(_1685689), tc_List_Olist(_1685691), hAPP(c_List_Omap(_1685687, _1685689), _1685693)), hAPP(c_List_Omap(_1685691, _1685687), _1685695)) = hAPP(c_List_Omap(_1685691, _1685689), hAPP(c_Fun_Ocomp(_1685687, _1685689, _1685691, _1685693), _1685695)))], (5360 ^ _779854) ^ [_861923, _861925] : [_861925 = _861923, -(c_Groups_Oone__class_Oone(_861925) = c_Groups_Oone__class_Oone(_861923))], (39964 ^ _779854) ^ [_1556284, _1556286, _1556288, _1556290, _1556292] : [hBOOL(hAPP(hAPP(_1556284, _1556286), _1556288)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1556290, _1556292, _1556284), _1556286)))], (52183 ^ _779854) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (42837 ^ _779854) ^ [_1631303, _1631305, _1631307, _1631309] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631303), tc_List_Olist(_1631303))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631303), tc_List_Olist(_1631303)), _1631305), _1631307)), c_List_Olistrel(_1631303, _1631309))), 42840 ^ _779854 : [(42843 ^ _779854) ^ [_1631639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631303, _1631303)), _1631639), hAPP(c_List_Oset(tc_prod(_1631303, _1631303)), hAPP(hAPP(c_List_Ozip(_1631303, _1631303), _1631305), _1631307)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1631303, _1631303, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1631303, tc_fun(tc_prod(_1631303, _1631303), tc_HOL_Obool), tc_fun(_1631303, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1631303, tc_fun(tc_fun(tc_prod(_1631303, _1631303), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1631303, _1631303), tc_HOL_Obool), tc_fun(_1631303, tc_HOL_Obool)), _1631303), c_COMBC(_1631303, tc_fun(tc_prod(_1631303, _1631303), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1631303, tc_prod(_1631303, _1631303)), tc_fun(_1631303, tc_fun(tc_fun(tc_prod(_1631303, _1631303), tc_HOL_Obool), tc_HOL_Obool)), _1631303), hAPP(c_COMBB(tc_prod(_1631303, _1631303), tc_fun(tc_fun(tc_prod(_1631303, _1631303), tc_HOL_Obool), tc_HOL_Obool), _1631303), c_member(tc_prod(_1631303, _1631303)))), c_Product__Type_OPair(_1631303, _1631303)))), _1631309)), _1631639)))], (42841 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631303)), _1631305) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631303)), _1631307))]]], (22009 ^ _779854) ^ [_1177299, _1177301, _1177303] : [class_Rings_Odivision__ring(_1177299), -(_1177301 = c_Groups_Ozero__class_Ozero(_1177299)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1177299), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177299), _1177303), _1177301)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177299), _1177303), hAPP(c_Groups_Ouminus__class_Ouminus(_1177299), _1177301)))], (33743 ^ _779854) ^ [_1400715, _1400717, _1400719, _1400721, _1400723] : [-(_1400715 = c_Orderings_Obot__class_Obot(tc_fun(_1400717, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400719, tc_HOL_Obool)), _1400721), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400717, tc_fun(_1400719, tc_HOL_Obool)), _1400715), _1400723)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400717, tc_fun(_1400719, tc_HOL_Obool)), _1400715), hAPP(hAPP(c_COMBB(tc_fun(_1400719, tc_HOL_Obool), tc_fun(_1400719, tc_HOL_Obool), _1400717), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400719, tc_HOL_Obool)), _1400721)), _1400723)))], (9046 ^ _779854) ^ [_930748, _930750, _930752, _930754, _930756] : [class_Orderings_Olinorder(_930748), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_930748, _930750), _930752) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_930748, _930754), _930756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930748), _930750), _930752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930748), _930754), _930756)), -(_930750 = _930754)], (28928 ^ _779854) ^ [_1302183, _1302185] : [_1302183 = hAPP(c_Int_Onat, _1302185), 28931 ^ _779854 : [(28938 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302185))), -(_1302183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28932 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302185)), -(_1302185 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1302183))]]], (32255 ^ _779854) ^ [_1360207, _1360209, _1360211] : [class_Fields_Olinordered__field(_1360207), -(_1360209 = c_Groups_Ozero__class_Ozero(_1360207)), -(hAPP(c_Groups_Oabs__class_Oabs(_1360207), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360207), _1360211), _1360209)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360207), hAPP(c_Groups_Oabs__class_Oabs(_1360207), _1360211)), hAPP(c_Groups_Oabs__class_Oabs(_1360207), _1360209)))], (34225 ^ _779854) ^ [_1413620, _1413622, _1413624, _1413626, _1413628] : [c_Fun_Oinj__on(_1413620, _1413622, _1413624, c_Orderings_Otop__class_Otop(tc_fun(_1413620, tc_HOL_Obool))), c_Fun_Oinj__on(_1413626, _1413620, _1413628, c_Orderings_Otop__class_Otop(tc_fun(_1413626, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1413626, _1413622, hAPP(c_Fun_Ocomp(_1413620, _1413622, _1413626, _1413624), _1413628), c_Orderings_Otop__class_Otop(tc_fun(_1413626, tc_HOL_Obool))))], (22063 ^ _779854) ^ [_1178265, _1178267, _1178269, _1178271] : [class_Groups_Ocomm__monoid__add(_1178265), 22066 ^ _779854 : [(22073 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1178267), _1178269))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178267, _1178265), _1178271), _1178269) = c_Groups_Ozero__class_Ozero(_1178265))], (22067 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1178267), _1178269)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178267, _1178265), _1178271), _1178269) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1178265, _1178267, c_Groups_Oplus__class_Oplus(_1178265)), _1178271), c_Groups_Ozero__class_Ozero(_1178265)), _1178269))]]], (41479 ^ _779854) ^ [_1593422, _1593424, _1593426, _1593428, _1593430] : [-(hAPP(c_Relation_Oconverse(_1593422, _1593424), hAPP(hAPP(c_Relation_Orel__comp(_1593422, _1593426, _1593424), _1593428), _1593430)) = hAPP(hAPP(c_Relation_Orel__comp(_1593424, _1593426, _1593422), hAPP(c_Relation_Oconverse(_1593426, _1593424), _1593430)), hAPP(c_Relation_Oconverse(_1593422, _1593426), _1593428)))], (52243 ^ _779854) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (33597 ^ _779854) ^ [_1396819, _1396821, _1396823, _1396825, _1396827] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396819, tc_fun(_1396821, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396819, tc_HOL_Obool)), _1396823), _1396825)), _1396827) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396821, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396819, tc_fun(_1396821, tc_HOL_Obool)), _1396823), _1396827)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396819, tc_fun(_1396821, tc_HOL_Obool)), _1396825), _1396827)))], (9560 ^ _779854) ^ [_940118, _940120, _940122] : [class_Orderings_Olinorder(_940118), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940118), _940120), hAPP(hAPP(c_Orderings_Oord__class_Omax(_940118), _940122), _940120))))], (24322 ^ _779854) ^ [_1220940, _1220942, _1220944, _1220946] : [class_Rings_Olinordered__semidom(_1220940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220942), _1220944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220940), c_Groups_Oone__class_Oone(_1220940)), _1220946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220940), hAPP(hAPP(c_Power_Opower__class_Opower(_1220940), _1220946), _1220942)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220940), _1220946), _1220944))))], (7447 ^ _779854) ^ [_902582, _902584] : [class_Lattices_Obounded__lattice__bot(_902582), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_902582), _902584), c_Orderings_Obot__class_Obot(_902582)) = c_Orderings_Obot__class_Obot(_902582))], (17322 ^ _779854) ^ [_1092845, _1092847, _1092849] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1092845, _1092847, c_Orderings_Obot__class_Obot(tc_fun(_1092845, tc_HOL_Obool))), _1092849))], (29429 ^ _779854) ^ [_1310717, _1310719] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1310717)), c_Int_OBit0(_1310719)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1310717), _1310719)))], (39776 ^ _779854) ^ [_1551291, _1551293] : [hAPP(hAPP(c_Relation_Orel__comp(_1551291, _1551291, _1551291), _1551293), _1551293) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551291, _1551291), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1551291, _1551293))], (21379 ^ _779854) ^ [_1165118, _1165120] : [21387 ^ _779854 : [(21390 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1165120, 21386 ^ [_1165118, _1165120])))], (21388 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21386 ^ [_1165118, _1165120]), _1165118)))]], 21380 ^ _779854 : [(21381 ^ _779854) ^ [_1165186] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1165186), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1165118))), hBOOL(hAPP(_1165120, _1165186))]]], (29007 ^ _779854) ^ [_1303449, _1303451] : [class_Groups_Omonoid__mult(_1303449), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1303449), _1303451), 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(_1303449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303449), _1303451), _1303451)), _1303451))], (52355 ^ _779854) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (12164 ^ _779854) ^ [_991768, _991770, _991772, _991774, _991776, _991778, _991780, _991782] : [c_Finite__Set_Ofolding__image__simple(_991768, _991770, _991772, _991774, _991776, _991778), hBOOL(hAPP(c_Finite__Set_Ofinite(_991770), _991780)), -(hBOOL(hAPP(hAPP(c_member(_991770), _991782), _991780))), -(hAPP(_991778, hAPP(hAPP(c_Set_Oinsert(_991770), _991782), _991780)) = hAPP(hAPP(_991772, hAPP(_991776, _991782)), hAPP(_991778, _991780)))], (18421 ^ _779854) ^ [_1113483] : [-(hAPP(c_Nat_OSuc, _1113483) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1113483))], (34495 ^ _779854) ^ [_1419691] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419691))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419691)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25705 ^ _779854) ^ [_1247152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247152), 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)), _1247152)), _1247152)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45294 ^ _779854) ^ [_1687031, _1687033] : [class_Groups_Oordered__ab__group__add__abs(_1687031), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1687031), hAPP(c_Groups_Oabs__class_Oabs(_1687031), hAPP(c_List_Omonoid__add__class_Olistsum(_1687031), _1687033))), hAPP(c_List_Omonoid__add__class_Olistsum(_1687031), hAPP(hAPP(c_List_Omap(_1687031, _1687031), c_Groups_Oabs__class_Oabs(_1687031)), _1687033)))))], (45410 ^ _779854) ^ [_1689585, _1689587] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1689585), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1689587), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45417 ^ _779854 : [(45424 ^ _779854) ^ [] : [_1689585 = _1689587, -(hAPP(c_Code__Numeral_Oof__nat, _1689585) = hAPP(c_Code__Numeral_Oof__nat, _1689587))], (45418 ^ _779854) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1689585) = hAPP(c_Code__Numeral_Oof__nat, _1689587), -(_1689585 = _1689587)]]], (1790 ^ _779854) ^ [_805181, _805183] : [-(class_Groups_Omonoid__mult(_805181)), _805183 = _805181, class_Groups_Omonoid__mult(_805183)], (8390 ^ _779854) ^ [_919946, _919948, _919950] : [class_Orderings_Olinorder(_919946), 8393 ^ _779854 : [(8394 ^ _779854) ^ [] : [-(_919948 = _919950), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919946), _919948), _919950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919946), _919950), _919948)))], (8404 ^ _779854) ^ [] : [8405 ^ _779854 : [(8408 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919946), _919950), _919948))], (8406 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919946), _919948), _919950))]], _919948 = _919950]]], (46607 ^ _779854) ^ [_1717523, _1717525] : [class_Groups_Omonoid__add(_1717523), -(hAPP(c_List_Ofoldl(_1717523, _1717523, c_Groups_Oplus__class_Oplus(_1717523), c_Groups_Ozero__class_Ozero(_1717523)), _1717525) = c_List_Ofoldr(_1717523, _1717523, c_Groups_Oplus__class_Oplus(_1717523), _1717525, c_Groups_Ozero__class_Ozero(_1717523)))], (16726 ^ _779854) ^ [_1081152, _1081154, _1081156, _1081158, _1081160, _1081162] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1081152, _1081154, _1081156, _1081158, _1081160), _1081162)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1081152), _1081160)))], (19907 ^ _779854) ^ [_1138941, _1138943] : [class_Groups_Olinordered__ab__group__add(_1138941), 19910 ^ _779854 : [(19917 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138941), _1138943), c_Groups_Ozero__class_Ozero(_1138941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138941), _1138943), hAPP(c_Groups_Ouminus__class_Ouminus(_1138941), _1138943))))], (19911 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138941), _1138943), hAPP(c_Groups_Ouminus__class_Ouminus(_1138941), _1138943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138941), _1138943), c_Groups_Ozero__class_Ozero(_1138941))))]]], (5132 ^ _779854) ^ [_858305, _858307, _858309, _858311, _858313, _858315, _858317, _858319] : [-(c_Product__Type_Ocurry(_858319, _858315, _858311, _858307) = c_Product__Type_Ocurry(_858317, _858313, _858309, _858305)), _858319 = _858317, _858315 = _858313, _858311 = _858309, _858307 = _858305], (27576 ^ _779854) ^ [_1279132] : [27578 ^ _779854 : [(27581 ^ _779854) ^ [] : [hBOOL(hAPP(_1279132, hAPP(c_Int_Onat, 27577 ^ [_1279132])))], (27579 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27577 ^ [_1279132])))]], 27582 ^ _779854 : [(27583 ^ _779854) ^ [_1279265] : [-(hBOOL(hAPP(_1279132, _1279265)))]]], (22105 ^ _779854) ^ [_1179004, _1179006, _1179008, _1179010, _1179012] : [class_Groups_Ocomm__monoid__mult(_1179004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1179006), _1179008)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1179006), _1179010)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179004), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1179004, _1179006, c_Groups_Otimes__class_Otimes(_1179004)), _1179012), c_Groups_Oone__class_Oone(_1179004)), _1179008)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1179004, _1179006, c_Groups_Otimes__class_Otimes(_1179004)), _1179012), c_Groups_Oone__class_Oone(_1179004)), _1179010)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179004), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1179004, _1179006, c_Groups_Otimes__class_Otimes(_1179004)), _1179012), c_Groups_Oone__class_Oone(_1179004)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179006, tc_HOL_Obool)), _1179008), _1179010))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1179004, _1179006, c_Groups_Otimes__class_Otimes(_1179004)), _1179012), c_Groups_Oone__class_Oone(_1179004)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1179006, tc_HOL_Obool)), _1179008), _1179010))))], (30779 ^ _779854) ^ [_1335566, _1335568, _1335570, _1335572] : [_1335566 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1335568), _1335570)), _1335572), -(_1335568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1335566, _1335568) = _1335572), 30786 ^ _779854 : [(30789 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335572), _1335568))], (30787 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335568)))]], 30794 ^ _779854 : [(30797 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335568), _1335572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335572), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (30795 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335568))]]], (3228 ^ _779854) ^ [_828099, _828101, _828103, _828105, _828107, _828109, _828111, _828113, _828115, _828117] : [-(c_Fun_Ofun__upd(_828117, _828113, _828109, _828105, _828101) = c_Fun_Ofun__upd(_828115, _828111, _828107, _828103, _828099)), _828117 = _828115, _828113 = _828111, _828109 = _828107, _828105 = _828103, _828101 = _828099], (17630 ^ _779854) ^ [_1099290, _1099292, _1099294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099290), _1099292)), 17633 ^ _779854 : [(17640 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099290), _1099294), _1099292))), -(hAPP(c_Finite__Set_Ocard(_1099290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099290, tc_HOL_Obool)), _1099292), hAPP(hAPP(c_Set_Oinsert(_1099290), _1099294), c_Orderings_Obot__class_Obot(tc_fun(_1099290, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1099290), _1099292))], (17634 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1099290), _1099294), _1099292)), -(hAPP(c_Finite__Set_Ocard(_1099290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099290, tc_HOL_Obool)), _1099292), hAPP(hAPP(c_Set_Oinsert(_1099290), _1099294), c_Orderings_Obot__class_Obot(tc_fun(_1099290, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1099290), _1099292)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (9484 ^ _779854) ^ [_938432, _938434, _938436] : [class_Orderings_Olinorder(_938432), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938432), _938434), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938432), _938434), _938436)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_938432), _938434), _938436))], (31728 ^ _779854) ^ [_1350987, _1350989, _1350991] : [class_Int_Oring__char__0(_1350987), 31731 ^ _779854 : [(31738 ^ _779854) ^ [] : [_1350989 = _1350991, -(hAPP(c_Int_Oring__1__class_Oof__int(_1350987), _1350989) = hAPP(c_Int_Oring__1__class_Oof__int(_1350987), _1350991))], (31732 ^ _779854) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1350987), _1350989) = hAPP(c_Int_Oring__1__class_Oof__int(_1350987), _1350991), -(_1350989 = _1350991)]]], (43564 ^ _779854) ^ [_1648033, _1648035] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648033), tc_List_Olist(_1648033))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648033), tc_List_Olist(_1648033)), c_List_Olist_ONil(_1648033)), c_List_Olist_ONil(_1648033))), c_List_Olistrel(_1648033, _1648035))))], (36187 ^ _779854) ^ [_1454995, _1454997, _1454999, _1455001] : [-(hAPP(c_Product__Type_Ofst(_1454995, _1454997), hAPP(hAPP(c_Product__Type_OPair(_1454995, _1454997), _1454999), _1455001)) = _1454999)], (51935 ^ _779854) ^ [_1830141, _1830143] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830141), _1830143)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830143), _1830141))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830143), _1830141)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830141), _1830143)))], (20782 ^ _779854) ^ [_1153856, _1153858, _1153860, _1153862] : [class_Rings_Olinordered__semiring(_1153856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153856), _1153858), _1153860)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153856), _1153858), _1153862))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153856), c_Groups_Ozero__class_Ozero(_1153856)), _1153858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153856), _1153860), _1153862)))], (28583 ^ _779854) ^ [_1296568, _1296570, _1296572] : [class_Rings_Osemiring__1(_1296568), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1296570), _1296572)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296568), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296568), _1296570)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296568), _1296572)))], (10699 ^ _779854) ^ [_962258, _962260, _962262, _962264, _962266] : [c_Fun_Oinj__on(_962258, _962260, _962262, _962264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962258, tc_HOL_Obool)), _962266), _962264)), -(c_Fun_Oinj__on(_962258, _962260, _962262, _962266))], (4644 ^ _779854) ^ [_850645, _850647, _850649, _850651, _850653, _850655, _850657, _850659] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_850659, _850655, _850651, _850647) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_850657, _850653, _850649, _850645)), _850659 = _850657, _850655 = _850653, _850651 = _850649, _850647 = _850645], (47010 ^ _779854) ^ [_1724895, _1724897, _1724899, _1724901, _1724903] : [class_Orderings_Olinorder(_1724895), c_List_Olinorder__class_Osorted(_1724895, hAPP(hAPP(c_List_Omap(_1724897, _1724895), _1724899), _1724901)), -(c_List_Olinorder__class_Osorted(_1724895, hAPP(hAPP(c_List_Omap(_1724897, _1724895), _1724899), c_List_Olinorder__class_Oinsort__insert__key(_1724897, _1724895, _1724899, _1724903, _1724901))))], (9094 ^ _779854) ^ [_931536, _931538, _931540] : [class_Complete__Lattice_Ocomplete__lattice(_931536), class_Orderings_Olinorder(_931536), 9101 ^ _779854 : [(9111 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931536), _931538), c_Complete__Lattice_OSup__class_OSup(_931536, _931540)))), 9112 ^ _779854 : [(9113 ^ _779854) ^ [_931842] : [hBOOL(hAPP(hAPP(c_member(_931536), _931842), _931540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931536), _931538), _931842))]]], (9102 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931536), _931538), c_Complete__Lattice_OSup__class_OSup(_931536, _931540))), 9106 ^ _779854 : [(9109 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931536), _931538), 9105 ^ [_931536, _931538, _931540])))], (9107 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_931536), 9105 ^ [_931536, _931538, _931540]), _931540)))]]]]], (52629 ^ _779854) ^ [_1838082, _1838084] : [-(hAPP(c_COMBI(_1838082), _1838084) = _1838084)], (20868 ^ _779854) ^ [_1155409, _1155411, _1155413] : [class_Rings_Olinordered__idom(_1155409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155409), c_Groups_Ozero__class_Ozero(_1155409)), _1155411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155409), c_Groups_Ozero__class_Ozero(_1155409)), _1155413)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155409), _1155413), c_Groups_Oone__class_Oone(_1155409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155409), _1155411), _1155413)), _1155411)))], (41511 ^ _779854) ^ [_1594254, _1594256, _1594258, _1594260] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594254, _1594254)), hAPP(hAPP(c_Product__Type_OPair(_1594254, _1594254), _1594256), _1594258)), c_Transitive__Closure_Ortrancl(_1594254, hAPP(c_Relation_Oconverse(_1594254, _1594254), _1594260)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594254, _1594254)), hAPP(hAPP(c_Product__Type_OPair(_1594254, _1594254), _1594258), _1594256)), c_Transitive__Closure_Ortrancl(_1594254, _1594260))))], (40541 ^ _779854) ^ [_1570131, _1570133] : [class_Complete__Lattice_Ocomplete__lattice(_1570131), c_Orderings_Oorder__class_Omono(_1570131, _1570131, _1570133), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1570131), c_Inductive_Ocomplete__lattice__class_Ogfp(_1570131, _1570133)), hAPP(_1570133, c_Inductive_Ocomplete__lattice__class_Ogfp(_1570131, _1570133)))))], (35074 ^ _779854) ^ [_1432229, _1432231, _1432233, _1432235, _1432237] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1432229, _1432231, _1432233), _1432235), _1432237)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1432229, _1432231)), hAPP(hAPP(c_Product__Type_OPair(_1432229, _1432231), _1432235), _1432237)), _1432233)))], (25693 ^ _779854) ^ [_1246920, _1246922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246920), _1246922)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246920), _1246922)))], (35360 ^ _779854) ^ [_1438584, _1438586] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1438584), _1438586)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1438584), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1438586)))], (16038 ^ _779854) ^ [_1067936, _1067938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067936), _1067938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067936), _1067938)))], (47858 ^ _779854) ^ [_1742589, _1742591, _1742593, _1742595] : [47860 ^ _779854 : [(47865 ^ _779854) ^ [] : [hBOOL(hAPP(_1742595, hAPP(hAPP(c_List_Onth(_1742591), _1742593), 47859 ^ [_1742589, _1742591, _1742593, _1742595])))], (47863 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47859 ^ [_1742589, _1742591, _1742593, _1742595]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742591)), _1742593))))], (47861 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47859 ^ [_1742589, _1742591, _1742593, _1742595]), _1742589)))]], 47868 ^ _779854 : [(47871 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1742595, hAPP(hAPP(c_List_Onth(_1742591), _1742593), _1742589))))], (47869 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742589), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742591)), _1742593))))]], -(c_List_OtakeWhile(_1742591, _1742595, _1742593) = hAPP(hAPP(c_List_Otake(_1742591), _1742589), _1742593))], (15790 ^ _779854) ^ [_1062775, _1062777] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1062775, _1062777))))], (19345 ^ _779854) ^ [_1128784, _1128786, _1128788] : [class_Rings_Oordered__cancel__semiring(_1128784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128784), c_Groups_Ozero__class_Ozero(_1128784)), _1128786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128784), _1128788), c_Groups_Ozero__class_Ozero(_1128784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128784), _1128788), _1128786)), c_Groups_Ozero__class_Ozero(_1128784))))], (32413 ^ _779854) ^ [_1363205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1363205), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1363205) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1363205))], (9552 ^ _779854) ^ [_939947, _939949, _939951, _939953, _939955] : [-(hAPP(c_Set_Oimage(_939947, _939949, _939951), hAPP(hAPP(c_Set_Oinsert(_939947), _939953), _939955)) = hAPP(hAPP(c_Set_Oinsert(_939949), hAPP(_939951, _939953)), hAPP(c_Set_Oimage(_939947, _939949, _939951), _939955)))], (31874 ^ _779854) ^ [_1353447, _1353449] : [class_Rings_Olinordered__idom(_1353447), 31877 ^ _779854 : [(31884 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1353449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353447), c_Groups_Ozero__class_Ozero(_1353447)), hAPP(c_Int_Oring__1__class_Oof__int(_1353447), _1353449))))], (31878 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353447), c_Groups_Ozero__class_Ozero(_1353447)), hAPP(c_Int_Oring__1__class_Oof__int(_1353447), _1353449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1353449)))]]], (31214 ^ _779854) ^ [_1342705] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1342705), c_Int_OMin) = c_Int_Opred(_1342705))], (1530 ^ _779854) ^ [_801931, _801933] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801931)), _801933 = _801931, class_Groups_Oordered__ab__semigroup__add__imp__le(_801933)], (33547 ^ _779854) ^ [_1393540, _1393542, _1393544, _1393546, _1393548, _1393550] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393540, tc_fun(_1393542, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1393540, tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_fun(_1393542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393542, tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_fun(_1393542, tc_HOL_Obool)), _1393540), c_COMBC(_1393542, tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393542, tc_prod(_1393540, _1393542)), tc_fun(_1393542, tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool)), _1393540), hAPP(c_COMBB(tc_prod(_1393540, _1393542), tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool), _1393542), c_member(tc_prod(_1393540, _1393542)))), c_Product__Type_OPair(_1393540, _1393542)))), _1393544)), hAPP(hAPP(c_COMBC(_1393540, tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_fun(_1393542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393542, tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_fun(_1393542, tc_HOL_Obool)), _1393540), c_COMBC(_1393542, tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393542, tc_prod(_1393540, _1393542)), tc_fun(_1393542, tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool)), _1393540), hAPP(c_COMBB(tc_prod(_1393540, _1393542), tc_fun(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool), tc_HOL_Obool), _1393542), c_member(tc_prod(_1393540, _1393542)))), c_Product__Type_OPair(_1393540, _1393542)))), _1393546)), _1393548), _1393550)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1393540, _1393542)), hAPP(hAPP(c_Product__Type_OPair(_1393540, _1393542), _1393548), _1393550)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1393540, _1393542), tc_HOL_Obool)), _1393544), _1393546))))], (13105 ^ _779854) ^ [_1010787, _1010789] : [-(hBOOL(hAPP(hAPP(c_member(_1010787), _1010789), c_Orderings_Otop__class_Otop(tc_fun(_1010787, tc_HOL_Obool)))))], (34781 ^ _779854) ^ [_1426305, _1426307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426305), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426307)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426305)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426307))], (4602 ^ _779854) ^ [_849958, _849960, _849962, _849964, _849966, _849968, _849970, _849972] : [-(c_Product__Type_Oscomp(_849972, _849968, _849964, _849960) = c_Product__Type_Oscomp(_849970, _849966, _849962, _849958)), _849972 = _849970, _849968 = _849966, _849964 = _849962, _849960 = _849958], (32493 ^ _779854) ^ [_1364550, _1364552, _1364554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1364550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364552), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1364554), 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), _1364554), _1364552))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1364550)))))], (49048 ^ _779854) ^ [_1768770, _1768772] : [-(c_List_Oconcat(_1768770, c_List_Oreplicate(tc_List_Olist(_1768770), _1768772, c_List_Olist_ONil(_1768770))) = c_List_Olist_ONil(_1768770))], (49582 ^ _779854) ^ [_1780964] : [-(c_Relation_Otrans(tc_fun(_1780964, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1780964)))], (37592 ^ _779854) ^ [_1488758, _1488760] : [c_Equiv__Relations_Oequivp(_1488758, _1488760), 37595 ^ _779854 : [(37602 ^ _779854) ^ [_1488951, _1488953] : [hAPP(_1488760, _1488953) = hAPP(_1488760, _1488951), -(hBOOL(hAPP(hAPP(_1488760, _1488953), _1488951)))], (37596 ^ _779854) ^ [_1488852, _1488854] : [hBOOL(hAPP(hAPP(_1488760, _1488854), _1488852)), -(hAPP(_1488760, _1488854) = hAPP(_1488760, _1488852))]]], (33589 ^ _779854) ^ [_1396297, _1396299, _1396301, _1396303, _1396305] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396297, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396299, tc_fun(_1396297, tc_HOL_Obool)), _1396301), _1396303)), _1396305) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396299, tc_fun(_1396297, tc_HOL_Obool)), _1396301), hAPP(hAPP(c_COMBC(_1396299, tc_fun(_1396297, tc_HOL_Obool), tc_fun(_1396297, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396297, tc_HOL_Obool), tc_fun(tc_fun(_1396297, tc_HOL_Obool), tc_fun(_1396297, tc_HOL_Obool)), _1396299), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396297, tc_HOL_Obool))), _1396303)), _1396305)))], (39355 ^ _779854) ^ [_1539592, _1539594, _1539596, _1539598] : [-(c_Product__Type_Oapfst(_1539592, _1539594, _1539596, _1539598) = c_Product__Type_Omap__pair(_1539592, _1539594, _1539596, _1539596, _1539598, c_Fun_Oid(_1539596)))], (46613 ^ _779854) ^ [_1717642, _1717644] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1717642))), c_List_Otranspose(_1717642, _1717644)) = c_List_Ofoldr(tc_List_Olist(_1717642), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1717642)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1717642))), _1717644, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (40603 ^ _779854) ^ [_1571366, _1571368, _1571370] : [class_Complete__Lattice_Ocomplete__lattice(_1571366), c_Orderings_Oorder__class_Omono(_1571366, _1571366, _1571368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1571366), _1571370), hAPP(_1571368, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1571366), _1571370), c_Inductive_Ocomplete__lattice__class_Ogfp(_1571366, _1571368))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1571366), _1571370), c_Inductive_Ocomplete__lattice__class_Ogfp(_1571366, _1571368))))], (28547 ^ _779854) ^ [_1295945, _1295947, _1295949] : [class_Rings_Olinordered__semidom(_1295945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295945), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295945), _1295947)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295945), _1295949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1295947), _1295949)))], (13631 ^ _779854) ^ [_1019569, _1019571, _1019573] : [class_Lattices_Olattice(_1019569), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019569), _1019571)), -(hBOOL(hAPP(hAPP(c_member(_1019569), _1019573), _1019571))), -(_1019571 = c_Orderings_Obot__class_Obot(tc_fun(_1019569, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1019569, hAPP(hAPP(c_Set_Oinsert(_1019569), _1019573), _1019571)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1019569), _1019573), c_Big__Operators_Olattice__class_OSup__fin(_1019569, _1019571)))], (17094 ^ _779854) ^ [_1088458, _1088460, _1088462, _1088464, _1088466] : [class_Groups_Ocomm__monoid__mult(_1088458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088460), _1088462)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088460), _1088464)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088460, tc_HOL_Obool)), _1088462), _1088464) = c_Orderings_Obot__class_Obot(tc_fun(_1088460, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088460, _1088458), _1088466), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088460, tc_HOL_Obool)), _1088462), _1088464)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088458), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088460, _1088458), _1088466), _1088462)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088460, _1088458), _1088466), _1088464)))], (16391 ^ _779854) ^ [_1074779, _1074781, _1074783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074783), _1074781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074779), _1074781)), _1074783)))], (32479 ^ _779854) ^ [_1364285] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1364285)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1364285)], (4886 ^ _779854) ^ [_854486, _854488, _854490, _854492] : [-(c_List_Olistrel(_854492, _854488) = c_List_Olistrel(_854490, _854486)), _854492 = _854490, _854488 = _854486], (10781 ^ _779854) ^ [_963884, _963886, _963888, _963890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963884, tc_HOL_Obool)), _963886), _963888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963884, tc_HOL_Obool)), _963888), _963890)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963884, tc_HOL_Obool)), _963888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963884, tc_HOL_Obool)), _963890), _963886)) = _963886)], (10085 ^ _779854) ^ [_950208, _950210, _950212] : [class_Orderings_Olinorder(_950208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950208), _950210), _950212)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_950208), _950212), _950210) = _950210)], (51120 ^ _779854) ^ [_1813447, _1813449, _1813451] : [hBOOL(hAPP(hAPP(c_member(_1813447), _1813449), c_Quotient_ORespects(_1813447, _1813451))), -(hBOOL(hAPP(hAPP(_1813451, _1813449), _1813449)))], (31948 ^ _779854) ^ [_1354634] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1354634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1354634)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28868 ^ _779854) ^ [_1301224, _1301226, _1301228] : [class_Rings_Oring__1(_1301224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1301226), _1301228)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1301224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1301228), _1301226)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1301224), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1301224), _1301228)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1301224), _1301226)))], (50457 ^ _779854) ^ [_1799502, _1799504, _1799506, _1799508, _1799510] : [c_Fun_Oinj__on(_1799502, _1799504, _1799506, c_Orderings_Otop__class_Otop(tc_fun(_1799502, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1799504, _1799508, _1799502, hAPP(c_Fun_Ocomp(_1799502, _1799508, _1799504, _1799510), c_Hilbert__Choice_Oinv__into(_1799502, _1799504, c_Orderings_Otop__class_Otop(tc_fun(_1799502, tc_HOL_Obool)), _1799506))), _1799506) = _1799510)], (452 ^ _779854) ^ [_786672, _786674, _786676, _786678, _786680, _786682] : [-(c_Relation_Osingle__valued(_786680, _786676, _786672)), c_Relation_Osingle__valued(_786682, _786678, _786674), _786682 = _786680, _786678 = _786676, _786674 = _786672], (16768 ^ _779854) ^ [_1082059, _1082061, _1082063, _1082065] : [class_Orderings_Olinorder(_1082059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082059), _1082061)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1082059, _1082059, c_Orderings_Oord__class_Omin(_1082059)), _1082063), hAPP(hAPP(c_Set_Oinsert(_1082059), _1082065), _1082061)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1082059), _1082065), hAPP(hAPP(c_Finite__Set_Ofold(_1082059, _1082059, c_Orderings_Oord__class_Omin(_1082059)), _1082063), _1082061)))], (9344 ^ _779854) ^ [_935776, _935778, _935780] : [class_Orderings_Oorder(_935776), 9347 ^ _779854 : [(9354 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935776), _935778), _935780))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_935776, _935778, _935780) = c_Orderings_Obot__class_Obot(tc_fun(_935776, tc_HOL_Obool)))], (9348 ^ _779854) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_935776, _935778, _935780) = c_Orderings_Obot__class_Obot(tc_fun(_935776, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935776), _935778), _935780))]]], (13807 ^ _779854) ^ [_1022752, _1022754, _1022756] : [class_Orderings_Olinorder(_1022752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022752), _1022754)), 13814 ^ _779854 : [(13821 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022752, tc_HOL_Obool)), _1022754), hAPP(hAPP(c_Set_Oinsert(_1022752), _1022756), c_Orderings_Obot__class_Obot(tc_fun(_1022752, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1022752, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1022752, hAPP(hAPP(c_Set_Oinsert(_1022752), _1022756), _1022754)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1022752), _1022756), c_Big__Operators_Olinorder__class_OMax(_1022752, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022752, tc_HOL_Obool)), _1022754), hAPP(hAPP(c_Set_Oinsert(_1022752), _1022756), c_Orderings_Obot__class_Obot(tc_fun(_1022752, tc_HOL_Obool)))))))], (13815 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022752, tc_HOL_Obool)), _1022754), hAPP(hAPP(c_Set_Oinsert(_1022752), _1022756), c_Orderings_Obot__class_Obot(tc_fun(_1022752, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1022752, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1022752, hAPP(hAPP(c_Set_Oinsert(_1022752), _1022756), _1022754)) = _1022756)]]], (52445 ^ _779854) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (1620 ^ _779854) ^ [_803056, _803058] : [-(class_Groups_Ocancel__semigroup__add(_803056)), _803058 = _803056, class_Groups_Ocancel__semigroup__add(_803058)], (48724 ^ _779854) ^ [] : [-(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)))], (52595 ^ _779854) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (47766 ^ _779854) ^ [_1740570, _1740572] : [-(c_List_OdropWhile(_1740570, _1740572, c_List_Olist_ONil(_1740570)) = c_List_Olist_ONil(_1740570))], (25759 ^ _779854) ^ [_1248098, _1248100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248098), _1248100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1248100), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21887 ^ _779854) ^ [_1175367, _1175369, _1175371] : [class_Rings_Odivision__ring(_1175367), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1175367), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175367), _1175369), _1175371)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175367), hAPP(c_Groups_Ouminus__class_Ouminus(_1175367), _1175369)), _1175371))], (548 ^ _779854) ^ [_788082, _788084] : [-(class_Lattices_Oab__semigroup__idem__mult(_788082)), _788084 = _788082, class_Lattices_Oab__semigroup__idem__mult(_788084)], (18685 ^ _779854) ^ [_1117797] : [class_Rings_Ozero__neq__one(_1117797), c_Groups_Ozero__class_Ozero(_1117797) = c_Groups_Oone__class_Oone(_1117797)], (16539 ^ _779854) ^ [_1077877, _1077879, _1077881] : [class_Lattices_Oab__semigroup__idem__mult(_1077877), hAPP(_1077879, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077877), 16544 ^ [_1077877, _1077879, _1077881]), 16545 ^ [_1077877, _1077879, _1077881])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077877), hAPP(_1077879, 16544 ^ [_1077877, _1077879, _1077881])), hAPP(_1077879, 16545 ^ [_1077877, _1077879, _1077881])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077877), _1077881)), -(_1077881 = c_Orderings_Obot__class_Obot(tc_fun(_1077877, tc_HOL_Obool))), -(hAPP(_1077879, hAPP(c_Finite__Set_Ofold1(_1077877, c_Groups_Otimes__class_Otimes(_1077877)), _1077881)) = hAPP(c_Finite__Set_Ofold1(_1077877, c_Groups_Otimes__class_Otimes(_1077877)), hAPP(c_Set_Oimage(_1077877, _1077877, _1077879), _1077881)))], (5238 ^ _779854) ^ [_859958, _859960, _859962, _859964, _859966, _859968] : [-(c_Lazy__Sequence_Obind(_859968, _859964, _859960) = c_Lazy__Sequence_Obind(_859966, _859962, _859958)), _859968 = _859966, _859964 = _859962, _859960 = _859958], (21483 ^ _779854) ^ [_1167204, _1167206, _1167208, _1167210, _1167212] : [class_Groups_Ocomm__monoid__add(_1167204), hBOOL(hAPP(c_Finite__Set_Ofinite(_1167206), _1167208)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1167206), _1167210)), 21497 ^ _779854 : [(21500 ^ _779854) ^ [] : [hAPP(_1167212, 21496 ^ [_1167204, _1167206, _1167208, _1167210, _1167212]) = c_Groups_Ozero__class_Ozero(_1167204)], (21498 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1167206), 21496 ^ [_1167204, _1167206, _1167208, _1167210, _1167212]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1167206, tc_HOL_Obool)), _1167208), _1167210))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1167206, _1167204), _1167212), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1167206, tc_HOL_Obool)), _1167208), _1167210)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167204), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1167206, _1167204), _1167212), _1167208)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1167206, _1167204), _1167212), _1167210)))], (1650 ^ _779854) ^ [_803431, _803433] : [-(class_Groups_Oab__semigroup__mult(_803431)), _803433 = _803431, class_Groups_Oab__semigroup__mult(_803433)], (49792 ^ _779854) ^ [_1786813, _1786815, _1786817, _1786819, _1786821] : [c_Predicate_Otransp(_1786813, _1786815), hBOOL(hAPP(hAPP(_1786815, _1786817), _1786819)), hBOOL(hAPP(hAPP(_1786815, _1786819), _1786821)), -(hBOOL(hAPP(hAPP(_1786815, _1786817), _1786821)))], (27677 ^ _779854) ^ [_1280787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1280787), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1280787) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34793 ^ _779854) ^ [_1426498, _1426500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426498), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1426500, _1426498) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426500), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426498)))], (43640 ^ _779854) ^ [_1649631, _1649633] : [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), _1649631), _1649633))), 43643 ^ _779854 : [(43650 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1649631), _1649633))), -(c_List_Oupto(_1649631, _1649633) = c_List_Olist_ONil(tc_Int_Oint))], (43644 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1649631), _1649633)), -(c_List_Oupto(_1649631, _1649633) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1649631), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1649631), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1649633)))]]], (17873 ^ _779854) ^ [_1103513, _1103515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103513), _1103515)), -(hAPP(c_Nat_OSuc, _1103513) = _1103515), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103513)), _1103515)))], (48459 ^ _779854) ^ [_1756255, _1756257, _1756259] : [c_List_Olist__ex(_1756255, _1756257, _1756259), 48463 ^ _779854 : [(48466 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1756257, 48462 ^ [_1756255, _1756257, _1756259])))], (48464 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756255), 48462 ^ [_1756255, _1756257, _1756259]), hAPP(c_List_Oset(_1756255), _1756259))))]]], (15832 ^ _779854) ^ [_1063650, _1063652] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063650), _1063652) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063652), _1063650))], (45468 ^ _779854) ^ [_1690794, _1690796, _1690798, _1690800, _1690802] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690794)), _1690796) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690798)), _1690800), 45471 ^ _779854 : [(45480 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1690794, _1690798), _1690796), _1690800) = _1690802), hAPP(hAPP(c_List_Omap(tc_prod(_1690794, _1690798), _1690794), c_Product__Type_Ofst(_1690794, _1690798)), _1690802) = _1690796, hAPP(hAPP(c_List_Omap(tc_prod(_1690794, _1690798), _1690798), c_Product__Type_Osnd(_1690794, _1690798)), _1690802) = _1690800], (45472 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Ozip(_1690794, _1690798), _1690796), _1690800) = _1690802, 45475 ^ _779854 : [(45478 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1690794, _1690798), _1690798), c_Product__Type_Osnd(_1690794, _1690798)), _1690802) = _1690800)], (45476 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1690794, _1690798), _1690794), c_Product__Type_Ofst(_1690794, _1690798)), _1690802) = _1690796)]]]]], (44987 ^ _779854) ^ [_1679608, _1679610, _1679612] : [-(c_List_Olast(_1679608, hAPP(hAPP(c_List_Oappend(_1679608), _1679610), hAPP(hAPP(c_List_Olist_OCons(_1679608), _1679612), c_List_Olist_ONil(_1679608)))) = _1679612)], (26705 ^ _779854) ^ [_1264854, _1264856, _1264858, _1264860] : [class_Divides_Osemiring__div(_1264854), -(_1264856 = c_Groups_Ozero__class_Ozero(_1264854)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1264854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264854), _1264856), _1264858)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264854), _1264856), _1264860)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1264854), _1264858), _1264860))], (38646 ^ _779854) ^ [_1516108, _1516110, _1516112, _1516114, _1516116, _1516118] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1516108, _1516110), _1516110, tc_prod(_1516112, _1516114), c_Product__Type_Osnd(_1516108, _1516110)), c_Product__Type_Omap__pair(_1516112, _1516108, _1516114, _1516110, _1516116, _1516118)) = hAPP(c_Fun_Ocomp(_1516114, _1516110, tc_prod(_1516112, _1516114), _1516118), c_Product__Type_Osnd(_1516112, _1516114)))], (45545 ^ _779854) ^ [_1692526] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1692526)) = _1692526)], (46659 ^ _779854) ^ [_1718704, _1718706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718704), _1718706)), -(c_List_Oupt(_1718704, _1718706) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1718704), c_List_Oupt(hAPP(c_Nat_OSuc, _1718704), _1718706)))], (28214 ^ _779854) ^ [_1290035, _1290037] : [_1290035 = _1290037, -(c_Int_OBit1(_1290035) = c_Int_OBit1(_1290037))], (5928 ^ _779854) ^ [_873703, _873705, _873707, _873709] : [class_Orderings_Oord(_873703), _873705 = _873707, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873703), _873707), _873709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873703), _873705), _873709)))], (17959 ^ _779854) ^ [_1104867, _1104869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104867), _1104869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104867)), hAPP(c_Nat_OSuc, _1104869))))], (41917 ^ _779854) ^ [_1604700, _1604702, _1604704, _1604706, _1604708] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604700, _1604700)), hAPP(hAPP(c_Product__Type_OPair(_1604700, _1604700), _1604702), _1604704)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604700, _1604700), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604706)), _1604708))), 41921 ^ _779854 : [(41924 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604700, _1604700)), hAPP(hAPP(c_Product__Type_OPair(_1604700, _1604700), 41920 ^ [_1604700, _1604702, _1604704, _1604706, _1604708]), _1604704)), _1604708)))], (41922 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604700, _1604700)), hAPP(hAPP(c_Product__Type_OPair(_1604700, _1604700), _1604702), 41920 ^ [_1604700, _1604702, _1604704, _1604706, _1604708])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604700, _1604700), tc_HOL_Obool), _1604706), _1604708))))]]], (26149 ^ _779854) ^ [_1255114, _1255116, _1255118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255114)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1255116), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1255118)), 26159 ^ _779854 : [(26165 ^ _779854) ^ [] : [-(_1255116 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26161 ^ [_1255114, _1255116, _1255118]), 26158 ^ [_1255114, _1255116, _1255118]))], (26163 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26161 ^ [_1255114, _1255116, _1255118]), _1255118)))], (26160 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26158 ^ [_1255114, _1255116, _1255118]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1255114))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1255116), _1255114) = _1255116)], (39945 ^ _779854) ^ [_1555675, _1555677, _1555679, _1555681] : [hBOOL(hAPP(hAPP(c_member(_1555675), _1555681), hAPP(c_Relation_ODomain(_1555675, _1555677), _1555679))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1555675, _1555677, hAPP(hAPP(c_COMBC(_1555675, tc_fun(tc_prod(_1555675, _1555677), tc_HOL_Obool), tc_fun(_1555677, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555677, tc_fun(tc_fun(tc_prod(_1555675, _1555677), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555675, _1555677), tc_HOL_Obool), tc_fun(_1555677, tc_HOL_Obool)), _1555675), c_COMBC(_1555677, tc_fun(tc_prod(_1555675, _1555677), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555677, tc_prod(_1555675, _1555677)), tc_fun(_1555677, tc_fun(tc_fun(tc_prod(_1555675, _1555677), tc_HOL_Obool), tc_HOL_Obool)), _1555675), hAPP(c_COMBB(tc_prod(_1555675, _1555677), tc_fun(tc_fun(tc_prod(_1555675, _1555677), tc_HOL_Obool), tc_HOL_Obool), _1555677), c_member(tc_prod(_1555675, _1555677)))), c_Product__Type_OPair(_1555675, _1555677)))), _1555679)), _1555681)))], (41084 ^ _779854) ^ [_1583948, _1583950] : [-(hAPP(c_Relation_ORange(_1583948, _1583948), c_Transitive__Closure_Ortrancl(_1583948, _1583950)) = c_Orderings_Otop__class_Otop(tc_fun(_1583948, tc_HOL_Obool)))], (6421 ^ _779854) ^ [_882245, _882247, _882249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882245, tc_HOL_Obool)), _882247), _882249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882245, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882245, tc_HOL_Obool)), _882249)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882245, tc_HOL_Obool)), _882247))))], (49261 ^ _779854) ^ [_1773223, _1773225, _1773227, _1773229] : [49262 ^ _779854 : [(49265 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1773223), _1773227), _1773229))], (49263 ^ _779854) ^ [] : [_1773225 = _1773229]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1773223), hAPP(hAPP(c_List_Olist_OCons(_1773223), _1773225), _1773227)), _1773229)))], (47258 ^ _779854) ^ [_1729738, _1729740, _1729742, _1729744, _1729746] : [class_Orderings_Olinorder(_1729738), c_Fun_Oinj__on(_1729740, _1729738, _1729742, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1729740, tc_HOL_Obool)), hAPP(c_List_Oset(_1729740), _1729744)), hAPP(c_List_Oset(_1729740), _1729746))), c_List_Olinorder__class_Osorted(_1729738, hAPP(hAPP(c_List_Omap(_1729740, _1729738), _1729742), _1729744)), hBOOL(hAPP(c_List_Odistinct(_1729738), hAPP(hAPP(c_List_Omap(_1729740, _1729738), _1729742), _1729744))), c_List_Olinorder__class_Osorted(_1729738, hAPP(hAPP(c_List_Omap(_1729740, _1729738), _1729742), _1729746)), hBOOL(hAPP(c_List_Odistinct(_1729738), hAPP(hAPP(c_List_Omap(_1729740, _1729738), _1729742), _1729746))), hAPP(c_List_Oset(_1729740), _1729744) = hAPP(c_List_Oset(_1729740), _1729746), -(_1729744 = _1729746)], (46232 ^ _779854) ^ [_1707579, _1707581, _1707583] : [-(hAPP(c_List_Oset(_1707579), hAPP(c_List_OremoveAll(_1707579, _1707581), _1707583)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1707579, tc_HOL_Obool)), hAPP(c_List_Oset(_1707579), _1707583)), hAPP(hAPP(c_Set_Oinsert(_1707579), _1707581), c_Orderings_Obot__class_Obot(tc_fun(_1707579, tc_HOL_Obool)))))], (28080 ^ _779854) ^ [_1287836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1287836)), -(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, _1287836))))], (31192 ^ _779854) ^ [_1342342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1342342)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1342342))))], (32916 ^ _779854) ^ [_1374950, _1374952, _1374954, _1374956] : [_1374950 = c_Orderings_Obot__class_Obot(tc_fun(_1374952, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1374952, tc_fun(_1374954, tc_HOL_Obool)), _1374950), hAPP(c_COMBK(tc_fun(_1374954, tc_HOL_Obool), _1374952), _1374956)) = c_Orderings_Otop__class_Otop(tc_fun(_1374954, tc_HOL_Obool)))], (39999 ^ _779854) ^ [_1556893, _1556895] : [-(hAPP(c_List_Olexn(_1556893, _1556895), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1556893), tc_List_Olist(_1556893)), tc_HOL_Obool)))], (52413 ^ _779854) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (31906 ^ _779854) ^ [_1353962, _1353964] : [class_Rings_Olinordered__idom(_1353962), 31909 ^ _779854 : [(31916 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1353964), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353962), hAPP(c_Int_Oring__1__class_Oof__int(_1353962), _1353964)), c_Groups_Ozero__class_Ozero(_1353962))))], (31910 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353962), hAPP(c_Int_Oring__1__class_Oof__int(_1353962), _1353964)), c_Groups_Ozero__class_Ozero(_1353962))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1353964), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (32101 ^ _779854) ^ [_1357354, _1357356] : [class_Groups_Oordered__ab__group__add__abs(_1357354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357354), c_Groups_Ozero__class_Ozero(_1357354)), _1357356)), -(hAPP(c_Groups_Oabs__class_Oabs(_1357354), _1357356) = _1357356)], (16449 ^ _779854) ^ [_1075921, _1075923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075921), _1075923)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075923), _1075921)), _1075921) = _1075923)], (52711 ^ _779854) ^ [_1839221, _1839223] : [-(hBOOL(_1839221)), -(hBOOL(hAPP(hAPP(c_fimplies, _1839221), _1839223)))], (34443 ^ _779854) ^ [_1418604, _1418606] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1418604) = hAPP(c_Nat_OSuc, _1418606), -(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(_1418604))), 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)), _1418606))))))], (3282 ^ _779854) ^ [_829010, _829012, _829014, _829016] : [-(c_Random_Oselect(_829016, _829012) = c_Random_Oselect(_829014, _829010)), _829016 = _829014, _829012 = _829010], (28114 ^ _779854) ^ [_1288463, _1288465] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1288463))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1288463)), _1288465) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1288465))], (39100 ^ _779854) ^ [_1529112, _1529114, _1529116, _1529118] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1529112, _1529114), _1529116), _1529118) = hAPP(c_Set_OCollect(tc_prod(_1529114, _1529114)), hAPP(c_Product__Type_Oprod_Oprod__case(_1529114, _1529114, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1529114, tc_fun(tc_prod(_1529112, _1529112), tc_HOL_Obool), tc_fun(_1529114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529114, tc_fun(tc_fun(tc_prod(_1529112, _1529112), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529112, _1529112), tc_HOL_Obool), tc_fun(_1529114, tc_HOL_Obool)), _1529114), c_COMBC(_1529114, tc_fun(tc_prod(_1529112, _1529112), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529114, tc_prod(_1529112, _1529112)), tc_fun(_1529114, tc_fun(tc_fun(tc_prod(_1529112, _1529112), tc_HOL_Obool), tc_HOL_Obool)), _1529114), hAPP(c_COMBB(tc_prod(_1529112, _1529112), tc_fun(tc_fun(tc_prod(_1529112, _1529112), tc_HOL_Obool), tc_HOL_Obool), _1529114), c_member(tc_prod(_1529112, _1529112)))), hAPP(hAPP(c_COMBC(_1529114, tc_fun(_1529114, _1529112), tc_fun(_1529114, tc_prod(_1529112, _1529112))), hAPP(hAPP(c_COMBB(tc_fun(_1529112, tc_prod(_1529112, _1529112)), tc_fun(tc_fun(_1529114, _1529112), tc_fun(_1529114, tc_prod(_1529112, _1529112))), _1529114), c_COMBB(_1529112, tc_prod(_1529112, _1529112), _1529114)), hAPP(hAPP(c_COMBB(_1529112, tc_fun(_1529112, tc_prod(_1529112, _1529112)), _1529114), c_Product__Type_OPair(_1529112, _1529112)), _1529118))), _1529118)))), _1529116))))], (18911 ^ _779854) ^ [_1121023, _1121025, _1121027] : [18912 ^ _779854 : [(18915 ^ _779854) ^ [] : [_1121025 = _1121027], (18913 ^ _779854) ^ [] : [_1121023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1121023), _1121025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1121023), _1121027))], (14701 ^ _779854) ^ [_1040442, _1040444, _1040446] : [class_Orderings_Olinorder(_1040442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040442), _1040444)), hBOOL(hAPP(hAPP(c_member(_1040442), _1040446), _1040444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040442), hAPP(c_Finite__Set_Ofold1(_1040442, c_Orderings_Oord__class_Omin(_1040442)), _1040444)), _1040446)))], (30503 ^ _779854) ^ [_1330693, _1330695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330693), _1330695)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330693, _1330695) = _1330693)], (49196 ^ _779854) ^ [_1771592, _1771594, _1771596] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1771592), _1771594))), -(hBOOL(hAPP(hAPP(_1771596, _1771592), _1771594))), 49203 ^ _779854 : [(49206 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 49201 ^ [_1771592, _1771594, _1771596]), 49202 ^ [_1771592, _1771594, _1771596]))), -(hBOOL(hAPP(hAPP(_1771596, 49201 ^ [_1771592, _1771594, _1771596]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 49202 ^ [_1771592, _1771594, _1771596]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49212 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1771596, 49201 ^ [_1771592, _1771594, _1771596]), 49202 ^ [_1771592, _1771594, _1771596]))], (49204 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 49201 ^ [_1771592, _1771594, _1771596]), 49202 ^ [_1771592, _1771594, _1771596]))))]]], (25661 ^ _779854) ^ [_1246346] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246346)) = _1246346)], (41765 ^ _779854) ^ [_1600431, _1600433] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600431, _1600431), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1600433) = _1600433)], (47681 ^ _779854) ^ [_1738751, _1738753, _1738755, _1738757, _1738759] : [class_Orderings_Olinorder(_1738751), c_List_Olinorder__class_Osorted(_1738751, hAPP(c_List_Orev(_1738751), hAPP(hAPP(c_List_Omap(_1738753, _1738751), _1738755), _1738757))), -(hAPP(c_List_Ofilter(_1738753, hAPP(hAPP(c_COMBB(_1738751, tc_HOL_Obool, _1738753), hAPP(c_Orderings_Oord__class_Oless(_1738751), _1738759)), _1738755)), _1738757) = c_List_OtakeWhile(_1738753, hAPP(hAPP(c_COMBB(_1738751, tc_HOL_Obool, _1738753), hAPP(c_Orderings_Oord__class_Oless(_1738751), _1738759)), _1738755), _1738757))], (18444 ^ _779854) ^ [_1114007, _1114009, _1114011, _1114013, _1114015] : [class_Groups_Ocomm__monoid__mult(_1114007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114009), _1114011)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114009), _1114013)), 18458 ^ _779854 : [(18461 ^ _779854) ^ [] : [hAPP(_1114015, 18457 ^ [_1114007, _1114009, _1114011, _1114013, _1114015]) = c_Groups_Oone__class_Oone(_1114007)], (18459 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1114009), 18457 ^ [_1114007, _1114009, _1114011, _1114013, _1114015]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1114009, tc_HOL_Obool)), _1114011), _1114013))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1114009, _1114007), _1114015), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1114009, tc_HOL_Obool)), _1114011), _1114013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114007), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1114009, _1114007), _1114015), _1114011)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1114009, _1114007), _1114015), _1114013)))], (46573 ^ _779854) ^ [_1716536, _1716538] : [-(c_Random_Oselect__weight(_1716536, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1716536), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1716536, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1716536, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1716536)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1716538)) = c_Random_Oselect__weight(_1716536, _1716538))], (29005 ^ _779854) ^ [_1303412] : [-(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, _1303412)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15262 ^ _779854) ^ [_1051986, _1051988, _1051990, _1051992] : [class_Groups_Oordered__ab__semigroup__add(_1051986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051986), _1051988), _1051990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051986), _1051988), _1051992)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051986), _1051990), _1051992))))], (36219 ^ _779854) ^ [_1455640, _1455642, _1455644, _1455646, _1455648, _1455650] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1455640, _1455642), _1455642, _1455644), hAPP(hAPP(c_COMBB(_1455646, tc_fun(_1455642, _1455644), tc_prod(_1455640, _1455642)), _1455648), hAPP(hAPP(c_COMBB(_1455640, _1455646, tc_prod(_1455640, _1455642)), _1455650), c_Product__Type_Ofst(_1455640, _1455642)))), c_Product__Type_Osnd(_1455640, _1455642)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1455640, _1455642, _1455644), hAPP(hAPP(c_COMBB(_1455646, tc_fun(_1455642, _1455644), _1455640), _1455648), _1455650)))], (33579 ^ _779854) ^ [_1395835, _1395837, _1395839] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395835, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1395835, tc_HOL_Obool), _1395837)), _1395839) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1395835, tc_HOL_Obool), tc_fun(_1395835, tc_HOL_Obool)), _1395837), hAPP(hAPP(c_COMBC(tc_fun(_1395835, tc_HOL_Obool), tc_fun(_1395835, tc_HOL_Obool), tc_fun(_1395835, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395835, tc_HOL_Obool))), _1395839)))], (21639 ^ _779854) ^ [_1170409, _1170411, _1170413] : [class_Rings_Oring__1(_1170409), hBOOL(hAPP(hAPP(c_member(_1170409), _1170411), c_Int_Oring__1__class_OInts(_1170409))), hBOOL(hAPP(hAPP(c_member(_1170409), _1170413), c_Int_Oring__1__class_OInts(_1170409))), -(hBOOL(hAPP(hAPP(c_member(_1170409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1170409), _1170411), _1170413)), c_Int_Oring__1__class_OInts(_1170409))))], (3250 ^ _779854) ^ [_828488, _828490, _828492, _828494, _828496, _828498, _828500, _828502] : [-(c_Nitpick_Osetsum_H(_828502, _828498, _828494, _828490) = c_Nitpick_Osetsum_H(_828500, _828496, _828492, _828488)), _828502 = _828500, _828498 = _828496, _828494 = _828492, _828490 = _828488], (38386 ^ _779854) ^ [_1508739, _1508741, _1508743, _1508745, _1508747, _1508749] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508739, _1508741)), hAPP(hAPP(c_Product__Type_OPair(_1508739, _1508741), _1508743), _1508745)), hAPP(hAPP(c_Product__Type_OSigma(_1508739, _1508741), _1508747), _1508749))), -(hBOOL(hAPP(hAPP(c_member(_1508739), _1508743), _1508747)))], (38807 ^ _779854) ^ [_1520025, _1520027] : [-(c_Relation_Orefl__on(_1520025, _1520027, c_Relation_OId__on(_1520025, _1520027)))], (25685 ^ _779854) ^ [] : [-(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))], (26554 ^ _779854) ^ [_1262526, _1262528, _1262530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262526)), 26560 ^ _779854 : [(26563 ^ _779854) ^ [] : [hBOOL(hAPP(_1262528, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26559 ^ [_1262526, _1262528, _1262530]), _1262526)))], (26561 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1262528, 26559 ^ [_1262526, _1262528, _1262530])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262530)), 26568 ^ _779854 : [(26569 ^ _779854) ^ [_1262815] : [hBOOL(hAPP(_1262528, _1262815)), -(hBOOL(hAPP(_1262528, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1262530), _1262526)))))]]], (12098 ^ _779854) ^ [_990613, _990615, _990617, _990619] : [hBOOL(hAPP(hAPP(c_member(_990613), _990615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990613, tc_HOL_Obool)), _990617), _990619))), hBOOL(hAPP(hAPP(c_member(_990613), _990615), _990619))], (51455 ^ _779854) ^ [_1821845, _1821847, _1821849, _1821851] : [-(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), _1821845, _1821847)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821849, _1821851)))), 51456 ^ _779854 : [(51459 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821849), _1821845)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821847), _1821851))], (51457 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821845), _1821847)))]]], (3638 ^ _779854) ^ [_834530, _834532, _834534, _834536, _834538, _834540, _834542, _834544, _834546, _834548] : [-(c_List_Ofoldr(_834548, _834544, _834540, _834536, _834532) = c_List_Ofoldr(_834546, _834542, _834538, _834534, _834530)), _834548 = _834546, _834544 = _834542, _834540 = _834538, _834536 = _834534, _834532 = _834530], (12696 ^ _779854) ^ [_1002245, _1002247, _1002249, _1002251, _1002253] : [c_Fun_Oinj__on(_1002245, _1002247, _1002249, hAPP(hAPP(c_Set_Oinsert(_1002245), _1002251), _1002253)), 12699 ^ _779854 : [(12702 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1002247), hAPP(_1002249, _1002251)), hAPP(c_Set_Oimage(_1002245, _1002247, _1002249), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002245, tc_HOL_Obool)), _1002253), hAPP(hAPP(c_Set_Oinsert(_1002245), _1002251), c_Orderings_Obot__class_Obot(tc_fun(_1002245, tc_HOL_Obool)))))))], (12700 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_1002245, _1002247, _1002249, _1002253))]]], (30129 ^ _779854) ^ [_1323476, _1323478, _1323480] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1323476), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323478, _1323480)), _1323480) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1323476), _1323478), _1323480))], (10009 ^ _779854) ^ [_948867, _948869, _948871, _948873] : [class_Orderings_Olinorder(_948867), 10012 ^ _779854 : [(10013 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948867), hAPP(hAPP(c_Orderings_Oord__class_Omin(_948867), _948869), _948871)), _948873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948867), _948869), _948873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948867), _948871), _948873)))], (10023 ^ _779854) ^ [] : [10024 ^ _779854 : [(10027 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948867), _948871), _948873))], (10025 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948867), _948869), _948873))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948867), hAPP(hAPP(c_Orderings_Oord__class_Omin(_948867), _948869), _948871)), _948873)))]]], (12314 ^ _779854) ^ [_994629, _994631, _994633, _994635] : [-(hBOOL(hAPP(hAPP(c_member(_994629), _994631), _994633))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994629, tc_HOL_Obool)), _994633), hAPP(hAPP(c_Set_Oinsert(_994629), _994631), _994635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994629, tc_HOL_Obool)), _994633), _994635))], (15198 ^ _779854) ^ [_1050494, _1050496, _1050498, _1050500, _1050502, _1050504] : [class_Rings_Oordered__ring(_1050494), 15201 ^ _779854 : [(15208 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050494), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050494), _1050496), _1050502)), _1050498)), _1050500)), _1050504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050494), _1050496), _1050498)), _1050500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050494), _1050502), _1050498)), _1050504))))], (15202 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050494), _1050496), _1050498)), _1050500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050494), _1050502), _1050498)), _1050504))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050494), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050494), _1050496), _1050502)), _1050498)), _1050500)), _1050504)))]]], (39170 ^ _779854) ^ [_1531992, _1531994, _1531996] : [class_Lattices_Odistrib__lattice(_1531992), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531992), _1531994)), -(_1531994 = c_Orderings_Obot__class_Obot(tc_fun(_1531992, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1531992), _1531996), c_Big__Operators_Olattice__class_OSup__fin(_1531992, _1531994)) = c_Big__Operators_Olattice__class_OSup__fin(_1531992, hAPP(c_Set_OCollect(_1531992), hAPP(hAPP(c_COMBB(tc_fun(_1531992, tc_HOL_Obool), tc_HOL_Obool, _1531992), c_HOL_OEx(_1531992)), hAPP(hAPP(c_COMBC(_1531992, tc_fun(_1531992, tc_HOL_Obool), tc_fun(_1531992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531992, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1531992, tc_HOL_Obool), tc_fun(_1531992, tc_HOL_Obool)), _1531992), c_COMBS(_1531992, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531992, tc_HOL_Obool), tc_fun(_1531992, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1531992), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531992), c_fconj)), hAPP(hAPP(c_COMBC(_1531992, tc_fun(_1531992, _1531992), tc_fun(_1531992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531992, tc_HOL_Obool), tc_fun(tc_fun(_1531992, _1531992), tc_fun(_1531992, tc_HOL_Obool)), _1531992), c_COMBB(_1531992, tc_HOL_Obool, _1531992)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1531992), _1531996))))), hAPP(hAPP(c_COMBC(_1531992, tc_fun(_1531992, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531992)), _1531994))))))], (29505 ^ _779854) ^ [_1312067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1312067))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1312067)))], (52661 ^ _779854) ^ [_1838605] : [-(hBOOL(_1838605)), -(hBOOL(hAPP(c_fNot, _1838605)))], (31220 ^ _779854) ^ [_1342782] : [class_Int_Onumber__ring(_1342782), c_Int_Oiszero(_1342782, hAPP(c_Int_Onumber__class_Onumber__of(_1342782), c_Int_OMin))], (52363 ^ _779854) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (42518 ^ _779854) ^ [_1622763, _1622765, _1622767, _1622769] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622763), tc_List_Olist(_1622763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622763), tc_List_Olist(_1622763)), _1622765), _1622767)), c_List_Olistrel(_1622763, _1622769))), 42521 ^ _779854 : [(42524 ^ _779854) ^ [_1622992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622992), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622763)), _1622765))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622763, _1622763)), hAPP(hAPP(c_Product__Type_OPair(_1622763, _1622763), hAPP(hAPP(c_List_Onth(_1622763), _1622765), _1622992)), hAPP(hAPP(c_List_Onth(_1622763), _1622767), _1622992))), _1622769)))], (42522 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622763)), _1622765) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622763)), _1622767))]]], (34397 ^ _779854) ^ [_1417458] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1417458) = 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), _1417458), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (3190 ^ _779854) ^ [_827508, _827510, _827512, _827514] : [-(c_Big__Operators_Olinorder__class_OMax(_827514, _827510) = c_Big__Operators_Olinorder__class_OMax(_827512, _827508)), _827514 = _827512, _827510 = _827508], (7517 ^ _779854) ^ [_903803, _903805, _903807] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_903803, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_903803, tc_HOL_Obool), tc_HOL_Obool)), _903805), _903807)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903803, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_903803, tc_HOL_Obool), _903805)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_903803, tc_HOL_Obool), _903807)))], (52621 ^ _779854) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (35974 ^ _779854) ^ [_1450139, _1450141, _1450143, _1450145, _1450147, _1450149] : [c_Finite__Set_Ofolding(_1450139, _1450141, _1450143, _1450145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450139), _1450147)), hBOOL(hAPP(hAPP(c_member(_1450139), _1450149), _1450147)), -(hAPP(_1450145, _1450147) = hAPP(c_Fun_Ocomp(_1450141, _1450141, _1450141, hAPP(_1450145, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1450139, tc_HOL_Obool)), _1450147), hAPP(hAPP(c_Set_Oinsert(_1450139), _1450149), c_Orderings_Obot__class_Obot(tc_fun(_1450139, tc_HOL_Obool)))))), hAPP(_1450143, _1450149)))], (41935 ^ _779854) ^ [_1605320, _1605322, _1605324, _1605326, _1605328] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605320, _1605320)), hAPP(hAPP(c_Product__Type_OPair(_1605320, _1605320), _1605322), _1605324)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605320, _1605320), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1605326)), _1605328))), 41939 ^ _779854 : [(41942 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605320, _1605320)), hAPP(hAPP(c_Product__Type_OPair(_1605320, _1605320), 41938 ^ [_1605320, _1605322, _1605324, _1605326, _1605328]), _1605324)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605320, _1605320), tc_HOL_Obool), _1605326), _1605328))))], (41940 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605320, _1605320)), hAPP(hAPP(c_Product__Type_OPair(_1605320, _1605320), _1605322), 41938 ^ [_1605320, _1605322, _1605324, _1605326, _1605328])), _1605328)))]]], (39629 ^ _779854) ^ [_1548684, _1548686, _1548688, _1548690] : [c_Wellfounded_Owf(_1548684, _1548686), c_Wellfounded_Owf(_1548688, _1548690), -(c_Wellfounded_Owf(tc_prod(_1548684, _1548688), c_Wellfounded_Olex__prod(_1548684, _1548688, _1548686, _1548690)))], (50682 ^ _779854) ^ [_1804592, _1804594, _1804596, _1804598, _1804600] : [c_Fun_Obij__betw(_1804592, _1804594, _1804596, c_Orderings_Otop__class_Otop(tc_fun(_1804592, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804594, tc_HOL_Obool))), c_Fun_Obij__betw(_1804598, _1804592, _1804600, c_Orderings_Otop__class_Otop(tc_fun(_1804598, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804592, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1804598, _1804594, c_Orderings_Otop__class_Otop(tc_fun(_1804598, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1804592, _1804594, _1804598, _1804596), _1804600)) = hAPP(c_Fun_Ocomp(_1804592, _1804598, _1804594, c_Hilbert__Choice_Oinv__into(_1804598, _1804592, c_Orderings_Otop__class_Otop(tc_fun(_1804598, tc_HOL_Obool)), _1804600)), c_Hilbert__Choice_Oinv__into(_1804592, _1804594, c_Orderings_Otop__class_Otop(tc_fun(_1804592, tc_HOL_Obool)), _1804596)))], (43662 ^ _779854) ^ [_1649945] : [-(c_List_Olistset(_1649945, c_List_Olist_ONil(tc_fun(_1649945, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1649945)), c_List_Olist_ONil(_1649945)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1649945), tc_HOL_Obool))))], (43969 ^ _779854) ^ [_1657260, _1657262, _1657264] : [_1657260 = hAPP(hAPP(c_List_Oappend(_1657262), _1657264), _1657260), -(_1657264 = c_List_Olist_ONil(_1657262))], (49816 ^ _779854) ^ [_1787180, _1787182] : [-(c_Equiv__Relations_Oequivp(_1787180, _1787182)), c_Predicate_Oreflp(_1787180, _1787182), c_Predicate_Osymp(_1787180, _1787182), c_Predicate_Otransp(_1787180, _1787182)], (20948 ^ _779854) ^ [_1156784, _1156786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1156784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1156786)), -(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), _1156786), _1156784))))], (2784 ^ _779854) ^ [_821265, _821267, _821269, _821271, _821273, _821275] : [-(c_Predicate_ORangeP(_821275, _821271, _821267) = c_Predicate_ORangeP(_821273, _821269, _821265)), _821275 = _821273, _821271 = _821269, _821267 = _821265], (49854 ^ _779854) ^ [_1787701, _1787703] : [c_Equiv__Relations_Oequivp(_1787701, _1787703), 49857 ^ _779854 : [(49862 ^ _779854) ^ [] : [-(c_Predicate_Otransp(_1787701, _1787703))], (49860 ^ _779854) ^ [] : [-(c_Predicate_Osymp(_1787701, _1787703))], (49858 ^ _779854) ^ [] : [-(c_Predicate_Oreflp(_1787701, _1787703))]]], (18831 ^ _779854) ^ [_1119850] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119850), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1119850)], (34689 ^ _779854) ^ [_1424159, _1424161, _1424163, _1424165] : [class_Rings_Ocomm__semiring__1(_1424159), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424159), c_Groups_Oone__class_Oone(_1424159)), c_Groups_Oone__class_Oone(_1424159))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424159), hAPP(hAPP(c_COMBB(_1424159, _1424159, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1424159), _1424161)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1424159, _1424159), hAPP(hAPP(c_COMBB(_1424159, tc_fun(_1424159, _1424159), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1424159)), c_Nat_Osemiring__1__class_Oof__nat(_1424159))), _1424163))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1424165))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424159), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1424159), _1424165)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424159), _1424161), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424159), _1424161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424159), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1424159), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1424165), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1424163)))))], (46457 ^ _779854) ^ [_1713286] : [-(c_List_Otranspose(_1713286, c_List_Olist_ONil(tc_List_Olist(_1713286))) = c_List_Olist_ONil(tc_List_Olist(_1713286)))], (46449 ^ _779854) ^ [_1713051, _1713053, _1713055] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1713051), tc_List_Olist(_1713051)), c_List_Opartition(_1713051, _1713053, _1713055)) = hAPP(c_List_Ofilter(_1713051, _1713053), _1713055))], (48275 ^ _779854) ^ [_1752494, _1752496, _1752498, _1752500, _1752502] : [-(hAPP(hAPP(c_List_Olist_OCons(_1752494), _1752496), _1752498) = hAPP(c_List_Ofilter(_1752494, _1752500), _1752502)), 48276 ^ _779854 : [(48277 ^ _779854) ^ [_1752622, _1752624] : [_1752502 = hAPP(hAPP(c_List_Oappend(_1752494), _1752624), hAPP(hAPP(c_List_Olist_OCons(_1752494), _1752496), _1752622)), 48283 ^ _779854 : [(48286 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1752500, 48282 ^ [_1752494, _1752496, _1752498, _1752500, _1752502, _1752622, _1752624])))], (48284 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752494), 48282 ^ [_1752494, _1752496, _1752498, _1752500, _1752502, _1752622, _1752624]), hAPP(c_List_Oset(_1752494), _1752624))))]], hBOOL(hAPP(_1752500, _1752496)), _1752498 = hAPP(c_List_Ofilter(_1752494, _1752500), _1752622)]]], (38957 ^ _779854) ^ [_1523956, _1523958, _1523960, _1523962, _1523964] : [c_Relation_Orefl__on(_1523956, _1523958, _1523960), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523956, _1523956)), hAPP(hAPP(c_Product__Type_OPair(_1523956, _1523956), _1523962), _1523964)), _1523960)), -(hBOOL(hAPP(hAPP(c_member(_1523956), _1523964), _1523958)))], (5030 ^ _779854) ^ [_856716, _856718] : [_856718 = _856716, -(c_Fun_Oid(_856718) = c_Fun_Oid(_856716))], (29313 ^ _779854) ^ [_1308814, _1308816] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308814) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308816), -(_1308814 = _1308816)], (42103 ^ _779854) ^ [_1609946, _1609948, _1609950] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609946)), c_List_Osublist(_1609946, _1609948, _1609950)) = 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(_1609946)), _1609948)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1609950)))))], (15066 ^ _779854) ^ [_1047712, _1047714, _1047716, _1047718] : [class_Groups_Oab__semigroup__mult(_1047712), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047712), _1047714), _1047716)), _1047718) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047712), _1047714), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047712), _1047716), _1047718)))], (45675 ^ _779854) ^ [_1695494, _1695496] : [-(hBOOL(hAPP(c_List_Olistsp(_1695494, _1695496), c_List_Olist_ONil(_1695494))))], (9784 ^ _779854) ^ [_943993, _943995, _943997, _943999, _944001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943993, tc_HOL_Obool)), _943995), hAPP(c_Set_Oimage(_943997, _943993, _943999), _944001))), 9788 ^ _779854 : [(9791 ^ _779854) ^ [] : [-(_943995 = hAPP(c_Set_Oimage(_943997, _943993, _943999), 9787 ^ [_943993, _943995, _943997, _943999, _944001]))], (9789 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943997, tc_HOL_Obool)), 9787 ^ [_943993, _943995, _943997, _943999, _944001]), _944001)))]]], (43191 ^ _779854) ^ [_1640703, _1640705, _1640707, _1640709] : [hBOOL(hAPP(c_List_Odistinct(_1640703), _1640705)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1640707, _1640703)), hAPP(hAPP(c_List_Ozip(_1640707, _1640703), _1640709), _1640705))))], (10995 ^ _779854) ^ [_968649, _968651, _968653, _968655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968649, tc_HOL_Obool)), _968651), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_968649, tc_HOL_Obool)), _968653), _968655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968649, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968649, tc_HOL_Obool)), _968651), _968653)), _968655)))], (50692 ^ _779854) ^ [_1804877, _1804879, _1804881, _1804883, _1804885, _1804887] : [c_Fun_Obij__betw(_1804877, _1804879, _1804881, c_Orderings_Otop__class_Otop(tc_fun(_1804877, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804879, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1804877, _1804879, _1804881), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1804883, tc_fun(_1804877, tc_HOL_Obool)), _1804885), _1804887)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1804883, tc_fun(_1804879, tc_HOL_Obool)), _1804885), hAPP(hAPP(c_COMBB(tc_fun(_1804877, tc_HOL_Obool), tc_fun(_1804879, tc_HOL_Obool), _1804883), c_Set_Oimage(_1804877, _1804879, _1804881)), _1804887)))], (32798 ^ _779854) ^ [_1370607, _1370609, _1370611, _1370613, _1370615, _1370617] : [hBOOL(hAPP(hAPP(c_member(_1370607), _1370609), _1370611)), hBOOL(hAPP(hAPP(c_member(_1370613), _1370615), hAPP(_1370617, _1370609))), -(hBOOL(hAPP(hAPP(c_member(_1370613), _1370615), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1370607, tc_fun(_1370613, tc_HOL_Obool)), _1370611), _1370617))))], (47358 ^ _779854) ^ [_1731904, _1731906, _1731908] : [_1731906 = hAPP(hAPP(c_List_Olist_OCons(_1731904), _1731908), c_List_Olist_ONil(_1731904)), -(hAPP(c_List_Orev(_1731904), _1731906) = hAPP(hAPP(c_List_Olist_OCons(_1731904), _1731908), c_List_Olist_ONil(_1731904)))], (39743 ^ _779854) ^ [_1550671, _1550673, _1550675] : [c_Wellfounded_Owf(_1550671, _1550673), c_Wellfounded_Owf(_1550671, _1550675), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1550671, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1550671, _1550671), _1550673)), hAPP(c_Relation_ORange(_1550671, _1550671), _1550675)) = c_Orderings_Obot__class_Obot(tc_fun(_1550671, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1550671, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1550671, _1550671), tc_HOL_Obool)), _1550673), _1550675)))], (36615 ^ _779854) ^ [_1464487, _1464489, _1464491] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1464487, tc_HOL_Obool), tc_fun(_1464487, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1464487, tc_HOL_Obool), tc_fun(_1464487, tc_HOL_Obool)), _1464489), _1464491)), c_Wellfounded_Ofinite__psubset(_1464487)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1464487, tc_HOL_Obool)), _1464489), _1464491)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464487), _1464491))], (51354 ^ _779854) ^ [_1820077, _1820079, _1820081] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1820077), _1820079)), -(_1820079 = c_Orderings_Obot__class_Obot(tc_fun(_1820077, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1820077, _1820081, _1820079), 51361 ^ [_1820077, _1820079, _1820081])))], (5342 ^ _779854) ^ [_861622, _861624, _861626, _861628, _861630, _861632, _861634, _861636] : [-(c_Lazy__Sequence_Omap(_861636, _861632, _861628, _861624) = c_Lazy__Sequence_Omap(_861634, _861630, _861626, _861622)), _861636 = _861634, _861632 = _861630, _861628 = _861626, _861624 = _861622], (41845 ^ _779854) ^ [_1602599, _1602601] : [-(c_Transitive__Closure_Ortrancl(_1602599, _1602601) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1602599, _1602599), 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(_1602599, _1602599), tc_HOL_Obool), tc_fun(tc_prod(_1602599, _1602599), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1602599, _1602599), tc_HOL_Obool)), _1602601)))], (4490 ^ _779854) ^ [_848242, _848244] : [_848244 = _848242, -(c_Lazy__Sequence_Oyield(_848244) = c_Lazy__Sequence_Oyield(_848242))], (28499 ^ _779854) ^ [_1295079, _1295081] : [class_Rings_Olinordered__semidom(_1295079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295079), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295079), _1295081)), c_Groups_Ozero__class_Ozero(_1295079)))], (46697 ^ _779854) ^ [_1719327, _1719329] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1719327), _1719329)) = c_List_Oupt(_1719327, _1719329))], (43031 ^ _779854) ^ [_1637011, _1637013, _1637015, _1637017, _1637019] : [-(_1637011 = _1637013), -(hAPP(hAPP(c_List_Onth(_1637015), hAPP(hAPP(c_List_Olist__update(_1637015, _1637017), _1637011), _1637019)), _1637013) = hAPP(hAPP(c_List_Onth(_1637015), _1637017), _1637013))], (38368 ^ _779854) ^ [_1508253, _1508255] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508253, _1508253), tc_HOL_Obool)), c_Relation_OId__on(_1508253, _1508255)), hAPP(hAPP(c_Product__Type_OSigma(_1508253, _1508253), _1508255), hAPP(c_COMBK(tc_fun(_1508253, tc_HOL_Obool), _1508253), _1508255)))))], (15822 ^ _779854) ^ [_1063383, _1063385, _1063387] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063383), _1063385)), _1063387) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063383), _1063387)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063385), _1063387)))], (39339 ^ _779854) ^ [_1539286, _1539288] : [-(c_Product__Type_Omap__pair(_1539286, _1539286, _1539288, _1539288, c_Fun_Oid(_1539286), c_Fun_Oid(_1539288)) = c_Fun_Oid(tc_prod(_1539286, _1539288)))], (37180 ^ _779854) ^ [_1478814, _1478816, _1478818, _1478820, _1478822] : [hBOOL(hAPP(hAPP(c_member(_1478814), _1478816), hAPP(c_Relation_OImage(_1478818, _1478814, _1478820), _1478822))), 37184 ^ _779854 : [(37187 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478818), 37183 ^ [_1478814, _1478816, _1478818, _1478820, _1478822]), _1478822)))], (37185 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1478818, _1478814)), hAPP(hAPP(c_Product__Type_OPair(_1478818, _1478814), 37183 ^ [_1478814, _1478816, _1478818, _1478820, _1478822]), _1478816)), _1478820)))]]], (24348 ^ _779854) ^ [_1221467, _1221469, _1221471] : [class_Rings_Olinordered__semidom(_1221467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221467), c_Groups_Ozero__class_Ozero(_1221467)), _1221469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221467), _1221469), c_Groups_Oone__class_Oone(_1221467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221467), _1221469), hAPP(hAPP(c_Power_Opower__class_Opower(_1221467), _1221469), _1221471))), hAPP(hAPP(c_Power_Opower__class_Opower(_1221467), _1221469), _1221471))))], (33523 ^ _779854) ^ [_1391062, _1391064, _1391066, _1391068] : [hAPP(hAPP(c_COMBC(_1391062, tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_fun(_1391064, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391064, tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_fun(_1391064, tc_HOL_Obool)), _1391062), c_COMBC(_1391064, tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391064, tc_prod(_1391062, _1391064)), tc_fun(_1391064, tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool)), _1391062), hAPP(c_COMBB(tc_prod(_1391062, _1391064), tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool), _1391064), c_member(tc_prod(_1391062, _1391064)))), c_Product__Type_OPair(_1391062, _1391064)))), _1391066) = hAPP(hAPP(c_COMBC(_1391062, tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_fun(_1391064, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391064, tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_fun(_1391064, tc_HOL_Obool)), _1391062), c_COMBC(_1391064, tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391064, tc_prod(_1391062, _1391064)), tc_fun(_1391064, tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool)), _1391062), hAPP(c_COMBB(tc_prod(_1391062, _1391064), tc_fun(tc_fun(tc_prod(_1391062, _1391064), tc_HOL_Obool), tc_HOL_Obool), _1391064), c_member(tc_prod(_1391062, _1391064)))), c_Product__Type_OPair(_1391062, _1391064)))), _1391068), -(_1391066 = _1391068)], (33561 ^ _779854) ^ [_1394927, _1394929] : [-(c_Fun_Oinj__on(_1394927, _1394927, c_COMBI(_1394927), _1394929))], (28428 ^ _779854) ^ [_1293846, _1293848, _1293850] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293846)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293848)), _1293850)) = 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), _1293846), _1293848))), _1293850))], (29817 ^ _779854) ^ [_1317556, _1317558, _1317560] : [class_Rings_Olinordered__semidom(_1317556), hAPP(hAPP(c_Power_Opower__class_Opower(_1317556), _1317558), 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(_1317556), _1317560), 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(_1317556), c_Groups_Ozero__class_Ozero(_1317556)), _1317558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317556), c_Groups_Ozero__class_Ozero(_1317556)), _1317560)), -(_1317558 = _1317560)], (16433 ^ _779854) ^ [_1075632, _1075634, _1075636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075632), _1075634)), 16436 ^ _779854 : [(16443 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1075636), _1075632)), _1075634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075634), _1075632))))], (16437 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075634), _1075632))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1075636), _1075632)), _1075634)))]]], (38078 ^ _779854) ^ [_1500263, _1500265, _1500267, _1500269, _1500271] : [hBOOL(hAPP(_1500269, hAPP(_1500267, _1500271))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1500263, _1500265, _1500267), _1500269), _1500271)))], (5612 ^ _779854) ^ [_865727, _865729, _865731, _865733, _865735, _865737] : [-(c_COMBC(_865737, _865733, _865729) = c_COMBC(_865735, _865731, _865727)), _865737 = _865735, _865733 = _865731, _865729 = _865727], (34009 ^ _779854) ^ [_1408027, _1408029, _1408031, _1408033, _1408035] : [class_Groups_Ocomm__monoid__add(_1408027), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1408027), _1408029), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408031), _1408033)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408035), _1408033))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1408027), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1408027, tc_Nat_Onat), _1408029), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1408033))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408031), _1408035)))], (52639 ^ _779854) ^ [_1838309, _1838311] : [hBOOL(hAPP(hAPP(c_fequal, _1838309), _1838311)), -(_1838309 = _1838311)], (31382 ^ _779854) ^ [_1345467, _1345469, _1345471] : [-(hBOOL(hAPP(_1345467, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1345469, _1345471)))), 31385 ^ _779854 : [(31388 ^ _779854) ^ [] : [hBOOL(hAPP(_1345467, _1345469))], (31386 ^ _779854) ^ [] : [-(_1345471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 31389 ^ _779854 : [(31394 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31392 ^ [_1345467, _1345469, _1345471]), _1345471)))], (31396 ^ _779854) ^ [] : [-(_1345469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1345471), 31391 ^ [_1345467, _1345469, _1345471])), 31392 ^ [_1345467, _1345469, _1345471]))], (31398 ^ _779854) ^ [] : [hBOOL(hAPP(_1345467, 31392 ^ [_1345467, _1345469, _1345471]))], (31390 ^ _779854) ^ [] : [_1345471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (282 ^ _779854) ^ [_784213, _784215, _784217, _784219] : [-(c_Nitpick_Orefl_H(_784217, _784213)), c_Nitpick_Orefl_H(_784219, _784215), _784219 = _784217, _784215 = _784213], (42167 ^ _779854) ^ [_1611811, _1611813, _1611815] : [-(c_List_Oset__Cons(_1611811, _1611813, _1611815) = hAPP(c_Set_OCollect(tc_List_Olist(_1611811)), hAPP(hAPP(c_COMBB(tc_fun(_1611811, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1611811)), c_HOL_OEx(_1611811)), hAPP(hAPP(c_COMBB(tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), tc_fun(_1611811, tc_HOL_Obool), tc_List_Olist(_1611811)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_HOL_Obool, _1611811), c_HOL_OEx(tc_List_Olist(_1611811)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1611811), tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1611811, tc_fun(tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool))), tc_fun(tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool))), tc_List_Olist(_1611811)), c_COMBS(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1611811, tc_fun(tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool))), tc_List_Olist(_1611811)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1611811), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), _1611811), c_COMBS(tc_List_Olist(_1611811), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1611811)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_List_Olist(_1611811), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1611811), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1611811)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1611811), tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_List_Olist(_1611811))), tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1611811), tc_List_Olist(_1611811)), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), tc_fun(tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_List_Olist(_1611811))), tc_fun(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool))), tc_List_Olist(_1611811)), c_COMBB(tc_fun(tc_List_Olist(_1611811), tc_List_Olist(_1611811)), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), _1611811)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1611811), tc_List_Olist(_1611811)), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), tc_List_Olist(_1611811)), c_COMBB(tc_List_Olist(_1611811), tc_HOL_Obool, tc_List_Olist(_1611811))), c_fequal))), c_List_Olist_OCons(_1611811)))))), hAPP(hAPP(c_COMBC(_1611811, tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool)), _1611811), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1611811))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1611811), c_fconj), hAPP(hAPP(c_COMBC(_1611811, tc_fun(_1611811, tc_HOL_Obool), tc_HOL_Obool), c_member(_1611811)), _1611813)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1611811), tc_fun(tc_List_Olist(_1611811), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1611811))), _1611815)))))))], (3314 ^ _779854) ^ [_829478, _829480] : [_829480 = _829478, -(c_Int_OBit1(_829480) = c_Int_OBit1(_829478))], (6499 ^ _779854) ^ [_883825, _883827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883825, tc_HOL_Obool)), _883827), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_883825, tc_HOL_Obool)), _883827))), -(_883827 = c_Orderings_Obot__class_Obot(tc_fun(_883825, tc_HOL_Obool)))], (5176 ^ _779854) ^ [_858989, _858991, _858993, _858995, _858997, _858999, _859001, _859003] : [-(c_Quotient_OBabs(_859003, _858999, _858995, _858991) = c_Quotient_OBabs(_859001, _858997, _858993, _858989)), _859003 = _859001, _858999 = _858997, _858995 = _858993, _858991 = _858989], (35778 ^ _779854) ^ [_1445852, _1445854, _1445856, _1445858, _1445860, _1445862, _1445864] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445852, _1445854), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445856), _1445858))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445860, _1445854), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445862), _1445864))), -(_1445854 = 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), _1445852), _1445860), _1445854), 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), _1445856), _1445862)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445858), _1445864)), _1445854))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445858), _1445864), _1445854)))))], (28262 ^ _779854) ^ [_1290907, _1290909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290907), _1290909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1290907)), c_Int_OBit1(_1290909))))], (35472 ^ _779854) ^ [_1440816, _1440818, _1440820, _1440822, _1440824, _1440826] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1440816, _1440818, _1440820, _1440822, c_Nitpick_Opair__box_OPairBox(_1440816, _1440818, _1440824, _1440826)) = hAPP(hAPP(_1440822, _1440824), _1440826))], (17566 ^ _779854) ^ [_1097957, _1097959, _1097961, _1097963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097957), _1097959)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097961), _1097963)), 17573 ^ _779854 : [(17574 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1097957), _1097959)), hAPP(c_Finite__Set_Ocard(_1097961), _1097963)))), 17575 ^ _779854 : [(17576 ^ _779854) ^ [_1098168] : [c_Fun_Oinj__on(_1097957, _1097961, _1098168, _1097959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097961, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1097957, _1097961, _1098168), _1097959)), _1097963))]]], (17584 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1097957), _1097959)), hAPP(c_Finite__Set_Ocard(_1097961), _1097963))), 17588 ^ _779854 : [(17591 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097961, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1097957, _1097961, 17587 ^ [_1097957, _1097959, _1097961, _1097963]), _1097959)), _1097963)))], (17589 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_1097957, _1097961, 17587 ^ [_1097957, _1097959, _1097961, _1097963], _1097959))]]]]], (45356 ^ _779854) ^ [_1688502, _1688504, _1688506, _1688508] : [class_Groups_Ocomm__monoid__add(_1688502), 45359 ^ _779854 : [(45366 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1688504), _1688506))), -(c_Nitpick_Osetsum_H(_1688504, _1688502, _1688508, _1688506) = c_Groups_Ozero__class_Ozero(_1688502))], (45360 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1688504), _1688506)), -(c_Nitpick_Osetsum_H(_1688504, _1688502, _1688508, _1688506) = hAPP(c_List_Omonoid__add__class_Olistsum(_1688502), hAPP(hAPP(c_List_Omap(_1688504, _1688502), _1688508), c_Hilbert__Choice_OEps(tc_List_Olist(_1688504), hAPP(hAPP(c_COMBS(tc_List_Olist(_1688504), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1688504)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1688504), tc_fun(_1688504, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1688504, tc_HOL_Obool), tc_fun(tc_fun(_1688504, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1688504)), c_fequal), c_List_Oset(_1688504))), _1688506))), c_List_Odistinct(_1688504))))))]]], (35169 ^ _779854) ^ [_1434889, _1434891, _1434893, _1434895, _1434897] : [hBOOL(hAPP(hAPP(_1434889, _1434891), _1434893)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1434895, _1434897, tc_HOL_Obool), _1434889), hAPP(hAPP(c_Product__Type_OPair(_1434895, _1434897), _1434891), _1434893))))], (5416 ^ _779854) ^ [_862785, _862787, _862789, _862791, _862793, _862795] : [-(c_SetInterval_Oord_OlessThan(_862795, _862791, _862787) = c_SetInterval_Oord_OlessThan(_862793, _862789, _862785)), _862795 = _862793, _862791 = _862789, _862787 = _862785], (8238 ^ _779854) ^ [_917857, _917859, _917861] : [class_Orderings_Opreorder(_917857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917857), _917859), _917861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917857), _917861), _917859))], (10981 ^ _779854) ^ [_968240, _968242, _968244, _968246, _968248] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968240, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968240, tc_HOL_Obool)), hAPP(c_Set_Oimage(_968242, _968240, _968244), _968246)), hAPP(c_Set_Oimage(_968242, _968240, _968244), _968248))), hAPP(c_Set_Oimage(_968242, _968240, _968244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968242, tc_HOL_Obool)), _968246), _968248)))))], (31272 ^ _779854) ^ [_1343656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1343656)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343656), c_Int_OMin)))], (32868 ^ _779854) ^ [_1372240, _1372242, _1372244, _1372246] : [c_Fun_Oinj__on(_1372240, _1372242, _1372244, c_Orderings_Otop__class_Otop(tc_fun(_1372240, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1372240, tc_fun(_1372246, _1372242), hAPP(hAPP(c_COMBB(_1372242, tc_fun(_1372246, _1372242), _1372240), c_COMBK(_1372242, _1372246)), _1372244), c_Orderings_Otop__class_Otop(tc_fun(_1372240, tc_HOL_Obool))))], (35226 ^ _779854) ^ [_1436166, _1436168, _1436170, _1436172, _1436174, _1436176] : [hAPP(hAPP(c_Product__Type_OPair(_1436166, _1436168), _1436170), _1436172) = hAPP(hAPP(c_Product__Type_OPair(_1436166, _1436168), _1436174), _1436176), 35229 ^ _779854 : [(35232 ^ _779854) ^ [] : [-(_1436172 = _1436176)], (35230 ^ _779854) ^ [] : [-(_1436170 = _1436174)]]], (29529 ^ _779854) ^ [_1312477, _1312479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1312477)), c_Int_OBit0(_1312479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1312477), _1312479)))], (43951 ^ _779854) ^ [_1656950, _1656952, _1656954] : [hAPP(hAPP(c_List_Oappend(_1656950), _1656952), _1656954) = c_List_Olist_ONil(_1656950), 43954 ^ _779854 : [(43957 ^ _779854) ^ [] : [-(_1656954 = c_List_Olist_ONil(_1656950))], (43955 ^ _779854) ^ [] : [-(_1656952 = c_List_Olist_ONil(_1656950))]]], (44121 ^ _779854) ^ [_1660676, _1660678, _1660680, _1660682, _1660684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660676), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660678)), _1660680))), -(hAPP(hAPP(c_List_Olist__update(_1660678, hAPP(hAPP(c_List_Oappend(_1660678), _1660680), _1660682)), _1660676), _1660684) = hAPP(hAPP(c_List_Oappend(_1660678), hAPP(hAPP(c_List_Olist__update(_1660678, _1660680), _1660676), _1660684)), _1660682))], (15828 ^ _779854) ^ [_1063542, _1063544, _1063546] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063544), _1063546)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063542), _1063544)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063542), _1063546)))], (45444 ^ _779854) ^ [_1690214, _1690216, _1690218] : [-(hAPP(hAPP(c_List_Ozip(_1690214, _1690216), hAPP(hAPP(c_List_Omap(tc_prod(_1690214, _1690216), _1690214), c_Product__Type_Ofst(_1690214, _1690216)), _1690218)), hAPP(hAPP(c_List_Omap(tc_prod(_1690214, _1690216), _1690216), c_Product__Type_Osnd(_1690214, _1690216)), _1690218)) = _1690218)], (9977 ^ _779854) ^ [_948309, _948311, _948313] : [class_Orderings_Olinorder(_948309), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_948309), _948311), _948313) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_948309), _948313), _948311))], (34415 ^ _779854) ^ [_1417810, _1417812, _1417814] : [-(hAPP(c_Divides_Oadjust(_1417810), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1417812), _1417814)) = 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), _1417814), _1417810)), 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)))), _1417812)), 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)))), _1417812)), _1417814))))], (26311 ^ _779854) ^ [_1258233, _1258235] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258233)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1258233)), _1258235)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1258233))), _1258235))], (16251 ^ _779854) ^ [_1071783, _1071785, _1071787] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071783), _1071785)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071787), _1071785)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1071783), _1071787)), _1071785))], (3514 ^ _779854) ^ [_832560, _832562] : [_832562 = _832560, -(c_SetInterval_Oord__class_OlessThan(_832562) = c_SetInterval_Oord__class_OlessThan(_832560))], (31844 ^ _779854) ^ [_1352914, _1352916] : [class_Rings_Oring__1(_1352914), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352914), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1352916)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1352914), _1352916))], (40469 ^ _779854) ^ [_1568891, _1568893, _1568895, _1568897, _1568899] : [_1568891 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1568893, tc_HOL_Obool), _1568895), c_Orderings_Oorder__class_Omono(tc_fun(_1568893, tc_HOL_Obool), tc_fun(_1568893, tc_HOL_Obool), _1568895), hBOOL(hAPP(hAPP(c_member(_1568893), _1568897), _1568899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1568893, tc_HOL_Obool)), _1568899), hAPP(_1568895, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1568893, tc_HOL_Obool)), _1568899), _1568891)))), -(hBOOL(hAPP(hAPP(c_member(_1568893), _1568897), _1568891)))], (50856 ^ _779854) ^ [_1808358, _1808360, _1808362, _1808364] : [c_Fun_Obij__betw(_1808358, _1808360, _1808362, _1808364, c_Orderings_Otop__class_Otop(tc_fun(_1808360, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1808358, _1808360, _1808362), c_Orderings_Otop__class_Otop(tc_fun(_1808358, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1808360, tc_HOL_Obool)))], (6937 ^ _779854) ^ [_893021, _893023, _893025, _893027] : [class_Lattices_Osemilattice__sup(_893021), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893021), _893023), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893021), _893025), _893027)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893021), _893025), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893021), _893023), _893027)))], (20401 ^ _779854) ^ [_1146990, _1146992, _1146994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146990), _1146992)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146994), _1146992))), 20404 ^ _779854 : [(20407 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146990), _1146994)))], (20405 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146992)))]]], (15984 ^ _779854) ^ [_1066851, _1066853, _1066855, _1066857, _1066859] : [class_Rings_Ocomm__semiring__1(_1066851), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066851), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066851), _1066853), _1066855)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066851), _1066857), _1066859)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066851), _1066853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066851), _1066855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066851), _1066857), _1066859))))], (20237 ^ _779854) ^ [_1144436, _1144438] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1144436), _1144438)), 20238 ^ _779854 : [(20245 ^ _779854) ^ [] : [_1144436 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1144438 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20239 ^ _779854) ^ [] : [_1144436 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (17971 ^ _779854) ^ [_1105081, _1105083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1105081), hAPP(c_Nat_OSuc, _1105083))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1105081), _1105083))), -(_1105081 = hAPP(c_Nat_OSuc, _1105083))], (52571 ^ _779854) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (8106 ^ _779854) ^ [_915791, _915793, _915795, _915797] : [class_Orderings_Olinorder(_915791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915791), _915793), _915795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915791), _915795), _915797)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915791, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_915791, _915793, _915795)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_915791, _915795), _915797)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_915791, _915793, _915797))], (31585 ^ _779854) ^ [_1349054, _1349056] : [c_Nat__Transfer_Ois__nat(_1349054), c_Nat__Transfer_Ois__nat(_1349056), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1349054), _1349056)))], (37162 ^ _779854) ^ [_1478213, _1478215, _1478217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1478213, _1478213), tc_HOL_Obool)), _1478215), _1478217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478213, tc_HOL_Obool)), hAPP(c_Relation_OField(_1478213), _1478215)), hAPP(c_Relation_OField(_1478213), _1478217))))], (25909 ^ _779854) ^ [_1250795, _1250797] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1250795, _1250797))))], (32656 ^ _779854) ^ [_1367762, _1367764, _1367766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1367762), _1367764)), -(c_Random_Ominus__shift(_1367766, _1367762, _1367764) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1367766), _1367762)), _1367764))], (41901 ^ _779854) ^ [_1604141, _1604143, _1604145, _1604147, _1604149] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604141, _1604141)), hAPP(hAPP(c_Product__Type_OPair(_1604141, _1604141), _1604143), _1604145)), c_Transitive__Closure_Ortrancl(_1604141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1604141, _1604141), tc_HOL_Obool)), _1604147), _1604149)))), 41907 ^ _779854 : [(41913 ^ _779854) ^ [] : [41909 ^ [_1604141, _1604143, _1604145, _1604147, _1604149] = 41906 ^ [_1604141, _1604143, _1604145, _1604147, _1604149]], (41911 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604141, _1604141)), hAPP(hAPP(c_Product__Type_OPair(_1604141, _1604141), 41909 ^ [_1604141, _1604143, _1604145, _1604147, _1604149]), 41906 ^ [_1604141, _1604143, _1604145, _1604147, _1604149])), _1604149)))], (41908 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604141, _1604141)), hAPP(hAPP(c_Product__Type_OPair(_1604141, _1604141), 41906 ^ [_1604141, _1604143, _1604145, _1604147, _1604149]), _1604145)), c_Transitive__Closure_Ortrancl(_1604141, _1604147))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604141, _1604141)), hAPP(hAPP(c_Product__Type_OPair(_1604141, _1604141), _1604143), _1604145)), c_Transitive__Closure_Ortrancl(_1604141, _1604147))))], (33238 ^ _779854) ^ [_1382689, _1382691, _1382693, _1382695] : [class_Groups_Oab__group__add(_1382689), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382691, _1382689), hAPP(hAPP(c_COMBB(_1382689, _1382689, _1382691), c_Groups_Ouminus__class_Ouminus(_1382689)), _1382693)), _1382695) = hAPP(c_Groups_Ouminus__class_Ouminus(_1382689), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382691, _1382689), _1382693), _1382695)))], (47975 ^ _779854) ^ [_1744946, _1744948] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1744946)), _1744948)), 47981 ^ _779854 : [(47984 ^ _779854) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1744946), 47980 ^ [_1744946, _1744948]))], (47982 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1744946)), 47980 ^ [_1744946, _1744948]), hAPP(c_List_Oset(tc_List_Olist(_1744946)), _1744948))))]], 47988 ^ _779854 : [(47992 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1744946)), 47990 ^ [_1744946, _1744948]), hAPP(c_List_Oset(tc_List_Olist(_1744946)), _1744948))))], (47994 ^ _779854) ^ [] : [47987 ^ [_1744946, _1744948] = 47990 ^ [_1744946, _1744948]], (47996 ^ _779854) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1744946, tc_HOL_Obool)), hAPP(c_List_Oset(_1744946), 47987 ^ [_1744946, _1744948])), hAPP(c_List_Oset(_1744946), 47990 ^ [_1744946, _1744948])) = c_Orderings_Obot__class_Obot(tc_fun(_1744946, tc_HOL_Obool))], (47989 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1744946)), 47987 ^ [_1744946, _1744948]), hAPP(c_List_Oset(tc_List_Olist(_1744946)), _1744948))))]], -(hBOOL(hAPP(c_List_Odistinct(_1744946), c_List_Oconcat(_1744946, _1744948))))], (28726 ^ _779854) ^ [_1298930, _1298932] : [28727 ^ _779854 : [(28728 ^ _779854) ^ [_1298986] : [_1298932 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298930), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1298986)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298930), _1298932)))], (3982 ^ _779854) ^ [_840166, _840168, _840170, _840172, _840174, _840176, _840178, _840180] : [-(c_Lazy__Sequence_Ohb__bind(_840180, _840176, _840172, _840168) = c_Lazy__Sequence_Ohb__bind(_840178, _840174, _840170, _840166)), _840180 = _840178, _840176 = _840174, _840172 = _840170, _840168 = _840166], (49743 ^ _779854) ^ [_1785189, _1785191, _1785193, _1785195] : [class_Complete__Lattice_Ocomplete__lattice(_1785189), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1785191, _1785189), _1785193), _1785195) = c_Complete__Lattice_OInf__class_OInf(_1785189, hAPP(c_Set_OCollect(_1785189), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1785191, _1785189), tc_HOL_Obool), tc_HOL_Obool, _1785189), c_HOL_OEx(tc_fun(_1785191, _1785189))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1785191, _1785189), tc_HOL_Obool), tc_fun(tc_fun(_1785191, _1785189), tc_HOL_Obool), _1785189), hAPP(c_COMBS(tc_fun(_1785191, _1785189), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1785191, _1785189)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1785191, _1785189), tc_fun(tc_fun(_1785191, _1785189), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1785191, _1785189))), _1785193)))), hAPP(hAPP(c_COMBC(_1785189, tc_fun(tc_fun(_1785191, _1785189), _1785189), tc_fun(tc_fun(_1785191, _1785189), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1785189, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1785191, _1785189), _1785189), tc_fun(tc_fun(_1785191, _1785189), tc_HOL_Obool)), _1785189), c_COMBB(_1785189, tc_HOL_Obool, tc_fun(_1785191, _1785189))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1785191, _1785189), _1785191, _1785189), c_COMBI(tc_fun(_1785191, _1785189))), _1785195)))))))], (49138 ^ _779854) ^ [_1770578, _1770580, _1770582, _1770584] : [-(hAPP(c_New__DSequence_Opos__union(_1770578, _1770580, _1770582), _1770584) = c_Lazy__Sequence_Oappend(_1770578, hAPP(_1770580, _1770584), hAPP(_1770582, _1770584)))], (41396 ^ _779854) ^ [_1591370, _1591372, _1591374, _1591376, _1591378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591370, _1591370)), hAPP(hAPP(c_Product__Type_OPair(_1591370, _1591370), hAPP(_1591372, hAPP(c_Nat_OSuc, 41397 ^ [_1591370, _1591372, _1591374, _1591376, _1591378]))), hAPP(_1591372, 41397 ^ [_1591370, _1591372, _1591374, _1591376, _1591378]))), c_Transitive__Closure_Ortrancl(_1591370, _1591374))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591370, _1591370)), hAPP(hAPP(c_Product__Type_OPair(_1591370, _1591370), hAPP(_1591372, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1591376), _1591378))), hAPP(_1591372, _1591376))), c_Transitive__Closure_Ortrancl(_1591370, _1591374))))], (44558 ^ _779854) ^ [_1671162, _1671164, _1671166] : [-(_1671162 = c_List_Olist_ONil(_1671164)), -(hAPP(c_List_Otl(_1671164), hAPP(hAPP(c_List_Oappend(_1671164), _1671162), _1671166)) = hAPP(hAPP(c_List_Oappend(_1671164), hAPP(c_List_Otl(_1671164), _1671162)), _1671166))], (51126 ^ _779854) ^ [_1813552, _1813554, _1813556] : [hBOOL(hAPP(hAPP(_1813556, _1813554), _1813554)), -(hBOOL(hAPP(hAPP(c_member(_1813552), _1813554), c_Quotient_ORespects(_1813552, _1813556))))], (36426 ^ _779854) ^ [_1459877, _1459879, _1459881, _1459883, _1459885, _1459887, _1459889, _1459891] : [c_Finite__Set_Ofolding__image(_1459877, _1459879, _1459881, _1459883, _1459885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459879), _1459887)), c_Fun_Oinj__on(_1459879, _1459879, _1459889, _1459887), -(hAPP(hAPP(_1459885, _1459891), hAPP(c_Set_Oimage(_1459879, _1459879, _1459889), _1459887)) = hAPP(hAPP(_1459885, hAPP(c_Fun_Ocomp(_1459879, _1459877, _1459879, _1459891), _1459889)), _1459887))], (50368 ^ _779854) ^ [_1797446, _1797448, _1797450, _1797452, _1797454] : [c_Fun_Oinj__on(_1797446, _1797448, _1797450, _1797452), hBOOL(hAPP(hAPP(c_member(_1797446), _1797454), _1797452)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1797446, _1797448, _1797452, _1797450), hAPP(_1797450, _1797454)) = _1797454)], (23011 ^ _779854) ^ [_1195786, _1195788, _1195790, _1195792, _1195794] : [class_Fields_Ofield(_1195786), -(_1195788 = c_Groups_Ozero__class_Ozero(_1195786)), -(_1195790 = c_Groups_Ozero__class_Ozero(_1195786)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195786), _1195792), _1195788)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195786), _1195794), _1195790)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195786), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195786), _1195792), _1195790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195786), _1195794), _1195788))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195786), _1195788), _1195790)))], (50338 ^ _779854) ^ [_1796827, _1796829, _1796831] : [hAPP(c_Fun_Ocomp(_1796829, _1796827, _1796827, c_Hilbert__Choice_Oinv__into(_1796827, _1796829, c_Orderings_Otop__class_Otop(tc_fun(_1796827, tc_HOL_Obool)), _1796831)), _1796831) = c_Fun_Oid(_1796827), -(c_Fun_Oinj__on(_1796827, _1796829, _1796831, c_Orderings_Otop__class_Otop(tc_fun(_1796827, tc_HOL_Obool))))], (43664 ^ _779854) ^ [_1649995, _1649997, _1649999, _1650001, _1650003] : [-(hAPP(hAPP(c_List_Ozip(_1649995, _1649997), hAPP(hAPP(c_List_Olist_OCons(_1649995), _1649999), _1650001)), _1650003) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1649995, _1649997)), _1649997, c_List_Olist_ONil(tc_prod(_1649995, _1649997)), hAPP(hAPP(c_COMBC(_1649997, tc_fun(tc_List_Olist(_1649997), tc_List_Olist(tc_prod(_1649995, _1649997))), tc_fun(tc_List_Olist(_1649997), tc_List_Olist(tc_prod(_1649995, _1649997)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1649995, _1649997)), tc_List_Olist(tc_prod(_1649995, _1649997))), tc_fun(tc_fun(tc_List_Olist(_1649997), tc_List_Olist(tc_prod(_1649995, _1649997))), tc_fun(tc_List_Olist(_1649997), tc_List_Olist(tc_prod(_1649995, _1649997)))), _1649997), c_COMBB(tc_List_Olist(tc_prod(_1649995, _1649997)), tc_List_Olist(tc_prod(_1649995, _1649997)), tc_List_Olist(_1649997))), hAPP(hAPP(c_COMBB(tc_prod(_1649995, _1649997), tc_fun(tc_List_Olist(tc_prod(_1649995, _1649997)), tc_List_Olist(tc_prod(_1649995, _1649997))), _1649997), c_List_Olist_OCons(tc_prod(_1649995, _1649997))), hAPP(c_Product__Type_OPair(_1649995, _1649997), _1649999)))), hAPP(c_List_Ozip(_1649995, _1649997), _1650001))), _1650003))], (39393 ^ _779854) ^ [_1540346, _1540348, _1540350, _1540352, _1540354] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1540346, _1540348, _1540350), _1540352), _1540354) = hAPP(c_Set_OCollect(tc_prod(_1540346, _1540350)), hAPP(c_Product__Type_Oprod_Oprod__case(_1540346, _1540350, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1540350, tc_fun(_1540348, tc_HOL_Obool)), tc_fun(_1540350, tc_HOL_Obool), _1540346), hAPP(c_COMBB(tc_fun(_1540348, tc_HOL_Obool), tc_HOL_Obool, _1540350), c_HOL_OEx(_1540348))), hAPP(hAPP(c_COMBC(_1540346, tc_fun(_1540350, tc_fun(_1540348, tc_HOL_Obool)), tc_fun(_1540350, tc_fun(_1540348, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540348, tc_HOL_Obool), tc_fun(_1540348, tc_HOL_Obool)), tc_fun(tc_fun(_1540350, tc_fun(_1540348, tc_HOL_Obool)), tc_fun(_1540350, tc_fun(_1540348, tc_HOL_Obool))), _1540346), c_COMBB(tc_fun(_1540348, tc_HOL_Obool), tc_fun(_1540348, tc_HOL_Obool), _1540350)), hAPP(hAPP(c_COMBB(tc_fun(_1540348, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1540348, tc_HOL_Obool), tc_fun(_1540348, tc_HOL_Obool)), _1540346), c_COMBS(_1540348, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540348, tc_HOL_Obool), tc_fun(_1540348, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1540346), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540348), c_fconj)), hAPP(hAPP(c_COMBC(_1540346, tc_fun(tc_prod(_1540346, _1540348), tc_HOL_Obool), tc_fun(_1540348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540348, tc_fun(tc_fun(tc_prod(_1540346, _1540348), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1540346, _1540348), tc_HOL_Obool), tc_fun(_1540348, tc_HOL_Obool)), _1540346), c_COMBC(_1540348, tc_fun(tc_prod(_1540346, _1540348), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540348, tc_prod(_1540346, _1540348)), tc_fun(_1540348, tc_fun(tc_fun(tc_prod(_1540346, _1540348), tc_HOL_Obool), tc_HOL_Obool)), _1540346), hAPP(c_COMBB(tc_prod(_1540346, _1540348), tc_fun(tc_fun(tc_prod(_1540346, _1540348), tc_HOL_Obool), tc_HOL_Obool), _1540348), c_member(tc_prod(_1540346, _1540348)))), c_Product__Type_OPair(_1540346, _1540348)))), _1540352))))), hAPP(hAPP(c_COMBC(_1540350, tc_fun(tc_prod(_1540348, _1540350), tc_HOL_Obool), tc_fun(_1540348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540348, tc_fun(tc_fun(tc_prod(_1540348, _1540350), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1540348, _1540350), tc_HOL_Obool), tc_fun(_1540348, tc_HOL_Obool)), _1540350), c_COMBC(_1540348, tc_fun(tc_prod(_1540348, _1540350), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540348, tc_prod(_1540348, _1540350)), tc_fun(_1540348, tc_fun(tc_fun(tc_prod(_1540348, _1540350), tc_HOL_Obool), tc_HOL_Obool)), _1540350), hAPP(c_COMBB(tc_prod(_1540348, _1540350), tc_fun(tc_fun(tc_prod(_1540348, _1540350), tc_HOL_Obool), tc_HOL_Obool), _1540348), c_member(tc_prod(_1540348, _1540350)))), hAPP(c_COMBC(_1540348, _1540350, tc_prod(_1540348, _1540350)), c_Product__Type_OPair(_1540348, _1540350))))), _1540354))))))], (28268 ^ _779854) ^ [_1291014, _1291016] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291014)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291016)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1291014), _1291016)))], (38060 ^ _779854) ^ [_1499775, _1499777, _1499779] : [-(hAPP(c_Set_Ovimage(_1499775, _1499777, _1499779), c_Orderings_Obot__class_Obot(tc_fun(_1499777, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1499775, tc_HOL_Obool)))], (22323 ^ _779854) ^ [_1183331, _1183333, _1183335, _1183337] : [class_Fields_Olinordered__field__inverse__zero(_1183331), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183331), _1183333), _1183335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183331), _1183337), c_Groups_Ozero__class_Ozero(_1183331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183331), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183331), _1183335), _1183337)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183331), _1183333), _1183337))))], (40070 ^ _779854) ^ [_1558370, _1558372] : [c_Wellfounded_OwfP(_1558370, hAPP(hAPP(c_COMBC(_1558370, tc_fun(tc_prod(_1558370, _1558370), tc_HOL_Obool), tc_fun(_1558370, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558370, tc_fun(tc_fun(tc_prod(_1558370, _1558370), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1558370, _1558370), tc_HOL_Obool), tc_fun(_1558370, tc_HOL_Obool)), _1558370), c_COMBC(_1558370, tc_fun(tc_prod(_1558370, _1558370), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558370, tc_prod(_1558370, _1558370)), tc_fun(_1558370, tc_fun(tc_fun(tc_prod(_1558370, _1558370), tc_HOL_Obool), tc_HOL_Obool)), _1558370), hAPP(c_COMBB(tc_prod(_1558370, _1558370), tc_fun(tc_fun(tc_prod(_1558370, _1558370), tc_HOL_Obool), tc_HOL_Obool), _1558370), c_member(tc_prod(_1558370, _1558370)))), c_Product__Type_OPair(_1558370, _1558370)))), _1558372)), -(c_Wellfounded_Owf(_1558370, _1558372))], (41286 ^ _779854) ^ [_1588840, _1588842, _1588844, _1588846] : [-(hBOOL(hAPP(hAPP(c_member(_1588840), _1588842), hAPP(c_Relation_ODomain(_1588840, _1588840), _1588844)))), 41289 ^ _779854 : [(41296 ^ _779854) ^ [] : [_1588842 = _1588846, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588840, _1588840)), hAPP(hAPP(c_Product__Type_OPair(_1588840, _1588840), _1588842), _1588846)), c_Transitive__Closure_Ortrancl(_1588840, _1588844))))], (41290 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588840, _1588840)), hAPP(hAPP(c_Product__Type_OPair(_1588840, _1588840), _1588842), _1588846)), c_Transitive__Closure_Ortrancl(_1588840, _1588844))), -(_1588842 = _1588846)]]], (15996 ^ _779854) ^ [_1067205, _1067207, _1067209, _1067211, _1067213] : [class_Rings_Ocomm__semiring__1(_1067205), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067205), _1067207), _1067209)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067205), _1067211), _1067213)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067205), _1067207), _1067211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067205), _1067209), _1067213)))], (34153 ^ _779854) ^ [_1411904, _1411906, _1411908, _1411910, _1411912] : [class_Groups_Ocomm__monoid__mult(_1411904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411906), _1411908)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1411904, _1411906, c_Groups_Otimes__class_Otimes(_1411904)), hAPP(hAPP(c_COMBS(_1411906, _1411904, _1411904), hAPP(hAPP(c_COMBB(_1411904, tc_fun(_1411904, _1411904), _1411906), c_Groups_Otimes__class_Otimes(_1411904)), _1411910)), _1411912)), c_Groups_Oone__class_Oone(_1411904)), _1411908) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411904), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1411904, _1411906, c_Groups_Otimes__class_Otimes(_1411904)), _1411910), c_Groups_Oone__class_Oone(_1411904)), _1411908)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1411904, _1411906, c_Groups_Otimes__class_Otimes(_1411904)), _1411912), c_Groups_Oone__class_Oone(_1411904)), _1411908)))], (43510 ^ _779854) ^ [_1647039, _1647041, _1647043] : [-(hAPP(hAPP(c_List_Olist__update(_1647039, c_List_Olist_ONil(_1647039)), _1647041), _1647043) = c_List_Olist_ONil(_1647039))], (39282 ^ _779854) ^ [_1536780, _1536782, _1536784, _1536786, _1536788, _1536790, _1536792] : [class_Rings_Osemiring__0(_1536780), c_Fun_Oinj__on(tc_prod(_1536782, _1536784), _1536780, hAPP(c_Product__Type_Oprod_Oprod__case(_1536782, _1536784, _1536780), hAPP(hAPP(c_COMBC(_1536782, tc_fun(_1536784, _1536780), tc_fun(_1536784, _1536780)), hAPP(hAPP(c_COMBB(tc_fun(_1536780, _1536780), tc_fun(tc_fun(_1536784, _1536780), tc_fun(_1536784, _1536780)), _1536782), c_COMBB(_1536780, _1536780, _1536784)), hAPP(hAPP(c_COMBB(_1536780, tc_fun(_1536780, _1536780), _1536782), c_Groups_Otimes__class_Otimes(_1536780)), _1536786))), _1536788)), hAPP(hAPP(c_Product__Type_OSigma(_1536782, _1536784), _1536790), hAPP(c_COMBK(tc_fun(_1536784, tc_HOL_Obool), _1536782), _1536792))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1536780), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536782, _1536780), _1536786), _1536790)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536784, _1536780), _1536788), _1536792)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536780, _1536780), c_Fun_Oid(_1536780)), hAPP(c_Set_OCollect(_1536780), hAPP(hAPP(c_COMBB(tc_fun(_1536782, tc_HOL_Obool), tc_HOL_Obool, _1536780), c_HOL_OEx(_1536782)), hAPP(hAPP(c_COMBB(tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool)), tc_fun(_1536782, tc_HOL_Obool), _1536780), hAPP(c_COMBB(tc_fun(_1536784, tc_HOL_Obool), tc_HOL_Obool, _1536782), c_HOL_OEx(_1536784))), hAPP(hAPP(c_COMBC(_1536780, tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool)), tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536782, tc_fun(tc_fun(_1536784, tc_HOL_Obool), tc_fun(_1536784, tc_HOL_Obool))), tc_fun(tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool)), tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool))), _1536780), c_COMBS(_1536782, tc_fun(_1536784, tc_HOL_Obool), tc_fun(_1536784, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536782, tc_fun(_1536784, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1536782, tc_fun(tc_fun(_1536784, tc_HOL_Obool), tc_fun(_1536784, tc_HOL_Obool))), _1536780), hAPP(c_COMBB(tc_fun(_1536784, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1536784, tc_HOL_Obool), tc_fun(_1536784, tc_HOL_Obool)), _1536782), c_COMBS(_1536784, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool)), tc_fun(_1536782, tc_fun(_1536784, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1536780), hAPP(c_COMBB(tc_fun(_1536784, tc_HOL_Obool), tc_fun(_1536784, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1536782), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536784), c_fconj))), hAPP(hAPP(c_COMBC(_1536780, tc_fun(_1536782, tc_fun(_1536784, _1536780)), tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1536784, _1536780), tc_fun(_1536784, tc_HOL_Obool)), tc_fun(tc_fun(_1536782, tc_fun(_1536784, _1536780)), tc_fun(_1536782, tc_fun(_1536784, tc_HOL_Obool))), _1536780), c_COMBB(tc_fun(_1536784, _1536780), tc_fun(_1536784, tc_HOL_Obool), _1536782)), hAPP(hAPP(c_COMBB(tc_fun(_1536780, tc_HOL_Obool), tc_fun(tc_fun(_1536784, _1536780), tc_fun(_1536784, tc_HOL_Obool)), _1536780), c_COMBB(_1536780, tc_HOL_Obool, _1536784)), c_fequal))), hAPP(hAPP(c_COMBC(_1536782, tc_fun(_1536784, _1536780), tc_fun(_1536784, _1536780)), hAPP(hAPP(c_COMBB(tc_fun(_1536780, _1536780), tc_fun(tc_fun(_1536784, _1536780), tc_fun(_1536784, _1536780)), _1536782), c_COMBB(_1536780, _1536780, _1536784)), hAPP(hAPP(c_COMBB(_1536780, tc_fun(_1536780, _1536780), _1536782), c_Groups_Otimes__class_Otimes(_1536780)), _1536786))), _1536788)))))), hAPP(hAPP(c_COMBC(_1536782, tc_fun(_1536784, tc_HOL_Obool), tc_fun(_1536784, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1536784, tc_HOL_Obool), tc_fun(_1536784, tc_HOL_Obool)), _1536782), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536784)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536782), c_fconj), hAPP(hAPP(c_COMBC(_1536782, tc_fun(_1536782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536782)), _1536790)))), hAPP(hAPP(c_COMBC(_1536784, tc_fun(_1536784, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536784)), _1536792))))))))], (38346 ^ _779854) ^ [_1507599, _1507601, _1507603, _1507605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507599), _1507601)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507603), _1507605)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1507599, _1507603)), hAPP(hAPP(c_Product__Type_OSigma(_1507599, _1507603), _1507601), hAPP(c_COMBK(tc_fun(_1507603, tc_HOL_Obool), _1507599), _1507605)))))], (31302 ^ _779854) ^ [_1344219, _1344221] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344219), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344221), _1344219)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1344221), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1344221, _1344219)))], (27121 ^ _779854) ^ [_1271571, _1271573] : [class_Int_Onumber__ring(_1271571), class_Rings_Olinordered__idom(_1271571), 27128 ^ _779854 : [(27135 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1271573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271571), c_Groups_Ozero__class_Ozero(_1271571)), hAPP(c_Int_Onumber__class_Onumber__of(_1271571), _1271573))))], (27129 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271571), c_Groups_Ozero__class_Ozero(_1271571)), hAPP(c_Int_Onumber__class_Onumber__of(_1271571), _1271573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1271573)))]]], (9394 ^ _779854) ^ [_936863, _936865] : [class_Lattices_Olattice(_936863), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936863), _936865), _936865) = _936865)], (2872 ^ _779854) ^ [_822617, _822619] : [_822619 = _822617, -(c_Nat_Ofunpow(_822619) = c_Nat_Ofunpow(_822617))], (25605 ^ _779854) ^ [_1245487, _1245489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245487), _1245489)), 25608 ^ _779854 : [(25611 ^ _779854) ^ [] : [_1245487 = _1245489], (25609 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245487), _1245489)))]]], (6967 ^ _779854) ^ [_893736, _893738, _893740, _893742] : [class_Lattices_Osemilattice__inf(_893736), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893736), _893738), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893736), _893740), _893742)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893736), _893740), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893736), _893738), _893742)))], (2168 ^ _779854) ^ [_811461, _811463, _811465, _811467] : [-(c_Random_Oinc__shift(_811467, _811463) = c_Random_Oinc__shift(_811465, _811461)), _811467 = _811465, _811463 = _811461], (8368 ^ _779854) ^ [_919692, _919694, _919696] : [class_Orderings_Olinorder(_919692), 8371 ^ _779854 : [(8372 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919692), _919694), _919696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919692), _919696), _919694))), -(_919694 = _919696)], (8382 ^ _779854) ^ [] : [8383 ^ _779854 : [(8386 ^ _779854) ^ [] : [_919694 = _919696], (8384 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919692), _919696), _919694))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919692), _919694), _919696))]]], (34223 ^ _779854) ^ [_1413545, _1413547, _1413549, _1413551, _1413553, _1413555] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413545, tc_fun(_1413547, tc_HOL_Obool)), _1413549), hAPP(c_Fun_Ocomp(_1413551, tc_fun(_1413547, tc_HOL_Obool), _1413545, _1413553), _1413555)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413551, tc_fun(_1413547, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1413545, _1413551, _1413555), _1413549)), _1413553))], (1900 ^ _779854) ^ [_806556, _806558] : [-(class_Int_Onumber(_806556)), _806558 = _806556, class_Int_Onumber(_806558)], (52329 ^ _779854) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (14808 ^ _779854) ^ [_1042385, _1042387, _1042389] : [class_Orderings_Olinorder(_1042385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042385), _1042387)), -(_1042387 = c_Orderings_Obot__class_Obot(tc_fun(_1042385, tc_HOL_Obool))), 14819 ^ _779854 : [(14829 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042385), hAPP(c_Finite__Set_Ofold1(_1042385, c_Orderings_Oord__class_Omin(_1042385)), _1042387)), _1042389))), 14830 ^ _779854 : [(14831 ^ _779854) ^ [_1042774] : [hBOOL(hAPP(hAPP(c_member(_1042385), _1042774), _1042387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042385), _1042774), _1042389))]]], (14820 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042385), hAPP(c_Finite__Set_Ofold1(_1042385, c_Orderings_Oord__class_Omin(_1042385)), _1042387)), _1042389)), 14824 ^ _779854 : [(14827 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042385), 14823 ^ [_1042385, _1042387, _1042389]), _1042389)))], (14825 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1042385), 14823 ^ [_1042385, _1042387, _1042389]), _1042387)))]]]]], (28276 ^ _779854) ^ [_1291161] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1291161) = 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)), _1291161)))], (50670 ^ _779854) ^ [_1804296, _1804298, _1804300] : [c_Fun_Obij__betw(_1804296, _1804298, _1804300, c_Orderings_Otop__class_Otop(tc_fun(_1804296, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804298, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1804298, _1804296, c_Hilbert__Choice_Oinv__into(_1804296, _1804298, c_Orderings_Otop__class_Otop(tc_fun(_1804296, tc_HOL_Obool)), _1804300), c_Orderings_Otop__class_Otop(tc_fun(_1804298, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804296, tc_HOL_Obool))))], (5685 ^ _779854) ^ [_869654, _869656, _869658, _869660] : [c_Hoare__Mirabelle_Ohoare__derivs(_869654, _869656, _869658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_869654), tc_HOL_Obool)), _869660), _869658)), -(c_Hoare__Mirabelle_Ohoare__derivs(_869654, _869656, _869660))], (34575 ^ _779854) ^ [_1421552, _1421554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421552)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421554))), -(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(_1421554))), 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), _1421552)), c_Int_Onat))))))], (39475 ^ _779854) ^ [_1543110, _1543112, _1543114, _1543116, _1543118, _1543120, _1543122, _1543124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1543110, _1543112), tc_HOL_Obool)), _1543114), hAPP(hAPP(c_Product__Type_OSigma(_1543110, _1543112), _1543116), hAPP(c_COMBK(tc_fun(_1543112, tc_HOL_Obool), _1543110), _1543118)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1543112, _1543120), tc_HOL_Obool)), _1543122), hAPP(hAPP(c_Product__Type_OSigma(_1543112, _1543120), _1543118), hAPP(c_COMBK(tc_fun(_1543120, tc_HOL_Obool), _1543112), _1543124)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1543110, _1543120), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1543110, _1543112, _1543120), _1543114), _1543122)), hAPP(hAPP(c_Product__Type_OSigma(_1543110, _1543120), _1543116), hAPP(c_COMBK(tc_fun(_1543120, tc_HOL_Obool), _1543110), _1543124)))))], (23487 ^ _779854) ^ [_1205270, _1205272, _1205274] : [class_Rings_Olinordered__idom(_1205270), -(c_Groups_Osgn__class_Osgn(_1205270, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205270), _1205272), _1205274)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205270), c_Groups_Osgn__class_Osgn(_1205270, _1205272)), c_Groups_Osgn__class_Osgn(_1205270, _1205274)))], (16618 ^ _779854) ^ [_1079598, _1079600, _1079602] : [class_Orderings_Olinorder(_1079598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079598), _1079600)), -(hBOOL(hAPP(hAPP(c_member(_1079598), _1079602), _1079600))), -(c_Big__Operators_Olattice_OSup__fin(_1079598, c_Orderings_Oord__class_Omax(_1079598), hAPP(hAPP(c_Set_Oinsert(_1079598), _1079602), _1079600)) = hAPP(hAPP(c_Finite__Set_Ofold(_1079598, _1079598, c_Orderings_Oord__class_Omax(_1079598)), _1079602), _1079600))], (18046 ^ _779854) ^ [_1106369] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106369), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1106369)], (27509 ^ _779854) ^ [_1278138, _1278140, _1278142] : [-(_1278138 = 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), _1278138), _1278140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1278138), _1278142)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1278140), _1278142))], (51039 ^ _779854) ^ [_1811711, _1811713, _1811715, _1811717, _1811719] : [51041 ^ _779854 : [(51044 ^ _779854) ^ [] : [c_Relation_Orefl__on(_1811715, hAPP(_1811717, 51040 ^ [_1811711, _1811713, _1811715, _1811717, _1811719]), hAPP(_1811719, 51040 ^ [_1811711, _1811713, _1811715, _1811717, _1811719]))], (51042 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811711), 51040 ^ [_1811711, _1811713, _1811715, _1811717, _1811719]), _1811713)))]], -(c_Relation_Orefl__on(_1811715, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1811711, tc_fun(_1811715, tc_HOL_Obool)), _1811713), _1811717), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1811711, tc_fun(tc_prod(_1811715, _1811715), tc_HOL_Obool)), _1811713), _1811719)))], (1958 ^ _779854) ^ [_808104, _808106, _808108, _808110, _808112, _808114, _808116, _808118] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_808118, _808114, _808110, _808106) = c_SetInterval_Oord_OgreaterThanLessThan(_808116, _808112, _808108, _808104)), _808118 = _808116, _808114 = _808112, _808110 = _808108, _808106 = _808104], (43574 ^ _779854) ^ [_1648412, _1648414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1648412), _1648414)), -(c_List_Oupto(_1648412, _1648414) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1648412), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1648412), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1648414)))], (14946 ^ _779854) ^ [_1045087, _1045089, _1045091] : [class_Orderings_Olinorder(_1045087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1045087), _1045089)), 14956 ^ _779854 : [(14959 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045087), 14955 ^ [_1045087, _1045089, _1045091]), _1045091))], (14957 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1045087), 14955 ^ [_1045087, _1045089, _1045091]), _1045089)))]], hBOOL(hAPP(hAPP(c_member(_1045087), _1045091), _1045089)), -(c_Big__Operators_Olinorder__class_OMax(_1045087, _1045089) = _1045091)], (42866 ^ _779854) ^ [_1633071, _1633073, _1633075, _1633077] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1633071, _1633073))), hAPP(hAPP(c_List_Ozip(_1633071, _1633073), _1633075), _1633077)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633071)), _1633075)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633073)), _1633077)))], (40363 ^ _779854) ^ [_1566194, _1566196] : [40364 ^ _779854 : [(40365 ^ _779854) ^ [_1566240] : [hBOOL(hAPP(_1566194, _1566240))]], -(hBOOL(hAPP(_1566194, c_Hilbert__Choice_OEps(_1566196, _1566194))))], (29783 ^ _779854) ^ [_1316943, _1316945] : [class_Fields_Olinordered__field__inverse__zero(_1316943), class_Int_Onumber__ring(_1316943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316943), c_Groups_Ozero__class_Ozero(_1316943)), _1316945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316943), c_Groups_Ozero__class_Ozero(_1316943)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316943), _1316945), hAPP(c_Int_Onumber__class_Onumber__of(_1316943), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (16962 ^ _779854) ^ [_1085917, _1085919] : [class_Complete__Lattice_Ocomplete__lattice(_1085917), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085917), _1085919)), -(c_Complete__Lattice_OSup__class_OSup(_1085917, _1085919) = hAPP(hAPP(c_Finite__Set_Ofold(_1085917, _1085917, c_Lattices_Osemilattice__sup__class_Osup(_1085917)), c_Orderings_Obot__class_Obot(_1085917)), _1085919))], (29279 ^ _779854) ^ [_1308164, _1308166] : [class_Rings_Oring__1(_1308164), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1308164), hAPP(c_Groups_Ouminus__class_Ouminus(_1308164), c_Groups_Oone__class_Oone(_1308164))), 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)))), _1308166))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1308164), c_Groups_Oone__class_Oone(_1308164)))], (40734 ^ _779854) ^ [_1574271, _1574273] : [class_Complete__Lattice_Ocomplete__lattice(_1574271), c_Orderings_Oorder__class_Omono(_1574271, _1574271, _1574273), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574271), hAPP(_1574273, c_Inductive_Ocomplete__lattice__class_Olfp(_1574271, _1574273))), c_Inductive_Ocomplete__lattice__class_Olfp(_1574271, _1574273))))], (52031 ^ _779854) ^ [_1831676, _1831678, _1831680] : [_1831676 = _1831678, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831678), _1831680)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831676), _1831680)))], (25497 ^ _779854) ^ [_1243622, _1243624, _1243626, _1243628, _1243630, _1243632, _1243634] : [hBOOL(hAPP(hAPP(c_member(_1243622), _1243624), _1243626)), c_Nitpick_Ofold__graph_H(_1243622, _1243628, _1243630, _1243632, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1243622, tc_HOL_Obool)), _1243626), hAPP(hAPP(c_Set_Oinsert(_1243622), _1243624), c_Orderings_Obot__class_Obot(tc_fun(_1243622, tc_HOL_Obool)))), _1243634), -(c_Nitpick_Ofold__graph_H(_1243622, _1243628, _1243630, _1243632, _1243626, hAPP(hAPP(_1243630, _1243624), _1243634)))], (43442 ^ _779854) ^ [_1645836, _1645838] : [-(c_List_Olistrelp(_1645836, _1645838, c_List_Olist_ONil(_1645836), c_List_Olist_ONil(_1645836)))], (3500 ^ _779854) ^ [_832339, _832341, _832343, _832345, _832347, _832349] : [-(c_List_Osublist(_832349, _832345, _832341) = c_List_Osublist(_832347, _832343, _832339)), _832349 = _832347, _832345 = _832343, _832341 = _832339], (33056 ^ _779854) ^ [_1378533, _1378535, _1378537, _1378539, _1378541] : [_1378533 = c_Orderings_Obot__class_Obot(tc_fun(_1378535, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1378537), _1378539), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378535, tc_fun(_1378537, tc_HOL_Obool)), _1378533), _1378541)) = hAPP(hAPP(c_Set_Oinsert(_1378537), _1378539), c_Orderings_Obot__class_Obot(tc_fun(_1378537, tc_HOL_Obool))))], (39647 ^ _779854) ^ [_1549029, _1549031] : [c_Wellfounded_Owf(_1549029, _1549031), -(c_Wellfounded_Owf(_1549029, hAPP(hAPP(c_Relation_Orel__comp(_1549029, _1549029, _1549029), _1549031), _1549031)))], (2798 ^ _779854) ^ [_821486, _821488, _821490, _821492] : [-(c_Wellfounded_Omax__ext(_821492, _821488) = c_Wellfounded_Omax__ext(_821490, _821486)), _821492 = _821490, _821488 = _821486], (33755 ^ _779854) ^ [_1401006, _1401008, _1401010, _1401012, _1401014] : [-(_1401006 = c_Orderings_Obot__class_Obot(tc_fun(_1401008, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401010, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401008, tc_fun(_1401010, tc_HOL_Obool)), _1401006), _1401012)), _1401014) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401008, tc_fun(_1401010, tc_HOL_Obool)), _1401006), hAPP(hAPP(c_COMBC(_1401008, tc_fun(_1401010, tc_HOL_Obool), tc_fun(_1401010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401010, tc_HOL_Obool), tc_fun(tc_fun(_1401010, tc_HOL_Obool), tc_fun(_1401010, tc_HOL_Obool)), _1401008), c_Groups_Ominus__class_Ominus(tc_fun(_1401010, tc_HOL_Obool))), _1401012)), _1401014)))], (34839 ^ _779854) ^ [_1427289, _1427291] : [34840 ^ _779854 : [(34843 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427291), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34841 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427289), _1427291))]], -(c_Divides_OposDivAlg(_1427289, _1427291) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427289))], (2570 ^ _779854) ^ [_817922, _817924, _817926, _817928] : [-(c_Nitpick_Onumber__of__frac(_817928, _817924) = c_Nitpick_Onumber__of__frac(_817926, _817922)), _817928 = _817926, _817924 = _817922], (7694 ^ _779854) ^ [_907716, _907718] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907716, tc_HOL_Obool)), _907718), c_Orderings_Otop__class_Otop(tc_fun(_907716, tc_HOL_Obool))) = _907718)], (49366 ^ _779854) ^ [_1775785, _1775787, _1775789] : [-(c_FunDef_OTHE__default(_1775787, _1775789, _1775785) = _1775789), 49368 ^ _779854 : [(49371 ^ _779854) ^ [_1775907] : [hBOOL(hAPP(_1775785, _1775907)), -(_1775907 = 49367 ^ [_1775785, _1775787, _1775789])], (49369 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1775785, 49367 ^ [_1775785, _1775787, _1775789])))]]], (15630 ^ _779854) ^ [_1059291, _1059293, _1059295, _1059297, _1059299] : [class_Groups_Ocomm__monoid__add(_1059291), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059293), _1059295)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059293, _1059291), _1059297), hAPP(hAPP(c_Set_Oinsert(_1059293), _1059299), _1059295)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059291), hAPP(_1059297, _1059299)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059293, _1059291), _1059297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059293, tc_HOL_Obool)), _1059295), hAPP(hAPP(c_Set_Oinsert(_1059293), _1059299), c_Orderings_Obot__class_Obot(tc_fun(_1059293, tc_HOL_Obool)))))))], (39985 ^ _779854) ^ [_1556661, _1556663] : [c_Wellfounded_Owf(_1556661, _1556663), -(c_Wellfounded_Owf(tc_List_Olist(_1556661), c_List_Olex(_1556661, _1556663)))], (44446 ^ _779854) ^ [_1669209, _1669211, _1669213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669209), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669211)), _1669213))), -(hAPP(hAPP(c_List_Oappend(_1669211), hAPP(hAPP(c_List_Otake(_1669211), _1669209), _1669213)), hAPP(hAPP(c_List_Olist_OCons(_1669211), hAPP(c_List_Ohd(_1669211), hAPP(hAPP(c_List_Odrop(_1669211), _1669209), _1669213))), c_List_Olist_ONil(_1669211))) = hAPP(hAPP(c_List_Otake(_1669211), hAPP(c_Nat_OSuc, _1669209)), _1669213))], (8918 ^ _779854) ^ [_928429, _928431, _928433] : [class_Groups_Oordered__ab__group__add(_928429), 8921 ^ _779854 : [(8928 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928429), _928433), hAPP(c_Groups_Ouminus__class_Ouminus(_928429), _928431))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928429), _928431), hAPP(c_Groups_Ouminus__class_Ouminus(_928429), _928433))))], (8922 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928429), _928431), hAPP(c_Groups_Ouminus__class_Ouminus(_928429), _928433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928429), _928433), hAPP(c_Groups_Ouminus__class_Ouminus(_928429), _928431))))]]], (39782 ^ _779854) ^ [_1551422, _1551424, _1551426] : [c_Wellfounded_Owf(_1551422, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551422, _1551422), tc_HOL_Obool)), _1551424), _1551426)), -(c_Wellfounded_Owf(_1551422, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551422, _1551422), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551422, _1551422), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1551422, _1551422, _1551422), _1551424), _1551424)), hAPP(hAPP(c_Relation_Orel__comp(_1551422, _1551422, _1551422), _1551426), _1551424))), _1551426)))], (39707 ^ _779854) ^ [_1550133, _1550135] : [c_Wellfounded_Owf(_1550133, _1550135), -(c_Wellfounded_Owf(tc_fun(_1550133, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1550133, _1550135)))], (52483 ^ _779854) ^ [_1836564, _1836566] : [-(class_Nat_Osize(tc_sum(_1836564, _1836566)))], (13897 ^ _779854) ^ [_1024524, _1024526, _1024528] : [class_Orderings_Olinorder(_1024524), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024524), _1024526)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024524), _1024528)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024524, tc_HOL_Obool)), _1024526), _1024528) = c_Orderings_Obot__class_Obot(tc_fun(_1024524, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1024524), c_Big__Operators_Olinorder__class_OMin(_1024524, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024524, tc_HOL_Obool)), _1024526), _1024528))), c_Big__Operators_Olinorder__class_OMin(_1024524, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024524, tc_HOL_Obool)), _1024526), _1024528))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1024524), c_Big__Operators_Olinorder__class_OMin(_1024524, _1024526)), c_Big__Operators_Olinorder__class_OMin(_1024524, _1024528)))], (36597 ^ _779854) ^ [_1463969, _1463971, _1463973, _1463975, _1463977, _1463979, _1463981] : [hBOOL(hAPP(_1463969, _1463971)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1463973, _1463973)), hAPP(hAPP(c_Product__Type_OPair(_1463973, _1463973), _1463975), _1463977)), hAPP(_1463979, _1463971))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1463981, _1463973), tc_prod(_1463981, _1463973))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1463981, _1463973), tc_prod(_1463981, _1463973)), hAPP(hAPP(c_Product__Type_OPair(_1463981, _1463973), _1463971), _1463975)), hAPP(hAPP(c_Product__Type_OPair(_1463981, _1463973), _1463971), _1463977))), c_Recdef_Osame__fst(_1463981, _1463973, _1463969, _1463979))))], (328 ^ _779854) ^ [_784884, _784886, _784888, _784890, _784892, _784894, _784896, _784898] : [-(c_Finite__Set_Ofolding(_784896, _784892, _784888, _784884)), c_Finite__Set_Ofolding(_784898, _784894, _784890, _784886), _784898 = _784896, _784894 = _784892, _784890 = _784888, _784886 = _784884], (41835 ^ _779854) ^ [_1602349, _1602351, _1602353] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602349, _1602349)), _1602351), c_Transitive__Closure_Otrancl(_1602349, _1602353)))), 41836 ^ _779854 : [(41837 ^ _779854) ^ [_1602428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1602428)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602349, _1602349)), _1602351), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1602349, _1602349), tc_HOL_Obool), _1602428), _1602353)))]]], (4314 ^ _779854) ^ [_845364, _845366] : [_845366 = _845364, -(c_Set_Oinsert(_845366) = c_Set_Oinsert(_845364))], (44061 ^ _779854) ^ [_1659158, _1659160, _1659162] : [-(c_List_Obutlast(_1659158, hAPP(hAPP(c_List_Oappend(_1659158), _1659160), hAPP(hAPP(c_List_Olist_OCons(_1659158), _1659162), c_List_Olist_ONil(_1659158)))) = _1659160)], (18329 ^ _779854) ^ [_1111497, _1111499] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1111497), _1111499) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1111497, _1111499))], (18629 ^ _779854) ^ [_1116927, _1116929] : [class_Rings_Omult__zero(_1116927), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116927), _1116929), c_Groups_Ozero__class_Ozero(_1116927)) = c_Groups_Ozero__class_Ozero(_1116927))], (42346 ^ _779854) ^ [_1617716, _1617718] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1617716), tc_List_Olist(_1617716)), tc_HOL_Obool)), c_List_Olistrel(_1617716, _1617718)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1617716), c_List_Olistrel1(_1617716, _1617718)))))], (33805 ^ _779854) ^ [_1402386, _1402388, _1402390, _1402392, _1402394] : [33807 ^ _779854 : [(33810 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402386, tc_HOL_Obool)), _1402388), hAPP(_1402394, 33806 ^ [_1402386, _1402388, _1402390, _1402392, _1402394])))], (33808 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1402390), 33806 ^ [_1402386, _1402388, _1402390, _1402392, _1402394]), _1402392)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402386, tc_HOL_Obool)), _1402388), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1402390, tc_fun(_1402386, tc_HOL_Obool)), _1402392), _1402394))))], (40954 ^ _779854) ^ [_1579985] : [-(c_Transitive__Closure_Otrancl(_1579985, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1579985, _1579985), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1579985, _1579985), tc_HOL_Obool)))], (20211 ^ _779854) ^ [_1144015, _1144017] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144015), hAPP(c_Nat_OSuc, _1144017)))), 20212 ^ _779854 : [(20215 ^ _779854) ^ [_1144103] : [_1144015 = hAPP(c_Nat_OSuc, _1144103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144103), _1144017))], (20213 ^ _779854) ^ [] : [_1144015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (52567 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (7786 ^ _779854) ^ [_909585, _909587, _909589] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909585, tc_HOL_Obool)), _909587), _909589) = c_Orderings_Obot__class_Obot(tc_fun(_909585, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909585, tc_HOL_Obool)), _909587), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_909585, tc_HOL_Obool)), _909589))))], (7700 ^ _779854) ^ [_907878, _907880] : [class_Lattices_Oboolean__algebra(_907878), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907878), _907880), hAPP(c_Groups_Ouminus__class_Ouminus(_907878), _907880)) = c_Orderings_Obot__class_Obot(_907878))], (24234 ^ _779854) ^ [_1219361, _1219363, _1219365] : [class_Rings_Olinordered__semidom(_1219361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219361), c_Groups_Oone__class_Oone(_1219361)), _1219363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219361), hAPP(hAPP(c_Power_Opower__class_Opower(_1219361), _1219363), _1219365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219361), _1219363), hAPP(hAPP(c_Power_Opower__class_Opower(_1219361), _1219363), _1219365)))))], (52291 ^ _779854) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (38021 ^ _779854) ^ [_1498911, _1498913, _1498915] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1498911), _1498913), _1498915) = c_Nitpick_OAbs__Frac(_1498911, c_Nitpick_Onorm__frac(_1498913, _1498915)))], (30927 ^ _779854) ^ [_1338317] : [c_Nat__Transfer_Onat__set(_1338317), 30930 ^ _779854 : [(30937 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1338317))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1338317)))], (30931 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1338317)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1338317))))]]], (9566 ^ _779854) ^ [_940225, _940227, _940229] : [class_Orderings_Olinorder(_940225), 9569 ^ _779854 : [(9576 ^ _779854) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_940225), _940227), _940229) = _940229, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940225), _940227), _940229)))], (9570 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940225), _940227), _940229)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_940225), _940227), _940229) = _940229)]]], (39977 ^ _779854) ^ [_1556525, _1556527, _1556529, _1556531] : [39978 ^ _779854 : [(39979 ^ _779854) ^ [_1556579] : [hBOOL(hAPP(hAPP(_1556529, _1556531), _1556579))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1556525, _1556527, _1556529), _1556531)))], (31597 ^ _779854) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (6151 ^ _779854) ^ [_877557] : [c_Orderings_Otop__class_Otop(tc_fun(_877557, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_877557, tc_HOL_Obool))], (40277 ^ _779854) ^ [_1564168, _1564170, _1564172, _1564174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1564168), _1564170)), 40283 ^ _779854 : [(40286 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1564172), hAPP(_1564174, 40282 ^ [_1564168, _1564170, _1564172, _1564174])))], (40284 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564168), 40282 ^ [_1564168, _1564170, _1564172, _1564174]), _1564170)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1564172), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1564168, tc_fun(_1564172, tc_HOL_Obool)), _1564170), _1564174))))], (49926 ^ _779854) ^ [_1789055, _1789057] : [c_Relation_Oantisym(_1789055, _1789057), -(c_Relation_Oantisym(_1789055, hAPP(c_Relation_Oconverse(_1789055, _1789055), _1789057)))], (52373 ^ _779854) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52415 ^ _779854) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (41788 ^ _779854) ^ [_1601024, _1601026, _1601028, _1601030] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601024, _1601024), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1601026), _1601028)), _1601030) = hAPP(hAPP(c_Relation_Orel__comp(_1601024, _1601024, _1601024), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601024, _1601024), tc_HOL_Obool), _1601026), _1601030)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601024, _1601024), tc_HOL_Obool), _1601028), _1601030)))], (18271 ^ _779854) ^ [_1110562, _1110564, _1110566] : [class_Groups_Ocomm__monoid__mult(_1110562), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1110564, _1110562), _1110566), c_Orderings_Obot__class_Obot(tc_fun(_1110564, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1110562))], (12004 ^ _779854) ^ [_988612, _988614, _988616, _988618, _988620, _988622] : [hBOOL(hAPP(hAPP(c_member(_988612), _988614), _988616)), _988618 = hAPP(_988620, _988614), -(hBOOL(hAPP(hAPP(c_member(_988622), _988618), hAPP(c_Set_Oimage(_988612, _988622, _988620), _988616))))], (33492 ^ _779854) ^ [_1390256, _1390258, _1390260, _1390262, _1390264] : [hBOOL(hAPP(hAPP(c_member(_1390256), _1390258), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390260, tc_fun(_1390256, tc_HOL_Obool)), _1390262), _1390264))), 33495 ^ _779854 : [(33496 ^ _779854) ^ [_1390380] : [hBOOL(hAPP(hAPP(c_member(_1390260), _1390380), _1390262)), -(hBOOL(hAPP(hAPP(c_member(_1390256), _1390258), hAPP(_1390264, _1390380))))]]], (4620 ^ _779854) ^ [_850259, _850261, _850263, _850265, _850267, _850269, _850271, _850273] : [-(c_Random__Sequence_ORandom(_850273, _850269, _850265, _850261) = c_Random__Sequence_ORandom(_850271, _850267, _850263, _850259)), _850273 = _850271, _850269 = _850267, _850265 = _850263, _850261 = _850259], (30111 ^ _779854) ^ [_1323045, _1323047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1323045), 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)))), _1323047)), 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)))), _1323045)) = 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), _1323047), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1323045))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29641 ^ _779854) ^ [_1314494, _1314496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1314494), _1314496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1314494)), c_Int_OBit1(_1314496))))], (22209 ^ _779854) ^ [_1181178, _1181180, _1181182, _1181184] : [class_Fields_Olinordered__field(_1181178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181178), c_Groups_Ozero__class_Ozero(_1181178)), _1181180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181178), _1181182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181178), _1181184), _1181180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181178), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181178), _1181182), _1181180)), _1181184)))], (43674 ^ _779854) ^ [_1650565, _1650567, _1650569] : [class_Orderings_Olinorder(_1650565), hBOOL(hAPP(c_Finite__Set_Ofinite(_1650565), _1650567)), -(c_List_Olinorder__class_Osorted__list__of__set(_1650565, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650565, tc_HOL_Obool)), _1650567), hAPP(hAPP(c_Set_Oinsert(_1650565), _1650569), c_Orderings_Obot__class_Obot(tc_fun(_1650565, tc_HOL_Obool))))) = c_List_Oremove1(_1650565, _1650569, c_List_Olinorder__class_Osorted__list__of__set(_1650565, _1650567)))], (25961 ^ _779854) ^ [_1251706, _1251708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251706), _1251708)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1251708, _1251706) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (45099 ^ _779854) ^ [_1682366, _1682368, _1682370, _1682372] : [_1682372 = c_List_Olist_ONil(_1682368), -(c_List_Olist_ONil(_1682366) = hAPP(hAPP(c_List_Omap(_1682368, _1682366), _1682370), _1682372))], (25549 ^ _779854) ^ [_1244654] : [-(_1244654 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25552 ^ _779854 : [(25559 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244654))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1244654) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25553 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244654)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1244654) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (10147 ^ _779854) ^ [_951268, _951270, _951272] : [class_Orderings_Olinorder(_951268), 10150 ^ _779854 : [(10157 ^ _779854) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_951268), _951270), _951272) = _951270, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951268), _951270), _951272)))], (10151 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951268), _951270), _951272)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_951268), _951270), _951272) = _951270)]]], (36279 ^ _779854) ^ [_1456926, _1456928, _1456930, _1456932, _1456934, _1456936] : [hBOOL(hAPP(_1456926, _1456928)), hBOOL(hAPP(_1456930, _1456932)), 36286 ^ _779854 : [(36289 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1456930, hAPP(c_Product__Type_Osnd(_1456934, _1456936), hAPP(hAPP(c_Product__Type_OPair(_1456934, _1456936), _1456928), _1456932)))))], (36287 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1456926, hAPP(c_Product__Type_Ofst(_1456934, _1456936), hAPP(hAPP(c_Product__Type_OPair(_1456934, _1456936), _1456928), _1456932)))))]]], (40381 ^ _779854) ^ [_1566495, _1566497, _1566499] : [-(c_Hilbert__Choice_OEps(tc_prod(_1566495, _1566497), _1566499) = c_Hilbert__Choice_OEps(tc_prod(_1566495, _1566497), hAPP(c_Product__Type_Oprod_Oprod__case(_1566495, _1566497, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1566497, tc_prod(_1566495, _1566497)), tc_fun(_1566497, tc_HOL_Obool), _1566495), hAPP(c_COMBB(tc_prod(_1566495, _1566497), tc_HOL_Obool, _1566497), _1566499)), c_Product__Type_OPair(_1566495, _1566497)))))], (13915 ^ _779854) ^ [_1024872, _1024874, _1024876] : [class_Orderings_Olinorder(_1024872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024872), _1024874)), -(_1024874 = c_Orderings_Obot__class_Obot(tc_fun(_1024872, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024872), _1024876)), -(_1024876 = c_Orderings_Obot__class_Obot(tc_fun(_1024872, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024872, tc_HOL_Obool)), _1024874), _1024876) = c_Orderings_Obot__class_Obot(tc_fun(_1024872, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1024872, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024872, tc_HOL_Obool)), _1024874), _1024876)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1024872), c_Big__Operators_Olinorder__class_OMax(_1024872, _1024874)), c_Big__Operators_Olinorder__class_OMax(_1024872, _1024876)))], (31657 ^ _779854) ^ [_1350011, _1350013] : [c_Nat__Transfer_Ois__nat(_1350011), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1350011, _1350013)))], (31952 ^ _779854) ^ [_1354687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354687)), 31956 ^ _779854 : [(31959 ^ _779854) ^ [] : [-(_1354687 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 31955 ^ [_1354687]))], (31957 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31955 ^ [_1354687])))]]], (51549 ^ _779854) ^ [_1823558, _1823560] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823558), _1823560)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1823558), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823560))))], (20922 ^ _779854) ^ [_1156357, _1156359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1156357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1156357), hAPP(c_Nat_OSuc, _1156359))), _1156357)))], (52357 ^ _779854) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (34329 ^ _779854) ^ [_1416069, _1416071, _1416073] : [class_Int_Onumber__ring(_1416069), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1416069), hAPP(c_Int_Onumber__class_Onumber__of(_1416069), _1416071)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1416073))) = hAPP(hAPP(c_HOL_OLet(_1416069, _1416069), hAPP(hAPP(c_Power_Opower__class_Opower(_1416069), hAPP(c_Int_Onumber__class_Onumber__of(_1416069), _1416071)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416073))), hAPP(hAPP(c_COMBS(_1416069, _1416069, _1416069), c_Groups_Otimes__class_Otimes(_1416069)), c_COMBI(_1416069))))], (14141 ^ _779854) ^ [_1029405, _1029407, _1029409, _1029411, _1029413] : [c_Fun_Ofun__upd(_1029405, _1029407, _1029409, _1029411, _1029413) = _1029409, -(hAPP(_1029409, _1029411) = _1029413)], (50517 ^ _779854) ^ [_1800946, _1800948, _1800950] : [hAPP(c_Set_Oimage(_1800946, _1800948, _1800950), c_Orderings_Otop__class_Otop(tc_fun(_1800946, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1800948, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1800946, _1800948, _1800948, _1800950), c_Hilbert__Choice_Oinv__into(_1800946, _1800948, c_Orderings_Otop__class_Otop(tc_fun(_1800946, tc_HOL_Obool)), _1800950)) = c_Fun_Oid(_1800948))], (8074 ^ _779854) ^ [_915097, _915099] : [class_Orderings_Olinorder(_915097), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915097, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915097), _915099), c_Orderings_Obot__class_Obot(tc_fun(_915097, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_915097), _915099)) = hAPP(c_SetInterval_Oord__class_OatLeast(_915097), _915099))], (18066 ^ _779854) ^ [_1106667, _1106669] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1106667), _1106669)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1106667)), hAPP(c_Nat_OSuc, _1106669)))], (49120 ^ _779854) ^ [_1770017, _1770019] : [class_Lazy__Sequence_Osmall__lazy(_1770017), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1770017), _1770019) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1770017), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1770017)), c_List_Olist_ONil(_1770017)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1770017))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1770019)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1770017, tc_List_Olist(_1770017)), tc_List_Olist(_1770017), c_Lazy__Sequence_Oproduct(_1770017, tc_List_Olist(_1770017), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1770017, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1770019), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1770017), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1770019), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1770017, tc_List_Olist(_1770017), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1770017))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1770017), tc_List_Olist(_1770017)), tc_fun(tc_List_Olist(_1770017), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1770017))), _1770017), hAPP(c_COMBB(tc_List_Olist(_1770017), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1770017)), tc_List_Olist(_1770017)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1770017)))), c_List_Olist_OCons(_1770017))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1770017)))))], (19939 ^ _779854) ^ [_1139483, _1139485] : [class_Groups_Olinordered__ab__group__add(_1139483), 19942 ^ _779854 : [(19949 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139483), c_Groups_Ozero__class_Ozero(_1139483)), _1139485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139483), hAPP(c_Groups_Ouminus__class_Ouminus(_1139483), _1139485)), _1139485)))], (19943 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139483), hAPP(c_Groups_Ouminus__class_Ouminus(_1139483), _1139485)), _1139485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139483), c_Groups_Ozero__class_Ozero(_1139483)), _1139485)))]]], (4922 ^ _779854) ^ [_855018, _855020, _855022, _855024] : [-(c_Hilbert__Choice_OEps(_855024, _855020) = c_Hilbert__Choice_OEps(_855022, _855018)), _855024 = _855022, _855020 = _855018], (9392 ^ _779854) ^ [_936781, _936783, _936785] : [-(hAPP(c_Set_OPow(_936781), hAPP(hAPP(c_Set_Oinsert(_936781), _936783), _936785)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_936781, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_936781), _936785)), hAPP(c_Set_Oimage(tc_fun(_936781, tc_HOL_Obool), tc_fun(_936781, tc_HOL_Obool), hAPP(c_Set_Oinsert(_936781), _936783)), hAPP(c_Set_OPow(_936781), _936785))))], (21895 ^ _779854) ^ [_1175545, _1175547, _1175549, _1175551] : [class_Rings_Odivision__ring(_1175545), -(_1175547 = c_Groups_Ozero__class_Ozero(_1175545)), 21902 ^ _779854 : [(21909 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175545), _1175549), _1175547) = _1175551, -(_1175549 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175545), _1175551), _1175547))], (21903 ^ _779854) ^ [] : [_1175549 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175545), _1175551), _1175547), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175545), _1175549), _1175547) = _1175551)]]], (49241 ^ _779854) ^ [_1772876, _1772878, _1772880] : [hBOOL(hAPP(hAPP(c_List_Omember(_1772876), _1772880), _1772878)), -(hBOOL(hAPP(hAPP(c_member(_1772876), _1772878), hAPP(c_List_Oset(_1772876), _1772880))))], (41190 ^ _779854) ^ [_1586593, _1586595, _1586597] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586593, _1586593)), hAPP(hAPP(c_Product__Type_OPair(_1586593, _1586593), _1586595), _1586597)), c_Relation_OId(_1586593))), -(_1586595 = _1586597)], (13323 ^ _779854) ^ [_1014659, _1014661, _1014663] : [class_Orderings_Olinorder(_1014659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014659), _1014661)), hBOOL(hAPP(hAPP(c_member(_1014659), _1014663), _1014661)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1014659), _1014663), c_Big__Operators_Olinorder__class_OMin(_1014659, _1014661)) = c_Big__Operators_Olinorder__class_OMin(_1014659, _1014661))], (31352 ^ _779854) ^ [_1344918] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1344918)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1344918)))], (32451 ^ _779854) ^ [_1363820, _1363822] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1363820), hAPP(hAPP(c_Power_Opower__class_Opower(_1363820), hAPP(c_Int_Onumber__class_Onumber__of(_1363820), c_Int_OMin)), _1363822)) = c_Groups_Oone__class_Oone(_1363820)), class_Int_Onumber__ring(_1363820), class_Rings_Olinordered__idom(_1363820)], (33294 ^ _779854) ^ [_1384578, _1384580, _1384582, _1384584, _1384586, _1384588] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384578, tc_fun(_1384580, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384582, tc_fun(_1384578, tc_HOL_Obool)), _1384584), _1384586)), _1384588) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384582, tc_fun(_1384580, tc_HOL_Obool)), _1384584), hAPP(hAPP(c_COMBC(_1384582, tc_fun(_1384578, tc_fun(_1384580, tc_HOL_Obool)), tc_fun(_1384580, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384578, tc_HOL_Obool), tc_fun(tc_fun(_1384578, tc_fun(_1384580, tc_HOL_Obool)), tc_fun(_1384580, tc_HOL_Obool)), _1384582), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384578, tc_fun(_1384580, tc_HOL_Obool))), _1384586)), _1384588)))], (23459 ^ _779854) ^ [_1204864, _1204866] : [class_Rings_Olinordered__idom(_1204864), -(c_Groups_Osgn__class_Osgn(_1204864, c_Groups_Osgn__class_Osgn(_1204864, _1204866)) = c_Groups_Osgn__class_Osgn(_1204864, _1204866))], (12594 ^ _779854) ^ [_1000170, _1000172, _1000174] : [class_Orderings_Olinorder(_1000170), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000170), _1000172)), hBOOL(hAPP(hAPP(c_member(_1000170), _1000174), _1000172)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1000170), _1000174), c_Big__Operators_Olattice_OInf__fin(_1000170, c_Orderings_Oord__class_Omin(_1000170), _1000172)) = c_Big__Operators_Olattice_OInf__fin(_1000170, c_Orderings_Oord__class_Omin(_1000170), _1000172))], (36760 ^ _779854) ^ [_1467655, _1467657, _1467659, _1467661, _1467663, _1467665] : [hAPP(c_Product__Type_Oapfst(_1467655, _1467657, _1467659, _1467661), _1467663) = hAPP(c_Product__Type_Oapfst(_1467655, _1467657, _1467659, _1467665), _1467663), -(hAPP(_1467661, hAPP(c_Product__Type_Ofst(_1467655, _1467659), _1467663)) = hAPP(_1467665, hAPP(c_Product__Type_Ofst(_1467655, _1467659), _1467663)))], (45346 ^ _779854) ^ [_1688253, _1688255, _1688257, _1688259, _1688261] : [class_Groups_Ocomm__monoid__add(_1688253), hBOOL(hAPP(hAPP(c_member(_1688255), _1688257), hAPP(c_List_Oset(_1688255), _1688259))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1688253), hAPP(hAPP(c_List_Omap(_1688255, _1688253), _1688261), _1688259)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1688253), hAPP(_1688261, _1688257)), hAPP(c_List_Omonoid__add__class_Olistsum(_1688253), hAPP(hAPP(c_List_Omap(_1688255, _1688253), _1688261), c_List_Oremove1(_1688255, _1688257, _1688259)))))], (8966 ^ _779854) ^ [_929278, _929280, _929282, _929284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929278, tc_HOL_Obool)), _929280), _929282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929278, tc_HOL_Obool)), _929282), _929284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929278, tc_HOL_Obool)), _929280), _929284)))], (29331 ^ _779854) ^ [_1309090, _1309092] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1309090) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1309092), -(_1309090 = _1309092)], (33879 ^ _779854) ^ [_1404182, _1404184, _1404186, _1404188, _1404190] : [hBOOL(hAPP(hAPP(c_member(_1404182), _1404184), _1404186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404188, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404182, tc_fun(_1404188, tc_HOL_Obool)), _1404186), _1404190)), hAPP(_1404190, _1404184))))], (48591 ^ _779854) ^ [_1758864, _1758866] : [-(c_FunDef_Ois__measure(_1758864, _1758866))], (44564 ^ _779854) ^ [_1671228, _1671230, _1671232] : [-(hAPP(hAPP(c_List_Otake(_1671228), _1671230), hAPP(c_List_Otl(_1671228), _1671232)) = hAPP(c_List_Otl(_1671228), hAPP(hAPP(c_List_Otake(_1671228), hAPP(c_Nat_OSuc, _1671230)), _1671232)))], (28414 ^ _779854) ^ [_1293584, _1293586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293584)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293586))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1293584), _1293586)))], (25577 ^ _779854) ^ [_1245090] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245090), _1245090)))], (49036 ^ _779854) ^ [_1768607, _1768609, _1768611, _1768613] : [hBOOL(hAPP(_1768607, _1768609)), -(hAPP(c_List_Ofilter(_1768611, _1768607), c_List_Oreplicate(_1768611, _1768613, _1768609)) = c_List_Oreplicate(_1768611, _1768613, _1768609))], (11568 ^ _779854) ^ [_980227, _980229, _980231] : [class_Orderings_Olinorder(_980227), hAPP(_980229, hAPP(hAPP(c_Orderings_Oord__class_Omin(_980227), 11573 ^ [_980227, _980229, _980231]), 11574 ^ [_980227, _980229, _980231])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_980227), hAPP(_980229, 11573 ^ [_980227, _980229, _980231])), hAPP(_980229, 11574 ^ [_980227, _980229, _980231])), hBOOL(hAPP(c_Finite__Set_Ofinite(_980227), _980231)), -(_980231 = c_Orderings_Obot__class_Obot(tc_fun(_980227, tc_HOL_Obool))), -(hAPP(_980229, c_Big__Operators_Olattice_OInf__fin(_980227, c_Orderings_Oord__class_Omin(_980227), _980231)) = c_Big__Operators_Olattice_OInf__fin(_980227, c_Orderings_Oord__class_Omin(_980227), hAPP(c_Set_Oimage(_980227, _980227, _980229), _980231)))], (33218 ^ _779854) ^ [_1382241, _1382243, _1382245, _1382247, _1382249, _1382251] : [-(c_Nitpick_Opair__box_OPairBox(_1382241, _1382243, _1382245, _1382247) = c_Nitpick_Opair__box_OPairBox(_1382241, _1382243, _1382249, _1382251)), _1382245 = _1382249, _1382247 = _1382251], (40645 ^ _779854) ^ [_1572415, _1572417, _1572419, _1572421, _1572423] : [_1572415 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1572417, tc_HOL_Obool), _1572419), c_Orderings_Oorder__class_Omono(tc_fun(_1572417, tc_HOL_Obool), tc_fun(_1572417, tc_HOL_Obool), _1572419), hBOOL(hAPP(hAPP(c_member(_1572417), _1572421), _1572423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1572417, tc_HOL_Obool)), _1572423), hAPP(_1572419, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1572417, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1572417, tc_HOL_Obool), tc_fun(_1572417, tc_HOL_Obool), tc_fun(_1572417, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572417, tc_HOL_Obool), tc_fun(tc_fun(_1572417, tc_HOL_Obool), tc_fun(_1572417, tc_HOL_Obool)), tc_fun(_1572417, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572417, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1572417, tc_HOL_Obool), tc_fun(_1572417, tc_HOL_Obool), tc_fun(_1572417, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572417, tc_HOL_Obool), tc_fun(tc_fun(_1572417, tc_HOL_Obool), tc_fun(_1572417, tc_HOL_Obool)), tc_fun(_1572417, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572417, tc_HOL_Obool))), _1572419)), _1572423))), _1572415))))), -(hBOOL(hAPP(hAPP(c_member(_1572417), _1572421), _1572415)))], (49755 ^ _779854) ^ [_1786075, _1786077, _1786079, _1786081] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1786075), _1786077)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1786075), _1786079)), -(_1786079 = c_Orderings_Obot__class_Obot(tc_fun(_1786075, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1786075, _1786081, _1786077, _1786079)), 49769 ^ _779854 : [(49772 ^ _779854) ^ [_1786420] : [hBOOL(hAPP(hAPP(c_member(_1786075), _1786420), _1786079)), hBOOL(hAPP(hAPP(_1786081, 49768 ^ [_1786075, _1786077, _1786079, _1786081]), _1786420))], (49770 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786075), 49768 ^ [_1786075, _1786077, _1786079, _1786081]), _1786077)))]]], (25669 ^ _779854) ^ [_1246485, _1246487, _1246489] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246487), _1246489)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246485), _1246489)))], (49527 ^ _779854) ^ [_1779582, _1779584, _1779586, _1779588, _1779590] : [c_Relation_Otrans(_1779582, _1779584), hBOOL(hAPP(hAPP(c_member(tc_prod(_1779582, _1779582)), hAPP(hAPP(c_Product__Type_OPair(_1779582, _1779582), _1779586), _1779588)), _1779584)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1779582, _1779582)), hAPP(hAPP(c_Product__Type_OPair(_1779582, _1779582), _1779588), _1779590)), _1779584)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779582, _1779582)), hAPP(hAPP(c_Product__Type_OPair(_1779582, _1779582), _1779586), _1779590)), _1779584)))], (3964 ^ _779854) ^ [_839865, _839867, _839869, _839871, _839873, _839875, _839877, _839879] : [-(c_New__DSequence_Opos__decr__bind(_839879, _839875, _839871, _839867) = c_New__DSequence_Opos__decr__bind(_839877, _839873, _839869, _839865)), _839879 = _839877, _839875 = _839873, _839871 = _839869, _839867 = _839865], (30404 ^ _779854) ^ [_1328863, _1328865] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328863, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1328865)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328863, _1328865) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (42671 ^ _779854) ^ [_1627019, _1627021, _1627023, _1627025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627019), _1627021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627023, tc_HOL_Obool)), hAPP(c_List_Oset(_1627023), hAPP(hAPP(c_List_Otake(_1627023), _1627019), _1627025))), hAPP(c_List_Oset(_1627023), hAPP(hAPP(c_List_Otake(_1627023), _1627021), _1627025)))))], (42919 ^ _779854) ^ [_1634505, _1634507, _1634509, _1634511, _1634513, _1634515] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634505, _1634507)), hAPP(hAPP(c_Product__Type_OPair(_1634505, _1634507), _1634509), _1634511)), hAPP(c_List_Oset(tc_prod(_1634505, _1634507)), hAPP(hAPP(c_List_Ozip(_1634505, _1634507), _1634513), _1634515)))), -(hBOOL(hAPP(hAPP(c_member(_1634507), _1634511), hAPP(c_List_Oset(_1634507), _1634515))))], (30163 ^ _779854) ^ [_1324215, _1324217, _1324219, _1324221] : [class_Divides_Oring__div(_1324215), -(c_Divides_Odiv__class_Omod(_1324215, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1324215), _1324217), _1324219), _1324221) = c_Divides_Odiv__class_Omod(_1324215, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1324215), _1324217), c_Divides_Odiv__class_Omod(_1324215, _1324219, _1324221)), _1324221))], (39808 ^ _779854) ^ [_1552120, _1552122, _1552124, _1552126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552120, _1552122), tc_HOL_Obool)), _1552124), _1552126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552120, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1552120, _1552122), _1552124)), hAPP(c_Relation_ODomain(_1552120, _1552122), _1552126))))], (28340 ^ _779854) ^ [_1292253] : [-(hBOOL(hAPP(_1292253, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28347 ^ [_1292253])))), 28341 ^ _779854 : [(28342 ^ _779854) ^ [_1292305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292305)), hBOOL(hAPP(_1292253, _1292305))]]], (26333 ^ _779854) ^ [_1258507] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1258507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258507)))], (3432 ^ _779854) ^ [_831285, _831287, _831289, _831291, _831293, _831295] : [-(c_List_Opartition(_831295, _831291, _831287) = c_List_Opartition(_831293, _831289, _831285)), _831295 = _831293, _831291 = _831289, _831287 = _831285], (9250 ^ _779854) ^ [_934262, _934264, _934266] : [class_Orderings_Oorder(_934262), _934264 = _934266, -(c_SetInterval_Oord__class_OatLeastAtMost(_934262, _934264, _934266) = hAPP(hAPP(c_Set_Oinsert(_934262), _934264), c_Orderings_Obot__class_Obot(tc_fun(_934262, tc_HOL_Obool))))], (35939 ^ _779854) ^ [_1449424] : [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), _1449424))), -(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), _1449424)) = 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), _1449424))))], (41485 ^ _779854) ^ [_1593675, _1593677] : [-(c_Transitive__Closure_Otrancl(_1593675, hAPP(c_Relation_Oconverse(_1593675, _1593675), _1593677)) = hAPP(c_Relation_Oconverse(_1593675, _1593675), c_Transitive__Closure_Otrancl(_1593675, _1593677)))], (7557 ^ _779854) ^ [_904628, _904630] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904628, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_904628, tc_HOL_Obool))), _904630) = c_Orderings_Obot__class_Obot(tc_fun(_904628, tc_HOL_Obool)))], (6847 ^ _779854) ^ [_890920, _890922, _890924, _890926] : [hBOOL(hAPP(_890920, _890922)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890924, tc_HOL_Obool)), _890926), _890920), _890922)))], (41362 ^ _779854) ^ [_1590638, _1590640] : [-(c_Relation_Oirrefl(_1590638, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1590638, _1590638), tc_HOL_Obool)), _1590640), c_Relation_OId(_1590638))))], (43834 ^ _779854) ^ [_1654331, _1654333, _1654335, _1654337] : [-(hAPP(hAPP(c_List_Oappend(_1654331), hAPP(hAPP(c_List_Oappend(_1654331), _1654333), _1654335)), _1654337) = hAPP(hAPP(c_List_Oappend(_1654331), _1654333), hAPP(hAPP(c_List_Oappend(_1654331), _1654335), _1654337)))], (38472 ^ _779854) ^ [_1510781, _1510783, _1510785, _1510787] : [-(_1510781 = c_Orderings_Obot__class_Obot(tc_fun(_1510783, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1510783, _1510785), _1510785, c_Product__Type_Osnd(_1510783, _1510785)), hAPP(hAPP(c_Product__Type_OSigma(_1510783, _1510785), _1510781), hAPP(c_COMBK(tc_fun(_1510785, tc_HOL_Obool), _1510783), _1510787))) = _1510787)], (18265 ^ _779854) ^ [_1110425, _1110427, _1110429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110427), _1110429)), -(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, _1110425)), _1110427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110425)), _1110429))))], (27625 ^ _779854) ^ [_1279896, _1279898] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1279896)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279896)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279898)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1279896)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1279898))))], (4730 ^ _779854) ^ [_852024, _852026, _852028, _852030] : [-(c_Product__Type_Osnd(_852030, _852026) = c_Product__Type_Osnd(_852028, _852024)), _852030 = _852028, _852026 = _852024], (52231 ^ _779854) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (4476 ^ _779854) ^ [_848021, _848023, _848025, _848027, _848029, _848031] : [-(c_Lazy__Sequence_Oanamorph(_848031, _848027, _848023) = c_Lazy__Sequence_Oanamorph(_848029, _848025, _848021)), _848031 = _848029, _848027 = _848025, _848023 = _848021], (23828 ^ _779854) ^ [_1211985, _1211987] : [-(_1211985 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211987), _1211985) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211987), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211987), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211985), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (20518 ^ _779854) ^ [_1148993] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1148993)) = 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), _1148993))))], (29409 ^ _779854) ^ [_1310394, _1310396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310394), _1310396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1310394)), c_Int_OBit0(_1310396))))], (23700 ^ _779854) ^ [_1209345, _1209347] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209345), _1209347)), 23706 ^ _779854 : [(23709 ^ _779854) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23707 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1209345), 23705 ^ [_1209345, _1209347]), _1209347)))]], -(hAPP(c_Finite__Set_Ocard(_1209345), _1209347) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2206 ^ _779854) ^ [_812084, _812086, _812088, _812090, _812092, _812094, _812096, _812098, _812100, _812102] : [-(c_Fun_Ooverride__on(_812102, _812098, _812094, _812090, _812086) = c_Fun_Ooverride__on(_812100, _812096, _812092, _812088, _812084)), _812102 = _812100, _812098 = _812096, _812094 = _812092, _812090 = _812088, _812086 = _812084], (17953 ^ _779854) ^ [_1104762, _1104764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104762)), hAPP(c_Nat_OSuc, _1104764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104762), _1104764)))], (29705 ^ _779854) ^ [_1315634] : [class_Rings_Osemiring__1(_1315634), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1315634), c_Groups_Ozero__class_Ozero(_1315634)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1315634))], (38805 ^ _779854) ^ [_1519986] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1519986, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1519986), hAPP(c_COMBK(tc_HOL_Obool, _1519986), c_fFalse)))], (27357 ^ _779854) ^ [_1275758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275758), 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), _1275758)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31029 ^ _779854) ^ [_1339877] : [c_Int_OMin = _1339877, -(c_Int_OMin = c_Int_OBit1(_1339877))], (43722 ^ _779854) ^ [_1651791, _1651793, _1651795, _1651797] : [-(c_List_Osublist(_1651791, hAPP(hAPP(c_List_Olist_OCons(_1651791), _1651793), _1651795), _1651797) = hAPP(hAPP(c_List_Oappend(_1651791), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1651791)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1651797)), hAPP(hAPP(c_List_Olist_OCons(_1651791), _1651793), c_List_Olist_ONil(_1651791))), c_List_Olist_ONil(_1651791))), c_List_Osublist(_1651791, _1651795, 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)), _1651797)))))], (52295 ^ _779854) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (39919 ^ _779854) ^ [_1554801, _1554803, _1554805, _1554807] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1554801, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1554801, _1554803), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1554801, _1554803), tc_HOL_Obool)), _1554805), _1554807))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1554801, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1554801, _1554803), _1554805)), hAPP(c_Relation_ODomain(_1554801, _1554803), _1554807)))))], (8054 ^ _779854) ^ [_914707, _914709, _914711] : [class_Orderings_Olinorder(_914707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914707), _914709), _914711)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914707, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_914707, _914709, _914711)), hAPP(c_SetInterval_Oord__class_OatLeast(_914707), _914711)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_914707), _914709))], (34581 ^ _779854) ^ [_1421697, _1421699] : [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(_1421699))), 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), _1421697)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421697)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421699))))], (39088 ^ _779854) ^ [_1528443, _1528445, _1528447, _1528449] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1528443), hAPP(c_Set_OCollect(_1528443), _1528445))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1528447), hAPP(c_Set_OCollect(_1528447), hAPP(hAPP(c_COMBB(tc_fun(_1528443, tc_HOL_Obool), tc_HOL_Obool, _1528447), c_HOL_OEx(_1528443)), hAPP(hAPP(c_COMBC(_1528447, tc_fun(_1528443, tc_HOL_Obool), tc_fun(_1528443, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528443, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1528443, tc_HOL_Obool), tc_fun(_1528443, tc_HOL_Obool)), _1528447), c_COMBS(_1528443, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528443, tc_HOL_Obool), tc_fun(_1528443, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1528447), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1528443), c_fconj)), hAPP(hAPP(c_COMBC(_1528447, tc_fun(_1528443, _1528447), tc_fun(_1528443, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528447, tc_HOL_Obool), tc_fun(tc_fun(_1528443, _1528447), tc_fun(_1528443, tc_HOL_Obool)), _1528447), c_COMBB(_1528447, tc_HOL_Obool, _1528443)), c_fequal)), _1528449)))), _1528445))))))], (41403 ^ _779854) ^ [_1591663, _1591665] : [-(c_Transitive__Closure_Ortrancl(_1591663, hAPP(c_Relation_Oconverse(_1591663, _1591663), _1591665)) = hAPP(c_Relation_Oconverse(_1591663, _1591663), c_Transitive__Closure_Ortrancl(_1591663, _1591665)))], (942 ^ _779854) ^ [_794001, _794003, _794005, _794007, _794009, _794011] : [-(c_Relation_Orefl__on(_794009, _794005, _794001)), c_Relation_Orefl__on(_794011, _794007, _794003), _794011 = _794009, _794007 = _794005, _794003 = _794001], (9212 ^ _779854) ^ [_933600, _933602, _933604] : [class_Orderings_Olinorder(_933600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933600), _933602), _933604)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933600, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_933600, _933602, _933604)), hAPP(hAPP(c_Set_Oinsert(_933600), _933604), c_Orderings_Obot__class_Obot(tc_fun(_933600, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_933600, _933602, _933604))], (2704 ^ _779854) ^ [_820033, _820035] : [_820035 = _820033, -(c_Int_Oint__ge__less__than2(_820035) = c_Int_Oint__ge__less__than2(_820033))], (22039 ^ _779854) ^ [_1177792, _1177794, _1177796, _1177798, _1177800, _1177802] : [class_Groups_Oab__semigroup__mult(_1177792), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177794), _1177796)), -(hBOOL(hAPP(hAPP(c_member(_1177794), _1177798), _1177796))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1177792, _1177794, c_Groups_Otimes__class_Otimes(_1177792)), _1177800), _1177802), hAPP(hAPP(c_Set_Oinsert(_1177794), _1177798), _1177796)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177792), hAPP(_1177800, _1177798)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1177792, _1177794, c_Groups_Otimes__class_Otimes(_1177792)), _1177800), _1177802), _1177796)))], (29071 ^ _779854) ^ [_1304509] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304509) = 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), _1304509))))], (36165 ^ _779854) ^ [_1454572, _1454574, _1454576, _1454578] : [-(_1454572 = _1454574), hAPP(c_Product__Type_Ofst(_1454576, _1454578), _1454572) = hAPP(c_Product__Type_Ofst(_1454576, _1454578), _1454574), hAPP(c_Product__Type_Osnd(_1454576, _1454578), _1454572) = hAPP(c_Product__Type_Osnd(_1454576, _1454578), _1454574)], (9426 ^ _779854) ^ [_937323, _937325, _937327, _937329] : [class_Orderings_Olinorder(_937323), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937323, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_937323), _937325)), c_SetInterval_Oord__class_OatLeastAtMost(_937323, _937327, _937329)) = c_SetInterval_Oord__class_OatLeastAtMost(_937323, hAPP(hAPP(c_Orderings_Oord__class_Omax(_937323), _937325), _937327), _937329))], (36556 ^ _779854) ^ [_1462747, _1462749, _1462751, _1462753, _1462755, _1462757, _1462759, _1462761] : [c_Fun_Oinj__on(_1462747, _1462749, _1462751, _1462753), 36562 ^ _779854 : [(36565 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462747, tc_HOL_Obool)), hAPP(_1462759, 36561 ^ [_1462747, _1462749, _1462751, _1462753, _1462755, _1462757, _1462759, _1462761])), _1462753))], (36563 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1462755), 36561 ^ [_1462747, _1462749, _1462751, _1462753, _1462755, _1462757, _1462759, _1462761]), _1462757)))]], hBOOL(hAPP(hAPP(c_member(_1462755), _1462761), _1462757)), -(hAPP(c_Set_Oimage(_1462747, _1462749, _1462751), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462755, tc_fun(_1462747, tc_HOL_Obool)), _1462757), _1462759)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462755, tc_fun(_1462749, tc_HOL_Obool)), _1462757), hAPP(hAPP(c_COMBB(tc_fun(_1462747, tc_HOL_Obool), tc_fun(_1462749, tc_HOL_Obool), _1462755), c_Set_Oimage(_1462747, _1462749, _1462751)), _1462759)))], (11061 ^ _779854) ^ [_970118, _970120] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_970118, tc_HOL_Obool)), _970120) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970118, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_970118, tc_HOL_Obool))), _970120))], (30611 ^ _779854) ^ [_1332420, _1332422] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332420), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1332422), _1332420)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332422), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332422, _1332420)))], (17935 ^ _779854) ^ [_1104480, _1104482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104480), hAPP(c_Nat_OSuc, _1104482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104480), _1104482))), -(_1104480 = hAPP(c_Nat_OSuc, _1104482))], (47334 ^ _779854) ^ [_1731461, _1731463] : [_1731463 = c_List_Olist_ONil(_1731461), -(c_List_Olist_ONil(_1731461) = hAPP(c_List_Orev(_1731461), _1731463))], (39788 ^ _779854) ^ [_1551621, _1551623, _1551625] : [c_Wellfounded_Owf(_1551621, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551621, _1551621), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551621, _1551621), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1551621, _1551621, _1551621), _1551623), _1551623)), hAPP(hAPP(c_Relation_Orel__comp(_1551621, _1551621, _1551621), _1551625), _1551623))), _1551625)), -(c_Wellfounded_Owf(_1551621, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551621, _1551621), tc_HOL_Obool)), _1551623), _1551625)))], (18593 ^ _779854) ^ [_1116409, _1116411, _1116413] : [class_Rings_Ono__zero__divisors(_1116409), -(_1116411 = c_Groups_Ozero__class_Ozero(_1116409)), -(_1116413 = c_Groups_Ozero__class_Ozero(_1116409)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116409), _1116411), _1116413) = c_Groups_Ozero__class_Ozero(_1116409)], (36778 ^ _779854) ^ [_1468142, _1468144, _1468146, _1468148, _1468150] : [-(hAPP(c_Product__Type_Osnd(_1468142, _1468144), hAPP(c_Product__Type_Oapfst(_1468146, _1468142, _1468144, _1468148), _1468150)) = hAPP(c_Product__Type_Osnd(_1468146, _1468144), _1468150))], (32111 ^ _779854) ^ [_1357509, _1357511] : [class_Groups_Oordered__ab__group__add__abs(_1357509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357509), c_Groups_Ozero__class_Ozero(_1357509)), _1357511)), -(hAPP(c_Groups_Oabs__class_Oabs(_1357509), _1357511) = _1357511)], (26773 ^ _779854) ^ [_1265893, _1265895] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1265893), _1265895) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1265895 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26782 ^ _779854 : [(26785 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265893), _1265895)))], (26783 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265893)))]], 26786 ^ _779854 : [(26789 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265895), _1265893)))], (26787 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1265893), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (50398 ^ _779854) ^ [_1798005, _1798007, _1798009, _1798011, _1798013] : [hBOOL(hAPP(hAPP(c_member(_1798005), _1798007), hAPP(c_Set_Oimage(_1798009, _1798005, _1798011), _1798013))), -(hBOOL(hAPP(hAPP(c_member(_1798009), hAPP(c_Hilbert__Choice_Oinv__into(_1798009, _1798005, _1798013, _1798011), _1798007)), _1798013)))], (45113 ^ _779854) ^ [_1682639, _1682641, _1682643, _1682645] : [_1682645 = c_List_Olist_ONil(_1682639), -(hAPP(hAPP(c_List_Omap(_1682639, _1682641), _1682643), _1682645) = c_List_Olist_ONil(_1682641))], (43227 ^ _779854) ^ [_1641443, _1641445] : [hAPP(c_Finite__Set_Ocard(_1641443), hAPP(c_List_Oset(_1641443), _1641445)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641443)), _1641445), -(hBOOL(hAPP(c_List_Odistinct(_1641443), _1641445)))], (2432 ^ _779854) ^ [_815691, _815693, _815695, _815697] : [-(c_Divides_OnegDivAlg(_815697, _815693) = c_Divides_OnegDivAlg(_815695, _815691)), _815697 = _815695, _815693 = _815691], (50170 ^ _779854) ^ [_1793643, _1793645] : [c_Predicate_Osymp(_1793643, _1793645), -(c_Relation_Osym(_1793643, hAPP(c_Set_OCollect(tc_prod(_1793643, _1793643)), hAPP(c_Product__Type_Oprod_Oprod__case(_1793643, _1793643, tc_HOL_Obool), _1793645))))], (434 ^ _779854) ^ [_786403, _786405, _786407, _786409, _786411, _786413] : [-(c_Relation_Ototal__on(_786411, _786407, _786403)), c_Relation_Ototal__on(_786413, _786409, _786405), _786413 = _786411, _786409 = _786407, _786405 = _786403], (30005 ^ _779854) ^ [_1320781, _1320783, _1320785] : [class_Int_Onumber__ring(_1320781), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1320781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320781), _1320783), _1320785)), 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(_1320781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320781), hAPP(hAPP(c_Power_Opower__class_Opower(_1320781), _1320783), 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(_1320781), _1320785), 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(_1320781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320781), hAPP(c_Int_Onumber__class_Onumber__of(_1320781), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1320783)), _1320785)))], (38460 ^ _779854) ^ [_1510531, _1510533, _1510535, _1510537] : [-(_1510531 = c_Orderings_Obot__class_Obot(tc_fun(_1510533, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1510535, _1510533), _1510535, c_Product__Type_Ofst(_1510535, _1510533)), hAPP(hAPP(c_Product__Type_OSigma(_1510535, _1510533), _1510537), hAPP(c_COMBK(tc_fun(_1510533, tc_HOL_Obool), _1510535), _1510531))) = _1510537)], (28631 ^ _779854) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (26357 ^ _779854) ^ [_1258815] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258815))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1258815) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52217 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (1290 ^ _779854) ^ [_798931, _798933] : [-(class_Int_Oring__char__0(_798931)), _798933 = _798931, class_Int_Oring__char__0(_798933)], (31298 ^ _779854) ^ [_1344099, _1344101, _1344103] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344099), _1344101)), _1344103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344099), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344101), _1344103))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1344099), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1344101, _1344103))), _1344103)))], (11969 ^ _779854) ^ [_987870, _987872, _987874, _987876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987870, tc_HOL_Obool)), _987872), _987874)), hBOOL(hAPP(hAPP(c_member(_987870), _987876), _987872)), -(hBOOL(hAPP(hAPP(c_member(_987870), _987876), _987874)))], (47540 ^ _779854) ^ [_1735797, _1735799] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735797), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1735797))), _1735799))), 47543 ^ _779854 : [(47550 ^ _779854) ^ [] : [-(_1735799 = c_List_Olist_ONil(tc_List_Olist(_1735797))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735797))), c_List_Otranspose(_1735797, _1735799)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735797)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1735797)), _1735799), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47544 ^ _779854) ^ [] : [_1735799 = c_List_Olist_ONil(tc_List_Olist(_1735797)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735797))), c_List_Otranspose(_1735797, _1735799)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (52115 ^ _779854) ^ [_1832869, _1832871] : [class_Orderings_Opreorder(_1832869), -(class_Orderings_Opreorder(tc_fun(_1832871, _1832869)))], (32824 ^ _779854) ^ [_1371184, _1371186, _1371188, _1371190] : [class_Groups_Oordered__ab__group__add__abs(_1371184), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371184), c_Groups_Ozero__class_Ozero(_1371184)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371186, _1371184), hAPP(hAPP(c_COMBB(_1371184, _1371184, _1371186), c_Groups_Oabs__class_Oabs(_1371184)), _1371188)), _1371190))))], (22393 ^ _779854) ^ [_1184648, _1184650, _1184652] : [class_Fields_Olinordered__field(_1184648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184648), c_Groups_Ozero__class_Ozero(_1184648)), _1184650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184648), _1184652), c_Groups_Ozero__class_Ozero(_1184648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184648), _1184650), _1184652)), c_Groups_Ozero__class_Ozero(_1184648))))], (52633 ^ _779854) ^ [_1838150, _1838152, _1838154, _1838156, _1838158, _1838160] : [-(hAPP(hAPP(hAPP(c_COMBB(_1838150, _1838152, _1838154), _1838156), _1838158), _1838160) = hAPP(_1838156, hAPP(_1838158, _1838160)))], (42257 ^ _779854) ^ [_1614847, _1614849, _1614851, _1614853, _1614855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614847), tc_List_Olist(_1614847))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614847), tc_List_Olist(_1614847)), _1614849), _1614851)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1614847), c_List_Olistrel1(_1614847, _1614853)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614847), tc_List_Olist(_1614847))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614847), tc_List_Olist(_1614847)), hAPP(hAPP(c_List_Olist_OCons(_1614847), _1614855), _1614849)), hAPP(hAPP(c_List_Olist_OCons(_1614847), _1614855), _1614851))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1614847), c_List_Olistrel1(_1614847, _1614853)))))], (41501 ^ _779854) ^ [_1593983, _1593985, _1593987] : [-(hAPP(c_Relation_ODomain(_1593983, _1593985), hAPP(c_Relation_Oconverse(_1593985, _1593983), _1593987)) = hAPP(c_Relation_ORange(_1593985, _1593983), _1593987))], (1040 ^ _779854) ^ [_795554, _795556, _795558, _795560, _795562, _795564] : [-(c_List_Olist__all(_795562, _795558, _795554)), c_List_Olist__all(_795564, _795560, _795556), _795564 = _795562, _795560 = _795558, _795556 = _795554], (5768 ^ _779854) ^ [_871134, _871136, _871138] : [-(_871134 = _871136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871138, tc_HOL_Obool)), _871134), _871136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871138, tc_HOL_Obool)), _871136), _871134))], (46514 ^ _779854) ^ [_1714477, _1714479, _1714481, _1714483] : [-(c_List_Otranspose(_1714477, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714479), tc_List_Olist(_1714477)), hAPP(c_List_Omap(_1714479, _1714477), _1714481)), _1714483)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714479), tc_List_Olist(_1714477)), hAPP(c_List_Omap(_1714479, _1714477), _1714481)), c_List_Otranspose(_1714479, _1714483)))], (5490 ^ _779854) ^ [_863924, _863926] : [_863926 = _863924, -(c_Groups_Ominus__class_Ominus(_863926) = c_Groups_Ominus__class_Ominus(_863924))], (42594 ^ _779854) ^ [_1624926, _1624928, _1624930, _1624932] : [-(hAPP(hAPP(c_List_Onth(_1624926), hAPP(hAPP(c_List_Olist_OCons(_1624926), _1624928), _1624930)), _1624932) = c_Nat_Onat_Onat__case(_1624926, _1624928, hAPP(c_List_Onth(_1624926), _1624930), _1624932))], (32938 ^ _779854) ^ [_1375405, _1375407, _1375409, _1375411] : [32940 ^ _779854 : [(32943 ^ _779854) ^ [] : [hAPP(_1375411, 32939 ^ [_1375405, _1375407, _1375409, _1375411]) = c_Orderings_Otop__class_Otop(tc_fun(_1375407, tc_HOL_Obool))], (32941 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375405), 32939 ^ [_1375405, _1375407, _1375409, _1375411]), _1375409)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375405, tc_fun(_1375407, tc_HOL_Obool)), _1375409), _1375411) = c_Orderings_Otop__class_Otop(tc_fun(_1375407, tc_HOL_Obool)))], (45714 ^ _779854) ^ [_1696335, _1696337, _1696339, _1696341] : [hBOOL(hAPP(c_List_Olistsp(_1696335, _1696337), _1696339)), hBOOL(hAPP(c_List_Olistsp(_1696335, _1696341), _1696339)), -(hBOOL(hAPP(c_List_Olistsp(_1696335, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1696335, tc_HOL_Obool)), _1696337), _1696341)), _1696339)))], (28232 ^ _779854) ^ [_1290360, _1290362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1290360)), c_Int_OBit1(_1290362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1290360), _1290362)))], (45601 ^ _779854) ^ [_1693462, _1693464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693462)), hAPP(c_Code__Numeral_Onat__of, _1693464))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1693462), _1693464)))], (34962 ^ _779854) ^ [_1429970, _1429972, _1429974, _1429976, _1429978, _1429980] : [hBOOL(hAPP(hAPP(_1429970, _1429972), _1429974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429976, tc_fun(_1429978, tc_HOL_Obool))), _1429970), _1429980)), -(hBOOL(hAPP(hAPP(_1429980, _1429972), _1429974)))], (35290 ^ _779854) ^ [_1437392, _1437394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437392)), 35293 ^ _779854 : [(35300 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437394))), 35303 ^ _779854 : [(35310 ^ _779854) ^ [] : [-(_1437392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1437392, _1437394) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1437392), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1437394))))], (35304 ^ _779854) ^ [] : [_1437392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1437392, _1437394) = 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)))]]], (35294 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437394)), -(c_Divides_Odivmod__int(_1437392, _1437394) = c_Divides_OposDivAlg(_1437392, _1437394))]]], (40155 ^ _779854) ^ [_1561186] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561186, tc_HOL_Obool) = c_Set_OBall(_1561186))], (35358 ^ _779854) ^ [_1438517, _1438519, _1438521, _1438523, _1438525, _1438527, _1438529] : [-(hAPP(c_Product__Type_Oapsnd(_1438517, _1438519, _1438521, _1438523), hAPP(c_Product__Type_Oapsnd(_1438525, _1438517, _1438521, _1438527), _1438529)) = hAPP(c_Product__Type_Oapsnd(_1438525, _1438519, _1438521, hAPP(c_Fun_Ocomp(_1438517, _1438519, _1438525, _1438523), _1438527)), _1438529))], (18567 ^ _779854) ^ [_1116039, _1116041] : [class_Rings_Ocomm__semiring__1(_1116039), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116039), _1116041), c_Groups_Ozero__class_Ozero(_1116039)) = c_Groups_Ozero__class_Ozero(_1116039))], (13979 ^ _779854) ^ [_1026141, _1026143] : [class_Orderings_Olinorder(_1026141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026141), _1026143)), -(_1026143 = c_Orderings_Obot__class_Obot(tc_fun(_1026141, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1026141), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1026141), 13992 ^ [_1026141, _1026143]), 13993 ^ [_1026141, _1026143])), hAPP(hAPP(c_Set_Oinsert(_1026141), 13992 ^ [_1026141, _1026143]), hAPP(hAPP(c_Set_Oinsert(_1026141), 13993 ^ [_1026141, _1026143]), c_Orderings_Obot__class_Obot(tc_fun(_1026141, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1026141), c_Big__Operators_Olinorder__class_OMin(_1026141, _1026143)), _1026143)))], (42024 ^ _779854) ^ [_1607646, _1607648, _1607650] : [-(c_Nitpick_Oplus__frac(_1607646, _1607648, _1607650) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1607646), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1607646), _1607648), hAPP(c_Nitpick_Odenom(_1607646), _1607650))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1607646), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1607646), tc_Int_Oint), c_Nitpick_Ofrac(_1607646)), 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(_1607646), _1607648))), 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(_1607646), _1607648))))), 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(_1607646), _1607650))), 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(_1607646), _1607650)))))), c_COMBI(tc_Int_Oint))))], (28537 ^ _779854) ^ [_1295770, _1295772, _1295774] : [class_Rings_Olinordered__semidom(_1295770), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1295772), _1295774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295770), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295770), _1295772)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295770), _1295774))))], (7662 ^ _779854) ^ [_907010, _907012, _907014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907010, tc_HOL_Obool)), _907012), _907014)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907010, tc_HOL_Obool)), _907012), _907014) = _907012)], (11350 ^ _779854) ^ [_975745, _975747] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975745), c_Complete__Lattice_OSup__class_OSup(tc_fun(_975745, tc_HOL_Obool), _975747))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_975745, tc_HOL_Obool)), _975747)))], (15524 ^ _779854) ^ [_1057131, _1057133, _1057135] : [class_Groups_Ogroup__add(_1057131), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057131), _1057133), hAPP(c_Groups_Ouminus__class_Ouminus(_1057131), _1057135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057131), _1057133), _1057135))], (14715 ^ _779854) ^ [_1040679, _1040681, _1040683] : [class_Orderings_Olinorder(_1040679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040679), _1040681)), -(_1040681 = c_Orderings_Obot__class_Obot(tc_fun(_1040679, tc_HOL_Obool))), 14726 ^ _779854 : [(14727 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040679), _1040683), hAPP(c_Finite__Set_Ofold1(_1040679, c_Orderings_Oord__class_Omin(_1040679)), _1040681))), 14730 ^ _779854 : [(14731 ^ _779854) ^ [_1040972] : [hBOOL(hAPP(hAPP(c_member(_1040679), _1040972), _1040681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040679), _1040683), _1040972)))]]], (14737 ^ _779854) ^ [] : [14739 ^ _779854 : [(14742 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040679), _1040683), 14738 ^ [_1040679, _1040681, _1040683]))], (14740 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1040679), 14738 ^ [_1040679, _1040681, _1040683]), _1040681)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040679), _1040683), hAPP(c_Finite__Set_Ofold1(_1040679, c_Orderings_Oord__class_Omin(_1040679)), _1040681))))]]], (31162 ^ _779854) ^ [_1341867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1341867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1341867)))], (470 ^ _779854) ^ [_786941, _786943] : [-(class_Rings_Oinverse(_786941)), _786943 = _786941, class_Rings_Oinverse(_786943)], (44699 ^ _779854) ^ [_1674113, _1674115, _1674117] : [class_Orderings_Olinorder(_1674113), -(c_Big__Operators_Olinorder__class_OMin(_1674113, hAPP(c_List_Oset(_1674113), hAPP(hAPP(c_List_Olist_OCons(_1674113), _1674115), _1674117))) = hAPP(c_List_Ofoldl(_1674113, _1674113, c_Orderings_Oord__class_Omin(_1674113), _1674115), _1674117))], (12836 ^ _779854) ^ [_1005158, _1005160] : [class_Orderings_Olinorder(_1005158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005158), _1005160)), -(_1005160 = c_Orderings_Obot__class_Obot(tc_fun(_1005158, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1005158), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1005158), 12849 ^ [_1005158, _1005160]), 12850 ^ [_1005158, _1005160])), hAPP(hAPP(c_Set_Oinsert(_1005158), 12849 ^ [_1005158, _1005160]), hAPP(hAPP(c_Set_Oinsert(_1005158), 12850 ^ [_1005158, _1005160]), c_Orderings_Obot__class_Obot(tc_fun(_1005158, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1005158), c_Big__Operators_Olattice_OSup__fin(_1005158, c_Orderings_Oord__class_Omax(_1005158), _1005160)), _1005160)))], (47615 ^ _779854) ^ [_1737459, _1737461, _1737463, _1737465, _1737467] : [-(hAPP(hAPP(c_List_Ozip(_1737459, _1737461), c_List_OtakeWhile(_1737459, _1737463, _1737465)), _1737467) = c_List_OtakeWhile(tc_prod(_1737459, _1737461), hAPP(c_Fun_Ocomp(_1737459, tc_HOL_Obool, tc_prod(_1737459, _1737461), _1737463), c_Product__Type_Ofst(_1737459, _1737461)), hAPP(hAPP(c_List_Ozip(_1737459, _1737461), _1737465), _1737467)))], (50940 ^ _779854) ^ [_1809835, _1809837, _1809839, _1809841] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1809835), _1809837)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1809839), _1809841)), 50947 ^ _779854 : [(50954 ^ _779854) ^ [] : [hAPP(c_Finite__Set_Ocard(_1809835), _1809837) = hAPP(c_Finite__Set_Ocard(_1809839), _1809841), -(c_Fun_Obij__betw(_1809835, _1809839, 50957 ^ [_1809835, _1809837, _1809839, _1809841], _1809837, _1809841))], (50948 ^ _779854) ^ [] : [50949 ^ _779854 : [(50950 ^ _779854) ^ [_1810024] : [c_Fun_Obij__betw(_1809835, _1809839, _1810024, _1809837, _1809841)]], -(hAPP(c_Finite__Set_Ocard(_1809835), _1809837) = hAPP(c_Finite__Set_Ocard(_1809839), _1809841))]]], (31005 ^ _779854) ^ [_1339470, _1339472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1339470, _1339472)), _1339470)))], (8044 ^ _779854) ^ [_914494, _914496, _914498] : [class_Orderings_Olinorder(_914494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914494), _914496), _914498)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914494, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_914494, _914496), _914498)), hAPP(hAPP(c_Set_Oinsert(_914494), _914498), c_Orderings_Obot__class_Obot(tc_fun(_914494, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_914494, _914496, _914498))], (20556 ^ _779854) ^ [_1149593, _1149595, _1149597] : [class_Groups_Oordered__comm__monoid__add(_1149593), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149593), _1149595), c_Groups_Ozero__class_Ozero(_1149593))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149593), _1149597), c_Groups_Ozero__class_Ozero(_1149593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149593), _1149595), _1149597)), c_Groups_Ozero__class_Ozero(_1149593))))], (43039 ^ _779854) ^ [_1637145, _1637147, _1637149, _1637151] : [_1637145 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637147)), _1637149)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1637147, hAPP(hAPP(c_List_Olist__update(_1637147, _1637149), _1637145), _1637151)) = c_List_Obutlast(_1637147, _1637149))], (32391 ^ _779854) ^ [_1362862] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1362862), hAPP(c_Int_Onumber__class_Onumber__of(_1362862), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1362862)), class_Int_Onumber__ring(_1362862), class_Rings_Olinordered__idom(_1362862)], (46398 ^ _779854) ^ [_1712037, _1712039, _1712041] : [hBOOL(hAPP(c_List_Odistinct(_1712037), _1712039)), -(hBOOL(hAPP(c_List_Odistinct(_1712037), hAPP(c_List_Ofilter(_1712037, _1712041), _1712039))))], (24294 ^ _779854) ^ [_1220410, _1220412, _1220414, _1220416] : [class_Rings_Olinordered__semidom(_1220410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220410), c_Groups_Oone__class_Oone(_1220410)), _1220412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220410), hAPP(hAPP(c_Power_Opower__class_Opower(_1220410), _1220412), _1220414)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220410), _1220412), _1220416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220414), _1220416)))], (2038 ^ _779854) ^ [_809484, _809486, _809488, _809490, _809492, _809494] : [-(c_Power_Opower_Opower(_809494, _809490, _809486) = c_Power_Opower_Opower(_809492, _809488, _809484)), _809494 = _809492, _809490 = _809488, _809486 = _809484], (6487 ^ _779854) ^ [_883624] : [class_Complete__Lattice_Ocomplete__lattice(_883624), -(c_Complete__Lattice_OInf__class_OInf(_883624, c_Orderings_Otop__class_Otop(tc_fun(_883624, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_883624))], (50114 ^ _779854) ^ [_1792816, _1792818, _1792820, _1792822] : [c_Relation_Osym(_1792816, _1792818), -(c_Relation_Osym(_1792820, hAPP(hAPP(c_Relation_Oinv__image(_1792816, _1792820), _1792818), _1792822)))], (1540 ^ _779854) ^ [_802056, _802058] : [-(class_Rings_Olinordered__comm__semiring__strict(_802056)), _802058 = _802056, class_Rings_Olinordered__comm__semiring__strict(_802058)], (48826 ^ _779854) ^ [_1763878, _1763880] : [-(c_List_Osplice(_1763878, c_List_Olist_ONil(_1763878), _1763880) = _1763880)], (33691 ^ _779854) ^ [_1399218, _1399220, _1399222] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1399218), _1399220), _1399222) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1399218), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1399218, tc_Int_Oint), _1399220), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1399222))), class_Groups_Ocomm__monoid__add(_1399218), class_Groups_Ocomm__monoid__mult(_1399218)], (39413 ^ _779854) ^ [_1541303, _1541305, _1541307, _1541309, _1541311, _1541313, _1541315] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541303, _1541305, _1541307), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541309, tc_fun(tc_prod(_1541303, _1541305), tc_HOL_Obool)), _1541311), _1541313)), _1541315) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541309, tc_fun(tc_prod(_1541303, _1541307), tc_HOL_Obool)), _1541311), hAPP(hAPP(c_COMBC(_1541309, tc_fun(tc_prod(_1541305, _1541307), tc_HOL_Obool), tc_fun(tc_prod(_1541303, _1541307), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1541303, _1541305), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1541305, _1541307), tc_HOL_Obool), tc_fun(tc_prod(_1541303, _1541307), tc_HOL_Obool)), _1541309), c_Relation_Orel__comp(_1541303, _1541305, _1541307)), _1541313)), _1541315)))], (12364 ^ _779854) ^ [_995633, _995635, _995637, _995639] : [hBOOL(hAPP(hAPP(c_member(_995633), _995635), _995637)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995633, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995633), _995635), _995639)), _995637) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995633, tc_HOL_Obool)), _995639), _995637))], (29251 ^ _779854) ^ [_1307592, _1307594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307592)), -(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)))), _1307594))), 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)))), _1307592)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1307594), _1307592))], (13475 ^ _779854) ^ [_1017023, _1017025, _1017027] : [class_Orderings_Olinorder(_1017023), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017023), _1017025)), -(_1017025 = c_Orderings_Obot__class_Obot(tc_fun(_1017023, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1017023, hAPP(hAPP(c_Set_Oinsert(_1017023), _1017027), _1017025)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1017023), _1017027), c_Big__Operators_Olinorder__class_OMax(_1017023, _1017025)))], (16127 ^ _779854) ^ [_1069426, _1069428, _1069430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069426), _1069428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069426), _1069430)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069428), _1069430))))], (44224 ^ _779854) ^ [_1663764, _1663766, _1663768] : [-(hAPP(hAPP(c_List_Oappend(_1663764), hAPP(hAPP(c_List_Otake(_1663764), _1663766), _1663768)), hAPP(hAPP(c_List_Odrop(_1663764), _1663766), _1663768)) = _1663768)], (7261 ^ _779854) ^ [_899353, _899355, _899357, _899359] : [class_Lattices_Osemilattice__inf(_899353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899353), _899355), _899357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899353), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_899353), _899359), _899355)), _899357)))], (48902 ^ _779854) ^ [_1765516, _1765518, _1765520, _1765522, _1765524] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1765516, _1765518, hAPP(hAPP(c_COMBC(_1765516, tc_fun(tc_prod(_1765516, _1765518), tc_HOL_Obool), tc_fun(_1765518, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1765518, tc_fun(tc_fun(tc_prod(_1765516, _1765518), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1765516, _1765518), tc_HOL_Obool), tc_fun(_1765518, tc_HOL_Obool)), _1765516), c_COMBC(_1765518, tc_fun(tc_prod(_1765516, _1765518), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1765518, tc_prod(_1765516, _1765518)), tc_fun(_1765518, tc_fun(tc_fun(tc_prod(_1765516, _1765518), tc_HOL_Obool), tc_HOL_Obool)), _1765516), hAPP(c_COMBB(tc_prod(_1765516, _1765518), tc_fun(tc_fun(tc_prod(_1765516, _1765518), tc_HOL_Obool), tc_HOL_Obool), _1765518), c_member(tc_prod(_1765516, _1765518)))), c_Product__Type_OPair(_1765516, _1765518)))), _1765520)), _1765522), _1765524)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765518, _1765516)), hAPP(hAPP(c_Product__Type_OPair(_1765518, _1765516), _1765522), _1765524)), hAPP(c_Relation_Oconverse(_1765516, _1765518), _1765520))))], (36645 ^ _779854) ^ [_1465118, _1465120, _1465122, _1465124, _1465126, _1465128, _1465130] : [c_Finite__Set_Ofolding__idem(_1465118, _1465120, _1465122, _1465124), -(hAPP(c_Fun_Ocomp(_1465120, _1465120, _1465126, hAPP(_1465122, _1465128)), hAPP(c_Fun_Ocomp(_1465120, _1465120, _1465126, hAPP(_1465122, _1465128)), _1465130)) = hAPP(c_Fun_Ocomp(_1465120, _1465120, _1465126, hAPP(_1465122, _1465128)), _1465130))], (26923 ^ _779854) ^ [_1268218, _1268220, _1268222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1268218), 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)), _1268220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268220), _1268222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268218), _1268220)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268218), _1268222))))], (38775 ^ _779854) ^ [_1519480, _1519482, _1519484] : [-(hAPP(c_Set_OCollect(_1519480), hAPP(hAPP(c_COMBS(_1519480, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519480), c_fconj), _1519482)), _1519484)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1519480, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1519480), _1519482)), hAPP(c_Set_OCollect(_1519480), _1519484)))], (18237 ^ _779854) ^ [_1109793, _1109795, _1109797] : [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, _1109793)), _1109795)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1109793)), _1109797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109795), _1109797)))], (38176 ^ _779854) ^ [_1502645, _1502647, _1502649, _1502651] : [c_Fun_Oinj__on(_1502645, _1502647, _1502649, c_Orderings_Otop__class_Otop(tc_fun(_1502645, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1502645, _1502647, _1502649), hAPP(c_Set_Oimage(_1502645, _1502647, _1502649), _1502651)) = _1502651)], (43289 ^ _779854) ^ [_1642904, _1642906] : [class_Groups_Ocomm__monoid__add(_1642904), hBOOL(hAPP(c_List_Odistinct(_1642904), _1642906)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1642904), _1642906) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1642904, _1642904), c_COMBI(_1642904)), hAPP(c_List_Oset(_1642904), _1642906)))], (16217 ^ _779854) ^ [_1071050, _1071052, _1071054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1071050), _1071052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071050), _1071054)), _1071052)))], (23659 ^ _779854) ^ [_1208640] : [class_Lattices_Osemilattice__inf(_1208640), -(c_Finite__Set_Ofun__left__comm__idem(_1208640, _1208640, c_Lattices_Osemilattice__inf__class_Oinf(_1208640)))], (46691 ^ _779854) ^ [_1719190, _1719192, _1719194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1719190), _1719192)), _1719194)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1719192), c_List_Oupt(_1719190, _1719194)) = c_List_Oupt(_1719190, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1719190), _1719192)))], (43153 ^ _779854) ^ [_1639808, _1639810, _1639812, _1639814] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639808), tc_List_Olist(_1639808))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639808), tc_List_Olist(_1639808)), _1639810), _1639812)), c_List_Olistrel1(_1639808, _1639814)))), 43154 ^ _779854 : [(43155 ^ _779854) ^ [_1639941, _1639943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1639808, _1639808)), hAPP(hAPP(c_Product__Type_OPair(_1639808, _1639808), hAPP(hAPP(c_List_Onth(_1639808), _1639810), _1639941)), _1639943)), _1639814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639941), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639808)), _1639810))), _1639812 = hAPP(hAPP(c_List_Olist__update(_1639808, _1639810), _1639941), _1639943)]]], (7656 ^ _779854) ^ [_906868, _906870] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906868, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_906868, tc_HOL_Obool))), _906870) = c_Orderings_Otop__class_Otop(tc_fun(_906868, tc_HOL_Obool)))], (34323 ^ _779854) ^ [_1415830, _1415832, _1415834, _1415836] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1415830), _1415832)), -(hAPP(c_Set_Oimage(_1415830, _1415834, _1415836), _1415832) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1415834, tc_HOL_Obool), _1415830, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415834, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1415830, tc_fun(_1415834, tc_HOL_Obool), tc_fun(_1415834, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1415834, tc_fun(tc_fun(_1415834, tc_HOL_Obool), tc_fun(_1415834, tc_HOL_Obool)), _1415830), c_Set_Oinsert(_1415834)), _1415836)), c_Orderings_Obot__class_Obot(tc_fun(_1415834, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1415834, tc_HOL_Obool))), _1415832))], (1870 ^ _779854) ^ [_806181, _806183] : [-(class_Groups_Ominus(_806181)), _806183 = _806181, class_Groups_Ominus(_806183)], (56 ^ _779854) ^ [_780652, _780654, _780656, _780658, _780660, _780662] : [-(c_Finite__Set_Ofolding__one__idem(_780660, _780656, _780652)), c_Finite__Set_Ofolding__one__idem(_780662, _780658, _780654), _780662 = _780660, _780658 = _780656, _780654 = _780652], (4788 ^ _779854) ^ [_852929, _852931, _852933, _852935] : [-(c_List_Olexord(_852935, _852931) = c_List_Olexord(_852933, _852929)), _852935 = _852933, _852931 = _852929], (49960 ^ _779854) ^ [_1789701, _1789703] : [49963 ^ _779854 : [(49968 ^ _779854) ^ [] : [49961 ^ [_1789701, _1789703] = 49962 ^ [_1789701, _1789703]], (49966 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1789701, _1789701)), hAPP(hAPP(c_Product__Type_OPair(_1789701, _1789701), 49962 ^ [_1789701, _1789703]), 49961 ^ [_1789701, _1789703])), _1789703)))], (49964 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1789701, _1789701)), hAPP(hAPP(c_Product__Type_OPair(_1789701, _1789701), 49961 ^ [_1789701, _1789703]), 49962 ^ [_1789701, _1789703])), _1789703)))]], -(c_Relation_Oantisym(_1789701, _1789703))], (12682 ^ _779854) ^ [_1001986, _1001988, _1001990] : [class_Orderings_Olinorder(_1001986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001986), _1001988)), hBOOL(hAPP(hAPP(c_member(_1001986), _1001990), _1001988)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1001986), _1001990), c_Big__Operators_Olattice_OSup__fin(_1001986, c_Orderings_Oord__class_Omax(_1001986), _1001988)) = _1001990)], (13443 ^ _779854) ^ [_1016501, _1016503, _1016505] : [class_Orderings_Olinorder(_1016501), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016501), _1016503)), -(_1016503 = c_Orderings_Obot__class_Obot(tc_fun(_1016501, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1016501, hAPP(hAPP(c_Set_Oinsert(_1016501), _1016505), _1016503)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1016501), _1016505), c_Big__Operators_Olinorder__class_OMin(_1016501, _1016503)))], (38773 ^ _779854) ^ [_1519450, _1519452] : [-(hAPP(c_Set_OCollect(_1519450), _1519452) = _1519452)], (38815 ^ _779854) ^ [_1520263, _1520265, _1520267] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520263, tc_HOL_Obool)), _1520265), _1520267) = hAPP(c_Set_OCollect(_1520263), hAPP(hAPP(c_COMBS(_1520263, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520263), c_fdisj), hAPP(hAPP(c_COMBC(_1520263, tc_fun(_1520263, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520263)), _1520265))), hAPP(hAPP(c_COMBC(_1520263, tc_fun(_1520263, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520263)), _1520267))))], (12104 ^ _779854) ^ [_990745, _990747, _990749, _990751, _990753, _990755] : [c_Fun_Oinj__on(_990745, _990747, _990749, _990751), -(_990753 = _990755), hBOOL(hAPP(hAPP(c_member(_990745), _990753), _990751)), hBOOL(hAPP(hAPP(c_member(_990745), _990755), _990751)), hAPP(_990749, _990753) = hAPP(_990749, _990755)], (52547 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (18391 ^ _779854) ^ [_1112779, _1112781, _1112783] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1112779), _1112781)), -(hAPP(c_Finite__Set_Ocard(_1112779), hAPP(hAPP(c_Set_Oinsert(_1112779), _1112783), _1112781)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1112779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1112779, tc_HOL_Obool)), _1112781), hAPP(hAPP(c_Set_Oinsert(_1112779), _1112783), c_Orderings_Obot__class_Obot(tc_fun(_1112779, tc_HOL_Obool)))))))], (9200 ^ _779854) ^ [_933367, _933369, _933371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933367, tc_HOL_Obool)), _933369), hAPP(hAPP(c_Set_Oinsert(_933367), _933371), c_Orderings_Obot__class_Obot(tc_fun(_933367, tc_HOL_Obool))))), -(_933369 = c_Orderings_Obot__class_Obot(tc_fun(_933367, tc_HOL_Obool))), -(_933369 = hAPP(hAPP(c_Set_Oinsert(_933367), _933371), c_Orderings_Obot__class_Obot(tc_fun(_933367, tc_HOL_Obool))))], (25665 ^ _779854) ^ [_1246402, _1246404] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246402), _1246404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246402)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246404)))], (47617 ^ _779854) ^ [_1737533, _1737535, _1737537, _1737539, _1737541] : [-(c_List_OtakeWhile(_1737533, _1737535, hAPP(hAPP(c_List_Omap(_1737537, _1737533), _1737539), _1737541)) = hAPP(hAPP(c_List_Omap(_1737537, _1737533), _1737539), c_List_OtakeWhile(_1737537, hAPP(c_Fun_Ocomp(_1737533, tc_HOL_Obool, _1737537, _1737535), _1737539), _1737541)))], (16714 ^ _779854) ^ [_1080915, _1080917, _1080919, _1080921] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1080915, _1080917, _1080919), _1080921), c_Orderings_Obot__class_Obot(tc_fun(_1080915, tc_HOL_Obool))) = _1080921)], (32611 ^ _779854) ^ [_1367028, _1367030] : [-(_1367028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1367030, _1367028) = c_Nitpick_Onat__gcd(_1367028, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1367030, _1367028)))], (47068 ^ _779854) ^ [_1726037, _1726039, _1726041] : [class_Orderings_Olinorder(_1726037), 47071 ^ _779854 : [(47084 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726037, hAPP(hAPP(c_List_Olist_OCons(_1726037), _1726039), _1726041))), c_List_Olinorder__class_Osorted(_1726037, _1726041), 47090 ^ _779854 : [(47093 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726037), _1726039), 47089 ^ [_1726037, _1726039, _1726041]))], (47091 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726037), 47089 ^ [_1726037, _1726039, _1726041]), hAPP(c_List_Oset(_1726037), _1726041))))]]], (47072 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1726037, hAPP(hAPP(c_List_Olist_OCons(_1726037), _1726039), _1726041)), 47075 ^ _779854 : [(47078 ^ _779854) ^ [_1726223] : [hBOOL(hAPP(hAPP(c_member(_1726037), _1726223), hAPP(c_List_Oset(_1726037), _1726041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726037), _1726039), _1726223)))], (47076 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726037, _1726041))]]]]], (7804 ^ _779854) ^ [_910008, _910010, _910012] : [class_Orderings_Olinorder(_910008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910008), _910010), _910012)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910008, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_910008), _910010)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_910008, _910010), _910012)) = hAPP(c_SetInterval_Oord__class_OlessThan(_910008), _910012))], (44939 ^ _779854) ^ [_1679004, _1679006, _1679008] : [-(_1679004 = c_List_Olist_ONil(_1679006)), -(c_List_Olast(_1679006, hAPP(hAPP(c_List_Olist_OCons(_1679006), _1679008), _1679004)) = c_List_Olast(_1679006, _1679004))], (6271 ^ _779854) ^ [_879460] : [class_Complete__Lattice_Ocomplete__lattice(_879460), -(c_Complete__Lattice_OInf__class_OInf(_879460, c_Orderings_Obot__class_Obot(tc_fun(_879460, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_879460))], (12044 ^ _779854) ^ [_989448, _989450, _989452, _989454] : [hBOOL(hAPP(hAPP(c_member(_989448), _989450), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989448, tc_HOL_Obool)), _989452), _989454))), 12047 ^ _779854 : [(12050 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989448), _989450), _989454)))], (12048 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989448), _989450), _989452)))]]], (45825 ^ _779854) ^ [_1699028, _1699030, _1699032, _1699034, _1699036, _1699038, _1699040] : [c_List_Olist__all2(_1699028, _1699036, hAPP(hAPP(c_COMBC(_1699028, tc_fun(_1699036, _1699030), tc_fun(_1699036, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1699030, tc_HOL_Obool), tc_fun(tc_fun(_1699036, _1699030), tc_fun(_1699036, tc_HOL_Obool)), _1699028), c_COMBB(_1699030, tc_HOL_Obool, _1699036)), _1699032)), _1699038), _1699034, _1699040), -(c_List_Olist__all2(_1699028, _1699030, _1699032, _1699034, hAPP(hAPP(c_List_Omap(_1699036, _1699030), _1699038), _1699040)))], (7537 ^ _779854) ^ [_904229, _904231] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904229, tc_HOL_Obool)), _904231), c_Orderings_Obot__class_Obot(tc_fun(_904229, tc_HOL_Obool))) = _904231)], (12960 ^ _779854) ^ [_1007785, _1007787, _1007789, _1007791, _1007793, _1007795] : [hBOOL(hAPP(hAPP(c_member(_1007785), _1007787), c_SetInterval_Oord_OatLeastLessThan(_1007785, _1007789, _1007791, _1007793, _1007795))), 12963 ^ _779854 : [(12966 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1007791, _1007787), _1007795)))], (12964 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1007789, _1007793), _1007787)))]]], (30195 ^ _779854) ^ [_1324903, _1324905, _1324907, _1324909] : [class_Divides_Osemiring__div(_1324903), -(c_Divides_Odiv__class_Omod(_1324903, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324903), _1324905), _1324907), _1324909) = c_Divides_Odiv__class_Omod(_1324903, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324903), c_Divides_Odiv__class_Omod(_1324903, _1324905, _1324909)), c_Divides_Odiv__class_Omod(_1324903, _1324907, _1324909)), _1324909))], (52297 ^ _779854) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (31635 ^ _779854) ^ [_1349718, _1349720] : [c_Nat__Transfer_Ois__nat(_1349718), c_Nat__Transfer_Ois__nat(_1349720), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1349718, _1349720)))], (26433 ^ _779854) ^ [_1260182, _1260184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1260182, _1260184))))], (18791 ^ _779854) ^ [_1119307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119307), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51791 ^ _779854) ^ [_1827776, _1827778, _1827780, _1827782] : [class_Rings_Ocomm__semiring__1(_1827776), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827776), _1827778), _1827780)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827776), _1827780), _1827782)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827776), _1827778), _1827782)))], (4158 ^ _779854) ^ [_843042, _843044] : [_843044 = _843042, -(c_New__Random__Sequence_Opos__single(_843044) = c_New__Random__Sequence_Opos__single(_843042))], (33369 ^ _779854) ^ [_1386620, _1386622, _1386624, _1386626, _1386628] : [c_Finite__Set_Ofun__left__comm(_1386620, _1386622, _1386624), -(c_Finite__Set_Ofun__left__comm(_1386626, _1386622, hAPP(hAPP(c_COMBB(_1386620, tc_fun(_1386622, _1386622), _1386626), _1386624), _1386628)))], (33431 ^ _779854) ^ [_1388500, _1388502] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1388500, tc_HOL_Obool)), _1388502)), -(hBOOL(hAPP(hAPP(c_member(_1388500), _1388502), c_Orderings_Obot__class_Obot(tc_fun(_1388500, tc_HOL_Obool)))))], (3330 ^ _779854) ^ [_829712, _829714, _829716, _829718] : [-(c_List_Olists(_829718, _829714) = c_List_Olists(_829716, _829712)), _829718 = _829716, _829714 = _829712], (29889 ^ _779854) ^ [_1318759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1318759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1318759 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1318759 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34251 ^ _779854) ^ [_1414111, _1414113, _1414115, _1414117, _1414119, _1414121] : [c_Fun_Oinj__on(_1414111, _1414113, _1414115, _1414117), c_Fun_Oinj__on(_1414113, _1414119, _1414121, hAPP(c_Set_Oimage(_1414111, _1414113, _1414115), _1414117)), -(c_Fun_Oinj__on(_1414111, _1414119, hAPP(c_Fun_Ocomp(_1414113, _1414119, _1414111, _1414121), _1414115), _1414117))], (27915 ^ _779854) ^ [_1284803, _1284805] : [27916 ^ _779854 : [(27919 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284805))], (27917 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284803))]], 27920 ^ _779854 : [(27927 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1284803), _1284805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1284803)), hAPP(c_Int_Onat, _1284805))))], (27921 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1284803)), hAPP(c_Int_Onat, _1284805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1284803), _1284805)))]]], (26329 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (46866 ^ _779854) ^ [_1722694, _1722696, _1722698] : [class_Orderings_Olinorder(_1722694), c_List_Olinorder__class_Osorted(_1722694, _1722696), -(c_List_Olinorder__class_Osorted(_1722694, hAPP(hAPP(c_List_Otake(_1722694), _1722698), _1722696)))], (11266 ^ _779854) ^ [_974122, _974124] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_974122), c_Orderings_Otop__class_Otop(tc_fun(_974122, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_974124), c_Orderings_Otop__class_Otop(tc_fun(_974124, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_974122, _974124)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_974122, _974124), tc_HOL_Obool)))))], (16054 ^ _779854) ^ [_1068145, _1068147] : [16055 ^ _779854 : [(16058 ^ _779854) ^ [] : [_1068145 = _1068147], (16056 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068145), _1068147))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068145), _1068147)))], (39991 ^ _779854) ^ [_1556748, _1556750, _1556752] : [c_Wellfounded_Owf(_1556748, _1556750), -(c_Wellfounded_Owf(tc_List_Olist(_1556748), hAPP(c_List_Olexn(_1556748, _1556750), _1556752)))], (52185 ^ _779854) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (3714 ^ _779854) ^ [_835706, _835708, _835710, _835712, _835714, _835716] : [-(c_List_Oinsert(_835716, _835712, _835708) = c_List_Oinsert(_835714, _835710, _835706)), _835716 = _835714, _835712 = _835710, _835708 = _835706], (52463 ^ _779854) ^ [_1836306, _1836308] : [-(class_Finite__Set_Ofinite(tc_sum(_1836306, _1836308))), class_Finite__Set_Ofinite(_1836306), class_Finite__Set_Ofinite(_1836308)], (6309 ^ _779854) ^ [_880117, _880119, _880121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_880117, tc_HOL_Obool), tc_HOL_Obool)), _880119), _880121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880117, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_880117, tc_HOL_Obool), _880121)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_880117, tc_HOL_Obool), _880119))))], (46733 ^ _779854) ^ [_1719989, _1719991, _1719993, _1719995] : [-(c_List_Oupt(_1719989, _1719991) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1719993), _1719995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719989), _1719991)), _1719989 = _1719993, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1719989), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1719991) = _1719995], (4264 ^ _779854) ^ [_844611, _844613, _844615, _844617] : [-(c_List_Ofilter(_844617, _844613) = c_List_Ofilter(_844615, _844611)), _844617 = _844615, _844613 = _844611], (11847 ^ _779854) ^ [_985605, _985607, _985609, _985611, _985613] : [11849 ^ _779854 : [(11855 ^ _779854) ^ [] : [hBOOL(hAPP(_985613, 11851 ^ [_985605, _985607, _985609, _985611, _985613]))], (11853 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985605), 11851 ^ [_985605, _985607, _985609, _985611, _985613]), hAPP(_985611, 11848 ^ [_985605, _985607, _985609, _985611, _985613]))))], (11850 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985607), 11848 ^ [_985605, _985607, _985609, _985611, _985613]), _985609)))]], 11856 ^ _779854 : [(11857 ^ _779854) ^ [_985915] : [hBOOL(hAPP(hAPP(c_member(_985605), _985915), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985607, tc_fun(_985605, tc_HOL_Obool)), _985609), _985611))), -(hBOOL(hAPP(_985613, _985915)))]]], (31290 ^ _779854) ^ [_1343947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1343947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1343947))))], (52585 ^ _779854) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (48726 ^ _779854) ^ [_1761466, _1761468] : [c_List_Olist__ex1(_1761466, _1761468, c_List_Olist_ONil(_1761466))], (28208 ^ _779854) ^ [_1289954, _1289956] : [c_Int_OBit1(_1289954) = c_Int_OBit1(_1289956), -(_1289954 = _1289956)], (27019 ^ _779854) ^ [_1269854, _1269856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1269854)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1269856))), 27022 ^ _779854 : [(27023 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1269854), _1269856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1269856)))], (27029 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1269854), _1269856)))]]], (8620 ^ _779854) ^ [_923453, _923455, _923457] : [class_Orderings_Opreorder(_923453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_923453), _923455), _923457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923453), _923455), _923457)))], (52349 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (24511 ^ _779854) ^ [_1224502, _1224504, _1224506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224502), _1224504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224506), _1224502)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224506), _1224504))))], (10679 ^ _779854) ^ [_961903, _961905, _961907, _961909, _961911] : [class_Groups_Oordered__ab__group__add(_961903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961903), _961905), _961907) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961903), _961909), _961911), 10686 ^ _779854 : [(10693 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961903), _961909), _961911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961903), _961905), _961907)))], (10687 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961903), _961905), _961907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961903), _961909), _961911)))]]], (49076 ^ _779854) ^ [_1769235, _1769237, _1769239, _1769241, _1769243] : [-(hAPP(hAPP(c_List_Omap(_1769235, _1769237), _1769239), c_List_Oreplicate(_1769235, _1769241, _1769243)) = c_List_Oreplicate(_1769237, _1769241, hAPP(_1769239, _1769243)))], (43061 ^ _779854) ^ [_1637616, _1637618, _1637620, _1637622, _1637624] : [-(hAPP(hAPP(c_List_Olist__update(_1637616, hAPP(hAPP(c_List_Olist__update(_1637616, _1637618), _1637620), _1637622)), _1637620), _1637624) = hAPP(hAPP(c_List_Olist__update(_1637616, _1637618), _1637620), _1637624))], (2852 ^ _779854) ^ [_822319, _822321, _822323, _822325] : [-(c_Relation_ORange(_822325, _822321) = c_Relation_ORange(_822323, _822319)), _822325 = _822323, _822321 = _822319], (25797 ^ _779854) ^ [_1248730] : [-(c_Int_Osucc(_1248730) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1248730), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29357 ^ _779854) ^ [_1309454] : [_1309454 = c_Int_OPls, -(c_Int_OBit0(_1309454) = c_Int_OPls)], (22567 ^ _779854) ^ [_1187488, _1187490, _1187492, _1187494] : [class_Fields_Ofield__inverse__zero(_1187488), -(_1187490 = c_Groups_Ozero__class_Ozero(_1187488)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187488), _1187490), _1187492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187488), _1187490), _1187494)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187488), _1187492), _1187494))], (30105 ^ _779854) ^ [_1322963, _1322965] : [-(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), _1322963)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1322965)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1322963))) = 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), _1322965)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1322963)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34875 ^ _779854) ^ [_1427840, _1427842, _1427844, _1427846, _1427848, _1427850] : [hBOOL(hAPP(hAPP(_1427840, _1427842), _1427844)), hBOOL(hAPP(hAPP(_1427846, _1427842), _1427844)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427848, tc_fun(_1427850, tc_HOL_Obool))), _1427840), _1427846), _1427842), _1427844)))], (5666 ^ _779854) ^ [_866548, _866550] : [_866550 = _866548, -(tc_Hoare__Mirabelle_Otriple(_866550) = tc_Hoare__Mirabelle_Otriple(_866548))], (25181 ^ _779854) ^ [_1237273, _1237275, _1237277, _1237279] : [class_Fields_Olinordered__field__inverse__zero(_1237273), class_Int_Onumber(_1237273), 25188 ^ _779854 : [(25189 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), _1237275), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237273), _1237277), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)))), 25192 ^ _779854 : [(25199 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), c_Groups_Ozero__class_Ozero(_1237273)), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)))), 25202 ^ _779854 : [(25209 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)), c_Groups_Ozero__class_Ozero(_1237273)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), _1237275), c_Groups_Ozero__class_Ozero(_1237273))))], (25203 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)), c_Groups_Ozero__class_Ozero(_1237273))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), _1237277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237273), _1237275), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)))))]]], (25193 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), c_Groups_Ozero__class_Ozero(_1237273)), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237273), _1237275), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279))), _1237277)))]]], (25215 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), _1237275), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237273), _1237277), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279))))), 25218 ^ _779854 : [(25221 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237273), _1237275), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279))), _1237277))], (25219 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), c_Groups_Ozero__class_Ozero(_1237273)), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279))))]], 25222 ^ _779854 : [(25225 ^ _779854) ^ [] : [25226 ^ _779854 : [(25229 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), _1237277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237273), _1237275), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279))))], (25227 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)), c_Groups_Ozero__class_Ozero(_1237273))))]], 25230 ^ _779854 : [(25233 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237273), _1237275), c_Groups_Ozero__class_Ozero(_1237273)))], (25231 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)), c_Groups_Ozero__class_Ozero(_1237273)))]]], (25223 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237273), c_Groups_Ozero__class_Ozero(_1237273)), hAPP(c_Int_Onumber__class_Onumber__of(_1237273), _1237279)))]]]]], (35205 ^ _779854) ^ [_1435685, _1435687, _1435689, _1435691] : [class_Rings_Osemiring__1(_1435685), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1435685, _1435687, hAPP(c_Nat_OSuc, _1435689), _1435691) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1435685, _1435687, _1435689, hAPP(_1435687, _1435691)))], (13205 ^ _779854) ^ [_1012810, _1012812] : [class_Lattices_Olattice(_1012810), -(c_Big__Operators_Olattice__class_OSup__fin(_1012810, hAPP(hAPP(c_Set_Oinsert(_1012810), _1012812), c_Orderings_Obot__class_Obot(tc_fun(_1012810, tc_HOL_Obool)))) = _1012812)], (28278 ^ _779854) ^ [_1291208, _1291210] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1291208), _1291210)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291208)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1291210))))], (20337 ^ _779854) ^ [_1145870, _1145872] : [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), _1145870), _1145872))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145872), _1145870)))], (33885 ^ _779854) ^ [_1404347, _1404349, _1404351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404347, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1404347, tc_fun(_1404347, tc_HOL_Obool), tc_HOL_Obool), c_member(_1404347)), _1404349)), hAPP(hAPP(c_COMBC(_1404347, tc_fun(_1404347, tc_HOL_Obool), tc_HOL_Obool), c_member(_1404347)), _1404351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404347, tc_HOL_Obool)), _1404349), _1404351)))], (6053 ^ _779854) ^ [_875736, _875738, _875740] : [class_Orderings_Olinorder(_875736), 6056 ^ _779854 : [(6063 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875736), _875740), _875738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875736, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_875736), _875738)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_875736), _875740))))], (6057 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875736, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_875736), _875738)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_875736), _875740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875736), _875740), _875738)))]]], (49517 ^ _779854) ^ [_1779429, _1779431, _1779433, _1779435] : [c_Relation_Otrans(_1779429, _1779431), c_Relation_Otrans(_1779433, _1779435), -(c_Relation_Otrans(tc_prod(_1779429, _1779433), c_Wellfounded_Olex__prod(_1779429, _1779433, _1779431, _1779435)))], (41569 ^ _779854) ^ [_1595882, _1595884, _1595886, _1595888, _1595890, _1595892] : [c_Relation_Osingle__valued(_1595882, _1595884, hAPP(c_Relation_Oconverse(_1595884, _1595882), _1595886)), -(_1595888 = c_Orderings_Obot__class_Obot(tc_fun(_1595890, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1595884, _1595882, _1595886), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595890, tc_fun(_1595884, tc_HOL_Obool)), _1595888), _1595892)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1595890, tc_fun(_1595882, tc_HOL_Obool)), _1595888), hAPP(hAPP(c_COMBB(tc_fun(_1595884, tc_HOL_Obool), tc_fun(_1595882, tc_HOL_Obool), _1595890), c_Relation_OImage(_1595884, _1595882, _1595886)), _1595892)))], (11260 ^ _779854) ^ [_974031] : [class_Finite__Set_Ofinite(_974031), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_974031), c_Orderings_Otop__class_Otop(tc_fun(_974031, tc_HOL_Obool)))))], (34675 ^ _779854) ^ [_1423884, _1423886, _1423888, _1423890, _1423892] : [class_Groups_Ocomm__monoid__mult(_1423884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423886), _1423888)), c_Fun_Oinj__on(_1423886, _1423886, _1423890, _1423888), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1423886, _1423884), _1423892), hAPP(c_Set_Oimage(_1423886, _1423886, _1423890), _1423888)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1423886, _1423884), hAPP(c_Fun_Ocomp(_1423886, _1423884, _1423886, _1423892), _1423890)), _1423888))], (46439 ^ _779854) ^ [_1712905, _1712907, _1712909, _1712911, _1712913, _1712915] : [class_Orderings_Olinorder(_1712905), -(hBOOL(hAPP(_1712907, _1712909))), -(hAPP(c_List_Ofilter(_1712911, _1712907), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712911, _1712905, _1712913), _1712909), _1712915)) = hAPP(c_List_Ofilter(_1712911, _1712907), _1712915))], (18183 ^ _779854) ^ [_1108862, _1108864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108862), _1108864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108862), hAPP(c_Nat_OSuc, _1108864))))], (10537 ^ _779854) ^ [_958805, _958807] : [class_Orderings_Oorder(_958805), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958805, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_958805), _958807), c_Orderings_Obot__class_Obot(tc_fun(_958805, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_958805), _958807)) = hAPP(hAPP(c_Set_Oinsert(_958805), _958807), c_Orderings_Obot__class_Obot(tc_fun(_958805, tc_HOL_Obool))))], (12942 ^ _779854) ^ [_1007422, _1007424, _1007426, _1007428, _1007430] : [hBOOL(hAPP(hAPP(c_member(_1007422), _1007424), c_SetInterval_Oord_OgreaterThanLessThan(_1007422, _1007426, _1007428, _1007430))), 12945 ^ _779854 : [(12948 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1007426, _1007424), _1007430)))], (12946 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1007426, _1007428), _1007424)))]]], (44254 ^ _779854) ^ [_1664375, _1664377, _1664379] : [-(hAPP(hAPP(c_List_Odrop(_1664375), _1664377), c_List_Obutlast(_1664375, _1664379)) = c_List_Obutlast(_1664375, hAPP(hAPP(c_List_Odrop(_1664375), _1664377), _1664379)))], (25507 ^ _779854) ^ [_1243861, _1243863] : [class_Int_Onumber__ring(_1243861), -(hAPP(c_Int_Onumber__class_Onumber__of(_1243861), c_Int_Osucc(_1243863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1243861), c_Groups_Oone__class_Oone(_1243861)), hAPP(c_Int_Onumber__class_Onumber__of(_1243861), _1243863)))], (9853 ^ _779854) ^ [_945609, _945611] : [class_Groups_Oordered__ab__group__add(_945609), -(hAPP(c_Set_Oimage(_945609, _945609, c_Groups_Ouminus__class_Ouminus(_945609)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_945609), _945611)) = hAPP(c_SetInterval_Oord__class_OlessThan(_945609), hAPP(c_Groups_Ouminus__class_Ouminus(_945609), _945611)))], (10709 ^ _779854) ^ [_962427, _962429, _962431, _962433, _962435] : [c_Fun_Oinj__on(_962427, _962429, _962431, c_Orderings_Otop__class_Otop(tc_fun(_962427, tc_HOL_Obool))), 10712 ^ _779854 : [(10719 ^ _779854) ^ [] : [_962433 = _962435, -(hAPP(_962431, _962433) = hAPP(_962431, _962435))], (10713 ^ _779854) ^ [] : [hAPP(_962431, _962433) = hAPP(_962431, _962435), -(_962433 = _962435)]]], (38725 ^ _779854) ^ [_1518378, _1518380, _1518382, _1518384] : [-(hAPP(c_Set_Ovimage(_1518378, _1518380, _1518382), hAPP(c_Set_OCollect(_1518380), _1518384)) = hAPP(c_Set_OCollect(_1518378), hAPP(hAPP(c_COMBB(_1518380, tc_HOL_Obool, _1518378), _1518384), _1518382)))], (27637 ^ _779854) ^ [] : [-(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))))], (24533 ^ _779854) ^ [_1224999, _1225001] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224999)), _1225001) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224999), _1225001)))], (29755 ^ _779854) ^ [] : [-(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)))))], (15348 ^ _779854) ^ [_1053651, _1053653, _1053655, _1053657] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1053651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053651), _1053653), _1053655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053651), _1053653), _1053657)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053651), _1053655), _1053657))))], (35834 ^ _779854) ^ [_1447073, _1447075] : [-(c_Divides_Odivmod__int__rel(_1447073, _1447075) = 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, _1447073))), 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), _1447075)))))), 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)), _1447075))), 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)), _1447075))))), 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)), _1447075)))), 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), _1447075))), 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))))))))], (31051 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (48614 ^ _779854) ^ [_1759304, _1759306, _1759308] : [c_FunDef_Ois__measure(_1759304, _1759306), -(c_FunDef_Ois__measure(tc_prod(_1759304, _1759308), hAPP(hAPP(c_COMBB(_1759304, tc_Nat_Onat, tc_prod(_1759304, _1759308)), _1759306), c_Product__Type_Ofst(_1759304, _1759308))))], (10369 ^ _779854) ^ [_955430, _955432, _955434, _955436, _955438] : [c_Orderings_Oorder__class_Omono(tc_fun(_955430, tc_HOL_Obool), tc_fun(_955432, tc_HOL_Obool), _955434), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955432, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_955432, tc_HOL_Obool)), hAPP(_955434, _955436)), hAPP(_955434, _955438))), hAPP(_955434, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_955430, tc_HOL_Obool)), _955436), _955438)))))], (45762 ^ _779854) ^ [_1697282, _1697284, _1697286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1697282, tc_HOL_Obool)), _1697284), _1697286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1697282), tc_HOL_Obool)), c_List_Olistsp(_1697282, _1697284)), c_List_Olistsp(_1697282, _1697286))))], (18863 ^ _779854) ^ [_1120321] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1120321) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34996 ^ _779854) ^ [_1430681, _1430683, _1430685, _1430687, _1430689, _1430691] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430681, tc_fun(_1430683, tc_HOL_Obool))), _1430685), _1430687), _1430689), _1430691)), -(hBOOL(hAPP(hAPP(_1430687, _1430689), _1430691)))], (37203 ^ _779854) ^ [_1479360, _1479362, _1479364] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479360), _1479362), _1479364) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1479360, tc_HOL_Obool), tc_HOL_Obool)), -(_1479362 = c_Orderings_Obot__class_Obot(tc_fun(_1479360, tc_HOL_Obool)))], (38915 ^ _779854) ^ [_1522614, _1522616, _1522618, _1522620, _1522622, _1522624, _1522626] : [class_Groups_Ocomm__monoid__add(_1522614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522616), _1522618)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522620), _1522622)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1522616, _1522614), hAPP(hAPP(c_COMBS(_1522616, tc_fun(_1522620, tc_HOL_Obool), _1522614), hAPP(hAPP(c_COMBB(tc_fun(_1522620, _1522614), tc_fun(tc_fun(_1522620, tc_HOL_Obool), _1522614), _1522616), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1522620, _1522614)), _1522624)), hAPP(hAPP(c_COMBB(tc_fun(_1522620, tc_HOL_Obool), tc_fun(_1522620, tc_HOL_Obool), _1522616), c_Set_OCollect(_1522620)), hAPP(hAPP(c_COMBB(tc_fun(_1522620, tc_HOL_Obool), tc_fun(_1522620, tc_HOL_Obool), _1522616), hAPP(c_COMBS(_1522620, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522620), c_fconj), hAPP(hAPP(c_COMBC(_1522620, tc_fun(_1522620, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522620)), _1522622)))), _1522626)))), _1522618) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1522620, _1522614), hAPP(hAPP(c_COMBS(_1522620, tc_fun(_1522616, tc_HOL_Obool), _1522614), hAPP(hAPP(c_COMBB(tc_fun(_1522616, _1522614), tc_fun(tc_fun(_1522616, tc_HOL_Obool), _1522614), _1522620), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1522616, _1522614)), hAPP(c_COMBC(_1522616, _1522620, _1522614), _1522624))), hAPP(hAPP(c_COMBB(tc_fun(_1522616, tc_HOL_Obool), tc_fun(_1522616, tc_HOL_Obool), _1522620), c_Set_OCollect(_1522616)), hAPP(hAPP(c_COMBB(tc_fun(_1522616, tc_HOL_Obool), tc_fun(_1522616, tc_HOL_Obool), _1522620), hAPP(c_COMBS(_1522616, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522616), c_fconj), hAPP(hAPP(c_COMBC(_1522616, tc_fun(_1522616, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522616)), _1522618)))), hAPP(c_COMBC(_1522616, _1522620, tc_HOL_Obool), _1522626))))), _1522622))], (26317 ^ _779854) ^ [_1258308, _1258310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258308), _1258310)), -(c_Nat__Transfer_Otsub(_1258310, _1258308) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1258310), _1258308))], (41499 ^ _779854) ^ [_1593938, _1593940, _1593942] : [-(hAPP(c_Relation_ORange(_1593938, _1593940), _1593942) = hAPP(c_Relation_ODomain(_1593940, _1593938), hAPP(c_Relation_Oconverse(_1593938, _1593940), _1593942)))], (6012 ^ _779854) ^ [_874961, _874963, _874965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874961, tc_HOL_Obool)), _874963), _874965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_874961, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_874961, _874963)), c_Predicate_OPowp(_874961, _874965))))], (14327 ^ _779854) ^ [_1033098, _1033100, _1033102, _1033104, _1033106] : [c_Finite__Set_Ofolding__one__idem(_1033098, _1033100, _1033102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033098), _1033104)), -(_1033106 = c_Orderings_Obot__class_Obot(tc_fun(_1033098, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033098, tc_HOL_Obool)), _1033106), _1033104)), -(hAPP(hAPP(_1033100, hAPP(_1033102, _1033106)), hAPP(_1033102, _1033104)) = hAPP(_1033102, _1033104))], (37328 ^ _779854) ^ [_1482645, _1482647, _1482649, _1482651, _1482653] : [c_Equiv__Relations_Oequiv(_1482645, _1482647, _1482649), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482645, tc_HOL_Obool)), _1482651), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482645), _1482647), _1482649))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482645, tc_HOL_Obool)), _1482653), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482645), _1482647), _1482649))), -(_1482651 = _1482653), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482645, tc_HOL_Obool)), _1482651), _1482653) = c_Orderings_Obot__class_Obot(tc_fun(_1482645, tc_HOL_Obool)))], (33617 ^ _779854) ^ [_1397309, _1397311, _1397313, _1397315, _1397317] : [_1397309 = c_Orderings_Obot__class_Obot(tc_fun(_1397311, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397313, tc_HOL_Obool)), _1397315), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397311, tc_fun(_1397313, tc_HOL_Obool)), _1397309), _1397317)) = _1397315)], (9899 ^ _779854) ^ [_946591, _946593, _946595, _946597] : [class_Orderings_Olinorder(_946591), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946591, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_946591, _946593, _946595)), hAPP(c_SetInterval_Oord__class_OatMost(_946591), _946597)) = c_SetInterval_Oord__class_OatLeastAtMost(_946591, _946593, hAPP(hAPP(c_Orderings_Oord__class_Omin(_946591), _946595), _946597)))], (35252 ^ _779854) ^ [_1436643, _1436645, _1436647, _1436649, _1436651, _1436653] : [_1436643 = _1436645, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1436647, _1436649, _1436651), _1436653), _1436643) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1436647, _1436649, _1436651), _1436653), _1436645))], (1220 ^ _779854) ^ [_798056, _798058] : [-(class_Rings_Olinordered__ring(_798056)), _798058 = _798056, class_Rings_Olinordered__ring(_798058)], (40958 ^ _779854) ^ [_1580067, _1580069] : [-(hAPP(c_Relation_ORange(_1580067, _1580067), c_Transitive__Closure_Otrancl(_1580067, _1580069)) = hAPP(c_Relation_ORange(_1580067, _1580067), _1580069))], (45228 ^ _779854) ^ [_1685551, _1685553, _1685555, _1685557, _1685559, _1685561] : [-(hAPP(hAPP(c_List_Omap(_1685551, _1685553), _1685555), hAPP(hAPP(c_List_Omap(_1685557, _1685551), _1685559), _1685561)) = hAPP(hAPP(c_List_Omap(_1685557, _1685553), hAPP(c_Fun_Ocomp(_1685551, _1685553, _1685557, _1685555), _1685559)), _1685561))], (48685 ^ _779854) ^ [_1760649, _1760651, _1760653] : [48687 ^ _779854 : [(48690 ^ _779854) ^ [] : [hBOOL(hAPP(_1760651, 48686 ^ [_1760649, _1760651, _1760653]))], (48688 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760649), 48686 ^ [_1760649, _1760651, _1760653]), hAPP(c_List_Oset(_1760649), _1760653))))]], -(c_List_Olist__all(_1760649, _1760651, _1760653))], (47434 ^ _779854) ^ [_1733583, _1733585, _1733587] : [_1733585 = hAPP(c_List_Orev(_1733583), _1733587), -(hAPP(c_List_Orev(_1733583), _1733585) = _1733587)], (11917 ^ _779854) ^ [_986921, _986923, _986925, _986927] : [-(hBOOL(hAPP(hAPP(c_member(_986921), _986923), _986925))), -(hBOOL(hAPP(hAPP(c_member(_986921), _986923), _986927))), 11924 ^ _779854 : [(11931 ^ _779854) ^ [] : [_986925 = _986927, -(hAPP(hAPP(c_Set_Oinsert(_986921), _986923), _986925) = hAPP(hAPP(c_Set_Oinsert(_986921), _986923), _986927))], (11925 ^ _779854) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_986921), _986923), _986925) = hAPP(hAPP(c_Set_Oinsert(_986921), _986923), _986927), -(_986925 = _986927)]]], (6381 ^ _779854) ^ [_881439, _881441] : [class_Orderings_Olinorder(_881439), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_881439, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_881439), _881441)) = hAPP(c_SetInterval_Oord__class_OatLeast(_881439), _881441))], (15157 ^ _779854) ^ [_1049437] : [15159 ^ _779854 : [(15162 ^ _779854) ^ [_1049547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 15158 ^ [_1049437, _1049547]), _1049547))], (15160 ^ _779854) ^ [_1049513] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 15158 ^ [_1049437, _1049513]), _1049437)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1049437)))], (48012 ^ _779854) ^ [_1745979, _1745981, _1745983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1745979, _1745979)), hAPP(hAPP(c_Product__Type_OPair(_1745979, _1745979), _1745981), _1745983)), c_List_Omeasures(_1745979, c_List_Olist_ONil(tc_fun(_1745979, tc_Nat_Onat)))))], (13763 ^ _779854) ^ [_1021927, _1021929, _1021931] : [class_Lattices_Olattice(_1021927), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021927), _1021929)), -(_1021929 = c_Orderings_Obot__class_Obot(tc_fun(_1021927, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021927), _1021931)), -(_1021931 = c_Orderings_Obot__class_Obot(tc_fun(_1021927, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1021927, tc_HOL_Obool)), _1021929), _1021931) = c_Orderings_Obot__class_Obot(tc_fun(_1021927, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1021927, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1021927, tc_HOL_Obool)), _1021929), _1021931)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1021927), c_Big__Operators_Olattice__class_OSup__fin(_1021927, _1021929)), c_Big__Operators_Olattice__class_OSup__fin(_1021927, _1021931)))], (16287 ^ _779854) ^ [_1072576, _1072578, _1072580, _1072582] : [class_Rings_Ocomm__semiring__1(_1072576), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072576), _1072578), _1072580)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072576), _1072582), _1072580)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072576), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072576), _1072578), _1072582)), _1072580))], (45081 ^ _779854) ^ [_1681437, _1681439] : [-(hAPP(hAPP(c_List_Ozip(_1681437, _1681437), _1681439), _1681439) = hAPP(hAPP(c_List_Omap(_1681437, tc_prod(_1681437, _1681437)), hAPP(hAPP(c_COMBS(_1681437, _1681437, tc_prod(_1681437, _1681437)), c_Product__Type_OPair(_1681437, _1681437)), c_COMBI(_1681437))), _1681439))], (8774 ^ _779854) ^ [_925738, _925740, _925742] : [class_Orderings_Olinorder(_925738), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925738), _925740), _925742))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925738), _925742), _925740)))], (34039 ^ _779854) ^ [_1408940, _1408942, _1408944, _1408946, _1408948] : [class_Groups_Ocomm__monoid__add(_1408940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408942), _1408944)), 34046 ^ _779854 : [(34053 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408942), _1408946), _1408944))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1408942, _1408940), hAPP(hAPP(c_COMBC(_1408942, _1408940, _1408940), hAPP(hAPP(c_COMBS(_1408942, _1408940, tc_fun(_1408940, _1408940)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1408940, tc_fun(_1408940, _1408940)), _1408942), c_If(_1408940)), hAPP(c_fequal, _1408946))), _1408948)), c_Groups_Ozero__class_Ozero(_1408940))), _1408944) = c_Groups_Ozero__class_Ozero(_1408940))], (34047 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1408942), _1408946), _1408944)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1408942, _1408940), hAPP(hAPP(c_COMBC(_1408942, _1408940, _1408940), hAPP(hAPP(c_COMBS(_1408942, _1408940, tc_fun(_1408940, _1408940)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1408940, tc_fun(_1408940, _1408940)), _1408942), c_If(_1408940)), hAPP(c_fequal, _1408946))), _1408948)), c_Groups_Ozero__class_Ozero(_1408940))), _1408944) = hAPP(_1408948, _1408946))]]], (20019 ^ _779854) ^ [_1140835, _1140837] : [class_Groups_Ogroup__add(_1140835), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140835), _1140837), hAPP(c_Groups_Ouminus__class_Ouminus(_1140835), _1140837)) = c_Groups_Ozero__class_Ozero(_1140835))], (13489 ^ _779854) ^ [_1017231, _1017233, _1017235] : [class_Lattices_Olattice(_1017231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017231), _1017233)), -(_1017235 = c_Orderings_Obot__class_Obot(tc_fun(_1017231, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017231, tc_HOL_Obool)), _1017235), _1017233)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1017231), c_Big__Operators_Olattice__class_OInf__fin(_1017231, _1017235)), c_Big__Operators_Olattice__class_OInf__fin(_1017231, _1017233)) = c_Big__Operators_Olattice__class_OInf__fin(_1017231, _1017233))], (42072 ^ _779854) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32045 ^ _779854) ^ [_1356492, _1356494] : [class_Groups_Oordered__ab__group__add__abs(_1356492), 32048 ^ _779854 : [(32055 ^ _779854) ^ [] : [_1356494 = c_Groups_Ozero__class_Ozero(_1356492), -(hAPP(c_Groups_Oabs__class_Oabs(_1356492), _1356494) = c_Groups_Ozero__class_Ozero(_1356492))], (32049 ^ _779854) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1356492), _1356494) = c_Groups_Ozero__class_Ozero(_1356492), -(_1356494 = c_Groups_Ozero__class_Ozero(_1356492))]]], (45212 ^ _779854) ^ [_1685214, _1685216, _1685218, _1685220, _1685222] : [-(hAPP(hAPP(c_List_Omap(_1685214, _1685216), _1685218), hAPP(hAPP(c_List_Olist_OCons(_1685214), _1685220), _1685222)) = hAPP(hAPP(c_List_Olist_OCons(_1685216), hAPP(_1685218, _1685220)), hAPP(hAPP(c_List_Omap(_1685214, _1685216), _1685218), _1685222)))], (33337 ^ _779854) ^ [_1385894, _1385896, _1385898, _1385900] : [-(hAPP(c_Set_OPow(_1385894), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385896, tc_fun(_1385894, tc_HOL_Obool)), _1385898), _1385900)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385896, tc_fun(tc_fun(_1385894, tc_HOL_Obool), tc_HOL_Obool)), _1385898), hAPP(hAPP(c_COMBB(tc_fun(_1385894, tc_HOL_Obool), tc_fun(tc_fun(_1385894, tc_HOL_Obool), tc_HOL_Obool), _1385896), c_Set_OPow(_1385894)), _1385900)))], (10253 ^ _779854) ^ [_953088] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_953088) = c_Orderings_Oord__class_Omin(_953088)), class_Lattices_Osemilattice__inf(_953088), class_Orderings_Olinorder(_953088)], (42253 ^ _779854) ^ [_1614744, _1614746] : [-(c_List_Olistrel1(_1614744, hAPP(c_Relation_Oconverse(_1614744, _1614744), _1614746)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1614744), tc_List_Olist(_1614744)), c_List_Olistrel1(_1614744, _1614746)))], (28974 ^ _779854) ^ [_1302877, _1302879] : [-(hBOOL(hAPP(_1302877, hAPP(c_Int_Onat, _1302879)))), 28978 ^ _779854 : [(28981 ^ _779854) ^ [] : [hBOOL(hAPP(_1302877, 28977 ^ [_1302877, _1302879]))], (28979 ^ _779854) ^ [] : [-(_1302879 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28977 ^ [_1302877, _1302879]))]], 28982 ^ _779854 : [(28985 ^ _779854) ^ [] : [hBOOL(hAPP(_1302877, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (28983 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302879), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25753 ^ _779854) ^ [_1247993, _1247995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247995), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1247993), _1247995)))], (36026 ^ _779854) ^ [_1451414, _1451416] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1451414, _1451416) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1451414, _1451416)))], (47556 ^ _779854) ^ [_1736107, _1736109, _1736111] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1736107), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1736107))), _1736109))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736111), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1736107))), _1736109))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1736107))), hAPP(c_List_Ofilter(tc_List_Olist(_1736107), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1736107)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736111)), c_Nat_Osize__class_Osize(tc_List_Olist(_1736107)))), c_List_Otranspose(_1736107, _1736109))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736107)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1736107)), _1736109), _1736111)))], (36892 ^ _779854) ^ [_1470213, _1470215, _1470217, _1470219, _1470221, _1470223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1470213, tc_HOL_Obool), tc_fun(_1470213, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1470213, tc_HOL_Obool), tc_fun(_1470213, tc_HOL_Obool)), _1470215), _1470217)), c_Wellfounded_Omax__ext(_1470213, _1470219))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1470213, tc_HOL_Obool), tc_fun(_1470213, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1470213, tc_HOL_Obool), tc_fun(_1470213, tc_HOL_Obool)), _1470221), _1470223)), c_Wellfounded_Omax__ext(_1470213, _1470219))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1470213, tc_HOL_Obool), tc_fun(_1470213, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1470213, tc_HOL_Obool), tc_fun(_1470213, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470213, tc_HOL_Obool)), _1470215), _1470221)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470213, tc_HOL_Obool)), _1470217), _1470223))), c_Wellfounded_Omax__ext(_1470213, _1470219))))], (34135 ^ _779854) ^ [_1411480, _1411482, _1411484, _1411486, _1411488] : [-(_1411480 = c_Orderings_Obot__class_Obot(tc_fun(_1411482, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411482, tc_fun(_1411484, tc_HOL_Obool)), _1411480), hAPP(hAPP(c_COMBB(tc_fun(_1411484, tc_HOL_Obool), tc_fun(_1411484, tc_HOL_Obool), _1411482), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411484, tc_HOL_Obool)), _1411486)), _1411488)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411484, tc_HOL_Obool)), _1411486), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411482, tc_fun(_1411484, tc_HOL_Obool)), _1411480), _1411488)))], (24384 ^ _779854) ^ [_1222125, _1222127, _1222129] : [class_Rings_Olinordered__semidom(_1222125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222125), c_Groups_Ozero__class_Ozero(_1222125)), _1222127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222125), _1222127), c_Groups_Oone__class_Oone(_1222125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222125), hAPP(hAPP(c_Power_Opower__class_Opower(_1222125), _1222127), hAPP(c_Nat_OSuc, _1222129))), c_Groups_Oone__class_Oone(_1222125))))], (46212 ^ _779854) ^ [_1707172, _1707174, _1707176] : [hBOOL(hAPP(hAPP(c_member(_1707172), _1707174), hAPP(c_List_Oset(_1707172), _1707176))), -(c_List_Oremdups(_1707172, hAPP(hAPP(c_List_Olist_OCons(_1707172), _1707174), _1707176)) = c_List_Oremdups(_1707172, _1707176))], (36028 ^ _779854) ^ [_1451449, _1451451, _1451453, _1451455, _1451457, _1451459, _1451461, _1451463] : [c_Finite__Set_Ofolding(_1451449, _1451451, _1451453, _1451455), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451449), _1451457)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451449), _1451459)), -(hAPP(c_Fun_Ocomp(_1451451, _1451451, _1451461, hAPP(_1451455, _1451459)), hAPP(c_Fun_Ocomp(_1451451, _1451451, _1451461, hAPP(_1451455, _1451457)), _1451463)) = hAPP(c_Fun_Ocomp(_1451451, _1451451, _1451461, hAPP(_1451455, _1451457)), hAPP(c_Fun_Ocomp(_1451451, _1451451, _1451461, hAPP(_1451455, _1451459)), _1451463)))], (29031 ^ _779854) ^ [_1303926, _1303928] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1303926) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1303928)), _1303926 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1303928)), 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), _1303928)))], (38785 ^ _779854) ^ [_1519749, _1519751] : [-(hBOOL(hAPP(_1519751, 38786 ^ [_1519749, _1519751]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1519749, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1519749), _1519751))], (7281 ^ _779854) ^ [_899693, _899695, _899697] : [class_Lattices_Osemilattice__sup(_899693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899693), _899695), _899697)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899693), _899695), _899697) = _899697)], (36766 ^ _779854) ^ [_1467804, _1467806, _1467808, _1467810, _1467812, _1467814] : [hAPP(_1467810, hAPP(c_Product__Type_Ofst(_1467804, _1467808), _1467812)) = hAPP(_1467814, hAPP(c_Product__Type_Ofst(_1467804, _1467808), _1467812)), -(hAPP(c_Product__Type_Oapfst(_1467804, _1467806, _1467808, _1467810), _1467812) = hAPP(c_Product__Type_Oapfst(_1467804, _1467806, _1467808, _1467814), _1467812))], (48802 ^ _779854) ^ [_1763121, _1763123, _1763125, _1763127] : [-(c_New__Random__Sequence_Opos__empty(_1763121, _1763123, _1763125, _1763127) = c_New__DSequence_Opos__empty(_1763121))], (28844 ^ _779854) ^ [_1300820] : [-(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), _1300820))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47782 ^ _779854) ^ [_1740876, _1740878, _1740880, _1740882, _1740884] : [hBOOL(hAPP(hAPP(c_member(_1740876), _1740878), hAPP(c_List_Oset(_1740876), _1740880))), -(hBOOL(hAPP(_1740882, _1740878))), -(c_List_OdropWhile(_1740876, _1740882, hAPP(hAPP(c_List_Oappend(_1740876), _1740880), _1740884)) = hAPP(hAPP(c_List_Oappend(_1740876), c_List_OdropWhile(_1740876, _1740882, _1740880)), _1740884))], (7978 ^ _779854) ^ [_913239, _913241] : [class_Lattices_Oboolean__algebra(_913239), -(hAPP(c_Groups_Ouminus__class_Ouminus(_913239), hAPP(c_Groups_Ouminus__class_Ouminus(_913239), _913241)) = _913241)], (44228 ^ _779854) ^ [_1663871, _1663873, _1663875] : [-(hAPP(hAPP(c_List_Odrop(_1663871), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1663871), _1663873), _1663875)) = _1663875)], (50582 ^ _779854) ^ [_1802718] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1802718), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1802718 = hAPP(c_Code__Numeral_Onat__of, 50585 ^ [_1802718]))], (242 ^ _779854) ^ [_783713, _783715] : [-(class_Fields_Olinordered__field__inverse__zero(_783713)), _783715 = _783713, class_Fields_Olinordered__field__inverse__zero(_783715)], (33567 ^ _779854) ^ [_1395280, _1395282, _1395284, _1395286, _1395288] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395280, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395282, tc_fun(_1395280, tc_HOL_Obool)), _1395284), _1395286)), _1395288) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395282, tc_fun(_1395280, tc_HOL_Obool)), _1395284), hAPP(hAPP(c_COMBC(_1395282, tc_fun(_1395280, tc_HOL_Obool), tc_fun(_1395280, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395280, tc_HOL_Obool), tc_fun(tc_fun(_1395280, tc_HOL_Obool), tc_fun(_1395280, tc_HOL_Obool)), _1395282), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395280, tc_HOL_Obool))), _1395286)), _1395288)))], (50207 ^ _779854) ^ [_1794228, _1794230] : [50208 ^ _779854 : [(50209 ^ _779854) ^ [_1794284] : [hBOOL(hAPP(hAPP(_1794228, _1794284), _1794284))]], c_Predicate_Osymp(_1794230, _1794228), c_Predicate_Otransp(_1794230, _1794228), -(c_Equiv__Relations_Opart__equivp(_1794230, _1794228))], (43055 ^ _779854) ^ [_1637536, _1637538, _1637540, _1637542, _1637544, _1637546] : [-(_1637536 = _1637538), -(hAPP(hAPP(c_List_Olist__update(_1637540, hAPP(hAPP(c_List_Olist__update(_1637540, _1637542), _1637536), _1637544)), _1637538), _1637546) = hAPP(hAPP(c_List_Olist__update(_1637540, hAPP(hAPP(c_List_Olist__update(_1637540, _1637542), _1637538), _1637546)), _1637536), _1637544))], (10349 ^ _779854) ^ [_955102, _955104, _955106] : [class_Groups_Olinordered__ab__group__add(_955102), -(hAPP(c_Groups_Ouminus__class_Ouminus(_955102), hAPP(hAPP(c_Orderings_Oord__class_Omin(_955102), _955104), _955106)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_955102), hAPP(c_Groups_Ouminus__class_Ouminus(_955102), _955104)), hAPP(c_Groups_Ouminus__class_Ouminus(_955102), _955106)))], (31230 ^ _779854) ^ [_1342915, _1342917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1342915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1342917, _1342915)), _1342915)))], (19275 ^ _779854) ^ [_1127467, _1127469, _1127471, _1127473] : [class_Rings_Oordered__comm__semiring(_1127467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127467), _1127469), _1127471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127467), c_Groups_Ozero__class_Ozero(_1127467)), _1127473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127467), _1127473), _1127469)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127467), _1127473), _1127471))))], (29217 ^ _779854) ^ [_1306995, _1306997] : [class_Int_Onumber__ring(_1306995), 29220 ^ _779854 : [(29227 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306997)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1306995), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1306997)) = hAPP(c_Int_Onumber__class_Onumber__of(_1306995), _1306997))], (29221 ^ _779854) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1306997))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1306995), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1306997)) = c_Groups_Ozero__class_Ozero(_1306995))]]], (49444 ^ _779854) ^ [_1777367, _1777369, _1777371] : [c_List_Oall__interval__int(_1777367, _1777369, _1777371), 49447 ^ _779854 : [(49448 ^ _779854) ^ [_1777445] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1777445), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1777369, _1777371))), -(hBOOL(hAPP(_1777367, _1777445)))]]], (46036 ^ _779854) ^ [_1703668, _1703670, _1703672] : [-(hAPP(c_List_Oset(tc_List_Olist(_1703668)), c_Enum_On__lists(_1703668, _1703670, _1703672)) = hAPP(c_Set_OCollect(tc_List_Olist(_1703668)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1703668), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1703668)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703668), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1703668)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1703668)))), _1703670))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703668), tc_fun(_1703668, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1703668, tc_HOL_Obool), tc_fun(tc_fun(_1703668, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1703668)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1703668, tc_HOL_Obool))), c_List_Oset(_1703668))), hAPP(c_List_Oset(_1703668), _1703672)))))], (50475 ^ _779854) ^ [_1799941, _1799943, _1799945, _1799947] : [c_Fun_Oinj__on(_1799941, _1799943, _1799945, c_Orderings_Otop__class_Otop(tc_fun(_1799941, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1799943, _1799941, c_Hilbert__Choice_Oinv__into(_1799941, _1799943, c_Orderings_Otop__class_Otop(tc_fun(_1799941, tc_HOL_Obool)), _1799945)), hAPP(c_Set_Oimage(_1799941, _1799943, _1799945), _1799947)) = _1799947)], (35824 ^ _779854) ^ [_1446851, _1446853, _1446855, _1446857, _1446859] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1446851, _1446853), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1446855), _1446857))), -(_1446853 = 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), _1446859), _1446851), _1446853), 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), _1446859), _1446855)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1446859), _1446857)), _1446853))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1446859), _1446857), _1446853)))))], (31212 ^ _779854) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (3604 ^ _779854) ^ [_834011, _834013, _834015, _834017, _834019, _834021] : [-(c_List_Oremove1(_834021, _834017, _834013) = c_List_Oremove1(_834019, _834015, _834011)), _834021 = _834019, _834017 = _834015, _834013 = _834011], (12308 ^ _779854) ^ [_994464, _994466, _994468, _994470] : [hBOOL(hAPP(hAPP(c_member(_994464), _994466), _994468)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994464, tc_HOL_Obool)), _994468), hAPP(hAPP(c_Set_Oinsert(_994464), _994466), _994470)) = hAPP(hAPP(c_Set_Oinsert(_994464), _994466), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994464, tc_HOL_Obool)), _994468), _994470)))], (45005 ^ _779854) ^ [_1679997, _1679999, _1680001, _1680003] : [-(hAPP(hAPP(c_List_Oappend(_1679997), _1679999), hAPP(hAPP(c_List_Olist_OCons(_1679997), _1680001), c_List_Olist_ONil(_1679997))) = _1680003), -(_1680003 = c_List_Olist_ONil(_1679997)), c_List_Obutlast(_1679997, _1680003) = _1679999, c_List_Olast(_1679997, _1680003) = _1680001], (52597 ^ _779854) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (46617 ^ _779854) ^ [_1717806, _1717808, _1717810, _1717812] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1717806, tc_Nat_Onat), _1717806), c_Product__Type_Ofst(_1717806, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1717806, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1717806, 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(_1717806, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1717806, tc_Nat_Onat))), _1717808)), hAPP(hAPP(c_List_Ozip(_1717806, tc_Nat_Onat), _1717810), c_List_Oupt(_1717812, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1717812), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717806)), _1717810)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1717806, tc_Nat_Onat), _1717806), c_Product__Type_Ofst(_1717806, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1717806, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1717806, 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(_1717806, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1717806, 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(_1717806, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1717806, tc_Nat_Onat))), _1717812))), _1717808)), hAPP(hAPP(c_List_Ozip(_1717806, tc_Nat_Onat), _1717810), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717806)), _1717810))))))], (47240 ^ _779854) ^ [_1729411, _1729413, _1729415, _1729417] : [class_Orderings_Olinorder(_1729411), c_List_Olinorder__class_Osorted(_1729411, _1729413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1729415), _1729417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729417), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729411)), _1729413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1729411), hAPP(hAPP(c_List_Onth(_1729411), _1729413), _1729415)), hAPP(hAPP(c_List_Onth(_1729411), _1729413), _1729417))))], (34287 ^ _779854) ^ [_1414950, _1414952, _1414954] : [class_Groups_Ocomm__monoid__add(_1414950), class_Groups_Ocomm__monoid__mult(_1414950), c_Nat__Transfer_Onat__set(_1414952), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1414950), _1414954), _1414952) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1414950), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1414950, tc_Nat_Onat), _1414954), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1414952)))], (44226 ^ _779854) ^ [_1663815, _1663817, _1663819, _1663821] : [-(hAPP(hAPP(c_List_Odrop(_1663815), hAPP(c_Nat_OSuc, _1663817)), hAPP(hAPP(c_List_Olist_OCons(_1663815), _1663819), _1663821)) = hAPP(hAPP(c_List_Odrop(_1663815), _1663817), _1663821))], (26641 ^ _779854) ^ [_1263943, _1263945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1263943), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 26644 ^ _779854 : [(26651 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1263945), _1263943)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26645 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1263945), _1263943)), 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)), _1263945)))]]], (48728 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49096 ^ _779854) ^ [_1769624, _1769626, _1769628] : [-(hAPP(hAPP(c_List_Oappend(_1769624), c_List_Oreplicate(_1769624, _1769626, _1769628)), hAPP(hAPP(c_List_Olist_OCons(_1769624), _1769628), c_List_Olist_ONil(_1769624))) = hAPP(hAPP(c_List_Olist_OCons(_1769624), _1769628), c_List_Oreplicate(_1769624, _1769626, _1769628)))], (40871 ^ _779854) ^ [_1578007, _1578009, _1578011, _1578013, _1578015, _1578017, _1578019] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1578007, _1578009, _1578011, _1578013), _1578015), _1578017), _1578019) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1578009, _1578011, _1578013), _1578017), hAPP(_1578015, _1578019)))], (37550 ^ _779854) ^ [_1487620, _1487622] : [c_Equiv__Relations_Oequiv(_1487620, c_Orderings_Otop__class_Otop(tc_fun(_1487620, tc_HOL_Obool)), _1487622), -(c_Equiv__Relations_Oequivp(_1487620, hAPP(hAPP(c_COMBC(_1487620, tc_fun(tc_prod(_1487620, _1487620), tc_HOL_Obool), tc_fun(_1487620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487620, tc_fun(tc_fun(tc_prod(_1487620, _1487620), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1487620, _1487620), tc_HOL_Obool), tc_fun(_1487620, tc_HOL_Obool)), _1487620), c_COMBC(_1487620, tc_fun(tc_prod(_1487620, _1487620), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487620, tc_prod(_1487620, _1487620)), tc_fun(_1487620, tc_fun(tc_fun(tc_prod(_1487620, _1487620), tc_HOL_Obool), tc_HOL_Obool)), _1487620), hAPP(c_COMBB(tc_prod(_1487620, _1487620), tc_fun(tc_fun(tc_prod(_1487620, _1487620), tc_HOL_Obool), tc_HOL_Obool), _1487620), c_member(tc_prod(_1487620, _1487620)))), c_Product__Type_OPair(_1487620, _1487620)))), _1487622)))], (52397 ^ _779854) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (44969 ^ _779854) ^ [_1679398, _1679400, _1679402] : [_1679398 = c_List_Olist_ONil(_1679400), -(c_List_Olast(_1679400, hAPP(hAPP(c_List_Oappend(_1679400), _1679402), _1679398)) = c_List_Olast(_1679400, _1679402))], (12326 ^ _779854) ^ [_994888, _994890, _994892, _994894] : [-(hBOOL(hAPP(hAPP(c_member(_994888), _994890), _994892))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994888, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_994888), _994890), _994894)), _994892) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994888, tc_HOL_Obool)), _994894), _994892))], (41726 ^ _779854) ^ [_1599504, _1599506, _1599508, _1599510, _1599512] : [c_Relation_Osingle__valued(_1599504, _1599506, hAPP(c_Relation_Oconverse(_1599506, _1599504), _1599508)), -(hAPP(c_Relation_OImage(_1599506, _1599504, _1599508), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599506, tc_HOL_Obool)), _1599510), _1599512)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599504, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1599506, _1599504, _1599508), _1599510)), hAPP(c_Relation_OImage(_1599506, _1599504, _1599508), _1599512)))], (49499 ^ _779854) ^ [_1778906, _1778908, _1778910, _1778912] : [-(hAPP(c_Relation_OImage(_1778906, _1778908, hAPP(c_Set_OCollect(tc_prod(_1778906, _1778908)), hAPP(c_Product__Type_Oprod_Oprod__case(_1778906, _1778908, tc_HOL_Obool), _1778910))), _1778912) = hAPP(c_Set_OCollect(_1778908), hAPP(hAPP(c_COMBB(tc_fun(_1778906, tc_HOL_Obool), tc_HOL_Obool, _1778908), c_HOL_OEx(_1778906)), hAPP(hAPP(c_COMBB(tc_fun(_1778906, tc_HOL_Obool), tc_fun(_1778906, tc_HOL_Obool), _1778908), hAPP(c_COMBS(_1778906, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1778906), c_fconj), hAPP(hAPP(c_COMBC(_1778906, tc_fun(_1778906, tc_HOL_Obool), tc_HOL_Obool), c_member(_1778906)), _1778912)))), hAPP(c_COMBC(_1778906, _1778908, tc_HOL_Obool), _1778910)))))], (22489 ^ _779854) ^ [_1186338, _1186340, _1186342, _1186344] : [class_Fields_Ofield__inverse__zero(_1186338), 22492 ^ _779854 : [(22493 ^ _779854) ^ [] : [_1186340 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186338), _1186342), _1186344), 22496 ^ _779854 : [(22503 ^ _779854) ^ [] : [_1186344 = c_Groups_Ozero__class_Ozero(_1186338), -(_1186340 = c_Groups_Ozero__class_Ozero(_1186338))], (22497 ^ _779854) ^ [] : [-(_1186344 = c_Groups_Ozero__class_Ozero(_1186338)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186338), _1186340), _1186344) = _1186342)]]], (22509 ^ _779854) ^ [] : [-(_1186340 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186338), _1186342), _1186344)), 22512 ^ _779854 : [(22515 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186338), _1186340), _1186344) = _1186342], (22513 ^ _779854) ^ [] : [_1186344 = c_Groups_Ozero__class_Ozero(_1186338)]], 22516 ^ _779854 : [(22519 ^ _779854) ^ [] : [_1186340 = c_Groups_Ozero__class_Ozero(_1186338)], (22517 ^ _779854) ^ [] : [-(_1186344 = c_Groups_Ozero__class_Ozero(_1186338))]]]]], (46022 ^ _779854) ^ [_1703247, _1703249] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1703247), tc_fun(_1703247, tc_HOL_Obool), c_List_Oset(_1703247)), hAPP(c_List_Oset(tc_List_Olist(_1703247)), c_Enum_Osublists(_1703247, _1703249))) = hAPP(c_Set_OPow(_1703247), hAPP(c_List_Oset(_1703247), _1703249)))], (5794 ^ _779854) ^ [_871573, _871575, _871577] : [_871573 = _871575, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871577, tc_HOL_Obool)), _871575), _871573)))], (23946 ^ _779854) ^ [_1214147, _1214149, _1214151, _1214153] : [class_Groups_Ocomm__monoid__mult(_1214147), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214147), _1214149), _1214151)), _1214153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214147), hAPP(hAPP(c_Power_Opower__class_Opower(_1214147), _1214149), _1214153)), hAPP(hAPP(c_Power_Opower__class_Opower(_1214147), _1214151), _1214153)))], (22981 ^ _779854) ^ [_1195252, _1195254, _1195256, _1195258] : [class_Fields_Ofield(_1195252), -(_1195254 = c_Groups_Ozero__class_Ozero(_1195252)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195252), _1195256), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195252), _1195258), _1195254)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195252), _1195254), _1195256)), _1195258)), _1195254))], (35945 ^ _779854) ^ [_1449541, _1449543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449543), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1449541, _1449543) = 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), _1449541), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1449543)))))], (40521 ^ _779854) ^ [_1569767, _1569769, _1569771, _1569773] : [hBOOL(hAPP(hAPP(c_member(_1569767), _1569769), _1569771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1569767, tc_HOL_Obool)), _1569771), hAPP(_1569773, _1569771))), -(hBOOL(hAPP(hAPP(c_member(_1569767), _1569769), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1569767, tc_HOL_Obool), _1569773))))], (33661 ^ _779854) ^ [_1398301, _1398303, _1398305, _1398307, _1398309, _1398311] : [-(hAPP(c_Set_Oimage(_1398301, _1398303, _1398305), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398307, tc_fun(_1398301, tc_HOL_Obool)), _1398309), _1398311)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398307, tc_fun(_1398303, tc_HOL_Obool)), _1398309), hAPP(hAPP(c_COMBB(tc_fun(_1398301, tc_HOL_Obool), tc_fun(_1398303, tc_HOL_Obool), _1398307), c_Set_Oimage(_1398301, _1398303, _1398305)), _1398311)))], (3886 ^ _779854) ^ [_838386, _838388, _838390, _838392, _838394, _838396, _838398, _838400, _838402, _838404, _838406, _838408, _838410, _838412] : [-(c_New__Random__Sequence_Oneg__decr__bind(_838412, _838408, _838404, _838400, _838396, _838392, _838388) = c_New__Random__Sequence_Oneg__decr__bind(_838410, _838406, _838402, _838398, _838394, _838390, _838386)), _838412 = _838410, _838408 = _838406, _838404 = _838402, _838400 = _838398, _838396 = _838394, _838392 = _838390, _838388 = _838386], (43891 ^ _779854) ^ [_1655625, _1655627, _1655629, _1655631, _1655633, _1655635] : [hAPP(hAPP(c_List_Oappend(_1655625), _1655627), _1655629) = _1655631, _1655633 = hAPP(hAPP(c_List_Oappend(_1655625), _1655629), _1655635), -(hAPP(hAPP(c_List_Oappend(_1655625), _1655627), _1655633) = hAPP(hAPP(c_List_Oappend(_1655625), _1655631), _1655635))], (39763 ^ _779854) ^ [_1551059, _1551061] : [hBOOL(hAPP(hAPP(c_member(_1551059), 39764 ^ [_1551059, _1551061]), c_Wellfounded_Oacc(_1551059, _1551061))), -(c_Wellfounded_Owf(_1551059, _1551061))], (30527 ^ _779854) ^ [_1331098, _1331100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1331098), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331100), _1331098)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331098, _1331100) = _1331098)], (39599 ^ _779854) ^ [_1548091, _1548093, _1548095, _1548097] : [39600 ^ _779854 : [(39601 ^ _779854) ^ [_1548145] : [hBOOL(hAPP(hAPP(_1548095, _1548145), _1548097))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1548091, _1548093, _1548095), _1548097)))], (52067 ^ _779854) ^ [_1832237, _1832239] : [class_Lattices_Obounded__lattice(_1832237), -(class_Lattices_Obounded__lattice(tc_fun(_1832239, _1832237)))], (23934 ^ _779854) ^ [_1213937, _1213939, _1213941] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1213937), _1213939)), _1213941) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1213937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1213939), _1213941)))], (29487 ^ _779854) ^ [_1311740, _1311742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311740), _1311742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1311740)), c_Int_OBit1(_1311742))))], (41449 ^ _779854) ^ [_1592561, _1592563, _1592565] : [-(hAPP(c_Relation_Oconverse(_1592561, _1592563), hAPP(c_Relation_Oconverse(_1592563, _1592561), _1592565)) = _1592565)], (40290 ^ _779854) ^ [_1564455, _1564457] : [40292 ^ _779854 : [(40295 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1564457), 40291 ^ [_1564455, _1564457]))], (40293 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 40291 ^ [_1564455, _1564457]), _1564455)))]], -(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)), _1564457), _1564455))], (23713 ^ _779854) ^ [_1209545, _1209547, _1209549, _1209551] : [class_Orderings_Olinorder(_1209545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209545), _1209547)), 23723 ^ _779854 : [(23726 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209545), 23722 ^ [_1209545, _1209547, _1209549, _1209551]), _1209549))], (23724 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1209545), 23722 ^ [_1209545, _1209547, _1209549, _1209551]), _1209547)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209545), hAPP(hAPP(c_Finite__Set_Ofold(_1209545, _1209545, c_Orderings_Oord__class_Omax(_1209545)), _1209551), _1209547)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209545), _1209549), _1209551))))], (33535 ^ _779854) ^ [_1392193, _1392195, _1392197, _1392199, _1392201, _1392203] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392193, tc_fun(_1392195, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1392193, tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_fun(_1392195, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392195, tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_fun(_1392195, tc_HOL_Obool)), _1392193), c_COMBC(_1392195, tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392195, tc_prod(_1392193, _1392195)), tc_fun(_1392195, tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool)), _1392193), hAPP(c_COMBB(tc_prod(_1392193, _1392195), tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool), _1392195), c_member(tc_prod(_1392193, _1392195)))), c_Product__Type_OPair(_1392193, _1392195)))), _1392197)), hAPP(hAPP(c_COMBC(_1392193, tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_fun(_1392195, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392195, tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_fun(_1392195, tc_HOL_Obool)), _1392193), c_COMBC(_1392195, tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392195, tc_prod(_1392193, _1392195)), tc_fun(_1392195, tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool)), _1392193), hAPP(c_COMBB(tc_prod(_1392193, _1392195), tc_fun(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool), tc_HOL_Obool), _1392195), c_member(tc_prod(_1392193, _1392195)))), c_Product__Type_OPair(_1392193, _1392195)))), _1392199)), _1392201), _1392203)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1392193, _1392195)), hAPP(hAPP(c_Product__Type_OPair(_1392193, _1392195), _1392201), _1392203)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1392193, _1392195), tc_HOL_Obool)), _1392197), _1392199))))], (38819 ^ _779854) ^ [_1520470, _1520472, _1520474, _1520476] : [hBOOL(hAPP(hAPP(c_member(_1520470), _1520472), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520470, tc_HOL_Obool)), _1520474), hAPP(c_Set_OCollect(_1520470), _1520476)))), 38822 ^ _779854 : [(38825 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1520476, _1520472)))], (38823 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520470), _1520472), _1520474)))]]], (33559 ^ _779854) ^ [_1394860, _1394862, _1394864] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1394860, tc_HOL_Obool)), _1394862), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1394860, tc_HOL_Obool), _1394864)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1394860, tc_HOL_Obool), tc_fun(_1394860, tc_HOL_Obool)), _1394864), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1394860, tc_HOL_Obool)), _1394862)))], (46485 ^ _779854) ^ [_1713855, _1713857, _1713859] : [46487 ^ _779854 : [(46490 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1713857, 46486 ^ [_1713855, _1713857, _1713859])))], (46488 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1713855), 46486 ^ [_1713855, _1713857, _1713859]), hAPP(c_List_Oset(_1713855), _1713859))))]], -(hAPP(c_List_Ofilter(_1713855, _1713857), _1713859) = c_List_Olist_ONil(_1713855))], (47153 ^ _779854) ^ [_1727699, _1727701, _1727703] : [class_Orderings_Olinorder(_1727699), 47156 ^ _779854 : [(47169 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727699, hAPP(hAPP(c_List_Olist_OCons(_1727699), _1727701), _1727703))), 47173 ^ _779854 : [(47176 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727699), _1727701), 47172 ^ [_1727699, _1727701, _1727703]))], (47174 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1727699), 47172 ^ [_1727699, _1727701, _1727703]), hAPP(c_List_Oset(_1727699), _1727703))))]], c_List_Olinorder__class_Osorted(_1727699, _1727703)], (47157 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1727699, hAPP(hAPP(c_List_Olist_OCons(_1727699), _1727701), _1727703)), 47160 ^ _779854 : [(47161 ^ _779854) ^ [_1727867] : [hBOOL(hAPP(hAPP(c_member(_1727699), _1727867), hAPP(c_List_Oset(_1727699), _1727703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727699), _1727701), _1727867)))], (47167 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727699, _1727703))]]]]], (39337 ^ _779854) ^ [_1539252, _1539254] : [-(hAPP(c_Set_Ovimage(_1539252, _1539252, c_Fun_Oid(_1539252)), _1539254) = _1539254)], (31494 ^ _779854) ^ [_1347525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347525)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1347525) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1347525), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20359 ^ _779854) ^ [_1146255, _1146257, _1146259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1146255), _1146257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146255), _1146259)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146257), _1146259))))], (29133 ^ _779854) ^ [_1305478, _1305480] : [class_Int_Onumber__ring(_1305478), class_Rings_Olinordered__idom(_1305478), 29140 ^ _779854 : [(29147 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1305480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305478), c_Groups_Oone__class_Oone(_1305478)), hAPP(c_Int_Onumber__class_Onumber__of(_1305478), _1305480))))], (29141 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305478), c_Groups_Oone__class_Oone(_1305478)), hAPP(c_Int_Onumber__class_Onumber__of(_1305478), _1305480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1305480)))]]], (48710 ^ _779854) ^ [_1761128, _1761130, _1761132, _1761134] : [-(c_List_Olist__ex1(_1761128, _1761130, hAPP(hAPP(c_List_Olist_OCons(_1761128), _1761132), _1761134))), 48713 ^ _779854 : [(48716 ^ _779854) ^ [] : [c_List_Olist__all(_1761128, hAPP(hAPP(c_COMBS(_1761128, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1761128), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1761128), c_fNot), _1761130))), hAPP(c_fequal, _1761132)), _1761134)], (48714 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1761130, _1761132)))]], 48717 ^ _779854 : [(48720 ^ _779854) ^ [] : [c_List_Olist__ex1(_1761128, _1761130, _1761134)], (48718 ^ _779854) ^ [] : [hBOOL(hAPP(_1761130, _1761132))]]], (29289 ^ _779854) ^ [_1308392, _1308394] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308392) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1308394), -(_1308392 = _1308394)], (30723 ^ _779854) ^ [_1334524, _1334526, _1334528, _1334530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334526), _1334528)), -(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), _1334528), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1334530, _1334524))), _1334526))))], (27161 ^ _779854) ^ [_1272181, _1272183] : [class_Int_Onumber__ring(_1272181), class_Rings_Olinordered__idom(_1272181), 27168 ^ _779854 : [(27175 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272183), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272181), hAPP(c_Int_Onumber__class_Onumber__of(_1272181), _1272183)), c_Groups_Ozero__class_Ozero(_1272181))))], (27169 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272181), hAPP(c_Int_Onumber__class_Onumber__of(_1272181), _1272183)), c_Groups_Ozero__class_Ozero(_1272181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272183), c_Int_OPls)))]]], (5760 ^ _779854) ^ [_870993, _870995, _870997] : [_870993 = _870995, 5763 ^ _779854 : [(5766 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870997, tc_HOL_Obool)), _870995), _870993)))], (5764 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870997, tc_HOL_Obool)), _870993), _870995)))]]], (48565 ^ _779854) ^ [_1758476, _1758478, _1758480, _1758482] : [c_List_Olist__all(_1758476, _1758478, hAPP(hAPP(c_List_Oappend(_1758476), _1758480), _1758482)), 48568 ^ _779854 : [(48571 ^ _779854) ^ [] : [-(c_List_Olist__all(_1758476, _1758478, _1758482))], (48569 ^ _779854) ^ [] : [-(c_List_Olist__all(_1758476, _1758478, _1758480))]]], (15966 ^ _779854) ^ [_1066422, _1066424, _1066426, _1066428] : [class_Rings_Ocomm__semiring__1(_1066422), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066422), _1066424), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066422), _1066426), _1066428)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066422), _1066424), _1066426)), _1066428))], (51367 ^ _779854) ^ [_1820243, _1820245] : [class_Rings_Ocomm__semiring__1(_1820243), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820243), _1820245), c_Groups_Ozero__class_Ozero(_1820243))))], (45607 ^ _779854) ^ [_1693573] : [-(hAPP(c_Code__Numeral_Onat__of, _1693573) = c_Code__Numeral_Onat__of__aux(_1693573, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (38330 ^ _779854) ^ [_1506853, _1506855, _1506857] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1506853, _1506855), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1506853, _1506855), c_Orderings_Otop__class_Otop(tc_fun(_1506853, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1506855, tc_HOL_Obool), _1506853), _1506857))) = hAPP(hAPP(c_Product__Type_OSigma(_1506853, _1506855), c_Orderings_Otop__class_Otop(tc_fun(_1506853, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1506855, tc_HOL_Obool), _1506853), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1506855, tc_HOL_Obool)), _1506857))))], (27867 ^ _779854) ^ [_1284053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1284053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284053)))], (19789 ^ _779854) ^ [_1136843, _1136845, _1136847, _1136849] : [class_Rings_Olinordered__ring__strict(_1136843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136843), _1136845), _1136847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136843), _1136849), c_Groups_Ozero__class_Ozero(_1136843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136843), _1136847), _1136849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136843), _1136845), _1136849))))], (46767 ^ _779854) ^ [_1720623, _1720625] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1720623, _1720625) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1720623), _1720625)))], (52053 ^ _779854) ^ [_1832025, _1832027] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832025), _1832027)), 52058 ^ _779854 : [(52061 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832027), _1832025))], (52059 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832025), _1832027)))]], -(_1832025 = _1832027)], (17076 ^ _779854) ^ [_1088063, _1088065, _1088067, _1088069, _1088071] : [class_Groups_Ocomm__monoid__mult(_1088063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088065), _1088067)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088065), _1088069)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088065, tc_HOL_Obool)), _1088067), _1088069) = c_Orderings_Obot__class_Obot(tc_fun(_1088065, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088065, _1088063), _1088071), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088065, tc_HOL_Obool)), _1088067), _1088069)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088063), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088065, _1088063), _1088071), _1088067)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088065, _1088063), _1088071), _1088069)))], (43987 ^ _779854) ^ [_1657569, _1657571, _1657573] : [_1657573 = c_List_Olist_ONil(_1657571), -(_1657569 = hAPP(hAPP(c_List_Oappend(_1657571), _1657569), _1657573))], (10239 ^ _779854) ^ [_952825, _952827, _952829, _952831, _952833] : [class_Lattices_Osemilattice__inf(_952825), class_Orderings_Olinorder(_952827), c_Orderings_Oorder__class_Omono(_952827, _952825, _952829), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952825), hAPP(_952829, hAPP(hAPP(c_Orderings_Oord__class_Omin(_952827), _952831), _952833))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952825), hAPP(_952829, _952831)), hAPP(_952829, _952833)))))], (31506 ^ _779854) ^ [_1347727] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1347727, 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, _1347727, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (22053 ^ _779854) ^ [_1178070, _1178072, _1178074, _1178076] : [class_Groups_Ocomm__monoid__add(_1178070), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178072), _1178074)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1178072, _1178070), _1178076), _1178074) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1178070, _1178072, c_Groups_Oplus__class_Oplus(_1178070)), _1178076), c_Groups_Ozero__class_Ozero(_1178070)), _1178074))], (25629 ^ _779854) ^ [_1245880, _1245882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1245880)), _1245882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245880), _1245882)))], (48145 ^ _779854) ^ [_1749198, _1749200, _1749202, _1749204] : [48147 ^ _779854 : [(48150 ^ _779854) ^ [] : [hBOOL(hAPP(_1749202, 48146 ^ [_1749198, _1749200, _1749202, _1749204]))], (48148 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749198), 48146 ^ [_1749198, _1749200, _1749202, _1749204]), hAPP(c_List_Oset(_1749198), _1749200))))]], -(c_List_OdropWhile(_1749198, _1749202, hAPP(hAPP(c_List_Oappend(_1749198), _1749200), _1749204)) = c_List_OdropWhile(_1749198, _1749202, _1749204))], (17278 ^ _779854) ^ [_1092036, _1092038, _1092040, _1092042, _1092044, _1092046] : [c_Finite__Set_Ofun__left__comm(_1092036, _1092038, _1092040), -(hAPP(hAPP(_1092040, _1092042), hAPP(hAPP(_1092040, _1092044), _1092046)) = hAPP(hAPP(_1092040, _1092044), hAPP(hAPP(_1092040, _1092042), _1092046)))], (43921 ^ _779854) ^ [_1656405, _1656407, _1656409] : [_1656405 = _1656407, -(_1656405 = hAPP(hAPP(c_List_Oappend(_1656409), c_List_Olist_ONil(_1656409)), _1656407))], (35732 ^ _779854) ^ [_1445231, _1445233, _1445235, _1445237] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1445231, _1445233), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445235), _1445237))), -(_1445233 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1445231, _1445233) = _1445237)], (24525 ^ _779854) ^ [_1224797, _1224799, _1224801] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224797), _1224799)), _1224801) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224797), _1224801)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224799), _1224801)))], (23982 ^ _779854) ^ [_1214935, _1214937, _1214939, _1214941] : [class_Rings_Olinordered__semidom(_1214935), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214935), _1214937), _1214939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214935), c_Groups_Ozero__class_Ozero(_1214935)), _1214937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214935), hAPP(hAPP(c_Power_Opower__class_Opower(_1214935), _1214937), _1214941)), hAPP(hAPP(c_Power_Opower__class_Opower(_1214935), _1214939), _1214941))))], (22847 ^ _779854) ^ [_1192787, _1192789, _1192791, _1192793] : [class_Fields_Olinordered__field(_1192787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192787), c_Groups_Ozero__class_Ozero(_1192787)), _1192789)), 22854 ^ _779854 : [(22861 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192787), _1192791), _1192789)), _1192793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192787), _1192791), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192787), _1192793), _1192789))))], (22855 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192787), _1192791), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192787), _1192793), _1192789))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192787), _1192791), _1192789)), _1192793)))]]], (9614 ^ _779854) ^ [_941040, _941042, _941044, _941046] : [class_Orderings_Olinorder(_941040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941040), _941042), _941044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941040), _941042), hAPP(hAPP(c_Orderings_Oord__class_Omax(_941040), _941046), _941044))))], (4412 ^ _779854) ^ [_847015, _847017] : [_847017 = _847015, -(c_Lazy__Sequence_Osingle(_847017) = c_Lazy__Sequence_Osingle(_847015))], (52419 ^ _779854) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (21230 ^ _779854) ^ [_1162150, _1162152, _1162154, _1162156, _1162158, _1162160] : [class_Rings_Olinordered__semiring__1__strict(_1162150), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162150), _1162152), _1162154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162150), _1162156), _1162154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162150), c_Groups_Ozero__class_Ozero(_1162150)), _1162158)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162150), c_Groups_Ozero__class_Ozero(_1162150)), _1162160)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162150), _1162158), _1162160) = c_Groups_Oone__class_Oone(_1162150), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162150), _1162158), _1162152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162150), _1162160), _1162156))), _1162154)))], (8020 ^ _779854) ^ [_914016, _914018, _914020, _914022] : [class_Orderings_Olinorder(_914016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914016), _914018), _914020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914016), _914020), _914022)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914016, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_914016, _914018, _914020)), c_SetInterval_Oord__class_OgreaterThanLessThan(_914016, _914020, _914022)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_914016, _914018), _914022))], (39397 ^ _779854) ^ [_1540869, _1540871, _1540873, _1540875, _1540877, _1540879, _1540881, _1540883] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540869, _1540871)), hAPP(hAPP(c_Product__Type_OPair(_1540869, _1540871), _1540873), _1540875)), _1540877)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1540871, _1540879)), hAPP(hAPP(c_Product__Type_OPair(_1540871, _1540879), _1540875), _1540881)), _1540883)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540869, _1540879)), hAPP(hAPP(c_Product__Type_OPair(_1540869, _1540879), _1540873), _1540881)), hAPP(hAPP(c_Relation_Orel__comp(_1540869, _1540871, _1540879), _1540877), _1540883))))], (33517 ^ _779854) ^ [_1390900, _1390902, _1390904] : [_1390902 = _1390904, -(hAPP(hAPP(c_COMBC(_1390900, tc_fun(_1390900, tc_HOL_Obool), tc_HOL_Obool), c_member(_1390900)), _1390902) = hAPP(hAPP(c_COMBC(_1390900, tc_fun(_1390900, tc_HOL_Obool), tc_HOL_Obool), c_member(_1390900)), _1390904))], (30809 ^ _779854) ^ [_1336031, _1336033] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1336031)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1336033))) = 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), _1336031), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1336033))))], (30999 ^ _779854) ^ [_1339412] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1339412)))), -(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), _1339412)) = 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), _1339412))))], (40925 ^ _779854) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40088 ^ _779854) ^ [_1559100, _1559102, _1559104, _1559106] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559100), _1559102))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559104), hAPP(c_Set_Oimage(_1559100, _1559104, _1559106), _1559102))), 40096 ^ _779854 : [(40099 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559100), hAPP(c_Set_OCollect(_1559100), hAPP(hAPP(c_COMBS(_1559100, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1559100), c_fconj), hAPP(hAPP(c_COMBC(_1559100, tc_fun(_1559100, tc_HOL_Obool), tc_HOL_Obool), c_member(_1559100)), _1559102))), hAPP(hAPP(c_COMBC(_1559100, _1559104, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1559104, tc_fun(_1559104, tc_HOL_Obool), _1559100), c_fequal), _1559106)), hAPP(_1559106, 40095 ^ [_1559100, _1559102, _1559104, _1559106]))))))], (40097 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559100), 40095 ^ [_1559100, _1559102, _1559104, _1559106]), _1559102)))]]], (23131 ^ _779854) ^ [_1198019, _1198021, _1198023, _1198025] : [class_Fields_Olinordered__field__inverse__zero(_1198019), 23134 ^ _779854 : [(23135 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1198019), _1198021), _1198023)), _1198025)), 23138 ^ _779854 : [(23145 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), c_Groups_Ozero__class_Ozero(_1198019)), _1198023))), 23148 ^ _779854 : [(23155 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), _1198023), c_Groups_Ozero__class_Ozero(_1198019)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), c_Groups_Ozero__class_Ozero(_1198019)), _1198025)))], (23149 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), _1198023), c_Groups_Ozero__class_Ozero(_1198019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198019), _1198025), _1198023)), _1198021)))]]], (23139 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), c_Groups_Ozero__class_Ozero(_1198019)), _1198023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), _1198021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198019), _1198025), _1198023))))]]], (23161 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1198019), _1198021), _1198023)), _1198025))), 23164 ^ _779854 : [(23167 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), _1198021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198019), _1198025), _1198023)))], (23165 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), c_Groups_Ozero__class_Ozero(_1198019)), _1198023)))]], 23168 ^ _779854 : [(23171 ^ _779854) ^ [] : [23172 ^ _779854 : [(23175 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198019), _1198025), _1198023)), _1198021))], (23173 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), _1198023), c_Groups_Ozero__class_Ozero(_1198019))))]], 23176 ^ _779854 : [(23179 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198019), c_Groups_Ozero__class_Ozero(_1198019)), _1198025))], (23177 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), _1198023), c_Groups_Ozero__class_Ozero(_1198019)))]]], (23169 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198019), c_Groups_Ozero__class_Ozero(_1198019)), _1198023))]]]]], (42404 ^ _779854) ^ [_1619684, _1619686, _1619688, _1619690] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619684), tc_List_Olist(_1619684))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619684), tc_List_Olist(_1619684)), _1619688), _1619690)), c_List_Olistrel(_1619684, _1619686))), -(c_List_Olistrelp(_1619684, hAPP(hAPP(c_COMBC(_1619684, tc_fun(tc_prod(_1619684, _1619684), tc_HOL_Obool), tc_fun(_1619684, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619684, tc_fun(tc_fun(tc_prod(_1619684, _1619684), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1619684, _1619684), tc_HOL_Obool), tc_fun(_1619684, tc_HOL_Obool)), _1619684), c_COMBC(_1619684, tc_fun(tc_prod(_1619684, _1619684), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619684, tc_prod(_1619684, _1619684)), tc_fun(_1619684, tc_fun(tc_fun(tc_prod(_1619684, _1619684), tc_HOL_Obool), tc_HOL_Obool)), _1619684), hAPP(c_COMBB(tc_prod(_1619684, _1619684), tc_fun(tc_fun(tc_prod(_1619684, _1619684), tc_HOL_Obool), tc_HOL_Obool), _1619684), c_member(tc_prod(_1619684, _1619684)))), c_Product__Type_OPair(_1619684, _1619684)))), _1619686), _1619688, _1619690))], (18207 ^ _779854) ^ [_1109289, _1109291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109289), _1109291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1109289)), _1109291)))], (25651 ^ _779854) ^ [_1246293, _1246295] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246293), _1246295))), -(_1246293 = _1246295), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246295), _1246293)))], (45089 ^ _779854) ^ [_1681919, _1681921, _1681923, _1681925, _1681927, _1681929, _1681931, _1681933] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1681919, _1681921), _1681923), _1681925), hAPP(hAPP(c_List_Ozip(_1681919, _1681921), _1681927), hAPP(hAPP(c_List_Omap(_1681929, _1681921), _1681931), _1681933))) = hAPP(hAPP(c_List_Omap(tc_prod(_1681919, _1681929), _1681923), hAPP(c_Product__Type_Oprod_Oprod__case(_1681919, _1681929, _1681923), hAPP(hAPP(c_COMBB(tc_fun(_1681929, tc_prod(_1681919, _1681921)), tc_fun(_1681929, _1681923), _1681919), hAPP(c_COMBB(tc_prod(_1681919, _1681921), _1681923, _1681929), _1681925)), hAPP(hAPP(c_COMBC(_1681919, tc_fun(_1681929, _1681921), tc_fun(_1681929, tc_prod(_1681919, _1681921))), hAPP(hAPP(c_COMBB(tc_fun(_1681921, tc_prod(_1681919, _1681921)), tc_fun(tc_fun(_1681929, _1681921), tc_fun(_1681929, tc_prod(_1681919, _1681921))), _1681919), c_COMBB(_1681921, tc_prod(_1681919, _1681921), _1681929)), c_Product__Type_OPair(_1681919, _1681921))), _1681931)))), hAPP(hAPP(c_List_Ozip(_1681919, _1681929), _1681927), _1681933)))], (44901 ^ _779854) ^ [_1678361, _1678363, _1678365, _1678367, _1678369] : [class_Orderings_Olinorder(_1678361), hBOOL(hAPP(hAPP(c_member(_1678361), hAPP(_1678363, _1678365)), hAPP(c_Set_Oimage(_1678367, _1678361, _1678363), hAPP(c_List_Oset(_1678367), _1678369)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1678367, _1678361, _1678363, _1678365, _1678369) = _1678369)], (9929 ^ _779854) ^ [_947237, _947239, _947241, _947243, _947245] : [class_Orderings_Olinorder(_947237), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947237, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_947237, _947239, _947241)), c_SetInterval_Oord__class_OgreaterThanAtMost(_947237, _947243, _947245)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_947237, hAPP(hAPP(c_Orderings_Oord__class_Omax(_947237), _947239), _947243), hAPP(hAPP(c_Orderings_Oord__class_Omin(_947237), _947241), _947245)))], (35175 ^ _779854) ^ [_1435018, _1435020, _1435022, _1435024, _1435026] : [hBOOL(hAPP(hAPP(_1435018, _1435020), _1435022)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1435024, _1435026, tc_HOL_Obool), _1435018), hAPP(hAPP(c_Product__Type_OPair(_1435024, _1435026), _1435020), _1435022))))], (46060 ^ _779854) ^ [_1704168, _1704170, _1704172] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1704168))), c_Enum_On__lists(_1704168, _1704170, _1704172)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704168)), _1704172)), _1704170))], (33413 ^ _779854) ^ [_1387939, _1387941, _1387943, _1387945, _1387947, _1387949] : [hBOOL(hAPP(hAPP(c_member(_1387939), _1387941), _1387943)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1387939, tc_fun(_1387945, tc_HOL_Obool)), _1387943), hAPP(hAPP(c_COMBB(tc_fun(_1387945, tc_HOL_Obool), tc_fun(_1387945, tc_HOL_Obool), _1387939), hAPP(c_Set_Oinsert(_1387945), _1387947)), _1387949)) = hAPP(hAPP(c_Set_Oinsert(_1387945), _1387947), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1387939, tc_fun(_1387945, tc_HOL_Obool)), _1387943), _1387949)))], (52091 ^ _779854) ^ [_1832553, _1832555] : [class_Lattices_Olattice(_1832553), -(class_Lattices_Osemilattice__sup(tc_fun(_1832555, _1832553)))], (44540 ^ _779854) ^ [_1670846, _1670848, _1670850] : [hAPP(c_List_Orotate(_1670846, _1670848), _1670850) = c_List_Olist_ONil(_1670846), -(_1670850 = c_List_Olist_ONil(_1670846))], (45972 ^ _779854) ^ [_1702185, _1702187, _1702189, _1702191, _1702193, _1702195] : [c_List_Olist__all2(_1702185, _1702187, _1702189, _1702191, _1702193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702195), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702187)), _1702193))), -(hBOOL(hAPP(hAPP(_1702189, hAPP(hAPP(c_List_Onth(_1702185), _1702191), _1702195)), hAPP(hAPP(c_List_Onth(_1702187), _1702193), _1702195))))], (34933 ^ _779854) ^ [_1429272, _1429274, _1429276, _1429278, _1429280, _1429282, _1429284] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429272, tc_fun(_1429274, tc_fun(_1429276, tc_HOL_Obool))), _1429278), _1429280), _1429282), _1429284)), 34936 ^ _779854 : [(34937 ^ _779854) ^ [_1429400] : [hBOOL(hAPP(hAPP(c_member(_1429272), _1429400), _1429278)), -(hBOOL(hAPP(hAPP(hAPP(_1429280, _1429400), _1429282), _1429284)))]]], (50973 ^ _779854) ^ [_1810383] : [-(c_Fun_Obij__betw(_1810383, _1810383, c_Fun_Oid(_1810383), c_Orderings_Otop__class_Otop(tc_fun(_1810383, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810383, tc_HOL_Obool))))], (52097 ^ _779854) ^ [_1832632, _1832634] : [class_Lattices_Olattice(_1832632), -(class_Lattices_Osemilattice__inf(tc_fun(_1832634, _1832632)))], (47398 ^ _779854) ^ [_1732887, _1732889, _1732891, _1732893, _1732895] : [c_List_Olist__all2(_1732887, _1732889, _1732891, _1732893, hAPP(c_List_Orev(_1732889), _1732895)), -(c_List_Olist__all2(_1732887, _1732889, _1732891, hAPP(c_List_Orev(_1732887), _1732893), _1732895))], (41154 ^ _779854) ^ [_1585676, _1585678, _1585680] : [-(c_Transitive__Closure_Ortrancl(_1585676, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585676, _1585676), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1585676, _1585678)), c_Transitive__Closure_Ortrancl(_1585676, _1585680))) = c_Transitive__Closure_Ortrancl(_1585676, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585676, _1585676), tc_HOL_Obool)), _1585678), _1585680)))], (39935 ^ _779854) ^ [_1555209, _1555211, _1555213] : [-(hAPP(c_Relation_ODomain(_1555209, _1555211), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1555209, _1555211), tc_HOL_Obool), _1555213)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1555209, _1555211), tc_HOL_Obool), tc_fun(_1555209, tc_HOL_Obool)), _1555213), c_Relation_ODomain(_1555209, _1555211)))], (18859 ^ _779854) ^ [_1120263] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120263), _1120263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52331 ^ _779854) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (13173 ^ _779854) ^ [_1012289, _1012291] : [class_Groups_Olinordered__ab__group__add(_1012289), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012289), _1012291)), -(_1012291 = c_Orderings_Obot__class_Obot(tc_fun(_1012289, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1012289), c_Big__Operators_Olinorder__class_OMin(_1012289, _1012291)) = c_Big__Operators_Olinorder__class_OMax(_1012289, hAPP(c_Set_Oimage(_1012289, _1012289, c_Groups_Ouminus__class_Ouminus(_1012289)), _1012291)))], (44264 ^ _779854) ^ [_1664666, _1664668] : [-(hAPP(hAPP(c_List_Odrop(_1664666), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1664668) = _1664668)], (49485 ^ _779854) ^ [_1778509, _1778511, _1778513, _1778515, _1778517, _1778519, _1778521] : [hBOOL(hAPP(hAPP(_1778509, hAPP(c_Product__Type_Osnd(_1778511, _1778513), _1778515)), hAPP(c_Product__Type_Ofst(_1778511, _1778513), _1778515))), 49492 ^ _779854 : [(49495 ^ _779854) ^ [] : [hBOOL(hAPP(_1778517, hAPP(hAPP(_1778519, 49490 ^ [_1778509, _1778511, _1778513, _1778515, _1778517, _1778519, _1778521]), 49491 ^ [_1778509, _1778511, _1778513, _1778515, _1778517, _1778519, _1778521])))], (49493 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1778509, 49491 ^ [_1778509, _1778511, _1778513, _1778515, _1778517, _1778519, _1778521]), 49490 ^ [_1778509, _1778511, _1778513, _1778515, _1778517, _1778519, _1778521])))]], -(hBOOL(hAPP(_1778517, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1778511, _1778513, _1778521), _1778519), _1778515))))], (42771 ^ _779854) ^ [_1629319, _1629321, _1629323] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1629319)), _1629321), c_List_Olists(_1629319, _1629323))), 42774 ^ _779854 : [(42775 ^ _779854) ^ [_1629427] : [hBOOL(hAPP(hAPP(c_member(_1629319), _1629427), hAPP(c_List_Oset(_1629319), _1629321))), -(hBOOL(hAPP(hAPP(c_member(_1629319), _1629427), _1629323)))]]], (3016 ^ _779854) ^ [_824777, _824779, _824781, _824783] : [-(c_List_Olenlex(_824783, _824779) = c_List_Olenlex(_824781, _824777)), _824783 = _824781, _824779 = _824777], (11384 ^ _779854) ^ [_976452, _976454, _976456, _976458] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976452, tc_HOL_Obool)), _976454), _976458))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976452, tc_HOL_Obool)), _976454), hAPP(hAPP(c_Set_Oinsert(_976452), _976456), _976458)))))], (38154 ^ _779854) ^ [_1502155, _1502157, _1502159, _1502161, _1502163] : [hAPP(c_Set_Oimage(_1502155, _1502157, _1502159), c_Orderings_Otop__class_Otop(tc_fun(_1502155, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1502157, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502155, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1502155, _1502157, _1502159), _1502161)), _1502163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502157, tc_HOL_Obool)), _1502161), hAPP(c_Set_Oimage(_1502155, _1502157, _1502159), _1502163))))], (20469 ^ _779854) ^ [_1148213, _1148215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148213), _1148215)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1148213), _1148215) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18919 ^ _779854) ^ [_1121181, _1121183] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1121181), _1121183) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1121181 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1121183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30269 ^ _779854) ^ [_1326262, _1326264, _1326266, _1326268, _1326270, _1326272] : [class_Divides_Osemiring__div(_1326262), c_Divides_Odiv__class_Omod(_1326262, _1326264, _1326266) = c_Divides_Odiv__class_Omod(_1326262, _1326268, _1326266), c_Divides_Odiv__class_Omod(_1326262, _1326270, _1326266) = c_Divides_Odiv__class_Omod(_1326262, _1326272, _1326266), -(c_Divides_Odiv__class_Omod(_1326262, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326262), _1326264), _1326270), _1326266) = c_Divides_Odiv__class_Omod(_1326262, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326262), _1326268), _1326272), _1326266))], (41503 ^ _779854) ^ [_1594028, _1594030, _1594032] : [-(hAPP(c_Relation_ORange(_1594028, _1594030), hAPP(c_Relation_Oconverse(_1594030, _1594028), _1594032)) = hAPP(c_Relation_ODomain(_1594030, _1594028), _1594032))], (19987 ^ _779854) ^ [_1140293, _1140295] : [class_Groups_Oordered__ab__group__add(_1140293), 19990 ^ _779854 : [(19997 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140293), _1140295), c_Groups_Ozero__class_Ozero(_1140293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140293), c_Groups_Ozero__class_Ozero(_1140293)), hAPP(c_Groups_Ouminus__class_Ouminus(_1140293), _1140295))))], (19991 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140293), c_Groups_Ozero__class_Ozero(_1140293)), hAPP(c_Groups_Ouminus__class_Ouminus(_1140293), _1140295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140293), _1140295), c_Groups_Ozero__class_Ozero(_1140293))))]]], (46791 ^ _779854) ^ [_1721194, _1721196, _1721198] : [46792 ^ _779854 : [(46795 ^ _779854) ^ [] : [_1721198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46793 ^ _779854) ^ [] : [-(_1721194 = c_List_Olist_ONil(tc_List_Olist(_1721196)))]], 46799 ^ _779854 : [(46802 ^ _779854) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721196)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1721196)), _1721194), 46798 ^ [_1721194, _1721196, _1721198])) = _1721198], (46800 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46798 ^ [_1721194, _1721196, _1721198]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1721196))), _1721194))))]], -(c_List_Otranspose(_1721196, _1721194) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1721196)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1721196)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1721196), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1721196)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1721196)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1721196), hAPP(hAPP(c_COMBB(tc_List_Olist(_1721196), tc_fun(tc_Nat_Onat, _1721196), tc_Nat_Onat), c_List_Onth(_1721196)), hAPP(c_List_Onth(tc_List_Olist(_1721196)), _1721194))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1721196))), _1721194)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1721198)))], (33351 ^ _779854) ^ [_1386277, _1386279, _1386281, _1386283, _1386285, _1386287] : [-(hAPP(hAPP(c_Fun_Ocomp(_1386277, _1386279, _1386281, _1386283), _1386285), _1386287) = hAPP(_1386283, hAPP(_1386285, _1386287)))], (14183 ^ _779854) ^ [_1030158, _1030160, _1030162, _1030164] : [c_Fun_Oinj__on(_1030158, _1030160, _1030162, _1030164), -(hAPP(c_Set_Oimage(_1030160, _1030158, c_Fun_Othe__inv__into(_1030158, _1030160, _1030164, _1030162)), hAPP(c_Set_Oimage(_1030158, _1030160, _1030162), _1030164)) = _1030164)], (46771 ^ _779854) ^ [_1720696, _1720698] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1720696), hAPP(c_List_Onth(_1720696), _1720698)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720696)), _1720698))) = _1720698)], (6913 ^ _779854) ^ [_892417, _892419, _892421, _892423] : [class_Lattices_Olattice(_892417), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892417), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892417), _892419), _892421)), _892423) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892417), _892419), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892417), _892421), _892423)))], (36076 ^ _779854) ^ [_1452521, _1452523, _1452525, _1452527, _1452529, _1452531] : [c_Finite__Set_Ofolding(_1452521, _1452523, _1452525, _1452527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452521), _1452529)), -(hAPP(hAPP(_1452527, _1452529), _1452531) = hAPP(hAPP(c_Finite__Set_Ofold(_1452521, _1452523, _1452525), _1452531), _1452529))], (39425 ^ _779854) ^ [_1541831, _1541833, _1541835, _1541837, _1541839, _1541841, _1541843] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541831, _1541833, _1541835), hAPP(hAPP(c_Relation_Orel__comp(_1541831, _1541837, _1541833), _1541839), _1541841)), _1541843) = hAPP(hAPP(c_Relation_Orel__comp(_1541831, _1541837, _1541835), _1541839), hAPP(hAPP(c_Relation_Orel__comp(_1541837, _1541833, _1541835), _1541841), _1541843)))], (46451 ^ _779854) ^ [_1713098, _1713100, _1713102] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1713098), tc_List_Olist(_1713098)), c_List_Opartition(_1713098, _1713100, _1713102)) = hAPP(c_List_Ofilter(_1713098, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1713098, c_fNot), _1713100)), _1713102))], (24422 ^ _779854) ^ [_1222818, _1222820, _1222822, _1222824] : [class_Lattices_Osemilattice__inf(_1222818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222818), _1222820)), 24432 ^ _779854 : [(24435 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222818), _1222822), 24431 ^ [_1222818, _1222820, _1222822, _1222824]))], (24433 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222818), 24431 ^ [_1222818, _1222820, _1222822, _1222824]), _1222820)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222818), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1222818), _1222822), _1222824)), hAPP(hAPP(c_Finite__Set_Ofold(_1222818, _1222818, c_Lattices_Osemilattice__inf__class_Oinf(_1222818)), _1222824), _1222820))))], (45982 ^ _779854) ^ [_1702402, _1702404, _1702406, _1702408, _1702410, _1702412, _1702414, _1702416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702402), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702404)), _1702406))), c_List_Olist__all2(_1702404, _1702408, _1702410, _1702406, _1702412), hBOOL(hAPP(hAPP(_1702410, _1702414), _1702416)), -(c_List_Olist__all2(_1702404, _1702408, _1702410, hAPP(hAPP(c_List_Olist__update(_1702404, _1702406), _1702402), _1702414), hAPP(hAPP(c_List_Olist__update(_1702408, _1702412), _1702402), _1702416)))], (33298 ^ _779854) ^ [_1384840, _1384842, _1384844, _1384846, _1384848] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384840, tc_fun(_1384842, tc_HOL_Obool)), _1384844), _1384846), _1384848)), 33302 ^ _779854 : [(33305 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1384846, 33301 ^ [_1384840, _1384842, _1384844, _1384846, _1384848]), _1384848)))], (33303 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384840), 33301 ^ [_1384840, _1384842, _1384844, _1384846, _1384848]), _1384844)))]]], (22019 ^ _779854) ^ [_1177447, _1177449, _1177451] : [class_Rings_Odivision__ring(_1177447), -(_1177449 = c_Groups_Ozero__class_Ozero(_1177447)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177447), hAPP(c_Groups_Ouminus__class_Ouminus(_1177447), _1177451)), hAPP(c_Groups_Ouminus__class_Ouminus(_1177447), _1177449)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1177447), _1177451), _1177449))], (50078 ^ _779854) ^ [_1792243, _1792245] : [c_Relation_Osym(_1792243, hAPP(c_Relation_Oconverse(_1792243, _1792243), _1792245)), -(c_Relation_Osym(_1792243, _1792245))], (46324 ^ _779854) ^ [_1709466, _1709468] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709466)), c_List_Oconcat(_1709466, _1709468)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1709466), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1709466))), _1709468)))], (6819 ^ _779854) ^ [_890206, _890208, _890210, _890212] : [6823 ^ _779854 : [(6826 ^ _779854) ^ [] : [hBOOL(hAPP(_890212, 6822 ^ [_890206, _890208, _890210, _890212]))], (6824 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890206), 6822 ^ [_890206, _890208, _890210, _890212]), _890208)))]], 6828 ^ _779854 : [(6831 ^ _779854) ^ [] : [hBOOL(hAPP(_890212, 6827 ^ [_890206, _890208, _890210, _890212]))], (6829 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890206), 6827 ^ [_890206, _890208, _890210, _890212]), _890210)))]], 6832 ^ _779854 : [(6833 ^ _779854) ^ [_890539] : [hBOOL(hAPP(hAPP(c_member(_890206), _890539), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890206, tc_HOL_Obool)), _890208), _890210))), -(hBOOL(hAPP(_890212, _890539)))]]], (16427 ^ _779854) ^ [_1075495, _1075497, _1075499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075495), _1075497)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1075499), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075497), _1075495)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1075499), _1075497)), _1075495))], (38029 ^ _779854) ^ [_1499091, _1499093, _1499095] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1499091, tc_HOL_Obool)), _1499093), hAPP(hAPP(c_Set_Oinsert(_1499091), _1499095), c_Orderings_Obot__class_Obot(tc_fun(_1499091, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1499091, _1499095, _1499093) = c_HOL_OThe(_1499091, hAPP(hAPP(c_COMBC(_1499091, tc_fun(_1499091, tc_HOL_Obool), tc_HOL_Obool), c_member(_1499091)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1499091, tc_HOL_Obool)), _1499093), hAPP(hAPP(c_Set_Oinsert(_1499091), _1499095), c_Orderings_Obot__class_Obot(tc_fun(_1499091, tc_HOL_Obool)))))))], (39891 ^ _779854) ^ [_1554079, _1554081] : [-(c_FunDef_Oreduction__pair(_1554079, _1554081)), c_Wellfounded_Owf(_1554079, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool), tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool)), _1554081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1554079, _1554079, _1554079), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool), tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool)), _1554081)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool), tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool)), _1554081))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool), tc_fun(tc_prod(_1554079, _1554079), tc_HOL_Obool)), _1554081)))], (16357 ^ _779854) ^ [_1074116, _1074118, _1074120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074116), _1074118)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074116), _1074120)), 16364 ^ _779854 : [(16371 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1074118), _1074120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074118), _1074116)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074120), _1074116))))], (16365 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074118), _1074116)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1074120), _1074116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1074118), _1074120)))]]], (45923 ^ _779854) ^ [_1701041, _1701043, _1701045, _1701047] : [c_List_Olist__all2(_1701041, _1701043, _1701045, c_List_Olist_ONil(_1701041), _1701047), -(_1701047 = c_List_Olist_ONil(_1701043))], (41312 ^ _779854) ^ [_1589357, _1589359, _1589361, _1589363] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589357, _1589357)), hAPP(hAPP(c_Product__Type_OPair(_1589357, _1589357), _1589359), _1589361)), c_Transitive__Closure_Ortrancl(_1589357, _1589363))), hBOOL(hAPP(hAPP(c_member(_1589357), _1589361), c_Wellfounded_Oacc(_1589357, _1589363))), -(hBOOL(hAPP(hAPP(c_member(_1589357), _1589359), c_Wellfounded_Oacc(_1589357, _1589363))))], (7099 ^ _779854) ^ [_896417, _896419, _896421, _896423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896417, tc_HOL_Obool)), _896423), _896419)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896417, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_896417, tc_HOL_Obool)), _896419), _896421)), _896423) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_896417, tc_HOL_Obool)), _896419), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896417, tc_HOL_Obool)), _896421), _896423)))], (15146 ^ _779854) ^ [_1049250] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1049250)), 15150 ^ _779854 : [(15151 ^ _779854) ^ [_1049330] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1049330), _1049250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049330), 15149 ^ [_1049250])))]]], (15114 ^ _779854) ^ [_1048552, _1048554, _1048556, _1048558] : [class_Groups_Ocancel__ab__semigroup__add(_1048552), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048552), _1048554), _1048556) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048552), _1048554), _1048558), -(_1048556 = _1048558)], (10287 ^ _779854) ^ [_953853, _953855, _953857] : [class_Orderings_Olinorder(_953853), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_953853), _953855), hAPP(hAPP(c_Orderings_Oord__class_Omax(_953853), _953855), _953857)) = _953855)], (6315 ^ _779854) ^ [_880266, _880268, _880270, _880272, _880274] : [class_Orderings_Olinorder(_880266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880266, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_880266, _880268), _880270)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_880266, _880272), _880274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880266), _880270), _880268))), 6326 ^ _779854 : [(6329 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880266), _880270), _880274)))], (6327 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880266), _880272), _880268)))]]], (43672 ^ _779854) ^ [_1650338, _1650340, _1650342, _1650344, _1650346] : [-(hAPP(hAPP(c_List_Ozip(_1650338, _1650340), _1650342), hAPP(hAPP(c_List_Olist_OCons(_1650340), _1650344), _1650346)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1650338, _1650340)), _1650338, c_List_Olist_ONil(tc_prod(_1650338, _1650340)), hAPP(hAPP(c_COMBC(_1650338, tc_fun(tc_List_Olist(_1650338), tc_List_Olist(tc_prod(_1650338, _1650340))), tc_fun(tc_List_Olist(_1650338), tc_List_Olist(tc_prod(_1650338, _1650340)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1650338, _1650340)), tc_List_Olist(tc_prod(_1650338, _1650340))), tc_fun(tc_fun(tc_List_Olist(_1650338), tc_List_Olist(tc_prod(_1650338, _1650340))), tc_fun(tc_List_Olist(_1650338), tc_List_Olist(tc_prod(_1650338, _1650340)))), _1650338), c_COMBB(tc_List_Olist(tc_prod(_1650338, _1650340)), tc_List_Olist(tc_prod(_1650338, _1650340)), tc_List_Olist(_1650338))), hAPP(hAPP(c_COMBB(tc_prod(_1650338, _1650340), tc_fun(tc_List_Olist(tc_prod(_1650338, _1650340)), tc_List_Olist(tc_prod(_1650338, _1650340))), _1650338), c_List_Olist_OCons(tc_prod(_1650338, _1650340))), hAPP(hAPP(c_COMBC(_1650338, _1650340, tc_prod(_1650338, _1650340)), c_Product__Type_OPair(_1650338, _1650340)), _1650344)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1650338), tc_List_Olist(_1650340), tc_List_Olist(tc_prod(_1650338, _1650340))), c_List_Ozip(_1650338, _1650340)), _1650346))), _1650342))], (47605 ^ _779854) ^ [_1737218, _1737220, _1737222, _1737224] : [hBOOL(hAPP(hAPP(c_member(_1737218), _1737220), hAPP(c_List_Oset(_1737218), c_List_OtakeWhile(_1737218, _1737222, _1737224)))), 47608 ^ _779854 : [(47611 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1737222, _1737220)))], (47609 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737218), _1737220), hAPP(c_List_Oset(_1737218), _1737224))))]]], (52501 ^ _779854) ^ [_1836792, _1836794] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1836792, _1836794))), class_Lazy__Sequence_Osmall__lazy(_1836792), class_Lazy__Sequence_Osmall__lazy(_1836794)], (48820 ^ _779854) ^ [_1763718, _1763720, _1763722] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763718)), c_List_Osplice(_1763718, _1763720, _1763722)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763718)), _1763720)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763718)), _1763722)))], (43354 ^ _779854) ^ [_1644365, _1644367, _1644369] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644365), tc_List_Olist(_1644365))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644365), tc_List_Olist(_1644365)), _1644367), c_List_Olist_ONil(_1644365))), c_List_Olistrel(_1644365, _1644369))), -(_1644367 = c_List_Olist_ONil(_1644365))], (22867 ^ _779854) ^ [_1193168, _1193170, _1193172, _1193174] : [class_Fields_Olinordered__field__inverse__zero(_1193168), 22870 ^ _779854 : [(22871 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193168), _1193170), _1193172)), _1193174)), 22874 ^ _779854 : [(22881 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), c_Groups_Ozero__class_Ozero(_1193168)), _1193172))), 22884 ^ _779854 : [(22891 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), _1193172), c_Groups_Ozero__class_Ozero(_1193168)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), c_Groups_Ozero__class_Ozero(_1193168)), _1193174)))], (22885 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), _1193172), c_Groups_Ozero__class_Ozero(_1193168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193168), _1193174), _1193172)), _1193170)))]]], (22875 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), c_Groups_Ozero__class_Ozero(_1193168)), _1193172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), _1193170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193168), _1193174), _1193172))))]]], (22897 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193168), _1193170), _1193172)), _1193174))), 22900 ^ _779854 : [(22903 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), _1193170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193168), _1193174), _1193172)))], (22901 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), c_Groups_Ozero__class_Ozero(_1193168)), _1193172)))]], 22904 ^ _779854 : [(22907 ^ _779854) ^ [] : [22908 ^ _779854 : [(22911 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193168), _1193174), _1193172)), _1193170))], (22909 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), _1193172), c_Groups_Ozero__class_Ozero(_1193168))))]], 22912 ^ _779854 : [(22915 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), c_Groups_Ozero__class_Ozero(_1193168)), _1193174))], (22913 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), _1193172), c_Groups_Ozero__class_Ozero(_1193168)))]]], (22905 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193168), c_Groups_Ozero__class_Ozero(_1193168)), _1193172))]]]]], (42074 ^ _779854) ^ [_1608752, _1608754, _1608756, _1608758, _1608760, _1608762] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1608752, _1608754, _1608756), _1608758), hAPP(hAPP(c_Product__Type_OPair(_1608752, _1608754), _1608760), _1608762)) = hAPP(hAPP(_1608758, _1608760), _1608762))], (43444 ^ _779854) ^ [_1645867, _1645869] : [-(c_List_Olistrelp(_1645867, _1645869, c_List_Olist_ONil(_1645867), c_List_Olist_ONil(_1645867)))], (22223 ^ _779854) ^ [_1181447, _1181449, _1181451, _1181453, _1181455] : [class_Fields_Ofield__inverse__zero(_1181447), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181447), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181447), _1181449), _1181451)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181447), _1181453), _1181455)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181447), _1181449), _1181453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181447), _1181451), _1181455)))], (46508 ^ _779854) ^ [_1714234, _1714236, _1714238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714234), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714236))), c_List_Otranspose(_1714236, _1714238)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714236)), c_List_Otranspose(_1714236, _1714238)), _1714234) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714236), _1714236), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714236), tc_Nat_Onat, _1714236), c_List_Onth(_1714236)), _1714234)), hAPP(c_List_Ofilter(tc_List_Olist(_1714236), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714236)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714234)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714236)))), _1714238)))], (18082 ^ _779854) ^ [_1106996, _1106998] : [class_Rings_Olinordered__semidom(_1106996), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106996), _1106998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106996), _1106998), c_Groups_Oone__class_Oone(_1106996)))))], (6143 ^ _779854) ^ [_877415, _877417] : [class_Orderings_Obot(_877415), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877415), c_Orderings_Obot__class_Obot(_877415)), _877417)))], (46854 ^ _779854) ^ [_1722519, _1722521, _1722523] : [class_Orderings_Olinorder(_1722519), c_List_Olinorder__class_Osorted(_1722519, _1722521), -(c_List_Olinorder__class_Osorted(_1722519, hAPP(hAPP(c_List_Odrop(_1722519), _1722523), _1722521)))], (48400 ^ _779854) ^ [_1754975, _1754977, _1754979] : [c_List_Olist__ex(_1754975, _1754977, _1754979), 48404 ^ _779854 : [(48407 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1754977, hAPP(hAPP(c_List_Onth(_1754975), _1754979), 48403 ^ [_1754975, _1754977, _1754979]))))], (48405 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48403 ^ [_1754975, _1754977, _1754979]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754975)), _1754979))))]]], (33393 ^ _779854) ^ [_1387210, _1387212, _1387214, _1387216, _1387218] : [class_Rings_Osemiring__0(_1387210), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387210), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387212, _1387210), _1387214), _1387216)), _1387218) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387212, _1387210), hAPP(hAPP(c_COMBC(_1387212, _1387210, _1387210), hAPP(hAPP(c_COMBB(_1387210, tc_fun(_1387210, _1387210), _1387212), c_Groups_Otimes__class_Otimes(_1387210)), _1387214)), _1387218)), _1387216))], (42563 ^ _779854) ^ [_1624171] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1624171)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1624171), tc_HOL_Obool))))], (33783 ^ _779854) ^ [_1401772, _1401774, _1401776, _1401778] : [class_Fields_Olinordered__field(_1401772), -(hAPP(c_Groups_Oabs__class_Oabs(_1401772), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401774, _1401772), _1401776), _1401778)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401774, _1401772), hAPP(hAPP(c_COMBB(_1401772, _1401772, _1401774), c_Groups_Oabs__class_Oabs(_1401772)), _1401776)), _1401778))], (42354 ^ _779854) ^ [_1617938, _1617940, _1617942, _1617944, _1617946] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617938), tc_List_Olist(_1617938))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617938), tc_List_Olist(_1617938)), _1617940), _1617942)), c_List_Olistrel(_1617938, c_Transitive__Closure_Ortrancl(_1617938, _1617944)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617938), tc_List_Olist(_1617938))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617938), tc_List_Olist(_1617938)), _1617942), _1617946)), c_List_Olistrel(_1617938, c_Transitive__Closure_Ortrancl(_1617938, _1617944)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617938), tc_List_Olist(_1617938))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617938), tc_List_Olist(_1617938)), _1617940), _1617946)), c_List_Olistrel(_1617938, c_Transitive__Closure_Ortrancl(_1617938, _1617944)))))], (41413 ^ _779854) ^ [_1591839, _1591841] : [c_Wellfounded_Oacyclic(_1591839, _1591841), -(c_Wellfounded_Oacyclic(_1591839, hAPP(c_Relation_Oconverse(_1591839, _1591839), _1591841)))], (29593 ^ _779854) ^ [_1313564, _1313566] : [class_Int_Onumber__ring(_1313564), -(hAPP(c_Int_Onumber__class_Onumber__of(_1313564), c_Int_OBit0(_1313566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1313564), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1313564), c_Groups_Ozero__class_Ozero(_1313564)), hAPP(c_Int_Onumber__class_Onumber__of(_1313564), _1313566))), hAPP(c_Int_Onumber__class_Onumber__of(_1313564), _1313566)))], (12986 ^ _779854) ^ [_1008311, _1008313, _1008315, _1008317, _1008319, _1008321] : [-(hBOOL(hAPP(hAPP(c_member(_1008311), _1008313), c_SetInterval_Oord_OgreaterThanAtMost(_1008311, _1008315, _1008317, _1008319, _1008321)))), hBOOL(hAPP(hAPP(_1008317, _1008319), _1008313)), hBOOL(hAPP(hAPP(_1008315, _1008313), _1008321))], (12092 ^ _779854) ^ [_990482, _990484, _990486, _990488] : [hBOOL(hAPP(hAPP(c_member(_990482), _990484), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990482, tc_HOL_Obool)), _990486), _990488))), -(hBOOL(hAPP(hAPP(c_member(_990482), _990484), _990486)))], (8668 ^ _779854) ^ [_924204, _924206, _924208] : [class_Orderings_Olinorder(_924204), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924204), _924206), _924208))), 8675 ^ _779854 : [(8682 ^ _779854) ^ [] : [_924206 = _924208, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924204), _924206), _924208)))], (8676 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924204), _924206), _924208)), -(_924206 = _924208)]]], (28507 ^ _779854) ^ [_1295229, _1295231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295229)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295231))))], (31071 ^ _779854) ^ [_1340454, _1340456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1340454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340456, _1340454)), _1340454)))], (44552 ^ _779854) ^ [_1671042] : [-(hAPP(c_List_Otl(_1671042), c_List_Olist_ONil(_1671042)) = c_List_Olist_ONil(_1671042))], (28673 ^ _779854) ^ [] : [-(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))))], (48830 ^ _779854) ^ [_1763958, _1763960, _1763962] : [-(hAPP(c_New__DSequence_Opos__single(_1763958, _1763960), _1763962) = hAPP(c_Lazy__Sequence_Osingle(_1763958), _1763960))], (50352 ^ _779854) ^ [_1797132, _1797134, _1797136, _1797138, _1797140] : [c_Fun_Oinj__on(_1797132, _1797134, _1797136, c_Orderings_Otop__class_Otop(tc_fun(_1797132, tc_HOL_Obool))), hAPP(_1797136, _1797138) = _1797140, -(hAPP(c_Hilbert__Choice_Oinv__into(_1797132, _1797134, c_Orderings_Otop__class_Otop(tc_fun(_1797132, tc_HOL_Obool)), _1797136), _1797140) = _1797138)], (32558 ^ _779854) ^ [_1365954, _1365956, _1365958] : [32560 ^ _779854 : [(32565 ^ _779854) ^ [] : [hBOOL(hAPP(_1365956, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 32559 ^ [_1365954, _1365956, _1365958]), _1365954)))], (32563 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1365956, 32559 ^ [_1365954, _1365956, _1365958])))], (32561 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32559 ^ [_1365954, _1365956, _1365958]), _1365954)))]], hBOOL(hAPP(_1365956, _1365958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1365958), _1365954)), -(hBOOL(hAPP(_1365956, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43668 ^ _779854) ^ [_1650251, _1650253, _1650255, _1650257] : [-(hAPP(c_List_Olist_Olist__case(_1650251, _1650253, _1650255, _1650257), c_List_Olist_ONil(_1650253)) = _1650255)], (43139 ^ _779854) ^ [_1639390, _1639392] : [-(c_List_Obutlast(_1639390, _1639392) = hAPP(hAPP(c_List_Otake(_1639390), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639390)), _1639392)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1639392))], (6901 ^ _779854) ^ [_892131, _892133, _892135, _892137] : [class_Lattices_Osemilattice__sup(_892131), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892131), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892131), _892133), _892135)), _892137) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892131), _892133), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892131), _892135), _892137)))], (37906 ^ _779854) ^ [_1496450, _1496452, _1496454, _1496456, _1496458] : [c_Typedef_Otype__definition(_1496450, _1496452, _1496454, _1496456, _1496458), -(hAPP(c_Set_Oimage(_1496452, _1496450, _1496456), _1496458) = c_Orderings_Otop__class_Otop(tc_fun(_1496450, tc_HOL_Obool)))], (36826 ^ _779854) ^ [_1469158] : [-(_1469158 = 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)), _1469158), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (31063 ^ _779854) ^ [_1340368, _1340370] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340368, _1340370)) = _1340370), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1340368), _1340370) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340368, _1340370)))], (12950 ^ _779854) ^ [_1007571, _1007573, _1007575, _1007577, _1007579] : [-(hBOOL(hAPP(hAPP(c_member(_1007571), _1007573), c_SetInterval_Oord_OgreaterThanLessThan(_1007571, _1007575, _1007577, _1007579)))), hBOOL(hAPP(hAPP(_1007575, _1007577), _1007573)), hBOOL(hAPP(hAPP(_1007575, _1007573), _1007579))], (50850 ^ _779854) ^ [_1808219, _1808221, _1808223] : [c_Fun_Obij__betw(_1808219, _1808221, _1808223, c_Orderings_Otop__class_Otop(tc_fun(_1808219, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808221, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1808219, _1808221, _1808223), c_Orderings_Otop__class_Otop(tc_fun(_1808219, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1808221, tc_HOL_Obool)))], (52695 ^ _779854) ^ [_1839040, _1839042] : [hBOOL(_1839040), -(hBOOL(hAPP(hAPP(c_fdisj, _1839042), _1839040)))], (26841 ^ _779854) ^ [_1266910, _1266912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266910)), 26844 ^ _779854 : [(26853 ^ _779854) ^ [] : [-(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), _1266910), _1266912)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1266912), _1266910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266912))], (26845 ^ _779854) ^ [] : [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), _1266910), _1266912))), 26848 ^ _779854 : [(26851 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266912)))], (26849 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1266912), _1266910)))]]]]], (19629 ^ _779854) ^ [_1133870, _1133872, _1133874] : [class_Rings_Olinordered__semiring__strict(_1133870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133870), c_Groups_Ozero__class_Ozero(_1133870)), _1133872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133870), c_Groups_Ozero__class_Ozero(_1133870)), _1133874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133870), c_Groups_Ozero__class_Ozero(_1133870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133870), _1133872), _1133874))))], (3456 ^ _779854) ^ [_831655, _831657, _831659, _831661, _831663, _831665, _831667, _831669] : [-(c_List_Olist_Olist__case(_831669, _831665, _831661, _831657) = c_List_Olist_Olist__case(_831667, _831663, _831659, _831655)), _831669 = _831667, _831665 = _831663, _831661 = _831659, _831657 = _831655], (23354 ^ _779854) ^ [_1202522, _1202524, _1202526] : [class_Fields_Olinordered__field__inverse__zero(_1202522), 23360 ^ _779854 : [(23365 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202522), 23359 ^ [_1202522, _1202524, _1202526]), _1202524)), _1202526))], (23363 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202522), 23359 ^ [_1202522, _1202524, _1202526]), c_Groups_Oone__class_Oone(_1202522))))], (23361 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202522), c_Groups_Ozero__class_Ozero(_1202522)), 23359 ^ [_1202522, _1202524, _1202526])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202522), _1202524), _1202526)))], (42269 ^ _779854) ^ [_1615337, _1615339, _1615341, _1615343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615337), tc_List_Olist(_1615337))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615337), tc_List_Olist(_1615337)), _1615339), _1615341)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1615337), c_List_Olistrel1(_1615337, _1615343)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615337)), _1615339) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615337)), _1615341))], (19891 ^ _779854) ^ [_1138667, _1138669] : [class_Groups_Oordered__ab__group__add(_1138667), 19894 ^ _779854 : [(19901 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138667), _1138669), c_Groups_Ozero__class_Ozero(_1138667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138667), c_Groups_Ozero__class_Ozero(_1138667)), hAPP(c_Groups_Ouminus__class_Ouminus(_1138667), _1138669))))], (19895 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138667), c_Groups_Ozero__class_Ozero(_1138667)), hAPP(c_Groups_Ouminus__class_Ouminus(_1138667), _1138669))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138667), _1138669), c_Groups_Ozero__class_Ozero(_1138667))))]]], (15490 ^ _779854) ^ [_1056430, _1056432, _1056434, _1056436] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1056430), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056430), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1056430), _1056432), _1056434)), _1056436) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1056430), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056430), _1056432), _1056436)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056430), _1056434), _1056436)))], (49780 ^ _779854) ^ [_1786601, _1786603] : [c_Predicate_Otransp(_1786601, _1786603), -(c_Relation_Otrans(_1786601, hAPP(c_Set_OCollect(tc_prod(_1786601, _1786601)), hAPP(c_Product__Type_Oprod_Oprod__case(_1786601, _1786601, tc_HOL_Obool), _1786603))))], (48812 ^ _779854) ^ [_1763454, _1763456, _1763458, _1763460, _1763462, _1763464, _1763466] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1763454, _1763456, _1763458, _1763460), _1763462), _1763464), _1763466) = c_New__DSequence_Opos__bind(_1763454, _1763456, hAPP(hAPP(hAPP(_1763458, _1763462), _1763464), _1763466), hAPP(hAPP(c_COMBC(_1763454, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1763456))), hAPP(hAPP(c_COMBC(_1763454, 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(_1763456)))), hAPP(hAPP(c_COMBC(_1763454, 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(_1763456))))), _1763460), _1763462)), _1763464)), _1763466)))], (39120 ^ _779854) ^ [_1529921, _1529923, _1529925] : [class_Groups_Olinordered__ab__semigroup__add(_1529921), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529921), _1529923)), -(_1529923 = c_Orderings_Obot__class_Obot(tc_fun(_1529921, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1529921), _1529925), c_Big__Operators_Olinorder__class_OMax(_1529921, _1529923)) = c_Big__Operators_Olinorder__class_OMax(_1529921, hAPP(c_Set_OCollect(_1529921), hAPP(hAPP(c_COMBB(tc_fun(_1529921, tc_HOL_Obool), tc_HOL_Obool, _1529921), c_HOL_OEx(_1529921)), hAPP(hAPP(c_COMBC(_1529921, tc_fun(_1529921, tc_HOL_Obool), tc_fun(_1529921, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529921, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1529921, tc_HOL_Obool), tc_fun(_1529921, tc_HOL_Obool)), _1529921), c_COMBS(_1529921, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529921, tc_HOL_Obool), tc_fun(_1529921, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1529921), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529921), c_fconj)), hAPP(hAPP(c_COMBC(_1529921, tc_fun(_1529921, _1529921), tc_fun(_1529921, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529921, tc_HOL_Obool), tc_fun(tc_fun(_1529921, _1529921), tc_fun(_1529921, tc_HOL_Obool)), _1529921), c_COMBB(_1529921, tc_HOL_Obool, _1529921)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1529921), _1529925))))), hAPP(hAPP(c_COMBC(_1529921, tc_fun(_1529921, tc_HOL_Obool), tc_HOL_Obool), c_member(_1529921)), _1529923))))))], (2228 ^ _779854) ^ [_812473, _812475] : [_812475 = _812473, -(c_SetInterval_Oord__class_OgreaterThan(_812475) = c_SetInterval_Oord__class_OgreaterThan(_812473))], (29457 ^ _779854) ^ [_1311205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1311205)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311205), c_Int_OPls)))], (9386 ^ _779854) ^ [_936609] : [-(hAPP(c_Set_OPow(_936609), c_Orderings_Obot__class_Obot(tc_fun(_936609, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_936609, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_936609, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_936609, tc_HOL_Obool), tc_HOL_Obool))))], (43045 ^ _779854) ^ [_1637276, _1637278, _1637280, _1637282] : [-(_1637276 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637278)), _1637280)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1637278, hAPP(hAPP(c_List_Olist__update(_1637278, _1637280), _1637276), _1637282)) = hAPP(hAPP(c_List_Olist__update(_1637278, c_List_Obutlast(_1637278, _1637280)), _1637276), _1637282))], (19461 ^ _779854) ^ [_1130838, _1130840, _1130842, _1130844] : [class_Rings_Olinordered__semidom(_1130838), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130838), c_Groups_Ozero__class_Ozero(_1130838)), _1130840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130838), _1130842), _1130844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130838), _1130842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130838), _1130840), _1130844))))], (52455 ^ _779854) ^ [_1836207] : [class_Lazy__Sequence_Osmall__lazy(_1836207), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1836207)))], (31238 ^ _779854) ^ [_1343067, _1343069] : [class_Int_Onumber__ring(_1343067), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343067), hAPP(c_Int_Onumber__class_Onumber__of(_1343067), c_Int_OMin)), _1343069) = hAPP(c_Groups_Ouminus__class_Ouminus(_1343067), _1343069))], (22577 ^ _779854) ^ [_1187650, _1187652, _1187654, _1187656, _1187658] : [class_Fields_Ofield(_1187650), -(_1187652 = c_Groups_Ozero__class_Ozero(_1187650)), -(_1187654 = c_Groups_Ozero__class_Ozero(_1187650)), 22588 ^ _779854 : [(22595 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187650), _1187656), _1187654) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187650), _1187658), _1187652), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187650), _1187656), _1187652) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187650), _1187658), _1187654))], (22589 ^ _779854) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187650), _1187656), _1187652) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187650), _1187658), _1187654), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187650), _1187656), _1187654) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187650), _1187658), _1187652))]]], (33096 ^ _779854) ^ [_1379484, _1379486, _1379488, _1379490, _1379492] : [-(_1379484 = c_Orderings_Obot__class_Obot(tc_fun(_1379486, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379488, tc_HOL_Obool)), _1379490), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379486, tc_fun(_1379488, tc_HOL_Obool)), _1379484), _1379492)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379486, tc_fun(_1379488, tc_HOL_Obool)), _1379484), hAPP(hAPP(c_COMBB(tc_fun(_1379488, tc_HOL_Obool), tc_fun(_1379488, tc_HOL_Obool), _1379486), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379488, tc_HOL_Obool)), _1379490)), _1379492)))], (50016 ^ _779854) ^ [_1791005, _1791007, _1791009, _1791011] : [c_Relation_Osym(_1791005, _1791007), hBOOL(hAPP(hAPP(c_member(tc_prod(_1791005, _1791005)), hAPP(hAPP(c_Product__Type_OPair(_1791005, _1791005), _1791009), _1791011)), _1791007)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1791005, _1791005)), hAPP(hAPP(c_Product__Type_OPair(_1791005, _1791005), _1791011), _1791009)), _1791007)))], (9847 ^ _779854) ^ [_945474, _945476, _945478] : [class_Groups_Oordered__ab__group__add(_945474), -(hAPP(c_Set_Oimage(_945474, _945474, c_Groups_Ouminus__class_Ouminus(_945474)), c_SetInterval_Oord__class_OgreaterThanAtMost(_945474, _945476, _945478)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_945474, hAPP(c_Groups_Ouminus__class_Ouminus(_945474), _945478)), hAPP(c_Groups_Ouminus__class_Ouminus(_945474), _945476)))], (46081 ^ _779854) ^ [_1704695, _1704697, _1704699, _1704701] : [46083 ^ _779854 : [(46086 ^ _779854) ^ [] : [hBOOL(hAPP(_1704699, hAPP(hAPP(c_List_Onth(_1704695), _1704697), 46082 ^ [_1704695, _1704697, _1704699, _1704701])))], (46084 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46082 ^ [_1704695, _1704697, _1704699, _1704701]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704695)), _1704697))))]], hBOOL(hAPP(hAPP(c_member(_1704695), _1704701), hAPP(c_List_Oset(_1704695), _1704697))), -(hBOOL(hAPP(_1704699, _1704701)))], (45524 ^ _779854) ^ [_1691985, _1691987] : [-(c_Random_Oselect(_1691985, _1691987) = 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(_1691985, 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(_1691985)), _1691987)))), hAPP(hAPP(c_COMBB(_1691985, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1691985, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1691985, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1691985, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1691985), _1691987)), c_Code__Numeral_Onat__of))))], (32617 ^ _779854) ^ [_1367076, _1367078] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1367076), _1367078) = 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), _1367076)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1367078)))))], (4042 ^ _779854) ^ [_841154, _841156, _841158, _841160, _841162, _841164, _841166, _841168] : [-(c_New__Random__Sequence_Oneg__map(_841168, _841164, _841160, _841156) = c_New__Random__Sequence_Oneg__map(_841166, _841162, _841158, _841154)), _841168 = _841166, _841164 = _841162, _841160 = _841158, _841156 = _841154], (13789 ^ _779854) ^ [_1022404, _1022406, _1022408] : [class_Lattices_Olattice(_1022404), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022404), _1022406)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022404), _1022408)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1022404, tc_HOL_Obool)), _1022406), _1022408) = c_Orderings_Obot__class_Obot(tc_fun(_1022404, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1022404), c_Big__Operators_Olattice__class_OSup__fin(_1022404, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1022404, tc_HOL_Obool)), _1022406), _1022408))), c_Big__Operators_Olattice__class_OSup__fin(_1022404, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1022404, tc_HOL_Obool)), _1022406), _1022408))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1022404), c_Big__Operators_Olattice__class_OSup__fin(_1022404, _1022406)), c_Big__Operators_Olattice__class_OSup__fin(_1022404, _1022408)))], (47340 ^ _779854) ^ [_1731573, _1731575] : [hAPP(c_List_Orev(_1731573), _1731575) = c_List_Olist_ONil(_1731573), -(_1731575 = c_List_Olist_ONil(_1731573))], (42430 ^ _779854) ^ [_1620640, _1620642, _1620644, _1620646, _1620648, _1620650] : [-(c_List_Olistrelp(_1620640, _1620642, hAPP(hAPP(c_List_Olist_OCons(_1620640), _1620644), _1620646), hAPP(hAPP(c_List_Olist_OCons(_1620640), _1620648), _1620650))), hBOOL(hAPP(hAPP(_1620642, _1620644), _1620648)), c_List_Olistrelp(_1620640, _1620642, _1620646, _1620650)], (18691 ^ _779854) ^ [_1117879] : [class_Rings_Ozero__neq__one(_1117879), c_Groups_Oone__class_Oone(_1117879) = c_Groups_Ozero__class_Ozero(_1117879)], (40927 ^ _779854) ^ [_1579426, _1579428] : [c_Wellfounded_Oacyclic(_1579426, _1579428), 40930 ^ _779854 : [(40931 ^ _779854) ^ [_1579511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579426, _1579426)), hAPP(hAPP(c_Product__Type_OPair(_1579426, _1579426), _1579511), _1579511)), c_Transitive__Closure_Otrancl(_1579426, _1579428)))]]], (30373 ^ _779854) ^ [_1328338, _1328340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328340, _1328338)), _1328338)))], (32768 ^ _779854) ^ [_1369941, _1369943, _1369945, _1369947, _1369949, _1369951] : [hBOOL(hAPP(hAPP(c_member(_1369941), _1369943), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369945, tc_fun(_1369941, tc_HOL_Obool)), _1369947), _1369949))), -(hBOOL(hAPP(hAPP(c_member(_1369941), _1369943), hAPP(_1369949, _1369951)))), hBOOL(hAPP(hAPP(c_member(_1369945), _1369951), _1369947))], (49152 ^ _779854) ^ [_1770865, _1770867, _1770869, _1770871, _1770873] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1770865, _1770867, _1770869) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1770865, _1770871, _1770873)), _1770867 = _1770871, _1770869 = _1770873], (11362 ^ _779854) ^ [_975976, _975978] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975976), _975978)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_975976, tc_HOL_Obool)), hAPP(c_Set_OPow(_975976), _975978))))], (45937 ^ _779854) ^ [_1701292, _1701294, _1701296, _1701298, _1701300] : [c_List_Olist__all2(_1701292, _1701294, _1701296, _1701298, _1701300), 45940 ^ _779854 : [(45943 ^ _779854) ^ [_1701455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701455), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701292)), _1701298))), -(hBOOL(hAPP(hAPP(_1701296, hAPP(hAPP(c_List_Onth(_1701292), _1701298), _1701455)), hAPP(hAPP(c_List_Onth(_1701294), _1701300), _1701455))))], (45941 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701292)), _1701298) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701294)), _1701300))]]], (18767 ^ _779854) ^ [_1118977] : [hAPP(c_Nat_OSuc, _1118977) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30351 ^ _779854) ^ [_1327985, _1327987, _1327989] : [class_Divides_Osemiring__div(_1327985), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1327985), c_Divides_Odiv__class_Omod(_1327985, _1327987, _1327989)), _1327989) = c_Groups_Ozero__class_Ozero(_1327985))], (39415 ^ _779854) ^ [_1541435, _1541437, _1541439, _1541441, _1541443, _1541445, _1541447] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541435, _1541437, _1541439), _1541441), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541443, tc_fun(tc_prod(_1541437, _1541439), tc_HOL_Obool)), _1541445), _1541447)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541443, tc_fun(tc_prod(_1541435, _1541439), tc_HOL_Obool)), _1541445), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1541437, _1541439), tc_HOL_Obool), tc_fun(tc_prod(_1541435, _1541439), tc_HOL_Obool), _1541443), hAPP(c_Relation_Orel__comp(_1541435, _1541437, _1541439), _1541441)), _1541447)))], (824 ^ _779854) ^ [_792238, _792240, _792242, _792244] : [-(c_Relation_Otrans(_792242, _792238)), c_Relation_Otrans(_792244, _792240), _792244 = _792242, _792240 = _792238], (18327 ^ _779854) ^ [_1111456, _1111458] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1111456, _1111458)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1111458), hAPP(c_Nat_OSuc, _1111456)))], (44963 ^ _779854) ^ [_1679332, _1679334, _1679336] : [-(_1679332 = c_List_Olist_ONil(_1679334)), -(c_List_Olast(_1679334, hAPP(hAPP(c_List_Oappend(_1679334), _1679336), _1679332)) = c_List_Olast(_1679334, _1679332))], (22155 ^ _779854) ^ [_1180147, _1180149, _1180151, _1180153] : [class_Fields_Olinordered__field(_1180147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180147), _1180149), c_Groups_Ozero__class_Ozero(_1180147))), 22162 ^ _779854 : [(22169 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180147), _1180153), _1180149)), _1180151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180147), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180147), _1180151), _1180149)), _1180153)))], (22163 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180147), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180147), _1180151), _1180149)), _1180153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180147), _1180153), _1180149)), _1180151)))]]], (4740 ^ _779854) ^ [_852173, _852175, _852177, _852179] : [-(c_Product__Type_Ofst(_852179, _852175) = c_Product__Type_Ofst(_852177, _852173)), _852179 = _852177, _852175 = _852173], (51284 ^ _779854) ^ [_1818726, _1818728, _1818730] : [c_List_Oall__interval__nat(_1818726, _1818728, _1818730), -(c_List_Olist__all(tc_Nat_Onat, _1818726, c_List_Oupt(_1818728, _1818730)))], (26825 ^ _779854) ^ [_1266660, _1266662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266660)), 26828 ^ _779854 : [(26835 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1266660), _1266662)), -(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), _1266662), _1266660))))], (26829 ^ _779854) ^ [] : [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), _1266662), _1266660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1266660), _1266662)))]]], (39532 ^ _779854) ^ [_1545387, _1545389, _1545391, _1545393] : [hBOOL(hAPP(hAPP(c_member(_1545389), _1545393), hAPP(c_Relation_ORange(_1545387, _1545389), _1545391))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1545387, _1545389, hAPP(hAPP(c_COMBC(_1545387, tc_fun(tc_prod(_1545387, _1545389), tc_HOL_Obool), tc_fun(_1545389, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545389, tc_fun(tc_fun(tc_prod(_1545387, _1545389), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545387, _1545389), tc_HOL_Obool), tc_fun(_1545389, tc_HOL_Obool)), _1545387), c_COMBC(_1545389, tc_fun(tc_prod(_1545387, _1545389), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545389, tc_prod(_1545387, _1545389)), tc_fun(_1545389, tc_fun(tc_fun(tc_prod(_1545387, _1545389), tc_HOL_Obool), tc_HOL_Obool)), _1545387), hAPP(c_COMBB(tc_prod(_1545387, _1545389), tc_fun(tc_fun(tc_prod(_1545387, _1545389), tc_HOL_Obool), tc_HOL_Obool), _1545389), c_member(tc_prod(_1545387, _1545389)))), c_Product__Type_OPair(_1545387, _1545389)))), _1545391)), _1545393)))], (45583 ^ _779854) ^ [_1693150, _1693152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693150)), hAPP(c_Code__Numeral_Onat__of, _1693152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1693150), _1693152)))], (14464 ^ _779854) ^ [_1035770, _1035772, _1035774, _1035776, _1035778] : [class_Groups_Oab__group__add(_1035770), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035772), _1035774)), 14471 ^ _779854 : [(14478 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1035772), _1035776), _1035774))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035772, _1035770), _1035778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1035772, tc_HOL_Obool)), _1035774), hAPP(hAPP(c_Set_Oinsert(_1035772), _1035776), c_Orderings_Obot__class_Obot(tc_fun(_1035772, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035772, _1035770), _1035778), _1035774))], (14472 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1035772), _1035776), _1035774)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035772, _1035770), _1035778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1035772, tc_HOL_Obool)), _1035774), hAPP(hAPP(c_Set_Oinsert(_1035772), _1035776), c_Orderings_Obot__class_Obot(tc_fun(_1035772, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035770), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035772, _1035770), _1035778), _1035774)), hAPP(_1035778, _1035776)))]]], (4102 ^ _779854) ^ [_842142, _842144, _842146, _842148] : [-(c_New__DSequence_Oneg__single(_842148, _842144) = c_New__DSequence_Oneg__single(_842146, _842142)), _842148 = _842146, _842144 = _842142], (9554 ^ _779854) ^ [_940011, _940013, _940015] : [class_Orderings_Olinorder(_940011), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940011), _940013), hAPP(hAPP(c_Orderings_Oord__class_Omax(_940011), _940013), _940015))))], (12284 ^ _779854) ^ [_993920, _993922, _993924, _993926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993920, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_993920), _993922), _993924)), _993926)), 12287 ^ _779854 : [(12290 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993920, tc_HOL_Obool)), _993924), _993926)))], (12288 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_993920), _993922), _993926)))]]], (28752 ^ _779854) ^ [_1299321, _1299323] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1299321) = _1299323), _1299321 = hAPP(c_Int_Onat, _1299323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299323))], (52539 ^ _779854) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (12244 ^ _779854) ^ [_993110, _993112, _993114, _993116, _993118, _993120] : [c_Finite__Set_Ofolding__image__simple(_993110, _993112, _993114, _993116, _993118, _993120), -(hAPP(_993120, c_Orderings_Obot__class_Obot(tc_fun(_993112, tc_HOL_Obool))) = _993116)], (26947 ^ _779854) ^ [_1268624, _1268626, _1268628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268624), _1268626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268624), _1268628)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268626), _1268628))))], (20327 ^ _779854) ^ [_1145696, _1145698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145698), _1145696)), _1145698)))], (18465 ^ _779854) ^ [_1114502, _1114504] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1114502, _1114504)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1114502, _1114504), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1114504), c_Orderings_Otop__class_Otop(tc_fun(_1114504, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1114502), c_Orderings_Otop__class_Otop(tc_fun(_1114502, tc_HOL_Obool)))))], (6153 ^ _779854) ^ [_877590, _877592, _877594] : [class_Orderings_Obot(_877590), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_877592, _877590)), _877594) = c_Orderings_Obot__class_Obot(_877590))], (45498 ^ _779854) ^ [_1691336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1691336)), _1691336 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5068 ^ _779854) ^ [_857323, _857325] : [_857325 = _857323, -(c_Orderings_Otop__class_Otop(_857325) = c_Orderings_Otop__class_Otop(_857323))], (46773 ^ _779854) ^ [_1720745, _1720747, _1720749, _1720751] : [class_Groups_Ocomm__monoid__add(_1720745), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1720745), _1720747), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1720749, _1720751))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1720745), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1720745), _1720747), c_List_Oupt(_1720749, _1720751))))], (19455 ^ _779854) ^ [_1130729, _1130731] : [class_Rings_Olinordered__ring(_1130729), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130729), c_Groups_Ozero__class_Ozero(_1130729)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130729), _1130731), _1130731))))], (39641 ^ _779854) ^ [_1548867, _1548869, _1548871, _1548873, _1548875] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548867, _1548869)), hAPP(hAPP(c_Product__Type_OPair(_1548867, _1548869), _1548871), _1548873)), _1548875)), -(hBOOL(hAPP(hAPP(c_member(_1548867), _1548871), hAPP(c_Relation_ODomain(_1548867, _1548869), _1548875))))], (31583 ^ _779854) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (49708 ^ _779854) ^ [_1783585, _1783587, _1783589] : [c_List_Olist__ex(_1783585, _1783587, _1783589), 49712 ^ _779854 : [(49715 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1783587, 49711 ^ [_1783585, _1783587, _1783589])))], (49713 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783585), 49711 ^ [_1783585, _1783587, _1783589]), hAPP(c_List_Oset(_1783585), _1783589))))]]], (27351 ^ _779854) ^ [_1275625, _1275627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1275625)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1275627)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275625)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1275627), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1275625))))], (18937 ^ _779854) ^ [_1121408] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1121408), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42925 ^ _779854) ^ [_1634686, _1634688, _1634690, _1634692, _1634694, _1634696] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634686, _1634688)), hAPP(hAPP(c_Product__Type_OPair(_1634686, _1634688), _1634690), _1634692)), hAPP(c_List_Oset(tc_prod(_1634686, _1634688)), hAPP(hAPP(c_List_Ozip(_1634686, _1634688), _1634694), _1634696)))), 42928 ^ _779854 : [(42931 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1634688), _1634692), hAPP(c_List_Oset(_1634688), _1634696))))], (42929 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1634686), _1634690), hAPP(c_List_Oset(_1634686), _1634694))))]]], (6925 ^ _779854) ^ [_892703, _892705, _892707, _892709] : [class_Lattices_Odistrib__lattice(_892703), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892703), _892705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892703), _892707), _892709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_892703), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892703), _892705), _892707)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892703), _892705), _892709)))], (52065 ^ _779854) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (41810 ^ _779854) ^ [_1601658, _1601660, _1601662, _1601664, _1601666, _1601668] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601658, _1601658)), hAPP(hAPP(c_Product__Type_OPair(_1601658, _1601658), _1601660), _1601662)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601658, _1601658), tc_HOL_Obool), _1601664), _1601666))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1601658, _1601658)), hAPP(hAPP(c_Product__Type_OPair(_1601658, _1601658), _1601662), _1601668)), _1601666)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601658, _1601658)), hAPP(hAPP(c_Product__Type_OPair(_1601658, _1601658), _1601660), _1601668)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601658, _1601658), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1601664)), _1601666))))], (5496 ^ _779854) ^ [_864009, _864011, _864013, _864015, _864017, _864019] : [-(c_Divides_Odiv__class_Omod(_864019, _864015, _864011) = c_Divides_Odiv__class_Omod(_864017, _864013, _864009)), _864019 = _864017, _864015 = _864013, _864011 = _864009], (51613 ^ _779854) ^ [_1824661, _1824663, _1824665] : [class_Rings_Ocomm__ring__1(_1824661), 51616 ^ _779854 : [(51623 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824661), _1824663), _1824665)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824661), hAPP(c_Groups_Ouminus__class_Ouminus(_1824661), _1824663)), _1824665)))], (51617 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824661), hAPP(c_Groups_Ouminus__class_Ouminus(_1824661), _1824663)), _1824665)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824661), _1824663), _1824665)))]]], (17965 ^ _779854) ^ [_1104978, _1104980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104978), _1104980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104978), hAPP(c_Nat_OSuc, _1104980))))], (41435 ^ _779854) ^ [_1592250, _1592252, _1592254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1592250, _1592252)), hAPP(c_Relation_Oconverse(_1592252, _1592250), _1592254))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1592252, _1592250)), _1592254)))], (44693 ^ _779854) ^ [_1673984, _1673986, _1673988] : [class_Lattices_Olattice(_1673984), -(c_Big__Operators_Olattice__class_OInf__fin(_1673984, hAPP(c_List_Oset(_1673984), hAPP(hAPP(c_List_Olist_OCons(_1673984), _1673986), _1673988))) = hAPP(c_List_Ofoldl(_1673984, _1673984, c_Lattices_Osemilattice__inf__class_Oinf(_1673984), _1673986), _1673988))], (34507 ^ _779854) ^ [_1419835, _1419837, _1419839] : [class_Fields_Ofield(_1419835), -(_1419837 = c_Groups_Oone__class_Oone(_1419835)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1419835), hAPP(c_Power_Opower__class_Opower(_1419835), _1419837)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1419839)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419835), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1419835), hAPP(hAPP(c_Power_Opower__class_Opower(_1419835), _1419837), _1419839)), c_Groups_Oone__class_Oone(_1419835))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1419835), _1419837), c_Groups_Oone__class_Oone(_1419835))))], (43959 ^ _779854) ^ [_1657079, _1657081, _1657083] : [-(hAPP(hAPP(c_List_Oappend(_1657079), _1657081), _1657083) = c_List_Olist_ONil(_1657079)), _1657081 = c_List_Olist_ONil(_1657079), _1657083 = c_List_Olist_ONil(_1657079)], (27435 ^ _779854) ^ [_1276902, _1276904] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1276902))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276902)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276904)) = 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), _1276904)))], (44729 ^ _779854) ^ [_1674812, _1674814, _1674816, _1674818] : [class_Complete__Lattice_Ocomplete__lattice(_1674812), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1674814, _1674812), hAPP(c_List_Oset(_1674814), _1674816)), _1674818) = hAPP(c_List_Ofoldl(_1674812, _1674814, hAPP(c_COMBC(_1674814, _1674812, _1674812), hAPP(hAPP(c_COMBB(_1674812, tc_fun(_1674812, _1674812), _1674814), c_Lattices_Osemilattice__inf__class_Oinf(_1674812)), _1674818)), c_Orderings_Otop__class_Otop(_1674812)), _1674816))], (3828 ^ _779854) ^ [_837519, _837521] : [_837521 = _837519, -(c_List_Odistinct(_837521) = c_List_Odistinct(_837519))], (51066 ^ _779854) ^ [_1812367, _1812369, _1812371, _1812373, _1812375] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1812367, _1812369, tc_HOL_Obool, _1812371), _1812373), _1812375)), -(hBOOL(hAPP(_1812371, hAPP(hAPP(c_Product__Type_OPair(_1812367, _1812369), _1812373), _1812375))))], (10163 ^ _779854) ^ [_951524, _951526, _951528] : [class_Orderings_Olinorder(_951524), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951524), hAPP(hAPP(c_Orderings_Oord__class_Omin(_951524), _951526), _951528)), _951528)))], (28284 ^ _779854) ^ [_1291313, _1291315] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1291313)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1291315))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1291313), _1291315)))], (22241 ^ _779854) ^ [_1181882, _1181884, _1181886] : [class_Fields_Olinordered__field__inverse__zero(_1181882), 22244 ^ _779854 : [(22259 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), c_Groups_Ozero__class_Ozero(_1181882)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181882), _1181884), _1181886)))), 22260 ^ _779854 : [(22267 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), _1181884), c_Groups_Ozero__class_Ozero(_1181882))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), _1181886), c_Groups_Ozero__class_Ozero(_1181882)))], (22261 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), c_Groups_Ozero__class_Ozero(_1181882)), _1181884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), c_Groups_Ozero__class_Ozero(_1181882)), _1181886))]]], (22245 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), c_Groups_Ozero__class_Ozero(_1181882)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181882), _1181884), _1181886))), 22250 ^ _779854 : [(22253 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), c_Groups_Ozero__class_Ozero(_1181882)), _1181886)))], (22251 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), c_Groups_Ozero__class_Ozero(_1181882)), _1181884)))]], 22254 ^ _779854 : [(22257 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), _1181886), c_Groups_Ozero__class_Ozero(_1181882))))], (22255 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181882), _1181884), c_Groups_Ozero__class_Ozero(_1181882))))]]]]], (43552 ^ _779854) ^ [_1647783, _1647785] : [-(_1647785 = c_List_Olist_ONil(_1647783)), -(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(_1647783)), _1647785))))], (27749 ^ _779854) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8350 ^ _779854) ^ [_919449, _919451, _919453, _919455] : [-(hAPP(hAPP(c_Set_Oinsert(_919449), _919451), hAPP(hAPP(c_Set_Oinsert(_919449), _919453), _919455)) = hAPP(hAPP(c_Set_Oinsert(_919449), _919453), hAPP(hAPP(c_Set_Oinsert(_919449), _919451), _919455)))], (4438 ^ _779854) ^ [_847398, _847400, _847402, _847404] : [-(c_Wellfounded_Oaccp(_847404, _847400) = c_Wellfounded_Oaccp(_847402, _847398)), _847404 = _847402, _847400 = _847398], (44656 ^ _779854) ^ [_1673254, _1673256] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1673254), _1673256) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1673254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44662 ^ _779854 : [(44665 ^ _779854) ^ [] : [44661 ^ [_1673254, _1673256] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44663 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44661 ^ [_1673254, _1673256]), hAPP(c_List_Oset(tc_Nat_Onat), _1673256))))]]], (44161 ^ _779854) ^ [_1661875, _1661877, _1661879, _1661881, _1661883, _1661885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661875), tc_List_Olist(_1661875))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661875), tc_List_Olist(_1661875)), hAPP(hAPP(c_List_Oappend(_1661875), _1661877), hAPP(hAPP(c_List_Olist_OCons(_1661875), _1661879), c_List_Olist_ONil(_1661875)))), hAPP(hAPP(c_List_Oappend(_1661875), _1661881), hAPP(hAPP(c_List_Olist_OCons(_1661875), _1661883), c_List_Olist_ONil(_1661875))))), c_List_Olistrel1(_1661875, _1661885))), 44166 ^ _779854 : [(44169 ^ _779854) ^ [] : [-(_1661879 = _1661883)], (44167 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661875), tc_List_Olist(_1661875))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661875), tc_List_Olist(_1661875)), _1661877), _1661881)), c_List_Olistrel1(_1661875, _1661885))))]], 44170 ^ _779854 : [(44173 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1661875, _1661875)), hAPP(hAPP(c_Product__Type_OPair(_1661875, _1661875), _1661879), _1661883)), _1661885)))], (44171 ^ _779854) ^ [] : [-(_1661877 = _1661881)]]], (48816 ^ _779854) ^ [_1763607, _1763609, _1763611, _1763613] : [-(c_New__Random__Sequence_Opos__map(_1763607, _1763609, _1763611, _1763613) = c_New__Random__Sequence_Opos__bind(_1763607, _1763609, _1763613, hAPP(c_Fun_Ocomp(_1763609, 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(_1763609))))), _1763607, c_New__Random__Sequence_Opos__single(_1763609)), _1763611)))], (15460 ^ _779854) ^ [_1055755, _1055757, _1055759] : [class_Rings_Oring(_1055755), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055755), hAPP(c_Groups_Ouminus__class_Ouminus(_1055755), _1055757)), hAPP(c_Groups_Ouminus__class_Ouminus(_1055755), _1055759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055755), _1055757), _1055759))], (38048 ^ _779854) ^ [_1499538, _1499540, _1499542, _1499544, _1499546, _1499548] : [hAPP(_1499538, _1499540) = _1499542, hBOOL(hAPP(hAPP(c_member(_1499544), _1499542), _1499546)), -(hBOOL(hAPP(hAPP(c_member(_1499548), _1499540), hAPP(c_Set_Ovimage(_1499548, _1499544, _1499538), _1499546))))], (33599 ^ _779854) ^ [_1396908, _1396910, _1396912, _1396914, _1396916] : [class_Lattices_Olattice(_1396908), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396910, _1396908)), _1396912), _1396914), _1396916) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396908), hAPP(_1396912, _1396916)), hAPP(_1396914, _1396916)))], (38745 ^ _779854) ^ [_1518769, _1518771, _1518773] : [hBOOL(hAPP(_1518773, _1518771)), -(hBOOL(hAPP(hAPP(c_member(_1518769), _1518771), hAPP(c_Set_OCollect(_1518769), _1518773))))], (19073 ^ _779854) ^ [_1123786, _1123788, _1123790, _1123792] : [class_Groups_Oordered__comm__monoid__add(_1123786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123786), c_Groups_Ozero__class_Ozero(_1123786)), _1123788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123786), _1123790), _1123792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123786), _1123790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123786), _1123788), _1123792))))], (38356 ^ _779854) ^ [_1507802, _1507804, _1507806] : [c_Equiv__Relations_Oequiv(_1507802, _1507804, _1507806), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507802, _1507802), tc_HOL_Obool)), _1507806), hAPP(hAPP(c_Product__Type_OSigma(_1507802, _1507802), _1507804), hAPP(c_COMBK(tc_fun(_1507802, tc_HOL_Obool), _1507802), _1507804)))))], (17704 ^ _779854) ^ [_1100846] : [hAPP(c_Nat_OSuc, _1100846) = _1100846], (32021 ^ _779854) ^ [_1355994, _1355996] : [class_Groups_Oordered__ab__group__add__abs(_1355994), -(hAPP(c_Groups_Oabs__class_Oabs(_1355994), hAPP(c_Groups_Oabs__class_Oabs(_1355994), _1355996)) = hAPP(c_Groups_Oabs__class_Oabs(_1355994), _1355996))], (6331 ^ _779854) ^ [_880547, _880549] : [class_Orderings_Olinorder(_880547), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_880547, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880547), _880549)) = hAPP(c_SetInterval_Oord__class_OatMost(_880547), _880549))], (31108 ^ _779854) ^ [_1340991, _1340993, _1340995] : [-(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), _1340991), _1340993)), _1340995), _1340993) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340995, _1340993))], (43544 ^ _779854) ^ [_1647623, _1647625, _1647627] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1647623, tc_HOL_Obool)), hAPP(c_List_Oset(_1647623), c_List_Oremove1(_1647623, _1647625, _1647627))), hAPP(c_List_Oset(_1647623), _1647627))))], (36142 ^ _779854) ^ [_1453899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1453899)), 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), _1453899)) = 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), _1453899))))))], (33573 ^ _779854) ^ [_1395569, _1395571, _1395573, _1395575, _1395577] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395569, tc_fun(_1395571, tc_HOL_Obool)), _1395573), hAPP(hAPP(c_COMBC(_1395569, tc_fun(_1395571, tc_HOL_Obool), tc_fun(_1395571, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395571, tc_HOL_Obool), tc_fun(tc_fun(_1395571, tc_HOL_Obool), tc_fun(_1395571, tc_HOL_Obool)), _1395569), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395571, tc_HOL_Obool))), _1395575)), _1395577)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395571, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395569, tc_fun(_1395571, tc_HOL_Obool)), _1395573), _1395575)), _1395577))], (3660 ^ _779854) ^ [_834919, _834921] : [_834921 = _834919, -(c_Orderings_Oord__class_Omax(_834921) = c_Orderings_Oord__class_Omax(_834919))], (10735 ^ _779854) ^ [_962851, _962853, _962855, _962857, _962859] : [c_Fun_Oinj__on(_962851, _962853, _962855, _962857), c_Fun_Oinj__on(_962851, _962853, _962855, _962859), -(c_Fun_Oinj__on(_962851, _962853, _962855, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962851, tc_HOL_Obool)), _962857), _962859)))], (47382 ^ _779854) ^ [_1732482, _1732484, _1732486] : [-(hAPP(c_List_Orev(_1732482), hAPP(c_List_Ofilter(_1732482, _1732484), _1732486)) = hAPP(c_List_Ofilter(_1732482, _1732484), hAPP(c_List_Orev(_1732482), _1732486)))], (12608 ^ _779854) ^ [_1000417, _1000419, _1000421] : [class_Orderings_Olinorder(_1000417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000417), _1000419)), hBOOL(hAPP(hAPP(c_member(_1000417), _1000421), _1000419)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1000417), _1000421), c_Big__Operators_Olattice_OSup__fin(_1000417, c_Orderings_Oord__class_Omax(_1000417), _1000419)) = c_Big__Operators_Olattice_OSup__fin(_1000417, c_Orderings_Oord__class_Omax(_1000417), _1000419))], (21353 ^ _779854) ^ [_1164621, _1164623] : [21355 ^ _779854 : [(21358 ^ _779854) ^ [] : [hBOOL(hAPP(_1164623, 21354 ^ [_1164621, _1164623]))], (21356 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 21354 ^ [_1164621, _1164623]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1164621))))]], 21359 ^ _779854 : [(21360 ^ _779854) ^ [_1164774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1164774), _1164621)), -(hBOOL(hAPP(_1164623, _1164774)))]]], (2078 ^ _779854) ^ [_810088, _810090, _810092, _810094] : [-(c_SMT_Oz3mod(_810094, _810090) = c_SMT_Oz3mod(_810092, _810088)), _810094 = _810092, _810090 = _810088], (19045 ^ _779854) ^ [_1123278, _1123280, _1123282] : [class_Groups_Oordered__comm__monoid__add(_1123278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123278), _1123280), c_Groups_Ozero__class_Ozero(_1123278))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123278), _1123282), c_Groups_Ozero__class_Ozero(_1123278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123278), _1123280), _1123282)), c_Groups_Ozero__class_Ozero(_1123278))))], (31358 ^ _779854) ^ [_1345034, _1345036, _1345038] : [hBOOL(hAPP(_1345034, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1345036, _1345038))), 31361 ^ _779854 : [(31368 ^ _779854) ^ [] : [-(_1345038 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31371 ^ _779854 : [(31372 ^ _779854) ^ [_1345282, _1345284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345282), _1345038)), _1345036 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1345038), _1345284)), _1345282), -(hBOOL(hAPP(_1345034, _1345282)))]]], (31362 ^ _779854) ^ [] : [_1345038 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1345034, _1345036)))]]], (40724 ^ _779854) ^ [_1574110, _1574112] : [class_Complete__Lattice_Ocomplete__lattice(_1574110), c_Orderings_Oorder__class_Omono(_1574110, _1574110, _1574112), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574110), c_Inductive_Ocomplete__lattice__class_Olfp(_1574110, _1574112)), hAPP(_1574112, c_Inductive_Ocomplete__lattice__class_Olfp(_1574110, _1574112)))))], (32545 ^ _779854) ^ [_1365714, _1365716] : [-(c_Nitpick_Onat__lcm(_1365714, _1365716) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1365714), _1365716)), c_Nitpick_Onat__gcd(_1365714, _1365716)))], (47697 ^ _779854) ^ [_1739079, _1739081] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1739079), _1739081) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1739079)), c_List_Oembed__list(_1739081))))], (11306 ^ _779854) ^ [_974960, _974962, _974964] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_974960), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974960, tc_HOL_Obool)), _974962), _974964))), 11309 ^ _779854 : [(11312 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_974960), _974964)))], (11310 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_974960), _974962)))]]], (47320 ^ _779854) ^ [_1731218, _1731220] : [hBOOL(hAPP(c_List_Odistinct(_1731218), _1731220)), -(hBOOL(hAPP(c_List_Odistinct(_1731218), hAPP(c_List_Orev(_1731218), _1731220))))], (41738 ^ _779854) ^ [_1599894, _1599896] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599894, _1599894)), hAPP(hAPP(c_Product__Type_OPair(_1599894, _1599894), 41739 ^ [_1599894, _1599896]), 41739 ^ [_1599894, _1599896])), c_Transitive__Closure_Otrancl(_1599894, _1599896)))), -(c_Wellfounded_Oacyclic(_1599894, _1599896))], (44216 ^ _779854) ^ [_1663477, _1663479] : [-(hAPP(c_List_Orotate1(_1663477), _1663479) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1663477), _1663477, c_List_Olist_ONil(_1663477), hAPP(hAPP(c_COMBB(tc_List_Olist(_1663477), tc_fun(tc_List_Olist(_1663477), tc_List_Olist(_1663477)), _1663477), hAPP(c_COMBC(tc_List_Olist(_1663477), tc_List_Olist(_1663477), tc_List_Olist(_1663477)), c_List_Oappend(_1663477))), hAPP(hAPP(c_COMBC(_1663477, tc_List_Olist(_1663477), tc_List_Olist(_1663477)), c_List_Olist_OCons(_1663477)), c_List_Olist_ONil(_1663477)))), _1663479))], (25687 ^ _779854) ^ [_1246815, _1246817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246815), _1246817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246815), _1246817)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27703 ^ _779854) ^ [_1281220, _1281222] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1281220)), hAPP(c_Int_Onat, _1281222)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281220), _1281222))], (32303 ^ _779854) ^ [_1361088, _1361090, _1361092] : [class_Rings_Oordered__ring__abs(_1361088), -(hAPP(c_Groups_Oabs__class_Oabs(_1361088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361088), _1361090), _1361092)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361088), hAPP(c_Groups_Oabs__class_Oabs(_1361088), _1361090)), hAPP(c_Groups_Oabs__class_Oabs(_1361088), _1361092))), 32310 ^ _779854 : [(32313 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361088), _1361090), c_Groups_Ozero__class_Ozero(_1361088)))], (32311 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361088), c_Groups_Ozero__class_Ozero(_1361088)), _1361090))]], 32314 ^ _779854 : [(32317 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361088), _1361092), c_Groups_Ozero__class_Ozero(_1361088)))], (32315 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361088), c_Groups_Ozero__class_Ozero(_1361088)), _1361092))]]], (24487 ^ _779854) ^ [_1224175] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1224175) = _1224175)], (32033 ^ _779854) ^ [_1356228, _1356230] : [class_Groups_Oordered__ab__group__add__abs(_1356228), -(hAPP(c_Groups_Oabs__class_Oabs(_1356228), hAPP(c_Groups_Ouminus__class_Ouminus(_1356228), _1356230)) = hAPP(c_Groups_Oabs__class_Oabs(_1356228), _1356230))], (43742 ^ _779854) ^ [_1652318, _1652320, _1652322, _1652324, _1652326] : [hAPP(hAPP(c_List_Olist_OCons(_1652318), _1652320), _1652322) = hAPP(hAPP(c_List_Oappend(_1652318), _1652324), _1652326), 43747 ^ _779854 : [(43750 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1652318), _1652320), _1652322) = _1652326)], (43748 ^ _779854) ^ [] : [-(_1652324 = c_List_Olist_ONil(_1652318))]], 43752 ^ _779854 : [(43755 ^ _779854) ^ [] : [-(_1652322 = hAPP(hAPP(c_List_Oappend(_1652318), 43751 ^ [_1652318, _1652320, _1652322, _1652324, _1652326]), _1652326))], (43753 ^ _779854) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1652318), _1652320), 43751 ^ [_1652318, _1652320, _1652322, _1652324, _1652326]) = _1652324)]]], (25675 ^ _779854) ^ [_1246627, _1246629] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246627), _1246629) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246627), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246629)))], (43995 ^ _779854) ^ [_1657723, _1657725, _1657727] : [c_List_Olist_ONil(_1657723) = hAPP(hAPP(c_List_Oappend(_1657723), _1657725), _1657727), 43998 ^ _779854 : [(44001 ^ _779854) ^ [] : [-(_1657727 = c_List_Olist_ONil(_1657723))], (43999 ^ _779854) ^ [] : [-(_1657725 = c_List_Olist_ONil(_1657723))]]], (31096 ^ _779854) ^ [_1340845, _1340847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1340845), _1340847)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340845, _1340847) = _1340845)], (39937 ^ _779854) ^ [_1555272, _1555274] : [-(c_HOL_OThe(_1555272, hAPP(c_fequal, _1555274)) = _1555274)], (41196 ^ _779854) ^ [_1586710, _1586712, _1586714] : [_1586712 = _1586714, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586710, _1586710)), hAPP(hAPP(c_Product__Type_OPair(_1586710, _1586710), _1586712), _1586714)), c_Relation_OId(_1586710))))], (13507 ^ _779854) ^ [_1017545, _1017547, _1017549] : [class_Orderings_Olinorder(_1017545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017545), _1017547)), -(_1017549 = c_Orderings_Obot__class_Obot(tc_fun(_1017545, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017545, tc_HOL_Obool)), _1017549), _1017547)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1017545), c_Big__Operators_Olinorder__class_OMin(_1017545, _1017549)), c_Big__Operators_Olinorder__class_OMin(_1017545, _1017547)) = c_Big__Operators_Olinorder__class_OMin(_1017545, _1017547))], (7712 ^ _779854) ^ [_908088, _908090] : [class_Lattices_Oboolean__algebra(_908088), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908088), _908090), hAPP(c_Groups_Ouminus__class_Ouminus(_908088), _908090)) = c_Orderings_Otop__class_Otop(_908088))], (22337 ^ _779854) ^ [_1183600, _1183602, _1183604, _1183606] : [class_Fields_Olinordered__field(_1183600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183600), _1183602), _1183604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183600), _1183606), c_Groups_Ozero__class_Ozero(_1183600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183600), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183600), _1183604), _1183606)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183600), _1183602), _1183606))))], (36774 ^ _779854) ^ [_1468013, _1468015, _1468017, _1468019, _1468021, _1468023, _1468025] : [-(hAPP(c_Product__Type_Oapfst(_1468013, _1468015, _1468017, _1468019), hAPP(c_Product__Type_Oapfst(_1468021, _1468013, _1468017, _1468023), _1468025)) = hAPP(c_Product__Type_Oapfst(_1468021, _1468015, _1468017, hAPP(c_Fun_Ocomp(_1468013, _1468015, _1468021, _1468019), _1468023)), _1468025))], (28180 ^ _779854) ^ [_1289484, _1289486] : [-(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, _1289484)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1289486))))], (15640 ^ _779854) ^ [_1059560, _1059562, _1059564, _1059566, _1059568] : [class_Groups_Ocomm__monoid__add(_1059560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059562), _1059564)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059562), _1059566)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1059562, tc_HOL_Obool)), _1059564), _1059566) = c_Orderings_Obot__class_Obot(tc_fun(_1059562, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059562, _1059560), _1059568), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1059562, tc_HOL_Obool)), _1059564), _1059566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059560), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059562, _1059560), _1059568), _1059564)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1059562, _1059560), _1059568), _1059566)))], (52473 ^ _779854) ^ [_1836435, _1836437] : [-(class_Enum_Oenum(tc_sum(_1836435, _1836437))), class_Enum_Oenum(_1836435), class_Enum_Oenum(_1836437)], (2846 ^ _779854) ^ [_822234, _822236] : [_822236 = _822234, -(c_Relation_OField(_822236) = c_Relation_OField(_822234))], (34375 ^ _779854) ^ [_1417108, _1417110] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1417108)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1417110)), hAPP(c_Int_Onat, _1417108)) = hAPP(c_Int_Onat, _1417110))], (49920 ^ _779854) ^ [_1788970, _1788972] : [c_Relation_Oantisym(_1788970, hAPP(c_Relation_Oconverse(_1788970, _1788970), _1788972)), -(c_Relation_Oantisym(_1788970, _1788972))], (34669 ^ _779854) ^ [_1423830, _1423832] : [-(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), _1423830)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1423832), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1423830))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (26575 ^ _779854) ^ [_1262938] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262938) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32027 ^ _779854) ^ [_1356099, _1356101, _1356103] : [class_Rings_Olinordered__idom(_1356099), -(hAPP(c_Groups_Oabs__class_Oabs(_1356099), hAPP(hAPP(c_Power_Opower__class_Opower(_1356099), _1356101), _1356103)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1356099), hAPP(c_Groups_Oabs__class_Oabs(_1356099), _1356101)), _1356103))], (7441 ^ _779854) ^ [_902487, _902489] : [class_Lattices_Obounded__lattice__bot(_902487), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902487), _902489), c_Orderings_Obot__class_Obot(_902487)) = _902489)], (32327 ^ _779854) ^ [_1361636, _1361638, _1361640, _1361642, _1361644] : [class_Groups_Oordered__ab__group__add__abs(_1361636), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361636), hAPP(c_Groups_Oabs__class_Oabs(_1361636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1361636), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361636), _1361638), _1361640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361636), _1361642), _1361644)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361636), hAPP(c_Groups_Oabs__class_Oabs(_1361636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1361636), _1361638), _1361642))), hAPP(c_Groups_Oabs__class_Oabs(_1361636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1361636), _1361640), _1361644))))))], (27683 ^ _779854) ^ [_1280890] : [hAPP(c_Int_Onat, _1280890) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1280890), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17450 ^ _779854) ^ [_1095361, _1095363, _1095365] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1095361), _1095363)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095361), _1095365)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095361), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095361, tc_HOL_Obool)), _1095363), _1095365))), hAPP(c_Finite__Set_Ocard(_1095361), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095361, tc_HOL_Obool)), _1095363), _1095365))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095361), _1095363)), hAPP(c_Finite__Set_Ocard(_1095361), _1095365)))], (1940 ^ _779854) ^ [_807052, _807054, _807056, _807058, _807060, _807062] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807060, _807056, _807052)), c_Hoare__Mirabelle_Ohoare__derivs(_807062, _807058, _807054), _807062 = _807060, _807058 = _807056, _807054 = _807052], (39621 ^ _779854) ^ [_1548554] : [-(c_Wellfounded_Owf(_1548554, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1548554, _1548554), tc_HOL_Obool))))], (39869 ^ _779854) ^ [_1553437, _1553439, _1553441, _1553443] : [39870 ^ _779854 : [(39871 ^ _779854) ^ [_1553512] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553437, _1553441)), hAPP(hAPP(c_Product__Type_OPair(_1553437, _1553441), _1553439), _1553512)), _1553443))]], -(hBOOL(hAPP(hAPP(c_member(_1553437), _1553439), hAPP(c_Relation_ODomain(_1553437, _1553441), _1553443))))], (35288 ^ _779854) ^ [] : [-(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)))))], (52615 ^ _779854) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (12668 ^ _779854) ^ [_1001751, _1001753, _1001755] : [class_Orderings_Olinorder(_1001751), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001751), _1001753)), hBOOL(hAPP(hAPP(c_member(_1001751), _1001755), _1001753)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1001751), _1001755), c_Big__Operators_Olattice_OInf__fin(_1001751, c_Orderings_Oord__class_Omin(_1001751), _1001753)) = _1001755)], (46555 ^ _779854) ^ [_1715469, _1715471, _1715473] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715469)), hAPP(c_List_Ofilter(_1715469, _1715471), _1715473)) = 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(_1715469)), _1715473)))), hAPP(hAPP(c_COMBB(_1715469, tc_HOL_Obool, tc_Nat_Onat), _1715471), hAPP(c_List_Onth(_1715469), _1715473))))))], (35694 ^ _779854) ^ [_1444539, _1444541, _1444543] : [35696 ^ _779854 : [(35699 ^ _779854) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1444539, _1444541), 35695 ^ [_1444539, _1444541, _1444543]))], (35697 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1444541, 35695 ^ [_1444539, _1444541, _1444543]), _1444543)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1444539, _1444541), _1444543)))], (47613 ^ _779854) ^ [_1737385, _1737387, _1737389, _1737391, _1737393] : [-(hAPP(hAPP(c_List_Ozip(_1737385, _1737387), _1737389), c_List_OtakeWhile(_1737387, _1737391, _1737393)) = c_List_OtakeWhile(tc_prod(_1737385, _1737387), hAPP(c_Fun_Ocomp(_1737387, tc_HOL_Obool, tc_prod(_1737385, _1737387), _1737391), c_Product__Type_Osnd(_1737385, _1737387)), hAPP(hAPP(c_List_Ozip(_1737385, _1737387), _1737389), _1737393)))], (38721 ^ _779854) ^ [_1518200, _1518202, _1518204, _1518206] : [-(hAPP(c_Set_OCollect(tc_prod(_1518200, _1518202)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518200, _1518202, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1518200, tc_fun(_1518202, tc_HOL_Obool), tc_fun(_1518202, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1518202, tc_HOL_Obool), tc_fun(_1518202, tc_HOL_Obool)), _1518200), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1518202)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518200), c_fconj), _1518204))), _1518206))) = hAPP(hAPP(c_Product__Type_OSigma(_1518200, _1518202), hAPP(c_Set_OCollect(_1518200), _1518204)), hAPP(hAPP(c_COMBB(tc_fun(_1518202, tc_HOL_Obool), tc_fun(_1518202, tc_HOL_Obool), _1518200), c_Set_OCollect(_1518202)), _1518206)))], (43408 ^ _779854) ^ [_1645287, _1645289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1645287), _1645289)), -(c_List_Oupto(_1645289, _1645287) = c_List_Olist_ONil(tc_Int_Oint))], (34517 ^ _779854) ^ [_1420037, _1420039] : [class_Rings_Ocomm__semiring__1(_1420037), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420037), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420037), c_Groups_Oone__class_Oone(_1420037)), c_Groups_Oone__class_Oone(_1420037))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1420037), c_Nat_Osemiring__1__class_Oof__nat(_1420037)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1420039))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420037), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1420037), _1420039)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420037), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1420037), _1420039)), c_Groups_Oone__class_Oone(_1420037))))], (29857 ^ _779854) ^ [_1318197, _1318199, _1318201] : [class_Rings_Olinordered__idom(_1318197), 29860 ^ _779854 : [(29869 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1318197), hAPP(hAPP(c_Power_Opower__class_Opower(_1318197), _1318199), 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(_1318197), _1318201), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1318197)), _1318199 = c_Groups_Ozero__class_Ozero(_1318197), _1318201 = c_Groups_Ozero__class_Ozero(_1318197)], (29861 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1318197), hAPP(hAPP(c_Power_Opower__class_Opower(_1318197), _1318199), 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(_1318197), _1318201), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1318197), 29864 ^ _779854 : [(29867 ^ _779854) ^ [] : [-(_1318201 = c_Groups_Ozero__class_Ozero(_1318197))], (29865 ^ _779854) ^ [] : [-(_1318199 = c_Groups_Ozero__class_Ozero(_1318197))]]]]], (33262 ^ _779854) ^ [_1383527, _1383529, _1383531, _1383533, _1383535, _1383537] : [class_Complete__Lattice_Ocomplete__lattice(_1383527), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383529, tc_fun(_1383531, _1383527)), _1383533), _1383535), _1383537) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383529, _1383527), _1383533), hAPP(hAPP(c_COMBC(_1383529, _1383531, _1383527), _1383535), _1383537)))], (44133 ^ _779854) ^ [_1660948, _1660950, _1660952, _1660954] : [-(c_List_Osublist(_1660948, hAPP(hAPP(c_List_Oappend(_1660948), _1660950), _1660952), _1660954) = hAPP(hAPP(c_List_Oappend(_1660948), c_List_Osublist(_1660948, _1660950, _1660954)), c_List_Osublist(_1660948, _1660952, 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(_1660948)), _1660950)))), _1660954)))))], (33353 ^ _779854) ^ [_1386327, _1386329, _1386331, _1386333, _1386335, _1386337, _1386339] : [-(hAPP(c_Fun_Ocomp(_1386327, _1386329, _1386331, _1386333), hAPP(c_Fun_Ocomp(_1386335, _1386327, _1386331, _1386337), _1386339)) = hAPP(c_Fun_Ocomp(_1386335, _1386329, _1386331, hAPP(c_Fun_Ocomp(_1386327, _1386329, _1386335, _1386333), _1386337)), _1386339))], (9314 ^ _779854) ^ [_935268, _935270] : [class_Complete__Lattice_Ocomplete__lattice(_935268), -(c_Complete__Lattice_OInf__class_OInf(_935268, hAPP(hAPP(c_Set_Oinsert(_935268), _935270), c_Orderings_Obot__class_Obot(tc_fun(_935268, tc_HOL_Obool)))) = _935270)], (28054 ^ _779854) ^ [_1287341, _1287343, _1287345] : [-(hBOOL(hAPP(_1287341, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1287343), _1287345)))), 28055 ^ _779854 : [(28062 ^ _779854) ^ [_1287509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1287345), _1287509)), _1287343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1287343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1287345), hAPP(c_Nat_OSuc, _1287509)))), hBOOL(hAPP(_1287341, _1287509))], (28056 ^ _779854) ^ [] : [_1287345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1287341, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19685 ^ _779854) ^ [_1134890, _1134892, _1134894] : [class_Rings_Olinordered__semiring__strict(_1134890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134890), c_Groups_Ozero__class_Ozero(_1134890)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134890), _1134892), _1134894))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134890), c_Groups_Ozero__class_Ozero(_1134890)), _1134894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134890), c_Groups_Ozero__class_Ozero(_1134890)), _1134892)))], (36474 ^ _779854) ^ [_1460684, _1460686, _1460688] : [class_Orderings_Owellorder(_1460684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460684), _1460686), c_Orderings_Oord__class_OLeast(_1460684, _1460688))), hBOOL(hAPP(_1460688, _1460686))], (3814 ^ _779854) ^ [_837298, _837300, _837302, _837304, _837306, _837308] : [-(c_List_OdropWhile(_837308, _837304, _837300) = c_List_OdropWhile(_837306, _837302, _837298)), _837308 = _837306, _837304 = _837302, _837300 = _837298], (20101 ^ _779854) ^ [_1142138, _1142140, _1142142] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1142138), _1142140)), 20104 ^ _779854 : [(20105 ^ _779854) ^ [] : [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(_1142138, tc_Nat_Onat), _1142142), _1142140))), 20108 ^ _779854 : [(20109 ^ _779854) ^ [_1142306] : [hBOOL(hAPP(hAPP(c_member(_1142138), _1142306), _1142140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1142142, _1142306))))]]], (20115 ^ _779854) ^ [] : [20117 ^ _779854 : [(20120 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1142142, 20116 ^ [_1142138, _1142140, _1142142])))], (20118 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1142138), 20116 ^ [_1142138, _1142140, _1142142]), _1142140)))]], -(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(_1142138, tc_Nat_Onat), _1142142), _1142140))))]]], (38837 ^ _779854) ^ [_1520852, _1520854, _1520856] : [hBOOL(hAPP(_1520852, _1520854)), -(hAPP(c_Set_OCollect(_1520856), hAPP(hAPP(c_COMBS(_1520856, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520856), c_fconj), hAPP(hAPP(c_COMBC(_1520856, _1520856, tc_HOL_Obool), c_fequal), _1520854))), _1520852)) = hAPP(hAPP(c_Set_Oinsert(_1520856), _1520854), c_Orderings_Obot__class_Obot(tc_fun(_1520856, tc_HOL_Obool))))], (38638 ^ _779854) ^ [_1515758, _1515760, _1515762, _1515764, _1515766, _1515768] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1515758, _1515760), _1515758, tc_prod(_1515762, _1515764), c_Product__Type_Ofst(_1515758, _1515760)), c_Product__Type_Omap__pair(_1515762, _1515758, _1515764, _1515760, _1515766, _1515768)) = hAPP(c_Fun_Ocomp(_1515762, _1515758, tc_prod(_1515762, _1515764), _1515766), c_Product__Type_Ofst(_1515762, _1515764)))], (2072 ^ _779854) ^ [_810003, _810005] : [_810005 = _810003, -(c_Nat_Osemiring__1__class_ONats(_810005) = c_Nat_Osemiring__1__class_ONats(_810003))], (7868 ^ _779854) ^ [_911310, _911312, _911314, _911316] : [class_Orderings_Oorder(_911310), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911310, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_911310, _911312, _911314)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_911310, _911314), _911316)) = c_Orderings_Obot__class_Obot(tc_fun(_911310, tc_HOL_Obool)))], (18072 ^ _779854) ^ [_1106793, _1106795] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1106793)), hAPP(c_Nat_OSuc, _1106795)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1106793), _1106795)))], (13337 ^ _779854) ^ [_1014894, _1014896, _1014898] : [class_Orderings_Olinorder(_1014894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014894), _1014896)), hBOOL(hAPP(hAPP(c_member(_1014894), _1014898), _1014896)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1014894), _1014898), c_Big__Operators_Olinorder__class_OMax(_1014894, _1014896)) = c_Big__Operators_Olinorder__class_OMax(_1014894, _1014896))], (2674 ^ _779854) ^ [_819578, _819580] : [_819580 = _819578, -(c_Wellfounded_Omeasure(_819580) = c_Wellfounded_Omeasure(_819578))], (48806 ^ _779854) ^ [_1763280, _1763282, _1763284, _1763286, _1763288] : [-(hAPP(c_New__DSequence_Opos__bind(_1763280, _1763282, _1763284, _1763286), _1763288) = hAPP(c_Lazy__Sequence_Obind(_1763280, _1763282, hAPP(_1763284, _1763288)), hAPP(hAPP(c_COMBC(_1763280, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1763282)), _1763286), _1763288)))], (45087 ^ _779854) ^ [_1681776, _1681778, _1681780, _1681782, _1681784, _1681786, _1681788, _1681790] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1681776, _1681778), _1681780), _1681782), hAPP(hAPP(c_List_Ozip(_1681776, _1681778), hAPP(hAPP(c_List_Omap(_1681784, _1681776), _1681786), _1681788)), _1681790)) = hAPP(hAPP(c_List_Omap(tc_prod(_1681784, _1681778), _1681780), hAPP(c_Product__Type_Oprod_Oprod__case(_1681784, _1681778, _1681780), hAPP(hAPP(c_COMBB(tc_fun(_1681778, tc_prod(_1681776, _1681778)), tc_fun(_1681778, _1681780), _1681784), hAPP(c_COMBB(tc_prod(_1681776, _1681778), _1681780, _1681778), _1681782)), hAPP(hAPP(c_COMBB(_1681776, tc_fun(_1681778, tc_prod(_1681776, _1681778)), _1681784), c_Product__Type_OPair(_1681776, _1681778)), _1681786)))), hAPP(hAPP(c_List_Ozip(_1681784, _1681778), _1681788), _1681790)))], (2646 ^ _779854) ^ [_819128, _819130, _819132, _819134, _819136, _819138, _819140, _819142] : [-(c_Product__Type_Oapfst(_819142, _819138, _819134, _819130) = c_Product__Type_Oapfst(_819140, _819136, _819132, _819128)), _819142 = _819140, _819138 = _819136, _819134 = _819132, _819130 = _819128], (27519 ^ _779854) ^ [_1278238] : [class_Rings_Osemiring__1(_1278238), c_Int_Oiszero(_1278238, c_Groups_Oone__class_Oone(_1278238))], (48350 ^ _779854) ^ [_1753916, _1753918, _1753920] : [class_Enum_Oenum(_1753916), class_Enum_Oenum(_1753918), 48357 ^ _779854 : [(48364 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753918), hAPP(hAPP(c_COMBB(tc_fun(_1753916, tc_HOL_Obool), tc_HOL_Obool, _1753918), c_Enum_Oenum__class_Oenum__all(_1753916)), hAPP(hAPP(c_COMBB(tc_fun(_1753916, tc_prod(_1753918, _1753916)), tc_fun(_1753916, tc_HOL_Obool), _1753918), hAPP(c_COMBB(tc_prod(_1753918, _1753916), tc_HOL_Obool, _1753916), _1753920)), c_Product__Type_OPair(_1753918, _1753916))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1753918, _1753916)), _1753920)))], (48358 ^ _779854) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1753918, _1753916)), _1753920)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1753918), hAPP(hAPP(c_COMBB(tc_fun(_1753916, tc_HOL_Obool), tc_HOL_Obool, _1753918), c_Enum_Oenum__class_Oenum__all(_1753916)), hAPP(hAPP(c_COMBB(tc_fun(_1753916, tc_prod(_1753918, _1753916)), tc_fun(_1753916, tc_HOL_Obool), _1753918), hAPP(c_COMBB(tc_prod(_1753918, _1753916), tc_HOL_Obool, _1753916), _1753920)), c_Product__Type_OPair(_1753918, _1753916))))))]]], (16403 ^ _779854) ^ [_1075027, _1075029, _1075031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075027), _1075029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075031), _1075029)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075031), _1075027))))], (52383 ^ _779854) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (51004 ^ _779854) ^ [_1811050, _1811052, _1811054, _1811056, _1811058, _1811060] : [c_Fun_Oinj__on(_1811050, _1811052, _1811054, _1811056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1811052, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1811050, _1811052, _1811054), _1811056)), _1811058)), c_Fun_Oinj__on(_1811052, _1811050, _1811060, _1811058), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1811050, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1811052, _1811050, _1811060), _1811058)), _1811056)), -(c_Fun_Obij__betw(_1811050, _1811052, 51019 ^ [_1811050, _1811052, _1811054, _1811056, _1811058, _1811060], _1811056, _1811058))], (46577 ^ _779854) ^ [_1716662] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1716662)), c_List_Otranspose__rel(_1716662)), c_List_Olist_ONil(tc_List_Olist(_1716662)))), -(c_List_Otranspose(_1716662, c_List_Olist_ONil(tc_List_Olist(_1716662))) = c_List_Olist_ONil(tc_List_Olist(_1716662)))], (28430 ^ _779854) ^ [_1293906, _1293908] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293906)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293908)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1293906), _1293908)))], (16133 ^ _779854) ^ [_1069549, _1069551, _1069553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069549), _1069551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069553), _1069549)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069553), _1069551))))], (40807 ^ _779854) ^ [_1576286, _1576288, _1576290, _1576292] : [hBOOL(hAPP(hAPP(c_member(_1576286), _1576288), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1576286, tc_HOL_Obool), _1576290))), c_Orderings_Oorder__class_Omono(tc_fun(_1576286, tc_HOL_Obool), tc_fun(_1576286, tc_HOL_Obool), _1576290), 40817 ^ _779854 : [(40820 ^ _779854) ^ [] : [hBOOL(hAPP(_1576292, 40816 ^ [_1576286, _1576288, _1576290, _1576292]))], (40818 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576286), 40816 ^ [_1576286, _1576288, _1576290, _1576292]), hAPP(_1576290, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1576286, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1576286, tc_HOL_Obool), _1576290)), hAPP(c_Set_OCollect(_1576286), _1576292))))))]], -(hBOOL(hAPP(_1576292, _1576288)))], (1058 ^ _779854) ^ [_795823, _795825, _795827, _795829, _795831, _795833] : [-(c_List_Olist__ex(_795831, _795827, _795823)), c_List_Olist__ex(_795833, _795829, _795825), _795833 = _795831, _795829 = _795827, _795825 = _795823], (5224 ^ _779854) ^ [_859737, _859739, _859741, _859743, _859745, _859747] : [-(c_Lazy__Sequence_Oappend(_859747, _859743, _859739) = c_Lazy__Sequence_Oappend(_859745, _859741, _859737)), _859747 = _859745, _859743 = _859741, _859739 = _859737], (894 ^ _779854) ^ [_793203, _793205, _793207, _793209, _793211, _793213, _793215, _793217] : [-(c_Fun_Oinj__on(_793215, _793211, _793207, _793203)), c_Fun_Oinj__on(_793217, _793213, _793209, _793205), _793217 = _793215, _793213 = _793211, _793209 = _793207, _793205 = _793203], (36215 ^ _779854) ^ [_1455544, _1455546] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1455544), _1455546) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1455544, _1455546)))], (8572 ^ _779854) ^ [_922851, _922853, _922855] : [class_Orderings_Oorder(_922851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922851), _922853), _922855)), -(_922853 = _922855), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922851), _922853), _922855)))], (23671 ^ _779854) ^ [_1208798] : [class_Orderings_Olinorder(_1208798), -(c_Finite__Set_Ofun__left__comm__idem(_1208798, _1208798, c_Orderings_Oord__class_Omax(_1208798)))], (7045 ^ _779854) ^ [_895283, _895285, _895287] : [class_Lattices_Olattice(_895283), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895283), _895285), _895287) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895283), _895287), _895285))], (47647 ^ _779854) ^ [_1738048] : [-(c_List_Oreturn__list(_1738048) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1738048))], (18142 ^ _779854) ^ [_1108088, _1108090] : [class_Rings_Ocomm__ring__1(_1108088), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1108088), _1108090) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108088), hAPP(c_Groups_Ouminus__class_Ouminus(_1108088), c_Groups_Oone__class_Oone(_1108088))), _1108090))], (52561 ^ _779854) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (47490 ^ _779854) ^ [_1734770, _1734772, _1734774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734770), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734772)), _1734774))), -(hAPP(hAPP(c_List_Onth(_1734772), hAPP(c_List_Orev(_1734772), _1734774)), _1734770) = hAPP(hAPP(c_List_Onth(_1734772), _1734774), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734772)), _1734774)), hAPP(c_Nat_OSuc, _1734770))))], (52619 ^ _779854) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (40394 ^ _779854) ^ [_1566876, _1566878, _1566880, _1566882, _1566884, _1566886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566876, tc_HOL_Obool)), _1566878), _1566880)), 40400 ^ _779854 : [(40403 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566882, tc_HOL_Obool)), hAPP(_1566884, 40399 ^ [_1566876, _1566878, _1566880, _1566882, _1566884, _1566886])), hAPP(_1566886, 40399 ^ [_1566876, _1566878, _1566880, _1566882, _1566884, _1566886])))], (40401 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566876), 40399 ^ [_1566876, _1566878, _1566880, _1566882, _1566884, _1566886]), _1566878)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566876, _1566882), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1566876, _1566882), _1566878), _1566884)), hAPP(hAPP(c_Product__Type_OSigma(_1566876, _1566882), _1566880), _1566886))))], (50112 ^ _779854) ^ [_1792771, _1792773] : [-(c_Relation_Osym(_1792771, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1792771, _1792771), tc_HOL_Obool)), _1792773), hAPP(c_Relation_Oconverse(_1792771, _1792771), _1792773))))], (44580 ^ _779854) ^ [_1671631, _1671633, _1671635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671631)), _1671633)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1671631, _1671635), _1671633) = _1671633)], (14359 ^ _779854) ^ [_1033643, _1033645, _1033647, _1033649] : [-(_1033643 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1033645, tc_HOL_Obool), tc_HOL_Obool))), 14365 ^ _779854 : [(14368 ^ _779854) ^ [] : [c_Fun_Oinj__on(_1033645, _1033647, _1033649, 14364 ^ [_1033643, _1033645, _1033647, _1033649])], (14366 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1033645, tc_HOL_Obool)), 14364 ^ [_1033643, _1033645, _1033647, _1033649]), _1033643)))]], -(c_Fun_Oinj__on(_1033645, _1033647, _1033649, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1033645, tc_HOL_Obool), _1033643)))], (45633 ^ _779854) ^ [_1693997, _1693999] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1693997), _1693999) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1693997, 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)))), _1693999))))], (2094 ^ _779854) ^ [_810322, _810324, _810326, _810328] : [-(c_Nat__Transfer_Otsub(_810328, _810324) = c_Nat__Transfer_Otsub(_810326, _810322)), _810328 = _810326, _810324 = _810322], (30737 ^ _779854) ^ [_1334771, _1334773, _1334775, _1334777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334773), _1334775)), -(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), _1334775), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1334777, _1334771))), _1334773)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1334775), _1334771))))], (19923 ^ _779854) ^ [_1139209, _1139211] : [class_Groups_Oordered__ab__group__add(_1139209), 19926 ^ _779854 : [(19933 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139209), c_Groups_Ozero__class_Ozero(_1139209)), _1139211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139209), hAPP(c_Groups_Ouminus__class_Ouminus(_1139209), _1139211)), c_Groups_Ozero__class_Ozero(_1139209))))], (19927 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139209), hAPP(c_Groups_Ouminus__class_Ouminus(_1139209), _1139211)), c_Groups_Ozero__class_Ozero(_1139209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139209), c_Groups_Ozero__class_Ozero(_1139209)), _1139211)))]]], (36020 ^ _779854) ^ [_1451251, _1451253, _1451255, _1451257, _1451259, _1451261, _1451263, _1451265, _1451267, _1451269, _1451271] : [c_Finite__Set_Ofolding(_1451251, _1451253, _1451255, _1451257), -(hAPP(c_Fun_Ocomp(_1451259, _1451261, _1451263, _1451265), hAPP(c_Fun_Ocomp(_1451267, _1451259, _1451263, _1451269), _1451271)) = hAPP(c_Fun_Ocomp(_1451267, _1451261, _1451263, hAPP(c_Fun_Ocomp(_1451259, _1451261, _1451267, _1451265), _1451269)), _1451271))], (14299 ^ _779854) ^ [_1032433, _1032435, _1032437, _1032439] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032433), _1032435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1032433, tc_HOL_Obool)), _1032435), _1032437)), hBOOL(hAPP(_1032439, c_Orderings_Obot__class_Obot(tc_fun(_1032433, tc_HOL_Obool)))), 14314 ^ _779854 : [(14315 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1032433), 14313 ^ [_1032433, _1032435, _1032437, _1032439])))], (14319 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1032433), 14312 ^ [_1032433, _1032435, _1032437, _1032439]), 14313 ^ [_1032433, _1032435, _1032437, _1032439]))], (14323 ^ _779854) ^ [] : [hBOOL(hAPP(_1032439, hAPP(hAPP(c_Set_Oinsert(_1032433), 14312 ^ [_1032433, _1032435, _1032437, _1032439]), 14313 ^ [_1032433, _1032435, _1032437, _1032439])))], (14321 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1032439, 14313 ^ [_1032433, _1032435, _1032437, _1032439])))], (14317 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1032433), 14312 ^ [_1032433, _1032435, _1032437, _1032439]), _1032437)))]], -(hBOOL(hAPP(_1032439, _1032435)))], (26589 ^ _779854) ^ [_1263136] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1263136), c_Int_OPls) = _1263136)], (41567 ^ _779854) ^ [_1595706, _1595708, _1595710] : [-(hAPP(c_Relation_Oconverse(_1595706, _1595708), _1595710) = hAPP(c_Set_OCollect(tc_prod(_1595708, _1595706)), hAPP(c_Product__Type_Oprod_Oprod__case(_1595708, _1595706, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1595708, tc_fun(tc_prod(_1595706, _1595708), tc_HOL_Obool), tc_fun(_1595706, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595706, tc_fun(tc_fun(tc_prod(_1595706, _1595708), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1595706, _1595708), tc_HOL_Obool), tc_fun(_1595706, tc_HOL_Obool)), _1595708), c_COMBC(_1595706, tc_fun(tc_prod(_1595706, _1595708), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1595706, tc_prod(_1595706, _1595708)), tc_fun(_1595706, tc_fun(tc_fun(tc_prod(_1595706, _1595708), tc_HOL_Obool), tc_HOL_Obool)), _1595708), hAPP(c_COMBB(tc_prod(_1595706, _1595708), tc_fun(tc_fun(tc_prod(_1595706, _1595708), tc_HOL_Obool), tc_HOL_Obool), _1595706), c_member(tc_prod(_1595706, _1595708)))), hAPP(c_COMBC(_1595706, _1595708, tc_prod(_1595706, _1595708)), c_Product__Type_OPair(_1595706, _1595708))))), _1595710))))], (51054 ^ _779854) ^ [_1812104, _1812106, _1812108, _1812110] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1812104, _1812106, _1812108), c_Product__Type_Ocurry(_1812104, _1812106, _1812108, _1812110)) = _1812110)], (6583 ^ _779854) ^ [_885245, _885247, _885249] : [class_Groups_Oordered__ab__group__add(_885245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885245), _885247), _885249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885245), hAPP(c_Groups_Ouminus__class_Ouminus(_885245), _885249)), hAPP(c_Groups_Ouminus__class_Ouminus(_885245), _885247))))], (6943 ^ _779854) ^ [_893164, _893166, _893168, _893170] : [class_Lattices_Olattice(_893164), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893164), _893166), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893164), _893168), _893170)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893164), _893168), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893164), _893166), _893170)))], (37942 ^ _779854) ^ [_1497079, _1497081, _1497083, _1497085, _1497087, _1497089, _1497091] : [c_Typedef_Otype__definition(_1497079, _1497081, _1497083, _1497085, _1497087), 37945 ^ _779854 : [(37952 ^ _779854) ^ [] : [_1497089 = _1497091, -(hAPP(_1497083, _1497089) = hAPP(_1497083, _1497091))], (37946 ^ _779854) ^ [] : [hAPP(_1497083, _1497089) = hAPP(_1497083, _1497091), -(_1497089 = _1497091)]]], (43542 ^ _779854) ^ [_1647592, _1647594] : [-(c_List_Osublist(_1647592, _1647594, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1647592))], (16010 ^ _779854) ^ [_1067524, _1067526] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067524), _1067526))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067524), _1067526)), -(_1067524 = _1067526)], (32662 ^ _779854) ^ [_1367877, _1367879, _1367881] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1367877), _1367879))), -(c_Random_Ominus__shift(_1367881, _1367877, _1367879) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1367877), _1367879))], (31218 ^ _779854) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (39439 ^ _779854) ^ [_1542207, _1542209, _1542211, _1542213] : [hAPP(hAPP(c_Relation_Orel__comp(_1542207, _1542207, _1542207), _1542209), _1542211) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542207, _1542207), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1542207, _1542207, _1542207), _1542209), _1542213) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542207, _1542207), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1542207, _1542207, _1542207), _1542209), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1542207, _1542207), tc_HOL_Obool)), _1542211), _1542213)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542207, _1542207), tc_HOL_Obool)))], (46755 ^ _779854) ^ [_1720381, _1720383] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1720381, _1720383) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1720381, hAPP(c_Nat_OSuc, _1720383))))], (42131 ^ _779854) ^ [_1610790, _1610792, _1610794] : [hAPP(hAPP(c_List_Olist_OCons(_1610790), _1610792), _1610794) = _1610794], (28687 ^ _779854) ^ [_1298311, _1298313] : [class_Int_Onumber__ring(_1298311), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298311), _1298313), hAPP(c_Int_Onumber__class_Onumber__of(_1298311), c_Int_OBit1(c_Int_OPls))) = _1298313)], (31128 ^ _779854) ^ [_1341308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1341308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1341308))))], (32686 ^ _779854) ^ [_1368182, _1368184, _1368186] : [-(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), _1368182)), 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))), _1368184))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1368186))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368186)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1368182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1368182), 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), _1368186), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1368184)))))], (52371 ^ _779854) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (17122 ^ _779854) ^ [_1089108, _1089110, _1089112] : [class_Groups_Oab__semigroup__mult(_1089108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089108), _1089110)), -(hBOOL(hAPP(hAPP(c_member(_1089108), _1089112), _1089110))), -(hAPP(c_Finite__Set_Ofold1(_1089108, c_Groups_Otimes__class_Otimes(_1089108)), hAPP(hAPP(c_Set_Oinsert(_1089108), _1089112), _1089110)) = hAPP(hAPP(c_Finite__Set_Ofold(_1089108, _1089108, c_Groups_Otimes__class_Otimes(_1089108)), _1089112), _1089110))], (49397 ^ _779854) ^ [_1776530, _1776532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1776530)), _1776532)), 49401 ^ _779854 : [(49402 ^ _779854) ^ [_1776631] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776530)), _1776631), _1776532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776530)), _1776631)), 49400 ^ [_1776530, _1776532])))]]], (33665 ^ _779854) ^ [_1398462, _1398464, _1398466, _1398468] : [-(hAPP(c_Set_Oimage(_1398462, _1398464, _1398466), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1398462, tc_HOL_Obool), _1398468)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1398462, tc_HOL_Obool), tc_fun(_1398464, tc_HOL_Obool)), _1398468), c_Set_Oimage(_1398462, _1398464, _1398466)))], (45330 ^ _779854) ^ [_1687895, _1687897, _1687899, _1687901] : [class_Groups_Ocomm__monoid__add(_1687895), hBOOL(hAPP(c_List_Odistinct(_1687897), _1687899)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687895), hAPP(hAPP(c_List_Omap(_1687897, _1687895), _1687901), _1687899)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1687897, _1687895), _1687901), hAPP(c_List_Oset(_1687897), _1687899)))], (30189 ^ _779854) ^ [_1324768, _1324770, _1324772, _1324774] : [class_Divides_Osemiring__div(_1324768), -(c_Divides_Odiv__class_Omod(_1324768, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324768), _1324770), c_Divides_Odiv__class_Omod(_1324768, _1324772, _1324774)), _1324774) = c_Divides_Odiv__class_Omod(_1324768, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324768), _1324770), _1324772), _1324774))], (28451 ^ _779854) ^ [_1294295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1294295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1294295))))], (18303 ^ _779854) ^ [_1111037, _1111039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111037), _1111039)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1111037), hAPP(c_Nat_OSuc, _1111039)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1111039), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1111037), _1111039)))], (50599 ^ _779854) ^ [_1802990] : [-(_1802990 = hAPP(c_Code__Numeral_Oof__nat, 50597 ^ [_1802990]))], (29373 ^ _779854) ^ [_1309725, _1309727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309725), _1309727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1309725)), c_Int_OBit0(_1309727))))], (34059 ^ _779854) ^ [_1409450, _1409452, _1409454, _1409456, _1409458] : [class_Groups_Ocomm__monoid__add(_1409450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409452), _1409454)), 34066 ^ _779854 : [(34073 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409452), _1409456), _1409454))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409452, _1409450), hAPP(hAPP(c_COMBC(_1409452, _1409450, _1409450), hAPP(hAPP(c_COMBS(_1409452, _1409450, tc_fun(_1409450, _1409450)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409450, tc_fun(_1409450, _1409450)), _1409452), c_If(_1409450)), hAPP(hAPP(c_COMBC(_1409452, _1409452, tc_HOL_Obool), c_fequal), _1409456))), _1409458)), c_Groups_Ozero__class_Ozero(_1409450))), _1409454) = c_Groups_Ozero__class_Ozero(_1409450))], (34067 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1409452), _1409456), _1409454)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409452, _1409450), hAPP(hAPP(c_COMBC(_1409452, _1409450, _1409450), hAPP(hAPP(c_COMBS(_1409452, _1409450, tc_fun(_1409450, _1409450)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409450, tc_fun(_1409450, _1409450)), _1409452), c_If(_1409450)), hAPP(hAPP(c_COMBC(_1409452, _1409452, tc_HOL_Obool), c_fequal), _1409456))), _1409458)), c_Groups_Ozero__class_Ozero(_1409450))), _1409454) = hAPP(_1409458, _1409456))]]], (45522 ^ _779854) ^ [_1691901, _1691903] : [-(c_Random_Oselect__weight(_1691901, _1691903) = 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(_1691901, 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, _1691901), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1691901)), _1691903)))), hAPP(hAPP(c_COMBB(_1691901, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1691901, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1691901, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1691901, _1691903))))], (48034 ^ _779854) ^ [_1746604, _1746606, _1746608, _1746610, _1746612] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1746604, _1746604)), hAPP(hAPP(c_Product__Type_OPair(_1746604, _1746604), _1746606), _1746608)), c_List_Omeasures(_1746604, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1746604, tc_Nat_Onat)), _1746610), _1746612))))), 48035 ^ _779854 : [(48038 ^ _779854) ^ [] : [hAPP(_1746610, _1746606) = hAPP(_1746610, _1746608), hBOOL(hAPP(hAPP(c_member(tc_prod(_1746604, _1746604)), hAPP(hAPP(c_Product__Type_OPair(_1746604, _1746604), _1746606), _1746608)), c_List_Omeasures(_1746604, _1746612)))], (48036 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1746610, _1746606)), hAPP(_1746610, _1746608)))]]], (52485 ^ _779854) ^ [_1836591] : [class_Finite__Set_Ofinite(_1836591), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1836591)))], (52559 ^ _779854) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (13239 ^ _779854) ^ [_1013371, _1013373] : [class_Orderings_Olinorder(_1013371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013371), _1013373)), -(_1013373 = c_Orderings_Obot__class_Obot(tc_fun(_1013371, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1013371), c_Big__Operators_Olinorder__class_OMin(_1013371, _1013373)), _1013373)))], (37556 ^ _779854) ^ [_1487941, _1487943] : [c_Equiv__Relations_Oequivp(_1487941, hAPP(hAPP(c_COMBC(_1487941, tc_fun(tc_prod(_1487941, _1487941), tc_HOL_Obool), tc_fun(_1487941, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487941, tc_fun(tc_fun(tc_prod(_1487941, _1487941), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1487941, _1487941), tc_HOL_Obool), tc_fun(_1487941, tc_HOL_Obool)), _1487941), c_COMBC(_1487941, tc_fun(tc_prod(_1487941, _1487941), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487941, tc_prod(_1487941, _1487941)), tc_fun(_1487941, tc_fun(tc_fun(tc_prod(_1487941, _1487941), tc_HOL_Obool), tc_HOL_Obool)), _1487941), hAPP(c_COMBB(tc_prod(_1487941, _1487941), tc_fun(tc_fun(tc_prod(_1487941, _1487941), tc_HOL_Obool), tc_HOL_Obool), _1487941), c_member(tc_prod(_1487941, _1487941)))), c_Product__Type_OPair(_1487941, _1487941)))), _1487943)), -(c_Equiv__Relations_Oequiv(_1487941, c_Orderings_Otop__class_Otop(tc_fun(_1487941, tc_HOL_Obool)), _1487943))], (43372 ^ _779854) ^ [_1644691, _1644693, _1644695] : [hBOOL(hAPP(c_List_Odistinct(_1644691), _1644693)), -(hBOOL(hAPP(c_List_Odistinct(_1644691), c_List_Oremove1(_1644691, _1644695, _1644693))))], (4208 ^ _779854) ^ [_843803, _843805] : [_843805 = _843803, -(c_List_Orev(_843805) = c_List_Orev(_843803))], (52041 ^ _779854) ^ [_1831829, _1831831] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831829), _1831831)), -(_1831829 = _1831831), 52048 ^ _779854 : [(52051 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831831), _1831829))], (52049 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831829), _1831831)))]]], (6561 ^ _779854) ^ [_884858] : [class_Lattices_Oboolean__algebra(_884858), -(hAPP(c_Groups_Ouminus__class_Ouminus(_884858), c_Orderings_Otop__class_Otop(_884858)) = c_Orderings_Obot__class_Obot(_884858))], (17216 ^ _779854) ^ [_1090673, _1090675, _1090677, _1090679, _1090681, _1090683] : [c_Finite__Set_Ofun__left__comm(_1090673, _1090675, _1090677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090673), _1090679)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1090673, _1090675, _1090677), _1090681), hAPP(hAPP(c_Set_Oinsert(_1090673), _1090683), _1090679)) = hAPP(hAPP(_1090677, _1090683), hAPP(hAPP(c_Finite__Set_Ofold(_1090673, _1090675, _1090677), _1090681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090673, tc_HOL_Obool)), _1090679), hAPP(hAPP(c_Set_Oinsert(_1090673), _1090683), c_Orderings_Obot__class_Obot(tc_fun(_1090673, tc_HOL_Obool)))))))], (52285 ^ _779854) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11294 ^ _779854) ^ [_974706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_974706)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_974706), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_974706), c_Orderings_Otop__class_Otop(tc_fun(_974706, tc_HOL_Obool)))))], (47314 ^ _779854) ^ [_1731119, _1731121] : [hBOOL(hAPP(c_List_Odistinct(_1731119), hAPP(c_List_Orev(_1731119), _1731121))), -(hBOOL(hAPP(c_List_Odistinct(_1731119), _1731121)))], (41340 ^ _779854) ^ [_1590041, _1590043, _1590045, _1590047] : [c_Wellfounded_Oacyclic(_1590041, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1590041, _1590041)), hAPP(hAPP(c_Product__Type_OPair(_1590041, _1590041), _1590043), _1590045)), _1590047)), 41343 ^ _779854 : [(41346 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590041, _1590041)), hAPP(hAPP(c_Product__Type_OPair(_1590041, _1590041), _1590045), _1590043)), c_Transitive__Closure_Ortrancl(_1590041, _1590047)))], (41344 ^ _779854) ^ [] : [-(c_Wellfounded_Oacyclic(_1590041, _1590047))]]], (24108 ^ _779854) ^ [_1217096, _1217098, _1217100, _1217102] : [class_Groups_Omonoid__mult(_1217096), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217096), _1217098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1217100), _1217102)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217096), hAPP(hAPP(c_Power_Opower__class_Opower(_1217096), _1217098), _1217100)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217096), _1217098), _1217102)))], (20958 ^ _779854) ^ [_1156955, _1156957, _1156959] : [hBOOL(hAPP(_1156955, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1156957), _1156959))), 20961 ^ _779854 : [(20968 ^ _779854) ^ [_1157140] : [_1156957 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1156959), _1157140), -(hBOOL(hAPP(_1156955, _1157140)))], (20962 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156957), _1156959)), -(hBOOL(hAPP(_1156955, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (37121 ^ _779854) ^ [_1477147, _1477149, _1477151, _1477153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1477147), _1477153)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1477151), _1477149))), -(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), _1477147), _1477149)), 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), _1477151), _1477153)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (9827 ^ _779854) ^ [_944993, _944995, _944997, _944999, _945001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944993, tc_HOL_Obool)), hAPP(c_Set_Oimage(_944995, _944993, _944997), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944995, tc_HOL_Obool)), _944999), _945001))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944993, tc_HOL_Obool)), hAPP(c_Set_Oimage(_944995, _944993, _944997), _944999)), hAPP(c_Set_Oimage(_944995, _944993, _944997), _945001)))))], (17694 ^ _779854) ^ [] : [-(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))], (32627 ^ _779854) ^ [_1367269, _1367271] : [-(c_Random_Olog(_1367269, _1367271) = 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(_1367269, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1367271), _1367269)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1367269), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1367271), _1367269)))], (42882 ^ _779854) ^ [_1633555, _1633557, _1633559] : [-(_1633555 = _1633557), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633559)), _1633555) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633559)), _1633557), 42888 ^ _779854 : [(42891 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1633559, _1633559, tc_HOL_Obool), c_fequal), 42887 ^ [_1633555, _1633557, _1633559]))], (42889 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633559, _1633559)), 42887 ^ [_1633555, _1633557, _1633559]), hAPP(c_List_Oset(tc_prod(_1633559, _1633559)), hAPP(hAPP(c_List_Ozip(_1633559, _1633559), _1633555), _1633557)))))]]], (25765 ^ _779854) ^ [] : [-(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))))], (42151 ^ _779854) ^ [_1611355, _1611357, _1611359, _1611361, _1611363, _1611365] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611355), tc_List_Olist(_1611355))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611355), tc_List_Olist(_1611355)), hAPP(hAPP(c_List_Olist_OCons(_1611355), _1611357), _1611359)), hAPP(hAPP(c_List_Olist_OCons(_1611355), _1611361), _1611363))), c_List_Olex(_1611355, _1611365)))), 42152 ^ _779854 : [(42159 ^ _779854) ^ [] : [_1611357 = _1611361, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611355), tc_List_Olist(_1611355))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611355), tc_List_Olist(_1611355)), _1611359), _1611363)), c_List_Olex(_1611355, _1611365)))], (42153 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611355, _1611355)), hAPP(hAPP(c_Product__Type_OPair(_1611355, _1611355), _1611357), _1611361)), _1611365)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611355)), _1611359) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611355)), _1611363)]]], (10115 ^ _779854) ^ [_950709, _950711, _950713, _950715] : [class_Orderings_Olinorder(_950709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950709), _950711), _950713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950709), hAPP(hAPP(c_Orderings_Oord__class_Omin(_950709), _950711), _950715)), _950713)))], (32283 ^ _779854) ^ [_1360712, _1360714] : [class_Rings_Olinordered__idom(_1360712), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360712), c_Groups_Osgn__class_Osgn(_1360712, _1360714)), hAPP(c_Groups_Oabs__class_Oabs(_1360712), _1360714)) = _1360714)], (34633 ^ _779854) ^ [_1423120, _1423122, _1423124] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1423120), _1423122))), 34636 ^ _779854 : [(34643 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1423124), _1423122))), -(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)), _1423120)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1423124), _1423122)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34637 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1423124), _1423122)), -(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)), _1423120)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1423124), _1423122)) = 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))))]]], (6253 ^ _779854) ^ [_879107, _879109] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879107, tc_HOL_Obool)), _879109), c_Orderings_Otop__class_Otop(tc_fun(_879107, tc_HOL_Obool)))))], (3916 ^ _779854) ^ [_838975, _838977, _838979, _838981, _838983, _838985, _838987, _838989] : [-(c_New__DSequence_Oneg__decr__bind(_838989, _838985, _838981, _838977) = c_New__DSequence_Oneg__decr__bind(_838987, _838983, _838979, _838975)), _838989 = _838987, _838985 = _838983, _838981 = _838979, _838977 = _838975], (51757 ^ _779854) ^ [_1827134, _1827136, _1827138, _1827140] : [class_Divides_Osemiring__div(_1827134), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827134), _1827136), _1827138)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827134), _1827136), _1827140)), 51768 ^ _779854 : [(51775 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827134), _1827138), _1827140)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827134), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827134), _1827138), _1827136)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827134), _1827140), _1827136))))], (51769 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827134), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827134), _1827138), _1827136)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827134), _1827140), _1827136))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827134), _1827138), _1827140)))]]], (19955 ^ _779854) ^ [_1139751, _1139753] : [class_Groups_Olinordered__ab__group__add(_1139751), 19958 ^ _779854 : [(19965 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139751), c_Groups_Ozero__class_Ozero(_1139751)), _1139753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139751), hAPP(c_Groups_Ouminus__class_Ouminus(_1139751), _1139753)), _1139753)))], (19959 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139751), hAPP(c_Groups_Ouminus__class_Ouminus(_1139751), _1139753)), _1139753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139751), c_Groups_Ozero__class_Ozero(_1139751)), _1139753)))]]], (12918 ^ _779854) ^ [_1006923, _1006925, _1006927, _1006929] : [hBOOL(hAPP(hAPP(_1006927, _1006929), _1006925)), -(hBOOL(hAPP(hAPP(c_member(_1006923), _1006925), c_SetInterval_Oord_OgreaterThan(_1006923, _1006927, _1006929))))], (29689 ^ _779854) ^ [_1315393, _1315395] : [class_Rings_Oring__1__no__zero__divisors(_1315393), 29692 ^ _779854 : [(29699 ^ _779854) ^ [] : [_1315395 = c_Groups_Ozero__class_Ozero(_1315393), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1315393), _1315395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1315393))], (29693 ^ _779854) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1315393), _1315395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1315393), -(_1315395 = c_Groups_Ozero__class_Ozero(_1315393))]]], (42951 ^ _779854) ^ [_1635392] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1635392) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42954 ^ _779854 : [(42955 ^ _779854) ^ [_1635467] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1635467), hAPP(c_List_Oset(tc_Nat_Onat), _1635392))), -(_1635467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5800 ^ _779854) ^ [_871672, _871674, _871676, _871678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871672, tc_HOL_Obool)), _871674), _871676)), hBOOL(hAPP(_871674, _871678)), -(hBOOL(hAPP(_871676, _871678)))], (10195 ^ _779854) ^ [_952096, _952098, _952100, _952102] : [class_Orderings_Olinorder(_952096), 10198 ^ _779854 : [(10199 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952096), hAPP(hAPP(c_Orderings_Oord__class_Omin(_952096), _952098), _952100)), _952102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952096), _952098), _952102))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952096), _952100), _952102)))], (10209 ^ _779854) ^ [] : [10210 ^ _779854 : [(10213 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952096), _952100), _952102))], (10211 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952096), _952098), _952102))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952096), hAPP(hAPP(c_Orderings_Oord__class_Omin(_952096), _952098), _952100)), _952102)))]]], (26745 ^ _779854) ^ [_1265434, _1265436, _1265438, _1265440] : [class_Divides_Osemiring__div(_1265434), 26748 ^ _779854 : [(26755 ^ _779854) ^ [] : [-(_1265436 = c_Groups_Ozero__class_Ozero(_1265434)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265434), _1265436), _1265438)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265434), _1265436), _1265440)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265434), _1265438), _1265440))], (26749 ^ _779854) ^ [] : [_1265436 = c_Groups_Ozero__class_Ozero(_1265434), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265434), _1265436), _1265438)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265434), _1265436), _1265440)) = c_Groups_Ozero__class_Ozero(_1265434))]]], (33717 ^ _779854) ^ [_1399914, _1399916, _1399918, _1399920, _1399922] : [class_Groups_Ominus(_1399914), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399916, _1399914)), _1399918), _1399920), _1399922) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1399914), hAPP(_1399918, _1399922)), hAPP(_1399920, _1399922)))], (12068 ^ _779854) ^ [_989949, _989951, _989953, _989955] : [hBOOL(hAPP(hAPP(c_member(_989949), _989951), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989949, tc_HOL_Obool)), _989953), _989955))), -(hBOOL(hAPP(hAPP(c_member(_989949), _989951), _989955)))], (43023 ^ _779854) ^ [_1636848, _1636850, _1636852, _1636854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636848)), _1636850)), _1636852)), -(hAPP(hAPP(c_List_Olist__update(_1636848, _1636850), _1636852), _1636854) = _1636850)], (27969 ^ _779854) ^ [_1285764, _1285766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285764), _1285766)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1285766), _1285764)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1285766)), hAPP(c_Int_Onat, _1285764)))], (51629 ^ _779854) ^ [_1824929, _1824931, _1824933] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824929), _1824931)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824929), _1824933)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824929), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1824931), _1824933))))], (18056 ^ _779854) ^ [_1106524, _1106526] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106524), _1106526) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1106524 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1106526 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (31979 ^ _779854) ^ [_1355184, _1355186] : [class_Rings_Olinordered__idom(_1355184), -(hAPP(c_Groups_Oabs__class_Oabs(_1355184), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1355184), _1355186)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1355184), _1355186))], (38344 ^ _779854) ^ [_1507498, _1507500, _1507502, _1507504] : [-(hAPP(c_Set_Oimage(tc_prod(_1507498, _1507500), tc_prod(_1507500, _1507498), hAPP(c_Product__Type_Oprod_Oprod__case(_1507498, _1507500, tc_prod(_1507500, _1507498)), hAPP(c_COMBC(_1507500, _1507498, tc_prod(_1507500, _1507498)), c_Product__Type_OPair(_1507500, _1507498)))), hAPP(hAPP(c_Product__Type_OSigma(_1507498, _1507500), _1507502), hAPP(c_COMBK(tc_fun(_1507500, tc_HOL_Obool), _1507498), _1507504))) = hAPP(hAPP(c_Product__Type_OSigma(_1507500, _1507498), _1507504), hAPP(c_COMBK(tc_fun(_1507498, tc_HOL_Obool), _1507500), _1507502)))], (37036 ^ _779854) ^ [_1474821, _1474823, _1474825, _1474827, _1474829, _1474831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1474821, _1474823), tc_HOL_Obool)), _1474825), _1474827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474821, tc_HOL_Obool)), _1474829), _1474831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474823, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474821, _1474823, _1474825), _1474829)), hAPP(c_Relation_OImage(_1474821, _1474823, _1474827), _1474831))))], (16079 ^ _779854) ^ [_1068576, _1068578] : [16080 ^ _779854 : [(16081 ^ _779854) ^ [_1068626] : [_1068578 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068576), _1068626)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068576), _1068578)))], (28426 ^ _779854) ^ [_1293800, _1293802] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293800)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1293802)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1293800), _1293802)))], (5588 ^ _779854) ^ [_865357, _865359, _865361, _865363] : [-(c_COMBK(_865363, _865359) = c_COMBK(_865361, _865357)), _865363 = _865361, _865359 = _865357], (48638 ^ _779854) ^ [_1759761, _1759763, _1759765, _1759767] : [c_List_Olist__all(_1759761, _1759763, hAPP(hAPP(c_List_Olist_OCons(_1759761), _1759765), _1759767)), 48641 ^ _779854 : [(48644 ^ _779854) ^ [] : [-(c_List_Olist__all(_1759761, _1759763, _1759767))], (48642 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1759763, _1759765)))]]], (7093 ^ _779854) ^ [_896232, _896234, _896236, _896238] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896232, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_896232, tc_HOL_Obool)), _896234), _896236)), _896238) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_896232, tc_HOL_Obool)), _896234), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896232, tc_HOL_Obool)), _896236), _896238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896232, tc_HOL_Obool)), _896238), _896234)))], (6018 ^ _779854) ^ [_875098, _875100, _875102, _875104] : [class_Orderings_Oord(_875098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875098), hAPP(_875100, 6023 ^ [_875098, _875100, _875102, _875104])), hAPP(_875102, 6023 ^ [_875098, _875100, _875102, _875104]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875104, _875098)), _875100), _875102)))], (45140 ^ _779854) ^ [_1683345, _1683347, _1683349, _1683351, _1683353, _1683355, _1683357] : [hAPP(hAPP(c_List_Omap(_1683345, _1683347), _1683349), _1683351) = hAPP(hAPP(c_List_Omap(_1683353, _1683347), _1683355), _1683357), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683345)), _1683351) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683353)), _1683357))], (6393 ^ _779854) ^ [_881673, _881675] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_881673, tc_HOL_Obool), hAPP(c_Set_OPow(_881673), _881675)) = _881675)], (11500 ^ _779854) ^ [_978678, _978680, _978682, _978684, _978686, _978688, _978690, _978692] : [c_Finite__Set_Ofolding__image__simple(_978678, _978680, _978682, _978684, _978686, _978688), hBOOL(hAPP(c_Finite__Set_Ofinite(_978680), _978690)), hBOOL(hAPP(c_Finite__Set_Ofinite(_978680), _978692)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978680, tc_HOL_Obool)), _978690), _978692) = c_Orderings_Obot__class_Obot(tc_fun(_978680, tc_HOL_Obool)), -(hAPP(_978688, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978680, tc_HOL_Obool)), _978690), _978692)) = hAPP(hAPP(_978682, hAPP(_978688, _978690)), hAPP(_978688, _978692)))], (24953 ^ _779854) ^ [_1232808, _1232810, _1232812, _1232814] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1232808, _1232810, _1232812), _1232814), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1232810)], (7746 ^ _779854) ^ [_908759, _908761] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_908759, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_908759, tc_HOL_Obool)), _908761)), _908761) = c_Orderings_Obot__class_Obot(tc_fun(_908759, tc_HOL_Obool)))], (47404 ^ _779854) ^ [_1733028, _1733030, _1733032, _1733034, _1733036] : [c_List_Olist__all2(_1733028, _1733030, _1733032, hAPP(c_List_Orev(_1733028), _1733034), hAPP(c_List_Orev(_1733030), _1733036)), -(c_List_Olist__all2(_1733028, _1733030, _1733032, _1733034, _1733036))], (18967 ^ _779854) ^ [_1121885] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1121885) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38511 ^ _779854) ^ [_1512218, _1512220, _1512222, _1512224] : [-(c_Fun_Oinj__on(_1512218, tc_prod(_1512220, _1512218), 38509 ^ [_1512218, _1512220, _1512222, _1512224], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512220, tc_fun(_1512218, tc_HOL_Obool)), _1512222), _1512224)))], (37189 ^ _779854) ^ [_1479038, _1479040] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479038), c_Orderings_Obot__class_Obot(tc_fun(_1479038, tc_HOL_Obool))), _1479040) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1479038, tc_HOL_Obool), tc_HOL_Obool)))], (33482 ^ _779854) ^ [_1389983, _1389985, _1389987, _1389989, _1389991] : [-(hBOOL(hAPP(hAPP(c_member(_1389983), _1389985), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389987, tc_fun(_1389983, tc_HOL_Obool)), _1389989), _1389991)))), 33483 ^ _779854 : [(33484 ^ _779854) ^ [_1390065] : [hBOOL(hAPP(hAPP(c_member(_1389987), _1390065), _1389989)), hBOOL(hAPP(hAPP(c_member(_1389983), _1389985), hAPP(_1389991, _1390065)))]]], (11228 ^ _779854) ^ [_973473, _973475, _973477] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_973473), hAPP(hAPP(c_Set_Oinsert(_973473), _973475), _973477))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973473), _973477)))], (10725 ^ _779854) ^ [_962684, _962686, _962688, _962690, _962692] : [c_Fun_Oinj__on(_962684, _962686, _962688, c_Orderings_Otop__class_Otop(tc_fun(_962684, tc_HOL_Obool))), hAPP(_962688, _962690) = hAPP(_962688, _962692), -(_962690 = _962692)], (49580 ^ _779854) ^ [_1780936, _1780938] : [-(c_Relation_Otrans(_1780936, c_Relation_OId__on(_1780936, _1780938)))], (25799 ^ _779854) ^ [_1248761, _1248763, _1248765, _1248767] : [-(c_Nitpick_Ofold__graph_H(_1248761, _1248763, _1248765, _1248767, c_Orderings_Obot__class_Obot(tc_fun(_1248761, tc_HOL_Obool)), _1248767))], (706 ^ _779854) ^ [_790499, _790501, _790503, _790505, _790507, _790509] : [-(c_List_Olist__ex1(_790507, _790503, _790499)), c_List_Olist__ex1(_790509, _790505, _790501), _790509 = _790507, _790505 = _790503, _790501 = _790499], (9360 ^ _779854) ^ [_935995, _935997, _935999] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_935995, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_935995, tc_HOL_Obool)), _935997), _935999)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_935995, tc_HOL_Obool)), _935997), c_Complete__Lattice_OInf__class_OInf(tc_fun(_935995, tc_HOL_Obool), _935999)))], (16477 ^ _779854) ^ [_1076428, _1076430, _1076432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076428), _1076430)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076430), _1076428)), _1076432) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076430), _1076432)), _1076428))], (31208 ^ _779854) ^ [_1342640] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1342640) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1342640))], (31015 ^ _779854) ^ [_1339623, _1339625] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1339623), _1339625) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1339623, _1339625)), _1339625))], (50487 ^ _779854) ^ [_1800231, _1800233, _1800235, _1800237, _1800239] : [c_Fun_Oinj__on(_1800231, _1800233, _1800235, _1800237), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800231, tc_HOL_Obool)), _1800239), _1800237)), -(hAPP(c_Set_Oimage(_1800233, _1800231, c_Hilbert__Choice_Oinv__into(_1800231, _1800233, _1800237, _1800235)), hAPP(c_Set_Oimage(_1800231, _1800233, _1800235), _1800239)) = _1800239)], (49070 ^ _779854) ^ [_1769142, _1769144, _1769146] : [_1769144 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1769142, _1769144, _1769146) = c_List_Olist_ONil(_1769142))], (28515 ^ _779854) ^ [_1295406] : [class_Rings_Osemiring__1(_1295406), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295406), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1295406))], (15332 ^ _779854) ^ [_1053344, _1053346, _1053348, _1053350] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1053344), 15335 ^ _779854 : [(15342 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053344), _1053348), _1053350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053344), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053344), _1053346), _1053348)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053344), _1053346), _1053350))))], (15336 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053344), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053344), _1053346), _1053348)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053344), _1053346), _1053350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053344), _1053348), _1053350)))]]], (52579 ^ _779854) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (40946 ^ _779854) ^ [_1579791, _1579793] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1579791, _1579791), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1579791, _1579793)), hAPP(hAPP(c_Product__Type_OSigma(_1579791, _1579791), hAPP(c_Relation_OField(_1579791), _1579793)), hAPP(c_COMBK(tc_fun(_1579791, tc_HOL_Obool), _1579791), hAPP(c_Relation_OField(_1579791), _1579793))))))], (18989 ^ _779854) ^ [_1122220, _1122222, _1122224] : [class_Rings_Olinordered__ring(_1122220), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122220), c_Groups_Ozero__class_Ozero(_1122220)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122220), _1122222), _1122222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122220), _1122224), _1122224)))))], (3784 ^ _779854) ^ [_836827, _836829] : [_836829 = _836827, -(c_Enum_Oenum__class_Oenum__ex(_836829) = c_Enum_Oenum__class_Oenum__ex(_836827))], (31069 ^ _779854) ^ [_1340427] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340427, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24462 ^ _779854) ^ [_1223661, _1223663, _1223665, _1223667, _1223669, _1223671, _1223673, _1223675] : [c_Finite__Set_Ofolding__image__simple__idem(_1223661, _1223663, _1223665, _1223667, _1223669, _1223671), hBOOL(hAPP(c_Finite__Set_Ofinite(_1223663), _1223673)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1223663), _1223675)), -(hAPP(_1223671, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1223663, tc_HOL_Obool)), _1223673), _1223675)) = hAPP(hAPP(_1223665, hAPP(_1223671, _1223673)), hAPP(_1223671, _1223675)))], (26001 ^ _779854) ^ [] : [-(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))))], (36042 ^ _779854) ^ [_1451774, _1451776, _1451778, _1451780, _1451782, _1451784] : [c_Finite__Set_Ofolding(_1451774, _1451776, _1451778, _1451780), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451774), _1451782)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451774), _1451784)), -(hAPP(c_Fun_Ocomp(_1451776, _1451776, _1451776, hAPP(_1451780, _1451784)), hAPP(_1451780, _1451782)) = hAPP(c_Fun_Ocomp(_1451776, _1451776, _1451776, hAPP(_1451780, _1451782)), hAPP(_1451780, _1451784)))], (11646 ^ _779854) ^ [_981783, _981785, _981787, _981789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981783, tc_HOL_Obool)), _981785), _981787)), hBOOL(hAPP(hAPP(c_member(_981783), _981789), _981785)), -(hBOOL(hAPP(hAPP(c_member(_981783), _981789), _981787)))], (15496 ^ _779854) ^ [_1056589, _1056591, _1056593, _1056595, _1056597] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1056589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056589), _1056591), _1056593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056589), _1056595), _1056597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056589), _1056591), _1056595)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056589), _1056593), _1056597))))], (33591 ^ _779854) ^ [_1396406, _1396408, _1396410, _1396412, _1396414, _1396416, _1396418] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396406, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396408, tc_fun(_1396406, tc_HOL_Obool)), _1396410), _1396412)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396414, tc_fun(_1396406, tc_HOL_Obool)), _1396416), _1396418)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396408, tc_fun(_1396406, tc_HOL_Obool)), _1396410), hAPP(hAPP(c_COMBB(tc_fun(_1396414, tc_fun(_1396406, tc_HOL_Obool)), tc_fun(_1396406, tc_HOL_Obool), _1396408), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396414, tc_fun(_1396406, tc_HOL_Obool)), _1396416)), hAPP(hAPP(c_COMBC(_1396408, tc_fun(_1396414, tc_fun(_1396406, tc_HOL_Obool)), tc_fun(_1396414, tc_fun(_1396406, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1396406, tc_HOL_Obool), tc_fun(_1396406, tc_HOL_Obool)), tc_fun(tc_fun(_1396414, tc_fun(_1396406, tc_HOL_Obool)), tc_fun(_1396414, tc_fun(_1396406, tc_HOL_Obool))), _1396408), c_COMBB(tc_fun(_1396406, tc_HOL_Obool), tc_fun(_1396406, tc_HOL_Obool), _1396414)), hAPP(hAPP(c_COMBB(tc_fun(_1396406, tc_HOL_Obool), tc_fun(tc_fun(_1396406, tc_HOL_Obool), tc_fun(_1396406, tc_HOL_Obool)), _1396408), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396406, tc_HOL_Obool))), _1396412))), _1396418))))], (8354 ^ _779854) ^ [_919561, _919563, _919565] : [class_Orderings_Olinorder(_919561), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919561), _919563), _919565))), -(_919563 = _919565), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919561), _919565), _919563)))], (29445 ^ _779854) ^ [_1311021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1311021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1311021)))], (43504 ^ _779854) ^ [_1646930, _1646932, _1646934, _1646936] : [_1646932 = c_List_Olist_ONil(_1646930), -(hAPP(hAPP(c_List_Olist__update(_1646930, _1646932), _1646934), _1646936) = c_List_Olist_ONil(_1646930))], (42070 ^ _779854) ^ [_1608699, _1608701, _1608703] : [-(c_Product__Type_Ointernal__split(_1608699, _1608701, _1608703) = c_Product__Type_Oprod_Oprod__case(_1608699, _1608701, _1608703))], (7081 ^ _779854) ^ [_895865, _895867, _895869, _895871] : [class_Lattices_Olattice(_895865), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895865), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895865), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895865), _895867), _895869)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895865), _895867), _895871))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_895865), _895867), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895865), _895869), _895871)))))], (14119 ^ _779854) ^ [_1029044, _1029046, _1029048, _1029050, _1029052, _1029054, _1029056] : [-(_1029044 = _1029046), -(c_Fun_Ofun__upd(_1029048, _1029050, c_Fun_Ofun__upd(_1029048, _1029050, _1029052, _1029044, _1029054), _1029046, _1029056) = c_Fun_Ofun__upd(_1029048, _1029050, c_Fun_Ofun__upd(_1029048, _1029050, _1029052, _1029046, _1029056), _1029044, _1029054))], (38779 ^ _779854) ^ [_1519641, _1519643] : [c_Orderings_Obot__class_Obot(tc_fun(_1519641, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1519641), _1519643), 38782 ^ _779854 : [(38783 ^ _779854) ^ [_1519726] : [hBOOL(hAPP(_1519643, _1519726))]]], (16814 ^ _779854) ^ [_1082986, _1082988, _1082990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082986), _1082988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1082990), _1082988))))], (31534 ^ _779854) ^ [_1348166, _1348168] : [c_Nat__Transfer_Ois__nat(_1348166), c_Nat__Transfer_Onat__set(_1348168), 31541 ^ _779854 : [(31548 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1348166)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1348168))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1348166), _1348168)))], (31542 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1348166), _1348168)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1348166)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1348168))))]]], (43606 ^ _779854) ^ [_1648946, _1648948, _1648950, _1648952] : [-(_1648946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1648948), _1648946), hAPP(hAPP(c_List_Olist_OCons(_1648948), _1648950), _1648952)) = hAPP(hAPP(c_List_Olist_OCons(_1648948), _1648950), hAPP(hAPP(c_List_Otake(_1648948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1648946), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1648952)))], (36987 ^ _779854) ^ [_1473633, _1473635] : [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)), _1473633), 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)), _1473635), 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)), _1473633), _1473635)), c_Int_Ointrel)))], (42382 ^ _779854) ^ [_1618740, _1618742, _1618744, _1618746] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618740), tc_List_Olist(_1618740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618740), tc_List_Olist(_1618740)), _1618742), _1618744)), c_List_Olistrel(_1618740, _1618746))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618740), tc_List_Olist(_1618740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618740), tc_List_Olist(_1618740)), _1618742), _1618744)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1618740), c_List_Olistrel1(_1618740, _1618746)))))], (7125 ^ _779854) ^ [_897009, _897011, _897013] : [class_Lattices_Osemilattice__sup(_897009), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897009), _897011), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897009), _897013), _897011))))], (14777 ^ _779854) ^ [_1041807, _1041809, _1041811] : [class_Orderings_Olinorder(_1041807), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041807), _1041809)), -(_1041809 = c_Orderings_Obot__class_Obot(tc_fun(_1041807, tc_HOL_Obool))), 14788 ^ _779854 : [(14789 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041807), _1041811), hAPP(c_Finite__Set_Ofold1(_1041807, c_Orderings_Oord__class_Omin(_1041807)), _1041809))), 14792 ^ _779854 : [(14793 ^ _779854) ^ [_1042100] : [hBOOL(hAPP(hAPP(c_member(_1041807), _1042100), _1041809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041807), _1041811), _1042100)))]]], (14799 ^ _779854) ^ [] : [14801 ^ _779854 : [(14804 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041807), _1041811), 14800 ^ [_1041807, _1041809, _1041811]))], (14802 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041807), 14800 ^ [_1041807, _1041809, _1041811]), _1041809)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041807), _1041811), hAPP(c_Finite__Set_Ofold1(_1041807, c_Orderings_Oord__class_Omin(_1041807)), _1041809))))]]], (8516 ^ _779854) ^ [_921978, _921980, _921982, _921984] : [class_Orderings_Opreorder(_921978), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921978), _921980), _921982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921978), _921982), _921984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921978), _921980), _921984)))], (16281 ^ _779854) ^ [_1072417, _1072419, _1072421, _1072423] : [class_Rings_Ocomm__semiring__1(_1072417), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072417), _1072419), _1072421)), _1072423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072417), _1072419), _1072423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072417), _1072421), _1072423)))], (23653 ^ _779854) ^ [_1208561] : [class_Lattices_Osemilattice__sup(_1208561), -(c_Finite__Set_Ofun__left__comm__idem(_1208561, _1208561, c_Lattices_Osemilattice__sup__class_Osup(_1208561)))], (41158 ^ _779854) ^ [_1585790, _1585792, _1585794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585790, _1585790), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585790, _1585790), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1585790, _1585792)), c_Transitive__Closure_Ortrancl(_1585790, _1585794))), c_Transitive__Closure_Ortrancl(_1585790, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585790, _1585790), tc_HOL_Obool)), _1585792), _1585794)))))], (52557 ^ _779854) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (2144 ^ _779854) ^ [_811091, _811093, _811095, _811097] : [-(c_Random_Olog(_811097, _811093) = c_Random_Olog(_811095, _811091)), _811097 = _811095, _811093 = _811091], (52421 ^ _779854) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (44424 ^ _779854) ^ [_1668486, _1668488, _1668490, _1668492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668486), _1668488)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668490)), _1668492))), -(hAPP(hAPP(c_List_Otake(_1668490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668486), _1668488)), _1668492) = hAPP(hAPP(c_List_Oappend(_1668490), hAPP(hAPP(c_List_Otake(_1668490), _1668486), _1668492)), hAPP(hAPP(c_List_Otake(_1668490), _1668488), hAPP(hAPP(c_List_Odrop(_1668490), _1668486), _1668492))))], (35101 ^ _779854) ^ [_1432851] : [-(c_Divides_Oadjust(_1432851) = 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)), _1432851))))), 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)), _1432851))))), 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))))))))], (43103 ^ _779854) ^ [_1638621, _1638623, _1638625, _1638627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638621), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638623)), _1638625))), 43106 ^ _779854 : [(43113 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Onth(_1638623), _1638625), _1638621) = _1638627, -(hAPP(hAPP(c_List_Olist__update(_1638623, _1638625), _1638621), _1638627) = _1638625)], (43107 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1638623, _1638625), _1638621), _1638627) = _1638625, -(hAPP(hAPP(c_List_Onth(_1638623), _1638625), _1638621) = _1638627)]]], (31798 ^ _779854) ^ [_1352044, _1352046, _1352048] : [class_Rings_Olinordered__idom(_1352044), 31801 ^ _779854 : [(31808 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352046), _1352048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352044), hAPP(c_Int_Oring__1__class_Oof__int(_1352044), _1352046)), hAPP(c_Int_Oring__1__class_Oof__int(_1352044), _1352048))))], (31802 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352044), hAPP(c_Int_Oring__1__class_Oof__int(_1352044), _1352046)), hAPP(c_Int_Oring__1__class_Oof__int(_1352044), _1352048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352046), _1352048)))]]], (46234 ^ _779854) ^ [_1707646, _1707648] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707646)), c_List_Oremdups(_1707646, c_List_Oconcat(_1707646, _1707648))) = hAPP(c_Finite__Set_Ocard(_1707646), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1707646), tc_fun(_1707646, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1707646)), _1707648)), c_List_Oset(_1707646))))], (44895 ^ _779854) ^ [_1678232, _1678234, _1678236] : [class_Orderings_Olinorder(_1678232), -(hAPP(c_List_Oset(_1678232), c_List_Olinorder__class_Oinsort__insert__key(_1678232, _1678232, c_COMBI(_1678232), _1678234, _1678236)) = hAPP(hAPP(c_Set_Oinsert(_1678232), _1678234), hAPP(c_List_Oset(_1678232), _1678236)))], (11069 ^ _779854) ^ [_970346, _970348] : [class_Orderings_Olinorder(_970346), hBOOL(hAPP(c_Finite__Set_Ofinite(_970346), _970348)), -(_970348 = c_Orderings_Obot__class_Obot(tc_fun(_970346, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970346), c_Big__Operators_Olattice_OInf__fin(_970346, c_Orderings_Oord__class_Omin(_970346), _970348)), c_Big__Operators_Olattice_OSup__fin(_970346, c_Orderings_Oord__class_Omax(_970346), _970348))))], (1120 ^ _779854) ^ [_796806, _796808] : [-(class_Lattices_Obounded__lattice(_796806)), _796808 = _796806, class_Lattices_Obounded__lattice(_796808)], (42980 ^ _779854) ^ [_1635907, _1635909, _1635911] : [class_Groups_Omonoid__add(_1635907), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1635907), hAPP(hAPP(c_List_Olist_OCons(_1635907), _1635909), _1635911)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1635907), _1635909), hAPP(c_List_Omonoid__add__class_Olistsum(_1635907), _1635911)))], (51587 ^ _779854) ^ [_1824196, _1824198, _1824200] : [class_Divides_Oring__div(_1824196), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824196), _1824198), _1824200)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824196), hAPP(c_Groups_Ouminus__class_Ouminus(_1824196), _1824200)), _1824198) = hAPP(c_Groups_Ouminus__class_Ouminus(_1824196), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824196), _1824200), _1824198)))], (44644 ^ _779854) ^ [_1673043, _1673045] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1673043), _1673045) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44647 ^ _779854 : [(44650 ^ _779854) ^ [_1673157] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673157), hAPP(c_List_Oset(tc_Nat_Onat), _1673045))), -(_1673157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44648 ^ _779854) ^ [] : [-(_1673043 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1850 ^ _779854) ^ [_805931, _805933] : [-(class_Rings_Osemiring(_805931)), _805933 = _805931, class_Rings_Osemiring(_805933)], (47456 ^ _779854) ^ [_1734066, _1734068, _1734070, _1734072] : [hAPP(c_List_Orev(_1734066), _1734068) = hAPP(hAPP(c_List_Olist_OCons(_1734066), _1734070), _1734072), -(_1734068 = hAPP(hAPP(c_List_Oappend(_1734066), hAPP(c_List_Orev(_1734066), _1734072)), hAPP(hAPP(c_List_Olist_OCons(_1734066), _1734070), c_List_Olist_ONil(_1734066))))], (47951 ^ _779854) ^ [_1744450, _1744452, _1744454] : [hBOOL(hAPP(c_List_Odistinct(_1744450), _1744452)), -(hBOOL(hAPP(c_List_Odistinct(_1744450), c_List_Oinsert(_1744450, _1744454, _1744452))))], (44272 ^ _779854) ^ [_1664874, _1664876] : [-(hAPP(c_List_Oset(_1664874), hAPP(c_List_Orotate1(_1664874), _1664876)) = hAPP(c_List_Oset(_1664874), _1664876))], (48135 ^ _779854) ^ [_1748741, _1748743, _1748745, _1748747, _1748749] : [48136 ^ _779854 : [(48139 ^ _779854) ^ [] : [hBOOL(hAPP(_1748749, hAPP(hAPP(c_List_Ozip(_1748741, _1748745), hAPP(hAPP(c_List_Otake(_1748741), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748741)), _1748743)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748745)), _1748747))), _1748743)), hAPP(hAPP(c_List_Otake(_1748745), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748741)), _1748743)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748745)), _1748747))), _1748747))))], (48137 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748741)), hAPP(hAPP(c_List_Otake(_1748741), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748741)), _1748743)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748745)), _1748747))), _1748743)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748745)), hAPP(hAPP(c_List_Otake(_1748745), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748741)), _1748743)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748745)), _1748747))), _1748747)))]], -(hBOOL(hAPP(_1748749, hAPP(hAPP(c_List_Ozip(_1748741, _1748745), _1748743), _1748747))))], (44354 ^ _779854) ^ [_1666685, _1666687, _1666689, _1666691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666685), _1666687)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666689)), _1666691))), -(hAPP(hAPP(c_List_Onth(_1666689), hAPP(hAPP(c_List_Odrop(_1666689), _1666685), _1666691)), _1666687) = hAPP(hAPP(c_List_Onth(_1666689), _1666691), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666685), _1666687)))], (50503 ^ _779854) ^ [_1800565, _1800567, _1800569, _1800571, _1800573, _1800575, _1800577] : [c_Fun_Oinj__on(_1800565, _1800567, _1800569, hAPP(c_Set_Oimage(_1800571, _1800565, _1800573), _1800575)), c_Fun_Oinj__on(_1800571, _1800565, _1800573, _1800575), hBOOL(hAPP(hAPP(c_member(_1800567), _1800577), hAPP(c_Set_Oimage(_1800565, _1800567, _1800569), hAPP(c_Set_Oimage(_1800571, _1800565, _1800573), _1800575)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1800571, _1800567, _1800575, hAPP(c_Fun_Ocomp(_1800565, _1800567, _1800571, _1800569), _1800573)), _1800577) = hAPP(hAPP(c_Fun_Ocomp(_1800565, _1800571, _1800567, c_Hilbert__Choice_Oinv__into(_1800571, _1800565, _1800575, _1800573)), c_Hilbert__Choice_Oinv__into(_1800565, _1800567, hAPP(c_Set_Oimage(_1800571, _1800565, _1800573), _1800575), _1800569)), _1800577))], (2610 ^ _779854) ^ [_818526, _818528, _818530, _818532, _818534, _818536, _818538, _818540] : [-(c_Nitpick_Oprod(_818540, _818536, _818532, _818528) = c_Nitpick_Oprod(_818538, _818534, _818530, _818526)), _818540 = _818538, _818536 = _818534, _818532 = _818530, _818528 = _818526], (31458 ^ _779854) ^ [_1346886, _1346888] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1346886))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1346888)) = 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)))), _1346886), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1346888)))], (18088 ^ _779854) ^ [_1107105, _1107107, _1107109] : [class_Rings_Olinordered__semidom(_1107105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107105), c_Groups_Oone__class_Oone(_1107105)), _1107107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107105), c_Groups_Oone__class_Oone(_1107105)), _1107109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107105), c_Groups_Oone__class_Oone(_1107105)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107105), _1107107), _1107109))))], (48900 ^ _779854) ^ [_1765423, _1765425, _1765427, _1765429] : [-(c_Predicate_Oconversep(_1765423, _1765425, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1765423, tc_fun(_1765425, tc_HOL_Obool))), _1765427), _1765429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1765425, tc_fun(_1765423, tc_HOL_Obool))), c_Predicate_Oconversep(_1765423, _1765425, _1765427)), c_Predicate_Oconversep(_1765423, _1765425, _1765429)))], (40902 ^ _779854) ^ [_1578834, _1578836] : [-(c_Wellfounded_Owf(_1578834, _1578836)), 40905 ^ _779854 : [(40908 ^ _779854) ^ [_1579054] : [hBOOL(hAPP(hAPP(c_member(_1578834), _1579054), 40903 ^ [_1578834, _1578836])), 40912 ^ _779854 : [(40915 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578834), 40911 ^ [_1578834, _1578836, _1579054]), 40903 ^ [_1578834, _1578836])))], (40913 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578834, _1578834)), hAPP(hAPP(c_Product__Type_OPair(_1578834, _1578834), 40911 ^ [_1578834, _1578836, _1579054]), _1579054)), _1578836)))]]], (40906 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578834), 40904 ^ [_1578834, _1578836]), 40903 ^ [_1578834, _1578836])))]]], (28298 ^ _779854) ^ [_1291562, _1291564] : [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)), _1291562)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1291564))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1291562), _1291564)))], (44410 ^ _779854) ^ [_1668193, _1668195, _1668197, _1668199] : [-(hAPP(c_List_Orotate1(_1668195), hAPP(hAPP(c_List_Olist_OCons(_1668195), _1668197), _1668199)) = hAPP(hAPP(c_List_Oappend(_1668195), _1668199), hAPP(hAPP(c_List_Olist_OCons(_1668195), _1668197), c_List_Olist_ONil(_1668195))))], (9764 ^ _779854) ^ [_943611, _943613, _943615, _943617] : [class_Orderings_Olinorder(_943611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943611), _943613), _943615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943611), _943613), hAPP(hAPP(c_Orderings_Oord__class_Omax(_943611), _943615), _943617))))], (51056 ^ _779854) ^ [_1812145, _1812147, _1812149, _1812151] : [-(c_Product__Type_Ocurry(_1812145, _1812147, _1812149, hAPP(c_Product__Type_Oprod_Oprod__case(_1812145, _1812147, _1812149), _1812151)) = _1812151)], (38843 ^ _779854) ^ [_1521025, _1521027, _1521029] : [-(hBOOL(hAPP(_1521025, _1521027))), -(hAPP(c_Set_OCollect(_1521029), hAPP(hAPP(c_COMBS(_1521029, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521029), c_fconj), hAPP(hAPP(c_COMBC(_1521029, _1521029, tc_HOL_Obool), c_fequal), _1521027))), _1521025)) = c_Orderings_Obot__class_Obot(tc_fun(_1521029, tc_HOL_Obool)))], (50497 ^ _779854) ^ [_1800434, _1800436, _1800438, _1800440, _1800442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800434, tc_HOL_Obool)), _1800436), hAPP(c_Set_Oimage(_1800438, _1800434, _1800440), _1800442))), -(c_Fun_Oinj__on(_1800434, _1800438, c_Hilbert__Choice_Oinv__into(_1800438, _1800434, _1800442, _1800440), _1800436))], (45899 ^ _779854) ^ [_1700607, _1700609, _1700611] : [c_List_Olist__all2(_1700611, _1700611, c_fequal, _1700607, _1700609), -(_1700607 = _1700609)], (44945 ^ _779854) ^ [_1679070, _1679072, _1679074] : [_1679070 = c_List_Olist_ONil(_1679072), -(c_List_Olast(_1679072, hAPP(hAPP(c_List_Olist_OCons(_1679072), _1679074), _1679070)) = _1679074)], (18339 ^ _779854) ^ [_1111720, _1111722, _1111724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111720), _1111722)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1111724), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1111722), _1111720))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111724), _1111720)), hAPP(c_Nat_OSuc, _1111722)))], (37107 ^ _779854) ^ [_1476698] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1476698) = 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), _1476698), 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))))))], (9887 ^ _779854) ^ [_946335, _946337] : [class_Orderings_Olinorder(_946335), -(c_Big__Operators_Olattice_OSup__fin(_946335, c_Orderings_Oord__class_Omax(_946335), hAPP(hAPP(c_Set_Oinsert(_946335), _946337), c_Orderings_Obot__class_Obot(tc_fun(_946335, tc_HOL_Obool)))) = _946337)], (40694 ^ _779854) ^ [_1573671, _1573673] : [class_Complete__Lattice_Ocomplete__lattice(_1573671), c_Orderings_Oorder__class_Omono(_1573671, _1573671, _1573673), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1573671, _1573673) = hAPP(_1573673, c_Inductive_Ocomplete__lattice__class_Olfp(_1573671, _1573673)))], (51543 ^ _779854) ^ [_1823457, _1823459] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1823457), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823459))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823457), _1823459)))], (49224 ^ _779854) ^ [_1772428, _1772430, _1772432, _1772434, _1772436, _1772438] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1772428, _1772430, _1772432, _1772434, c_Lazy__Sequence_Olazy__sequence_OInsert(_1772430, _1772436, _1772438)) = hAPP(hAPP(_1772434, _1772436), _1772438))], (44793 ^ _779854) ^ [_1676358, _1676360, _1676362, _1676364, _1676366] : [class_Orderings_Olinorder(_1676358), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676360)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676360, _1676358, _1676362), _1676364), _1676366)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676360)), _1676366)))], (6549 ^ _779854) ^ [_884656, _884658] : [class_Orderings_Olinorder(_884656), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_884656, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_884656), _884658)) = hAPP(c_SetInterval_Oord__class_OlessThan(_884656), _884658))], (36832 ^ _779854) ^ [_1469203] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1469203)), -(_1469203 = 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))), _1469203)), c_FunDef_Omax__strict)))], (47346 ^ _779854) ^ [_1731664, _1731666] : [_1731666 = c_List_Olist_ONil(_1731664), -(hAPP(c_List_Orev(_1731664), _1731666) = c_List_Olist_ONil(_1731664))], (31629 ^ _779854) ^ [_1349633, _1349635] : [c_Nat__Transfer_Ois__nat(_1349633), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1349633), _1349635)))], (18419 ^ _779854) ^ [_1113451] : [-(hAPP(c_Nat_OSuc, _1113451) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113451), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (33090 ^ _779854) ^ [_1379351, _1379353, _1379355, _1379357, _1379359] : [_1379351 = c_Orderings_Obot__class_Obot(tc_fun(_1379353, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379355, tc_HOL_Obool)), _1379357), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379353, tc_fun(_1379355, tc_HOL_Obool)), _1379351), _1379359)) = _1379357)], (38867 ^ _779854) ^ [_1521555, _1521557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521555), hAPP(c_Set_OCollect(_1521555), _1521557))), 38870 ^ _779854 : [(38877 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521555), c_Orderings_Otop__class_Otop(tc_fun(_1521555, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521555), hAPP(c_Set_OCollect(_1521555), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1521555), c_fNot), _1521557)))))], (38871 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521555), hAPP(c_Set_OCollect(_1521555), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1521555), c_fNot), _1521557)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521555), c_Orderings_Otop__class_Otop(tc_fun(_1521555, tc_HOL_Obool)))))]]], (6955 ^ _779854) ^ [_893450, _893452, _893454, _893456] : [class_Lattices_Osemilattice__inf(_893450), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893450), _893452), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893450), _893454), _893456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893450), _893454), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_893450), _893452), _893456)))], (18963 ^ _779854) ^ [_1121838] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1121838), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (31244 ^ _779854) ^ [_1343178, _1343180] : [class_Int_Onumber__ring(_1343178), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343178), _1343180), hAPP(c_Int_Onumber__class_Onumber__of(_1343178), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1343178), _1343180))], (11378 ^ _779854) ^ [_976299, _976301, _976303, _976305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976299, tc_HOL_Obool)), _976301), hAPP(hAPP(c_Set_Oinsert(_976299), _976303), _976305)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976299, tc_HOL_Obool)), _976301), _976305))))], (41732 ^ _779854) ^ [_1599687, _1599689, _1599691] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599687, _1599687)), _1599689), c_Transitive__Closure_Ortrancl(_1599687, _1599691))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599687, _1599687)), _1599689), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1599687, _1599687), 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(_1599687, _1599687), tc_HOL_Obool), tc_fun(tc_prod(_1599687, _1599687), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1599687, _1599687), tc_HOL_Obool)), _1599691)))))], (7658 ^ _779854) ^ [_906914, _906916, _906918] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906914, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906914, tc_HOL_Obool)), _906916), _906918)), _906916)))], (25943 ^ _779854) ^ [_1251348, _1251350, _1251352, _1251354, _1251356] : [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), _1251348), _1251350)), _1251352)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251348), _1251354)), _1251356))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251352), _1251348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251356), _1251348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251350), _1251354)))], (36665 ^ _779854) ^ [_1465540, _1465542, _1465544, _1465546, _1465548, _1465550] : [c_Finite__Set_Ofolding__idem(_1465540, _1465542, _1465544, _1465546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465540), _1465548)), -(hAPP(_1465546, hAPP(hAPP(c_Set_Oinsert(_1465540), _1465550), _1465548)) = hAPP(c_Fun_Ocomp(_1465542, _1465542, _1465542, hAPP(_1465546, _1465548)), hAPP(_1465544, _1465550)))], (22813 ^ _779854) ^ [_1192137, _1192139, _1192141, _1192143] : [class_Fields_Olinordered__field(_1192137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192137), c_Groups_Ozero__class_Ozero(_1192137)), _1192139)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192137), _1192141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192137), _1192143), _1192139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192137), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192137), _1192141), _1192139)), _1192143)))], (20192 ^ _779854) ^ [_1143733] : [_1143733 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143733), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (15414 ^ _779854) ^ [_1054920, _1054922, _1054924] : [class_Groups_Ogroup__add(_1054920), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054920), hAPP(c_Groups_Ouminus__class_Ouminus(_1054920), _1054922)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054920), _1054922), _1054924)) = _1054924)], (27409 ^ _779854) ^ [_1276475, _1276477] : [class_Int_Onumber__ring(_1276475), 27412 ^ _779854 : [(27419 ^ _779854) ^ [] : [c_Int_Oiszero(_1276475, hAPP(c_Int_Onumber__class_Onumber__of(_1276475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1276477)))), -(c_Groups_Ozero__class_Ozero(_1276475) = hAPP(c_Int_Onumber__class_Onumber__of(_1276475), _1276477))], (27413 ^ _779854) ^ [] : [c_Groups_Ozero__class_Ozero(_1276475) = hAPP(c_Int_Onumber__class_Onumber__of(_1276475), _1276477), -(c_Int_Oiszero(_1276475, hAPP(c_Int_Onumber__class_Onumber__of(_1276475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1276477)))))]]], (43933 ^ _779854) ^ [_1656617, _1656619, _1656621] : [_1656619 = c_List_Olist_ONil(_1656617), -(hAPP(hAPP(c_List_Oappend(_1656617), _1656619), _1656621) = _1656621)], (30418 ^ _779854) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (50004 ^ _779854) ^ [_1790605, _1790607, _1790609, _1790611, _1790613, _1790615] : [-(c_Partial__Function_Ofun__lub(_1790605, _1790607, _1790609, _1790611, _1790613, _1790615) = hAPP(_1790611, hAPP(c_Set_OCollect(_1790605), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1790609, _1790605), tc_HOL_Obool), tc_HOL_Obool, _1790605), c_HOL_OEx(tc_fun(_1790609, _1790605))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1790609, _1790605), tc_HOL_Obool), tc_fun(tc_fun(_1790609, _1790605), tc_HOL_Obool), _1790605), hAPP(c_COMBS(tc_fun(_1790609, _1790605), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1790609, _1790605)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1790609, _1790605), tc_fun(tc_fun(_1790609, _1790605), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1790609, _1790605))), _1790613)))), hAPP(hAPP(c_COMBC(_1790605, tc_fun(tc_fun(_1790609, _1790605), _1790605), tc_fun(tc_fun(_1790609, _1790605), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1790605, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1790609, _1790605), _1790605), tc_fun(tc_fun(_1790609, _1790605), tc_HOL_Obool)), _1790605), c_COMBB(_1790605, tc_HOL_Obool, tc_fun(_1790609, _1790605))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1790609, _1790605), _1790609, _1790605), c_COMBI(tc_fun(_1790609, _1790605))), _1790615)))))))], (23079 ^ _779854) ^ [_1197066, _1197068, _1197070, _1197072] : [class_Fields_Olinordered__field__inverse__zero(_1197066), 23082 ^ _779854 : [(23083 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), _1197068), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1197066), _1197070), _1197072))), 23086 ^ _779854 : [(23093 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), c_Groups_Ozero__class_Ozero(_1197066)), _1197072))), 23096 ^ _779854 : [(23103 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), _1197072), c_Groups_Ozero__class_Ozero(_1197066)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), _1197068), c_Groups_Ozero__class_Ozero(_1197066))))], (23097 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), _1197072), c_Groups_Ozero__class_Ozero(_1197066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), _1197070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197066), _1197068), _1197072))))]]], (23087 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), c_Groups_Ozero__class_Ozero(_1197066)), _1197072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197066), _1197068), _1197072)), _1197070)))]]], (23109 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), _1197068), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1197066), _1197070), _1197072)))), 23112 ^ _779854 : [(23115 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197066), _1197068), _1197072)), _1197070))], (23113 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), c_Groups_Ozero__class_Ozero(_1197066)), _1197072)))]], 23116 ^ _779854 : [(23119 ^ _779854) ^ [] : [23120 ^ _779854 : [(23123 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), _1197070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197066), _1197068), _1197072)))], (23121 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), _1197072), c_Groups_Ozero__class_Ozero(_1197066))))]], 23124 ^ _779854 : [(23127 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197066), _1197068), c_Groups_Ozero__class_Ozero(_1197066)))], (23125 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), _1197072), c_Groups_Ozero__class_Ozero(_1197066)))]]], (23117 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1197066), c_Groups_Ozero__class_Ozero(_1197066)), _1197072))]]]]], (30430 ^ _779854) ^ [_1329278, _1329280] : [c_Nat__Transfer_Onat__set(_1329278), c_Nat__Transfer_Onat__set(_1329280), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1329278), _1329280)))], (33363 ^ _779854) ^ [_1386562, _1386564, _1386566, _1386568, _1386570, _1386572] : [-(_1386562 = _1386564), -(hAPP(c_Fun_Ofun__upd(_1386566, _1386568, _1386570, _1386564, _1386572), _1386562) = hAPP(_1386570, _1386562))], (35012 ^ _779854) ^ [_1431023, _1431025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431023)), _1431025)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1431023), _1431025)))], (16211 ^ _779854) ^ [_1070997, _1070999] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070997), _1070999))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070997), _1070999)) = _1070997)], (7003 ^ _779854) ^ [_894504, _894506, _894508] : [class_Lattices_Osemilattice__inf(_894504), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894504), _894506), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894504), _894506), _894508)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_894504), _894506), _894508))], (39341 ^ _779854) ^ [_1539327, _1539329] : [-(c_Product__Type_Omap__pair(_1539327, _1539327, _1539329, _1539329, c_COMBI(_1539327), c_COMBI(_1539329)) = c_Fun_Oid(tc_prod(_1539327, _1539329)))], (27797 ^ _779854) ^ [_1282762, _1282764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1282762)), 27800 ^ _779854 : [(27807 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1282764), _1282762))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1282764), _1282762) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1282764), _1282762)), _1282762)))], (27801 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1282764), _1282762)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1282764), _1282762) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (28886 ^ _779854) ^ [_1301561] : [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), _1301561))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1301561)))], (29019 ^ _779854) ^ [_1303680, _1303682] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1303680)))), _1303682) = 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)))), _1303680)), _1303682))], (29999 ^ _779854) ^ [_1320637, _1320639, _1320641] : [class_Rings_Olinordered__idom(_1320637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320637), hAPP(hAPP(c_Power_Opower__class_Opower(_1320637), _1320639), 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(_1320637), _1320641), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1320637)))], (21462 ^ _779854) ^ [_1166709, _1166711, _1166713, _1166715, _1166717] : [class_Groups_Ocomm__monoid__add(_1166709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166711), _1166713)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166711), _1166715)), 21476 ^ _779854 : [(21479 ^ _779854) ^ [] : [hAPP(_1166717, 21475 ^ [_1166709, _1166711, _1166713, _1166715, _1166717]) = c_Groups_Ozero__class_Ozero(_1166709)], (21477 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1166711), 21475 ^ [_1166709, _1166711, _1166713, _1166715, _1166717]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1166711, tc_HOL_Obool)), _1166713), _1166715))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1166711, _1166709), _1166717), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1166711, tc_HOL_Obool)), _1166713), _1166715)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166709), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1166711, _1166709), _1166717), _1166713)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1166711, _1166709), _1166717), _1166715)))], (14646 ^ _779854) ^ [_1039464, _1039466] : [class_Orderings_Olinorder(_1039464), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039464), _1039466)), -(c_Big__Operators_Olattice_OSup__fin(_1039464, c_Orderings_Oord__class_Omax(_1039464), _1039466) = hAPP(c_Finite__Set_Ofold1(_1039464, c_Orderings_Oord__class_Omax(_1039464)), _1039466))], (42476 ^ _779854) ^ [_1621839, _1621841, _1621843] : [c_Equiv__Relations_Oequiv(_1621839, _1621841, _1621843), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1621839), c_List_Olists(_1621839, _1621841), c_List_Olistrel(_1621839, _1621843)))], (39665 ^ _779854) ^ [_1549310, _1549312, _1549314] : [c_Wellfounded_Owf(_1549310, _1549312), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549310, _1549310), tc_HOL_Obool)), _1549314), _1549312)), -(c_Wellfounded_Owf(_1549310, _1549314))], (11658 ^ _779854) ^ [_982005, _982007, _982009, _982011, _982013, _982015] : [_982005 = hAPP(_982007, _982009), hBOOL(hAPP(hAPP(c_member(_982011), _982009), _982013)), -(hBOOL(hAPP(hAPP(c_member(_982015), _982005), hAPP(c_Set_Oimage(_982011, _982015, _982007), _982013))))], (6283 ^ _779854) ^ [_879646, _879648, _879650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879646, tc_HOL_Obool)), _879648), _879650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_879646, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_879646), _879648)), hAPP(c_Set_OPow(_879646), _879650))))], (48932 ^ _779854) ^ [_1766726, _1766728, _1766730] : [-(hAPP(c_List_Orev(_1766726), c_List_Oreplicate(_1766726, _1766728, _1766730)) = c_List_Oreplicate(_1766726, _1766728, _1766730))], (34033 ^ _779854) ^ [_1408764, _1408766, _1408768] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408764, tc_Nat_Onat), _1408766), _1408768) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408764, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1408764), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1408766)), _1408768)))], (34703 ^ _779854) ^ [_1424650, _1424652] : [-(c_Divides_OnegDivAlg(_1424650, _1424652) = hAPP(c_Divides_Oadjust(_1424652), c_Divides_OnegDivAlg(_1424650, 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)))), _1424652)))), -(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), _1424650), _1424652)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424652), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44572 ^ _779854) ^ [_1671432, _1671434, _1671436] : [-(hAPP(c_List_Otl(_1671432), hAPP(hAPP(c_List_Oappend(_1671432), _1671434), _1671436)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1671432), _1671432, hAPP(c_List_Otl(_1671432), _1671436), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1671432), tc_List_Olist(_1671432)), _1671432), hAPP(hAPP(c_COMBC(tc_List_Olist(_1671432), tc_List_Olist(_1671432), tc_List_Olist(_1671432)), c_List_Oappend(_1671432)), _1671436))), _1671434))], (2052 ^ _779854) ^ [_809705, _809707, _809709, _809711] : [-(c_SMT_Oz3div(_809711, _809707) = c_SMT_Oz3div(_809709, _809705)), _809711 = _809709, _809707 = _809705], (20666 ^ _779854) ^ [_1151626, _1151628, _1151630, _1151632, _1151634] : [class_Rings_Olinordered__semiring__strict(_1151626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151626), _1151628), _1151630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151626), _1151632), _1151634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151626), c_Groups_Ozero__class_Ozero(_1151626)), _1151630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151626), c_Groups_Ozero__class_Ozero(_1151626)), _1151632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151626), _1151628), _1151632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151626), _1151630), _1151634))))], (18813 ^ _779854) ^ [_1119596, _1119598] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119596), _1119598) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18816 ^ _779854 : [(18819 ^ _779854) ^ [] : [-(_1119598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18817 ^ _779854) ^ [] : [-(_1119596 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25911 ^ _779854) ^ [_1250826] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1250826) = _1250826)], (46494 ^ _779854) ^ [_1713972, _1713974, _1713976, _1713978, _1713980] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713972)), hAPP(c_List_Ofilter(_1713972, _1713974), hAPP(hAPP(c_List_Omap(_1713976, _1713972), _1713978), _1713980))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713976)), hAPP(c_List_Ofilter(_1713976, hAPP(c_Fun_Ocomp(_1713972, tc_HOL_Obool, _1713976, _1713974), _1713978)), _1713980)))], (25405 ^ _779854) ^ [_1241639, _1241641, _1241643, _1241645, _1241647, _1241649, _1241651, _1241653] : [c_Finite__Set_Ofolding__image__simple__idem(_1241639, _1241641, _1241643, _1241645, _1241647, _1241649), hBOOL(hAPP(c_Finite__Set_Ofinite(_1241641), _1241651)), hBOOL(hAPP(hAPP(c_member(_1241641), _1241653), _1241651)), -(hAPP(hAPP(_1241643, hAPP(_1241647, _1241653)), hAPP(_1241649, _1241651)) = hAPP(_1241649, _1241651))], (17428 ^ _779854) ^ [_1094921, _1094923, _1094925, _1094927, _1094929, _1094931] : [c_Finite__Set_Ofun__left__comm(_1094921, _1094923, _1094925), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1094921, _1094923, _1094925, _1094927, _1094929), _1094931)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1094921, _1094923, _1094925), _1094927), _1094929) = _1094931)], (23525 ^ _779854) ^ [_1205933, _1205935] : [class_Rings_Olinordered__idom(_1205933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205933), c_Groups_Ozero__class_Ozero(_1205933)), _1205935)), -(c_Groups_Osgn__class_Osgn(_1205933, _1205935) = c_Groups_Oone__class_Oone(_1205933))], (7395 ^ _779854) ^ [_901714, _901716, _901718, _901720] : [class_Lattices_Osemilattice__inf(_901714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901714), _901716), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_901714), _901718), _901720))), 7402 ^ _779854 : [(7405 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901714), _901716), _901720)))], (7403 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901714), _901716), _901718)))]]], (52689 ^ _779854) ^ [_1838953, _1838955] : [hBOOL(_1838953), -(hBOOL(hAPP(hAPP(c_fdisj, _1838953), _1838955)))], (32547 ^ _779854) ^ [_1365757, _1365759, _1365761] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365757, _1365759) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1365761, _1365759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1365761), _1365757)), -(_1365757 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1365761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1365759), 32554 ^ [_1365757, _1365759, _1365761])))], (39639 ^ _779854) ^ [_1548837, _1548839] : [-(c_Wellfounded_Owf(_1548837, hAPP(c_Wellfounded_Omeasure(_1548837), _1548839)))], (17919 ^ _779854) ^ [_1104222, _1104224] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104222)), _1104224) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1104222), hAPP(c_Nat_OSuc, _1104224)))], (26169 ^ _779854) ^ [_1255453, _1255455, _1255457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255453)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1255455), _1255457)), 26176 ^ _779854 : [(26177 ^ _779854) ^ [_1255649] : [26179 ^ _779854 : [(26185 ^ _779854) ^ [] : [-(_1255649 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26181 ^ [_1255453, _1255455, _1255457, _1255649]), 26178 ^ [_1255453, _1255455, _1255457, _1255649]))], (26183 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26181 ^ [_1255453, _1255455, _1255457, _1255649]), _1255457)))], (26180 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26178 ^ [_1255453, _1255455, _1255457, _1255649]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1255453))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255649), _1255455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1255649), _1255453)), _1255455)))]]], (44248 ^ _779854) ^ [_1664264, _1664266, _1664268] : [hBOOL(hAPP(c_List_Odistinct(_1664264), _1664266)), -(hBOOL(hAPP(c_List_Odistinct(_1664264), hAPP(hAPP(c_List_Odrop(_1664264), _1664268), _1664266))))], (30519 ^ _779854) ^ [_1330949, _1330951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330949), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30522 ^ _779854 : [(30525 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330949), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330951, _1330949))))], (30523 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330951, _1330949)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30450 ^ _779854) ^ [_1329582] : [30452 ^ _779854 : [(30455 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30451 ^ [_1329582]))], (30453 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30451 ^ [_1329582]), _1329582)))]], -(c_Nat__Transfer_Onat__set(_1329582))], (35272 ^ _779854) ^ [_1437068, _1437070] : [-(c_Divides_Odivmod__nat(_1437070, _1437068) = 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), _1437070), _1437068), _1437068))), -(_1437068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1437070), _1437068)))], (32121 ^ _779854) ^ [_1357664, _1357666] : [class_Groups_Oordered__ab__group__add__abs(_1357664), 32124 ^ _779854 : [(32131 ^ _779854) ^ [] : [-(_1357666 = c_Groups_Ozero__class_Ozero(_1357664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357664), c_Groups_Ozero__class_Ozero(_1357664)), hAPP(c_Groups_Oabs__class_Oabs(_1357664), _1357666))))], (32125 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357664), c_Groups_Ozero__class_Ozero(_1357664)), hAPP(c_Groups_Oabs__class_Oabs(_1357664), _1357666))), _1357666 = c_Groups_Ozero__class_Ozero(_1357664)]]], (33228 ^ _779854) ^ [_1382408, _1382410, _1382412, _1382414] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1382408, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382410, tc_fun(_1382408, tc_HOL_Obool)), _1382412), _1382414)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382410, tc_fun(_1382408, tc_HOL_Obool)), _1382412), hAPP(hAPP(c_COMBB(tc_fun(_1382408, tc_HOL_Obool), tc_fun(_1382408, tc_HOL_Obool), _1382410), c_Groups_Ouminus__class_Ouminus(tc_fun(_1382408, tc_HOL_Obool))), _1382414)))], (23952 ^ _779854) ^ [_1214306, _1214308, _1214310] : [class_Groups_Omonoid__mult(_1214306), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214306), hAPP(hAPP(c_Power_Opower__class_Opower(_1214306), _1214308), _1214310)), _1214308) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214306), _1214308), hAPP(hAPP(c_Power_Opower__class_Opower(_1214306), _1214308), _1214310)))], (48892 ^ _779854) ^ [_1765257, _1765259, _1765261, _1765263, _1765265] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1765257, _1765259, _1765261), _1765263), _1765265)), -(hBOOL(hAPP(hAPP(_1765261, _1765265), _1765263)))], (51825 ^ _779854) ^ [_1828328, _1828330, _1828332] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828328), _1828330)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828330), _1828328))), 51840 ^ _779854 : [(51843 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828332), _1828328))], (51841 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828328), _1828332)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828330), _1828332)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828332), _1828330)))], (18865 ^ _779854) ^ [_1120365, _1120367, _1120369] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120365), _1120367) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1120369), _1120367), -(_1120365 = _1120369), -(_1120367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39242 ^ _779854) ^ [_1535192, _1535194, _1535196] : [class_Orderings_Olinorder(_1535192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535192), _1535194)), -(_1535194 = c_Orderings_Obot__class_Obot(tc_fun(_1535192, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535192), _1535196)), -(_1535196 = c_Orderings_Obot__class_Obot(tc_fun(_1535192, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1535192), c_Big__Operators_Olattice_OInf__fin(_1535192, c_Orderings_Oord__class_Omin(_1535192), _1535194)), c_Big__Operators_Olattice_OInf__fin(_1535192, c_Orderings_Oord__class_Omin(_1535192), _1535196)) = c_Big__Operators_Olattice_OInf__fin(_1535192, c_Orderings_Oord__class_Omin(_1535192), hAPP(c_Set_OCollect(_1535192), hAPP(hAPP(c_COMBB(tc_fun(_1535192, tc_HOL_Obool), tc_HOL_Obool, _1535192), c_HOL_OEx(_1535192)), hAPP(hAPP(c_COMBB(tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool)), tc_fun(_1535192, tc_HOL_Obool), _1535192), hAPP(c_COMBB(tc_fun(_1535192, tc_HOL_Obool), tc_HOL_Obool, _1535192), c_HOL_OEx(_1535192))), hAPP(hAPP(c_COMBC(_1535192, tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool)), tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535192, tc_fun(tc_fun(_1535192, tc_HOL_Obool), tc_fun(_1535192, tc_HOL_Obool))), tc_fun(tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool)), tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool))), _1535192), c_COMBS(_1535192, tc_fun(_1535192, tc_HOL_Obool), tc_fun(_1535192, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535192, tc_fun(_1535192, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1535192, tc_fun(tc_fun(_1535192, tc_HOL_Obool), tc_fun(_1535192, tc_HOL_Obool))), _1535192), hAPP(c_COMBB(tc_fun(_1535192, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1535192, tc_HOL_Obool), tc_fun(_1535192, tc_HOL_Obool)), _1535192), c_COMBS(_1535192, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool)), tc_fun(_1535192, tc_fun(_1535192, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1535192), hAPP(c_COMBB(tc_fun(_1535192, tc_HOL_Obool), tc_fun(_1535192, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1535192), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535192), c_fconj))), hAPP(hAPP(c_COMBC(_1535192, tc_fun(_1535192, tc_fun(_1535192, _1535192)), tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1535192, _1535192), tc_fun(_1535192, tc_HOL_Obool)), tc_fun(tc_fun(_1535192, tc_fun(_1535192, _1535192)), tc_fun(_1535192, tc_fun(_1535192, tc_HOL_Obool))), _1535192), c_COMBB(tc_fun(_1535192, _1535192), tc_fun(_1535192, tc_HOL_Obool), _1535192)), hAPP(hAPP(c_COMBB(tc_fun(_1535192, tc_HOL_Obool), tc_fun(tc_fun(_1535192, _1535192), tc_fun(_1535192, tc_HOL_Obool)), _1535192), c_COMBB(_1535192, tc_HOL_Obool, _1535192)), c_fequal))), c_Orderings_Oord__class_Omax(_1535192)))))), hAPP(hAPP(c_COMBC(_1535192, tc_fun(_1535192, tc_HOL_Obool), tc_fun(_1535192, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1535192, tc_HOL_Obool), tc_fun(_1535192, tc_HOL_Obool)), _1535192), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1535192)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535192), c_fconj), hAPP(hAPP(c_COMBC(_1535192, tc_fun(_1535192, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535192)), _1535194)))), hAPP(hAPP(c_COMBC(_1535192, tc_fun(_1535192, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535192)), _1535196))))))))], (28699 ^ _779854) ^ [_1298511] : [_1298511 = 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), _1298511)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32343 ^ _779854) ^ [_1362022, _1362024] : [class_Groups_Oordered__ab__group__add__abs(_1362022), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362022), hAPP(c_Groups_Ouminus__class_Ouminus(_1362022), hAPP(c_Groups_Oabs__class_Oabs(_1362022), _1362024))), c_Groups_Ozero__class_Ozero(_1362022))))], (43598 ^ _779854) ^ [_1648770] : [-(c_List_Olists(_1648770, c_Orderings_Obot__class_Obot(tc_fun(_1648770, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1648770)), c_List_Olist_ONil(_1648770)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1648770), tc_HOL_Obool))))], (48804 ^ _779854) ^ [_1763157, _1763159, _1763161, _1763163, _1763165, _1763167, _1763169] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1763157, _1763159, _1763161, _1763163), _1763165), _1763167), _1763169) = c_New__DSequence_Oneg__bind(_1763157, _1763159, hAPP(hAPP(hAPP(_1763161, _1763165), _1763167), _1763169), hAPP(hAPP(c_COMBC(_1763157, 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(_1763159)))), hAPP(hAPP(c_COMBC(_1763157, 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(_1763159))))), hAPP(hAPP(c_COMBC(_1763157, 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(_1763159)))))), _1763163), _1763165)), _1763167)), _1763169)))], (39353 ^ _779854) ^ [_1539549, _1539551, _1539553, _1539555] : [-(c_Product__Type_Oapsnd(_1539549, _1539551, _1539553, _1539555) = c_Product__Type_Omap__pair(_1539553, _1539553, _1539549, _1539551, c_Fun_Oid(_1539553), _1539555))], (39270 ^ _779854) ^ [_1536544, _1536546] : [c_Predicate_Oreflp(_1536544, _1536546), -(c_Relation_Orefl__on(_1536544, c_Orderings_Otop__class_Otop(tc_fun(_1536544, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1536544, _1536544)), hAPP(c_Product__Type_Oprod_Oprod__case(_1536544, _1536544, tc_HOL_Obool), _1536546))))], (38929 ^ _779854) ^ [_1523307, _1523309, _1523311, _1523313, _1523315, _1523317] : [-(hAPP(c_Set_Oimage(_1523307, _1523309, hAPP(hAPP(c_COMBS(_1523307, _1523309, _1523309), hAPP(hAPP(c_COMBS(_1523307, _1523309, tc_fun(_1523309, _1523309)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1523309, tc_fun(_1523309, _1523309)), _1523307), c_If(_1523309)), _1523311)), _1523313)), _1523315)), _1523317) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523309, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1523307, _1523309, _1523313), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523307, tc_HOL_Obool)), _1523317), hAPP(c_Set_OCollect(_1523307), _1523311)))), hAPP(c_Set_Oimage(_1523307, _1523309, _1523315), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523307, tc_HOL_Obool)), _1523317), hAPP(c_Set_OCollect(_1523307), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523307), c_fNot), _1523311))))))], (29655 ^ _779854) ^ [_1314756, _1314758] : [class_Int_Onumber__ring(_1314756), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1314756), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1314756), c_Groups_Oone__class_Oone(_1314756)), c_Groups_Oone__class_Oone(_1314756))), hAPP(c_Int_Onumber__class_Onumber__of(_1314756), _1314758)) = hAPP(c_Int_Onumber__class_Onumber__of(_1314756), c_Int_OBit0(_1314758)))], (43656 ^ _779854) ^ [_1649881, _1649883, _1649885] : [-(_1649881 = c_List_Olist_ONil(_1649883)), -(hBOOL(hAPP(hAPP(c_member(_1649883), hAPP(c_Product__Type_Ofst(_1649883, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1649883, _1649881), _1649885))), hAPP(c_List_Oset(_1649883), _1649881))))], (9546 ^ _779854) ^ [_939830, _939832, _939834, _939836] : [_939836 = c_Orderings_Obot__class_Obot(tc_fun(_939830, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_939830, _939832, _939834), _939836) = c_Orderings_Obot__class_Obot(tc_fun(_939832, tc_HOL_Obool)))], (4764 ^ _779854) ^ [_852543, _852545, _852547, _852549, _852551, _852553, _852555, _852557] : [-(c_Wellfounded_Olex__prod(_852557, _852553, _852549, _852545) = c_Wellfounded_Olex__prod(_852555, _852551, _852547, _852543)), _852557 = _852555, _852553 = _852551, _852549 = _852547, _852545 = _852543], (52189 ^ _779854) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (52287 ^ _779854) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (18114 ^ _779854) ^ [_1107650, _1107652] : [class_Rings_Ocomm__semiring__1(_1107650), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107650), _1107652), _1107652) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107650), c_Groups_Oone__class_Oone(_1107650)), c_Groups_Oone__class_Oone(_1107650))), _1107652))], (16223 ^ _779854) ^ [_1071161, _1071163, _1071165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1071161), _1071163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1071161), _1071165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071165), _1071163)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071165), _1071161))))], (44288 ^ _779854) ^ [_1665220, _1665222] : [_1665222 = c_List_Olist_ONil(_1665220), -(hAPP(c_List_Orotate1(_1665220), _1665222) = c_List_Olist_ONil(_1665220))], (26511 ^ _779854) ^ [_1261771, _1261773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261773)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1261773), _1261771)), _1261773) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1261773), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1261771), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (15942 ^ _779854) ^ [_1065850, _1065852, _1065854, _1065856] : [class_Rings_Ocomm__semiring__1(_1065850), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065850), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065850), _1065852), _1065854)), _1065856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065850), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065850), _1065852), _1065856)), _1065854))], (8784 ^ _779854) ^ [_925856, _925858, _925860] : [class_Orderings_Olinorder(_925856), 8787 ^ _779854 : [(8794 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925856), _925860), _925858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925856), _925858), _925860))], (8788 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925856), _925858), _925860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925856), _925860), _925858)))]]], (4856 ^ _779854) ^ [_854031, _854033, _854035, _854037, _854039, _854041] : [-(c_Relation_Orel__comp(_854041, _854037, _854033) = c_Relation_Orel__comp(_854039, _854035, _854031)), _854041 = _854039, _854037 = _854035, _854033 = _854031], (47468 ^ _779854) ^ [_1734366, _1734368] : [-(_1734366 = c_List_Olist_ONil(_1734368)), -(c_List_Olast(_1734368, hAPP(c_List_Orev(_1734368), _1734366)) = hAPP(c_List_Ohd(_1734368), _1734366))], (18159 ^ _779854) ^ [_1108409, _1108411] : [18160 ^ _779854 : [(18161 ^ _779854) ^ [_1108462] : [_1108411 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108409), _1108462))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108409), _1108411)))], (45460 ^ _779854) ^ [_1690557, _1690559] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1690557)), hAPP(c_Code__Numeral_Oof__nat, _1690559)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1690557), _1690559)))], (6343 ^ _779854) ^ [_880769, _880771, _880773] : [class_Orderings_Oorder(_880769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880769), _880771), _880773)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_880769, _880773), _880771) = c_Orderings_Obot__class_Obot(tc_fun(_880769, tc_HOL_Obool)))], (14405 ^ _779854) ^ [_1034508, _1034510, _1034512] : [class_Orderings_Olinorder(_1034508), -(_1034510 = c_Orderings_Obot__class_Obot(tc_fun(_1034508, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1034508, tc_HOL_Obool)), _1034510), _1034512)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034508), _1034512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1034508), hAPP(c_Finite__Set_Ofold1(_1034508, c_Orderings_Oord__class_Omin(_1034508)), _1034512)), hAPP(c_Finite__Set_Ofold1(_1034508, c_Orderings_Oord__class_Omin(_1034508)), _1034510))))], (40571 ^ _779854) ^ [_1570768, _1570770, _1570772, _1570774] : [class_Complete__Lattice_Ocomplete__lattice(_1570768), _1570770 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1570768, _1570772), c_Orderings_Oorder__class_Omono(_1570768, _1570768, _1570772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1570768), _1570774), hAPP(_1570772, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1570768), _1570774), _1570770)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1570768), _1570774), _1570770)))], (15004 ^ _779854) ^ [_1046307, _1046309, _1046311, _1046313, _1046315, _1046317] : [class_Rings_Oring(_1046307), 15007 ^ _779854 : [(15014 ^ _779854) ^ [] : [_1046313 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046307), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046307), _1046315), _1046309)), _1046311)), _1046317), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046307), _1046309), _1046311)), _1046313) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046307), _1046315), _1046311)), _1046317))], (15008 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046307), _1046309), _1046311)), _1046313) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046307), _1046315), _1046311)), _1046317), -(_1046313 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046307), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046307), _1046315), _1046309)), _1046311)), _1046317))]]], (17330 ^ _779854) ^ [_1092987, _1092989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1092987), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1092989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092989), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1092987))))), -(_1092987 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1092989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092989), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1092987))))], (25721 ^ _779854) ^ [_1247400, _1247402] : [25722 ^ _779854 : [(25725 ^ _779854) ^ [] : [_1247400 = _1247402], (25723 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247400), _1247402))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247402), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (6683 ^ _779854) ^ [_887073, _887075, _887077, _887079] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887073, tc_HOL_Obool)), _887075), _887077), _887079)), -(hBOOL(hAPP(_887075, _887079))), -(hBOOL(hAPP(_887077, _887079)))], (33062 ^ _779854) ^ [_1378686, _1378688, _1378690, _1378692, _1378694] : [-(_1378686 = c_Orderings_Obot__class_Obot(tc_fun(_1378688, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1378690), _1378692), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378688, tc_fun(_1378690, tc_HOL_Obool)), _1378686), _1378694)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378688, tc_fun(_1378690, tc_HOL_Obool)), _1378686), hAPP(hAPP(c_COMBB(tc_fun(_1378690, tc_HOL_Obool), tc_fun(_1378690, tc_HOL_Obool), _1378688), hAPP(c_Set_Oinsert(_1378690), _1378692)), _1378694)))], (24050 ^ _779854) ^ [_1216062, _1216064, _1216066] : [class_Rings_Olinordered__semidom(_1216062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1216062), c_Groups_Oone__class_Oone(_1216062)), _1216064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1216062), c_Groups_Oone__class_Oone(_1216062)), hAPP(hAPP(c_Power_Opower__class_Opower(_1216062), _1216064), _1216066))))], (29547 ^ _779854) ^ [_1312804, _1312806] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1312804)), c_Int_OBit0(_1312806)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1312804), _1312806)))], (30069 ^ _779854) ^ [_1322278, _1322280, _1322282] : [class_Rings_Olinordered__idom(_1322278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322278), _1322280), c_Groups_Ozero__class_Ozero(_1322278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322278), hAPP(hAPP(c_Power_Opower__class_Opower(_1322278), _1322280), 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)))), _1322282)))), c_Groups_Ozero__class_Ozero(_1322278))))], (30183 ^ _779854) ^ [_1324633, _1324635, _1324637, _1324639] : [class_Divides_Osemiring__div(_1324633), -(c_Divides_Odiv__class_Omod(_1324633, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324633), c_Divides_Odiv__class_Omod(_1324633, _1324635, _1324637)), _1324639), _1324637) = c_Divides_Odiv__class_Omod(_1324633, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324633), _1324635), _1324639), _1324637))], (28074 ^ _779854) ^ [_1287751] : [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, _1287751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1287751)))], (12062 ^ _779854) ^ [_989818, _989820, _989822, _989824] : [hBOOL(hAPP(hAPP(c_member(_989818), _989820), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989818, tc_HOL_Obool)), _989822), _989824))), -(hBOOL(hAPP(hAPP(c_member(_989818), _989820), _989822)))], (12458 ^ _779854) ^ [_997349, _997351, _997353] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997349, tc_HOL_Obool)), _997351), hAPP(c_Set_OPow(_997349), _997353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997349, tc_HOL_Obool)), _997351), _997353)))], (48818 ^ _779854) ^ [_1763670, _1763672, _1763674, _1763676, _1763678] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1763670), _1763672), _1763674), _1763676), _1763678) = c_New__DSequence_Opos__single(_1763670, _1763672))], (39319 ^ _779854) ^ [_1538955, _1538957, _1538959] : [-(hAPP(c_Fun_Ocomp(_1538955, _1538957, _1538955, _1538959), c_Fun_Oid(_1538955)) = _1538959)], (52393 ^ _779854) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (46054 ^ _779854) ^ [_1704120, _1704122] : [-(_1704120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1704122, _1704120, c_List_Olist_ONil(_1704122)) = c_List_Olist_ONil(tc_List_Olist(_1704122)))], (47969 ^ _779854) ^ [_1744802, _1744804, _1744806, _1744808] : [-(c_List_Omaps(_1744802, _1744804, _1744806, _1744808) = c_List_Oconcat(_1744804, hAPP(hAPP(c_List_Omap(_1744802, tc_List_Olist(_1744804)), _1744806), _1744808)))], (51733 ^ _779854) ^ [_1826744, _1826746, _1826748, _1826750] : [class_Divides_Osemiring__div(_1826744), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826744), _1826746), c_Divides_Odiv__class_Omod(_1826744, _1826748, _1826750))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826744), _1826746), _1826750)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826744), _1826746), _1826748)))], (38434 ^ _779854) ^ [_1510031, _1510033, _1510035, _1510037] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1510031, _1510033)), hAPP(hAPP(c_Product__Type_OSigma(_1510031, _1510033), _1510035), hAPP(c_COMBK(tc_fun(_1510033, tc_HOL_Obool), _1510031), _1510037)))), -(_1510037 = c_Orderings_Obot__class_Obot(tc_fun(_1510033, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1510031), _1510035)))], (51164 ^ _779854) ^ [_1814251, _1814253, _1814255, _1814257, _1814259, _1814261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814251, tc_HOL_Obool)), _1814253), _1814255)), 51170 ^ _779854 : [(51173 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814257, tc_HOL_Obool)), hAPP(_1814259, 51169 ^ [_1814251, _1814253, _1814255, _1814257, _1814259, _1814261])), hAPP(_1814261, 51169 ^ [_1814251, _1814253, _1814255, _1814257, _1814259, _1814261])))], (51171 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1814251), 51169 ^ [_1814251, _1814253, _1814255, _1814257, _1814259, _1814261]), _1814255)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814257, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1814251, tc_fun(_1814257, tc_HOL_Obool)), _1814255), _1814259)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1814251, tc_fun(_1814257, tc_HOL_Obool)), _1814255), _1814261))))], (17264 ^ _779854) ^ [_1091681, _1091683, _1091685, _1091687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1091681), _1091683)), hBOOL(hAPP(hAPP(c_member(_1091681), _1091685), _1091683)), hBOOL(hAPP(hAPP(c_member(_1091681), _1091687), _1091683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1091681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1091681, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1091681, tc_HOL_Obool)), _1091683), hAPP(hAPP(c_Set_Oinsert(_1091681), _1091685), c_Orderings_Obot__class_Obot(tc_fun(_1091681, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1091681), _1091687), c_Orderings_Obot__class_Obot(tc_fun(_1091681, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1091681), _1091683))))], (39292 ^ _779854) ^ [_1538057, _1538059, _1538061, _1538063, _1538065, _1538067] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538057), _1538059)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538061), _1538063)), 39302 ^ _779854 : [(39305 ^ _779854) ^ [] : [hAPP(c_Finite__Set_Ocard(_1538057), hAPP(c_Set_OCollect(_1538057), hAPP(hAPP(c_COMBS(_1538057, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538057), c_fconj), hAPP(hAPP(c_COMBC(_1538057, tc_fun(_1538057, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538057)), _1538059))), hAPP(hAPP(c_COMBC(_1538057, _1538061, tc_HOL_Obool), _1538065), 39301 ^ [_1538057, _1538059, _1538061, _1538063, _1538065, _1538067])))) = hAPP(_1538067, 39301 ^ [_1538057, _1538059, _1538061, _1538063, _1538065, _1538067])], (39303 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538061), 39301 ^ [_1538057, _1538059, _1538061, _1538063, _1538065, _1538067]), _1538063)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538057, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1538061, tc_HOL_Obool), tc_Nat_Onat, _1538057), c_Finite__Set_Ocard(_1538061)), hAPP(hAPP(c_COMBB(tc_fun(_1538061, tc_HOL_Obool), tc_fun(_1538061, tc_HOL_Obool), _1538057), c_Set_OCollect(_1538061)), hAPP(hAPP(c_COMBB(tc_fun(_1538061, tc_HOL_Obool), tc_fun(_1538061, tc_HOL_Obool), _1538057), hAPP(c_COMBS(_1538061, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538061), c_fconj), hAPP(hAPP(c_COMBC(_1538061, tc_fun(_1538061, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538061)), _1538063)))), _1538065)))), _1538059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538061, tc_Nat_Onat), _1538067), _1538063))], (1190 ^ _779854) ^ [_797681, _797683] : [-(class_Rings_Olinordered__semiring__1(_797681)), _797683 = _797681, class_Rings_Olinordered__semiring__1(_797683)], (42974 ^ _779854) ^ [_1635786, _1635788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1635786), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1635788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1635788), _1635786)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1635788))))], (36936 ^ _779854) ^ [_1471838, _1471840, _1471842, _1471844] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1471838), _1471844) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1471842), _1471840), -(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), _1471838), _1471840)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1471842), _1471844))), c_Int_Ointrel)))], (14590 ^ _779854) ^ [_1038388, _1038390, _1038392, _1038394] : [hBOOL(hAPP(hAPP(c_member(_1038388), _1038390), _1038392)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038388, tc_Nat_Onat), _1038394), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038388, tc_HOL_Obool)), _1038392), hAPP(hAPP(c_Set_Oinsert(_1038388), _1038390), c_Orderings_Obot__class_Obot(tc_fun(_1038388, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1038388, tc_Nat_Onat), _1038394), _1038392)), hAPP(_1038394, _1038390)))], (48632 ^ _779854) ^ [_1759645, _1759647, _1759649] : [c_List_Olist__all(_1759645, _1759647, _1759649), -(c_List_Olist__all(_1759645, _1759647, hAPP(c_List_Orev(_1759645), _1759649)))], (44711 ^ _779854) ^ [_1674371, _1674373, _1674375] : [class_Orderings_Olinorder(_1674371), -(c_Big__Operators_Olattice_OInf__fin(_1674371, c_Orderings_Oord__class_Omin(_1674371), hAPP(c_List_Oset(_1674371), hAPP(hAPP(c_List_Olist_OCons(_1674371), _1674373), _1674375))) = hAPP(c_List_Ofoldl(_1674371, _1674371, c_Orderings_Oord__class_Omin(_1674371), _1674373), _1674375))], (44735 ^ _779854) ^ [_1674983, _1674985] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1674983), hAPP(c_List_Oset(tc_Nat_Onat), _1674985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1674983), 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)), _1674985))))], (13547 ^ _779854) ^ [_1018208, _1018210, _1018212] : [class_Orderings_Olinorder(_1018208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018208), _1018210)), -(_1018212 = c_Orderings_Obot__class_Obot(tc_fun(_1018208, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1018208, tc_HOL_Obool)), _1018212), _1018210)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1018208), c_Big__Operators_Olinorder__class_OMax(_1018208, _1018212)), c_Big__Operators_Olinorder__class_OMax(_1018208, _1018210)) = c_Big__Operators_Olinorder__class_OMax(_1018208, _1018210))], (31454 ^ _779854) ^ [_1346796, _1346798] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1346796, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1346798)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1346796, 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)))), _1346798)))], (46575 ^ _779854) ^ [_1716599, _1716601] : [-(c_Random_Opick(_1716599, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1716599), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1716599, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1716599, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1716599)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1716601)) = c_Random_Opick(_1716599, _1716601))], (45734 ^ _779854) ^ [_1696748, _1696750, _1696752, _1696754] : [-(hBOOL(hAPP(c_List_Olistsp(_1696748, _1696750), hAPP(hAPP(c_List_Olist_OCons(_1696748), _1696752), _1696754)))), hBOOL(hAPP(_1696750, _1696752)), hBOOL(hAPP(c_List_Olistsp(_1696748, _1696750), _1696754))], (6391 ^ _779854) ^ [_881632] : [-(hAPP(c_Set_OPow(_881632), c_Orderings_Otop__class_Otop(tc_fun(_881632, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_881632, tc_HOL_Obool), tc_HOL_Obool)))], (50350 ^ _779854) ^ [_1797095] : [-(c_Hilbert__Choice_Oinv__into(_1797095, _1797095, c_Orderings_Otop__class_Otop(tc_fun(_1797095, tc_HOL_Obool)), c_Fun_Oid(_1797095)) = c_Fun_Oid(_1797095))], (6433 ^ _779854) ^ [_882561, _882563, _882565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882561, tc_HOL_Obool)), _882565), _882563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882561, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882561, tc_HOL_Obool)), _882563)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882561, tc_HOL_Obool)), _882565))))], (37912 ^ _779854) ^ [_1496563, _1496565, _1496567, _1496569, _1496571, _1496573, _1496575] : [c_Typedef_Otype__definition(_1496563, _1496565, _1496567, _1496569, _1496571), hBOOL(hAPP(hAPP(c_member(_1496565), _1496573), _1496571)), hBOOL(hAPP(hAPP(c_member(_1496565), _1496575), _1496571)), 37923 ^ _779854 : [(37930 ^ _779854) ^ [] : [_1496573 = _1496575, -(hAPP(_1496569, _1496573) = hAPP(_1496569, _1496575))], (37924 ^ _779854) ^ [] : [hAPP(_1496569, _1496573) = hAPP(_1496569, _1496575), -(_1496573 = _1496575)]]], (50156 ^ _779854) ^ [_1793435, _1793437, _1793439] : [-(c_Equiv__Relations_Oequiv(_1793435, _1793437, _1793439)), c_Relation_Orefl__on(_1793435, _1793437, _1793439), c_Relation_Osym(_1793435, _1793439), c_Relation_Otrans(_1793435, _1793439)], (46062 ^ _779854) ^ [_1704221, _1704223, _1704225, _1704227] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704221)), _1704223), hAPP(c_List_Oset(tc_List_Olist(_1704221)), c_Enum_On__lists(_1704221, _1704225, _1704227)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704221)), _1704223) = _1704225)], (29565 ^ _779854) ^ [_1313151] : [-(c_Int_Opred(c_Int_OBit1(_1313151)) = c_Int_OBit0(_1313151))], (7301 ^ _779854) ^ [_900015, _900017, _900019] : [class_Lattices_Osemilattice__sup(_900015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900015), _900017), _900019)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900015), _900019), _900017) = _900019)], (25979 ^ _779854) ^ [_1251955, _1251957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251957)), -(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), _1251955), _1251957))))], (33655 ^ _779854) ^ [_1398108, _1398110, _1398112] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398108, tc_Nat_Onat), _1398110), _1398112)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398108, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1398108), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1398110)), _1398112))], (16820 ^ _779854) ^ [_1083097, _1083099, _1083101, _1083103, _1083105] : [c_Finite__Set_Ofolding__one__idem(_1083097, _1083099, _1083101), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083097), _1083103)), -(hAPP(_1083101, hAPP(hAPP(c_Set_Oinsert(_1083097), _1083105), _1083103)) = hAPP(hAPP(c_Finite__Set_Ofold(_1083097, _1083097, _1083099), _1083105), _1083103))], (9472 ^ _779854) ^ [_938214, _938216, _938218] : [class_Orderings_Olinorder(_938214), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938214), _938216), _938218) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_938214), _938218), _938216))], (1460 ^ _779854) ^ [_801056, _801058] : [-(class_Orderings_Otop(_801056)), _801058 = _801056, class_Orderings_Otop(_801058)], (3572 ^ _779854) ^ [_833473, _833475, _833477, _833479, _833481, _833483, _833485, _833487, _833489, _833491] : [-(c_List_Olinorder__class_Oinsort__insert__key(_833491, _833487, _833483, _833479, _833475) = c_List_Olinorder__class_Oinsort__insert__key(_833489, _833485, _833481, _833477, _833473)), _833491 = _833489, _833487 = _833485, _833483 = _833481, _833479 = _833477, _833475 = _833473], (46926 ^ _779854) ^ [_1723556] : [class_Orderings_Olinorder(_1723556), -(c_List_Olinorder__class_Osorted(_1723556, c_List_Olist_ONil(_1723556)))], (40271 ^ _779854) ^ [_1563977] : [-(_1563977 = hAPP(c_Int_OAbs__Integ, 40269 ^ [_1563977]))], (27713 ^ _779854) ^ [_1281387, _1281389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281387)), 27716 ^ _779854 : [(27723 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281389), _1281387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1281389)), hAPP(c_Int_Onat, _1281387))))], (27717 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1281389)), hAPP(c_Int_Onat, _1281387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281389), _1281387)))]]], (43311 ^ _779854) ^ [_1643372, _1643374, _1643376, _1643378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1643372), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643374)), _1643376))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1643372), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643374)), _1643378))), 43321 ^ _779854 : [(43324 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Onth(_1643374), _1643376), 43320 ^ [_1643372, _1643374, _1643376, _1643378]) = hAPP(hAPP(c_List_Onth(_1643374), _1643378), 43320 ^ [_1643372, _1643374, _1643376, _1643378])], (43322 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43320 ^ [_1643372, _1643374, _1643376, _1643378]), _1643372)))]], -(hAPP(hAPP(c_List_Otake(_1643374), _1643372), _1643376) = hAPP(hAPP(c_List_Otake(_1643374), _1643372), _1643378))], (44675 ^ _779854) ^ [_1673625, _1673627] : [class_Complete__Lattice_Ocomplete__lattice(_1673625), -(c_Complete__Lattice_OSup__class_OSup(_1673625, hAPP(c_List_Oset(_1673625), _1673627)) = hAPP(c_List_Ofoldl(_1673625, _1673625, c_Lattices_Osemilattice__sup__class_Osup(_1673625), c_Orderings_Obot__class_Obot(_1673625)), _1673627))], (30319 ^ _779854) ^ [_1327379, _1327381, _1327383] : [-(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, _1327379, _1327381)), _1327383), _1327381) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1327379), _1327383), _1327381))], (24210 ^ _779854) ^ [_1218881, _1218883, _1218885, _1218887] : [class_Rings_Olinordered__semidom(_1218881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218881), hAPP(hAPP(c_Power_Opower__class_Opower(_1218881), _1218883), hAPP(c_Nat_OSuc, _1218885))), hAPP(hAPP(c_Power_Opower__class_Opower(_1218881), _1218887), hAPP(c_Nat_OSuc, _1218885)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218881), c_Groups_Ozero__class_Ozero(_1218881)), _1218887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218881), _1218883), _1218887)))], (52653 ^ _779854) ^ [] : [-(hBOOL(c_fTrue))], (29421 ^ _779854) ^ [_1310597, _1310599] : [_1310597 = _1310599, -(c_Int_OBit0(_1310597) = c_Int_OBit0(_1310599))], (29599 ^ _779854) ^ [_1313724, _1313726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1313724)), c_Int_OBit0(_1313726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1313724), _1313726)))], (25905 ^ _779854) ^ [_1250731, _1250733] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1250731), _1250733))))], (45248 ^ _779854) ^ [_1686108, _1686110, _1686112, _1686114, _1686116] : [c_Fun_Oinj__on(_1686108, _1686110, _1686112, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1686108, tc_HOL_Obool)), hAPP(c_List_Oset(_1686108), _1686114)), hAPP(c_List_Oset(_1686108), _1686116))), 45251 ^ _779854 : [(45258 ^ _779854) ^ [] : [_1686114 = _1686116, -(hAPP(hAPP(c_List_Omap(_1686108, _1686110), _1686112), _1686114) = hAPP(hAPP(c_List_Omap(_1686108, _1686110), _1686112), _1686116))], (45252 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Omap(_1686108, _1686110), _1686112), _1686114) = hAPP(hAPP(c_List_Omap(_1686108, _1686110), _1686112), _1686116), -(_1686114 = _1686116)]]], (38084 ^ _779854) ^ [_1500376, _1500378, _1500380, _1500382, _1500384] : [-(hAPP(c_Set_Ovimage(_1500376, _1500378, _1500380), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500378, tc_HOL_Obool)), _1500382), _1500384)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500376, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1500376, _1500378, _1500380), _1500382)), hAPP(c_Set_Ovimage(_1500376, _1500378, _1500380), _1500384)))], (23936 ^ _779854) ^ [_1213988, _1213990, _1213992] : [class_Rings_Oring__1__no__zero__divisors(_1213988), -(_1213990 = c_Groups_Ozero__class_Ozero(_1213988)), hAPP(hAPP(c_Power_Opower__class_Opower(_1213988), _1213990), _1213992) = c_Groups_Ozero__class_Ozero(_1213988)], (42040 ^ _779854) ^ [_1608087, _1608089] : [-(c_Nitpick_Ouminus__frac(_1608087, _1608089) = c_Nitpick_OAbs__Frac(_1608087, 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(_1608087), _1608089))), hAPP(c_Nitpick_Odenom(_1608087), _1608089))))], (32738 ^ _779854) ^ [_1369290, _1369292, _1369294, _1369296, _1369298, _1369300] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1369290, tc_fun(_1369292, tc_HOL_Obool)), _1369294), _1369296), _1369298)), -(hBOOL(hAPP(hAPP(_1369296, _1369300), _1369298))), hBOOL(hAPP(hAPP(c_member(_1369290), _1369300), _1369294))], (8288 ^ _779854) ^ [_918629, _918631, _918633] : [class_Orderings_Oorder(_918629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918629), _918631), _918633)), _918631 = _918633], (15896 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (46785 ^ _779854) ^ [_1721031, _1721033, _1721035, _1721037, _1721039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721031), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1721033), _1721035))), -(hAPP(hAPP(c_List_Onth(_1721037), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1721037), _1721039), c_List_Oupt(_1721035, _1721033))), _1721031) = hAPP(_1721039, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1721035), _1721031)))], (19059 ^ _779854) ^ [_1123533, _1123535, _1123537, _1123539] : [class_Groups_Oordered__comm__monoid__add(_1123533), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123533), c_Groups_Ozero__class_Ozero(_1123533)), _1123535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123533), _1123537), _1123539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123533), _1123537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123533), _1123539), _1123535))))], (7131 ^ _779854) ^ [_897116, _897118, _897120] : [class_Lattices_Olattice(_897116), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897116), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_897116), _897118), _897120)), _897118)))], (52011 ^ _779854) ^ [_1831374, _1831376] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831374), _1831376)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831376), _1831374)), -(_1831374 = _1831376)], (2968 ^ _779854) ^ [_824067, _824069, _824071, _824073] : [-(c_Nitpick_Ouminus__frac(_824073, _824069) = c_Nitpick_Ouminus__frac(_824071, _824067)), _824073 = _824071, _824069 = _824067], (24555 ^ _779854) ^ [_1225337, _1225339, _1225341] : [class_Int_Onumber(_1225337), 24558 ^ _779854 : [(24565 ^ _779854) ^ [] : [_1225341 = hAPP(c_Int_Onumber__class_Onumber__of(_1225337), _1225339), -(hAPP(c_Int_Onumber__class_Onumber__of(_1225337), _1225339) = _1225341)], (24559 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1225337), _1225339) = _1225341, -(_1225341 = hAPP(c_Int_Onumber__class_Onumber__of(_1225337), _1225339))]]], (50529 ^ _779854) ^ [_1801250, _1801252, _1801254, _1801256, _1801258] : [c_Fun_Oinj__on(_1801250, _1801252, _1801254, c_Orderings_Otop__class_Otop(tc_fun(_1801250, tc_HOL_Obool))), 50535 ^ _779854 : [(50538 ^ _779854) ^ [] : [hBOOL(hAPP(_1801256, hAPP(c_Hilbert__Choice_Oinv__into(_1801250, _1801252, c_Orderings_Otop__class_Otop(tc_fun(_1801250, tc_HOL_Obool)), _1801254), 50534 ^ [_1801250, _1801252, _1801254, _1801256, _1801258])))], (50536 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801252), 50534 ^ [_1801250, _1801252, _1801254, _1801256, _1801258]), hAPP(c_Set_Oimage(_1801250, _1801252, _1801254), c_Orderings_Otop__class_Otop(tc_fun(_1801250, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1801256, _1801258)))], (45340 ^ _779854) ^ [_1688094, _1688096, _1688098, _1688100] : [class_Rings_Osemiring__1(_1688094), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1688094), hAPP(hAPP(c_List_Omap(_1688096, _1688094), hAPP(c_COMBK(_1688094, _1688096), _1688098)), _1688100)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1688094), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1688094), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688096)), _1688100))), _1688098))], (17742 ^ _779854) ^ [_1101401] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101401)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1101401)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101401)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (42849 ^ _779854) ^ [_1632032, _1632034, _1632036, _1632038] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632032), tc_List_Olist(_1632032))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632032), tc_List_Olist(_1632032)), _1632034), _1632036)), c_List_Olistrel(_1632032, _1632038)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632032)), _1632034) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632032)), _1632036), 42855 ^ _779854 : [(42858 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1632032, _1632032, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1632032, tc_fun(tc_prod(_1632032, _1632032), tc_HOL_Obool), tc_fun(_1632032, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1632032, tc_fun(tc_fun(tc_prod(_1632032, _1632032), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1632032, _1632032), tc_HOL_Obool), tc_fun(_1632032, tc_HOL_Obool)), _1632032), c_COMBC(_1632032, tc_fun(tc_prod(_1632032, _1632032), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1632032, tc_prod(_1632032, _1632032)), tc_fun(_1632032, tc_fun(tc_fun(tc_prod(_1632032, _1632032), tc_HOL_Obool), tc_HOL_Obool)), _1632032), hAPP(c_COMBB(tc_prod(_1632032, _1632032), tc_fun(tc_fun(tc_prod(_1632032, _1632032), tc_HOL_Obool), tc_HOL_Obool), _1632032), c_member(tc_prod(_1632032, _1632032)))), c_Product__Type_OPair(_1632032, _1632032)))), _1632038)), 42854 ^ [_1632032, _1632034, _1632036, _1632038]))], (42856 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632032, _1632032)), 42854 ^ [_1632032, _1632034, _1632036, _1632038]), hAPP(c_List_Oset(tc_prod(_1632032, _1632032)), hAPP(hAPP(c_List_Ozip(_1632032, _1632032), _1632034), _1632036)))))]]], (19833 ^ _779854) ^ [_1137664, _1137666, _1137668] : [class_Groups_Oordered__ab__group__add(_1137664), 19836 ^ _779854 : [(19843 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137664), _1137666), _1137668)), c_Groups_Ozero__class_Ozero(_1137664))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137664), _1137666), _1137668)))], (19837 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137664), _1137666), _1137668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137664), _1137666), _1137668)), c_Groups_Ozero__class_Ozero(_1137664))))]]], (34365 ^ _779854) ^ [_1416884, _1416886, _1416888, _1416890] : [class_Complete__Lattice_Ocomplete__lattice(_1416884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416886), _1416888)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416886, _1416884), _1416888), _1416890) = hAPP(hAPP(c_Finite__Set_Ofold(_1416886, _1416884, hAPP(hAPP(c_COMBB(_1416884, tc_fun(_1416884, _1416884), _1416886), c_Lattices_Osemilattice__inf__class_Oinf(_1416884)), _1416890)), c_Orderings_Otop__class_Otop(_1416884)), _1416888))], (46206 ^ _779854) ^ [_1707053, _1707055, _1707057] : [hBOOL(hAPP(c_List_Odistinct(_1707053), _1707055)), -(c_List_Oremove1(_1707053, _1707057, _1707055) = hAPP(c_List_OremoveAll(_1707053, _1707057), _1707055))], (33148 ^ _779854) ^ [_1380736, _1380738, _1380740, _1380742] : [c_Orderings_Obot__class_Obot(tc_fun(_1380736, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380738, tc_fun(_1380736, tc_HOL_Obool)), _1380740), _1380742), 33151 ^ _779854 : [(33152 ^ _779854) ^ [_1380852] : [hBOOL(hAPP(hAPP(c_member(_1380738), _1380852), _1380740)), -(hAPP(_1380742, _1380852) = c_Orderings_Obot__class_Obot(tc_fun(_1380736, tc_HOL_Obool)))]]], (31500 ^ _779854) ^ [_1347636] : [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, _1347636, 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, _1347636, 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))], (5758 ^ _779854) ^ [_870940, _870942] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870940, tc_HOL_Obool)), _870942), _870942)))], (20989 ^ _779854) ^ [_1157542, _1157544, _1157546] : [hBOOL(hAPP(_1157542, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1157544), _1157546))), 20992 ^ _779854 : [(20999 ^ _779854) ^ [_1157733] : [_1157544 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1157546), _1157733), -(hBOOL(hAPP(_1157542, _1157733)))], (20993 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157544), _1157546)), -(hBOOL(hAPP(_1157542, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (26657 ^ _779854) ^ [_1264199, _1264201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264199), 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)), _1264201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1264199), _1264201)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45635 ^ _779854) ^ [_1694035, _1694037, _1694039, _1694041, _1694043] : [c_List_Opartition(_1694035, _1694037, _1694039) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694035), tc_List_Olist(_1694035)), _1694041), _1694043), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1694035, tc_HOL_Obool)), hAPP(c_List_Oset(_1694035), _1694041)), hAPP(c_List_Oset(_1694035), _1694043)) = hAPP(c_List_Oset(_1694035), _1694039))], (36780 ^ _779854) ^ [_1468193, _1468195, _1468197, _1468199, _1468201, _1468203, _1468205] : [-(hAPP(c_Product__Type_Oapsnd(_1468193, _1468195, _1468197, _1468199), hAPP(c_Product__Type_Oapfst(_1468201, _1468197, _1468193, _1468203), _1468205)) = hAPP(c_Product__Type_Oapfst(_1468201, _1468197, _1468195, _1468203), hAPP(c_Product__Type_Oapsnd(_1468193, _1468195, _1468201, _1468199), _1468205)))], (38809 ^ _779854) ^ [_1520054] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1520054, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1520054), hAPP(c_COMBK(tc_HOL_Obool, _1520054), c_fTrue)))], (52325 ^ _779854) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (17002 ^ _779854) ^ [_1086635, _1086637, _1086639] : [class_Lattices_Olattice(_1086635), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086635), _1086637)), -(c_Big__Operators_Olattice__class_OInf__fin(_1086635, hAPP(hAPP(c_Set_Oinsert(_1086635), _1086639), _1086637)) = hAPP(hAPP(c_Finite__Set_Ofold(_1086635, _1086635, c_Lattices_Osemilattice__inf__class_Oinf(_1086635)), _1086639), _1086637))], (9502 ^ _779854) ^ [_938825, _938827, _938829, _938831] : [class_Orderings_Olinorder(_938825), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938825), _938827), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938825), _938829), _938831)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_938825), _938829), hAPP(hAPP(c_Orderings_Oord__class_Omax(_938825), _938827), _938831)))], (50102 ^ _779854) ^ [_1792610, _1792612, _1792614] : [c_Relation_Osym(_1792610, _1792612), c_Relation_Osym(_1792610, _1792614), -(c_Relation_Osym(_1792610, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1792610, _1792610), tc_HOL_Obool)), _1792612), _1792614)))], (40357 ^ _779854) ^ [_1566088, _1566090] : [40358 ^ _779854 : [(40359 ^ _779854) ^ [_1566134] : [hBOOL(hAPP(_1566088, _1566134))]], -(hBOOL(hAPP(_1566088, c_Hilbert__Choice_OEps(_1566090, _1566088))))], (44765 ^ _779854) ^ [_1675716, _1675718, _1675720, _1675722] : [class_Orderings_Olinorder(_1675716), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675718, _1675716, _1675720), _1675722), c_List_Olist_ONil(_1675718)) = hAPP(hAPP(c_List_Olist_OCons(_1675718), _1675722), c_List_Olist_ONil(_1675718)))], (25513 ^ _779854) ^ [_1243980, _1243982] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1243980)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1243982)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243980), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243982))))], (7515 ^ _779854) ^ [_903736, _903738, _903740] : [-(hAPP(c_Set_OPow(_903736), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903736, tc_HOL_Obool)), _903738), _903740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_903736, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_903736), _903738)), hAPP(c_Set_OPow(_903736), _903740)))], (43085 ^ _779854) ^ [_1638259, _1638261, _1638263, _1638265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638259, tc_HOL_Obool)), hAPP(c_List_Oset(_1638259), hAPP(hAPP(c_List_Olist__update(_1638259, _1638261), _1638263), _1638265))), hAPP(hAPP(c_Set_Oinsert(_1638259), _1638265), hAPP(c_List_Oset(_1638259), _1638261)))))], (10795 ^ _779854) ^ [_964225, _964227, _964229, _964231] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964225, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964225, tc_HOL_Obool)), _964227), _964229)), _964231) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964225, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964225, tc_HOL_Obool)), _964227), _964231)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964225, tc_HOL_Obool)), _964229), _964231)))], (50734 ^ _779854) ^ [_1805770, _1805772, _1805774, _1805776, _1805778, _1805780, _1805782, _1805784] : [c_Fun_Obij__betw(_1805770, _1805772, _1805774, _1805776, _1805778), c_Fun_Obij__betw(_1805772, _1805780, _1805782, _1805778, _1805784), -(c_Fun_Obij__betw(_1805770, _1805780, hAPP(c_Fun_Ocomp(_1805772, _1805780, _1805770, _1805782), _1805774), _1805776, _1805784))], (36924 ^ _779854) ^ [_1471559, _1471561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1471559), _1471561)), -(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), _1471559), _1471561)), c_Wellfounded_Oless__than)))], (41483 ^ _779854) ^ [_1593583, _1593585, _1593587, _1593589, _1593591] : [-(hAPP(c_Relation_Oconverse(_1593583, _1593585), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593587, tc_fun(tc_prod(_1593583, _1593585), tc_HOL_Obool)), _1593589), _1593591)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1593587, tc_fun(tc_prod(_1593585, _1593583), tc_HOL_Obool)), _1593589), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1593583, _1593585), tc_HOL_Obool), tc_fun(tc_prod(_1593585, _1593583), tc_HOL_Obool), _1593587), c_Relation_Oconverse(_1593583, _1593585)), _1593591)))], (4284 ^ _779854) ^ [_844909, _844911] : [_844911 = _844909, -(c_List_Oappend(_844911) = c_List_Oappend(_844909))], (12302 ^ _779854) ^ [_994302, _994304, _994306, _994308, _994310] : [hBOOL(hAPP(hAPP(c_member(_994302), _994304), _994306)), -(hAPP(hAPP(c_Set_Oinsert(_994308), hAPP(_994310, _994304)), hAPP(c_Set_Oimage(_994302, _994308, _994310), _994306)) = hAPP(c_Set_Oimage(_994302, _994308, _994310), _994306))], (4916 ^ _779854) ^ [_854933, _854935] : [_854935 = _854933, -(c_HOL_OEx(_854935) = c_HOL_OEx(_854933))], (40369 ^ _779854) ^ [_1566298, _1566300] : [40370 ^ _779854 : [(40371 ^ _779854) ^ [_1566344] : [hBOOL(hAPP(_1566298, _1566344))]], -(hBOOL(hAPP(_1566298, c_Hilbert__Choice_OEps(_1566300, _1566298))))], (38120 ^ _779854) ^ [_1501305, _1501307, _1501309, _1501311] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501305, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1501307, _1501305, _1501309), hAPP(c_Set_Ovimage(_1501307, _1501305, _1501309), _1501311))), _1501311)))], (42137 ^ _779854) ^ [_1610957, _1610959, _1610961, _1610963, _1610965, _1610967] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610957), tc_List_Olist(_1610957))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610957), tc_List_Olist(_1610957)), hAPP(hAPP(c_List_Olist_OCons(_1610957), _1610959), _1610961)), hAPP(hAPP(c_List_Olist_OCons(_1610957), _1610963), _1610965))), c_List_Olex(_1610957, _1610967))), 42142 ^ _779854 : [(42145 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610957)), _1610961) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610957)), _1610965))], (42143 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610957, _1610957)), hAPP(hAPP(c_Product__Type_OPair(_1610957, _1610957), _1610959), _1610963)), _1610967)))]], 42146 ^ _779854 : [(42149 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610957), tc_List_Olist(_1610957))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610957), tc_List_Olist(_1610957)), _1610961), _1610965)), c_List_Olex(_1610957, _1610967))))], (42147 ^ _779854) ^ [] : [-(_1610959 = _1610963)]]], (49749 ^ _779854) ^ [_1785632, _1785634, _1785636, _1785638] : [class_Complete__Lattice_Ocomplete__lattice(_1785632), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1785634, _1785632), _1785636), _1785638) = c_Complete__Lattice_OInf__class_OInf(_1785632, hAPP(c_Set_OCollect(_1785632), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1785634, _1785632), tc_HOL_Obool), tc_HOL_Obool, _1785632), c_HOL_OEx(tc_fun(_1785634, _1785632))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1785634, _1785632), tc_HOL_Obool), tc_fun(tc_fun(_1785634, _1785632), tc_HOL_Obool), _1785632), hAPP(c_COMBS(tc_fun(_1785634, _1785632), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1785634, _1785632)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1785634, _1785632), tc_fun(tc_fun(_1785634, _1785632), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1785634, _1785632))), _1785636)))), hAPP(hAPP(c_COMBC(_1785632, tc_fun(tc_fun(_1785634, _1785632), _1785632), tc_fun(tc_fun(_1785634, _1785632), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1785632, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1785634, _1785632), _1785632), tc_fun(tc_fun(_1785634, _1785632), tc_HOL_Obool)), _1785632), c_COMBB(_1785632, tc_HOL_Obool, tc_fun(_1785634, _1785632))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1785634, _1785632), _1785634, _1785632), c_COMBI(tc_fun(_1785634, _1785632))), _1785638)))))))], (20570 ^ _779854) ^ [_1149848, _1149850, _1149852, _1149854] : [class_Groups_Oordered__comm__monoid__add(_1149848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149848), c_Groups_Ozero__class_Ozero(_1149848)), _1149850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149848), _1149852), _1149854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149848), _1149852), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149848), _1149850), _1149854))))], (28812 ^ _779854) ^ [_1300324, _1300326] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1300324)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1300326))))), _1300324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1300326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15960 ^ _779854) ^ [_1066279, _1066281, _1066283, _1066285] : [class_Rings_Ocomm__semiring__1(_1066279), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066279), _1066281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066279), _1066283), _1066285)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066279), _1066283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066279), _1066281), _1066285)))], (32501 ^ _779854) ^ [_1364743, _1364745, _1364747, _1364749] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1364743, _1364745, _1364747, c_Code__Numeral_OSuc__code__numeral(_1364749)) = hAPP(_1364747, _1364749))], (30059 ^ _779854) ^ [_1322083, _1322085, _1322087] : [class_Rings_Olinordered__idom(_1322083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322083), c_Groups_Ozero__class_Ozero(_1322083)), hAPP(hAPP(c_Power_Opower__class_Opower(_1322083), _1322085), 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)))), _1322087))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322083), c_Groups_Ozero__class_Ozero(_1322083)), _1322085)))], (39379 ^ _779854) ^ [_1540079, _1540081] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540079), _1540081)), -(_1540081 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1540079, 39383 ^ [_1540079, _1540081]), 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)), 39382 ^ [_1540079, _1540081]))))], (18573 ^ _779854) ^ [_1116138, _1116140] : [class_Rings_Ocomm__semiring__1(_1116138), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116138), c_Groups_Ozero__class_Ozero(_1116138)), _1116140) = c_Groups_Ozero__class_Ozero(_1116138))], (47971 ^ _779854) ^ [_1744850, _1744852, _1744854] : [-(c_List_Omaps(_1744850, _1744852, _1744854, c_List_Olist_ONil(_1744850)) = c_List_Olist_ONil(_1744852))], (46390 ^ _779854) ^ [_1711857, _1711859, _1711861] : [-(hAPP(c_List_Ofilter(_1711857, _1711859), c_List_Oconcat(_1711857, _1711861)) = c_List_Oconcat(_1711857, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711857), tc_List_Olist(_1711857)), c_List_Ofilter(_1711857, _1711859)), _1711861)))], (51415 ^ _779854) ^ [_1821069, _1821071, _1821073, _1821075, _1821077] : [class_Rings_Ocomm__semiring__1(_1821069), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821069), _1821071), _1821073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1821075), _1821077)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821069), hAPP(hAPP(c_Power_Opower__class_Opower(_1821069), _1821071), _1821075)), hAPP(hAPP(c_Power_Opower__class_Opower(_1821069), _1821073), _1821077))))], (16421 ^ _779854) ^ [_1075384, _1075386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1075384), _1075386)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1075384), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075386), _1075384)) = _1075386)], (36066 ^ _779854) ^ [_1452308, _1452310, _1452312, _1452314, _1452316, _1452318] : [c_Finite__Set_Ofolding(_1452308, _1452310, _1452312, _1452314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452308), _1452316)), -(hAPP(c_Fun_Ocomp(_1452310, _1452310, _1452310, hAPP(_1452312, _1452318)), hAPP(_1452314, _1452316)) = hAPP(c_Fun_Ocomp(_1452310, _1452310, _1452310, hAPP(_1452314, _1452316)), hAPP(_1452312, _1452318)))], (38751 ^ _779854) ^ [_1518878, _1518880] : [-(hAPP(c_Set_OCollect(_1518878), hAPP(hAPP(c_COMBC(_1518878, tc_fun(_1518878, tc_HOL_Obool), tc_HOL_Obool), c_member(_1518878)), _1518880)) = _1518880)], (22557 ^ _779854) ^ [_1187326, _1187328, _1187330, _1187332] : [class_Fields_Ofield__inverse__zero(_1187326), -(_1187328 = c_Groups_Ozero__class_Ozero(_1187326)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187326), _1187330), _1187328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187326), _1187332), _1187328)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187326), _1187330), _1187332))], (43440 ^ _779854) ^ [_1645791, _1645793, _1645795, _1645797] : [-(c_List_Oremove1(_1645791, _1645793, c_List_Oremove1(_1645791, _1645795, _1645797)) = c_List_Oremove1(_1645791, _1645795, c_List_Oremove1(_1645791, _1645793, _1645797)))], (43448 ^ _779854) ^ [_1645941, _1645943, _1645945] : [-(hAPP(hAPP(c_List_Ozip(_1645941, _1645943), c_List_Olist_ONil(_1645941)), _1645945) = c_List_Olist_ONil(tc_prod(_1645941, _1645943)))], (47097 ^ _779854) ^ [_1726562, _1726564, _1726566] : [class_Orderings_Olinorder(_1726562), 47100 ^ _779854 : [(47119 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726562, hAPP(hAPP(c_List_Oappend(_1726562), _1726564), _1726566))), c_List_Olinorder__class_Osorted(_1726562, _1726564), c_List_Olinorder__class_Osorted(_1726562, _1726566), 47129 ^ _779854 : [(47135 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726562), 47128 ^ [_1726562, _1726564, _1726566]), 47131 ^ [_1726562, _1726564, _1726566]))], (47133 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726562), 47131 ^ [_1726562, _1726564, _1726566]), hAPP(c_List_Oset(_1726562), _1726566))))], (47130 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726562), 47128 ^ [_1726562, _1726564, _1726566]), hAPP(c_List_Oset(_1726562), _1726564))))]]], (47101 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1726562, hAPP(hAPP(c_List_Oappend(_1726562), _1726564), _1726566)), 47104 ^ _779854 : [(47109 ^ _779854) ^ [_1726798] : [hBOOL(hAPP(hAPP(c_member(_1726562), _1726798), hAPP(c_List_Oset(_1726562), _1726564))), 47112 ^ _779854 : [(47113 ^ _779854) ^ [_1726908] : [hBOOL(hAPP(hAPP(c_member(_1726562), _1726908), hAPP(c_List_Oset(_1726562), _1726566))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726562), _1726798), _1726908)))]]], (47107 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726562, _1726566))], (47105 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726562, _1726564))]]]]], (45372 ^ _779854) ^ [_1688890, _1688892, _1688894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688890), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688892)), _1688894))), -(hAPP(c_Random_Opick(_1688892, hAPP(hAPP(c_List_Omap(_1688892, tc_prod(tc_Code__Numeral_Ocode__numeral, _1688892)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1688892), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1688894)), hAPP(c_Code__Numeral_Oof__nat, _1688890)) = hAPP(hAPP(c_List_Onth(_1688892), _1688894), _1688890))], (4214 ^ _779854) ^ [_843888, _843890] : [_843890 = _843888, -(c_List_Otake(_843890) = c_List_Otake(_843888))], (32407 ^ _779854) ^ [_1363106] : [_1363106 = 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), _1363106)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35424 ^ _779854) ^ [_1439848, _1439850, _1439852, _1439854] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1439848, _1439850), _1439852)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1439848, _1439850), _1439854)), -(_1439852 = _1439854)], (38238 ^ _779854) ^ [_1504306, _1504308, _1504310, _1504312, _1504314, _1504316] : [-(hAPP(c_Set_Oimage(_1504306, tc_prod(_1504308, _1504310), hAPP(hAPP(c_COMBS(_1504306, _1504310, tc_prod(_1504308, _1504310)), hAPP(hAPP(c_COMBB(_1504308, tc_fun(_1504310, tc_prod(_1504308, _1504310)), _1504306), c_Product__Type_OPair(_1504308, _1504310)), _1504312)), _1504314)), _1504316) = hAPP(hAPP(c_Product__Type_OSigma(_1504308, _1504310), hAPP(c_Set_Oimage(_1504306, _1504308, _1504312), _1504316)), hAPP(hAPP(c_COMBB(tc_fun(_1504306, tc_HOL_Obool), tc_fun(_1504310, tc_HOL_Obool), _1504308), c_Set_Oimage(_1504306, _1504310, _1504314)), hAPP(hAPP(c_COMBC(_1504308, tc_fun(_1504306, tc_HOL_Obool), tc_fun(_1504306, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504306, tc_HOL_Obool), tc_fun(tc_fun(_1504306, tc_HOL_Obool), tc_fun(_1504306, tc_HOL_Obool)), _1504308), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1504306, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1504308, tc_HOL_Obool), tc_fun(_1504306, tc_HOL_Obool), _1504308), c_Set_Ovimage(_1504306, _1504308, _1504312)), hAPP(hAPP(c_COMBC(_1504308, tc_fun(_1504308, tc_HOL_Obool), tc_fun(_1504308, tc_HOL_Obool)), c_Set_Oinsert(_1504308)), c_Orderings_Obot__class_Obot(tc_fun(_1504308, tc_HOL_Obool)))))), _1504316))))], (43570 ^ _779854) ^ [_1648255, _1648257, _1648259] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648255), tc_List_Olist(_1648255))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648255), tc_List_Olist(_1648255)), _1648257), c_List_Olist_ONil(_1648255))), c_List_Olex(_1648255, _1648259)))], (10585 ^ _779854) ^ [_959919, _959921, _959923, _959925, _959927] : [c_Fun_Oinj__on(_959919, _959921, _959923, _959925), -(c_Fun_Oinj__on(_959919, _959921, _959923, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959919, tc_HOL_Obool)), _959925), _959927)))], (31354 ^ _779854) ^ [_1344951] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1344951)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1344951)))], (2770 ^ _779854) ^ [_821044, _821046, _821048, _821050, _821052, _821054] : [-(c_Predicate_ODomainP(_821054, _821050, _821046) = c_Predicate_ODomainP(_821052, _821048, _821044)), _821054 = _821052, _821050 = _821048, _821046 = _821044], (41232 ^ _779854) ^ [_1587646, _1587648, _1587650, _1587652] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587646, _1587646)), hAPP(hAPP(c_Product__Type_OPair(_1587646, _1587646), _1587648), _1587650)), c_Transitive__Closure_Ortrancl(_1587646, _1587652))), -(_1587648 = _1587650), 41239 ^ _779854 : [(41242 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587646, _1587646)), hAPP(hAPP(c_Product__Type_OPair(_1587646, _1587646), _1587648), _1587650)), c_Transitive__Closure_Otrancl(_1587646, _1587652))))], (41240 ^ _779854) ^ [] : [_1587648 = _1587650]]], (52277 ^ _779854) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (19521 ^ _779854) ^ [_1131912, _1131914, _1131916] : [class_Groups_Oordered__comm__monoid__add(_1131912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131912), _1131914), c_Groups_Ozero__class_Ozero(_1131912))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131912), _1131916), c_Groups_Ozero__class_Ozero(_1131912))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131912), _1131914), _1131916)), c_Groups_Ozero__class_Ozero(_1131912))))], (4984 ^ _779854) ^ [_856011, _856013] : [_856013 = _856011, -(c_Set_OCollect(_856013) = c_Set_OCollect(_856011))], (10769 ^ _779854) ^ [_963591, _963593, _963595] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963591, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963591, tc_HOL_Obool)), _963593), _963595)), _963593)))], (37026 ^ _779854) ^ [_1474408, _1474410, _1474412, _1474414, _1474416] : [-(hAPP(c_Relation_OImage(_1474408, _1474410, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1474408, _1474410), tc_HOL_Obool)), _1474412), _1474414)), _1474416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474410, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1474408, _1474410, _1474412), _1474416)), hAPP(c_Relation_OImage(_1474408, _1474410, _1474414), _1474416)))], (36906 ^ _779854) ^ [_1470663, _1470665, _1470667, _1470669] : [c_Wellfounded_Omax__extp(_1470663, hAPP(hAPP(c_COMBC(_1470663, tc_fun(tc_prod(_1470663, _1470663), tc_HOL_Obool), tc_fun(_1470663, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470663, tc_fun(tc_fun(tc_prod(_1470663, _1470663), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470663, _1470663), tc_HOL_Obool), tc_fun(_1470663, tc_HOL_Obool)), _1470663), c_COMBC(_1470663, tc_fun(tc_prod(_1470663, _1470663), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470663, tc_prod(_1470663, _1470663)), tc_fun(_1470663, tc_fun(tc_fun(tc_prod(_1470663, _1470663), tc_HOL_Obool), tc_HOL_Obool)), _1470663), hAPP(c_COMBB(tc_prod(_1470663, _1470663), tc_fun(tc_fun(tc_prod(_1470663, _1470663), tc_HOL_Obool), tc_HOL_Obool), _1470663), c_member(tc_prod(_1470663, _1470663)))), c_Product__Type_OPair(_1470663, _1470663)))), _1470665), _1470667, _1470669), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1470663, tc_HOL_Obool), tc_fun(_1470663, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1470663, tc_HOL_Obool), tc_fun(_1470663, tc_HOL_Obool)), _1470667), _1470669)), c_Wellfounded_Omax__ext(_1470663, _1470665))))], (46689 ^ _779854) ^ [_1719164] : [-(c_List_Oupt(_1719164, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (14139 ^ _779854) ^ [_1029330, _1029332, _1029334, _1029336, _1029338, _1029340] : [-(c_Fun_Ofun__upd(_1029330, _1029332, c_Fun_Ofun__upd(_1029330, _1029332, _1029334, _1029336, _1029338), _1029336, _1029340) = c_Fun_Ofun__upd(_1029330, _1029332, _1029334, _1029336, _1029340))], (18973 ^ _779854) ^ [_1121958] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1121958) = _1121958)], (8898 ^ _779854) ^ [_928071, _928073, _928075, _928077] : [class_Lattices_Osemilattice__inf(_928071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928071), _928073), _928075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928071), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928071), _928073), _928077)), _928075)))], (49420 ^ _779854) ^ [_1777017, _1777019, _1777021] : [c_List_Olist__all(tc_Int_Oint, _1777017, c_List_Oupto(_1777019, _1777021)), -(c_List_Oall__interval__int(_1777017, _1777019, _1777021))], (46886 ^ _779854) ^ [_1722980, _1722982] : [class_Orderings_Olinorder(_1722980), c_List_Olinorder__class_Osorted(_1722980, _1722982), -(c_List_Olinorder__class_Osorted(_1722980, hAPP(c_List_Otl(_1722980), _1722982)))], (32982 ^ _779854) ^ [_1376526, _1376528, _1376530, _1376532] : [_1376526 = c_Orderings_Obot__class_Obot(tc_fun(_1376528, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1376528, _1376530, hAPP(c_COMBK(_1376530, _1376528), _1376532)), _1376526) = c_Orderings_Obot__class_Obot(tc_fun(_1376530, tc_HOL_Obool)))], (40561 ^ _779854) ^ [_1570537, _1570539, _1570541, _1570543] : [c_Orderings_Oorder__class_Omono(tc_fun(_1570537, tc_HOL_Obool), tc_fun(_1570537, tc_HOL_Obool), _1570539), hBOOL(hAPP(hAPP(c_member(_1570537), _1570541), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1570537, tc_HOL_Obool), _1570539))), -(hBOOL(hAPP(hAPP(c_member(_1570537), _1570541), hAPP(_1570539, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1570537, tc_HOL_Obool)), _1570543), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1570537, tc_HOL_Obool), _1570539))))))], (21446 ^ _779854) ^ [_1166468, _1166470] : [class_Groups_Olinordered__ab__group__add(_1166468), 21449 ^ _779854 : [(21456 ^ _779854) ^ [] : [_1166470 = c_Groups_Ozero__class_Ozero(_1166468), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166468), _1166470), _1166470) = c_Groups_Ozero__class_Ozero(_1166468))], (21450 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166468), _1166470), _1166470) = c_Groups_Ozero__class_Ozero(_1166468), -(_1166470 = c_Groups_Ozero__class_Ozero(_1166468))]]], (33563 ^ _779854) ^ [_1394956, _1394958, _1394960, _1394962, _1394964] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394956, tc_fun(_1394958, tc_HOL_Obool)), _1394960), hAPP(hAPP(c_COMBS(_1394956, tc_fun(_1394958, tc_HOL_Obool), tc_fun(_1394958, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1394958, tc_HOL_Obool), tc_fun(tc_fun(_1394958, tc_HOL_Obool), tc_fun(_1394958, tc_HOL_Obool)), _1394956), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394958, tc_HOL_Obool))), _1394962)), _1394964)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394958, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394956, tc_fun(_1394958, tc_HOL_Obool)), _1394960), _1394962)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394956, tc_fun(_1394958, tc_HOL_Obool)), _1394960), _1394964)))], (28705 ^ _779854) ^ [_1298604] : [class_Int_Onumber__ring(_1298604), -(hAPP(c_Int_Onumber__class_Onumber__of(_1298604), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1298604))], (10801 ^ _779854) ^ [_964466, _964468, _964470, _964472] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964466, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964466, tc_HOL_Obool)), _964468), _964470)), _964472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964466, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964466, tc_HOL_Obool)), _964468), _964472)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964466, tc_HOL_Obool)), _964470), _964472)))], (16169 ^ _779854) ^ [_1070175, _1070177, _1070179, _1070181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070175), _1070177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070179), _1070181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070175), _1070179)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070177), _1070181))))], (25803 ^ _779854) ^ [_1248837, _1248839] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248837)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248839)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1248837), _1248839)))], (20938 ^ _779854) ^ [_1156625, _1156627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1156625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1156627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156625), _1156627))))], (25903 ^ _779854) ^ [_1250700, _1250702] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1250700, _1250702))))], (27635 ^ _779854) ^ [_1280050] : [-(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), _1280050)) = 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), _1280050))))], (5252 ^ _779854) ^ [_860179, _860181, _860183, _860185] : [-(c_Lazy__Sequence_Oflat(_860185, _860181) = c_Lazy__Sequence_Oflat(_860183, _860179)), _860185 = _860183, _860181 = _860179], (33635 ^ _779854) ^ [_1397701, _1397703, _1397705, _1397707, _1397709] : [-(_1397701 = c_Orderings_Obot__class_Obot(tc_fun(_1397703, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397705, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397703, tc_fun(_1397705, tc_HOL_Obool)), _1397701), _1397707)), _1397709) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397703, tc_fun(_1397705, tc_HOL_Obool)), _1397701), hAPP(hAPP(c_COMBC(_1397703, tc_fun(_1397705, tc_HOL_Obool), tc_fun(_1397705, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397705, tc_HOL_Obool), tc_fun(tc_fun(_1397705, tc_HOL_Obool), tc_fun(_1397705, tc_HOL_Obool)), _1397703), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397705, tc_HOL_Obool))), _1397707)), _1397709)))], (37154 ^ _779854) ^ [_1477967] : [-(_1477967 = 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), 37151 ^ [_1477967]), 37152 ^ [_1477967])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (12038 ^ _779854) ^ [_989296, _989298, _989300, _989302] : [hBOOL(hAPP(hAPP(c_member(_989296), _989298), _989300)), -(hBOOL(hAPP(hAPP(c_member(_989296), _989298), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989296, tc_HOL_Obool)), _989302), _989300))))], (43558 ^ _779854) ^ [_1647832, _1647834, _1647836] : [-(hAPP(hAPP(c_List_Otake(_1647832), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1647832), _1647834), _1647836)) = hAPP(hAPP(c_List_Olist_OCons(_1647832), _1647834), c_List_Olist_ONil(_1647832)))], (20886 ^ _779854) ^ [_1155732] : [class_Rings_Olinordered__semidom(_1155732), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155732), c_Groups_Ozero__class_Ozero(_1155732)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155732), c_Groups_Oone__class_Oone(_1155732)), c_Groups_Oone__class_Oone(_1155732)))))], (52305 ^ _779854) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (11474 ^ _779854) ^ [_978177, _978179, _978181, _978183, _978185] : [c_Finite__Set_Ofolding__one(_978177, _978179, _978181), hBOOL(hAPP(c_Finite__Set_Ofinite(_978177), _978183)), -(_978183 = c_Orderings_Obot__class_Obot(tc_fun(_978177, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978177), _978185)), -(_978185 = c_Orderings_Obot__class_Obot(tc_fun(_978177, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978177, tc_HOL_Obool)), _978183), _978185) = c_Orderings_Obot__class_Obot(tc_fun(_978177, tc_HOL_Obool)), -(hAPP(_978181, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978177, tc_HOL_Obool)), _978183), _978185)) = hAPP(hAPP(_978179, hAPP(_978181, _978183)), hAPP(_978181, _978185)))], (33643 ^ _779854) ^ [_1397926, _1397928, _1397930, _1397932, _1397934, _1397936] : [hBOOL(hAPP(hAPP(c_member(_1397926), _1397928), _1397930)), -(hAPP(c_Fun_Ooverride__on(_1397926, _1397932, _1397934, _1397936, _1397930), _1397928) = hAPP(_1397936, _1397928))], (15536 ^ _779854) ^ [_1057369, _1057371, _1057373] : [class_Groups_Ogroup__add(_1057369), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057369), _1057371), _1057373) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057369), _1057371), hAPP(c_Groups_Ouminus__class_Ouminus(_1057369), _1057373)))], (7644 ^ _779854) ^ [_906577, _906579, _906581, _906583, _906585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906577, tc_HOL_Obool)), _906579), _906581)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906577, tc_HOL_Obool)), _906583), _906585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906577, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906577, tc_HOL_Obool)), _906579), _906583)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906577, tc_HOL_Obool)), _906581), _906585))))], (44875 ^ _779854) ^ [_1677894, _1677896, _1677898, _1677900, _1677902] : [class_Orderings_Olinorder(_1677894), hBOOL(hAPP(c_List_Odistinct(_1677896), _1677898)), -(hBOOL(hAPP(c_List_Odistinct(_1677896), c_List_Olinorder__class_Oinsort__insert__key(_1677896, _1677894, _1677900, _1677902, _1677898))))], (23281 ^ _779854) ^ [_1201041, _1201043, _1201045, _1201047, _1201049] : [class_Groups_Ocomm__monoid__mult(_1201041), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201043), _1201045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201043, tc_HOL_Obool)), _1201047), _1201045)), 23295 ^ _779854 : [(23298 ^ _779854) ^ [] : [hAPP(_1201049, 23294 ^ [_1201041, _1201043, _1201045, _1201047, _1201049]) = c_Groups_Oone__class_Oone(_1201041)], (23296 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201043), 23294 ^ [_1201041, _1201043, _1201045, _1201047, _1201049]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201043, tc_HOL_Obool)), _1201045), _1201047))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1201043, _1201041), _1201049), _1201047) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1201043, _1201041), _1201049), _1201045))], (558 ^ _779854) ^ [_788207, _788209, _788211, _788213, _788215, _788217] : [-(c_Finite__Set_Ofun__left__comm__idem(_788215, _788211, _788207)), c_Finite__Set_Ofun__left__comm__idem(_788217, _788213, _788209), _788217 = _788215, _788213 = _788211, _788209 = _788207], (33595 ^ _779854) ^ [_1396730, _1396732, _1396734, _1396736, _1396738] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396730, tc_fun(_1396732, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396730, tc_HOL_Obool)), _1396734), _1396736)), _1396738) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396732, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396730, tc_fun(_1396732, tc_HOL_Obool)), _1396734), _1396738)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396730, tc_fun(_1396732, tc_HOL_Obool)), _1396736), _1396738)))], (18607 ^ _779854) ^ [_1116629, _1116631, _1116633] : [class_Rings_Oring__no__zero__divisors(_1116629), 18610 ^ _779854 : [(18611 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116629), _1116631), _1116633) = c_Groups_Ozero__class_Ozero(_1116629), -(_1116631 = c_Groups_Ozero__class_Ozero(_1116629)), -(_1116633 = c_Groups_Ozero__class_Ozero(_1116629))], (18621 ^ _779854) ^ [] : [18622 ^ _779854 : [(18625 ^ _779854) ^ [] : [_1116633 = c_Groups_Ozero__class_Ozero(_1116629)], (18623 ^ _779854) ^ [] : [_1116631 = c_Groups_Ozero__class_Ozero(_1116629)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116629), _1116631), _1116633) = c_Groups_Ozero__class_Ozero(_1116629))]]], (2366 ^ _779854) ^ [_814688, _814690, _814692, _814694, _814696, _814698, _814700, _814702] : [-(c_Nitpick_Opair__box_OPairBox(_814702, _814698, _814694, _814690) = c_Nitpick_Opair__box_OPairBox(_814700, _814696, _814692, _814688)), _814702 = _814700, _814698 = _814696, _814694 = _814692, _814690 = _814688], (33733 ^ _779854) ^ [_1400365, _1400367, _1400369, _1400371, _1400373] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400365, tc_HOL_Obool)), _1400367), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1400369, tc_fun(_1400365, tc_HOL_Obool)), _1400371), _1400373)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400369, tc_fun(_1400365, tc_HOL_Obool)), _1400371), hAPP(hAPP(c_COMBB(tc_fun(_1400365, tc_HOL_Obool), tc_fun(_1400365, tc_HOL_Obool), _1400369), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400365, tc_HOL_Obool)), _1400367)), _1400373)))], (42823 ^ _779854) ^ [_1630550, _1630552] : [-(hAPP(c_List_Oset(_1630550), _1630552) = hAPP(c_Set_OCollect(_1630550), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1630550), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1630550, 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)), _1630550), 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)), _1630550), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1630550, tc_fun(tc_Nat_Onat, _1630550), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630550, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1630550), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1630550), c_COMBB(_1630550, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1630550), _1630552))))), 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(_1630550)), _1630552))))))], (27369 ^ _779854) ^ [_1275907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275907), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275907)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (26667 ^ _779854) ^ [_1264360] : [-(_1264360 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1264360), _1264360) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (39925 ^ _779854) ^ [_1555018, _1555020, _1555022, _1555024] : [c_Wellfounded_Owf(_1555018, _1555020), c_Fun_Oinj__on(_1555018, _1555022, _1555024, c_Orderings_Otop__class_Otop(tc_fun(_1555018, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1555022, hAPP(c_Set_Oimage(tc_prod(_1555018, _1555018), tc_prod(_1555022, _1555022), c_Product__Type_Omap__pair(_1555018, _1555022, _1555018, _1555022, _1555024, _1555024)), _1555020)))], (32904 ^ _779854) ^ [_1374361, _1374363, _1374365, _1374367, _1374369, _1374371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1374363, _1374365)), hAPP(hAPP(c_Product__Type_OPair(_1374363, _1374365), _1374369), _1374371)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1374361, tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1374361, tc_HOL_Obool))), _1374367))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1374361, tc_fun(_1374363, tc_fun(_1374365, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1374361, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool), tc_fun(_1374363, tc_fun(_1374365, tc_HOL_Obool)), _1374361), hAPP(c_COMBC(_1374363, tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool), tc_fun(_1374365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374365, tc_fun(tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool), tc_fun(_1374365, tc_HOL_Obool)), _1374363), c_COMBC(_1374365, tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374365, tc_prod(_1374363, _1374365)), tc_fun(_1374365, tc_fun(tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool), tc_HOL_Obool)), _1374363), hAPP(c_COMBB(tc_prod(_1374363, _1374365), tc_fun(tc_fun(tc_prod(_1374363, _1374365), tc_HOL_Obool), tc_HOL_Obool), _1374365), c_member(tc_prod(_1374363, _1374365)))), c_Product__Type_OPair(_1374363, _1374365))))), _1374367)), _1374369), _1374371)))], (38068 ^ _779854) ^ [_1500039, _1500041] : [-(hAPP(c_Set_Ovimage(_1500039, _1500039, c_COMBI(_1500039)), _1500041) = _1500041)], (18527 ^ _779854) ^ [_1115418, _1115420] : [class_Groups_Ocomm__monoid__add(_1115418), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115418), _1115420), c_Groups_Ozero__class_Ozero(_1115418)) = _1115420)], (41172 ^ _779854) ^ [_1586152, _1586154, _1586156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586152, _1586152), tc_HOL_Obool)), c_Relation_OId(_1586152)), _1586154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586152, _1586152), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1586152, _1586152, _1586152), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1586152, _1586152), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1586152, _1586156)), _1586154)), _1586156)), _1586154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586152, _1586152), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1586152, _1586156)), _1586154)))], (39102 ^ _779854) ^ [_1529353] : [-(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)))), _1529353)) = 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), _1529353), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (49426 ^ _779854) ^ [_1777102, _1777104, _1777106] : [c_List_Oall__interval__int(_1777102, _1777104, _1777106), -(c_List_Olist__all(tc_Int_Oint, _1777102, c_List_Oupto(_1777104, _1777106)))], (13667 ^ _779854) ^ [_1020043, _1020045, _1020047] : [class_Orderings_Olinorder(_1020043), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020043), _1020045)), -(hBOOL(hAPP(hAPP(c_member(_1020043), _1020047), _1020045))), -(_1020045 = c_Orderings_Obot__class_Obot(tc_fun(_1020043, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1020043, hAPP(hAPP(c_Set_Oinsert(_1020043), _1020047), _1020045)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1020043), _1020047), c_Big__Operators_Olinorder__class_OMin(_1020043, _1020045)))], (41926 ^ _779854) ^ [_1605012, _1605014, _1605016, _1605018, _1605020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605012, _1605012)), hAPP(hAPP(c_Product__Type_OPair(_1605012, _1605012), _1605014), _1605016)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605012, _1605012), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1605018)), _1605020))), 41930 ^ _779854 : [(41933 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605012, _1605012)), hAPP(hAPP(c_Product__Type_OPair(_1605012, _1605012), 41929 ^ [_1605012, _1605014, _1605016, _1605018, _1605020]), _1605016)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605012, _1605012), tc_HOL_Obool), _1605018), _1605020))))], (41931 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605012, _1605012)), hAPP(hAPP(c_Product__Type_OPair(_1605012, _1605012), _1605014), 41929 ^ [_1605012, _1605014, _1605016, _1605018, _1605020])), _1605020)))]]], (52199 ^ _779854) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (45724 ^ _779854) ^ [_1696524, _1696526, _1696528] : [-(c_List_Olistsp(_1696524, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1696524, tc_HOL_Obool)), _1696526), _1696528)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1696524), tc_HOL_Obool)), c_List_Olistsp(_1696524, _1696526)), c_List_Olistsp(_1696524, _1696528)))], (7533 ^ _779854) ^ [_904108, _904110, _904112] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904108, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904108, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_904108, tc_HOL_Obool), _904110)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_904108, tc_HOL_Obool), _904112))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_904108, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_904108, tc_HOL_Obool), tc_HOL_Obool)), _904110), _904112)))))], (50770 ^ _779854) ^ [_1806482, _1806484, _1806486, _1806488] : [c_Fun_Obij__betw(_1806482, _1806484, _1806486, c_Orderings_Otop__class_Otop(tc_fun(_1806482, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1806484, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1806482, _1806484, _1806486), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1806482, tc_HOL_Obool)), _1806488)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1806484, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1806482, _1806484, _1806486), _1806488)))], (48922 ^ _779854) ^ [_1766462, _1766464, _1766466] : [-(c_List_Oreplicate(_1766462, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766462)), hAPP(c_List_Ofilter(_1766462, hAPP(c_fequal, _1766464)), _1766466)), _1766464) = hAPP(c_List_Ofilter(_1766462, hAPP(c_fequal, _1766464)), _1766466))], (38863 ^ _779854) ^ [_1521406, _1521408] : [-(hAPP(c_Set_OCollect(_1521406), hAPP(c_fequal, _1521408)) = hAPP(hAPP(c_Set_Oinsert(_1521406), _1521408), c_Orderings_Obot__class_Obot(tc_fun(_1521406, tc_HOL_Obool))))], (378 ^ _779854) ^ [_785623, _785625] : [-(c_Nitpick_Ounknown(_785623)), _785625 = _785623, c_Nitpick_Ounknown(_785625)], (35382 ^ _779854) ^ [_1438918, _1438920] : [-(_1438918 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35385 ^ _779854 : [(35392 ^ _779854) ^ [] : [-(_1438920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1438918, _1438920) = 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, _1438920))), 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, _1438918)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1438920))), c_Divides_Opdivmod(_1438918, _1438920)), 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), _1438920))))), c_Divides_Opdivmod(_1438918, _1438920)))))], (35386 ^ _779854) ^ [] : [_1438920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1438918, _1438920) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1438918))]]], (22779 ^ _779854) ^ [_1191487, _1191489, _1191491, _1191493] : [class_Fields_Olinordered__field(_1191487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191487), _1191489), c_Groups_Ozero__class_Ozero(_1191487))), 22786 ^ _779854 : [(22793 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191487), _1191493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191487), _1191491), _1191489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191487), _1191491), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191487), _1191493), _1191489))))], (22787 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191487), _1191491), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191487), _1191493), _1191489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191487), _1191493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191487), _1191491), _1191489))))]]], (33048 ^ _779854) ^ [_1378353, _1378355, _1378357, _1378359, _1378361] : [-(_1378353 = c_Orderings_Obot__class_Obot(tc_fun(_1378355, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378355, tc_fun(_1378357, tc_HOL_Obool)), _1378353), hAPP(hAPP(c_COMBB(tc_fun(_1378357, tc_HOL_Obool), tc_fun(_1378357, tc_HOL_Obool), _1378355), hAPP(c_Set_Oinsert(_1378357), _1378359)), _1378361)) = hAPP(hAPP(c_Set_Oinsert(_1378357), _1378359), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378355, tc_fun(_1378357, tc_HOL_Obool)), _1378353), _1378361)))], (46502 ^ _779854) ^ [_1714102, _1714104, _1714106] : [-(c_List_Oremdups(_1714102, hAPP(c_List_Ofilter(_1714102, _1714104), _1714106)) = hAPP(c_List_Ofilter(_1714102, _1714104), c_List_Oremdups(_1714102, _1714106)))], (11722 ^ _779854) ^ [_983254, _983256, _983258] : [-(hBOOL(hAPP(hAPP(c_member(_983254), _983256), _983258))), -(hBOOL(hAPP(hAPP(c_member(_983254), _983256), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_983254, tc_HOL_Obool)), _983258))))], (4586 ^ _779854) ^ [_849724, _849726, _849728, _849730] : [-(c_List_Oupto(_849730, _849726) = c_List_Oupto(_849728, _849724)), _849730 = _849728, _849726 = _849724], (25531 ^ _779854) ^ [_1244356, _1244358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244356)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244358))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244356), _1244358)))], (41419 ^ _779854) ^ [_1591948, _1591950, _1591952] : [c_Relation_Orefl__on(_1591948, _1591950, hAPP(c_Relation_Oconverse(_1591948, _1591948), _1591952)), -(c_Relation_Orefl__on(_1591948, _1591950, _1591952))], (48938 ^ _779854) ^ [_1766864, _1766866, _1766868] : [-(_1766864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1766866), c_List_Oreplicate(_1766866, _1766864, _1766868)) = _1766868)], (32974 ^ _779854) ^ [_1376250] : [-(c_Fun_Oinj__on(_1376250, tc_fun(_1376250, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1376250, tc_fun(_1376250, tc_HOL_Obool), tc_fun(_1376250, tc_HOL_Obool)), c_Set_Oinsert(_1376250)), c_Orderings_Obot__class_Obot(tc_fun(_1376250, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1376250, tc_HOL_Obool))))], (41708 ^ _779854) ^ [_1599114, _1599116, _1599118, _1599120, _1599122] : [c_Relation_Osingle__valued(_1599114, _1599114, _1599116), hBOOL(hAPP(hAPP(c_member(tc_prod(_1599114, _1599114)), hAPP(hAPP(c_Product__Type_OPair(_1599114, _1599114), _1599118), _1599120)), c_Transitive__Closure_Ortrancl(_1599114, _1599116))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1599114, _1599114)), hAPP(hAPP(c_Product__Type_OPair(_1599114, _1599114), _1599118), _1599122)), c_Transitive__Closure_Ortrancl(_1599114, _1599116))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599114, _1599114)), hAPP(hAPP(c_Product__Type_OPair(_1599114, _1599114), _1599120), _1599122)), c_Transitive__Closure_Ortrancl(_1599114, _1599116)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599114, _1599114)), hAPP(hAPP(c_Product__Type_OPair(_1599114, _1599114), _1599122), _1599120)), c_Transitive__Closure_Ortrancl(_1599114, _1599116))))], (37221 ^ _779854) ^ [_1479781, _1479783, _1479785, _1479787] : [c_Fun_Oinj__on(_1479781, tc_fun(tc_fun(_1479781, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1479781, tc_fun(tc_prod(_1479781, _1479781), tc_HOL_Obool), tc_fun(tc_fun(_1479781, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479781, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1479781, _1479781), tc_HOL_Obool), tc_fun(tc_fun(_1479781, tc_HOL_Obool), tc_HOL_Obool)), _1479781), c_Equiv__Relations_Oquotient(_1479781)), hAPP(hAPP(c_COMBC(_1479781, tc_fun(_1479781, tc_HOL_Obool), tc_fun(_1479781, tc_HOL_Obool)), c_Set_Oinsert(_1479781)), c_Orderings_Obot__class_Obot(tc_fun(_1479781, tc_HOL_Obool))))), _1479783), _1479785), hBOOL(hAPP(hAPP(c_member(_1479781), _1479787), _1479785)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479781), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1479781, tc_HOL_Obool)), _1479785), hAPP(hAPP(c_Set_Oinsert(_1479781), _1479787), c_Orderings_Obot__class_Obot(tc_fun(_1479781, tc_HOL_Obool))))), _1479783) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1479781, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479781), _1479785), _1479783)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1479781), hAPP(hAPP(c_Set_Oinsert(_1479781), _1479787), c_Orderings_Obot__class_Obot(tc_fun(_1479781, tc_HOL_Obool)))), _1479783)))], (14498 ^ _779854) ^ [_1036565, _1036567, _1036569] : [14500 ^ _779854 : [(14503 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1036565), _1036569), 14499 ^ [_1036565, _1036567, _1036569]))], (14501 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1036565, tc_HOL_Obool)), 14499 ^ [_1036565, _1036567, _1036569]), _1036567)))]], -(hBOOL(hAPP(hAPP(c_member(_1036565), _1036569), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1036565, tc_HOL_Obool), _1036567))))], (1480 ^ _779854) ^ [_801306, _801308] : [-(class_Groups_Ouminus(_801306)), _801308 = _801306, class_Groups_Ouminus(_801308)], (21314 ^ _779854) ^ [_1163845, _1163847] : [21316 ^ _779854 : [(21319 ^ _779854) ^ [] : [hBOOL(hAPP(_1163847, 21315 ^ [_1163845, _1163847]))], (21317 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21315 ^ [_1163845, _1163847]), _1163845)))]], 21320 ^ _779854 : [(21321 ^ _779854) ^ [_1163996] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1163996), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1163845))), -(hBOOL(hAPP(_1163847, _1163996)))]]], (33773 ^ _779854) ^ [_1401485, _1401487, _1401489, _1401491] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1401485, tc_HOL_Obool), hAPP(c_Set_Oimage(_1401487, tc_fun(_1401485, tc_HOL_Obool), _1401489), _1401491)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401487, tc_fun(_1401485, tc_HOL_Obool)), _1401491), _1401489))], (23260 ^ _779854) ^ [_1200498, _1200500, _1200502, _1200504, _1200506] : [class_Groups_Ocomm__monoid__mult(_1200498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1200500), _1200502)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1200500), _1200504)), 23274 ^ _779854 : [(23277 ^ _779854) ^ [] : [hAPP(_1200506, 23273 ^ [_1200498, _1200500, _1200502, _1200504, _1200506]) = c_Groups_Oone__class_Oone(_1200498)], (23275 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200500), 23273 ^ [_1200498, _1200500, _1200502, _1200504, _1200506]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1200500, tc_HOL_Obool)), _1200502), _1200504))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1200498, _1200500, c_Groups_Otimes__class_Otimes(_1200498)), _1200506), c_Groups_Oone__class_Oone(_1200498)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1200500, tc_HOL_Obool)), _1200502), _1200504)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200498), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1200498, _1200500, c_Groups_Otimes__class_Otimes(_1200498)), _1200506), c_Groups_Oone__class_Oone(_1200498)), _1200502)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1200498, _1200500, c_Groups_Otimes__class_Otimes(_1200498)), _1200506), c_Groups_Oone__class_Oone(_1200498)), _1200504)))], (44015 ^ _779854) ^ [_1658062, _1658064, _1658066] : [_1658062 = c_List_Olist_ONil(_1658064), -(c_List_Obutlast(_1658064, hAPP(hAPP(c_List_Oappend(_1658064), _1658066), _1658062)) = c_List_Obutlast(_1658064, _1658066))], (50284 ^ _779854) ^ [_1795696, _1795698, _1795700, _1795702] : [c_Equiv__Relations_Opart__equivp(_1795696, _1795698), hBOOL(hAPP(hAPP(_1795698, _1795700), _1795702)), -(hBOOL(hAPP(hAPP(_1795698, _1795702), _1795700)))], (838 ^ _779854) ^ [_792431, _792433, _792435, _792437] : [-(c_Relation_Osym(_792435, _792431)), c_Relation_Osym(_792437, _792433), _792437 = _792435, _792433 = _792431], (17512 ^ _779854) ^ [_1096792, _1096794, _1096796] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096792), _1096794)), -(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(_1096792), _1096796)), hAPP(c_Finite__Set_Ocard(_1096792), _1096794))), hAPP(c_Finite__Set_Ocard(_1096792), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1096792, tc_HOL_Obool)), _1096796), _1096794)))))], (38164 ^ _779854) ^ [_1502398, _1502400, _1502402, _1502404] : [-(hAPP(c_Set_Oimage(_1502398, _1502400, _1502402), hAPP(c_Set_Ovimage(_1502398, _1502400, _1502402), _1502404)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502400, tc_HOL_Obool)), _1502404), hAPP(c_Set_Oimage(_1502398, _1502400, _1502402), c_Orderings_Otop__class_Otop(tc_fun(_1502398, tc_HOL_Obool)))))], (19867 ^ _779854) ^ [_1138285] : [class_Rings_Olinordered__semidom(_1138285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138285), c_Groups_Oone__class_Oone(_1138285)), c_Groups_Ozero__class_Ozero(_1138285)))], (39582 ^ _779854) ^ [_1547735, _1547737, _1547739, _1547741, _1547743, _1547745, _1547747] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1547735, _1547737, _1547739, _1547741, _1547743), _1547745), _1547747))), 39583 ^ _779854 : [(39584 ^ _779854) ^ [_1547806] : [hBOOL(hAPP(hAPP(_1547741, _1547745), _1547806)), hBOOL(hAPP(hAPP(_1547743, _1547806), _1547747))]]], (16097 ^ _779854) ^ [_1068869, _1068871, _1068873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068871), _1068873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068869), _1068871)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1068869), _1068873))))], (16489 ^ _779854) ^ [_1076702, _1076704, _1076706, _1076708, _1076710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076702), _1076704)), 16492 ^ _779854 : [(16499 ^ _779854) ^ [] : [_1076708 = 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), _1076704), _1076702)), _1076706)), _1076710), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1076702), _1076706)), _1076708) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1076704), _1076706)), _1076710))], (16493 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1076702), _1076706)), _1076708) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1076704), _1076706)), _1076710), -(_1076708 = 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), _1076704), _1076702)), _1076706)), _1076710))]]], (3834 ^ _779854) ^ [_837604, _837606, _837608, _837610, _837612, _837614] : [-(c_List_OtakeWhile(_837614, _837610, _837606) = c_List_OtakeWhile(_837612, _837608, _837604)), _837614 = _837612, _837610 = _837608, _837606 = _837604], (52235 ^ _779854) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (8298 ^ _779854) ^ [_918775, _918777, _918779] : [class_Orderings_Olinorder(_918775), -(_918777 = _918779), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918775), _918777), _918779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918775), _918779), _918777)))], (1690 ^ _779854) ^ [_803931, _803933] : [-(class_Rings_Ono__zero__divisors(_803931)), _803933 = _803931, class_Rings_Ono__zero__divisors(_803933)], (51891 ^ _779854) ^ [_1829443, _1829445] : [_1829445 = _1829443, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829443), _1829445)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829445), _1829443)))], (40003 ^ _779854) ^ [_1556954, _1556956, _1556958, _1556960] : [40005 ^ _779854 : [(40008 ^ _779854) ^ [] : [c_Wellfounded_Owf(_1556956, hAPP(_1556958, 40004 ^ [_1556954, _1556956, _1556958, _1556960]))], (40006 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1556954, 40004 ^ [_1556954, _1556956, _1556958, _1556960])))]], -(c_Wellfounded_Owf(tc_prod(_1556960, _1556956), c_Recdef_Osame__fst(_1556960, _1556956, _1556954, _1556958)))], (33777 ^ _779854) ^ [_1401599, _1401601, _1401603, _1401605] : [class_Groups_Oordered__ab__group__add__abs(_1401599), -(hAPP(c_Groups_Oabs__class_Oabs(_1401599), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1401601, _1401599), hAPP(hAPP(c_COMBB(_1401599, _1401599, _1401601), c_Groups_Oabs__class_Oabs(_1401599)), _1401603)), _1401605)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1401601, _1401599), hAPP(hAPP(c_COMBB(_1401599, _1401599, _1401601), c_Groups_Oabs__class_Oabs(_1401599)), _1401603)), _1401605))], (20612 ^ _779854) ^ [_1150609, _1150611, _1150613] : [class_Groups_Oordered__comm__monoid__add(_1150609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150609), c_Groups_Ozero__class_Ozero(_1150609)), _1150611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150609), c_Groups_Ozero__class_Ozero(_1150609)), _1150613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150609), c_Groups_Ozero__class_Ozero(_1150609)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150609), _1150611), _1150613))))], (50886 ^ _779854) ^ [_1808914, _1808916, _1808918, _1808920, _1808922] : [c_Fun_Obij__betw(_1808914, _1808916, _1808918, _1808920, _1808922), -(c_Fun_Oinj__on(_1808914, _1808916, _1808918, _1808920))], (18325 ^ _779854) ^ [_1111424] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111424)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1111424))], (6261 ^ _779854) ^ [_879275, _879277] : [_879277 = c_Orderings_Obot__class_Obot(tc_fun(_879275, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879275, tc_HOL_Obool)), _879277), c_Orderings_Obot__class_Obot(tc_fun(_879275, tc_HOL_Obool)))))], (30151 ^ _779854) ^ [_1323937, _1323939, _1323941, _1323943] : [class_Divides_Oring__div(_1323937), -(c_Divides_Odiv__class_Omod(_1323937, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1323937), _1323939), _1323941), _1323943) = c_Divides_Odiv__class_Omod(_1323937, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1323937), c_Divides_Odiv__class_Omod(_1323937, _1323939, _1323943)), c_Divides_Odiv__class_Omod(_1323937, _1323941, _1323943)), _1323943))], (46386 ^ _779854) ^ [_1711488, _1711490, _1711492, _1711494] : [-(c_List_Otranspose(_1711488, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711488)), hAPP(hAPP(c_List_Olist_OCons(_1711488), _1711490), _1711492)), _1711494)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711488)), hAPP(hAPP(c_List_Olist_OCons(_1711488), _1711490), c_List_Oconcat(_1711488, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711488), tc_List_Olist(_1711488)), c_List_Olist_Olist__case(tc_List_Olist(_1711488), _1711488, c_List_Olist_ONil(_1711488), hAPP(hAPP(c_COMBB(tc_List_Olist(_1711488), tc_fun(tc_List_Olist(_1711488), tc_List_Olist(_1711488)), _1711488), c_COMBK(tc_List_Olist(_1711488), tc_List_Olist(_1711488))), hAPP(hAPP(c_COMBC(_1711488, tc_List_Olist(_1711488), tc_List_Olist(_1711488)), c_List_Olist_OCons(_1711488)), c_List_Olist_ONil(_1711488))))), _1711494)))), c_List_Otranspose(_1711488, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711488)), _1711492), c_List_Oconcat(tc_List_Olist(_1711488), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711488), tc_List_Olist(tc_List_Olist(_1711488))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1711488)), _1711488, c_List_Olist_ONil(tc_List_Olist(_1711488)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1711488), tc_List_Olist(tc_List_Olist(_1711488))), _1711488), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711488), tc_List_Olist(tc_List_Olist(_1711488)), tc_List_Olist(tc_List_Olist(_1711488))), c_List_Olist_OCons(tc_List_Olist(_1711488))), c_List_Olist_ONil(tc_List_Olist(_1711488)))))), _1711494))))))], (26877 ^ _779854) ^ [_1267477, _1267479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1267477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267479), 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), _1267477), _1267479)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32957 ^ _779854) ^ [_1375885, _1375887, _1375889, _1375891] : [32959 ^ _779854 : [(32962 ^ _779854) ^ [] : [hAPP(_1375891, 32958 ^ [_1375885, _1375887, _1375889, _1375891]) = c_Orderings_Otop__class_Otop(tc_fun(_1375885, tc_HOL_Obool))], (32960 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375887), 32958 ^ [_1375885, _1375887, _1375889, _1375891]), _1375889)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1375885, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375887, tc_fun(_1375885, tc_HOL_Obool)), _1375889), _1375891))], (43438 ^ _779854) ^ [_1645758, _1645760] : [-(c_List_Oremove1(_1645758, _1645760, c_List_Olist_ONil(_1645758)) = c_List_Olist_ONil(_1645758))], (41358 ^ _779854) ^ [_1590462, _1590464] : [-(c_Relation_Orefl__on(_1590462, c_Orderings_Otop__class_Otop(tc_fun(_1590462, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1590462, _1590462), tc_HOL_Obool)), _1590464), c_Relation_OId(_1590462))))], (49515 ^ _779854) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (41451 ^ _779854) ^ [_1592600, _1592602] : [-(hAPP(c_Relation_OField(_1592600), hAPP(c_Relation_Oconverse(_1592600, _1592600), _1592602)) = hAPP(c_Relation_OField(_1592600), _1592602))], (4750 ^ _779854) ^ [_852322, _852324, _852326, _852328, _852330, _852332] : [-(c_Relation_OImage(_852332, _852328, _852324) = c_Relation_OImage(_852330, _852326, _852322)), _852332 = _852330, _852328 = _852326, _852324 = _852322], (11548 ^ _779854) ^ [_979812, _979814, _979816] : [class_Orderings_Olinorder(_979812), hAPP(_979814, hAPP(hAPP(c_Orderings_Oord__class_Omax(_979812), 11553 ^ [_979812, _979814, _979816]), 11554 ^ [_979812, _979814, _979816])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_979812), hAPP(_979814, 11553 ^ [_979812, _979814, _979816])), hAPP(_979814, 11554 ^ [_979812, _979814, _979816])), hBOOL(hAPP(c_Finite__Set_Ofinite(_979812), _979816)), -(_979816 = c_Orderings_Obot__class_Obot(tc_fun(_979812, tc_HOL_Obool))), -(hAPP(_979814, c_Big__Operators_Olattice_OSup__fin(_979812, c_Orderings_Oord__class_Omax(_979812), _979816)) = c_Big__Operators_Olattice_OSup__fin(_979812, c_Orderings_Oord__class_Omax(_979812), hAPP(c_Set_Oimage(_979812, _979812, _979814), _979816)))], (48844 ^ _779854) ^ [_1764299, _1764301, _1764303, _1764305] : [-(c_Predicate_Oconversep(_1764299, _1764301, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1764299, tc_fun(_1764301, tc_HOL_Obool))), _1764303), _1764305)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1764301, tc_fun(_1764299, tc_HOL_Obool))), c_Predicate_Oconversep(_1764299, _1764301, _1764303)), c_Predicate_Oconversep(_1764299, _1764301, _1764305)))], (49118 ^ _779854) ^ [_1769965, _1769967, _1769969] : [-(hAPP(c_List_Oset(_1769965), c_List_Oreplicate(_1769965, hAPP(c_Nat_OSuc, _1769967), _1769969)) = hAPP(hAPP(c_Set_Oinsert(_1769965), _1769969), c_Orderings_Obot__class_Obot(tc_fun(_1769965, tc_HOL_Obool))))], (41302 ^ _779854) ^ [_1589136, _1589138, _1589140, _1589142] : [hBOOL(hAPP(hAPP(c_member(_1589136), _1589138), c_Wellfounded_Oacc(_1589136, _1589140))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589136, _1589136)), hAPP(hAPP(c_Product__Type_OPair(_1589136, _1589136), _1589142), _1589138)), c_Transitive__Closure_Ortrancl(_1589136, _1589140))), -(hBOOL(hAPP(hAPP(c_member(_1589136), _1589142), c_Wellfounded_Oacc(_1589136, _1589140))))], (1830 ^ _779854) ^ [_805681, _805683] : [-(class_Rings_Omult__zero(_805681)), _805683 = _805681, class_Rings_Omult__zero(_805683)], (16906 ^ _779854) ^ [_1084849, _1084851, _1084853, _1084855] : [class_Lattices_Osemilattice__sup(_1084849), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084849), _1084851)), hBOOL(hAPP(hAPP(c_member(_1084849), _1084853), _1084851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1084849), _1084853), _1084855)), hAPP(hAPP(c_Finite__Set_Ofold(_1084849, _1084849, c_Lattices_Osemilattice__sup__class_Osup(_1084849)), _1084855), _1084851))))], (39957 ^ _779854) ^ [_1556119, _1556121, _1556123, _1556125] : [hBOOL(hAPP(hAPP(c_member(_1556119), _1556121), hAPP(c_Relation_ODomain(_1556119, _1556123), _1556125))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556119, _1556123)), hAPP(hAPP(c_Product__Type_OPair(_1556119, _1556123), _1556121), 39960 ^ [_1556119, _1556121, _1556123, _1556125])), _1556125)))], (49572 ^ _779854) ^ [_1780825, _1780827] : [-(c_Relation_Otrans(_1780825, c_Transitive__Closure_Otrancl(_1780825, _1780827)))], (33925 ^ _779854) ^ [_1406342, _1406344, _1406346, _1406348, _1406350] : [class_Groups_Ocomm__monoid__add(_1406342), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406344), _1406346)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406344, _1406342), hAPP(hAPP(c_COMBS(_1406344, _1406342, _1406342), hAPP(hAPP(c_COMBB(_1406342, tc_fun(_1406342, _1406342), _1406344), c_Groups_Oplus__class_Oplus(_1406342)), _1406348)), _1406350)), _1406346) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1406342), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406344, _1406342), _1406348), _1406346)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406344, _1406342), _1406350), _1406346)))], (6269 ^ _779854) ^ [_879427, _879429] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_879427, _879429, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_879427), tc_HOL_Obool))))], (44041 ^ _779854) ^ [_1658708, _1658710, _1658712, _1658714] : [hBOOL(hAPP(hAPP(c_member(_1658708), _1658710), hAPP(c_List_Oset(_1658708), _1658712))), -(c_List_Oremove1(_1658708, _1658710, hAPP(hAPP(c_List_Oappend(_1658708), _1658712), _1658714)) = hAPP(hAPP(c_List_Oappend(_1658708), c_List_Oremove1(_1658708, _1658710, _1658712)), _1658714))], (41800 ^ _779854) ^ [_1601345, _1601347, _1601349, _1601351, _1601353, _1601355] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601345, _1601345)), hAPP(hAPP(c_Product__Type_OPair(_1601345, _1601345), _1601347), _1601349)), _1601351)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1601345, _1601345)), hAPP(hAPP(c_Product__Type_OPair(_1601345, _1601345), _1601349), _1601353)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601345, _1601345), tc_HOL_Obool), _1601355), _1601351))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601345, _1601345)), hAPP(hAPP(c_Product__Type_OPair(_1601345, _1601345), _1601347), _1601353)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1601345, _1601345), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1601355)), _1601351))))], (25429 ^ _779854) ^ [_1242131, _1242133, _1242135, _1242137, _1242139, _1242141, _1242143, _1242145] : [c_Finite__Set_Ofolding__image__simple__idem(_1242131, _1242133, _1242135, _1242137, _1242139, _1242141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1242133), _1242143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1242133, tc_HOL_Obool)), _1242145), _1242143)), -(hAPP(hAPP(_1242135, hAPP(_1242141, _1242145)), hAPP(_1242141, _1242143)) = hAPP(_1242141, _1242143))], (52283 ^ _779854) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (39831 ^ _779854) ^ [_1552720, _1552722] : [39833 ^ _779854 : [(39834 ^ _779854) ^ [_1552745] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1552720, _1552720)), hAPP(hAPP(c_Product__Type_OPair(_1552720, _1552720), hAPP(39832 ^ [_1552720, _1552722], hAPP(c_Nat_OSuc, _1552745))), hAPP(39832 ^ [_1552720, _1552722], _1552745))), _1552722)))]], -(c_Wellfounded_Owf(_1552720, _1552722))], (6415 ^ _779854) ^ [_882121] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_882121, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_882121, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_882121, tc_HOL_Obool)))], (9803 ^ _779854) ^ [_944442, _944444, _944446, _944448, _944450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944442, tc_HOL_Obool)), _944444), _944446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944448, tc_HOL_Obool)), hAPP(c_Set_Oimage(_944442, _944448, _944450), _944444)), hAPP(c_Set_Oimage(_944442, _944448, _944450), _944446))))], (8950 ^ _779854) ^ [_928995, _928997, _928999] : [class_Groups_Oordered__ab__group__add(_928995), 8953 ^ _779854 : [(8960 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928995), _928999), _928997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928995), hAPP(c_Groups_Ouminus__class_Ouminus(_928995), _928997)), hAPP(c_Groups_Ouminus__class_Ouminus(_928995), _928999))))], (8954 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928995), hAPP(c_Groups_Ouminus__class_Ouminus(_928995), _928997)), hAPP(c_Groups_Ouminus__class_Ouminus(_928995), _928999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928995), _928999), _928997)))]]], (28625 ^ _779854) ^ [_1297211, _1297213] : [class_Rings_Oring__1(_1297211), -(hBOOL(hAPP(hAPP(c_member(_1297211), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1297211), _1297213)), c_Int_Oring__1__class_OInts(_1297211))))], (11899 ^ _779854) ^ [_986623, _986625, _986627, _986629] : [hBOOL(hAPP(hAPP(c_member(_986623), _986625), hAPP(hAPP(c_Set_Oinsert(_986623), _986627), _986629))), -(_986625 = _986627), -(hBOOL(hAPP(hAPP(c_member(_986623), _986625), _986629)))], (7908 ^ _779854) ^ [_912148, _912150, _912152, _912154] : [class_Orderings_Oorder(_912148), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912148, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_912148, _912150, _912152)), c_SetInterval_Oord__class_OgreaterThanLessThan(_912148, _912152, _912154)) = c_Orderings_Obot__class_Obot(tc_fun(_912148, tc_HOL_Obool)))], (11891 ^ _779854) ^ [_986456, _986458, _986460] : [_986456 = c_Orderings_Obot__class_Obot(tc_fun(_986458, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_986458), _986460), _986456))], (15472 ^ _779854) ^ [_1056013, _1056015, _1056017] : [class_Rings_Oring(_1056013), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1056013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056013), _1056015), _1056017)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056013), hAPP(c_Groups_Ouminus__class_Ouminus(_1056013), _1056015)), _1056017))], (38064 ^ _779854) ^ [_1499893, _1499895, _1499897, _1499899, _1499901, _1499903] : [-(hAPP(c_Set_Ovimage(_1499893, _1499895, _1499897), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1499899, tc_fun(_1499895, tc_HOL_Obool)), _1499901), _1499903)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1499899, tc_fun(_1499893, tc_HOL_Obool)), _1499901), hAPP(hAPP(c_COMBB(tc_fun(_1499895, tc_HOL_Obool), tc_fun(_1499893, tc_HOL_Obool), _1499899), c_Set_Ovimage(_1499893, _1499895, _1499897)), _1499903)))], (21723 ^ _779854) ^ [_1171876, _1171878, _1171880, _1171882] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1171876, _1171878)), c_Sum__Type_OPlus(_1171876, _1171878, _1171880, _1171882))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171878), _1171882)))], (12382 ^ _779854) ^ [_996039, _996041, _996043] : [class_Complete__Lattice_Ocomplete__lattice(_996039), hBOOL(hAPP(hAPP(c_member(_996039), _996041), _996043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996039), _996041), c_Complete__Lattice_OSup__class_OSup(_996039, _996043))))], (7559 ^ _779854) ^ [_904674, _904676] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904674, tc_HOL_Obool)), _904676), c_Orderings_Obot__class_Obot(tc_fun(_904674, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_904674, tc_HOL_Obool)))], (19733 ^ _779854) ^ [_1135781, _1135783, _1135785] : [class_Rings_Olinordered__ring__strict(_1135781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135781), _1135783), c_Groups_Ozero__class_Ozero(_1135781))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135781), _1135785), c_Groups_Ozero__class_Ozero(_1135781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135781), c_Groups_Ozero__class_Ozero(_1135781)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135781), _1135783), _1135785))))], (27327 ^ _779854) ^ [_1275250, _1275252, _1275254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275250), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1275252)), _1275254)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6159 ^ _779854) ^ [_877687, _877689, _877691] : [class_Orderings_Otop(_877687), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_877689, _877687)), _877691) = c_Orderings_Otop__class_Otop(_877687))], (52461 ^ _779854) ^ [_1836282] : [-(class_Nat_Osize(tc_List_Olist(_1836282)))], (28866 ^ _779854) ^ [_1301190] : [-(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, _1301190))))))], (46601 ^ _779854) ^ [_1717390, _1717392, _1717394] : [class_Groups_Omonoid__add(_1717390), -(hAPP(c_List_Ofoldl(_1717390, _1717390, c_Groups_Oplus__class_Oplus(_1717390), _1717392), _1717394) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1717390), _1717392), c_List_Ofoldr(_1717390, _1717390, c_Groups_Oplus__class_Oplus(_1717390), _1717394, c_Groups_Ozero__class_Ozero(_1717390))))], (52251 ^ _779854) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (18152 ^ _779854) ^ [_1108296, _1108298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108296), _1108298)), -(_1108298 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108296), 18155 ^ [_1108296, _1108298])))], (17150 ^ _779854) ^ [_1089546, _1089548, _1089550] : [class_Lattices_Olattice(_1089546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089546), _1089548)), -(hBOOL(hAPP(hAPP(c_member(_1089546), _1089550), _1089548))), -(c_Big__Operators_Olattice__class_OInf__fin(_1089546, hAPP(hAPP(c_Set_Oinsert(_1089546), _1089550), _1089548)) = hAPP(hAPP(c_Finite__Set_Ofold(_1089546, _1089546, c_Lattices_Osemilattice__inf__class_Oinf(_1089546)), _1089550), _1089548))], (27091 ^ _779854) ^ [_1271093, _1271095, _1271097] : [class_Divides_Osemiring__div(_1271093), -(_1271095 = c_Groups_Ozero__class_Ozero(_1271093)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271093), _1271095), _1271097)), _1271095) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271093), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271093), _1271097), _1271095)), c_Groups_Oone__class_Oone(_1271093)))], (28396 ^ _779854) ^ [_1293237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293237), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1293237)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17921 ^ _779854) ^ [_1104274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104274)), _1104274))], (9450 ^ _779854) ^ [_937835, _937837, _937839, _937841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937835, tc_HOL_Obool)), _937837), _937839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937835, tc_HOL_Obool)), _937839), _937841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937835, tc_HOL_Obool)), _937837), _937841)))], (28292 ^ _779854) ^ [_1291457, _1291459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1291457), _1291459)), -(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)), _1291457)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1291459))))], (9905 ^ _779854) ^ [_946734, _946736, _946738, _946740, _946742] : [class_Orderings_Olinorder(_946734), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946734, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_946734, _946736, _946738)), c_SetInterval_Oord__class_OgreaterThanLessThan(_946734, _946740, _946742)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_946734, hAPP(hAPP(c_Orderings_Oord__class_Omax(_946734), _946736), _946740), hAPP(hAPP(c_Orderings_Oord__class_Omin(_946734), _946738), _946742)))], (2878 ^ _779854) ^ [_822702, _822704, _822706, _822708] : [-(c_Nitpick_Oint__lcm(_822708, _822704) = c_Nitpick_Oint__lcm(_822706, _822702)), _822708 = _822706, _822704 = _822702], (37255 ^ _779854) ^ [_1480796, _1480798, _1480800, _1480802] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1480796, _1480796)), hAPP(hAPP(c_Product__Type_OPair(_1480796, _1480796), _1480798), _1480800)), c_Relation_OId__on(_1480796, _1480802)))), _1480798 = _1480800, hBOOL(hAPP(hAPP(c_member(_1480796), _1480798), _1480802))], (43907 ^ _779854) ^ [_1655973, _1655975, _1655977] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655973)), hAPP(hAPP(c_List_Oappend(_1655973), _1655975), _1655977)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655973)), _1655975)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655973)), _1655977)))], (28469 ^ _779854) ^ [_1294592, _1294594] : [class_Rings_Olinordered__semidom(_1294592), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294592), c_Groups_Ozero__class_Ozero(_1294592)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294592), _1294594))))], (31057 ^ _779854) ^ [_1340269, _1340271] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1340269, _1340271)) = _1340271, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1340269), _1340271) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29629 ^ _779854) ^ [_1314271, _1314273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1314271), _1314273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1314271)), c_Int_OBit1(_1314273))))], (32928 ^ _779854) ^ [_1375176, _1375178, _1375180, _1375182] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375176, tc_fun(_1375178, tc_HOL_Obool)), _1375180), _1375182) = c_Orderings_Otop__class_Otop(tc_fun(_1375178, tc_HOL_Obool)), 32931 ^ _779854 : [(32932 ^ _779854) ^ [_1375292] : [hBOOL(hAPP(hAPP(c_member(_1375176), _1375292), _1375180)), -(hAPP(_1375182, _1375292) = c_Orderings_Otop__class_Otop(tc_fun(_1375178, tc_HOL_Obool)))]]], (34717 ^ _779854) ^ [_1424842, _1424844, _1424846] : [-(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), _1424842)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1424844))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1424846))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1424846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1424842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1424842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1424846), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1424844)))))], (46475 ^ _779854) ^ [_1713650, _1713652, _1713654] : [hAPP(c_List_Ofilter(_1713650, _1713652), _1713654) = c_List_Olist_ONil(_1713650), 46478 ^ _779854 : [(46479 ^ _779854) ^ [_1713747] : [hBOOL(hAPP(hAPP(c_member(_1713650), _1713747), hAPP(c_List_Oset(_1713650), _1713654))), hBOOL(hAPP(_1713652, _1713747))]]], (18331 ^ _779854) ^ [_1111533, _1111535] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1111533)), _1111535) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1111533, _1111535))], (11738 ^ _779854) ^ [_983511, _983513, _983515, _983517] : [hBOOL(hAPP(hAPP(c_member(_983511), _983513), c_Complete__Lattice_OInf__class_OInf(tc_fun(_983511, tc_HOL_Obool), _983515))), hBOOL(hAPP(hAPP(c_member(tc_fun(_983511, tc_HOL_Obool)), _983517), _983515)), -(hBOOL(hAPP(hAPP(c_member(_983511), _983513), _983517)))], (52149 ^ _779854) ^ [_1833314, _1833316] : [class_Orderings_Oord(_1833314), -(class_Orderings_Oord(tc_fun(_1833316, _1833314)))], (41441 ^ _779854) ^ [_1592365, _1592367, _1592369] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1592367, _1592365)), _1592369)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1592365, _1592367)), hAPP(c_Relation_Oconverse(_1592367, _1592365), _1592369))))], (8186 ^ _779854) ^ [_917040, _917042, _917044, _917046] : [class_Orderings_Oord(_917040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917040), _917042), _917044)), _917044 = _917046, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917040), _917042), _917046)))], (11155 ^ _779854) ^ [_972113] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_972113), c_Orderings_Obot__class_Obot(tc_fun(_972113, tc_HOL_Obool)))))], (15830 ^ _779854) ^ [_1063599, _1063601, _1063603] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063599), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063601), _1063603)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063599), _1063603)))], (46342 ^ _779854) ^ [_1709913, _1709915, _1709917] : [46344 ^ _779854 : [(46347 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1709913), tc_List_Olist(_1709913), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1709913), tc_fun(tc_List_Olist(_1709913), tc_Nat_Onat), tc_fun(tc_List_Olist(_1709913), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1709913), tc_Nat_Onat), tc_fun(tc_List_Olist(_1709913), tc_HOL_Obool)), tc_List_Olist(_1709913)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1709913))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1709913)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1709913))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1709913)))), 46343 ^ [_1709913, _1709915, _1709917]))], (46345 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709913), tc_List_Olist(_1709913))), 46343 ^ [_1709913, _1709915, _1709917]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1709913), tc_List_Olist(_1709913))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1709913), tc_List_Olist(_1709913)), _1709915), _1709917)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1709913))), _1709915) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1709913))), _1709917), 46352 ^ _779854 : [(46359 ^ _779854) ^ [] : [_1709915 = _1709917, -(c_List_Oconcat(_1709913, _1709915) = c_List_Oconcat(_1709913, _1709917))], (46353 ^ _779854) ^ [] : [c_List_Oconcat(_1709913, _1709915) = c_List_Oconcat(_1709913, _1709917), -(_1709915 = _1709917)]]], (16668 ^ _779854) ^ [_1080285, _1080287] : [-(_1080285 = _1080287), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080285), _1080287))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080287), _1080285)))], (4990 ^ _779854) ^ [_856096, _856098] : [_856098 = _856096, -(c_Lattices_Osemilattice__inf__class_Oinf(_856098) = c_Lattices_Osemilattice__inf__class_Oinf(_856096))], (33268 ^ _779854) ^ [_1383678, _1383680, _1383682, _1383684, _1383686, _1383688, _1383690, _1383692, _1383694, _1383696, _1383698] : [hAPP(_1383678, hAPP(_1383680, _1383682)) = hAPP(_1383684, hAPP(_1383686, _1383688)), -(hAPP(hAPP(c_Fun_Ocomp(_1383690, _1383692, _1383694, _1383678), _1383680), _1383682) = hAPP(hAPP(c_Fun_Ocomp(_1383696, _1383692, _1383698, _1383684), _1383686), _1383688))], (34357 ^ _779854) ^ [_1416658, _1416660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1416658), _1416660)), -(hAPP(c_Finite__Set_Ocard(_1416658), _1416660) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1416658, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1416658), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1416660))], (4564 ^ _779854) ^ [_849335, _849337, _849339, _849341, _849343, _849345, _849347, _849349, _849351, _849353] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_849353, _849349, _849345, _849341, _849337) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_849351, _849347, _849343, _849339, _849335)), _849353 = _849351, _849349 = _849347, _849345 = _849343, _849341 = _849339, _849337 = _849335], (49106 ^ _779854) ^ [_1769847, _1769849, _1769851] : [-(_1769847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1769849), c_List_Oreplicate(_1769849, _1769847, _1769851)) = hAPP(hAPP(c_Set_Oinsert(_1769849), _1769851), c_Orderings_Obot__class_Obot(tc_fun(_1769849, tc_HOL_Obool))))], (2690 ^ _779854) ^ [_819812, _819814, _819816, _819818, _819820, _819822] : [-(c_Wellfounded_Omlex__prod(_819822, _819818, _819814) = c_Wellfounded_Omlex__prod(_819820, _819816, _819812)), _819822 = _819820, _819818 = _819816, _819814 = _819812], (16247 ^ _779854) ^ [_1071681, _1071683, _1071685] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071681), _1071683)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071681), _1071685)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071683), _1071685))], (49699 ^ _779854) ^ [_1783407, _1783409, _1783411] : [c_List_Olist__ex(_1783407, _1783411, _1783409), 49703 ^ _779854 : [(49706 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1783411, 49702 ^ [_1783407, _1783409, _1783411])))], (49704 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783407), 49702 ^ [_1783407, _1783409, _1783411]), hAPP(c_List_Oset(_1783407), _1783409))))]]], (42661 ^ _779854) ^ [_1626790, _1626792, _1626794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1626790, tc_HOL_Obool)), hAPP(c_List_Oset(_1626790), _1626792)), hAPP(c_List_Oset(_1626790), hAPP(hAPP(c_List_Olist_OCons(_1626790), _1626794), _1626792)))))], (43452 ^ _779854) ^ [_1646015] : [class_Groups_Omonoid__add(_1646015), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1646015), c_List_Olist_ONil(_1646015)) = c_Groups_Ozero__class_Ozero(_1646015))], (52545 ^ _779854) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (20974 ^ _779854) ^ [_1157239, _1157241, _1157243] : [-(hBOOL(hAPP(_1157239, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1157241), _1157243)))), 20977 ^ _779854 : [(20980 ^ _779854) ^ [] : [hBOOL(hAPP(_1157239, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20978 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157241), _1157243)))]], 20982 ^ _779854 : [(20985 ^ _779854) ^ [] : [hBOOL(hAPP(_1157239, 20981 ^ [_1157239, _1157241, _1157243]))], (20983 ^ _779854) ^ [] : [-(_1157241 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1157243), 20981 ^ [_1157239, _1157241, _1157243]))]]], (33671 ^ _779854) ^ [_1398621, _1398623, _1398625, _1398627, _1398629, _1398631] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398621, tc_fun(_1398623, tc_HOL_Obool)), _1398625), hAPP(hAPP(c_COMBB(_1398627, tc_fun(_1398623, tc_HOL_Obool), _1398621), _1398629), _1398631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398627, tc_fun(_1398623, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398621, _1398627, _1398631), _1398625)), _1398629))], (5550 ^ _779854) ^ [_864804, _864806] : [_864806 = _864804, -(tc_Option_Ooption(_864806) = tc_Option_Ooption(_864804))], (33138 ^ _779854) ^ [_1380581, _1380583, _1380585, _1380587] : [class_Complete__Lattice_Ocomplete__lattice(_1380581), -(_1380583 = c_Orderings_Obot__class_Obot(tc_fun(_1380585, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380585, _1380581), _1380583), hAPP(c_COMBK(_1380581, _1380585), _1380587)) = _1380587)], (34924 ^ _779854) ^ [_1429019, _1429021, _1429023, _1429025, _1429027] : [34926 ^ _779854 : [(34929 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1429025, 34925 ^ [_1429019, _1429021, _1429023, _1429025, _1429027]), _1429027))], (34927 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429019), 34925 ^ [_1429019, _1429021, _1429023, _1429025, _1429027]), _1429023)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429019, tc_fun(_1429021, tc_HOL_Obool)), _1429023), _1429025), _1429027)))], (51344 ^ _779854) ^ [_1819896, _1819898, _1819900] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1819896), _1819898)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1819896), _1819900))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1819896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1819898), _1819900)))], (2 ^ _779854) ^ [_779881] : [-(_779881 = _779881)], (36782 ^ _779854) ^ [_1468260, _1468262, _1468264, _1468266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1468260), _1468262)), -(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), _1468260), _1468264)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1468262), _1468266))), c_FunDef_Opair__less)))], (39220 ^ _779854) ^ [_1534075, _1534077, _1534079] : [class_Orderings_Olinorder(_1534075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534075), _1534077)), -(_1534077 = c_Orderings_Obot__class_Obot(tc_fun(_1534075, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534075), _1534079)), -(_1534079 = c_Orderings_Obot__class_Obot(tc_fun(_1534075, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1534075), c_Big__Operators_Olattice_OSup__fin(_1534075, c_Orderings_Oord__class_Omax(_1534075), _1534077)), c_Big__Operators_Olattice_OSup__fin(_1534075, c_Orderings_Oord__class_Omax(_1534075), _1534079)) = c_Big__Operators_Olattice_OSup__fin(_1534075, c_Orderings_Oord__class_Omax(_1534075), hAPP(c_Set_OCollect(_1534075), hAPP(hAPP(c_COMBB(tc_fun(_1534075, tc_HOL_Obool), tc_HOL_Obool, _1534075), c_HOL_OEx(_1534075)), hAPP(hAPP(c_COMBB(tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool)), tc_fun(_1534075, tc_HOL_Obool), _1534075), hAPP(c_COMBB(tc_fun(_1534075, tc_HOL_Obool), tc_HOL_Obool, _1534075), c_HOL_OEx(_1534075))), hAPP(hAPP(c_COMBC(_1534075, tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool)), tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534075, tc_fun(tc_fun(_1534075, tc_HOL_Obool), tc_fun(_1534075, tc_HOL_Obool))), tc_fun(tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool)), tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool))), _1534075), c_COMBS(_1534075, tc_fun(_1534075, tc_HOL_Obool), tc_fun(_1534075, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534075, tc_fun(_1534075, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1534075, tc_fun(tc_fun(_1534075, tc_HOL_Obool), tc_fun(_1534075, tc_HOL_Obool))), _1534075), hAPP(c_COMBB(tc_fun(_1534075, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1534075, tc_HOL_Obool), tc_fun(_1534075, tc_HOL_Obool)), _1534075), c_COMBS(_1534075, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool)), tc_fun(_1534075, tc_fun(_1534075, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1534075), hAPP(c_COMBB(tc_fun(_1534075, tc_HOL_Obool), tc_fun(_1534075, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1534075), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534075), c_fconj))), hAPP(hAPP(c_COMBC(_1534075, tc_fun(_1534075, tc_fun(_1534075, _1534075)), tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534075, _1534075), tc_fun(_1534075, tc_HOL_Obool)), tc_fun(tc_fun(_1534075, tc_fun(_1534075, _1534075)), tc_fun(_1534075, tc_fun(_1534075, tc_HOL_Obool))), _1534075), c_COMBB(tc_fun(_1534075, _1534075), tc_fun(_1534075, tc_HOL_Obool), _1534075)), hAPP(hAPP(c_COMBB(tc_fun(_1534075, tc_HOL_Obool), tc_fun(tc_fun(_1534075, _1534075), tc_fun(_1534075, tc_HOL_Obool)), _1534075), c_COMBB(_1534075, tc_HOL_Obool, _1534075)), c_fequal))), c_Orderings_Oord__class_Omin(_1534075)))))), hAPP(hAPP(c_COMBC(_1534075, tc_fun(_1534075, tc_HOL_Obool), tc_fun(_1534075, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534075, tc_HOL_Obool), tc_fun(_1534075, tc_HOL_Obool)), _1534075), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534075)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534075), c_fconj), hAPP(hAPP(c_COMBC(_1534075, tc_fun(_1534075, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534075)), _1534077)))), hAPP(hAPP(c_COMBC(_1534075, tc_fun(_1534075, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534075)), _1534079))))))))], (50912 ^ _779854) ^ [_1809366, _1809368, _1809370, _1809372] : [c_Fun_Obij__betw(_1809366, _1809368, _1809370, c_Orderings_Obot__class_Obot(tc_fun(_1809366, tc_HOL_Obool)), _1809372), -(_1809372 = c_Orderings_Obot__class_Obot(tc_fun(_1809368, tc_HOL_Obool)))], (44681 ^ _779854) ^ [_1673740, _1673742] : [class_Complete__Lattice_Ocomplete__lattice(_1673740), -(c_Complete__Lattice_OInf__class_OInf(_1673740, hAPP(c_List_Oset(_1673740), _1673742)) = hAPP(c_List_Ofoldl(_1673740, _1673740, c_Lattices_Osemilattice__inf__class_Oinf(_1673740), c_Orderings_Otop__class_Otop(_1673740)), _1673742))], (52351 ^ _779854) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (13193 ^ _779854) ^ [_1012596, _1012598] : [class_Orderings_Olinorder(_1012596), -(c_Big__Operators_Olinorder__class_OMin(_1012596, hAPP(hAPP(c_Set_Oinsert(_1012596), _1012598), c_Orderings_Obot__class_Obot(tc_fun(_1012596, tc_HOL_Obool)))) = _1012598)], (6727 ^ _779854) ^ [_887883, _887885, _887887] : [class_Lattices_Oboolean__algebra(_887883), -(hAPP(c_Groups_Ouminus__class_Ouminus(_887883), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_887883), _887885), _887887)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_887883), hAPP(c_Groups_Ouminus__class_Ouminus(_887883), _887885)), hAPP(c_Groups_Ouminus__class_Ouminus(_887883), _887887)))], (8874 ^ _779854) ^ [_927571, _927573, _927575, _927577] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927571, tc_HOL_Obool)), _927573), hAPP(hAPP(c_Set_Oinsert(_927571), _927575), _927577)) = hAPP(hAPP(c_Set_Oinsert(_927571), _927575), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927571, tc_HOL_Obool)), _927573), _927577)))], (45380 ^ _779854) ^ [_1689096, _1689098] : [hAPP(c_Code__Numeral_Oof__nat, _1689096) = hAPP(c_Code__Numeral_Oof__nat, _1689098), -(_1689096 = _1689098)], (45831 ^ _779854) ^ [_1699231, _1699233, _1699235, _1699237, _1699239, _1699241] : [c_List_Olist__all2(_1699231, _1699233, _1699235, _1699237, _1699239), -(c_List_Olist__all2(_1699231, _1699233, _1699235, hAPP(hAPP(c_List_Odrop(_1699231), _1699241), _1699237), hAPP(hAPP(c_List_Odrop(_1699233), _1699241), _1699239)))], (42060 ^ _779854) ^ [_1608512, _1608514, _1608516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1608512), c_Nitpick_Oplus__frac(_1608512, _1608514, c_Nitpick_Ouminus__frac(_1608512, _1608516)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1608512, _1608514, _1608516))], (30811 ^ _779854) ^ [_1336083, _1336085, _1336087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336083)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336085, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1336087), _1336083)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1336087), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1336085), _1336087), _1336083))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1336085, _1336087)))], (33381 ^ _779854) ^ [_1386846, _1386848, _1386850, _1386852, _1386854] : [class_Groups_Ocomm__monoid__mult(_1386846), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386848, _1386846), hAPP(hAPP(c_COMBS(_1386848, _1386846, _1386846), hAPP(hAPP(c_COMBB(_1386846, tc_fun(_1386846, _1386846), _1386848), c_Groups_Otimes__class_Otimes(_1386846)), _1386850)), _1386852)), _1386854) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386846), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386848, _1386846), _1386850), _1386854)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386848, _1386846), _1386852), _1386854)))], (32079 ^ _779854) ^ [_1356998, _1357000] : [class_Groups_Oordered__ab__group__add__abs(_1356998), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356998), c_Groups_Ozero__class_Ozero(_1356998)), hAPP(c_Groups_Oabs__class_Oabs(_1356998), _1357000))))], (9148 ^ _779854) ^ [_932456, _932458, _932460, _932462, _932464] : [class_Orderings_Oorder(_932456), class_Orderings_Oorder(_932458), c_Orderings_Oorder__class_Ostrict__mono(_932458, _932456, _932460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932458), _932462), _932464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932456), hAPP(_932460, _932462)), hAPP(_932460, _932464))))], (46946 ^ _779854) ^ [_1723886, _1723888, _1723890, _1723892] : [class_Orderings_Olinorder(_1723886), 46949 ^ _779854 : [(46958 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1723886, hAPP(hAPP(c_List_Olist_OCons(_1723886), _1723888), hAPP(hAPP(c_List_Olist_OCons(_1723886), _1723890), _1723892)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723886), _1723888), _1723890)), c_List_Olinorder__class_Osorted(_1723886, hAPP(hAPP(c_List_Olist_OCons(_1723886), _1723890), _1723892))], (46950 ^ _779854) ^ [] : [c_List_Olinorder__class_Osorted(_1723886, hAPP(hAPP(c_List_Olist_OCons(_1723886), _1723888), hAPP(hAPP(c_List_Olist_OCons(_1723886), _1723890), _1723892))), 46953 ^ _779854 : [(46956 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1723886, hAPP(hAPP(c_List_Olist_OCons(_1723886), _1723890), _1723892)))], (46954 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723886), _1723888), _1723890)))]]]]], (35965 ^ _779854) ^ [_1449909, _1449911, _1449913] : [35967 ^ _779854 : [(35970 ^ _779854) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1449913, 35966 ^ [_1449909, _1449911, _1449913]))], (35968 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1449909), 35966 ^ [_1449909, _1449911, _1449913]), _1449911)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1449909, tc_Int_Oint), _1449913), _1449911) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1449909, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1449909), c_Int_Onat), _1449913)), _1449911)))], (42713 ^ _779854) ^ [_1627935, _1627937, _1627939, _1627941] : [-(hAPP(hAPP(c_List_Otake(_1627935), hAPP(c_Nat_OSuc, _1627937)), hAPP(hAPP(c_List_Olist_OCons(_1627935), _1627939), _1627941)) = hAPP(hAPP(c_List_Olist_OCons(_1627935), _1627939), hAPP(hAPP(c_List_Otake(_1627935), _1627937), _1627941)))], (30011 ^ _779854) ^ [_1320996, _1320998, _1321000] : [class_Rings_Olinordered__idom(_1320996), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320996), c_Groups_Ozero__class_Ozero(_1320996)), hAPP(hAPP(c_Power_Opower__class_Opower(_1320996), _1320998), 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)))), _1321000)))))], (43666 ^ _779854) ^ [_1650196, _1650198, _1650200, _1650202, _1650204, _1650206] : [-(hAPP(c_List_Olist_Olist__case(_1650196, _1650198, _1650200, _1650202), hAPP(hAPP(c_List_Olist_OCons(_1650198), _1650204), _1650206)) = hAPP(hAPP(_1650202, _1650204), _1650206))], (44811 ^ _779854) ^ [_1676759, _1676761, _1676763, _1676765, _1676767, _1676769] : [class_Orderings_Olinorder(_1676759), -(hAPP(_1676761, _1676763) = hAPP(_1676761, _1676765)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676767, _1676759, _1676761), _1676765), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676767, _1676759, _1676761), _1676763), _1676769)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676767, _1676759, _1676761), _1676763), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1676767, _1676759, _1676761), _1676765), _1676769)))], (51290 ^ _779854) ^ [_1818817, _1818819, _1818821, _1818823, _1818825] : [-(c_Lazy__Sequence_Omap(_1818817, _1818819, _1818821, c_Lazy__Sequence_Olazy__sequence_OInsert(_1818817, _1818823, _1818825)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1818819, hAPP(_1818821, _1818823), c_Lazy__Sequence_Omap(_1818817, _1818819, _1818821, _1818825)))], (42602 ^ _779854) ^ [_1625103, _1625105, _1625107, _1625109] : [-(_1625103 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1625105), hAPP(hAPP(c_List_Olist_OCons(_1625105), _1625107), _1625109)), _1625103) = hAPP(hAPP(c_List_Onth(_1625105), _1625109), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1625103), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9420 ^ _779854) ^ [_937180, _937182, _937184, _937186] : [class_Orderings_Olinorder(_937180), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937180, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_937180, _937182, _937184)), hAPP(c_SetInterval_Oord__class_OatLeast(_937180), _937186)) = c_SetInterval_Oord__class_OatLeastAtMost(_937180, hAPP(hAPP(c_Orderings_Oord__class_Omax(_937180), _937182), _937186), _937184))], (19873 ^ _779854) ^ [_1138381] : [class_Rings_Olinordered__semidom(_1138381), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138381), c_Groups_Ozero__class_Ozero(_1138381)), c_Groups_Oone__class_Oone(_1138381))))], (19699 ^ _779854) ^ [_1135145, _1135147, _1135149, _1135151] : [class_Rings_Olinordered__ring__strict(_1135145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135145), _1135147), c_Groups_Ozero__class_Ozero(_1135145))), 19706 ^ _779854 : [(19713 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135145), _1135151), _1135149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135145), _1135147), _1135149)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135145), _1135147), _1135151))))], (19707 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135145), _1135147), _1135149)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135145), _1135147), _1135151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135145), _1135151), _1135149)))]]], (49669 ^ _779854) ^ [_1782740, _1782742] : [c_Relation_Otrans(_1782740, _1782742), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1782740, _1782740), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1782740, _1782740, _1782740), _1782742), _1782742)), _1782742)))], (39737 ^ _779854) ^ [] : [-(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)))))], (36221 ^ _779854) ^ [_1455741, _1455743, _1455745, _1455747, _1455749] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1455741, _1455743, _1455745), _1455747), _1455749) = hAPP(hAPP(_1455747, hAPP(c_Product__Type_Ofst(_1455741, _1455743), _1455749)), hAPP(c_Product__Type_Osnd(_1455741, _1455743), _1455749)))], (34557 ^ _779854) ^ [_1421111, _1421113] : [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(_1421113))), 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), _1421111)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421111)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421113))))], (26285 ^ _779854) ^ [_1257705, _1257707, _1257709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257705)), 26288 ^ _779854 : [(26289 ^ _779854) ^ [_1257839] : [26291 ^ _779854 : [(26297 ^ _779854) ^ [] : [-(_1257839 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26293 ^ [_1257705, _1257707, _1257709, _1257839]), 26290 ^ [_1257705, _1257707, _1257709, _1257839]))], (26295 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26293 ^ [_1257705, _1257707, _1257709, _1257839]), _1257707)))], (26292 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26290 ^ [_1257705, _1257707, _1257709, _1257839]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1257705))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257839), _1257709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1257839), _1257705)), _1257709)))]]], (31304 ^ _779854) ^ [_1344266, _1344268] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1344266, _1344268) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1344266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1344266), _1344268)), _1344268)))], (13225 ^ _779854) ^ [_1013144, _1013146, _1013148] : [class_Orderings_Olinorder(_1013144), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013144), _1013146)), hBOOL(hAPP(hAPP(c_member(_1013144), _1013148), _1013146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013144), c_Big__Operators_Olinorder__class_OMin(_1013144, _1013146)), _1013148)))], (31310 ^ _779854) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (29647 ^ _779854) ^ [] : [-(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))))], (44274 ^ _779854) ^ [_1664914, _1664916, _1664918, _1664920] : [hBOOL(hAPP(hAPP(c_member(_1664914), _1664916), hAPP(c_List_Oset(_1664914), hAPP(hAPP(c_List_Odrop(_1664914), _1664918), _1664920)))), -(hBOOL(hAPP(hAPP(c_member(_1664914), _1664916), hAPP(c_List_Oset(_1664914), _1664920))))], (37111 ^ _779854) ^ [_1476843, _1476845] : [-(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), _1476843), _1476845)), 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), _1476843), _1476845))], (5886 ^ _779854) ^ [_873046, _873048, _873050, _873052] : [class_Orderings_Oorder(_873046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873046), _873048), _873050)), _873048 = _873052, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873046), _873052), _873050)))], (38811 ^ _779854) ^ [_1520093, _1520095, _1520097] : [-(hAPP(hAPP(c_Set_Oinsert(_1520093), _1520095), _1520097) = hAPP(c_Set_OCollect(_1520093), hAPP(hAPP(c_COMBS(_1520093, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520093), c_fdisj), hAPP(hAPP(c_COMBC(_1520093, _1520093, tc_HOL_Obool), c_fequal), _1520095))), hAPP(hAPP(c_COMBC(_1520093, tc_fun(_1520093, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520093)), _1520097))))], (43011 ^ _779854) ^ [_1636534, _1636536, _1636538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1636534), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1636536))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1636536), _1636534), _1636538)) = 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), _1636536)), _1636538)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1636536), _1636534)))], (12250 ^ _779854) ^ [_993237, _993239, _993241] : [hBOOL(hAPP(hAPP(c_member(_993237), _993239), hAPP(hAPP(c_Set_Oinsert(_993237), _993241), c_Orderings_Obot__class_Obot(tc_fun(_993237, tc_HOL_Obool))))), -(_993239 = _993241)], (14235 ^ _779854) ^ [_1031140, _1031142, _1031144] : [class_Lattices_Olattice(_1031140), hAPP(_1031142, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1031140), 14240 ^ [_1031140, _1031142, _1031144]), 14241 ^ [_1031140, _1031142, _1031144])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1031140), hAPP(_1031142, 14240 ^ [_1031140, _1031142, _1031144])), hAPP(_1031142, 14241 ^ [_1031140, _1031142, _1031144])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031140), _1031144)), -(_1031144 = c_Orderings_Obot__class_Obot(tc_fun(_1031140, tc_HOL_Obool))), -(hAPP(_1031142, c_Big__Operators_Olattice__class_OSup__fin(_1031140, _1031144)) = c_Big__Operators_Olattice__class_OSup__fin(_1031140, hAPP(c_Set_Oimage(_1031140, _1031140, _1031142), _1031144)))], (43618 ^ _779854) ^ [_1649194, _1649196] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649194)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649196)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649194), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1649196)) = c_List_Olist_ONil(tc_Int_Oint))], (15786 ^ _779854) ^ [_1062719] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1062719))))], (39735 ^ _779854) ^ [_1550569, _1550571] : [-(hAPP(c_Relation_ODomain(_1550569, _1550569), c_Relation_OId__on(_1550569, _1550571)) = _1550571)], (28220 ^ _779854) ^ [_1290137, _1290139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1290137)), c_Int_OBit1(_1290139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1290137), _1290139)))], (17781 ^ _779854) ^ [_1102084, _1102086] : [class_Groups_Ocomm__monoid__mult(_1102084), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102084), _1102086), c_Groups_Oone__class_Oone(_1102084)) = _1102086)], (35234 ^ _779854) ^ [_1436309, _1436311, _1436313, _1436315, _1436317, _1436319] : [-(hAPP(hAPP(c_Product__Type_OPair(_1436309, _1436311), _1436313), _1436315) = hAPP(hAPP(c_Product__Type_OPair(_1436309, _1436311), _1436317), _1436319)), _1436313 = _1436317, _1436315 = _1436319], (48952 ^ _779854) ^ [_1767045, _1767047, _1767049, _1767051] : [48959 ^ _779854 : [(48962 ^ _779854) ^ [] : [_1767047 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48960 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1767051, _1767049)))]], 48953 ^ _779854 : [(48954 ^ _779854) ^ [_1767117] : [hBOOL(hAPP(hAPP(c_member(_1767045), _1767117), hAPP(c_List_Oset(_1767045), c_List_Oreplicate(_1767045, _1767047, _1767049)))), hBOOL(hAPP(_1767051, _1767117))]]], (21366 ^ _779854) ^ [_1164890, _1164892] : [21374 ^ _779854 : [(21377 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1164892, 21373 ^ [_1164890, _1164892])))], (21375 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 21373 ^ [_1164890, _1164892]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1164890))))]], 21367 ^ _779854 : [(21368 ^ _779854) ^ [_1164958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1164958), _1164890)), hBOOL(hAPP(_1164892, _1164958))]]], (11538 ^ _779854) ^ [_979549, _979551, _979553, _979555, _979557, _979559, _979561, _979563] : [c_Finite__Set_Ofolding__image__simple(_979549, _979551, _979553, _979555, _979557, _979559), hBOOL(hAPP(c_Finite__Set_Ofinite(_979551), _979561)), -(hAPP(_979559, hAPP(hAPP(c_Set_Oinsert(_979551), _979563), _979561)) = hAPP(hAPP(_979553, hAPP(_979557, _979563)), hAPP(_979559, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979551, tc_HOL_Obool)), _979561), hAPP(hAPP(c_Set_Oinsert(_979551), _979563), c_Orderings_Obot__class_Obot(tc_fun(_979551, tc_HOL_Obool)))))))], (42207 ^ _779854) ^ [_1613393, _1613395, _1613397, _1613399] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613393), tc_List_Olist(_1613393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613393), tc_List_Olist(_1613393)), _1613395), _1613397)), c_List_Olex(_1613393, _1613399))), 42210 ^ _779854 : [(42213 ^ _779854) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613393)), _1613395) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613393)), _1613397))], (42211 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613393), tc_List_Olist(_1613393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613393), tc_List_Olist(_1613393)), _1613395), _1613397)), c_List_Olexord(_1613393, _1613399))))]]], (28256 ^ _779854) ^ [_1290806, _1290808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1290806)), c_Int_OBit1(_1290808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290806), _1290808)))], (30605 ^ _779854) ^ [_1332225, _1332227, _1332229] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332225), _1332227)), _1332229) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332225), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1332227), _1332229))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332225), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332227, _1332229))), _1332229)))], (29803 ^ _779854) ^ [_1317293, _1317295, _1317297] : [class_Rings_Olinordered__semidom(_1317293), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317293), hAPP(hAPP(c_Power_Opower__class_Opower(_1317293), _1317295), 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(_1317293), _1317297), 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(_1317293), c_Groups_Ozero__class_Ozero(_1317293)), _1317297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317293), _1317295), _1317297)))], (36217 ^ _779854) ^ [_1455581, _1455583, _1455585, _1455587, _1455589] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1455581, _1455583, _1455585), _1455587), _1455589) = hAPP(hAPP(_1455587, hAPP(c_Product__Type_Ofst(_1455581, _1455583), _1455589)), hAPP(c_Product__Type_Osnd(_1455581, _1455583), _1455589)))], (16678 ^ _779854) ^ [_1080347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080347), _1080347))], (51327 ^ _779854) ^ [_1819491, _1819493, _1819495, _1819497, _1819499, _1819501, _1819503, _1819505] : [c_Finite__Set_Ofolding__image(_1819491, _1819493, _1819495, _1819497, _1819499), hBOOL(hAPP(c_Finite__Set_Ofinite(_1819493), _1819501)), 51337 ^ _779854 : [(51340 ^ _779854) ^ [] : [hAPP(_1819503, 51336 ^ [_1819491, _1819493, _1819495, _1819497, _1819499, _1819501, _1819503, _1819505]) = hAPP(_1819505, 51336 ^ [_1819491, _1819493, _1819495, _1819497, _1819499, _1819501, _1819503, _1819505])], (51338 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819493), 51336 ^ [_1819491, _1819493, _1819495, _1819497, _1819499, _1819501, _1819503, _1819505]), _1819501)))]], -(hAPP(hAPP(_1819499, _1819503), _1819501) = hAPP(hAPP(_1819499, _1819505), _1819501))], (10633 ^ _779854) ^ [_960877, _960879, _960881, _960883, _960885] : [c_Fun_Oinj__on(_960877, _960879, _960881, c_Orderings_Otop__class_Otop(tc_fun(_960877, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_960877, _960879, _960881), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960877, tc_HOL_Obool)), _960883), _960885)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960879, tc_HOL_Obool)), hAPP(c_Set_Oimage(_960877, _960879, _960881), _960883)), hAPP(c_Set_Oimage(_960877, _960879, _960881), _960885)))], (9478 ^ _779854) ^ [_938323, _938325, _938327] : [class_Orderings_Olinorder(_938323), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938323), _938325), _938327) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_938323), _938327), _938325))], (23794 ^ _779854) ^ [_1211329, _1211331, _1211333] : [class_Rings_Ocomm__semiring__1(_1211329), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211329), hAPP(hAPP(c_Power_Opower__class_Opower(_1211329), _1211331), _1211333)), _1211331) = hAPP(hAPP(c_Power_Opower__class_Opower(_1211329), _1211331), hAPP(c_Nat_OSuc, _1211333)))], (20155 ^ _779854) ^ [_1143107, _1143109, _1143111, _1143113] : [class_Rings_Ocomm__semiring__1(_1143107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1143109), _1143111)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1143109, _1143107), _1143113), _1143111) = c_Groups_Ozero__class_Ozero(_1143107)), 20164 ^ _779854 : [(20165 ^ _779854) ^ [_1143288] : [hBOOL(hAPP(hAPP(c_member(_1143109), _1143288), _1143111)), hAPP(_1143113, _1143288) = c_Groups_Ozero__class_Ozero(_1143107)]]], (45492 ^ _779854) ^ [_1691304] : [-(_1691304 = 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)), _1691304)))], (41774 ^ _779854) ^ [_1600645, _1600647, _1600649] : [41775 ^ _779854 : [(41776 ^ _779854) ^ [_1600721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600645, _1600645)), _1600647), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600645, _1600645), tc_HOL_Obool), _1600721), _1600649)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600645, _1600645)), _1600647), c_Transitive__Closure_Ortrancl(_1600645, _1600649))))], (20536 ^ _779854) ^ [_1149279, _1149281] : [-(_1149279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1149279), _1149281) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1149279), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1149281)))], (8870 ^ _779854) ^ [_927464, _927466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927464, tc_HOL_Obool)), _927466), c_Orderings_Obot__class_Obot(tc_fun(_927464, tc_HOL_Obool))))], (8852 ^ _779854) ^ [_927022, _927024, _927026] : [hAPP(hAPP(c_Set_Oinsert(_927022), _927024), _927026) = c_Orderings_Obot__class_Obot(tc_fun(_927022, tc_HOL_Obool))], (51325 ^ _779854) ^ [_1819446, _1819448, _1819450, _1819452, _1819454] : [-(c_New__DSequence_Opos__map(_1819446, _1819448, _1819450, _1819452, _1819454) = c_Lazy__Sequence_Omap(_1819446, _1819448, _1819450, hAPP(_1819452, _1819454)))], (25293 ^ _779854) ^ [_1239456, _1239458, _1239460, _1239462] : [class_Fields_Olinordered__field__inverse__zero(_1239456), class_Int_Onumber(_1239456), 25300 ^ _779854 : [(25301 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239456), _1239458), _1239460)), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462))), 25304 ^ _779854 : [(25311 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), c_Groups_Ozero__class_Ozero(_1239456)), _1239460))), 25314 ^ _779854 : [(25321 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), _1239460), c_Groups_Ozero__class_Ozero(_1239456)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), c_Groups_Ozero__class_Ozero(_1239456)), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462))))], (25315 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), _1239460), c_Groups_Ozero__class_Ozero(_1239456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239456), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462)), _1239460)), _1239458)))]]], (25305 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), c_Groups_Ozero__class_Ozero(_1239456)), _1239460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), _1239458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239456), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462)), _1239460))))]]], (25327 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239456), _1239458), _1239460)), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462)))), 25330 ^ _779854 : [(25333 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), _1239458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239456), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462)), _1239460)))], (25331 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), c_Groups_Ozero__class_Ozero(_1239456)), _1239460)))]], 25334 ^ _779854 : [(25337 ^ _779854) ^ [] : [25338 ^ _779854 : [(25341 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239456), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462)), _1239460)), _1239458))], (25339 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), _1239460), c_Groups_Ozero__class_Ozero(_1239456))))]], 25342 ^ _779854 : [(25345 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239456), c_Groups_Ozero__class_Ozero(_1239456)), hAPP(c_Int_Onumber__class_Onumber__of(_1239456), _1239462)))], (25343 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), _1239460), c_Groups_Ozero__class_Ozero(_1239456)))]]], (25335 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239456), c_Groups_Ozero__class_Ozero(_1239456)), _1239460))]]]]], (33856 ^ _779854) ^ [_1403688, _1403690, _1403692, _1403694, _1403696] : [class_Complete__Lattice_Ocomplete__lattice(_1403688), 33859 ^ _779854 : [(33860 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403688), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403690, _1403688), _1403692), _1403694)), _1403696)), 33863 ^ _779854 : [(33864 ^ _779854) ^ [_1403869] : [hBOOL(hAPP(hAPP(c_member(_1403690), _1403869), _1403692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403688), hAPP(_1403694, _1403869)), _1403696)))]]], (33870 ^ _779854) ^ [] : [33872 ^ _779854 : [(33875 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403688), hAPP(_1403694, 33871 ^ [_1403688, _1403690, _1403692, _1403694, _1403696])), _1403696))], (33873 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403690), 33871 ^ [_1403688, _1403690, _1403692, _1403694, _1403696]), _1403692)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403688), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403690, _1403688), _1403692), _1403694)), _1403696)))]]], (33042 ^ _779854) ^ [_1378190, _1378192, _1378194, _1378196, _1378198] : [_1378190 = c_Orderings_Obot__class_Obot(tc_fun(_1378192, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378192, tc_fun(_1378194, tc_HOL_Obool)), _1378190), hAPP(hAPP(c_COMBB(tc_fun(_1378194, tc_HOL_Obool), tc_fun(_1378194, tc_HOL_Obool), _1378192), hAPP(c_Set_Oinsert(_1378194), _1378196)), _1378198)) = c_Orderings_Obot__class_Obot(tc_fun(_1378194, tc_HOL_Obool)))], (52607 ^ _779854) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (42590 ^ _779854) ^ [_1624827, _1624829, _1624831, _1624833] : [-(hAPP(hAPP(c_List_Onth(_1624827), hAPP(hAPP(c_List_Olist_OCons(_1624827), _1624829), _1624831)), hAPP(c_Nat_OSuc, _1624833)) = hAPP(hAPP(c_List_Onth(_1624827), _1624831), _1624833))], (46599 ^ _779854) ^ [_1717323, _1717325, _1717327, _1717329, _1717331, _1717333, _1717335] : [-(c_List_Ofoldr(_1717323, _1717325, _1717327, hAPP(hAPP(c_List_Omap(_1717329, _1717323), _1717331), _1717333), _1717335) = c_List_Ofoldr(_1717329, _1717325, hAPP(c_Fun_Ocomp(_1717323, tc_fun(_1717325, _1717325), _1717329, _1717327), _1717331), _1717333, _1717335))], (45091 ^ _779854) ^ [_1682100, _1682102, _1682104, _1682106, _1682108, _1682110] : [-(hAPP(hAPP(c_List_Ozip(_1682100, _1682102), _1682104), hAPP(hAPP(c_List_Omap(_1682106, _1682102), _1682108), _1682110)) = hAPP(hAPP(c_List_Omap(tc_prod(_1682100, _1682106), tc_prod(_1682100, _1682102)), hAPP(c_Product__Type_Oprod_Oprod__case(_1682100, _1682106, tc_prod(_1682100, _1682102)), hAPP(hAPP(c_COMBC(_1682100, tc_fun(_1682106, _1682102), tc_fun(_1682106, tc_prod(_1682100, _1682102))), hAPP(hAPP(c_COMBB(tc_fun(_1682102, tc_prod(_1682100, _1682102)), tc_fun(tc_fun(_1682106, _1682102), tc_fun(_1682106, tc_prod(_1682100, _1682102))), _1682100), c_COMBB(_1682102, tc_prod(_1682100, _1682102), _1682106)), c_Product__Type_OPair(_1682100, _1682102))), _1682108))), hAPP(hAPP(c_List_Ozip(_1682100, _1682106), _1682104), _1682110)))], (46392 ^ _779854) ^ [_1711912, _1711914, _1711916, _1711918, _1711920] : [class_Orderings_Olinorder(_1711912), -(hAPP(c_List_Ofilter(_1711914, _1711916), c_List_Olinorder__class_Osort__key(_1711914, _1711912, _1711918, _1711920)) = c_List_Olinorder__class_Osort__key(_1711914, _1711912, _1711918, hAPP(c_List_Ofilter(_1711914, _1711916), _1711920)))], (9466 ^ _779854) ^ [_938123, _938125] : [class_Orderings_Olinorder(_938123), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_938123), _938125), _938125) = _938125)], (25443 ^ _779854) ^ [_1242414, _1242416] : [class_Int_Onumber__ring(_1242414), -(hAPP(c_Int_Onumber__class_Onumber__of(_1242414), c_Int_Opred(_1242416)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1242414), hAPP(c_Groups_Ouminus__class_Ouminus(_1242414), c_Groups_Oone__class_Oone(_1242414))), hAPP(c_Int_Onumber__class_Onumber__of(_1242414), _1242416)))], (39065 ^ _779854) ^ [_1527795, _1527797, _1527799, _1527801] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527795), hAPP(c_Set_OCollect(_1527795), _1527797))), 39068 ^ _779854 : [(39069 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527799), hAPP(c_Set_OCollect(_1527799), hAPP(hAPP(c_COMBB(tc_fun(_1527795, tc_HOL_Obool), tc_HOL_Obool, _1527799), c_HOL_OEx(_1527795)), hAPP(hAPP(c_COMBB(tc_fun(_1527795, tc_HOL_Obool), tc_fun(_1527795, tc_HOL_Obool), _1527799), hAPP(c_COMBS(_1527795, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527795), c_fconj), _1527797))), _1527801))))), 39072 ^ _779854 : [(39073 ^ _779854) ^ [_1528078] : [hBOOL(hAPP(_1527797, _1528078)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1527799), hAPP(c_Set_OCollect(_1527799), hAPP(hAPP(c_COMBC(_1527799, _1527795, tc_HOL_Obool), _1527801), _1528078)))))]]], (39079 ^ _779854) ^ [] : [39081 ^ _779854 : [(39084 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527799), hAPP(c_Set_OCollect(_1527799), hAPP(hAPP(c_COMBC(_1527799, _1527795, tc_HOL_Obool), _1527801), 39080 ^ [_1527795, _1527797, _1527799, _1527801]))))], (39082 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1527797, 39080 ^ [_1527795, _1527797, _1527799, _1527801])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1527799), hAPP(c_Set_OCollect(_1527799), hAPP(hAPP(c_COMBB(tc_fun(_1527795, tc_HOL_Obool), tc_HOL_Obool, _1527799), c_HOL_OEx(_1527795)), hAPP(hAPP(c_COMBB(tc_fun(_1527795, tc_HOL_Obool), tc_fun(_1527795, tc_HOL_Obool), _1527799), hAPP(c_COMBS(_1527795, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527795), c_fconj), _1527797))), _1527801))))))]]], (5522 ^ _779854) ^ [_864400, _864402] : [_864402 = _864400, -(c_Power_Opower__class_Opower(_864402) = c_Power_Opower__class_Opower(_864400))], (25449 ^ _779854) ^ [_1242543, _1242545, _1242547, _1242549] : [class_Rings_Olinordered__semidom(_1242543), 25455 ^ _779854 : [(25458 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242543), c_Groups_Ozero__class_Ozero(_1242543)), hAPP(_1242549, 25454 ^ [_1242543, _1242545, _1242547, _1242549])))], (25456 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1242545), 25454 ^ [_1242543, _1242545, _1242547, _1242549]), _1242547)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242543), c_Groups_Ozero__class_Ozero(_1242543)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1242545, _1242543), _1242549), _1242547))))], (43975 ^ _779854) ^ [_1657355, _1657357, _1657359] : [_1657359 = c_List_Olist_ONil(_1657357), -(_1657355 = hAPP(hAPP(c_List_Oappend(_1657357), _1657359), _1657355))], (31760 ^ _779854) ^ [_1351454, _1351456] : [class_Int_Oring__char__0(_1351454), 31763 ^ _779854 : [(31770 ^ _779854) ^ [] : [_1351456 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1351454) = hAPP(c_Int_Oring__1__class_Oof__int(_1351454), _1351456))], (31764 ^ _779854) ^ [] : [c_Groups_Ozero__class_Ozero(_1351454) = hAPP(c_Int_Oring__1__class_Oof__int(_1351454), _1351456), -(_1351456 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (52497 ^ _779854) ^ [_1836741] : [-(class_Nat_Osize(tc_Option_Ooption(_1836741)))], (41493 ^ _779854) ^ [_1593825, _1593827, _1593829] : [c_Equiv__Relations_Oequiv(_1593825, _1593827, _1593829), -(hAPP(hAPP(c_Relation_Orel__comp(_1593825, _1593825, _1593825), hAPP(c_Relation_Oconverse(_1593825, _1593825), _1593829)), _1593829) = _1593829)], (30765 ^ _779854) ^ [_1335307, _1335309, _1335311, _1335313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335309), _1335311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335311), 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), _1335309), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1335313, _1335307))), _1335311)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6441 ^ _779854) ^ [_882756, _882758, _882760] : [class_Complete__Lattice_Ocomplete__lattice(_882756), 6444 ^ _779854 : [(6445 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882756), c_Complete__Lattice_OSup__class_OSup(_882756, _882758)), _882760)), 6448 ^ _779854 : [(6449 ^ _779854) ^ [_882914] : [hBOOL(hAPP(hAPP(c_member(_882756), _882914), _882758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882756), _882914), _882760)))]]], (6455 ^ _779854) ^ [] : [6457 ^ _779854 : [(6460 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882756), 6456 ^ [_882756, _882758, _882760]), _882760))], (6458 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_882756), 6456 ^ [_882756, _882758, _882760]), _882758)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882756), c_Complete__Lattice_OSup__class_OSup(_882756, _882758)), _882760)))]]], (47584 ^ _779854) ^ [_1736766, _1736768, _1736770] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736766)), c_List_OtakeWhile(_1736766, _1736768, _1736770))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736766)), _1736770))))], (41755 ^ _779854) ^ [_1600195, _1600197, _1600199, _1600201] : [-(hAPP(hAPP(c_Nat_Ocompow(_1600195, _1600195), _1600197), hAPP(hAPP(c_Nat_Ocompow(_1600195, _1600195), _1600199), _1600201)) = hAPP(hAPP(c_Nat_Ocompow(_1600195, _1600195), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1600199), _1600197)), _1600201))], (41757 ^ _779854) ^ [_1600257, _1600259, _1600261] : [c_Wellfounded_Owf(_1600257, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1600257, _1600257), tc_HOL_Obool), _1600259), _1600261)), -(c_Wellfounded_Owf(_1600257, _1600261))], (8144 ^ _779854) ^ [_916355, _916357, _916359, _916361] : [class_Orderings_Oorder(_916355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916355), _916357), _916359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916355), _916361), _916357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916355), _916361), _916359)))], (30327 ^ _779854) ^ [_1327535, _1327537, _1327539] : [class_Divides_Osemiring__div(_1327535), -(c_Divides_Odiv__class_Omod(_1327535, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327535), _1327537), _1327539), _1327539) = c_Groups_Ozero__class_Ozero(_1327535))], (52521 ^ _779854) ^ [_1837050, _1837052] : [-(class_Enum_Oenum(tc_prod(_1837050, _1837052))), class_Enum_Oenum(_1837050), class_Enum_Oenum(_1837052)], (51719 ^ _779854) ^ [_1826503, _1826505, _1826507, _1826509] : [class_Divides_Osemiring__div(_1826503), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826503), _1826505), _1826507)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826503), _1826505), _1826509)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826503), _1826505), c_Divides_Odiv__class_Omod(_1826503, _1826507, _1826509))))], (10797 ^ _779854) ^ [_964309, _964311, _964313, _964315] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964309, tc_HOL_Obool)), _964311), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964309, tc_HOL_Obool)), _964313), _964315)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964309, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964309, tc_HOL_Obool)), _964311), _964313)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964309, tc_HOL_Obool)), _964311), _964315)))], (35262 ^ _779854) ^ [_1436870, _1436872, _1436874, _1436876, _1436878, _1436880] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1436870, _1436872, _1436874), _1436876), hAPP(hAPP(c_Product__Type_OPair(_1436870, _1436872), _1436878), _1436880)) = hAPP(hAPP(_1436876, _1436878), _1436880))], (23645 ^ _779854) ^ [_1208453] : [-(c_Finite__Set_Ofun__left__comm__idem(_1208453, tc_fun(_1208453, tc_HOL_Obool), c_Set_Oinsert(_1208453)))], (52207 ^ _779854) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (26461 ^ _779854) ^ [_1260640] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1260640))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1260640)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34591 ^ _779854) ^ [_1421986, _1421988, _1421990] : [class_Int_Onumber__ring(_1421986), 34594 ^ _779854 : [(34601 ^ _779854) ^ [] : [-(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), _1421988)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421986), _1421990), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1421988))) = c_Groups_Oone__class_Oone(_1421986))], (34595 ^ _779854) ^ [] : [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), _1421988))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421986), _1421990), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1421988))) = hAPP(hAPP(c_HOL_OLet(_1421986, _1421986), hAPP(hAPP(c_Power_Opower__class_Opower(_1421986), _1421990), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421988))), hAPP(hAPP(c_COMBS(_1421986, _1421986, _1421986), hAPP(hAPP(c_COMBB(_1421986, tc_fun(_1421986, _1421986), _1421986), c_Groups_Otimes__class_Otimes(_1421986)), hAPP(c_Groups_Otimes__class_Otimes(_1421986), _1421990))), c_COMBI(_1421986))))]]], (34313 ^ _779854) ^ [_1415509, _1415511, _1415513, _1415515, _1415517] : [class_Groups_Ocomm__monoid__add(_1415509), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415511), _1415513)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1415511, _1415509), _1415515), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415511, tc_HOL_Obool)), _1415513), _1415517)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1415511, _1415509), hAPP(hAPP(c_COMBC(_1415511, _1415509, _1415509), hAPP(hAPP(c_COMBS(_1415511, _1415509, tc_fun(_1415509, _1415509)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1415509, tc_fun(_1415509, _1415509)), _1415511), c_If(_1415509)), hAPP(hAPP(c_COMBC(_1415511, tc_fun(_1415511, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415511)), _1415517))), _1415515)), c_Groups_Ozero__class_Ozero(_1415509))), _1415513))], (2604 ^ _779854) ^ [_818441, _818443] : [_818443 = _818441, -(c_Equiv__Relations_Oquotient(_818443) = c_Equiv__Relations_Oquotient(_818441))], (6389 ^ _779854) ^ [_881594, _881596] : [hAPP(c_Set_OPow(_881594), _881596) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_881594, tc_HOL_Obool), tc_HOL_Obool))], (45887 ^ _779854) ^ [_1700379, _1700381, _1700383, _1700385, _1700387, _1700389] : [c_List_Olist__all2(_1700379, _1700381, _1700383, _1700385, _1700387), -(c_List_Olist__all2(_1700379, _1700381, _1700383, hAPP(hAPP(c_List_Otake(_1700379), _1700389), _1700385), hAPP(hAPP(c_List_Otake(_1700381), _1700389), _1700387)))], (20455 ^ _779854) ^ [_1147965, _1147967] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1147965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1147965), _1147967)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9400 ^ _779854) ^ [_936954, _936956] : [class_Lattices_Olattice(_936954), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936954), _936956), _936956) = _936956)], (42422 ^ _779854) ^ [_1620483, _1620485, _1620487, _1620489, _1620491, _1620493] : [c_List_Olistrelp(_1620483, _1620485, hAPP(hAPP(c_List_Olist_OCons(_1620483), _1620487), _1620489), hAPP(hAPP(c_List_Olist_OCons(_1620483), _1620491), _1620493)), 42425 ^ _779854 : [(42428 ^ _779854) ^ [] : [-(c_List_Olistrelp(_1620483, _1620485, _1620489, _1620493))], (42426 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1620485, _1620487), _1620491)))]]], (40375 ^ _779854) ^ [_1566402, _1566404, _1566406] : [hBOOL(hAPP(_1566402, _1566404)), -(hBOOL(hAPP(_1566402, c_Hilbert__Choice_OEps(_1566406, _1566402))))], (23970 ^ _779854) ^ [_1214685, _1214687, _1214689, _1214691] : [class_Fields_Ofield__inverse__zero(_1214685), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214685), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214685), _1214687), _1214689)), _1214691) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214685), hAPP(hAPP(c_Power_Opower__class_Opower(_1214685), _1214687), _1214691)), hAPP(hAPP(c_Power_Opower__class_Opower(_1214685), _1214689), _1214691)))], (39512 ^ _779854) ^ [_1544191, _1544193, _1544195, _1544197] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544191, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1544191, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544193, _1544191), _1544195)), hAPP(c_Relation_ORange(_1544193, _1544191), _1544197))), hAPP(c_Relation_ORange(_1544193, _1544191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1544193, _1544191), tc_HOL_Obool)), _1544195), _1544197)))))], (42085 ^ _779854) ^ [_1608988, _1608990] : [-(c_List_Olenlex(_1608988, _1608990) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1608988)), tc_List_Olist(_1608988)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1608988), c_Wellfounded_Oless__than, c_List_Olex(_1608988, _1608990))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1608988), tc_List_Olist(_1608988), tc_prod(tc_Nat_Onat, tc_List_Olist(_1608988))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1608988), tc_prod(tc_Nat_Onat, tc_List_Olist(_1608988))), tc_List_Olist(_1608988)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1608988))), c_Nat_Osize__class_Osize(tc_List_Olist(_1608988)))), c_COMBI(tc_List_Olist(_1608988)))))], (36999 ^ _779854) ^ [_1473901, _1473903, _1473905, _1473907, _1473909] : [class_Groups_Ocomm__monoid__add(_1473901), class_Groups_Ocomm__monoid__mult(_1473901), _1473903 = _1473905, c_Nat__Transfer_Onat__set(_1473905), 37017 ^ _779854 : [(37020 ^ _779854) ^ [] : [hAPP(_1473907, 37016 ^ [_1473901, _1473903, _1473905, _1473907, _1473909]) = hAPP(_1473909, 37016 ^ [_1473901, _1473903, _1473905, _1473907, _1473909])], (37018 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37016 ^ [_1473901, _1473903, _1473905, _1473907, _1473909])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1473901), _1473907), _1473903) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1473901), _1473909), _1473905))], (33355 ^ _779854) ^ [_1386394, _1386396, _1386398, _1386400, _1386402, _1386404] : [-(hAPP(hAPP(c_Fun_Ocomp(_1386394, _1386396, _1386398, _1386400), _1386402), _1386404) = hAPP(_1386400, hAPP(_1386402, _1386404)))], (8214 ^ _779854) ^ [_917478, _917480, _917482, _917484] : [class_Orderings_Oord(_917478), _917480 = _917482, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917478), _917482), _917484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917478), _917480), _917484)))], (26527 ^ _779854) ^ [_1262059] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262059), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1262059)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1262059)))], (28128 ^ _779854) ^ [] : [-(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))))], (806 ^ _779854) ^ [_791969, _791971, _791973, _791975, _791977, _791979] : [-(c_Equiv__Relations_Oequiv(_791977, _791973, _791969)), c_Equiv__Relations_Oequiv(_791979, _791975, _791971), _791979 = _791977, _791975 = _791973, _791971 = _791969], (2254 ^ _779854) ^ [_812856, _812858, _812860, _812862] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_812862, _812858) = c_Code__Numeral_Odiv__mod__code__numeral(_812860, _812856)), _812862 = _812860, _812858 = _812856], (30949 ^ _779854) ^ [_1338628, _1338630] : [c_Nat__Transfer_Onat__set(_1338628), c_Nat__Transfer_Onat__set(_1338630), 30956 ^ _779854 : [(30963 ^ _779854) ^ [] : [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), _1338628)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1338630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1338628), _1338630)))], (30957 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1338628), _1338630)), -(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), _1338628)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1338630))))]]], (34147 ^ _779854) ^ [_1411733, _1411735, _1411737] : [class_Int_Onumber__ring(_1411733), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1411733), _1411735), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1411737))) = hAPP(hAPP(c_HOL_OLet(_1411733, _1411733), hAPP(hAPP(c_Power_Opower__class_Opower(_1411733), _1411735), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411737))), hAPP(hAPP(c_COMBS(_1411733, _1411733, _1411733), c_Groups_Otimes__class_Otimes(_1411733)), c_COMBI(_1411733))))], (6267 ^ _779854) ^ [_879394, _879396] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_879394, _879396, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_879394), tc_HOL_Obool))))], (33675 ^ _779854) ^ [_1398775, _1398777, _1398779, _1398781, _1398783, _1398785] : [-(hAPP(c_Set_Oimage(_1398775, _1398777, hAPP(c_Fun_Ocomp(_1398779, _1398777, _1398775, _1398781), _1398783)), _1398785) = hAPP(c_Set_Oimage(_1398779, _1398777, _1398781), hAPP(c_Set_Oimage(_1398775, _1398779, _1398783), _1398785)))], (22629 ^ _779854) ^ [_1188609, _1188611, _1188613, _1188615, _1188617] : [class_Fields_Olinordered__field(_1188609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188609), c_Groups_Ozero__class_Ozero(_1188609)), _1188611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188609), _1188611), _1188613)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188609), c_Groups_Ozero__class_Ozero(_1188609)), _1188615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188609), _1188615), _1188617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188609), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188609), _1188611), _1188617)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188609), _1188613), _1188615))))], (1140 ^ _779854) ^ [_797056, _797058] : [-(class_Groups_Oordered__ab__group__add__abs(_797056)), _797058 = _797056, class_Groups_Oordered__ab__group__add__abs(_797058)], (25475 ^ _779854) ^ [_1243135, _1243137, _1243139] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1243135), _1243137)), hBOOL(hAPP(_1243139, c_Orderings_Obot__class_Obot(tc_fun(_1243135, tc_HOL_Obool)))), 25486 ^ _779854 : [(25489 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1243135), 25484 ^ [_1243135, _1243137, _1243139]), 25485 ^ [_1243135, _1243137, _1243139]))], (25491 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1243139, 25485 ^ [_1243135, _1243137, _1243139])))], (25493 ^ _779854) ^ [] : [hBOOL(hAPP(_1243139, hAPP(hAPP(c_Set_Oinsert(_1243135), 25484 ^ [_1243135, _1243137, _1243139]), 25485 ^ [_1243135, _1243137, _1243139])))], (25487 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1243135), 25485 ^ [_1243135, _1243137, _1243139])))]], -(hBOOL(hAPP(_1243139, _1243137)))], (45077 ^ _779854) ^ [_1681319, _1681321, _1681323, _1681325] : [-(hAPP(hAPP(c_List_Omap(_1681319, _1681321), _1681323), hAPP(c_List_Otl(_1681319), _1681325)) = hAPP(c_List_Otl(_1681321), hAPP(hAPP(c_List_Omap(_1681319, _1681321), _1681323), _1681325)))], (34079 ^ _779854) ^ [_1409988, _1409990, _1409992, _1409994, _1409996] : [hBOOL(hAPP(hAPP(c_member(_1409988), _1409990), _1409992)), -(hAPP(c_Set_Oimage(_1409988, _1409994, hAPP(c_COMBK(_1409994, _1409988), _1409996)), _1409992) = hAPP(hAPP(c_Set_Oinsert(_1409994), _1409996), c_Orderings_Obot__class_Obot(tc_fun(_1409994, tc_HOL_Obool))))], (4724 ^ _779854) ^ [_851939, _851941] : [_851941 = _851939, -(c_Random__Sequence_Osingle(_851941) = c_Random__Sequence_Osingle(_851939))], (37312 ^ _779854) ^ [_1482329, _1482331, _1482333] : [c_Equiv__Relations_Oequiv(_1482329, _1482331, _1482333), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1482329, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482329), _1482331), _1482333)) = _1482331)], (10805 ^ _779854) ^ [_964634, _964636, _964638, _964640] : [class_Orderings_Oorder(_964634), class_Orderings_Olinorder(_964636), c_Orderings_Oorder__class_Ostrict__mono(_964636, _964634, _964638), -(c_Fun_Oinj__on(_964636, _964634, _964638, _964640))], (11314 ^ _779854) ^ [_975107, _975109, _975111] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_975107), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_975107, tc_HOL_Obool)), _975109), _975111)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_975107), _975109)), hBOOL(hAPP(c_Finite__Set_Ofinite(_975107), _975111))], (46258 ^ _779854) ^ [_1708131, _1708133, _1708135, _1708137] : [class_Orderings_Olinorder(_1708131), -(hAPP(c_List_Oset(_1708133), c_List_Olinorder__class_Osort__key(_1708133, _1708131, _1708135, _1708137)) = hAPP(c_List_Oset(_1708133), _1708137))], (11979 ^ _779854) ^ [_988079, _988081, _988083, _988085, _988087] : [hBOOL(hAPP(hAPP(c_member(_988079), _988081), hAPP(c_Set_Oimage(_988083, _988079, _988085), _988087))), 11983 ^ _779854 : [(11986 ^ _779854) ^ [] : [-(_988081 = hAPP(_988085, 11982 ^ [_988079, _988081, _988083, _988085, _988087]))], (11984 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_988083), 11982 ^ [_988079, _988081, _988083, _988085, _988087]), _988087)))]]], (28645 ^ _779854) ^ [_1297586, _1297588] : [class_Rings_Osemiring__1(_1297586), -(hBOOL(hAPP(hAPP(c_member(_1297586), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1297586), _1297588)), c_Nat_Osemiring__1__class_ONats(_1297586))))], (16716 ^ _779854) ^ [_1080959, _1080961, _1080963, _1080965, _1080967] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1080959, _1080961, _1080963, _1080965, c_Orderings_Obot__class_Obot(tc_fun(_1080959, tc_HOL_Obool))), _1080967)), -(_1080967 = _1080965)], (39041 ^ _779854) ^ [_1526801, _1526803, _1526805] : [class_Orderings_Olinorder(_1526801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526801), _1526803)), -(_1526803 = c_Orderings_Obot__class_Obot(tc_fun(_1526801, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1526801), _1526805), c_Big__Operators_Olattice_OInf__fin(_1526801, c_Orderings_Oord__class_Omin(_1526801), _1526803)) = c_Big__Operators_Olattice_OInf__fin(_1526801, c_Orderings_Oord__class_Omin(_1526801), hAPP(c_Set_OCollect(_1526801), hAPP(hAPP(c_COMBB(tc_fun(_1526801, tc_HOL_Obool), tc_HOL_Obool, _1526801), c_HOL_OEx(_1526801)), hAPP(hAPP(c_COMBC(_1526801, tc_fun(_1526801, tc_HOL_Obool), tc_fun(_1526801, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526801, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1526801, tc_HOL_Obool), tc_fun(_1526801, tc_HOL_Obool)), _1526801), c_COMBS(_1526801, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526801, tc_HOL_Obool), tc_fun(_1526801, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1526801), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526801), c_fconj)), hAPP(hAPP(c_COMBC(_1526801, tc_fun(_1526801, _1526801), tc_fun(_1526801, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526801, tc_HOL_Obool), tc_fun(tc_fun(_1526801, _1526801), tc_fun(_1526801, tc_HOL_Obool)), _1526801), c_COMBB(_1526801, tc_HOL_Obool, _1526801)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1526801), _1526805))))), hAPP(hAPP(c_COMBC(_1526801, tc_fun(_1526801, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526801)), _1526803))))))], (6755 ^ _779854) ^ [_888699, _888701, _888703, _888705] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888699, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888699, tc_HOL_Obool)), _888701), _888703)), _888705) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888699, tc_HOL_Obool)), _888701), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888699, tc_HOL_Obool)), _888703), _888705)))], (47312 ^ _779854) ^ [_1731071, _1731073] : [-(c_Fun_Oinj__on(tc_List_Olist(_1731071), tc_List_Olist(_1731071), c_List_Orev(_1731071), _1731073))], (28238 ^ _779854) ^ [_1290461, _1290463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1290461), _1290463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1290461)), c_Int_OBit1(_1290463))))], (34627 ^ _779854) ^ [_1422968, _1422970, _1422972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1422968), _1422970)), -(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)), _1422968)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1422972), _1422970)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1422972), _1422968)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1422970), _1422968)))], (50424 ^ _779854) ^ [_1798602, _1798604, _1798606, _1798608] : [hAPP(c_Set_Oimage(_1798602, _1798604, _1798606), c_Orderings_Otop__class_Otop(tc_fun(_1798602, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1798604, tc_HOL_Obool)), -(hAPP(_1798606, hAPP(c_Hilbert__Choice_Oinv__into(_1798602, _1798604, c_Orderings_Otop__class_Otop(tc_fun(_1798602, tc_HOL_Obool)), _1798606), _1798608)) = _1798608)], (44512 ^ _779854) ^ [_1670284, _1670286, _1670288] : [hBOOL(hAPP(c_List_Odistinct(_1670284), hAPP(c_List_Orotate(_1670284, _1670286), _1670288))), -(hBOOL(hAPP(c_List_Odistinct(_1670284), _1670288)))], (7814 ^ _779854) ^ [_910207, _910209, _910211, _910213] : [class_Orderings_Olinorder(_910207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910207), _910209), _910211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910207), _910211), _910213)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910207, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_910207, _910209, _910211)), c_SetInterval_Oord__class_OgreaterThanAtMost(_910207, _910211, _910213)) = c_SetInterval_Oord__class_OatLeastAtMost(_910207, _910209, _910213))], (50676 ^ _779854) ^ [_1804447, _1804449, _1804451] : [c_Fun_Obij__betw(_1804447, _1804449, _1804451, c_Orderings_Otop__class_Otop(tc_fun(_1804447, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804449, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1804449, _1804447, c_Orderings_Otop__class_Otop(tc_fun(_1804449, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1804447, _1804449, c_Orderings_Otop__class_Otop(tc_fun(_1804447, tc_HOL_Obool)), _1804451)) = _1804451)], (52443 ^ _779854) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (23223 ^ _779854) ^ [_1199734, _1199736, _1199738, _1199740, _1199742, _1199744, _1199746] : [c_Big__Operators_Ocomm__monoid__big(_1199734, _1199736, _1199738, _1199740, _1199742), 23226 ^ _779854 : [(23233 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1199736), _1199744))), -(hAPP(hAPP(_1199742, _1199746), _1199744) = _1199740)], (23227 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1199736), _1199744)), -(hAPP(hAPP(_1199742, _1199746), _1199744) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1199734, _1199736, _1199738), _1199746), _1199740), _1199744))]]], (49172 ^ _779854) ^ [_1771242, _1771244] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1771242), _1771244))), -(c_Lazy__Sequence_Osmall__lazy_H(_1771242, _1771244) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1771244), c_Lazy__Sequence_Osmall__lazy_H(_1771242, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1771244), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (9406 ^ _779854) ^ [_937045, _937047, _937049] : [class_Rings_Olinordered__idom(_937045), -(_937047 = _937049), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937045), _937047), _937049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937045), _937049), _937047)))], (28607 ^ _779854) ^ [_1296949] : [class_Rings_Osemiring__1(_1296949), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1296949), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1296949))], (8558 ^ _779854) ^ [_922677, _922679, _922681] : [class_Orderings_Oorder(_922677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922677), _922679), _922681)), -(_922681 = _922679), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922677), _922679), _922681)))], (14051 ^ _779854) ^ [_1027764, _1027766, _1027768, _1027770, _1027772, _1027774] : [c_Fun_Oinj__on(_1027764, _1027766, _1027768, _1027770), hBOOL(hAPP(hAPP(c_member(_1027766), _1027772), hAPP(c_Set_Oimage(_1027764, _1027766, _1027768), _1027770))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027764, tc_HOL_Obool)), _1027770), _1027774)), -(hBOOL(hAPP(hAPP(c_member(_1027764), hAPP(c_Fun_Othe__inv__into(_1027764, _1027766, _1027770, _1027768), _1027772)), _1027774)))], (39526 ^ _779854) ^ [_1545036, _1545038, _1545040, _1545042] : [hBOOL(hAPP(c_Predicate_ORangeP(_1545036, _1545038, hAPP(hAPP(c_COMBC(_1545036, tc_fun(tc_prod(_1545036, _1545038), tc_HOL_Obool), tc_fun(_1545038, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545038, tc_fun(tc_fun(tc_prod(_1545036, _1545038), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545036, _1545038), tc_HOL_Obool), tc_fun(_1545038, tc_HOL_Obool)), _1545036), c_COMBC(_1545038, tc_fun(tc_prod(_1545036, _1545038), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545038, tc_prod(_1545036, _1545038)), tc_fun(_1545038, tc_fun(tc_fun(tc_prod(_1545036, _1545038), tc_HOL_Obool), tc_HOL_Obool)), _1545036), hAPP(c_COMBB(tc_prod(_1545036, _1545038), tc_fun(tc_fun(tc_prod(_1545036, _1545038), tc_HOL_Obool), tc_HOL_Obool), _1545038), c_member(tc_prod(_1545036, _1545038)))), c_Product__Type_OPair(_1545036, _1545038)))), _1545040)), _1545042)), -(hBOOL(hAPP(hAPP(c_member(_1545038), _1545042), hAPP(c_Relation_ORange(_1545036, _1545038), _1545040))))], (4258 ^ _779854) ^ [_844526, _844528] : [_844528 = _844526, -(c_List_Onth(_844528) = c_List_Onth(_844526))], (34387 ^ _779854) ^ [_1417277, _1417279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417277), 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)), _1417279)), -(c_Divides_OnegDivAlg(_1417277, _1417279) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1417277), _1417279)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1417277, _1417279)))], (7828 ^ _779854) ^ [_910472, _910474, _910476] : [class_Orderings_Oorder(_910472), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_910472, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_910472), _910474)), c_SetInterval_Oord__class_OatLeastAtMost(_910472, _910474, _910476)) = c_Orderings_Obot__class_Obot(tc_fun(_910472, tc_HOL_Obool)))], (50072 ^ _779854) ^ [_1792141, _1792143] : [c_Relation_Osym(_1792141, _1792143), -(c_Relation_Osym(tc_List_Olist(_1792141), c_List_Olistrel(_1792141, _1792143)))], (43398 ^ _779854) ^ [_1645117, _1645119, _1645121, _1645123] : [-(_1645117 = _1645119), -(c_List_Oremove1(_1645121, _1645117, hAPP(hAPP(c_List_Olist_OCons(_1645121), _1645119), _1645123)) = hAPP(hAPP(c_List_Olist_OCons(_1645121), _1645119), c_List_Oremove1(_1645121, _1645117, _1645123)))], (36251 ^ _779854) ^ [_1456320, _1456322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1456320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1456322), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1456320), _1456322) = 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), _1456320), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1456322)))))], (7880 ^ _779854) ^ [_911572, _911574, _911576] : [class_Orderings_Oorder(_911572), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911572, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_911572, _911574, _911576)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_911572), _911576)) = c_Orderings_Obot__class_Obot(tc_fun(_911572, tc_HOL_Obool)))], (12190 ^ _779854) ^ [_992210, _992212, _992214] : [hBOOL(hAPP(hAPP(c_member(_992210), _992212), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_992210, tc_HOL_Obool)), _992214))), hBOOL(hAPP(hAPP(c_member(_992210), _992212), _992214))], (33611 ^ _779854) ^ [_1397182, _1397184, _1397186, _1397188, _1397190, _1397192] : [c_Fun_Oinj__on(_1397182, _1397184, hAPP(c_Fun_Ocomp(_1397186, _1397184, _1397182, _1397188), _1397190), _1397192), -(c_Fun_Oinj__on(_1397182, _1397186, _1397190, _1397192))], (16397 ^ _779854) ^ [_1074904, _1074906, _1074908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074904), _1074906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074906), _1074908)), _1074904))))], (38194 ^ _779854) ^ [_1502975, _1502977, _1502979, _1502981] : [-(hAPP(c_Set_Ovimage(_1502975, _1502977, _1502979), _1502981) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502977, tc_fun(_1502975, tc_HOL_Obool)), _1502981), hAPP(hAPP(c_COMBB(tc_fun(_1502977, tc_HOL_Obool), tc_fun(_1502975, tc_HOL_Obool), _1502977), c_Set_Ovimage(_1502975, _1502977, _1502979)), hAPP(hAPP(c_COMBC(_1502977, tc_fun(_1502977, tc_HOL_Obool), tc_fun(_1502977, tc_HOL_Obool)), c_Set_Oinsert(_1502977)), c_Orderings_Obot__class_Obot(tc_fun(_1502977, tc_HOL_Obool))))))], (28351 ^ _779854) ^ [_1292423] : [28352 ^ _779854 : [(28353 ^ _779854) ^ [_1292480] : [hBOOL(hAPP(_1292423, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292480)))]], 28355 ^ _779854 : [(28358 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1292423, 28354 ^ [_1292423])))], (28356 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28354 ^ [_1292423])))]]], (30625 ^ _779854) ^ [_1332689, _1332691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332689)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1332689, _1332691)))], (26533 ^ _779854) ^ [_1262114, _1262116, _1262118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262114)), 26539 ^ _779854 : [(26542 ^ _779854) ^ [] : [hBOOL(hAPP(_1262116, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26538 ^ [_1262114, _1262116, _1262118]), _1262114)))], (26540 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1262116, 26538 ^ [_1262114, _1262116, _1262118])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262118)), 26547 ^ _779854 : [(26548 ^ _779854) ^ [_1262403] : [hBOOL(hAPP(_1262116, _1262403)), -(hBOOL(hAPP(_1262116, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1262403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1262118), _1262114)))))]]], (41202 ^ _779854) ^ [_1586833, _1586835, _1586837, _1586839, _1586841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586833, _1586833)), hAPP(hAPP(c_Product__Type_OPair(_1586833, _1586833), _1586835), _1586837)), c_Transitive__Closure_Ortrancl(_1586833, _1586839))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586833, _1586833)), hAPP(hAPP(c_Product__Type_OPair(_1586833, _1586833), _1586837), _1586841)), c_Transitive__Closure_Otrancl(_1586833, _1586839))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586833, _1586833)), hAPP(hAPP(c_Product__Type_OPair(_1586833, _1586833), _1586835), _1586841)), c_Transitive__Closure_Otrancl(_1586833, _1586839))))], (9698 ^ _779854) ^ [_942533, _942535, _942537, _942539] : [class_Orderings_Olinorder(_942533), 9701 ^ _779854 : [(9702 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942533), _942535), hAPP(hAPP(c_Orderings_Oord__class_Omax(_942533), _942537), _942539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942533), _942535), _942537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942533), _942535), _942539)))], (9712 ^ _779854) ^ [] : [9713 ^ _779854 : [(9716 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942533), _942535), _942539))], (9714 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942533), _942535), _942537))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942533), _942535), hAPP(hAPP(c_Orderings_Oord__class_Omax(_942533), _942537), _942539))))]]], (18769 ^ _779854) ^ [_1119012] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1119012)], (4252 ^ _779854) ^ [_844441, _844443] : [_844443 = _844441, -(c_Orderings_Oord__class_Omin(_844443) = c_Orderings_Oord__class_Omin(_844441))], (45996 ^ _779854) ^ [_1702701, _1702703, _1702705, _1702707, _1702709, _1702711, _1702713, _1702715] : [c_List_Olist__all2(_1702701, _1702703, _1702705, _1702707, _1702709), hBOOL(hAPP(hAPP(_1702705, _1702711), _1702713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702715), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702703)), _1702709))), -(c_List_Olist__all2(_1702701, _1702703, _1702705, hAPP(hAPP(c_List_Olist__update(_1702701, _1702707), _1702715), _1702711), hAPP(hAPP(c_List_Olist__update(_1702703, _1702709), _1702715), _1702713)))], (24132 ^ _779854) ^ [_1217619, _1217621] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217619), _1217621) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1217621 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1217619 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41615 ^ _779854) ^ [_1596743, _1596745] : [-(c_Relation_Ototal__on(_1596743, c_Orderings_Obot__class_Obot(tc_fun(_1596743, tc_HOL_Obool)), _1596745))], (39875 ^ _779854) ^ [_1553597] : [class_Orderings_Owellorder(_1553597), -(c_Wellfounded_Owf(_1553597, hAPP(c_Set_OCollect(tc_prod(_1553597, _1553597)), hAPP(c_Product__Type_Oprod_Oprod__case(_1553597, _1553597, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1553597)))))], (33254 ^ _779854) ^ [_1383164, _1383166, _1383168, _1383170] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383164, tc_fun(_1383166, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1383164, tc_HOL_Obool), _1383168)), _1383170) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1383164, tc_HOL_Obool), tc_fun(_1383166, tc_HOL_Obool)), _1383168), hAPP(hAPP(c_COMBC(tc_fun(_1383164, tc_HOL_Obool), tc_fun(_1383164, tc_fun(_1383166, tc_HOL_Obool)), tc_fun(_1383166, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383164, tc_fun(_1383166, tc_HOL_Obool))), _1383170)))], (35624 ^ _779854) ^ [_1443487, _1443489, _1443491] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1443487, _1443487), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1443489), _1443491))), -(_1443487 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1443491 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7021 ^ _779854) ^ [_894847, _894849, _894851] : [class_Lattices_Osemilattice__sup(_894847), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894847), _894849), _894851) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894847), _894851), _894849))], (8800 ^ _779854) ^ [_926065, _926067, _926069] : [class_Orderings_Olinorder(_926065), 8803 ^ _779854 : [(8810 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926065), _926069), _926067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926065), _926067), _926069))], (8804 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926065), _926067), _926069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926065), _926069), _926067)))]]], (52173 ^ _779854) ^ [_1833630, _1833632] : [-(class_Enum_Oenum(tc_fun(_1833630, _1833632))), class_Enum_Oenum(_1833630), class_Enum_Oenum(_1833632)], (45949 ^ _779854) ^ [_1701608, _1701610, _1701612, _1701614, _1701616] : [-(c_List_Olist__all2(_1701608, _1701610, _1701612, _1701614, _1701616)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701608)), _1701614) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701610)), _1701616), 45955 ^ _779854 : [(45958 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1701612, hAPP(hAPP(c_List_Onth(_1701608), _1701614), 45954 ^ [_1701608, _1701610, _1701612, _1701614, _1701616])), hAPP(hAPP(c_List_Onth(_1701610), _1701616), 45954 ^ [_1701608, _1701610, _1701612, _1701614, _1701616])))], (45956 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45954 ^ [_1701608, _1701610, _1701612, _1701614, _1701616]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701608)), _1701614))))]]], (28432 ^ _779854) ^ [_1293967, _1293969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293967), _1293969)), -(_1293969 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1293967), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28435 ^ [_1293967, _1293969])))], (26983 ^ _779854) ^ [_1269282, _1269284] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269282), _1269284), hAPP(c_Int_Onumber__class_Onumber__of(_1269282), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1269282)), class_Fields_Ofield__inverse__zero(_1269282), class_Int_Onumber__ring(_1269282)], (45386 ^ _779854) ^ [_1689181, _1689183] : [_1689181 = _1689183, -(hAPP(c_Code__Numeral_Oof__nat, _1689181) = hAPP(c_Code__Numeral_Oof__nat, _1689183))], (33541 ^ _779854) ^ [_1392850, _1392852, _1392854, _1392856, _1392858, _1392860] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1392850, _1392852)), hAPP(hAPP(c_Product__Type_OPair(_1392850, _1392852), _1392858), _1392860)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool)), _1392854), _1392856))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392850, tc_fun(_1392852, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1392850, tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_fun(_1392852, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392852, tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_fun(_1392852, tc_HOL_Obool)), _1392850), c_COMBC(_1392852, tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392852, tc_prod(_1392850, _1392852)), tc_fun(_1392852, tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool)), _1392850), hAPP(c_COMBB(tc_prod(_1392850, _1392852), tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool), _1392852), c_member(tc_prod(_1392850, _1392852)))), c_Product__Type_OPair(_1392850, _1392852)))), _1392854)), hAPP(hAPP(c_COMBC(_1392850, tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_fun(_1392852, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392852, tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_fun(_1392852, tc_HOL_Obool)), _1392850), c_COMBC(_1392852, tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392852, tc_prod(_1392850, _1392852)), tc_fun(_1392852, tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool)), _1392850), hAPP(c_COMBB(tc_prod(_1392850, _1392852), tc_fun(tc_fun(tc_prod(_1392850, _1392852), tc_HOL_Obool), tc_HOL_Obool), _1392852), c_member(tc_prod(_1392850, _1392852)))), c_Product__Type_OPair(_1392850, _1392852)))), _1392856)), _1392858), _1392860)))], (38328 ^ _779854) ^ [_1506761, _1506763, _1506765] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1506761, _1506763), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1506761, _1506763), _1506765), hAPP(c_COMBK(tc_fun(_1506763, tc_HOL_Obool), _1506761), c_Orderings_Otop__class_Otop(tc_fun(_1506763, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1506761, _1506763), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1506761, tc_HOL_Obool)), _1506765)), hAPP(c_COMBK(tc_fun(_1506763, tc_HOL_Obool), _1506761), c_Orderings_Otop__class_Otop(tc_fun(_1506763, tc_HOL_Obool)))))], (27617 ^ _779854) ^ [_1279750] : [-(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)), _1279750)) = hAPP(c_Int_Onat, _1279750))], (38274 ^ _779854) ^ [_1505211, _1505213, _1505215, _1505217, _1505219, _1505221] : [hBOOL(hAPP(hAPP(c_member(_1505211), _1505213), _1505215)), 38277 ^ _779854 : [(38284 ^ _779854) ^ [] : [_1505219 = _1505221, -(hAPP(hAPP(c_Product__Type_OSigma(_1505217, _1505211), _1505219), hAPP(c_COMBK(tc_fun(_1505211, tc_HOL_Obool), _1505217), _1505215)) = hAPP(hAPP(c_Product__Type_OSigma(_1505217, _1505211), _1505221), hAPP(c_COMBK(tc_fun(_1505211, tc_HOL_Obool), _1505217), _1505215)))], (38278 ^ _779854) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1505217, _1505211), _1505219), hAPP(c_COMBK(tc_fun(_1505211, tc_HOL_Obool), _1505217), _1505215)) = hAPP(hAPP(c_Product__Type_OSigma(_1505217, _1505211), _1505221), hAPP(c_COMBK(tc_fun(_1505211, tc_HOL_Obool), _1505217), _1505215)), -(_1505219 = _1505221)]]], (30241 ^ _779854) ^ [_1325842] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1325842, _1325842) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (1350 ^ _779854) ^ [_799681, _799683] : [-(class_Rings_Oidom(_799681)), _799683 = _799681, class_Rings_Oidom(_799683)], (17192 ^ _779854) ^ [_1090188, _1090190, _1090192, _1090194, _1090196, _1090198] : [c_Finite__Set_Ofun__left__comm(_1090188, _1090190, _1090192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090188), _1090194)), hBOOL(hAPP(hAPP(c_member(_1090188), _1090196), _1090194)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1090188, _1090190, _1090192), _1090198), _1090194) = hAPP(hAPP(_1090192, _1090196), hAPP(hAPP(c_Finite__Set_Ofold(_1090188, _1090190, _1090192), _1090198), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090188, tc_HOL_Obool)), _1090194), hAPP(hAPP(c_Set_Oinsert(_1090188), _1090196), c_Orderings_Obot__class_Obot(tc_fun(_1090188, tc_HOL_Obool)))))))], (28675 ^ _779854) ^ [_1298065, _1298067] : [class_Int_Onumber__ring(_1298065), -(hAPP(c_Int_Onumber__class_Onumber__of(_1298065), c_Int_OBit1(_1298067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298065), c_Groups_Oone__class_Oone(_1298065)), hAPP(c_Int_Onumber__class_Onumber__of(_1298065), _1298067))), hAPP(c_Int_Onumber__class_Onumber__of(_1298065), _1298067)))], (23591 ^ _779854) ^ [_1207145, _1207147, _1207149, _1207151, _1207153, _1207155] : [c_Finite__Set_Ofun__left__comm__idem(_1207145, _1207147, _1207149), hBOOL(hAPP(c_Finite__Set_Ofinite(_1207145), _1207151)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1207145, _1207147, _1207149), _1207153), hAPP(hAPP(c_Set_Oinsert(_1207145), _1207155), _1207151)) = hAPP(hAPP(c_Finite__Set_Ofold(_1207145, _1207147, _1207149), hAPP(hAPP(_1207149, _1207155), _1207153)), _1207151))], (34185 ^ _779854) ^ [_1412620, _1412622, _1412624, _1412626, _1412628] : [class_Complete__Lattice_Ocomplete__lattice(_1412620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412622), _1412624)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1412620), _1412626), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412622, _1412620), _1412624), _1412628)) = hAPP(hAPP(c_Finite__Set_Ofold(_1412622, _1412620, hAPP(hAPP(c_COMBB(_1412620, tc_fun(_1412620, _1412620), _1412622), c_Lattices_Osemilattice__sup__class_Osup(_1412620)), _1412628)), _1412626), _1412624))], (38240 ^ _779854) ^ [_1504503, _1504505] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1504503), c_Int_OInteg)), hBOOL(hAPP(_1504505, hAPP(c_Int_ORep__Integ, 38245 ^ [_1504503, _1504505]))), -(hBOOL(hAPP(_1504505, _1504503)))], (388 ^ _779854) ^ [_785748, _785750, _785752, _785754] : [-(c_Wellfounded_OwfP(_785752, _785748)), c_Wellfounded_OwfP(_785754, _785750), _785754 = _785752, _785750 = _785748], (20626 ^ _779854) ^ [_1150864, _1150866, _1150868, _1150870] : [class_Rings_Olinordered__ring__strict(_1150864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150864), c_Groups_Ozero__class_Ozero(_1150864)), _1150866)), 20633 ^ _779854 : [(20640 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150864), _1150868), _1150870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150864), _1150866), _1150868)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150864), _1150866), _1150870))))], (20634 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150864), _1150866), _1150868)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150864), _1150866), _1150870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150864), _1150868), _1150870)))]]], (43486 ^ _779854) ^ [_1646606, _1646608] : [hAPP(c_List_Oset(_1646606), _1646608) = c_Orderings_Obot__class_Obot(tc_fun(_1646606, tc_HOL_Obool)), -(_1646608 = c_List_Olist_ONil(_1646606))], (1420 ^ _779854) ^ [_800556, _800558] : [-(class_Lattices_Osemilattice__inf(_800556)), _800558 = _800556, class_Lattices_Osemilattice__inf(_800558)], (38300 ^ _779854) ^ [_1506011, _1506013, _1506015, _1506017] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1506011, _1506013)), hAPP(hAPP(c_Product__Type_OSigma(_1506011, _1506013), _1506015), hAPP(c_COMBK(tc_fun(_1506013, tc_HOL_Obool), _1506011), _1506017))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1506011), _1506015)), hAPP(c_Finite__Set_Ocard(_1506013), _1506017)))], (30489 ^ _779854) ^ [_1330463, _1330465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330463)), -(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, _1330465, _1330463))))], (37176 ^ _779854) ^ [_1478534, _1478536] : [-(c_Relation_OId__on(_1478534, _1478536) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478534, tc_fun(tc_prod(_1478534, _1478534), tc_HOL_Obool)), _1478536), hAPP(hAPP(c_COMBC(_1478534, tc_fun(tc_prod(_1478534, _1478534), tc_HOL_Obool), tc_fun(tc_prod(_1478534, _1478534), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1478534, _1478534), tc_fun(tc_fun(tc_prod(_1478534, _1478534), tc_HOL_Obool), tc_fun(tc_prod(_1478534, _1478534), tc_HOL_Obool)), _1478534), c_Set_Oinsert(tc_prod(_1478534, _1478534))), hAPP(hAPP(c_COMBS(_1478534, _1478534, tc_prod(_1478534, _1478534)), c_Product__Type_OPair(_1478534, _1478534)), c_COMBI(_1478534)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1478534, _1478534), tc_HOL_Obool)))))], (3766 ^ _779854) ^ [_836526, _836528, _836530, _836532, _836534, _836536, _836538, _836540] : [-(c_List_Ofoldl(_836540, _836536, _836532, _836528) = c_List_Ofoldl(_836538, _836534, _836530, _836526)), _836540 = _836538, _836536 = _836534, _836532 = _836530, _836528 = _836526], (44927 ^ _779854) ^ [_1678841, _1678843] : [-(_1678841 = c_List_Olist_ONil(_1678843)), -(c_List_Olast(_1678843, _1678841) = hAPP(hAPP(c_List_Onth(_1678843), _1678841), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678843)), _1678841)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (43470 ^ _779854) ^ [_1646309] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646309)), c_List_Olist_ONil(_1646309)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4140 ^ _779854) ^ [_842741, _842743, _842745, _842747, _842749, _842751, _842753, _842755] : [-(c_New__Random__Sequence_Opos__bind(_842755, _842751, _842747, _842743) = c_New__Random__Sequence_Opos__bind(_842753, _842749, _842745, _842741)), _842755 = _842753, _842751 = _842749, _842747 = _842745, _842743 = _842741], (29567 ^ _779854) ^ [_1313180] : [-(c_Int_Opred(c_Int_OBit0(_1313180)) = c_Int_OBit1(c_Int_Opred(_1313180)))], (48468 ^ _779854) ^ [_1756409, _1756411, _1756413] : [-(c_List_Olist__ex(_1756409, _1756411, _1756413)), 48469 ^ _779854 : [(48470 ^ _779854) ^ [_1756466] : [hBOOL(hAPP(hAPP(c_member(_1756409), _1756466), hAPP(c_List_Oset(_1756409), _1756413))), hBOOL(hAPP(_1756411, _1756466))]]], (39395 ^ _779854) ^ [_1540794, _1540796, _1540798] : [-(hAPP(c_Relation_ORange(_1540794, _1540796), hAPP(c_Set_OCollect(tc_prod(_1540794, _1540796)), hAPP(c_Product__Type_Oprod_Oprod__case(_1540794, _1540796, tc_HOL_Obool), _1540798))) = hAPP(c_Set_OCollect(_1540796), hAPP(hAPP(c_COMBB(tc_fun(_1540794, tc_HOL_Obool), tc_HOL_Obool, _1540796), c_HOL_OEx(_1540794)), hAPP(c_COMBC(_1540794, _1540796, tc_HOL_Obool), _1540798))))], (36888 ^ _779854) ^ [] : [-(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)))], (29535 ^ _779854) ^ [_1312578, _1312580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1312578), _1312580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1312578)), c_Int_OBit0(_1312580))))], (33461 ^ _779854) ^ [_1389373, _1389375, _1389377, _1389379] : [hBOOL(hAPP(hAPP(c_member(_1389373), _1389379), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389373, tc_HOL_Obool)), _1389375), _1389377))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389373, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1389373, tc_fun(_1389373, tc_HOL_Obool), tc_HOL_Obool), c_member(_1389373)), _1389375)), hAPP(hAPP(c_COMBC(_1389373, tc_fun(_1389373, tc_HOL_Obool), tc_HOL_Obool), c_member(_1389373)), _1389377)), _1389379)))], (31987 ^ _779854) ^ [_1355321, _1355323, _1355325] : [class_Groups_Oordered__ab__group__add__abs(_1355321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355321), hAPP(c_Groups_Oabs__class_Oabs(_1355321), _1355323)), _1355325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355321), _1355323), _1355325)))], (880 ^ _779854) ^ [_793010, _793012, _793014, _793016] : [-(c_Equiv__Relations_Opart__equivp(_793014, _793010)), c_Equiv__Relations_Opart__equivp(_793016, _793012), _793016 = _793014, _793012 = _793010], (10873 ^ _779854) ^ [_965774, _965776, _965778, _965780, _965782] : [c_Fun_Oinj__on(_965774, _965776, _965778, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965774, tc_HOL_Obool)), _965780), _965782)), 10876 ^ _779854 : [(10881 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965776, tc_HOL_Obool)), hAPP(c_Set_Oimage(_965774, _965776, _965778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965774, tc_HOL_Obool)), _965780), _965782))), hAPP(c_Set_Oimage(_965774, _965776, _965778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965774, tc_HOL_Obool)), _965782), _965780))) = c_Orderings_Obot__class_Obot(tc_fun(_965776, tc_HOL_Obool)))], (10879 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_965774, _965776, _965778, _965782))], (10877 ^ _779854) ^ [] : [-(c_Fun_Oinj__on(_965774, _965776, _965778, _965780))]]], (10057 ^ _779854) ^ [_949710, _949712, _949714, _949716] : [class_Orderings_Olinorder(_949710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949710), _949712), _949714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949710), _949712), _949716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949710), _949712), hAPP(hAPP(c_Orderings_Oord__class_Omin(_949710), _949714), _949716))))], (38513 ^ _779854) ^ [_1512272, _1512274, _1512276, _1512278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512274, _1512272), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512272, tc_prod(_1512274, _1512272), 38509 ^ [_1512272, _1512274, _1512276, _1512278]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512274, tc_fun(_1512272, tc_HOL_Obool)), _1512276), _1512278))), hAPP(hAPP(c_Product__Type_OSigma(_1512274, _1512272), _1512276), _1512278))))], (35881 ^ _779854) ^ [_1448173, _1448175, _1448177, _1448179] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1448173, _1448173)), hAPP(hAPP(c_Product__Type_OPair(_1448173, _1448173), _1448175), _1448177)), hAPP(c_Wellfounded_Omeasure(_1448173), _1448179))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1448179, _1448175)), hAPP(_1448179, _1448177))))], (52223 ^ _779854) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (3484 ^ _779854) ^ [_832105, _832107, _832109, _832111] : [-(c_Random_Opick(_832111, _832107) = c_Random_Opick(_832109, _832105)), _832111 = _832109, _832107 = _832105], (28521 ^ _779854) ^ [_1295493, _1295495, _1295497] : [class_Rings_Olinordered__semidom(_1295493), 28524 ^ _779854 : [(28531 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1295495), _1295497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295493), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295493), _1295495)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295493), _1295497))))], (28525 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295493), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295493), _1295495)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295493), _1295497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1295495), _1295497)))]]], (22229 ^ _779854) ^ [_1181624, _1181626, _1181628] : [class_Fields_Ofield__inverse__zero(_1181624), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181624), hAPP(c_Groups_Ouminus__class_Ouminus(_1181624), _1181626)), hAPP(c_Groups_Ouminus__class_Ouminus(_1181624), _1181628)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181624), _1181626), _1181628))], (23806 ^ _779854) ^ [_1211555, _1211557, _1211559, _1211561] : [class_Rings_Ocomm__semiring__1(_1211555), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211555), hAPP(hAPP(c_Power_Opower__class_Opower(_1211555), _1211557), _1211559)), hAPP(hAPP(c_Power_Opower__class_Opower(_1211555), _1211557), _1211561)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1211555), _1211557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1211559), _1211561)))], (32015 ^ _779854) ^ [_1355855, _1355857, _1355859] : [class_Rings_Olinordered__idom(_1355855), -(hAPP(c_Groups_Oabs__class_Oabs(_1355855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355855), _1355857), _1355859)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355855), hAPP(c_Groups_Oabs__class_Oabs(_1355855), _1355857)), hAPP(c_Groups_Oabs__class_Oabs(_1355855), _1355859)))], (10929 ^ _779854) ^ [_966954, _966956, _966958] : [class_Lattices_Oboolean__algebra(_966954), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966954), _966956), _966958) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_966954), _966956), hAPP(c_Groups_Ouminus__class_Ouminus(_966954), _966958)))], (26577 ^ _779854) ^ [_1262964, _1262966] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1262964), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1262966)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1262964)), _1262966))], (48563 ^ _779854) ^ [_1758427, _1758429] : [-(c_List_Olist__all(_1758427, _1758429, c_List_Olist_ONil(_1758427)))], (45613 ^ _779854) ^ [_1693673, _1693675] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1693673), _1693675) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1693673)), hAPP(c_Code__Numeral_Onat__of, _1693675))))], (25741 ^ _779854) ^ [_1247762, _1247764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247762), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1247764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247762), _1247764)))], (5444 ^ _779854) ^ [_863227, _863229, _863231, _863233, _863235, _863237] : [-(c_SetInterval_Oord_OatLeast(_863237, _863233, _863229) = c_SetInterval_Oord_OatLeast(_863235, _863231, _863227)), _863237 = _863235, _863233 = _863231, _863229 = _863227], (29481 ^ _779854) ^ [_1311639, _1311641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1311639)), c_Int_OBit1(_1311641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311639), _1311641)))], (12900 ^ _779854) ^ [_1006569, _1006571, _1006573, _1006575] : [hBOOL(hAPP(hAPP(c_member(_1006569), _1006571), c_SetInterval_Oord_OlessThan(_1006569, _1006573, _1006575))), -(hBOOL(hAPP(hAPP(_1006573, _1006571), _1006575)))], (28003 ^ _779854) ^ [_1286403, _1286405] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1286403, _1286405)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1286405), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1286403), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (5528 ^ _779854) ^ [_864485, _864487] : [_864487 = _864485, -(c_Rings_Odvd__class_Odvd(_864487) = c_Rings_Odvd__class_Odvd(_864485))], (6353 ^ _779854) ^ [_880936, _880938, _880940, _880942, _880944] : [class_Orderings_Oorder(_880936), 6356 ^ _779854 : [(6369 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880936, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_880936, _880938, _880940)), c_SetInterval_Oord__class_OatLeastAtMost(_880936, _880942, _880944)))), 6370 ^ _779854 : [(6373 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880942), _880938)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880940), _880944))], (6371 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880938), _880940)))]]], (6357 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880936, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_880936, _880938, _880940)), c_SetInterval_Oord__class_OatLeastAtMost(_880936, _880942, _880944))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880938), _880940)), 6364 ^ _779854 : [(6367 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880940), _880944)))], (6365 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880936), _880942), _880938)))]]]]], (34301 ^ _779854) ^ [_1415213, _1415215, _1415217] : [hBOOL(hAPP(c_Predicate_OPowp(_1415213, hAPP(hAPP(c_COMBC(_1415213, tc_fun(_1415213, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415213)), _1415215)), _1415217)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1415213, tc_HOL_Obool)), _1415217), hAPP(c_Set_OPow(_1415213), _1415215))))], (27981 ^ _779854) ^ [_1285996, _1285998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285996)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1285996)), _1285998) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1285996), _1285998)))], (13827 ^ _779854) ^ [_1023222, _1023224, _1023226] : [class_Lattices_Olattice(_1023222), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023222), _1023224)), -(_1023224 = c_Orderings_Obot__class_Obot(tc_fun(_1023222, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023222), _1023226)), -(_1023226 = c_Orderings_Obot__class_Obot(tc_fun(_1023222, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1023222, tc_HOL_Obool)), _1023224), _1023226) = c_Orderings_Obot__class_Obot(tc_fun(_1023222, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1023222, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1023222, tc_HOL_Obool)), _1023224), _1023226)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1023222), c_Big__Operators_Olattice__class_OInf__fin(_1023222, _1023224)), c_Big__Operators_Olattice__class_OInf__fin(_1023222, _1023226)))], (24635 ^ _779854) ^ [_1226786, _1226788, _1226790] : [class_Int_Onumber__ring(_1226786), -(hAPP(c_Int_Onumber__class_Onumber__of(_1226786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226788), _1226790)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226786), hAPP(c_Int_Onumber__class_Onumber__of(_1226786), _1226788)), hAPP(c_Int_Onumber__class_Onumber__of(_1226786), _1226790)))], (11943 ^ _779854) ^ [_987391, _987393, _987395] : [hBOOL(hAPP(hAPP(c_member(_987391), _987393), _987395)), -(hAPP(hAPP(c_Set_Oinsert(_987391), _987393), _987395) = _987395)], (28711 ^ _779854) ^ [_1298691] : [class_Int_Onumber__ring(_1298691), -(c_Groups_Oone__class_Oone(_1298691) = hAPP(c_Int_Onumber__class_Onumber__of(_1298691), c_Int_OBit1(c_Int_OPls)))], (52323 ^ _779854) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (48868 ^ _779854) ^ [_1764789, _1764791, _1764793, _1764795, _1764797] : [hBOOL(hAPP(hAPP(_1764793, _1764797), _1764795)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1764789, _1764791, _1764793), _1764795), _1764797)))], (31180 ^ _779854) ^ [_1342146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342146), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1342146)), c_Int_OMin)))], (41847 ^ _779854) ^ [_1602670] : [-(c_Nat_Ofunpow(_1602670) = c_Nat_Ocompow(_1602670, _1602670))], (25915 ^ _779854) ^ [_1250876, _1250878, _1250880] : [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), _1250876), _1250878)), _1250880))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250880), _1250876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250878)))], (32880 ^ _779854) ^ [_1372627, _1372629, _1372631, _1372633] : [hBOOL(hAPP(hAPP(c_member(_1372629), _1372633), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372627, tc_fun(_1372629, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1372627, tc_HOL_Obool))), _1372631))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372627, tc_fun(_1372629, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1372627, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1372629, tc_HOL_Obool), tc_fun(_1372629, tc_HOL_Obool), _1372627), hAPP(c_COMBC(_1372629, tc_fun(_1372629, tc_HOL_Obool), tc_HOL_Obool), c_member(_1372629))), _1372631)), _1372633)))], (8854 ^ _779854) ^ [_927077, _927079, _927081] : [c_Orderings_Obot__class_Obot(tc_fun(_927077, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_927077), _927079), _927081)], (41623 ^ _779854) ^ [_1596883, _1596885, _1596887] : [c_Relation_Ototal__on(_1596883, _1596885, _1596887), -(c_Relation_Ototal__on(_1596883, _1596885, hAPP(c_Relation_Oconverse(_1596883, _1596883), _1596887)))], (50918 ^ _779854) ^ [_1809473, _1809475, _1809477, _1809479] : [c_Fun_Obij__betw(_1809473, _1809475, _1809477, _1809479, c_Orderings_Obot__class_Obot(tc_fun(_1809475, tc_HOL_Obool))), -(_1809479 = c_Orderings_Obot__class_Obot(tc_fun(_1809473, tc_HOL_Obool)))], (27554 ^ _779854) ^ [_1278756] : [-(hBOOL(hAPP(_1278756, 27561 ^ [_1278756]))), 27555 ^ _779854 : [(27556 ^ _779854) ^ [_1278808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1278808)), hBOOL(hAPP(_1278756, hAPP(c_Int_Onat, _1278808)))]]], (15886 ^ _779854) ^ [_1064689, _1064691, _1064693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064691), _1064693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064689), _1064691)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064689), _1064693))))], (29929 ^ _779854) ^ [_1319329, _1319331, _1319333] : [class_Rings_Oring__1(_1319329), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1319329), hAPP(c_Groups_Ouminus__class_Ouminus(_1319329), _1319331)), 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)))), _1319333)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1319329), _1319331), 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)))), _1319333)))], (6439 ^ _779854) ^ [_882714] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_882714, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_882714, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_882714, tc_HOL_Obool)))], (5002 ^ _779854) ^ [_856266, _856268, _856270, _856272] : [-(c_Quickcheck_Obeyond(_856272, _856268) = c_Quickcheck_Obeyond(_856270, _856266)), _856272 = _856270, _856268 = _856266], (16758 ^ _779854) ^ [_1081836, _1081838, _1081840, _1081842] : [class_Lattices_Osemilattice__inf(_1081836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081836), _1081838)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1081836, _1081836, c_Lattices_Osemilattice__inf__class_Oinf(_1081836)), _1081840), hAPP(hAPP(c_Set_Oinsert(_1081836), _1081842), _1081838)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1081836), _1081842), hAPP(hAPP(c_Finite__Set_Ofold(_1081836, _1081836, c_Lattices_Osemilattice__inf__class_Oinf(_1081836)), _1081840), _1081838)))], (23493 ^ _779854) ^ [_1205397, _1205399] : [class_Rings_Olinordered__idom(_1205397), 23496 ^ _779854 : [(23503 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205397), _1205399), c_Groups_Ozero__class_Ozero(_1205397))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205397), c_Groups_Osgn__class_Osgn(_1205397, _1205399)), c_Groups_Ozero__class_Ozero(_1205397))))], (23497 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205397), c_Groups_Osgn__class_Osgn(_1205397, _1205399)), c_Groups_Ozero__class_Ozero(_1205397))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205397), _1205399), c_Groups_Ozero__class_Ozero(_1205397))))]]], (48429 ^ _779854) ^ [_1755638, _1755640, _1755642] : [-(hBOOL(hAPP(hAPP(c_member(_1755638), _1755640), hAPP(c_List_Oset(_1755638), _1755642)))), 48430 ^ _779854 : [(48431 ^ _779854) ^ [_1755727] : [48432 ^ _779854 : [(48433 ^ _779854) ^ [_1755800] : [_1755642 = hAPP(hAPP(c_List_Oappend(_1755638), _1755727), hAPP(hAPP(c_List_Olist_OCons(_1755638), _1755640), _1755800))]], -(hBOOL(hAPP(hAPP(c_member(_1755638), _1755640), hAPP(c_List_Oset(_1755638), _1755727))))]]], (24571 ^ _779854) ^ [_1225578, _1225580, _1225582, _1225584, _1225586, _1225588, _1225590] : [c_Finite__Set_Ofolding__image__simple__idem(_1225578, _1225580, _1225582, _1225584, _1225586, _1225588), -(hAPP(hAPP(_1225582, _1225590), _1225590) = _1225590)], (46040 ^ _779854) ^ [_1703844, _1703846, _1703848] : [hBOOL(hAPP(c_List_Odistinct(_1703844), _1703846)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1703844)), c_Enum_On__lists(_1703844, _1703848, _1703846))))], (38865 ^ _779854) ^ [_1521452, _1521454, _1521456] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521452, tc_HOL_Obool)), _1521454), _1521456) = hAPP(c_Set_OCollect(_1521452), hAPP(hAPP(c_COMBS(_1521452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521452), c_fconj), hAPP(hAPP(c_COMBC(_1521452, tc_fun(_1521452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521452)), _1521454))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1521452), c_fNot), hAPP(hAPP(c_COMBC(_1521452, tc_fun(_1521452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521452)), _1521456)))))], (32265 ^ _779854) ^ [_1360365, _1360367, _1360369] : [class_Rings_Olinordered__idom(_1360365), -(hAPP(c_Groups_Oabs__class_Oabs(_1360365), hAPP(hAPP(c_Power_Opower__class_Opower(_1360365), hAPP(c_Groups_Ouminus__class_Ouminus(_1360365), _1360367)), _1360369)) = hAPP(c_Groups_Oabs__class_Oabs(_1360365), hAPP(hAPP(c_Power_Opower__class_Opower(_1360365), _1360367), _1360369)))], (24647 ^ _779854) ^ [_1227056, _1227058, _1227060, _1227062] : [class_Int_Onumber__ring(_1227056), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227056), hAPP(c_Int_Onumber__class_Onumber__of(_1227056), _1227058)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227056), hAPP(c_Int_Onumber__class_Onumber__of(_1227056), _1227060)), _1227062)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227056), hAPP(c_Int_Onumber__class_Onumber__of(_1227056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1227058), _1227060))), _1227062))], (37109 ^ _779854) ^ [_1476742, _1476744, _1476746, _1476748] : [-(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), _1476742), _1476744)), 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), _1476746), _1476748)), 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), _1476742), _1476746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1476744), _1476748))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (34207 ^ _779854) ^ [_1413133, _1413135, _1413137, _1413139, _1413141] : [hAPP(c_Set_Oimage(_1413133, _1413135, _1413137), c_Orderings_Otop__class_Otop(tc_fun(_1413133, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1413135, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1413135, _1413139, _1413141), c_Orderings_Otop__class_Otop(tc_fun(_1413135, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1413139, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1413133, _1413139, hAPP(c_Fun_Ocomp(_1413135, _1413139, _1413133, _1413141), _1413137)), c_Orderings_Otop__class_Otop(tc_fun(_1413133, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1413139, tc_HOL_Obool)))], (11220 ^ _779854) ^ [_973340, _973342] : [class_Finite__Set_Ofinite(_973340), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973340), _973342)))], (40972 ^ _779854) ^ [_1580342, _1580344, _1580346, _1580348, _1580350] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580342, _1580342)), hAPP(hAPP(c_Product__Type_OPair(_1580342, _1580342), _1580344), _1580346)), c_Transitive__Closure_Otrancl(_1580342, _1580348))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580342, _1580342)), hAPP(hAPP(c_Product__Type_OPair(_1580342, _1580342), _1580346), _1580350)), c_Transitive__Closure_Otrancl(_1580342, _1580348))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580342, _1580342)), hAPP(hAPP(c_Product__Type_OPair(_1580342, _1580342), _1580344), _1580350)), c_Transitive__Closure_Otrancl(_1580342, _1580348))))], (12344 ^ _779854) ^ [_995113, _995115, _995117, _995119] : [hBOOL(hAPP(hAPP(c_member(_995113), _995115), _995117)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995113, tc_HOL_Obool)), _995117), hAPP(hAPP(c_Set_Oinsert(_995113), _995115), _995119)) = hAPP(hAPP(c_Set_Oinsert(_995113), _995115), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_995113, tc_HOL_Obool)), _995117), _995119)))], (31418 ^ _779854) ^ [_1346188, _1346190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346190)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1346188, _1346190)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1346188), hAPP(c_Int_Onat, _1346190)))], (37388 ^ _779854) ^ [_1483868, _1483870, _1483872, _1483874, _1483876, _1483878, _1483880] : [c_Equiv__Relations_Oequiv(_1483868, _1483870, _1483872), hBOOL(hAPP(hAPP(c_member(tc_fun(_1483868, tc_HOL_Obool)), _1483874), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483868), _1483870), _1483872))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1483868, tc_HOL_Obool)), _1483876), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483868), _1483870), _1483872))), hBOOL(hAPP(hAPP(c_member(_1483868), _1483878), _1483874)), hBOOL(hAPP(hAPP(c_member(_1483868), _1483880), _1483876)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1483868, _1483868)), hAPP(hAPP(c_Product__Type_OPair(_1483868, _1483868), _1483878), _1483880)), _1483872)), -(_1483874 = _1483876)], (46108 ^ _779854) ^ [_1705353, _1705355] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705353)), c_List_Oremdups(_1705353, _1705355))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705353)), _1705355))))], (43348 ^ _779854) ^ [_1644218, _1644220, _1644222] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644218), tc_List_Olist(_1644218))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644218), tc_List_Olist(_1644218)), c_List_Olist_ONil(_1644218)), _1644220)), c_List_Olistrel(_1644218, _1644222))), -(_1644220 = c_List_Olist_ONil(_1644218))], (23369 ^ _779854) ^ [_1202871, _1202873] : [class_Rings_Olinordered__idom(_1202871), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202871), _1202873), c_Groups_Ozero__class_Ozero(_1202871))), -(c_Groups_Osgn__class_Osgn(_1202871, _1202873) = hAPP(c_Groups_Ouminus__class_Ouminus(_1202871), c_Groups_Oone__class_Oone(_1202871)))], (11998 ^ _779854) ^ [_988481, _988483, _988485, _988487, _988489] : [hBOOL(hAPP(hAPP(c_member(_988481), _988483), _988485)), -(hBOOL(hAPP(hAPP(c_member(_988487), hAPP(_988489, _988483)), hAPP(c_Set_Oimage(_988481, _988487, _988489), _988485))))], (29153 ^ _779854) ^ [_1305783, _1305785] : [class_Int_Onumber__ring(_1305783), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305783), c_Groups_Oone__class_Oone(_1305783)), hAPP(c_Int_Onumber__class_Onumber__of(_1305783), _1305785)) = hAPP(c_Int_Onumber__class_Onumber__of(_1305783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1305785)))], (38144 ^ _779854) ^ [_1501954, _1501956, _1501958, _1501960] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501954), hAPP(c_Set_Ovimage(_1501954, _1501956, _1501958), _1501960))), hAPP(c_Set_Oimage(_1501954, _1501956, _1501958), c_Orderings_Otop__class_Otop(tc_fun(_1501954, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1501956, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1501956), _1501960)))], (46404 ^ _779854) ^ [_1712144, _1712146, _1712148] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1712144, tc_HOL_Obool)), hAPP(c_List_Oset(_1712144), hAPP(c_List_Ofilter(_1712144, _1712146), _1712148))), hAPP(c_List_Oset(_1712144), _1712148))))], (34477 ^ _779854) ^ [_1419336, _1419338, _1419340, _1419342, _1419344, _1419346, _1419348, _1419350] : [class_Groups_Ocomm__monoid__mult(_1419336), c_Fun_Oinj__on(_1419338, _1419340, _1419342, _1419344), _1419346 = hAPP(c_Set_Oimage(_1419338, _1419340, _1419342), _1419344), _1419348 = hAPP(c_Fun_Ocomp(_1419340, _1419336, _1419338, _1419350), _1419342), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1419340, _1419336), _1419350), _1419346) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1419338, _1419336), _1419348), _1419344))], (32852 ^ _779854) ^ [_1371790, _1371792, _1371794, _1371796] : [class_Rings_Osemiring__1(_1371790), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1371790), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371792, tc_Nat_Onat), _1371794), _1371796)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371792, _1371790), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1371790, _1371792), c_Nat_Osemiring__1__class_Oof__nat(_1371790)), _1371794)), _1371796))], (44669 ^ _779854) ^ [_1673480, _1673482, _1673484, _1673486, _1673488] : [c_Finite__Set_Ofun__left__comm__idem(_1673480, _1673482, _1673484), -(hAPP(hAPP(c_Finite__Set_Ofold(_1673480, _1673482, _1673484), _1673486), hAPP(c_List_Oset(_1673480), _1673488)) = hAPP(c_List_Ofoldl(_1673482, _1673480, hAPP(c_COMBC(_1673480, _1673482, _1673482), _1673484), _1673486), _1673488))], (31677 ^ _779854) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (16315 ^ _779854) ^ [_1073147, _1073149, _1073151, _1073153, _1073155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073147), _1073149)), 16318 ^ _779854 : [(16325 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073153), 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), _1073149), _1073147)), _1073151)), _1073155))), -(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), _1073147), _1073151)), _1073153)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073149), _1073151)), _1073155))))], (16319 ^ _779854) ^ [] : [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), _1073147), _1073151)), _1073153)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073149), _1073151)), _1073155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073153), 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), _1073149), _1073147)), _1073151)), _1073155))))]]], (39573 ^ _779854) ^ [_1547545, _1547547, _1547549, _1547551, _1547553, _1547555, _1547557] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1547545, _1547547, _1547549, _1547551, _1547553), _1547555), _1547557)), 39577 ^ _779854 : [(39580 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1547553, 39576 ^ [_1547545, _1547547, _1547549, _1547551, _1547553, _1547555, _1547557]), _1547557)))], (39578 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(_1547551, _1547555), 39576 ^ [_1547545, _1547547, _1547549, _1547551, _1547553, _1547555, _1547557])))]]], (49883 ^ _779854) ^ [_1788253, _1788255, _1788257, _1788259] : [-(c_Wellfounded_Omax__extp(_1788253, _1788255, _1788257, _1788259)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788253), _1788257)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788253), _1788259)), -(_1788259 = c_Orderings_Obot__class_Obot(tc_fun(_1788253, tc_HOL_Obool))), 49897 ^ _779854 : [(49900 ^ _779854) ^ [_1788598] : [hBOOL(hAPP(hAPP(c_member(_1788253), _1788598), _1788259)), hBOOL(hAPP(hAPP(_1788255, 49896 ^ [_1788253, _1788255, _1788257, _1788259]), _1788598))], (49898 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788253), 49896 ^ [_1788253, _1788255, _1788257, _1788259]), _1788257)))]]], (31868 ^ _779854) ^ [_1353354] : [class_Int_Onumber__ring(_1353354), -(hAPP(c_Int_Oring__1__class_Oof__int(_1353354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1353354), c_Int_OMin))], (35887 ^ _779854) ^ [_1448320, _1448322, _1448324, _1448326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1448326, _1448322)), hAPP(_1448326, _1448324))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448320, _1448320)), hAPP(hAPP(c_Product__Type_OPair(_1448320, _1448320), _1448322), _1448324)), hAPP(c_Wellfounded_Omeasure(_1448320), _1448326))))], (11284 ^ _779854) ^ [_974497, _974499] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_974497, _974499)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_974497, _974499), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_974497), c_Orderings_Otop__class_Otop(tc_fun(_974497, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_974499), c_Orderings_Otop__class_Otop(tc_fun(_974499, tc_HOL_Obool))))], (47062 ^ _779854) ^ [_1725922, _1725924, _1725926] : [class_Orderings_Olinorder(_1725922), -(c_List_Olinorder__class_Osorted(_1725922, hAPP(c_List_Ofilter(_1725922, hAPP(hAPP(c_COMBC(_1725922, _1725922, tc_HOL_Obool), c_fequal), hAPP(_1725924, _1725926))), _1725926)))], (33317 ^ _779854) ^ [_1385252, _1385254] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385252, tc_HOL_Obool), _1385254) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1385252, tc_HOL_Obool), tc_fun(_1385252, tc_HOL_Obool)), _1385254), c_COMBI(tc_fun(_1385252, tc_HOL_Obool))))], (40960 ^ _779854) ^ [_1580122, _1580124] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580122, _1580122)), c_Transitive__Closure_Otrancl(_1580122, _1580124))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580122, _1580122)), _1580124)))], (50404 ^ _779854) ^ [_1798146, _1798148, _1798150, _1798152, _1798154, _1798156] : [hAPP(c_Hilbert__Choice_Oinv__into(_1798146, _1798148, _1798150, _1798152), _1798154) = hAPP(c_Hilbert__Choice_Oinv__into(_1798146, _1798148, _1798150, _1798152), _1798156), hBOOL(hAPP(hAPP(c_member(_1798148), _1798154), hAPP(c_Set_Oimage(_1798146, _1798148, _1798152), _1798150))), hBOOL(hAPP(hAPP(c_member(_1798148), _1798156), hAPP(c_Set_Oimage(_1798146, _1798148, _1798152), _1798150))), -(_1798154 = _1798156)], (18775 ^ _779854) ^ [_1119117] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1119117)], (5540 ^ _779854) ^ [_864655, _864657, _864659, _864661] : [-(tc_sum(_864661, _864657) = tc_sum(_864659, _864655)), _864661 = _864659, _864657 = _864655], (18078 ^ _779854) ^ [_1106923] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1106923)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1106923)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1106923)))], (29113 ^ _779854) ^ [_1305164, _1305166] : [class_Int_Onumber__ring(_1305164), class_Rings_Olinordered__idom(_1305164), 29120 ^ _779854 : [(29127 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305166), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305164), hAPP(c_Int_Onumber__class_Onumber__of(_1305164), _1305166)), c_Groups_Oone__class_Oone(_1305164))))], (29121 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305164), hAPP(c_Int_Onumber__class_Onumber__of(_1305164), _1305166)), c_Groups_Oone__class_Oone(_1305164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305166), c_Int_OBit1(c_Int_OPls))))]]], (4366 ^ _779854) ^ [_846224, _846226, _846228, _846230, _846232, _846234, _846236, _846238, _846240, _846242, _846244, _846246] : [-(c_New__Random__Sequence_Opos__union(_846246, _846242, _846238, _846234, _846230, _846226) = c_New__Random__Sequence_Opos__union(_846244, _846240, _846236, _846232, _846228, _846224)), _846246 = _846244, _846242 = _846240, _846238 = _846236, _846234 = _846232, _846230 = _846228, _846226 = _846224], (2862 ^ _779854) ^ [_822468, _822470, _822472, _822474] : [-(c_Relation_ODomain(_822474, _822470) = c_Relation_ODomain(_822472, _822468)), _822474 = _822472, _822470 = _822468], (48990 ^ _779854) ^ [_1767750, _1767752, _1767754, _1767756] : [48991 ^ _779854 : [(48994 ^ _779854) ^ [] : [_1767752 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48992 ^ _779854) ^ [] : [hBOOL(hAPP(_1767756, _1767754))]], 48995 ^ _779854 : [(48996 ^ _779854) ^ [_1767875] : [hBOOL(hAPP(hAPP(c_member(_1767750), _1767875), hAPP(c_List_Oset(_1767750), c_List_Oreplicate(_1767750, _1767752, _1767754)))), -(hBOOL(hAPP(_1767756, _1767875)))]]], (44598 ^ _779854) ^ [_1672007, _1672009] : [class_Lattices_Oab__semigroup__idem__mult(_1672007), -(_1672009 = c_List_Olist_ONil(_1672007)), -(hAPP(c_Finite__Set_Ofold1(_1672007, c_Groups_Otimes__class_Otimes(_1672007)), hAPP(c_List_Oset(_1672007), _1672009)) = hAPP(c_List_Ofoldl(_1672007, _1672007, c_Groups_Otimes__class_Otimes(_1672007), hAPP(c_List_Ohd(_1672007), _1672009)), hAPP(c_List_Otl(_1672007), _1672009)))], (1730 ^ _779854) ^ [_804431, _804433] : [-(class_Divides_Osemiring__div(_804431)), _804433 = _804431, class_Divides_Osemiring__div(_804433)], (34539 ^ _779854) ^ [_1420691, _1420693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420691)), hAPP(c_Nat_OSuc, _1420693))), -(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(_1420691))), 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)), _1420693)))))], (36195 ^ _779854) ^ [_1455167, _1455169] : [hAPP(c_Int_ORep__Integ, _1455167) = hAPP(c_Int_ORep__Integ, _1455169), -(_1455167 = _1455169)], (50601 ^ _779854) ^ [_1803018] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50597 ^ [_1803018]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (18793 ^ _779854) ^ [_1119341] : [-(_1119341 = 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)), _1119341)))], (33767 ^ _779854) ^ [_1401358, _1401360, _1401362, _1401364, _1401366] : [-(_1401358 = c_Orderings_Obot__class_Obot(tc_fun(_1401360, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401360, tc_fun(_1401362, tc_HOL_Obool)), _1401358), hAPP(hAPP(c_COMBC(_1401360, tc_fun(_1401362, tc_HOL_Obool), tc_fun(_1401362, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401362, tc_HOL_Obool), tc_fun(tc_fun(_1401362, tc_HOL_Obool), tc_fun(_1401362, tc_HOL_Obool)), _1401360), c_Groups_Ominus__class_Ominus(tc_fun(_1401362, tc_HOL_Obool))), _1401364)), _1401366)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401362, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401360, tc_fun(_1401362, tc_HOL_Obool)), _1401358), _1401364)), _1401366))], (2284 ^ _779854) ^ [_813311, _813313, _813315, _813317, _813319, _813321, _813323, _813325] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_813325, _813321, _813317, _813313) = c_Nat_Osemiring__1__class_Oof__nat__aux(_813323, _813319, _813315, _813311)), _813325 = _813323, _813321 = _813319, _813317 = _813315, _813313 = _813311], (48860 ^ _779854) ^ [_1764623, _1764625, _1764627] : [-(c_Predicate_Oconversep(_1764623, _1764625, c_Predicate_Oconversep(_1764625, _1764623, _1764627)) = _1764627)], (6853 ^ _779854) ^ [_891031, _891033, _891035, _891037] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_891031, tc_HOL_Obool)), _891033), _891035), _891037)), -(hBOOL(hAPP(_891033, _891037)))], (19971 ^ _779854) ^ [_1140019, _1140021] : [class_Groups_Oordered__ab__group__add(_1140019), 19974 ^ _779854 : [(19981 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140019), c_Groups_Ozero__class_Ozero(_1140019)), _1140021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140019), hAPP(c_Groups_Ouminus__class_Ouminus(_1140019), _1140021)), c_Groups_Ozero__class_Ozero(_1140019))))], (19975 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140019), hAPP(c_Groups_Ouminus__class_Ouminus(_1140019), _1140021)), c_Groups_Ozero__class_Ozero(_1140019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140019), c_Groups_Ozero__class_Ozero(_1140019)), _1140021)))]]], (41557 ^ _779854) ^ [_1595551, _1595553] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1595551, _1595551)), _1595553)), c_Wellfounded_Oacyclic(_1595551, _1595553), -(c_Wellfounded_Owf(_1595551, hAPP(c_Relation_Oconverse(_1595551, _1595551), _1595553)))], (6719 ^ _779854) ^ [_887674, _887676, _887678] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_887674, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_887674, tc_HOL_Obool), tc_HOL_Obool)), _887676), _887678)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887674, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_887674, tc_HOL_Obool), _887676)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_887674, tc_HOL_Obool), _887678)))], (40786 ^ _779854) ^ [_1575845, _1575847, _1575849, _1575851, _1575853] : [_1575845 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1575847, tc_HOL_Obool), _1575849), c_Orderings_Oorder__class_Omono(tc_fun(_1575847, tc_HOL_Obool), tc_fun(_1575847, tc_HOL_Obool), _1575849), hBOOL(hAPP(hAPP(c_member(_1575847), _1575851), _1575845)), 40800 ^ _779854 : [(40803 ^ _779854) ^ [] : [hBOOL(hAPP(_1575853, 40799 ^ [_1575845, _1575847, _1575849, _1575851, _1575853]))], (40801 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575847), 40799 ^ [_1575845, _1575847, _1575849, _1575851, _1575853]), hAPP(_1575849, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575847, tc_HOL_Obool)), _1575845), hAPP(c_Set_OCollect(_1575847), _1575853))))))]], -(hBOOL(hAPP(_1575853, _1575851)))], (51653 ^ _779854) ^ [_1825353, _1825355, _1825357, _1825359] : [class_Divides_Osemiring__div(_1825353), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825353), _1825355), _1825357)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1825353), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825353), _1825357), _1825355)), _1825359) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825353), hAPP(hAPP(c_Power_Opower__class_Opower(_1825353), _1825357), _1825359)), hAPP(hAPP(c_Power_Opower__class_Opower(_1825353), _1825355), _1825359)))], (17470 ^ _779854) ^ [_1095875, _1095877, _1095879, _1095881, _1095883, _1095885] : [c_Fun_Oinj__on(_1095875, _1095877, _1095879, _1095881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095877, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1095875, _1095877, _1095879), _1095881)), _1095883)), c_Fun_Oinj__on(_1095877, _1095875, _1095885, _1095883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095875, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1095877, _1095875, _1095885), _1095883)), _1095881)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095875), _1095881)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095877), _1095883)), -(hAPP(c_Finite__Set_Ocard(_1095875), _1095881) = hAPP(c_Finite__Set_Ocard(_1095877), _1095883))], (26607 ^ _779854) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (8172 ^ _779854) ^ [_916821, _916823, _916825, _916827] : [class_Orderings_Oorder(_916821), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916821), _916823), _916825)), _916823 = _916827, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916821), _916827), _916825)))], (30975 ^ _779854) ^ [_1339029, _1339031] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339029))), -(c_SMT_Oz3mod(_1339031, _1339029) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1339031, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1339029)))], (36494 ^ _779854) ^ [] : [-(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))], (37215 ^ _779854) ^ [_1479600, _1479602] : [-(c_Relation_OId__on(_1479600, _1479602) = hAPP(c_Product__Type_Oprod_Oprod__case(_1479600, _1479600, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1479600, tc_HOL_Obool, tc_fun(_1479600, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479600, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1479600, tc_HOL_Obool)), _1479600), c_COMBC(_1479600, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479600, tc_HOL_Obool), tc_fun(_1479600, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1479600), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1479600), c_fconj)), c_fequal))), _1479602)))], (40863 ^ _779854) ^ [_1577721, _1577723, _1577725, _1577727, _1577729, _1577731, _1577733, _1577735, _1577737] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1577721, _1577723, _1577725, _1577727), hAPP(hAPP(c_Product__Type_Oscomp(_1577721, _1577729, _1577731, tc_prod(_1577723, _1577725)), _1577733), _1577735)), _1577737) = hAPP(hAPP(c_Product__Type_Oscomp(_1577721, _1577729, _1577731, _1577727), _1577733), hAPP(hAPP(c_COMBC(_1577729, tc_fun(_1577723, tc_fun(_1577725, _1577727)), tc_fun(_1577731, _1577727)), hAPP(hAPP(c_COMBB(tc_fun(_1577731, tc_prod(_1577723, _1577725)), tc_fun(tc_fun(_1577723, tc_fun(_1577725, _1577727)), tc_fun(_1577731, _1577727)), _1577729), c_Product__Type_Oscomp(_1577731, _1577723, _1577725, _1577727)), _1577735)), _1577737)))], (12332 ^ _779854) ^ [_994963, _994965, _994967, _994969] : [-(hBOOL(hAPP(hAPP(c_member(_994963), _994965), _994967))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994963, tc_HOL_Obool)), _994967), hAPP(hAPP(c_Set_Oinsert(_994963), _994965), _994969)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994963, tc_HOL_Obool)), _994967), _994969))], (17726 ^ _779854) ^ [_1101184, _1101186] : [class_Groups_Oone(_1101184), 17729 ^ _779854 : [(17736 ^ _779854) ^ [] : [_1101186 = c_Groups_Oone__class_Oone(_1101184), -(c_Groups_Oone__class_Oone(_1101184) = _1101186)], (17730 ^ _779854) ^ [] : [c_Groups_Oone__class_Oone(_1101184) = _1101186, -(_1101186 = c_Groups_Oone__class_Oone(_1101184))]]], (13743 ^ _779854) ^ [_1021457, _1021459, _1021461] : [class_Orderings_Olinorder(_1021457), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021457), _1021459)), 13750 ^ _779854 : [(13757 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021457, tc_HOL_Obool)), _1021459), hAPP(hAPP(c_Set_Oinsert(_1021457), _1021461), c_Orderings_Obot__class_Obot(tc_fun(_1021457, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1021457, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1021457, hAPP(hAPP(c_Set_Oinsert(_1021457), _1021461), _1021459)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1021457), _1021461), c_Big__Operators_Olinorder__class_OMin(_1021457, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021457, tc_HOL_Obool)), _1021459), hAPP(hAPP(c_Set_Oinsert(_1021457), _1021461), c_Orderings_Obot__class_Obot(tc_fun(_1021457, tc_HOL_Obool)))))))], (13751 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021457, tc_HOL_Obool)), _1021459), hAPP(hAPP(c_Set_Oinsert(_1021457), _1021461), c_Orderings_Obot__class_Obot(tc_fun(_1021457, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1021457, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1021457, hAPP(hAPP(c_Set_Oinsert(_1021457), _1021461), _1021459)) = _1021461)]]], (34857 ^ _779854) ^ [_1427499, _1427501, _1427503, _1427505, _1427507, _1427509] : [34858 ^ _779854 : [(34861 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1427505, _1427501), _1427503))], (34859 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(_1427499, _1427501), _1427503))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427507, tc_fun(_1427509, tc_HOL_Obool))), _1427505), _1427499), _1427501), _1427503)))], (33833 ^ _779854) ^ [_1403194, _1403196, _1403198, _1403200, _1403202] : [class_Complete__Lattice_Ocomplete__lattice(_1403194), 33836 ^ _779854 : [(33837 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403194), _1403196), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1403198, _1403194), _1403200), _1403202))), 33840 ^ _779854 : [(33841 ^ _779854) ^ [_1403375] : [hBOOL(hAPP(hAPP(c_member(_1403198), _1403375), _1403200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403194), _1403196), hAPP(_1403202, _1403375))))]]], (33847 ^ _779854) ^ [] : [33849 ^ _779854 : [(33852 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403194), _1403196), hAPP(_1403202, 33848 ^ [_1403194, _1403196, _1403198, _1403200, _1403202])))], (33850 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403198), 33848 ^ [_1403194, _1403196, _1403198, _1403200, _1403202]), _1403200)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403194), _1403196), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1403198, _1403194), _1403200), _1403202))))]]], (44013 ^ _779854) ^ [_1658015, _1658017] : [-(hAPP(hAPP(c_List_Oappend(_1658015), c_List_Olist_ONil(_1658015)), _1658017) = _1658017)], (28274 ^ _779854) ^ [] : [-(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))))], (42543 ^ _779854) ^ [_1623615, _1623617, _1623619, _1623621] : [42546 ^ _779854 : [(42551 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623615, _1623615)), hAPP(hAPP(c_Product__Type_OPair(_1623615, _1623615), 42545 ^ [_1623615, _1623617, _1623619, _1623621]), 42544 ^ [_1623615, _1623617, _1623619, _1623621])), _1623617))], (42549 ^ _779854) ^ [] : [42544 ^ [_1623615, _1623617, _1623619, _1623621] = 42545 ^ [_1623615, _1623617, _1623619, _1623621]], (42547 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623615, _1623615)), hAPP(hAPP(c_Product__Type_OPair(_1623615, _1623615), 42544 ^ [_1623615, _1623617, _1623619, _1623621]), 42545 ^ [_1623615, _1623617, _1623619, _1623621])), _1623617))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623615), tc_List_Olist(_1623615))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623615), tc_List_Olist(_1623615)), _1623619), _1623621)), c_List_Olexord(_1623615, _1623617)))), -(_1623619 = _1623621), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623615), tc_List_Olist(_1623615))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623615), tc_List_Olist(_1623615)), _1623621), _1623619)), c_List_Olexord(_1623615, _1623617))))], (52301 ^ _779854) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52375 ^ _779854) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (13685 ^ _779854) ^ [_1020280, _1020282, _1020284] : [class_Orderings_Olinorder(_1020280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020280), _1020282)), -(hBOOL(hAPP(hAPP(c_member(_1020280), _1020284), _1020282))), -(_1020282 = c_Orderings_Obot__class_Obot(tc_fun(_1020280, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1020280, hAPP(hAPP(c_Set_Oinsert(_1020280), _1020284), _1020282)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1020280), _1020284), c_Big__Operators_Olinorder__class_OMax(_1020280, _1020282)))], (50632 ^ _779854) ^ [_1803583, _1803585, _1803587, _1803589, _1803591, _1803593] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1803583, _1803585, _1803587, _1803589, c_Lazy__Sequence_Olazy__sequence_OInsert(_1803585, _1803591, _1803593)) = hAPP(hAPP(hAPP(_1803589, _1803591), _1803593), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1803583, _1803585, _1803587, _1803589, _1803593)))], (29851 ^ _779854) ^ [_1318087, _1318089] : [class_Rings_Olinordered__idom(_1318087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318087), hAPP(hAPP(c_Power_Opower__class_Opower(_1318087), _1318089), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1318087)))], (51845 ^ _779854) ^ [_1828671, _1828673] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828671), _1828673)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828673), _1828671))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828673), _1828671)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828671), _1828673)))], (10553 ^ _779854) ^ [_959142, _959144, _959146, _959148] : [c_Fun_Oinj__on(_959142, _959144, _959146, _959148), 10556 ^ _779854 : [(10557 ^ _779854) ^ [_959250] : [hBOOL(hAPP(hAPP(c_member(_959142), _959250), _959148)), 10560 ^ _779854 : [(10561 ^ _779854) ^ [_959352] : [hBOOL(hAPP(hAPP(c_member(_959142), _959352), _959148)), hAPP(_959146, _959250) = hAPP(_959146, _959352), -(_959250 = _959352)]]]]], (18481 ^ _779854) ^ [_1114752, _1114754] : [class_Groups_Ozero(_1114752), 18484 ^ _779854 : [(18491 ^ _779854) ^ [] : [_1114754 = c_Groups_Ozero__class_Ozero(_1114752), -(c_Groups_Ozero__class_Ozero(_1114752) = _1114754)], (18485 ^ _779854) ^ [] : [c_Groups_Ozero__class_Ozero(_1114752) = _1114754, -(_1114754 = c_Groups_Ozero__class_Ozero(_1114752))]]], (9809 ^ _779854) ^ [_944593, _944595, _944597, _944599, _944601] : [-(hAPP(c_Set_Oimage(_944593, _944595, _944597), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_944593, tc_HOL_Obool)), _944599), _944601)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_944595, tc_HOL_Obool)), hAPP(c_Set_Oimage(_944593, _944595, _944597), _944599)), hAPP(c_Set_Oimage(_944593, _944595, _944597), _944601)))], (26411 ^ _779854) ^ [_1259719, _1259721, _1259723] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259719))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259719)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259721)), _1259723)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1259721)), _1259723))], (33175 ^ _779854) ^ [_1381405, _1381407, _1381409, _1381411] : [-(_1381405 = c_Orderings_Obot__class_Obot(tc_fun(_1381407, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381407, tc_fun(_1381409, tc_HOL_Obool)), _1381405), hAPP(c_COMBK(tc_fun(_1381409, tc_HOL_Obool), _1381407), _1381411)) = _1381411)], (34719 ^ _779854) ^ [_1424923, _1424925, _1424927, _1424929, _1424931, _1424933, _1424935] : [c_Fun_Oinj__on(_1424923, _1424925, _1424927, hAPP(c_Set_Oimage(_1424929, _1424923, _1424931), _1424933)), c_Fun_Oinj__on(_1424929, _1424923, _1424931, _1424933), hBOOL(hAPP(hAPP(c_member(_1424925), _1424935), hAPP(c_Set_Oimage(_1424923, _1424925, _1424927), hAPP(c_Set_Oimage(_1424929, _1424923, _1424931), _1424933)))), -(hAPP(c_Fun_Othe__inv__into(_1424929, _1424925, _1424933, hAPP(c_Fun_Ocomp(_1424923, _1424925, _1424929, _1424927), _1424931)), _1424935) = hAPP(hAPP(c_Fun_Ocomp(_1424923, _1424929, _1424925, c_Fun_Othe__inv__into(_1424929, _1424923, _1424933, _1424931)), c_Fun_Othe__inv__into(_1424923, _1424925, hAPP(c_Set_Oimage(_1424929, _1424923, _1424931), _1424933), _1424927)), _1424935))], (44314 ^ _779854) ^ [_1665777, _1665779, _1665781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665777)), _1665781)), _1665779)), -(hAPP(hAPP(c_List_Odrop(_1665777), _1665779), _1665781) = c_List_Olist_ONil(_1665777))], (46765 ^ _779854) ^ [_1720582, _1720584] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1720582, _1720584) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1720582), hAPP(c_Nat_OSuc, _1720584))))], (16836 ^ _779854) ^ [_1083387, _1083389, _1083391, _1083393, _1083395] : [class_Groups_Ocomm__monoid__mult(_1083387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083389), _1083391)), -(hBOOL(hAPP(hAPP(c_member(_1083389), _1083393), _1083391))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083389, _1083387), _1083395), hAPP(hAPP(c_Set_Oinsert(_1083389), _1083393), _1083391)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083387), hAPP(_1083395, _1083393)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1083389, _1083387), _1083395), _1083391)))], (15392 ^ _779854) ^ [_1054507, _1054509, _1054511, _1054513] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1054507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054507), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054507), _1054509), _1054511)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054507), _1054509), _1054513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054507), _1054511), _1054513)))], (31832 ^ _779854) ^ [_1352692] : [class_Rings_Oring__1(_1352692), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352692), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1352692))], (10545 ^ _779854) ^ [_959004, _959006, _959008] : [-(c_Fun_Oinj__on(_959004, _959006, _959008, c_Orderings_Obot__class_Obot(tc_fun(_959004, tc_HOL_Obool))))], (20075 ^ _779854) ^ [_1141781, _1141783, _1141785] : [class_Groups_Ocomm__monoid__add(_1141781), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1141783, _1141781), _1141785), c_Orderings_Obot__class_Obot(tc_fun(_1141783, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1141781))], (36878 ^ _779854) ^ [_1470046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1470046)), -(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))), _1470046)), c_FunDef_Omax__weak)))], (46365 ^ _779854) ^ [_1710640, _1710642, _1710644] : [c_List_Oconcat(_1710640, _1710642) = c_List_Oconcat(_1710640, _1710644), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710640))), _1710642) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710640))), _1710644), 46375 ^ _779854 : [(46378 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1710640), tc_List_Olist(_1710640), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710640), tc_fun(tc_List_Olist(_1710640), tc_Nat_Onat), tc_fun(tc_List_Olist(_1710640), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1710640), tc_Nat_Onat), tc_fun(tc_List_Olist(_1710640), tc_HOL_Obool)), tc_List_Olist(_1710640)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1710640))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1710640)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1710640))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1710640)))), 46374 ^ [_1710640, _1710642, _1710644]))], (46376 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710640), tc_List_Olist(_1710640))), 46374 ^ [_1710640, _1710642, _1710644]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1710640), tc_List_Olist(_1710640))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1710640), tc_List_Olist(_1710640)), _1710642), _1710644)))))]], -(_1710642 = _1710644)], (31448 ^ _779854) ^ [_1346711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346711)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1346711) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (40551 ^ _779854) ^ [_1570292, _1570294, _1570296, _1570298, _1570300, _1570302] : [hBOOL(hAPP(hAPP(c_member(_1570292), _1570294), _1570296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570298, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1570292, _1570298, _1570300), _1570296)), hAPP(_1570302, hAPP(c_Set_Oimage(_1570292, _1570298, _1570300), _1570296)))), -(hBOOL(hAPP(hAPP(c_member(_1570298), hAPP(_1570300, _1570294)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1570298, tc_HOL_Obool), _1570302))))], (21659 ^ _779854) ^ [_1170759, _1170761] : [class_Rings_Oring__1(_1170759), hBOOL(hAPP(hAPP(c_member(_1170759), _1170761), c_Int_Oring__1__class_OInts(_1170759))), -(hBOOL(hAPP(hAPP(c_member(_1170759), hAPP(c_Groups_Ouminus__class_Ouminus(_1170759), _1170761)), c_Int_Oring__1__class_OInts(_1170759))))], (23964 ^ _779854) ^ [_1214546, _1214548, _1214550, _1214552] : [class_Groups_Omonoid__mult(_1214546), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214546), _1214548), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214550), _1214552)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1214546), hAPP(hAPP(c_Power_Opower__class_Opower(_1214546), _1214548), _1214550)), _1214552))], (9821 ^ _779854) ^ [_944796, _944798, _944800, _944802, _944804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944796, tc_HOL_Obool)), hAPP(c_Set_Oimage(_944798, _944796, _944800), _944802)), _944804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_944796, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_944798, tc_HOL_Obool), tc_fun(_944796, tc_HOL_Obool), c_Set_Oimage(_944798, _944796, _944800)), hAPP(c_Set_OPow(_944798), _944802))), hAPP(c_Set_OPow(_944796), _944804))))], (2928 ^ _779854) ^ [_823463, _823465, _823467, _823469] : [-(c_Nitpick_Oinverse__frac(_823469, _823465) = c_Nitpick_Oinverse__frac(_823467, _823463)), _823469 = _823467, _823465 = _823463], (43197 ^ _779854) ^ [_1640824, _1640826, _1640828, _1640830] : [hBOOL(hAPP(c_List_Odistinct(_1640824), _1640826)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1640824, _1640828)), hAPP(hAPP(c_List_Ozip(_1640824, _1640828), _1640826), _1640830))))], (37024 ^ _779854) ^ [_1474364, _1474366, _1474368] : [-(hAPP(c_Relation_OImage(_1474364, _1474366, _1474368), c_Orderings_Obot__class_Obot(tc_fun(_1474364, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1474366, tc_HOL_Obool)))], (34904 ^ _779854) ^ [_1428524, _1428526, _1428528, _1428530, _1428532, _1428534, _1428536] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428524, tc_fun(_1428526, tc_fun(_1428528, tc_HOL_Obool))), _1428530), _1428532), _1428534), _1428536))), 34905 ^ _779854 : [(34906 ^ _779854) ^ [_1428609] : [hBOOL(hAPP(hAPP(c_member(_1428524), _1428609), _1428530)), hBOOL(hAPP(hAPP(hAPP(_1428532, _1428609), _1428534), _1428536))]]], (30579 ^ _779854) ^ [_1331865, _1331867] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331865, _1331867) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331865, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1331867)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48583 ^ _779854) ^ [_1758762] : [class_Nat_Osize(_1758762), -(c_FunDef_Ois__measure(_1758762, c_Nat_Osize__class_Osize(_1758762)))], (17835 ^ _779854) ^ [_1102919, _1102921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102919), _1102921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1102919)), hAPP(c_Nat_OSuc, _1102921))))], (6949 ^ _779854) ^ [_893307, _893309, _893311, _893313] : [class_Lattices_Osemilattice__sup(_893307), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893307), _893309), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893307), _893311), _893313)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893307), _893311), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893307), _893309), _893313)))], (36689 ^ _779854) ^ [_1466018, _1466020, _1466022, _1466024, _1466026, _1466028] : [class_Groups_Oordered__ab__group__add(_1466018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466020), _1466022)), 36699 ^ _779854 : [(36702 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1466018), c_Groups_Ozero__class_Ozero(_1466018)), hAPP(_1466024, 36698 ^ [_1466018, _1466020, _1466022, _1466024, _1466026, _1466028])))], (36700 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466020), 36698 ^ [_1466018, _1466020, _1466022, _1466024, _1466026, _1466028]), _1466022)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466020, _1466018), _1466024), _1466022) = _1466026, hBOOL(hAPP(hAPP(c_member(_1466020), _1466028), _1466022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1466018), hAPP(_1466024, _1466028)), _1466026)))], (29669 ^ _779854) ^ [] : [-(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)))))], (45962 ^ _779854) ^ [_1701968, _1701970, _1701972, _1701974, _1701976, _1701978] : [c_List_Olist__all2(_1701968, _1701970, _1701972, _1701974, _1701976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701978), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701968)), _1701974))), -(hBOOL(hAPP(hAPP(_1701972, hAPP(hAPP(c_List_Onth(_1701968), _1701974), _1701978)), hAPP(hAPP(c_List_Onth(_1701970), _1701976), _1701978))))], (52439 ^ _779854) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (36946 ^ _779854) ^ [_1472091, _1472093, _1472095, _1472097] : [c_FunDef_Oreduction__pair(_1472091, _1472093), -(c_FunDef_Oreduction__pair(_1472095, hAPP(hAPP(c_FunDef_Orp__inv__image(_1472091, _1472095), _1472093), _1472097)))], (24717 ^ _779854) ^ [_1228536, _1228538, _1228540, _1228542] : [class_Int_Onumber__ring(_1228536), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228536), hAPP(c_Int_Onumber__class_Onumber__of(_1228536), _1228538)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1228536), _1228540), hAPP(c_Int_Onumber__class_Onumber__of(_1228536), _1228542))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228536), hAPP(c_Int_Onumber__class_Onumber__of(_1228536), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228538), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228542)))), _1228540))], (43017 ^ _779854) ^ [_1636695, _1636697, _1636699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1636695), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636697)), _1636699))), -(c_List_Obutlast(_1636697, hAPP(hAPP(c_List_Otake(_1636697), _1636695), _1636699)) = hAPP(hAPP(c_List_Otake(_1636697), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1636695), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1636699))], (4496 ^ _779854) ^ [_848327, _848329] : [_848329 = _848327, -(c_List_Olist_ONil(_848329) = c_List_Olist_ONil(_848327))], (3494 ^ _779854) ^ [_832254, _832256] : [_832256 = _832254, -(c_List_Otranspose__rel(_832256) = c_List_Otranspose__rel(_832254))], (34217 ^ _779854) ^ [_1413392, _1413394, _1413396] : [class_Groups_Ocomm__monoid__add(_1413392), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1413392), _1413394), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1413396))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1413392), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1413392), _1413394), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1413396))), hAPP(_1413394, _1413396)))], (17338 ^ _779854) ^ [_1093174, _1093176] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1093174, _1093176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1093176), _1093174))], (1370 ^ _779854) ^ [_799931, _799933] : [-(class_Orderings_Owellorder(_799931)), _799933 = _799931, class_Orderings_Owellorder(_799933)], (9028 ^ _779854) ^ [_930441, _930443, _930445, _930447, _930449] : [class_Orderings_Olinorder(_930441), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_930441, _930443), _930445) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_930441, _930447), _930449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930441), _930443), _930445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930441), _930447), _930449)), -(_930445 = _930449)], (8158 ^ _779854) ^ [_916588, _916590, _916592, _916594] : [class_Orderings_Opreorder(_916588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916588), _916590), _916592)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916588), _916592), _916594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916588), _916590), _916594)))], (48046 ^ _779854) ^ [_1746927, _1746929, _1746931, _1746933, _1746935, _1746937, _1746939, _1746941] : [48048 ^ _779854 : [(48051 ^ _779854) ^ [] : [hAPP(c_Fun_Ocomp(_1746931, _1746931, _1746933, hAPP(_1746935, 48047 ^ [_1746927, _1746929, _1746931, _1746933, _1746935, _1746937, _1746939, _1746941])), _1746937) = hAPP(c_Fun_Ocomp(_1746933, _1746931, _1746933, _1746937), hAPP(_1746939, 48047 ^ [_1746927, _1746929, _1746931, _1746933, _1746935, _1746937, _1746939, _1746941]))], (48049 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746927), 48047 ^ [_1746927, _1746929, _1746931, _1746933, _1746935, _1746937, _1746939, _1746941]), hAPP(c_List_Oset(_1746927), _1746929))))]], -(hAPP(c_List_Ofoldl(_1746931, _1746927, hAPP(c_COMBC(_1746927, _1746931, _1746931), _1746935), hAPP(_1746937, _1746941)), _1746929) = hAPP(_1746937, hAPP(c_List_Ofoldl(_1746933, _1746927, hAPP(c_COMBC(_1746927, _1746933, _1746933), _1746939), _1746941), _1746929)))], (9538 ^ _779854) ^ [_939654, _939656, _939658] : [-(hAPP(c_Set_Oimage(_939654, _939656, _939658), c_Orderings_Obot__class_Obot(tc_fun(_939654, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_939656, tc_HOL_Obool)))], (49222 ^ _779854) ^ [_1772395] : [-(c_Lazy__Sequence_Oyieldn(_1772395) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1772395), _1772395, c_Lazy__Sequence_Oyield(_1772395)))], (7724 ^ _779854) ^ [_908298, _908300, _908302, _908304] : [class_Orderings_Olinorder(_908298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908298), _908300), _908302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908298), _908302), _908304)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908298, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_908298, _908300), _908302)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_908298, _908302), _908304)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_908298, _908300), _908304))], (10421 ^ _779854) ^ [_956644] : [class_Orderings_Oord(_956644), -(c_Orderings_Oord__class_Omin(_956644) = c_Orderings_Oord_Omin(_956644, c_Orderings_Oord__class_Oless__eq(_956644)))], (18080 ^ _779854) ^ [_1106964] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1106964)) = hAPP(c_Nat_OSuc, _1106964))], (49806 ^ _779854) ^ [_1787057, _1787059] : [c_Equiv__Relations_Oequivp(_1787057, _1787059), 49809 ^ _779854 : [(49814 ^ _779854) ^ [] : [-(c_Predicate_Otransp(_1787057, _1787059))], (49812 ^ _779854) ^ [] : [-(c_Predicate_Osymp(_1787057, _1787059))], (49810 ^ _779854) ^ [] : [-(c_Predicate_Oreflp(_1787057, _1787059))]]], (39802 ^ _779854) ^ [_1552001, _1552003, _1552005] : [_1552005 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1552001, _1552003), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1552001, _1552003), _1552005) = c_Orderings_Obot__class_Obot(tc_fun(_1552001, tc_HOL_Obool)))], (48218 ^ _779854) ^ [_1750908, _1750910, _1750912, _1750914, _1750916] : [hAPP(c_List_Ofilter(_1750908, _1750910), _1750912) = hAPP(hAPP(c_List_Olist_OCons(_1750908), _1750914), _1750916), 48223 ^ _779854 : [(48232 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1750910, _1750914)))], (48234 ^ _779854) ^ [] : [-(_1750916 = hAPP(c_List_Ofilter(_1750908, _1750910), 48222 ^ [_1750908, _1750910, _1750912, _1750914, _1750916]))], (48226 ^ _779854) ^ [_1751222] : [hBOOL(hAPP(hAPP(c_member(_1750908), _1751222), hAPP(c_List_Oset(_1750908), 48221 ^ [_1750908, _1750910, _1750912, _1750914, _1750916]))), hBOOL(hAPP(_1750910, _1751222))], (48224 ^ _779854) ^ [] : [-(_1750912 = hAPP(hAPP(c_List_Oappend(_1750908), 48221 ^ [_1750908, _1750910, _1750912, _1750914, _1750916]), hAPP(hAPP(c_List_Olist_OCons(_1750908), _1750914), 48222 ^ [_1750908, _1750910, _1750912, _1750914, _1750916])))]]], (2302 ^ _779854) ^ [_813612, _813614, _813616, _813618] : [-(c_Groups_Osgn__class_Osgn(_813618, _813614) = c_Groups_Osgn__class_Osgn(_813616, _813612)), _813618 = _813616, _813614 = _813612], (33707 ^ _779854) ^ [_1399572, _1399574] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1399572, 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(_1399572, tc_HOL_Obool)), tc_fun(_1399572, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1399572, tc_HOL_Obool)), tc_fun(_1399572, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1399572, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1399574)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1399572, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1399574))], (37170 ^ _779854) ^ [_1478425, _1478427] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1478425, _1478425)), _1478427)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1478425), hAPP(c_Relation_OField(_1478425), _1478427))))], (52211 ^ _779854) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (9438 ^ _779854) ^ [_937589, _937591] : [class_Groups_Oordered__ab__group__add(_937589), -(hAPP(c_Set_Oimage(_937589, _937589, c_Groups_Ouminus__class_Ouminus(_937589)), hAPP(c_SetInterval_Oord__class_OatLeast(_937589), _937591)) = hAPP(c_SetInterval_Oord__class_OatMost(_937589), hAPP(c_Groups_Ouminus__class_Ouminus(_937589), _937591)))], (33120 ^ _779854) ^ [_1380131, _1380133, _1380135, _1380137, _1380139] : [-(_1380131 = c_Orderings_Obot__class_Obot(tc_fun(_1380133, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380133, tc_fun(_1380135, tc_HOL_Obool)), _1380131), hAPP(hAPP(c_COMBB(tc_fun(_1380135, tc_HOL_Obool), tc_fun(_1380135, tc_HOL_Obool), _1380133), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380135, tc_HOL_Obool)), _1380137)), _1380139)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380135, tc_HOL_Obool)), _1380137), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380133, tc_fun(_1380135, tc_HOL_Obool)), _1380131), _1380139)))], (30609 ^ _779854) ^ [_1332359, _1332361, _1332363] : [-(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), _1332359), _1332361)), _1332361)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332359, _1332361))), _1332363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332359), _1332363))], (42717 ^ _779854) ^ [_1628054, _1628056, _1628058, _1628060] : [-(hAPP(hAPP(c_List_Otake(_1628054), _1628056), hAPP(hAPP(c_List_Otake(_1628054), _1628058), _1628060)) = hAPP(hAPP(c_List_Otake(_1628054), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1628056), _1628058)), _1628060))], (21005 ^ _779854) ^ [_1157834, _1157836, _1157838] : [-(hBOOL(hAPP(_1157834, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1157836), _1157838)))), 21008 ^ _779854 : [(21011 ^ _779854) ^ [] : [hBOOL(hAPP(_1157834, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21009 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157836), _1157838)))]], 21013 ^ _779854 : [(21016 ^ _779854) ^ [] : [hBOOL(hAPP(_1157834, 21012 ^ [_1157834, _1157836, _1157838]))], (21014 ^ _779854) ^ [] : [-(_1157836 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1157838), 21012 ^ [_1157834, _1157836, _1157838]))]]], (38682 ^ _779854) ^ [_1517271, _1517273, _1517275] : [-(c_Relation_Orefl__on(_1517271, _1517273, _1517275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517271, _1517271), tc_HOL_Obool)), _1517275), hAPP(hAPP(c_Product__Type_OSigma(_1517271, _1517271), _1517273), hAPP(c_COMBK(tc_fun(_1517271, tc_HOL_Obool), _1517271), _1517273)))), 38688 ^ _779854 : [(38691 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517271, _1517271)), hAPP(hAPP(c_Product__Type_OPair(_1517271, _1517271), 38687 ^ [_1517271, _1517273, _1517275]), 38687 ^ [_1517271, _1517273, _1517275])), _1517275))], (38689 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1517271), 38687 ^ [_1517271, _1517273, _1517275]), _1517273)))]]], (38792 ^ _779854) ^ [_1519821, _1519823] : [hAPP(c_Set_OCollect(_1519821), _1519823) = c_Orderings_Obot__class_Obot(tc_fun(_1519821, tc_HOL_Obool)), 38795 ^ _779854 : [(38796 ^ _779854) ^ [_1519906] : [hBOOL(hAPP(_1519823, _1519906))]]], (35917 ^ _779854) ^ [_1449069, _1449071] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1449069, _1449071) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1449069, _1449071)))], (36464 ^ _779854) ^ [_1460529, _1460531, _1460533] : [class_Orderings_Owellorder(_1460529), hBOOL(hAPP(_1460531, _1460533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460529), c_Orderings_Oord__class_OLeast(_1460529, _1460531)), _1460533)))], (22379 ^ _779854) ^ [_1184393, _1184395, _1184397] : [class_Fields_Olinordered__field(_1184393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184393), _1184395), c_Groups_Ozero__class_Ozero(_1184393))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184393), c_Groups_Ozero__class_Ozero(_1184393)), _1184397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184393), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184393), _1184395), _1184397)), c_Groups_Ozero__class_Ozero(_1184393))))], (2406 ^ _779854) ^ [_815308, _815310, _815312, _815314] : [-(c_Nitpick_Onat__gcd(_815314, _815310) = c_Nitpick_Onat__gcd(_815312, _815308)), _815314 = _815312, _815310 = _815308], (42372 ^ _779854) ^ [_1618523, _1618525, _1618527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618523, _1618523), tc_HOL_Obool)), _1618525), _1618527)), c_Relation_Orefl__on(_1618523, c_Orderings_Otop__class_Otop(tc_fun(_1618523, tc_HOL_Obool)), _1618527), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1618523), tc_List_Olist(_1618523)), tc_HOL_Obool)), c_List_Olistrel1(_1618523, _1618525)), c_List_Olistrel(_1618523, _1618527))))], (12996 ^ _779854) ^ [_1008504, _1008506] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1008504, tc_HOL_Obool)), _1008506)), 13002 ^ _779854 : [(13005 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008504), 13001 ^ [_1008504, _1008506]))], (13003 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1008504, tc_HOL_Obool)), 13001 ^ [_1008504, _1008506]), _1008506)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1008504), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1008504, tc_HOL_Obool), _1008506))))], (41629 ^ _779854) ^ [_1596980, _1596982, _1596984, _1596986, _1596988, _1596990] : [c_Relation_Osingle__valued(_1596980, _1596982, _1596984), hBOOL(hAPP(hAPP(c_member(tc_prod(_1596980, _1596982)), hAPP(hAPP(c_Product__Type_OPair(_1596980, _1596982), _1596986), _1596988)), _1596984)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1596980, _1596982)), hAPP(hAPP(c_Product__Type_OPair(_1596980, _1596982), _1596986), _1596990)), _1596984)), -(_1596988 = _1596990)], (49432 ^ _779854) ^ [_1777211, _1777213, _1777215] : [c_List_Olist__ex(tc_Int_Oint, _1777211, c_List_Oupto(_1777213, _1777215)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1777211), _1777213, _1777215)], (25913 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (4782 ^ _779854) ^ [_852844, _852846] : [_852846 = _852844, -(c_Wellfounded_Ofinite__psubset(_852846) = c_Wellfounded_Ofinite__psubset(_852844))], (14656 ^ _779854) ^ [_1039627, _1039629, _1039631] : [class_Lattices_Osemilattice__inf(_1039627), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039627), _1039629)), hBOOL(hAPP(hAPP(c_member(_1039627), _1039631), _1039629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039627), hAPP(c_Finite__Set_Ofold1(_1039627, c_Lattices_Osemilattice__inf__class_Oinf(_1039627)), _1039629)), _1039631)))], (44436 ^ _779854) ^ [_1668806, _1668808, _1668810, _1668812, _1668814] : [-(hAPP(hAPP(c_List_Ozip(_1668806, _1668808), _1668810), hAPP(hAPP(c_List_Oappend(_1668808), _1668812), _1668814)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1668806, _1668808)), hAPP(hAPP(c_List_Ozip(_1668806, _1668808), hAPP(hAPP(c_List_Otake(_1668806), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668808)), _1668812)), _1668810)), _1668812)), hAPP(hAPP(c_List_Ozip(_1668806, _1668808), hAPP(hAPP(c_List_Odrop(_1668806), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668808)), _1668812)), _1668810)), _1668814)))], (32988 ^ _779854) ^ [_1376647, _1376649, _1376651, _1376653] : [-(_1376647 = c_Orderings_Obot__class_Obot(tc_fun(_1376649, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1376649, _1376651, hAPP(c_COMBK(_1376651, _1376649), _1376653)), _1376647) = hAPP(hAPP(c_Set_Oinsert(_1376651), _1376653), c_Orderings_Obot__class_Obot(tc_fun(_1376651, tc_HOL_Obool))))], (31673 ^ _779854) ^ [] : [-(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))], (47288 ^ _779854) ^ [_1730321, _1730323, _1730325] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1730321), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1730321))), _1730323))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1730321))), _1730323))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1730321), _1730321), hAPP(hAPP(c_COMBC(tc_List_Olist(_1730321), tc_Nat_Onat, _1730321), c_List_Onth(_1730321)), _1730325)), hAPP(c_List_Ofilter(tc_List_Olist(_1730321), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1730321)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730325)), c_Nat_Osize__class_Osize(tc_List_Olist(_1730321)))), c_List_Otranspose(_1730321, _1730323))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1730321)), _1730323), _1730325))], (20309 ^ _779854) ^ [_1145442, _1145444] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145442), _1145444) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20312 ^ _779854 : [(20315 ^ _779854) ^ [] : [-(_1145444 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20313 ^ _779854) ^ [] : [-(_1145442 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8976 ^ _779854) ^ [_929475, _929477, _929479, _929481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929475, tc_HOL_Obool)), _929477), _929479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929475, tc_HOL_Obool)), _929479), _929481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929475, tc_HOL_Obool)), _929477), _929481)))], (46593 ^ _779854) ^ [_1717210, _1717212, _1717214] : [class_Groups_Oab__semigroup__add(_1717210), -(c_List_Ofoldr(_1717210, _1717210, c_Groups_Oplus__class_Oplus(_1717210), _1717212, _1717214) = hAPP(c_List_Ofoldl(_1717210, _1717210, c_Groups_Oplus__class_Oplus(_1717210), _1717214), _1717212))], (47754 ^ _779854) ^ [_1740395, _1740397, _1740399, _1740401] : [hBOOL(hAPP(_1740395, _1740397)), -(c_List_OdropWhile(_1740399, _1740395, hAPP(hAPP(c_List_Olist_OCons(_1740399), _1740397), _1740401)) = c_List_OdropWhile(_1740399, _1740395, _1740401))], (33577 ^ _779854) ^ [_1395768, _1395770, _1395772] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395768, tc_HOL_Obool)), _1395770), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1395768, tc_HOL_Obool), _1395772)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1395768, tc_HOL_Obool), tc_fun(_1395768, tc_HOL_Obool)), _1395772), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395768, tc_HOL_Obool)), _1395770)))], (23812 ^ _779854) ^ [_1211710, _1211712, _1211714] : [class_Rings_Oring__1(_1211710), hBOOL(hAPP(hAPP(c_member(_1211710), _1211712), c_Int_Oring__1__class_OInts(_1211710))), -(hBOOL(hAPP(hAPP(c_member(_1211710), hAPP(hAPP(c_Power_Opower__class_Opower(_1211710), _1211712), _1211714)), c_Int_Oring__1__class_OInts(_1211710))))], (37219 ^ _779854) ^ [_1479733, _1479735, _1479737] : [-(hAPP(c_Relation_OImage(_1479733, _1479733, c_Relation_OId__on(_1479733, _1479735)), _1479737) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479733, tc_HOL_Obool)), _1479735), _1479737))], (52451 ^ _779854) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52167 ^ _779854) ^ [_1833551, _1833553] : [class_Groups_Ominus(_1833551), -(class_Groups_Ominus(tc_fun(_1833553, _1833551)))], (32922 ^ _779854) ^ [_1375087, _1375089, _1375091, _1375093] : [-(_1375087 = c_Orderings_Obot__class_Obot(tc_fun(_1375089, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375089, tc_fun(_1375091, tc_HOL_Obool)), _1375087), hAPP(c_COMBK(tc_fun(_1375091, tc_HOL_Obool), _1375089), _1375093)) = _1375093)], (31236 ^ _779854) ^ [_1343014, _1343016, _1343018] : [-(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), _1343014), _1343016)), _1343018)), _1343016) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1343018), _1343016))], (37265 ^ _779854) ^ [_1480993, _1480995, _1480997] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1480993), hAPP(hAPP(c_Set_Oinsert(_1480993), _1480995), c_Orderings_Obot__class_Obot(tc_fun(_1480993, tc_HOL_Obool)))), _1480997) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1480993, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1480993, _1480993, _1480997), hAPP(hAPP(c_Set_Oinsert(_1480993), _1480995), c_Orderings_Obot__class_Obot(tc_fun(_1480993, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1480993, tc_HOL_Obool), tc_HOL_Obool))))], (24739 ^ _779854) ^ [_1229123, _1229125, _1229127, _1229129] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1229123), _1229125), _1229127)), hAPP(c_Int_Onumber__class_Onumber__of(_1229123), _1229129)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1229123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229123), _1229125), hAPP(c_Int_Onumber__class_Onumber__of(_1229123), _1229129))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229123), _1229127), hAPP(c_Int_Onumber__class_Onumber__of(_1229123), _1229129)))), class_Int_Onumber(_1229123), class_Rings_Oring(_1229123)], (43716 ^ _779854) ^ [_1651497, _1651499, _1651501, _1651503, _1651505] : [-(_1651497 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1651499, _1651501, _1651503), _1651497), _1651505) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1651501), _1651499), tc_prod(_1651501, _1651499), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651501), _1651499), c_List_Olist_ONil(_1651501)), _1651505), hAPP(c_Product__Type_Oprod_Oprod__case(_1651501, _1651499, tc_prod(tc_List_Olist(_1651501), _1651499)), hAPP(hAPP(c_COMBC(_1651501, tc_fun(_1651499, tc_prod(tc_List_Olist(_1651501), _1651499)), tc_fun(_1651499, tc_prod(tc_List_Olist(_1651501), _1651499))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1651501), _1651499), tc_prod(tc_List_Olist(_1651501), _1651499)), tc_fun(tc_fun(_1651499, tc_prod(tc_List_Olist(_1651501), _1651499)), tc_fun(_1651499, tc_prod(tc_List_Olist(_1651501), _1651499))), _1651501), c_COMBB(tc_prod(tc_List_Olist(_1651501), _1651499), tc_prod(tc_List_Olist(_1651501), _1651499), _1651499)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1651501), tc_fun(_1651499, tc_prod(tc_List_Olist(_1651501), _1651499))), tc_fun(tc_prod(tc_List_Olist(_1651501), _1651499), tc_prod(tc_List_Olist(_1651501), _1651499)), _1651501), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1651501), _1651499, tc_prod(tc_List_Olist(_1651501), _1651499))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1651501), tc_List_Olist(_1651501)), tc_fun(tc_List_Olist(_1651501), tc_fun(_1651499, tc_prod(tc_List_Olist(_1651501), _1651499))), _1651501), hAPP(c_COMBB(tc_List_Olist(_1651501), tc_fun(_1651499, tc_prod(tc_List_Olist(_1651501), _1651499)), tc_List_Olist(_1651501)), c_Product__Type_OPair(tc_List_Olist(_1651501), _1651499))), c_List_Olist_OCons(_1651501))))), hAPP(c_Lazy__Sequence_Oanamorph(_1651499, _1651501, _1651503), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1651497), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1651503, _1651505)))], (4348 ^ _779854) ^ [_845923, _845925, _845927, _845929, _845931, _845933, _845935, _845937] : [-(c_Lazy__Sequence_Oproduct(_845937, _845933, _845929, _845925) = c_Lazy__Sequence_Oproduct(_845935, _845931, _845927, _845923)), _845937 = _845935, _845933 = _845931, _845929 = _845927, _845925 = _845923], (24617 ^ _779854) ^ [_1226347, _1226349, _1226351] : [class_Int_Onumber__ring(_1226347), -(hAPP(c_Int_Onumber__class_Onumber__of(_1226347), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226349), _1226351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226347), hAPP(c_Int_Onumber__class_Onumber__of(_1226347), _1226349)), hAPP(c_Int_Onumber__class_Onumber__of(_1226347), _1226351)))], (46647 ^ _779854) ^ [_1718547, _1718549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718547), _1718549)), -(c_List_Oupt(_1718547, _1718549) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1718547), c_List_Oupt(hAPP(c_Nat_OSuc, _1718547), _1718549)))], (21587 ^ _779854) ^ [_1169499, _1169501, _1169503, _1169505] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1169499, _1169503)), c_Sum__Type_OPlus(_1169499, _1169503, _1169501, _1169505)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1169499), _1169501)), hAPP(c_Finite__Set_Ocard(_1169503), _1169505))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169499), _1169501)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169503), _1169505))], (7453 ^ _779854) ^ [_902681, _902683] : [class_Lattices_Obounded__lattice__bot(_902681), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902681), c_Orderings_Obot__class_Obot(_902681)), _902683) = _902683)], (24629 ^ _779854) ^ [_1226617, _1226619, _1226621, _1226623] : [class_Int_Onumber__ring(_1226617), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226617), hAPP(c_Int_Onumber__class_Onumber__of(_1226617), _1226619)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226617), hAPP(c_Int_Onumber__class_Onumber__of(_1226617), _1226621)), _1226623)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226617), hAPP(c_Int_Onumber__class_Onumber__of(_1226617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226619), _1226621))), _1226623))], (7353 ^ _779854) ^ [_900923, _900925, _900927, _900929] : [class_Lattices_Osemilattice__sup(_900923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900923), _900925), _900927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900923), _900929), _900927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900923), _900925), _900929)), _900927)))], (24723 ^ _779854) ^ [_1228711, _1228713, _1228715, _1228717] : [class_Int_Onumber__ring(_1228711), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228711), hAPP(c_Int_Onumber__class_Onumber__of(_1228711), _1228713)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1228711), hAPP(c_Int_Onumber__class_Onumber__of(_1228711), _1228715)), _1228717)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1228711), hAPP(c_Int_Onumber__class_Onumber__of(_1228711), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228713), _1228715))), _1228717))], (9644 ^ _779854) ^ [_941541, _941543, _941545, _941547] : [class_Orderings_Olinorder(_941541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941541), _941543), _941545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941541), _941547), _941545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941541), hAPP(hAPP(c_Orderings_Oord__class_Omax(_941541), _941543), _941547)), _941545)))], (29203 ^ _779854) ^ [_1306720, _1306722, _1306724] : [-(hBOOL(hAPP(_1306720, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1306722), _1306724))))), 29206 ^ _779854 : [(29209 ^ _779854) ^ [] : [hBOOL(hAPP(_1306720, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306722)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306724))))], (29207 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1306724), _1306722)))]], 29210 ^ _779854 : [(29213 ^ _779854) ^ [] : [hBOOL(hAPP(_1306720, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29211 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306722), _1306724)))]]], (31009 ^ _779854) ^ [_1339528, _1339530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1339528), _1339530)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1339528, _1339530) = _1339528)], (51373 ^ _779854) ^ [_1820336] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1820336)))], (32137 ^ _779854) ^ [_1357879, _1357881] : [class_Groups_Oordered__ab__group__add__abs(_1357879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357879), hAPP(c_Groups_Oabs__class_Oabs(_1357879), _1357881)), c_Groups_Ozero__class_Ozero(_1357879)))], (52321 ^ _779854) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (29263 ^ _779854) ^ [_1307856, _1307858] : [class_Rings_Osemiring__1(_1307856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307858)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1307856), 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)))), _1307858))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1307856), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1307856), hAPP(c_Int_Onat, _1307858))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1307856), hAPP(c_Int_Onat, _1307858))))], (34427 ^ _779854) ^ [_1418109, _1418111, _1418113] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1418109), _1418111)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1418109, tc_HOL_Obool)), _1418113), _1418111) = hAPP(hAPP(c_Finite__Set_Ofold(_1418109, tc_fun(_1418109, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1418109, tc_HOL_Obool), tc_fun(tc_fun(_1418109, tc_HOL_Obool), tc_fun(_1418109, tc_HOL_Obool)), _1418109), hAPP(c_COMBC(tc_fun(_1418109, tc_HOL_Obool), tc_fun(_1418109, tc_HOL_Obool), tc_fun(_1418109, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1418109, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1418109, tc_fun(_1418109, tc_HOL_Obool), tc_fun(_1418109, tc_HOL_Obool)), c_Set_Oinsert(_1418109)), c_Orderings_Obot__class_Obot(tc_fun(_1418109, tc_HOL_Obool))))), _1418113), _1418111))], (38096 ^ _779854) ^ [_1500759, _1500761, _1500763, _1500765, _1500767] : [hBOOL(hAPP(hAPP(c_member(_1500759), hAPP(_1500761, _1500763)), _1500765)), -(hBOOL(hAPP(hAPP(c_member(_1500767), _1500763), hAPP(c_Set_Ovimage(_1500767, _1500759, _1500761), _1500765))))], (38332 ^ _779854) ^ [_1506945, _1506947, _1506949, _1506951, _1506953, _1506955] : [class_Groups_Ocomm__monoid__mult(_1506945), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1506947, _1506945), hAPP(hAPP(c_COMBC(_1506947, tc_fun(_1506949, tc_HOL_Obool), _1506945), hAPP(hAPP(c_COMBB(tc_fun(_1506949, _1506945), tc_fun(tc_fun(_1506949, tc_HOL_Obool), _1506945), _1506947), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1506949, _1506945)), _1506951)), _1506953)), _1506955) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1506947, _1506949), _1506945), hAPP(c_Product__Type_Oprod_Oprod__case(_1506947, _1506949, _1506945), _1506951)), hAPP(hAPP(c_Product__Type_OSigma(_1506947, _1506949), _1506955), hAPP(c_COMBK(tc_fun(_1506949, tc_HOL_Obool), _1506947), _1506953))))], (778 ^ _779854) ^ [_791583, _791585, _791587, _791589] : [-(c_Wellfounded_Oacyclic(_791587, _791583)), c_Wellfounded_Oacyclic(_791589, _791585), _791589 = _791587, _791585 = _791583], (51503 ^ _779854) ^ [_1822715, _1822717] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1822715), 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)))), _1822717)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822715), _1822717)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822717), _1822715)))], (48552 ^ _779854) ^ [_1758201, _1758203, _1758205] : [48554 ^ _779854 : [(48557 ^ _779854) ^ [] : [hBOOL(hAPP(_1758203, hAPP(hAPP(c_List_Onth(_1758201), _1758205), 48553 ^ [_1758201, _1758203, _1758205])))], (48555 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48553 ^ [_1758201, _1758203, _1758205]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758201)), _1758205))))]], -(c_List_Olist__all(_1758201, _1758203, _1758205))], (40336 ^ _779854) ^ [_1565745, _1565747, _1565749] : [40337 ^ _779854 : [(40338 ^ _779854) ^ [_1565799] : [hBOOL(hAPP(_1565745, _1565799))]], _1565747 = c_Hilbert__Choice_OEps(_1565749, _1565745), -(hBOOL(hAPP(_1565745, _1565747)))], (23183 ^ _779854) ^ [_1198972, _1198974, _1198976, _1198978] : [class_Fields_Olinordered__field(_1198972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198972), c_Groups_Ozero__class_Ozero(_1198972)), _1198974)), 23190 ^ _779854 : [(23197 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198972), _1198976), _1198974)), _1198978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198972), _1198976), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1198972), _1198978), _1198974))))], (23191 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198972), _1198976), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1198972), _1198978), _1198974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198972), _1198976), _1198974)), _1198978)))]]], (17903 ^ _779854) ^ [_1103924, _1103926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103924)), _1103926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103924), _1103926)))], (52499 ^ _779854) ^ [_1836765, _1836767] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1836765, _1836767)))], (47182 ^ _779854) ^ [_1728225, _1728227] : [class_Orderings_Olinorder(_1728225), hBOOL(hAPP(c_Finite__Set_Ofinite(_1728225), _1728227)), 47189 ^ _779854 : [(47194 ^ _779854) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1728225), c_List_Olinorder__class_Osorted__list__of__set(_1728225, _1728227))))], (47192 ^ _779854) ^ [] : [-(c_List_Olinorder__class_Osorted(_1728225, c_List_Olinorder__class_Osorted__list__of__set(_1728225, _1728227)))], (47190 ^ _779854) ^ [] : [-(hAPP(c_List_Oset(_1728225), c_List_Olinorder__class_Osorted__list__of__set(_1728225, _1728227)) = _1728227)]]], (4952 ^ _779854) ^ [_855473, _855475, _855477, _855479] : [-(c_Orderings_Oord__class_OLeast(_855479, _855475) = c_Orderings_Oord__class_OLeast(_855477, _855473)), _855479 = _855477, _855475 = _855473], (47637 ^ _779854) ^ [_1737862, _1737864] : [-(c_List_OtakeWhile(_1737862, _1737864, c_List_Olist_ONil(_1737862)) = c_List_Olist_ONil(_1737862))], (51911 ^ _779854) ^ [_1829749, _1829751] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829749), _1829751)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829751), _1829749))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829751), _1829749)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829749), _1829751)))], (42133 ^ _779854) ^ [_1610840, _1610842, _1610844] : [_1610840 = hAPP(hAPP(c_List_Olist_OCons(_1610842), _1610844), _1610840)], (24150 ^ _779854) ^ [_1217861, _1217863] : [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), _1217861), _1217863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217861))), -(_1217863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10937 ^ _779854) ^ [_967156, _967158, _967160, _967162] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967156, tc_HOL_Obool)), _967158), hAPP(hAPP(c_Set_Oinsert(_967156), _967160), _967162)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967156, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967156, tc_HOL_Obool)), _967158), hAPP(hAPP(c_Set_Oinsert(_967156), _967160), c_Orderings_Obot__class_Obot(tc_fun(_967156, tc_HOL_Obool))))), _967162))], (33024 ^ _779854) ^ [_1377712, _1377714, _1377716, _1377718, _1377720] : [-(_1377712 = c_Orderings_Obot__class_Obot(tc_fun(_1377714, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377714, tc_fun(_1377716, tc_HOL_Obool)), _1377712), hAPP(hAPP(c_COMBB(tc_fun(_1377716, tc_HOL_Obool), tc_fun(_1377716, tc_HOL_Obool), _1377714), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377716, tc_HOL_Obool)), _1377718)), _1377720)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377716, tc_HOL_Obool)), _1377718), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377714, tc_fun(_1377716, tc_HOL_Obool)), _1377712), _1377720)))], (26993 ^ _779854) ^ [_1269449] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1269449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269449), c_Int_OPls)))], (2244 ^ _779854) ^ [_812707, _812709, _812711, _812713] : [-(c_Orderings_Oord_Omin(_812713, _812709) = c_Orderings_Oord_Omin(_812711, _812707)), _812713 = _812711, _812709 = _812707], (49992 ^ _779854) ^ [_1790411, _1790413] : [c_Relation_Oantisym(_1790411, _1790413), -(c_Relation_Oantisym(_1790411, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1790411, _1790411), tc_HOL_Obool)), _1790413), c_Relation_OId(_1790411))))], (39970 ^ _779854) ^ [_1556410, _1556412, _1556414, _1556416] : [hBOOL(hAPP(c_Predicate_ODomainP(_1556410, _1556412, _1556414), _1556416)), -(hBOOL(hAPP(hAPP(_1556414, _1556416), 39973 ^ [_1556410, _1556412, _1556414, _1556416])))], (42183 ^ _779854) ^ [_1612672, _1612674, _1612676, _1612678, _1612680, _1612682] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612672), tc_List_Olist(_1612672))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612672), tc_List_Olist(_1612672)), hAPP(hAPP(c_List_Olist_OCons(_1612672), _1612674), _1612676)), hAPP(hAPP(c_List_Olist_OCons(_1612672), _1612678), _1612680))), c_List_Olexord(_1612672, _1612682))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612672, _1612672)), hAPP(hAPP(c_Product__Type_OPair(_1612672, _1612672), _1612674), _1612678)), _1612682))), 42190 ^ _779854 : [(42193 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612672), tc_List_Olist(_1612672))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612672), tc_List_Olist(_1612672)), _1612676), _1612680)), c_List_Olexord(_1612672, _1612682))))], (42191 ^ _779854) ^ [] : [-(_1612674 = _1612678)]]], (38380 ^ _779854) ^ [_1508578, _1508580, _1508582, _1508584, _1508586, _1508588] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508578, _1508580)), hAPP(hAPP(c_Product__Type_OPair(_1508578, _1508580), _1508582), _1508584)), hAPP(hAPP(c_Product__Type_OSigma(_1508578, _1508580), _1508586), _1508588))), -(hBOOL(hAPP(hAPP(c_member(_1508580), _1508584), hAPP(_1508588, _1508582))))], (38813 ^ _779854) ^ [_1520178, _1520180, _1520182] : [-(hAPP(hAPP(c_Set_Oinsert(_1520178), _1520180), _1520182) = hAPP(c_Set_OCollect(_1520178), hAPP(hAPP(c_COMBS(_1520178, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520178), c_fdisj), hAPP(hAPP(c_COMBC(_1520178, _1520178, tc_HOL_Obool), c_fequal), _1520180))), hAPP(hAPP(c_COMBC(_1520178, tc_fun(_1520178, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520178)), _1520182))))], (48516 ^ _779854) ^ [_1757264, _1757266, _1757268] : [48517 ^ _779854 : [(48518 ^ _779854) ^ [_1757341, _1757343] : [_1757268 = hAPP(hAPP(c_List_Oappend(_1757264), _1757343), hAPP(hAPP(c_List_Olist_OCons(_1757264), _1757266), _1757341))]], -(hBOOL(hAPP(hAPP(c_member(_1757264), _1757266), hAPP(c_List_Oset(_1757264), _1757268))))], (25663 ^ _779854) ^ [_1246375] : [-(c_Int_Osucc(c_Int_Opred(_1246375)) = _1246375)], (29499 ^ _779854) ^ [_1311954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311954), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1311954)), c_Int_OPls)))], (24535 ^ _779854) ^ [_1225042, _1225044, _1225046] : [class_Int_Onumber__ring(_1225042), class_Int_Oring__char__0(_1225042), 24542 ^ _779854 : [(24549 ^ _779854) ^ [] : [_1225044 = _1225046, -(hAPP(c_Int_Onumber__class_Onumber__of(_1225042), _1225044) = hAPP(c_Int_Onumber__class_Onumber__of(_1225042), _1225046))], (24543 ^ _779854) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1225042), _1225044) = hAPP(c_Int_Onumber__class_Onumber__of(_1225042), _1225046), -(_1225044 = _1225046)]]], (18977 ^ _779854) ^ [] : [-(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))))], (18673 ^ _779854) ^ [_1117607, _1117609] : [class_Groups_Ogroup__add(_1117607), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117607), _1117609), _1117609) = c_Groups_Ozero__class_Ozero(_1117607))], (41405 ^ _779854) ^ [_1591706] : [-(hAPP(c_Relation_Oconverse(_1591706, _1591706), c_Relation_OId(_1591706)) = c_Relation_OId(_1591706))], (11368 ^ _779854) ^ [_976087, _976089, _976091, _976093, _976095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976087), _976089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976091, tc_HOL_Obool)), _976093), hAPP(c_Set_Oimage(_976087, _976091, _976095), _976089))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976091), _976093)))], (46384 ^ _779854) ^ [_1711368, _1711370, _1711372] : [-(c_Enum_On__lists(_1711368, hAPP(c_Nat_OSuc, _1711370), _1711372) = c_List_Oconcat(tc_List_Olist(_1711368), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711368), tc_List_Olist(tc_List_Olist(_1711368))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711368), tc_List_Olist(_1711368), tc_List_Olist(tc_List_Olist(_1711368))), hAPP(hAPP(c_COMBB(tc_fun(_1711368, tc_List_Olist(_1711368)), tc_fun(tc_List_Olist(_1711368), tc_List_Olist(tc_List_Olist(_1711368))), tc_List_Olist(_1711368)), c_List_Omap(_1711368, tc_List_Olist(_1711368))), hAPP(c_COMBC(_1711368, tc_List_Olist(_1711368), tc_List_Olist(_1711368)), c_List_Olist_OCons(_1711368)))), _1711372)), c_Enum_On__lists(_1711368, _1711370, _1711372))))], (37046 ^ _779854) ^ [_1475084, _1475086, _1475088, _1475090, _1475092] : [hBOOL(hAPP(hAPP(c_member(_1475084), _1475086), hAPP(c_Relation_OImage(_1475088, _1475084, _1475090), _1475092))), 37050 ^ _779854 : [(37053 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475088, _1475084)), hAPP(hAPP(c_Product__Type_OPair(_1475088, _1475084), 37049 ^ [_1475084, _1475086, _1475088, _1475090, _1475092]), _1475086)), _1475090)))], (37051 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475088), 37049 ^ [_1475084, _1475086, _1475088, _1475090, _1475092]), _1475092)))]]], (21301 ^ _779854) ^ [_1163590, _1163592] : [21309 ^ _779854 : [(21312 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1163592, 21308 ^ [_1163590, _1163592])))], (21310 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21308 ^ [_1163590, _1163592]), _1163590)))]], 21302 ^ _779854 : [(21303 ^ _779854) ^ [_1163659] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1163659), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1163590))), hBOOL(hAPP(_1163592, _1163659))]]], (45911 ^ _779854) ^ [_1700832, _1700834, _1700836, _1700838] : [c_List_Olist__all2(_1700832, _1700834, _1700836, _1700838, c_List_Olist_ONil(_1700834)), -(_1700838 = c_List_Olist_ONil(_1700832))], (43133 ^ _779854) ^ [_1639243, _1639245, _1639247, _1639249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639243), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639245)), _1639247))), -(hBOOL(hAPP(hAPP(c_member(_1639245), _1639249), hAPP(c_List_Oset(_1639245), hAPP(hAPP(c_List_Olist__update(_1639245, _1639247), _1639243), _1639249)))))], (24707 ^ _779854) ^ [_1228293, _1228295, _1228297, _1228299] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228293), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228293), _1228295), _1228297)), hAPP(c_Int_Onumber__class_Onumber__of(_1228293), _1228299)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228293), _1228295), hAPP(c_Int_Onumber__class_Onumber__of(_1228293), _1228299))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228293), _1228297), hAPP(c_Int_Onumber__class_Onumber__of(_1228293), _1228299)))), class_Int_Onumber(_1228293), class_Rings_Osemiring(_1228293)], (48874 ^ _779854) ^ [_1764926, _1764928, _1764930, _1764932, _1764934] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1764926, _1764928, _1764930), _1764932), _1764934)), -(hBOOL(hAPP(hAPP(_1764930, _1764934), _1764932)))], (45312 ^ _779854) ^ [_1687486, _1687488, _1687490] : [c_Fun_Oinj__on(tc_List_Olist(_1687486), tc_List_Olist(_1687488), hAPP(c_List_Omap(_1687486, _1687488), _1687490), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1687486), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1687486, _1687488, _1687490, c_Orderings_Otop__class_Otop(tc_fun(_1687486, tc_HOL_Obool))))], (11334 ^ _779854) ^ [_975467, _975469, _975471] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975467), _975469)), 11337 ^ _779854 : [(11344 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975467), _975471)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_975467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975467, tc_HOL_Obool)), _975471), _975469))))], (11338 ^ _779854) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975467, tc_HOL_Obool)), _975471), _975469))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_975467), _975471)))]]], (29463 ^ _779854) ^ [_1311300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311300), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1311300)), c_Int_OPls)))], (31312 ^ _779854) ^ [_1344406, _1344408] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1344406), _1344408) = c_Groups_Oone__class_Oone(tc_Int_Oint), 31317 ^ _779854 : [(31320 ^ _779854) ^ [] : [-(_1344408 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (31318 ^ _779854) ^ [] : [-(_1344406 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 31321 ^ _779854 : [(31324 ^ _779854) ^ [] : [-(_1344408 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (31322 ^ _779854) ^ [] : [-(_1344406 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (47056 ^ _779854) ^ [_1725759, _1725761, _1725763, _1725765, _1725767] : [class_Orderings_Olinorder(_1725759), -(c_List_Olinorder__class_Osorted(_1725759, hAPP(hAPP(c_List_Omap(_1725761, _1725759), _1725763), hAPP(c_List_Ofilter(_1725761, hAPP(hAPP(c_COMBC(_1725761, _1725759, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1725759, tc_fun(_1725759, tc_HOL_Obool), _1725761), c_fequal), _1725763)), hAPP(_1725765, _1725767))), _1725767))))], (39024 ^ _779854) ^ [_1526111, _1526113, _1526115, _1526117, _1526119, _1526121] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526111), _1526113)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526115), _1526117)), 39034 ^ _779854 : [(39037 ^ _779854) ^ [] : [hAPP(c_Finite__Set_Ocard(_1526111), hAPP(c_Set_OCollect(_1526111), hAPP(hAPP(c_COMBS(_1526111, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526111), c_fconj), hAPP(hAPP(c_COMBC(_1526111, tc_fun(_1526111, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526111)), _1526113))), hAPP(hAPP(c_COMBC(_1526111, _1526115, tc_HOL_Obool), _1526119), 39033 ^ [_1526111, _1526113, _1526115, _1526117, _1526119, _1526121])))) = _1526121], (39035 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526115), 39033 ^ [_1526111, _1526113, _1526115, _1526117, _1526119, _1526121]), _1526117)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526111, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1526115, tc_HOL_Obool), tc_Nat_Onat, _1526111), c_Finite__Set_Ocard(_1526115)), hAPP(hAPP(c_COMBB(tc_fun(_1526115, tc_HOL_Obool), tc_fun(_1526115, tc_HOL_Obool), _1526111), c_Set_OCollect(_1526115)), hAPP(hAPP(c_COMBB(tc_fun(_1526115, tc_HOL_Obool), tc_fun(_1526115, tc_HOL_Obool), _1526111), hAPP(c_COMBS(_1526115, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526115), c_fconj), hAPP(hAPP(c_COMBC(_1526115, tc_fun(_1526115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526115)), _1526117)))), _1526119)))), _1526113) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1526121), hAPP(c_Finite__Set_Ocard(_1526115), _1526117)))], (44149 ^ _779854) ^ [_1661406, _1661408, _1661410, _1661412, _1661414, _1661416, _1661418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1661406, _1661406)), hAPP(hAPP(c_Product__Type_OPair(_1661406, _1661406), _1661408), _1661410)), _1661412)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661406), tc_List_Olist(_1661406))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661406), tc_List_Olist(_1661406)), hAPP(hAPP(c_List_Oappend(_1661406), _1661414), hAPP(hAPP(c_List_Olist_OCons(_1661406), _1661408), _1661416))), hAPP(hAPP(c_List_Oappend(_1661406), _1661414), hAPP(hAPP(c_List_Olist_OCons(_1661406), _1661410), _1661418)))), c_List_Olexord(_1661406, _1661412))))], (45284 ^ _779854) ^ [_1686844, _1686846, _1686848, _1686850] : [-(hBOOL(hAPP(c_List_Odistinct(_1686844), hAPP(hAPP(c_List_Omap(_1686846, _1686844), _1686848), _1686850)))), hBOOL(hAPP(c_List_Odistinct(_1686846), _1686850)), c_Fun_Oinj__on(_1686846, _1686844, _1686848, hAPP(c_List_Oset(_1686846), _1686850))], (26241 ^ _779854) ^ [_1256847, _1256849, _1256851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256847)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1256849), _1256851)), 26248 ^ _779854 : [(26249 ^ _779854) ^ [_1257037] : [26251 ^ _779854 : [(26257 ^ _779854) ^ [] : [-(_1257037 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26253 ^ [_1256847, _1256849, _1256851, _1257037]), 26250 ^ [_1256847, _1256849, _1256851, _1257037]))], (26255 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26253 ^ [_1256847, _1256849, _1256851, _1257037]), _1256851)))], (26252 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26250 ^ [_1256847, _1256849, _1256851, _1257037]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1256847))))]], -(_1257037 = _1256849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1257037), _1256847) = _1256849]]], (7063 ^ _779854) ^ [_895592, _895594] : [class_Lattices_Osemilattice__sup(_895592), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895592), _895594), _895594) = _895594)], (52631 ^ _779854) ^ [_1838112, _1838114, _1838116, _1838118] : [-(hAPP(hAPP(c_COMBK(_1838112, _1838114), _1838116), _1838118) = _1838116)], (42695 ^ _779854) ^ [_1627530, _1627532, _1627534, _1627536] : [hBOOL(hAPP(hAPP(c_member(_1627530), _1627532), hAPP(c_List_Oset(_1627530), c_List_Osublist(_1627530, _1627534, _1627536)))), -(hBOOL(hAPP(hAPP(c_member(_1627530), _1627532), hAPP(c_List_Oset(_1627530), _1627534))))], (51274 ^ _779854) ^ [_1818545] : [-(c_Lazy__Sequence_Oflat(_1818545, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1818545))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1818545))], (25525 ^ _779854) ^ [_1244230, _1244232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244230), _1244232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244230)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244232))))], (18213 ^ _779854) ^ [_1109392, _1109394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109392), _1109394)), 18216 ^ _779854 : [(18223 ^ _779854) ^ [] : [_1109394 = _1109392, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109394), hAPP(c_Nat_OSuc, _1109392))))], (18217 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109394), hAPP(c_Nat_OSuc, _1109392))), -(_1109394 = _1109392)]]], (37133 ^ _779854) ^ [_1477560, _1477562, _1477564, _1477566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1477560), _1477566)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1477564), _1477562))), -(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), _1477560), _1477562)), 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), _1477564), _1477566)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (3676 ^ _779854) ^ [_835153, _835155, _835157, _835159] : [-(c_List_Obutlast(_835159, _835155) = c_List_Obutlast(_835157, _835153)), _835159 = _835157, _835155 = _835153], (50176 ^ _779854) ^ [_1793746, _1793748] : [c_Relation_Osym(_1793746, hAPP(c_Set_OCollect(tc_prod(_1793746, _1793746)), hAPP(c_Product__Type_Oprod_Oprod__case(_1793746, _1793746, tc_HOL_Obool), _1793748))), -(c_Predicate_Osymp(_1793746, _1793748))], (1760 ^ _779854) ^ [_804806, _804808] : [-(class_Rings_Ozero__neq__one(_804806)), _804808 = _804806, class_Rings_Ozero__neq__one(_804808)], (21408 ^ _779854) ^ [_1165638, _1165640, _1165642] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1165638), _1165640)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165638), _1165642)), 21418 ^ _779854 : [(21421 ^ _779854) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21419 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1165638), 21417 ^ [_1165638, _1165640, _1165642]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1165638, tc_HOL_Obool)), _1165640), _1165642))))]], -(hAPP(c_Finite__Set_Ocard(_1165638), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1165638, tc_HOL_Obool)), _1165640), _1165642)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1165638), _1165640)), hAPP(c_Finite__Set_Ocard(_1165638), _1165642)))], (31134 ^ _779854) ^ [_1341409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1341409)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1341409), c_Int_OMin)))], (45214 ^ _779854) ^ [_1685282, _1685284, _1685286, _1685288, _1685290] : [-(hAPP(hAPP(c_List_Omap(_1685282, _1685284), _1685286), hAPP(hAPP(c_List_Oappend(_1685282), _1685288), _1685290)) = hAPP(hAPP(c_List_Oappend(_1685284), hAPP(hAPP(c_List_Omap(_1685282, _1685284), _1685286), _1685288)), hAPP(hAPP(c_List_Omap(_1685282, _1685284), _1685286), _1685290)))], (28178 ^ _779854) ^ [_1289445, _1289447] : [-(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), _1289445))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1289447))))], (38717 ^ _779854) ^ [_1518048] : [-(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)), _1518048)))))], (32684 ^ _779854) ^ [_1368120, _1368122, _1368124, _1368126, _1368128, _1368130] : [-(c_Nitpick_Opair__box_Opair__box__size(_1368120, _1368122, _1368124, _1368126, c_Nitpick_Opair__box_OPairBox(_1368120, _1368122, _1368128, _1368130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1368124, _1368128)), hAPP(_1368126, _1368130))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26897 ^ _779854) ^ [_1267797, _1267799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267797), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 26900 ^ _779854 : [(26907 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267799), 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), _1267799), _1267797))))], (26901 ^ _779854) ^ [] : [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), _1267799), _1267797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267799), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (21869 ^ _779854) ^ [_1174970, _1174972, _1174974, _1174976] : [class_Rings_Odivision__ring(_1174970), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174970), _1174972), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174970), _1174974), _1174976)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174970), _1174972), _1174974)), _1174976))], (7251 ^ _779854) ^ [_899174, _899176, _899178, _899180] : [class_Lattices_Osemilattice__inf(_899174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899174), _899176), _899178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899174), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_899174), _899176), _899180)), _899178)))], (52403 ^ _779854) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (38727 ^ _779854) ^ [_1518434, _1518436, _1518438] : [hBOOL(hAPP(hAPP(c_member(_1518434), _1518436), hAPP(c_Set_OCollect(_1518434), _1518438))), -(hBOOL(hAPP(_1518438, _1518436)))], (32039 ^ _779854) ^ [_1356333, _1356335, _1356337] : [class_Groups_Oordered__ab__group__add__abs(_1356333), -(hAPP(c_Groups_Oabs__class_Oabs(_1356333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356333), hAPP(c_Groups_Oabs__class_Oabs(_1356333), _1356335)), hAPP(c_Groups_Oabs__class_Oabs(_1356333), _1356337))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356333), hAPP(c_Groups_Oabs__class_Oabs(_1356333), _1356335)), hAPP(c_Groups_Oabs__class_Oabs(_1356333), _1356337)))], (49251 ^ _779854) ^ [_1773089, _1773091, _1773093, _1773095] : [hBOOL(hAPP(hAPP(c_List_Omember(_1773089), hAPP(hAPP(c_List_Olist_OCons(_1773089), _1773091), _1773093)), _1773095)), -(_1773091 = _1773095), -(hBOOL(hAPP(hAPP(c_List_Omember(_1773089), _1773093), _1773095)))], (21542 ^ _779854) ^ [_1168557, _1168559, _1168561, _1168563, _1168565] : [class_Groups_Ocomm__monoid__add(_1168557), class_Groups_Oordered__ab__semigroup__add(_1168557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168559), _1168561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1168559, tc_HOL_Obool)), _1168563), _1168561)), 21560 ^ _779854 : [(21563 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168557), c_Groups_Ozero__class_Ozero(_1168557)), hAPP(_1168565, 21559 ^ [_1168557, _1168559, _1168561, _1168563, _1168565])))], (21561 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1168559), 21559 ^ [_1168557, _1168559, _1168561, _1168563, _1168565]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1168559, tc_HOL_Obool)), _1168561), _1168563))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168557), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168559, _1168557), _1168565), _1168563)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168559, _1168557), _1168565), _1168561))))], (49100 ^ _779854) ^ [_1769746, _1769748, _1769750] : [_1769746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1769748), c_List_Oreplicate(_1769748, _1769746, _1769750)) = c_Orderings_Obot__class_Obot(tc_fun(_1769748, tc_HOL_Obool)))], (13033 ^ _779854) ^ [_1009269, _1009271, _1009273] : [class_Lattices_Olattice(_1009269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009269), _1009271)), hBOOL(hAPP(hAPP(c_member(_1009269), _1009273), _1009271)), 13044 ^ _779854 : [(13051 ^ _779854) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009269, tc_HOL_Obool)), _1009271), hAPP(hAPP(c_Set_Oinsert(_1009269), _1009273), c_Orderings_Obot__class_Obot(tc_fun(_1009269, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1009269, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1009269, _1009271) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009269), _1009273), c_Big__Operators_Olattice__class_OSup__fin(_1009269, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009269, tc_HOL_Obool)), _1009271), hAPP(hAPP(c_Set_Oinsert(_1009269), _1009273), c_Orderings_Obot__class_Obot(tc_fun(_1009269, tc_HOL_Obool)))))))], (13045 ^ _779854) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009269, tc_HOL_Obool)), _1009271), hAPP(hAPP(c_Set_Oinsert(_1009269), _1009273), c_Orderings_Obot__class_Obot(tc_fun(_1009269, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1009269, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1009269, _1009271) = _1009273)]]], (6127 ^ _779854) ^ [_877113, _877115, _877117, _877119, _877121] : [class_Complete__Lattice_Ocomplete__lattice(_877113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877115, tc_HOL_Obool)), _877117), _877119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877113), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_877115, _877113), _877119), _877121)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_877115, _877113), _877117), _877121))))], (2396 ^ _779854) ^ [_815159, _815161, _815163, _815165] : [-(c_Divides_Odivmod__int__rel(_815165, _815161) = c_Divides_Odivmod__int__rel(_815163, _815159)), _815165 = _815163, _815161 = _815159], (18277 ^ _779854) ^ [_1110671, _1110673, _1110675] : [class_Groups_Ocomm__monoid__mult(_1110671), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1110673, _1110671), _1110675), c_Orderings_Obot__class_Obot(tc_fun(_1110673, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1110671))], (7706 ^ _779854) ^ [_907983, _907985] : [class_Lattices_Oboolean__algebra(_907983), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907983), hAPP(c_Groups_Ouminus__class_Ouminus(_907983), _907985)), _907985) = c_Orderings_Obot__class_Obot(_907983))], (48796 ^ _779854) ^ [_1762917, _1762919, _1762921, _1762923, _1762925, _1762927, _1762929] : [-(c_New__Random__Sequence_Opos__decr__bind(_1762917, _1762919, _1762921, _1762923, _1762925, _1762927, _1762929) = c_New__DSequence_Opos__decr__bind(_1762917, _1762919, hAPP(hAPP(hAPP(_1762921, _1762925), _1762927), _1762929), hAPP(hAPP(c_COMBC(_1762917, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1762919))), hAPP(hAPP(c_COMBC(_1762917, 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(_1762919)))), hAPP(hAPP(c_COMBC(_1762917, 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(_1762919))))), _1762923), _1762925)), _1762927)), _1762929)))], (36442 ^ _779854) ^ [_1460204] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1460204) = _1460204)], (17923 ^ _779854) ^ [_1104314, _1104316] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104314), _1104316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104316)), _1104314)))], (7798 ^ _779854) ^ [_909877, _909879, _909881, _909883] : [class_Orderings_Oorder(_909877), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909877, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_909877, _909879), _909881)), c_SetInterval_Oord__class_OatLeastAtMost(_909877, _909881, _909883)) = c_Orderings_Obot__class_Obot(tc_fun(_909877, tc_HOL_Obool)))], (25537 ^ _779854) ^ [_1244461, _1244463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244461), _1244463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244461)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244463))))], (52273 ^ _779854) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (46506 ^ _779854) ^ [_1714191, _1714193] : [-(c_List_Otranspose(_1714191, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1714191)), c_List_Olist_ONil(_1714191)), _1714193)) = c_List_Otranspose(_1714191, _1714193))], (15868 ^ _779854) ^ [_1064330, _1064332, _1064334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064330), _1064332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064330), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064334), _1064332))))], (51805 ^ _779854) ^ [_1828009, _1828011] : [class_Rings_Ocomm__semiring__1(_1828009), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828009), _1828011), _1828011)))], (16121 ^ _779854) ^ [_1069303, _1069305, _1069307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069303), _1069305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1069303), _1069307)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1069305), _1069307))))], (21739 ^ _779854) ^ [_1172200, _1172202] : [class_Int_Oring__char__0(_1172200), hBOOL(hAPP(hAPP(c_member(_1172200), _1172202), c_Int_Oring__1__class_OInts(_1172200))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172200), c_Groups_Oone__class_Oone(_1172200)), _1172202)), _1172202) = c_Groups_Ozero__class_Ozero(_1172200)], (7674 ^ _779854) ^ [_907252, _907254, _907256, _907258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907252, tc_HOL_Obool)), _907254), _907256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907252, tc_HOL_Obool)), _907254), _907258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907252, tc_HOL_Obool)), _907254), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907252, tc_HOL_Obool)), _907256), _907258))))], (43051 ^ _779854) ^ [_1637355, _1637357, _1637359, _1637361, _1637363, _1637365, _1637367] : [-(hAPP(hAPP(c_List_Ozip(_1637355, _1637357), hAPP(hAPP(c_List_Olist__update(_1637355, _1637359), _1637361), _1637363)), hAPP(hAPP(c_List_Olist__update(_1637357, _1637365), _1637361), _1637367)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1637355, _1637357), hAPP(hAPP(c_List_Ozip(_1637355, _1637357), _1637359), _1637365)), _1637361), hAPP(hAPP(c_Product__Type_OPair(_1637355, _1637357), _1637363), _1637367)))], (4946 ^ _779854) ^ [_855388, _855390] : [_855390 = _855388, -(c_Groups_Otimes__class_Otimes(_855390) = c_Groups_Otimes__class_Otimes(_855388))], (10883 ^ _779854) ^ [_966041, _966043, _966045, _966047, _966049] : [-(c_Fun_Oinj__on(_966041, _966043, _966045, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_966041, tc_HOL_Obool)), _966047), _966049))), c_Fun_Oinj__on(_966041, _966043, _966045, _966047), c_Fun_Oinj__on(_966041, _966043, _966045, _966049), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_966043, tc_HOL_Obool)), hAPP(c_Set_Oimage(_966041, _966043, _966045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966041, tc_HOL_Obool)), _966047), _966049))), hAPP(c_Set_Oimage(_966041, _966043, _966045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966041, tc_HOL_Obool)), _966049), _966047))) = c_Orderings_Obot__class_Obot(tc_fun(_966043, tc_HOL_Obool))], (31035 ^ _779854) ^ [_1339970] : [c_Int_OBit1(_1339970) = c_Int_OMin, -(_1339970 = c_Int_OMin)], (42255 ^ _779854) ^ [_1614791, _1614793] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1614791), tc_List_Olist(_1614791)), tc_HOL_Obool)), c_List_Olistrel1(_1614791, c_Transitive__Closure_Ortrancl(_1614791, _1614793))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1614791), c_List_Olistrel1(_1614791, _1614793)))))], (19475 ^ _779854) ^ [_1131091, _1131093] : [class_Groups_Olinordered__ab__group__add(_1131091), 19478 ^ _779854 : [(19485 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131091), c_Groups_Ozero__class_Ozero(_1131091)), _1131093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131091), c_Groups_Ozero__class_Ozero(_1131091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131091), _1131093), _1131093))))], (19479 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131091), c_Groups_Ozero__class_Ozero(_1131091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131091), _1131093), _1131093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131091), c_Groups_Ozero__class_Ozero(_1131091)), _1131093)))]]], (10803 ^ _779854) ^ [_964550, _964552, _964554, _964556] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964550, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964550, tc_HOL_Obool)), _964552), _964554)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964550, tc_HOL_Obool)), _964556), _964554)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964550, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964550, tc_HOL_Obool)), _964552), _964554)), _964556))], (42331 ^ _779854) ^ [_1617330, _1617332, _1617334] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617330, _1617330)), hAPP(hAPP(c_Product__Type_OPair(_1617330, _1617330), 42332 ^ [_1617330, _1617332, _1617334]), 42332 ^ [_1617330, _1617332, _1617334])), _1617332))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617330), tc_List_Olist(_1617330))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617330), tc_List_Olist(_1617330)), _1617334), _1617334)), c_List_Olexord(_1617330, _1617332)))], (630 ^ _779854) ^ [_789315, _789317, _789319, _789321, _789323, _789325, _789327, _789329, _789331, _789333] : [-(c_List_Olist__all2(_789331, _789327, _789323, _789319, _789315)), c_List_Olist__all2(_789333, _789329, _789325, _789321, _789317), _789333 = _789331, _789329 = _789327, _789325 = _789323, _789321 = _789319, _789317 = _789315], (36271 ^ _779854) ^ [_1456696, _1456698, _1456700, _1456702, _1456704] : [-(c_Product__Type_Oprod_Oprod__size(_1456696, _1456698, _1456700, _1456702, _1456704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1456700, hAPP(c_Product__Type_Ofst(_1456696, _1456698), _1456704))), hAPP(_1456702, hAPP(c_Product__Type_Osnd(_1456696, _1456698), _1456704)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25579 ^ _779854) ^ [_1245114, _1245116] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245114), _1245116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1245116), _1245114)))], (31820 ^ _779854) ^ [_1352456, _1352458] : [class_Int_Onumber__ring(_1352456), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352456), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1352458)) = hAPP(c_Int_Onumber__class_Onumber__of(_1352456), _1352458))], (48810 ^ _779854) ^ [_1763406, _1763408, _1763410, _1763412, _1763414] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1763406), _1763408), _1763410), _1763412), _1763414) = c_New__DSequence_Oneg__single(_1763406, _1763408))], (48832 ^ _779854) ^ [_1764011, _1764013] : [c_Wellfounded_Oacyclic(_1764011, hAPP(c_Set_OCollect(tc_prod(_1764011, _1764011)), hAPP(c_Product__Type_Oprod_Oprod__case(_1764011, _1764011, tc_HOL_Obool), c_Predicate_Oconversep(_1764011, _1764011, _1764013)))), -(c_Wellfounded_Oacyclic(_1764011, hAPP(c_Set_OCollect(tc_prod(_1764011, _1764011)), hAPP(c_Product__Type_Oprod_Oprod__case(_1764011, _1764011, tc_HOL_Obool), _1764013))))], (24398 ^ _779854) ^ [_1222386, _1222388, _1222390, _1222392] : [class_Rings_Olinordered__semidom(_1222386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222388), _1222390)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222386), c_Groups_Ozero__class_Ozero(_1222386)), _1222392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222386), _1222392), c_Groups_Oone__class_Oone(_1222386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222386), hAPP(hAPP(c_Power_Opower__class_Opower(_1222386), _1222392), _1222390)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222386), _1222392), _1222388))))], (18515 ^ _779854) ^ [_1115228, _1115230] : [class_Rings_Ocomm__semiring__1(_1115228), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115228), _1115230), c_Groups_Ozero__class_Ozero(_1115228)) = _1115230)], (26305 ^ _779854) ^ [_1258122, _1258124] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1258122))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1258122)), _1258124)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1258124))], (48694 ^ _779854) ^ [_1760852, _1760854, _1760856, _1760858] : [c_List_Olist__ex1(_1760852, _1760854, hAPP(hAPP(c_List_Olist_OCons(_1760852), _1760856), _1760858)), 48697 ^ _779854 : [(48704 ^ _779854) ^ [] : [-(hBOOL(hAPP(_1760854, _1760856))), -(c_List_Olist__ex1(_1760852, _1760854, _1760858))], (48698 ^ _779854) ^ [] : [hBOOL(hAPP(_1760854, _1760856)), -(c_List_Olist__all(_1760852, hAPP(hAPP(c_COMBS(_1760852, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1760852), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760852), c_fNot), _1760854))), hAPP(c_fequal, _1760856)), _1760858))]]], (27141 ^ _779854) ^ [_1271876, _1271878] : [class_Int_Onumber__ring(_1271876), class_Rings_Olinordered__idom(_1271876), 27148 ^ _779854 : [(27155 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1271878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271876), c_Groups_Ozero__class_Ozero(_1271876)), hAPP(c_Int_Onumber__class_Onumber__of(_1271876), _1271878))))], (27149 ^ _779854) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271876), c_Groups_Ozero__class_Ozero(_1271876)), hAPP(c_Int_Onumber__class_Onumber__of(_1271876), _1271878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1271878)))]]], (1440 ^ _779854) ^ [_800806, _800808] : [-(class_Lattices_Oboolean__algebra(_800806)), _800808 = _800806, class_Lattices_Oboolean__algebra(_800808)], (42577 ^ _779854) ^ [_1624512, _1624514, _1624516] : [-(_1624512 = _1624514), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624516)), _1624512) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624516)), _1624514), 42583 ^ _779854 : [(42586 ^ _779854) ^ [] : [hAPP(hAPP(c_List_Onth(_1624516), _1624512), 42582 ^ [_1624512, _1624514, _1624516]) = hAPP(hAPP(c_List_Onth(_1624516), _1624514), 42582 ^ [_1624512, _1624514, _1624516])], (42584 ^ _779854) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42582 ^ [_1624512, _1624514, _1624516]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624516)), _1624512))))]]], (46459 ^ _779854) ^ [_1713320, _1713322] : [-(hAPP(c_List_Ofilter(_1713320, _1713322), c_List_Olist_ONil(_1713320)) = c_List_Olist_ONil(_1713320))], (15484 ^ _779854) ^ [_1056271, _1056273, _1056275, _1056277] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1056271), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056271), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1056271), _1056273), _1056275)), _1056277) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1056271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056271), _1056273), _1056277)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056271), _1056275), _1056277)))], (37160 ^ _779854) ^ [_1478172] : [-(hAPP(c_Relation_OField(_1478172), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1478172, _1478172), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1478172, tc_HOL_Obool)))], (2990 ^ _779854) ^ [_824386, _824388] : [_824388 = _824386, -(c_Nitpick_ORep__Frac(_824388) = c_Nitpick_ORep__Frac(_824386))], (4122 ^ _779854) ^ [_842440, _842442, _842444, _842446, _842448, _842450, _842452, _842454] : [-(c_New__Random__Sequence_Opos__map(_842454, _842450, _842446, _842442) = c_New__Random__Sequence_Opos__map(_842452, _842448, _842444, _842440)), _842454 = _842452, _842450 = _842448, _842446 = _842444, _842442 = _842440], (46136 ^ _779854) ^ [_1705846, _1705848] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705846)), c_List_Oremdups(_1705846, _1705848)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705846)), _1705848), -(c_List_Oremdups(_1705846, _1705848) = _1705848)], (52317 ^ _779854) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11758 ^ _779854) ^ [_983905, _983907, _983909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983905, tc_HOL_Obool)), _983907), _983909)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_983905, tc_HOL_Obool)), _983907), hAPP(c_Set_OPow(_983905), _983909))))], (52723 ^ _779854) ^ [_1839348, _1839350] : [hBOOL(hAPP(hAPP(c_fimplies, _1839348), _1839350)), hBOOL(_1839348), -(hBOOL(_1839350))]], input).
% 47.10/46.11  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, 52734 ^ [], v_ts)],start(52738 ^ 0)).
% 47.10/46.11  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, 52734 ^ [], v_ts)), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts), c_Hoare__Mirabelle_Ohoare__derivs(t_a, 52734 ^ [], v_G_H)],extension(5695 ^ 1,bind([[_869819, _869821, _869823, _869825], [t_a, v_G_H, v_ts, 52734 ^ []]]))).
% 47.10/46.11  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts))],extension(52733 ^ 2)).
% 47.10/46.11  ncf('1.1.2',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, 52734 ^ [], v_G_H)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), 52734 ^ []))],extension(5679 ^ 2,bind([[_869549, _869551, _869553], [t_a, v_G_H, 52734 ^ []]]))).
% 47.10/46.11  ncf('1.1.2.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), 52734 ^ [])))],extension(52736 ^ 3)).
% 47.10/46.11  %-----------------------------------------------------
% 47.10/46.11  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------